Question 1 (Multiple Choice Worth 2 points)
(Multiplying Linear Expressions MC)
Simplify ---
O
45
m²
8.
45
8
45
2
m²-m
35
2
-m² + m
35
8
45
2
·m² + m
35

Answer: Let's start by finding the dimensions of the original rectangular room.

We know that the area of the room is 60m², so we can write:

length x width = 60

We want to find the length and width of the original room, so let's call them "L" and "W", respectively. Then we can write:

L x W = 60

Now let's consider the modified room, where the length is 25% less and the width is 4m more. If the room is a square, that means the length and width are equal. Let's call this side length "S". Then we can write:

S x S = (L - 0.25L) x (W + 4)

Simplifying, we get:

S² = 0.75LW + 4(L - 0.25L)

Simplifying further, we get:

S² = 0.75LW + 3L

Now we can use the fact that LW = 60 to eliminate one variable. Substituting, we get:

S² = 45 + 3L

We want to find the length of the longest stick that can be put on the floor of the original room. This is the diagonal of the rectangle, which we can find using the Pythagorean theorem:

diagonal² = L² + W²

Substituting LW = 60, we get:

diagonal² = L² + (60/L)²

To maximize the diagonal, we can take the derivative of the right-hand side with respect to L and set it equal to zero:

d/dL (L² + (60/L)²) = 2L - 7200/L³ = 0

Solving for L, we get:

L³ = 3600

L = 15

Therefore, the length of the longest stick that can be put on the floor of the room is the diagonal, which is:

diagonal = sqrt(15² + (60/15)²) = sqrt(225 + 16) = sqrt(241) ≈ 15.52 meters

Step-by-step explanation:

Step-by-step explanation:

Find the frontal area = triangle PLUS square...then multiply by depth ,a.

  1/2 * a * b     +    a * a       all of this times the depth  'a'

 [ 1/2 ( 7 *5)  +  7*7 ]  *  7   = 465.5 units^3

The ratio for tanx is 7/24.

To find the ratio for tanx, we need to use the given values of sinx and cosx.

The formula for tanx is:
tanx = sinx / cosx
Given, sinx = 7/25 and cosx = 24/25.
Now, let's substitute these values in the formula:
tanx = (7/25) / (24/25)
To divide these fractions, multiply the first fraction by the reciprocal of the second fraction:
tanx = (7/25) * (25/24)
Now, simplify the fractions:
tanx = (7 * 25) / (25 * 24)
The 25 in the numerator and denominator will cancel out:
tanx = 7 / 24.

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Answer:

A

Step-by-step explanation:

Cost for x shirts in a week (4x+150)  divided by the shirts made in a week (x)

 would be represented by  A

Answer:

A is correct.

Step-by-step explanation:

The expression 4x + 150 represents the cost of manufacturing x shirts in a week. If x shirts are made in a week, the expression [tex]\frac{4x+150}{x}[/tex] (Answer A) represents the manufacturing cost per t-shirt (that's why we divide by x) where x shirts are made in a week (that's why we divide by just x, not 7x, because we're talking about 1 week, not 7 days)!

The mean absolute deviation of the data given in the pictograph is found to be 1, as the mean of the data is 3.5. MAD=1

What is MAD?

MAD acronym for mean absolute deviation of a data given in any form is the average magnitue between each data point and the mean of the given data. Stpeps for evaluating the mean absolute deviation:

Step i: Calculate the mean of the observations from the data given.

Step ii: Calculate magnitude between each observation & its mean. These are called absolute deviations.

Step iii: finally find the mean of the absolute deviations found.

The observations or frequency of the data in given pictograph is 2,3,4 and 5

The mean of the given data = (sum of data) ÷ (number of observations)

                                             =[tex]\frac{2+3+4+5}{4}[/tex]

                                              =[tex]\frac{14}{4}[/tex]

                                              =3.5

Absolute Deviations of each observation:

|3.5 - 2| = 1.5

|3.5 - 3| = 0.5

|3.5 - 4| = 0.5

|3.5 - 5| = 1.5

Mean of absolute deviations(MAD)= (sum of data) ÷ (number of observations)

                                                        =[tex]\frac{1.5+0.5+0.5+1.5}{4}[/tex]

                                                        =[tex]\frac{4}{4}[/tex]

                                                        =1

MAD of given data is 1.

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Refer to the attachment for complete question.

Answer: the corect answer is B

Step-by-step explanation: Please give me brainly

Step-by-step explanation:

h=-16t^2+136t+8        For this quadratic  a = -16     b= 136     c = 8

 will reach max height at t = - b/2a = -  136/ (2*-16) = 4.25 s

Plug in 4.25 into the equation for 't' to find max height = 297 ft

The soil will reach about 27 cm up the pot when it fills 75% of the pot's volume.

To determine how far up the pot the soil will reach, we need to first find the volume of the pot, then find 75% of that volume, and finally calculate the height of soil in the pot.
Step 1: Calculate the volume of the pot
The volume of a pyramid can be calculated using the formula V = (1/3) * B * h,

where V is the volume, B is the area of the base, and h is the height.

Since the base is a square with a side length of 36 cm, the area of the base (B) is 36 cm * 36 cm = 1296 cm².

Now, plug the values into the formula:
V = (1/3) * 1296 cm² * 36 cm = 15552 cm³
Step 2: Calculate 75% of the pot's volume
75% of the pot's volume can be calculated as:
Soil volume = 15552 cm³ * 0.75 = 11664 cm³
Step 3: Calculate the height of the soil in the pot
To find the height of the soil, we can use the same formula for the volume of the pyramid, but we will solve for the height[tex](h_soil)[/tex] this time:
11664 cm³ = (1/3) * 1296 cm² * [tex]h_soil[/tex]
Solve for h_soil:
[tex]h_soil[/tex] = (11664 cm³ * 3) / 1296 cm² ≈ 27 cm.

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a) It takes 350 cubic centimetres to fill the rectangular prism.

b) The capacity of the rectangular prism is 350 cm³.

c) It takes 340 square centimetres to cover the rectangular prism.

d) The rectangular prism contains 350 cm³.

a) We need to find the volume of the rectangular prism to determine how much it takes to fill it. The following formula provides the volume:

V = l × w × h

where the prism's length, breadth, and height are indicated by l, w, and h, respectively.

Substituting the given values, we get:

V = 5 cm × 7 cm × 10 cm

V = 350 cm³

Therefore, it takes 350 cubic centimetres to fill the rectangular prism.

b) The capacity of the rectangular prism is the same as its volume, which we calculated in part (a) to be 350 cm³.

c) To cover the rectangular prism, we need to find its surface area. The following formula determines a rectangular prism's surface area:

SA = 2lw + 2lh + 2wh

where the prism's length, breadth, and height are indicated by l, w, and h, respectively.

Substituting the given values, we get:

SA = 2(5 cm × 7 cm) + 2(5 cm × 10 cm) + 2(7 cm × 10 cm)

SA = 340 cm²

Therefore, it takes 340 square centimetres to cover the rectangular prism.

d) The rectangular prism contains the same amount of volume as its capacity, which we calculated in part (b) to be 350 cm³.

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Assuming the shape of the balloon remains the same, the volume of the balloon is directly proportional to the cube of its height. Therefore, we can use the following proportion:

(air volume)₁ / (height)₁³ = (air volume)₂ / (height)₂³

where:

(air volume)₁ = 108 in.³ (when the height is 4 in.)

(height)₁ = 4 in.

(height)₂ = 8 in.

We can solve for (air volume)₂ as follows:

(air volume)₂ = (air volume)₁ × (height)₂³ / (height)₁³

(air volume)₂ = 108 in.³ × (8 in.)³ / (4 in.)³

(air volume)₂ = 108 in.³ × 64 / 64

(air volume)₂ = 108 in.³

Therefore, the balloon must hold 108 in.³ of air for the clown's face to be 8 in. tall.

The final answer is: 5 quarts, 1 pint, and 0.5 cups based on conversion.

To add these two quantities, we first need to convert all of the measurements to a common unit. Since we are adding pints and cups, we can convert everything to cups, and then convert back to pints and quarts as needed.

5 pints is equal to 5 x 2 = 10 cups (since there are 2 cups in a pint).

2 cups is 2 cups.

3 pints is equal to 3 x 2 = 6 cups.

3 cups is 3 cups.

Now we can add the quantities:

10 cups + 2 cups + 6 cups + 3 cups = 21 cups

To convert 21 cups back to pints and quarts, we can use the fact that there are 2 cups in a pint, and 4 cups in a quart.

First, we can divide 21 by 4 to find the number of quarts:

21 cups ÷ 4 = 5 with a remainder of 1 cup

So we have 5 quarts and 1 cup. To convert the remaining cup to pints, we can divide by 2:

1 cup ÷ 2 = 0.5 pints

Therefore, the final answer is:

5 quarts, 1 pint, and 0.5 cups.

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In the given Sample Space, there are 80 red gumballs in the entire population of 200 gumballs.

What exactly is a sample space?

In probability theory, a sample space is the set of all possible outcomes or results of an experiment or random process. It is denoted by the symbol "S". The sample space depends on the nature of the experiment or process and consists of all the possible values or events that could occur.

Now,

If the random sample of 25 gumballs contains 10 red gumballs, we can estimate the proportion of red gumballs in the entire population of 200 gumballs by using the formula:

proportion of red gumballs = number of red gumballs in sample / sample size

Substituting the given values, we get:

proportion of red gumballs = 10 / 25

= 0.4

This means that the proportion of red gumballs in the entire population of 200 gumballs is estimated to be 0.4. To find the estimated number of red gumballs in the entire population, we can use the formula:

number of red gumballs in population = proportion of red gumballs x population size

Substituting the given values, we get:

number of red gumballs in population = 0.4 x 200

= 80

Therefore, based on the random sample results, it is estimated that there are 80 red gumballs in the entire population of 200 gumballs.

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Answer:

3 is greater than or equal to value a.

Step-by-step explanation:

With the given values, the surface area of the rectangular prism is 544 square units.

A prism is a three-dimensional geometric shape that consists of two identical parallel polygonal bases and a set of parallelograms connecting the corresponding sides of the two bases.

In general, the area of any prism can be found by adding together the areas of its bases and lateral faces.

To find the surface area of the rectangular prism represented by the given net, we need to calculate the area of each face and add them together. The rectangular prism has six faces, so we need to find the area of each face.

The top and bottom faces are rectangles with dimensions 8 x 6, so each has an area of 8 x 6 = 48 square units. There are two of these faces, so their combined area is 2 x 48 = 96 square units.

The front and back faces are rectangles with dimensions 8 x 16, so each has an area of 8 x 16 = 128 square units. There are two of these faces, so their combined area is 2 x 128 = 256 square units.

The left and right faces are rectangles with dimensions 16 x 6, so each has an area of 16 x 6 = 96 square units. There are two of these faces, so their combined area is 2 x 96 = 192 square units.

Therefore, the total surface area of the rectangular prism represented by the given net is:

96 (top and bottom) + 256 (front and back) + 192 (left and right) = 544 square units.

So, the surface area of the rectangular prism is 544 square units.

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The 95% confidence interval for the percentage of people with diabetes is equals to the (0.335, 0.1652).

We have, a sample of adults with

Sample size = 1000

Sample proportion, p = 25% = 0.25

We have to determine 95% confidence interval for the percentage of people with diabetes.Confidence interval formula for known value of sample proportion is written as CI = p ± Z ( √(p(1 - p)/n)

Now, for the 95% of confidence level or significance level, α = 1- 0.95 = 0.05 or α/2 = 0.25.

Using the normal distribution table, Z₀.₀₂₅ is 1.96. From above formula, confidence interval, CI = 0.25 ± 1.96( √0.25× 0.75/1000)

= 0.25 ± 1.96 ( 0.0433)

= 0.25 ± 0.0848

= ( 0.335, 0.1652)

Hence, required confidence interval is (0.335, 0.1652) .

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the coordinate that represents the cost when renting from either company would be the same is (10, 50). This means that if Carmen rents a bike for 10 hours, she would pay the same amount whether she rented from Company A or Company B.

How to determine the point?

To determine the point where the cost of renting a bike from Company A and Company B is the same, we need to find the values of h and y that satisfy the equations y = 2h + 30 and y = 4h + 10. We can solve for h by setting the two equations equal to each other:

2h + 30 = 4h + 10

Simplifying this equation, we get:

20 = 2h

h = 10

Now that we know h is 10, we can substitute that value into either equation to find y. Using the first equation:

y = 2h + 30 = 2(10) + 30 = 50

Therefore, the coordinate that represents the cost when renting from either company would be the same is (10, 50). This means that if Carmen rents a bike for 10 hours, she would pay the same amount whether she rented from Company A or Company B.

It's worth noting that as the number of hours rented increases, the difference in cost between the two companies becomes greater. For example, if Carmen rented a bike for 20 hours, the cost would be $70 from Company A and $90 from Company B. Therefore, it's important for Carmen to consider how long she plans to rent the bike for when deciding which company to rent from.

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The calculated surface area of the figure is 3100.8 square feet

from the question, we have the following parameters that can be used in our computation:

SA = hp + 2B

From the figure, we have

B = 1/2 * (10 + 34) * 24.7 = 543.4

p = 2 * (34 + 19) = 106

h = 19

So, we have

SA = 19 * 106 + 2 *  543.4

Evaluate

SA = 3100.8

Hence, the surface area is 3100.8 square feet

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Part A: The side length of triangle EF = 10.35.

Part B: ∠E = 78

Sine rule :

e/sinE = f/sinF = d/sinD

Where D, E, and F are the angles and d,e and f are the angles' opposing sides.

Put the values:

DF/sinE = 11.7/sin55 = EF/sin47

Part A: EF = ?

11.7/sin55 = EF/sin47

EF = 11.7 * sin47 / sin55

EF = 10.35

Part B: ∠E = ?

Using angle sum property of triangles.

∠E + ∠D + ∠F = 180

∠E + 47 + 55 = 180

∠E = 78

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The parts of the circle when named are listed below

An inscribed angle is an angle between two chords

So, we have

inscribed angle = Angle GJI

A major arc is an arc with the greater central angle

So, we have

Major arc = AJG

Minor arc = GFH

Next, we have

GH = 55 degrees i.e angle at center = arc

GJI = 180 degrees i.e. semicircle

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FIFA created a football with a 21 cm circumference out of leather. If 10% of the leather is wasted, the cost of leather with labour is Rs. 25 per square centimetre. All total, Rs. 31,173.90 worth of leather was purchased to produce one football.

The diameter of the leather used to make the football is 21 cm, so its radius is 10.5 cm (half of the diameter).

The formula for calculating a sphere's surface area can be used to determine how much leather is required to produce a football:

Surface area = [tex]4\pi r^2[/tex]

Surface area = 4π[tex](10.5)^2[/tex]

Surface area = 1385.44 sq. cm

If 10% of the leather is wasted, then the actual amount of leather used is 90% of the total leather bought. So, we need to calculate the cost of 90% of the leather:

Cost of leather = 90% of the total leather cost

Cost of leather = 0.9 x 1385.44 sq.cm x Rs. 25/sq.cm

Cost of leather = Rs. 31,173.90

Therefore, the total cost of the leather bought to make the football, including the labour cost, is Rs. 31,173.90.

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The decision to use a one-tailed or two-tailed test depends on the specific research question and the directionality of the hypothesis.

When testing a hypothesis about a population mean, researchers may use a one-tailed or two-tailed test. A one-tailed test is used when the research question only focuses on one direction of an effect, for example, if the researcher is interested in whether the population mean is greater than a specific value. In contrast, a two-tailed test is used when the research question is interested in any significant difference between the sample mean and the hypothesized population mean, regardless of the direction of the difference.

The decision to use a one-tailed or two-tailed test should be based on the specific research question, and it is essential to clearly define the directionality of the hypothesis before selecting the appropriate test.

Therefore, the choice of a one-tailed or two-tailed test should be based on the research question and the specific direction of the hypothesis.

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Answer:

57.5 cm × 8 mi./cm = 460 miles

The probability that the exam scores are at least 37 is 0.4013 or 40.13%

The probability that the exam scores are at least 37 can be calculated using the normal distribution function. To calculate the probability, we first need to standardize the variable using the formula z = (x - μ) / σ, where x is the value of interest (in this case, x = 37), μ is the mean, and σ is the standard deviation.

z = (37 - 36.12) / 3.53 = 0.25

Using a standard normal distribution table or a calculator, we can find the probability that a standard normal random variable is greater than or equal to 0.25, which is approximately 0.4013.

Therefore, the probability that the exam scores are at least 37 is 0.4013 or 40.13%

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The surface area of the composite figure is 446 cm².

Surface area is the sum of the areas of all faces (or surfaces) on a 3D object. It is a two-dimensional measure of the space occupied by the object, and is measured in units of square units, such as square inches, square feet, and square meters. Surface area is often used to determine the amount of material needed for a solid object or the amount of paint needed to cover it.

The surface area of the composite figure can be calculated using the formula SA = 2(L x W) + (2 x H x L) + (2 x H x W). In this case, L = 9 cm, W = 10 cm, and H = 7 cm.

Therefore, the surface area of the composite figure is SA = 2(9 cm x 10 cm) + (2 x 7 cm x 9 cm) + (2 x 7 cm x 10 cm) = 180 cm²+ 126 cm²+ 140 [tex]cm^2[/tex] = 446 cm².

Therefore, the surface area of the composite figure is 446 [tex]cm^{2}[/tex].

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Complete questions as follows-

Surface Area of Composite Figures Acellus Find the surface area of the composite figure. 1 9 cm 10 cm cm 7 cm 8 cm 2 cm SA [? ] cm? Enter Copyright 02003 2021 Acellus Corporation. All Rights Reserved:'

a) A and B are independent events.

b) The outcome of each game is independent of the other games so, Rachel's loss = p.

c) The probability of all marbles being red is 4

a) Given that a first marble is red and the second marble is also red, such that

P(1) = P(2) = 0.2, P(3) = P(5) = P(6) = 0.1 and P(4) = 0.3 and die is thrown two times. Also given that:

A1 = red

B1 = red.

So, P(A) = [P(1, 1) + P(2, 2) + P(3, 3) + P(4, 4) + P(5, 5) + P(6, 6)]

= P(1).P(1) + P(2).P(2) + P(3).P(3) + P(4).P(4) + P(5).P(5) + P(6).P(6)

= 0.2 x 0.2 + 0.2 x 0.2 + 0.1 x 0.1 + 0.3 x 0.3 + 0.1 x 0.1 + 0.1 x 0.1

= 0.04 + 0.04 + 0.01 + 0.09 + 0.01 + 0.01 = 0.20

Now, B = [(4, 6), (6, 4), (5, 5), (5, 6), (6, 5), (6, 6)]

P(B) = [P(4).P(6) + P(6).P(4) + P(5).P(5) + P(5).P(6) + P(6).P(5) + P(6).P(6)]

= 0.3 x 0.1 + 0.1 x 0.3 + 0.1 x 0.1 + 0.1 x 0.1 + 0.1 x 0.1 + 0.1 x 0.1

= 0.03 + 0.03 + 0.01 + 0.01 + 0.01 + 0.01 = 0.10

A and B both events will be independent if

P(A ⋂ B) = P(A).P(B) …. (i)

And, here (A ⋂ B) = {(5, 5), (6, 6)}

So, P(A ⋂ B) = P(5, 5) + P(6, 6) = P(5).P(5) + P(6).P(6)

= 0.1 x 0.1 + 0.1 x 0.1 = 0.02

From equation (i) we get,

0.02 = 0.20 x 0.10

0.02 = 0.02

Therefore, we can say that A and B are independent events.

b) We know that the outcome of each game is independent of the other games. Rachel's loss = p. As per the given information, the games in the series are unrelated, indicating the application of the probability multiplication principle.

c) The probability of all marbles being red is 4

Let a be the probability that the first player (ultimately) wins if the two players are tied in wins. Let b be the probability that she wins if she is 1 ahead. And let c be the probability she wins if she is 1 behind. We have the equations

a = rb + 1 - r x c

b = r + 1 - r x a

c = r x a

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Answer:

9q + 18

Step-by-step explanation:

Heres each step by step process to simplify:

[tex]9(q+2)[/tex]

[tex]9\times q +9\times 2[/tex]

[tex]9q+18[/tex]

Answer:

28cm

Step-by-step explanation:

see image for explanation.

Answer:

45

Step-by-step explanation:

Since 5 x 3 is 15, 15 x 3 = 45

45sq

Answer:

45 squared units

Step-by-step explanation:

So we know that the width of the rectangle is 3 units, and that the length of the rectangle is 5 times greater than the width. With simply maths we can find that the length we use the equation 3 multipled 5 = 15.

So we now know the length of the triangle is 15 units, so to find the area of a rectangle the equation would be: Length times width

3 units multiped by 15 units = x

x = 45 squared units

Based on the calculated z-score of 17.07, and a corresponding p-value, the process would be considered out of control at the 0.05 significance level.

To determine whether the process is in control or out of control, we can use a hypothesis test with a significance level of 0.05. The null hypothesis (H0) is that the process is in control, and the alternative hypothesis (Ha) is that the process is out of control.

We can calculate the z-score as follows:

z = (x - μ) / (σ / sqrt(n))

where x is the observed value (118), μ is the mean (104), σ is the standard deviation (8.2), and n is the sample size (1).

Plugging in the values, we get:

z = (118 - 104) / (8.2 / sqrt(1)) = 17.07

The corresponding p-value for this z-score is virtually zero. Since the p-value is less than 0.05, we reject the null hypothesis and conclude that the process is out of control.

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