Two model cars race in a straight line. The distance in feet of car A from the starting line is modeled by the function f(t) = 0.25t^2 + 22t - 1, where t is the time in seconds since the start of the race. The distance in feet of car B from the starting line is modeled by the function g(t) = -0.1t^2 + 25t.
Write a model for the difference in feet between car A and car B.
What is the difference in feet between car A and car B after 10 seconds? How can you tell which car is in the lead?

Answer:

18 cm

Step-by-step explanation:

Range = Largest Number - Smallest Number

We know the following from the original data set:

Largest Number = 32 cm

Smallest Number = 3 cm

Original Range = 32 cm - 3 cm = 29 cm

The outlier is 3 cm because all the other numbers are relatively close to ine another in their 20s and 30s. If we remove 3 cm from the data set, we know the following:

Largest Number = 32 cm (Doesn't change)

Smallest Number = 21 cm

New Range = 32 cm - 21 cm = 11 cm

We can compare the two ranges by subtracting the larger range from the smaller range:

Range Difference = 29 cm - 11 cm = 18 cm

Therefore, the range decreases by 18 cm when we remove the outlier.

The measurement that is closest to the volume of the cylinder in cubic feet is: 15.7 Feet. (Option B)

Recall that volume is

V = πr²h

Given:

h = 5 feet

r = 2/2 = 1

Hence

V = 5 x 1 x 22/7

= 15.7142857143

Hence, the cylinders volume in cubic feet is given as:

[tex]$\approx$[/tex] 15.7 ft

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Answer: 15.7 ft3

Step-by-step explanation:

Answer:

a good estimation is 190

Step-by-step explanation:

(2x25)+(3x12)+(7x8)+(9x5)=187

187 rounds to 190

Answer: (a) 0-2 (b) 3.2

Step-by-step explanation:

modal = the number that appears the most

mean = average

(a) modal class interval: 0 - 2

(b) first, find the mean of each class interval (number of letters delivered):

1, 3.5, 6 and 9

1 x 25 = 25

3.5 x 12 = 42

6 x 8 = 48

9 x 5 =45

25 + 42 + 48 + 45 = 160

number of houses:

25 + 12 + 8 + 5 =50

mean:

160 / 50 = 3.2

Answer:

(a) 1/2

(b) $1,080,000

(c) 72°

Step-by-step explanation:

We have to find the ratio in which the money is being distributed

To do this first add up the individual values in the ratio 5:3:2 which represents the ratio C:D:E for apportioning savings

5 + 3 + 2 = 10

Chris's share = 5/10 = 1/2

Danny's share = 3/10

Evelyn's share = 2/10 = 1/5

Answers

(a) Fraction of Danny's share = 1/2

(b) If Danny is to receive $540,000 and his share is 1/2 of total savings then the total savings = 2 x 540,000 = $1,080,000

(c) The ratio of the angles in a pie chart will be the same as the ratio of the division. A pie chart shows the relative shares as part of a circle. Since a circle contains 360° , the angle of the sector that represents Evelyn's share will be 1/5 x 360 = 72°

Answer:

false

Step-by-step explanation:

Answer: so Justin pays 0.49 per pound for each pumpkin

Give me brainliest if it is correct

Step-by-step explanation: so Justin a 20 purchased a pound Pumpkin for 9.80 so first

you put [tex]\frac{9.8}{20}[/tex] and when you divide you get  0.49

Answer:

2

Step-by-step explanation:

to solve this equation you must find what you multiply A to to equal A'

you can solve this by dividing 18 by 9

18 / 9 = 2

that is your answer

Answer:

-2 <= y <= 4

Step-by-step explanation:

-3 <= 2y + 1 <= 9

-4 <= 2y <= 8

-2 <= y <= 4

Answer:

-2 <= y <= 4

Step-by-step explanation:

-3 <= 2y + 1 <= 9

-4 <= 2y <= 8

-2 <= y <= 4

Answer:

50 69 600 5.2 2

Step-by-step explanation:

this is because this is simple interest i=pxrxt

Answer: triangle 4  MNO≅JKL

Step-by-step explanation:

Answer:

-2.04

Step-by-step explanation:

it'll be

-1.34 - 0.7 = y

- 2.04 = y

You can just try out all the answers but I'll give you a solution.

We will expand out the middle term to 5x^2 - 30x - 6x + 36, then we group the first 2 terms together, and the last 2 terms together.

= 5x (x - 6) - 6(x - 6)

And we put x-6 out : (x-6)(5x-6) = 0

Now, we can just set the value of one bracket to 0 and find out the value of x, and do the same for the other one

x - 6 = 0 -> x = 6
5x - 6 = 0 -> x = 6/5

Because 6 is not a possible option, the answer is x = 1.2

The form of a periodic function is H(t) = 20cos(π/12(t+12))+ 60.

What do periodic functions mean?

A function that periodically returns to the same value. Despite the similarity in sound between periodic motion and oscillatory motion, not all periodic motions are oscillatory motion.

Since the values of H oscillates between two values, then the choices of the function are either sine or cosine. However, since the variable measures the time from 4 AM, and 4 AM represents the trough of the oscillation, then cosine is the more appropriate choice. Recall the form of a periodic function

y =A cos(B(x +C))+D

It is given that the peak of desert temperature is at 80F, and the lowest is 40F. Note that the distance between the two temperatures is

80F − 40F =40F

Since the amplitude is the distance from the middle line to either peak or trough, then it is half the distance from the trough to the peak. Hence

A = 40/2= 20

Notice that one full oscillation occurs after one day or 24 hours. Hence the period is

B =2π/24 = π/12

The graph of the cosine function begins at the peak, whereas the function needs to begin at the trough, since the variable t represents the number of hours after 4 AM. Thus, the graph must be shifted horizontally to the left one half-cycle, which is

C = 12

Since the original cosine function has the centerline at x= 0  the centerline of the function must be shifted by the number of units corresponding to the midway point of the peak and the trough. Hence

D= 80 + 40/2 = 120/2 = 60

ubstituting

A =20, B = π/12. C= 12 , and  D= 60 into

The form of a periodic function

                    H(t) = 20cos(π/12(t+12))+ 60

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The function is 4|x-4|.

It is required to find the  function g.

A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given:

The original function is:

f(x)=|x|

Translation 4 units to the right we get,

f(x-4)=|x-4|

Horizontal stretch by a factor of 4

Multiplying by 4, so:

g(x)=4f(x-4)=4|x-4|

Therefore, the function is 4|x-4|.

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In linear equation, y = \frac{x}{r} - \frac{z}{mr} + \frac{t}{r} is  simple form .

What is a formula for linear equations?

Ry+ z/m-t=x

Ry = x - z/m + t

[tex]y = \frac{x - \frac{z}{m}+ t }{r}[/tex]

[tex]y = \frac{x}{r} - \frac{z}{mr} + \frac{t}{r}[/tex]

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The product of 12 and √17 is not a rational number.

Any number that can be expressed as a fraction and where the denominator (the bottom number) and the numerator (the top number) are both integers is considered a rational number.

The product of ant two rational numbers is always a rational number , but product of a irrational number and a rational number is not a rational number.

Hence only the third option is correct.

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Answer:

1. = 96

2. = -158

Step-by-step explanation:

When you multiply two negatives the answer is positive, and when you multiply one negative and one positive the answer is negative

a. Interest of the first year = $26.93

b. Balance after the first year = $1256.93

c. Interest for the second year = $27.52

d. Balance after the second year = $1284.45

Although a part of your question is missing, you might refer to this full question: Gerry deposited $1230 in an account that pays 2.19% simple interest for one year.

a. How much interest will he earn in one year?

b. What will be his balance after one year?

c. Gerry withdraws all of the principal and interest after the first year and deposits into another one-year account at the same rate. What will be his interest for the second year?

d. What will his balance be after two years?

Principal = $1230

Rate = 2.19%

Formula to be used:

Simple interest = (P*R*T)/100

where P = principal

R = rate

T = time in years

Calculating interest for the first year:

S.I = (1230*2.19*1)/100

S.I = 26.93

So, he will earn $26.93 as interest in the first year

And balance after the first year will be $1256.93

Solving for the second year:

P = 1256.93

S.I = (1256.93*2.19*1)/100

= 27.52

So, interest for the second year will be $27.52

And balance after the second year will be $1284.45

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Attribute data is data that logically can be only whole numbers and can be expressed as control charts.

Therefore, attribute data is data that logically can be only whole numbers and can be expressed as control charts.

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Answer: Is 86 your welcome have a nice labor day

Step-by-step explanation:

Answer:

12, 20, 5, 30, 10, 14, 10, 20, 10, 16

Step-by-step explanation:

1.) 21-9=12

2.)35-15=20

3.) 30-25=5

4.) 40-10=30

5.) 30-20=10

11.) 34-20=14

12.) 22-12=10

13.) 30-10=20

14.) 19-9=10

15.) 28-12=16

Answer:

Step-by-step explanation:

1.

1) =7+(-4)=3

2) =13-8=5

3) =11+5=16

4) =-5-9=-14

5) =-8-1=-9

6) =-1-(-7)=6

7) =-10+13=3

8) =15-7=8

9) =-2+6=4

10) =9-4=5

11) =-1-8=-9

2.

[tex]\sqrt{12.8+25.4}= \sqrt{38.2}\approx 6.18[/tex]

Option C: At margin of error of 0.44, we are 90% confident that the true proportion of seniors who will attend homecoming is within 0.044 of the sample proportion.

The formula for confidence interval of proportions is;

CI = p^ ± z√((p^(1 - p^)/n)

where;

CI is confidence interval

p^ is sample proportion

z is test statistic at confidence level

n is sample size

We are given;

n = 95

x = 88

Thus;

p^ = 88/95 = 0.9263

z at CL of 90% = 1.645

Now, margin of error is;

E = z√((p^(1 - p^)/n)

Thus;

E = 1.645√((0.9263(1 - 0.9263)/95)

E ≈ 0.044

Thus, at margin of error of 0.44, we are 90% confident that the true proportion of seniors who will attend homecoming is within 0.044 of the sample proportion.

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Answer:

128

Step-by-step explanation:

x³y²if x = 2 and y = 4

x³*y²

[tex](2)^{3} * (4)^{2}[/tex]

(2*2*2)*(4*4)

(8)*(16)

128

I believe the answer is 200.

If we have the x and y components of a vector, the trigonometry function that can be used to determine its angle relative to the x-axis is cosine function.

For given question,

Let α be an angle between vector a and vector b.

The angles between two vectors is given by,

cos(α) = [tex]\frac{\vec a . \vec b}{|\vec a | | \vec b|}[/tex]

The x component of vector is usually denoted by [tex]\vec i[/tex]

Let vector be [tex]x\vec i + y\vec j[/tex]

Let [tex]\vec a=\vec i, ~ \vec b=x\vec i + y\vec j[/tex]

[tex]\vec a . \vec b=x[/tex]

[tex]|\vec a|=1[/tex]

[tex]|\vec b|=\sqrt{x^2+y^2}[/tex]

So, the angle between the vector and x-axis is [tex]cos^{-1}(\frac{x}{\sqrt{x^2+y^2} } )[/tex]

Therefore, if we have the x and y components of a vector, the trigonometry function that can be used to determine its angle relative to the x-axis is cosine function.

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Answer:

total inner angle of quadrilateral is 360 so

66 is remaining angle.

Please mark me as brainlist answer.

You has promised. Don't broke promise that you will give brainlist answer.

Answer:

The sum of the interior angle of a quadrilateral is given by the formula

(n-2)×180°

n represent the number of sides

(4-2)×180°

2×180°

=360°

then equate the angle to 360°

The required requirement of the density curve is should be equal to 1 and the ordinate should not be zero.

Given that,
Two requirements of a density curve are to be determined.

A density curve is defined as a curve on a graph that represents the distribution of values in a dataset.

Here,

The two requirements of a density curve should be,

a. The area under the density curve should be equal to 1.

b. The ordinate of the curve should not be zero i.e. they should always have the vertical height.

Thus, the required requirement of the density curve is mentioned above.

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