Q9. Alice worked 52 hours this week. She gets paid $9.35 per hour for the
first 40 hours and then gets time-and-a-half for the rest of the time. How
much money did she make this week?

Hunter and three friends spent a total $41 of money.

Addition is the process used to combine things and count them as a single, large group. Addition in mathematics is the process of combining two or more numbers. The term "sum" refers to the result of the process, and "addends" refers to the numbers that are added.

Given, Hunter and three friends were going to the movies.

The movie tickets cost $10 each.

So, cost of movie ticket is 3 times $10 = $30.

And they bought three popcorn at $7.25, and three drinks at $2.75.

That means, the expenditure other than movie is;

$7.25 + $2.75 = $11

To find the total money they spent:

Add all the expenditures,

$30 + $11 = $41.

Therefore, they spent $41.

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 The inverse of the matrix. A^-1(b) =

[-2/5, -1/5, -1/5]

[1/5, 1/5, 1/5]

[3/5, 2/5, -1/5]

The value of x,y,z are:

x = 2/5,

y = -1/5,

z = -2/5.

To find the inverse of the matrix A, we use the formula A-1 = (1/det A) × adj(A). We calculate the determinant as det A = (1)(-2)(-1) - (-2)(1)(-1) + (3)(1)(-2) = 1 + 2 - 6 = -5. Then, the inverse of the matrix A is A-1 = (-1/5) × adj(A) = (-1/5) ×

[-2, 1, 3]

[1, -1, -2]

[-1, 1, -1]

= (-1/5) ×

[-2, -1, -1]

[1, 1, 1]

[3, 2, -1]

=

[-2/5, -1/5, -1/5]

[1/5, 1/5, 1/5]

[3/5, 2/5, -1/5]

Now, we use the inverse matrix to solve the system:

x - 2y + 3z = 1

-x + y - 2z = -2

x - y - z = -1

A-1A = I, so A-1 × [x y z] = [1 -2 -1], so

[x y z] = A-1 × [1 -2 -1] =

[-2/5, -1/5, -1/5] × [1 -2 -1]

+ [1/5, 1/5, 1/5] × [1 -2 -1]

+ [3/5, 2/5, -1/5] × [1 -2 -1]

= [2/5 -1/5 -2/5]

Therefore, x = 2/5, y = -1/5, z = -2/5.

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Answer:

x =48° because it alternates with angle a

Alternate angles are equal.

Answer:

21

Step-by-step explanation:

straight line = 180 degrees ( H,D,R)

180 = 7x - 3 + 2x  - 6    

180 = 7x + 2x - 3 - 6     (group the same type number together)

180 = 9x -9           (simplify the numbers)

189 = 9x    (+9)

21 = x    (divide by 9)

Answer:

1000-0=1/2(2000-0)

y= 1/2x

-1x + 2y = 0

The total profit will be maximized by using the objective function Z = 22x₁ + 53x₂ + 124x₃ + 25x₄ + 156x₅ + 37x₆ + 108x₇ + x₈

To formulate this problem mathematically, we need to define the decision variables, objective function, and constraints.

We will define a binary decision variable, \(x_i\), which indicates whether or not to invest in project i. If \(x_i\) = 1, the project i will be funded, and if \(x_i\) = 0, the project i will not be funded.

The objective is to maximize the total profit earned by investing in the selected projects. Thus, the objective function can be written as:

Maximize Z = 22x₁ + 53x₂ + 124x₃ + 25x₄ + 156x₅ + 37x₆ + 108x₇ + x₈

This objective function adds the profit of all the projects that will be funded based on the decision variable \(x_i\).

The total investment cannot exceed the available investment budget of $1 million, which can be written as:

0.50x₁ + 1.40x₂ + 1.70x₃ + 1.10x₄ + 4.00x₅ + 0.60x₆ + 2.50x₇ + 1.10x₈ <= 1

Additionally, the decision variables are binary, which means that x_i can only be either 0 or 1. Therefore, we can add binary constraints for each decision variable as follows:

x_i = 0 or 1 for i = 1,2,3,4,5,6,7,8

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The definitional formula is easy to use when the mean is a whole number, the range of scores is small, and there are either relatively few scores or many of them are zero.

The definitional formula is an equation used to calculate the mean of a set of scores. It is easy to use when the mean of the scores is a whole number, meaning there is no need to round. Additionally, if the range of scores is small, it is easier to find the mean, as there is less data to consider. Furthermore, the formula is easier to use when there are either relatively few scores or many of them are zero. This is because there is less data to consider, meaning the mean can be found more quickly. When there are many scores, and the range is large, it can be difficult to calculate the mean using the definitional formula. In this case, it is often more efficient to use an alternate method such as the arithmetic mean.

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The complete question is

Under what circumstances is the definitional formula easy to use

-When the mean is a whole number and there are relatively few scores

-When the mean is a whole number and the range is small

-When the mean is a whole number and there are many scores

-When there are relatively few scores and many of them are zero

Answer:

7 is the answer

mark as the Brainliest

Answer:

The expression i think Gabriel might have written is

3x + 6

Step-by-step explanation:

i may not be right

The Sun is approximately 9.2661 x 10^7 miles farther than the Moon from Earth.

The distance between the Sun and the Earth is approximately 9.29 x 10^7 miles, and the distance between the Moon and the Earth is approximately 2.389 x 10^5 miles.

To find how much farther the Sun is from the Earth than the Moon, we can subtract the distance between the Moon and the Earth from the distance between the Sun and the Earth:

9.29 x 10^7 miles - 2.389 x 10^5 miles = 9.2661 x 10^7 miles

Therefore, the Sun is approximately 9.2661 x 10^7 miles farther than the Moon from Earth.

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(1) The probability that a randomly selected car has a cd player is 0.7575.

(2) The probability that a randomly selected car either is a mercedes or has a cd player is 0.8475.

(1) Let P(CD) be the probability that a randomly selected car has a CD player. Then, using the law of total probability, we have:

P(CD) = P(CD | Lexus) x P(Lexus) + P(CD | Infinity) x P(Infinity) + P(CD | Mercedes) x P(Mercedes)

where P(Lexus), P(Infinity), and P(Mercedes) are the probabilities of selecting a Lexus, Infinity, or Mercedes respectively.

Substituting the given values, we get:

P(CD) = 0.35 x 0.25 + 0.85 x 0.3 + 0.8 x 0.45 = 0.7575

Therefore, the probability that a randomly selected car has a CD player is 0.7575.

(2) Let P(Mercedes) be the probability of selecting a Mercedes and P(CD) be the probability of selecting a car with a CD player, as calculated above. Then, using the addition rule of probability, we have:

P(Mercedes or CD) = P(Mercedes) + P(CD) - P(Mercedes and CD)

To find P(Mercedes and CD), we can use the multiplication rule of probability:

P(Mercedes and CD) = P(CD | Mercedes) x P(Mercedes) = 0.8 x 0.45 = 0.36

Substituting the given and calculated values, we get:

P(Mercedes or CD) = 0.45 + 0.7575 - 0.36 = 0.8475

Therefore, the probability that a randomly selected car either is a Mercedes or has a CD player is 0.8475.

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Option-B is correct that is exponential growth. The new Malthusians fear that a lack of food will result from the population's exponential growth.

Given that,

The new Malthusians worry that ______ of the population will lead to a scarcity of food.

We have to fill the blank.

We know that,

A pattern of data that exhibits larger increases over time, forming the curve of an exponential function, is said to exhibit exponential growth.

The formula for the exponential growth is

V=S×(1+R\()^{T}\)

The starting value, S, of an initial starting point subject to exponential growth can be multiplied by the sum of one plus the interest rate, R, raised to the power of T, or the number of periods that have passed, to get the current value, V.

Therefore, Option-B is correct that is exponential growth. The new Malthusians fear that a lack of food will result from the population's exponential growth.

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In degrees Celsius, the difference between Michigan's record low temperature and Colorado's record low temperature  to the nearest tenth if necessary is 5.50°C

The concept that wil be used here is temperature conversion. The degrees Celsius,  of Michigan's record low temperature can be calculated as

-51.7 °F we can convert to  °C,Using the equation below

F=1.8C+32

-51.7 ° = 1.8C+32

1.8C=-51.7 ° - 32

1.8C= -83.7

°C= -83.7/1.8

=-45.5°C

The degrees Celsius,  of Michigan's record low temperature can be calculated as -51. °C

The difference, in degrees Celsius, between colorado's record=( -45.5°C)  -(-51. °C) = 5.5°C

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The probability of a Type II error is represented by beta. Thus, the correct answer is option B.

Beta represents the probability of failing to reject the null hypothesis when it is false.

On the other hand, Type I error (alpha) represents the probability of rejecting the null hypothesis when it is true. A Type II error occurs when a false null hypothesis is not rejected. Hence, beta is the probability of making a Type II error.

The null hypothesis is rejected when the p-value is less than or equal to the level of significance, not exceeds it.

The p-value is the probability of obtaining a result as extreme as or more extreme than the observed result when the null hypothesis is true. If the p-value is less than the level of significance, the null hypothesis is rejected, and vice versa.

Hence, the statement "The null hypothesis is rejected when the p-value exceeds the level of significance" is false.

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To find out how far a car will travel (in feet) before a driver reacts to an obstacle, given that the car is moving at 34 miles per hour in a residential neighborhood, we need to convert the speed of the car from miles per hour to feet per second. This can be done using the conversion factor that 1 mile per hour is equal to 1.46667 feet per second. Therefore, 34 miles per hour is equal to 34 x 1.46667 = 49.86678 feet per second.

We know that the average reaction time of the driver is 1.2 seconds, and we can use the following formula to calculate the distance traveled by the car before the driver reacts to the obstacle:

d = v x t

where d is the distance, v is the velocity, and t is the time taken. Using the formula above, we can calculate the distance traveled by the car before the driver reacts to the obstacle as:

d = 49.86678 x 1.2 = 59.84014 feet

Therefore, the car will travel 59.84014 feet before a driver reacts to an obstacle.

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Answer:

Step-by-step explanation:

This two point should be pass in the point (0,0)

So, we will write it like this :

y2 - y1 over X2 - X1 :-

8-0 over -4-0 = -2

then we will write it like that to find what is X :

3-0 over X-0 = 3/X

we know that the answer is -2 So, the 3/X should be equal to -2

So, X = -1.5

The P-value of the test statistic is approximately 0.0445. To determine the P-value, we need to perform a hypothesis test. The null hypothesis (H₀) is that the actual percentage of chips that do not fail is equal to or less than the stated percentage of 73%.

The alternative hypothesis (H₁) is that the actual percentage is greater than 73%.

We can use the normal approximation to the binomial distribution since the sample size is large (1300) and both expected proportions (73% and 74%) are reasonably close. We calculate the test statistic using the formula:

z = (P - p₀) / √[(p₀ * (1 - p₀)) / n]

where P is the sample proportion (74% or 0.74), p₀ is the hypothesized proportion (73% or 0.73), and n is the sample size (1300).

Substituting the values, we get:

z = (0.74 - 0.73) / √[(0.73 * 0.27) / 1300]

Calculating this expression, we find that z is approximately 1.556.

Since we are testing if the actual percentage is more than the stated percentage, we are interested in the right-tailed area under the standard normal curve. We find this area by looking up the z-value in the standard normal distribution table or using statistical software. The corresponding area is approximately 0.0596.

The P-value is the probability of observing a test statistic as extreme as, or more extreme than, the one obtained under the null hypothesis. Since the P-value (0.0596) is less than the significance level of 0.05, we have enough evidence to reject the null hypothesis.

Therefore, there is sufficient evidence at the 0.05 significance level to support the quality control manager's claim that the actual percentage of chips that do not fail in the first 1000 hours is more than the stated percentage.

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Answer:

10.17 Seconds

Step-by-step explanation:

Answer:

5n^3

Step-by-step explanation:

For this type of problem, you can do the numbers and the variables separately and then combine them at the end.

First, lets do the variables:

n^4 has the following factors: n^1, n^2, n^3, n^4

n^3 has the following factors: n^1, n^2, n^3

The greatest common factor is n^3

Now for the numbers.

5 has the following factors: 1,5

30 has the following factors: 1,2,3,5,6,10,15,30

The greatest common factor is 5

Put it all together and the answer is 5n^3

Answer:

the greatest common factor between those is 5n^3

Step-by-step explanation:

So if you factor out 5n^3 you would have,

5n^3(n+ 6)

Answer:

16.028 yards

Step-by-step explanation:

1 inch=0.0833333 foot

24 inches=0.0833333×24

=1.9999992 foot

The mirror is square shaped and each side is 24 inches

If each 24 inches=1.9999992 foot

Then,

4 sides of 24 inches=1.9999992×24

=47.9999808 foot

Maria has 1 foot of trim left

Total Length of trim when she started=47.9999808+0.0833333

=48.0833141 foot

=16.02777136667 yards

Approximately,

16.028 yards

(a) correctly describes the relationship between a parameter and a statistic.

The correct description is:

a) A statistic is calculated from sample data and is generally used to estimate a parameter.

In statistics, a parameter refers to a characteristic or measure that describes a population, while a statistic is a characteristic or measure calculated from sample data. Statistics are often used to estimate or infer the corresponding parameters of the population. Therefore, option (a) correctly describes the relationship between a parameter and a statistic.

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Infinitely many position vectors with length 2 in xyz-space are orthogonal to the nonzero position vector v. (D)

A position vector in xyz-space is a vector that starts at the origin and ends at a point in xyz-space. The length of a position vector is the distance from the origin to the point it ends at.

If we want to find position vectors with length 2 that are orthogonal (perpendicular) to a given nonzero position vector v, we can use the dot product.

Let w be a position vector with length 2 that is orthogonal to v. Then, the dot product of v and w must be zero, since they are orthogonal. That is, v · w = 0. Since the length of w is 2, we can write w as 2u for some unit vector u. Thus, v · w = v · (2u) = 2(v · u) = 0.

This means that v and u are orthogonal as well, since the dot product of two vectors is zero if and only if they are orthogonal.

There are infinitely many unit vectors u that are orthogonal to v, and therefore, there are infinitely many position vectors with length 2 that are orthogonal to v. Therefore, the answer is (d) infinitely many.

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Based on the information provided, we have a simple random sample of eight classes and their corresponding numbers of students. However, it is not clear what the numbers are or what the sample mean and sample standard deviation values are. Without this information, it is difficult to determine if it is appropriate to perform a hypothesis test about the population mean.

In general, when conducting hypothesis tests about the population mean, it is important to consider the sample size, the distribution of the data, and the assumptions of the test. For smaller sample sizes, it is typically recommended to have a normal distribution in the population or use statistical tests that are robust to violations of normality assumptions. In this case, it is mentioned that the sample size is small, but without further information about the distribution of the data or the specific hypothesis being tested, it is not possible to definitively determine if it is appropriate to perform a hypothesis test about the population mean.

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It will cost $8,783.69 to complete this prank.

To get number of balls needed, we will calculate volume of the room and divide it by the volume of a single ball.

Volume of the room = Length * Width * Height

Volume of the room = 10ft * 10ft × 3ft

Volume of the room = 300 cubic feet

Radius = diameter / 2

Radius = 3in / 2

Radius = 1.5in

Radius = 1.5/12ft

Radius = 0.125ft

Volume of a single ball = (4/3) * π * (radius)^3

Volume of a single ball = (4/3) * π * (0.125ft)^3

Volume of a single ball ≈ 0.013 cubic feet

Number of balls needed = Volume of the room / Volume of a single ball

Number of balls needed = 300 cubic feet / 0.013 cubic feet

Number of balls needed =  23,077 balls

Since a 100 pack is purchased for $37.99:

Number of packs needed = Number of balls needed / 100

Number of packs needed ≈ 23,077 balls / 100 balls per pack

Number of packs needed ≈ 231 packs

Total cost = Number of packs needed × Cost per pack

Total cost ≈ 231 packs × $37.99 per pack

Total cost = $8,783.69

Full question:

Bri is doing her schoolwork in a room that is 10ft by 10ft. Since it’s the end of the year we’ve decided to fill this room with 3” diameter plastic balls to a depth of 3ft. Estimate the number of balls needed to fill her office space. To keep things consistent round the volumes of the plastic ball to the nearest thousandths.

A 100 pack of multi colored 3in plastic balls can be purchased at Walmart for 37.99. How much would it cost us to complete this prank.

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In recent years, the poverty rate in the United States was approximately a percentage of the total population.

The poverty rate in the United States refers to the proportion of the population that falls below the poverty threshold, which is determined by the federal government. The poverty rate is calculated by comparing a household's income to the poverty guidelines set by the Department of Health and Human Services. The exact percentage of the poverty rate can vary from year to year and is influenced by various economic and social factors.

To provide an accurate answer to the question, it is necessary to refer to specific data from recent years. However, as an AI language model, I do not have access to real-time or up-to-date information. I recommend referring to reliable sources such as government reports or reputable research organizations to obtain the most current data on the poverty rate in the United States.

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Given :

Magnitude of vector is 30 units.

Direction of vector from x-axis is 116°.

To Find :

The component form of the vector.

Solution :

We know, vector in component form is given by :

\(\vec{v} = (Acos\ \theta) \hat{i} + (Asin\ \theta)\hat{j}\)

Putting given values,

\(\vec{v} = (30\times cos\ 116^o) \hat{i} + (30\times sin\ 116^o)\hat{j}\\\\\vec{v} = -13.15 \hat{i} + 0.90 \hat{j}\)

Hence, this is the required solution.

To identify the restaurant with the distribution closest to normal for sodium, we can calculate the goodness-of-fit measures, such as the Anderson-Darling test or the Shapiro-Wilk test, for each restaurant's sodium distribution and select the one with the highest p-value indicating the closest agreement to normality.

To answer the probability questions and identify the restaurant with the distribution closest to normal for sodium, we need access to the dataset and perform statistical calculations using R programming language. Unfortunately, as a text-based AI, I don't have direct access to external datasets or the capability to execute code. However, I can provide you with an outline of the steps you can follow to conduct the analysis:

1. Load the dataset: Import the dataset containing information about the restaurants, including the variable of interest (sodium levels).

2. Probability questions: Formulate two probability questions related to the dataset. For example:

  a) What is the probability that a randomly selected restaurant has sodium levels above a certain threshold?

  b) What is the probability that a randomly selected restaurant has sodium levels within a specific range?

3. Theoretical normal distribution: Assuming that the sodium variable follows a normal distribution, calculate the probabilities using the theoretical normal distribution. You will need to estimate the mean and standard deviation from the dataset.

4. Empirical distribution: Calculate the probabilities using the empirical distribution. This involves computing the sample mean and sample standard deviation from the dataset and using these estimates to calculate the probabilities.

5. Compare the results: Compare the probabilities obtained from the theoretical normal distribution and the empirical distribution. Assess the agreement between the two methods by examining the differences in probabilities.

6. Identify closest to normal distribution: Analyze the sodium variable for each restaurant and assess which restaurant's distribution exhibits the closest resemblance to a normal distribution. This can be done by visually inspecting histograms or using statistical tests such as the Shapiro-Wilk test.

By following these steps and implementing the necessary code in R, you will be able to answer the probability questions and determine which restaurant's sodium distribution is closest to normal.

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Answer:

Each side of the triangle is 1/24 unit.

Step-by-step explanation:

Equilateral triangle is a triangle with equal sides  and perimeter is given by the formula:

P = 3a

where a is the length of one side

Given: P = 1/8 unit

Solve for a:

P = 3a

1/8 unit = 3a

Divide both sides of the equation by 3 to get the value of a

(1/8unit)/3 = 3a/3

1/24 unit = a

a = 1/24 unit

The length of each side of the triangle is 1/24 unit.

Perimeter is the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).

We are given that;

Perimeter= 1/8unit

Now,

To find the length of each side of an equilateral triangle, you need to divide the perimeter by 3, since all three sides are equal.

In this case, the perimeter is 1/8 unit, so you need to divide 1/8 by 3.

You can do this by multiplying 1/8 by the reciprocal of 3, which is 1/3:

8/1​÷3=8/1​×3/1​

=1/8×3/1×1​

=1/24​

Therefore, by the given perimeter the answer will be 1/24 unit.

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