PLEASE HELP V=1/3a^2h solve for h

Answer: FOIL method

1. (a + b)(a + b) =

= a² + ab + b² + ab

= a² + 2ab + b²

2. (3a-2b) (3a - 2b) =

= 9a² - 6ab - 6ab + 4b²

= 9a² -12ab + 4b²

3. (x - 4y)(-3x - 2y) =

= -3x² -2xy +12xy +8y²

= -3x² + 10xy + 8y²

4.(-y-2z)(y-2z) =

= -y² + 2yz -2yz + 4z²

= -y² + 4z²

Step-by-step explanation:

Step-by-step explanation:

6×(2.5)+1.5

15+1.5

16.5

or

f(x)= 6x+1.5

f(2.5)= 6(2.5)+15

f(2.5)=16.5

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Answer:

I think it's -35

Step-by-step explanation:

sorry if its wrong

Answer:

b = (F - g)/2M

Step-by-step explanation:

2Mb = F - g

Divide each side by 2M

2Mb/2M = (F - g)/2M

b = (F - g)/2M

Answer: Answer in steps

Step-by-step explanation:

2Mb =f-g    Divide both sides by 2M

b= \(\frac{f}{2M} - \frac{g}{2M}\)

In question 1;

The student multiplied without flipping the second expression.

In second question;

The negative should only be distributed to the numerator.

In third question,

3/2 should be remove from the x - value which make the expression undefined.

In fourth student;

Neither student is correct.

In fifth question,;

Sarah didn't cancel incorrectly in step 3.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

In question 1;

The expression is,

⇒ x² + 2x - 3 / (x² - 3x - 10) ÷ (2x + 12) / (8x + 16)

= (2x³ + 16x² + 18x - 36) / (8x³ - 8x² - 128x - 100)

Cleary, The student multiplied without flipping the second expression.

In question 2;

⇒ (-2y - 2) / (y² + 2y - 8) - (y - 1) / (2 - y)

⇒ (-2y - 2) / (y² + 2y - 8) + (-y + 1) / (-2 + y)

Clearly, The negative should only be distributed to the numerator.

In Question 3;

The student make mistake is ''3/2 should be remove from the x - value which make the expression undefined.''

In fourth student;

Neither student is doing correct solution.

In fifth question,;

Sarah didn't cancel incorrectly in step 3.

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Answer:

Olha,pirmieiro voce adiciona o AAS com o AABC e depois divide por 2. depois, voce ai ter que simplificar. eu iria simplificar por 2 mas vcque sabe.

Step-by-step explanation:

Answer:

y  >  2  −  x

Step-by-step explanation:

The area of the shaded region which is a semi-circle is 157ft.

What is semi-circle?

In geometry, a semicircle can be defined as a half of a circle formed by cutting the circle into two halves. It is formed when a line or cut passes through the center and touches the two end positions of the circle and the line is called the diameter of the circle.

The shaded region is a semi- circle.

The radius is 10 ft.

The formula for the area of semi- circle is π×r²/2 where π= 3.14 and r is the radius.

So, the area of the semi- circle is {3.14× (10)²}/ 2

                                                      = 157 ft.

Hence, the area of the shaded region which is a semi-circle is 157ft.

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The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is \($\sqrt{301}$\).

For part (a), we can find a nonzero vector orthogonal to the plane through the points P, Q, and R by constructing a normal vector to the plane using the cross product of two vectors in the plane. The two vectors in the plane are \($\vec{PQ} = (1- (-2), 0-1, 1-3) = (3, -1, -2)$\) and \($\vec{PR} = (1-4, 0-2, 1-5) = (-3, -2, -4)$\). Taking the cross product of the two vectors gives us the normal vector to the plane, \($\vec{n} = \vec{PQ} \times \vec{PR} = (8, -8, 12)$\). Therefore, the vector orthogonal to the plane is \($\vec{n} = (8, -8, 12)$.\)

For part (b), the area of triangle PQR can be found using the formula for Heron's Formula, which states that the area of a triangle with sides a, b,and c is given by

\($A = \sqrt{s(s-a)(s-b)(s-c)}$\)

where \($s = \frac{a+b+c}{2}$\) . In this case, the sides are \($a = \|\vec{PQ}\| = \sqrt{3^2 + (-1)^2 + (-2)^2} = \sqrt{14}$, $b = \|\vec{QR}\| = \sqrt{(-2-4)^2 + (1-2)^2 + (3-5)^2} = \sqrt{14}$\), and\($c = \|\vec{PR}\| = \sqrt{(-3)^2 + (-2)^2 + (-4)^2} = \sqrt{29}$\). Plugging these values into the formula, we get

\(= \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{\frac{7(7-\sqrt{14})(7-\sqrt{14})(7-\sqrt{29})}{4}} = \sqrt{7(7-\sqrt{14})^2(7-\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2(\sqrt{14}+\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2\sqrt{43}} = \sqrt{301}$\)Therefore, the area of triangle PQR is \($\sqrt{301}$\)

The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is \($\sqrt{301}$\).

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The transformation of C(9, 3) when dilated by a scale factor of 3, using the origin as the centre of dilation is C'(27,9).

The given coordinate is C(9, 3) and a scale factor is 3.

Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.

If any figure is dilated by a scale factor k with the centre of dilation as the origin.

Then the change pr transformation in each of the vertices of the figure is given by (x,y) ⇒ (kx, ky).

Here, k=3.

So, C(9,3) ⇒ C'(9×3,3×3)

= C(9,3) ⇒ C'(27,9)

Therefore, the transformation of C(9, 3) when dilated by a scale factor of 3, using the origin as the centre of dilation is C'(27,9).

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The number is 14. Dividing both sides by 4 gives -4 = 4 × number, which can be further simplified to number = -4 ÷ 4. This means that the number is 14.

20 = 4 × (number + 6)

20 = 4 × number + 24

20 - 24 = 4 × number

-4 = 4 × number

number = -4 ÷ 4

number = -1

The equation provided is 20 = 4 × (number + 6). Rearranging this equation gives 20 = 4 × number + 24. Subtracting 24 from both sides gives 20 - 24 = 4 × number. Dividing both sides by 4 gives -4 = 4 × number. Dividing both sides by 4 once again gives number = -4 ÷ 4. Therefore, the number is 14.

To find the number in the equation given, we can first rearrange the equation so it is in the form of 20 = 4 × number + 24. Then, subtracting 24 from both sides gives us 20 - 24 = 4 × number. Dividing both sides by 4 gives -4 = 4 × number, which can be further simplified to number = -4 ÷ 4. This means that the number is 14.

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32 miles. ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

We can expect the probability of an event of drawing two red cards to occur approximately 39 times in 300 simulations of the experiment.

We are provided that a deck contains 3 red and 2 yellow cards. this means that out exhaustible events, i.e., the number of total outcomes is 5 in an event. We are asked to find out the probability of drawing red cards:

P(red) = No. of possible outcomes/ Total number of outcomes

p(red) = 3/5

Since, we are asked the probability drawing two red cards in a row:

P(red and red) = (3/5) x (3/5) = 9/25

The probability of any particular outcome occurring twice in a row is the square of the probability of that outcome occurring once. Therefore, the probability of drawing two red cards in a row twice in a row is:

P(red and red) twice = (9/25)² = 81/625

To estimate how many times this event will occur in 300 simulations, we can use the expected value of the number of times this event will occur. The expected value is given by:

E(number of times) = number of simulations x probability of event

= 300 x 81/625

= 39

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Answer:  The sum of the interior angles of a heptagon is 900 degrees.

To estimate the integral √(ln(2)) ln(x) dx within an accuracy of 0.01 using upper and lower sums for a uniform partition of the interval [1, e], we need to divide the interval into at least n subintervals. The answer is obtained by finding the minimum value of n that satisfies the given accuracy condition.

We start by determining the interval [1, e], where e is approximately 2.718. The function ln(x)^2 is increasing, meaning that its values increase as x increases. To estimate the integral, we use upper and lower sums with a uniform partition. In this case, the width of each subinterval is (e - 1)/n, where n is the number of subintervals.

To find the minimum value of n that ensures the accuracy condition S - S < 0.01, we need to evaluate the difference between the upper sum (S) and the lower sum (S) for the given partition. The upper sum is the sum of the maximum values of the function within each subinterval, while the lower sum is the sum of the minimum values.

Since ln(x)^2 is increasing, the maximum value of ln(x)^2 within each subinterval occurs at the right endpoint. Therefore, the upper sum can be calculated as the sum of ln(e)^2, ln(e - (e - 1)/n)^2, ln(e - 2(e - 1)/n)^2, and so on, up to ln(e - (n - 1)(e - 1)/n)^2.

Similarly, the minimum value of ln(x)^2 within each subinterval occurs at the left endpoint. Therefore, the lower sum can be calculated as the sum of ln(1)^2, ln(1 + (e - 1)/n)^2, ln(1 + 2(e - 1)/n)^2, and so on, up to ln(1 + (n - 1)(e - 1)/n)^2.

We need to find the minimum value of n such that the difference between the upper sum and the lower sum is less than 0.01. This can be done by iteratively increasing the value of n until the condition is satisfied. Once the minimum value of n is determined, we have the required number of subintervals for the given accuracy.

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Answer:

64 ft

Step-by-step explanation:

The missing word is "modulus". The statement should read: Twelve is congruent to 60 (modulus 8) because both 12 and 60 have 4 as a remainder when divided by 8.

The modulus function, also known as the modulo operation or mod function, is a mathematical operation that returns the remainder when one integer is divided by another. The modulo operation is a quick and efficient way to find the remainder of a division. For example, if we want to know the remainder when 23 is divided by 5, we can simply compute 23 % 5, which equals 3. The symbol "%" is often used to represent the modulo operation in computer programming, while "mod" is used in mathematical notation to indicate congruence. In either case, the statement means that 12 and 60 leave the same remainder when divided by 8.

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7 pieces of paper were cut into part

Answer:

5 pieces

Step-by-step explanation:

original pieces of paper = 11

some cut into = 3 parts

new pieces of paper = 21

21 / 3 = 7 pieces were cut into three parts to make 21 pieces of paper,

but according to the question some of the paper got cut into three parts,

so we will stick to  5 pieces that were cut into three parts

as,

5*3 = 15 pieces

pieces left = 6

total = 21 pieces

thus, 5 pieces were cut into three equal parts

Answer:

35

Step-by-step explanation:

Add them together and then divide

Answer:

b + b + h + h

Step-by-step explanation:

You are finding the perimeter of the given rectangle. Note that by definition of a rectangle, the opposite parallel sides will have the same measurement. In this case, Terrance gives the expression of 2b + 2h, and so simply just expand the expression:

2b + 2h = b + b + h + h

~

Answer:7x−23=7x−23

49°=7x−23

3x=3x

11y−1=11y−1

Step-by-step explanation:

The conditions and assumptions for inference are reasonably satisfied, particularly with regard to random sampling, independence, and sample sizes.

To show that the conditions and assumptions for inference are satisfied, we need to assess whether the sample meets the necessary requirements. In this case, we are examining the support for the principal among white and minority students in a large school.

1. Random Sampling: The statement mentions that students were randomly chosen for the survey. Random sampling helps ensure that the sample is representative of the larger population. If the students were truly selected randomly, this condition is satisfied.

2. Independence: To conduct inference, it is essential to assume that the responses from different students are independent of each other. If students were selected randomly and surveyed independently without any influence from one another, this condition is likely to be satisfied.

3. Sample Size: The sample sizes for both white and minority students are given: 56 white students and 33 minority students. While sample size alone does not guarantee inference validity, larger samples tend to provide more reliable estimates.

4. Normality: For inference methods such as hypothesis testing or constructing confidence intervals, the sample data should follow an approximately normal distribution. Since we don't have information about the underlying population or the distribution of the responses, we cannot directly assess the normality assumption. However, if the sample sizes are sufficiently large (typically around 30 or more), the Central Limit Theorem suggests that the sampling distribution will tend to be approximately normal, even if the underlying population is not.

5. Random Assignment (for experiments): The statement doesn't mention whether this study is an experiment with a randomly assigned treatment. Since it only involves surveying students' opinions, this assumption is not applicable in this case.

Based on the information provided, it appears that the conditions and assumptions for inference are reasonably satisfied, particularly with regard to random sampling, independence, and sample sizes. However, without additional information or data, it cannot definitively confirm the exact nature of the population or distribution.

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The diameter of the sphere with a volume of 2171 m3, to the nearest tenth of a meter, is 16.1 m.

To find the diameter of a sphere with a volume of 2171 m³, we'll use the following formula for the volume of a sphere:

V = (4/3)πr³

Here, V is the volume and r is the radius of the sphere. We need to solve for r, then find the diameter (d), which is twice the radius (d = 2r).

Step 1: Substitute the given volume (2171 m³) into the formula:
r = (3V/4π)^(1/3)

Plugging in the given volume of 2171 m3, we get:

2171 = (4/3)πr³

Step 2: Solve for r³:

r³ = 2171 × (3/4) / π

r³ ≈ 520.44

Step 3: Find the cube root of r³ to get r:

r ≈ 8.05

Step 4: Find the diameter (d) by multiplying r by 2:

d = 2 × 8.05

d ≈ 16.1

To the nearest tenth of a meter, the diameter of the sphere is approximately 16.1 meters.

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Answer: 0

Step-by-step explanation:

Range = Highest number - lowest number

range = 6 - 6

range = 0

When dealing with figures that are round to the closest tenth, such as 5.460, it may be simpler to round the number to 5.5.

We must look at the hundredth digit, which is 6, in order to round 5.460 to the nearest tenth. We must round up to the next higher digit, which is 4, because 6 is bigger than or equal to 5. The result is 5.5, which has been rounded to the nearest tenth.

If the digit in the hundredths place is 5 or above, we round up the tenths digit; if it is less than 5, we leave the tenths digit as is. This is the basic rule we use when rounding numbers to the closest tenth. In this instance, we round up the tenths digit from 4 to 5 because the hundredths digit is 6. When we want to streamline calculations or explain numbers in a more understandable or natural way, rounding might be helpful.

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The number 7 emerged in human history through cultural and mathematical developments.

The significance of the number 7 can be observed in various aspects of human history. One of the earliest instances is found in ancient Mesopotamia, where the Sumerians developed a base-60 numeral system called sexagesimal.

This system contributed to the use of 60 as a highly divisible number and influenced the concept of dividing the day into 24 hours, each consisting of 60 minutes.

In ancient Egypt, the division of the week into seven days was based on the observation of celestial bodies.

The Egyptians associated each day with a different planet or celestial object, namely Sunday (Sun), Monday (Moon), Tuesday (Mars), Wednesday (Mercury), Thursday (Jupiter), Friday (Venus), and Saturday (Saturn). These planetary associations were later adopted by the Romans, and their names in English still reflect these origins.

The number 7 also holds religious and symbolic significance. In Judaism, the seventh day of the week, Saturday, is considered a day of rest, known as the Sabbath.

This tradition is rooted in the biblical story of creation, where God rested on the seventh day. In Christianity, the Book of Genesis describes the world being created in six days, with the seventh day being designated as holy.

Furthermore, the number 7 appears in mathematics and geometry. The seven colors of the rainbow, the seven musical notes, and the seven wonders of the ancient world are all examples of the cultural significance attributed to this number.

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Answer:

1

Step-by-step explanation:

Answer:

uh what is this address for or am i not supposed to be in this

Step-by-step explanation:

sorry if im getting in your buisness

a) If the true rate of rejection is 10%, then the probability that the production will be suspended based on a sample of 15 bearings is 10%.

b)  The assumptions made in part a are that the sample of 15 bearings is representative of the population of bearings produced, and that each bearing is independent of the others.

To ensure that the production process is producing quality products, samples of 15 bearings are taken periodically and carefully inspected. If more than 2 bearings in a sample of 15 fail to meet the required specifications, production is suspended for necessary adjustments.

a) If the true rate of rejection is 10%, what is the probability that the production will be suspended based on a sample of 15 bearings? To answer this question, we need to use the binomial distribution. The binomial distribution is used to calculate the probability of a certain number of successes in a fixed number of independent trials. In this case, the number of trials is 15, and the probability of success (i.e., a bearing not meeting the required specifications) is 10%.

b) The assumptions allow us to use the binomial distribution to calculate the probability of having a certain number of bearings fail to meet the required specifications in a sample of 15. Additionally, we assume that the true rate of rejection is 10%, which may not always be the case.

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The exact values of all angles in the interval [0, 360°) that satisfy the given equations are:

data = 45°, 135°, 315°.

To solve the given trigonometric equations, we will consider each equation separately.

tan²(data) - 1 = 0:

First, let's rewrite tan²(data) as (sin(data)/cos(data))²:

(sin(data)/cos(data))² - 1 = 0

Now, we can factor the equation:

(sin²(data) - cos²(data)) / cos²(data) = 0

Using the Pythagorean identity sin²(data) + cos²(data) = 1, we can substitute sin²(data) with 1 - cos²(data):

((1 - cos²(data)) - cos²(data)) / cos²(data) = 0

Simplifying further:

1 - 2cos²(data) = 0

Rearranging the equation:

2cos²(data) - 1 = 0

Now, we solve for cos(data):

cos²(data) = 1/2

cos(data) = ± √(1/2)

cos(data) = ± 1/√2

cos(data) = ± 1/√2 * √2/√2

cos(data) = ± √2/2

From the unit circle, we know that cos(data) = √2/2 corresponds to angles 45° and 315° in the interval [0, 360°). Therefore, the solutions for data are:

data = 45° and data = 315°.

cos(data)sin(data) = 1:

Since cos(data) ≠ 0 (otherwise the equation wouldn't hold), we can divide both sides by cos(data):

sin(data) = 1/cos(data)

sin(data) = 1/√2

From the unit circle, we know that sin(data) = 1/√2 corresponds to angles 45° and 135° in the interval [0, 360°). Therefore, the solutions for data are:

data = 45° and data = 135°.

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