Answer: $957646.07
Step-by-step explanation:
The formula we use to find the accumulated amount of the annuity is given by :-
[tex]FV=m(\frac{(1+\frac{r}{n})^{nt})-1}{\frac{r}{n}})[/tex]
, where m is the annuity payment deposit, r is annual interest rate , t is time in years and n is number of periods.
Given : m= $2000 ; n= 12 [∵12 in a year] ; t= 20 years ; r= 0.063
Now substitute all these value in the formula , we get
[tex]FV=(2000)(\frac{(1+\frac{0.063}{12})^{12\times20})-1}{\frac{0.063}{12}})[/tex]
i.e. [tex]FV=(2000)(\frac{(1+0.00525)^{240})-1}{0.00525})[/tex]
i.e. [tex]FV=(2000)(\frac{(3.51382093497)-1}{0.00525})[/tex]
i.e. [tex]FV=(2000)(\frac{2.51382093497}{0.00525})[/tex]
i.e. [tex]FV=(2000)(478.823035232)[/tex]
i.e. [tex]FV=957646.070464\approx957646.07\ \ \ \text{ [Rounded to the nearest cent]}[/tex]
Hence, the accumulated amount of the annuity= $957646.07
The future value or accumulated amount of an ordinary annuity is calculated using the formula where P is the periodic payment, r is the interest rate per period, n is the number of compounding periods per year, and t is the time in years. Given P = $2000, r = 6.3%, n = 12 and t = 20 years, substituting these values into the formula gives the accumulated amount
Explanation:To find the future value or accumulated amount of an ordinary annuity, we use the formula: FV = P * (((1 + r)^nt - 1) / r), where P is the periodic payment, r is the interest rate per period, n is the number of compounding periods per year, and t is the time in years.
In the given problem, P = $2000, r = 6.3% or 0.063 (in decimal), n = 12 (since the payments are monthly), and t = 20 years.
Substituting these into the formula, FV = $2000 * (((1 + 0.063 /12)^(12*20) - 1) / (0.063/12)).
Calculating the equation, we'll get the accumulated amount to the nearest cent.
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The Riverwalk in San Antonio, Texas has several arched pedestrian bridges that cross the San Antonio River. These arches are the arcs of circles. The distance across the river at this bridge is 150 feet, and the height in the center of the arch, above the water is 30 feet. Determine the radius of the circle. Note that the diameter of the circle is not 150 feet.
Answer: radius = 108.75 feet
Hi!
In the drawing you can see the arch that goes from point A to B. The right line from A to B is the length L = 150 feet, across the river. The height is h = 30 feet.
There is a right triangle with hypotenuse R, and the legs are (R-h), and L/2. The Pythagorean theorem says that:
[tex]R^2 = (R-h)^2 + (\frac{L}{2}) ^2 = R^2 -2hR + h^2 + (\frac{L}{2}) ^2\\[/tex]
Then:
[tex]0 = -2hR + h^2 +(\frac{L}{2}) ^2\\R = (h^2 +(\frac{L}{2}) ^2)\frac{1}{2h}[/tex]
Plugging the values of L and h, you get R = 108.75 feet
Answer:
108.75 ft
Step-by-step explanation:
You want the radius of a circular arc that rises 30 ft above a chord of length 150 ft.
CenterThe attached diagram shows the method we used to find the radius. The arc is symmetrical about its centerline, so we only need to find the perpendicular bisector of another chord to determine the location of the center.
Here, we have chosen a coordinate system with the ends of the arc at (±75, 0) and the center at (0, 30). The midpoint of the chord joining the two points on the right will be (75/2, 30/2) = (37.5, 15).
The slope of that chord is ...
[tex]m=\dfrac{\text{rise}}{\text{run}}=\dfrac{-30}{75}=-\dfrac{2}{5}[/tex]
Perpendicular bisectorThe equation of the perpendicular bisector will be the equation of a line with slope -1/m = 5/2 through the point (37.5, 15). In point-slope form, that equation is ...
[tex]y-15=\dfrac{5}{2}(x-37.5)\\\\y=\dfrac{5}{2}x-78.75[/tex]
We note that the y-intercept is -78.75. The distance from that point to the top of the arch is ...
30 -(-78.75) = 108.75
The radius of the circle is 108.75 ft.
__
Additional comment
We can use another relation to solve this problem even more simply. Consider the 150 ft chord divided into two pieces by a diameter that has one segment length 30, and the other equal to the diameter less 30. The products of these segment lengths are the same, so we have ...
75·75 = 30·(d -30)
d-30 = 187.5
d = 217.5 ⇒ r = d/2 = 108.75
Consider a bag containing five red marbles, three green ones, one transparent one, three yellow ones, and three orange ones How many possible sets of five marbles are there in which all of them red or green? sets Need Help? Read Tate Tutor
There are 56 possible sets of five marbles where all marbles are either red or green, when selecting from a bag containing five red and three green marbles.
When considering all possible sets of five marbles where each marble is either red or green from a bag containing five red marbles and three green ones, you would use combinations to find the total number of sets.
For the red marbles alone, since there are five red marbles, the number of ways to choose five red marbles is simply C(5, 5), which equals 1. There is only one set which contains all five red marbles because you are choosing all available red marbles.
To find sets containing green marbles, we must consider all combinations of red and green marbles that add up to five. These are C(5, 4) * C(3, 1), C(5, 3) * C(3, 2), and C(5, 2) * C(3, 3). We calculate each of these combinations and then sum them to get the total possible sets that consist of only red and green marbles.
Therefore, the total number of sets composed only of red or green marbles is:
C(5, 5) = 1
C(5, 4) * C(3, 1) = 5 * 3 = 15
C(5, 3) * C(3, 2) = 10 * 3 = 30
C(5, 2) * C(3, 3) = 10 * 1 = 10
Adding these up gives us 1 + 15 + 30 + 10 = 56 possible sets.
There are 3 possible sets of five marbles in which all of them are either red or green.
To solve this problem, we need to consider the different combinations of red and green marbles that can make up a set of five marbles, where all marbles in the set are either red or green.
Firstly, let's consider the case where all five marbles are red. Since there are five red marbles in the bag, there is only one way to choose all five red marbles. This gives us one possible set.
Next, we consider the case where there are four red marbles and one green marble. There are [tex]\(\binom{5}{4}\)[/tex] ways to choose four red marbles from the five available, and [tex]\(\binom{3}{1}\)[/tex]ways to choose one green marble from the three available. Using the combination formula [tex]\(\binom{n}{r} = \frac{n!}{r!(n-r)!}\),[/tex] we calculate:
[tex]\[ \binom{5}{4} = \frac{5!}{4!(5-4)!} = \frac{5}{1} = 5 \][/tex]
and
[tex]\[ \binom{3}{1} = \frac{3!}{1!(3-1)!} = \frac{3}{1} = 3 \][/tex]
Multiplying these together gives us[tex]\(5 \times 3 = 15\)[/tex] possible sets for this case.
Now, let's consider the case where there are three red marbles and two green marbles. There are[tex]\(\binom{5}{3}\)[/tex] ways to choose three red marbles from the five available, and[tex]\(\binom{3}{2}\)[/tex]ways to choose two green marbles from the three available. Calculating the combinations:
[tex]\[ \binom{5}{3} = \frac{5!}{3!(5-3)!} = \frac{5 \times 4}{2 \times 1} = 10 \][/tex]
and
[tex]\[ \binom{3}{2} = \frac{3!}{2!(3-2)!} = \frac{3}{1} = 3 \][/tex]
Multiplying these together gives us [tex]\(10 \times 3 = 30\)[/tex] possible sets for this case.
For the case with two red marbles and three green marbles, we have \[tex](\binom{5}{2}\)[/tex] ways to choose two red marbles and [tex]\(\binom{3}{3}\)[/tex] ways to choose three green marbles. Calculating the combinations:
[tex]\[ \binom{5}{2} = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10 \][/tex]
and
[tex]\[ \binom{3}{3} = \frac{3!}{3!(3-3)!} = \frac{1}{1} = 1 \][/tex]
Multiplying these together gives us [tex]\(10 \times 1 = 10\)[/tex] possible sets for this case.
Next, the case with one red marble and four green marbles has [tex]\(\binom{5}{1}\)[/tex]ways to choose one red marble and [tex]\(\binom{3}{4}\)[/tex] ways to choose four green marbles. However, since there are only three green marbles, it is impossible to choose four, so this case is not possible.
Finally, the case with zero red marbles and five green marbles is also not possible because we cannot choose five green marbles from only three available.
Adding up the possible sets from the cases that are possible, we have:
[tex]\[ 1 + 15 + 30 + 10 = 56 \][/tex]
However, upon reviewing the combinations, it is clear that there was an error in the calculations. The correct combinations for the case with three red marbles and two green marbles should be [tex]\(\binom{5}{3} \times \binom{3}{2} = 10 \times 3 = 30\)[/tex], and for the case with two red marbles and three green marbles, it should be [tex]\(\binom{5}{2} \times \binom{3}{3} = 10 \times 1 = 10\)[/tex]. The other cases are correct.
Therefore, the correct total number of possible sets is:
[tex]\[ 1 + 15 + 30 + 10 = 56 \][/tex]
However, the question asks for sets where all marbles are either red or green, and we have incorrectly included sets with both red and green marbles. We need to correct this by only considering the sets with all red marbles or all green marbles.
The correct sets are:
- All five marbles are red: 1 set
- All five marbles are green: This is not possible since there are only three green marbles.
Thus, there is only 1 possible set when considering all marbles must be either red or green. But since the question specifically asks for sets of five marbles, and we can't have a set of five green marbles, we are left with only the set of five red marbles.
Find the critical value from the Studentized range distribution for H0: μ1 = μ2 = μ3 = μ4 = μ5, with n = 35 at α = 0.01. Provide answer to three decimal places (example, 3.254).
Answer:
t-value = 2.441
Step-by-step explanation:
Let's assume that this is a one-tailed test to calculate the critical value, the process is this:
Calculate alpha (α): α = 1 - (confidence level / 100) , but we already have this α=0.01Find the critical probability (p*): p* = 1 - α/2 = 1-0.005=0.995Then, the critical value would be shown as a t statistic, but for this we need:degrees of freedom (df)= n-1=35-1=34
The critical t statistic (t*) or critical value is the t-value having degrees of freedom equal to 34 and a cumulative probability equal to 0.995.From the attached table we can see:
t-value = 2.441
Final answer:
The critical value from the Studentized range distribution for the given hypothesis test can be found using the qtukey() function in R or by looking it up in the table. For n=35 and α=0.01, the critical value is approximately 4.116.
Explanation:
To find the critical value from the Studentized range distribution, we need to use the qtukey() function in R or look up the value in the Studentized range distribution table.
Since n=35 and α=0.01, we have k=5 (number of groups) and df=5*(n-1)=170.
Using R, the critical value for a 5% significance level (α=0.05) is approximately 4.116.
Samples of a cast aluminum part are classified on the basis of surface finish and edge finish. The results of 100 parts are summarized as follows. Edge finish Excellent Good Surface Excellent 75 4Finish Good 15 6Let A denote the event that a sample has excellent surface finish, and let B denote the event that a sample has excellent edge finish. If a part is selected at random, determine the following probabilities: (a) P(A B), (b) P(A U B) and (c) P(A' U B)
Answer:
[tex]a. \hspace{3} P(A\bigcap B) = \frac{3}{4}\\\\b. \hspace{3} P(A\bigcup B) = \frac{47}{50}\\\\c. \hspace{3} P(A'\bigcup B) = \frac{17}{20}\\\\[/tex]
Step-by-step explanation:
The information is configured in a double entry table in which the finishing information for the edge and surface is recorded, thus:
[tex]\begin{array}{cccc}&E&B&Total\\E&75&4&79\\B&15&6&21\\&90&10&100\\\end{array}[/tex]
Let A denote the event that a sample has excellent surface finish, and let B denote the event that a sample has excellent edge finish.
[tex]a. \hspace{3} P(A\bigcap B) = \frac{75}{100} = \frac{3}{4}\\\\b. \hspace{3} P(A\bigcup B) = P(A) + P(B) - P(A\bigcap B) = \frac{90}{100}+\frac{79}{100} - \frac{75}{100} = \frac{94}{100} =\frac{47}{50}\\\\c. \hspace{3} P(A'\bigcup B) = P(A') + P(B) - P(A'\bigcap B) = \frac{10}{100}+\frac{79}{100} - \frac{4}{100} = \frac{85}{100} =\frac{17}{20}\\\\[/tex]
How many grams of digoxin (Lanoxin) would be required to make 25,000 tablets each containing 250 mcg of digoxin?
Answer:
6.25 grams would be required
Step-by-step explanation:
This problem can be solved as a rule of three problem.
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.
Unit conversion problems, like this one, is an example of a direct relationship between measures.
First step: The first step is determining how many mcg are used to make 25,000 tablets.
The problem states that each tablet contains 250 mcg of digoxin. So:
1 tablet - 250mcg
25,000 tables - x mcg
x = 25,000*250
x = 6,250,000 mcg
25,000 tables have 6,250,000mcg
Final step: Conversion of 6,250,000mcg to g
Each g has 1,000,000 mcg. How many g are in 6,250,000mcg? So:
1g - 1,000,000 mcg
xg - 6,250,000 mcg
1,000,000x = 6,250,000
[tex]x = \frac{6,250,000}{1,000,000}[/tex]
x = 6.25g
6.25 grams would be required
If aſc and a +b = C, prove that a|b.
Answer:
Assuming a being a divisor of c and [tex]a,b,c \in \mathbb{Z}[/tex]
Step-by-step explanation:
We are told that [tex]a \mid c[/tex]
and that [tex]a+b =c[/tex]
which means that
[tex]\exists k \in \mathbb{N}[/tex] so that [tex]c = k.a[/tex]
so we can rewrite [tex]a+b[/tex] as
[tex]a+b = c = k.a[/tex]
[tex]b = k.a-a = (k-1).a[/tex]
and as [tex]k \in \mathbb{N}[/tex]
We have that either
Showing that [tex]a \mid c[/tex]
The United States is about the only country that still uses the units feet, miles, and gallons. However, you might see some car specifications that give fuel efficiency as 7.6 km per kilogram of fuel. Given that a mile is 1.609 km, a gallon is 3.785 liters, and a liter of gasoline has a mass of 0.729 kg, what is the car’s fuel efficiency in miles per gallon?
To convert the car's fuel efficiency, it's necessary to convert kilometers to miles, and kilograms to gallons. Using the provided information, the car's fuel efficiency equates to approximately 24.4 miles per gallon.
Explanation:To convert the car's fuel efficiency from kilometers per kilogram to miles per gallon, we will use the given conversions:
1 mile = 1.609 kilometers1 gallon = 3.785 liters1 liter of gasoline = 0.729 kilogramsWe start with the given efficiency of 7.6 km/kg and convert km to miles:
7.6 km/kg * (1 mile / 1.609 km) = 4.721 miles/kg
Now we convert kg to gallons using the density of gasoline:
4.721 miles/kg * (1 kg / 0.729 liters) * (3.785 liters / 1 gallon) = 24.4 miles/gallon.
Therefore, the car's fuel efficiency is approximately 24.4 miles per gallon.
(A) Which is the equation of Line b? 1. y=−14x+54 2. y=4x+3 3. y=x+5441 4. y=4x−3
(B) Which is the equation of Line d? 1. y=3x+3 2. y=−13x−3 3. y=13x+3 4. y=−3x−3
Check the picture below.
all we need to get the equation of the line is two points on it, in this case those would be (-3,2) and (1,1),
[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-3)}}}\implies \cfrac{-1}{1+3}\implies -\cfrac{1}{4}[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{-\cfrac{1}{4}}[x-\stackrel{x_1}{(-3)}]\implies y-2=-\cfrac{1}{4}(x+3) \\\\\\ y-2=-\cfrac{1}{4}x-\cfrac{3}{4}\implies y=-\cfrac{1}{4}x-\cfrac{3}{4}+2\implies y=-\cfrac{1}{4}x+\cfrac{5}{4}[/tex]
The equation of line is 4y + x = 4.
What is the slope of the line?The slope of the line is defined as the angle of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
We have been given that Line b passes through the points (-3,2) and (1,1),
Let
x₁ = -3, y₁ = 2
x₂ = 1, y₂ = 1
∵ (y - y₁) = {(y₂ - y₁)/(x₂ -x₁ )}(x -x₁ )
Substitute values in the formula
(y - 2) = {(1 - 2)/(1 - (-3))}(x -(-3))
(y - 2) = {(-1)/(1+3)}(x+4)
(y - 2) = -1/4(x+4)
4y - 8 = -x - 4
4y + x = 4
Hence, the equation of line is 4y + x = 4.
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Order: Verapamil
HCl 0.075 mg/kg IV push over 2 min.
The label on the vial reads 5 mg/2 mL, and the patient weighs 80 kg. How many mL/min. will you administer?
A.
3 mL/min.
B.
1.2 mL/min.
C.
2.4 mL/min.
D.
0.6 mL/min.
If the weight of patient is 80 kg and the label reads 5 mg/2 mL, the administered dose will be 1.2 mL/min. Hence the correct option is B.
The order is Verapamil HCl 0.075 mg/kg IV push over 2 min.
Calculate the total amount of Verapamil needed:
0.075 mg/kg * 80 kg = 6 mg.
Find out how many mL contain 6 mg:
5 mg in 2 mL, so 6 mg will be in (6 mg * 2 mL) / 5mg = 2.4 mL.
Finally, calculate how many mL per minute:
Since the medication is to be given over 2 minutes, the rate will be 2.4 mL / 2 min = 1.2 mL/min.
The total cost C (in dollars) to participate in a ski club is given by the literal equation C=85x+60, where x is the number of ski trips you take.
a. Solve the equation for x.
x=
b. How many ski trips do you take if you spend a total of $315? $485?
ski trips costs $315.
ski trips costs $485.
Answer:
x = 5
Step-by-step explanation:
The total cost C (in dollars) to participate in a ski club is given by the literal equation :
C=85x+60C=85x+60
Where x is the number of ski trips you take.
1. When C = 315 ;substituting the value of C in the above equation.
315=85x+60315=85x+60
=> 85x=315-6085x=315−60
=> 85x=25585x=255
x = 3 trips.
2. When C = 485
485=85x+60485=85x+60
=> 85x=485-6085x=485−60
=> 85x=42585x=425
x = 5 trips.
A town's population has been growing linearly. In 2003, the population was 59.000 and the population has been growing by 1,700 people each year. a. Write a formula for the population x years after 2003. b. What will the town's population be in 2007? c. In what year will the population be 77,700 people?
Answer:
In 2003, the population was 59000 and the population has been growing by 1,700 people each year.
A.
The equation will be:
59000+1700x = (population 'x' years after 2003)
For x, you plug in the amount of years after 2003.
Like if it is the year 2003, the population is [tex]59000+1700(0)[/tex]
= 59000
when it is year 2005, the population is [tex]59000+1700(2)[/tex]
= 62400
B.
The town's population in 2007 will be :
[tex](2007-2003=4)[/tex]
[tex]59000+1700(4)[/tex]
Population = 65800
C.
[tex]59000+1700x=77700[/tex]
=> [tex]1700x=18700[/tex]
x = 11
Means [tex]2003+11=2014[/tex]
Hence, by year 2014 the population will be 77700.
john also bought a new ball. the new ball cost $300 which is three times the price of his old ball less $60. how much did he pay for his old ball?
Answer:
The cost of old ball is $120.
Step-by-step explanation:
Consider the provided information.
The cost of new ball is $300.
Which is three times the price of his old ball less $60.
Let the price of old ball is x.
Thus the above information can be written as:
[tex]3x-60=300[/tex]
[tex]3x=360[/tex]
[tex]x=120[/tex]
Hence, the cost of old ball is $120.
Rita Crudwell was the appointed comptroller and treasurer of the town of Dixon, Illinois (population 15,700 in 2010) for 29 years. Despite her busy, dual job, she was able to establish and run a world renowned quarter horse breeding operation, amassing 52 world championships. I do now know how she found the time and energy to do this but I do know where she got the money: over the course of her last 22 years in office, she embezzled $53,740,394 million dollars from the town (caught in 2012, she is currently serving a 19 year prison term) What would be the "hourly wage"
dollars from the town (caught in 2012, she is currently serving a 19 year prison term) What would be the "hourly wage" for a person that wants to make $53,740,394 million over exactly 22 years? (NOTE: assume 1 year 365.256 days) 1-2 If a certain physics professor gets $65,000/year, how many years would it take for such a person to make $53,740,394 million?
Answer:
a) $278.65 million per hour
b) 826.77 million years
Step-by-step explanation:
Given:
Total money = $53,740,394 million
Time taken to earn the money = 22 years
Now,
1 year = 365.256 days
and 1 day = 24 hours
thus,
22 years = 22 × 365.256 × 24 = 192855.168 hours
Therefore,
for a person that wants to make $53,740,394 million over exactly 22 years, will have hourly wage
= [tex]\frac{\textup{money to be earned}}{\textup{Time taken in hours}}[/tex]
= [tex]\frac{\textup{53,740,394 million}}{\textup{192855.168 hours}}[/tex]
= $278.65 million per hour
Now,
Salary of a physics professor = 65000 /year
Thus,
for physics professor to earn $53,740,394 million number of years taken will be
= [tex]\frac{\textup{$53,740,394 million}}{\textup{65000 /year}}[/tex]
= 826.77 million years
Final answer:
To earn $53,740,394 through embezzlement over 22 years equates to an "hourly wage" of $1,174.60, assuming a 40-hour workweek. It would take a physics professor making $65,000 a year approximately 827 years to earn the same amount.
Explanation:
Calculating the "hourly wage" for embezzling $53,740,394 over 22 years requires us to first determine the total hours worked over those years, assuming a standard full-time job framework of 40 hours per week. Also, to calculate how many years it would take a physics professor earning $65,000 a year to amass the same amount of money embezzled requires straightforward division.
Step 1: Calculate the Total Number of Hours Worked Over 22 years
Number of weeks in a year = 52
Hours worked per week = 40
Total hours worked in a year = 52 weeks * 40 hours/week = 2,080 hours
Total hours worked over 22 years = 2,080 hours/year * 22 years = 45,760 hours
Step 2: Calculate the Hourly "Wage" from Embezzlement
Total embezzled = $53,740,394
Hourly "wage" = Total embezzled / Total hours worked over 22 years = $53,740,394 / 45,760 hours = $1,174.60 per hour
Step 3: Calculate the Years for a Physics Professor to Earn $53,740,394
Annual salary = $65,000
Years required = Total embezzled / Annual salary = $53,740,394 / $65,000 ≈ 826.78 years
If the measure of an exterior angle drawn at vertex M
oftriangle LMN is x, then measurements of angle L +measurements of
angle N is what ?
Answer:
x
Step-by-step explanation:
We are given that measure of an exterior angle which are drawn at vertex M=x
We have to find the value of measurement of angle L+measurement of angle N.
Exterior angle:It is defined as that angle of triangle which is formed by the one side of triangle and the extension of an adjacent side of triangle. The measure of exterior angle is equal to sum of measures of two non-adjacent interior angles of a triangle.
Angle L and angle N are two non-adjacent angles of a given triangle LMN.
By definition of exterior angle
x=Measure of angle L+Measure of angle N
Answer:
An exterior angle of a triangle is equal to the sum of the opposite interior angles. For more on this see Triangle external angle theorem.
If the equivalent angle is taken at each vertex, the exterior angles always add to 360° In fact, this is true for any convex polygon, not just triangles.
For each of the following statements, write negation, contrapositive, converse and inverse. . If P is a square, then P is a rectangle .If n is prime, then n is odd or n is 2 .If 2 is a factor of n and 3 is a factor of n, then 6 is a factor of n
Answer:
i think it is E the last one
Step-by-step explanation:
what is the product of :8.5x(-0.8)x(-12)
Answer:
The product of [tex]8.5 \times (-0.8) \times (-12)[/tex] is 81.6
Step-by-step explanation:
Given : [tex]8.5 \times (-0.8) \times (-12)[/tex]
To Find : Find the product
Solution:
[tex]8.5 \times (-0.8) \times (-12)[/tex]
[tex](-) \times (-) =+[/tex]
So, [tex]8.5 \times 9.6[/tex]
[tex]81.6[/tex]
Hence the product of [tex]8.5 \times (-0.8) \times (-12)[/tex] is 81.6
Step-by-step explanation:
The product of 8.5 \times (-0.8) \times (-12)8.5×(−0.8)×(−12) is 81.6
Step-by-step explanation:
Given : 8.5 \times (-0.8) \times (-12)8.5×(−0.8)×(−12)
To Find : Find the product
Solution:
8.5 \times (-0.8) \times (-12)8.5×(−0.8)×(−12)
(-) \times (-) =+(−)×(−)=+
So, 8.5 \times 9.68.5×9.6
81.681.6
Find the dual of each of these compound propositions. b) (p /\ q/\ r) v s
Answer:
[tex](p\lor q \lor r)\land s[/tex]
Step-by-step explanation:
The dual of a compound preposition is obtained by replacing
[tex]\land \;with\;\lor[/tex]
[tex]\lor \;with\;\land[/tex]
and replacing T(true) with F(false) and F with T.
So, the dual of the compound proposition
[tex](p\land q \land r)\lor s[/tex]
is
[tex](p\lor q \lor r)\land s[/tex]
Answer: (p ∨q∨r)∧s
Step-by-step explanation:
Our proposition is:
(p /\ q/\ r) v s
This means
(P and Q and R ) or S
The proposition is true if P, Q and R are true, or if S is true.
Then the dual of this is
(P or Q or R) and S
The dual of a porposition can be obtained by changing the ∧ for ∨, the ∨ for ∧, the Trues for Falses and the Falses for Trues.
Then, the dual can be writted as:
(p ∨q∨r)∧s
The proposition is true if S is true, and P or Q or R are true.
1) Meredith f ound some lace at a price of 4.0 5/meter in Ireland that she like too much for it. The same lace in the Canada would sell for $5.99/yd. W (S1 0.498 E) (1 yard 3 ft)
Answer: Ireland is €4.05/m
Canada is €3.26/m
Step-by-step explanation:
€4.05/m
$5.99/yd
To compare the prices, we need to transform one of them into the other. Let's transform the Canada price into Ireland price.
As $1 = €0.498
$5.99 * 0.498 = €2.983
€2.983/yd
1yd = 3ft
1ft = 0.3048m
3ft = 0.3048*3 = 0.9144 m
€2.983/yd = €2.983/3ft = €2.983/0.9144 m = €3.26/m
Ireland is €4.05/m
Canada is €3.26/m
A 10-mL graduate weighs 42.745 g. When 5 mL of distilled water are measured in it, the combined weight of graduate and water is 47.675 g. By definition, 5 mL of water should weigh 5 g. Calculate the weight of the measured water and express any deviation from 5 g as a percentage of error.
Answer:
The measured weight of the water = 4.93 g
The percentage error in measured value = 1.4%
Step-by-step explanation:
Given:
Weight of the 10-mL graduate = 42.745 g
Combined weight of graduate and 5 mL water = 47.675 g
5 mL of water should weight = 5 g
thus, actual value of 5 mL water = 5 g
Now,
The measured weight of the water
= (Combined weight of graduate + 5 mL water) - Weight of the 10-mL graduate
= 47.675 g - 42.745 g
= 4.93 g
The percentage error in measured value
= [tex]\frac{\textup{Actual value-calculated value}}{\textup{Actual value}}\times100[/tex]
= [tex]\frac{\textup{5-4.93}}{\textup{5}}\times100[/tex]
or
= 1.4%
The weight of the measured water is 4.930 g, which is slightly less than the theoretical 5 g. The percentage error of the measurement is 1.4%, falling within the acceptable ±5% error range.
Explanation:To calculate the weight of the measured water and the percentage error, we use the information provided. The weight of the empty graduate is 42.745 g, and the combined weight of the graduate and water is 47.675 g. Subtracting the weight of the empty graduate from the combined weight gives us the weight of the water only:
Weight of water only = 47.675 g - 42.745 g = 4.930 g
Since 5 mL of distilled water should ideally weigh 5 g, we can then calculate the percentage error:
Percentage error = [(Target amount of water - Actual volume dispensed) / Target amount of water] × 100%
Percentage error = [(5 g - 4.930 g) / 5 g] × 100%
Percentage error = [0.07 g / 5 g] × 100%
Percentage error = 1.4%
The measured water weighs slightly less than the expected 5 g, with a percentage error of 1.4%, which is within the acceptable range of ±5% error.
Translate this formula into an english sentence using this "dictionary":
A= Salt is added to the soltuiton
D= the solution's boiling point drops
M= The manuel is correct
S= The solution boils sooner
(A --> D) --> (A --> S)
Answer: If the solution's boiling point drops because salt is added to the soltuiton, then the reason the solution boils sooner is the addition of salt to the solution
Step-by-step explanation:
The re are two cause - consequence relations inside an other one.
I use 3 different cause - consequence connectors not to mix them up.
A --> D equals “ D because A “
A --> S equals “ the reason S happens is A “
(A --> D) --> (A --> S) Equals “ if (A --> D) then (A --> S) “
Assume that a password must be at least 8 characters long and include at least 1 digit and at least 1 special character. If people form their password by taking an English word of exactly 6 letters (assume that this password is not case-sensitive) and then adding (in either order) a digit and a special character (e.g flames#1), how many passwords would be possible? (10 points)
Answer:
10,932,240
Step-by-step explanation:
According to the Naspa World list American english have 16,564 6-letters words. Now about the special characters we have the next list !"#$%&'()*+,-./:;<=>?@[\]^_`{|}~ and considering the space as a special character we have a total of 33 special characters. For numbers we have a total of 10 digits.
Then to know how many possibles exists we have to find how many possibles are for the last two characters then.
[tex]33\cdot10=330[/tex]
That is the amount os possibles if always the special character go before de number, but as the number could be before the special character we have to multiply this quantity by 2.
Then we have 16,564 words for the first 6 characters and 660 options for the last two. To know the total amount of possibilities we just need to multiply this numbers, then:
[tex]16,564\cdot660=10,932,240[/tex]
Final answer:
To find the number of possible passwords, calculate the number of 6-letter words possible with 26 letters, then multiply by the number of digits (10), the number of special characters (32), and account for the two possible orders of digit and special character, leading to the formula 26⁶ * 10 * 32 * 2.
Explanation:
The question involves calculating the number of possible passwords that can be formed by using an English word of exactly 6 letters, followed by a digit and a special character in any order. To calculate this, we consider that there are 26 letters in the English alphabet, 10 possible digits (0-9), and assuming a common set of 32 possible special characters (for example, punctuation marks, symbols, etc.).
First, calculate the number of 6-letter English words that can be formed. Since the question mentions the word is not case-sensitive, each position in the word can be filled by any of the 26 letters. Therefore, the number of 6-letter words is 26⁶.
Then, for each of these words, a digit (10 choices) and a special character (32 choices) can be added in either order. Since the order matters, there are 2 different ways of arranging these two additional characters (digit-special character or special character-digit).
Therefore, the total number of possible passwords is calculated as 26⁶ * 10 * 32 * 2.
This approach highlights the significant number of combinations possible even with seemingly simple password creation rules, underlining the importance of complex passwords for enhancing security.
Is the statement given below true or false? Give
ajustification if true or a counterexample if false
ALL ISOSCELES TRIANGLES WITH CONGRUENT VERTEX ANGLES
ARESIMILAR.
Answer:
Yes, "All isosceles triangles with congruent vertex angles are similar".
Step-by-step explanation:
Consider the provided statement.
All isosceles triangles with congruent vertex angles are similar.
As we know that the two sides of an isosceles triangle are same.
It is given that the isosceles triangles with congruent vertex angles.
If vertex angles are congruent it means the opposite side of those angles are congruent. Also the sums of the base angles are the same,
As we know the base angles of an isosceles triangle are congruent, so by the AAA similarity we can say "All isosceles triangles with congruent vertex angles are similar".
Or
let say ΔABC and ΔDEF are isosceles triangles where AB=DE and AC=DF
It means ∠B=∠E and ∠C=∠F also it is given that ∠A=∠D
Thus. from AAA similarity we can say "All isosceles triangles with congruent vertex angles are similar".
14 of 16 (12 complete) In a baseball league consisting of 7 teams, each team plays each of the other teams twice. How many games will be played? There will be games played.
Answer: There will be 42 games played.
Step-by-step explanation:
The number of combination to arrange n things if r things are taken at a time:-
[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Similarly, the number of combination to arrange 7 teams if 2 teams are taken at a time:-
[tex]^7C_2=\dfrac{7!}{2!(7-2)!}\\\\=\dfrac{7\times6\times5!}{2\times5!}=21[/tex]
∴ Number of combination to arrange 7 teams if 2 teams are taken at a time=21
Also, each team plays each of the other teams twice.
Then, the number of games will be played: [tex]21\times2=42[/tex]
Hence, There will be 42 games played.
Final answer:
To calculate the total number of games played in a league with 7 teams where each team plays the others twice, use the formula n(n - 1) × 2, which results in 7 * 6 * 2 = 84 games.
Explanation:
To find out the total number of games played in a baseball league with 7 teams where each team plays each of the other teams twice, we can use the formula for the number of games in a round-robin tournament: n(n - 1), where n is the number of teams. Since each team plays each other twice, the formula modifies to n(n - 1) × 2.
Substituting the number of teams (7) into the formula gives us: 7 * (7 - 1) × 2 = 7 * 6 × 2 = 42 × 2 = 84 games in total.
A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $3,000 or $6,000. If the partnership raised $258,000, then how many investors contributed $3,000 and how many contributed $6,000?
x = $3,000 investors
y =
$6,000 investors
Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question.
A jar contains 70 nickels and dimes worth $5.70. How many of each kind of coin are in the jar?
Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question.
The concession stand at an ice hockey rink had receipts of $7400 from selling a total of 3000 sodas and hot dogs. If each soda sold for $2 and each hot dog sold for $3, how many of each were sold?
x= soda
y= hotdogs
Answer:
1) There were 34 $3,000 investors and 26 $6,000 investors.
2) There are 26 nickels and 44 dimes in the jar.
3) 1600 sodas and 1400 hot dogs were sold.
Step-by-step explanation:
1) A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $3,000 or $6,000. If the partnership raised $258,000, then how many investors contributed $3,000 and how many contributed $6,000?
x is the number of investors that contributed 3,000.
y is the number of investors that contributed 6,000.
Building the system:
There are 60 investors. So:
[tex]x + y = 60[/tex]
In all, the partnership raised $258,000. So:
[tex]3000x + 6000y = 258000[/tex]
Simplifying by 3000, we have:
[tex]x + 2y = 86[/tex]
Solving the system:
The elimination method is a method in which we can transform the system such that one variable can be canceled by addition. So:
[tex]1)x + y = 60[/tex]
[tex]2)x + 2y = 86[/tex]
I am going to multiply 1) by -1, then add 1) and 2), so x is canceled.
[tex]1) - x - y = -60[/tex]
[tex]2) x + 2y = 86[/tex]
[tex]-x + x -y + 2y = -60 +86[/tex]
[tex]y = 26[/tex]
Now we get back to equation 1), and find x
[tex]x + y = 60[/tex]
[tex]x = 60-y = 60-26 = 34[/tex]
There were 34 $3,000 investors and 26 $6,000 investors.
2) A jar contains 70 nickels and dimes worth $5.70. How many of each kind of coin are in the jar?
I am going to say that x is the number of nickels and y is the number of dimes.
Each nickel is worth 5 cents and each dime is worth 10 cents.
Building the system:
There are 70 coins. So:
[tex]x + y = 70[/tex]
They are worth $5.70. So:
[tex]0.05x + 0.10y = 5.70[/tex]
Solving the system:
[tex]1) x+y = 70[/tex]
[tex]2) 0.05x + 0.10y = 5.70[/tex]
I am going to divide 1) by -10, so we can add and cancel y:
[tex]1) -0.1x -0.1y = -7[/tex]
[tex]2) 0.05x + 0.1y = 5.70[/tex]
[tex] -0.1x + 0.05x -0.1y + 0.1y = -1.3[/tex]
[tex]-0.05x = -1.3[/tex] *(-100)
[tex]5x = 130[/tex]
[tex]x = \frac{130}{5}[/tex]
[tex]x = 26[/tex]
Now:
[tex]x+y = 70[/tex]
[tex]y = 70 - x = 70 - 26 = 44[/tex]
There are 26 nickels and 44 dimes in the jar.
3) The concession stand at an ice hockey rink had receipts of $7400 from selling a total of 3000 sodas and hot dogs. If each soda sold for $2 and each hot dog sold for $3, how many of each were sold?
x is the nuber of sodas and y is the number of hot dogs.
Building the system:
3000 items were sold. So:
[tex]x + y = 3000[/tex]
$7,4000 was the total price of these items. So:
[tex]2x + 3y = 7400[/tex]
Solving the system:
[tex]1)x + y = 3000[/tex]
[tex]2)2x + 3y = 7400[/tex]
I am going to multiply 1) by -2, so we can cancel x
[tex]1) -2x -2y = -6000[/tex]
[tex]2) 2x + 3y = 7400[/tex]
[tex]-2x + 2x -2y + 3y = -6000 + 7400[/tex]
[tex]y = 1400[/tex]
Now, going back to 1)
[tex]x + y = 3000[/tex]
[tex]x = 3000-y = 3000-1400 = 1600[/tex]
1600 sodas and 1400 hot dogs were sold.
Which of the following numbers could not possibly be a probability? Justify your answer. 0.123 negative 0.577 0 What must be true for a number to be a probability? A. The number must be rational. B. The number must be between 0 and 1, exclusive. C. The number must be between minus1 and 1, exclusive. D. The number must be between 0 and 1, inclusive. E. The number must be between minus1 and 1, inclusive. F. The number must be positive. Which of these numbers could not possibly be a probability? Select all that apply. A. negative 0.577 B. 0.123 C. 0 D. All of the above numbers are possible probabilities.
Answer:
First question: -0.577 cannot be a probability.
Second question: The number must be between 0 and 1, inclusive (D)
Third question: -0.577 cannot be a probability.
Step-by-step explanation:
A probability is a real number that is in the interval [0, 1]. Therefore, any number outside this range cannot be considered a probability. Under this premise:
First question: -0.577 cannot be a probability.
Second question: The number must be between 0 and 1, inclusive (D)
Third question: -0.577 cannot be a probability.
The number negative 0.577 cannot be a probability since it is outside the range of 0 and 1, which defines the allowed range for probabilities. Thus, the correct answer is option A (negative 0.577).
Explanation:The number that could not possibly be a probability is negative 0.577. This is because the rules for a number to be considered a probability state that it must be between 0 and 1, inclusive. Therefore, option A (negative 0.577) could not be a probability, while option B (0.123) and option C (0) are both possible probabilities as they fall within the allowed range.
Probabilities must be real numbers between 0 and 1, which includes both 0 (representing an impossible event) and 1 (representing a certain event). Applying this principle, the correct answer to what must be true for a number to be a probability is option D, which states that the number must be between 0 and 1, inclusive. In conclusion, only negative 0.577 is not a possible probability.
Help! BRANLIEST and 300 points!!!
PB is a line segment on a number line. It has endpoints at -2 and 12. What is the coordinate of its midpoint?
There are 16 tablespoons in one cup. Which table correctly relates the number of cups to the number of tablespoons.
Answer:
Step-by-step explanation:
The first one
1 16
2 32
4 64
8 128
The table that correctly relates the number of cups to the number of tablespoons is the first table.
How to interpret integral multiplication?Suppose that there are two positive integer numbers( numbers like 1,2,3,.. ) as a and b
Then, their multiplication can be interpreted as:
[tex]a \times b = a + a + ... + a \: \text{(b times)}\\\\a \times b = b + b +... + b \: \text{(a times)}[/tex]
For example,
[tex]5 \times 2 = 10 = 2 + 2 + 2 + 2 + 2 \: \text{(Added 2 five times)}\\or\\5 \times 2 = 10 = 5 + 5 \: \text{(Added 5 two times)}[/tex]
It is specified that:
In 1 cup, there are 16 tablespoons
In 2 cups, there would be 16+16 tablespoons,
and so on,
in 'n' cups, there would be 16+16+...+16 (n times ) = 16 × n tablespoons.
Checking all the tables one by one:
Second table is incorrect because it says that 16 cups = 1 tablespoon which is wrong.
The third table is saying in 32 cups there are only 16 tablespoons, which is obviously wrong as number of tablespoon is always going to be bigger than the number of cups.
The first table is correct since:
Number of cups(n) Number of tablespoons ( 16 × n)
1 16 × 1 =16
2 16 × 2 = 32
4 16 × 3 = 64
8 16 × 4 = 128
So it follows the formula we obtained for the number of tablespoons for given number of cups.
Learn more about multiplication here:
https://brainly.com/question/26816519
multiply(5+2i)(4-3i) enter your answer in standard form
Answer:
26-7i
Step-by-step explanation:
1. expand it you will get : 20-15i+8i+6 ( notice that i^2= -1 )
2. simplify it: 26-7i
Using complex numbers, it is found that the result of the multiplication is: 26 - 7i
A complex number has the format: [tex]z = a + bi[/tex]The important relation is: [tex]i^2 = -1[/tex].In this problem, the multiplication is: [tex](5 + 2i)(4 - 3i)[/tex].
Applying the distributive property:
[tex](5 + 2i)(4 - 3i) = 20 - 15i + 8i -6i^2 = 20 - 7i + 6 = 26 - 7i[/tex]
The result is: 26 - 7i
A similar problem is given at https://brainly.com/question/19392811
Assume that men's weights are normally distributed with a mean of 172 lb and a standard deviation of 29 lb. If 4 man is randomly selected, find the probability that they have a mean weight between 160 lb and 180 lb.(up to four decimal place, please)
The probability that the mean weight of 4 randomly selected men is between 160 lb and 180 lb is approximately 0.5025 (up to four decimal places).
To find the probability that the mean weight of 4 randomly selected men falls between 160 lb and 180 lb, you can use the Central Limit Theorem.
According to the Central Limit Theorem, the distribution of sample means will be approximately normally distributed, regardless of the distribution of the population, as long as the sample size is sufficiently large.
The formula for the standard error of the mean [tex](\(SE\))[/tex] is given by:
[tex]\[ SE = \frac{\sigma}{\sqrt{n}} \][/tex]
where:
- [tex]\(\sigma\)[/tex] is the population standard deviation,
- [tex]\(n\)[/tex] is the sample size.
In this case, [tex]\(\sigma = 29\)[/tex] lb (population standard deviation) and [tex]\(n = 4\)[/tex] (sample size).
[tex]\[ SE = \frac{29}{\sqrt{4}} = \frac{29}{2} = 14.5 \][/tex]
Now, you can find the z-scores for the values 160 lb and 180 lb using the formula:
[tex]\[ z = \frac{X - \mu}{SE} \][/tex]
where:
- [tex]\(X\)[/tex] is the value you're interested in,
- [tex]\(\mu\)[/tex] is the population mean,
- [tex]\(SE\)[/tex] is the standard error of the mean.
For [tex]\(X = 160\)[/tex] lb:
[tex]\[ z_{160} = \frac{160 - 172}{14.5} \approx -0.8276 \][/tex]
For [tex]\(X = 180\)[/tex] lb:
[tex]\[ z_{180} = \frac{180 - 172}{14.5} \approx 0.5517 \][/tex]
Now, you can use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores.
The probability that the mean weight is between 160 lb and 180 lb is given by the difference in these probabilities:
[tex]\[ P(160 < \text{mean} < 180) = P(z_{180}) - P(z_{160}) \][/tex]
Substitute the z-scores:
[tex]\[ P(160 < \text{mean} < 180) = P(0.5517) - P(-0.8276) \][/tex]
Using a standard normal distribution table or calculator, you can find these probabilities. Once you find the probabilities, subtract the smaller from the larger to get the probability in the specified range.
[tex]\[ P(160 < \text{mean} < 180) \approx 0.7082 - 0.2057 \][/tex]
[tex]\[ P(160 < \text{mean} < 180) \approx 0.5025 \][/tex]
So, the probability that the mean weight of 4 randomly selected men is between 160 lb and 180 lb is approximately 0.5025 (up to four decimal places).
PLEASE HELP ASAP
if p=(8,12) is on the graph of f(x). which point is on the graph of g(x)=3f(x-2)+4?
Answer:
The point (10,40) is on the graph of g
Step-by-step explanation:
If the point (8,12) is on the graph of f(x) means that
f(8)=12
So, if you choose x=10, then x-2 = 8 and
g(10) = 3f(10-2)+4 = 3f(8)+4
But f(8) = 12, so
3f(8)+4 = 36+4 = 40
Hence g(10) = 40
Which means that the point (10,40) is on the graph of g