Proof:
Prove that for every positive integer n, there aren consecutive composite integers.
[Hint: Consider the n consecutive integers starting with(n+1)! + 2]

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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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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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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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.

hope it helps!

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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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

The mean response of the randomly selected 30 students is x, which is also the mean response of the entire class.

To find the mean response for the randomly selected students, we need to use the formula:

mean = (sum of all responses) / (number of students)

Since we are given that the # of students is 30, not 463, we need to adjust our calculation accordingly.

Let's say the sum of all the responses for the 30 students is S. Then the formula becomes:

mean = S / 30

We don't know the exact value of S, but we can use the information given to make an estimate. The mean response of the 30+463 students is x, so we can write:

(x) = (S + 463y) / (30+463)

where y is the mean response of the remaining 463 students. We want to solve for x, so we need to isolate it on one side of the equation:

(x) = (S + 463y) / (30+463)

x(30+463) = S + 463y

30x + 463x = S + 463y

493x = S + 463y

x = (S + 463y) / 493

Now we need to use the fact that y is not given, but we can make an assumption based on the information given. The mean response of the entire class is likely to be somewhere between the mean response of the randomly selected 30 students and the mean response of the remaining 463 students. So we can assume that:

y is close to x

This allows us to simplify the equation:

x = (S + 463x) / 493

Multiplying both sides by 493 gives:

493x = S + 463x

30x = S

So we can see that the sum of the responses for the 30 students is 30 times the mean response, which is x. Therefore:

S = 30x

Plugging this back into the formula for the mean, we get:

mean = S / 30

mean = (30x) / 30

mean = x

So the mean response of the randomly selected 30 students is x, which is also the mean response of the entire class.

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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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According to the World Health Organization (WHO), the European and Mediterranean populations over the age of 20 have a high percentage of overweight people. In fact, the WHO estimates that approximately 55% of the population in this region is overweight or obese.

This is a significant percentage, and it is important to note that being overweight or obese can increase the risk of numerous health problems, including cardiovascular disease, diabetes, and certain types of cancer.

There are a number of factors that contribute to the high prevalence of overweight and obesity in this region, including changes in diet, decreased physical activity levels, and cultural factors. For example, many people in these regions consume a diet that is high in calories, fat, and sugar, while also engaging in sedentary behaviors.

Overall, the high percentage of overweight and obese individuals in the European and Mediterranean populations over the age of 20 is a cause for concern. It highlights the need for effective public health interventions to promote healthy lifestyles and prevent chronic disease.

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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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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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For Aₙ = aₙ₋₁ + n and a₁ = 4, the first four terms will be 4, 6, 9, 13 respectively.

We will use the recursive formula  aₙ = aₙ₋₁ + n for the recursive series to get the first four terms of the sequence, with a₁ set to 4 for the series.

a₁ = 4 (given),

a₂ = a₁+2

⇒ a₂ = 4+2

⇒ a₂ = 6,

a₃ = a₂+3

⇒ a₂ = 6+3

⇒ a₃ = 9,

a₄ = a₃+4

⇒ a₄ = 9+4

⇒ a₄ = 13,

As can be seen, one term is utilized to locate the next term in the sequence, which is why it is referred to as recursive. So the series' first four terms are 4, 6, 9, 13.

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The given statement " using an empirical (resampling) distribution includes sampling values outside the range of the actual data. " is True because while resampling techniques may generate values outside the range of the original data, this is not necessarily a cause for concern.

Resampling techniques, such as bootstrapping or permutation tests, involve repeatedly sampling from the observed data to create an empirical distribution. This empirical distribution can then be used to make statistical inferences and hypothesis testing.

In some cases, resampling may generate values that are outside the range of the original data. This occurs because the resampling process is not constrained by the actual data values, but rather by the probability distribution of the observed data.

While sampling values outside the range of the actual data may seem counterintuitive, it is not necessarily a problem. In fact, resampling can be a powerful tool for testing statistical hypotheses and estimating uncertainty, particularly when the underlying population distribution is unknown or complex.

However, it is important to be aware of the limitations and assumptions of resampling techniques, particularly when making inferences or drawing conclusions. For example, if the original data is highly skewed or contains outliers, resampling may not accurately capture the underlying distribution.

Overall, while resampling techniques may generate values outside the range of the original data, this is not necessarily a cause for concern. Instead, it highlights the flexibility and power of empirical methods for statistical analysis.

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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 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 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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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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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 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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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 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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The sentence "After Tiara's lawn had been mowed, she cooled off in the swimming pool." contains a remote reference because the pronoun "she" is ambiguous and could refer to either Tiara or someone else. The sentence "After her lawn had been mowed, Tiara cooled off in the swimming pool." would avoid the remote reference by explicitly stating who cooled off in the pool.

The probability that the mean life of 7 items will be longer than 7 years is approximately 0.0059, or 0.59%.

To solve this problem, we need to use the central limit theorem, which tells us that the sample mean of a normally distributed population is also normally distributed, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

So, in this case, the mean of the sample mean lifespan is also 5.6 years, and the standard deviation is 1.7 years / sqrt(7) = 0.644 years.

To find the probability that the mean life of 7 items is longer than 7 years, we need to standardize the sample mean using the z-score formula:

z = (x - mu) / (sigma / sqrt(n))
where x is the desired mean (in this case, 7 years), mu is the population mean (5.6 years), sigma is the population standard deviation (1.7 years), and n is the sample size (7).

Plugging in the values, we get:
z = (7 - 5.6) / (1.7 / sqrt(7)) = 2.52

Using a standard normal distribution table or calculator, we can find that the probability of a z-score being greater than 2.52 is approximately 0.0059.

Therefore, the probability that the mean life of 7 items will be longer than 7 years is approximately 0.0059, or 0.59%.

To answer your question, we need to find the probability that the mean life of 7 randomly purchased items will be longer than 7 years, given that their normally distributed lifespan has a mean of 5.6 years and a standard deviation of 1.7 years.

To do this, we first need to find the standard deviation of the sample mean, which is calculated as the population standard deviation divided by the square root of the sample size:

Standard deviation of the sample mean = 1.7 / √7 ≈ 0.642

Next, we'll calculate the z-score for the desired mean lifespan of 7 years:

Z = (7 - 5.6) / 0.642 ≈ 2.18

Now, we need to find the probability of having a z-score greater than 2.18, which represents the probability that the mean life of the 7 items will be longer than 7 years. You can use a standard normal (Z) table or an online calculator to find the area to the right of 2.18. This area represents the probability:

P(Z > 2.18) ≈ 0.0146

So, the probability that the mean life of the 7 randomly purchased items will be longer than 7 years is approximately 1.46%.

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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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The mean absolute deviation of the data is of:

1.25.

It represents the average by which the shoe sizes deviate from the mean shoe size.

The mean of the data-set in this problem is given as follows:

Mean = (6 + 8.5 + 6 + 9 + 10 + 7 + 8 + 9.5)/8

Mean = 8.

Then the deviations are given as follows:

Hence the MAD for the data-set is given as follows:

MAD = (2 + 0.5 + 2 + 1 + 2 + 1 + 0 + 1.5)/8

MAD = 1.25.

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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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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:

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

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:

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Step-by-step explanation:

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