The management of Hartman Rent-A-Car has allocated $2.52 million to buy a fleet of new automobiles consisting of compact, intermediate-size, and full-size cars. Compacts cost $18,000 each, intermediate-size cars cost $27,000 each, and full-size cars cost $36,000 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 100, determine how many cars of each type will be purchased. (Assume that the entire budget will be used. Let x, y, and z denote the number of compact, intermediate-sized, and full-size cars purchased, respectively.)

Answer: The pages in the book can be found with the following method;

Step-by-step explanation:

Step 1

Given that the book starts on page 1 and is numbered on every page.

a)

9 digits are used for numbering pages from 1 to 9

4 digits are used for numbering pages 10 and 11

Then the first eleven pages contain thirteen digits.

b)

9 digits are used for numbering pages from 1 to 9

2×90=180 digits are used for numbering pages 10 and 99

Since the total number of digits used is 516 digits, then

From page 100 to the end of the book, the number of digits used is

516-9-180= 327 digits

Since 3 digits are used for every page, the number of pages is

327 \3 = 109 pages.

Number of pages in the book is

9+90+109= 208 pages.

The equation of the quartic polynomial in

standard form. f(x) = -4x^4 - 8x^3 + 4x^2 + 64x + 64

Since the zeros of the quartic function are -4, -2, -1, and 2, we know that the function can be factored as:

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

where a is some constant.

To find the value of a, we can use the fact that the y-intercept of the function is 64. The y-intercept occurs when x = 0, so we have:

f(0) = a(4)(2)(1)(-2) = -16a = 64

Solving for a, we get a = -4.

Substituting this into the factored form of the function, we get:

f(x) = -4(x + 4)(x + 2)(x + 1)(x - 2)

Expanding this expression, we get:

f(x) = -4x^4 - 8x^3 + 4x^2 + 64x + 64

This is the quartic polynomial in standard form.

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Answer:

\( \frac{3}{2} \)

Step-by-step explanation:

I'm not sure how to answer this but try to put the "5's" in Fraction form as 5/1 and divide them with 15/2. Which would be 3/2

Answer:

Step-by-step explanation:

yes since they are both divisible by their denominators and equal the same thing

Answer:

yes, they are equivalent

Step-by-step explanation:

2/2 = (2/2)x(4/4) = 8/8 = 1

The probability that the individual must stop at at least one light that is 0.45.

Probability is the mathematical tool or procedure of predicting how likely a given event is going to happen.

Given is that there are two traffic lights on the route used by a certain individual to go from home to work. Let {E} denote the event that the individual must stop at the first light, and define the event {F} in a similar manner for the second light. Suppose that -

We can write -

P{E ∪ F} = P{E} + P{F} - P{E ∩ F}

P{E ∪ F} = 0.4 + 0.2 - 0.15

P{E ∪ F} = 0.6 - 0.15

P{E ∪ F} = 0.45

Therefore, the probability that the individual must stop at at least one light that is 0.45.

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The number line that shows the solutions of x < 5

A number line is a visual representation of the real numbers, ordered from left to right, with zero in the middle. It is typically a straight line that extends infinitely in both directions, with evenly spaced markings that represent specific points along the line.

The solution of x < 5 should consist of number less than 5

The inequality used is less than and hence should have values saying less than

Other options has numbers more than 5 such as 6 except option B

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Answer:

3x

Step-by-step explanation:

gradient is slope.

rise/run = 3/1x = 3x

Answer:

with wut XD

Step-by-step explanation:

Answer:

0.5041 = 50.41% probability of getting 2 of the same colour

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

What is the probability of getting 2 of the same colour?

Both blue or both red

Since they are replaced, we have, in each trial:

6 blue from a set of 6 + 5 = 11

5 red from a set of 6 + 5 = 11

Probability of both blue:

Each with 6/11 probability. So

\(P = (\frac{6}{11})^2 = \frac{36}{121}\)

Probability of both red:

Each with 5/11 probability. So

\(P = (\frac{5}{11})^2 = \frac{25}{121}\)

Total:

\(p = \frac{36}{121} + \frac{25}{121} = \frac{61}{121} = 0.5041\)

0.5041 = 50.41% probability of getting 2 of the same colour

The temperature at 8:00 A.M. was 15°C.

Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.

We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C

3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.

Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C

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Answer:

A. Cendric is correct because he used the inverse of subtraction and added 4.5

Step-by-step explanation:

To solve for x, all we needed to do was to make x stand alone. To do this, we have to apply addition property of equality. This means we would add 4.5 to both sides for the equation to balance. Thus, we would have z standing alone which equals 3.

Therefore, Cendric was correct because he used the inverse of subtraction of -4.5, which is 4.5 that was later added to both sides of the equation.

Answer:

B my friend

Step-by-step explanation:

Answer:

Try contacting the Help center located at the bottom part of the home page of this site. It is recoverable as long as no violation committed

(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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The exact value of sin(5π/12) is (√6 + √2)/4

From the question, we have the following parameters that can be used in our computation:

sin 5pi/12

Express properly

So, we have

sin(5π/12)

Convert the angle to degrees

This gives

sin(5π/12) = sin(5/12 * 180)

Evaluate

sin(5π/12) = sin(75)

The actual value of sin(75) is (√6 + √2)/4

This means that

sin(5π/12) = (√6 + √2)/4

Hence, the exact value of sin(5π/12) is (√6 + √2)/4

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The exact value of sin 5π/12 is (√6 + √2)/4

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Angle in trigonometry can be measured in either degree or radian.

π is a measurement in radian which is equivalent to 180° in degrees.

Therefore:

5π/12 = 5 × 180/12

= 75°

Therefore sin5π/12 = sin75°

sin75 = sin( 45+30) = sin45cos30+ cos 45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= √3/2√2 + 1/2√2

= (√3+1)/2√2

rationalizing;

(2√6 + 2√2)/8

dividing through by 2

=(√6 + √2)/4

therefore tan75 =(√6 + √2)/4

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Answer:

1711

Step-by-step explanation:

\(4\cdot(14+8)^2-9\cdot(9-4)^2\\=4\cdot(22)^2-9\cdot(5)^2\\=4(484)-9(25)\\=1936-225\\=1711\)

Make sure to follow order of operations!

Answer:

9 ft

Step-by-step explanation:

You can use cosine to solve this, which is adjacent over hypotenuse. The ladder forms a triangle with the house, and the side you need to solve for is adjacent to the angle. You can set up the equation:

cos(50)=x/14

Then you multiply 14 by cos(50) and get almost 9 ft (rounding to the nearest tenth of a foot).

7x²+5x​

(9x²+8x)-(2x²+3x)

We will subtract the like terms. That means that we will subtract \(2x^{2}\) from \(9x^{2}\) and 3x from 8x.

To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer:

The height is 1.25m.

Step-by-step explanation:

Volume = 1/3 πr²h

Given:

V = 13.4 m³

r = 3.2 m

Asked: height (h)

Substitute the formula with the given values then solve

13.4m³ = 1/3π(3.2m)²h

13.4(3) = 10.24πh

40.2 = 10.24πh

h = 40.2/10.24π

h = 1.25m

The height of the cone is 1.25 meters.

We know that the volume of the cone is given by

V = (1 / 3) * π * r ^2 * h................equation 1

where,

V is the volume of the cone.

r is the radius of the cone's base

h is the height

The volume and radius of the cone are given,

V = 13.4 m

r = 3.2m

substituting these values in equation 1 we get,

13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h

on simplifying further

13.4 = 10.717  * h

h = 1.25m

The height of the cone is 1.25 meters.

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Answer:

b = 20 when a = 8.

Step-by-step explanation:

For this problem, we will simply plug the value of a=8 into the given equation for b, to find the value of b.

b = [ (a)^2 / 4 ] + 4

b = [ (8)^2 / 4 ] + 4

b = [ 64 / 4 ] + 4

b = [ 16 ] + 4

b = 20

Hence, when the value of a=8, then the value of b=20.

Cheers.

Answer:

20

Step-by-step explanation:

b = a^2/4 +4

Let a =8

b = 8^2 /4 +4

  = 64/4 +4

   = 16 +4

   = 20

The probability of Event A is 1/360 and the probability of Event B is 1/15.

For Event A, we can calculate the probability by considering the order in which the acts are scheduled.

There are 6 acts, so there are 6 possible choices for the first act. After the first act is scheduled, there are 5 remaining acts, so there are 5 possible choices for the second act.

Similarly, there are 4 possible choices for the third act, and 3 possible choices for the fourth act.

Finally, there are 2 possible choices for the fifth act, and only 1 choice remains for the last act.

Therefore, the total number of possible ways to schedule all 6 acts is:

6 x 5 x 4 x 3 x 2 x 1 = 720

Since we are only interested in one specific order of the first four acts, we need to count the number of ways to schedule the remaining two acts after the first four have been scheduled in the desired order.

There are 2 remaining acts, so there are 2 possible choices for the fifth act.

Only one act remains for the last slot.

Therefore, the total number of ways to schedule all 6 acts such that the acrobat is first, the singer is second, the violinist is third, and the whistler is fourth is:

1 x 1 x 1 x 1 x 2 x 1 = 2

Thus, the probability of Event A is:

P(A) = 2/720 = 1/360

For Event B, we want to count the number of ways to schedule the first four acts as the whistler, the acrobat, the guitarist, and the dancer, in any order.

There are 4 acts, so there are 4 possible choices for the first act. After the first act is scheduled, there are 3 remaining acts, so there are 3 possible choices for the second act.

Similarly, there are 2 possible choices for the third act, and only one choice remains for the fourth act.

Therefore, the total number of possible ways to schedule the first four acts is:

4 x 3 x 2 x 1 = 24

Since we do not care about the order in which the last two acts are scheduled, we can simply choose any two acts from the remaining 2. There are 2 ways to do this.

Therefore, the total number of ways to schedule all 6 acts such that the first four acts are the whistler, the acrobat, the guitarist, and the dancer, in any order is:

24 x 2 = 48

Thus, the probability of Event B is:

P(B) = 48/720 = 1/15

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Answer:$39

Step-by-step explanation:

The discounted price is going to be 60% of the original price because 100 - 40 = 60. So we want to find 60% of the original price, or 65. 65 x . 6 = 39, so the pair of rollerskates will be $39 at the discounted price.

Step-by-step explanation:

\( - \frac{3}{2} < 3x\)

\(3x > - \frac{3}{2} \)

\(x > - \frac{3}{2} \div 3\)

\(x > - \frac{1}{2} \)

9514 1404 393

Answer:

  46 games

Step-by-step explanation:

Let g represent the number of games played at 30 points per game. Then Jordan's total score would be

  32292 +30g

We want to find the value of g that makes this total 33,643:

  32292 +30g = 33643

  30g = 1351

  g ≈ 45.03

Jordan would have to  play 46 games to regain 3rd place.

_____

After 45 games, Jordan's point total would be 33,642, which is 1 point short of Bryant's record.

Answer:

Thank you so much! Always appreciated ! Happy early V day! Hope you the best <3

Step-by-step explanation: