Which linear function has the greatest rate of change?

A. The Equation

B. The Table

C. The graph

To generate the most money, the stadiums might set the price at $11.50.A mathematical equation known as a demand function expresses consumer demand as a function of a product or service's pricing and .

The price that customers are prepared to pay and the amount that they're willing to purchase are generally correlated through a demand function. Since the profit function is the sum of these two amounts, this relationship can be converted into one.

m=5−836−30=−36=−1

This is the number of tickets sold that will maximize the revenue because the second derivative is, in fact, negative. Let's go back to the demand function to determine the appropriate ticket price.

R=−x+23\s−x+23=0x=23

R=−1\sp=−12(23)+23=11.5

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The graph of each given piecewise function is shown below .

In the question,

a piece wise function is given ,

we have to sketch the graph of the piecewise function ,

the piecewise function f(x) is  = [tex]\left \{ {-2x-1 , {x\leq 2} \atop -x+4 , {x > 2}} \right.[/tex]

when x ≤ 2 ,

we put x =2 , we get , f(2) = -2*2-1  = -5 .

So , the point is (2,-5) .

when we put x = 0 , f(0) = -2*0 - 1 = -1

so , the second point is (0,-1) .

Now , for x>2  

we put x= 4 , we get f(4) = 0

the point will, be (4,0)

we put x = 6 , we get , f(6) = -2 .

the point will be = (6,-2) .

On plotting all the four points , we get the graph as sketched below .

Therefore , the given piecewise function's graph is shown below.

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Answer:

C. C and E

Step-by-step explanation:

As per the graph, both points C and E are points that are located on both the red and purple graphs.

Answer:

C.  point C and point E

Step-by-step explanation:

The solutions to the given linear-quadratic system of equations are the points where the line and curve intersect.

From inspection of the given graph, the points of intersection are:

1)test the claim that women and men have the same mean diastolic blood pressure .Let p1 be the mean diastolic blood pressure for women and let u2 be the mean diastolic blood pressure for men

there for we test

H0: u1 = u2

H1 : u1 =!u2

2)t= overline X 1 - overline X 2 sqrt((S_{1} ^ 2)/n_{1} + (S_{2} ^ 2)/n_{2})

= (69.81 - 69.35)/(sqrt((10.46 ^ 2)/26 + (11.2l ^ 2)/26)

= 0.153

3) P-value.

t-statistic value = 0.153 , alpha=0.05 then

p-value for two tail test = 0.879 which is greater than n = 0.05(0.879 > 0.05) So we do not reject H0.

4)Make a conclusion about the null hypothesis and a final conclusion that addresses the original claim.

we concluded that the null hypothesis not rejected, at 95 % confidence H0:u1= u2 accepted.

that is we accept the claim that women and men have the same mean diastolic blood pressure.at 0.05 significance level.

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The solution of the inequality 42 > g + 27 is 25 > g  and the graph of the inequality has been plotted on a number line

The given inequality is

42 > g + 27

The inequality is the mathematical statement that shows the relationship between two expression with and inequality sign. The inequality maybe less than, less than or equal, greater than, greater than or equal etc. The equal sign will not be a part of inequality

Th given inequality is

42 > g + 27

Subtract both side of the inequality by 27

42 - 27 > g + 27 - 27

25 > g

Plot the inequality in number line

Therefore, the solution is 25 > g and the inequality has been plotted on the number line

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Answer:

8<r

Step-by-step explanation:

5 > r – 3

+3      +3

add 3 to both sides

8>r

move variable to the left and flip the sign

8<r

A height with a z-score of 1 is the lowest, a height with a percentile rank of 80 percent is in the middle, and a height at the third quartile Q₃ is the highest.

A bell-shaped distribution is also known as a normal distribution. It is a symmetrical distribution where the mean, median, and mode are all equal. The distribution has two tails that extend out from the mean in either direction. A height with a z-score of 1 is the lowest because a z-score of 1 is one standard deviation below the mean. A height with a percentile rank of 80 percent is in the middle because it is the 80th percentile, meaning that 80 percent of the data is lower than it. A height at the third quartile Q₃ is the highest because it is the 75th percentile, meaning that 75 percent of the data is lower than it. In ascending order, the heights arranged are III, II, and I.

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By analyzing the question, we find that there are a total of 5 * 4 * 3 = 60 different shows that Elodie can put on.

A permutation is an arrangement of a set of items in a specific order. Permutations are typically denoted using the notation "P" followed by the number of items being permuted and the number of items being chosen at a time.

The formula for calculating permutations is as follows:

P(n,r) = n! / (n-r)!

where:

P(n,r) is the number of permutations of r items from a set of n items.

n! is the factorial of n, which is the product of all positive integers less than or equal to n.

There are five fashion models and three remaining outfits, which means there are 5 ways to choose the model who wears the first outfit, 4 ways to choose the model who wears the second outfit, and 3 ways to choose the model who wears the third outfit. Therefore, there are a total of 5 * 4 * 3 = 60 different shows that Elodie can put on.

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$76.25 will be the total cost of four games including discount.

Percent, A relative value that specifies one hundredth of an arbitrary amount. A percentage (representing 1%) is 1 in 100. So 100% represents the whole and 200% represents double the amount.

For example, 1 percent of 1,000 chickens is 1/100 of 1,000 or 10 chickens. 20% of the crowd is 20/100 1,000 or 200.

For the given case:

Original cost of each game = $30.50

75% of $30.50

(75/100) × 30.50

= $22.875

The cost of second game = 30.50 - 22.875

= $7.625

Since, 4 games are bought at once; this means 2 set of games with one on original price and another on discount price each.

Total cost of four games:

2 games at original price = 2 × 30.5

= $61

2 games at discount price = 2 × 7.625

= $15.25

Total = $61 + $15.25

= $76.25

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Answer: 2/9 = 0.22

Step-by-step explanation: This is rounded to the nearest hundredth which is in the 2nd place after the decimal point.

Hazel's new balance in the account is $1197

From the question, we have the following parameters that can be used in our computation:

Previous balance = $876.21.

$2.39 in interest,

$616.46 in deposits,

$298.06 in withdrawals

Her new balance can be calculated using

New balance = Previous balance + interest + deposits - withdrawals

Substitute the known values in the above equation, so, we have the following representation

New balance = 876.21 + 2.39 + 616.46 - 298.06

Evaluate

New balance = 1197

Hence, the new balance is $1197

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Answer:

90%

Step-by-step explanation:

63 of 70 can be written as:

63/70

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

63/70 × 100/100 = (63 × 100/70) × 1/100 = 90/100

Therefore, the answer is 90%

If you are using a calculator, simply enter 63÷70×100 which will give you 90 as the answer.

The conclusion of the hypothesis test is;

B: Reject H₀. At the 10% significance level, the data provides sufficient evidence to conclude that the mean time is less than 9 minutes.

We are given;

Null Hypothesis; H₀: μ = 9;

Alternative Hypothesis; Hₐ: μ < 9

Significance level; α = 0.1

The critical value; z_0.1 = 1.28

Test statistic; z = -4.5

Now, the rejection rule here is that if the test statistic is below the critical value, we reject the null hypothesis at the significance level.

In this case, the the test statistic is less than the critical value and as such we reject the null hypothesis and conclude that the data provides sufficient evidence to conclude that the mean time is less than 9 minutes

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The largest value of these integers is 68

We are given that the average of 5 positive integers is 60

Let the five numbers be [tex]x_{1}, x_{2}, x_{3}, x_{4}, x_{5}[/tex]

Therefore,

[tex]\frac{x_{1}+ x_{2}+ x_{3}+ x_{4}+ x_{5}}{5} = 60[/tex]

[tex]{x_{1}+ x_{2}+ x_{3}+ x_{4}+ x_{5}} = (60)(5)[/tex]

[tex]{x_{1}+ x_{2}+ x_{3}+ x_{4}+ x_{5}} = 300[/tex]

Now, let the first (smallest) number be [tex]x[/tex]

Therefore, the last (largest) number will be equal to [tex]x + 10[/tex]

To maximise a number in the sum equation, we'll have to minimise all the other numbers.

Therefore, let it be

[tex]x + x + x + x + (x + 10) = 300[/tex]

[tex]5x + 10 = 300[/tex]

[tex]5x = 290[/tex]

Therefore, [tex]x = 58[/tex]

Now, we took the largest number as [tex](x + 10)[/tex]

Therefore, the largest number is (58 + 10)

The correct answer is 68

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Answer:

C) An exponential model is suitable because the scatterplot of log(weeks) against log(stock price) shows a curved relationship.

Step-by-step explanation:

Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.

a) To find the type I error probability, we need to find the probability of rejecting the null hypothesis (H0) when it is actually true. In this case,

Since the foam height is approximately normally distributed with a standard deviation of 20 millimeters and we are taking a sample of size n = 10, the standard error of the mean is:

20 : [tex]\sqrt{10}[/tex] = 6.3 millimeters.

This means that the mean of the sampling distribution of the mean is approximately normally distributed with a mean of 175 millimeters and a standard deviation of 6.3 millimeters.

To find the probability of rejecting the null hypothesis when it is actually true, we can use a z-score.

In this case, the z-score for a value of 185 millimeters is:

(185-175)/6.3 = 1.6

We can use a z-table or a calculator to find the probability of getting a value greater than 1.6 standard deviations above the mean in a normal distribution. This probability is equal to 1 - the probability of getting a value less than or equal to 1.6 standard deviations above the mean, which is:

1 - 0.9495 = 0.0505.

Therefore, the type I error probability, or the probability of rejecting the null hypothesis when it is actually true, is 0.0505 if the critical region is x > 185.

b) To find the boundary point of the acceptance region if alpha = 0.05, we need to find the critical value that corresponds to a type I error probability of 0.05.

To find the critical value, we can use the z-score formula:

z = (x - mean) / standard deviation

We can rearrange this formula to solve for x:

x = z * standard deviation + mean

Since we want the probability of getting a sample mean greater than x to be 0.05, we can use a z-table or a calculator to find the z-score that corresponds to a probability of 0.05 in a normal distribution. This z-score is approximately 1.645.

Substituting this value into the formula above, we get:

x = 1.645 * 6.3 + 175 = 185.095

Therefore, the boundary point of the acceptance region if alpha = 0.05 is approximately 185.095 millimeters.

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No such c exist from 1 and hence mean value theorem fails, an example is given below.

Consider f(x)=[x] on [-1,1]

Then, f is not differentiable on x=0

Note that,

f'(x)=1  for x>0 and f'(x)=-1 for x<0

The Mean Value Theorem states that if a feature f is non-stop at the closed interval [a,b] and differentiable at the open interval (a,b), then there exists a factor c withinside the interval (a,b) such that f'(c) is same to the feature's common price of extrade over [a,b].

According to near value theorem we need,

a c (-1,1).

f'(c)= f(1)-f(-1)/1-(-1)

=|1|-|-1|/2

=1-1/2=0

i.e., f'(c)=0

While, no such c exist from 1 and hence mean value theorem fails.

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The given matrix has no solution.

What is the system of equations?

system of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns. Even then a solution is not guaranteed.

According to the question, the matrix is:

[tex]\left[\begin{array}{ccc}1&-5&-4\\0&0&7\\ \end{array}\right][/tex]

The linear equation will be:

x - 5y = -4

and

0x + 0y = 7

i.e,

   0 = 7       (Not possible)

Hence, the above given matrix has no solution.

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The 3-year Weighted Moving Average (WMA) for predicting the amount of sports equipment sales in 2022 is 1.7.

A Weighted Moving Average gives more weight to recent data and less weight to historical data. This is accomplished by multiplying the price of each bar by a weighting factor. WMA will track prices more precisely than a related Simple Moving Average due to its unique formula. A Weighted Moving Average (WMA) is a sort of moving average that prioritizes recent data over historical data. A moving average is a technical indicator that displays how the price has moved on average over a given time period.

Here,

weights=0.5, 0.3, and 0.2

(0.5×1+0.3×2+0.2×3) / (0.5+0.3+0.2) = 1.7

The 3-year Weighted Moving Average (WMA) to predict the number of sports equipment that will be sold in 2022 is 1.7.

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On solving the provided question we can say that he probability of getting the following result using the binomial probability formula and the normal curve approximation is P(4, 16, 1/2) = 0.0280.

Probability is the possibility or chance that something will happen. Probability = how many different paths there are to success/the total number of events that might occur. A coin flip, for instance, has a 50% chance of coming up heads since there is only one method to acquire a head and there are a total of two possible outcomes (a head or tail). P(heads) = 1/2 is the formula.

P(4,16,1/2) = C(16,4)(1/2) 4(1 - 1/2)16 - 4 = C(16,4)(1/2)16 = 0.02777;

by help of table - P(4, 16, 1/2) = 0.0280

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DB will appear at outputs A, and B.

Step 1

D flip flop stands for a delay flip flop that produces output that is identical to input after a brief delay. The flip flop's input and next state are equal.

Z is an output, and x and x inputs.

x'y + xA = DA= A*

B* = x'B + xA

z=A (output is independent of input) (output is independent of input)

The next states are A(t+1) and B(t+1). We must provide the next state value to D of the D flip flop in order to obtain the next states A(t+1), and B(t+1) for A, B(present state). So the sequential circuit will be:

Step 2

To get the next state as A(t+1)= x’A + xA, B(t+1)= x’B + xA, we have to give them to DA, DB of D flip flop because for D flip flop whatever is given to DA, DB will appear at output A, B.

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Answer: 7

Step-by-step explanation: cause I took the quiz…

The value of s for the given right angle triangle by Pythagoras' theorem will be 17.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

As per the given triangle, ABD is a right-angle triangle thus to Pythagora's theorem,

s² = 15² + 8²

s = 17

Hence "According to Pythagoras' Theorem, the value of s for the given right angle triangle is 17.".

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Answer: Radius or Diameter

Step-by-step explanation: The formula for circumference is diameter times pi. Since radius is half of diameter, you could still easily find the circumference. You could also find it with area, but that involves multiple formulas and a lot of math. I hope this helped :)

Answer:

Step-by-step explanation:

You want to know the least-cost path of a pipeline from 3 km offshore to 4 km east of the closest point on shore. The cost of pipe in the water is $0.5M/km, and onshore is $0.3M/km.

The solution in the general case for this kind of question is that the sine of the angle between the route directly to shore and the least-cost route is the ratio of the onshore cost to the in-water cost.

  sin(α) = (0.3M/km)/(0.5M/km) = 3/5

The distance from the closest point onshore (E) to the least-cost onshore point is the product of the distance from shore and the tangent of this angle:

  distance downshore = (3 km)·tan(arccos(3/5)) = 2.25 km

Since the refinery is 4 km downshore, this point is 1.75 km from the refinery.

The pipe should follow a direct path underwater from the well to a point 1.75 km west of the refinery, then downshore the remaining 1.75 km to the refinery.

If x represents the distance from the refinery to the point where the pipeline comes ashore, the cost of the route in millions will be ...

  c = 0.5√(3² +(4-x)²) +0.3x

where the square root function is calculating the underwater length of the pipeline using the Pythagorean theorem.

This cost function will be minimized when its derivative with respect to x is zero.

  c' = 0.5(1/2)(2x -8)/√(x² -8x +25) +0.3 = 0

  0 = 0.5(x -4) +0.3√(x² -8x +25) . . . . . . numerator of the combined terms

  4 -x = 0.6√(x² -8x +25) . . . . multiply by 2, add 4-x

  16 -8x +x² = 0.36x² -2.88x +9 . . . . . . square both sides

  0.64x² -5.12x +7 = 0 . . . . . subtract the right side

  x = (5.12 -√(5.12² -4(0.64)(7)))/(2(0.64)) = 2.24/1.28 = 1.75

The route with lowest cost comes ashore 1.75 km from the refinery.

__

Additional comment

The cost of the pipeline will be ...

  c = 0.5√(9 +(4-1.75)²) +0.3(1.75) = 0.5√14.0625 +0.525

  c = 2.4 . . . . million dollars

The attached graph shows the cost function has a minimum of 2.4M at a distance of 1.75 km from the refinery. The cost is only 2.5M if the pipe runs directly from the well to the refinery (x=0).

The simplified form of the given expression is [x² - 5x -24]/[x² + 8x -9].

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

Given expression is

(x-8)(x+3)/(x+9)(x-1)

Now applying the formula (x - a)(x + b) = x² -(a - b)x -ab in the numerator:

= [x² - (8 - 3)x -8×3]/(x+9)(x-1)

= [x² - 5x -24]/(x+9)(x-1)

Again applying the formula (x - a)(x + b) = x² -(a - b)x - ab in the denominator:

= [x² - 5x -24]/[x² - (1 - 9)x -9×1]

= [x² - 5x -24]/[x² + 8x -9]

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x be the distance (in miles) between point p and where the boat lands on the lakeshore.x = (7 - 3)/(3/4) = 4.5 miles.The boat should be landed 4.5 miles down the shore from point p.

The woman needs to get to a town 7 miles down the shore from point P. She can row the boat 3 miles per hour, and walk 4 miles per hour. The boat needs to be landed 4.5 miles down the shore from point P so she can get to the town in the least time. To figure out this distance, we subtract the 3 miles between the island and point P from the 7 miles between the town and point P. This gives us 4 miles. We then divide 4 miles by the ratio of her rowing rate (3) to her walking rate (4) to get 4.5 miles. Therefore, the boat should be landed 4.5 miles down the shore from point P.

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Answer:

Area = Length * Width

Area = 5 units * 3 units

Area = 15 units²

(see attachment picture for the graph)

Step-by-step explanation:

Answer: 15 sq units

Step-by-step explanation:

1. graph it out, this will help visually.

2. find the distance/difference between the y's of (3,1) and (3, -2) to find the width, or (-2, -2) and (-2, 1). it is 3.

3. find the distance between the x's of (3,1) and (-2,1), or (3, -2) and (-2, -2). the distance is 5.

4. multiply the lengths together to find the area. :)

Large sample significance tests for a single proportion are based on the  statistic binomial. the correct option is A

Significance test can be defined as tests for statistical significance indicate whether observed differences between assessment results occur because of sampling error. Significance tests give a formal process for using sample data to evaluate the likelihood of some claim about a population value.

Therefore a Large sample significance tests for a single proportion are based on the  statistic binomial.

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