The expression (h) (b, + b₂) gives the area of a trapezoid, with b, and b, representing the two base lengths of a trapezoid and h representing the height. Find the area of a trapezoid with base lengths 4 in. and 6 in. and a height of 8 in. (Lesson 10.2)​

The expression in terms of the first power of sine is 1 + 3[tex]sin^{4}[/tex]x - 3[tex]sin^{2}[/tex]x - [tex]sin^{6}[/tex]x. The solution has been obtained by using the trigonometric identities.

What are trigonometric identities?

All possible values of the variables in the equation must satisfy the equality condition known as a trigonometric identity. A triangle's side length and angle can be used to express a variety of unusual trigonometric identities.

We are given expression as [tex]cos^{6}[/tex] (x).

This can be written as a cosine function as  [tex](cos^{2} x)^{3}[/tex].

We know that [tex]sin^{2}[/tex]x + [tex]cos^{2}[/tex]x = 1.

So, we get

⇒ (1 - [tex]sin^{2}[/tex]x[tex])^{3}[/tex]

⇒ 1 + 3[tex]sin^{4}[/tex]x - 3[tex]sin^{2}[/tex]x - [tex]sin^{6}[/tex]x

Hence, the required expression has been obtained.

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Answer:

2.07 cm

Step-by-step explanation:

Hypotenuse = 2 cm

Adjacent side = a

Formula

cos θ = Hypotenuse/Adjacent side

cos 15 = 2/a

Note

The value of cos 15 is approximately 0.965.

0.965 = 2/a

a = 2/0.965

a = 2.07 cm ( approximately )

Answer: there is only one number

Answer:

Solo hay un número primo que se puede escribir como suma de dos números primos y también como diferencia de dos números primos.

Espero haber ayudado :D

The probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.

a. The exponential distribution with a mean of 2.725 hours can be expressed as λ = 1/2.725. Using this parameter, we can calculate the probabilities as follows:

P(X ≥ 2) = [tex]e^{(-λ2) }= e^{(-1/2.7252)[/tex] ≈ 0.4800

P(X ≤ 3) = 1 - [tex]e^{(-λ3)} = 1 - e^{(-1/2.7253)[/tex] ≈ 0.6674

P(2 ≤ X ≤ 3) = [tex]e^{(-λ2)} - e^{(-λ3)} = e^{(-1/2.7252)} - e^{(-1/2.7253)}[/tex] ≈ 0.1474

b. The standard deviation of an exponential distribution is equal to the mean, so 2 standard deviations above the mean would be 2*2.725 = 5.45 hours. The probability that a rainfall event exceeds this duration can be calculated as follows:

P(X > 5.45) =[tex]e^{(-λ5.45)} = e^{(-1/2.7255.45)}[/tex] ≈ 0.0498

Therefore, the probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.

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Complete Question:

Suppose that rainfall duration follows an exponential distribution with mean value 2.725 hours.

a. What is the probability that the duration of a particular rainfall event is at least 2 hours? At most 3 hours? Between 2 and 3 hours? (.4800, .6674, .1474)

b. What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations? (.0498)

Answer:

The answer is 7 pens

Donna Mosier should use an Individuals control chart to set control limits for the data entry process.

An Individuals control chart is a type of process control chart used to monitor the process when the sample size is one. In this case, Mosier is examining 100 records entered by each of the 20 clerks, making the sample size one.

To set control limits that include 99.73% of the random variation in the data entry process, Mosier can use the following steps:

By using an Individuals control chart, Mosier can set control limits to monitor the data entry process and detect any issues before they become major problems.

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To determine if each ordered pair is a point of intersection between the line x - y = 6 and the circle y² - 26 = -x², we need to substitute the values of x and y in both equations and see if they are true for both.

For the ordered pair (1, -5):

x - y = 6 becomes 1 - (-5) = 6, which is true.

y² - 26 = -x² becomes (-5)² - 26 = -(1)², which is false.

Therefore, (1, -5) is not a point of intersection.

For the ordered pair (1, 5):

x - y = 6 becomes 1 - 5 = -4, which is false.

y² - 26 = -x² becomes (5)² - 26 = -(1)², which is true.

Therefore, (1, 5) is a point of intersection.

For the ordered pair (5, -1):

x - y = 6 becomes 5 - (-1) = 6, which is true.

y² - 26 = -x² becomes (-1)² - 26 = -(5)², which is false.

Therefore, (5, -1) is not a point of intersection.

So the answer is:

(1,-5) - No

(1,5) - Yes

(5,-1) - No

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If y is proportional to the square root of x and y = 60 when x = 36, then the value of x when y = 80 is 64

We are given that y is proportional to the square root of x, or y ∝ √x.

Using the constant of proportionality k, we can write this relationship as:

y = k√x

To solve for k, we can use the values given in the problem

y = 60, x = 36

60 = k√36

60 = k × 6

k = 60 / 6

Divide the numbers

k = 10

Now that we know k, we can use the same equation to find x when y = 80

80 = 10√x

Squaring both sides, we get

6400 = 100x

x = 64

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The given question is incomplete, the complete question is:

y ∝ √x If y = 60 when x = 36, find x when y = 80​.

When two coins are repeatedly flipped, the probability of getting two heads is 1/4, the probability of getting a head and a tail is 1/2, and the probability of getting two tails is also 1/4.

Therefore, the expected ratio of two heads : heads/tails : tails/heads : two tails is 1:2:2:1, respectively. This means that out of every six flips, we would expect to see one outcome of two heads, two outcomes of heads/tails and tails/heads each, and one outcome of two tails.

However, it is important to note that this is only a prediction and the actual results may differ due to chance.

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The perimeter and the area of the regular polygon are 20 inches and 27.53 square inches.

The figure representing a regular polygon with five sides of same length, whose perimeter and area is well described by following formulas:

Perimeter

p = n · l

Area

A = (n · l · a) / 2

Where:

Where the apothema is:

a = 0.5 · l / tan (180° / n)

If we know that l = 4 in and n = 5, then the perimeter and the area of the polygon are:

Perimeter

p = 5 · (4 in)

p = 20 in

Area

a = 0.5 · (4 in) / tan (180° / 5)

a = 0.5 · (4 in) / tan 36°

a = 2.753 in

A = [5 · (4 in) · (2.753 in)] / 2

A = 27.53 in²

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Therefore, the correct answer is (B) No, she needs 1/2 cup more.

To determine if Patricia has enough rice cereal for her recipe, we need to calculate the total amount of rice cereal she has after all her actions and compare it to the 3 cups required for the cereal clusters.

Initially, Patricia had 5 cups of rice cereal. She used 3 cups to make granola bars, leaving her with 2 cups. She then borrowed 0.5 cup from her friend, which brings her total to 2.5 cups.

Finally, she needs 3 cups of rice cereal for the cereal clusters recipe. Since she only has 2.5 cups, she does not have enough rice cereal and needs to get more. Therefore, the correct answer is B) No, she needs 1/2 cup more.

She then borrows 0.5 cup, so she now has 2 + 0.5 = 2.5 cups.

needs 3 - 2.5 = 0.5 cups more.

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[tex]7^{(1/3)}[/tex] is the equivalent expression to ∛7 with rational exponents.

What are rational exponents?

Rational exponents are exponents that are expressed as fractions. Specifically, a rational exponent of the form m/n is equivalent to taking the nth root of a number and then raising it to the power of m.

When we talk about rational exponents, we are referring to exponents that are written as fractions. Specifically, a rational exponent of the form m/n is equivalent to taking the nth root of a number and then raising it to the power of m.

So, in the case of ∛7, we can rewrite the cube root symbol (∛) as a rational exponent with a denominator of 3. That is, ∛7 can be expressed as [tex]7^{(1/3)}[/tex] , where the 1/3 exponent means "take the cube root of 7".

Therefore, [tex]7^{(1/3)}[/tex] is the equivalent expression to ∛7 with rational exponents.

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The statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

The expression 100 - 0.4m represents the amount of medicine in Evan's bloodstream after m minutes, where the amount of medicine decreases by 0.4 milligrams each minute.

The coefficient of the variable m (-0.4) represents the rate of change of the amount of medicine in Evan's bloodstream per minute. It tells us that for every one minute that passes, the amount of medicine in his bloodstream decreases by 0.4 milligrams.

The constant term (100) represents the initial amount of medicine in Evan's bloodstream before the medicine starts to decrease.

Therefore, the statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.

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Answer:150°

Step-by-step explanation:

The surface area of the cylinder is approximately 94.2 ft².

Surface area refers to the total area of the external or outer part of an object. It is the sum of the areas of all the individual surfaces or faces of the object. Surface area is typically measured in square units, such as square inches (in²), square feet (ft²), or square meters (m²), depending on the unit of measurement used.

According to the given information:

The surface area of a cylinder is the sum of the lateral surface area (the curved surface) and the area of the two circular bases.

The formula for the lateral surface area of a cylinder is given:

Lateral Surface Area = 2πrh

where r is the radius of the cylinder and h is the height of the cylinder.

Plugging in the given values for the radius (r = 3 ft) and height (h = 2 ft), we can calculate the lateral surface area:

Lateral Surface Area = 2π * 3 * 2 = 12π ft²

The formula for the area of a circle (which represents the bases of the cylinder) is given:

Circle Area = πr²

Plugging in the given value for the radius (r = 3 ft), we can calculate the area of each circular base:

Circle Area = π * 3² = 9π ft²

Since there are two bases in a cylinder, we multiply this by 2 to account for both bases:

2 * Circle Area = 2 * 9π = 18π ft²

Now, we can add the lateral surface area and the area of the two bases to find the total surface area of the cylinder:

Total Surface Area = Lateral Surface Area + 2 * Circle Area

= 12π + 18π

= 30π ft²

As a decimal rounded to the nearest tenth, the surface area of the cylinder is approximately 94.2 ft²

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Answer:

x=2

Step-by-step explanation:

x^4=16

x=[tex]\sqrt[4]{16}[/tex]

x=[tex]2[/tex]

Using the fact that the triangles are similar we can see that the value of x is  36

We can see that the triangles are similar due to the same interior angles, then ther is a scale factor k between them.

So we can write:

20*k = 48

k = 48/20 = 2.4

Then:

x = 15*2.4

x = 36

That is the value of x.

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The H. C. F of 80,215,245 and 720 using long division method is 5.

The long division method to find the Highest Common Factor (H.C.F.) of 80, 215, 245, and 720.

Divide the largest number by the smallest number.

720 ÷ 80 = 9 with a remainder of 0

Divide the smallest number by the remainder from the previous step.

80 ÷ 40 = 2 with a remainder of 0

Divide the remainder from the previous step by the next smallest number.

40 ÷ 5 = 8 with a remainder of 0

Divide the remainder from the previous step by the next smallest number.

5 ÷ 5 = 1 with a remainder of 0

We have reached a remainder of 0, which means that 5 is the H.C.F. of the given numbers.

Therefore, the H.C.F. of 80, 215, 245, and 720 is 5.

We can also verify this by listing the factors of each number and finding the common factors:

80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

215: 1, 5, 43, 215

245: 1, 5, 7, 35, 49, 245

720: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720

The common factors are 1, 5, and 40.

The largest common factor is 5, which is the same as what we obtained using the long division method.

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Answer:

Step-by-step explanation:

5989.87

Answer:see below

Step-by-step explanation:

10.600

11.80000

12.17

13.48

14.4000

21. 1km=100m;0.5km=500m;0.1km=100m

22.50m=5000cm; 5m=500cm; 0.5m=50cm

Answer:

C and D

Step-by-step explanation:

cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{4}{5}[/tex] ⇒ C

sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{3}{5}[/tex] ⇒ D

The answer to the trigonometry question in the picture attached is:

   = cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

Simplify 1-csc θ as follows:

1 - csc θ = (1 - csc θ)(1 + csc θ) / (1 + csc θ)

= 1 - csc^2 θ / (1 + csc θ)

= 1 - 1/sin^2 θ / (1 + 1/sin θ)

= 1 - sin^2 θ / (sin θ + 1)

= (sin θ - sin^2 θ) / (sin θ + 1)

Simplify 1+csc θ as follows:

1 + csc θ = (1 + csc θ)(1 - csc θ) / (1 - csc θ)

= 1 - csc^2 θ / (1 - csc θ)

= 1 - 1/sin^2 θ / (1 - 1/sin θ)

= 1 - sin^2 θ / (sin θ - 1)

= (sin θ + sin^2 θ) / (sin θ - 1)

Substitute the above simplifications in the expression cos θ/(1-csc θ) * 1+csc θ/(1+ csc θ) to get:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

Simplify the expression by canceling out the sin^2 θ terms:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

= cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

Simplify further by factoring out common terms in the numerator and denominator:

cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

= cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

Finally, simplify the expression by factoring out a sin θ term from the denominator:

cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

= cos θ * (1 + sin θ) / [sin θ * (1 - sin θ) * (sin θ + 1)]

= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

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Weight cannot be represented as a function of height.

No, the weight of Karim's friends cannot be represented as a function of their height.

To represent weight as a function of height, there should be a consistent relationship between the height and weight values.

However, from the given data, we can see that for the same height, there are different weight values, and for the same weight, there are different height values.

This indicates that there is no one-to-one relationship between height and weight, and hence weight cannot be represented as a function of height.

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Every day, the number of views of the video increases by 80% of the previous day's views.

Every day, the number of views of the video increases by a certain percentage. To find the daily percent change in the views, we can use the formula for percent change, which is given by:

percent change = ((new value - old value) / old value) * 100

In this case, the old value is the number of views at the start, which is 500, and the new value is the number of views after one day, which is given by:

V(1) = 500*(1.8)^1 = 900

Substituting these values into the formula, we get:

percent change = ((900 - 500) / 500) * 100 = 80%

In other words, for every day that passes, the number of views of the video is multiplied by a factor of 1.8.

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The inequality represented by the given number line is: -60 ≥ m.

We can see the values that an inequality represents by placing it on a number line.

On a number line, inequalities are represented by drawing a straight line and designating the end points as an open or closed circle.

On a number line, inequality is represented as follows:

For the given number line,

-6 is shown with the closed circle, with lines extending towards +∞

Thus, the inequality represented by the given number line is: -60 ≥ m.

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The number of tiles that will be required to cover a floor with dimensions 2 meters by 3 meters is given as follows:

D. 120 tiles.

To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:

Area = Length x Width

The area of the floor is given as follows:

2 x 3 = 6 m².

The area in m² of each tile is given as follows:

0.25 x 0.2 = 0.05.

Hence the number of tiles that will be required to cover the floor is given as follows:

6/0.05 = 120 tiles.

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This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.

The confidence interval estimate of the population means examination score can be calculated using the sample mean and the margin of error. The margin of error depends on the level of confidence and the sample size.

For example, if a sample of 100 applications provided a sample mean score of 80, and a 95% confidence level is used, the confidence interval estimate of the population mean examination score would be:

Margin of error = (critical value) x (standard error)

The critical value for a 95% confidence level with 99 degrees of freedom is 1.984. The standard error can be calculated using the formula:

Standard error = (standard deviation) / sqrt(sample size)

If the standard deviation of the examination scores is known, it can be used in the formula. If not, the sample standard deviation can be used as an estimate.

Assuming a sample standard deviation of 10, the standard error would be:

[tex]Standard\  error = \frac{10} { \sqrt{(100)}} = 1[/tex]

Therefore, the margin of error would be:

Margin of error = 1.984 x 1 = 1.984

The confidence interval estimate of the population means examination score would be:

80 ± 1.984, or between 78.016 and 81.984.

This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.

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The 95% confidence interval for the population mean examination score would be between 72.23 and 77.77, to the

nearest whole number.

To determine the confidence interval estimate of the population mean examination score based on a sample mean

provided to the nearest whole number, we need to know the sample size and the level of confidence.

Assuming a normal distribution and a level of confidence of 95%, we can use the following formula to calculate the

confidence interval estimate:

Confidence interval = sample mean +/- (critical value) x (standard error)

The critical value can be found using a t-distribution table or a calculator, based on the sample size and degrees of

freedom (n-1). For a sample size of 30 or more, we can use the z-score instead of the t-score.

The standard error is the standard deviation of the sample divided by the square root of the sample size.

For example, if a sample of 50 applications provided a sample mean of 75, and the standard deviation was 10, the

standard error would be 10/sqrt(50) = 1.41.

Assuming a level of confidence of 95%, the critical value for a sample size of 50 and degrees of freedom of 49 would be 1.96.

Therefore, the confidence interval estimate would be:

75 +/- 1.96 x 1.41 = 75 +/- 2.77

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Both functions have the same axis of symmetry equation, which is x = -3.

Given that, Maxine graphs a function m(x) which has a vertex of (-3,4) and passes through the point (-1,-8).

Ricardo graphs p(x) = (x+3)² + 4

We need to check if both the function axis of symmetry equation.

So,

Both functions have a vertex of (-3,4), which means that the axis of symmetry must be a vertical line passing through x = -3.

Axis of symmetry = The axis of symmetry is an imaginary straight line that divides the shape into two identical parts or that makes the shape symmetrical.

For the function p(x) = (x+3)² +4, the axis of symmetry is indeed x = -3.

For the function m(x), since it has a vertex of (-3,4), the equation of the axis of symmetry is x = -3.

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The psychologist finds that the estimated Cohen's d is  0.32, the t statistic is 2. 83, and r² is 0.073.  Using r² and the extension of Cohen's guidelines for interpreting the effect size using r², there is a small treatment effect.   job seeker finds that the estimated Cohen's d is 0.88, the t statistic is 7. 78, and r² is 0.479.Using r² and the extension of Cohen's guidelines for interpreting the effect size with r², there is a large treatment effect

To calculate the estimated Cohen's d, we use the formula

d = (M - M0) / SD

where M is the mean of the treatment group (job seekers who received training on using the Internet to find job listings), M0 is the mean of the control group (typical job seeker), and SD is the pooled standard deviation of the two groups. Using the given values, we have

M = 8.7 months

M0 = 7.4 months

SD = 4.1 months

So, d = (8.7 - 7.4) / 4.1 = 0.32

Using Cohen's guidelines for interpreting effect size with Cohen's d, a value of 0.2 is considered a small effect, 0.5 a medium effect, and 0.8 a large effect. Therefore, with an estimated Cohen's d of 0.32, there is a small treatment effect.

To calculate r², we use the formula

r² = t² / (t² + df)

where t is the t statistic, df is the degrees of freedom (n-2 for a two-group design), and n is the sample size. Using the given values for the Internet training group, we have

t = 2.83

n = 81

df = 79

So, r² = 2.83² / (2.83² + 79) = 0.073

Using the extension of Cohen's guidelines for interpreting effect size with r², a value of 0.01 is considered a small effect, 0.09 a medium effect, and 0.25 a large effect. Therefore, with an r² of 0.073, there is a small treatment effect.

For the job seekers who received training on interview skills, we can calculate Cohen's d and r² in a similar way

d = (M - M0) / SD = (8.1 - 7.4) / 0.8 = 0.88

t = 7.78

n = 81

df = 79

r² = 7.78² / (7.78² + 79) = 0.479

Using Cohen's guidelines for interpreting effect size with Cohen's d, a value of 0.2 is considered a small effect, 0.5 a medium effect, and 0.8 a large effect. Therefore, with an estimated Cohen's d of 0.88, there is a large treatment effect.

Using the extension of Cohen's guidelines for interpreting effect size with r², a value of 0.01 is considered a small effect, 0.09 a medium effect, and 0.25 a large effect. Therefore, with an  r² of 0.479, there is a medium to large treatment effect.

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Answer:.317

.091

Small to med

Med

.875

.431

Large

Large

Step-by-step explanation: