**Answer:**

156 bundles

**Step-by-step explanation:**

Total area of the roof = 2(70 x 30) = 4200 sf

(4200 sf) / (27sf/bundle) = 155.56 ≈ 156 bundles

Niamh was driving back home following a business trip.

She looked at her Sat Nav at 17:30

Time: 17:30

Distance: 143 miles

Niamh arrived home at 19:42

Work out the average speed of the car, in mph, from 17:30 to 19:42

You need to show all your working

:)

**Answer:**

65 mph

**Step-by-step explanation:**To calculate the average speed of Niamh's car, we need to use the formula:

Average speed = Total distance ÷ Total time

First, we need to calculate the total time elapsed from 17:30 to 19:42:

Total time = 19:42 - 17:30 = 2 hours and 12 minutes

To convert the minutes to decimal form, we divide by 60:

2 hours and 12 minutes = 2 + (12 ÷ 60) = 2.2 hours

Now we can calculate the average speed:

Average speed = Total distance ÷ Total time

Average speed = 143 miles ÷ 2.2 hours

Average speed = 65 mph

Therefore, the average speed of Niamh's car from 17:30 to 19:42 was 65 mph.

A cylinder has a base area of 64π m2. Its height is equal to twice the radius. Identify the volume of the cylinder to the nearest tenth

The **volume** of the cylinder is approximately 1024π cubic meters.

We are given the base area of the cylinder as 64π square meters, which means that the radius of the **cylinder** is 8 meters (since the area of a circle is given by πr^2). We are also given that the height of the cylinder is twice the radius, which means that the height is 16 meters.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the **height**. Substituting the given values, we get V = π(8^2)(16) = 1024π cubic meters. Therefore, the volume of the cylinder is approximately 1024π cubic meters.

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**Answer:**

[tex]3217.0 m ^{3}[/tex]

**Step-by-step explanation:**

H 고 Assignment Law of Cosli Progress saved Submit and End Assignment Law of Cosines 5 points possible 0/5 answered 6 VO : Question 1 > 1 pt 1 Details A pilot flies in a straight path for 1 hour 45 minutes. She then makes a course correction, heading 35 degrees to the right of her original course, and flies 2 hours 15 minutes in the new direction. If she maintains a constant speed of 235 mi/h, how far is she from her starting position? Give your answer to the nearest mile. She is miles from her starting position

Round the answer to the nearest **mile**: She is 398 miles from her starting position.

To solve this problem, we'll use the **Law of Cosines**.

Here are the steps to find the distance from the starting position:

1. Convert the given time to hours: 1 hour 45 minutes = 1.75 hours 2 hours 15 minutes = 2.25 hours

2. Calculate the distance traveled in each direction:

Distance1 = Speed × Time1 = 235 mi/h × 1.75 h = 411.25 miles

Distance2 = Speed × Time2 = 235 mi/h × 2.25 h = 528.75 miles

3. Use the Law of Cosines to find the distance between the starting position and her final position:

Distance = √(Distance1² + Distance2² - 2 × Distance1 × Distance2 × cos(35°))

4. Plug in the values and solve for the distance:

Distance = √(411.25² + 528.75² - 2 × 411.25 × 528.75 × cos(35°))

Distance ≈ 397.69 miles

5. Round the answer to the nearest mile: She is 398 miles from her starting position.

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The cost to produce x cases of Thingamabobs is given by the function C = 50x + 1000 where Cis in hundreds of dollars. If production is growing at a rate of 20 cases per day when the production level is x= 50 cases, find the rate at which the cost of production is changing.

The rate at which the cost of **production **is changing is **1000 hundred dollars per day **or** $100,000 per day.**

To find the rate at which the** cost** of production is changing, we'll use the given cost function C = 50x + 1000, and the information that production is growing at a rate of 20 cases per day when x = 50 cases.

First, differentiate the** cost function** with respect to x to get the rate of change of the cost with respect to the number of cases produced (dC/dx):

dC/dx = 50

The derivative, 50, tells us that the cost increases by 50 hundred dollars for each additional case produced.

Now, we're given that dx/dt = 20 cases per day when x = 50 cases. To find dC/dt, the rate at which the cost of production is changing, multiply the rate of change of the cost with respect to the number of cases (dC/dx) by the rate of change of the number of **cases** with respect to time (dx/dt):

[tex]dC/dt = (dC/dx) × (dx/dt) = 50 × 20[/tex]

dC/dt = 1000

So, the rate at which the cost of production is changing is 1000 hundred dollars per day or $100,000 per day.

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Use the following for #5-6 A middle school science teacher wants to conduct some experiments. There are 15 students in the class. The teacher selects the students randomly to work together in groups of five. 5) In how many ways can the teacher combine five of the students for the first group if the order is not important? 6) After the first group of five is selected, in how many ways can the teacher combine five of the remaining students if the order is not important?

**Answer:**

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

5) Use the **combination formula**:

In this case, n = 15 (total students) and r = 5 (students in a group).

**Substitute and calculate**:

The teacher can combine the students in **3003 ways** for the first group.

6) After the first group of five is selected, there are **10 students remaining.**

Again use the **combination formula, **with n = 10 and r = 5:

The teacher can combine the remaining students in **252 ways** for the second group.

Which of the following tables represent a proportional relationship?

verbal:

a. y/x= 40/1 76/2 112/3 148/4

b. y/x= 48/2 96/3 144/4 192/5

c. y/x= 18/1 54/3 90/5 126/7

d. 24/1 21/2 18/3 15/4

picture:

a. y/x = 40/1, 76/2, 112/3, 148/4 does not represent a proportional relationship. . y/x = 48/2, 96/3, 144/4, 192/5 does not represent a proportional relationship. c. y/x = 18/1, 54/3, 90/5, 126/7 represents a proportional relationship.

How to determine a proportional relationshipA proportional relationship means that the **ratio **of y to x is constant throughout the table. Let's check each table:

a. y/x = 40/1, 76/2, 112/3, 148/4

If we simplify the fractions, we get y/x = 40, 38, 37.33, 37. This is not a constant ratio, so this table does** not represent** a proportional relationship.

b. y/x = 48/2, 96/3, 144/4, 192/5

If we simplify the fractions, we get y/x = 24, 32, 36, 38.4. This is not a constant ratio, so this table does** not represent **a proportional relationship.

c. y/x = 18/1, 54/3, 90/5, 126/7

If we simplify the fractions, we get y/x = 18, 18, 18, 18. This is a constant ratio, so this table r**epresents **a proportional relationship.

d. y/x = 24/1, 21/2, 18/3, 15/4

If we simplify the** fractions**, we get y/x = 24, 10.5, 6, 3.75. This is not a constant ratio, so this table does not represent a proportional relationship.

Therefore, the table that represents a** proportional relationship** is c. y/x = 18/1, 54/3, 90/5, 126/7.

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true or false

Solids can be "unfolded" to form different net arrangements.

**Solids **can be "unfolded" to form different net arrangements is a **true statement.**

A net refers to a flat, two-**dimensional **shape that can be transformed or manipulated to form a three-dimensional object. A solid has the potential to create a variety of nets through various unfolding methods.

The term "net" for a solid refers to a flat shape that can be folded to form the solid object. it is possible to **manipulate **a three-dimensional object in various manners in order to produce distinct two-dimensional patterns. One can create various nets by cutting different edges of a cube and arranging the resultant faces.

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Use linear approximation to approximate √125.04 as follows Let f(x) = ³√ x, and find the linearization of f(x) at x = 125 in the form y = mx+ b Note: The values of m and bare rational numbers which can be computed by hand. You need to enter expressions which give m and b exactly You should not have a decimal point in the answers to either of these parts m= b = Using these values, find the approximation Also, for this part you should be entering a rational number, not a decimal approximation ²√ 125.04≈

To approximate √125.04 using linear approximation, first find the linearization of f(x) = ³√x at x = 125. Then use the point-slope form of the equation to find the equation of the **tangent line **and plug in x = 125.04 to get the approximation.

To approximate √125.04 using linear **approximation** and the function f(x) = ³√x, first find the linearization of f(x) at x = 125 in the form y = mx + b. Calculate f(125) and f'(x).Calculate f'(125): Use the** **point-slope form of the equation

1: Calculate f(125) and f'(x).

f(125) = ³√125 = 5

f'(x) = (1/3)x^(-2/3)

2: Calculate f'(125).

f'(125) = (1/3)(125)^(-2/3) = 1/15

3: Use the** point-slope** form of the equation y - y1 = m(x - x1) to find the equation of the tangent line.

y - 5 = (1/15)(x - 125)

4: Rearrange to find y in terms of x.

y = (1/15)(x - 125) + 5

5: **Determine** the values of m and b.

m = 1/15

b = (1/15)(-125) + 5

6: Plug in x = 125.04 to approximate √125.04.

²√125.04 ≈ (1/15)(125.04 - 125) + 5

The **linearization** of f(x) at x = 125 is y = (1/15)x + b, with m = 1/15 and b = (1/15)(-125) + 5. Using these values, the approximation of √125.04 is (1/15)(125.04 - 125) + 5.

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Work out the size of an exterior angle of a regular hexagon

The size of an **exterior **angle of a **regular hexagon** is 60 degrees.

In a **regular hexagon**, all the interior angles are equal and are given by the formula:

Interior angle = (n-2) x 180 / n

where n is the number of **sides **of the **polygon**.

For a hexagon, n = 6, so the **interior **angle is:

Interior angle = (6-2) x 180 / 6 = 120 degrees

An exterior angle is the **supplement** of an **interior angle**, which means it is the angle that when added to the interior angle, will equal 180 degrees.

So, exterior angle = 180 - interior angle = 180 - 120 = 60 degrees.

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A cat falls from a tree (with zero initial velocity) at time t = 0. How far does the cat fall between t = 0.5 s and t=1.4 s? Use Galileo's formula u(t) = -32t ft/s.

Answer = _______

The** distance** is negative because it's a fall, so the cat falls 27.36 ft between t = 0.5 s and t = 1.4 s.

To find the **distance** the cat falls between t = 0.5 s and t = 1.4 s, we need to use the formula for velocity and distance.

we first need to find the position at each of these **times **using the given formula u(t) = -32t ft/s.

The formula for distance fallen is:

distance(t) = initial position + initial velocity × t + (1/2) × **acceleration** × t²

Since the cat falls with zero initial velocity and starts from the tree, we can simplify the formula:

distance(t) = (1/2) × acceleration × t²

First, let's find the **velocity** of the cat at t = 0.5 s and t = 1.4 s using Galileo's formula:

u(0.5) = -32(0.5) = -16 ft/s

and, u(1.4) = -32(1.4) = -44.8 ft/s

Now, we can use the formula for distance:

distance = (velocity at t = 0.5 s + velocity at t = 1.4 s) / 2 x (t = 1.4 s - t = 0.5 s)

⇒ distance = (-16 ft/s + (-44.8 ft/s)) / 2 x (1.4 s - 0.5 s)

⇒ distance = (-60.8 ft/s) / 2 x (0.9 s)

⇒ distance = -27.36 ft/s x s

Therefore, the cat falls 27.36 feet between t = 0.5 s and t = 1.4 s.

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145 student are in the auditorium. Of the students in the auditorium, about 86% of the students play a sport. About 45% of the students are in the school play. How many students play a sport? How many students are in the play? Round your answer to the nearest whole

About 125 students play a **sport **and about 65 students are in the play.

To find the number of **students **who play a sport and those who are in the play, we need to use the given percentages and round the answers to the nearest whole.

Find the number of students who play a sport:

Multiply the total number of students (145) by the **percentage **of students who play a sport (86%).

145 × 0.86 = 124.7

Round the answer to the nearest whole number:

Approximately 125 students play a sport.

Find the number of students who are in the play:

Multiply the total number of students (145) by the percentage of students who are in the play (45%).

145 × 0.45 = 65.25

Round the answer to the **nearest **whole number:

Approximately 65 students are in the play.

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A fisherman kept records of the weight in pounds of the fish caught on the fishing trip 10, 9, 2, 12, 10, 12, 8, 14, 11, 3, 6, 9, 7, 15. What does the shape of the distribution in the histogram tell you about the situation

The shape of the **distribution **in the **histogram **can tell us about the distribution of weights of fish caught by the fisherman.

Looking at the given **data set,** we can see that the weights of the fish caught vary from as low as 2 pounds to as high as 15 pounds. The histogram of this data set can help us to fantasize the distribution of these weights. Grounded on the shape of the histogram, we can see that the distribution is kindly slanted to the right, with a long tail extending towards the **advanced **end of the weights.

This suggests that there were further fish caught that counted lower than the mean weight of the catch, with smaller fish caught that counted further than the **mean **weight. also, the presence of a many outliers( similar as the fish that counted 15 pounds) suggests that there may have been some larger or unusual fish caught on the trip.

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Question 3

3.1 simplify the following ratios:

3.1.1 500g : 3 kg

3.1.2 12cm : 1m

The simplified** ratios** are: 1:6 & 3:25

To simplify the first ratio, we need to convert the **units **so they are the same. We can either convert 500g to **kilograms **or 3kg to grams. Let's convert 3kg to grams since it will be easier to compare with 500g.

3 kg = 3000g

Now the ratio becomes:

500g : 3000g

We can simplify this ratio by dividing both sides by 500:

500g/500 = 1 and 3000g/500 = 6

So the simplified** **ratio is:

1 : 6

For the second** **ratio, we need to convert either 12cm to meters or 1m to **centimeters**. Let's convert 1m to centimeters since it will be easier to compare with 12cm.

1m = 100cm

Now the ratio becomes:

12cm : 100cm

We can simplify this** **ratio by dividing both sides by 4:

12cm/4 = 3 and 100cm/4 = 25

So the simplified** **ratio is:

3 : 25

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An athletic Beld is a 50 yd-by-100 yd rectangle, with a semicircle at each of the short sides. Arunning track 10 yd wide surrounds the field. If the track is divided into eight lanes of equal width, with lane 1 being the inner-most and lane 8 being the outer-most lane, what is the distance around the along the inside edge of each lane?

The **distance** along the inside edge of each **lane** is 170 yards, 180 yards, 190 yards, 200 yards, 210 yards, 220 yards, 230 yards, and 240 yards.

Length of the Beld = 100 yd

Width of the Beld = 50 yd

The **radius** of the lane = 50/2 = 25 yards

To calculate the **length** of the overall length of the lane including semicircles is:

100 yards + 2 × 25 yards = 150 yards

The length of the **innermost lane** is:

150 yards + 2 × 10 yards = 170 yards

To calculate the length of the other lanes is:

170 yards + 10 yards = 180 yards

The length of **lane 3 **is:

180 yards + 10 yards = 190 yards

The distance between the two lanes is 10 yards. Then the remaining lengths of the lanes will be 200 yards, 210 yards, 220 yards, 230 yards, and 240 yards

Therefore, we can conclude that the distance between the two lanes along the inside edge of each lane is **10 yards.**

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Use this data set, which shows how many miles Tisha ran each week for 10 weeks

4,9,8,6,14,8,16,12

Find the statistical measures that you need tomake a box plot of Tisha's running distances.

(what’s a statistical measure)

Statistical measures, you can construct a box plot that shows the range, median, and quartiles of Tisha's running **distances** over the 10 weeks.

A statistical measure is a numerical value that provides information about a specific aspect of a dataset's distribution, such as its central tendency, spread, or **variability**. Box plots require several statistical measures to be constructed, including:

Minimum: The smallest value in the dataset. In this case, the minimum value is 4.

Maximum: The largest value in the **dataset**. In this case, the maximum value is 16.

Median: The middle value of the dataset when it is arranged in numerical order. In this case, the median is the average of the two middle values, which are 8 and 9. The median is therefore (8 + 9) / 2 = 8.5.

First Quartile (Q1): The value below which 25% of the data falls. In this case, the first quartile is the **median** of the first half of the data, which is 6.

Third Quartile (Q3): The value below which 75% of the data falls. In this case, the **third quartile** is the median of the second half of the data, which is 14.

With these statistical measures, you can construct a box plot that shows the range, median, and quartiles of Tisha's running distances over the 10 weeks.

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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2

**Answer:**

The three equivalent equations are x+1=4, -5+x=-2, and 2+x=5. The x equals 3.

**Step-by-step explanation:**

This question: 1 pt

15 of 30

identify the type 1 error. the epa claims that fluoride in children's drinking water should be at a mean level of less than 1. 2 ppm, or parts per million, to reduce the number of dental cavities.

The** type 1 error** in this scenario would be rejecting the null hypothesis that the mean level of fluoride in children's drinking water is less than 1.2 ppm, when in reality it is true.

The EPA claims that fluoride in children's drinking water should have a mean level of less than 1.2 ppm to reduce the number of dental cavities. A **type 1 error** occurs when we reject the **null hypothesis** when it is actually true. In this case, the null hypothesis (H0) would be that the mean fluoride level is less than or equal to 1.2 ppm, and the **alternative hypothesis** (H1) would be that the mean fluoride level is greater than 1.2 ppm.

A type 1 error would occur if we incorrectly conclude that the mean fluoride level is greater than 1.2 ppm when, in reality, it is less than or equal to 1.2 ppm. This could lead to unnecessary actions being taken to reduce fluoride levels when they are already at an acceptable level.

In other words, falsely concluding that the mean level of fluoride in the water is above 1.2 ppm and therefore causing harm to the children's dental health by not reducing the number of dental cavities.

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9. define a relation r on the integers, ∀m, n ∈ z, mean if m n is even. is r a partial order relation? prove or give counterexample.

No, the relation r is not a **partial order relation.**

To prove this, we need to show that r is not reflexive, not **antisymmetric,** or not transitive.

Since r fails to satisfy the** antisymmetric property**, it is not a partial order relation.

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Set up the partial fraction decomposition for a given function. Do not evaluate the coefficients. f(x) = 16x3 + 12x2 + 10x + 2 / (x4 – 4x2)(x2 + x + 1)2(x2 – 3x + 2)(x4 + 3x2 + 2)

We can **decompose **the given **rational function** as follows:

f(x) = (16x^3 + 12x^2 + 10x + 2) / [(x^4 – 4x^2)(x^2 + x + 1)^2(x^2 – 3x + 2)(x^4 + 3x^2 + 2)]

To find the partial fraction decomposition, we first factor the **denominator **completely:

x^4 – 4x^2 = x^2(x^2 – 4) = x^2(x – 2)(x + 2)

x^2 + x + 1 = (x + 1/2)^2 + 3/4

x^2 – 3x + 2 = (x – 1)(x – 2)

x^4 + 3x^2 + 2 = (x^2 + 1)(x^2 + 2)

Substituting these **factorizations **into the **denominator**, we get:

f(x) = (16x^3 + 12x^2 + 10x + 2) / [x^2(x – 2)(x + 2)(x + 1/2)^2(3/4)^2(x – 1)(x – 2)(x^2 + 1)(x^2 + 2)]

We can now write the partial fraction decomposition as:

f(x) = A/x + Bx + C/(x – 2) + D/(x + 2) + E/(x + 1/2) + F/(x + 1/2)^2 + G/(x – 1) + H/(x^2 + 1) + I/(x^2 + 2)

where A, B, C, D, E, F, G, H, and I are constants to be determined.

Note that the term E/(x + 1/2) has a repeated **linear factor** (x + 1/2)^2, so we need to include a second term F/(x + 1/2)^2 in the decomposition.

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The foutain in the of a park is circular with a diameter of 16 feet. There is a walk way that is 3 feet wide that goes around the fountain what is the approximate are of the walkway?

The **approximate area **of the walkway is 179 square feet.

To find the area of the walkway, we need to subtract the area of the inner circle (fountain) from the area of the outer circle (walkway + fountain).

The** radius** of the fountain is half the diameter, which is 16/2 = 8 feet.

The radius of the outer circle is the radius of the fountain + the width of the walkway, which is 8 + 3 = 11 feet.

The area of a circle is πr², where π (pi) is approximately 3.14.

So, the **area** of the fountain is:

π(8)² ≈ 201 square feet

And the area of the walkway plus fountain is:

π(11)² ≈ 380 square feet

To find the area of just the walkway, we **subtract** the area of the fountain from the area of the walkway plus fountain:

380 - 201 ≈ 179 square feet

So, the approximate area of the walkway is 179 square feet.

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4. Let A be a 3 x 4 matrix and B be a 4 x 5 matrix such that ABx = 0 for all x € R5. a. Show that R(B) C N(A) and deduce that rank(B) < null(A) b. Use the Rank-Nullity theorem to prove that rank(A) + rank(B) < 4.

**a. To show that R(B) is a subset of N(A), let y be any vector in R(B):**

This means that there exists a vector x in R4 such that Bx = y.

Now, since ABx = 0 for all x in R5, we can write:**A(Bx) = 0**

But we know that **Bx = y**, so we have:**Ay = 0**

This shows that y is in N(A), and therefore **R(B) is a subset of N(A). **

To deduce that rank(B) is less than null(A), recall that by the

rank(B) + null(B) = dim(R5) = 5

rank(A) + null(A) = dim(R4) = 4

Since R(B) is a subset of N(A), we have

Therefore, using the above equations, we get:

rank(B) + null(A) <= null(B) + null(A) = 5

which implies:**rank(B) <= 5 - null(A) = 5 - (4 - rank(A)) = 1 + rank(A)**

This shows that **rank(B) is less than or equal to 1** plus the rank of A.

Since the rank of A can be at most 3 (since A is a 3 x 4 matrix),

we conclude that:**rank(B) < null(A)****b. To use the Rank-Nullity theorem to prove that rank(A) + rank(B) < 4**

We simply add the equations:**rank(A) + null(A) = 4rank(B) + null(B) = 5**

to get:

rank(A) + rank(B) + null(A) + null(B) = 9

But since R(B) is a subset of N(A), we know that

rank(A) + rank(B) + 2null(A) <= 9

Using the first equation above, we can write

rank(A) + rank(B) + 2(4 - rank(A)) <= 9

which simplifies to:

Since

we conclude that:**rank(A) + rank(B) < 4**

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3

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.

the measurement of an angle is 40°, and the length of a line segment is 8 centimeters.

the number of unique rhombuses that can be constructed using this information is _____

please hurry

The number of **unique rhombuses** that can be constructed using this information is three.

When given a 40° **angle** and an 8 cm line segment, we can construct three distinct rhombuses. A rhombus is a quadrilateral with all sides of equal length, and opposite angles are congruent.

In this scenario, the given 40° angle determines the orientation of the rhombus, while the 8 cm line segment determines its side length. By connecting the endpoints of the line segment with **congruent** opposite angles, we can create three different rhombuses.

Each rhombus formed will possess an** **angle measure of 40° and a side length of 8 cm. However, these rhombuses will vary in terms of their overall shape and orientation. Each one represents a unique configuration that satisfies the given angle and side length **criteria**.

Therefore, the correct answer is that three distinct rhombuses can be constructed using the given information.

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4 km 20) Determine the distance across the lake? 6 km Lake 6

hope this helps you

Two different box-filling machines are used to fill cerealboxes on the assembly line. The critical measurement influenced bythese machines is the weight of the product in the machines. Engineers are quite certain that the variance of the weight ofproduct is σ^2=1 ounce. Experiments are conducted using bothmachines with sample sizes of 36 each. The sample averages formachine A and B are xA=4. 5 ounces and xB =4. 7 ounces. Engineers seemed surprisedthat the two sample averages for the filling machines were sodifferent.

a. Use the central limit theorem to determine

P(XB- XA >= 0. 2)

under the condition that μA=μB

b. Do the aforementioned experiments seem to, in any way,strongly support a conjecture that the two population means for thetwo machines are different?

a. By **central limit theorem**, P(XB- XA >= 0. 2) is approximately 0.0228 under the condition that μA=μB.

b. Yes, we can conclude that the observed difference in sample means does provide evidence that the two population means for the two machines are different.

a. Using the** central limit theorem**, we know that the sampling distribution of the difference in means (XB - XA) is approximately normal with mean (μB - μA) and standard deviation (σ/√n), where σ is the population standard deviation (σ=1 ounce) and n is the sample size (n=36 for both machines).

So, P(XB - XA >= 0.2) can be calculated by standardizing the difference in **means**:

Z = (XB - XA - (μB - μA)) / (σ/√n)

Z = (4.7 - 4.5 - 0) / (1/√36)

Z = 2

Looking up the **probability** of Z being greater than or equal to 2 in a standard normal distribution table, we find P(Z >= 2) = 0.0228.

Therefore, P(XB - XA >= 0.2) is approximately 0.0228 under the condition that μA=μB.

b. The difference in sample means (XB - XA = 0.2) is relatively small compared to the population standard deviation (σ=1 ounce). However, the calculated probability in part a (0.0228) suggests that the observed difference in sample means is** statistically significant** at a significance level of 0.05 (since P(XB - XA >= 0.2) < 0.05).

Therefore, we can conclude that the observed difference in sample means does provide evidence that the two population means for the two machines are different. However, further testing or analysis may be necessary to confirm this conclusion.

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Need help on unit 2 review

Use the pythagorean theorem:

a^2+b^2=c^2

12 is the hypotenuse because it is opposite the right angle.

10^2+b^2=144

100+b^2=144

b^2=44

b=sqrt44

a^2+b^2=c^2

12 is the hypotenuse because it is opposite the right angle.

10^2+b^2=144

100+b^2=144

b^2=44

b=sqrt44

ASAP THX!!! ANSWER GETS BRAINLIEST

Rachel went to the grocery store and spent $68. She now has only $23 to get gasoline with before she returns home. How much money did Rachel have before she went grocery shopping? Create an equation to represent the situation. Make sure to identify and label your variable. Solve for the variable and describe your answer. Show your work and prove your solution to be correct

The **solution** is correct, as both sides of the equation are equal.

To find out how much money Rachel had before she went grocery shopping, we can create an equation using a **variable.**

Let x represent the **amount** of money Rachel had before grocery shopping.

The **equation** for the situation would be: x - $68 = $23

Now, let's solve for x:

Step 1: Add $68 to both sides of the equation:

x = $23 + $68

Step 2: Calculate the sum:

x = $91

So, Rachel had $91 before she went grocery shopping.

To prove the solution is correct, we can plug the value of x back into the equation:

$91 - $68 = $23

$23 = $23

Hence, both are** equal.**

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Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

The **dot plot** that most accurately displays Miss Little's class data is illustrated below.

To create a dot plot, we first need to determine the range of the data, which is the **difference **between the highest and lowest values. In this case, the range is from 8 to 16. We then draw a number line that spans the range, and mark each data point along the line with a dot.

Let's take a look at the first data set: 13, 14, 9, 12, 16, 11, and 10. The range is from 9 to 16, so we draw a number **line **from 9 to 16. We then mark each data point with a dot above its corresponding value on the number line. So, there will be one dot above 13, one dot above 14, two dots above 9, one dot above 12, one dot above 16, one dot above 11, and one dot above 10.

We repeat this process for the second data set: 9, 8, 10, 10, 11, 15, and 10. The range is from 8 to 15, so we draw a number line from 8 to 15. We then mark each data point with a dot above its corresponding value on the **number line. **So, there will be one dot above 9, one dot above 8, three dots above 10, one dot above 11, one dot above 15, and zero dots above 14.

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**Complete Question:**

Miss. Little wants to know how many pairs of shoes each of her students owns. She decides to ask each of her students to write the number of pairs of shoes that he or she owns. This data is displayed in the provided chart. Plot the dot plot that most accurately displays Miss Little's class data.

13 14 9 12 16 11 10

9 8 10 10 11 15 10

8-73.

For each diagram below, write and solve an equation for x

**Answer:**

a.x=100 equation: 540=(125·2)+90+(2x)

b. x=3 equation: 6x+18=2x+30

**Step-by-step explanation:**

a. We know that the interior angles of a pentagon have to equal 540 degrees.

So:

540=125+125+90 (hence the square) + x + x

simplify:

540=340+2x

simplify:

200=2x

x=100

b. Using the alternate exterior angles theorem we can say:

6x+18=2x+30

simplify:

4x+18=30

4x=12

x=3

2. A social media company claims that over 1 million people log onto their app daily. To test this claim, you record the number of people who log onto the app for 65 days. The mean number of people to log in and use the social media app was discovered to be 998,946 users a day, with a standard deviation of 23,876. 23. Test the hypothesis using a 1% level of significance.

The **hypothesis test **suggests that there is not enough evidence to reject the claim made by the social media company that over 1 million people log onto their app daily, as the t-value (-1.732) is less than the critical value (-2.429).

**Null hypothesis**, The true mean number of people who log onto the app daily is equal to or less than 1 million.

Alternative hypothesis, The true mean number of people who log onto the app daily is greater than 1 million.

Level of significance = 1%

We can use a one-sample **t-test **to test the hypothesis.

t = (X - μ) / (s / √n)

where X is the sample mean, μ is the hypothesized population mean, s is the sample **standard deviation**, and n is the sample size.

Substituting the values, we get

t = (998,946 - 1,000,000) / (23,876 / √65)

t = -1.732

Using a t-distribution table with 64 degrees of freedom and a one-tailed test at a 1% level of significance, the **critical value** is 2.429.

Since the calculated t-value (-1.732) is less than the critical value (-2.429), we fail to reject the null hypothesis. There is not enough evidence to support the claim that more than 1 million people log onto the app daily.

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Select the correct answer from each drop-down menu.

The three vertices of a triangle drawn on a complex plane are represented by 0 + 0i, 4 + 0i, and 0+ 3i.

The length of the hypotenuse is

units, and the area of the triangle is

square units. (Hint: Use the Pythagorean theorem.)

The **area **of the triangle is **6 square units.**

Once you have the** points **they make a 3-4-5 triangle.

The two legs are 3 and 4, so the **hypotenuse **has to be 5.

Or you could use the **Pythagorean theorem** a² + b² = c² 3² + 4² = c² 25 = c² c = 5

then find area

A=1/2bh

1/2(3*4)

6

Thus, the **area **of the triangle is **6 square units.**

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