The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0

The length of river C and river D are 2005miles and 2505miles.

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

This word problem are interpreted into mathematical equation or expression

represent the length of river C by x and the length of river D by y

x = 500+y

x+y = 5510

substitute 500+y for x

500+y+y = 5510

2y =5510-500

2y = 5010

divide both sides by 2

y = 5010/2

y = 2505miles

x = 500+y

x= 500+2505

x= 3050miles

therefore the length of river C and D are 3005miles and 2505miles respectively

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Answer:

fraction:26/100

decimal:0.26

The correct linear inequality would be y > 2x + 1.

Option (A) is correct.

What is linear inequality?

A linear inequality is an inequality that can be written in the form of a linear equation with an inequality symbol, such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

We can see that the line passes through the points (-1, -1) and (0, 1), and has a positive slope. The equation of the line can be found using the point-slope form:

y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the points on the line.

Using the point (-1, -1) and the slope 2, we get:

y - (-1) = 2(x - (-1))

y + 1 = 2x + 2

y = 2x + 1

Since the line is dashed, the inequality is not inclusive of the points on the line. Therefore, we use the inequality symbol > rather than ≥.

so the linear inequality would be  y > 2x + 1.

Therefore, the correct linear inequality would be y > 2x + 1.

Option (A) is correct.

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There are 160 tree in each row.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.

To calculate the number of students in the seventh grade, you must divide the number of students in the Environmental Club by the percentage they represent. The answer is 8 divided by 0.05, which equals 160. Therefore, there are 160 students in the seventh grade.

The Environmental Club provides students with an opportunity to learn more about the natural environment and how to help protect it. The club members work together to come up with ideas to promote environmental awareness and action in their school and community. They plan activities such as tree-planting, trash clean-ups, and educational presentations. The club also participates in activities like field trips to local parks and nature preserves.

By joining the Environmental Club, students can gain a better understanding of their local environment and how to protect it. This can help them become more aware of their actions and how they can make a difference in the world. They can also develop leadership and communication skills, as well as an understanding of the importance of teamwork. Furthermore, they can make friendships and connections with other students who share the same values and interests.

Overall, the Environmental Club is an important part of the school community and provides great benefits to its members. It allows students to gain knowledge, build skills, and make a positive difference in their communities.

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Answer:

there is an error in the question. if you compute ac - ab = 4 you get -2x+4 =4 that leads to x=0.

if so, ab = -6 and this is not allowed.

Answer: When y=1, x=[tex]\frac{1}{2}[/tex]

It will be a point with the coordinates ([tex]\frac{1}{2}[/tex], 1)

Step-by-step explanation:

- Start plotting points from the y-intercept, in this case, -1.

- Since the function is written in the form y=mx+b, where the slope is b which is in this case 4. Meaning to say that from the y-intercept -1 you have to go 4 units up and 1 unit right.

- Continue plotting 2 or 3 points, then connect them with a straight line.

- For the value of x when y=1, we can substitute y with 1 and solve the equation for x.

1=4x-1  (Add 1 to both sides)

2=4x  (Divide by 4)

[tex]\frac{1}{2}[/tex]=x Write the solution.

Financial plan - The cost of a jug of squeezed orange is $2.00 and the cost of pop is $1.00. These information propose that Sharon is augmenting her utility from the given fixed spending plan

A written financial program offers you a quantifiable objective to strive for. By monitoring your progress, you can eliminate doubt or uncertainty regarding your choices and make necessary adjustments to help you get past potential roadblocks.

Budgeting is the most crucial first step in financial planning. Making a budget is fairly simple; keeping one is more challenging! What matters is having the self-control to take the time as well as care to track and reconcile your spending in some way.

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Answer:

your answer is explained below

Step-by-step explanation:

To find the proportion of cities with a vacancy rate of more than 9%, we need to add the relative frequencies for the classes with vacancy rates greater than 9%. These classes are 9 < x ≤ 12 and 12 < x ≤ 15.

Proportion of cities with a vacancy rate of more than 9%:

= Relative frequency for 9 < x ≤ 12 + Relative frequency for 12 < x ≤ 15

= 0.24 + 0.42

= 0.66

Therefore, 66% of the cities had a vacancy rate of more than 9%.

Rounding this answer to two decimal places, we get 0.66 as the final answer.

  tanθ   = √3 are the values of cos and tan in Trigonometric Ratios .

How are trigonometric ratios defined?

As specified by the definition of a right-angled triangle's side ratio, trigonometric ratios are the values of all trigonometric functions. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.

Sinθ =  -√3/2

  cosθ = √1 - sin²θ

        = √1 - (-√3/2)²

       = √ 1 - 3/4

       = √4-3/4

     = √1/4

 cosθ = 1/2

since π<θ<3π/2 in third quadrant.

 We know, cosθ in third quadrant is negative.

   cosθ = -1/2

  tanθ = sinθ/cosθ

     tanθ = -√3/2/-1/2

       tanθ   = √3

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Answer: The value of a=29/23 and b=124/23

Step-by-step explanation:

Given equations are,

2b-3a=7       _(1)

3b+7a=25     _(2)

Multiplying (1) by 7

14b-21a=49

Multiplying (2) by 3

9b+21a=75

solving the above equations,

14b-21a=49

9b+21a=75

23b      =124

b=124/23

Substituting the value of b in eq. (1)

a=29/23

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The height of the flagpole based on the information is 23 feet.

Let's start by converting the height of the person's shadow to feet, since the length of the flagpole's shadow is given in feet. There are 12 inches in a foot, so 54 inches is 54/12 = 4.5 feet.

Now we can set up a proportion to solve for the height of the flagpole:

(person's height) / (person's shadow length) = (flagpole height) / (flagpole shadow length)

Plugging in the values we know, we get:

5.75 / 4.5 = x / 18

5.75 * 18 = 4.5 * x

103.5 = 4.5x

Dividing both sides by 4.5, we get:

x = 103.5 / 4.5

x = 23

So the height of the flagpole is 23 feet.

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We have given the constraints to the given equations:

1.  $10,000 ≤ x1 ≤ 50

2. $25,000 ≤ x2 ≤ 75.6

3. $30,000 ≤ x3 ≤ 150

4. $35,000 ≤ x4 ≤ 50

5. x1 + x2 ≤ x3

What is linear inequality?

A linear inequality is an inequality that can be written in the form of a linear equation with an inequality symbol, such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

If we are lowering all amounts by a factor of 1,000, then we would replace $150,000 with 150.

So the constraint equations would be:

1.) $10,000 ≤ x1 ≤ 50 (since the customer can deposit up to 1/3 of her money in CD#1)

2.) $25,000 ≤ x2 ≤ 75.6 (since the customer can deposit up to 1/3 of her money in CD#2 and she wants to deposit exactly three times as much in CD#2 as in CD#1)

3.) $30,000 ≤ x3 ≤ 150 (since the customer can deposit up to 1/3 of her money in CD#3)

4.) $35,000 ≤ x4 ≤ 50 (since the customer can deposit up to 1/3 of her money in CD#4)

5.) x1 + x2 ≤ x3 (since the sum of the first and the second CDs must be less than or equal to the third CD)

Hence, we have given the constraints to the given equations:

1.  $10,000 ≤ x1 ≤ 50

2. $25,000 ≤ x2 ≤ 75.6

3. $30,000 ≤ x3 ≤ 150

4. $35,000 ≤ x4 ≤ 50

5. x1 + x2 ≤ x3

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Therefore , the solution of the given problem of plotting data comes out to be  their line plot is given below table.

The most typical technique to present data using a chart is to graph the connection between two extra variables. Diagrams created manually or digitally are also acceptable. Starting at the origin, move three pieces up and two types to the right. It is essential to show the numbers of rows 2, 3, & 4 just on standard system. Be sure to expression yourself clearly. The letter P is represented by the pinkish squiggle next to the number 2.3.

Here,

In the given problem, Jessica and her friend measured the lengths of the fish they caught one day.

The measurements in inches are given in the table:

Jessica's Fish (inches) Friend's Fish(inches)

13.2                       12.5

14.3                      15.6

15.1                   13.7

12.4                          14.1

13.9                          13.0

Thus , their line plot is given above.

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This is a valid example of stringing arguments together using conditional statements.

The first statement establishes a conditional relationship between Martin shooting the sheriff and Martin shooting first.

The second statement also establishes a conditional relationship, but this time between Martin using his best pistol and Martin shooting first.

By combining the two conditional statements, we can conclude that if Martin didn't use his best pistol, then he didn't shoot first.

This follows from the fact that not using his best pistol would mean Martin didn't shoot first (according to statement 2), and if he didn't shoot first, then he couldn't have shot the sheriff (according to statement 1).

Therefore, the conclusion of the argument, which is that if Martin didn't use his best pistol, then he didn't shoot the sheriff, follows logically from the two conditional statements.

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The interior angles of the triangle are in terms of t=15.

what are interior angles ?

In a polygon, an interior angle is an angle formed by two adjacent sides of the polygon inside the polygon. For example, in a triangle, the interior angles are the angles formed by the three sides of the triangle inside the triangle.

The formula for the sum of the interior angles of a polygon with n sides is:

(n-2) x 180 degrees

In other words, to find the sum of the interior angles of a polygon, you take the number of sides, subtract 2, and then multiply the result by 180 degrees.

For example, a triangle has 3 sides, so the sum of its interior angles is:

(3-2) x 180 = 1 x 180 = 180 degrees

Given by the question:
The sum of the interior angles of a triangle is 180 degrees. Therefore:

w + x + y = 180

(5t + 3) + (3t + 7) + 50 = 180

8t + 60 = 180

8t = 120

t = 15

So the value of t is 15.

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Answer:

Step-by-step explanation:

To find an integer n so that the interval of the form [n, n+1] contains the solution to the equation x^2 + 1/x = 1, we can first rewrite the equation as x^3 - x^2 + 1 = 0.

Next, we can use the Intermediate Value Theorem to find such an n. Since f(x) = x^3 - x^2 + 1 is a continuous function, if we can find two values of x, a and b, such that f(a) and f(b) have opposite signs, then there must exist a value of x between a and b for which f(x) = 0.

(a) Evaluating f(n) and f(n+1), we have:

f(n) = n^3 - n^2 + 1

f(n+1) = (n+1)^3 - (n+1)^2 + 1

(b) Since f(x) is a polynomial, it is continuous for all x, and so the largest possible interval on which f(x) is continuous is (-∞, ∞).

Thus, we want to find values a and b such that f(a) and f(b) have opposite signs. We can plot the function to get an idea of where the roots might be                          

   |                              

   |                 __          

   |                 /  \        

   |                /    \        

   |              ./      \.      

   |             /          \    

   |           ./            \.  

   |          /                \  

   |        ./                  \.

   |      ./                      \

   |    ./                          \

   |---------------------------------

        a                           b

From the graph, it appears that there is a root between 0 and 1, and another root between -1 and 0. We can use this information to choose a and b. Since we want the largest possible interval, we can take a = -1 and b = 1, so that the interval is (-∞, ∞).

Thus, the integer n such that [n, n+1] contains a root of x^2 + 1/x = 1 is given by n = 0.

The theorem that tells us that the solution must be in the interval [n, n+1] is the Intermediate Value Theorem.

The integer 'n' that fits the solution of the equation x^2 + 1/x = 1 within the interval [n, n+1] is 0. Using n=0 for the function f(x) = x^2 + 1/x - 1 it is undefined, but for n+1, it equals 1. The function f is continuous for all x ≠ 0 which is represented by the interval (-∞, 0) ∪ (0, ∞). This conclusion is established by the Intermediate Value Theorem.

The task involves solving the equation x2 + 1/x = 1 to find an integer 'n' such that the solution fits within the interval [n, n+1]. For this equation, rearranging to x2 - x + 1 = 0, we can use the quadratic formula to find x = (1±√(1-4))/2. This gives us two solutions x = 0.5 and x = -0.5.

However, only x=0.5 is found in the interval [0, 1], where n = 0.

For the function f(x) = x2 + 1/x - 1, at n = 0, the function is undefined. However, for f(n+1) it yields a value of 1.

The function f is continuous everywhere on its domain and the function is defined for all x ≠ 0, hence the function is continuous on the interval (-∞, 0) ∪ (0, ∞).

The theorem that ensures the solution is within the interval [n, n+1] is known as the Intermediate Value Theorem.

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The best table, Observed Values | Expected Values, for a chi-square goodness-of-fit test for an independent assortment model, displays the expected values in the f2 generation.

When evaluating how well observed values fit a model of independent assortment, the chi-square goodness-of-fit test is used. The test necessitates comparing the observed values to what would be expected in the f2 generation.

The best option for this comparison is Observed Values | Expected Values since it gives a direct comparison between the observed and expected numbers. As any discrepancies between the observed and expected values can be attributed to the model's performance, this comparison enables an evaluation of the model's goodness-of-fit.

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The average baggage-related revenue per passenger is $29.80, using the variance the standard deviation of the baggage-related revenue is $27.35 and  the airline should expect about $3874 in revenue from baggage fees for a flight of 130 passengers (rounded to the nearest dollar).

a) To find the average baggage-related revenue per passenger, we need to calculate the expected value of the baggage fees. Let X be the random variable that represents the number of checked bags per passenger. Then the expected value of the baggage fees per passenger is:

E[Baggage Fees] = E[20X + 40(max(0, X-1))]

= 20E[X] + 40E[max(0, X-1)]

= 20(0.31 + 0.14(2)) + 40(0.14 + 0.31)

= 29.80

Therefore, the average baggage-related revenue per passenger is $29.80

b) To find the standard deviation of the baggage-related revenue, we can use the formula for the variance:

Var[Baggage Fees] = E[(Baggage Fees - E[Baggage Fees])^2]

= E[(20X + 40(max(0, X-1)) - 29.80)^2]

= E[(20X - 40(max(0, X-1)))^2]

= E[400X^2 - 1600X(max(0, X-1)) + 1600(max(0, X-1))^2]

= 400E[X^2] - 1600E[X(max(0, X-1))] + 1600E[(max(0, X-1))^2]

To calculate these expected values, we can use the fact that:

E[X^2] = Var[X] + (E[X])^2

E[X(max(0, X-1))] = E[X^2] - E[X]

E[(max(0, X-1))^2] = Var[X] + (E[X])^2 - 2E[X] + 1/4

Plugging in the values, we get:

Var[Baggage Fees] = 400(0.31 + 0.14(4)) - 1600(0.31 + 0.14) + 1600(0.31 + 0.14 + 1/4)

= 748

Therefore, the standard deviation of the baggage-related revenue is $27.35 (rounded to the nearest cent).

c) For a flight of 130 passengers, the total revenue from baggage fees can be found by multiplying the average baggage-related revenue per passenger by the number of passengers:

Total revenue = 130($29.80)

= $3874

Therefore, the airline should expect about $3874 in revenue from baggage fees for a flight of 130 passengers (rounded to the nearest dollar).

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It would take approximately 6.5 years for an investment to double at a simple interest rate of 11%.

To find the number of years necessary for an investment to double at a simple interest rate of 11%, we can use the following formula:

n = 72 / r

where n is the number of years required for the investment to double, and r is the interest rate.

Plugging in the values, we get:

n = 72 / 11

n ≈ 6.5 years (rounded to the nearest tenth)

Therefore, it would take approximately 6.5 years for an investment to double at a simple interest rate of 11%.

Simple interest is a type of interest that is calculated on the principal amount of a loan or investment. It is a fixed percentage of the original amount borrowed or invested, and it is not compounded over time.

The formula for calculating simple interest is:

I = P * r * t

where I is the interest, P is the principal amount, r is the interest rate, and t is the time period.

For example, if you borrow $1,000 for two years at a simple interest rate of 5%, the interest you would pay is calculated as follows:

I = 1,000 * 0.05 * 2

I = $100

So, you would have to pay back the $1,000 principal plus $100 in interest, for a total of $1,100.

Simple interest is commonly used in short-term loans or investments, and it is usually easier to calculate and understand than compound interest, which takes into account the effect of earning interest on previously earned interest.

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The trignometric ratios are given by1. B = 180 - (90 + 58) (sum of triangles)

B = 32°

Let's find a and b using trigonometric ratios:

Reference angle = 58°

Opposite = a = ?

Hypotenuse = c = 27

Adjacent = b = ?

✔️To find a, apply SOH:

Sin 58 = Opp/Hyp

Sin 58 = a/27

a = 27*Sin 58

a = 22.8972986 ≈ 22.9 (nearest tenth)

✔️To find b, apply CAH:

Cos 58 = Adj/Hyp

Cos 58 = b/27

b = 27*Cos58

b = 14.3 (nearest tenth)

2. B = 180 - (90 + 63) (sum of triangles)

B = 27°

Let's find a and b using trigonometric ratios:

Reference angle = 63°

Opposite = a = 11

Hypotenuse = c = ?

Adjacent = b = ?

✔️To find b, apply TOA:

Tan 63 = Opp/Adj

Tan 63 = 11/b

b = 11/Tan 63

b = 5.6 (nearest tenth)

✔️To find c, apply SOH:

Sin 63 = Opp/Hyp

Sin 63 = 11/c

c = 11/Sin 63

c = 12.3 (nearest tenth)

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The smallest number in our sample of 11 numbers that is greater than or equal to 40% of the numbers.

In arithmetic, a percentage is a ratio or ratio that is presented as a part of 100. Usually, the acronyms "pct.," "pct," and "pc" are also utilized. Yet it is broadly classified into the following by the percent sign, "%." The % sum has no dimensions. Rates are essentially fractions when the sum is 100. Use the percent sign (%) to indicate that a number seems to be a percentage by placing it next to it. For illustrate, you score a 75% if you properly answer 75 out of 100 respondents on a test (75/100). Divide the money by total and multiply it by 100 to calculate percentages. The formula for calculating the percentage is (value/total) x 100%.

given

The 40th percentile's ordinal rank is equal to (40/100) X 10 (or 4).

50 is the 40th percentile and the following rank is 5 with 50 as the data value.

We observe that 50 is greater than 10, 20, 30, or 40% of the data,

4/10 = 0.4.

The smallest number in our sample of 11 numbers that is greater than or equal to 40% of the numbers.

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Answer:  a

Step-by-step explanation:

karabee kailash

The standard error tells us how much we can expect the sample proportion to vary from the true proportion in repeated samples of the same size. Option (d) correctly states that "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion." This means that if we were to take many samples of 100 students from the same school and calculate the proportion of students who bring a reusable water bottle from home in each sample, about 95% of the sample proportions would fall within +/-0.048 of the true proportion.

The correct option is (d) "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion."

The standard error of the sample proportion can be calculated using the formula:

SE = √[p*(1-p) / n]

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 37/100 = 0.37 and the sample size is 100. Plugging in these values, we get:

SE = sqrt[0.37*(1-0.37) / 100] = 0.048

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The probability he will get less than $283 from a random customer is 0.93. 2. The standard deviation for the payments from the customers is 50678.88. 3. The median job payment amount is 120.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.

The probability of 0 is given as:

p(0) = 1 - (0.42 + 0.08 + 0.05 + 0.02) = 0.43

1. The probability he will get less than $283 from a random customer:

p(x < 283) = p(0) + p(8) + p(120)

= 0.43 + 0.42 + 0.08

= 0.93

2. The standard deviation for the payments from the customers is:

E(x²) = ∑x²p(x) = (0)²(0.43) + (8)²(0.42) + (120)²(0.008) + (300)²(0.05) + (1500)²0.02

= 50678.88

3. The median job payment amount is 120.

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Answer:

[tex]3p + 5p = 8p + 7[/tex]

Step-by-step explanation:

I don't know how to explain it, but

[tex]3p + 5p = 8p + 7[/tex]

Simplifying this

[tex]8p = 8p + 7[/tex]

It will never equal because no matter what number you put for P, one will always be 7 greater than the other

The expected weight left after the next customer's order shipped is 92 pounds, and the variance of the weight left is 51.2 lb²

What is the probability mass function?

A probability mass function (PMF) is a mathematical function that describes the probability of each possible value of a discrete random variable. In simpler terms, the PMF gives the likelihood of a specific outcome occurring when you randomly select an item from a finite set of possible outcomes.

The PMF assigns a probability to each outcome, such that the sum of all probabilities equals 1. The PMF is often presented in a table or a graph to show the probabilities associated with each possible value of the random variable.

The given probability mass function (pmf) for the number of batches ordered by a randomly chosen customer, X, is:

X P(X)

0 0.3

1 0.5

2 0.1

3 0.1

To calculate the expected value of X, we use the formula:

E(X) = Σ [x * P(X=x)]

E(X) = (0 * 0.3) + (1 * 0.5) + (2 * 0.1) + (3 * 0.1)

E(X) = 0 + 0.5 + 0.2 + 0.3

E(X) = 1

To calculate the variance of X, we first need to calculate the squared values of X:

X²

0² = 0

1²  = 1

2² = 4

3² = 9

Then, we use the formula:

Var(X) = E(X²) - [E(X)]²

E(X²) = Σ [x² * P(X=x)]

E(X²) = (0² * 0.3) + (1² * 0.5) + (2² * 0.1) + (3² * 0.1)

E(X²) = 0 + 0.5 + 0.4 + 0.9

E(X²) = 1.8

Var(X) = E(X²) - [E(X)]²

Var(X) = 1.8 - 1²

Var(X) = 0.8 batches²

The expected number of pounds left after the next customer's order is shipped can be calculated as:

E(Weight left) = 100 - 8X

where X is the number of batches ordered by the next customer.

Using the formula for the expected value of X that we found earlier, we can write:

E(Weight left) = 100 - 8E(X)

E(Weight left) = 100 - 8(1)

E(Weight left) = 92 lb

To calculate the variance of the number of pounds left, we first need to find the variance of X, which we already calculated as 0.8 batches² Then, we use the formula for the variance of a linear function of a random variable:

Var(aX + b) = a² * Var(X)

where a = -8 (the negative sign indicates that the weight left decreases as X increases) and b = 100.

Var(Weight left) = (-8)² * Var(X)

Var(Weight left) = 64 * 0.8

Var(Weight left) = 51.2 lb^2

Therefore, the expected weight left after the next customer's order is shipped is 92 pounds, and the variance of the weight left is 51.2 pounds squared.

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The value of y is given as follows:

y = 4.3 cm.

The value of y is obtained applying the two secant segment theorem, which means that the following equation will hold true:

3(3 + y) = 2(2 + 9).

Applying the distributive property and solving for y, the value of y is obtained as follows:

9 + 3y = 22

3y = 13

y = 13/3

y = 4.3 cm.

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Refer to the attached image.