The number of pizzas consumed per month by university students is normally distributed with a mean of 12 and a standard deviation of 3. A. What proportion of students consume more than 13 pizzas per month? Probability = = B. What is the probability that in a random sample of size 10, a total of more than 110 pizzas are consumed? Probability = Note: You can earn partial credit on this problem.

The area to the right of x in the normal distribution is 0.229, or 22.9% when expressed as a percentage. This means that the probability of observing a value greater than x is 0.229.

In a normal distribution, the total area under the curve represents the probability of all possible outcomes occurring, and it is equal to 1. When we refer to the area to the left or right of a specific value, we are essentially calculating the cumulative probability up to that value.

Given that the area to the left of a certain value, x, is 0.771, we want to determine the area to the right of x. This can be done by subtracting the area to the left of x from 1.

To explain this further, let's consider the standard normal distribution, which has a mean of 0 and a standard deviation of 1. The cumulative distribution function (CDF) of the standard normal distribution gives us the probability of observing a value less than or equal to a given value.

In this case, the area to the left of x represents the cumulative probability up to x. So, if the area to the left of x is 0.771, it means that the probability of observing a value less than or equal to x is 0.771.

Now, to find the area to the right of x, we can subtract the area to the left from 1. This is because the total area under the curve is equal to 1, so the remaining area to the right of x can be calculated by taking the complement of the area to the left.

Area to the right of x = 1 - Area to the left of x

Area to the right of x = 1 - 0.771

Area to the right of x = 0.229

Therefore, the area to the right of x in the normal distribution is 0.229, or 22.9% when expressed as a percentage. This means that the probability of observing a value greater than x is 0.229.

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Answer:

x=127

Step-by-step explanation:

total sum of all angle of triangle is 180 degree

Now,

taking angle A let interior angle be Y

taking angle C let interior angle be Z

Again, In angle A

the sum of interior angle and exterior angle is 180 degree being staright line

Or, y+(x+5)=180

or,x+y=180-5

or, x+y=175

or,y=175-x --------eqn 1

In angle C

the sum of interior angle and exterior angle is 180 degree being staright line

or, x+z=180

or, z=180-x ----------eqn2

Again, In triangle ABC

total sum of all angle of triangle is 180 degree.

Angle A+ Angle B + AngleC=180

Or, y+79+z=180 -------eqn3

putting the value of eqn-1 and eqn-2 in eqn-3

Or, 175-x+79+180-x=180

Or, 431-180= 2x

Or, 254÷2=x

hence X= 127 degree

Answer:

c127

Step-by-step explanation:

Answer:

$20.25 Dollars

Step-by-step explanation:

keep in mind:

1 pint = 2cups

1 quart = 4cups

according to the story, she buys 2 pints of blue(4 cups), 3 cups of green(3cups),

1 1/2 quarts (6cups), and 1/2 cups(I am assuming cups because it wasn't stated)

so now we just add up all the cups using the measurements I stated at the beginning.

13.5 cups is the amount she is buying, but we need to know the price, so we simply add $1.50 for every cup she bought!

1.50 x 13.5 = 20.25

So the answer is $20.25 Dollars

The influence of all these risks are explained below in the sequential manner.

The DREAD risk methodology is a quantitative approach for evaluating the risk posed by security vulnerabilities. This methodology assigns a numerical value to each vulnerability based on the likelihood of it being exploited and the potential impact of an exploit. The DREAD methodology is based on the following five factors:

Damage: The extent of harm that an attack could cause.

Reproducibility: The ease with which an attack can be replicated.

Exploitability: The level of effort required to launch an attack.

Affected users: The number of people who could be impacted by the attack.

Discoverability: The ease with which the threat can be discovered.

To calculate the risk value, the DREAD formula multiplies the sum of the damage and affected users by the sum of the reproducibility, exploitability, and discoverability. The resulting risk value is then compared to predefined thresholds to determine the risk level.

This methodology provides a systematic and objective way of evaluating risk, which can help organizations prioritize their security efforts and make informed decisions about which vulnerabilities to address first. However, like any methodology, the DREAD approach has its limitations, and it is important to consider other factors, such as the likelihood of an attack, when evaluating risk.

Therefore, The influence of all these risks is explained above in a sequential manner.

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Answer:

The total number of hardwood mulch is 48 and pine bark mulch is 128 and this can be determine by forming the linear equation in two variables.

Given :

A local boys club sold 176 bags of mulch and made a total of $520.

Sold two types of mulch : hardwood for $3.50 a bag and pine bark for $2.75 a bag.

Let the number of hardwood mulch be x and the number of pine bark mulch be y then the total number of mulch will be:

  --- (1)

And the total amount is given by the equation:

   ----  (2)

Substitute the value of y in equation (2).

y = 128

Now, put the value of y in equation (1).

x = 176 - 128

x = 48

So, the total number of hardwood mulch is 48 and pine bark mulch is 128

Step-by-step explanation:

The statement "The Gradient Vector Of F(X,Y)=Yx−2xy2 At (2,−1) Is ∇F(2,−1) Is Equal To <2−3,4>" is False.

The function is:

f(x,y) = yx - 2x(y^2)

To find the gradient vector ∇f(x,y), we need to take the partial derivatives of f with respect to x and y, and evaluate them at the point (2,-1).

∂f/∂x = y - 4xy

∂f/∂y = x - 4x^2y

Evaluating these at (2,-1), we get:

∂f/∂x(2,-1) = (-1) - 4(2)(-1) = 9

∂f/∂y(2,-1) = 2 - 4(2)^2(-1) = 4

So the gradient vector ∇f(2,-1) is <9,4>.

Therefore, the statement "The Gradient Vector Of F(X,Y)=Yx−2xy2 At (2,−1) Is ∇F(2,−1) Is Equal To <2−3,4>" is False.

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Answer:

1/3

Step-by-step explanation:

If you add all the n's, it would make 3n=1.  Divide both sides by 3 and get n=1/3

Answer:

0.333 or 1/3

Step-by-step explanation:

0.333*3=1

Answer:

$8

Step-by-step explanation:

Let x represent the amount of money he has to save each week.

We can use this to set up an equation:

\(7x=56\)

Now, we have to "isolate the variable". This means we must have a resulting equation of \(x=\text{something}\).

In this case, we can use the Division Property of Equality to divide both sides by 7:

\(\frac{7x}{7}=\frac{56}{7}\\x=8\)

Therefore he must say $8 each week for 7 weeks so that he can buy the guitar.

Part a)Given, utility function of the consumer as:U(x1, x2) = log(x1) + log(x2)X1 ≤ 0.5Let p2 = 1 and m = 1, and p1 is unknown. The consumer has a budget constraint as: p1x1 + p2x2 = m = 1Now we have to find the minimal p1 such that the consumer consumes x1 strictly less than 0.5.

We need to find the value of p1 such that the consumer spends the entire budget (m = 1) on the two goods, but purchases only less than 0.5 units of the first good. In other words, the consumer spends all his money on the two goods, but still cannot afford more than 0.5 units of good 1.

Mathematically we can represent this as:

p1x1 + p2x2 = 1......(1)Where, x1 < 0.5, p2 = 1 and m = 1

Substituting the given value of p2 in (1), we get:

p1x1 + x2 = 1x1 = (1 - x2) / p1Given, x1 < 0.5 => (1 - x2) / p1 < 0.5 => 1 - x2 < 0.5p1 => p1 > (1 - x2) / 0.5

Now we know, 0 < x2 < 1.So, we will maximize the expression (1 - x2) / 0.5 for x2 ∈ (0,1) which gives the minimum value of p1 such that x1 < 0.5.On differentiating the expression w.r.t x2, we get:d/dx2 [(1-x2)/0.5] = -1/0.5 = -2

Therefore, (1-x2) / 0.5 is maximum at x2 = 0.

Now, substituting the value of x2 = 0 in the above equation, we get:p1 > 1/0.5 = 2So, the minimal value of p1 is 2.Part b)Now, we have to show mathematically that whether the threshold on p1 found in Part a increases/decreases/stays the same when p2 increases.

That is, if p2 increases then the minimum value of p1 will increase/decrease/stay the same.Since p2 = 1, the consumer’s budget constraint is given by:

p1x1 + x2 = m = 1Suppose that p2 increases to p2′.

The consumer’s new budget constraint is:

p1x1 + p2′x2 = m = 1.

Now we will find the minimal p1 denoted by pi, such that the consumer purchases less than 0.5 units of good 1. This can be expressed as:

p1x1 + p2′x2 = 1Where, x1 < 0.5

The budget constraint is the same as that in Part a, except that p2 has been replaced by p2′. Now, using the same argument as in Part a, the minimum value of p1 is given by:

p1 > (1 - x2) / 0.5.

We need to maximize (1 - x2) / 0.5 w.r.t x2.

As discussed in Part a, this occurs when x2 = 0.Therefore, minimal value of p1 is:

pi > 1/0.5 = 2

This value of pi is independent of the value of p2′.

Hence, the threshold on p1 found in Part a stays the same when p2 increases.

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Answer:

(1,-1)

Step-by-step explanation:

Find the middle between the two points:

4 to -2=6, so the middle would be 3

4-3=1

-8 to 6=14, so the middle would be 7

-8+7=-1

Answer:

\(\displaystyle (1,-1)\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point G(4, -8)

Point H(-2, 6)

Step 2: Find Midpoint

Simply plug in your coordinates into the midpoint formula to find midpoint

Answer:

wait.

Step-by-step explanation:

what do u really mean by zombies

When dealing with the simultaneous occurrence of two events A and B, the probability can be determined by using the probability of one event and the conditional probability of the other event given that the first event has occurred. Both P(A) * P(B|A) and P(B) * P(A|B) are valid ways to calculate this probability.

The concept of probability is fundamental in various fields such as mathematics, statistics, and even in everyday life. The probability of the simultaneous occurrence of two events A and B is a critical concept in probability theory. According to the definition, the probability of A and B occurring at the same time is equal to the probability of A multiplied by the conditional probability of B given that A has occurred. This equation is also valid in the reverse case, where the probability of B and A occurring simultaneously is equal to the probability of B multiplied by the conditional probability of A given that B has occurred.

Understanding the relationship between the probability of two events and their conditional probabilities is essential in predicting the likelihood of these events happening together. In real-life situations, this concept can be used to determine the probability of two events such as the success of a product launch and the corresponding increase in sales. The probability of these two events occurring simultaneously can be predicted by analyzing the probability of the product launch's success and the conditional probability of sales increasing given that the product launch is successful.

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Shaquille has the highest typing speed of 45 WPM, making him the fastest typist among the four individuals. Therefore, the answer is d).

To determine the fastest typist among Ella, Harper, Owen, and Shaquille, we need to calculate their typing speeds in words per minute (WPM). Typing speed is calculated by dividing the number of words typed by the minutes spent typing.

For Ella, she typed 640 words in 16 minutes, resulting in a typing speed of 640/16 = 40 WPM.

For Harper, she typed 450 words in 15 minutes, resulting in a typing speed of 450/15 = 30 WPM.

For Owen, he typed 560 words in 14 minutes, resulting in a typing speed of 560/14 = 40 WPM.

For Shaquille, he typed 540 words in 12 minutes, resulting in a typing speed of 540/12 = 45 WPM.

Comparing the typing speeds, we find that Shaquille has the highest typing speed of 45 WPM, making him the fastest typist among the four individuals.

Therefore, the answer is d) Shaquille.

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According to the information in the table, who is the fastest typist?

Words Typed by Four Typists

Typist         Words Typed       Minutes Typing

Ella                   640                             16

Harper            450                             15

Owen               560                              14

Shaquille        540                             12

a) Ella

b) Harper

c) Owen

d) Shaquille

Based on the data in the table, Ella is the fastest typist because she has typed 640 words in 16 minutes.

According to the table given, Ella is the fastest typist with a typing speed of 40 words per minute.

She typed a total of 640 words in 16 minutes which is twice the number of words typed by Harper, who is the second fastest typist.

Harper has a typing speed of 30 words per minute and typed 450 words in 15 minutes.

Owen and Shaquille have typing speeds of 28 and 45 words per minute, respectively.

Owen typed 560 words in 14 minutes, whereas Shaquille typed 540 words in 12 minutes.

Therefore, Ella is the fastest typist among all the typists mentioned in the table and Shaquille is the fastest among Owen and Shaquille.

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The number of jars of jam that has to be sold in order to break even is 106,250.

The minimum sales price is $24.36.

The monthly profit is $5,097.12.

The price per customer is $205.34.

The ROI is 106.68%.

Breakeven quantity = fixed cost / price – variable cost per unit

$42500 / (1.2 - 0.8) = 106,250

Minimum price = (fixed cost / breakeven sales) + variable cost

($562,795.00 / 61,755) + $15.25 = $24.36

Profit = revenue - total cost

Revenue = 443 x 28.99 = $12,842.57

Total cost = $3692 + (9.15 x 443) = $7,745.45

Profit = $12,842.57 - $7,745.45 = $5097.12

Price = (profit +  total cost) / number of customers

Total cost = $2,345 + (16.90 x 45) = $3,105.50

($6,135.00 - 3105.50) / 45 = $205.34

ROI = (profit / cost of the investment) x 100

Cost = fixed cost + variable cost

$5,750 + (0.80 x 4175) = $9090

Profit = total revenue - cost

(4.5 x 4175) - 9090 = $9,697.50

ROI = $9,697.50 /  $9090 = 106.68%

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Answer:

72

Step-by-step explanation:

this number sentence will be represented as,

72 is 8 times as many as 9

The information shows that Larry is incorrect as a composite number is a positive integer that has at least one positive divisor.

It should be noted that composite numbers are those numbers that have more than two factors. Composite numbers have factors other than 1 and itself

Larry is incorrect. A composite number is a positive integer that has at least one positive divisor other than one and itself. For example, 4 is composite because it can be divided by 2 (and 1). However, a number's ones place simply refers to the digit in the units place and has no bearing on whether a number is prime or composite.

For example, the number 22 is composite because it is divisible by 2 and 11, but the number 12 is composite because it is divisible by 2,3,4 and 6.

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We have

As we can see in order to find the shaded area of the figure, we only need to calculate the area of a square.

the shaded area is 400 mm^2

Since the triangle is dilated, the sides of the original triangle are stretched. Since J'K' is the length of one side of the triangle after the dilation, we have that:

Then, the answer is 10.125

Answer:

c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

put 12.4* 20 and you get D

The produce a 95% confidence interval with a margin of error of 4% sample size of 451 the proportion of people eating breakfast is 75%.

The required sample size for a 95% confidence interval with a margin of error of 4% (0.04) and a proportion of 75%,

n = (Z² × p × (1-p)) / E²

where:

n = sample size

Z = Z-score corresponding to the desired confidence level (95% confidence level corresponds to a Z-score of approximately 1.96)

p = proportion of people eating breakfast (expressed as a decimal, so 75% is 0.75)

E = margin of error (0.04)

n = (1.9² × 0.75 × (1-0.75)) / 0.04²

n =(3.8416 × 0.75 × 0.25) / 0.0016

n = 0.7209 / 0.0016

n = 450.56

a fractional sample size, to round up to the nearest whole number.

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Answer: 17.888543819998

Step-by-step explanation:

Answer:

17.8885

Step-by-step explanation:

find the geometric mean between 16 and 20, we need to multiply the numbers and take the square root of the result. That is:

Geometric Mean = √(16 × 20)

Geometric Mean = √320

Geometric Mean ≈ 17.8885

Therefore, the geometric mean between 16 and 20 is approximately 17.8885.

Answer:

z^2 = -12y

or y = -(z^2/12)

Step-by-step explanation:

Answer:

z^2 = -12y

Step-by-step explanation:

Given the vertex at origin;

This is same as (0,0)

The focus (0,-3)

The general form is;

(z-h)^2 = 4p(y-k)

(h,k) is the vertex (0,0); so h = 0 and k = 0

The focus is given as;

(h,k + p)

so ;

k + p = -3

but k =0

so p = -3

Thus, the equation of the parabola is;

(z-0)^2 = 4(-3)(y-0)

z^2 = -12y

Answer:

4.0 atm

Step-by-step explanation:

it looks to be a proportional ratio so for every meter pressure increases by .1 atm so if you add .8 to 3.2 you get 4 atm

The vector PQ, which connects the points P(0,0) and Q(-5,-3), can be visualized as an arrow pointing from P to Q in the xy-coordinate system. The magnitude of vector PQ is √34 (approximately 5.83) .

To sketch the vector PQ, we start at the origin (point P) and move 5 units to the left along the x-axis and 3 units downward along the y-axis to reach point Q. This creates an arrow that represents the direction and magnitude of the vector. The arrow starts at P(0,0) and ends at Q(-5,-3).

To compute the magnitude of vector PQ, we can use the distance formula derived from the Pythagorean theorem. The distance formula states that the distance between two points (x₁,y₁) and (x₂,y₂) in a Cartesian coordinate system is given by the square root of the sum of the squares of the differences in their x and y coordinates:

Magnitude = √(\((x₂ - x₁)² + (y₂ - y₁)²)\)

In this case, substituting the coordinates of P(0,0) and Q(-5,-3) into the formula, we get:

Magnitude = √((\(-5 - 0)² + (-3 - 0)²)\)\(-5 - 0)² + (-3 - 0)²)\)

= √\(sqrt{((-5)² + (-3)²)}\)

= √(25 + 9)

= √34

Therefore, the magnitude of vector PQ is √34 (approximately 5.83)

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The equation 61 * 61 * 61 = (** 61 *)^2 can be replaced with 0 through 9 in various ways for the decimal equation to be correct.

In this equation, we have three instances of the number 61 being multiplied together on the left-hand side, and on the right-hand side, we have a square of a number that contains two unknown digits. We need to determine the values of these unknown digits (represented by the stars) by replacing them with digits from 0 to 9, such that the equation holds true.

To find the possible combinations, we can start by calculating the left-hand side of the equation. 61 * 61 * 61 equals 226,981. Now, we need to find two-digit numbers whose square is equal to 226,981. By taking the square root of 226,981, we find that it is approximately 476.383.

Since the square of the number on the right-hand side should be equal to 226,981, the two digits represented by the stars must be 7 and 6 in some order. Therefore, the equation can be written as 61 * 61 * 61 = (7*61 + 6)^2 or as 61 * 61 * 61 = (6*61 + 7)^2, depending on the order of the digits.

By replacing the stars with 7 and 6 in either order, we find a valid solution for the equation. It is important to note that there might be other combinations that satisfy the equation as well, but the specific values of the stars being 7 and 6 are valid options.

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The statement "a paired samples test for the difference between two means can be used for segmentation purposes " is true

The given statement is

"A paired samples test for the difference between two means can be used for segmentation purposes"

The segmentation is the process of dividing the similar characteristics objects and group them together.

Here the a paired sample test for the difference between two mean is used for the segmentation process. It can be used for the segmentation purpose because A paired samples test for the difference between two means are  samples in which natural or matched couplings occur

Therefore, the give statement is true

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