4. In a large public university, the number of sections of calculus to be offered in a given year depends on the proportion of students completing the prerequisite course. The mathematics department must decide how many calculus sections to create before students begin to register for classes. To help them decide, the department decides to survey a random sample of students currently enrolled in the prerequisite course. If more than 80% of these students plan to take calculus, the department will need to increase the number of sections offered. They survey 130 students, 125 of whom respond. Of these 125, 108 say they intend to take calculus in the following year.


A. On the basis of these data, would you recommend to the mathematics department that they increase the number of sections of calculus for the following year? Use appropriate statistical evidence to support your answer.


B. Suppose the five missing responses from the original 130 had simply gotten lost on the department secretary's desk while the rest were being analyzed. In what way could the inclusion of these five responses have affected your recommendation?

99% confidence interval is (0.5034,0.5566).

Given that,

sample size n = 2434

proportion of adults who watched digitally streamed TV = 53%

⇒ p = 0.53

We know the formula for the 99% confidence interval,

p ± Zstat\(\sqrt{\frac{p(1-p)}{n} }\)

Zcritical at α₀.₀₁ = ± 2.58

Putting all the values we get,

0.53 ± 2.58(\(\sqrt{\frac{0.53(1-0.53)}{2343} }\))

= 0.53 ± 0.0266

= (0.5034, 0.5566).

Therefore the confidence interval is (0.5034,0.5566).

A 99% confidence interval would be wider than a 95% confidence interval.

Given question is incomplete.

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The Mean, Median, Mode, and Range of the data is 4.2, 2.5, 2 and 10 respectively.

1) The mean of the data set is 4.2, indicating that if we were to sum up all the values and divide by the total number of values (6 in this case), the average would be 4.2.

2) The median of the data set is 2.5, which means that when the values are arranged in ascending order, the middle value is 2.5. In this case, the median is calculated by taking the average of the two middle values, which are 2 and 3.

3) The mode of the data set is 2, indicating that the value 2 appears most frequently among the given numbers. In this case, 2 appears twice, while all the other values appear only once.

4) The range of the data set is 10, which is calculated by subtracting the smallest value (0) from the largest value (10). This indicates the spread or the difference between the maximum and minimum values in the data set.

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Answer:

(B

The given system of equations are:

y=x^2+3x+3y=x

2

+3x+3 (1)

and y=x^2+x+2y=x

2

+x+2 (2)

Subtracting equation (2) from (1), we get

0=2x+10=2x+1

⇒2x=-12x=−1

⇒x={\frac{-1}{2}}x=

2

−1

⇒x=-0.5x=−0.5

Now, substituting the value of x=-0.5 in equation (2), we get

y=0.25-0.5+2y=0.25−0.5+2

⇒y=1.7y=1.7

Thus, the values of x and y are -0.5 and 1.7.

Therefore, the approximate solution of the given system of the equation is (-0.5, 1.7).

Hence, option (B) is correct.

Answer:

Property of Equality

Step-by-step explanation:

Answer:Property of Equality

STEP BY STEP EXPLANATION HAS BEEN CANCELED ITS EASY:

PLEB

this means that y can be equal to 7.9 or any other number above

The temperature of the fired Raku pot is about 1612°F

An equation is used to show the relationship between numbers and variables. An equation can be linear, quadratic depending on the degree.

Water boils at 212°F. A raku pot is at a temperature that is 128°F more than 7 times the temperature at which water boils. Hence:

Temperature of Raku pot = 7(212) + 128 = 1612°F

The temperature of the fired Raku pot is about 1612°F

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0.45 or %45 is left of the circular cake.

Hope this helps; have a great day!

Answer:

B - The correct answer is graph B

Step-by-step explanation:

Answer:

the correct choice is graph B. (see attachment below)

Answer:

1.   3(-7 - 14) + 4 (10)            2. -23

Step-by-step explanation:

Answer:

x intercept - = 11/2 (5.50000 as a decimal)

y intercept - = 11/1 (11.00000 as a decimal)

Step-by-step explanation:

There are 5 choices left), and 5 ways to choose the remaining element of Y. This gives us a total of 7 × 5 × 5 = 175 ordered pairs (X,Y).

Let's first consider the possible values of |X ∪ Y|.

If |X ∪ Y| = 1, it means that X and Y have no elements in common, and each set has only one element. There are 7 such sets: {1},{2},{3},{4},{5},{6},{7}.

If |X ∪ Y| = 2, it means that X and Y have one element in common. There are 7 ways to choose the common element, and 6 ways to choose the remaining element of X (it cannot be the same as the common element, so there are only 6 choices left), and 6 ways to choose the remaining element of Y (again, it cannot be the same as the common element or the element of X, so there are only 6 choices left). This gives us a total of 7 × 6 × 6 = 252 ordered pairs (X,Y).

If |X ∪ Y| = 3, it means that X and Y have two elements in common. There are 7 ways to choose the common elements, and 5 ways to choose the remaining element of X (it cannot be any of the common elements, so there are 5 choices left), and 5 ways to choose the remaining element of Y. This gives us a total of 7 × 5 × 5 = 175 ordered pairs (X,Y).

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Answer:

80 miles per an hour

Step-by-step explanation:

400 divided by 5 equals= 80 so 80miles = 1 hour

Answer:

80 miles per hour.

Step-by-step explanation:

Start with the speed formula.

\(speed=\frac{distance}{time}\)

In this scenario, the distance is \(400\) miles, and the time is \(5\) hours.

Substitute:

\(speed=\frac{400}{5}\)

Divide.

\(400\) ÷ \(5\)

Solve:

\(400\) ÷ \(5=80\)

Answer:

rounded to the nearest tenth is 0.4

The correct answer is (D) If A is the given matrix, then the augmented matrix represents the equation Ax =0. The reduced echelon form of this matrix indicates that Ax =0 has only the trivial solution. Therefore, the columns of A form a linearly independent set.

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital applications as well.

Mathematically, assume that B = {v₁, v₂, v₃, ........} is the set of vectors. Then B will be linearly independent if the vector equation

y₁v₁ + y₂v₂ + y₃v₃ + ........ = 0 possesses the trivial solution such that

y₁ = y₂ = y₃ = ........ = 0.

Let A be a matrix, then columns of A will be linearly independent if the equation Ax = 0 possesses the trivial solution. In other words, The row space of matrix A is the span of its rows. The column space denoted by

C(A) is the span of A’s columns. The dimension of the row and column spaces is always the same, which is known as the rank of A.

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Answer:

D. it passes through the point (-12)

Let x represent the number of chickens and y represent the number of sheep.There is no proper system equation so such farms does not exist as this equations contradict.

A system of equations is a set of multiple equations with multiple variables that are related to each other. It is a mathematical problem that requires a solution for each equation in the system.

The total number of legs on the farm is given as "4x + 2y". What's more, we are told that the total number of animals is "x + y".

4x + 2y means the total legs

x + y = the number of total of animals

We'll now use the Elimination method to identify x and y.

One method is to multiply the first equation by 2 and subtract it from the second:

(2) * legs = (4x + 2y)

2x + 2y = the total number of animals

Legs = (2x + 2y)

0 = number of legs - 2 * the amount of animals

When we solve for the number of animals we get:

animal count = legs / 2

So, if we connect this back into either equation, we can find x and y.

Let's look at the first equation:

4x + 2y means the total legs

legs / 2 = x + y

When we substitute legs / 2 in the second equation for "number of animals," we get:

legs / 2 = x + y

Now we'll use substitution to find x. In the first equation, we'll substitute x = legs / 2 - y:

4x + 2y means the total legs

legs = 4(legs / 2 - y) + 2y

legs = 2 * legs - 4y + 2y

2 times legs = legs

There are no solutions due to this contradiction, and no such farm exists under the given conditions.

As a result, the answer to the system of equations is that no such farm occurs under the given conditions.

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\(\huge\underline\mathtt\colorbox{cyan}{Graph B}\)

\(\huge\mathsf\colorbox{white}{}\)

Graph B consists of a parabola that opens downward. If a parabola opens downward, the the coefficient of x will be negative.

There is an easy way to tell whether the graph of a quadratic function opens upward or downward: if the leading coefficient is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward.

Answer:

- 1 7/8's of a cup

Step-by-step explanation:

1/2 = 4/8

1 4/8 + 3/8 = 1 7/8

Make it negative because it is REMOVING or TAKING AWAY from something

Answer:1 1/2

Step-by-step explanation: if your asking which is a change 1 1/2 is a change in the sugar making the total of sugar go down, 3/8 has nothing to do with sugar since it’s the sprinkle quantity, hope this helps!

Answer:

a

Step-by-step explanation:

The correct statement is that the solution to an absolute value equation must always be greater than or equal to zero. The absolute value of a number is its distance from zero on the number line. Thus, the absolute value of any number is always greater than or equal to zero.

The correct option is-C

The absolute value of a negative number is its opposite, which is always positive. The absolute value of a positive number is the same number.To solve an absolute value equation, you must isolate the absolute value first, then write two equations using the positive and negative versions of the absolute value expression. You can then solve for the variable in each equation to obtain two solutions. Therefore, not every absolute value equation has two solutions. It's possible for an absolute value equation to have one solution as well as no solution.

Additionally, the solutions to an absolute value equation can be negative as well. In summary, data markers are used in charts to represent individual data points. They are often used in combination with other chart elements, such as axes, gridlines, and legends, to help viewers understand the data being presented. The column, bar, area, dot, pie slice, or other symbol in a chart that represents a single data point is a data marker. Data markers provide you with a visual representation of the data in a chart. For example, in a column chart, each column represents a single data point.

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The probability is approximately 45.4% (rounded to the nearest tenth of a percent).

To find the probability that a randomly selected point within the circle falls in the white area, we need to find the area of the white region and divide it by the total area of the circle.

The total area of the circle is:

A = πr² = π(4 cm)² = 16π cm²

The area of the white region can be found by subtracting the area of the two semicircles from the area of the circle:

White area = A - 2(1/2π(2.5 cm)²) = 16π - 2(4.375π) = 7.25π cm²

So, the probability that a randomly selected point within the circle falls in the white area is:

P(white area) = (white area)/(total area) = (7.25π)/(16π) ≈ 45.4%

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The derivative of the function f(x) is:

\(f'(x) = 8 tan((8x)^5)\)

To find the derivative of the function f(x), we can use the fundamental theorem of calculus, which states that if a function f(x) is defined as an integral with variable limits of integration, then its derivative is given by the integrand function evaluated at the upper limit of integration.

In this case, we have:

\(f(x) = \int 8x tan(t^5) dt\)

Taking the derivative with respect to x, we get:

\(f'(x) = d/dx [ \int 8x $ tan(t^5) dt ]\)

Using the chain rule, we have:

\(f'(x) = tan((8x)^5) d/dx (8x) - tan(0) d/dx (0)\)

The second term is zero, since the integral evaluated at 0 is 0.

For the first term, we can simplify using the power rule:

\(f'(x) = tan((8x)^5) \times 8.\)

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To use the fundamental theorem of calculus to find the derivative of f(x)=∫8xtan(t5)dt, we need to apply the chain rule and the fundamental theorem of calculus. The derivative of f(x) using the Fundamental Theorem of Calculus is f'(x) = 8 * tan(x^5).

First, let's rewrite the integral in terms of x:

f(x) = ∫8xtan(t^5)dt

Next, we can use the chain rule to find the derivative of the integral:

f'(x) = d/dx [∫8xtan(t^5)dt]

= tan(8x^5) * d/dx [8x^5]

= 40x^4 tan(8x^5)

Finally, we can use the fundamental theorem of calculus to verify that our answer is correct:

f(x) = ∫8xtan(t^5)dt

= F(t)|8x - F(t)|0

where F(t) = -1/40 cos(8t^5) + C

Therefore,

f'(x) = F'(8x) * d/dx [8x] - F'(0) * d/dx [0]

= -1/5 cos(8x^5) * 8 + 0

= -8/5 cos(8x^5)

Since -8/5 cos(8x^5) = 40x^4 tan(8x^5), we have verified that our answer is correct.

To use the Fundamental Theorem of Calculus to find the derivative of f(x) = ∫(8x * tan(t^5)) dt, you need to evaluate the integral with respect to t and then differentiate the result with respect to x. However, it seems there is a missing detail in the question, which should specify the limits of integration.

Assuming the limits are from a constant 'a' to a variable 'x', the problem becomes:

f(x) = ∫(8x * tan(t^5)) dt from 'a' to 'x'

According to the Fundamental Theorem of Calculus, if F(t) is an antiderivative of the function f(t), then the derivative of F(x) with respect to x is:

f'(x) = d(F(x))/dx = f(x)

So in this case, you need to differentiate the integrand with respect to x:

f'(x) = d(8x * tan(t^5))/dx

Since 't' is a constant with respect to 'x', the derivative becomes:

f'(x) = 8 * tan(x^5)

Therefore, the derivative of f(x) using the Fundamental Theorem of Calculus is f'(x) = 8 * tan(x^5).

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Answer:

Step-by-step explanation:

Volume of prism = length * width * height

= 6*2.5*4.5

= 67 1/2 cm^3

Answer:

Step-by-step explanation:

vol = length*width height

= 6*2.5*4.5

= 67.5cm^3

Answer:

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

12*4=48

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Answer:

y= 16, 64, 256, 1024

y/x= 16/2, 64/3, 256/4, 1024/5,

Step-by-step explanation:

    This is just like any other equation, except instead of x being a number, it is an exponent. For example, when x equals 2, y equals 16 because y always equals four to the power of x.  This applies to all of the parts in your table. when x equals 3, y equals 4^3 (4 times 4 times 4) which is 64, and when x equals 4, y equals 4^4 (4 times 4 times 4 times 4), which is 256.

    For the y over x part that is just the value y, divided by the value x. For the first line on the table x equals 2, and we know y equals 16 (4^2 is 4 times 4, which is 16) so 16 divided by 2 is 8. That is the answer.

Hope this helps :)

Answer:

Nuestra masa ejerce una fuerza de 931,665 newtons por efecto de la gravedad terrestre.

Step-by-step explanation:

Nuestro peso puede determinarse mediante la definición de peso (\(W\)), medido en newtons, representado por la siguiente fórmula:

\(W = m\cdot g\) (1)

Where:

\(m\) - Masa, medida en kilogramos.

\(g\) - Aceleración gravitacional, medida en metros por segundo cuadrado.

Si sabemos que \(m = 95\,kg\) y \(g = 9,807\, \frac{m}{s^{2}}\), entonces la fuerza que ejerce sobre nuestra masa es:

\(W = (95\,kg)\cdot \left(9,807\,\frac{m}{s^{2}} \right)\)

\(W = 931,665\,N\)

Nuestra masa ejerce una fuerza de 931,665 newtons por efecto de la gravedad terrestre.

Answer:

Step-by-step explanation:

18+(-4)= 18 - 4 = 14

-5 + (-18) = - 5 - 18 = - 23  

9 + (-18) = 9 - 18 = - 9  

-18 + 18 = 0