The figure below is made up of a square with height, h units, and a right triangle with height, h units, and base length, b units. The area of this figure is 80 square units. Write an equation that solves for the height, h, in terms of b. Show all work necessary to justify your answer.

The probability that six people in the group wear glasses is at most 0.3646.

We have,

(a)

The expected number of people who wear glasses is 2, so the probability that a person chosen at random from the group wears glasses is.

= 2/total number of people in the group.

We don't know the total number of people in the group, so we can't find the exact probability.

(b)

Let X be the number of people in the group who wear glasses.

X follows a binomial distribution with n = total number of people in the group and p = probability that a person wears glasses

= 2/total number of people in the group.

We know that the variance of X is 1.6,

So the standard deviation of X.

= √(variance)

= √(1.6)

= 1.2649 (rounded to four decimal places).

We want to find the probability that six people in the group wear glasses. That is, P(X = 6).

Using the binomial probability formula, we have:

P(X = 6) = (n choose 6) x p^6 x (1 - p)^(n - 6)

We don't know the value of n, so we can't find the exact probability. However, we can use Chebyshev's inequality to find an upper bound on the probability.

Chebyshev's inequality states that for any random variable X with finite mean mu and finite standard deviation sigma, the probability that X deviates from its mean by more than k standard deviations is at most 1/k². In symbols:

P(|X - mu| > k x sigma) <= 1/k²

Let X be the number of people in the group who wear glasses, with mean mu = np and standard deviation sigma = √(n x p x (1 - p)).

We want to find an upper bound on the probability that six people wear glasses, which means we want to find an upper bound on P(X = 6).

We can rewrite the event {X = 6} as {X - mu = 6 - np}.

Then:

P(X = 6) = P(X - mu = 6 - np)

= P(|X - mu| > |6 - np|)

= 1 / ((6 - np) / sigma)²

We want to find an upper bound on this expression, so we want to minimize (6 - np) / sigma.

Since p = 2/n, we have:

= (6 - np) / sigma

= (6 - 2) / √(n x 2/n (1 - 2/n))

= 4 / √(2n - 4)

This is minimized when n is maximized.

The total number of people in the group must be an integer, so we choose the smallest integer n such that 2/n > 0.5 (since the probability that a person wears glasses is 2/n).

This is n = 5.

Then:

= (6 - np) / sigma

= (6 - 2) / √(5 x 2/5 x (1 - 2/5))

= 4 / √(6)

= 1.63299 (rounded to five decimal places)

So,

P(X = 6)  ≤ 1 / (1.63299)² ≤ 0.3646 (rounded to four decimal places)

Thus,

The probability that six people in the group wear glasses is at most 0.3646.

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If 28 people were surveyed, 7 more people voted for spinach than for broccoli.

The amounts are obtained applying the proportions in the context of the problem.

The fractions for each vegetable are given as follows:

Then the amounts, out of 28 people, are given as follows:

Then the difference between spinach and broccoli is given as follows:

14 - 7 = 7.

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Chen's condition does not take into consideration the impact of gravity on the ball's height, so the calculation of the ball's height at any point in time is incorrect. 

Based on the information given, Chen used the following formula to determine the height of the ball.

[tex]h(t) = -16t^2 + vt + h0[/tex]

where h(t)= height of the ball at time t, v = initial velocity (16 feet/second), and h0 = initial height (6 feet).

However, Chen's equation is flawed. The sign of acceleration due to gravity being a constant factor of [tex]-32 ft/s^2[/tex] is wrong. The correct formula is:

[tex]h(t) = -16t^2 + vt + h0 - (1/2)gt^2[/tex]

where g is the acceleration due to gravity [tex](-32 ft/s^2).[/tex]

hence, Chen's condition does not take into consideration the impact of gravity on the ball's height, so the calculation of the ball's height at any point in time is incorrect. 

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Answer:

Sarah can have the plumber work on her faucet for six (6) hours maximum

Step-by-step explanation:

Answer:

Step-by-step explanation:

sorrry

Measures of central tendency are summary statistics that represent the center point or typical value of a dataset. Examples of these measures include the mean, median, and mode. These statistics indicate where most values in a distribution fall and are also referred to as the central location of a distribution.

The answer is central because measures of central tendency, such as mean, median, and mode, are the values that summarize the center of a distribution of data. They provide a single value around which the data tend to cluster, making them useful for describing the overall characteristics of a dataset. The mean is the arithmetic average of a set of values, while the median is the middle value when the data are ordered, and the mode is the most frequently occurring value in the dataset. All of these measures provide a central or typical value for the data.

~~~Harsha~~~

On adding the provided equations, 4x +7y= 17 and 9x + 13y = 46 the resultant equation we will be getting is 13x + 20y = 63.

In order to perform addition of two equations together, we are needed to add the left-hand side of each equation and the right-hand side of each equation separately. This gives us:

(4x + 7y) + (9x + 13y) = 17 + 46

Combining like terms on both the sides, we will be getting ,

13x + 20y = 63

Therefore, from the above calculations this inference can be drawn that the overall equation is calculated to be  13x + 20y = 63.

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The complete question is :

4x +7y= 17

9x + 13y = 46

when these equations are added together, what will the overall equation be? assume that no equations need to be reversed.

Answer: A

Step-by-step explanation:

hope this helps

Answer: The next number is 22

Hope it helped :D

Good luck!

The answer of the given question based on line plot graph is , the data points are , 1,6,9,12,18.

A box-and-whisker plot, also known as a box plot, is a graphical representation of a data set that shows the distribution of the data and provides information about its central tendency and variability.

To construct a box-and-whisker plot from the given line plot, we need to find the following five data points:

The minimum value, which is the smallest number of miles Habib hiked in the past 18 days.

The first quartile (Q1), which is  median of  lower half of  data set.

The median, which is  middle value of data set.

The third quartile (Q3), which is the median of the upper half of the data set.

The maximum value, which is the largest number of miles Habib hiked in the past 18 days.

Based on the line plot, we can estimate the five data points as follows:

The minimum value appears to be 1 miles.

The first quartile appears to be around 6 miles, which is the median of the data points from day 1 to day 9.

The median appears to be around 9 miles, which is the middle value of the entire data set.

The third quartile appears to be around 12 miles, which is the median of the data points from day 10 to day 18.

The maximum value appears to be 18 miles.

These five data points can be used to construct a box-and-whisker plot that summarizes the distribution of the data.

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Inequality: In mathematics, an inequality is a statement that compares two values, expressions, or quantities using a relation symbol such as "greater than" (>), "less than" (<), "greater than or equal to" (≥), "less than or equal to" (≤), or "not equal to" (≠). An inequality indicates that the values or expressions being compared are not equal.

Combining like terms: In algebra, combining like terms refers to the process of simplifying an expression by adding or subtracting terms that have the same variable raised to the same power.

Inverse operations to isolate: In algebra, inverse operations are operations that undo each other. For example, addition and subtraction are inverse operations, as are multiplication and division. To isolate a variable in an equation or inequality, you can use inverse operations to undo the operations that are being performed on the variable.

To solve the inequality -13x + 46 > -45, you need to isolate the variable (x) on one side of the inequality.

1. First, you can subtract 46 from both sides of the inequality to get:

[tex]-13x > -91[/tex]

2. Then, divide both sides of the inequality by -13 (remember that when you divide or multiply by a negative number, you need to flip the inequality sign) to get:

[tex]x < 7[/tex]

Therefore, the solution to the inequality is x < 7. To check, you can substitute any value less than 7 into the inequality to see if it's true. For example, if you plug in x = 5, you get:

[tex]-13(5) +46 > -45[/tex]

[tex]-19 > -45[/tex]

This is true, so x < 7 is indeed a valid solution to the inequality.

The probability that their first child will not roll its tongue and will have the normal number of fingers is 25%.

To determine the probability that their first child will not roll its tongue and will have the normal number of fingers, we need to know the probability of each event separately and then multiply them together.

Assuming that rolling the tongue is a dominant trait and the father is homozygous recessive for the finger trait, the probabilities are:

The probability that the first child will not roll its tongue is 25% (or 0.25), as both parents are heterozygous and carry the dominant allele.

The probability that the first child will have the normal number of fingers is 100% (or 1), as the father is homozygous recessive for the trait and will only pass on the normal allele.

Multiplying the two probabilities together, we get

0.25 x 1 = 0.25 or 25%

Therefore, there is probability of 25% that their first child will have the normal number of fingers and will not roll its tongue.

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Answer:

A. 400 ounces is 25lbs so yeah

Step-by-step explanation:

Answer:

50% If there's only black and white pieces. If there's more, please mention them.

Answer:

The general rule for the seth ethic sequence is to add 7 to the previous term to get the next term.

Domain: The sequence is defined for all integer values of n where n is greater than or equal to 1.

Range: {-12, -5, 2, 9}

The interval that has the greatest average rate of change is given as follows:

B. Between 5 and 7 tires

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.

For each interval, the change in the input is of 2 tires.

The outputs are given as follows:

The rate is only positive between 5 and 7 tires, hence it has the greatest average rate of change.

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Answer:

10 × 3.5 = 35

22 × 3.5 = 77

The dimensions of the new rectangle are 35 and 77.

A function requires that each input or independent variable has exactly one output or dependent variable, which is not the case if Brent weighs himself every week and his weight changes every time. The correct option is No/false.

Independent variable and dependent variable are two sets of values that explain a connection in mathematics. Each input value in a function corresponds to exactly one output value.

Therefore, the input is the week and the output is Brent's weight, but there are multiple outputs for the same input week which violates the definition of a function.

Therefore, The answer is No/false

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Answer: The surface area of the triangular prism with dimensions 30 ft, 36 ft, 30 ft, 32 ft, and 24 ft is 4116 square feet.

Step-by-step explanation:Area = 0.5 x base x height

The first triangular face has a base of 30 ft and a height of 36 ft. So, its area is:

Area of first triangle = 0.5 x 30 ft x 36 ft = 540 square feet

The second triangular face has a base of 32 ft and a height of 24 ft. So, its area is:

Area of second triangle = 0.5 x 32 ft x 24 ft = 384 square feet

Next, we need to find the area of the three rectangular faces. Each rectangular face has an area equal to the length times the width. We have three rectangular faces with dimensions:

30 ft x 36 ft

30 ft x 32 ft

36 ft x 32 ft

So, the area of each rectangular face is:

Area of first rectangular face = 30 ft x 36 ft = 1080 square feet

Area of second rectangular face = 30 ft x 32 ft = 960 square feet

Area of third rectangular face = 36 ft x 32 ft = 1152 square feet

Finally, we can find the total surface area by adding up the areas of all the faces:

Total surface area = Area of first triangle + Area of second triangle + Area of first rectangular face + Area of second rectangular face + Area of third rectangular face

Total surface area = 540 sq ft + 384 sq ft + 1080 sq ft + 960 sq ft + 1152 sq ft

Total surface area = 4116 square feet

Therefore, the surface area of the triangular prism with dimensions 30 ft, 36 ft, 30 ft, 32 ft, and 24 ft is 4116 square feet.

Answer:

5/6

Step-by-step explanation:

divide each by 6 and you get 5/6

have a good day :)

The mass of African elephant is 30 times of Silverback gorilla, so, the value of m is found to be 30 which is an integer.

The mass of an African elephant is about 6 x 10⁶ grams. The mass of a silverback gorilla is about 2 x 10⁵ grams. Solution using unitary method,

Mass of elephant = 6 x 10⁶ grams

Mass of gorilla = 2 x 10⁵ grams

Let us say that m gorillas are weighting equal to one elephant. We need to find the value of m, such that,

6 x 10⁶ = m x 2 x 10⁵

Dividing both sides by 2 x 10⁵, we get:

m = 6 x 10⁶ / 2 x 10⁵

m  = 30

Therefore, the value of m is 30.

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Complete question - The mass of an African elephant is  6 x 10⁶ grams. The mass of a silverback gorilla is 2 x 10⁵ grams.

A. Using these estimated values, the mass of the African elephant is about 3 x 10 times the mass of the silverback gorilla, where m is an integer.

What is the value of m?

the statement that is true is that Desmond's aquarium has a higher concentration of chemical solution than Megan's aquarium, even though they added the same amount of water and chemical solution.

How to solve the question?

To compare the chemical concentration of the two aquariums, we need to convert the amount of chemical added to a common unit of measurement. Let's convert Megan's chemical solution to mL per 2 gallons, which is equivalent to 7.57 L per 3785.41 mL of water. This means that Megan added 7.57 mL of the chemical solution for every 2 gallons of water in her aquarium.

Desmond added 8 mL of the chemical solution for every 2 gallons of water in his aquarium. So, both Megan and Desmond added the same amount of chemical to their aquariums.

However, the concentration of the chemical in the water would be different since Megan added the chemical at a higher rate than Desmond. Megan added 7.57 mL of chemical per 2 gallons of water, while Desmond added 8 mL of chemical per 2 gallons of water. This means that the concentration of the chemical in Megan's aquarium would be lower than that in Desmond's aquarium.

Therefore, the statement that is true is that Desmond's aquarium has a higher concentration of chemical solution than Megan's aquarium, even though they added the same amount of water and chemical solution.

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YOUR COMPLETE QUESTION IS ;-Morgan and Desmond each added the same amount of water to their aquariums. Megan mixed 5 mL of a chemical solution with every gallon of water for her aquarium. Desmond mixed 8 mL of the chemical solution with every 2 gallons of water for his aquarium.Which of these statements is true?

There is enough evidence to reject the null hypothesis and conclude that the true population mean delivery time is indeed longer than 2 days.

Set up the null hypothesis (H0), alternative hypothesis (Ha).

In this case, our null hypothesis would be that the average delivery time for U.S. packages are pending to be delivered during December is equal to 2 days:

H0: μ = 2

Our alternative hypothesis would be that the average delivery time for U.S. packages to be delivered during December is longer than 2 days:

Ha: μ > 2

Where μ represents the population mean delivery time.

So our hypotheses would be:

H0: μ = 2 (null hypothesis)

Ha: μ > 2 (alternative hypothesis)

We will then conduct a statistical test to determine if there is enough evidence to reject the null hypothesis and conclude that the true population mean delivery time is indeed longer than 2 days.

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If someone claims that the average delivery time for U.S. packages during December is 2 days, and you believe it takes longer than that, then you can conduct a hypothesis test to determine if your belief is statistically significant or not.

Your hypotheses for this test would be as follows:

Null Hypothesis (H0): The average delivery time for US packages during December is equal to 2 days.

Alternative Hypothesis (Ha): The average delivery time for U.S. packages during December is greater than 2 days.

The null hypothesis represents the status quo or the claim that is being made. The alternative hypothesis represents your belief or the claim that you are testing. To conduct the hypothesis test, you would need to collect a sample of delivery times during December and use statistical analysis to determine if the sample mean is significantly different from 2 days.

If the sample mean is significantly greater than 2 days, then you would reject the null hypothesis and conclude that the average delivery time is longer than 2 days during December. However, if the sample mean is not significantly different from 2 days, then you would fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the average delivery time is longer than 2 days during December.

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It's important to remember that using the binomial approximation assumes a large population size, which may not be the case here.

To answer your questions, we will use R commands to calculate the probabilities.

(a) To find the probability that exactly 6 of the students will be full-time, we can use the "dhyper" function in R. The parameters are x = 6, m = 30 (number of full-time students), n = 20 (number of part-time students), and k = 10 (sample size).

R command:
```R
dhyper(x = 6, m = 30, n = 20, k = 10)
```

(b) To find the probability that at most 8 of the students will be full-time, we can use the "phyper" function in R, which calculates the cumulative probability. We need to calculate P(X ≤ 8).

R command:
```R
phyper(q = 8, m = 30, n = 20, k = 10)
```

(c) To use the binomial approximation, we can use the "dbinom" function in R with p = 0.6 (probability of full-time student) and n = 10 (sample size). We want to calculate P(X = 6).

R command:
```R
dbinom(x = 6, size = 10, prob = 0.6)
```

Compare this result with the answer in part (a). If the difference is relatively small, it's appropriate to use the binomial approximation in this scenario.

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The diameter of the circle is 3 miles.

Given that, a circle with circumference of 9.42 miles, we need to find diameter of the circle,

Circumference = π × diameter

9.42 = 3.14 × diameter

Diameter = 9.42 / 3.14

Diameter = 3

Hence, the diameter of the circle is 3 miles.

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839 square miles of land was burned by the fire.

To determine how many square miles the Wallow Fire burned in 2011, we can divide the total number of acres burned by the number of acres in one square mile.

538,000 acres / 640 acres per square mile = 839 square miles

Therefore, the Wallow Fire burned approximately 839 square miles of land in eastern Arizona. This was a devastating wildfire that caused significant damage to the environment and local communities. The fire started on May 29, 2011, and was not fully contained until July 8, 2011. The cause of the fire was determined to be human-caused, and it serves as a reminder of the importance of being cautious and responsible with fire in areas prone to wildfires.

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Answer:

a. 1.26

b. 0.1038

Step-by-step explanation:

The p-value is 1.0000 (rounded to four decimal places). This means that we fail to reject the null hypothesis, which in this case would be that the population mean is equal to the sample mean of 26.2.

To find the test statistic, we need to use the formula:

test statistic = (sample mean - population mean) / (standard deviation / square root of sample size)

Since the population standard deviation is given as 6, we can plug in the values:

test statistic = (26.2 - population mean) / (6 / √40)

To find the population mean, we can use the fact that the sample mean is an unbiased estimator of the population mean, so:

population mean = sample mean = 26.2

Plugging in the values, we get:

test statistic = (26.2 - 26.2) / (6 / √40) = 0

The test statistic is 0.

To find the p-value, we need to use a t-distribution table or calculator. Since we have a sample size of 40, we can use the t-distribution with 39 degrees of freedom.

Using a calculator or table, we can find that the area to the right of 0 (since the test statistic is 0) is 0.5. Since this is a two-tailed test, we need to double this value to get the p-value:

p-value = 2 * 0.5 = 1.0000
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The measure of angle x is given as follows:

x = 39.6º.

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

For angle x, we have that:

Applying the cosine, the measure is obtained as follows:

cos(x) = 64/83

x = arccos(64/83)

x = 39.6º.

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The coterminal angle of tetha is 240°

Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. For example, the angles 60,-300 are coterminal.

If tetha = -8π/3

and π is 180

therefore, tetha = -8×180/3

= - 8 × 60 = -480°

since tetha is -480°, the coterminal angle is calculated as;

-480° +360 = -120°

The positive angle of -120° = 360-120 = 240°

therefore the coterminal angle that is greater than 0 but less than 360 is 240°

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