Answer:
[tex]x_{1}=\frac{-13+\sqrt{153}}{2}\\x_{2}=\frac{-13-\sqrt{153}}{2}[/tex]
Step-by-step explanation:
The given expression is
[tex]x^{2}=-13x-4[/tex]
To solve this quadratic equation, we first need to place all terms in one side of the equation sign
[tex]x^{2} +13x+4=0[/tex]
Now, to find all solutions of this expression, we have to use the quadratic formula
[tex]x_{1,2}=\frac{-b\±\sqrt{b^{2}-4ac}}{2a}[/tex]
Where [tex]a=1[/tex], [tex]b=13[/tex] and [tex]c=4[/tex]
Replacing these values in the formula, we have
[tex]x_{1,2}=\frac{-13\±\sqrt{(13)^{2}-4(1)(4)}}{2(1)}\\x_{1,2}=\frac{-13\±\sqrt{169-16}}{2}=\frac{-13\±\sqrt{153}}{2}[/tex]
So, the solutions are
[tex]x_{1}=\frac{-13+\sqrt{153}}{2}\\x_{2}=\frac{-13-\sqrt{153}}{2}[/tex]
If we approximate each solution, it would be
[tex]x_{1}=\frac{-13+\sqrt{153}}{2}\approx -0.32\\\\x_{2}=\frac{-13-\sqrt{153}}{2} \approx -12.68[/tex]
Answer:
D on Edge
Step-by-step explanation:
A statistical procedure used to determine whether observed frequencies at each level of one categorical variable are similar to or different from frequencies expected, is called the chi-square:
Answer:
This statement is true.In statistics, the chi-square test is used to prove a specific hypothesis, accepting or rejecting the null one. In order to find enough evidence to prove the hypothesis, we compare two group of frequencies, which belongs to two different groups (like a quasi-experimental design, with a control and experimental group). The researcher have set an expected frequency, based on the hypothesis, and then he/she will observe a frequency from the data recollected.
Therefore, by comparing this two frequencies (the expected with the observed), the researcher is able to demonstrate the hypothesis.
Find the probability of each outcome when a biased die is rolled, if rolling a 2 or rolling a 4 is three times as likely as rolling each of the other four numbers on the die and it is equally likely to roll a 2 or a 4.
Answer:
Let's x be the probability for 1, 3, 5 and 6.
The probability for 2 and 4 is going to be 3x.
The sum of the probabilities of all possible outcomes is always 1.
P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1
x + 3x + x + 3x + x + x = 1
10x = 1
x = 1/10
The probability of obtaining 1, 3, 5 or 6 is 1/10
The probability for 2 and 4 is 3/10
The probability of rolling a 2 or a 4 is [tex]$\frac{3}{14}$[/tex], and the probability of rolling any of the other numbers (1, 3, 5, or 6) is [tex]$\frac{1}{14}$.[/tex]
To solve this problem, we need to distribute the total probability of 1 (since the sum of all probabilities must equal 1) among the six outcomes of the die according to the given conditions.
Let's denote the probability of rolling a 2 or a 4 as $p$. According to the problem, rolling a 2 or rolling a 4 is three times as likely as rolling each of the other four numbers. Therefore, the probability of rolling a 1, 3, 5, or 6 is [tex]$\frac{p}{3}$.[/tex]
Since there are two outcomes with probability $p$ (rolling a 2 and rolling a 4) and four outcomes with probability $\frac{p}{3}$ (rolling a 1, 3, 5, or 6), we can set up the following equation to represent the total probability:
[tex]\[ 2p + 4\left(\frac{p}{3}\right) = 1 \][/tex]
Now, let's solve for $p$:
[tex]\[ 2p + \frac{4p}{3} = 1 \][/tex]
[tex]\[ \frac{6p + 4p}{3} = 1 \][/tex]
[tex]\[ \frac{10p}{3} = 1 \][/tex]
[tex]\[ 10p = 3 \][/tex]
[tex]\[ p = \frac{3}{10} \][/tex]
So, the probability of rolling a 2 or a 4 is[tex]$p = \frac{3}{10}$.[/tex]
The probability of rolling a 1, 3, 5, or 6 is [tex]$\frac{p}{3} = \frac{3}{10} \times[/tex] [tex]\frac{1}{3} = \frac{1}{10}$.[/tex]
However, we must remember that the total probability must be distributed equally between rolling a 2 and rolling a 4. Since they are equally likely, each has a probability of half of $p$:
[tex]\[ p_{2} = p_{4} = \frac{p}{2} = \frac{3}{10} \times \frac{1}{2} = \frac{3}{20} \][/tex]
Now, we can state the final probabilities for each outcome:
- The probability of rolling a 1 is [tex]$\frac{1}{10}$.[/tex]
- The probability of rolling a 2 is [tex]$\frac{3}{20}$.[/tex]
- The probability of rolling a 3 is [tex]$\frac{1}{10}$.[/tex] - The probability of rolling a 4 is [tex]$\frac{3}{20}$.[/tex]
The probability of rolling a 5 is [tex]$\frac{1}{10}$.[/tex]
help me with out this one thanks!
Answer:
9.5
Step-by-step explanation:
It keeps repeating the line goes all the way up then it keeps going to 9 then to 9.5 in the middle of 9 so it means its in between 10 so its 9.5 to 9 then 9.5 it repeats so mostly the answer is 9.5
hope i helped
please mark me as brainliest please
Hey guys, how would i write this? Thank youuuu
Answer:
(x-4)² - 11
Step-by-step explanation:
You find half of 8 which is 4 and half of x² which is x. this forms (x - 4).
However this would expand as
x²-8x+16 which isn't the expression. So to make it 5, you have to take away 11 leaving you with
(x-4)²-11
Answer:
(x - 4)^2 - 11.
Step-by-step explanation:
x^2 - 8x + 5
Note that x^2 - 8x = (x - 4)^2 - 16 so we have:
(x - 4)^2 - 16 + 5
= (x - 4)^2 - 11.
To get (x - 4)^2 - 16 I used the identity:
x^2 + ax = ( x + a/2)^2 - a^2/4 with a = -8.
The length of the escalator is 30 feet and the distance between the floors is 12 feet. Find the distance from the base of the escalator to the point on the first floor directly below the top of the escalator.
Answer:
Distance from the base of the escalator to the point on the first floor directly below the top of the escalator = 27.5 feet
Step-by-step explanation:
Given:
Length of escalator = 30 feet
Distance between the floors = 12 feet
To find the distance from base of escalator to the point on the first floor directly below the top of the escalator we will create the figure for the situation.
From the figure we see that a triangle ABC is formed.
We see that the Δ ABC is a right triangle.
Applying Pythagorean theorem for right triangle ABC to find the missing side.
[tex]AB^2=BC^2+AC^2[/tex]
AB = 30 feet
BC = 12 feet
Plugging in values in the theorem.
[tex]30^2=12^2+AC^2[/tex]
Solving for AC.
[tex]900=144+AC^2[/tex]
Subtracting both sides by 144.
[tex]900-144=144+AC^2-144[/tex]
[tex]756=AC^2[/tex]
Taking square root both sides.
[tex]\sqrt{756}=\sqrt{AC^2}[/tex]
[tex]27.5=AC[/tex]
∴ [tex]AC=27.5[/tex] feet.
∴ Distance from the base of the escalator to the point on the first floor directly below the top of the escalator = 27.5 feet
To find the distance from the base of the escalator to the point on the first floor directly below the top of the escalator, we can use the Pythagorean theorem. The distance is approximately 27 feet.
Explanation:To find the distance from the base of the escalator to the point on the first floor directly below the top of the escalator, we can use the Pythagorean theorem. The length of the escalator represents the hypotenuse of a right triangle, and the distance between the floors represents one of the legs.
We can use the formula a^2 + b^2 = c^2, where a and b are the legs of the triangle and c is the hypotenuse. Substituting the given values, we have 12^2 + b^2 = 30^2. Simplifying the equation, we get b^2 = 30^2 - 12^2. Calculating the value, we find that b^2 = 756, which means b is equal to the square root of 756. Rounding to the nearest foot, the distance from the base of the escalator to the point on the first floor directly below the top of the escalator is approximately 27 feet.
Learn more about Distance calculation here:
https://brainly.com/question/34212393
#SPJ3
The balance in the office supplies account on January 1 was $6,791, the supplies purchased during January were $3,205, and the supplies on hand on January 31 were $2,155. The amount to be used for the appropriate adjusting entry is?
Answer:
$7,661
Step-by-step explanation:
Closing balance = Opening balance + purchases - Issued items
Given
Office supplies account on January 1 = $6,791 - Opening balance
Purchases = $3,205
Supplies on hand on January 31 = $2,155 - Closing balance
Substituting into the formula above
2155 = 6791 + 3025 - Issued items
Issued items = 6791 + 3025 - 2155
= $7,661
The amount to be used for the appropriate adjusting entry is $7,661
Final answer:
The adjusting entry for the used office supplies for the month of January is $7,841, which is calculated by subtracting the supplies on hand at the month's end from the sum of the starting balance and purchases made during the month.
Explanation:
To calculate the adjusting entry for office supplies, you need to calculate the cost of supplies that were used during the month. Start with the balance of supplies on hand at the beginning of the month, add the purchases made during the month, and then subtract the balance of supplies on hand at the end of the month.
The calculation is as follows:
Starting balance on January 1: $6,791
Add purchases during January: $3,205
Subtract ending balance on January 31: $2,155
The adjusting entry for supplies used = (Starting balance + Purchases) - Ending balance
= ($6,791 + $3,205) - $2,155
= $9,996 - $2,155
= $7,841
Therefore, the adjusting entry to record the office supplies used would be for $7,841.
The profit function p(x) of a tour operator is modeled by p(x) = −2x^2 + 700x − 10000, where x is the average number of tours he arranges per day. What is the range of the average number of tours he must arrange per day to earn a monthly profit of at least $50,000?
Answer: The correct answer is D). Between 150 and 200; exclusive
Step-by-step explanation:
Given profit function p(x) of a tour operator is modeled by
p(x)=[tex](-2)x^{2} +700x-10000[/tex]
Where, x is the average number of tours he arranges per day.
To find number of tours to arrange per day to get monthly profit of at least 50,000$:
Now, he should make at-least 50000$ profit.
we can write as p(x)>50000$
[tex](-2)x^{2} +700x-10000\geq50000[/tex]
[tex](-2)x^{2} +700x-60000\geq0[/tex]
Roots are x is 150 and 200
(x-150)(x-200)>0
Case 1 : x>150 and x>200
x>150 also satisfy the x>200.
Case2: x<100 and x<200
x<200 also satisfy the x<100
Thus, the common range is 150<x<200
The correct answer is D). Between 150 and 200; exclusive
Answer: between 150 and 200; inclusive
Step-by-step explanation:
The answer is 'inclusive' NOT 'exclusive.'
Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 3x boxes?
Answer:
6 minutes
Step-by-step explanation:
Machine A produces x boxes in 10 minutes
In one minute, the machine produces x/10 boxes
Machine B produces 2x boxes in 5 minutes
In one minute, the machine produces 2x/5 boxes
Therefore in one minutes, both boxes working together will produce
= 2x/5 + x/10
=5x/10
=x/2 boxes
To produce 3x boxes, the time required
= 3x/(x/2)
= 3 × 2
= 6
It take machines A and B, working simultaneously at their respective constant rates, to produce 3x boxes in 6 minutes
You measure 20 dogs' weights, and find they have a mean weight of 64 ounces. Assume the population standard deviation is 11.5 ounces. Based on this, construct a 95% confidence interval for the true population mean dog weight.
95% confidence interval would be (58.96, 69.04).
Step-by-step explanation:
Since we have given that
Number of dogs' weight = 20
Mean = 64 ounces
Standard deviation = 11.5 ounces
We need to find the 95% confidence interval.
So, z = 1.96
so, interval would be
[tex]\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=64\pm 1.96\times \dfrac{11.5}{\sqrt{20}}\\\\=64\pm 5.04\\\\=(64-5.04,64+5.04)\\\\=(58.96,69.04)[/tex]
Hence, 95% confidence interval would be (58.96, 69.04).
Suppose you buy flour and corn meal in bulk to make flour tortillas and corn tortillas flour cost $1.50 per pound and corn meal cost $2.50 per pound do you want to spend masking $25 on flour and corn meal but you need at least 6 pounds altogether Write a system of linear equalities
Answer:
1.50X+2.50Y=25&X+Y=6 are required systems(Solution: X=16 and Y=-10)
Explanation:
》Total money that will be spent on flour and corn meal altogether(T)
=$25
》Since it is not mentioned that whether corn and flour are bought in same quantity or not, we will assume them of different quantity.
i.e.,Suppose
》X pound of flour is bought
&
》Y pound of corn is bought.
So,
》Cost of flour(F)=$1.50X
》Cost of corn(C)=$2.50Y
So total cost will be sum of cost of flour and corn altogether,
Writing it in equation(linear),
F+C=T
1.50X+2.50Y=25Also,
Total pounds=6
ie,
X+Y=6The system of linear equations is x + y = 6 and 1.5x + 2.5y = 25.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Assume you purchase flour and corn dinner in mass to make flour tortillas and corn tortillas flour cost $1.50 per pound and corn feast cost $2.50 per pound would you like to spend veiling $25 on flour and corn feast yet you want somewhere around 6 pounds by and large
Let x be the number of pounds of flour and y be the number of pounds of corn meal. Then the system of linear equalities is given as,
x + y = 6
1.5x + 2.5y = 25
The system of linear equations is x + y = 6 and 1.5x + 2.5y = 25.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ5
pls help asap
Given the number of people that are going on the trip, what is the total amount you will you spend on food and lodging each day?
$525 each day
Given the number of people that are going on the trip, what is the total amount you will spend on luggage for everybody?
$230 for everyone
Now use the amount you spend on Daily expenses to make an equation in y=mx+b form that will give you the expenses (y) for any amount of days (x).
Total Expense equation:
Answer:
y=525x+230
Step-by-step explanation:
525 is spent everyday. x is the number of days, so with each day $525 is spent.
$230 is a one time cost, regardless of how many days they stay on the trip.
how do i set it up ?
Answer:
m∠A = m∠D = 40°
Step-by-step explanation:
Angles A and D are corresponding angles in the congruent triangles, so have the same measure. You set one measure equal to the other:
x + 20 = 2x
To solve this, subtract x from both sides:
20 = x
Then both angle measures are 2x = 40°.
A rancher has 280 feet of fence with which to enclose three sides of a rectangular field (the fourth side is a cliff wall and will not require fencing). Find the dimensions of the field with the largest possible area. (For the purpose of this problem, the width will be the smaller dimension (needing two sides); the length with be the longer dimension (needing one side).)
length = feet
width = feet
What is the largest area possible for this field?
area = feet-squared
Enter your answers as numbers. If necessary, round to the nearest hundredths.
Answer:
x = 140 ft
w = 70 ft
A(max) = 9800 ft²
Step-by-step explanation:
We have:
280 feet of fence to enclose three sides of a rectangular area
perimeter of the rectangle ( 3 sides ) is
p = L = x +2w w = (L - x ) / 2 w = ( 280 - x ) / 2
where:
x is the longer side
w is the width
A(x,w) = x*w ⇒ A(x) = x* ( 280 - x ) / 2 ⇒ A(x) = (280x -x²)/2
Taking derivatives on bth sides of the equation
A´(x) = ( 280 -2x)*2 /4 A´(x) = 0 ( 280 -2x) = 0
280 -2x = 0 x = 280/2
x = 140 ft
And w = ( 280 - x ) / 2 ⇒ w =( 280 -140 )/ 2
w = 70 ft
A(max) = 9800 ft²
Which of the following is a radical equation? x + StartRoot 5 EndRoot = 12 x squared = 16 3 + x StartRoot 7 EndRoot = 13 7 StartRoot x EndRoot = 14
Answer:
The equation [tex]7\,\sqrt{x} =14[/tex] is a radical equation.
Step-by-step explanation:
If the equations given are (as I can read them from your typing):
a) [tex]x+\sqrt{5} =12[/tex]
b) [tex]x^2=16[/tex]
c) [tex]3+x\,\sqrt{7} =13[/tex]
d) [tex]7\,\sqrt{x} =14[/tex]
The only radical equation is the last one : [tex]7\,\sqrt{x} =14[/tex], because it is the only one where the unknown appears inside the root. The name "radical equations" is associated with the fact that the unknown is contained inside the root and therefore the process involved in solving for the unknown will need to include the elimination of the root via algebraic methods to free the unknown.
Notice that the options a) and c) have roots, but what appears inside them are numbers (5 and 7 respectively), and not an unknown like "x". Equation b) doesn't contain a root, and wouldn't classify as a radical equation.
A radical equation is one which contains roots in it, specially those which has root over variables or things whose values changes.
Thus, by above definition, we will have the fourth option: [tex]7\sqrt{x} = 14[/tex] as a radical equation.
Given the equations: [tex]x + \sqrt{5} = 12\\[/tex] [tex]x^2 = 16[/tex] [tex]3 + x\sqrt{7} = 13\\[/tex] [tex]7\sqrt{x} = 14[/tex]Explanation:A radical equation is one which contains roots in it, specially those which has root over variables or things whose values changes.
Since only in the fourth option we see there's root over x which is a variable here, thus the fourth option: [tex]7\sqrt{x} = 14[/tex] is a radical equation.
Rest of the options, although containing roots, aren't having variables inside the root, thus they aren't classified as radical equations.
Learn more about radical equations here:
https://brainly.com/question/8606917
The fraction 6/12 can be written as which decimal?
A) 0.2
B) 0.25
C) 0.33
D) 0.5
Mr. Ruiz was a principal at Wilson high for 6 years. He became principal after teaching at the school for 13 years. He first began teaching two years after graduating from college in 1973. During what years was Mr. Ruiz principal of Wilson high
Answer:
From years 1988 to 1994
Step-by-step explanation:
The trick in this question is to start from last conditions.
Mr. Ruiz graduated in 1973. Started to teach 2 years after, which means, 1975.
He taught for 13 years, which means from 1975 to (1975 + 13)1988.
He became principle only after teaching for 13 years, which means he started to be principle for 1988. And he continued to be for 6 years which means, (1988 + 6) 1994.
Thus, years for which Mr. Ruiz was principle were From 1988 to 1994.
A furniture company is introducing a new line of lounge chairs next quarter. These are the cost and revenue functions, where x represents the number of chairs to be manufactured and sold: R(x) = 1,248x – 8.32x2 C(x) = 36,400 – 83.2x For the company to make a profit on the chairs, the selling price can go no lower than $ and no higher than $.
Answer:
lower limit: $208upper limit: $956.80Step-by-step explanation:
For cost and revenue functions C(x) = 36400-83.2x and R(x) = 1248-8.32x², you want to know the selling price limits that will let the company make a profit.
ProfitProfit is the difference between revenue and cost.
P(x) = R(x) -C(x)
P(x) = 1248-8.32x² -(36400-83.2x) . . . . . . use the given functions
P(x) = -8.32(x² -160x +4375) . . . . . . . . remove common factor
P(x) = -8.32(x -35)(x -125) . . . . . . factor
The profit will be zero when the factors are zero, for x = 35 and x = 125.
PriceWe have to assume the demand function is found by dividing the revenue by the number of chairs sold.
R(x) = x(price) = x(1248 -8.32x)
Then the price is ...
price = 1248 -8.32x . . . . . . . . . . . where x is the number of chairs sold
When selling 125 chairs, the price is ...
1248 -8.32(125) = 208 . . . . . dollars
When selling 35 chairs, the price is ...
1248 -8.32(35) = 956.80 . . . . dollars
For the company to make a profit, the selling price can go no lower than $208 and no higher than $956.80.
__
Additional comment
These prices will result in 0 profit, as the number of chairs sold makes the revenue equal to the cost. If we require sales of 36 to 124 chairs, so profit is positive, then the price limits are $216.32 and $948.48. Profit will be maximized when 80 chairs are sold for $582.40 each.
If [tex]x-12\sqrt{x} +36=0[/tex], what is the value of x?
A. [tex]6[/tex]
B. [tex]6^{2}[/tex]
C. [tex]6^{3}[/tex]
D. [tex]6^{4}[/tex]
Answer:
x = 36
Step-by-step explanation:
[tex] x - 12\sqrt{x} + 36 = 0 [/tex]
Subtract x and 36 from both sides.
[tex] -12\sqrt{x} = -x - 36 [/tex]
Divide both sides by -1.
[tex] 12\sqrt{x} = x + 36 [/tex]
Square both sides.
[tex] 144x = x^2 + 72x + 1296 [/tex]
Subtract 144x from both sides.
[tex] 0 = x^2 - 72x + 1296 [/tex]
Factor the right side.
[tex] 0 = (x - 36)^2 [/tex]
[tex] x - 36 = 0 [/tex]
[tex] x = 36 [/tex]
Since the solution of the equation involved squaring both sides, we musty check the answer for possible extraneous solutions.
Check x = 36:
[tex] x - 12\sqrt{x} + 36 = 0 [/tex]
[tex] 36 - 12\sqrt{36} + 36 = 0 [/tex]
[tex] 36 - 12\times 6 + 36 = 0 [/tex]
[tex] 36 - 72 + 36 = 0 [/tex]
[tex] 0 = 0 [/tex]
Since 0 = 0 is a true statement, the solution x = 36 is a valid solution.
Alberto has 2 cats. The smaller cat weighs 10 3/4 pounds. The larger cat weighs 15 1/3 pounds. How much do the cats weigh altogether? A.26 1/12 B.26 11/12 C.25 4/7 D.25 7/12
The total weight of the smaller and the bigger cat Alberto has is 26 1/12 pounds.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Alberto has 2 cats.
The smaller cat weighs 10 3/4 pounds and the larger cat weighs 15 1/3 pounds.
Therefore, The weights of the cats together is the sum of their individual
weights which is,
= (10 3/4 + 15 1/3) pounds.
= (43/4 + 46/3) pounds.
= [(3×43 + 4×46)/12] pounds.
= (129 + 184)/12 pounds.
= 313/12 pounds.
= 26 1/12 pounds.
So, Together the cats weigh 26 1/12 pounds.
learn more about fractions here :
https://brainly.com/question/10354322
#SPJ5
Gabe went ot lunch with his best friend the bill costs 16.40 dollers before trax and tip he paid a 9 persent tax and left a 20 persent tip howm much did gabe spend
Answer:
Step-by-step explanation:
Gabe went out for lunch with his best friend the bill costs $16.40
This amount was before tax and the tip that he wanted to give.
He paid a 9 percent tax on the bill. The amount of the 9 percent tax is 9/100 × 16.40 = 0.09 × 16.40 = $1.476
He left a 20 percent tip. This means that amount left as tip is 20/100 × 16.40 = 0.2×16.40 = $3.28
The amount that Gabe paid would be the sum of the bill, the tip and the amount paid on tax. It becomes
16.40 + 1.476 + 3.28 = $21.156
Stella likes to run laps around the edge of the yard if Miss bridgeyard is 24 ft by 42 ft how many feet does Stella run with each lap? How many feet after five laps?
Answer: she runs 132 feets in each lap and 660 feets in 5 laps
Step-by-step explanation:
Stella runs laps around the edge of the yard. This means she runs round the entire shape of the yard.
Miss bridgeyard is 24 ft by 42 ft. This means that the length and width of Miss bridgeyard are not the same. Therefore, Miss bridgeyard has the shape of a rectangle. The distance that stella covers in one lap is the perimeter of the rectangular Miss bridgeyard.
Perimeter of a rectangle = 2( L + W )
If length,L = 42 feets and
Width ,W = 24 feets, the perimeter would be
2(42+24)/= 2×66 = 132 feets
She runs a distance of 132 feets in one lap.
Distance in 5 laps would be
132 × 5 = 660 feets
In a canoe race, A team paddles downstream 480 m in 60 seconds. The same team makes the trip upstream and 80 seconds. Find the teammates rate in Stillwater and the rate of the current period
Answer: The rate in still water is 8m/s
The rate in current period is is 6 m/s
Step-by-step explanation:
In a canoe race, A team paddles downstream 480 m in 60 seconds. The same team makes the trip upstream and 80 seconds.
We observe that it took the team more time paddling upstream than paddling downstream even though it was the same distance.
Let us assume that on paddling downstream, they paddled in the same direction with the current. This means that they paddled on still water. On paddling upstream, they paddled in the opposite direction of the current.
Let the speed of the boat or teammates be
x m/s
Let the speed of the current be
y m/s
Distance = speed × time
Distance travelled on still water or downstream
= (x+y) × 60 = 60(x+y)
Distance travelled on upstream
= (x-y) × 80 = 80(x-y)
Since the distance is 480 miles for both upstream and downstream,
60(x+y) = 480
x + y = 480/60 = 8 - - - - - -1
80(x-y) = 480
x - y = 480/80 = 6 - - - - - -2
Adding equation 1 and 2,it becomes
2x = 14
x = 14/2 = 7 m/s
y = 8 - x = 8-7
y = 1 m/s
Rate in still water = x +y = 7+1 = 8m/s
Rate in current period = x - y = 7 - 1 = 6m/s
Evaluate the function f(x)=10-x for the domain {-2, 0, 2}
For this case we have a function of the form [tex]y = f (x)[/tex], where:
[tex]f (x) = 10-x[/tex]
We must find the value of the function when:
[tex]x = -2,0,2[/tex]
For [tex]x = -2:[/tex][tex]f (-2) = 10 - (- 2) = 10 + 2 = 12[/tex]
For [tex]x = 0[/tex]:[tex]f (0) = 10-0 = 10[/tex]
For [tex]x = 2[/tex]:[tex]f (2) = 10-2 = 8[/tex]
Thus, we have that the function has a value of [tex]y = {12,10,8}[/tex] when [tex]x = {- 2,0,2}[/tex]
Answer:
[tex]y = {12,10,8}[/tex]
At the ritz concert tickets for adults cost $6 and tickets for students cost $4. How many of each ticket were purchased if 480 tickets were bought for $2340?
Answer: the number of adult tickets is 210
The number if student tickets is 270
Step-by-step explanation:
Let x represent the number of adult tickets that were purchased.
Let y represent the number of student tickets that were purchased.
At the ritz, concert tickets for adults cost $6 and tickets for students cost $4. If the cost of total tickets purchased is $2340, then,
6x + 4y = 2340 - - - - - - - -1
Total number of tickets purchased is 480. This means that
x + y = 480
x = 480 - y
Substituting x = 480 - y into equation 1, it becomes
6(480 - y) + 4y = 2340
2880 - 6y + 4y = 2340
- 6y + 4y = 2340 - 2880
-2y = - 540
y = - 540/-2 = 270
x = 480 - 270
x = 210
Determine the temperature of 2.6 moles of gas contained in a 5.00-L vessel at a pressure of 1.2atm.
Answer:
28.108 K.
Step-by-step explanation:
Given: Pressure (P)= 1.2atm
Number of moles (n)= 2.6 moles
Volume (V)= 5.00-L
Now finding the temperature (T).
Formula; T= [tex]\frac{P\times V}{n\times R}[/tex]
R is a constant factor which makes other factors work together.
There is a numerical value for R which we use is [tex]0.0821 \times \frac{L.atm}{mole.K}[/tex]
∴ Temperature (T)= [tex]\frac{1.2\times 5}{2.6\times 0.0821 \frac{L.atm}{mol.K} }[/tex]
⇒ Temperature (T)= [tex]\frac{6}{0.21346} = 28.1083\ K[/tex]
∴ Temperature is 28.108 K
What is the interest earned on $3000 at a rate of 0.04 for three years? The formula is interest equals (principal) (rate) (time) Substitute and multiply
Answer:
The interest after 3 years is $360
Explanation:
Given the principal amount (P) = $3000
Rate of interest (R) = 0.04
Time period (T) is given as 3 years
The Simple Interest is calculated by the formula;
[tex]SI = Principal \times Rate of Interest \times Time[/tex]
Substituting the values in the above formula,
[tex]SI = 3000 \times 0.04 \times 3[/tex]
SI = $360
Therefore, the interest after 3 years is $360
Answer:
$360
Step-by-step explanation:
Use the graph below to fill in the blank with the correct number: f(0) = _______ X, Y graph. Plotted points negative 3, 0; negative 2, 2; 0, 1; and 1, negative 2.
Answer:
f(0) = 1
Step-by-step explanation:
The ordered pair with first number 0 has second number 1. Each pair corresponds to (x, f(x)), so that pair has x=0 and f(0) = 1.
Answer:
[tex]f(0)=1[/tex]
Step-by-step explanation:
The given points are
[tex](-3,0), (-2,2),(0,1),(1,-2)[/tex]
Remember that each point has the form [tex](x,y)[/tex], where [tex]y=f(x)[/tex].
That means if we need to find [tex]f(0)[/tex], then we just need to look for the pair that belong to [tex]x=0[/tex].
If you observe, the pair we are looking for is [tex](0,1)[/tex], which relation is
[tex]f(0)=1[/tex].
Therefore, the answer is 1, that is, [tex]f(0)=1[/tex].
The perimeter of kite LMNO is 36 feet. Side MN = 8x – 3 and side NO = 2x + 1. Find the value of x.
Answer: 85.333 or 256 over 3.
Answer: x = 2
Step-by-step explanation:
The diagram of the kite is shown in the attached photo.
The perimeter of the kite is the distance around the kite.
The kite has 2 pairs of equal sides.
This means that
Side ML = side MN and side NO =
side LO
If Side MN = 8x – 3 and side NO = 2x + 1, then The perimeter of the kite is ML + MN + NO + LO
The perimeter of kite LMNO is given as 36 feet.
Therefore
ML + MN + NO + LO = 36
8x – 3 + 2x + 1 +8x – 3 + 2x + 1 = 36
8x + 8x + 2x+ 2x -3 +1 - 3 + 1
20x -4 = 36
20x = 40
x = 40/20 = 2
Leo practices his violin 12.5 hours each week you are so practices singing for 3.5 hours each week if you buy this is the same amount of time each week how many hours does your practice in 10 weeks
Answer: You would spend 160 hours in total of ten weeks.
Step-by-step explanation: Just add 12.5 + 3.5 which = 16. Then multiply 16 times 10 which is 160, and that is your answer.
Which fraction is equivalent to 0.65?
A) 5/13
B) 13/20
C) 19/25
D) 27/35