Jenna works in an ice cream shop. When she starts her shift, the tub of chocolate ice cream is 23 full. When she finishes her shift 612 hours later, there is only 16 of the tub left. What was the average hourly change in tub fullness?

Answer: 7/80

Step-by-step explanation: because you would have to multiply the values of a and b, 7 times 1=7 and 8 times 10=80, so an= 7/80

To find two divergent series, summation from n equals 1 to infinity of a_n and summation from n equals 1 to infinity of b_n, such that their product converges, we can consider the following series:

1. Summation from n equals 1 to infinity of a_n = ∑(1/n)
2. Summation from n equals 1 to infinity of b_n = ∑n

Solution:

1. The first series, ∑(1/n), is known as the harmonic series. It is a famous example of a divergent series, meaning that its sum approaches infinity as n approaches infinity.

2. The second series, ∑n, is an arithmetic series where the terms increase linearly. This series is also divergent, as the sum increases without bound as n approaches infinity.

Now, we need to verify that the product of these series converges:

3. Summation from n equals 1 to infinity of (a_n * b_n) = ∑((1/n) * n)

4. Simplifying the expression, we get ∑(1), which is a constant series with all terms equal to 1.

5. The sum of the constant series converges, as it approaches a finite value when n approaches infinity.

In conclusion, the two divergent series summation from n equals 1 to infinity of a_n = ∑(1/n) and

summation from n equals 1 to infinity of b_n = ∑n, have a product that converges, as their product ∑((1/n) * n) simplifies to a constant series ∑(1), which has a finite sum.

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Answer:

A

Step-by-step explanation: got 100 on it

The underlying distribution for the independent groups t-test is the sampling distribution of the difference between means, assuming it's approximately normally distributed. The correct answer is C).

The underlying distribution for the independent groups t-test is the sampling distribution of the difference between means. The independent groups t-test is used to compare the means of two independent groups, and it assumes that the sampling distribution of the difference between the means is approximately normally distributed.

The t-test uses the sample means and sample standard deviations to estimate the population means and population standard deviations, and it tests the null hypothesis that the difference between the population means is zero. The correct option is C).

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Answer:

A single number would be the total amount of goals which would be the sum.

Population: All American households.

Sample: The 1780 American households surveyed.

Individuals: The American households participating in the survey.

In the given scenario, we have a survey of 1780 American households that found 59% of the households own a computer. Let's identify the population, sample, and individuals in the study:

Population: The population refers to the entire group or larger set of individuals that we are interested in. In this case, the population would be all American households.

Sample: The sample is a subset of the population that is chosen to represent the population accurately. In this situation, the survey includes 1780 American households. Therefore, the sample is the 1780 households that were surveyed.

Individuals: The individuals in the study are the specific units or elements being surveyed or examined. In this case, the individuals are the American households that participated in the survey. Each household represents an individual within the study.

To summarize:

Population: All American households.

Sample: The 1780 American households surveyed.

Individuals: The American households participating in the survey.

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Answer:

Cantidad total de lapices= 76

Step-by-step explanation:

Dada la siguiente información:

Costo por docena= $0.79

Presupuesto total= $5

Para calcular la cantidad total de lapiceras que se pueden comprar con $5, debemos usar la siguiente formula:

Cantidad total de lapices= presupuesto total / costo por docena

Cantidad total de lapices=  5 / 0.79

Cantidad total de lapices= 6.33

Para ser mas exactos:

0.33*12= 4

Cantidad total de lapices= 6*12 + 4

Cantidad total de lapices= 76

Answer:

Yes

Step-by-step explanation:

They are just in the opposite side

a. The median number of calls = 55

b. The first and third quartiles, Q1 = 48 and Q3 = 66

c. The first decile and the ninth decile, D1 = 45 and D9 = 71.

d. The 33rd percentile = 52.5

To answer the questions, let's first organize the data in ascending order:

38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57 59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79

(a) The median is the middle value of a dataset when arranged in ascending order.

Since we have 40 observations, the median is the value at the 20th position.

In this case, the median is the 55th visit.

(b) The quartiles divide the data into four equal parts.

To find the first quartile (Q1), we need to locate the position of the 25th percentile, which is 40 * (25/100) = 10.

The first quartile is the value at the 10th position, which is 48.

To find the third quartile (Q3), we need to locate the position of the 75th percentile, which is 40 * (75/100) = 30.

The third quartile is the value at the 30th position, which is 66.

Therefore, Q1 = 48 and Q3 = 66.

(c) The deciles divide the data into ten equal parts.

To find the first decile (D1), we need to locate the position of the 10th percentile, which is 40 * (10/100) = 4.

The first decile is the value at the 4th position, which is 45.

To find the ninth decile (D9), we need to locate the position of the 90th percentile, which is 40 * (90/100) = 36.

The ninth decile is the value at the 36th position, which is 71.

Therefore, D1 = 45 and D9 = 71.

(d) To find the 33rd percentile, we need to locate the position of the 33rd percentile, which is 40 * (33/100) = 13.2 (rounded to 13). The 33rd percentile is the value at the 13th position.

Since the value at the 13th position is between 52 and 53, we can calculate the percentile using interpolation:

Lower value: 52

Upper value: 53

Position: 13

Percentage: (13 - 12) / (13 - 12 + 1) = 1 / 2 = 0.5

33rd percentile = Lower value + (Percentage * (Upper value - Lower value))

                = 52 + (0.5 * (53 - 52))

                = 52.5

Therefore, the 33rd percentile is 52.5.

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Answer:

Step-by-step explanation:

Begin by grouping the x terms and the y terms together and separating the constants out.

\((x^2-2x)+(y^2-8y)=-8\)

Now we'll complete the square on those x and y terms. Take half the linear term of each, square it, and add it to both sides. Our linear x term is 2, half of 2 is 1 and 1 squared is 1, so we add that in. Likewise, half the linear y term (which is 8) is 4, and 4 squared is 16, so we add that in, too. Like this:

\((x^2-2x+1)+(y^2-8x+16)=-8+1+16\)

Doing this gives us the perfect square binomials for each of the x and y terms, and then gives us the radius on the right:

\((x-1)^2+(y-4)^2=9\)

This is a circle with a center of (1, 4) and a radius of 3.

17 minutes

hope this helps!

Step-by-step explanation:

61 pounds for 8 acres

1 pound for 8/61 = 0.131147541... ≈ 0.13 acres

6 pounds for $4

$1 for 6/4 = 3/2 = 1.5 pounds

We can conclude that there are no nontrivial clean pulsations for the given left-mounted beam with a simple support on the right.

To find the equation of clean pulsations for a left-mounted beam with a simple support on the right, we can use the differential equation that describes the deflection of the beam. Assuming the beam is subject to a distributed load and has certain boundary conditions, the equation governing the deflection can be written as:

d^2y/dx^2 + (chx)^2 * y = 0

Where:

y(x) is the deflection of the beam at position x,

d^2y/dx^2 is the second derivative of y with respect to x,

ch(x) is the hyperbolic cosine function.

To solve this differential equation, we can assume a solution in the form of y(x) = A * cosh(kx) + B * sinh(kx), where A and B are constants, and k is a constant to be determined.

Substituting this assumed solution into the differential equation, we get:

k^2 * (A * cosh(kx) + B * sinh(kx)) + (chx)^2 * (A * cosh(kx) + B * sinh(kx)) = 0

Simplifying the equation and applying the given identity (chx)^2 - (shx)^2 = 1, we have:

(A + A * chx^2) * cosh(kx) + (B + B * chx^2) * sinh(kx) = 0

For this equation to hold for all values of x, the coefficients of cosh(kx) and sinh(kx) must be zero. Therefore, we get the following equations:

A + A * chx^2 = 0

B + B * chx^2 = 0

Simplifying these equations, we have:

A * (1 + chx^2) = 0

B * (1 + chx^2) = 0

Since we are looking for nontrivial solutions (A and B not equal to zero), the expressions in parentheses must be zero:

1 + chx^2 = 0

Using the identity (sinx)^2 + (cosx)^2 = 1, we can rewrite this equation as:

1 + (1 - (sinx)^2) = 0

Simplifying further, we get:

2 - (sinx)^2 = 0

Solving for (sinx)^2, we find:

(sin x)^2 = 2

Since the square of the sine function cannot be negative, there are no real solutions to this equation. Therefore, we can conclude that there are no nontrivial clean pulsations for the given left-mounted beam with a simple support on the right.

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Answer:

what are the choices?? if you don't mind me asking

The bottom of the ladder is 9 feet from the wall.

Using the Pythagorean Theorem, we can calculate the distance from the wall. The Pythagorean Theorem states that for a right triangle, the sum of the squares of the sides is equal to the square of the hypotenuse. In this case, the hypotenuse is 15 feet and the side adjacent to the wall is 12 feet.

The formula for the Pythagorean Theorem is a^2 + b^2 = c^2.

We can solve for the distance from the wall (a). a^2 = c^2 - b^2, so a^2 = 15^2 - 12^2, which equals a^2 = 225 - 144, so a^2 = 81. Taking the square root of both sides, a = 9 feet.

Therefore, the bottom of the ladder is 9 feet from the wall.

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Answer:

Watermelon A weighs 2 kg, watermelon B weighs 4 kg and watermelon C weighs 10 kg.

Step-by-step explanation:

Watermelon A is 2 kg lighter than watermelon B and 5 times lighter than watermelon C. This means that:

A = B - 2

and

A = C / 5 => C = 5A

Watermelons A and C together are 3 times heavier than watermelon B. This means that:

A + C = 3*B = 3B

Put C = 5A:

A + 5A = 3B

6A = 3B

=> B = 6/3 A = 2A

=> A = 2A - 2

=> 2A - A = 2

=> A = 2 kg

B = 2 * 2 = 4 kg

C = 5 * 2 = 10 kg

Therefore, watermelon A weighs 2 kg, watermelon B weighs 4 kg and watermelon C weighs 10 kg.

In linear equation, $ 442.54 tall is the tower.

What are a definition and an example of a linear equation?

Suppose A is the window, B is the top of the tower, C is the bottom of the tower, and D is the point on the tower at the same horizontal level as the window.

Find BD, DC then add these together to give this°.

For BD :  AD is 350 ft, the angle CAD is 42.  

So BD/350 = tan 42°.  

      BD =  0.9004 × 350

      BD  = 315.14

   AD/350  =  tan20°

    AD =   0.364 × 350

    AD =  127.4

AD + BD =   315.14 +   127.4  =  $ 442.54

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Answer: -3

Step-by-step explanation: 15 - 18 = -3

\( \huge \boxed{Answer \hookleftarrow}\)

=》1² + 3²

=》1 + 9

=》10

The Frisbee following a parabolic path will take  8.5 seconds to hit the ground.

Given that:

h(t) = â€" 0.07t2 - 0.007t - 5

The given equation is the parabolic equation showing the path traced by the frisbee. from the equation

h = height from ground

t = time consumed in seconds

time it takes to hit the ground will be at h = 0.  we therefore solve as follows:

h(t) = â€" 0.07t2 - 0.007t - 5

0 = 0.07t2 + 0.007t + 5

\(=\frac{-0.007+or-\sqrt{0.007^{2}-4*0.07*-5 } }{2*0.07}\)

\(=\frac{-0.007+or-\sqrt{0.0049+1.4 } }{0.14}\)

\(=\frac{-0.007+or-\sqrt{1.3951 } }{0.14}\)

=8.5 or -8.5 seconds

≅ 8.5 seconds

We choose the positive which is 8.5 seconds and can therefore say that the first option is the correct option.

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The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Answer:

CD = 13

Step-by-step explanation:

it is given that both the triangles are congruent so ,

DA = CD = 13

therefore, CD is 13.

hope this answer helps you dear take care!

Answer:

yes its linear

Step-by-step explanation:

Answer:

555.1 ft

Step-by-step explanation:

Your question is...?

First, divide the money that Miguel made (264) by the number of hours worked (12)

264/12 = $22 per hour

For 7 hours:

22 x 7 = $154