The value V of a certain automobile that is t years old can be modeled by V(t) = 14,651(0.81). According to the model, when will the car be worth each of the following amounts?
(a) $8000
(b) $6000
(c) $1000
- The car will be worth $8000 after years.
(Type an integer or a decimal rounded to the nearest tenth as needed.)

The inequality used to determine the maximum number of days Miguel can afford to rent while staying within his budget is 202.5 + 36.39x ≤ 480.

What is an inequality?

An inequality is a comparison between two or more mathematical expressions. It can be of the form ≤, ≥, < or >.

We are given per day charges as $36.39 and the charges per mile as $0.90.

Also, it is given that in total 225 miles have been driven.

So, the charges of 225 miles are:

⇒225 x 0.90

⇒$202.5

It is given that he can spend maximum $480.

So, for the maximum number of x days, we get the inequality as

202.5 + 36.39x ≤ 480

Hence, the inequality used to determine the maximum number of days Miguel can afford to rent while staying within his budget is

202.5 + 36.39x ≤ 480.

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6. B. 2x + 6

7. A. 4x + 5

8. B. 3x + 10

9. C. This is because like terms are terms that have the same variables, for example: 6x - 9x, 12y - 4y, 3a + 5a. In the other choices, we can see that they are unlike terms, not like terms.

Answer:

a 30÷5=6

Step-by-step explanation:

Because from the fact the numbers that were used were 5,6and30.

they solved for 5×6=30,30÷6=5and6×5=30. which means it is left with 30÷5=6.

hope this helps.

Answer:

As given,

I = \(\int\limits {\frac{3x}{x^{2} - 2x} } \, dx\)

Since the degree of the numerator is less than the degree of the denominator, we don't need to divide.

We factor the denominator as x(x-2)

The partial fraction decomposition is

\(\frac{3x}{x^{2} - 2x} = \frac{3x}{x(x-2)} = \frac{A}{x} + \frac{B}{x-2}\\ = \frac{A(x-2) + B(x)}{x(x-2)} \\\)

we get

3x = A(x-2) + B(x)

⇒3x = x(A+B) - 2A

By comparing , we get

A+ B = 3 , -2A = 0

⇒A = 0 and B = 3- A = 3-0 = 3

∴ we get

A = 0, B = 3

Therefore, the integral become \(\int\limits {\frac{3x}{x^{2} - 2x} } \, dx = \int\limits {[\frac{0}{x} + \frac{3}{x-2} ] } \, dx\)

Answer:

the required answer are -8,0,4

There are 360 ways tο assign fοur taxi drivers tο six cars.

A permutatiοn is an arrangement οf οbjects in a definite οrder. The members οr elements οf sets are arranged here in a sequence οr linear οrder. Fοr example, the permutatiοn οf set A={1,6} is 2, such as {1,6}, {6,1}. As yοu can see, there are nο οther ways tο arrange the elements οf set A.

In permutatiοn, the elements shοuld be arranged in a particular οrder whereas in cοmbinatiοn the οrder οf elements dοes nοt matter. Alsο, read: Permutatiοn And Cοmbinatiοn

We wοuld use a permutatiοn tο determine hοw many ways fοur taxi drivers can be assigned tο six cars. This is because the οrder in which the drivers are assigned tο the cars matters - assigning driver A tο car 1 is different frοm assigning driver A tο car 2.

The permutatiοn nοtatiοn fοr this prοblem is P(6,4), which represents the number οf permutatiοns οf 6 οbjects taken 4 at a time. Using the fοrmula fοr permutatiοns, we have:

P(6,4) = 6! / (6-4)! = 6! / 2! = 720 / 2 = 360

Therefοre, there are 360 ways tο assign fοur taxi drivers tο six cars.

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The correct value of 2f(a-1) is 2a^2 - 12a + 10.

To find the value of 2f(a-1), we need to substitute (a-1) into the function f(x) and then multiply the result by 2.

Given: f(x) = x^2 - 4x

Substituting (a-1) into the function:

f(a-1) = (a-1)^2 - 4(a-1)

Expanding and simplifying:

f(a-1) = (a^2 - 2a + 1) - (4a - 4)

f(a-1) = a^2 - 2a + 1 - 4a + 4

f(a-1) = a^2 - 6a + 5

Now, we multiply the result by 2:

2f(a-1) = 2(a^2 - 6a + 5)

Expanding:

2f(a-1) = 2a^2 - 12a + 10

Therefore, the value of 2f(a-1) is 2a^2 - 12a + 10.

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Answer:

a -> 3

b -> 4

c -> 1

d -> 5

e -> 2

Step-by-step explanation:

We apply the properties to solve this question.

a. √4x^2y^4

\(\sqrt{4x^2y^4} = \sqrt{4}\sqrt{x^2}\sqrt{y^4} = 2xy^2\)

So a -> 3

b. √8x^2y

\(\sqrt{8x^2y} = \sqrt{8}\sqrt{x^2}\sqrt{y} = \sqrt{4*2}x\sqrt{y} = \sqrt{4}\sqrt{2}x\sqrt{y} = 2x\sqrt{2}\sqrt{y} = 2x\sqrt{2y}\)

So b -> 4

c. √4x^2y

\(\sqrt{4x^2y} = \sqrt{4}\sqrt{x^2}\sqrt{y} = 2x\sqrt{y}\)

So c -> 1

d. √16xy^2

\(\sqrt{16xy^2} = \sqrt{16}\sqrt{x}\sqrt{y^2} = 4\sqrt{x}y = 4y\sqrt{x}\)

So d -> 5

e. √8xy^2

\(\sqrt{8xy^2} = \sqrt{8}\sqrt{x}\sqrt{y^2} = \sqrt{4*2}\sqrt{x}y = \sqrt{4}\sqrt{2}\sqrt{x}y = 2y\sqrt{2}\sqrt{x} = 2y\sqrt{2x}\)

So e -> 2

Answer:

7.534g ring is heavier, by 2.234g

Step-by-step explanation:

Note: mg =

\( {10}^{ - 3} grams\)

\(5300mg = ( \frac{5300}{ {10}^{3} } )g \\ = ( \frac{5300}{1000} )g \\ = 5.3g\)

From here we can see Ring A (7.534g) is heavier than Ring B(5,300mg)

Difference in Mass = 7.534g - 5.3g

= 2.234g

Answer:

maybe 0 dollars doesn't know

Answer:

-240.75

Step-by-step explanation:

-70.12-100.50=30.38

30.38- 271.13= -240.75

This is a sum of squares, which cannot be factored over the real numbers. You'll need to involve complex numbers to be able to factor, though its likely your teacher hasn't covered that topic yet (though I could be mistaken and your teacher has mentioned it).

Choice B can be factored through the difference of squares rule. Therefore, choice B is not prime.

Choice C and D can be factored by pulling out the GCF and then use the difference of squares rule afterward. So we can rule out C and D as well.

Answer:

A

Step-by-step explanation:

because it has a + sign

Answer:

19. 25 chocolate bars

Step-by-step explanation:

77 divided by 4=19. 25

Answer:

b) no

Step-by-step explanation:

let's put all these options in columns to visualize:

   shirts:                            pants:

    red                               khaki

    white                            black

    black                            white

now i'll list all the combos without matching colors (shirt, pants)

red, khaki;

red, black;

red, white;

white, khaki;

white, black;

white, white;

black, khaki;

black, black;

black, white;

now, we need to get rid of any combos that consist of the same color and combos that consist of black and white paired together.

and we're left with:

red, khaki;

red, black;

red, white;

white, khaki;

black, khaki;

that's only 5 options, so no, she cannot make 8 outfits

Answer:

(1,0), (2,1), (4,2), (8,3), (16,4)

Step-by-step explanation:

For every point (a,b) that lies on the graph of function f, the point (b,a) must lie on the graph of its inverse. The points (1,0), (2,1), (4,2), (8,3), (16,4) and lie on the graph of function f. The points shown in the table lie on the graph of the inverse function,f^-1

Plato's Explanation.

Hope this helps!

The quadratic functions are: f(x) = 0.03x² for Design A and g(x) = 0.024x² for Design B.

A quadratic function is a type of polynomial function of the form f(x) = ax² + bx + c, where a, b, and c are constants and x is the variable. In a quadratic function, the highest power of the variable is 2.

The graph of a quadratic function is a parabola, which is a U-shaped curve that opens either upwards or downwards depending on the sign of the coefficient a. If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards. The vertex of the parabola, which is the point where the curve changes direction, is given by the coordinates (-b/2a, f(-b/2a)).

Quadratic functions have a wide range of applications in various fields such as physics, engineering, economics, and finance. For example, they can be used to model the motion of projectiles, the trajectory of a rocket, the shape of a bridge arch, the optimization of business profits, and the behavior of financial markets.

Let's assume that each side of the cube has a length of x inches. Then, the surface area of the cube is 6x² square inches.

a. For Design A with a cost of $0.005 per square inch, the total cardboard cost can be calculated using the quadratic function:

f(x) = 0.005(6x²) = 0.03x²

b. For Design B with a cost of $0.004 per square inch, the total cardboard cost can be calculated using the quadratic function:

g(x) = 0.004(6x²) = 0.024x²

Therefore, the quadratic functions are:

f(x) = 0.03x² for Design A

g(x) = 0.024x² for Design B

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The complete question is:

Answer:

Ok, so with this problem, you would start with the equation 6/10=x/38.

Then, cross multiply:

38(6)=10x

After, you would:

38 x 6 = 228

Then:

228/10

Lastly:

x=22.8m which when rounded equals 23 ft.

The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Answer:

x= 5 , y = 34

Step-by-step explanation:

8x-6=5x+9

3x-6=9

3x=15

x=5

-

8(x5) - 6 =

34

25(x5) +9 =

34

Answer:

x = 5 and y = 34

Step-by-step explanation:

I used substitution method and did this ;

8x - 6 = 5x + 9 .....put like terms together

8x - 5x = 9 + 6

3x = 15

x = 5

y = 8 (5) - 6

y = 40 - 6

y = 34

Answer: 0.41

Step-by-step explanation:
To find the decimal point of a fraction, divide the numerator (the top half of the fraction) by the denominator (the bottom half of the fraction).

41 over 100 as a decimal point would be 41 divided by 100

Which produces the equivalent decimal, 0.41

P.S this is also how you find the percent of a number. To get the percent, move the decimal point 2 digits over (0.41 to 41.) and then add the percentage sign to the end of the number (41%)

0.41 = 41%

so 41 over 100 is 0.41, and 41 is also 41% of 100 (per cent means per 100)

Best of luck in 5th grade :)

Using it's concept, it is found that the sample space of T and S is:

{{8, [850-1500]}, {9, [850-1500]}, {10, [850-1500]}, {11, [850-1500]}, {12, [850-1500]}, {13, [850-1500]}, {14, [850-1500]}}

The sample space is the set that contains all possible outcomes for an experiment.

In this problem:

Considering that for each time, the cost will be between $850 and $1500, the sample space for T and S is:

{{8, [850-1500]}, {9, [850-1500]}, {10, [850-1500]}, {11, [850-1500]}, {12, [850-1500]}, {13, [850-1500]}, {14, [850-1500]}}

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The number of days until Stephen and John are on the same page would be 6 days

The page they would be on would be 64 pages

Assuming that the number of days can be denoted as x, the equation for the number of pages that Stephen has read in total is:

= 22 + 7 x

The number of pages that John has read in total is:

= 10 + 9 x

To find the number of pages, equate these:

22 + 7 x = 10 + 9x

22 - 10 = 9x - 7 x

12 = 2 x

x = 12 / 2

x = 6 days

The page they would be on is:

= 10 + 9 x

= 10 + 9 ( 6 )

= 64 pages

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Explanation

Step 1

Let

x represents the number

Four times a number=4x

two times that same number=2x

is equal = "="

Step 2

replace

"Four times a number is equal to two times that same number and 16"

Step 3

solve for x

I hope this helps you

Answer:

You are correct

Step-by-step explanation:

You are correct sir. They want the answer in feet, so everything on that triangle has to be converted into feet.

There are 12 inches in a foot. If we do 108/12 we get 9 feet.

Elisa's savings account has the greater average rate of change between 2005 and 2015.

For Darlene's savings account, the initial amount in 2005 is $500. To calculate the value of the account in 2015, we need to know how many years have passed. Since 2015 is 10 years after 2005, we can substitute t = 10 into the equation given:

f(t) = 500(1 + 0.04t)

f(10) = 500(1 + 0.04(10))

f(10) = 500(1.4)

f(10) = 700

Therefore, the amount in Darlene's savings account in 2015 is $700. The average rate of change between 2005 and 2015 is the slope of the line connecting the points (0, 500) and (10, 700):

slope = (700 - 500) / (10 - 0) = 20

For Elisa's savings account, we are given the values of the function at several points, but we need to determine the slope of the line connecting the points (0, 600) and (10, 977), since this represents the change between 2005 and 2015. The slope is:

slope = (977 - 600) / (10 - 0) = 37.7

Therefore, Elisa's savings account has the greater average rate of change between 2005 and 2015.

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9514 1404 393

Answer:

  The lines are neither parallel nor perpendicular. They intersect in the 2nd quadrant.

Step-by-step explanation:

You have provided no descriptions, so we have shown the lines to let you draw your own conclusion regarding the description that best fits.

The probability that the third largest observation in the sample is less than 0.7 is  0.2401 =  24.01%.

The sample size n = 5,

Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.

Probability that X₃ is less than 0.7:

Since X₃ is the third largest observation =  (X₁ and X₂) < 0.7.

The probability that X₃ is less than 0.7 is (0.7)² = 0.49.

.

The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.

We then get the product of both cases:

Probability = 0.49 * 0.49 = 0.2401

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ANSWER:

6

STEP-BY-STEP EXPLANATION:

The area of a triangle is given by the following equation:

We replace and solve for h (height)

The height of the triangle is 6 inches

Answer: for 10. the answer is 29y and 49y and for 11 the answer is 119 x 146y

Step-by-step explanation: Tutor verified) If you take 1-3x 57y92 you get 29y and if you get 5-4y 178x1 -119 wich is 146y

Step-by-step explanation:

What is 45% of 150?

Y is 45% of 150

Equation: Y = P% * X

Solving our equation for Y

Y = P% * X

Y = 45% * 150

Converting percent to decimal:

p = 45%/100 = 0.45

Y = 0.45 * 150

Y = 67.5

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