Mathematics College

## Answers

**Answer 1**

Understanding and applying **mathematics** to daily **life** is essential for success in various fields and personal growth.

Mathematics is a fundamental tool in our **daily lives**, from simple tasks such as counting money, cooking, or measuring ingredients to more complex tasks such as budgeting, managing finances, and making informed decisions.

**Math** is an essential part of fields such as science, technology, engineering, and economics. It helps us understand and solve problems, analyze data, and make predictions.

By learning and applying **math**, we can make better decisions and achieve our goals more efficiently.

Therefore, understanding and applying **mathematics** to daily life is essential for success in various fields and personal growth.

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## Related Questions

c) The group is planning to build a fence around the garden. How many yards of

fencing materials do they need for the fence? Show your work. (3 points-2 points for

finding the value of side b and 1 point for finding the perimeter of the garden)

I

### Answers

Based on the information, it should be noted that the **perimeter** that they need is 130 yds to build up the fence.

How to explain the value

Attached you can find a **picture** that will guide the explanation. We will assume that each line is supposed to be a fence. We will assume also that the diagonals that cross any subfield that has the same vegetable is unnecessary.

On the same fashion, the diagonal of the spinach-celery sector is 10. Recall that the field is a rectangle, so the perimeter of the outter fence is 2*(12+6)+2*(8+9) = 70 yds. Then, the total **perimeter** is given by

outter fence (70)+

fence spinach-watermelon (8) +

fence red peppers-watermelon(12)+

fence red peppers-carrots (15)+

fence carrots-tomatoes (9)+

fence celery-tomatoes(6) +

fence **spinach-celery(10)**

= 130 yds

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A student claims that a given point is located in Quadrant III. The x-coordinate is −5

, and the cos(θ)

of the angle is −513

. Use a unit circle to complete the table with numbers that support the student's claim. Enter your answer in the table.

### Answers

**Answer:**

sin(θ) = -12/13

**Step-by-step explanation:**

You want the **sine** of the **third-quadrant angle** whose **cosine** is **-5/13**.

3rd Quadrant

In* *the third quadrant, both the sine and the cosine are negative. The sine of the angle can be found from your knowledge of the {5, 12, 13} Pythagorean triple, or using the Pythagorean trig identity:

sin(θ) = -√(1 -cos(θ)²)

sin(θ) = -√(1 -(-5/13)²) = -√(144/169)

** sin(θ) = -12/13**

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PLEASE HELP !!!!!!!

The lengths of two sides of a triangle are shown.

Side 1: 8x2 − 5x − 2

Side 2: 7x − x2 + 3

The perimeter of the triangle is 4x3 − 3x2 + 2x − 6.

Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work. (4 points)

Part B: What is the length of the third side of the triangle? Show your work. (4 points)

Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)

### Answers

**Answer:**

Part A: -x^2 + 15x + 1

Part B: 4x^3 - 2x^2 - 13x - 7

Part C: No

**Step-by-step explanation:**

Part A:

To find the total length of the two sides, we simply add them together:

(8x^2 - 5x - 2) + (7x - x^2 + 3)

= -x^2 + 15x + 1

Therefore, the total length of the two sides is -x^2 + 15x + 1.

Part B:

To find the length of the third side, we need to use the fact that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So we set up an inequality:

(8x^2 - 5x - 2) + (7x - x^2 + 3) > (length of third side)

Simplifying, we get:

6x^2 + 2x + 1 > (length of third side)

Now we use the fact that the perimeter of the triangle is equal to the sum of the lengths of all three sides:

(length of side 1) + (length of side 2) + (length of third side) = 4x^3 - 3x^2 + 2x - 6

Substituting in the expressions for side 1 and side 2, we get:

(8x^2 - 5x - 2) + (7x - x^2 + 3) + (length of third side) = 4x^3 - 3x^2 + 2x - 6

Simplifying, we get:

-x^2 + 15x + 1 + (length of third side) = 4x^3 - 3x^2 + 2x - 6

Now we can solve for the length of the third side:

length of third side = 4x^3 - 2x^2 - 13x - 7

Therefore, the length of the third side is 4x^3 - 2x^2 - 13x - 7.

Part C:

To see if the polynomials are closed under addition and subtraction, we need to check whether the sum or difference of any two polynomials in the form given will also be of that form.

For Part A, we found that the total length of the two sides was -x^2 + 15x + 1. To check if this polynomial is of the same form, we compare it to the general form of a polynomial in this problem:

ax^2 + bx + c

We can see that the polynomial -x^2 + 15x + 1 is indeed of this form, with a = -1, b = 15, and c = 1. Therefore, the polynomials are closed under addition.

For Part B, we found that the length of the third side was 4x^3 - 2x^2 - 13x - 7. To check if this polynomial is of the same form, we again compare it to the general form of a polynomial in this problem:

ax^2 + bx + c

We can see that the polynomial 4x^3 - 2x^2 - 13x - 7 is not of this form, since it has a degree of 3 rather than 2. Therefore, the polynomials are not closed under subtraction.

Overall, we can say that the polynomials are closed under addition, but not under subtraction.

Question 3 (1 point)

A store is having a sale where everything is 25% off. A shirt has an original price of

$20. When paying for the shirt you are offered an additional discount of 10% after

the first discount is taken. What is the final sale price of the shirt?

Round your answer to two decimal places and do not include the $ sign.

### Answers

Given statement solution:- The **final sale price** of the shirt is $13.50.

To calculate the final sale price of the shirt, we need to apply the discounts** sequentially.**

First, let's calculate the price after the** initial **25% discount. The discount is calculated by multiplying the original price by (1 - discount percentage):

25% discount = 0.25

Price after the initial discount = $20 * (1 - 0.25) = $20 * 0.75 = $15.

Next, we need to calculate the additional discount of 10% after the first discount is taken. Again, we'll use the same formula:

10% discount = 0.10

Price after the additional discount = $15 * (1 - 0.10) = $15 * 0.90 = $13.50.

Therefore, the **final sale price** of the shirt is $13.50.

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Find the product.

3/8 times4/5

### Answers

**Answer:**

3/10

**Step-by-step explanation:**

In XYZ, the measure of Z=90°, XZ = 20, YX = 29, and ZY = 21. What is the value of the cosine of X to the nearest hundredth?

### Answers

The value of the **cosine X **is 0.724

How to determine the value

We need to know the different **trigonometric identities**.

These identities are written as;

sinecosinetangentcotangentsecantcosecant

From the information given, we have that;

Z=90°, XZ = 20, YX = 29, and ZY = 21.

The ratio for the** cosine identity** is;

cos θ = adjacent/hypotenuse

Adjacent side = XZ = 20

Hypotenuse side; YX = 29

then, we have;

cos X = 21/29

cos X = 0.724

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A raised garden is shown below. Use a formula to find the area of the garden.

24 ft

18 ft

O 432 P

46812

O 504ff

O 576

A

4 ft

32 ft-

### Answers

By using definition of area of Trapezoid, The **area **of **garden **is,

⇒ Area = 504 feet²

We have to given that;

A **raised **garden is shown below.

Since, The **multiply **means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Since, Garden is in shape of **trapezoid**.

And, Bases of garden are,

⇒ a = 26 feet

⇒ b = 32 feet

Height of garden is,

⇒ h = 18 feet

Since, We know that;

**Area **of trapezoid is,

A = (a + b) h/2

Where, a and b are base and h is **height**

Hence, We can formulate;

The **area **of garden is,

Area = (24 + 32) × 18 / 2

Area = 504 feet²

Therefore, The **area **of **garden **would be,

⇒ Area = 504 feet²

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4. If A = 2x - 7x² +3 and B = 4x² - 12x, what is A + B?

### Answers

**Answer: -7x² - 10x + 3**

**Step-by-step explanation: To find A + B, we need to add the like terms. Combining the terms of A and B, we get: -7x² - 10x + 3. Therefore, the sum of A and B is -7x² - 10x + 3.**

Simplify √24 (square root of 24)

33 points

6√2

2√12

2√6

3√2

### Answers

**Answer:**

2√6

**Step-by-step explanation:**

√24=√2*2*2*3 the square root is to all numbers

√24=2√6

100 POINTS+ BRAINLIEST+ 5 STAR RATING! HELP ME WITH THESE MATH EQUATIONS PLEASE! I DONT WANT TO FAIL!

A deli wraps its cylindrical containers of hot food items with plastic wrap. The containers have a diameter of 4.5 inches and a height of 3 inches. What is the minimum amount of plastic wrap needed to completely wrap 6 containers? Round your answer to the nearest tenth and approximate using π = 3.14.

A fair 6-sided die is rolled 480 times. What is a reasonable prediction for the number of times the event of landing on an odd number will occur?

A streetlamp illuminates a circular area that is 19 meters across through the center. How many square meters of the street is covered by the light? Round to the nearest hundredth and approximate using π = 3.14.

A label is placed on a soup can during manufacturing. If the label is represented by the rectangle in the figure, how many square inches is the label? Answer in terms of π. Image of a net drawing of a cylinder is shown as two circles each with a radius labeled 3 inches and a rectangle with a height labeled 8.4 inches

### Answers

The minimum amount of **plastic wrap **needed is 445.08 square inches

How much plastic wrap is needed?

To get **minimum **amount of plastic wrap needed to completely wrap 6 containers, we have to get total **surface area **of all 6 containers.

The **surface area **of one container is found using [tex]SA = 2\pi r^2 + 2\pi rh[/tex]

The **diameter **of each container is 4.5 inches

The **radius **is half of diameter = 2.25 inches.

The **height **of each container is 3 inches.

Substituting these **values**.

SA = 2 x 3.14 x 2.25^2 + 2 x 3.14 x 2.25 x 3

SA = 74.1825

SA = 74.18 square inches

The total **surface area **of 6 containers is:

= 6 x 74.18

= 445.08 square inches.

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STION 1: GEOMETRIC THEOREMS Theorem 1

1.1.1 A line drawn from the centre of a circle perpendicular to a chord ..... the chord. (1)

1.1.2 In the diagram drawn below, O is the centre of the circle XCY. COT 1 XY. OC = r and XY = 3/2 r

Prove, stating reasons, that CT: = 4+√7₂ 4 -Y. (6)

### Answers

The length of the **hypotenuse **AC is 5 units.

The correct answer is: A) 5 units.

In the given** right triangle** ABC, we are given the lengths of the two legs, AB and BC, as 3 units and 4 units, respectively.

We need to determine the length of the hypotenuse, AC.

According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Mathematically, it can be expressed as :

[tex]AC^2 = AB^2 + BC^2[/tex]

Substituting the given lengths, we have:

[tex]AC^2 = (3 units)^2 + (4 units)^2[/tex]

[tex]AC^2 = 9 units^2 + 16 units^2[/tex]

[tex]AC^2 = 25 units^2[/tex]

To find the length of AC, we take the **square root** of both sides:

AC = √(25 [tex]units^2[/tex])

AC = 5 units.

Therefore, the length of the hypotenuse AC is 5 units.

The correct answer is:

A) 5 units.

The Pythagorean theorem is a fundamental concept in geometry that relates the sides of a right triangle.

It is commonly used to find missing side **lengths **or to determine if a triangle is a right triangle.

In this case, by applying the theorem, we were able to calculate the length of the hypotenuse AC based on the given side lengths.

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The complete question may be like:

In a right triangle ABC, angle B is a right angle. The lengths of the two legs are given by AB = 3 units and BC = 4 units. The length of the hypotenuse AC can be determined using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. What is the length of the hypotenuse AC?

A) 5 units

B) 7 units

C) 9 units

D) 12 units

The histogram below shows information about the masses of gold in the rings in a

jewellery shop.

a) Work out an estimate for the number of rings that contain between 1.4 g and

3 g of gold.

b) Write a sentence to explain why the value you calculated in part a) is only an

estimate.

Back to task

Frequency density

100

44

50

25

Mass (g)

Watch video

Answer

### Answers

a) We estimate that there are approximately 4700 rings **weighing **between 1.4 g and 3 g of gold. b) Because we are using the histogram to approximate the number of rings in each mass range, the value we calculated in part a) is only an estimate.

How to answer the aforementoned questions

a) To estimate the number of rings that contain between 1.4 g and 3 g of gold, we need to find the area of the** bars **in the histogram that correspond to this range. We can do this by multiplying the height of each bar by its width and adding up the results.

From the histogram, we can see that the height of the bar for the range 1.4 g to 2 g is 44 and its width is 50, while the height of the bar for the range 2 g to 3 g is 25 and its width is 100. So, the estimate for the number of rings that contain between 1.4 g and 3 g of gold is:

44 × 50 + 25 × 100 = 2200 + 2500 = 4700

Therefore, we estimate that there are around **4700 rings **that contain between 1.4 g and 3 g of gold.

b) Because we are using the histogram to approximate the number of rings in each mass range, the value we calculated in part a) is only an estimate.

The **frequency density** is represented by the histogram, which is the frequency divided by the width of each bar. To calculate the true frequency, multiply the frequency density by the width of the bar. This, however, assumes that the mass of gold in each ring is distributed evenly across the range of the bar, which may not be the case.

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45 points!!!

solve questions 14 and 15

### Answers

The **measure** of DF is 82 and measure of ∠PQR is 59°.

We know that,

For the first figure,

The secant- **secant** angle CEG is half the difference of the measures of the **intercepted** arcs, that is

∠ CEG = (1/2) (CG - DF)

44° = (1/2)( 170 - DF)

**Multiply** both sides by 2 to clear the fraction

88° = 170 - DF

**subtract** 170 from both sides

- 82 = - DF

multiply both sides by - 1

DF = 82°

For the second figure,

The **tangen**t- tangent angle PQR is half the difference of the measures of the intercepted arcs.

the intercepted arcs are PSR and RP

the **sum **of the arcs in a circle = 360° , so

Hence,

PSR = 360° - RP = 360° - 121° = 239°

Therefore,

∠ PQR = (1/2)( 239 - 121)° = (1/2) × 118° = 59°

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46°

A

Determine the measure of the missing angle.

A/

O

B

E

### Answers

**Answer:**

*44 degrees*.

**Step-by-step explanation:**

Interior angles in a triangle add up to 180 degrees. The little square in the top right hand corner of the right-angled triangle indicates a right angle. Right angles are always equal to 90 degrees. Do 180-90-46=44, because there are three angles in the triangle that have a cumulative value of 180 degrees, and we know the value of two of them (90 and 46), so 44 degrees must be the value of the remaining angle.

NO LINKS!!! URGENT HELP PLEASE!!!!!

Write a rule for the nth term of the arithmetic sequence that has the two given terms.

7. a_2 = 17, a_11 = 35

8. a_9 = 89, a_15 = 137

### Answers

**Answer:**

[tex]\textsf{7.} \quad a_n=2n+13[/tex]

[tex]\textsf{8.} \quad a_n=8n+17[/tex]

**Step-by-step explanation:**

To write a rule for the **nth term** of a **arithmetic sequence**, we can use the following **formula**:

[tex]\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

[tex]\hrulefill[/tex]

Question 7

Given terms:

a₂ = 17a₁₁ = 35

**Substitute **the given **values **into the **formula **to create **two equations**:

[tex]\begin{aligned}a_2=a+(2-1)d&=17\\a+d&=17\end{aligned}[/tex]

[tex]\begin{aligned}a_{11}=a+(11-1)d&=35\\a+10d&=35\end{aligned}[/tex]

**Rearrange **the first equation to** isolate d**:

[tex]d=17-a[/tex]

**Substitute **this into the second equation and **solve for a**:

[tex]\begin{aligned}a+10(17-a)&=35\\a+170-10a&=35\\170-9a&=35\\-9a&=-135\\a&=15\end{aligned}[/tex]

**Substitute **the found **value of a** into the **equation for d** and **solve for d**:

[tex]d=17-15=2[/tex]

Therefore, the **rule **for the **nth term** of the given **arithmetic sequence** is:

[tex]\begin{aligned}a_n&=15+(n-1)2\\ &=15+2n-2\\&=2n+13\end{aligned}[/tex]

[tex]\hrulefill[/tex]

Question 8

Given terms:

a₉ = 89a₁₅ = 137

**Substitute **the given **values **into the **formula **to create **two equations**:

[tex]\begin{aligned}a_9=a+(9-1)d&=89\\a+8d&=89\end{aligned}[/tex]

[tex]\begin{aligned}a_{15}=a+(15-1)d&=137\\a+14d&=137\end{aligned}[/tex]

**Rearrange **the first equation to** isolate a**:

[tex]a=89-8d[/tex]

**Substitute **this into the second equation and **solve for d**:

[tex]\begin{aligned}a+14d&=137\\(89-8d)+14d&=137\\89+6d&=137\\6d&=48\\d&=8\end{aligned}[/tex]

**Substitute **the found **value of d** into the **equation for a** and **solve for a**:

[tex]\begin{aligned}a&=89-8(8)\\&=89-64\\&=25\end{aligned}[/tex]

Therefore, the **rule **for the **nth term** of the given **arithmetic sequence** is:

[tex]\begin{aligned}a_n&=25+(n-1)8\\ &=25+8n-8\\&=8n+17\end{aligned}[/tex]

In the figure below, mZ2-66". Find m21, mZ3, and mZ4

*

m23-

#24-

%

### Answers

The value of the **angles** in the** figure** are:

m∠1 = 114°

m∠3 = 114°

m∠4 = 66°

How to find m∠1, m∠3 and m∠4 in the figure?

To answer the question, we need some angle** geometry** knowledge:

We have:

**m∠2** = 66°

Thus, we can find the angles in the** figure** as follow:

m∠1 = 180° - 66° (sum of** angles** on a straight line is 180°)

m∠1 = 114°

m∠3 = m∠1 (vertically opposite angles are equal)

m∠3 = 114°

m∠4 = m∠2 (vertically opposite angles are equal)

m∠4 = 66°

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find “h” if r=5 and V=100π

### Answers

**Answer:**

**Step-by-step explanation:**

**V = π.**[tex]r^{2}[/tex]**.h**

**100π = π.**[tex](5)^{2}[/tex]**.h**

**h = 4**

**Answer:**

4

**Step-by-step explanation:**

The equation for the volume of a cylinder is [tex]V=\pi r^{2} h[/tex]. So if V is 100[tex]\pi[/tex], it means that [tex]\pi hr^{2}[/tex] is [tex]100\pi[/tex]. So the you plug in the information you know [tex]25h\pi =100\pi[/tex]. The pi cancels out and you end up with [tex]25h=100[/tex] meaning that h=4

In the beginning of BS 2077, Dolma deposited Rs 1,20,000 in her account at the rate of 9% p.a. If she paid 5% of her interest as income tax, how much total amount did she receive in the beginning of BS 2080

### Answers

Dolma received a total **amount **of Rs 1,29,260 at the **beginning **of BS 2080.

Given:

**Principal **amount (P) = Rs 1,20,000

**Interest **rate (R) = 9% per annum

Income **tax **rate (T) = 5% of the interest earned

First, we calculate the **interest **earned

Interest (I) = P x R/100

= 1,20,000 * 9/100

= 10,800

Next, we calculate the **income tax**

Income Tax = I x T/100

= 10,800 x 5/100

= 540

Now, **Total **amount = P + I - Income Tax

= 1,20,000 + 10,800 - 540

= Rs 1,29,260

Therefore, Dolma received a total **amount **of Rs 1,29,260 at the **beginning **of BS 2080.

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Isaiah scores with 50% of his penalty kicks in soccer. He flips two fair coins to conduct a simulation with 20 trials to determine the likelihood that he will make his next two penalty kicks, as shown. Heads up (H) represents a goal. What is the probability that Isaiah will make both penalty kicks? Give the probability as a percent. Enter your answer in the box. TH HH TT HT TH HH HH TT HT TH TT HH HT HH HH TT HT HH TH TT P(two goals) = %

### Answers

The **probability **that Isaiah will make both **penalty kicks,** as simulated by flipping two fair coins 20 times, is 25%.

Since Isaiah scores with a 50% success rate on penalty kicks, the probability of him** scoring **a goal on any given penalty kick is 0.5 or 50%.

If he flips **two fair coins** to simulate 20 trials, there are four possible outcomes: HH (two goals), HT (one goal and one miss), TH (one goal and one miss), and TT (two misses).

Out of the 20 trials, there are two possible ways for Isaiah to score both of his penalty kicks: HH and HH. The probability of getting** HH** on two coin flips is (0.5) x (0.5) = 0.25 or 25%.

Therefore, the probability that Isaiah will make both penalty kicks, as simulated by** flipping **two fair coins 20 times, is 25%.

Expressed as a percentage, this is:

P(two goals) = 25%

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Here is a cuboid.

The two largest faces are blue.

The other four faces are green.

9 cm

Is the total blue area greater than the total green area?

You must show your working.

3 cm

5 cm

### Answers

Given the difference that exists between the the total** blue area** and the total** green area,** we can see that the blue area is larger

How to solve for the larger area

We have to solve for the **blue area**

2 {area of the largest face}

The largest face is 9 x 5

2[9 * 5]

= 90 cm²

Then total** green area **calculation

= 2{5 * 3} + 2{9 * 3}

= 84 cm²

Hence given the difference that exists between the the total blue area and the **total green area**, we can see that the blue area is larger

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Find f(0) for the piece-wise function. f(x) = {-x-2 if x < -2, x+4 if x > -2

### Answers

**Answer: **f(0) = 4

**Step-by-step explanation:**

First, we see that 0 is greater than -2, so we will **substitute **0 for x into the x + 4 part of the **piece-wise function**. Then we will **simplify**.

f(x > -2) = x + 4

f(0) = 0 + 4

f(0) = 4

I really need the answer!! PLS HELP!!!!

Which set of ordered pairs represents a linear relation. Explain your answer. {(0, 3600), (4, 3526), (8, 3353.5), (12, 3147.5)) or ((15, 2988.5), (21, 2670.5), (27, 2352.5), (33, 2034.5)}

### Answers

**Answer:**

{(15, 2988.5), (21, 2670.5), (27, 2352.5), (33, 2034.5)}

**Step-by-step explanation:**

Let's analyze both sets of ordered pairs:

Set 1: {(0, 3600), (4, 3526), (8, 3353.5), (12, 3147.5)}

The x-values in this set increase by a constant amount of 4: 0, 4, 8, 12.

Now let's examine the corresponding y-values:

3600, 3526, 3353.5, 3147.5

To determine the rate of change between the y-values, we subtract consecutive pairs:

3526 - 3600 = -74

3353.5 - 3526 = -172.5

3147.5 - 3353.5 = -206

The y-values in this set decrease, but the rate of change is not constant. The differences between consecutive y-values are not the same, indicating that the relation is not linear.

Set 2: {(15, 2988.5), (21, 2670.5), (27, 2352.5), (33, 2034.5)}

The x-values in this set also increase by a constant amount of 6: 15, 21, 27, 33.

Now let's examine the corresponding y-values:

2988.5, 2670.5, 2352.5, 2034.5

Again, we calculate the differences between consecutive y-values:

2670.5 - 2988.5 = -318

2352.5 - 2670.5 = -318

2034.5 - 2352.5 = -318

In this set, the y-values decrease by a constant rate of 318. The rate of change between consecutive y-values is the same, indicating that the relation is linear.

Therefore, the set of ordered pairs {(15, 2988.5), (21, 2670.5), (27, 2352.5), (33, 2034.5)} represents a linear relation.

in a study researching how to donating to charity can affect a person's happiness, 96 participants were given $5 a d for one week. Each participant was randomly assigned to one of two groups. Those assigned to the first group were asked to spend the money on themselves, and those assigned to the second group were asked to donate the money to charity. at the end of the week, all of the participant were asked to rate their overall level of happiness on a scale from 0 to 100, higher score indicating greater levels of happiness. Which of the following are the appropriate null and alternative hypotheses to test weather the sample data provide convincing statistical evidence that donating to charity results in greater happiness than spending on oneself, on average?

### Answers

If there is no significant difference found, then the null hypothesis can be accepted, indicating that donating to **charity** does not necessarily lead to greater happiness levels compared to spending on oneself.

The appropriate null **hypothesis** for this study is that there is no significant difference in happiness levels between those who donate to charity and those who spend money on themselves.

The alternative hypothesis, on the other hand, is that donating to charity results in greater happiness levels than spending on oneself, on average. In order to test these hypotheses, **statistical** methods such as a t-test or ANOVA can be used to analyze the data collected from the participants.

If the results of the statistical analysis indicate a significant difference in happiness levels between the two groups, then the alternative hypothesis can be accepted, providing convincing evidence that donating to charity can lead to greater **happiness** levels.

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Find (g o g)(x) if g(x) = –x^ 2 + 5.

### Answers

Solution:

(g o g)(x) = -((-x^2 + 5)^2) + 5

Answer:

(g o g)(x) = -x^4 + 10x^2 - 20

Can someone help meee please

### Answers

a. The **function** (f o g)(x) = 3/(3 + x)

b. In** interval notation**, the** domain** of the** function** (f o g)(x) is (-3, ∞).

What is a function?

A** function** is a mathematical equation that shows the relationship between two variables.

a. Given the** functions **f(x) = x/x + 2 and g(x) = 6/x, we desire to find (f o g)(x). We proceed as follows

We know that (f o g)(x) is a **composite function** and (f o g)(x) = f(g(x))

Since f(x) = x/x + 2 and g(x) = 6/x,

So f(g(x)) = x/(x + 2)

= g(x)/[g(x) + 2]

= 6/x ÷ (6/x + 2)

= 6/x ÷ (6 + 2x)/x

= 6/x × x/(6 + 2x)

= 6/(6 + 2x)

= 6/2(3 + x)

= 3/(3 + x)

So, f(g(x)) = 3/(3 + x)

b. To find the** domain** of (f o g)(x) in** interval notation, **we proceed as follows

Since (f o g)(x) = f(g(x)) = 3/(3 + x)

Now, f(g(x)) is valid when (3 + x) > 0

So, 3 + x > 0

x > - 3

So, in interval notation, the domain of (f o g)(x) is (-3, ∞). We use the open bracket on the left side of the - 3 since -3 is not included.

So, in interval notation, the domain of (f o g)(x) is (-3, ∞).

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To find the height of an object that is dropped off a 320 foot cliff t seconds after it is

dropped, you can use the polynomial -16t² + 320. Find the height of the object at

t = 3 seconds after it is dropped.

Height feet

### Answers

The **height** of an object dropped off a 350 foot cliff after 1.5 seconds is 314 feet

We have,

An **equation **is an expression that shows the relationship between two or more numbers and variables.

Let h(t) represent th**e height **of an object after t seconds, hence:

h(t) = -16t² + 350

Hence:

At time t = 1.5:

h(1.5) = -16(1.5)² + 350 = 314 feet

The** height **of an object dropped off a 350 foot cliff after 1.5 seconds is 314 feet

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Nicole is 1.55 meters tall. At 2 p.m., she measures the length of a tree's shadow to be 30.05 meters. She stands 25.6 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

### Answers

approximately 1.81 meters.

Step-by-step explanation:

Let's call the height of the tree "h". We can set up a proportion based on the similar triangles formed by Nicole, her shadow, the tree, and the tree's shadow:

(height of Nicole) / (length of Nicole's shadow) = (height of tree) / (length of tree's shadow)

Substituting the given values, we get:

1.55 / 25.6 = h / 30.05

Simplifying and solving for h, we get:

h = (1.55 / 25.6) * 30.05

= 1.81181640625

Rounding to the nearest hundredth, we get:

h ≈ 1.81 meters

the height of the tree is approximately 1.81 meters.

what would you do if yes said would go

An invoice is dated 18 January and offers terms of 6/10, 4/20, 1/30, n/50. Find

the three final discount dates.

the net payment date.

### Answers

The three final discount dates are 28 January, 7 February, and 17 February, and the net payment date is 9 March, based on the given **invoice** terms.

To determine the three final discount dates and the net payment date based on the invoice** terms** provided (6/10, 4/20, 1/30, n/50), we need to understand the meaning of the terms.

The format for these terms is a discount percentage followed by the number of days within which the discount can be availed. The final discount date is calculated by adding the specified number of days to the invoice date, while the net payment date is determined by adding the maximum number of days for payment.

Given that the invoice is dated 18 January, we can calculate the final discount dates and net **payment **date as follows:

6/10: This term offers a 6% discount if paid within 10 days. The final discount date is calculated by adding 10 days to the invoice date (18 January + 10 days), resulting in 28 January.

4/20: This term **offers** a 4% discount if paid within 20 days. The final discount date is calculated by adding 20 days to the invoice date (18 January + 20 days), resulting in 7 February.

1/30: This term offers a 1% discount if paid within 30 days. The final discount date is calculated by adding 30 days to the invoice date (18 January + 30 days), resulting in 17 February.

n/50: This term does not specify a discount percentage but offers a payment period of 50 days. The net payment date is calculated by adding 50 days to the invoice date (18 January + 50 days), resulting in 9 March.

The three final discount dates are 28 January, 7 February, and 17 February, and the net payment date is 9 March, based on the given invoice terms.

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For a segment of a radio show, a disc jockey can play 6 records. If there are 10 records to select from, in how many ways can the program for this segment be arranged?

### Answers

There would be 210 **Different combinations** of 6 records that could be played out of the 10 available records.

The number of ways the **program **for this radio show segment can be arranged, we need to use the formula for permutations, which is:nPr = n! / (n - r)!

where n is the total number of items to choose from and r is the **number **of items to be selected.

In this case, the disc jockey can play 6 records out of a total of 10. So, we can plug in n = 10 and r = 6 into the formula and calculate the number of permutations:

10P6 = 10! / (10 - 6)!

= 10! / 4!

= (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (4 x 3 x 2 x 1)

= (10 x 9 x 8 x 7 x 6 x 5)

= 151,200

Therefore, there are 151,200 ways that the program for this radio show segment can be **arranged **from the 10 available records.

It's important to note that the order in which the records are played matters, so this is a case of permutations rather than combinations. If the order didn't matter and we were simply selecting 6 records out of 10, we would use the formula for combinations instead:

nCr = n! / (r! * (n - r)!)

In this case, we would have:

10C6 = 10! / (6! * (10 - 6)!)

= 10! / (6! * 4!)

= (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1)

= 210

Therefore, there would be 210 different combinations of 6 records that could be played out of the 10 available records.

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4. Find the area Molly needs to paint. Show your work, and be sure to include units

with your answer. (3 points)

### Answers

The** total area** that Molly needs to paint is: 300 sq. inches

How to find the total surface area?

To find the **total surface area **of the given figure, we will add all surface areas together.

**Prism**: 6 surfaces

**Surface area**:

Front = 6 x 6 = 36

Back = 6 x 6 = 36

Top = 6 x 6 = 36

Bottom (base) = 6 x 6 = 36

Side = 6 x 6 = 36

Other side = 6 x 6 = 36

Total = 216 square inches

**Pyramid**: 5 surfaces

**Surface area**:

Bottom (base) = 6 x 6 = 36

Front triangle = (6 x 4)/2 = 12

Back = (6 x 4)/2 = 12

Side = (6 x 4)/2 = 12

Other side = (6 x 4)/2 = 12

Surface area = 84 square inches

Thus:

**TOTAL surface area** = 216 sq. inches + 84 sq. inches

= 300 sq. inches

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