Year No. of cars sold
in (hundreds)
2000 45
2002 51
2004 53
2006 60
2008 77
A car manufacturer's sales figures for 2000 to 2008 are shown in the table. Estimate the average rate of change in the number of cars the manufacturer sold between 2002 and 2006.

A.
450 cars per year
B.
225 cars per year
C.
2,900 cars per year
D.
600 cars per year

Answer: In photo below

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The budget of KT's Restaurant for newspaper advertising for the coming year is $58,533,500

Given,

The length of advertisement of KT's Restaurant in Vidalia Times in week days = 5,000

The length of advertisement of KT's Restaurant in Vidalia Times in Saturdays = 10,000

The cost of daily column = $27.55 per column inch

The cost of Saturdays = $29.35 per column inch

We have to find the budget of KT's Restaurant for newspaper advertising for the coming year;

Here,

There are approximately 53 Saturdays in a year.

So,

365 - 53 = 312

Then,

The budget of advertisement on daily column = 312 × 5000 × 27.55 = $42,978,000

The budget of advertisement on Saturday column = 53 × 10,000 × 29.35 = $1,555,500

Therefore,

The total budget for advertisement = 42,978,000 + 1,555,500 = $58,533,500

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The equation of the line that passes through (3, 1) and (1,2) in slope intercept form is y = - 2 / 2 x + 5 / 2.

The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.

Therefore, let's write the equation of a line that passes through (3, 1) and (1, 2).

using slope intercept form,

y = mx + b

where

Therefore, let's find slope

m = 2 - 1 / 1 - 3

m = 1 / - 2

m = - 1 / 2

Let's find y-intercept using (1, 2)

2 = - 1 / 2(1) + b

b = 2 + 1 / 2

b = 5 / 2

Therefore, the equation is y = - 2 / 2 x + 5 / 2

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Answer:

a. 17 - 2 × 3 - 8 = 3

b. 33 ÷ 3 - 2 × 5 = 1

Step-by-step explanation:

a. 17 - 2 × 3 - 8 = 3

b. 33 ÷ 3 - 2 × 5 = 1

The time taken to reaches its maximum height is 3s.

In the question,

It is given that,

Height, h(t) = [tex]96t - 16t^{2}[/tex]

The maximum value of the function is obtained if the first derivative of the function h (t) = 0.

[tex]\frac{dh(t)}{dt} = 96 - 32t = 0[/tex]

⇒ [tex]t = 3[/tex]

So, time taken to reach its max height is 3 seconds.

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If a man is 6 feet 2 inches tall, his z-score is equal to 1.82.

If a woman is 5 feet 10 inches tall, her z-score is equal to 2.92.

The 5 feet 10 inches American woman is relatively taller.

In a normal distribution, the z-score of a given sample score can be calculated by using this formula:

Z-score = (x - μ)/σ

Where:

Next, we would convert the height in feet to inches as follows:

American man = 6 × 12 + 2 = 74 inches.

American woman = 5 × 12 + 10 = 70 inches.

For the American man's z-score, we have:

Z-score = (74 - 69.2)/2.64

Z-score = 4.8/2.64

Z-score = 1.82

For the American woman's z-score, we have:

Z-score = (70 - 64.2)/2.53

Z-score = 5.8/2.53

Z-score = 2.92

Therefore, the 5 feet 10 inches American woman is relatively taller because she has a higher z-score (2.92 > 1.82).

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Complete Question:

The heights of adult men in America are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.64 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.2 inches and a standard deviation of 2.53 inches.

a) If a man is 6 feet 2 inches tall, what is his z-score (to two decimal places)?

b) If a woman is 5 feet 10 inches tall, what is her z-score (to two decimal places)?

c) Who is relatively taller?

The 6 feet 2 inches American man

The 5 feet 10 inches American woman

The number of tongue depressors = 56

The number of Band-Aids = 128

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Let x be the number of tongue depressors.

Let y be the number of Band-Aids

Convert cents to dollars

1 cent = $0.01

So, 4 cents = 0.01*4 = $0.04

     8 cents = 0.01* = $0.08

The materials are worth $12.48 .

This means, 0.04x+0.08y=12.48......(1)

There are 184 individual packages in total.

This means,  x+y=184.......(2) => x=184-y.....(3)

Substitute (3) in (1),

0.04(184-y)+0.08y=12.48

7.36-0.04y+0.08y=12.48

=> y= 128

(3) => x=184-128=56

So, the number of tongue depressors = 56

     The number of Band-Aids = 128

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By the sequence of term to term rule the value of : a)  [tex]U_{1}[/tex]= [tex](U_{0})^{2}[/tex] + 3 =[tex]1^{2}[/tex] + 3 = 4    b). [tex]U_{2}[/tex] = [tex](U_{1})^{2}[/tex] + 3 = [tex]4^{2}[/tex] + 3 =19     c). [tex]U_{3}[/tex] = [tex](U_{2})^{2}[/tex] + 3 = [tex]19^{2}[/tex] + 3 = 364 .

Give the first number in the sequence and then describe the pattern of the numbers to get the term-to-term rule. Three is the first number. The rule for terms to terms is "add 4." All of the terms in the series can be located once the initial term and term to

[tex]$$\mathrm{u}_0=1$$[/tex]

The difference is given by[tex]$u_{n+1}=\left(u_n\right)^2[/tex]+ 3

We have to simply put the value in their places to get the proper answer -

a). Put the [tex]$u_{n+1}=u_1$[/tex]

n+1 = 1  ⇒ n = 0

put n = 0in the formula[tex]$\mathrm{u}_{n+1}=\left(\mathrm{u}_n\right)^2[/tex] +3

we wil get

[tex]$$u_1=\left(u_0\right)^2[/tex] + 3 = [tex]1^{2}[/tex] =3 = 4

b). Put the [tex]$u_{n+1}=u_2$[/tex]

n + 1 = 2 => n = 1

put  n=1 in the formula [tex]$u_{n+1}=\left(u_n\right)^2[/tex]+3

we wil get:

[tex]$$u_2=\left(u_1\right)^2[/tex]+3= [tex]4^2[/tex]+3=19

c). Put the  [tex]$u_{n+1}=u_3$[/tex]

n + 1 = 3 => n = 2

Put n=2 in the formula+3

we wil get :

[tex]$$u_3=\left(u_2\right)^2[/tex] +3= [tex](19)^2[/tex] +3 =364

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The angle x will be 34°.

From the properties of circles we get to know that the angle at the center and the angle between two tangents are always supplementary.

Supplementary angles are those which always sum to to 180°.

For example ∠HJK is supplementary to ∠HIK the their sum will come out to be 180°.

similarly ∠ROP + ∠RQP = 180°

∠RQP = 180° - ∠ROP

∠ROP is given to us 146°

After putting it in the equation above we get ∠RQP = 34°

Therefore x comes out to be 34°.

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The cost of plastering the rectangle walls at rate of Rs.15/[tex]m^2[/tex] is Rs.5565.

What is rectangle?

  With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The opposite sides of a quadrilateral are equal and parallel, and all the angles are equal. Around us, there are several rectangle-shaped items. Two dimensions, the length and breadth, define each rectangle shape. The width and length of a rectangle are its longer and shorter sides, respectively.

Given,

Length of room =12m

Breadth of room =10m

Height of room =6m

So, Area of four walls =2(l+b)×h

=>area of four wall=2(12+10)×6=264[tex]m^2[/tex]

Now Area of 2 doors and 3 windows =(2×1×2+3×2×1.5)

=> area of 2 doors and 3 windows = 13[tex]m^2[/tex]

Area of ceiling =l×b=12×10=120 [tex]m^2[/tex]

Thus, total area for plastering =(264−13+120)= 371[tex]m^2[/tex]

Hence, the cost of whitewashing =Rs.(371×15)=Rs.5565.

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-1.5 is the difference in the sequence

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms are the same.

The difference is usually called the common difference. For example, the sequence 3, 6, 9, 12 have a common difference of 3 i.e. 6-3 = 3 or 9-6 = 3

Given: the sequence 4.5,3,1.5,0

The difference = 3 - 4.5 = -1.5 or 1.5-3 = -1.5

Note: You can pick any two consecutive terms to get the difference

Therefore, the difference in the sequence is -1.5

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The statements about lines that is true are

A. Line 11y = 55 is vertical.

C. For both lines, all points on the line have an x and a y-coordinate.

D. For either line, one of the coordinates of all of the points is always the same value.

Lines given to us are

1. 7x = -21

x = -3

2. 11y = 55

y = 5

Now let us check the statements.

A. Line 11y = 55 is vertical.

Yes, it is absolutely true as y = 5 will be a straight vertical line from origin of the graph (0 , 0) to (0 , 5)

B. Line 7x= -21 is vertical.

No, this statement is not true as this will be a horizontal line from (0 , 0) to (-3 , 0)

C. For both lines, all points on the line have an x- and a y-coordinate.

Yes, for both the lines there will be both x and y coordinate as every point on graph has x and y coordinates to represent them.

D. For either line, one of the coordinates of all of the points is always the same value.

Yes, this statement is true as for first line x coordinate is a constant value of 0 and for second line y is a constant value of 0.

Therefore the statements about lines that is true are A, C and D.

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The integers that would make the inequality true is the set of integers less than 20.

From the question we are to determine the integer that would make the given inequality true

The given inequality is

x - 4 < 16

To determine the integer that would make the inequality true, we will solve the inequality for the variable x

Solving the inequality

x - 4 < 16

Add 4 to both sides of the inequality

x - 4 + 4 < 16 + 4

x < 20

Hence, the solution to the given inequality is x < 20. All integers less than 20 will make the inequality true.

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The number of ways that there are to get dealt exactly a single pair is; 6,589,440 ways

The combination in probability selection is defined as a method where we count the number of ways a certain number of objects can be arranged in "n" different ways. If the number of different objects are "n", then it means that the number of ways that we can select "r" number of different objects is expressed as:

nCr = n!/(r!(n - r)!)

The total number of cards that we have in a deck of cards = 52.

There total number of different cards are 13 in number and this tells us that we can possibly have a pair of any one of the 13 cards. There are also 4 cards of the same rank and this means that the number of ways of selecting two cards of the same rank is; 4C2 = 6 ways

After selecting a card for the pair, we have 48 different cards as an option for the third card. Thereafter, we will have a total of 44 cards as an option for the fourth card and then 40 cards will be an option for the fifth card (due to the fact that none of the cards can be of same rank except for the pair of cards).

Therefore, the total number of ways that we can deal with exactly a single pair can be expressed as:

Number of ways = number of ways for the pair × number of ways for the third card × number of ways for the fourth card × number of ways for the fifth card

Plugging in the relevant values gives;

Number of ways = (13 × 6) × 48 × 44 × 40

= 6,589,440 ways

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Answer:

13.9375

Step-by-step explanation:

this is your answer 1234

The dimensions of the rectangle is 83 feet x 46 feet

What is the Perimeter of a Rectangle?

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

The perimeter P of the rectangle = 258 feet

Let the length of the rectangle be = L

Let the width of the rectangle be = W

And , The width is 37 feet less than the length. ,

So , W = L - 37

Perimeter P = 2 ( Length + Width )

Substituting the values of L and W in the equation , we get

Perimeter P = 2 ( L + L - 37 )

2 ( L + L - 37 ) = 258

( L + L - 37 ) = 129

2L - 37 = 129

Adding 37 on both sides , we get

2L = 166

Divide by 2 on both sides , we get

Length L of the rectangle = 83 feet

Substituting the value of L in equation ,we get

W = L - 37

Width W of the rectangle = 46 feet

Therefore , Length = 83 feet and Width = 46 feet

Hence , the dimensions of the rectangle is 83 feet x 46 feet

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Answer: [tex]\frac{3}{5}[/tex]of the class like blue

Step-by-step explanation:

There are : 40 - 12 - 4 = 24 ( students like blue )

[tex]\frac{24}{40}[/tex]= [tex]\frac{3}{5}[/tex]

Answer:

D.) 11

Step-by-step explanation:

-9=-k^2-7k+k Plugging in k for x

-9=k^2-6k Combine like terms

0=k^2-6k+9 Add 9 to both sides

0=(k-3)(k-3) Factor

k=3

The equation is now

f(x)=x^2-7x+3

so

f(-1)=(-1)^2-7(-1)+3

f(-1)=1+7+3

f(-1)=11

Answer:

$12,312

Step-by-step explanation:

$2,052 * 6 = $12,312

The answer to the questions from 4 through 12 are below:

4. z³ + 5z + 3z² + 1 - 4 - 2z²

= z³ + 5z² + 5z + - 3

5. Perimeter of the square = Addition of all the sides

= (2d - 3) + (3c) + (2d - 3) + (3c)

= 2d - 3 + 3c + 2d - 3 + 3c

= 4d + 6c - 6

6. Perimeter of the triangle = Addition of all the sides

= (4a - 2b) + (9a - 4) + (7a + 3)

= 4a - 2b + 9a - 4 + 7a + 3

= 20a - 2b - 1

7. Perimeter of a square = 4 × side length

= 4 × 10x

= 40x

8. Perimeter of a rectangle = 2(length + width)

= 2{(2x + 7) + (3x + 8y)}

= 2(2x + 7 + 3x + 8y)

= 2(5x + 8y + 7)

= 10x + 16y + 14

Simplify the following

9. 3a + a² + 5(a - 2)

= 3a + a² + 5a - 10

= a² + 8a - 10

10. 8(v + w) + 7(v + 2w)

= 8v + 8w + 7v + 14w

= 15v + 22w

11. 4c² + 6(c + c²) - 2c

= 4c² + 6c + 6c² - 2c

= 10c² + 4c

12. z³ + 5(z + 3) + 4(2 - 2z²)

= z³ + 5z + 15 + 8 - 8z²

= z³ - 8z² + 5z + 23

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Answer:

The Number is -5

Step-by-step explanation:

We will form the Equation and solve for the Number

Let the Number be x

Product of 30 and a Number = 30x

75 less than the Product of 30 and a Number = 30x - 75

75 less than the Product of 30 and a Number is -225

Then 30x - 75 = -225

Now solve for x (the Number)

add 75 for both sides

30x = -225 + 75 = -150

Divide both sides by 30

x = -150 / 30 = -5

Glad to Help

The values of x and y are -1 and 6 respectively, this forms an ordered pair of (-3,6) and (-1,2).

Given the equation and ordered pair in the question;

Find the y-value by substituting the x-value into the equation and solving for y.

y = 4x + 6

Plug in x = -3

y = 4( -3 ) + 6

y = -12 + 6

y = 6

Find the x-value by substituting the y-value into the equation and solving for x.

y = 4x + 6

Plug in y = 2

2 = 4x + 6

2 - 6 = 4x

-4 = 4x

x = -4/4

x = -1

Therefore, the ordered pair are (-3,6) and (-1,2).

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The age of the three brothers, based on the relationship between the ages of Frankenstein, Pugsley, Gomez, is:

Frankenstein is older than Pugsley and so is not the youngest. Pugsley is not the youngest according to the question so Gomez must be the youngest.

Assuming Gomez's age is x, the relationship between their ages is:

Gomez age + Pugsley age + Frankenstein age = 34
x + x + 5 + x + 8 = 34

3x + 13 = 34

x = (34 - 13) / 3

x = 7 years

Pugsley's age is:

= x + 5

= 7 + 5

= 12 years

Frankenstein's age is:
= x + 8

= 7 + 8

= 15 years

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The critical points of the given inequality are; x=-6 and x=2

1) When the denominator is equal to zero, at that point, we will have a critical point.

We are given the inequality;

(2x + 5)/(x - 2) ≥ (x - 1)/(x - 2)

Thus, x - 2 = 0

x = 2.

Thus, x = 2 is a critical point

2) Simplify the numerator to get the expression such that p(x) ≥ 0 or p(x) ≤ 0.

Thus, at p(x) = zero, we have other critical point(s)

Multiply both sides by (x - 2) to get;

2x + 5 = x - 1

2x - x = - 1 - 5

x = - 6

Then, the two critical points are x = 2 and x = - 6.

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Answer:

45

Step-by-step explanation:

the pattern adds 3 if you look at it care fully

The value of the variables in the right triangle are as follows;

A right triangle is a triangle that has one of its angles as 90 degrees.

The side of a right triangle can be found by using trigonometric ratios.

Therefore, let's find the variable length of the right triangle as follows;

sin 30 = opposite / hypotenuse

sin 30 = v / 3√2

1 / 2 = v / 3√2

cross multiply

3√2 = 2v

divide both sides by 2

v = 3√2 / 2

Let's find the variable w.

cos 30 = adjacent  / hypotenuse

cos 30 = w  / 3√2

√3 / 2 = w  / 3√2

cross multiply

√3 × 3√2 = 2w

3√6 = 2w

divide both sides by 2

w = 3√6 / 2

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Answer:

3 units left 7 units down

Step-by-step explanation:

if the sign is inside the bracket opposite sign

if the sign is outside the bracket leave it as it is

so (x+3)=0 which means x= -3 so 3 units left since it is on x axis. 7 is on y axis and since it is negative so 7 units down.

Answer:

20 units

Step-by-step explanation:

we find the side lengths by looking at the coordinates and just counting up

Sides are 6,4,6,4

So we just add

6+4+6+4

10+10

20

Hopes this helps please mark brainliest

Answer: Your answer is 20 units, because the height is 6 units, and the length is 4 units, so we then multiply by 2 for both numbers, then add them together, having a sum of 20 units.

Hope that helps.