Libby starts draining the pool for cleaning. The function y = 10,080 - 720x represents the


gallons of water y remaining in the pool after x hours. Find the zero and explain what it means in the context of the situation

If elijah and riley are playing a board game elijah choses the dragon for his game piece and rily choses the cat for hers. the measure of angle B is : B. 49.734 degrees.

To find the measure of angle B, we can use the law of cosines, which relates the lengths of the sides of a triangle to the cosine of the angles. Specifically, we can use the following formula:

c^2 = a^2 + b^2 - 2ab*cos(C)

where a, b, and c are the lengths of the sides of the triangle opposite to the angles A, B, and C, respectively.

In this case, we know the lengths of sides b and c, and the measure of angle A. We want to find the measure of angle B. So we can rearrange the formula above to solve for cos(B):

cos(B) = (a^2 + b^2 - c^2) / 2ab

Then we can take the inverse cosine of both sides to get the measure of angle B:

B = cos^-1[(a^2 + b^2 - c^2) / 2ab]

Substituting the given values, we have:

a = ?

b = 10

c = 13

A = 33 degrees

To find side a, we can use the law of sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. Specifically, we can use the following formula:

a / sin(A) = b / sin(B) = c / sin(C)

Solving for a, we have:

a = sin(A) * c / sin(C)

Substituting the given values, we have:

a = sin(33 degrees) * 13 / sin(C)

To find sin(C), we can use the fact that the angles in a triangle add up to 180 degrees:

C = 180 - A - B

Substituting the given values, we have:

C = 180 - 33 - B

C = 147 - B

So, we can write:

sin(C) = sin(147 - B)

Substituting into the equation for a, we have:

a = sin(33 degrees) * 13 / sin(147 - B)

Now, substituting all the values in the equation for cos(B), we get:

cos(B) = (a^2 + b^2 - c^2) / 2ab

cos(B) = [sin(33 degrees)^2 * 13^2 + 10^2 - 13^2] / 2 * sin(33 degrees) * 10

cos(B) = (169 * sin(33 degrees)^2 + 100 - 169) / (20 * sin(33 degrees))

cos(B) = (169 * sin(33 degrees)^2 - 69) / (20 * sin(33 degrees))

Now, we can substitute this into the equation for B, and use a calculator to find the value of B:

B = cos^-1[(a^2 + b^2 - c^2) / 2ab]

B = cos^-1[(169 * sin(33 degrees)^2 - 69) / (20 * sin(33 degrees))]

B ≈ 49.734 degrees

Therefore, the measure of angle B is approximately 49.734 degrees. The answer is (B) 49.734°.

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The derivative of the function is y' = 50e^(-0.06x) - 3xe^(-0.06x). The x-intercept is approximately x ≈ 16.273. The y-intercept is y = 0. The horizontal asymptote is y = 0, which occurs as x approaches infinity.

To find the derivative of the function y = 50xe^-0.06x, we can use the product rule and the chain rule.

y' = 50e^-0.06x - 50xe^-0.06x(0.06)

Simplifying, we get y' = 50e^-0.06x(1-0.06x)

To find the x-intercept, we need to set y=0 and solve for x:

0 = 50xe^-0.06x

Since e^-0.06x is never zero, we can divide both sides by it:

0 = 50x

So the x-intercept is x=0.

To find the y-intercept, we need to set x=0 and solve for y:

y = 50(0)e^0

So the y-intercept is y=0.

To find the horizontal asymptote, we can take the limit as x approaches infinity:

lim (x→∞) 50xe^-0.06x = 0

So the horizontal asymptote is y=0. This horizontal asymptote occurs as x approaches infinity.

1. Consider the function: y = 50xe^(-0.06x)

2. Find the derivative of the function:
To find the derivative, use the product rule (uv)' = u'v + uv':
y' = (50)'(e^(-0.06x)) + (50)(e^(-0.06x))(-0.06)
y' = 50e^(-0.06x) - 3xe^(-0.06x)

3. The x-intercept is:
To find the x-intercept, set y = 0 and solve for x:
0 = 50xe^(-0.06x)
This equation cannot be solved algebraically, but using numerical methods, we find x ≈ 16.273

4. The y-intercept is:
To find the y-intercept, set x = 0 and solve for y:
y = 50(0)e^(-0.06(0))
y = 0

5. Find the horizontal asymptote, y:
As x approaches infinity, y approaches the horizontal asymptote. In this case, the exponential term (e^(-0.06x)) approaches 0:
y = 50xe^(-0.06x)
y ≈ 50x(0)
y ≈ 0

The horizontal asymptote is y = 0, and it occurs as x approaches infinity.

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The formula for the function h(x) is given as follows:

h(x) = g(x + 5).

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The function h(x) is a translation left 5 units of the function g(x), hence it is defined as follows:

h(x) = g(x + 5).

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Answer:

15 cubic centimeters

Step-by-step explanation:

The figure is in the shape of a rectangular and the formula for volume of such a rectangular box is

V=lwh, where V is the volume, l is the length, and h is the height.

Since each cube is 1 cm, we see that the length is 5 cm (1 cm cube * 5 = 5 cm), the width is 3 cm (1 cm cube * 3 = 3 cm), and the height is 1 cm (1 cm cube * 1 = 1 cm).

Thus, we the product of our length, width, and height will give us the volume of the figure:

V = 5 * 3 * 1

V = 15 cubic centimeters

The quadratic equation where the squares had been completed is:

(x + 2)² = 27/5

Remember the perfect square trinomial:

(a + b)² = a² + 2ab + b²

now we have the quadratic equation:

5x² + 20x - 7 = 0

If we divide it all by 5, we will get.

x² + 4x - 7/5 = 0

Now we can rewrite this as:

(x² + 2*2*x )  - 7/5 = 0

Now we need to add 2² in both sides, we will get:

(x² + 2*2x + 2²) - 7/5 = 2²

(x + 2)² = 4 + 7/5

(x + 2)² = 27/5

There the square is completed.

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The initial condition y(5) = 4 tells us that we should use the positive square root.

To find the particular solution to the given differential equation, we can use separation of variables. First, we rearrange the equation to get:

y dy = 2x dx

Next, we integrate both sides with respect to their respective variables:

∫y dy = ∫2x dx

This gives us:

y^2/2 = x^2 + C

where C is the constant of integration. To find the value of C, we use the initial condition y(5) = 4:

4^2/2 = 5^2 + C

8 = 25 + C

C = -17

So the particular solution to the differential equation dy/dx = 2x/y with the initial condition y(5) = 4 is:

y^2/2 = x^2 - 17

or

y = ±√(2x^2 - 34)

Note that there are two possible solutions, one with a positive square root and one with a negative square root, but the initial condition y(5) = 4 tells us that we should use the positive square root.

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The mean score for the test Phyllis scored 84, exactly one standard deviation above the mean is  78.

One of the statistics used in the generalised Cochran-Mantel-Haenszel tests is the mean score statistic. When the answer levels (columns) are assessed using an ordinal scale, it is applicable.

The chi-square distribution with (R-1) degrees of freedom, where R is the number of treatment groups, serves as the asymptotic distribution of the mean score statistic if the two variables are independent of one another in all strata (rows).

If the mean scores of the response differ between the treatment groups in at least one stratum, the mean score statistic tends to have larger values. The term "nonparametric ANOVA statistic" also applies to this statistic.

x = 84

[tex]\sigma=6[/tex]

since, x is 1 standard deviation above mean so,

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]1=\frac{84-\mu}{6}\\ \\[/tex]

[tex]\mu[/tex] = 84-6

[tex]\mu[/tex] =78.

therefore, mean = 78.

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Option (B) x + 6 < 10 and (C) 5x < 20 have same graph.

From the given set of inequalities;

(A) x < 2 represents x ∈ (-∞, 2)

(B) X + 6 < 10 ⇒ x < 4

    represents x ∈ (-∞, 4)

(C) 5x < 20 ⇒ x < 4

     represents x ∈ (-∞, 4)

(D) x - 2 > 2 ⇒ x > 4

     represents x ∈ (4, ∞)

(E) x < 4 represents x ∈ (-∞, 8)

We can see that inequalities (B) and (C) both represents x ∈ (-∞, 4)

Thus, the graph of both inequalities are same.

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Based on simultaneous equations, the number of children and adults who swam at the public pool that hot summer's day is as follows:

Simultaneous equations are two or more equations solved concurrently.

Simultaneous equations are also referred to as a system of equations because the equations are solved at the same time.

The total number of people who used the public swimming pool = 670

The unit price for children = $1.25

The unit price for adults = $2.00

The total amount collected that day = $1,118

Let the number of children who swam at the public pool that day = x

Let the number of adults who swam at the pool that day = y

x + y = 670 ... Equation 1

1.25x + 2y = 1,118 ... Equation 2

Multiply Equation 1 by 2:

2x + 2y = 1,340 Equation 3

Subtract Equation 2 from Equation 3:

2x + 2y = 1,340

-

1.25x + 2y = 1,118

0.75x = 222

x = 296

y = 670 - 296

= 374

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The polynomial is factored to y²(x³ - 7³y³)

Note that polynomials are described as expressions that are made up of terms, variables, coefficients, factors and constants.

Also, they have a degree greater than one.

Index forms are also seen as forms used to represent values that are too large or small in more convenient forms.

From the information given, we have that;

x³y²-343y⁵

Now, find the cube value of 343, we have;

343 = 7³

Substitute the value

x³y²- 7³y⁵

Factorize the common terms, we have;

y²(x³ - 7³y³)

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The extreme value theorem states that if a function f(x) is continuous on a closed interval [a, b], then there exists at least one point c in [a, b] where f(c) is the absolute maximum value and at least one point d in [a, b] where f(d) is the absolute minimum value.

A. f(x)=x2 over(-5,0] - This function is continuous on the closed interval [-5,0], so by the extreme value theorem, there exists at least one absolute maximum and one absolute minimum.

B. g(x) over [-5,0] - We do not have information about the function g(x), so we cannot determine whether it is continuous on the closed interval [-5,0]. Therefore, we cannot determine whether the extreme value theorem applies.

C. h(x)=1x-1 lover [-5.0] - This function is not continuous at x=0 because it has a vertical asymptote there. Therefore, the extreme value theorem does not apply.

D. k( x) = Vx + 1 over [- 5,0] - This function is continuous on the closed interval [-5,0], so by the extreme value theorem, there exists at least one absolute maximum and one absolute minimum.

E. None of the above - Only options A and D satisfy the conditions for the extreme value theorem, so the correct answer is none of the above.

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a. The area of Priya's scalp is ≈ [tex]615.75 cm^2[/tex]. b. Priya has approximately 92,363 strands of hair on her head.

a. The area of Priya's scalp can be estimated using the formula for the area of a circle, which is A = π[tex]r^2[/tex] ,where r is the radius (half the diameter) of the circle. Since Priya's diameter is 28cm, her radius would be 14cm. So, the area of her scalp would be:

A = π[tex](14cm)^2[/tex]
A ≈[tex]615.75 cm^2[/tex]

b. To estimate how many strands of hair Priya has on her head, we can multiply the number of hairs per square cm by the total area of her scalp. So, if Priya has approximately 150 hairs per square cm and her scalp has an estimated area of 615.75 cm^2, then:

Total number of hairs ≈ [tex]150 hairs/cm^2 * 615.75 cm^2[/tex]
Total number of hairs ≈ 92,362.5 hairs

Therefore, we can estimate that Priya has approximately 92,363 strands of hair on her head.

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To compare Ralph's and Frank's t-shirt companies, let's calculate the total cost of buying a certain number of t-shirts from each company.

1. Ralph's t-shirt company:

- Price per t-shirt: $5.00

- Shipping and design fee: $20.00

Total cost for Ralph's t-shirts = (number of t-shirts * $5.00) + $20.00

2. Frank's t-shirt company:

- Price per t-shirt: $10.00

- No additional fees

Total cost for Frank's t-shirts = number of t-shirts * $10.00

Now you can compare the total costs for each company depending on the number of t-shirts you want to buy.

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The instantaneous rate of change in revenue at x=14 is $860 per camera.

The average change in revenue is $85 per camera [(ΔR/Δx) = 255/3].

a. The average change in revenue if production is changed from x=14 to x=17 is equal to the average rate of change of the revenue function over this interval:

Δx = 17 - 14 = 3

ΔR = R(17) - R(14) = (100017 - 517^2) - (100014 - 514^2) = $255

Therefore, the average change in revenue is $85 per camera [(ΔR/Δx) = 255/3].

b. The instantaneous rate of change in revenue at x=14 is equal to the derivative of the revenue function evaluated at x=14:

R(x) = 1000x - 5x^2

R'(x) = 1000 - 10x

R'(14) = 1000 - 10(14) = $860

Therefore, the instantaneous rate of change in revenue at x=14 is $860 per camera.

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The probability to get 5 and blue that is the value of P(5 and blue) = 1/24.

Hence the correct option is (B).

From the definition of Probability we can know that,

Probability of an event = (The number of outcomes favorable to the event)/(Total number of outcomes)

Here, Sample space if we roll a dice = {1, 2, 3, 4, 5, 6}

Total number of outcomes = 6

5 is one of the face value of dice.

The probability to get 5 on dice as face value = 1/6.

So, P(5) = 1/6

In picture we can see that there is total 4 space that are one blue and two yellow and one green space.

So the probability spinner land on blue space = 1/4

So, P(blue) = 1/4

Roll of dice and spin a spinner are two independent events as their outcomes do noy rely on each other.

Now the probability to get 5 and blue is given by,

= P(5 and blue)

= P(5)*P(blue)

= (1/6)*(1/4)

= 1/(6*4)

= 1/24

Hence the correct option is (B).

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Answer:

12

325

Step-by-step explanation:

When it mentions the word "fit", you use TSA.

TSA cuboid = 2[LH+BH+LH] = 2 [ (2×3/2)+(3/2×7/2)+(2×7/2)] = 2 [ 3 + 21/4 + 7] = 2 [5¼+10] = 2 [15¼] = 2 × 61/4 = 61/2 = 30½ ft²

TSA ½ foot cube = 6L² = 6(½)² = 6×¼ = 2½

Number of cubes = 30.5÷2.5 = 12.2 = 12

TSA ⅛ foot cube = 6(⅛)² = 6×1/64 = 3/32

Number of cubes = 30.5÷3/32 = 325⅓ = 325

If the area of the hallway is 250 square feet, it would cost $625 to carpet the hallway with $2.50 per square foot carpet.

To find the cost of carpeting the hallway, we need to know the area of the hallway first. Let's assume that the length of the hallway is 50 feet and the width is 5 feet.

The area of the hallway = length x width
= 50 feet x 5 feet
= 250 square feet

Now that we know  we can find the cost of carpeting it.

Cost of carpeting = area x cost per square foot
= 250 square feet x $2.50 per square foot
= $625

Therefore, it would cost $625 to carpet the hallway with $2.50 per square foot carpet.

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The experimental probability of weather causing school to be canceled in at least three of the next four school years is (3+1)/24, which simplifies to 1/6 or approximately 0.1667.

To find the experimental probability of weather causing school to be canceled in at least three of the next four school years, we need to count the number of times there were three or more cancellations in each set of four years and divide that by the total number of sets of four years.

According to the table of simulated values, there are 24 sets of four years. Out of these, there were three or more cancellations in three sets of four years, and there were four cancellations in one set of four years.  Therefore, the experimental probability of weather causing school to be canceled in at least three of the next four school years is 20%.

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Total cost = VC(80) + Fixed cost = 1325.34 + 200 = $1525.34

To find the total cost of producing 80 barstools, we need to calculate the variable cost and add it to the fixed cost.

First, integrate the marginal cost function to find the variable cost function:

VC(x) = ∫[tex](20 - 0.5\sqrt{x dx} )[/tex]

VC(x) = [tex]20x - (1/3)x^(^3^/^2^) + C[/tex]

The constant C is irrelevant in this case, as we are interested in the difference between VC(80) and VC(0).

Now, evaluate the variable cost function at x = 80:

VC(80) = 20(80) - [tex](1/3)(80^(^3^/^2^))[/tex]

VC(80) = 1600 - [tex](1/3)(80\sqrt{80} )[/tex]

VC(80) ≈ 1325.34

Finally, add the fixed cost:

Total cost = VC(80) + Fixed cost = 1325.34 + 200 = $1525.34

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To calculate the cost for Design A and Design B, we need to know the size of each design in square inches. Once we have that information, we can multiply the size of each design by the cost per square inch of wood to determine the total cost.

Let's say Design A is 10 inches by 10 inches, which is a total of 100 square inches. To calculate the cost for Design A, we would multiply 100 by 0.15, which gives us a total cost of $15.

Similarly, let's say Design B is 8 inches by 12 inches, which is a total of 96 square inches. To calculate the cost for Design B, we would multiply 96 by 0.15, which gives us a total cost of $14.40.

Therefore, the cost for Design A is $15 and the cost for Design B is $14.40.

In summary, the cost of a wooden design can be calculated by multiplying the size of the design in square inches by the cost per square inch of wood. In this case, we used a cost of 0.15 per square inch and calculated the cost for Design A and Design B. It is important to know the size of the design before calculating the cost.

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The student from the first class performs better when comparing their scores using z-scores.

To compare the students' performances, we will calculate their z-scores, which show how many standard deviations away their scores are from the mean of their respective classes.

For the student from the first class:
z-score = (Score - Mean) / Standard Deviation
z-score = (62 - 56) / 9
z-score ≈ 0.67

For the student from the second class:
z-score = (83 - 75) / 15
z-score ≈ 0.53

The student from the first class has a higher z-score (0.67) compared to the student from the second class (0.53). This means the student from the first class performed better relative to their classmates.

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we find that the solutions to the equation are:x ≈ -1.283, x ≈ 4.283.

To solve the equation 2x(x+0.5) = -(x+2.5)² + 5.5 by graphing, we can first rearrange it to the standard form:

x² - 3x - 2 = 0.5(x+2.5)²

Then we can plot the two functions y = x² - 3x - 2 and y = 0.5(x+2.5)² - 5.5 on the same graph and find their intersection points, which represent the solutions to the equation.

Enter the two functions in separate equations:

[tex]y_1 = x^2 - 3x - 2[/tex]

[tex]y_2 = 0.5(x+2.5)^2 - 5.5[/tex]

Adjust the zoom level and position of the graph to see the intersection points.

Click on the intersection points to see their coordinates.

Round the coordinates to the nearest thousandth.

After following these steps, we find that the solutions to the equation are:

x ≈ -1.283

x ≈ 4.283

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The effective utilization for the XYZ medical facility provides medical services to patients in Russellville is 81.63%, option B.

The percentage of your available resources that are now being used is known as resource utilization. To make sure your business is as productive as possible, it might assist to plan how to use your resources more wisely.

Employers and workers may both benefit from efficient resource management. On one side of the spectrum, it may also avoid overworking and burnout, resulting in a more balanced work life overall. On the other, it makes sure that workers have enough work to keep their position sustainable and lucrative.

Design capacity = 40 patients per hour,

Effective capacity is 35 patients per hour

Actual capacity is given by,

200/7 patients per hour

Effective utilization is given by = 200 x 100 /7 x 35

= 20000/245

= 81.63%.

Therefore, the effective utilization is 81.63%.

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Step-by-step explanation:

[tex]6x + 26 = 16x\\ 16x - 6x = 26 \\ 10x = 26 \\ x = 2.6[/tex]

a. The down payment is $22,500.

b. The mortgage is $202,500.

c. The monthly mortgage payment is $1,027.

a. The down payment is 10% of the home price, which is $225,000 x 0.1 = $22,500.

b. The mortgage is the remaining amount that you need to pay, which is $225,000 - $22,500 = $202,500.

c. The monthly mortgage payment can be calculated using the formula for a fixed-rate mortgage:

Monthly Payment = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

where P is the principal amount (the mortgage), i is the monthly interest rate (4.5% / 12 = 0.375%), and n is the total number of monthly payments (30 years x 12 months/year = 360).

Plugging in the values, we get:

Monthly Payment = $202,500 [ 0.00375(1 + 0.00375)^360 ] / [ (1 + 0.00375)^360 – 1] = $1,027.

Therefore, your monthly mortgage payment will be $1,027.

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To determine the value of x, y, and the line segment lengths and angle measures, we need more information such as the given figure or problem. Without any context or image, it is impossible to provide a solution. However, in general, to find the values of x and y, we need to have equations or information about the relationship between them.

Similarly, to find line segment lengths and angle measures, we need to have given figures or diagrams and use appropriate formulas and rules to calculate them.

For example, if we have a right triangle with one side length of 5 and the hypotenuse of 13, we can use the Pythagorean theorem to find the other side's length, which is 12. Then, we can use trigonometric functions like sine, cosine, and tangent to find the angles' measures.

Therefore, the approach to finding x, y, and other geometric properties depends on the given information and the type of problem. It is essential to carefully read and understand the problem's instructions before attempting to solve it and show all your work for clarity and accuracy.

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x² + 10x + 25 is the expression of (x+5)^2 in trinomial in standard form

A trinomial is a polynomial that consists of three terms. It is a type of algebraic expression that contains three algebraic terms separated by either plus or minus signs.

For example, the expression 2x^2 + 5x - 3 is a trinomial because it has three terms: 2x^2, 5x, and -3. Similarly, the expression 4a^3 - 7a^2 + 2a is also a trinomial because it has three terms: 4a^3, -7a^2, and 2a.

We have to expand this

x² + 2(x)(5) + 5²

= x² + 10x + 25

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Assuming the population of times is normally distributed, and using the 0. 01 level of significance, we can conclude that the new booklet is effective.

To determine if the new instructional booklet is effective in reducing the assembly time for novices, we will perform a one-sample t-test using the given information.

1. State the null hypothesis (H0) and the alternative hypothesis (H1):

H0: There is no difference in the mean assembly time with the new booklet (µ = 3.15 hours).

H1: The mean assembly time with the new booklet is less than 3.15 hours (µ < 3.15 hours).

2. Identify the level of significance, sample size, sample mean, and sample standard deviation:

α = 0.01

n = 25

x = 2.98 hours

s = 0.23 hours

3. Calculate the test statistic:

t = (x - µ) / (s / √n) = (2.98 - 3.15) / (0.23 / √25) = -0.17 / 0.046 = -3.70

4. Find the p-value for the test:

Using a t-distribution table or calculator, the p-value for a one-tailed test with t = -3.70 and degrees of freedom (df) = 24 is approximately 0.0005.

5. Compare the p-value with the level of significance:

Since the p-value (0.0005) is less than α (0.01), we reject the null hypothesis.

Based on the p-value, we have enough evidence to conclude that the new instructional booklet is effective in reducing the assembly time for novices at the 0.01 level of significance.

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The student that correctly translates Mrs. Tucker's fraction into a percentage is Elvin and the percentage is  2.75%, under the condition that Mrs. Tucker writes the fraction 1 and tells her students to convert  the fraction into a percentage

Elvin's response is correct. Ferdinand's response is incorrect due to the application of multiplication of fraction by 100 and then added a percent sign.
Gertrude's response is incorrect due to the reason of  converting the fraction to a decimal and then multiplied by 100. nt sign to

Henrietta's response is incorrect due to the fact that she added a percepercentnt sign to the decimal equivalent of the fraction instead of multiplying it by 100.
Now To convert 1/36 to a percentage, we have to  first divide the numerator by the denominator:
1 / 36
= 0.0277777777778

Secondly , we have to  multiply the result by 100 to get the percentage
0.0277777777778 × 100
= 2.7778%

Then, the correct response is 2.75% which is the percentage equivalent of 1/36 given by Elvin.

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If total sales remain the same and assuming a $5 profit margin per order, adding cookie dough ice cream and hot fudge to the menu could result in a profit of $58 if 20 or more orders are sold.

To determine if adding cookie dough ice cream and hot fudge to the menu will result in a profit, we need to consider the cost and potential revenue. If the cost of adding these items is $42, we need to calculate how many orders of cookie dough ice cream with hot fudge we need to sell to cover that cost and make a profit.

Assuming the profit margin on each order of cookie dough ice cream with hot fudge is $5 (for example), we would need to sell at least 9 orders (rounding up from 8.4) to cover the $42 cost and break even. If we sell more than 9 orders, we would make a profit.

Assuming we sell 20 orders of cookie dough ice cream with hot fudge, the total revenue generated would be $100 ($5 profit per order x 20 orders). Subtracting the $42 cost of adding these items, the net profit would be $58.

Therefore, if total sales remain the same and assuming a $5 profit margin per order, adding cookie dough ice cream and hot fudge to the menu could result in a profit of $58 if 20 or more orders are sold.

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