I have k quarters, five less quarters than nickels and one more than twice as many dimes as quarters. Find the value of the coins in cents in terms of k.

Answer:

The results of the hypothesis test suggests that there is no difference in productivity level of two warehouses (East Coast and the Midwest Coast).

p-value = 0.0473

Step-by-step explanation:

To perform this test we first define the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, we want to test if there is a difference in productivity level of the two warehouses (East Coast and the Midwest Coast).

Hence, the null hypothesis would be that there isn't significant evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast). That is, there is no difference in the productivity level of two warehouses (East Coast and the Midwest Coast).

The alternative hypothesis is that there is significant evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast).

Mathematically, if the average productivity level of the East Coast group is μ₁, the average productivity level of the Midwest group is μ₂ and the difference in productivity level is μ = μ₂ - μ₁

The null hypothesis is represented as

H₀: μ = 0 or μ₂ = μ₁

The alternative hypothesis is represented as

Hₐ: μ ≠ 0 or μ₂ ≠ μ₁

So, to perform this test, we need to compute the test statistic

Test statistic for 2 sample mean data is given as

Test statistic = (μ₂ - μ₁)/σ

σ = √[(s₂²/n₂) + (s₁²/n₁)]

μ₁ = average productivity level of the East Coast group = 1299 parts shipped

n₁ = sample size of East Coast group surveyed = 35

s₁ = standard deviation of the East Coast group sampled = 350

μ₂ = average productivity level of the Midwest group = 1456 parts shipped

n₂ = sample size of Midwest group surveyed = 35

s₂ = standard deviation of the Midwest group sampled = 297

σ = √[(297²/35) + (350²/35)] = 77.5903160379 = 77.59

We will use the t-distribution as no information on population standard deviation is provided

t = (1456 - 1299) ÷ 77.59

= 2.02

checking the tables for the p-value of this t-statistic

Degree of freedom = df = n₁ + n₂ - 2 = 35 + 35 - 2 = 68

Significance level = 0.01

The hypothesis test uses a two-tailed condition because we're testing in both directions.

p-value (for t = 2.02, at 0.01 significance level, df = 68, with a two tailed condition) = 0.047326

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.01

p-value = 0.047326

0.047326 > 0.01

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & say that there isn't enough evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast).

Hope this Helps!!!

Answer:

56 46 38 2 12

Step-by-step explanation:

Answer:

Divide by 7 or multiply by 1/7

Step-by-step explanation:

7x = 12

Divide each side by 7

7x/7 = 12/7

x = 12/7

We could also multiply each side by 1/7

7x * 1/7 = 12*1/7

x = 12/7

Answer:

4

Step-by-step explanation:

I used Desmos

We will see that the y-intercept of g(x) is larger than the y-intercept of f(x).

For a function y = f(x), the y-intercept is the value that takes y when we evaluate in x = 0.

So, for the first function:

[tex]f(x) = (1/5)*|x - 15|[/tex]

The y-intercept is:

[tex]f(0) =  (1/5)*|0 - 15| = 15/5 = 3[/tex]

For the second function:

[tex]g(x) = (x - 2)^2[/tex]

The y-intercept is:

[tex]g(0) = (0 - 2)^2 = (-2)^2 = 4[/tex]

Then we can see that g(x) has a greater y-intercept than f(x).

If you want to learn more about y-intercepts:

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Answer:

Result = 9b/25 or 36b/100

Step-by-step explanation:

The number is b

step 1

b is decreased by 40%

value of 40% of b = 40/100 *b = 4b/10

New value after this change = b - 40% decreased value of b = b -4b/10

= (10b-4b)/10 = 6b/10

Step 2 The new value obtained is again decreased by 40%

value of 40%  number found in step 1 =  40% of value found in step 1

value of 40%  number found in step 1 =  40/100 * 6b/10 = 24b/100

This value (24b/100) is subtracted from value found in step 1(6b/10) as given that  value obtained is decreased by 40%

new value found after 40% decrease = 6b/10 - 24b/100

new value found after 40% decrease = 60b/100 - 24b/100= 36b/100

new value found after 40% decrease =  36b/100 = 9b/25

Thus, the result of b is decreased by 40% and decreased again by 40% is 9b/25

Answer:

35/42 = b/7    and b= 35/6

Step-by-step explanation:

Our base is unkhown so it will be the variable in our equation :

so b is 35/6 cm

Multiply both sides of the ODE

[tex]x'+2tx+5t[/tex]

by [tex]e^{t^2}[/tex]:

[tex]e^{t^2}x'+2te^{t^2}x=5te^{t^2}[/tex]

Now the left side can be condensed as the derivative of a product:

[tex]\left(e^{t^2}x\right)'=5te^{t^2}[/tex]

Integrate both sides, then solve for x :

[tex]e^{t^2}x=\dfrac52e^{t^2}+C[/tex]

[tex]\implies x(t)=\dfrac52+Ce^{-t^2}[/tex]

Given that x(0) = 8, we find

[tex]8=\dfrac52+Ce^0\implies C=\dfrac{11}2[/tex]

so that the particular solution to this IVP is

[tex]\boxed{x(t)=\dfrac{5+11e^{-t^2}}2}[/tex]

Answer:

The answer is

Step-by-step explanation:

63, 360 inches = 1 mile

126,720 = 126,720 / 63 , 360 × 1 mile

Which is equal to

2 miles

Hope this helps you

Answer:

C. 105° = (5x - 70)°

Step-by-step explanation:

Vertically opposite angles are equal in size.

105° = (5x - 70)°

The correct answer is choice C.

Meant to put the letter C

Answer:

x=1/2, y=5

Step-by-step explanation:

This can be solved using substitution!

Hope this helped!

Answer:

{x,y}={ 1/2, 5)

Step-by-step explanation:

[1]    8x + 7y = 39

[2]    4x - 14y = -68

Solve equation [2] for the variable  x

 [2]    4x = 14y - 68

 [2]    x = 7y/2 - 17

// Plug this in for variable  x  in equation [1]

  [1]    8•(7y/2-17) + 7y = 39

  [1]    35y = 175

// Solve equation [1] for the variable  y

  [1]    35y = 175

  [1]    y = 5

// By now we know this much :

   x = 7y/2-17

   y = 5

// Use the  y  value to solve for  x

   x = (7/2)(5)-17 = 1/2

Answer:

double

Step-by-step explanation:

Answer:

9.110434

Step-by-step explanation:

√83 ≈ 9.110434

If [tex]a = 0[/tex], then [tex]y = ax^2+bx+c[/tex] turns into [tex]y = 0x^2+bx+c[/tex]. That [tex]0x^2[/tex] term goes away because it turns into 0, and adding 0 onto anything does not change the expression.

So  [tex]y = 0x^2+bx+c[/tex] turns into [tex]y = bx+c[/tex] which is a linear equation (b is the slope, c is the y intercept). It is no longer a quadratic as quadratic equations always graph out a curved parabola.

As an example, you could graph out [tex]y = 0x^2+3x+4[/tex] and note how it's the exact same as [tex]y = 3x+4[/tex], both of which are straight lines through the two points (0,4) and (1,7).

Answer:

4x

Step-by-step explanation:

The Taylor series of a function f(x) about a value x = a is given by f(x) = f(a) + f'(a)(x - a)/1! + f''(a)(x - a)²/2! + f'''(a)(x - a)³/3! + ... where the terms in f prime f'(a) represent the derivatives of x valued at a.

For the given function, f(x) = 4x and a = -2

So, f(a) = f(-2) = 4(-2) = -8

f'(a) = f'(-2) = 4

All the higher derivatives of f(x) evaluated at a are equal to zero. That is f''(a) = f'"(a) =...= 0

Substituting the values of a = -2, f(a) = f(-2) = -8 and f'(-2) = 4 into the Taylor series, we have

f(x) = f(-2) + f'(-2)(x - (-2))/1! + f''(-2)(x - (-2))²/2! + f'''(-2)(x - (-2))³/3! +...

= -8 + 4(x + 2)/1! + (0)(x + 2)²/2! + (0)(x + 2)³/3! +...

= -8 + 4(x + 2) + 0 + 0

= -8 + 4x + 8

= 4x

Answer:

yes

Step-by-step explanation:

2b+b=3b because2+1 = 3

Answer:

the answer is yes

Step-by-step explanation:

yes it is equivalent expression because 2b+b and 3b have the same value and length or numerator which equals yes.

Answer:

C - 3 (negative 64 divided by 8) + 25 =1

Step-by-step explanation:

Answer:

C is correct answer

Step-by-step explanation:

We assume that we need to simplify the expression in two different ways.

Answer:

One way: Raise both, the numerator and denominator, to the third power, and then simplify the expression.

Second way: Simplify the terms inside parentheses, and then raise the result to the third power.

The result of both ways is the same: [tex] \\8x^{9}[/tex]

Step-by-step explanation:

One way

Raise both, the numerator and denominator, to the third power, and then simplify the expression:

[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]

[tex] \\ (\frac{64x^{5*3}}{8x^{2*3}})[/tex]

[tex] \\ (\frac{64x^{15}}{8x^{6}})[/tex]

[tex] \\ \frac{64}{8}\frac{x^{15}}{x^{6}}[/tex]

[tex] \\8x^{9}[/tex]

This is the first simplification.

Second way

Simplify the terms inside parentheses, and then raise the result to the third power.

[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]

[tex] \\ (\frac{4}{2}*\frac{x^{5}}{x^{2}})^{3}[/tex]

[tex] \\ (2*x^{5-2})^{3}[/tex]

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

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

[tex] \\ (8*x^{9})[/tex]

or [tex] \\ 8x^{9}[/tex].

Answer:

Every decade, the number of species decays by a factor of 0.0834.

Step-by-step explanation:

Let be [tex]S(t) = 25,000,000\cdot 0.78^{t}[/tex], [tex]\forall t \geq 0[/tex]. The decay rate per decay is deducted from the following relation:

[tex]\frac{S(t+10)}{S(t)} = \frac{25,000,000\cdot 0.78^{t+10}}{25,000,000\cdot 0.78^{t}}[/tex]

[tex]\frac{S(t+10)}{S(t)} = 0.78^{t+10-t}[/tex]

[tex]\frac{S(t+10)}{S(t)} = 0.78^{10}[/tex]

[tex]\frac{S(t+10)}{S(t)} = 0.0834[/tex]

Every decade, the number of species decays by a factor of 0.0834.

Answer:

28% subtracted

Step-by-step explanation:

khan

Answer:  see proof below

Step-by-step explanation:

Proof by exhaustion means to input several numbers that satisfy the claim and if they all prove to be true then you have proven the claim.

Claim: (2x³ + 3x² + x)/(6) ∈ Z (integer)

Let's choose x = {1, 2, 3, 4)

Case 1: x = 1

2(1)³ + 3(1)² + (1) = 12

12/6 = 2

2 ∈ Z [tex]\checkmark[/tex]

Case 2: x = 2

2(2)³ + 3(2)² + (2) = 30

30/6 = 5

5 ∈ Z [tex]\checkmark[/tex]

Case 3: x = 3

2(3)³ + 3(3)² + (3) = 84

84/6 = 14

14 ∈ Z [tex]\checkmark[/tex]

Case 4: x = 4

2(4)³ + 3(4)² + (4) = 180

180/6 = 30

30 ∈ Z [tex]\checkmark[/tex]

Since each case was shown to be true we have proven the claim is true by exhaustion.

Answer:

work is shown and pictured

answer is c

Answer:

the correct answer among the choices is C

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

We already have the zeros, so we can write the cubic polynomial in this general form:

[tex]y = a(x - x_1)(x - x_2)(x - x_3)[/tex]

Where:

[tex]x_1 = 5[/tex]

[tex]x_2 = 5i[/tex]

[tex]x_3 = -5i[/tex]

So we have that:

[tex]y = a(x -5)(x - 5i)(x + 5i)[/tex]

[tex]y = a(x -5)(x^2 + 25)[/tex]

To find the value of the leading coefficient 'a', we can use the point (1, -208) given:

[tex]-208 = a(1 -5)(1 + 25)[/tex]

[tex]-208 = a(-4)(26)[/tex]

[tex]a = -208 / (-104) = 2[/tex]

So the leading coefficient is 2.

Answer:

99% one-sided lower confidence bound = 26.77

Step-by-step explanation:

We have to calculate a 99% one-sided lower confidence bound for the population variance.

The sample size is n=25.

The degrees of freedom are then:

[tex]df=n-1=25-1=24[/tex]

The critical value of the chi-square for this confidence bound is:

[tex]\chi^2_{0.01, \,24}=42.98[/tex]

Then, the lower confidence bound can be calculated as:

[tex]LB=\dfrac{(n-1)s^2}{\chi^2_{0.01,24}}=\dfrac{24\cdot(6.9)^2}{42.98}=\dfrac{1,142.64}{42.68}=26.77[/tex]

Answer:

slope is m=1. y-intercept is -1

Answer:

Slope is 1 and intercept is -1. Slope can be found by taking the rise and run of 2 points on a graph. and intercept is just when x = 0

Answer:

20*19*18 = 6840

UNLESS...............  

he is allowed to ride the same ride again , over and over....  

then it is 20 x 20 x 20 = 8000

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

factors of 13 : 1, 13

factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

factors of 49: 1, 7, 49

factors of 65: 1, 5, 13, 65

factors of 87: 1, 3, 29, 87

Answer:

A

Step-by-step explanation:

6r - 17r = -66

Subtract like terms.

-11r = -66

Divide both sides by -11.

r = -66/-11

r = 6

Answer:

6

Step-by-step explanation:

6r-17r=-66

-11r=-66

r=6

Hey there! :)

Answer:

2nd choice. (x - 2)

Step-by-step explanation:

Given in the question:

(x²-4) ÷ (x + 2) = x-2

This is an example of difference of squares.

We can rearrange the equation by multiplying both sides by (x+2) to become:

(x² - 4) = x - 2 (x + 2)

Therefore, the binomial that must be multiplied by (x+2) is the second choice, x-2.

Answer: B

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

The table shows the result of the statement given below.

A data table is a range of cells in which you can change values in some of the cells and come up with different answers to a problem.

here, we have,

Given that,

the chef at a school cafeteria asked 100 male and 100 female students whether they like peas.

42 of the males said they like peas. 64 of the females said they dislike peas.

The number of males who like peas=42 and the number of males who dislikes peas=58.

The number of females who like peas=36 and the number of females who dislikes peas=64.

The table shows the result of the statement given below.

To learn more about the data table visit:

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Answer:

210 vegetable in 7 rows

Step-by-step explanation:

first step is to figure out how many vegetable can she grow in one row:

convert feet to inches : 6.25 feet* 12 inches=75 inches

(75/2 1/2)                (2 /12 is 3/2 or  2.5)

(75/2.5)= 30 vegetable in one row

in 7 rows : 30*7=210 vegetable in 7 rows