Someone help plss/a. Consider the cube shown below. Identify the two-dimensional shape of the cross-section if the
cube is sliced horizontally.
b. Starting with the same cube, identify the two-dimensional shape of the cross-section if the cube is
sliced vertically.
c. Explain why the shapes are the same or different.

Answer:

457

Step-by-step explanation:

220+237=457

a) The probability that the demand will exceed 200 cfs during the early after- noon on a randomly selected day is 0.1353.

b)  The water-pumping capacity that the station should maintain during early afternoons is 460.52 cfs, so that the probability that demand will exceed capacity on a randomly selected day is only 0.01.

a) The given probability distribution of the demand for water during the early afternoon hours is given as exponentially distributed with a mean of 100 cfs. Therefore, the random variable X, representing the demand for water during early afternoon hours, follows exponential distribution with parameter λ = 1/100. We are required to find the probability that the demand will exceed 200 cfs during the early afternoon on a randomly selected day. By definition of probability density function of exponential distribution, the probability that the demand for water during early afternoon hours will exceed 200 cfs on a randomly selected day is:  

P(X > 200) = e-2  ≈ 0.1353

b) Given that the probability that demand will exceed capacity on a randomly selected day is only 0.01, we can write this in terms of the probability density function of exponential distribution as:

P(X > c) ≤ 0.01, where c is the water-pumping capacity that the station should maintain during early afternoons.

If X ~ Exponential distribution with parameter λ, the probability density function is given by:

f(x) = λ e-λx;  x > 0

For the probability P(X > c) ≤ 0.01, we have:

P(X > c) = e-λc ≤ 0.01 (probability distribution function of exponential distribution)

⇒ e-λc = 0.01

⇒ λc = ln(100) = 4.6052

⇒ c = 4.6052 * 100 = 460.52 cfs

Therefore, the station should maintain a pumping capacity of 460.52 cfs.

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Step-by-step explanation:

BRO I USE TO DO THIS IN 7TH GRADE I GOT YOU.

Answer:

234

Step-by-step explanation:

Answer:

Step-by-step explanation:

Equation of circle: [tex](x-a)^2+(y-b)^2=r^2[/tex]  where (a,b) is center and r is radius.

This is a circle with center [tex](\frac{5}{2} ,4)[/tex] and radius [tex]\sqrt{60}[/tex].

Diameter [tex]=2 \times radius=2\sqrt{60} =4\sqrt{15}[/tex]

Answer: When dividing a polynomial by a monomial, we can simply divide each term in the polynomial by the monomial.

So, dividing (8zy² - 28z¹y5 + 12z³y7) by (4z¹y³) gives:

(8zy²)/(4z¹y³) - (28z¹y5)/(4z¹y³) + (12z³y7)/(4z¹y³)

Simplifying each term by canceling out any common factors gives:

2y^(-1)z^(1-1) - 7y^(5-3)z^(1-1) + 3y^(7-3)z^(3-1)

which simplifies to:

2yz^0 - 7y^2z + 3y^4z^2

Therefore, (8zy² - 28z¹y5 + 12z³y7) ÷ (4z¹y³) = 2yz^0 - 7y^2z + 3y^4z^2.

Step-by-step explanation:

Polynomial functions can only have 2 terms which is true.

Monomials are polynomials that contain only one term. Examples: 15x 2, 3b, and 12y 4 Binomials are polynomials that contain only two terms. Examples: x + y, 4x – 7, and 9x + 2

Therefore, Polynomial functions can only have 2 terms which is true.

Answer:

False

Step-by-step explanation:

Polynomial functions contain two or more terms.

Hope this helps

The demeaned approach's advantages over the LSDV approach are it gives more accurate coefficient estimates, as it accounts for variations in the intercepts across different units because it can prevent multicollinearity, which is the correlation between two independent variables.

The demeaned approach refers to subtracting the unit means from every variable in the dataset. By subtracting the means from every variable in the dataset, this approach simplifies the regression model's interpretation and can enhance its estimation accuracy.

The LSDV approach involves adding a dummy variable for every single unit in the dataset. By adding a dummy variable for each unit, the LSDV approach keeps the data unaltered and estimates coefficients for each unit individually. However, this method can be inconvenient if the data includes many units.

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Answer: 70km

Step-by-step explanation: 280/4=70

Let's have a couple of examples:

You're going to drive at an average of 70km/h for 4 hours. Distance is speed multiplied by time, so: 70km/h * 4 hours = 280km.

You are going to run for 80km in 6 hours  80/6=13.33. You will run 13.33 km an hour 13.33x6= 80km

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The experiment has not been repeated.

The answer to the question:1. (a) The sum of squares for the factor is 14.18.2. (b) The number of degrees of freedom for the single factor in the experiment is 1.3. (c) The number of degrees of freedom for the error is 23.4. (d) The mean square for error is 1.64.5. (e) The value of the test statistic is 8.63.6. (f) If the significance level is 0.05, the conclusion is to reject the null hypothesis. Yes.7. (g) The p-value for the test statistic is 0.0086.8. (i) Laura used how many levels of the factor in this experiment? One.9. (j) Laura replicated this experiment how many times? The experiment has not been repeated.A complete randomized design with a single factor was conducted by physics graduate student Laura van Iertia. She is hoping to solve the mystery of the unified theory and complete her dissertation with the results of this experiment. The results of this experiment are summarized in the following ANOVA display:Source df SS MS F Factor 1 14.18 14.18 8.63 Error 23 37.75 1.64 - Total 24 52.93 - The questions and answers based on this experiment are given below:(a) The sum of squares for the factor is 14.18.(b) The number of degrees of freedom for the single factor in the experiment is 1.(c) The number of degrees of freedom for the error is 23.(d) The mean square for error is 1.64.(e) The value of the test statistic is 8.63.(f) If the significance level is 0.05, the conclusion is to reject the null hypothesis. Yes.(g) The p-value for the test statistic is 0.0086.(i) Laura used how many levels of the factor in this experiment? One.(j) Laura replicated this experiment how many times? The experiment has not been repeated.

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In a trapezoid, the height is the perpendicular distance between the two parallel bases. It is usually denoted as "h".

In order to determine the height of a trapezoid, we need to know the lengths of the two parallel bases or have additional information about the trapezoid's dimensions.

The lengths of the bases of a trapezoid are crucial for calculating the height using various formulas. Without the lengths of the bases or any other relevant information, we cannot determine the height of the trapezoid.

To determine the height of a trapezoid, we need more information. The height of a trapezoid is typically defined as the perpendicular distance between the two parallel bases. In this case, we would need to know the lengths of the two parallel bases or have additional information about the trapezoid's dimensions. Without that information, we cannot determine the height of the trapezoid.

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Answer: 5 units

Step-by-step explanation:

A motorboat with a speed of 10 km/hr in still water travels 35 km upstream on a river and 18 km up an adjacent stream for 8 hours. The speed of the river's current is approximately 5.55 km/hr.

Let's call the speed of the stream's current "v" km/hr, and the speed of the river's current "v - 1" km/hr (since it is 1 km/hr slower than the stream's current). Let's also call the speed of the motorboat in still water "s" km/hr.

When the motorboat is traveling upstream (against the current), its effective speed is:

s - (v - 1)

When the motorboat is traveling downstream (with the current), its effective speed is:

s + (v - 1)

Using the formula distance = speed x time, we can set up two equations based on the distances traveled upstream and downstream:

35 = (s - (v - 1))t1

18 = (s + (v - 1))t2

We also know that the total time spent on the trip is 8 hours:

t1 + t2 = 8

We can use the first equation to solve for t1:

t1 = 35 / (s - (v - 1))

We can use the second equation to solve for t2:

t2 = 18 / (s + (v - 1))

Substituting these expressions for t1 and t2 into the third equation, we get:

35 / (s - (v - 1)) + 18 / (s + (v - 1)) = 8

Multiplying both sides by (s - (v - 1))(s + (v - 1)), we get:

35(s + (v - 1)) + 18(s - (v - 1)) = 8(s - (v - 1))(s + (v - 1))

Expanding and simplifying, we get:

53s - 17v + 17 = 4s^2 - 4v^2 + 6s + 6v

Rearranging and simplifying, we get:

4s^2 - 47s + 4v^2 + 23v - 17 = 0

We have two unknowns (s and v), so we need another equation. We can use the fact that the speed of the motorboat in still water is 10 km/hr:

s - v = 10

We can solve this equation for s:

s = v + 10

Substituting this expression for s into the previous equation, we get:

4(v + 10)^2 - 47(v + 10) + 4v^2 + 23v - 17 = 0

Expanding and simplifying, we get:

4v^2 + 74v - 477 = 0

Solving this quadratic equation using the quadratic formula, we get:

v ≈ 5.55 km/hr (rounded to two decimal places)

Therefore, the speed of the river's current is approximately 5.55 km/hr.

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Answer: To sketch all the possible rectangles that Kay could make with 16 small squares and 1 large square, we can arrange them in different configurations. For example:

One possible rectangle could have a length of 8 small squares and a width of 2 small squares. The large square would be used to fill in the empty space at one end of the rectangle.

 8 small squares

8 small squares

1 large square

The area of this rectangle is (8)(2) + 1 = 17. We can write this in standard form as 17 and in factored form as 17 = 17(1).

Another possible rectangle could have a length of 4 small squares and a width of 4 small squares. The large square would be used to fill in the empty space at one end of the rectangle.

4 small squares 4 small squares

4 small squares 4 small squares

1 large square

The area of this rectangle is (4)(4) + 1 = 17. We can write this in standard form as 17 and in factored form as 17 = 1(17).

A third possible rectangle could have a length of 8 small squares and a width of 1 small square. The large square would be used to fill in the empty space at one end of the rectangle.

8 small squares

1 large square

The area of this rectangle is (8)(1) + 1 = 9. We can write this in standard form as 9 and in factored form as 9 = 9(1).

A fourth possible rectangle could have a length of 4 small squares and a width of 2 small squares. The large square would be used to fill in the empty space at one end of the rectangle.

4 small squares 2 small squares

4 small squares 2 small squares

1 large square

The area of this rectangle is (4)(2) + 1 = 9. We can write this in standard form as 9 and in factored form as 9 = 3(3).

So, there are four possible rectangles that Kay could make with 16 small squares and 1 large square, and the area of each rectangle can be expressed in both standard form and factored form as shown above.

Step-by-step explanation:

A significant difference between the theoretical and experimental probabilities in this case may be due to the relatively small sample size of 25 spins.

According to the law of large numbers, as the sample size (the number of times the experiment is repeated) increases, the experimental probability of an event approaches its theoretical probability.

The law of large numbers can be expressed mathematically using the following formula:

P(E) ≈ n(E)/n

where P(E) is the experimental probability of event E, n(E) is the number of times event E occurs in the experiment, and n is the total number of trials (or spins, in this case).

As n (the sample size) increases, the experimental probability P(E) approaches the theoretical probability of the event, which we can represent as P'(E). Mathematically, we can write:

lim P(E) = P'(E)

n→∞

In other words, as the sample size approaches infinity, the experimental probability approaches the theoretical probability.

Therefore, if Jess had spun the pointer many more times, the experimental probability of the pointer landing on 3 would have approached the theoretical probability of 25%. On the other hand, the relatively small sample size of only 25 spins may have introduced some chance variation that caused the experimental probability of 16% to differ significantly from the theoretical probability.

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This equation involves a cosine function shifted to the right by pi/2 units [tex]y = cos(x - \pi /2) - 1[/tex]

Explain about cosine function ?

The cosine function is a mathematical function that describes the relationship between the angles and the adjacent sides of a right triangle. It is defined as the ratio of the adjacent side of a right triangle to its hypotenuse.

In trigonometry, the cosine function is often represented as cos(θ), where θ is the angle of interest. The value of the cosine function for a given angle θ can range from -1 to 1, depending on the angle's position relative to the x-axis.

According to the question:
Based on the description you provided, it seems like option (c) is the correct answer:

[tex]y = cos(x - \pi /2) - 1[/tex]

This equation involves a cosine function shifted to the right by pi/2 units, which causes the wave to start below the x-axis. The additional -1 at the end of the equation causes the entire graph to be shifted downward by one unit.

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The missing side of the right triangle is 12 feet

The Pythagorean theorem is a mathematical theorem that states that the length of the longest leg or side of a given triangle is equal to the sum of the squares of the other two sides.

The other two sides of the triangle are the opposite and the adjacent side.

From the information given in the diagram, we have;

Hypotenuse = 37

Opposite side = 35

Adjacent side = x

Substitute the values

37² = 35² + x²

find the squares

1369 = 1225 + x²

make 'x' the subject of formula

x² = 144

Find the square root

x = 12 feet

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Answer:

Carl used a total of 3 liters of coffee in all.

Step-by-step explanation:

There are 1000 milliliters (mL) in a liter, so to convert from milliliters to liters, you need to divide by 1000.

To find the total amount of coffee used, you can multiply the number of mugs by the volume of each mug:

12 mugs x 250 mL/mug = 3000 mL

To convert this to liters, you divide by 1000:

3000 mL ÷ 1000 = 3 L

Therefore, Carl used 3 liters of coffee in all.

Answer:

Carl used 3 liters of coffee in all

Step-by-step explanation:

Step 1: multiply 12 by 250 to determine how mL are in all the mugs of coffee which gets you 3000

Step 2 convert: There are 1000 milliliters (mL) in a liter, so to convert from milliliters to liters, you need to divide by 1000. So divide 3000 by 1000 to find how much liters Carl uses in all. Which gets you 3

Therefore, Carl used 3 liters of coffee in all

The measure of angle B is in the given cyclic quadrilateral is 140 ⁰.

The measure of angle B is calculated by applying the principle of circle geometry for cyclic quadrilateral.

From the given figure, we will have the following equation;

angle D + angle B = 180 (opposite angles of a cyclic quadrilateral are supplementary)

x + ( 4x - 20 ) = 180

5x - 20 = 180

5x = 200

x = 200/5

x = 40

The measure of angle B is calculated as;

∠B = 4x - 20

∠B = 4 (40) - 20

∠B = 160 - 20

∠B = 140 ⁰

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Jake interpreted the mean as the mode. Half the cats weighed less than pounds and half weighed more.

What is mean and mode?

In statistics, mean and mode are two common measures of central tendency used to describe a set of data:

Mean: The mean, also known as the average, is calculated by adding up all the values in a data set and dividing the sum by the total number of values. It is a measure of the central location of the data, and it gives us an idea of the typical value of the data set. For example, the mean weight of a group of cats can tell us the typical weight of a cat in that group.

Mode: The mode is the value that appears most frequently in a data set. It is a measure of the most common value or values in the data, and it is useful for describing the shape of the distribution of the data. For example, the mode of the weights of a group of cats can tell us the most common weight among the cats in that group. It is possible for a data set to have more than one mode (bimodal or multimodal).

Jake's error is that he interpreted the mean as the mode, which is the most frequent value in a data set. The mean, however, is the average value of a data set and is calculated by adding all the values and dividing by the total number of values. Therefore, his interpretation that half the cats weighed less than the mean and half weighed more is incorrect. In reality, the mean only tells us the average weight of all the cats in the data set, but it does not indicate anything about the distribution of weights.

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Ross's profit percentage is 17%.

How to calculate the percentages?

To calculate a percentage, you need to divide the part by the whole and then multiply the result by 100. The formula is:

Percentage = (part/whole) x 100

Let's work through the problem step by step:

Ross bought the chair for 1000.

1. He marked it up by 30%, which means he added 30% of 1000 to the original price:

[tex]1000 + 0.3 * 1000 = 1300[/tex]

2. He gave a discount of 10%, which means he subtracted 10% of the marked-up price:

[tex]1300 - 0.1 * 1300 = 1170[/tex]

3. The customer paid 1228.50 inclusive of a 5% tax, which means the original price before tax was:

1228.50 / 1.05 = 1170

4. Ross's profit was the difference between the price he sold the chair for and the price he bought it for:

1170 - 1000 = 170

5. To find the profit percentage, we divide the profit by the cost and multiply by 100:

[tex](170 / 1000) * 100 = 17%[/tex]

Hence, Ross's profit percentage is 17%.

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Yes, there is a correlation between the number of hours per week a student works outside of school and how many units the student takes in a quarter.

The cluster sample of 482 students is chosen in order to examine the relationship between these two variables. The statistical relationship between two variables is known as correlation.

The correlation coefficient r is used to determine the degree and direction of the correlation between two variables. The correlation coefficient is a numerical value that ranges from -1 to +1.

A negative correlation exists when one variable decreases as the other variable increases. A positive correlation exists when both variables increase or decrease together.

In this case, if the number of hours per week a student works outside of school increases, the number of units the student takes in a quarter may decrease, indicating a negative correlation between the two variables. Similarly, if the number of hours per week a student works outside of school decreases, the number of units the student takes in a quarter may increase, indicating a positive correlation between the two variables.

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The probability that fewer than five of the 11 randomly selected adult smartphone users will use their phones during meetings or classes is 0.6747

When adults with smartphones are randomly selected, 53% use them during meetings or classes. You need to find the probability that fewer than five of the 11 selected adults use their smartphones during meetings or classes. Here's how to calculate the probability that fewer than five of the 11 randomly selected adult smartphone users will use their phones during meetings or classes:

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

Where X represents the number of smartphone users in the selected group who use their phones in meetings or classes. Using the binomial probability formula, you can calculate each of these probabilities separately.

[tex]P(X = 0) = (11C0)(0.53)^0(1 - 0.53)^11 = 0.0026\\P(X = 1) = (11C1)( 0.53)^1(1 - 0.53)^10 = 0.0247\\P(X = 2) = (11C2)(0.53)^2(1 - 0.53)^9 = 0.1012\\P(X = 3) = (11C3)(0.53) ^3(1 - 0.53)^8 = 0.2346\\P(X = 4) = (11C4)(0.53)^4(1 - 0.53)^7 = 0.3116\\[/tex]

Therefore, the probability that fewer than five of the 11 randomly selected adult smartphone users will use their phones during meetings or classes is:

[tex]P(X < 5) = 0.0026 + 0.0247 + 0.1012 + 0.2346 + 0.3116 = 0.6747[/tex]

Therefore, the probability is 0.6747.

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A = 3800(1.0675)11,  will the investment be worth after 14 years.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

According to our question-

A = p(r)t,

where t = years that have passed,

A = amount of money after t years,

p = principal amount of money, and

r = rate of growth (interest plus 1)

Hence, A = 3800(1.0675)11,  will the investment be worth after 14 years.

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Answer:

Answer below :)

Step-by-step explanation:

Question 1:

When comparing the two sets of data in the histograms to determine the location with the most consistent temperature, we should use IQR as the measure of variability. The reason for this is that IQR is a robust measure of dispersion that is not affected by outliers and is especially useful when the data is skewed. In this case, the data in Sunny Town is skewed, and therefore the range may not be the best measure of variability. IQR is not affected by the shape of the data and provides a better measure of variability in both symmetric and skewed datasets.

Therefore, the correct answer is: IQR, because Sunny Town is skewed.

Question 2:

To determine which coffee shop typically sells the most amount of coffee per hour, we need to find the measure of center that best represents the data. Both the mean and the median can be used as measures of center, but the appropriate one depends on the distribution of the data. If the data is skewed, the median is more appropriate, and if it is symmetric, the mean is more appropriate.

Comparing the data from the two coffee shops, we find that Coffee Ground has a mean value of about 5 gallons, while Wide Awake has a median value of 4.5 gallons. The mean value for Coffee Ground is higher, but since the data is not given, it is not possible to determine the distribution of the data. Therefore, we should use the median as the measure of center for both coffee shops. In this case, we find that the median for Coffee Ground is 5 gallons, while the median for Wide Awake is 4.5 gallons.

Therefore, the correct answer is: Coffee Ground, with a median value of 5 gallons.

Question 3:

To determine which drive-thru is able to estimate their wait time more consistently, we need to compare the variability of the wait times between the two drive-thrus. We can use either the range or IQR as a measure of variability. The smaller the range or IQR, the more consistent the wait times.

Comparing the box plots for Super Fast Food and Burger Quick, we find that Super Fast Food has a smaller IQR of 4.5 (15.5 - 12), while Burger Quick has an IQR of 14.5 (24 - 9.5). Therefore, Super Fast Food has a more consistent wait time.

Therefore, the correct answer is: Super Fast Food, because it has a smaller IQR.

Question 4:

To determine which bus has the most consistent travel times, we need to compare the variability of the travel times between Bus 47 and Bus 14. We can use either the range or IQR as a measure of variability. The smaller the range or IQR, the more consistent the travel times.

Comparing the line plots for Bus 47 and Bus 14, we find that Bus 14 has a smaller IQR of 6 (18 - 12), while Bus 47 has an IQR of 8 (22 - 14). Therefore, Bus 14 has more consistent travel times.

Therefore, the correct answer is: Bus 14, with an IQR of 6.

Question 5:

To determine which girls' basketball team typically has the tallest players, we need to find the measure of center that best represents the data. Both the mean and the median can be used as measures of center, but the appropriate one depends on the distribution of the data. If the data is skewed, the median is more appropriate, and if it is symmetric, the mean is more appropriate.

Comparing the data from the two girls' basketball teams, we find that the Allstars have a median height of 68 inches, while the Champs have a median height of 67

Answer: C

Step-by-step explanation:

To firgure out if a graph is a function, do the vertical line test. If the line ahs more than 1 intersection anywhere on the graph, it is not a function.

The sales tax rate is 7% in Allegheny County. The sales tax rate in Warren County is 6%. And the book was bought in Allegheny County.

A math teacher bought a book for $ 24.99, and the sales tax on the book was $ 1.75. The teacher was able to determine whether the book was purchased in Allegheny County or Warren County by figuring out the sales tax rate. Because the total sales tax on the book was $1.75, which is equivalent to 7% of the purchase price of $24.99, the book was purchased in Allegheny County.

Sales tax rate = Total sales tax / Purchase price

Using the above formula,

Total sales tax = Sales tax rate * Purchase price

Let's calculate the sales tax using the above formula;

For Warren County, Sales tax rate = 6% = 0.06

Total sales tax = Sales tax rate * Purchase price= 0.06 * 24.99= $1.4994 ≈ $1.50

For Allegheny County,Sales tax rate = 7% = 0.07

Total sales tax = Sales tax rate * Purchase price= 0.07 * 24.99= $1.7493 ≈ $1.75

As we can see, the total sales tax on the book was $1.75, which corresponds to the sales tax rate of 7%. Therefore, the book was bought in Allegheny County.

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Each box weighs 11.5 pounds. The answer is option B.

Pound is a unit of measurement of mass or weight commonly used in the United States and some other countries, abbreviated as "lb".

To solve the problem, we need to use some basic algebraic equations. Let x be the weight of each box in pounds. Then, we can set up the following equation:

5x + 7.5 = 65

Simplifying this equation, we get:

5x = 57.5

Dividing both sides by 5, we get:

x = 11.5

Therefore, each box weighs 11.5 pounds. The answer is option B.

Pound is a unit of measurement of mass or weight commonly used in the United States and some other countries, abbreviated as "lb". One pound is equal to 16 ounces, and approximately 0.45 kilograms. It is commonly used to measure the weight of objects, such as people, animals, and goods.

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Answer: Width of the moving truck is 1.5 ft.

Step-by-step explanation:

Step 1: Volume of the moving truck = 300 ft³, length = 25 ft and height = 8ft. Since the truck is in the shape of a cuboid, use the formula of volume of the cuboid to find width.

⇒ Volume of truck = length × width × height

⇒ 300 = 25 × width × 8

⇒ 300 = 200 × width

⇒ width = 300/200 = 3/2 = 1.5 ft

a) If you were to list the sample space for this problem, there would be 36 equally likely outcomes. b) The probability of getting a sum of 9 on both dice is 136. c) The probability of getting a 5 on the first die is 16. d) The probability of getting a sum of 9 on both dice and a 5 on the first die is 1216. e) The probability of getting a sum of 9 on both dice or a 5 on the first die is 736. f) The probability of getting doubles is 16. g) The probability of getting both dice to be odd numbers is 936. h) The probability of getting doubles and both dice to be odd numbers is 136. i) The probability of getting doubles or both dice to be odd numbers is 1036.

a) The sample space of two fair dice would be 6 x 6 = 36 outcomes.

b) To get a sum of 9 on both dice, there is only one possible outcome which is rolling two 4's. Hence, the probability of getting a sum of 9 on both dice is 1/36.

c) To get 5 on the first die, there are 6 possible outcomes because the first die can show 1, 2, 3, 4, 5, or 6. Hence, the probability of getting 5 on the first die is 6/36 or 1/6.

d) The probability of getting both 9 and 5 is 1/6 x 1/36 = 1/216.

e) The probability of getting the sum of 9 on both dice or 5 on the first die is (4/36) + (1/6 - 1/36) = 11/36.

f) There are 6 possible doubles: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6). So, the probability of getting doubles is 6/36 or 1/6.

g) To get both dice to be odd numbers, we have to get either (1, 3), (1, 5), (3, 1), (3, 5), (5, 1), (5, 3). So, there are 6 possible outcomes to get both dice to be odd. Hence, the probability of getting both dice to be odd is 6/36 or 1/6.

h) The probability of getting doubles and both dice to be odd numbers is zero because we cannot roll doubles and odd numbers at the same time.

i) The probability of getting doubles or both dice to be odd numbers is the sum of their individual probabilities minus their intersection. Therefore, it is (1/6) + (1/6) - (1/6 x 1/6) = 11/36.

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