For x=9 movies, the costs of A and B are equal and the equation in terms of A is A=22+2x.
What is meant by an equation?When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. For instance, an equation in French is described as having one or more variables, whereas in English, an equation is any properly written formula that consists of two expressions linked by the equals sign.
Determine which values of the variables result in the equality to be true in order to solve an equation with variables.
For plan A, cost is $22 and $2 per movie then, for x movies
A=22+2x
For plan B, cost $13 and $3 per movie then, for x movies
B=13+3x
The costs of A and B equal then,
22+2x=13+3x
x=9
For x=9 movies, the costs of A and B are equal and the equation in terns of A is A=22+2x.
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Use the product property to rewrite log2 256b
The solution for the given logarithmic expression would be x = 8.
What are the logarithms?
In mathematics, the logarithm is the inverse function of exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.
Given:
[tex]log_2(256)[/tex]
Let
[tex]x=log_2(256)[/tex]
By using the property of logarithms we can write
[tex]2^x=256\\\\2^x=2^8\\[/tex]
Since the bases are the same, the two expressions are only equal if the exponents are also equal.
x = 8.
Hence, the solution for the given logarithmic expression would be x = 8.
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Which expression is equivalent to 225/625m⁴n⁶
A. 1/20m²|n³|
B. 1/20m²n⁴
C. 3/5m²|n³|
D. 3/5m²n⁴
The equivalent expression of 225/625m⁴n⁶ is 3/5m²n³.
What is the square root?
A number y such that y = x², or a number y whose square is x, is referred to as the square root of a number x in mathematics. For instance, since 4² = 2 = 16, 4 and -4 are the square roots of 16.
We have,
225/625m⁴n⁶
So, simplifying the given equation,
= 225/625m⁴n⁶
dividing the numerator and denominator by 25 we get,
= 9/25m⁴n⁶
again by taking the square root of the numerator and denominator we get,
= 3/5m²n³.
Hence, the equivalent expression of 225/625m⁴n⁶ is 3/5m²n³.
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The sum of two mixed fractions is 12 3/35
If one mixed fractions is 5 31/35 find the other mixed fraction.
let's convert the mixed fractions to improper fractions and then let's proceed.
[tex]\stackrel{mixed}{12\frac{3}{35}}\implies \cfrac{12\cdot 35+3}{35}\implies \stackrel{improper}{\cfrac{423}{35}} ~\hfill \stackrel{mixed}{5\frac{31}{35}}\implies \cfrac{5\cdot 35+31}{35}\implies \stackrel{improper}{\cfrac{206}{35}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]12\frac{3}{35}~~ + ~~x~~ = ~~5\frac{31}{35}\implies \cfrac{423}{35}+x=\cfrac{206}{35}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{35}}{35\left( \cfrac{423}{35}+x \right)=35\left( \cfrac{206}{35} \right)} \\\\\\ 423+35x=206\implies 35x=-217 \\\\\\ x=\cfrac{-217}{35}\implies x=\cfrac{-31}{5}\implies {\Large \begin{array}{llll} x=- 6\frac{1}{5} \end{array}}[/tex]
to convert an improper fraction like -31/5 to a mixed fraction, well, first off, we nevermind the sign, so we only use 31/5 and then we divide 31 ÷ 5.
hmm 31 ÷ 5 gives us a quotient of 6, and a remainder of 1, we put the quotient upfront and the remainder as the numerator, with the old denominator and sign back in.
Please help! Thank you!
The median weekly gross income for someone with a bachelor's degree was $2,117.00. If they continued their education and training and earned a master's degree, they had an increase in their median weekly income of about 46.1%. Determine the median weekly income for someone with a master's degree.
$2,856.12
$3,092.94
$3,153.76
$2,908.45
A master's degree earner's typical weekly salary is $3,092.94.
What is the meaning of percentage?
A percentage in mathematics is a number or ratio that may be stated as a fraction of 100.In determining a percentage of a number, we should first divide it by 100 before multiply the outcome by 100. As a result, the proportion refers to a part per 100. The word "percent" refers to a fraction of one hundred. The letter "%" stands for it.
Considering that the median gross weekly wage for a bachelor's degree holder was $2,117.00.
If any one had mater degree, then an increase in the median weekly income of about 46.1%.
To find the increment multiply $2,117.00 with increase rate:
The increment is $2,117.00 × 46.1% = 2,117.00 × 46.1/100= $975.937
The total the median weekly income is
$975.937 + $2,117.00
= $3,092.937
≈ $3,092.94
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a) Work out the minimum number of dogs that could have a mass of more than 24 kg
b) Work out the maximum number of dogs that could have a mass of more than 24 kg}.
Mass(kg) Frequency
0≤x<10 2
10≤x<20 7
20≤x<30 12
30≤x<40 6
a) The minimum number of dogs that could have a mass of more than 24 kg is 6.
b) The maximum number of dogs that could have a mass of more than 18 kg is 20.
How to find the minimum and maximum value mean?We will first of all have to rearrange the function with the aid of fundamental algebraic concepts that makes us calculate the value of x in the event that the derivative is equal to 0.
Now, the response above will give us the x-coordinate of the function's vertex. This vertex x-coordinate is the point at which the maximum or minimum will occur. To find the minimum or maximum, we will start by rewriting the solution into the original function.
From the given figures in the question, it is clear that the minimum of the values present in the interval 20 to 40 is 6
From the given figures in the question, it is clear that the maximum of the values present in the interval 20 to 40 is;
(12 + 6) = 18
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The equation y = 1.5x describes a proportional relationship and is shown in the graph.
graph of a line beginning at point 0 comma 0 and going through 9 comma 6
Which of the following statements is true about the graph shown?
The graph is incorrect and the line should go through the point (6, 9).
The graph is incorrect and the line should go through the point (1.5, 1.5).
The graph does not show a proportional relationship.
The equation y = 1.5x is correctly represented by the graph.
PLEASE HELP, also its not B I got it wrong the first time
The source explains where you found the information that is in your graph. X-Axis Bar graphs have an x-axis and a y-axis. Y-Axis
What is a graph simple definition?In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.Statistical Graphs (bar graph, pie graph, line graph, etc.)Exponential Graphs.Logarithmic Graphs.Trigonometric Graphs.Frequency Distribution Graph.Graph is defined as to create a diagram that shows a relationship between two or more things. An example of graph is to create a series of bars on graphing paper. YourDictionary. To put in the form of, or represent by, a graph. Webster's New World.The word "chart" is usually used as a catchall term for the graphical representation of data. "Graph" refers to a chart that specifically plots data along two dimensions, as shown in figure 1.Given equation of the line,
If x = 0,
f(x)=-1.5+6
f(x)=-1.5(o)+6=6
Thus, the line intersects the y - axis at (0, 6)
If f(x) = 0,
o=-1.5+6= -1.5*=-6=x=4
Thus, the line intersects the x-axis at (4,0)
Plotting theses points in the given graph,
Then join them,
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multiply v by 2, then divide 8 by the result
2 * V is equal to 2 v you divide 2 from 8 and your answer is 4
for this problem use the data in sheet wages in the excel file hw5data2020 to estimate a simple regression explaining
With the use of regression analysis, you may determine which of the independent factors actually has an effect statistically and learn how the dependent variable changes when one of the independent variables changes.
What is linear regression?Regression analysis is used in statistical modeling to determine the associations between two or more variables:
The fundamental element you are attempting to comprehend and anticipate is the dependent variable. The elements that could have an impact on the dependent variable are known as independent variables.
Regression analysis enables you to statistically ascertain which of the independent variables actually has an impact and explains how the dependent variable changes when one of the independent variables changes. There is a difference between a simple and multiple linear regression in statistics. A dependent variable and one independent variable are modeled using a linear function in simple linear regression. Multiple linear regression is used when there are two or more explanatory variables used to predict the dependent variable.
Here,
estimate a simple regression in excel:
On the Data tab, in the Analysis group, click the Data Analysis button.
Select Regression and click OK.
In the Regression dialog box, configure the following settings: Select the Input Y Range, which is your dependent variable.
Click OK and observe the regression analysis output created by Excel.
Regression analysis illustrates how the dependent variable changes when one of the independent factors changes and allows you to statistically determine which of the independent variables actually has an impact.
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Need help solving this. Please help
Answer:
Step-by-step explanation:
Reason 2: The box in the corner of the angle indicates that the angle is a right angle, which is 90 degrees.
Statement 3:
m<abd +m<dbc=m<abc
Rewrite the expression in terms of the given function. (sec x - csc x) / (1 - tan x) in terms of sin x (sec x - csc x) / (1-tan x) =
The trigonometric expression (sec x - csc x) / (1 - tan x) is equivalent by trigonometric formulas and algebra properties to - sin x.
How to rewrite a trigonometric expression in terms of sine function
Herein we find a trigonometric expression that must be rewritten in terms of sin x by means of trigonometric formulas and algebra properties. The original expression is shown below:
(sec x - csc x) / (1 - tan x)
First, the original expression is written:
(sec x - csc x) / (1 - tan x)
Second, use the definitions of secant, cosecant and tangent:
[(1 / cos x) - (1 / sin x)] / [1 - (sin x / cos x)]
Third, use algebraic properties to simplify the expression:
[(sin x - cos x) / (sin x · cos x)] / [(cos x - sin x) / cos x]
[(sin x - cos x) · cos x] / [sin x · cos x · (cos x - sin x)]
- sin x
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Using the methods provided in the text for computing confidence intervals for population proportions, a marketing analyst takes a survey of 1000 randomly selected consumers. She asks if they prefer low-sodium soup products. Using the results, she provides a 95% confidence interval for the population proportion of consumers who prefer low-sodium soup products. The interval has a margin of error of 03. Which of the following is an appropriate interpretation of these results? (a) The sample proportion from the survey differs from the population proportion by at most 03. (b) 95% of all possible values of the population proportion are contained in the interval provided. (c) The analyst is 95% confident that all possible values for the sample proportion from a sample of 1000 consumers are in the interval provided. (d) Using these methods, 95% of all possible confidence intervals from a sample of 1000 consumers will contain the population proportion. (e) The reported confidence interval will contain the population proportion 95% of the time.
The reported confidence interval will contain the population proportion of consumers 95% of the time.
In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. Therefore, it can be concluded that there is a 95% probability that the true value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.
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what is the slope of a line with a y intercept of 5 and an x intercept of -4
Answer:
slope = [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 5 ) ← coordinates of y- intercept
and (x₂, y₂ ) = (- 4, 0 ) ← coordinates of x- intercept
m = [tex]\frac{0-5}{-4-0}[/tex] = [tex]\frac{-5}{-4}[/tex] = [tex]\frac{5}{4}[/tex]
Wyatt is deciding between two different movie streaming sites to subscribe to. Plan A costs $ 19 per month plus $0.50 per movie watched. Plan B costs $ 13 per month plus $1.50 per movie watched. Let A represent the monthly cost of Plan A if Wyatt watches x per month, and let B represent the monthly cost of Plan B if Wyatt watches x movies per month. Write an equation for each situation, in terms of x, and determine the number of monthly movies watched, x, that would make the two plans have an equal monthly cost.
A=
B=
Answer=
Equations representing the total costs for plan A and B are A = 19 + 0.50x and B = 13 + 1.5x, respectively, where x is the number of movies watches.
Cost of both the plans will be equal for 6 movies.
What is a linear equation?
A linear function is defined as a function that has either one or two variables without exponents.Given that, Wyatt is deciding between two different film streaming sites to subscribe to, plan A costs $19 per month plus $0.50 per film watched, plan B costs $13 per month plus $1.50 per film watched.
According to question,
A = 19 + 0.50x and
B = 13 + 1.5x
For costs being equal, we have,
A = B
19 + 0.50x = 13 + 1.5x
x = 6
Hence, for 6 films the costs of both the plans will be equal and equation for both the plans are A = 19 + 0.50x and B = 13 + 1.5x
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Dos cuadrados de lado 10 cm se sobreponen formando un rectángulo de 17 cm de largo, como se muestra en la figura. ¿Cuál es el área de la franja amarilla en centímetros cuadrados?
The area of the rectangular yellow region is of:
30 cm².
How to obtain the area of a rectangle?The area of a rectangle of base b and height h is obtained as the multiplication of these dimensions, as follows:
Area = base x height.
From the image given at the end of the answer, these dimensions are given as follows:
Height = 10 cm, which is the side length of the square.Base = 3 cm, as the two squares would combine for a side length of 20 cm, but they combine for 17 cm, hence 20 - 17 = 3 cm.Then the area of the yellow region is calculated as follows:
Area = 10 x 3 = 30 cm².
TranslationThe problem asks to obtain the area of the rectangular region, considering that:
The squares have side length of 10.The combined squared combine for a side length of 17.Missing InformationThe region is given by the image shown at the end of the answer.
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The bottom of a 50 foot straight ladder is set into the ground 14 feet away from a house. When the top of the ladder is leaned against the house, which of the following is the distance above the ground the ladder will reach?
A. 25 feet
B. 36 feet
C. 48 feet
D. 64 feet
Answer:
You need to subtract
Step-by-step explanation:
50 minus 14 will give you 36
Suppose Dariya is an avid reader and buys only reusable tote bagses. Dariya deposits $4,000 into a savings account that pays an annual nominal interest rate of 5%. Assume this interest rate is fixed, and so it will not change over time. On the day she makes her deposit, suppose that a reusable tote bags has a price of $10.00.
The price of reusable tote bags and the interest rate may change over time, which could affect the length of time that Dariya's savings will last.
What is the interest rate?
The proportion of a loan that is charged as interest to the borrower is typically expressed as an annual percentage of the loan outstanding.
If Dariya deposits $4,000 into a savings account with an annual nominal interest rate of 5%, the amount of interest she earns each year will be $4,000 * 5% = $200.
If the price of a reusable tote bag is $10.00 and Dariya wants to buy one every year, the cost of buying one reusable tote bag every year will be $10.00/year.
To determine how long Dariya's savings will last, you can divide the amount of her annual interest earnings by the cost of buying a reusable tote bag each year.
In this case, Dariya's savings will last for 200/10 = 20 years.
Keep in mind that this calculation assumes that the price of reusable tote bags remains constant at $10.00/year and that the nominal interest rate remains fixed at 5% per year.
Hence, the price of reusable tote bags and the interest rate may change over time, which could affect the length of time that Dariya's savings will last.
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Exactly 10% of the students in a school are left-handed. Select 15 students at random from the school and define W = the number who are left-handed.
a. yes
b. no
c. unsure
The statement is true , that the given sample follows binomial distribution.
If a random variable has two alternative outcomes (success or failure), it has a binomial distribution.
Each draw must be separate from the ones that came before it.
There is a set number of drawn components.
We randomly select 15 students, and since the sample size of 15 is less than 10% of the total population, we can assume that each draw is independent.
Because X has a binomial distribution, success is determined by whether the student is left-handed (failure is determined by whether the student is not left-handed).
The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for success or failure as the possible outcomes of an experiment.
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plase help me out tanks
Answer: x = 4
Step-by-step explanation:
5x - 3 ≥ 13
Substitute x with 4
5(4) - 3 ≥ 13
20 - 3 ≥ 13
17 ≥ 13
17 is greater than or equal to 13
I REALLY NEED HELP PLEASE
Which of the following is the dilation of scale factor 2 about the center (4, -2)?
If the scale factor is less than 1, the dilated figure is smaller than the original, if it is greater than 1 the dilated figure is larger than the original.
What is the dilation of scale factor?Image result for Which of the following is the dilation of scale factor Scale Factor (Dilation) The scale factor in the dilation of a mathematical object determines how much larger or smaller the image will be (compared to the original object). When the absolute value of the scale factor is greater than one, an expansion occurs. if we have a scale factor of 1/4, we just multiply each of those by 1/4. So instead of going to the left eight, we would go to the left two. Eight times 1/4 is two. Instead of going up four, we would go up one.A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).The location of the point (4, 2) is to the right of the triangle RST, therefore,A dilation from the left or a contraction from the right is required.The dilation of ΔRST that would result in a line segment with slope of 2That passes through (4, 2) is C. A dilation with a scale factor of 0.5 centered at
The given vertex of the line are;
R(-2, 6), T(-6, -2), S(6, -4)
Point on the lint RT that has the same y-coordinate as the point (4, 2) is (-4, 2)Taking the center of dilation as the point (12, 2), we have;Coordinates of the point (-4, 2) relative to the point (12, 2) is found asfollows;(-4 - 12, 2 - 2) = (-16, 0)Therefore, dilating (-16, 0) by a scale factor of 0.5, with a center at (12,2) gives;0.5 × (-16, 0) = (-8, 0)The actual location of the point (-8, 0) is (-8 + 12, 0 + 2 ) = (4, 2)Therefore, the dilation of ΔRST that would result in a line segment withslope of 2 that passes through (4, 2) is C. A dilation with a scale factor of 0.5 centered atTo learn more about scale refer to:
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Solve the system below by substitution
6x-y=-23
2x+5y=-13
Answer:
x= -4 y= -1
6x - y = - 23
-y=-23-6x
y=6x+23, use this to plug in for y in the second equation.
2x + 5y = -13
2x + 5(6x+23) = -13
2x+30x+115=-13
x= -4, use this to plug in for x in the first equation.
6x - y = - 23
6(-4)-y=-23
-24-y=-23
-y=-23+24
-y=1
y= -1
Step-by-step explanation: not doing this to steal points
Answer:
here is your solution.
Step-by-step explanation:
x=4 & y=1
The equation c = 13.99p represents the proportional relationship between the total cost (c) and the number of pounds (p) of shrimp at a grocery store. Which description is true, based on the equation of the proportional relationship?
each pound of shimp costs $13.99
Whats the simplified version of √(√21-2√3)^2
The required simplified solution of the given expression is given as √3(√7 - 2).
Given that,
To determine the simplified solution of the √(√21-2√3)²
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
= √(√21-2√3)²
=√21-2√3 (√a² = a)
= √3(√7 - 2)
Thus, the required simplified solution of the given expression is given as √3(√7 - 2).
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For what values of a does the equation 2a-4x=4-a^2*x have a solution in the interval (-8,-2)?
The values of a such that the linear equation 2 · a - 4 · x = 4 - a² · x have a solution in the interval (- 8, - 2) is a = 2 and - 7 / 4 ≤ a ≤ - 1.
How to find the values of a variable associated to an equation
In this problem we find the case of a linear equation whose values of variable a must be determined in terms of an interval of values of variable x. First, write the defined equation:
2 · a - 4 · x = 4 - a² · x
Second, form the standard form of a quadratic equation in terms of a:
x · a² + 2 · a - 4 · (x + 1) = 0
Third, use the quadratic formula:
a = - 2 / (2 · x) ± [1 / (2 · x)] · √[4 - 4 · x · [- 4 · (x + 1)]]
a = - 1 / x ± (1 / x) · √[1 + 4 · x · (x + 1)]
a = - 1 / x ± (1 / x) · √(4 · x² + 4 · x + 1)
There are two cases for the given interval:
Case 1
a = - 1 / x + (1 / x) · √(4 · x² + 4 · x + 1)
x = - 8
a = - 1 / (- 8) + [1 / (- 8)] · √[4 · (- 8)² + 4 · (- 8) + 1]
a = - 7 / 4
a = - 1 / (- 2) + [1 / (- 2)] · √[4 · (- 2)² + 4 · (- 2) + 1]
a = - 1
Case 2
a = - 1 / x - (1 / x) · √(4 · x² + 4 · x + 1)
x = - 8
a = - 1 / (- 8) - [1 / (- 8)] · √[4 · (- 8)² + 4 · (- 8) + 1]
a = 2
a = - 1 / (- 2) - [1 / (- 2)] · √[4 · (- 2)² + 4 · (- 2) + 1]
a = 2
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I need help with my math homework
Answer:
1. 2
2. 7
3. 15
4. 80
5. 70
Step-by-step explanation:
Answer:
1st question's answer is 2 x 90 = 180
2nd question's answer is 70 x 7 =490
3rd question's answer is 240 = 4 x 60
4th question's answer is 9 x 80 = 720
5th question's answer is 70 x 8 =560
these are easy questions for anyone who would like answer them just don’t put random answers
Help i need help with this question.
Based on the SAS, SSS, and the transitive property of congruence, the reason why ΔABC ≅ ΔGHJ is because of option B.
What is SAS and SSS?The SAS is a triangle theorem that states that two triangles are congruent if they both have two pairs of congruent sides and a pair of included congruent angles.
On the other hand, the SSS states that two triangles that have three pairs of congruent sides are equal.
What is the Transitive Property of Congruence?The transitive property of congruence states that if two triangles are congruent to a third triangle, then all three triangles are congruent to each other.
Based on the SSS, triangle ABC is congruent to triangle DEF.
Based on the SAS, triangle DEF is congruent to GHJ.
Therefore, based on the transitive property of congruence, triangle ABC is congruent to triangle GHJ.
Therefore, the reason why ΔABC ≅ ΔGHJ is because of the reason given in option B.
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Would greatly appreciate if any of you can answer the question in the attached image with full explanation including a strategy for solving it. Thanks in advance!
Answer:
B) a = - 3------------------
Multiply both sides by ax - 2 to clear fractions:
24x² + 25x - 47 = (ax - 2)(- 8x - 3) - 5324x² + 25x - 47 = - 8ax² - 3ax + 16x + 6 - 5324x² + 25x - 47 = - 8ax² - (3a - 16)x - 47Comparing both sides we can guess that -8a = 24 ⇒ a = - 3, then:
- (3*(-3) - 16) = - (- 9 - 16) = - (-25) = 25.We see both coefficients match, hence a = - 3 is a right choice.
the number k if 3/11 (fraction) of k is 12
Answer:
k = 44
Step-by-step explanation:
[tex]\frac{3}{4}[/tex]k = 12 Multiple both sides by [tex]\frac{4}{3}[/tex]
k = 44
Answer:
k = 44
Explanation:
You can write this into an equation, where k x 3/11 = 12. If you multiply both sides of the equation by 11 and divide by 3, you get k by itself.
k x 3/11 = 12
3k/11 = 12
3k = 132
k = 44
Please can anyone answer this percentage question cor grade 7
well, we know it was 480, then we reduce it by 50.
a)if we take 480 to be the 100%, what's 50 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 480 & 100\\ 50& x \end{array} \implies \cfrac{480}{50}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 48 }{ 5 } ~~=~~ \cfrac{ 100 }{ x }\implies 48x=500\implies x=\cfrac{500}{48}\implies x=\cfrac{125}{12}\implies \boxed{x\approx 10.4}[/tex]
now, the TV is only 480 - 50 = 430, then it gets reduced another 50.
if we take 430 to be the 100%, what's 50 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 430 & 100\\ 50& y \end{array} \implies \cfrac{430}{50}~~=~~\cfrac{100}{y} \\\\\\ \cfrac{ 43 }{ 5 } ~~=~~ \cfrac{ 100 }{ y }\implies 43y=500\implies y=\cfrac{500}{43}\implies \boxed{y\approx 11.6}[/tex]
b)hmmm the absolute change of the reductions? that sounds like 480 - 50 - 50 = 380.
c)well, the overall percentage hmmm well, that's the $100 reduction total.
if we take $480 as the 100%, what's $100 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 480 & 100\\ 100& z \end{array} \implies \cfrac{480}{100}~~=~~\cfrac{100}{z} \\\\\\ \cfrac{ 24 }{ 5 } ~~=~~ \cfrac{ 100 }{ z }\implies 24z=500\implies z=\cfrac{500}{24}\implies z=\cfrac{125}{6}\implies \boxed{z\approx 20.8}[/tex]