Determine the number of degrees of freedom for the two sample test or Clin each of the following situations. (Round your answers down to the nearest whole number) (m. 12, n = 15.5, -40.52 - 5,0 X (6)

The value of a in the equation X^2 - 10x + 25 = (X-a)^2 is 5

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

X^2 - 10x + 25 = (X-a)^2

When the equation on the left hand side is factorized

We have

(X - 5)^2 = (X - a)

By comparing both sides of the equation, we have

-5 = -a

This gives

a = 5

Hence, the solution is a = 5

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The radius of the grain silo is approximately 1.8 feet.

To solve this problem, we need to use the formula for the volume of a cylinder and the volume of a hemisphere.

The volume of a cylinder is given by V = πr^2h, where r is the radius and h is the height.

The volume of a hemisphere is given by V = (2/3)πr^3.

Since the silo consists of a cylindrical main section and a hemispherical roof, we can find the total volume by adding the volume of the cylinder and the volume of the hemisphere.

So,

Total volume = V_cylinder + V_hemisphere

= πr^2h + (2/3)πr^3

= πr^2(3h/3) + (2/3)πr^3

= (3πr^2h + 2πr^3)/3

We know that the total volume of the silo is given, so we can set up an equation:

(3πr^2h + 2πr^3)/3 = given volume

Simplifying this equation, we get:

3πr^2h + 2πr^3 = 3 x given volume

Dividing both sides by π and factoring out r^2, we get:

3rh + 2r^2 = 3 x (given volume)/π

Now we can plug in the given values and solve for r.

Let's assume the given volume is 1000 cubic feet and the height of the cylindrical part is 20 feet.

Then,

3rh + 2r^2 = 3 x 1000/π

3r x 20 + 2r^2 = 955.03

60r + 2r^2 = 955.03

2r^2 + 60r - 955.03 = 0

Using the quadratic formula, we get:

r = (-60 ± sqrt(60^2 - 4 x 2 x (-955.03)))/4

r = (-60 ± 67.2)/4

r = 1.8 or r = -33

Since the radius cannot be negative, we choose the positive solution:

r = 1.8 feet (rounded to the nearest tenth of a foot).

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Answer:

0.06

Step-by-step explanation:

The smallest alpha you can reject the null hypothesis under when you have a p-value of 0.054 is 0.06.

In hypothesis testing, we compare the p-value to the level of significance (alpha) to determine whether to reject or fail to reject the null hypothesis. If the p-value is less than or equal to alpha, we reject the null hypothesis. If the p-value is greater than alpha, we fail to reject the null hypothesis.

In this case, the p-value is greater than 0.05 (the commonly used alpha level), but it is less than 0.06. Therefore, we can reject the null hypothesis at the 0.06 alpha level, but not at the 0.05 alpha level.

The smallest alpha you can reject the null hypothesis under when you have a p-value of 0.054 is option (d) 0.056.

The smallest alpha at which you can reject the null hypothesis when you have a p-value of 0.054 is:
b.) 0.055
The p-value must be less than or equal to the chosen alpha level to reject the null hypothesis. Since 0.054 is greater than 0.05 but less than 0.055, you can reject the null hypothesis at an alpha level of 0.055.

This is because the p-value (0.054) is greater than the usual significance level of 0.05, but it is less than 0.056. Therefore, if you set your significance level to 0.056 or greater, you can reject the null hypothesis.

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To estimate the number of households in the sample that lost electricity, we can use the mean of the relevant distribution,

A) The relevant random variable is the number of households in the sample that lost electricity. Since we know that 7% of households in the city lost electricity, we can use this as the probability of any one household in the sample losing electricity. Therefore, the mean of the relevant distribution is:

Mean = np = 50 * 0.07 = 3.5 households

B) To find the standard deviation of the distribution, we use the formula:

Standard deviation = √(np(1-p))

where n is the sample size and p is the probability of success (in this case, the probability of a household losing electricity). Plugging in the values, we get:

Standard deviation = √(50 * 0.07 * (1 - 0.07)) = 1.51 households

Therefore, our estimate is that the sample will have an average of 3.5 households that lost electricity, with a standard deviation of 1.51 households.

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The statement which is not True is

The independent variable is c and dependent variable is n.

We have a table shows the total cost for different numbers of nights at a campground

So, the rate of change is

= (80- 32)/ (5-2)

= 48/ 3

= 16

and, the y intercept is

32 = 16(2)+ b

b= 0

Then, the equation is y= 16n.

and, The independent variable is n and dependent variable is c.

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According to the discount, the price of the tablet computer after the markup is $610.30.

In this problem, a store offered a 30% discount on a tablet computer that originally sold for $670. We can calculate the discounted price of the tablet computer by finding 30% of its original price and subtracting it from the original price.

Discounted price = Original price - Discount

Discounted price = $670 - 30% of $670

Discounted price = $670 - $201

Discounted price = $469

So, the discounted price of the tablet computer is $469.

The problem then asks us to find the price of the tablet computer after it is marked up by 30%. To do this, we need to add 30% of the discounted price to the discounted price.

Markup price = Discounted price + Markup

Markup price = $469 + 30% of $469

Markup price = $469 + $141.30

Markup price = $610.30

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Answer:

In Triangle A all angles are equal and in B only angles q and a are equal

Step-by-step explanation:

Triangle A is an equilateral triangle which means all angles are the same but since Triangle B is an Isosceles Traiangle means only two angles are equal

The measure of angles which are equal in each triangle  

Using the definition,

"the angles opposite to the legs are equal to each other."

Two Triangles are given names as Triangle A and Triangle B.

As, in first triangle all the sides are equal and angles opposite to the sides are equal to each other.

So, x = y = z

Now, in second triangle two sides are equal and angles opposite to the sides are equal to each other.

So, <q = <s

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The flag pole's shadow extends six feet above the ground from the top of the pole.

This issue may be resolved with triangles that are comparable. Let's use the letters "x" for the flag pole's height and "y" for the distance from the pole to the top of its shadow. Hence, we may establish the ratio shown below:

x / y = 10 / 6

To solve for y, we can cross-multiply:

y * 10 = x * 6

y = (x * 6) / 10

Now, we just need to substitute the known values and solve for y:

y = (10 * 6) / 10 = 6

Therefore, the distance from the top of the flag pole to the top of its shadow is 6 feet.

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The row mean values represent a sample mean for each student, as they are the average of the 10 rolls for each individual.

To calculate the row mean for each student in the survey data, follow these steps:

1. For each student, locate the values of rolls 1 through 10.
2. Add up the values of rolls 1 through 10 for that particular student.
3. Divide the sum obtained in step 2 by the total number of rolls (10) to get the mean.
4. Record this mean value in that student's "row mean" column.

This process should be repeated for each student in the dataset. The row mean values represent a sample mean for each student, as they are the average of the 10 rolls for each individual.

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To determine if a function is independent, we need to analyze whether one variable can be expressed as a function of the other variable(s).

In the given function f(x,y) = 4(x + xy), let's see if either x or y can be isolated.

f(x,y) = 4(x + xy)
f(x,y) = 4x + 4xy

Now, let's try to isolate y:

f(x,y) - 4x = 4xy
(f(x,y) - 4x) / 4x = y

From the above equation, we can see that y is expressed as a function of x and f(x,y). Since y depends on both x and f(x,y), the variables x and y are not independent in this function.

In conclusion, for the given function f(x,y) = 4(x + xy), x and y are not independent variables. The relationship between x and y is dependent, as the value of y relies on both x and f(x,y).

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The probability of at least one pet owner out of 18 having their pet bathed professionally is:
P(X ≥ 1) = 1 - P(X = 0) = 1 - 0.0052 = 0.9948

Given that 25% of pet owners have their pets bathed professionally, the probability of a single pet owner having their pet bathed professionally is 0.25. Conversely, the probability of a pet owner not having their pet bathed professionally is 1 - 0.25 = 0.75.

To find the probability that at least one pet owner out of 18 randomly selected has their pet bathed professionally, we can first find the probability that none of the 18 pet owners have their pets bathed professionally and then subtract it from 1.

Step 1: Find the probability that none of the 18 pet owners have their pets bathed professionally.
The probability of one pet owner not having their pet bathed professionally is 0.75. Since we're considering 18 independent pet owners, we need to multiply this probability 18 times.

Probability (none have pets bathed professionally) = (0.75)^18

Step 2: Subtract the probability found in step 1 from 1.
The probability that at least one pet owner has their pet bathed professionally is the complement of the probability found in step 1.
The probability of a pet owner having their pet bathed professionally is 25%, which can be written as 0.25. The probability of a pet owner not having their pet bathed professionally is 1 - 0.25 = 0.75.

Using the binomial probability formula, we can calculate the probability of no pet owners out of 18 having their pet bathed professionally:

P(X = 0) = (0.75)^18 = 0.0052

Therefore, the probability of at least one pet owner out of 18 having their pet bathed professionally is:

P(X ≥ 1) = 1 - P(X = 0) = 1 - 0.0052 = 0.9948
Probability (at least one has pet bathed professionally) = 1 - (0.75)^18

Now, you can calculate the probability using a calculator. The result will be the probability that at least one of the 18 randomly selected pet owners has their pet bathed professionally.

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The expression that has a value less than 1 is 3/4 x 4/4, the correct answer is option C. To decide which expression contains esteem less than 1, we got to rearrange each expression and compare it to 1.

A. 3/4 x 4/3

Increasing these divisions, we get:

(3/4) x (4/3) = 12/12 = 1

This expression rearranges to 1, which isn't less than 1.

B. 3/4 x 6/3

Duplicating these divisions, we get:

(3/4) x (6/3) = 18/12 = 3/2

This expression disentangles to 3/2, which is more prominent than 1.

C. 3/4 x 4/4

Duplicating these divisions, we get:

(3/4) x (4/4) = 12/16 = 3/4

This expression streamlines to 3/4, which is less than 1.

D. 3/4 x 8/4

Increasing these divisions, we get:

(3/4) x (8/4) = 24/16 = 3/2

This expression rearranges to 3/2, which is more prominent than 1.

thus, the expression that incorporates esteem less than 1 is alternative C, 3/4 x 4/4. 

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In mathematical modeling, some values are considered fixed and cannot vary without consequence. These values are often referred to as constants or parameters, and they represent physical or environmental properties that are assumed to be constant throughout the problem.

For example, in a mathematical model of the motion of a pendulum, the length of the pendulum, the mass of the weight, and the force of gravity are typically considered constants that cannot vary without consequence. If any of these values were to change, the motion of the pendulum would be affected, and the solution to the problem would be different.

Similarly, in a mathematical model of heat transfer, the thermal conductivity of the material, the heat source or sink, and the boundary conditions are typically considered constants that cannot vary without consequence. If any of these values were to change, the temperature distribution and heat transfer rate within the system would be affected, and the solution to the problem would be different.

The choice of which values to consider as constants or parameters depends on the specific problem being modeled and the assumptions made.

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Answer:

1/4

Step-by-step explanation:

.25 has two numbers after the decimal so we put 25 over 100

25/100

We can simplify this fraction by dividing the top and bottom by 25

25÷25 =1

100 ÷25 =4

The fraction becomes 1/4

Answer: 1/4

Step-by-step explanation:

You can think of 0.25 as 25 hundredths to convert it to a fraction. In other words, you have 25 of 100 equal parts.

So, the fraction will be 25/100

We can simplify that fraction by dividing both the numerator and denominator by the greatest common factor, which is 25.

25/100 ÷ 25 = 1/4

This gives us 1/4.

So, 0.25 is equal to 1/4.

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On rolling a die, the sample space is {1,2,3,4,5,6}. To find the probability of certain events, we can use mathematical statements.

(a) The probability of rolling a 5 or a number greater than 3 can be mathematically stated as:

P(rolling a 5 or rolling a number greater than 3) = P(rolling a 5) + P(rolling a 4) + P(rolling a 6)

However, we notice that the probability of rolling a 5 is repeated, so we need to remove the repetition:

P(rolling a 5 or rolling a number greater than 3) = P(rolling a 4) + P(rolling a 5) + P(rolling a 6) = 1/6 + 1/6 + 1/6 = 3/6 = 1/2

Therefore, the probability of rolling a 5 or a number greater than 3 is 1/2.

(b) The probability of rolling a number less than 5 or an even number can be mathematically stated as:

P(rolling a number less than 5 or an even number) = P(rolling a 1) + P(rolling a 2) + P(rolling a 3) + P(rolling a 4) + P(rolling a 6)

Adding up the probabilities, we get:

P(rolling a number less than 5 or an even number) = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 5/6

Therefore, the probability of rolling a number less than 5 or an even number is 5/6.

(c) The probability of rolling a six or an odd number can be mathematically stated as:

P(rolling a six or an odd number) = P(rolling a 1) + P(rolling a 3) + P(rolling a 5) + P(rolling a 6)

Adding up the probabilities, we get:

P(rolling a six or an odd number) = 1/6 + 1/6 + 1/6 + 1/6 = 4/6 = 2/3

Therefore, the probability of rolling a six or an odd number is 2/3.
Based on your question, here are the answers incorporating the terms you've mentioned:

(a) The probability of rolling a 5 or a number greater than 3 can be mathematically stated as:
P(5 or >3) = P(4) + P(5) + P(6) = 1/6 + 1/6 + 1/6 = 3/6 = 1/2

(b) The probability of rolling a number less than 5 or an even number is:
P(<5 or even) = P(1) + P(2) + P(3) + P(4) + P(6) = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 5/6

(c) The probability of rolling a six or an odd number is:
P(6 or odd) = P(1) + P(3) + P(5) + P(6) = 1/6 + 1/6 + 1/6 + 1/6 = 4/6 = 2/3

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The value of tan I = √12/9

To determine the value of tan I from the diagram, we have to take note of the different trigonometric identities in mathematics;

These includes;

Also, the ratios of these identities are;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given, we have;

Substitute the values

Opposite = √12

Adjacent = 9

Now, add the values, we get

tan I = √12/9

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The calculated volume of the sphere is 113.04 in³

What is a sphere?

Recall that a sphere is a three-dimensional round-shaped object that does not have any vertices or edges.

the volume of the sphere is given as V.

Where V = 4/3 * π*r³

Where r = 3 inch

The volume V. = 4/3 * 3.14 * 3*3*3

Volume = 339.12/3

Volume of the sphere = 113.04 in³

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Answer:

Each employee worked for 8 regular hours and 2 overtime hours, so each employee worked for a total of 10 hours. The regular pay rate is $15.50 per hour, so each employee earned 8 hours x $15.50 = $124 for regular pay. For overtime pay, each employee worked for 2 hours x ($15.50 + $7.00) = $44 in total.

Step-by-step explanation:

Therefore, each employee earned a total of $124 + $44 = $168.

Since there are 3 employees, the total amount that the company paid the employees is $168 x 3 = $504.

Therefore, the company paid a total of $504 to its employees.

Answer:

$507

Step-by-step explanation:

The total rate for overtime work is $7.00 + $15.50 = $22.50

1 employee worked:

8 hours at $15.50 per hour

2 hours at $22.50 per hour

total for 1 employee:

8 × $15.50 + 2 × $22.50 = $124 + $45 = $169

total for 3 employees:

3 × $169 = $507

Answer:

length-7 width-5

Step-by-step explanation:

I used to guess and check so if you give a good guess you can get it in two attempts

Since the calculated t-value (2.24) is greater than the critical value (2.074), we reject the null hypothesis and conclude that there is convincing evidence that the average food intake is different for the patients in the treatment group. In other words, playing solitaire while eating lunch seems to have an effect on the amount of food consumed.

To determine whether there is convincing evidence that the average food intake is different for the patients in the treatment group, we can conduct a two-sample t-test. The null hypothesis is that the means of the two groups are equal, and the alternative hypothesis is that they are different.

H0: μa = μb

Ha: μa ≠ μb

where μa is the mean amount of biscuits consumed in the treatment group and μb is the mean amount of biscuits consumed in the control group.

We can use the following formula to calculate the test statistic:

t = (Xa - Xb) / √[(Sa²/n) + (Sb²/n)]

where Xa and Xb are the sample means, Sa and Sb are the sample standard deviations, and n is the sample size.

Plugging in the values from the question, we get:

t = (52.1 - 27.1) / √[(45.1²/22) + (26.4²/22)]

= 2.24

Using a two-tailed t-distribution with 22 degrees of freedom and a significance level of 0.05, the critical values are ±2.074.

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a P(both can accommodate) = 0.225 or 22.5%  ,P(event must be postponed) = 0.775 or 77.5%

a. The probability that both venues can accommodate the event is found by multiplying the individual probabilities together, since they are assumed to be independent:
P(both can accommodate) = P(first venue can accommodate) x P(second venue can accommodate)
P(both can accommodate) = 0.75 x 0.30
P(both can accommodate) = 0.225 or 22.5%

b. The probability that at least one venue can accommodate the event is found by using the complement rule:
P(at least one can accommodate) = 1 - P(neither can accommodate)
Since the only two possible outcomes are that either both venues can accommodate or neither can, we can use the probabilities from part a to find the probability that neither can accommodate:
P(neither can accommodate) = 1 - P(both can accommodate)
P(neither can accommodate) = 1 - 0.225
P(neither can accommodate) = 0.775
Now we can use the complement rule to find the probability that at least one venue can accommodate:
P(at least one can accommodate) = 1 - P(neither can accommodate)
P(at least one can accommodate) = 1 - 0.775
P(at least one can accommodate) = 0.225 or 22.5%

c. The probability that the event must be postponed because neither venue can accommodate is simply the complement of the probability that at least one venue can accommodate:
P(event must be postponed) = 1 - P(at least one can accommodate)
P(event must be postponed) = 1 - 0.225
P(event must be postponed) = 0.775 or 77.5%

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Given that in ∠ABC and ∠DEF, ∠C and ∠F are right angles and sinA = cos D.

The tabla can be completed as follows:

Angle Pair Related as

∠A and ∠D Complementary

∠B and ∠F Complementary

∠B and ∠E Neither

∠A and ∠E Congruent

∠E and ∠D Neither

∠B and ∠D Congruent

Complementary angles are two angles whose sum is 90 degrees.

Congruent angles are two or more angles whose values are the same.

Considering the given angles:

∠A and ∠D are complementary angles since sinA = cos D.

∠B and ∠F are complementary angles since they are both right angles

∠A and ∠E are congruent angles since sinA = sinE and both angles are acute angles.

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Answer:

The solution to the equation x^2=2 is an irrational number. Specifically, the exact value of the solution is the square root of 2, which cannot be expressed as a fraction of two integers and has a decimal expansion that goes on infinitely without repeating. Therefore, the correct answer is D.

Step-by-step explanation:

The equation x^2=2 can be solved by taking the square root of both sides of the equation. However, since the square root of 2 is not a rational number (meaning it cannot be expressed as a fraction of two integers), the solution to this equation is an irrational number.

To see why the square root of 2 is irrational, suppose it could be expressed as a fraction a/b, where a and b are integers with no common factors. Then, squaring both sides of this equation gives:

(a/b)^2 = 2

a^2/b^2 = 2

Multiplying both sides by b^2 gives:

a^2 = 2b^2

This means that a^2 is an even number, since it is equal to twice an integer (namely, 2b^2). But this implies that a itself must be even, since the square of an odd number is odd and the square of an even number is even. Therefore, we can write a=2k for some integer k.

Substituting this expression for a into the equation a^2=2b^2 gives:

(2k)^2 = 2b^2

4k^2 = 2b^2

2k^2 = b^2

This implies that b^2 is even, which means that b itself must be even (using the same argument as before). But this contradicts our assumption that a/b is a fraction with no common factors. Therefore, we have shown that the square root of 2 cannot be expressed as a fraction of two integers and is therefore an irrational number.

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The difference between an implicitly defined function and an explicitly defined function lies in how the relationship between the variables is expressed.

In an explicitly defined function, the dependent variable (usually y) is expressed directly in terms of the independent variable (usually x), such as y = f(x). In an implicitly defined function, the relationship between the variables is expressed indirectly through an equation involving both variables, such as F(x, y) = 0, making it not straightforward to solve for y in terms of x.

Explicitly defined functions provide a clear and explicit expression for the dependent variable in terms of the independent variable, allowing for direct evaluation and computation. They are commonly used when the relationship between variables can be easily represented by a formula or equation.

On the other hand, implicitly defined functions are often used when the relationship between variables is more complex or cannot be easily expressed in a single equation. They require additional manipulation or solving techniques to determine the relationship between the variables.

Implicit functions are commonly encountered in calculus and differential equations, where the relationships may involve derivatives or multiple variables.

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The cosine of angle X is given as follows:

cos(X) = 4/5.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For angle X, we have that:

Hence the cosine of angle X is obtained as follows:

cos(X) = 32/40

cos(X) = 4/5.

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Answer:

E. 9, F. 10

Step-by-step explanation:

Area of the rectangle: 3b

Area of the white triangle: 3b/3

Area of shaded region: 3b/2

3b/2 > 12

3b > 24

b > 8

Answer: E. 9, F. 10

Answer: value of RT is 4√3.

Step-by-step explanation: To solve for the value of RT, we can use the fact that the tangent to a circle is perpendicular to the radius drawn to the point of tangency.

In this case, we can draw a radius from the center of the circle (point O) to point T and label it OT. Since RT is tangent to the circle at point T, it is perpendicular to the radius OT.

We can then use the Pythagorean theorem to relate the lengths of the line segments in the right triangle OTR:

OT^2 = OR^2 + RT^2

Substituting the given values, we have:

13^2 = 11^2 + RT^2

169 = 121 + RT^2

RT^2 = 48

Taking the square root of both sides, we get:

RT = √48 = 4√3

Therefore, the value of RT is 4√3.

The solution of the given parabola is (0, -2) and equation is  y=a(x+1)²

The equation of parabola in standard form is y=a(x-h)²+k

Where (h, k) are the coordinates of vertex

The value of (h, k) is (-1, 0)

Now plug in the values in equation

y=a(x+1)²+0

y=a(x+1)²

The point (0, -2) is in parabola

Hence, the solution of the given parabola is (0, -2)

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At Ying Ying's bakery, there's an 8% probability that a customer will report a food allergy.

When dealing with 12 customers, we can calculate the probability that at least one customer will report a food allergy by first finding the probability that none of them report a food allergy, and then subtracting that value from 1.

The probability that a single customer doesn't report a food allergy is 1 - 0.08 = 0.92. For all 12 customers not to report a food allergy, the probability is 0.92^12 = 0.3981 (rounded to four decimal places).

Now, subtract this probability from 1: 1 - 0.3981 = 0.6019.

Therefore, the probability that at least one customer will report a food allergy is 0.6019 or 60.19%.

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Answer: 74

Step-by-step explanation:

Mean means average.  Add all the numbers and divide by how many there are.

(86+45+93+77+63+80)/6

444/6

=74