4(3x + 2) < 5(3x − 2)

The point estimate of the population standard deviation is 5.91 (Option A)

Standard deviation refers to the spread of a data distribution and measures the distance between each data point and the mean. The sample standard deviation (s) is a point estimate of the population standard deviation σ.

The mean of the population ẋ = sum of all values/ total number of values = 97/6 ≈ 16

The point estimate of the population standard deviation S =√(∑(xi - ẋ)^2/n-1)

∑(xi - µ)^2 = (9 – 16)^2 + (13– 16)^2 + (15– 16)^2 + (15– 16)^2 + (21– 16)^2 + (24– 16)^2 = 79 + 9 + 1 + 1 + 25 + 64 = 179

s = √(179/5) = 5.98

Note: The question is incomplete. The complete question probably is: The following information was collected from a simple random sample of a population. 9 13 15 15 21 24 The point estimate of the population standard deviation is Select one: O a. 5.91. O b. 7.688. O C. 7.018. O d. 4.925.

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Answer: 8.77

Step-by-step explanation:

When the cost of a gallon of milk increases from $2.81 to $3.48 over a period of 10 years the annual inflation rate is 2.15 percent.

What is a annual inflation rate?

A percentage is used to represent the inflation rate. For instance, a yearly inflation rate of 2% indicates that the cost of products and services as a whole has increased by 2%. As an illustration, a product that cost $10 last year will cost $10.20 this year.

Here, we have

Given

The cost of the gallon of milk earlier was $2.81

The cost of a gallon of milk now is $3.48.

The total time period is 10 years.

r = (F/P)ⁿ⁻¹ - 1

r = {(3.48/2.81)^(1/10) - 1}×100

r = {(1.238)^(1/10) - 1}×100

r = 0.0215 ×100

r = 2.15

Hence, when the cost of a gallon of milk increases from $2.81 to $3.48 over a period of 10 years the annual inflation rate is 2.15 percent.

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Answer:

9x + 1

Step-by-step explanation:

45x + 5

-------------

     5

Coefficient of x in the expression given is 0.

In any given expression when a variable has a constant or number written before itself it is called the coefficient of the variable. Coefficients are always numbers.

Solution:

Given expression: \(5x^{3}+7x^{2}+5\) (Assumption since question is not clear)

Now coefficient of x³ is 5, x² is 7 and x=0  and constant is 5

Over here we have been asked the coefficient of variable x and not \(x^{2}\) or \(x^{3}\) so we write the expression as

\(5x^{3}+7x^{2}+0x+5\)

∴ Coefficient of x = 0

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107, y = 25Step-by-step explanation:z and 73 are same- side interior angles and are supplementary, sum to 180°z + 73 = 180 ( subtract 73 from both sides )z = 107z and (3y + 32) are vertical angles and are congruent, then3y + 32 = 107 ( subtract 32 from both sides )3y = 75 ( divide both sides by 3 )y = 25

Answer:

I believe the answer is A.

Step-by-step explanation:

Correct me if im wrong plz thanks

Answer:

I think the answer is A

Length of longer piece of rope is 11.7 m.

Define Equation.

A mathematical statement known as an equation is one that places the symbol "equal to" between two expressions with the same values. In any mathematical equation, we have LHS = RHS (left hand side = right hand side). Equations can be solved to find the value of an unknown variable that represents an unknown quantity.

Given data-

Length of a rope = 20.6 m

First piece of rope is 2.8 shorter than other.

As rope is cut into two pieces

Let the first piece of rope be x m and second piece of rope be (x - 2.8) m.

As per the given data, we can create an equation

x + (x - 2.8) = 20.6

2x - 2.8 = 20.6

2x = 23.4

x = 11.7

Length of first piece of rope is 11.7 m

Length of second piece of rope = (x - 2.8)

= 11.7 - 2.8

= 8.9 m.

Length of longer piece of rope is 11.7 m.

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Answer:

B. x = 3

Step-by-step explanation:

3³ = 27

3 · 3 · 3 = 27

9 · 3 = 27

This is an example of interviewer bias where the gender of the interviewer may have impacted the replies of the unmarried males in the poll.

This is an example of interviewer bias, where the gender of the interviewer may have influenced the responses of the unmarried men in the survey. The results may not accurately reflect the true opinions of the participants as their answers could have been affected by their desire to impress or please the interviewer.

This situation is an example of response bias, specifically interviewer bias, which occurs when the respondent's answer is influenced by the gender or characteristics of the interviewer, rather than their true preferences or opinions.

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Answer:

1

Step-by-step explanation:

3 divided by 1/3 is 9, and 9-9=0

0+1=1

1

Step-by-step explanation:

To show that A is diagonalizable over the real numbers, we can choose any real numbers a, b, and c such that the matrix A can be diagonalized. One example is choosing a = 7, b = 0, and c = 2, which leads to a diagonal matrix D.

To show that matrix A is diagonalizable over the real numbers, we need to find infinitely many real numbers a, b, and c such that A can be diagonalized.

Let's consider the characteristic equation of matrix A:

| A - λI | = 0

Substituting the values of A and the identity matrix I:

| 7-a a b |

| 0 2-c c |

| 0 0 3-λ |

Expanding the determinant, we get:

(7-a)(2-c)(3-λ) - a(b)(0) = 0

(7-a)(2-c)(3-λ) = 0

For A to be diagonalizable, the characteristic equation should have infinitely many distinct real eigenvalues.

From the equation (7-a)(2-c)(3-λ) = 0, we can choose any real values for a, b, and c, and we can set λ = 3.

For example, let a = 7, b = 0, c = 2, and λ = 3:

| 7-7 7 0 |

| 0 2-2 2 |

| 0 0 3-3 |

Simplifying the matrix A:

| 0 7 0 |

| 0 0 2 |

| 0 0 0 |

This matrix A is already in a diagonal form, so it is diagonalizable.

To find the invertible matrix M such that M^-1 AM = D, we can choose:

M = | 7 0 0 |

| 0 2 0 |

| 0 0 1 |

Taking the inverse of M:

M^-1 = | 1/7 0 0 |

| 0 1/2 0 |

| 0 0 1 |

Calculating M^-1 AM:

M^-1 AM = | 1/7 0 0 | | 7 0 0 | | 7 0 0 |

| 0 1/2 0 | * | 0 2 0 | = | 0 1 0 |

| 0 0 1 | | 0 0 1 | | 0 0 1 |

The resulting matrix is a diagonal matrix D, which verifies that A is diagonalizable with the invertible matrix M.

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The correct answer is b). Yes, the p-value for testing for a positive correlation between age and body fat percentage is 0.039. Since the p-value is small we reject the null hypothesis of no relationship.

In statistics, the p-value is used to determine the likelihood that the observed relationship between two variables occurred by chance. If the p-value is small, it means that the relationship is statistically significant and unlikely to have occurred by chance. In this case, the p-value of 0.039 indicates that there is a statistically significant positive relationship between age and body fat percentage.

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Answer:

Step-by-step explanation:

The value of each variable in the given polygon is x = 4 and y = 3.

Triangles that resemble one another but may not be precisely the same size are said to be comparable triangles. When two items have the same shape but different sizes, they can be considered to be comparable. This indicates that comparable forms superimpose one another when amplified or demagnified. The term "Similarity" refers to this characteristic of like forms. If the sides are in the same ratio or proportion and the angles are equal (corresponding angles), two triangles will be comparable (corresponding sides). Similar triangles may have varied side lengths when compared individually, but they must all have equal angles and the same ratio of their side lengths.

The two triangles are similar hence, the ratio of the lengths of their sides are also equal.

Here,

5 / 10 = y / 6

Using cross multiplication we have:

y = 5/10 (6)

y = 3

Also,

5/10 = x/8

x = 5/10(8)

x = 4

Hence, the value of each variable in the given polygon is x = 4 and y = 3.

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Container 1: The unit rate for Container 1 from Home Depot is $14.98 per gallon. Container 2: The unit rate for Container 2 from Lowes is $115.00 per gallon. The unit rate for each container tells us how much one gallon of paint costs from each store.

The unit rate for the paint from Home Depot is $14.98 per gallon and the unit rate for the paint from Lowes is $115.00 per gallon. This tells us that the paint from Home Depot is cheaper than the paint from Lowes.

Step 1: To calculate the rate for each container, divide the cost of the container by the number of gallons in the container.

Container 1: $14.98 per gallon = $14.98 / 1 gallon

Container 2: $115.00 per gallon = $115.00 / 1 gallon

Step 2: To calculate the unit rate for each container, divide the cost of the container by the number of units in the container.

Container 1: $14.98 per gallon = $14.98 / 1 unit

Container 2: $115.00 per gallon = $115.00 / 1 unit

Step 3: The unit rate for each container tells us how much one gallon of paint costs from each store.

Container 1: The unit rate for Container 1 from Home Depot is $14.98 per gallon.

Container 2: The unit rate for Container 2 from Lowes is $115.00 per gallon.

The theory used in this question is the concept of unit rate, which is used to compare the prices of different products.

Unit rate is defined as the cost per unit of measure (e.g., price per gallon, price per pound, etc.).

In this case, we are using the unit rate of price per gallon to compare the prices of paint from Home Depot and Lowes.

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Answer: 1,666,666.666666667

The result is approximately 0.037, which means that 1 cubic foot is equal to approximately 0.037 cubic yards.

In measurement, "cf" stands for cubic feet, while "cy" stands for cubic yards. To convert cubic feet to cubic yards, you can use the following conversion factor:

1 cubic yard = 27 cubic feet

To convert 1 cubic foot to cubic yards, divide the number of cubic feet by 27. Therefore:

1 cubic foot = 1/27 cubic yards

So 1 cubic foot is equal to approximately 0.037 cubic yards (rounded to three decimal places).

Therefore, to convert 1 cf to cy, you simply need to divide 1 by 27. The result is approximately 0.037, which means that 1 cubic foot is equal to approximately 0.037 cubic yards.

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Answer:

950

Step-by-step explanation:

19 ×5

then add the zero

Answer:

6

Step-by-step explanation:

To calculate x+10, we first need to find x. To do this, we can use the first equation.

We are given the equation:

\(x^2-8x=48\)

To solve for x, turn one side of the equation into 0 and solve. Therefore:

\(x^2-8x=48\\x^2-8x-48=0\\(x-12)(x+4)=0\\x=-4, 12\)

So, the possible values for x are -4 and 12.

However, we are also told that x<0. In other words, x must be negative. Thus, we can remove 12. That leaves us with: x=-4.

So:

\(x+10\\(-4)+10\\=6\)

Answer:

8%

Step-by-step explanation:

8 out of 100 are green

8/100  * 100% = 8 %

Answer:

8% of the beads are green

Step-by-step explanation:

Step 1:  Determine what percentage of the beads are green

This problem is known as a probability problem which basically tries to determine the proportionality between certain numbers.  In this example we are trying to figure out the proportionality between the green beads and the total sample.  

(8 green beads) / (100 total beads)

0.08

0.08 is the probability but if we want to determine what the percentage is of the number we just multiply it by 100.

0.08 * 100 = 8%

Answer:  8% of the beads are green

The mean (μ) is 105, the variance (σ^2) is 17.64, and the standard deviation (σ) is approximately 4.2.

To find the mean, variance, and standard deviation of a binomial distribution, you can use the following formulas:

Mean (μ) = n  p

Variance (σ^2) = n p  (1 - p)

Standard Deviation (σ) = √(n p  (1 - p)

Given n = 125 and p = 0.84, we can calculate the mean, variance, and standard deviation as follows:

Mean (μ) = 125  0.84 = 105

Variance (σ^2) = 125  0.84  (1 - 0.84) = 17.64

Standard Deviation (σ) = √(125 0.84  (1 - 0.84)=4.2

Therefore, the mean (μ) is 105, the variance (σ^2) is 17.64, and the standard deviation (σ) is approximately 4.2.

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Sarah earns $120 per week from her part-time job. To complete the table, we need to list her expenses.  Sarah's expenses may vary, but here are some common examples she might have:

1. Transportation: Sarah may spend money on bus fare or gas if she drives. This expense depends on her mode of transportation and how far she travels.
2. Food: Sarah needs to eat, so she may spend money on groceries or meals outside. The amount spent on food will depend on her eating habits and whether she eats out frequently or cooks at home.
3. Utilities: Sarah may have to pay for utilities like electricity, water, and internet. The cost of utilities can vary depending on the region and the size of her living space.

4. Rent/ Mortgage: If Sarah lives independently or contributes to household expenses, she may have to pay rent or contribute to a mortgage payment.
5. Entertainment: Sarah may have expenses related to leisure activities such as going to the movies, concerts, or other entertainment events.
These are just a few examples, and Sarah's actual expenses may differ. It's important for her to track her spending to understand where her money goes. By doing so, she can budget effectively and make informed financial decisions.

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The given equation is W(s,t) = F(u(s,t), v(s,t)), where F, u, and v are differentiable functions. The values of u, u_s, u_t, v, v_s, v_t, F_u, and F_v at the point (3,0) are provided. We need to find the value of t.

To find the value of t, we can substitute the given values into the equation and solve for t. Let's substitute the values:

u(3,0) = -3

u_s(3,0) = -7

u_t(3,0) = 4

v(3,0) = 3

v_s(3,0) = -8

v_t(3,0) = -2

F_u(-3,3) = 6

F_v(-3,3) = -1

Substituting these values into the equation, we have:

W(3,t) = F(u(3,t), v(3,t))

W(3,t) = F(-3,3)

Now, since F_u(-3,3) = 6 and F_v(-3,3) = -1, we can rewrite the equation as:

W(3,t) = 6 * (-3) + (-1) * 3

W(3,t) = -18 - 3

W(3,t) = -21

Therefore, the value of t that satisfies the given conditions is t = -21.

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The width of the rectangle is approximately 9.66 meters.

The formula for the area of a rectangle is:

Area = length * width

Let's assume the width of the rectangle as x meters.

According to the problem, the length of the rectangle is 4 meters longer than its width.

So,

the length of the rectangle would be (x+4) meters.

Substituting the given values, we get:

117 = (x+4) * x

\(117 = x^2 + 4x\)

Rearranging the terms, we get a quadratic equation in standard form:

\(x^2 + 4x - 117 = 0\)

To solve for x, we can use the quadratic formula:

x = [-b ± (\(\sqrt{ b^2 - 4ac\))] / 2a

Where a = 1, b = 4, and c = -117.

Substituting the values, we get:

x = [-4 ± \(\sqrt{4^2 - 4(1)(-117)\))] / 2(1)

x = [-4 ± √472)] / 2

x = (-4 ± 2√118)) / 2

x = -2 ± √118

The width of the rectangle cannot be negative. Therefore, we take the positive root:

x = -2 + √118

x ≈ 9.66 meters (rounded to two decimal places)

Therefore, the width of the rectangle is approximately 9.66 meters.

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In school suspension

Using a proportional relationship, it is found that she would be able to drive 240 miles on 8 gallons of gasoline.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

Researching the problem on the internet, it is found that she drives 30 miles per gallon, hence the function for the distance driven considering the number of gallons in the tank is given by:

D(n) = 30n.

She has n = 8 gallons, hence the distance is given by:

D(8) = 30 x 8 = 240 miles.

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Answer:

81

Step-by-step explanation:

Area is multiplying all side

9 x 9 = 81