(1 point) Consider the function f(x) - on the interval [4, 9] (A) Find the average or mean slope of the function on this interval. Average Slope = (B) By the Mean Value Theorem, we know there exists a c in the open interval (4, 9) such that f (c) is equal to this mean slope. Find all values of c that work and list them (separated by commas) in the box below. List of values

Answer:

Each friend will get 1/9 of the pizza (I think).

Step-by-step explanation:

I believe you would divide 1/3 by 3, or in other words, multiply 1/3 * 1/3:

1/3 * 1/3 = 1/9

Have a nice day!! It would be TOTALLY RAD if I could get brainliest!!!

Answer:

x=5 y=130

Step-by-step explanation:

27x-5 and 11x-5 = 180

27x-5 + 11x-5 = 180

38x- 10= 180

38x= 190

x=5

11(5)-5 = 50

50 + y= 180

y= 130

We can estimate that about 74 people voted in the election, which is the same as the actual number of voters.

What are the voters?

To estimate the number of people who voted in the election, we can use the proportion of registered voters who actually voted.

If we know that there are 8,246 registered voters in the town of Mayfield and 74 voters cast their vote, we can calculate the proportion of registered voters who voted as follows:

Proportion of voters = Number of voters / Number of registered voters

Proportion of voters = 74 / 8,246

Proportion of voters = 0.00897

We can then use this proportion to estimate the number of people who voted by multiplying it by the total number of registered voters:

Estimated number of voters = Proportion of voters x Number of registered voters

Estimated number of voters = 0.00897 x 8,246

Estimated number of voters = 73.9 (rounded to the nearest whole number)

Therefore, we can estimate that about 74 people voted in the election, which is the same as the actual number of voters.

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Complete question is: There are 8,246 registered to vote in the town of mayfield, about 74 people voted in the election, which is the same as the actual number of voters.

Answer:

There were 10 flies originally

Step-by-step explanation:

Since we have an exponential growth, we will be having a constant percentage of increase and we can set up the increase at any day using the following equation;

V = I(1+r)^d

where V is the number of flies on a particular day

I is the initial number of flies

r is the constant increase in percentage

and d is the number of days.

So we have for the second day;

60 = I(1+r)^2 ••••••(i)

For the fourth day, we have;

360 = I(1+r)^4 ••••••••(ii)

divide equation ii by i; we have;

360/60 = (1+r)^4/(1+r)^2

6 = (1+r)^2

(√6)^2 = (1+r)^2

1 + r = √6

r = √6 - 1

So we can substitute the value of r in any of the equations to get I which is the initial number of flies

Let’s use equation 1

60 = I(1 + r)^2

60 = I(1 + √6 -1)^2

60 = I(√6)^2

60 = 6I

I = 60/6

I = 10 flies

The expression represents the difference of 7 and twice the product of a and b is 7 - 2ab

Let's break down the given problem step by step. First, we need to find the product of a and b, which is done by multiplying the two variables together using the multiplication symbol (*). Then, we need to multiply this result by 2, which is done by placing the entire product inside parentheses and then multiplying it by 2 using the multiplication symbol again.

Once we have found twice the product of a and b, we need to subtract it from 7. This can be done using the subtraction symbol (-), which we place between 7 and the expression we just found.

Putting it all together, the expression we get is:

7 - 2ab

where a and b are the two variables we were given.

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The optimal solution of the objective function is cost = 5x + 7y.

To solve this problem, we need to determine the optimal amounts of material to be taken from each pit in order to minimize the overall cost while meeting the minimum sand content requirement. Let's break down the problem step by step:

Step 1: Define the decision variables:

Let's define:

x = amount of material (in cubic meters) taken from Bloomingdale Pit

y = amount of material (in cubic meters) taken from Valley Springs Pit

Step 2: Write the constraints in mathematical form:

We have two constraints to consider:

Total volume constraint:

x + y = 100,000 (the total volume of mixed material needed for the project)

Minimum sand content constraint:

The mix should contain a minimum of 30% sand. We can express this constraint as follows:

(0.25x + 0.50y) / (x + y) ≥ 0.30

Step 3: Write the objective function in mathematical form:

The objective is to minimize the overall cost of material. We can express the cost as follows:

Cost = 5x + 7y

Step 4: Find the optimum solution using the graphical method:

To find the optimum solution, we need to plot the feasible region defined by the constraints and identify the point that minimizes the objective function within that region.

First, let's rearrange the minimum sand content constraint:

0.25x + 0.50y ≥ 0.30(x + y)

0.25x + 0.50y ≥ 0.30x + 0.30y

0.20x - 0.20y ≥ 0

Now, we can plot the feasible region using the given constraints. The region will be bounded by the lines x + y = 100,000 and 0.20x - 0.20y ≥ 0. However, since the region is defined in terms of the total volume, we can simplify the plot by considering only the positive quadrant (x ≥ 0, y ≥ 0).

By substituting x = 0 and y = 100,000 into the minimum sand content constraint, we can check if the constraint is satisfied:

(0.25 * 0 + 0.50 * 100,000) / (0 + 100,000) ≥ 0.30

50,000 / 100,000 ≥ 0.30

0.50 ≥ 0.30

Since the constraint is satisfied at this point, we know the feasible region lies above or on the line x = 0, y = 100,000.

Now, by substituting x = 100,000 and y = 0 into the minimum sand content constraint, we can check if the constraint is satisfied:

(0.25 * 100,000 + 0.50 * 0) / (100,000 + 0) ≥ 0.30

25,000 / 100,000 ≥ 0.30

0.25 ≥ 0.30

Since the constraint is not satisfied at this point, we know the feasible region lies below the line x = 100,000, y = 0.

Finally, we can plot these two lines and shade the feasible region between them. The point that minimizes the objective function within this region will be the optimal solution.

Step 5: Calculate the savings:

If the contractor had used 60,000 m3 from Bloomingdale and 40,000 m3 from Valley Springs, we can calculate the cost for that scenario and compare it with the cost of the optimal solution.

Cost with the contractor's plan:

Cost = 5(60,000) + 7(40,000)

Cost with the optimal solution (as determined in Step 4):

Calculate the values of x and y from the optimal solution and substitute them into the objective function Cost = 5x + 7y.

The savings can be calculated as:

Savings = Cost with the contractor's plan - Cost with the optimal solution

By comparing the costs, you can determine the amount saved by giving the expert advice.

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The probability that the hand contains exactly 0 aces or exactly 2 kings is  0.0742.

To find the probability of being dealt a 13-card bridge hand containing exactly 0 aces or exactly 2 kings, we need to first determine the total number of possible bridge hands, and then determine the number of hands that meet the given conditions. We can then use these values to calculate the probability.

Step 1: Calculate the total number of possible bridge hands

There are 52 cards in a standard deck, so the total number of possible bridge hands is:

C(52,13) = 52!/(13!(52-13)!) = 635,013,559,600

Step 2: Calculate the number of hands with exactly 0 aces

There are 4 aces in the deck, so the number of ways to choose a 13-card hand with exactly 0 aces is:

C(48,13) = 48!/(13!(48-13)!) = 33,854,775,456

Step 3: Calculate the number of hands with exactly 2 kings

There are 4 kings in the deck, so the number of ways to choose a 13-card hand with exactly 2 kings is:

C(4,2) × C(48,11) = 6 × (48!/(11!(48-11)!)) = 13,247,856,896

Step 4: Add the number of hands with exactly 0 aces and the number of hands with exactly 2 kings

To find the total number of hands that meet the given conditions, we need to add the number of hands with exactly 0 aces and the number of hands with exactly 2 kings:

33,854,775,456 + 13,247,856,896 = 47,102,632,352

Step 5: Calculate the probability

To find the probability of being dealt a 13-card bridge hand containing exactly 0 aces or exactly 2 kings, we divide the number of hands that meet the given conditions by the total number of possible hands:

P = 47,102,632,352 / 635,013,559,600 ≈ 0.0742

Therefore, the probability of being dealt a 13-card bridge hand containing exactly 0 aces or exactly 2 kings is approximately 0.0742, or about 7.42%.

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Using the assembly line balancing procedure, we find that the balance delay of the workstation is 0, we cannot improve the line by balancing it further.

Task times for the six tasks that make up the job = 4, 6, 7, 2, 6, and 5 minutes Cycle time = 9 minutes The first step in solving assembly line balance problems is to calculate the number of work stations needed to meet product demand while maintaining the desired cycle time

The following are the steps to balance an assembly line using assigned task times: Calculate the task times for each work station. Calculate the theoretical minimum number of workstations needed. Here is the formula: = sum of task times / cycle time. Round to the next highest integer. In this case it will be 6 + 7 + 4 + 6 + 2 + 5 = 30 minutes; 30 minutes/9 minutes = 3.33 or 4.

Therefore, the theoretical minimum number of workstations is 4. Examine the balance late percentage by comparing it to the balance late occurrence, which is the difference between the cycle time and the sum of the task times for one workstation This is the maximum amount of idle time that can be allocated to each workstation. Since the balance delay of the workstation is 0, we can't improve the line by balancing it further.

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Answer:

The hand moved \(\bf \frac{3}{4}\) of a complete turn.

Step-by-step explanation:

The hand moved from 3 to 12, that is, it moved:

12 - 3 = 9 hours

In a clock, 12 hours represent a complete turn.

∴ Using the unitary method:

12 hours    ⇒     1 turn

1 hour        ⇒     \(\frac{1}{12}\) turns

9 hours     ⇒     \(\frac{1}{12}\)  × 9 = \(\frac{9}{12}\)

                                     = \(\bf \frac{3}{4}\) turns    (simplified)

∴ The hand moved \(\bf \frac{3}{4}\) of a complete turn.

The answer is  \(\boxed{\frac{3}{4}}\).

To find the fraction of a complete turn it moved in this case, take the ratio between hours covered between 3 and 12, and the hours covered in a complete turn.

16 + 16 = 32

X * 4.75 = ?

32 + X = Y

You would add 16 plus 16 because there are TWO new books being bought, you multiply however many used books there are (X) by 4.5 then add that answer to 16+16, solve that, and you have your answer = Y

Hope this helps ^-^

The number of aluminium balls with a radius of 4.5 in will be 200.

The amount of space that a sphere can occupy is measured by its volume. The three-dimensional shape of a sphere lacks vertices and edges.

Given that Amy's company makes solid balls out of scrap metal for various industrial uses. Her current task is to make a batch of aluminium balls with a radius of 4.5 in. The total volume of the aluminium is 76302 cubic inches.

The number of spheres with a radius of 4.5 inches will be calculated as:-

Number = ( Total volume of aluminium) / ( Volume of the small sphere)

The volume of small sphere = ( 4 / 3 ) πr³

The volume of small sphere = ( 4 / 3 ) π x 4.5³

The volume of the small sphere = 381.7 cubic inches

Number = ( Total volume of aluminium) / ( Volume of the small sphere)

Number = 76302 / 381.7

Number = 200

Hence, the number of spheres will be 200.

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Answer:

amplitude = |-4| =4

period = 2 pi/3

phase shift = pi / 3

midline = 2

Step-by-step explanation:

f(x)=-4 cos (3x-pi)+2

The equation is in the form

f(x) = a cos (bx -c) +d  where |a| is the amplitude

period  is 2 pi /b

phase shift:  c/b

midline = d

amplitude = |-4| =4

period = 2 pi/3

phase shift = pi / 3

midline = 2

Answer:

  (x, y) = (1, 4)

Step-by-step explanation:

You want the solution to the equation (x²-2x+1)⁷⁷ +(3x-2y+5)⁸⁸ = 0​.

The first term can be rewritten as ...

  \((x^2-2x+1)^{77}=((x-1)^2)^{77}=(x-1)^{154}\)

This means both of the terms are being raised to even powers. Any non-zero value of the base expression will result in a positive value for the term. That is, each term is non-negative.

The sum of two non-negative terms will be zero if and only if each of the terms individually is zero. That means the equation resolves to two equations:

The solution to the first equation is x=1. Using this value in the second equation, it becomes ...

  3 -2y +5 = 0

  8 = 2y . . . . . . . . add 2y

  4 = y . . . . . . . divide by 2

The values of x and y that will make the equation true are ...

  (x, y) = (1, 4)

Therefore, the figure's volume is 32 times Prism A's length less 40 cubic feet.

In three dimensions, each object takes up some space. What is being assessed is the size of this region. The volume of an item is the region that fills its three-dimensional boundaries. It is additionally known as an object's potential.

To determine the volume of the figure, we need to find the dimensions of both prisms and then add their volumes together.

Let's start by finding the width of Prism A. Since Prism A and Prism B are attached to each other, they must share a common width. We know the width of Prism B is 4 feet, so the width of Prism A must also be 4 feet.

Now we can calculate the volume of Prism A:

Volume of Prism A = length x width x height

Volume of Prism A = unknown x 4 feet x 8 feet (since we don't know the length of Prism A)

We don't know the length of Prism A, but we do know that it is connected to Prism B, which has a length of 2 feet. Therefore, the length of Prism A must be the remaining distance between the two prisms, which is:

Length of Prism A = total length - length of Prism B

Length of Prism A = unknown - 2 feet

Now we can substitute this value into the volume equation for Prism A:

Volume of Prism A = (unknown - 2 feet) x 4 feet x 8 feet

Next, we can calculate the volume of Prism B:

Volume of Prism B = length x width x height

Volume of Prism B = 2 feet x 4 feet x 3 feet

Volume of Prism B = 24 cubic feet

Finally, we can add the volumes of the two prisms together to get the total volume of the figure:

Total volume = Volume of Prism A + Volume of Prism B

Total volume = (unknown - 2 feet) x 4 feet x 8 feet + 24 cubic feet

Without knowing the value of "unknown", we cannot calculate the exact volume of the figure. However, we can simplify the equation by multiplying out the terms:

Total volume = (32 x unknown - 64) cubic feet + 24 cubic feet

Total volume = 32 x unknown - 40 cubic feet

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Answer:

a and b

Step-by-step explanation:

The margin of error for the survey, rounded to the nearest tenth, is approximately 4.0% when expressed as a percentage.

To determine the margin of error for a survey at the 95% confidence level, we need to calculate the standard error. The margin of error represents the range within which the true population proportion is likely to fall.

The formula for calculating the standard error is:

Standard Error = sqrt((p * (1 - p)) / n)

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 64% (or 0.64) since 64% of the 1350 surveyed residents support the plan.

Plugging in the values:

Standard Error = \(\sqrt{(0.64 * (1 - 0.64)) / 1350)}\)

\(= \sqrt{(0.2304 / 1350)} \\= \sqrt{(0.0001707)}\)

≈ 0.0131

Now, to find the margin of error, we multiply the standard error by the appropriate critical value for a 95% confidence level. The critical value corresponds to the z-score, which is approximately 1.96 for a 95% confidence level.

Margin of Error = z * Standard Error

= 1.96 * 0.0131

≈ 0.0257

Finally, to express the margin of error as a percentage, we divide it by the sample proportion and multiply by 100:

Margin of Error as Percentage = (Margin of Error / Sample Proportion) * 100

= (0.0257 / 0.64) * 100

≈ 4.0%

Therefore, the margin of error for this survey, expressed as a percentage to the nearest tenth, is approximately 4.0%.

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The high temperature for today using a 3-day moving average is 92 degrees.

To calculate the high temperature for today using a 3-day moving average, we take the average of the temperatures from the past three days, including today.

Given the daily high temperatures in St. Louis for the last week:

92, 92, 93, 95, 95, 86, 95 (yesterday)

To find the 3-day moving average for today's high temperature, we consider the temperatures from yesterday, the day before yesterday, and three days ago.

(95 + 86 + 95) / 3 = 92

Therefore, the high temperature for today, calculated using a 3-day moving average, is approximately 92 degrees Fahrenheit, rounded to one decimal place.

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Given:

Angle A = 18.6°

Angle B = 93°

Length of side AB = 646 meters

To find:

the distance across the river, distance between BC

Steps:

Since we know the measure of 2 angles of a triangle we can find the measure of the third angle.

18.6° + 93° + ∠C = 180°

        111.6° + ∠C = 180°

                    ∠C = 180° - 111.6°

                    ∠C = 68.4°

Therefore the measure of angle C is 68.4°.

now we can use the law of Sines,

\(\frac{BC}{sinA}=\frac{AB}{SinC}\)

\(\frac{BC}{sin(18.6)}= \frac{646}{sin(68.4)}\)

\(BC[sin(68.4)] = 646 [sin(18.6)]\)

\(BC = \frac{646*sin(18.6)}{sin(68.4)}\)

\(BC = \frac{646 * 0.3190}{0.9298}\)

\(BC = 221.63\)

\(BC = 222\) meters

Therefore, the distance across the river is 222 meters.

Happy to help :)

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The value of x the function when x = -7.5 is 34.5

Functions are written in terms of variables

Given the expression  –3.8x + 6, when the value of x is -7.5, hence;

f(x) =  –3.8x + 6

f(-7.5) = -3.8(-7.5) + 6

f(-7.5) = 28.5 + 6

f(-7.5) = 34.5

Hence the value of x the function when x = -7.5 is 34.5

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Answer: 3,9,7,1,3,9,7,1

Step-by-step explanation: In the powers of 3 table, the ones digits form the repeating pattern

Answer:

4+8

Step-by-step explanation:

oh and the answer to the whole equation is 153

Answer:

hope help you stay happy

Answer:

An example would be... slope intercept form is y=mx+b m being the slope b equal the y-intercept. so an equation would be y=3x+7 3 is the slope and 7 in the y-intercept. I am giving you this way because i do not know what points the graph are going through. And do not know what the graph looks like.

The sample of size 36 provides the strongest evidence to reject H0 in favor of Ha

B) = 27, S = 4.

An testing whether the population mean (μ) is less than 30 based on a sample of size 36. The test statistic commonly used in this scenario is the t-statistic which follows a t-distribution.

The formula for the t-statistic is

t = (X - μ) / (S / √(n))

where:

X is the sample mean

μ is the hypothesized population mean under H0

S is the sample standard deviation

n is the sample size

A smaller t-statistic value indicates stronger evidence against H0 and in favor of Ha.

calculate the t-statistic for each sample result

A) X= 28, S = 6, n = 36

t = (28 - 30) / (6 / √(36)) = -2 / (6/6) = -2

B) X= 27, S = 4, n = 36

t = (27 - 30) / (4 / √(36)) = -3 / (4/6) = -4.5

C) X = 32, S = 2, n = 36

t = (32 - 30) / (2 / √(36)) = 2 / (2/6) = 6

D) X = 26, S = 9, n = 36

t = (26 - 30) / (9 / √(36)) = -4 / (9/6) = -8/3 ≈ -2.67

Comparing the t-statistics,  that option B) with t = -4.5 gives the strongest evidence against H0. A more negative t-value indicates a larger deviation from the hypothesized mean of 30, which supports the alternative hypothesis that the true mean is less than 30.

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The p-value for the hypothesis test H₀:μ = 10 against H₁:μ<10 with variance unknown and n = 10 is approximately 0.047.

To determine the p-value, the test statistic is calculated as follows:

t = (sample mean - hypothesized mean) / (standard error of the mean)

The sample mean is calculated as follows:

x = Σx / n

where Σx is the sum of the sample values and n is the sample size.

The hypothesized mean is 10.

The standard error of the mean is calculated as follows:

SE = σ / √n

where σ is the population standard deviation and n is the sample size.

Plugging in the values for the sample mean, hypothesized mean, sample standard deviation, and sample size, we get the following test statistic:

t = (2.5 - 10) / (1.5 / √10) = -4.66

The critical value is found using the t-distribution with n-1 degrees of freedom. The t-distribution is a probability distribution that is used to calculate the p-value for a hypothesis test when the population standard deviation is unknown. The degrees of freedom is the number of data points minus the number of parameters estimated. In this case, the degrees of freedom is 10-1=9.

The critical value for a two-tailed hypothesis test with a significance level of 0.05 and 9 degrees of freedom is 2.306.

The test statistic (-4.66) is less than the critical value (2.306). Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.

The p-value is the probability of obtaining a test statistic that is at least as extreme as the one observed, assuming that the null hypothesis is true. The p-value for the test statistic -4.66 is approximately 0.047. This means that there is a 4.7% chance of obtaining a test statistic that is at least as extreme as -4.66 if the population mean is actually 10.

Therefore, the best approximation for the p-value for the test statistic is 0.047.

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The dual for the given linear programming problems are as follows:

(i) Minimize Z' = 10a + 12b Subject to: a + 7b ≥ 3 2a + 3b ≥ 4 a + 9b ≥ 5 a, b ≥ 0.

(ii) Maximize Z' = 5a + 6b + 2c Subject to: 3a + 2b + c ≤ 1 4a + 6b + c ≤ 2 a + b ≤ 0 a, b, c ≥ 0.

In the first problem, we have a maximization problem with three variables (x, y, z) and two constraints. The dual formulation involves minimizing a new objective function with two variables (a, b) and four constraints. The coefficients of the variables and the constraints are transformed according to the rules of duality.

The primal problem is:

Maximize Z = 3x + 4y + 5z

Subject to:

x + 2y + z ≤ 10

7x + 3y + 9z ≤ 12

x, y, z ≥ 0

To find the dual, we introduce the dual variables a and b for the constraints:

Minimize Z' = 10a + 12b

Subject to:

a + 7b ≥ 3

2a + 3b ≥ 4

a + 9b ≥ 5

a, b ≥ 0

In the second problem, we have a minimization problem with two variables (y1, y2) and three constraints. The dual formulation requires maximizing a new objective function with three variables (a, b, c) and four constraints. Again, the coefficients and constraints are transformed accordingly.

The primal problem is:

Minimize Z = y1 + 2y2

Subject to:

3y1 + 4y2 > 5

2y1 + 6y2 ≥ 6

y1 + y2 ≥ 2

To find the dual, we introduce the dual variables a, b, and c for the constraints:

Maximize Z' = 5a + 6b + 2c

Subject to:

3a + 2b + c ≤ 1

4a + 6b + c ≤ 2

a + b ≤ 0

a, b, c ≥ 0

The duality principle in linear programming allows us to find a lower bound (for maximization) or an upper bound (for minimization) on the optimal objective value by solving the dual problem. It provides useful insights into the relationships between the primal and dual variables, as well as the economic interpretation of the problem.

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Answer:

Slope: 3/2

Y-Intercept: 3

Step-by-step explanation:

The y-intercept is very easy to discover as it is just the Y coordinate when X is zero or "intercepts" the x axis. So if you look directly above the origin you see that the line has the point (0, 3).

The Y Intercept is 3

The slope is found using the slope formula of y2-y1/x2-x1

Lets take two points from the line. We have the (0, 3) point that I mentioned earlier and we can get the x-intercept of (-2, 0)

Lets Solve!

3- 0 = 3

0-(-2) = 2

3/2 is the slope

So the formula is Y = 3/2 + 3