The depreciating value of a semi-truck can be modeled by y = Ao(0.87)x, where y is the remaining value of the semi, x is the time in years, and it depreciates at 13% per year. What is the value of the truck initially, Ao, and how would the graph change if the initial value was only $67,000?

Answer:

Step-by-step explanation:

Any equation that is equivalent to V = x(12 - 2x)(8 - 2x) is accepted. Any graph that is similar to the graph of the function is accepted.

Sample Student Response:

The box is a cube, so the volume is the length × width × height. The height is the side length of the cardboard, which is x.

The length is the original length minus two side lengths of the cutout, so the length is 12 - 2x.

Similarly, the width is the original width minus two side lengths of the cutout, so the width is 8 - 2x.

the greatest possible error for meters is 1/2 the increments

 since 18.9 is to the tenths place

 1/2 x 1/10 = 0.05

 so greatest possible error for 18.9 is 0.05m

Answer:

Step-by-step explanation:

D

Answer:

First straight line joins ordered pairs 0, 0 and 1, 60; second straight line joins 1, 60 and 3, 60; third straight line joins 3, 60 and 6, 100; and fourth straight line joins 6, 100 and 8.5, 0.

Step-by-step explanation:

Starting at home is starting at (0, 0).

Traveling at the same velocity for an hour will connect (0, 0) to (1, 60).

Stopping at the mall for 2 hours will connect (1, 60) to (3, 60).

Going ahead again at a constant velocity for 3 hours will connect (3, 60) to (6, 100).

Returning to the starting point for 2.5 hours will connect (6, 100) to (8.5, 0).

It will take 1.5 hours (or 1 hour and 30 minutes) before Taylor and Blair are 225 miles apart.

To find out how many hours it will be before Taylor and Blair are 225 miles apart, we can set up an equation based on the distance they travel.

Since they are driving away from each other in opposite directions, their distances add up to the total distance they will be apart.

Let t be the number of hours it takes for them to be 225 miles apart.

Distance traveled by Blair = Blair's speed * time (d = r * t)

Distance traveled by Taylor = Taylor's speed * time (d = r * t)

The total distance they will be apart is 225 miles:

Blair's distance + Taylor's distance = 225 miles

(70 mph * t) + (80 mph * t) = 225 miles

Now, solve for t:

70t + 80t = 225

150t = 225

t = 225 / 150

t = 1.5

So, it will take 1.5 hours (or 1 hour and 30 minutes) before Taylor and Blair are 225 miles apart.

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Mr. Chavez spent $299.97 altogether. The estimated total matches approximately with the calculated total, confirming the accuracy of our answer.

To find the total amount Mr. Chavez spent, we need to add the costs of the smartphone, carrying case, and accessories.

Total amount = |-199.99| + |-39.99| + |-59.99|

Now, let's evaluate each absolute value:

|-199.99| = 199.99

|-39.99| = 39.99

|-59.99| = 59.99

Now, let's add them together:

Total amount = 199.99 + 39.99 + 59.99

Total amount = 299.97

So, Mr. Chavez spent $299.97 altogether.

Now, let's check the answer using estimation:

Round each amount to the nearest ten:

- $199.99 is approximately $200.00

- $39.99 is approximately $40.00

- $59.99 is approximately $60.00

Now, let's add them together:

Total estimation = $200.00 + $40.00 + $60.00

Total estimation = $300.00

The estimated total matches closely with the calculated total, confirming the accuracy of our answer.

The complete question is:

Mr. Chavez spent $199.99 for a new smart phone,$39 .99 on a carrying case, and $59.99 on accessories. The expression |-199.99|+|-39.99|+|-59.99| represents the total amount that Mr. Chavez spent. How much did Mr. Chavez spend altogether? Check your answer using estimation.

9/15 = 12/x =

x = 180/9 = 20

answer is 20

Final answer:

the employee would need to work approximately 32.3 hours per month to pay for their health insurance.

Explanation:

The student has inquired about the number of hours they would need to work each month to pay for the cost of single coverage medical insurance.

Given that the insurance costs $322.77 per month and the employee earns $10 per hour, we can find the number of hours required by dividing the total cost of the insurance by the hourly wage.

To calculate:
Hours required = Total cost of insurance ÷ Hourly wage

Hours required = $322.77 ÷ $10 = 32.277

Therefore, the employee would need to work approximately 32.3 hours per month (rounding to the nearest tenth of an hour) to pay for their health insurance.

Answer:

[tex]4p^{2}+6p-8[/tex]

Step-by-step explanation:

Being a subtraction of polynomials, the second polynomial will change the signs of its terms and then the algebraic sum is done.

[tex]2p^{2} -3p-4 - (-2p^{2} -3p+4)[/tex]

changing the signs

[tex]2p^{2} -3p-4 +2p^{2}+3p-4[/tex]

performing indicated operations

[tex]4p^{2}+6p-8[/tex]

The subject of this question is Mathematics.

The subject of this question is Mathematics.

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True, A conjecture becomes a theorem after it has been proven true by logic.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The sentence is,

''A conjecture becomes a theorem after it has been proven true by logic.''

Now, We know that;

Conjectures are unproven claims.

Hence, Once someone proves a conjecture, it is called a theorem.

Thus, A conjecture becomes a theorem after it has been proven true by logic.

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An example of a compound inequality that has no solution:

x >5 and x < -4.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

 |____|____|____|____|____|____|____|____|____|____|

-5       -4      -3      -2       -1        0       1        2       3        4       5

Here is an example of a compound inequality that has no solution:

x >5 and x < -4.

x may be both higher than 5 and less than -4.

Here it is not possible that x can be both lower than -4 and larger than 5.

Hence, these inequalities have no solution.

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Answer:

52

Step-by-step explanation:

Suppose Joe had $J$ dollars to start with. Then Mary had $J + 2$ dollars. Since they both spent the same amount on their shirts, $\frac{2}{5} J - 1 = \frac{1}{3} (J + 2)$. Distributing, we get $\frac{2}{5} J - 1 = \frac{1}{3}J + \frac{2}{3}$. Isolating $J$ on the left side, $\frac{1}{15}J = \frac{5}{3}$. Therefore, $J = 25$. Thus, their original total amount of money was $J + (J + 2) = \boxed{52}$ dollars.

Final answer:

A committee of 5 can be chosen in 126 different ways from 10 people if Jones must be one of them, by using the combination formula C(9, 4) to choose the remaining four committee members from the other nine people.

Explanation:

To determine in how many ways a committee of 5 can be chosen from 10 people given that Jones must be one of them, we need to apply the concept of combinations in probability and combinatorics. Since Jones must be on the committee, we are actually choosing the remaining 4 members from the remaining 9 people.

The number of ways to choose 4 people out of 9 is calculated using the combination formula, which is:

C(n, k) = n! / (k!(n - k)!), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.

Applying this to our scenario:

C(9, 4) = 9! / (4! * (9 - 4)!) = 126

Therefore, there are 126 different ways to form the committee if Jones is already chosen as one member.

Answer:

Justin should have Multiplied 3.8 and 7.9 first

Step-by-step explanation:

Because all these people that have the wrong answer got me mad

Justin should have multiplied 3.8 and 7.9 first. Therefore, option C is the correct answer.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is 12.5 + 3.8x.

When x=7.9 in the given expression, we get

12.5+3.8(7.9)

= 12.5+30.02

= 42.52

Justin should have multiplied 3.8 and 7.9 first. Therefore, option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Justin is evaluating the expression 12.5 + 3.8x, when x is 7.9.

12.5+3.8(7.9)

16.3(7.9)

128.77

What was Justin's error?

1) Justin should have multiplied 12.5 and 7.9 first.

2)  Justin should have added 12.5 and 7.9 first.

3)  Justin should have multiplied 3.8 and 7.9 first.

4)  Justin should have added 3.8 and 7.9 first.

The sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2 is 5.9765625

Series are the sum of sequences. The sum of geometric series is expressed as:

Sn = a(1-r^n)/1-r

Given the following

n = 8

a = 3

r = 1/2

Substitute

S8 = 3(1-(1/2)^8)/0.5
S8 = 3(1-1/256)/0.5
S8 = 3(255/256)/0.5
S8 = 5.9765625

Hence the sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2 is 5.9765625

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Answer:

[tex]x^{3}-(\sqrt{x} )^3[/tex]

Step-by-step explanation:

The given expression is x³ - 3√3

We have to rewrite the expression in the forem of difference of cubes.

x³ - 3√3 = x³ - √(3)³

             = [tex]x^3-(3)^{\frac{3}{2}}[/tex]

             = [tex]x^{3}-(\sqrt{x} )^3[/tex]

Therefore, we can rewrite the expression as

[tex]x^{3}-(\sqrt{x} )^3[/tex]

Answer:

To show: [tex]\sqrt{21}[/tex] is between 4 and 5

We know:

21 is lies between two consecutive integer  i.e, 16 and 25

We can write this as:

[tex]16 < 21 < 25[/tex]

or

[tex]\sqrt{16} <\sqrt{21}<\sqrt{25}[/tex]

Simplify:

[tex]4 < \sqrt{21} < 5[/tex]

⇒[tex]\sqrt{21}[/tex] lies between 4 and 5.

Therefore,  [tex]\sqrt{21}[/tex] is between [tex]\sqrt{16}[/tex] and [tex]\sqrt{25}[/tex] this means [tex]\sqrt{21}[/tex] lies between 4 and 5.

Answer:

We know that

[tex]16<21<25[/tex]

Because, 16 is less than 21 and 25 is more than 21.

Now, if we apply a square root to each part, we would have

[tex]\sqrt{16} < \sqrt{21}<\sqrt{25}[/tex]

Then, we solve each square root, except the square root of 21, because it doesn't have an exact result

[tex]4<\sqrt{21}<5[/tex], because [tex]\sqrt{16}=4[/tex] and [tex]\sqrt{25}=5[/tex]

So, basically, the reason why [tex]\sqrt{21}[/tex] is between 4 and 5 is beacuse 21 is between 16 and 25. Then, when you apply square roots to each part, you would find that the square root of 21 is between 4 and 5. That's the reason, the position.