Erica wants to fill the bottom of a planter with 2 in. of rocks, then fill the rest of the planter with soil all the way to the top. She wants the volume of the soil to be exactly 640 in.³. What could be the shape of Erica's planter? 12 in. 0- 1 10 in. 10 in. 8 in. 8 in. 10 in. 8 in. 10 in. 12 in. 8 in. 8 in. 10 in.​

The value of the identities are;

1. sin M = 3√39/20

2. sin M = √3/5

3. sin M = 3√19/14

4. sin M = √3/2

The different trigonometric identities and their ratios are written as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the information given, we have;

1. opposite = 3√39

Hypotenuse = 20

Then, sin M = 3√39/20

2. Opposite = 4√3

Hypotenuse = 20

sin M =  4√3/20

Divide the values

sin M = √3/5

3. The Opposite side = 3√19

Hypotenuse = 14

sin M = 3√19/14

4. Opposite = 6√3

Hypotenuse = 12

sin M =  6√3/12

Divide the values

sin M = √3/2

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The surface area of the triangular prism is 312 ft².

In order to calculate the surface area of a prism, we  twice the perimeter of base of the prism to twice the area of the base of the prism

To calculate the surface area of the triangular prism in the question, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the surface area is 312 ft².

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The equation that represents the cost of the rental truck is y = 0.42x + 71. The Option C is correct.

Let x be the number of miles driven

Let y be the cost of the rental truck.

We can set up a system of equations to represent the given information:

For Bob:

y = mx + b

112.96 = 138m + b

For Carl:

y = mx + b

142.78 = 209m + b

Solving for b in both equations, we get:

b = 112.96 - 138m

b = 142.78 - 209m

Setting the two expressions for b equal to each other, we get:

112.96 - 138m = 142.78 - 209m

209m - 138m  = 142.78 - 112.96

71 m = 29.82

m = 0.42

Substituting m into equation for b:

b = 71.

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If in an Bernoulli experiment the chance of picking red ball is 3.2 times higher than to pick a blue ball, the probability of picking a red ball is approximately 0.7619, or 76.19%.

A Bernoulli experiment is a statistical experiment that has only two possible outcomes, usually referred to as success and failure. In this case, the outcomes are picking a red ball or picking a blue ball.

Let's assume that the probability of picking a blue ball is P(B), and the probability of picking a red ball is P(R). We are given that the chance of picking a red ball is 3.2 times higher than the chance of picking a blue ball. Mathematically, this can be expressed as:

P(R) = 3.2 * P(B)

We also know that the sum of the probabilities of all possible outcomes must be 1, so:

P(R) + P(B) = 1

We can use these two equations to solve for P(R):

P(R) + (1/3.2) * P(R) = 1

(4.2/3.2) * P(R) = 1

P(R) = 3.2/4.2 = 0.7619

This means that out of every 10 balls, about 7.6 will be red and 2.4 will be blue.

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Complete question is:

In an Bernoulli experiment the chance of picking red ball is 3.2 times higher than to pick a blue ball. What is the probability of picking the red ball?

Based on the equation 441 + b² = 3011.81, the value of b is equal to 50.7032.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

Based on the given equation, we have the following;

441 + b² = 3011.81

By subtracting 441 from both sides of the equation, we have the following:

441 + b² - 441 = 3011.81 - 441

b² = 3011.81 - 441

b² = 2570.81

b = √2570.81

b = 50.7032.

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If the total trip takes 12 hours, the speed of the current is 1 mph.

The speed of an object is described as  the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time.

The downstream trip:

distance = rate × time

96 = (18 + x) × t ( 18 + x)

The upstream trip:

distance = rate × time

96 = (18 - x) × (12 - t)

96 = (18 - x) × (12 - t)

8 = x - (x/6)t

We have two equations and two unknowns, so we can solve for x and t.

We solve for x by making t subject fomula and substituting into the equation.

Where x = 1

In conclusion, if the total trip takes 12 hours, the speed of the current is 1 mph.

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Results from the Simple Interest:

1. The amount Tucker will receive in interest after 5 years = $1,165.50.

2 The simple interest rate Wilson would need to make his $9,000 grow to $85,000 in 16 years =  53%.

3. The number of years it will take for $7,000 to double in an account with 2.8% simple interest = ≈36 years.

4. The ending balance after 6 years = $25,472.

Using Simple interest formula: S.I. = P × R × T

Simple interest (SI) formular = Interest (I) = Principal (P) * Rate (R) * Time(T)

Given:

P= $7,400

R = 3.15% or 0.0315

T = 5 years

Plugging in the values:

Interest = ($7,400 * 0.0315 * 5)

Interest = $1,165.50

2) Using SI  formular: I = P* R * T

Given:

P = $9,000

I = $85,000 - $9,000 = $76,000 (as the total cost is the principal plus interest)

T = 16 years

Plugging in the values:

$76,000 = $9,000 * Rate * 16

R = $76,000 / ($9,000 * 16)

To convert  to percentage, we multiply by 100:

Rate = 0.531 * 100

Rate = 53.1%.

3) Using SI  formular: I = P* R * T

Given:

P = $7,000

R = 2.8%

I = P

T = ?

Plugging in the values and solving for Time (T):

$7,000 = $7,000 * 0.028 * T

T = $7,000 / ($7,000 * 0.028) = 35.7

T  ≈36 years

4. Using SI  formular: I = P* R * T

Given:

P = $20,000

R = 4.56%

T = 6 years

Plugging in the values:

P = $20,000

R = 4.56% or 0.0456

T = 6 years

Ending Balance (EB) = P + (Pl *  R * T)

EB = $20,000 + ($20,000 * 0.0456 * 6)

EB = $20,000 + $5,472

EB = $25,472

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The equation of this circle in general form is: (x - 1)^2 + (y - 3)^2 = 36

To find the equation of a circle in general form, we need to complete the square for both x and y terms.

x^2 + y^2 - 2x - 6y - 26 = 0

First, we will complete the square for x terms:

x^2 - 2x + y^2 - 6y - 26 = 0

(x - 1)^2 - 1 + y^2 - 6y - 26 = 0

(x - 1)^2 + y^2 = 27

Now, we will complete the square for y terms:

(x - 1)^2 + (y - 3)^2 = 36

Therefore, the equation of this circle in general form is: (x - 1)^2 + (y - 3)^2 = 36

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Answer:

x2+y2−2x−6y−26=0

Step-by-step explanation:

Just took the test.

Based on the given options and the information provided, the missing answer for "Reason 3" is option D, ASA.

The proof mentioned is based on the fact that the two triangles have two pairs of congruent angles and one pair of congruent sides.

This corresponds to the criteria for the ASA postulate, which states that if two triangles have two pairs of congruent angles and one pair of congruent sides, then the triangles are congruent.

Therefore, by using the ASA postulate, we can conclude that the two given triangles are congruent.

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The null hypothesis represents the default assumption or the status quo, while the alternative hypothesis represents the alternative possibility or the hypothesis that is being tested.

These two hypotheses are mutually exclusive, meaning that if one is true, the other must be false.

The null and alternative hypotheses divide all possibilities into two non-overlapping sets.

In statistical hypothesis testing, the null and alternative hypotheses divide all possibilities into two non-overlapping sets.

These two hypotheses represent different explanations or theories about the data, and they are used to make inferences about the population from the sample data.

The null hypothesis represents the default assumption or the status quo. It states that there is no significant difference or relationship between two variables, or that the observed data is due to random chance alone. The alternative hypothesis, on the other hand, represents an alternative explanation or theory about the data.

It states that there is a significant difference or relationship between two variables, or that the observed data is not due to random chance alone.

The null and alternative hypotheses are mutually exclusive, meaning that if one hypothesis is true, the other hypothesis must be false.

They are also exhaustive, meaning that they cover all possible explanations for the observed data.

By dividing all possibilities into two non-overlapping sets, the null and alternative hypotheses allow us to make a decision about which hypothesis is more likely to be true based on the evidence provided by the sample data.

In order to test the null and alternative hypotheses, we use statistical methods to calculate the probability of obtaining the observed data if the null hypothesis were true.

This probability is called the p-value, and it represents the likelihood of obtaining the observed data or a more extreme result if there were no true effect or relationship in the population.

If the p-value is small enough, we reject the null hypothesis in favor of the alternative hypothesis.

The null and alternative hypotheses divide all possibilities into two non-overlapping sets and provide a framework for making inferences about the population based on sample data.

By testing the null hypothesis and calculating the p-value, we can make decisions about which hypothesis is more likely to be true based on the evidence provided by the sample data.

In statistical hypothesis testing, we use evidence from the data to decide whether to reject the null hypothesis in favor of the alternative hypothesis or not.

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Answer: Assuming a significance level of 0.05 for each hypothesis test, the probability of committing a Type I error (rejecting the null hypothesis when it is actually true) in any given test is 0.05.

Therefore, the expected number of Type I errors in 1,900 hypothesis tests is:

Expected number of Type I errors = (0.05) x (1,900) = 95

So, we would expect to commit a Type I error about 95 times in 1,900 hypothesis tests, assuming the null hypothesis were true.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve this problem, we can use the formula:

distance = rate x time

Since Tina bicycles at a constant speed, we can simplify the formula to:

distance = speed x time

For the first 2 hours, Tina bicycles at a constant speed, so the distance she travels is:

distance = speed x time = s x 2

After taking a 1-hour break, Tina continues to bicycle at the same speed for another 2 hours, so the distance she travels is:

distance = speed x time = s x 2

Therefore, the total distance Tina travels over the 5-hour period is:

total distance = 2s + 2s = 4s

This means that the total distance Tina bicycles is directly proportional to the speed at which she travels. In other words, if Tina travels twice as fast, she will cover twice the distance in the same amount of time.

With this in mind, we can eliminate choices (A) and (B), which show linear relationships between distance and time. Since Tina is traveling at a constant speed, the graph of her distance should be a straight line with a positive slope.

Choice (C) shows a straight line with a positive slope, but the slope is too steep. This graph would indicate that Tina is traveling at a much faster speed than she actually is.

Choice (D) shows a straight line with a positive slope that is not as steep as (C). This graph accurately represents Tina's constant speed and shows the increase in distance after the break. Therefore, the correct graph is (D).

Example

It took Markus half an hour to drive home from work.  He averaged 34 miles per hour.  How far does Markus live from his work?

Solution

We are given that it takes 1/2 an hour for the trip.  This is a time:

       t  =  1/2

We are given that he averages 34 miles per hour.  This is a rate:

       r  =  34

We are asked how few he has traveled.  This is a distance.  We use the d=rt equation:

       d  =  rt

           =  (34)(1/2)

           =  17

Markus lives 17 miles from work.

The probability that a randomly selected student from this class has four or more pets at home is 4/31 ≈ 0.13 when rounded to the nearest two decimal places.

Explain probability

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, with 0 indicating no chance and 1 indicating certainty. Probability is calculated by dividing the number of desired outcomes by the total number of possible outcomes. It is used in many fields, including mathematics, statistics, science, and engineering.

According to the given information

Based on the data provided, there are a total of 4 students who have four or more pets at home

(0 with 4 pets + 1 with 5 pets + 2 with 6 pets + 1 with 7 pets).

Since there are a total of 31 students in the class, the probability that a randomly selected student from this class has four or more pets at home is 4/31 ≈ 0.13 when rounded to the nearest two decimal places.

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The value of k given the absolute value functions is (a) k = -5

Given that

graph = f(x)

table = g(x)

Since the vertex of the function f(x) is at (0,1), we have f(0) = 1.

Also, from the given table, we have g(0) = -4.

Therefore, if g(x) = f(x) + k, we must have g(0) = f(0) + k = 1 + k.

But we also know that g(0) = -4. Thus, we have:

1 + k = -4

Solving for k, we get:

k = -5

Therefore, the value of k is -5.

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The volume of the cheese head is 192 cubic inches.

Explain the term volume

Volume refers to the amount of space that an object or substance occupies in three dimensions. It is typically measured in units such as cubic meters or cubic feet. The volume of an object can be calculated using various formulas, depending on its shape and dimensions.

According to the given information

The volume V of a triangular prism is given by the formula:

V = (1/2) * b * h * L

In this case, the base of the triangle is 12 inches, the height of the triangle is 8 inches, and the length of the prism (depth of the 3D shape) is 4 inches. Substituting these values into the formula, we get:

V = (1/2) * 12 * 8 * 4

V = 192 cubic inches

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Answer: To find the coordinates of F' and G', we need to reflect points F and G across the line y = 5, since point D is located on this line.

For point F, the y-coordinate changes from 11 to -1, since the distance between the line y = 5 and point F is 6 units (2 times the distance between D and the line). Therefore, the coordinates of F' are (3,-1).

For point G, the y-coordinate changes from 8 to 2, since the distance between the line y = 5 and point G is 3 units (1.5 times the distance between D and the line). Therefore, the coordinates of G' are (2,2).

Thus, the coordinates of F' are (3,-1) and the coordinates of G' are (2,2).

The image vertices of N'M'O' after reflecting triangle NMO over x = -2 are N'(1, 2), M'(-2, 1), and O'(-1, 3).

What is meant by vertices?

Vertices (singular: vertex) are the points where two or more edges meet in a geometric shape or object. They are also known as corners and are a defining feature of many shapes, including polygons, polyhedra, and graphs.

What is meant by a triangle?

A triangle is a geometric shape with three sides and three angles. It is a fundamental shape in geometry and has many practical applications in mathematics, science, and engineering.

According to the given information

In this case, the line of reflection is x = -2. The distance from N's x-coordinate to the line of reflection is |-5 - (-2)| = 3. So the x-coordinate of N' is -2 + 3 = 1. The y-coordinate of N' remains the same as N's y-coordinate, so N' = (1, 2).

The distance from M's x-coordinate to the line of reflection is |-2 - (-2)| = 0. So the x-coordinate of M' is -2 + 0 = -2. The y-coordinate of M' remains the same as M's y-coordinate, so M' = (-2, 1).

The distance from O's x-coordinate to the line of reflection is |-3 - (-2)| = 1. So the x-coordinate of O' is -2 + 1 = -1. The y-coordinate of O' remains the same as O's y-coordinate, so O' = (-1, 3).

So the image vertices of N'M'O' after reflecting triangle NMO over x = -2 are N'(1, 2), M'(-2, 1), and O'(-1, 3).

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Answer:

x=2

Step-by-step explanation:

This is a system of equations that we can solve by using substitution.

We know that y=7. We know that y is also equal to 8x-9.

Since y is equal to both 7 and 8x-9, this must mean that 7 is also equal to 8x-9.

Let's set them equal and solve for x, like so:

[tex]y=8x-9=\\7=8x-9=\\16=8x=\\2=x[/tex]

So, x=2.

The value of the functions are;

f(-4) = 1/16

f(-3) = 1/8

f(-2) = 1/4

f(-1) = 1/2

f(0) = 1

It is important to note that functions are described as equations or expressions that shows the relationship between two variables.

From the information given, we have that;

The function, f(x) = 2ˣ

To determine the value of f(x) for -4, we have to substitute the value

f(x) = 2⁻⁴

find the value

f(-4) = 1/2⁴ = 1/16

For the value of f(-3)

f(-3) =2⁻³

find the value

f(-3) = 1/2³ = 1/8

For the value of -2

f(-2) = 2⁻²

f(-2) = 1/2² = 1/4

For the value of -1

f(-1) = 2⁻¹

f(-1) = 1/2¹ = 1/2

For the value of 0

f(0) = 2⁰

f(0) = 1

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Answer:

6/6=1

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

512 / 4 = 128

128 / 4 = 32

32 / 4 = 8

8 / 4 = 2

ans. (c) 1/2

given line,

y = 1/2 x -2

we know that the slope form of the line is given by

y =mx+c

comparing both equations we get

m= 1/2

hence, the slope is 1/2

Answer:

The answer to your problem is, B. 0.125

Step-by-step explanation:

Here is something that is simple so you will not forget easily.

( Just replace the numbers like how you shown in fraction )

= [tex]\frac{125}{1000}[/tex]

= 125 ÷ 1000

= 0.125

Simple but effective

0.125 is the answer.

Thus the answer to your problem is, B. 0.125

(a) The simplified and correct expression is (6×7)-(5 +4) = 16

(b) The simplified and correct expression is (-2x²) + (24÷12)-4 = 2

a. 6×7-5 +4= 16

In this calculation, we need to use brackets to ensure the correct order of operations, which is typically remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division [from left to right], Addition and Subtraction [from left to right]).

Without brackets, the calculation would be evaluated as follows:

6×7-5 +4 = 42-5 +4 (applying multiplication first)

= 37 +4 (applying subtraction)

= 41 (applying addition)

However, the desired result is 16. To achieve this, we can use brackets to group the addition and subtraction operations together, like this:

(6×7)-(5 +4) = 42 - 9 (applying addition within the brackets first)

= 33 (applying subtraction)

b. -2x²+24÷12-4=2

Similarly, in this calculation, we need to use brackets to ensure the correct order of operations.

Without brackets, the calculation would be evaluated as follows:

-2x²+24÷12-4 = -2x²+2-4 (applying division first)

= -2x²-2 (applying addition and subtraction)

However, the desired result is 2. To achieve this, we can use brackets to group the division and subtraction operations together, like this:

-2x²+(24÷12)-4 = -2x²+2-4 (applying division within the brackets first)

= -2x²-2 (applying addition and subtraction)

By adding brackets to each calculation to ensure the desired order of operations, we arrive at the correct results of 16 and 2, respectively.

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Answer: 7/9

Step-by-step explanation: 3 + 4 = 9

add the /9 = 7/9

If you know that a girl plays soccer, then the probability that she also plays basketball = 0.23

The correct answer is an option (c)

Let's assume that event S: a girl plays soccer

event B: a girl plays basketball

Here, the probability that the girl plays soccer would be,

P(S) = P(SB) + P(SB')

where B' means a girl does not play basketball

here, P(SB) = 0.075 and P(SB') = 0.250

So, P(S) = 0.075 + 0.250

P(S) = 0.325

We need to find the probability that a girl plays basketball knowing that she plays a soccer.

i.e., the conditional probability P(B|S)

Using formula for the conditional probability,

P(B|S) = P(BS) / P(S)

           = 0.075 / 0.325

           = 0.23

Therefore, the correct answer is an option (c)

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Find the complete question below.

A value of 26 is 2.5 standard deviations away from the mean.

To find the number of standard deviations away from the mean, we can use the formula:

z = (x - μ) / σ

where x is the value we want to convert to a z-score, μ is the population mean, and σ is the population standard deviation.

In this case, the value we want to convert is x = 26, the population mean is μ = 16, and the population standard deviation is σ = 4. Substituting these values into the formula, we get:

z = (26 - 16) / 4 = 2.5

This means that the value of 26 is 2.5 standard deviations away from the mean. Since the z-score is positive, we know that the value of 26 is above the mean. Therefore, the answer is option D, 2.5.

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Answer: 71

Step-by-step explanation: to get the answer you have to know that all the angles of a triangle have to add up to 180 so therefore you add the angles they gave you and then you minus them from 180 and you get 71

To construct a confidence interval for the proportion of defectives, we should use the plus four method.

Since the sample size is 20, which is not very large, the large-sample interval is not appropriate. Instep, we ought to utilize a strategy that's suitable for little test sizes. 

The plus four method is one such method that is commonly used when the sample size is small. Therefore, to construct a confidence interval for the proportion of defectives, we should use the plus four method.

The plus four strategies may be a strategy for building a certainty interim for an extent when the test estimate is little.

To utilize this strategy, we to begin with include four fanciful perceptions to our test, two of which are flawed and two of which are not imperfect.

This increments the test estimate to 24, which permits us to utilize the typical guess to the binomial dispersion to build the certainty interim.

The equation for the certainty interim utilizing the also four strategies is:

p ± zα/2 √((p + 2) (1 - p + 2) / n + 4)

where:

p is the test extent (number of defectives/test estimate)

zα/2 is the basic esteem from the standard typical dissemination at the level of importance α/2

n is the test estimate (counting the included four nonexistent perceptions)

Therefore, to construct a confidence interval for the proportion of defectives, we should use the plus four method.

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Answer:

12000 In 12 days

Step-by-step explanation:

12÷4=3

4000×3=12000