Cincinnati Paint Company sells quality brands of paints through hardware stores throughout the United States. The company maintains a large sales force whose job it is to call on existing customers as well as look for new business. The national sales manager is investigating the relationship between the number of sales calls made and the miles driven by the sales representative. Also, do the sales representatives who drive the most miles and make the most calls necessarily earn the most in sales commissions? To investigate, the vice president of sales selected a sample of 25 sales representatives and determined:
%u2022 The amount earned in commissions last month (Y).
%u2022 The number of miles driven last month (X2)
%u2022 The number of sales calls made last month (X1)
($000) Calls Driven Commissions
($000) Calls Driven
22 139 2,371 38 146 3,290
13 132 2,226 44 144 3,103
33 144 2,731 29 147 2,122
38 142 3,351 38 144 2,791
23 142 2,289 37 149 3,209
47 142 3,449 14 131 2,287
29 138 3,114 34 144 2,848
38 139 3,342 25 132 2,690
41 144 2,842 27 132 2,933
32 134 2,625 25 127 2,671
20 135 2,121 43 154 2,988
13 137 2,219 34 147 2,829
47 146 3,463
Click here for the Excel Data File
Develop a regression equation including an interaction term. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)
Commissions = + Calls + Miles - X1X2
Complete the following table. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)
Predictor Coef SE Coef T P
Constant
Calls
Miles
X1X2
Compute the value of the test statistic corresponding to the interaction term. (Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)
Value of the test statistic
Is there a significant interaction between the number of sales calls and the miles driven?

Answer:

[2.5 ,4]

Step-by-step explanation:

The graph in this interval has a vertex while opening up wich means it's a minimum

Answer:

239 who are you

Step-by-step explanation:

Answer:

TRUE

Step-by-step explanation:

We are given 2 triangles, ∆ABC and ∆DEF.

For the two trinagles to be considered similar, both must have their set of corresponding angles congruent to each other. That is, their corresponding angles are equal.

From the information given, the following are the set of corresponding angles:

<B = <E = 31°

<B = <D = 90°

<C = <F = 59° [180 - (90+31)]

The corresponding angles of both triangles are congruent. Therefore, it is guaranteed that ∆ABC is similar to ∆DEF (∆ABC ~ DEF).

Answer: $1500

Step-by-step explanation:

6% commission on $25,000

= 25000 x .06

= 1500

Answer: 1/5

Step-by-step explanation:

given data;

chances of winning = 1/3

chances of losing = 1/3

chances of tying in a given round = 1/3

solution:

probability that you would win atleast 2 in any 3 matches without a tied match is

1/3 /  ( 2 - 1/3 )

= 1/3 / 5/3

= 1/5

the probability of winning 2 of 3 games without a tie is 1/5

Answer:

19

Step-by-step explanation:

7 supersricpt 8

Answer:

Step-by-step explanation:

Using the formula for calculating the distance between two points to calculate the length of WX.

D = √(y₂-y₁)²+(x₂-x₁)²

Given the endpoints W(2,-7) and X(5,-4), x₁ = 2, y₁ = -7, x₂ = 5 and y₂ = -4

Substituting this values into the formula to get the length of WX will give;

WX = √(-4-(-7))²+(5-2)²

WX = √(-4+7)²+3²

WX = √3²+3²

WX = √18

WX = √2*9

WX = 3√2 units

Hence the length of WX is 3√2 units.

Answer:

3[tex]\sqrt{2}[/tex]

Hope this helps!

Step-by-step explanation:

Answer:

There are 2 * 32 = 64 possible ways for choosing three course meal.

Step-by-step explanation:

1-If we choose an appetizer, main course and a soup then there are 32 ways to choose this three course meal. 4 * 2 * 4 = 32 ways. There will be an appetizer, main course and a soup in the meal.

2-If we choose a soup, main course and a dessert then there are 32 ways to choose this three course meal. 4 * 2 * 4 = 32 ways. There will be a soup, main course and a dessert in the meal.

There are 2 possible ways to choose either an appetizer or dessert in a 3 course meal. There will be 64 ways in total for the three course meal.

Answer:

Angle L is a base angle and measures 72°.

Step-by-step explanation:

Triangle JKL is isosceles.

The measure of angle J is 72°

The measure of angle K is 36°

Angles in a trinagle add up to 180° so angle L is;

180° - (36° + 72°) = 72°

An isosceles triangle means that two of its sides are equal and two base angles are equal. So base  angles are angles J and L and measures 72° each.

Answer:

I think it's B

Step-by-step explanation:

I hope this helps.

Answer:

Step-by-step explanation:

when h(t)=0

-4.9 t²+19.6t=0

4.9t(-t+4)=0

either t=0 or t=4

so domain is 0≤t≤4

for range

h(t)=-4.9t²+19.6t

=-4.9(t²-4t+4-4)

=-4.9(t-2)²+19.6

so range is 0≤h≤19.6

Domain = 0<t<4, make sure to use less than or equal to signs not just less than signs.

Range = 0<h<19.6, again, use less than or equal to signs.

Answer:

4.24m³

Step-by-step explanation:

The inside diameter of 1.2 m of the pipe

Radius of the inside pipe = Diameter/2 = 1.2/2 = 0.6m

The outside diameter of 1.8 m

Radius of the outer of the pipe = 1.8/2 = 0.9m

Height of the pipe = 3.0m

A Pipe looks like the shape of the cylinder. Hence,

Volume of concrete in the pipe = Volume of the outer section of the Pipe - Volume of the inner section of the pipe

Volume of the outer section of the Pipe = πr²h

h = 3.0m

r = 0.9

= π × 0.9² × 3.0

= 7.63m³

Volume of the inner section of the Pipe = πr²h

h = 3.0m

r = 0.6

= π × 0.6² × 3.0

= 3.39m³

Volume of concrete in the pipe = Volume of the outer section of the Pipe - Volume of the inner section of the pipe

= 7.63m³ - 3.39m³

= 4.24m³

Therefore, volume of concrete in the pipe is 4.24m³

Answer:

B. Y = -3X

C. Y = 4 - 3X

Step-by-step explanation:

Y = -3X + 2

This is in the form y= mx +b where m is the slope

The slope is -3

Parallel lines have the same slope

A. Y = 1/3 X - 2   the slope is 1/3

B. Y = -3X   The slope is -3  

C. Y = 4 - 3X Y = -3x+4  the slope is -3

Answer:

D

Step-by-step explanation:

we let that,

(3,2)=(x,y)

given the equation that,

x-4y=10

so,we substitute the values of (x,y)=(3,2)it become

3-4(2)=-5

and test another coordinates(-3,3)

-3-4(3)=-15

botha answers doesn't give 10 as the answer so the answer is D(neither)

answer: 1020000

step-by-step explanation:

(7.8*10^5+(2.4*10^5)                                         given expression

(7.8*10^5)+(2.4*10^5)                                        group with parenthesis

(7.8+2.4)*10^5                                                   combine like terms

10.2*10^5                                                           preform addition

10.2*100000                                                     evaluate the exponent

1020000                                                           multiply out

Use the binomial theorem:

[tex](1+1)^{16}=\displaystyle\sum_{k=0}^{16}\binom{16}k1^{16-k}1^k[/tex]

So

[tex]\dbinom{16}0+\dbinom{16}1+\cdots+\dbinom{16}{16}=\boxed{2^{16}}[/tex]

More generally,

[tex]\displaystyle\sum_{k=0}^n\binom nk=2^n[/tex]

Answer:

F, J, and K

Step-by-step explanation:

The others are negative so they can't be exponential

The exponential function can't be negative or irrational, so options A, D, and E are correct.

The exponential function in mathematics is represented by the symbol eˣ (where the argument x is written as an exponent). The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras. The idea of exponentiation, or repeated multiplication, is where the exponential function got its start, but more recent definitions—there are several that are equivalent—allow it to be rigorously extended to all real arguments, including irrational values.

As we discussed above, the exponential function can't be negative or irrational  so, look at the options only,

f(x) = 10(1/7)ˣ,

j(x) = 8(4.13)ˣ,

k(x) = 12(8)ˣ are the exponential functions, whereas

g(x) = 4(-3)ˣ,

h(x) = 4(-13)ˣ are negative, so they can't be exponential functions.

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Answer:

It is not normally distributed as it has it main concentration in only one side.

Step-by-step explanation:

So, we are given that the class width is equal to 0.2. Thus we will have that the first class is 0.00 - 0.20, second class is 0.20 - 0.40 and so on(that is 0.2 difference).

So, let us begin the groupings into their different classes, shall we?

Data given:

0.31 0.31 0 0 0 0.19 0.19 0 0.150.15 0 0.01 0.01 0.19 0.19 0.53 0.53 0 0.

(1). 0.00 - 0.20: there are 15 values that falls into this category. That is 0 0 0 0.19 0.19 0 0.15 0.15 0 0.01 0.01 0.19 0.19 0 0.

(2). 0.20 - 0.40: there are 2 values that falls into this category. That is 0.31 0.31

(3). 0.4 - 0.6 : there are 2 values that falls into this category.

(4). 0.6 - 0.8: there 0 values that falls into this category. That is 0.53 0.53.

Class interval            frequency.

0.00 - 0.20.                   15.

0.20 - 0.40.                    2.

0.4 - 0.6.                        2.

Answer:

1). 18

Step-by-step explanation:

1). The numbers above are real numbers but on a care ful look the number below it is a squrea of the number above but it's position ois swapped.

What am I saying., Let's take for example the number 4.

4² = 16 but what's written is 61

Let's take 5

5² = 25 but what's written is 52

Let's take 6

6² = 36bl but what's written is 63.

So as for 9

9²= 81 but what will be in the box = 18

2).this number two is something special

Answer:

The cheap one is 8 while the costly one is 17.5

Step-by-step explanation:

Let the cheaper candle be x

And the costly candle b y

X+y = 25.5.... equation one

2.20x +7.3y = 25.5(5.7)

2.2x + 7.3y = 145.35....equation two

Solving simultaneously

X+y = 25.5

2.2x + 7.3y = 145.35

2.2X+2.2y = 56.1

2.2x + 7.3y = 145.35

5.1y= 89.25

Y= 17.5

X+y = 25.5

X+ 17.5 = 25.5

X= 25.5-17.5

X= 8

The cheap one is 8 while the costly one is 17.5

Answer:

[tex]x=-\frac{11}{6}[/tex]

Step-by-step explanation:

8x2=6x=5

16+6x=5

6x=5-16

6x=-11

[tex]x=-\frac{11}{6}[/tex]

Answer:

See below.

Step-by-step explanation:

[tex]8x^2+6x=5[/tex]

Reformat this so the equation equals zero:

[tex]8x^2+6x-5=0[/tex]

[tex]a=8, b=6, c=-5[/tex]

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-(6)\pm\sqrt{(6)^2-4(8)(-5)} }{2(8)}[/tex]

[tex]x=\frac{-6\pm\sqrt{36+160} }{16}[/tex]

[tex]x=\frac{-6\pm\sqrt{196} }{16}[/tex]

[tex]x=\frac{-6\pm14 }{16}[/tex]

[tex]x=\frac{-6+14}{16}=8/16=1/2[/tex] or

[tex]x=\frac{-6-14}{16}=-20/16=-5/4[/tex]

Answer:

40091.

Step-by-step explanation:

Multiply 40.091 by 10 three times to get the answer.

40.091 * 10 = 400.91

400.91 * 10 = 4009.1

4009.1 * 10 = 40091.

The expression 40.091 x 10³ can be represented as 40091.

The term xⁿ, read as x to the power n, shows an exponent n, which implies x is multiplied by itself n times.

In the question, we are asked to arrange the cards showing '.', '0', '0', '1', '4', and '9', to show the solution to the expression 40.091 x 10³.

Now, 10³ is 10 to the power 3, where 3 is the exponent, so 10 is multiplied by itself 3 times = 10*10*10 = 1000.

Now, the expression 40.091 x 10³ = 40.091 * 1000 = 40091.

∴ The expression 40.091 x 10³ can be represented as 40091.

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Answer:

t ≤ 15

Step-by-step explanation:

Let t = tables

6 * 15 + 2* t ≤ 120

90 + 2t ≤ 120

2t ≤ 30

t ≤ 15

Answer:

170.67

Step-by-step explanation:

Answer:

171

Step-by-step explanation:

Modeling the situation

If we fill the pyramid mold 2\text{ cm}2 cm2, start text, space, c, m, end text from the top, we have a smaller pyramid that's similar to the original pyramid.

Since the pyramids are similar, we can set up a proportional equation to find the side lengths and height of the smaller pyramid, and then find its volume.

Hint #22 / 4

Base and height of smaller pyramid

The height of the smaller pyramid is 10-2=8\text{ cm}10−2=8 cm10, minus, 2, equals, 8, start text, space, c, m, end text.

We can solve for the length \blueE{\ell}ℓstart color #0c7f99, ell, end color #0c7f99 in the smaller pyramid using a proportional equation.

\begin{aligned} \dfrac{\blueE{\ell}}{10} &= \dfrac{8}{10} \\\\ \blueE{\ell} &= \blueE{8} \end{aligned}  

10

ℓ

​  

ℓ

​  

=  

10

8

​  

=8

​  

Hint #33 / 4

Volume of smaller pyramid

\begin{aligned} \text{volume}_{\text{pyramid}} &= \dfrac13(\text{base area})(\text{height}) \\\\ &= \dfrac13 \cdot (\blueE{\ell})^2\cdot (\text{height}) \\\\ &= \dfrac13 \cdot \blueE{8}^2\cdot(8)\\\\ &= \dfrac{512}{3}=170.\overline{6}\\\\ &\approx \purpleD{170.67} \end{aligned}  

volume  

pyramid

​  

​  

=  

3

1

​  

(base area)(height)

=  

3

1

​  

⋅(ℓ)  

2

⋅(height)

=  

3

1

​  

⋅8  

2

⋅(8)

=  

3

512

​  

=170.  

6

≈170.67

​  

Hint #44 / 4

To the nearest cubic centimeter, the volume of the smaller pyramid is about 171\text{ cm}^3171 cm  

3

171, start text, space, c, m, end text, cubed.

Plug in a = 2 m/s^2 and d = 10 m, and solve for t (in s):

[tex]a=\dfrac{2d}{t^2}\iff2\dfrac{\rm m}{\mathrm s^2}=\dfrac{2\cdot10\,\mathrm m}{t^2}[/tex]

[tex]\implies t^2=\dfrac{20\,\rm m}{2\frac{\rm m}{\mathrm s^2}}=10\,\mathrm s^2[/tex]

[tex]\implies t=\sqrt{10}\,\mathrm s[/tex]

So the answer is C.

Answer:

The sum is 66  

Step-by-step explanation:

There are a couple formulas to remember.

aₙ = a₁ + d(n-1)

Sₙ = [tex]\frac{n}{2}[/tex] · (a₁ + aₙ)

In your case "d" equals 4 and a₁ equals 1, that's how we know what the sequence will progress.

Let's plug in the values for the first equation:

aₙ = 1 + 4 (n-1)

Next we can simplify:

aₙ = 1 + 4n-4

aₙ = 4n - 3

Now we can plug in the value for "n" which is 6 for this particular problem:

a₆ = 4 · 6 - 3

a₆ = 21

We can now use the second equation to find the sum:

S₆ = [tex]\frac{6}{2}[/tex] · (1 + 21)

S₆ = 66    

Hope this helps =)

Answer:

B

Step-by-step explanation:

Since the vertex of the function is (-6, -3), we know the equation must be y = |x + 6| - 3.

Answer:

B. |x+6|-3

Step-by-step explanation:

Well we can tell by looking at the graph that the line has a y-intercept of +3,

meaning we can cross out choices A and C.

Now we can graph B and D,

Look at the image below ↓

By looking at the graphed lines we can tell that y = |x+6|-3 is the correct answer.

Wel can also conclude that choice B is correct because of its vertex being at (-6,-3).

Thus,

answer choice B is the correct answer.

Hope this helps :)

Answer:

Empirical Rule

Step-by-step explanation:

The Empirical Rule is also known as the Sigma rule or the 68-95-99.7% rule. The rule state that for a given data set, 68% of all data values will fall within the first standard deviation from the mean. The rule also states that 95% of all data values would fall within two standard deviations, while almost all the data which amounts to about 99.7% will fall within three standard deviations.

The empirical rule is used in forecasting based on the given datasets because it is a certainty that after obtaining the standard deviation, data values can be assigned to the categories they fall into, under the Empirical rule.

Answer:

(assuming all members of the gang get equal percentages)

For a gang of 8: 12.5% (100/8)

If 2 are killed: 16.67% (100/6), so percentage increases by roughly 4.2% (16.67-12.5)

Percent that belongs to 3: 12.5%*3=37.5%

Percent that belongs to 3 if 2 are killed: 16.67%*3=50.0%

Each robber's share still increases by 4.2% (50%-37.5%=12.5%, 12.5%/3=4.2%)

If you would like additional help with math or another subject, check out growthinyouth.org!

Step-by-step explanation:

Answer:

undefined! one cannot divide by 0

Step-by-step explanation:

Answer:

undefined!

Step-by-step explanation: