Answers
13) 5 + 8log_7 (v + 10) = 298log_7 (v + 10) = 24log_7 (v + 10) = 37^3 = v + 10343 = v + 10v = 333
14) log_5 (x^2) + log_5 (4) = 1log_5 (4x^2) = 15^1 = 4x^25/4 = x^2x = +/- sqrt(5) / 2 = +/-1.1180
*No extraneous solutions here, since the equation only uses x^2, not x.
15) -6*12^(b+7) +1 = -6-6*12^(b+7) = -712^(b+7) = 7/6
log 12^(b+7) = log(7/6)(b+7) log 12 = log (7/6)b+7 = log(7/6) / log(12) = 0.06203b = -6.9380
Related Questions
Find all the factors of 211.
a.1 and 211
b.It has no factors
c.1, 3, 11, 20, 71, and 211
d.1, 11, 20, and 211
Answers
___________
Final answer:
The factors of the number 211 are only 1 and 211 itself, indicating that it is a prime number. Thus, the correct answer is option a (1 and 211).
Explanation:
To find all the factors of 211, you need to determine all whole numbers that can divide 211 without leaving a remainder. Starting with the smallest factor, which is always 1, and ending with the number itself, because any number is divisible by itself, we iterate through the numbers between 1 and 211 to check if they are factors.
Through inspection or a process of trial and error, we find that there are no numbers other than 1 and 211 that can divide 211 evenly, indicating that 211 is a prime number. Therefore, the correct answer to the question 'Find all the factors of 211.' is option a. 1 and 211 are the only factors of 211
A salesperson has to drive 500 miles. For the first three hours she drove at 65 mi/h. For the next two hours she drove at 55 miles per hour. How many more miles does she have to drive?
Answers
First, you do 65 times 3 and that gives you 195 miles.
Then you do 55 times 2 and that gives you 110 miles.
You add both answers and get 305.
Do 500-305 and you get =195.
What is the square root 25 multiplied by 40 divided by 2
Answers
[tex] \frac{ \sqrt{25}* 40 }{2} [/tex]
[tex] \sqrt{25} = 5[/tex]
Simplify
[tex] \frac{5*40}{2} [/tex]
Multiply
[tex] \frac{200}{2} = 100[/tex]
The answer is 100
Hope this helps!
Square root:
a number that produces a specified quantity when multiplied by itself."7 is a square root of 49"
The square root of 25 is - 5, therefore:
5 x 40 divided by 2 equals - 100
therefore your answer is 100
Hope this helps you!
~DL
Experts/ace/geniuses helppp asapp
Answers
3au -2bv > 60
Then add 2bv-60
3au -60 > 2bv
Now, divide by 2b
(3au -60)/(2b) > v
This can be rearranged to match the 4th selection.
v < (3au - 60)/(2b)
A group would like to estimate the percentage of town residents who would support a teen curfew.
Which statement describes a method that will help the group accurately estimate this percentage?
Take a random sample of towns in the state. Ask an administrator in the city office whether the town has a teen curfew, and then calculate the percentage of the total who say "yes."
Identify all nearby towns that have a teen curfew. Contact the mayor of each of those towns and ask whether he or she thinks the curfew is a good policy. Calculate the percentage of the total who say "yes."
Contact every parent who lives in the town and ask whether they support a teen curfew. Calculate the percentage of the total who say "yes."
Take a random sample of residents in the town, and ask each resident in the sample whether or not they support a teen curfew. Then calculate the percentage of the total who say "yes."
Answers
Your best answer here would be:
Take a random sample of residents in the town, and ask each resident in the sample whether or not they support a teen curfew. Then calculate the percentage of the total who say "yes."
This is because you are taking a sample of votes from residents.
Hope this helps!
The correct statement that describes a method that will help the group accurately estimate this percentage is;
⇒ Take a random sample of residents in the town, and ask each resident in the sample whether or not they support a teen curfew. Then calculate the percentage of the total who say "yes."
What is Random Sampling?Random sampling is defined as a sampling method that utilizes randomization of sample selection.
In random sampling, each sample has the same probability of being selected as that of other samples to be selected to serve as a representation of an entire population.
Now, in this question, since the group would like to estimate the percentage of town residents who would support a teen curfew, then the sampling method they should use is random sampling which is in option C.
Learn more about Random Sampling visit:
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Cameron used 1 3/4 ounces of hydrochloric acid in one experiment. She used 2 1/8 ounces of the acid in a second experiment. How much more acid did Cameron use in the second experiment?
Answers
2 1/8 -1 3/4 =
17/8 - 14/8 = 3/8ths
Answer:
Amount required is [tex]x=\frac{3}{8}[/tex]
Step-by-step explanation:
Given : Cameron used [tex]1\frac{3}{4}[/tex] ounces of hydrochloric acid in one experiment. She used [tex]2\frac{1}{8}[/tex] ounces of the acid in a second experiment.
To find : How much more acid did Cameron use in the second experiment?
Solution :
In one experiment,
Cameron used [tex]1\frac{3}{4}[/tex] ounces of hydrochloric acid
i.e [tex]1\frac{3}{4}=\frac{7}{4}[/tex]
In second experiment,
She used [tex]2\frac{1}{8}[/tex] ounces of the acid.
i.e. [tex]2\frac{1}{8}=\frac{17}{8}[/tex]
Let x amount more she used then experiment 1 in experiment 2.
So, the equation became
[tex]\frac{7}{4}+x=\frac{17}{8}[/tex]
[tex]x=\frac{17}{8}-\frac{7}{4}[/tex]
[tex]x=\frac{17-14}{8}[/tex]
[tex]x=\frac{3}{8}[/tex]
Therefore, Amount required is [tex]x=\frac{3}{8}[/tex]
find the surface area of a triangular prism that is 16 inches long 12 inches wide and 5 inches high
A. 714in2
B. 644 in2
C. 960 in2
D. 689 in2
Answers
The number tiles containing the numbers 11-20 are in a bag. One tile is pulled from the bag. Determine each probability. 3a. P(prime number)= ? / 3b. p(multiple of 3)= ?
Answers
[tex] |\Omega|=10\\ [/tex]
3a
[tex] |A|=4\\\\P(A)=\dfrac{4}{10}=\dfrac{2}{5}=40\% [/tex]
3b
[tex] |A|=3\\\\P(A)=\dfrac{3}{10}=30\% [/tex]
Meg needs to have her car repaired. Parts will cost $905, and the labor cost for the job is $499. What will be the total cost for the job? Check your answer using the inverse operation
Answers
+499
----------
1,404
1404
-499
-----------
905
We know that Me will pay:
$905 for parts and $499 for labor cost
This means that:
Total amount paid = price for parts + labor cost
Total amount paid = 905 + 499
Total amount paid = $1404
2- checking using inverse operation:
Assume Meg pays $1404 for her car repairs. This cost includes both the price of parts and the labor cost.
Given that the price of parts = $905:
labor cost = 1404 - 905 = $499
Hope this helps :)
what are the zeroes of 2x squared plus 6x minus 8
Answers
3.
Every 6 months, Reuben Lopez puts $420 into an account paying 10% compounded semiannually.
Find the account balance after 15 years.
$29,299.53
$27,904.32
$31,500.00
$29,315.00
Answers
where
[tex]FV[/tex] is the future value
[tex]P[/tex] is the periodic deposit
[tex]r[/tex] is the interest rate in decimal form
[tex]n[/tex] is the number of times the interest is compounded per year
[tex]k[/tex] is the number of deposits per year
We know for our problem that [tex]P=420[/tex] and [tex]t=15[/tex]. To convert the interest rate to decimal form, we are going to divide the rate by 100%: [tex]r= \frac{10}{100} =0.1[/tex]. Since Ruben makes the deposits every 6 months, [tex]k=2[/tex]. The interest is compounded semiannually, so 2 times per year; therefore, [tex]k=2[/tex].
Lets replace the values in our formula:
[tex]FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n})^{kt}-1 }{ \frac{r}{n} } ][/tex]
[tex]FV=(1+ \frac{0.1}{2} )*420[ \frac{(1+ \frac{0.1}{2})^{(2)(15)}-1 }{ \frac{01}{2} } ][/tex]
[tex]FV=29299.53[/tex]
We can conclude that the correct answer is $29,299.53
Which equation could have been used to create this function table? 1 2,3 6,4 8,5 10, 10 20 A. y = 5x B. y = x + 1 C. y = x + 2 D. y = 2x
Answers
The correct equation used to create the function table provided is Option D: y = 2x, which indicates a linear relationship where y is twice the value of x.
The function table given in the question indicates the relationship between values of x and their corresponding y values. To determine which equation was used to create this table, you can compare the differences between these values. In the given pairs (1, 2), (3, 6), (4, 8), (5, 10), and (10, 20), it is observed that the y values are exactly twice the x values. Therefore, the equation representing this relationship must be y = 2x, which is a linear function with a slope of 2.
Looking at the options provided, Option D: y = 2x is the correct one, as it fits the pattern shown in the function table: for every unit increase in x, y increases by 2 units, implying a line with a slope of 2.
What is the following sum? 4(5 sqrt x^2y)+3(5 sqrt x^2y)
Answers
[tex]4(5 \sqrt{ {x}^{2}y } ) + 3(5 \sqrt{ {x}^{2} y} ) = 35x\sqrt{y}[/tex]
EXPLANATION
The given expression is
[tex]4(5 \sqrt{ {x}^{2}y } ) + 3(5 \sqrt{ {x}^{2} y} )[/tex]
We need to simplify the above expression first before, we add them.
Let us deal with the expressions within the parenthesis first,
[tex]4(5 \sqrt{ {x}^{2}y } ) + 3(5 \sqrt{ {x}^{2} y} ) = 4(5 \sqrt{ {x}^{2}}\times \sqrt{y} ) + 3(5 \sqrt{ {x}^{2} } \times \sqrt{y} )[/tex]
This will simplify to,
[tex]4(5 \sqrt{ {x}^{2}y } ) + 3(5 \sqrt{ {x}^{2} y} ) = 4(5 x\times \sqrt{y} ) + 3(5 x \times \sqrt{y} )[/tex]
We now multiply out the brackets to obtain,
[tex]4(5 \sqrt{ {x}^{2}y } ) + 3(5 \sqrt{ {x}^{2} y} ) = 20 x\times \sqrt{y} + 15 x \times \sqrt{y} )[/tex]
This implies that,
[tex]4(5 \sqrt{ {x}^{2}y } ) + 3(5 \sqrt{ {x}^{2} y} ) = 20 x\sqrt{y} + 15 x \sqrt{y} )[/tex]
This will give us,
[tex]4(5 \sqrt{ {x}^{2}y } ) + 3(5 \sqrt{ {x}^{2} y} ) = 35x\sqrt{y}[/tex]
Answer:
7(5 sqrt x^2y) or C
Step-by-step explanation:
The definition of an angle uses the undefined term
Answers
Write the linear equation 5x-15y=-8 in slope-intercept form.
Answers
15y = 5x - 8
Answer: 15y = 5x - 8
Slope-intercept form is y = mx + b
You have to get the equation into this format
5x - 15y = -8
Subtract 5x from both sides
-15y = -5x - 8
Divide both sides by -15
y = 1/3x + 8/15
The answer is [tex]y = \frac{1}{3} x + \frac{8}{15} [/tex]
Hope this helps!
hey can you please help me posted picture of question
Answers
One way to check if a function is inverse of the other is to take their composition. The composition of two inverse functions will always result in x.
[tex]F(x) = x-2 \\ \\ F^{-1}(x)=x+2 \\ \\ F(F^{-1}(x)) = F(x+2) \\ \\ F(F^{-1}(x)) = (x+2) -2 = x [/tex]
Thus x - 2 and x + 2 are the inverse of each other.
If it takes 2 nurses 2 minutes to measure the blood pressure of 2 patients, how long would it take 200 nurses to measure the blood pressure of 200 patients (in minutes)?
Answers
Answer:
it will take 2 minutes for 200 nurses to measure the blood pressure of 200 patients .
Step-by-step explanation:
We know that the work-time and number of labor and efficiency formula is given by:
[tex]Efficiency=\dfrac{Number\ of\ labor\times Time}{Work\ done}[/tex]formula is given by:
Here Number of labor=Number of nurses.
Work=Number of patients whose blood pressure were noted.
As the efficiency will be same this means that:
[tex]\dfrac{2\times 2}{2}=\dfrac{200\times x}{200}[/tex]
where x denotes the number of time taken by 200 nurses.
Hence,
[tex]x=2[/tex]
Hence, the answer is:
2 minutes.
Factor the expression. 40z – 20
a) 2z - 1
b) 2(20z-10)
c) 20(2z-1)
d) 20(2Z-20)
Answers
20 is the greatest common factor. Then divide.
Answer:
[tex]\bf\pink{20(2z-1)}[/tex]Step-by-step explanation:
Given Expression :-[tex]\rm\gray{40z-20}[/tex]Steps to factorise :-[tex]\\\to\:\:\to\:\:\rm\red{40z - 20}[/tex]
Factor out [tex]\bf\blue{20}[/tex] from the expression[tex]\\\to\:\:\to\:\:\rm\green{20(2z-1)} \\ [/tex]
(Refer the attachment for graph representation)
Graph Details :-[tex]\bigstar\:\:\bf\purple{y = 40z-20} \\ [/tex]
[tex]\rm{Root \: \bigg( \dfrac{1}{2}, \:0\bigg) }[/tex][tex]\rm{ Domain \: \:z \: \in\:{\mathbb{R}}}[/tex][tex]\rm{Range \: \:y \: \in\:{\mathbb{R}}}[/tex][tex]\rm{Vertical \: intercept\:\:(0,\:-20)}[/tex]Lena made 32 ounces of a fruit drink mix using pineapple juice and grapefruit juice. The number of ounces of pineapple juice in the fruit drink mix is 5 more than 2 times the number of ounces of grapefruit juice in the fruit drink mix. Which graph shows the number of ounces of pineapple juice, x, and the number of ounces of grapefruit juice, y, in the fruit drink mix?
Answers
let
x-------> the number of ounces of pineapple juice
y------> the number of ounces of grapefruit juice
we know that
x+y=32
x=2y+5-----> x-5=2y
using a graph tool
see the attached figure N 2
the solution is
x=23 ounces (pineapple juice)
y=9 ounces (grapefruit juice)
therefore
the answer is the option a
Past experience indicates that the time re- quired for high school seniors to complete a standard- ized test is a normal random variable with a standard deviation of 6 minutes. test the hypothesis that σ = 6 against the alternative that σ < 6 if a random sample of the test times of 20 high school seniors has a standard deviation s = 4.51. use a 0.05 level of significance.
Answers
At 0.05 level of significance, there is sufficient evidence to support the alternative hypothesis that [tex]\sigma[/tex] < 6.
To test the hypothesis that the standard deviation ([tex]\sigma = 6[/tex] ) against the alternative that ( [tex]\sigma = 6[/tex] ), we can use a chi-square test.
The test statistic for a chi-square test is given by ( [tex]\chi^2 = \frac{(n-1)s2}{\sigma2}[/tex]), where:
The sample size = [tex]n[/tex]
The sample standard deviation = [tex]s[/tex]
The hypothesized standard deviation = [tex]\sigma[/tex]
The sample size, n = 20
The sample standard deviation, s = 4.51
The hypothesized standard deviation, [tex]\sigma[/tex] = 6
Substituting these values into the formula:
[tex][ \chi^2 = \frac{(20-1)(4.51)2}{62} \approx 14.13 ][/tex]
The degrees of freedom for the test is ( n - 1 = 20 - 1 = 19 ).
The test statistic for our chi-square test is ([tex][ \chi^2 = \frac{(20-1)(4.51)2}{62} \approx 14.13 ][/tex] ).
The critical value for a chi-square distribution with 19 degrees of freedom at the 0.05 level of significance is approximately 30.14.
Since our test statistic ([tex]\chi^2 = 14.13[/tex] ) is less than the critical value (30.14), we reject the null hypothesis that [tex]\sigma[/tex] = 6 at the 0.05 level of significance.
Thus, we have sufficient evidence to support the alternative hypothesis that [tex]\sigma[/tex] < 6, suggesting that the standard deviation of the time required for high school seniors to complete the standardized test is less than 6 minutes.
Mrs. Wilton is planning a rectangular flower box for her front window. She wants the flower box to hold exactly 16 cubic feet of soil. How many different flower boxes, all with the whole-number dimensions and a different-size base, will hold exactly 16 cubic feet of soil.
Answers
There are 3 different sizes of flower boxes that have different dimensions. Then the dimensions will be 2 by 1, 2by 3, and 2 by 4.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Mrs. Wilton is planning a rectangular flower box for her front window.
She wants the flower box to hold exactly 16 cubic feet of soil.
Let the height of the flower boxes will be 1 foot.
Then the number of the flower boxes with the whole dimensions and different-size base will be
Volume = Area × 1
Area = 16 square ft.
There are 3 different sizes of flower boxes that have different dimensions. Then the dimensions will be
Area = 16
Area = 2 + 6 + 8
Area = 2 × 1 + 3 × 2 + 2 × 4
Then the dimensions are 2 by 1, 2by 3, and 2 by 4.
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If point (4,5) is in the graph of a function, which equation must be true?
Answers
Answer:
Step-by-step explanation:
C) f(4)=5
they travelled 551 km from Bagani to Zimbabwe N.R at an average speed of 75km/h and their car has an average petrol consumption of 12 litres per 100 km . calculate the following .
1. the time that it will take them to complete the journey , convert to hours & minutes .
2. the amount that they will spend on petrol if the petrol costs is R7.25 per litre ?
Answers
Time=(distance)/(speed)
distance=551
speed=75 km/h
thus
time=551/75=7 26/75 hours
=7 hours (26/75×60) min
=7 hours 21 min
2] the amount that they will spend on petrol if the petrol costs is R7.25 per litre ?
Total amount spent on petrol will be as follows:
Cost of petrol R7.25 per Km
Consumption=12 liters per 100 km
thus amount of liters used:
12/100×551
=66.12 liters
thus total cost of petrol used:
66.12×7.25
=R479.37
the weight of an object on mars varies directly with its weight on earth. an object that weighs 50 pounds on mars weighs 150 pounds on earth. if an object weighs 120 pounds on earth, write and solve a direct variation equation to find how much an object would weigh on mars.
Answers
Wm α We => Wm = kWe, Where Wm = Weight on mars, We = Weight on earth, k = constant of proportionality.
For Wm = 50 pounds, We = 150 pounds;
k = Wm/We = 50/150 = 1/3
Now, for 120 pounds on earth;
Wm = k*We
Substituting;
Wm = 1/3 * 120 = 40 pounds
To find the weight of an object on Mars, we can use a direct variation equation. By finding the constant ratio from the given values, we can then solve for the weight on Mars when the weight on Earth is known. In this case, the object would weigh 40 pounds on Mars if it weighs 120 pounds on Earth.
Explanation:To solve this problem, we will use the concept of direct variation. The weight of an object on Mars varies directly with its weight on Earth. This means that the weight on Mars can be found by multiplying the weight on Earth by a constant ratio. Let's represent the weight on Mars as WM and the weight on Earth as WE. According to the problem, an object that weighs 50 pounds on Mars weighs 150 pounds on Earth. This gives us the following direct variation equation:
WM = k * WE
where k is the constant ratio.
We can now substitute the given values: 50 pounds for WM and 150 pounds for WE.
50 = k * 150
To solve for k, divide both sides of the equation by 150:
k = 50 / 150
k = 1 / 3
Now that we have the value of the constant ratio, we can find the weight of an object on Mars when it weighs 120 pounds on Earth. Let's represent the weight on Mars as x and the weight on Earth as 120:
x = (1 / 3) * 120
x = 40
Therefore, the object would weigh 40 pounds on Mars.
Graph the inequality y<|x+2|. Which point is not part of the solution?
A) -1,-2
B) 1,2
C) 0,0
D) -1,2
Answers
Answer:
D) (-1, 2)
Step-by-step explanation:
See the graph below. The indicated point is not in the shaded region, hence not part of the solution.
Make up an equation of the form y = kx +b, the graph of which passes through the following points:
P (4, 1) and Q (3, –5)
Answers
The given points are
[tex] P(4,1) , Q(3,-5) [/tex]
First we find the slope using slope formula which is
[tex] m= \frac{y_{2} - y_{1}}{x_{2}- x_{1}} [/tex]
Substituting the values of x1,y1 and x2, y2, we will get
[tex] m = \frac{-5-1}{3-4} = 6 [/tex]
Now we use slope point form, which is
[tex] y-y_{1} = m (x-x_{1}) [/tex]
Using the values of m,x1 and y1, we will get
[tex] y-1=6(x-4) \\
y-1=6x-24 \\
y = 6x-23 [/tex]
The Pyramid of Giza is one of the largest pyramid structures still standing in Egypt. It is a right pyramid with a square base, a base length of 230 m, and height of 150 m. The base is ___ m2. The volume is ___ m3.
Answers
Volume = (Area of the Base * Height) ÷ 3
Volume = (52,900 * 150) / 3
Volume = 2,645,000 cubic meters
The base area of the pyramid is 52900 m².
The volume of the pyramid is 2645000 m³.
Volume of a square based pyramidv = 1 / 3 B h
where
B = base area
h = height
Therefore,
Base area = 230 × 230
Base area = 52900 m²
h = 150m
B = 52900 m²
Therefore,
V = 1 / 3 × 52900 × 150
V = 7935000 / 3
V = 2645000 m³
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Victor is enlarging a poster for a school baseball match. The graph below shows the size y of the poster after x enlargements: graph of y equals 1.8 to the power of x What does the y-intercept of the graph represent?
Answers
y = 1.8 ^ x
The intersection with the y axis occurs when x = 0.
We have then:
y = 1.8 ^ 0
y = 1
In this case, the intersection with the y-axis represents the original size of the poster.
Answer:
the y-intercept of the graph represents:
the original size of the poster.
Answer:C
Step-by-step explanation:
Original size of the picture
Two sides of a parallelogram measure 60 centimeters and 40 centimeters. If one angle of the parallelogram measures 132 degrees, find the length of each diagonal.
Answers
Final answer:
The lengths of the diagonals in the parallelogram can be calculated using the properties of vectors and the law of cosines with the given side lengths and angle.
Explanation:
To find the length of each diagonal in a parallelogram with sides measuring 60 centimeters and 40 centimeters and one angle of 132 degrees, we can leverage the properties of vectors and the law of cosines. It is known that one diagonal is the vector sum of the sides, while the other diagonal is the vector difference of the sides.
First, let's compute the length of the shorter diagonal, which is the vector sum of the two sides:
Shorter diagonal (Ñ) = A + B
Using the law of cosines for finding the length of a diagonal, we get:
Ѳ = 60² + 40² - 2 * 60 * 40 * cos(132°)
After computing this, we find the length of the shorter diagonal.
Next, we calculate the length of the longer diagonal, which is found by subtracting the vectors of the two sides:
Longer diagonal (D) = A - B
Again using the law of cosines:
D² = 60² + 40² - 2 * 60 * 40 * cos(48°)
After computation, we find the length of the longer diagonal.
Through these calculations using the provided formulae and the law of cosines, both diagonals' lengths can be established.
Two different bacteria are growing in a lab. The following functions represents the bacteria.
Bacteria A: f(x) = 1000 . 3^x, where x is number of hours.
Bacteria B: g(x) = 3000 . 2^x, where x is number of hours.
Which of the following statements are true? Select all that apply.
( )Bacteria B is growing at a fasster rate than Bacteria A.
( ) Baccteria B started with 3000 bacteria.
( ) Bacteria A doubles every three hours.
( ) Bacteria B doubles every hour.
( ) In three hours, the amount of bacteria A will be greater than the amount of Bacteria B.
Answers
y = A (b) ^ x
Where,
A: initial amount
b: growth rate
x: time
We then have the following functions:
f (x) = 1000. 3 ^ x
g (x) = 3000. 2 ^ x
For x = 3 we have:
f (3) = 1000. 3 ^ 3 = 1000 * 27 = 27000
g (3) = 3000. 2 ^ 3 = 3000 * 8 = 24000
Answer:
the following statements are true:
Baccteria B started with 3000 bacteria
Bacteria B doubles every hour.
In three hours, the amount of bacteria A will be greater than the amount of Bacteria B.