A local restaurant recently began to offer an eat-in pizza promotion for their famous double-decker pizza. When priced at $17.99/person, the promotion attracted 112 customers per day on average. When they raised the price to $19.99/person they attracted an average of only 96 customers per day.
What price should the promotion be set at to generate the maximum daily profit?

Answer:

f(x) = -x -11

    = -9-11 = -20

f(x) = -x-11

    = -6-11= -17

Step-by-step explanation:

The number described in the question, whose stated percentage difference is 36, is 80.

Let us represent the number as x. So, the increased number will be -

Increased number = x + 20%×x

Simplify percentage

Increases number = x + 0.2x

Add the digits

Increased number = 1.2x

Similarly, decreased number = x - 25%×x

Converting percentage

Decreased number = x - 0.25x

Subtract the digits

Decreased number = 0.75x

Representing the difference

1.2x - 0.75x = 36

Subtract

0.45x = 36

Divide

x = 80

Hence, the number is 80.

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Answer: Slope: 1/3

Y-intercept: 0 (since there is no constant term)

The probability that it is yellow is 1/4.

What is probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: A bag with 8 marbles has 2 yellow marbles, 3 red marbles, and 3 blue marbles. A marble is chosen from the bag at random.

We have to find the probability that it is yellow.

the probability that it is yellow:

= 2/8

= 1/4

Hence, the probability that it is yellow is 1/4.

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To convert the score of 14 to a z-score, we use the formula:

z = (x - μ) / σ

where x is the raw score, μ is the population mean, and σ is the population standard deviation.

Substituting the given values, we get:

z = (14 - 20) / 2.8

z = -2.14

The z-score of -2.14 indicates that the score of 14 is quite far from the mean of 20, which makes it an unusual score. To determine how unusual it is, we can compare the z-score to the standard normal distribution table.

The table shows that a z-score of -2.14 corresponds to a probability of approximately 0.016. This means that only about 1.6% of contestants would receive a score of 14 or lower in this cooking contest. Therefore, we can conclude that the score of 14 is unusual.

The 43rd term of the sequence is 149.

Arithmetic progression is a sequence of numbers in which the difference between any two consecutive numbers is a constant value. The constant value is called a common difference.

We can see that the common difference between consecutive terms in the sequence is 4. So, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where a1 is the first term, d is the common difference, and n is the term number we want to find.

To find the 43rd term, we plug in the values:

a1 = -19, d = 4, n = 43

an = -19 + (43 - 1)4

an = -19 + 42(4)

an = -19 + 168

an = 149

Therefore, the 43rd term of the sequence is 149.

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a) The anomalous result in the table is the Durablast battery in the second trial, which recorded a time taken of 768 seconds.

b) The mean averages for each brand of battery are 955.33, 852 and 908 seconds.

c) the amount of charge stored by each brand of battery is 1098.6 coulombs, 1065 coulombs and 1089.6 coulombs.

d) The results of this experiment can be presented in a table format, showing the current flowing, the mean time taken, and the amount of charge stored for each brand of battery.

It is an unexpected or unusual outcome that does not agree with the expected or accepted outcome. It may be a result of a mistake, an anomaly in the data, or a misinterpretation of the data.

a) The anomalous result in the table is the Durablast battery in the second trial, which recorded a time taken of 768 seconds.

b) The mean averages for each brand of battery are:

Longalast: 955.33 seconds

Durablast: 852 seconds

Morelife: 908 seconds

c) The amount of charge stored by each brand of battery can be calculated by multiplying the current flowing into the toothbrush (amps) by the mean time taken (seconds) for each battery:

Longalast: 1.15 amps x 955.33 seconds = 1098.6 coulombs

Durablast: 1.25 amps x 852 seconds = 1065 coulombs

Morelife: 1.20 amps x 908 seconds = 1089.6 coulombs

d) The results of this experiment can be presented in a table format, showing the current flowing, the mean time taken, and the amount of charge stored for each brand of battery. This would allow the reader to easily compare the performance of each battery, as well as to identify any anomalous results.

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The probability of not getting a clay pot or a cactus when randomly picking a plant and a pot from a selection of 4 plants and 4 pots is 0.75 or 75%.

There are a total of 4 x 4 = 16 possible outcomes when randomly picking a plant and a pot. Out of these, we need to count the number of outcomes where we don't get a clay pot or a cactus.

Let's start by counting the number of outcomes where we get a clay pot or a cactus. There are 4 possible outcomes for the plant (cactus or one of the three other plants) and 1 possible outcome for the pot (clay pot). So there are 4 x 1 = 4 outcomes where we get a cactus or a clay pot.

Therefore, the number of outcomes where we don't get a cactus or a clay pot is:

16 - 4 = 12

So the probability of getting a plant and a pot where neither the plant is a cactus nor the pot is a clay pot is:

P = number of outcomes where we don't get a cactus or a clay pot / total number of outcomes

= 12 / 16

= 0.75

Therefore, the probability of not getting a clay pot or a cactus is 0.75 or 75%.

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Answer:

It would be true

Step-by-step explanation:

A linear pair is two angles that are adjacent and whose non-common sides form a straight line. If two angles are a linear pair, then it would be supplementary.

There were approximately 304,657,600 Americans in July 2009.

To find out how many Americans were there in July 2009, we'll use the given data in the student question:
Initial population (July 2008): 302,000,000 people
Growth rate (2008): 0.88%
Step 1: Convert the growth rate percentage to a decimal.
0.88% = 0.0088
Step 2: Calculate the population increase for 2009.
Increase = Initial population × Growth rate
Increase = 302,000,000 × 0.0088
Increase ≈ 2,657,600 people
Step 3: Add the population increase to the initial population to get the population in July 2009.
Population (July 2009) = Initial population + Increase
Population (July 2009) ≈ 302,000,000 + 2,657,600
Population (July 2009) ≈ 304,657,600 people.

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The measure of the exterior angle at vertex A is equal to the sum of the measures of angles BAC and BCA, which is angle A + angle C.

An exterior angle is an angle that forms a linear pair with an interior angle of a polygon. It is formed by extending one of the sides of the polygon. In other words, it is the angle formed between a side of a polygon and the extension of an adjacent side.

Based on the problem description, we can see that the exterior angle at vertex A is equal to the sum of the measures of angles BAC and BCA. Therefore, we need to find the measure of the exterior angle at vertex A.

We know that the sum of the measures of the angles in a triangle is 180 degrees. So, we can find the measure of angle BAC by subtracting the measures of angles BCA and ABC from 180 degrees:

angle BAC = 180 - angle BCA - angle ABC

We can find the measure of angle ABC by subtracting the measure of angle A from 180 degrees:

angle ABC = 180 - angle A

Similarly, we can find the measure of angle BCA by subtracting the measure of angle C from 180 degrees:

angle BCA = 180 - angle C

Substituting these expressions into the equation for angle BAC, we get:

angle BAC = 180 - (180 - angle A) - (180 - angle C)

         = angle A + angle C

Therefore, the measure of the exterior angle at vertex A is equal to the sum of the measures of angles BAC and BCA, which is angle A + angle C.

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Answer:

25

Step-by-step explanation:

Formula 1/2(B1+B2)H

1/2(10)5

1/2 x 10=5

5 x 5 =25

Answer:

Therefore, P(X = 2) ≈ 0.1247 - 0.0337 ≈ 0.091, or about 9.1%.

Step-by-step explanation:

We can use the Poisson approximation to the binomial distribution when n (the number of trials) is large and p (the probability of success) is small. In this case, n = 100 and p = 0.05, so np = 5, which is not too small. However, we can still use the approximation as long as we adjust for continuity, by adding and subtracting 0.5 from the number of successes we're interested in.

Let X be the number of books with defective bindings out of 100. We want to find the probability that X = 2. Using the Poisson approximation, we have:

λ = np = 5

P(X = 2) ≈ P(1.5 < Y < 2.5), where Y is a Poisson random variable with parameter λ

To find this probability, we can use the cumulative distribution function (CDF) of Y:

P(X = 2) ≈ P(1.5 < Y < 2.5) = F(2.5) - F(1.5), where F(x) is the CDF of Y evaluated at x

The CDF of a Poisson distribution with parameter λ is given by:

F(x) = e^(-λ) * Σ(λ^k / k!, k = 0 to floor(x))

where floor (x) is the greatest integer less than or equal to x. Using this formula, we can calculate:

F(1.5) = e^(-5) * Σ(5^k / k!, k = 0 to 1) ≈ 0.0337

F(2.5) = e^(-5) * Σ(5^k / k!, k = 0 to 2) ≈ 0.1247

Therefore, P(X = 2) ≈ 0.1247 - 0.0337 ≈ 0.091, or about 9.1%.

The probability that 2 of the 100 books bound by this bindery will have defective bindings using the poisson approximation to the binomial distribution is  0.0842.

Since the number of books bound, n = 100, is large and the probability of defective bindings, p = 0.05, is small, we can use the Poisson approximation to the binomial distribution.

The mean, µ, of the Poisson distribution is µ = np = 100 x 0.05 = 5.

The probability of 2 defective bindings can be calculated using the Poisson probability formula:

P(X = 2) = (e^-µ) * (µ^x) / x!

= (e^-5) * (5^2) / 2!

= 0.0842 (rounded to four decimal places)

Using the Poisson approximation to the binomial distribution, the likelihood that 2 of the 100 volumes bound by this bindery will have faulty bindings is roughly 0.0842.

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Since the mid 1950s, both men and women in the U.S. have experienced an increase in the proportion of the population never married. The correct answer is "increase".

This trend has been attributed to various factors such as the rise of individualism, changing gender roles, economic factors, and the decline of traditional social norms. In 1960, only 9% of women and 6% of men aged 25-34 had never been married, while in 2020, these numbers increased to 33% for women and 23% for men.

Therefore, it is evident that the proportion of the U.S. population never married has increased steadily over the past few decades

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The missing numbers to fill the question marks are 2.1 and 7.11

To solve the question, we need to look for a pattern or relationship between the given numbers. One way to approach this is to consider the decimal representation of each number.

If we look at the first number, 0.13, we can see that it has 2 digits after the decimal point.

The second number, 6.02, has 2 digits before the decimal point.

So, it's possible that the missing numbers also follow a pattern where one number has 2 digits before the decimal point, and the other has n digits after the decimal point.

Using the decimal points, one possible pattern is 2, 2.1, 0.13, 6.02, 7.11

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Answer:

C) x² + y² = 25

Step-by-step explanation:

the center is (0, 0).

so, the generic circle equation

(x−h)² + (y−k)² = r². The center is (h, k) and the radius is r units.

for (h, k) = (0, 0) this gives us the equation above.

and r we can easily see as the distance from the center to one of the points on the circle arc. which is 5, as the coordinates tell us.

Answer:

[tex]6.45ft^{2}[/tex]

Step-by-step explanation:

Answer: a ≤ 2

Step-by-step explanation:

How to write an inequality statement:

Step 1: Write the two values being compared in the problem.

Step 2: Determine whether the first value is larger or smaller than the second value.

Step 3: Express the inequality with the right symbols:

≤ = less than or equal to

≥ = greater than or equal to

Therefore, the answer would be a≤2.

Hope this helped!

The average speed of a falling object during the first 3 seconds of its fall is h(3)-h(0)/3.

The model of the motion of the body is given by, and the function of the motion of the body is given by h(t) = 300 - 16t².

The speed of object after 3 seconds is given by . The falling speed of object during the first 3 seconds of falling is calculated as follows, v = dh(t)/dt = -32t.

So now the average speed of the movement is calculated as follows,

v = h(3)-h(0)/3.

Option d is therefore the correct option.

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Complete question - the height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function . what is the average rate at which the object falls during the first 3 seconds?

A.) h(3) – h(0)

B.) h(3/3)-h(0/3)

C.) h(3)/3

D.) (h(3)-h(0))/3

Answer: To find how many free throw shots Shawn makes out of 300 shots, we can first find how many he makes out of 100 shots, and then multiply by 3 to get the number of shots he makes out of 300.

If he makes 15 1/5 shots out of 100, we can convert this to a decimal by dividing 15 by 100 and adding 1/5, which is the same as adding 0.2. This gives:

15/100 + 1/5 = 0.15 + 0.2 = 0.35

So, on average, Shawn makes 35% of the free throw shots he attempts.

To find how many shots he makes out of 300, we can multiply this percentage by 300:

0.35 x 300 = 105

Therefore, Shawn makes about 105 free throw shots out of 300 shots.

Step-by-step explanation:

The volume of the cylinder is 18.0864 cubic cm and the surface area of the cylinder is 39.1872 square cm.

What is a cylinder?

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry.

We are given that the radius of the cylinder is 1.2 cm and the height is 4 cm.

So,

⇒ Volume = π[tex]r^{2}[/tex]h

⇒ Volume = π * [tex](1.2)^{2}[/tex] * 4

⇒ Volume = 3.14 * 5.76

⇒ Volume = 18.0864 cubic cm

Similarly,

⇒ Total surface area = 2πrh + 2π[tex]r^{2}[/tex]

⇒ Total surface area = 2π * 1.2 * 4 + 2π[tex](1.2)^{2}[/tex]

⇒ Total surface area = 2π * 4.8 + 2π * 1.44

⇒ Total surface area = 2π * (4.8 + 1.44)

⇒ Total surface area = 2 * 3.14 * 6.24

⇒ Total surface area = 39.1872 square cm

Hence, the  volume of the cylinder is 18.0864 cubic cm and the surface area of the cylinder is 39.1872 square cm.

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Thus, the value of y for the given direct variation is found as y = 34.96 (Rounded up to two decimal places).

When two quantities, including such time and distance or hours and compensation, change directly, they do so at a predictable rate.

The constant of variation is another name for the constant rate of increase or decline. We will examine three different methods of showing direct variation in this lesson: an equation, a table, and just a graph.

For the given question:

y varies directly as the square root of x.

y ∝ √x

y = k√x  

Here, k is the constant of proportionality

Now,

y=43 when x=289 .

43 = k√289

k = 43/√289

k = 2.53

Now, y when  x=191.

y = k√x  

y = 2.53√191

y = 34.96

Thus, the value of y for the given direct variation is found as y = 34.96 (Rounded up to two decimal places).

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Answer: -32.00

Step-by-step explanation:

Answer:

A) -32.00

Step-by-step explanation:

-32.00 would be more debt than -25

Helping in the name of Jesus.

The table of values when completed using y = 10x is a linear function

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

The incomplete table

When completed, we have

Levels    Toothpicks

1                     10

2                   20

3                   30

4                   40

5                   50

6                   60

7                   70

8                   80

The means that

Toothpicks = 10 * Level

So, we have the equation to be

y = 10x

This is a linear function

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The work done pulling the bucket to the top of the well of depth 76 feet is equals to the 346.56 pounds/ feet.

Work is the product of force and distance, W=F×d. A Riemann Sum is a collection of rectangles used to approximate the area underneath a curve. In this case the "height" of the rectangle will be the force being exerted, and the "width" of the rectangle will be the amount of distance it moved. The work done by the force on the object can be expressed as an integral, [tex]W = \int_{a}^{b}F(x)dx[/tex]

Weigh of bucket = 5 pounds

A rope with negligible weight is used to draw water from a well. The depth of well = 76 feet.

Initially, Water in bucket = 37 pounds

Rate of pulling rope = 1.8 feet per second

Rate of water leaking in bucket = 0.25 pounds per second

Changing rate of leaking from pounds/sec to pounds/ feet : Q = 0.25/1.8 pounds/feet

= 0.139 pounds per feet

Thus, the rate of water leak from bucket hole is 0.12 pounds per feet. Let 'x' be height of bucket in feet from bottom of well. So, the total water leaked from hole = 0.12x

After leakage Remaining water in bucket = (37 - 0.12x )pounds

Also, add the weigh of buket in above expression. The limits of integration varies with depth of well that is 0 to 76 feet. Using Riemann sum method, work done pulling the bucket to the top of the well, [tex]W = \int_{0}^{76} ( 37 - 0.12x + 5 ) dx [/tex]

=>[tex]W = \int_{0}^{76} ( 42 - 0.12x ) dx [/tex]

=> [tex]W = [0 - \frac{0.12x²}{2}]_{0}^{76} \\ [/tex]

=> [tex]W = \frac{0.12×76²}{2} - 0 [/tex]

=> W = 0.12× 38×76 = 346.56 pounds/ feet. Hence required work done is 346.56 pounds/ feet.

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The solution to the inequality 32 ≤ −5z − 32 is z ≥ -12.8.

To solve for z in the inequality 32 ≤ -5z - 32, we first add 32 to both sides:

32 + 32 ≤ -5z

64 ≤ -5z

Then, we can divide both sides by -5, but we need to reverse the inequality since we are dividing by a negative number:

-5z ≤ 64

z ≥ -64/5

z ≥ -12.8

Therefore, the solution to the inequality is z ≥ -12.8.

Option (d) is correct: z ≥ -12.8.

The complete question is:

Solve 32 ≤ −5z − 32.

Answer choices:

a) z ≤ 0

b) z ≥ 0

c) z ≤ −12.8

d) z ≥ −12.8

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The relationship of those who attend religious services regularly are less likely to consume alcohol regularly.

Yes, there can be a relationship between attendance at religious services and alcohol consumption. In the given random sample of 1000 adults, both their attendance at religious services and daily alcohol consumption were recorded.

To analyze the relationship, you can follow these steps:

1. Organize the data: Create a contingency table that displays the frequency of each combination of attendance at religious services and alcohol consumption.

2. Calculate percentages: Determine the percentage of adults who attend religious services and drink alcohol daily, as well as the percentages for the other categories (e.g., attend services and don't drink daily, don't attend services and drink daily, etc.).

3. Identify trends or patterns: Compare the percentages to see if there is a relationship between attendance at religious services and daily alcohol consumption.

For example,

If the percentage of adults who attend religious services and drink daily is significantly lower than the percentage of those who don't attend services and drink daily, this suggests a relationship.

4. Statistical testing: Perform a chi-square test to determine if the observed relationship is statistically significant.

This test compares the observed frequencies in the contingency table to the frequencies that would be expected if there was no relationship between attendance at religious services and alcohol consumption.

5. Interpret the results: If the chi-square test shows that the relationship is statistically significant, this supports the hypothesis that there is a relationship between attendance at religious services and alcohol consumption in the sample of 1000 adults.

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The interval over which the function f(x) increase is {∞, 1}.

The interval over which the function f(x) decrease is {1, ∞}.

The interval over which the function g(x) increase is {3, ∞}.

The interval over which the function g(x) decrease is {∞, 3}.

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph of f(x), we can logically deduce that the function f(x) increases over the interval {∞, 1}. On the other hand, the function f(x) decreases over the interval {1, ∞}.

By critically observing the graph of g(x), we can logically deduce that the function f(x) increases over the interval {3, ∞}. On the other hand, the function f(x) decreases over the interval {∞, 3}.

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To check the normality of the sampling distribution for a one-sample z confidence interval for proportions, the sample size should be large (typically n > 30), and the number of successes and failures in the sample should both be at least 10.

To check for normality of the sampling distribution for a one-sample z confidence interval for proportions, we need to ensure that the following conditions are met:

Large sample size: The sample size should be sufficiently large (typically n > 30). This is because the central limit theorem states that for large enough sample sizes, the sampling distribution of the sample proportion will be approximately normal, regardless of the underlying distribution of the population.

Success-Failure Condition: The number of successes (np) and failures (n(1-p)) in the sample should both be at least 10. This condition ensures that the binomial distribution of the sample proportion is approximately normal.

If these conditions are met, then we can assume that the sampling distribution of the sample proportion is approximately normal, and we can proceed to construct a one-sample z confidence interval for proportions.

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