1. Draw the solid, showing the 10 x 8 face as the base. Find:

a. The lateral area

b. The total area

c. The volume

2. Repeat Exercise 1, but show the 10 x 3 face as the base.

a.

b.

c.

We are adjusting the original rectangular solid and here is what we have:

1. Rectangular solid showing 10x8 face as the base(a) **The lateral area** is the sum of the areas of the four sides, which are all rectangles. The two sides with dimensions 8 x 3 have an area of 8 x 3 = 24 square units each, and the two sides with dimensions 10 x 3 have an area of 10 x 3 = 30 square units each. Therefore, the lateral area is:

2(24) + 2(30) = 48 + 60 = 1**08 square units**

(b) **The total area** is the sum of the areas of all six faces. The two faces with dimensions 10 x 8 have an area of 10 x 8 = 80 square units each, the two faces with dimensions 8 x 3 have an area of 8 x 3 = 24 square units each, and the two faces with dimensions 10 x 3 have an area of 10 x 3 = 30 square units each. Therefore, the total area is:

2(80) + 2(24) + 2(30) = 160 + 48 + 60 = **268 square units**

(c) The **volume** is the product of the length, width, and height of the rectangular solid. Therefore, the volume is:

10 x 8 x 3 = **240 cubic units**

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330 men took 30 days to finish a work then how many men will be required to finish the same work in 11 days...???

In your birthday party there was food for 20 friends for 2 hours but 30 friends attened the party. Till how long did the food last...???

**Step-by-step explanation:**

data given

men 330 ,days30

men? ,days11

from

men(m) are inversely proportional todays (d)

m=k/d

330×30=k

k=9900

now,

m=9900/11m

m=900

data given

friends 20, time 2hours

friends 30, time?

from

friends (f) are inversely proportional to time (t)

f=k/t

k=20×2

k=40

now,

t=40/30

t=1.3(1:18)

answer ,men required are900answer the food will last for1:18. (Adapted from Terence Blows, Northern Arizona University.) Classify as in Exercise 6 but for the following circumstances. a. The amount of caffeine in the bloodstream decreases by 50% every 5 hours or so after stopping drinking coffee. b. The amount of trash in a landfill increases by 350 tons per week. c. The amount of alcohol in the bloodstream decreases by 10 grams (the amount in a standard drink) per hour after stopping drinking. d. Your age increases every day.

The statements are classified as **Exponential decay **and **Linear growth.**

a. **Exponential decay**: The amount of caffeine in the bloodstream decreases by 50% every 5 hours, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.

b. **Linear growth**: The amount of trash in a landfill increases by 350 tons per week, which indicates a linear growth process where the quantity increases by a constant amount over time.

c.** Exponential decay**: The amount of alcohol in the bloodstream decreases by 10 grams (the amount in a standard drink) per hour after stopping drinking, which indicates an exponential decay process where the quantity decreases at a constant percentage rate over time.

d.** Linear growth:** Your age increases every day, which indicates a linear growth process where the quantity (age) increases by a constant amount (1 day) over time.

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6. Two out of every five Canadians read at least 10 books a year. What percent of Canadians read at least 10 books a year?

**Answer:**

40%

**Step-by-step explanation:**

2/5=x/100

cross multiply and you get 5x=200

by isolation the variable you will get x=40

therefore, 40% of Canadians read at least 10 books a year

Peanuts sell for Php 10.00 per gram. Cashews sell for Php 8.00 per gram. How many grams of cashews should be mixed with 12 g of peanuts to obtain a mixture that sells for Php 9.00 per gram?

PEANUTS CASHEWS MIXTURE Number of Grams (g) 12 X 12+ X Price per grams Php 10.00 Php 8.00 Php 9.00 Total Price Phn10x12 = Php 120 8x 9 [12+x]

**Answer:**

Phn10x12

**Step-by-step explanation:**

PEANUTS CASHEWS MIXTURE Number of Grams (g) 12 X 12+ X Price per grams Php 10.00 Php 8.00 Php 9.00 Total Price Phn10x12 = Php 120 8x 9 [12+x]

On the Y axis, we have the profit from the trucking company and on the X axis, we have the miles the truck has traveled. The company decided that they needed to start paying for a driver at a price of 0.25 cents a mile. After this change what will happen to the x and y axis/slope?

A. Y intercept will be less and X will be less

B. Y intercept will be less and X intercept will be greater

C. Y intercept will be greater and X will be greater

D. Y intercept will be greater and X will be less

**Answer:**

B.

**Step-by-step explanation:**

**Answer:**

B.

**Step-by-step explanation:**

the description is very confusing and lacks any hint about the behavior of the curve before the change.

but ok, let's assume that the curve (line ?) is in general going up. in other words, if the traveled miles go up, so does the profit.

I also don't know how they could drive the miles without paying the driver, but again, let's assume they did.

now they pay the driver. $0.25 per mile.

this has to come out of their profit.

so, the Y (profit) values all go down by 0.25.

therefore, the y-intercept is going down too.

that eliminates C. and D.

for this to be true they have to have some overhead costs that apply even if there are 0 miles traveled (which is the meaning of the y-intercept : the y-value when x = 0).

so, the line must be in a form

y = ax + b

with "b" <> 0.

and since we assumed the line to go up (positive slope), a "sinking" line means that the x-intercept (the break-even point, where the line goes from below the x-axis and therefore negative (y) profit up into positive profit) will move to the right (become greater).

because now that they have additional costs (paying the driver), it takes longer (more driven miles) to make a positive profit.

and that eliminates A, leaving B. as the right answer.

The diameter of a circle is 5 centimeters. What’s the radius? Give the exact answer in simplest form

**Answer:**

2.5cm

**Step-by-step explanation:**

you half the diameter to get the radius

^4√p7

in exponential form.

**Answer:1111**

**Step-by-step explanation:**

please help fill in these..

**Answer:**

Vertex: (-2, -1)

Axis of Symmetry: x = -2

Y-intercept: (0, 3)

Min/Max: Min

Domain: All Real

Range: y ≥ -1

**Step-by-step explanation:**

**Given the graph:**

**Answer:**

So, the answers to the question is:

Vertex: (-2, -1)

Axis of Symmetry: x = -2

Y-intercept: (0, 3)

Min/Max: Min

Domain: All Real

Range: y ≥ -1

What is the perimeter of the triangle?

**Answer:**

40 units

**Step-by-step explanation:**

a = 8

b = 15

To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]8^{2} +15^{2} =x^{2}[/tex]

64 + 225 = c^2

289 = c^2

c = 17

a + b + c = perimeter

8 + 15 + 17 = 40

**Answer:**

40 units

**Step-by-step explanation:**

You want the **perimeter** of the **triangle** shown in the **graph**.

You can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.

The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:

c² = a² +b²

c² = 8² +15² = 64 +225 = 289

c = √289 = 17

The long side of the triangle is 17 units.

PerimeterThe perimeter of the triangle is the sum of the lengths of its sides:

P = 8 + 15 + 17 = 40

**The perimeter is 40 units**.

__

*Additional comment*

A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...

{3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}

You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.

The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)

coordinate plane with points at A 0 comma 2 and B 2 comma 0 intersected by line f Dilate line f by a scale factor of one half with the center of dilation at the origin to create line f′. Where are points A′ and B′ located after dilation, and how are lines f and f′ related? The locations of A′ and B′ are A′ (0, 2) and B′ (0, 0); lines f and f′ intersect at point A. The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel. The locations of A′ and B′ are A′ (0, 0) and B′ (2, 0); lines f and f′ intersect at point B. The locations of A′ and B′ are A′ (0, 2) and B′ (2, 0); lines f and f′ are the same line.

The answer of the given question based on the **graph** is , The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.

A scale factor is a number that scales, or multiplies, a quantity by some **factor**. It is used in mathematics to describe the relationship between corresponding measurements of two similar figures, such as triangles or rectangles.

To dilate line f by scale factor of one half with **center of dilation** at origin, we multiply coordinates of each point on line f by 1/2.

The equation of line f can be found by using the points A and B:

slope of line f = (0 - 2)/(2 - 0) = -1

y-intercept of line f = 2

Therefore, the equation of line f is y = -x + 2.

To find the coordinates of A' and B' after dilation, we can apply the dilation factor to each point:

A' = (0, 2)*1/2 =(0, 1)

B' = (2, 0)*1/2 =(1, 0)

So A' is located at (0, 1) and B' is located at (1, 0) after dilation.

Now let's analyze the relationship between lines f and f'. The dilation was centered at the origin, so the origin is a fixed point of the dilation. This means that the point where lines f and f' intersect must be the origin.

If we plug in x = 0 into the equation of line f, we get y = 2. This means that point A is located at (0, 2) and intersects with line f at y = 2. After dilation, point A' is located at (0, 1), which means that lines f and f' intersect at point A.

To determine the relationship between lines f and f', we can compare their equations. The equation of f' can be found by using the points A' and B':

slope of f' = (0 - 1)/(1 - 0) = -1

y-intercept of f' = 0

Therefore, the equation of f' is y = -x.

Comparing the equations of f and f', we can see that they have the same slope of -1, which means they are parallel. Therefore, the correct answer is: The locations of A′ and B′ are A′ (0, 1) and B′ (1, 0); lines f and f′ are parallel.

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Hurry help Greg plants a seed and as soon as the plant sprouts, he measures its height each day and records his data for two weeks. If the plant continues to grow the whole two weeks, what would a line graph of Greg's data look like?

It would be flat.

It would move downward.

It would go up and down.

It would move upward.

The **line graph** of Greg's data wood look like "It would move upward."

A **graph** is a visual representation of data that shows the relationship between two or more variables. There are several types of graphs that can be used to display data

If Greg is measuring the **height** of the plant each day and the plant is **continuing** to grow for two weeks, then the line graph of his data would move upward. The graph would show an increasing trend as the plant grows taller each day. Therefore, the correct answer is "It would move upward."

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(01.08)

Let f(x) = 3x² + x - 3 and g(x) = x² - 5x +

1. Find f(x) - g(x).

**Answer:**

f(x) - g(x) = 2x² + 6x - 4

**Step-by-step explanation:**

f(x) - g(x)

= 3x² + x - 3 - (x² - 5x + 1) ← distribute parenthesis by - 1

= 3x² + x - 3 - x² + 5x - 1 ← collect like terms

= 2x² + 6x - 4

You have a bag with 4 red marbles, 3 green marbles, 2 blue marbles, and 1 purple marble. What is the probability of drawing a red marble out of the bag?

**Answer:**

40%

**Step-by-step explanation:**

**We Know**

**You have a bag with 4 red marbles, 3 green marbles, 2 blue marbles, and 1 purple marble.**

**4 + 3 + 2 + 1 = 10 marbles total**

**What is the probability of drawing a red marble out of the bag?**

We Take

(4 ÷ 10) x 100 = 40%

So, 40% of drawing a red marble out of the bag.

i have 60 square feet of paper to wrap a box in the shape of a right rectangular prism the height of the box is 1 2/3 feet the width is 4 feet and the length is 5 1/2 feet what percent of the box will remain unwrapped if i use all the paper i has available

The **percent** of the **box** that will **remain** unwrapped by the 60 square feet of paper is about 20.70%

A **percentage** is a **proportion** of a number expressed as **fraction** of a 100

The **dimensions** in mixed fractions can be expressed as follows;

**Height** of the box = 1 2/3 feet = 5/3 feet

**Width** of the box = 4 feet

**Length** of the box = 5 1/2 feet = 11/2 feet

**Surface area** of the **box**, *A* = 2 × (5/3) × 4 + 2 × 4 × 11/2 + 2 × (5/3) × 11/2 = 227/3 = 75 2/3 square inches

The percent of the box that will remain unwrapped is therefore;

Percentage = 60/(227/3) × 100 ≈ 79.3%

The **percentage** of the box that will remain unwrapped is about (100 - 79.3)% = 20.70%

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12. The length of a rectangle is 6 meters longer than the width. If the total area of the rectangle is 16m², find the dimensions of the rectangle.

**Answer: Let's say that the width of the rectangle is x meters. Then, according to the problem, the length of the rectangle is 6 meters longer than the width, which means that the length is (x + 6) meters.**

**The formula for the area of a rectangle is:**

**Area = Length x Width**

**We are given that the total area of the rectangle is 16m². Substituting the expressions for length and width, we get:**

**(x + 6) x = 16**

**Expanding the product and rearranging, we get a quadratic equation:**

**x² + 6x - 16 = 0**

**We can solve this equation by factoring or by using the quadratic formula. Factoring, we get:**

**(x + 8) (x - 2) = 0**

**This equation is satisfied when either x + 8 = 0 or x - 2 = 0. Therefore, the possible values for the width are x = -8 or x = 2. However, since the width of a rectangle cannot be negative, we reject the solution x = -8.**

**Therefore, the width of the rectangle is x = 2 meters. The length is 6 meters longer than the width, so the length is (2 + 6) = 8 meters.**

**Therefore, the dimensions of the rectangle are 2 meters by 8 meters.**

**Step-by-step explanation:**

Can someone help me with this problem, and explain how to solve it?

Thus, the **height of flagpole** from the ground is found as 23.34 feet.

The measurement of the angle between a person's eyes' line of sight to anything above and the horizontal line is known as the angle of elevation.

The movement of the observer's eyes determines the elevation angle. The angle of elevation is the angle formed by the line of sight and the horizontal line when a viewer is looking up at an object.

Given data:

height of boy = 5 ftDistance of boy from flagpole = 30 ftUsing the **trigonometric ratios** in the right triangle ABE.

tan 35 = h / 30

h = 30* tan(35)

h = 18.34

Height of flagpole = 18.34 + 5 = 23.34 feet

Thus, the height of the flagpole from the ground is found as 23.34 feet.

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whats the answer to 102-38x14 divided by 7+162= help plss

**Answer:**

-2.5

**Step-by-step explanation:**

follow BIMDAS.

like my answer if you find it helpful

Cylinder M and cylinder N are similar. The radius of cylinder N is equal to its height, and the ratio of the height of cylinder N to the height of cylinder M is 5: 3. The surface area of cylinder N is 256 square feet greater than the surface area of cylinder M. Find the surface area of each cylinder.

The surface area of **cylinder **M is approximately 131.95 square feet and the surface **area **of cylinder N is approximately 319.77 square feet.

**What is a cylinder?**

A cylinder is a three-dimensional geometric shape that consists of two congruent **parallel bases** in the shape of circles or ellipses, and a curved surface that connects the bases. The height of a cylinder is the perpendicular distance between the bases. A cylinder is a type of prism, and it can be classified as either a right cylinder or an oblique cylinder depending on whether or not its axis is perpendicular to its bases. Right cylinders have circular bases and their axis is perpendicular to the bases, while oblique cylinders have elliptical bases and their axis is not **perpendicular **to the bases.

Now,

Let the radius of cylinder M be r and its height be h. Then, the radius and height of cylinder N are both 2r, since the **radius **is equal to the height.

Since the cylinders are similar, their dimensions are proportional, which means:

(height of N) / (height of M) = 5/3

(radius of N) / (radius of M) = (2r) / r = 2

Using the formula for the surface area of a cylinder, we can write:

Surface area of cylinder M: 2πr² + 2πrh

Surface area of cylinder N: 2π(2r)² + 2π(2r)(5/3)h

We are told that the surface area of cylinder N is 256 square feet greater than the surface area of cylinder M. So we can set up the equation:

2π(2r)² + 2π(2r)(5/3)h = 2πr² + 2πrh + 256

Simplifying and solving for h, we get:

4r² + 20rh/3 = r² + rh + 128

3r² - rh - 128 = 0

(3r + 32)(r - 4) = 0

Since the **height **of the cylinder cannot be negative, we take the positive solution r = 4. Then, the height of cylinder M is (3/5)(4) = 12/5, and the height of cylinder N is 2(4) = 8.

Using the formulas for surface area, we can find the surface areas of both cylinders:

Surface area of cylinder M: 2π(4)² + 2π(4)(12/5) = 131.95 square feet

Surface area of cylinder N: 2π(2(4))² + 2π(2(4))(8) = 319.77 square feet

Therefore, the surface area of cylinder M is approximately 131.95 square feet and the **surface area** of cylinder N is approximately 319.77 square feet.

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If P(A)=0.3, P(B)=0.2 and P(A∩B)=0.2 determine the following probabilities:

(a) P(A')

(b) P(A∪B)

(c) P(A'∩B)

(d) P(A∩B')

(e) P[(A∪B)']

The **probabilities **are as follows:

(a) P(A')= 0.7

(b) P(A∪B) = 0.3

(c) P(A'∩B) = 0

(d) P(A∩B') = 0.1

(e) P[(A∪B)'] = 0.7

**What is probability?**

Probability is a **measure** of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is **impossible** and 1 means the event is certain to happen.

(a) P(A') = 1 - P(A) = 1 - 0.3 = 0.7

(b) P(A∪B) = P(A) + P(B) - P(A∩B) = 0.3 + 0.2 - 0.2 = 0.3

(c) P(A'∩B) = P(B) - P(A∩B) = 0.2 - 0.2 = 0

(d) P(A∩B') = P(A) - P(A∩B) = 0.3 - 0.2 = 0.1

(e) P[(A∪B)'] = 1 - P(A∪B) = 1 - 0.3 = 0.7

Note: P(A) represents the probability of event A occurring, P(B) **represents** the probability of event B occurring, and P(A∩B) represents the probability of both events A and B occurring simultaneously. The symbol '∪' represents the union of two events, and the symbol '∩' represents the intersection of two **events**. The complement of an event A is represented by A'.

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An insurance company reported that 70% of all automobile damage claims were made by people under the age of 25. If 5 automobile damage claims were selected at random, determine the probability that exactly 4 of them were made by someone under the age of 25.

I need the method more than the answer, as detailed as possible, please.

There is a 0.00567 **percent **chance that 4 out of the 5 auto damage claims were submitted by individuals under the age of 25.

An expression that has been raised to any finite power can be expanded using the binomial theorem. A** binomial theorem** is a potent expansionary technique with uses in probability, algebra, and other fields.

A binomial expression is an **algebraic **expression with two terms that are not the same. For instance, a+b, a3+b3, etc.

Let n = N, x, y, R, then the binomial theorem holds.

(x + y)n = nΣr=0 where, nCr xn - r yr

what is a probability?The likelihood of an event happening is gauged by probability. Several things are impossible to completely predict in advance. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening. The **probability **might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty. A crucial subject for pupils in class 10, probability explains all the fundamental ideas of the subject. A **sample space** has an overall probability of 1 for all events.

This is a binomial probability problem, where each automobile damage claim is a Bernoulli trial with a probability of success (a claim made by someone under the age of 25) of p=0.70. We want to find the probability of getting exactly 4 successes out of 5 trials.

The probability of getting exactly k successes out of n trials in a binomial experiment with probability of success p is given by the binomial probability formula:

P(k successes out of n trials) = (n choose k) * [tex]p^k[/tex] * [tex](1-p)^(n-k)[/tex]

where (n choose k) = n! / (k! * (n-k)!) is the number of ways to choose k items out of n items.

In this case, we have n=5 and p=0.70. So, the probability of getting exactly 4 successes out of 5 trials is:

P(4 out of 5 claims made by someone under 25) = (5 choose 4) * [tex]0.70^4[/tex] *[tex](1-0.70)^(5-4)[/tex]

P(4 out of 5 claims made by someone under 25) = 5 * [tex]0.70^4[/tex] *[tex]0.30^1[/tex]

P(4 out of 5 claims made by someone under 25) = 0.00567 (rounded to 5 decimal places)

Therefore, the probability that exactly 4 of the 5 automobile damage claims were made by people under the age of 25 is approximately 0.00567.

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A company is going to make an oil container in the shape of a cylinder. As shown below, the container will have a height of 8 m and a diameter of 10 m. The container will be made from steel (including its top and bottom). Suppose the total cost of the steel will be $13,062.40. How much will the steel cost per square meter? Use 3.14 for it, and do not round your answer.

The per square meter cost of steel will be $32. The solution has been obtained by using the **cylinder**.

**What is a cylinder?**

The cylinder, one of the most basic curvilinear **geometric** shapes, has long been considered to be a three-dimensional solid. It is regarded as a prism with a circle as its basis in elementary geometry.

We are given that the height of cylinder is 8 m and diameter is 10 m.

So, the **radius** is 5 m.

Now, using the surface area formula, we get

⇒ S = 2πrh + 2π[tex]r^{2}[/tex]

⇒ S = 2π * 5 * 8 + 2π * [tex]5^{2}[/tex]

⇒ S = 2 * 3.14 * 5 * 8 + 2 * 3.14 * 25

⇒ S = 251.2 + 157

⇒ S = 408.2 square meter

Now, it is given that the total cost of the steel will be $13,062.40.

So, per square meter cost will be:

⇒ Cost = [tex]\frac{13,062.40}{408.2\\}[/tex]

⇒ Cost = $32

Hence, the per square meter cost of steel for the **cylinder** will be $32.

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Calculate Volume of Air passing through Filter HEPA Filter 100ft/min *- Airflow 4ft 2ft Volume = Filter Area x Airflow Velocity

The formula for calculating the volume of air passing through a filter is:

Volume = Filter Area x Airflow Velocity

Given that the airflow velocity is 100 ft/min and the dimensions of the filter are 4 ft x 2 ft, we can calculate the filter area as:

Filter Area = Length x Width

Filter Area = 4 ft x 2 ft

Filter Area = 8 square feet

Now we can substitute the values into the formula:

Volume = Filter Area x Airflow Velocity

Volume = 8 sq ft x 100 ft/min

Volume = 800 cubic feet per minute (CFM)

Therefore, the volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).

Volume = Filter Area x Airflow Velocity

Given that the airflow velocity is 100 ft/min and the dimensions of the filter are 4 ft x 2 ft, we can calculate the filter area as:

Filter Area = Length x Width

Filter Area = 4 ft x 2 ft

Filter Area = 8 square feet

Now we can substitute the values into the formula:

Volume = Filter Area x Airflow Velocity

Volume = 8 sq ft x 100 ft/min

Volume = 800 cubic feet per minute (CFM)

Therefore, the volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).

Final answer:

The **volume** of air passing through the filter is 800 cubic feet per minute. It is calculated by multiplying the air flow speed (100ft/min) by the area of the filter (8ft²).

The volume of air passing through the **HEPA filter** can be calculated using the formula for the speed of air flow multiplied by area. The **speed** of the air flow is given as 100ft/min and the area of the filter is given as 4ft x 2ft, which equals 8 square feet. Therefore, the volume of the air passing through the filter can be calculated as **8ft2 x 100ft/min = 800 cubic feet per minute**.

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3. How many ways can you line up 7 books on a shelf?

**Answer:**

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

Use the formula for **permutations**:

The **number of objects** is n = 7 books.

**Calculate **the factorial:

In the coordinate plane, a square has vertices (4, 3), (-3, 3), (-3, - 4). What is the location of the fourth vertex?

The two **possible** locations for the fourth vertex are (4, -4) and (-3, -1).

**What is quadratic equation?**

it's a second-degree quadratic equation which is an **algebraic** equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the **variable**, and c is the constant term, is the quadratic equation in its standard form.

To find the location of the fourth vertex of the square, we need to use the fact that a **square** has four equal sides and four right angles.

The first two vertices given are (4, 3) and (-3, 3), which lie on a horizontal line segment of length 7.

The third vertex is (-3, -4), which is 7 units away from the first two vertices and lies on a **vertical** line segment.

Since the square has four equal sides, the distance between the third vertex and the fourth vertex must also be 7 units.

And since the square has four right angles, the fourth vertex must be located on a vertical line passing through the first two vertices or on a horizontal line passing through the third vertex.

So, there are two possible locations for the fourth vertex:

(4, -4): This point is located 7 units below the first vertex (4, 3) on the vertical line passing through it.

(-3, -1): This point is located 7 units to the right of the third vertex (-3, -4) on the **horizontal** line passing through it.

Therefore, the two possible locations for the fourth vertex are (4, -4) and (-3, -1).

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Pls help with this question

The **plane **degrees off **course **is 6.79 degrees off at a speed of 541. 92 km / hr relative to the ground.

To find the **airplane's course** **deviation **and its ground speed, we need to first determine the velocity vectors of the airplane and the wind.

W x = W x cos(225) = 90 x cos(225) = -63.64 km/hr

Wy = W x sin(225) = 90 x sin(225) = -63.64 km/hr

**Magnitude**: |R| = sqrt(Rx^2 + Ry^2) = √(536.36^2 + (-63.64)^2) = 541.92 km/hr

Direction: θ = arctan(Ry / Rx) ≈ arctan (-63.64 / 536.36) = -6.79 degrees

So, the airplane is 6.79 degrees off course, and its **ground speed **is 541.92 km/hr.

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1. You go to the ice cream shop with your friends and you can choose an ice cream, a topping

and sprinkles. How many different sundaes can you make when you order one flavor of ice

cream, one topping and one color of sprinkles from the chart below? Show all possible

outcomes in a tree diagram.

Ice Cream

Chocolate

Vanilla

Strawberry

Topping

Fudge

Marshmallow

Sprinkles

Chocolate

Rainbow

How many sample spaces are there? HINT: How many possible combinations?

b. P (Chocolate, Fudge, Rainbow)

**Answer:**

**Step-by-step explanation:**

**Answer:**

You can make 12 possible sundaes with these toppings.

**Step-by-step explanation:**

Chocolate, Vanilla, and Strawberry all have 4 possible outcomes:

1. Fudge & Chocolate Sprinkles

2. Fudge & Rainbow Sprinkles

3. Marshmallow & Chocolate Sprinkles

4. Marshmallow & Rainbow Sprinkles

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

4 x 3 will equal 12, the total possible sundaes you can make with these toppings and ice cream flavors.

1. All numbered streets runs parallel to each other. Both 3rd and 4th Streets are intersected by King Ave. as shown:

(a) Suppose a car is traveling east on 4th Street and turns onto King Avenue heading northeast. What is the measure of the angle created by the car's turning? Explain your answer.

(b) Suppose a car is traveling southwest on King Avenue and turns left onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.

(c) Suppose a car is traveling northeast on King Avenue and turns right onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.

When the car travels **east **on 4th Street and turns onto King Avenue heading northeast, the** angle **created by the car's turning is a 45-degree angle.

When the car travels **southwest **on King Avenue and turns left onto 3rd Street, the angle created by the car's turning is a 135-degree angle.

When the car travels northeast on King Avenue and turns right onto 3rd Street, the angle created by the car's turning is a 45-degree angle.

How to get the Angle?(a) When the car travels east on 4th Street and turns onto King Avenue heading northeast, the angle created by the car's turning is a 45-degree angle. This is because the **intersection **of 4th Street and King Avenue creates a right angle, and the car turns northeast, creating another 45-degree angle with the horizontal 4th Street.

(b) When the car travels southwest on King Avenue and turns left onto 3rd Street, the angle created by the car's turning is a 135-degree angle. This is because the intersection of King Avenue and 3rd Street creates a **right** **angle**, and the car turns left, creating an additional 90-degree angle. Therefore, the total angle is 90 degrees + 45 degrees = 135 degrees.

(c) When the car travels northeast on King Avenue and turns right onto 3rd Street, the angle created by the car's turning is a 45-degree angle. This is because the intersection of King Avenue and 3rd Street creates a right angle, and the car turns right, creating another 45-degree angle with the horizontal 3rd Street.

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Hello, I am confused on how to answer this question.

**Answer: x=14**

**Step-by-step explanation:**

cb=10.

ac=14

The value of X will be **14.**

This is a simple mathematics problem that can be solved by using** ratios.**

**Given, AC : BC : AB = 7 : 5 : 8**

AC = X ; BC = 10 ; AB = X + 2

AC/ BC = X/ 10 = 7/5 (Ratios can also be represented as fractions)

X/10 = 7/5

On Transposing,

5X = 70

X = 70/5

**X = 14**

**Alternatively,**

BC/AB = 5/8 = 10/ (X + 2)

5/8 = 10/ (X + 2)

On Transposing,

80 = 5X + 10

5X = 70

**X = 14**

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Determine which relation is a function.

A: {(–3, 2), (–1, 3), (–1, 2), (0, 4), (1, 1)}

B: {(–3, 2), (–2, 3), (–1, 1), (0, 4), (0, 1)}

C: {(–3, 3), (–2, 3), (–1, 1), (0, 4), (0, 1)}

D: {(–3, 2), (–2, 3), (–1, 2), (0, 4), (1, 1)}

The **relation **that is a **function **is D: {(–3, 2), (–2, 3), (–1, 2), (0, 4), (1, 1)}.

A **function **is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. In other words, for a relation to be a **function**, each input can only be related to one output.

In relation D, each input (x-value) has a unique **output **(y-value), meaning that each x-value is only paired with one y-value. In contrast, relations A, B, and C have repeated x-values with different y-values, which means that they are not functions.

In relation A, the input -1 is paired with two different **outputs **(2 and 3). In relation B, both inputs 0 and -1 are each paired with two different outputs. In relation C, both inputs 0 and -3 are each paired with two different outputs. Therefore, only relation D satisfies the definition of a function.

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3√b in exponential form

3sqrt(b) is 3b^1/2 in exponential form.

When you want to change a square root to exponential form, simply change it to the power of 1/2. And if you want to get rid of a square root, square the whole thing.

When you want to change a square root to exponential form, simply change it to the power of 1/2. And if you want to get rid of a square root, square the whole thing.

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