Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)
The area to the left of z = 0.54 is
.
Answers
Area under the standard normal curve of z - score :
P(z < 0.54) = 0.7054
Given:
The area under the standard normal curve left is z = 0.54.
and, also sketch the area of normal curve and allocate the area left to the z - score .
What do z-scores mean?
Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean. Standard deviation is essentially a reflection of the amount of variability within a given data set.
Now,
The area under the curve represents the probability, therefore, the total area under the curve is equal to 1.
The Area under the standard normal curve of z - score :
P(z < 0.54) = 0.7054
Here, The sketch the under the standard normal curve over the indicated interval.
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Related Questions
Maths problem in indices. Pls help
Answers
Answer:
x = 9
Step-by-step explanation:
using the rule of indices
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]5^{x}[/tex] = [tex]\frac{5^{8} }{5^{-1} }[/tex] = [tex]5^{(8-(-1))}[/tex] = [tex]5^{(8+1)}[/tex] = [tex]5^{9}[/tex]
since bases on both sides are equal, both 5 , then equate indices
x = 9
Use slope to determine if lines AB and CD are parallel, perpendicular, or neither 10. A(3, 1), B(3,-4), C(-4,1), D (-4,5)m(AB) m(CD) Types of lines
Answers
Neither parallel nor perpendicular
Explanations:The points are:
A(3, 1), B(3,-4), C(-4,1), D (-4,5)
The slope of a line is given as:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]The slope of the line AB, m(AB), with gthe points A(3, 1), B(3,-4) is given as:
[tex]\begin{gathered} m(AB)\text{ = }\frac{-4-1}{3-3} \\ m(AB)\text{ = }\frac{-5}{0} \\ m(AB)\text{ =- }\infty \end{gathered}[/tex]The slope of the line CD, m(CD), with the points C(-4,1), D (-4,5) is given as:
[tex]\begin{gathered} m(CD)\text{ = }\frac{5-1}{-4-(-4)} \\ m(CD)\text{ = }\frac{4}{-4+4} \\ m(CD)\text{ = }\frac{4}{0} \\ m(CD)\text{ = }\infty \end{gathered}[/tex]A line that has an infinite slope is a vertical line
For the two lines to be parallel, m(AB) should be equal to m(CD)
For the two lines to be perpendicular, m(AB) = -1 / m(CD)
None of the conditions for paralleleism and perpendicularity is met, the lines AB and CD are neither parallel nor perpendicular
Please answer fast
The boxplot displays the arm spans for 44 students.
Which of the following is not a true statement?
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
Answers
The statements The range of the distribution is around 60 cm and
the center of the distribution is around 180 cm are true.
What is statistics?Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.
In the given statements
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
The statement "The range of the distribution is around 60 cm" is true.
The range is the spread of your data from the lowest to the highest value in the distribution.
In the given graph
Range=200-140
=60
So it is true.
The center of the distribution is around 180 cm is also true.
Hence the statements The range of the distribution is around 60 cm and
the center of the distribution is around 180 cm are true.
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11. FINANCIAL LITERACY The surf shop has a weekly overhead of $2300. b. How many skimboards and longboards must the shop sell each week to make a profit a. Write an inequality to represent the number of skimboards and longboards the shop sells each week to make a profit.
Skimboard costs 115 longboard costs 685
Answers
Can someone pls answer thiss!! rlly need help asap
Answers
The inverse of f(x) will be a relation if the original function's graph contains any location where a horizontal line would cross itself twice, but the inverse of that function won't be a function in and of itself.
Does a function's inverse always represent a relationship?
Essentially, obtaining an inverse is only a matter of changing the x and y coordinates. Although it might not always be a function, this newly generated inverse will be a relation. Sometimes a function's inverse isn't actually a function!
The inverse will also be a function if all horizontal lines only ever intersect one place on the original graph.
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solve the equation, and enter the solutions from least to greatest. If there is only one solution, enter “n.a” for the second solution. (picture of equation listed below)
Answers
Answer
x = 1 or x = n.a.
Step-by-step explanation
[tex]\frac{1}{x}+\frac{1}{x-10}=\frac{x-9}{x-10}[/tex]Multiplying by (x - 10) at both sides of the equation:
[tex]\begin{gathered} (x-10)(\frac{1}{x}+\frac{1}{x-10})=\frac{x-9}{x-10}(x-10) \\ \text{ Distributing and simplifying:} \\ \frac{x-10}{x}+\frac{x-10}{x-10}=x-9 \\ \frac{x-10}{x}+1=x-9 \end{gathered}[/tex]Multiplying by x at both sides of the equation:
[tex]\begin{gathered} x(\frac{x-10}{x}+1)=x(x-9) \\ \text{ Distributing and simplifying:} \\ \frac{x(x-10)}{x}+x=x^2-9x \\ x-10+x=x^2-9x \\ 2x-10=x^2-9x \end{gathered}[/tex]Subtracting 2x and adding 10 at both sides of the equation:
[tex]\begin{gathered} 2x-10-2x+10=x^2-9x-2x+10 \\ 0=x^2-11x+10 \end{gathered}[/tex]We can solve this equation with the help of the quadratic formula with the coefficients a = 1, b = -11, and c = 10, as follows:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm{}\sqrt{b^2-4ac}}{2a} \\ x_{1,2}=\frac{11\pm\sqrt{(-11)^2-4\cdot1\operatorname{\cdot}10}}{2\operatorname{\cdot}1} \\ x_{1,2}=\frac{11\pm\sqrt{81}}{2} \\ x_1=\frac{11+9}{2}=10 \\ x_2=\frac{11-9}{2}=1 \end{gathered}[/tex]The solution x = 10 is not possible because it makes zero the denominator in 2 of the rational expressions of the original equation. In consequence, it must be discarded.
Please help me with 24For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes.
Answers
Given the equation,
[tex]-9x^2+72x+16y^2+16y+4=0[/tex]Complete squares as shown below,
[tex]\begin{gathered} -9x^2+72x-a^2=-(9x^2-72x+a^2)=-9(x^2-8x+b^2) \\ \end{gathered}[/tex]Thus,
[tex]\begin{gathered} \Rightarrow-9x^2+72x-a^2=-9(x^{}-4)^2 \\ \Rightarrow a^2=16\cdot9=144\Rightarrow a=12 \\ \Rightarrow-9x^2+72x-144=-9(x^{}-4)^2 \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} 16y^2+16y=16(y^2+y) \\ \Rightarrow16(y+\frac{1}{2})^2=16(y^2+y+\frac{1}{4}) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} -9x^2+72x+16y^2+16y+4=0 \\ \Rightarrow-9(x-4)^2+16(y+\frac{1}{2})^2+4=-144+4 \\ \Rightarrow-9(x-4)^2+16(y+\frac{1}{2})^2=-144 \end{gathered}[/tex]Finally, the standard form is.
[tex]\begin{gathered} \Rightarrow-\frac{(x-4)^2}{16}+\frac{(y+\frac{1}{2})^2}{9}=-1 \\ \Rightarrow\frac{(x-4)^2}{16}-\frac{(y+\frac{1}{2})^2}{9}=1 \end{gathered}[/tex]As for the vertices, foci, and asymptotes,
[tex]\begin{gathered} c=\pm\sqrt[]{16+9}=\pm5 \\ \text{center:}(4,-\frac{1}{2}) \\ \Rightarrow\text{foci:}(4-5,-\frac{1}{2})_{},(4+5,-\frac{1}{2})_{} \\ \Rightarrow\text{foci:}(-1,-\frac{1}{2}),(9,-\frac{1}{2}) \end{gathered}[/tex]Foci: (-1,-1/2), (9,-1/2)
Vertices
[tex]\begin{gathered} \text{center:}(4,-\frac{1}{2}),\text{vertices:}(4\pm a,-\frac{1}{2}) \\ \text{vertices:}(4+4,-\frac{1}{2}),(4-4,-\frac{1}{2}) \\ \text{vertices:}(8,-\frac{1}{2}),(0,-\frac{1}{2}) \end{gathered}[/tex]Vertices: (8,-1/2), (0,-1/2)
Asymptotes:
[tex]\begin{gathered} y=\pm\frac{3}{4}(x-4)-\frac{1}{2} \\ \Rightarrow y=\frac{3}{4}x-\frac{7}{2} \\ \text{and} \\ y=-\frac{3}{4}x+\frac{5}{2} \end{gathered}[/tex]Asymptotes: y=3x/4-7/2 and y=-3x/4+5/2
Need help on this asap
Answers
Answer:
K=0 N=3 and I=-2
it's
3+-20= -17
Give an example of a percent problem involving the simple interest formula. Then solve your problem.
Answers
The example of the simple interest problem is: What will be the simple interest on $2500 invested at an interest rate of 6% for 2 years?
What is simple interest?
Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
Solution for the above problem is:
The formula to calculate simple interest is:
[tex]S.I. = P \times I \times T[/tex]
Here, S.I. is simple interest, P = principal amount, I = interest rate, T = time
Given in the question:
P = $2500
I = 6% = 0.06 (in decimals)
T = 2
Putting the value in the question:
S.I. = 2500(0.06)(2)
S.I. = 300
Therefore, the simple interest is $300.
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PLEASE HELP RIGHT NOW, THIS IS SUPER URGENT
The graph shows the proportional relationship between the number of gems collected and the number of levels that have been completed in a video game.
Graph with x axis labeled game levels and y axis labeled gems collected. A line begins at 0 comma 0 and goes through points 6 comma 450 and 8 comma 600.
Determine the constant of proportionality for the relationship.
p equals 2 over 150
p = 0.0133
p = 75
p = 150
Answers
The constant of proportionality for the graph will be P=75. The correct option is C.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
The proportionality of the constant determines the linear relation between two variables. as one increases the another also increases with the same factor.
To calculate the constant of proportionality for the given graph finds the slope of the graph with the points.
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 600 - 450 ) / ( 8 - 6 )
Slope = ( 150 / 2
Slope= 75
Therefore, the constant of proportionality for the graph will be P=75. The correct option is C.
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write an equation in slope-intercept form for the line with slope 4/3 and y-intercept -5
Answers
Remember the slope-intercept of a line is
[tex]y=mx+b[/tex]where:
• m ,is the slope of the line
,• b, is the y-intercept of the line
Now, let's substitute the data we're given. Thereby, the equation would be
[tex]y=\frac{4}{3}x-5[/tex]Parallel lines investigation
Answers
From the given figure the value of x is 6 and the measure of angle 3 is 57°.
From the given figure, m∠4=(20x+3)° and m∠6=(9x+3)°.
What are angles of parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
22). From the given figure
m∠4+m∠6=180° (Coointerior angles sum is equal to 180°)
(20x+3)°+(9x+3)°=180°
⇒ 29x+6=180
⇒ 29x=174
⇒ x=6
m∠4=(20x+3)°=123°
m∠3+m∠4=180° (Adjacent angles sum is equal to 180°)
m∠3+123=180
m∠3=57°
23). From the given figure
m∠3=m∠6 (Alternate interior angles are congruent)
x+10 = 4x-20
⇒ 3x=30
⇒ x=10
Now, m∠6=4x-20
=20
m∠6+m∠8=180° (Adjacent angles sum is equal to 180°)
20+m∠8=180°
⇒ m∠8=160
Therefore, from the given figure the value of x is 6 and the measure of angle 3 is 57°.
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A farm is being divided so that each section of land has equal access
to the canal running through the property for watering crops. If the road on the
opposite side of the property runs parallel to the canal, explain how this can be
done.
Answers
The best way to divide the land having canal and road parallel, is divide land with the line perpendicular to the road and canal.
What is parallel and perpendicular?
In simple geometry, two geometric objects cross at a right angle (90 degrees or /2 radians) if they are perpendicular to one another. The perpendicular symbol,⟂, can be used to graphically depict the condition of perpendicularity. It can be defined between two planes, between two lines (or line segments), and between two lines.
In geometry, parallel lines are coplanar, straight lines that never intersect. Any parallel planes in the same three-dimensional space are those that never intersect. Parallel curves are those that have a predetermined minimum separation between them and do not touch or intersect.
We need to give equal access of canal to each section of land so, the best way to divide land is divide land perpendicularly to canal and the road.
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hi I need help with this question anyone got answers??? please its due tmrrrr!!!!!
5 1/4 ÷ 2/4
Answers
21/4 / 2/4 = 21/4 • 4/2 = 84/8 = 10 1/2
7/12 x 4x3 =? I need help
Answers
Cyphon, this is the solution:
We have to multiply the following fractions:
7/12 * 4/3
7 * 4 / 12 * 3
28/36
Simplifying, we have:
7/9 (Dividing by 4 numerator and denominator)
We have to add the following fractions:
- 1/2 + 4/9
Let's find the lowest common denominator between 2 and 9, as follows:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
9, 18, 27, 36
The lowest common denominator is 18
if square one is the largest of the three squares in the model,which statement is true?
Answers
_______________
I'm reading your question
___________________
According to the Pythagorean theorem
Hypotenuse ^2 = Side 1 ^2 + Side 2 ^2
The hypotenuse is the case (Square 1 )
area of the sqaure= side of the square^2
________________________
That means the area of 1 is = area of square 2 + area fo square3 (J is false)
_______________________________
We are not sure about the relation between square 2 and 3 just the addition is the square 1 (F and H we have no certainty)
______________________________
G is true
______________________________
Answer
G
What is the linear equation for the line graphed below?
Answers
Answer:
y = -3x + 7
Step-by-step explanation:
Hello!
Slope-Intercept Form: y = mx + b
m = slopeb = y-interceptThe y-intercept of the graph, or the point where the graph intersects the y-axis, is 7.
We can find the slope by finding the Rise/Run.
The graph rises negatively by 3 units as it runs positively by 1 unit, so the slope is -3/1 or -3.
Given the slope and y-intercept, the equation of the line is y = -3x + 7.
what does x = to in the equation 4x +4<9x +8?
Answers
The given inequality is expressed as
[tex]4x\text{ + 4 }\leq\text{ 9x + 8}[/tex]The first step is to collect like terms. Thus, we have
[tex]\begin{gathered} 4x\text{ - 9x }\leq\text{ 8 - 4} \\ -\text{ 5x }\leq\text{ 4} \\ \end{gathered}[/tex]We would find x by dividing both sides of the inequality by - 5. Since - 5 is negative, the inequality symbol would be reversed. Thus, we have
[tex]\begin{gathered} \frac{-\text{ 5x}}{-\text{ 5}}\ge\frac{4}{-\text{ 5}} \\ x\text{ }\ge\text{ }\frac{-\text{ 4}}{5} \end{gathered}[/tex]darnel is the executive chef at a mediterranean restaurant famous for its spicy tomato sauce. every week, he takes inventory and then places an order for what he needs. since his spicy tomato sauce is so popular, darnel needs to order more tomatoes every week. there is a proportional relationship between the amount of tomatoes he orders (in pounds), x, and their cost (in dollars), y. x (pounds) y (dollars) 22 $88 23 $92 24 $96 25 $100 what is the constant of proportionality? write your answer as a whole number or decimal. dollars per pound
Answers
The constant of proportionality between the amount of tomatoes he orders (in pounds), and their cost (in dollars) is: 4 dollars per pound
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
pounds , dollars
22, $8823, $9224, $9625, $100Calculating the proportion of the amount of tomatoes he orders and their cost we get:
Proportion dollars per pound = Dollars / pound
Proportion dollars per pound = $88/ 22 pounds = 4 $/pound
Proportion dollars per pound = $92/ 23 pounds = 4 $/pound
Proportion dollars per pound = $96/ 24 pounds = 4 $/pound
Proportion dollars per pound = $100/ 25pounds = 4 $/pound
As we could get the constant of proportionality is 4 $/pound
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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a. cos x b. tan x c. sec x d. cot x Simplify the expression
Answers
First, multiply by 1:
cos x * 1 + cos x tan^2 x
Factor cos x out of cos x tan^2 x
cos x * 1 + cos x (tan ^2 x)
Factor again
cos x (1+ tan^2 x)
Rearrange:
cos x (tan^2 x +1 )
Apply Pythagorean identity:
cos x * sec ^2 x
Rewrite Sec x in terms of sin and cos
cos x * (1 / cos x )^2
Apply product rule:
cos x * 1^2 / cos^2 x
cos x * (1/ cos^2 x )
Cancel common factor cos x
1 / cos x
1/cosx = sec x
Answer : sec x (option c)
If Susie's age is 8 less than 3 times her brother's age, and Susie is 13. How old is her brother?
Answers
Answer:
correct me if im wrong but my answer is x=7, or in other words, 7.
Step-by-step explanation:
Answer:
7 years old
Step-by-step explanation:
You would start by going backward. If 13 is 8 less, then you would first add 8. You would have 21. Now all you have to do is divide by three. So your answer would be 7. If you would want to check you could plug it back in. 7 multiplied by 3 is 21. 21 - 8=13
The Answer, 7 years old
Which one of these expressions doesn’t have a value less than 1 please help thank you if u do
Answers
The fourth option [tex](3^{5)^{2} }[/tex]/[tex](3)^{4}[/tex] does not have value less than 1.
What is Power or Exponent?Power of a number is defined as how many times to use the number in a multiplication. We also call Powers as Exponents or Indices. For example, [tex]8^{2}[/tex] could be called “8 to the power 2” or “8 to the second power”, or simply “8 squared”.
Step-by-step explanation:
In first option, [tex]4^{11}[/tex]/[tex]4^{14[/tex], if we solve this, the answer comes out to be 1/[tex]4^{3}[/tex] which will be 1/64 which is 0.015 that is lesser than 1.
In second option, [tex](5^{4)^{2} }[/tex]×[tex]5^{-11}[/tex],if we solve this, the answer comes out to be 1/[tex]5^{3}[/tex] which will be 1/125 which is 0.008 that is lesser than 1
In third option,[tex](2^{3)^{-2} }[/tex],if we solve this, the answer comes out to be 1/[tex]2^{6}[/tex] which will be 1/64 which is 0.015 that is lesser than 1
in Fourth option ,[tex](3^{5)^{2} }[/tex]/[tex]3^{4}[/tex] , if solve this, the answer comes out to be [tex]3^{6}[/tex] which will be 729 that is larger than 1
∴fourth option will be the answer.
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Berti is the Shape Factory's top employee. She has received awards every month for having the top sales
figures so far for the year. If she stays on top, she will receive a $5000 bonus for excellence. She currently has
sold 16, 250 shapes and continues to sell 340 per month.
EMPL
Since there are eight months left in the sales year, Sarita is working hard to catch up. While she has only sold
8,830 shapes, she is working overtime and on weekends so that she can sell 1, 082 per month. Will Sarita
catch up with Berti before the end of the sales year? If so, when?
Answers
No, Sarita will not be able to catch up with Berti before the end of the sales year.
Berti currently has sold 16, 250 shapes
She continues to sell 340 per month.
In eight months she will be able to sell
16250 + 8 x 340
= 16250 + 2720
= 18970
Sharita has only sold 8,830 shapes
Working overtime and on weekends so that she can sell 1, 082 per month
In eight months she will be able to sell
8830 + 8 x 1082
8830 + 8656
17486
No, Sarita will not be able to catch up with Berti before the end of the sales year.
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Write a linear equation to represent the given problem and then solve the problem.
The perimeter of a college basketball court is 96 meters and the length is 14 meters more than the width. What are the dimensions?
Perimeter = 2 x Length + 2 x Width
Answers
Answer:
Step-by-step explanation:
Let L be the length and W the width
Perimeter of a rectangle is P = 2L + 2W
We are told that L = W + 14 (m) [the length is 14 meters more than the width]
Area of a rectangle is A = L*W
We learn that A = 96 m^2
L*W = 96
Since L = W + 14, we can substitute:
L*W = 96
(W + 14)*W = 96 m^2
W^2 + 14W = 96
W^2 + 14W - 96 = 0
The solution to W in the above equation is 5.04 m
This means L = 5.04 m + 14 m
L = 19.04 meters
Perimeter = 2W + 2L
Perimeter = 2(5.04) + 2(19.04) = 96 m^2
Find the area of thisirregular figure.9 ft8 ft15 ft26 ft
Answers
The area of the irregular figure will be equal to the sum of area of triangle and the area of the rectangle.
The required area can be determined as,
[tex]\begin{gathered} A=A_t+A_r \\ =(\frac{1}{2}\times8\text{ ft}\times9\text{ ft)+(15 ft}\times26\text{ ft)} \\ =36ft^2+390ft^2 \\ =426ft^2 \end{gathered}[/tex]Thus, the required area of the irregular figure is 426 square feet.
NOBODY IS ANSWERING!! I WILL GIVE BRAINLIEST!! PLS HELP!!
Answers
You invest $8,000 in 3 investment accounts. The accounts are: paper, metal and glass. Paper returns 2% income, metal returns 4% income, and glass returns 5% income. The amount invested in the glass account was double the amount invested in the metal account. The yield was a total of $280 at the end of one year. How much was invested in each account?
Answers
The following investments were done:
Metal account: $ 1,500Glass account: $ 3,000Paper account: $ 3,500How much money has a person invested in three accounts?
In this problem we must determine how much money from a $ 8,000 investment has been deposited in each account based on overall yield after a period of one year. In accordance with the statement, the person deposited the following quantities in each account:
Metal: x
Glass: 2 · x
Paper: 8,000 - 3 · x
And the yield function is equal to:
280 = x · (4 / 100) + 2 · x · (5 / 100) + (8,000 - 3 · x) · (2 / 100)
280 = 0.04 · x + 0.1 · x + 160 - 0.06 · x
120 = 0.08 · x
x = 1500
The person made an investment of $ 1,500 in the metal account, $ 3,000 in the glass account and $ 3,500 in the paper account.
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The sum of two consecutive integers is 97. What is the smaller integer?
Answers
Answer: 48 is the smaller integer
Step-by-step explanation: 48+49=97 48 and 49 are the two integers, 48 is smaller than 49.
Find the value of each variable
Answers
Step by step
The two “x” variable angles are supplementary so combined they will equal 180 degrees
2(5x -5) + (3x -5) = 180
Distribute
10x -10 + 3x -5 = 180
Combine
13x -15 = 180
Add 15 to both sides to isolate variable
13x -15 + 15 = 180 + 15
Combine
13x = 195
Divide both sides by 13 to solve for x
13/13 x = 195/13
x = 15
The two “y” variable angles are supplementary so combined they will equal 180 degrees
5y + 5 + 20y = 180
Combine
25y + 5 = 180
Subtract 5 from both sides to isolate y
25y +5 -5 = 180 -5
25y = 175
Divide both sides by 25 to solve for y
25/25 y = 175/25
y = 7
PLSS HELP I DO NOT UNDERSTAND THIS PLSSS
Answers
The rate of change is 18 units and 24 ≤ x ≤ 96 is 24 < 42, 60, 78 < 96.
What is the rate of change?The rate at which a variable alters over a predetermined amount of time. It is frequently used when discussing momentum and is typically expressed as a ratio of one variable's change to another's corresponding change. This ratio is graphically represented by a line's slope.So, the rate of change in column 'x':
24 - 6 = 18The rate of change per unit is 18.
Now, 24 ≤ x ≤ 96.
Between 24 and 96, there are three values given in the column which are:
426078So, x can be 42, 60, and 78.
Therefore, the rate of change is 18 units and 24 ≤ x ≤ 96 is 24 < 42, 60, 78 < 96.
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