Mathematics College

## Answers

**Answer 1**

**Answer:**

{ } or empty set.

**Step-by-step explanation:**

The solutions should be where the two lines intersect, but in this case, the parallel lines never intersect. That means that they have no solutions.

Hope this helps!

**Answer 2**

**Answer:**

{ } or empty set

**Step-by-step explanation:**

It's because these lines are parallel so they don't intersect to give you a coordinate.

## Related Questions

Simplify the expression.

16 • 4^-4

A. 256

B. -256

C. 1/16

D. -4,096

### Answers

**Answer:**

C. 1/16

**Step-by-step explanation:**

[tex]16 * 4^{-4}[/tex]

16 can be written as a power of 4.

[tex]4^2 * 4^{-4}[/tex]

The bases are same, add exponents.

[tex]4^{2+-4}[/tex]

[tex]4^{-2}[/tex]

Simplify negative exponent.

[tex]\frac{1}{4^2 }[/tex]

[tex]\frac{1}{16}[/tex]

Help ASAP

Picking the first second and third place winners at a track meet is an independent event￼.

False

Or

True

### Answers

**false, an independent event is an event that isn't affected**

The statement given is **false**

**What is a dependent event?**

Two events are **dependent, **when the outcome of the first event **influences **the outcome of the second event.

Given that, Picking the first second and third place winners at a track meet is an **independent **even,

This statement is not correct.

The event is a **dependant **variable, the 1st person is picked based on the 1st mark on the track, so is the second and the 3rd. their position **influence **the outcome of the other.

the position of the 1st, 2nd or 3rd is **influenced **by time and speed, so the positions will be picked based on the participant scores /effect of time or speed of the 1st person to reach the track meet.

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3/4 (1/2x - 12) + 4/5 HELP

### Answers

**Answer:**

3/8x - 9 4/5

**Step-by-step explanation:**

Well we need to simplify the following expression,

[tex]\frac{3}{4} (\frac{1}{2}x - 12) + \frac{4}{5}[/tex]

So we need to distribute 3/4 to (1/2x - 12)

3/8x - 9 + 4/5

**3/8x - 9 4/5**

*Thus,*

*the answer is 3/8x - 9 4/5.*

*Hope this helps :)*

Which of the following shows the graph of y = –(2)x – 1? On a coordinate plane, a curve is level at y = 0 in quadrant 2 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 0.5). On a coordinate plane, a curve is level at y = negative 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 2). On a coordinate plane, a curve is level at y = 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, 0).

### Answers

**Answer:**

On a coordinate plane, a curve is level at y = -1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, -2).

**Step-by-step explanation:**

y = -2 ^x -1

On a **coordinate plane**, a **curve **is level at y = – 1 in** quadrant 3** and then decreases rapidly into **quadrant 4**. It crosses the **y-axis** at (0, -2). Option **C** is correct.

What is Cartesian coordinate plane?

The **Cartesian coordinate** plane is a two-dimensional **plane **with infinite dimensions. On an endless 2d **plane**, any two-**dimensional **figure can be drawn. A **location **is assigned to each **point **on a **Cartesian plane.**

On a coordinate **plane**, a **curve **is level at y = – 1 in **quadrant 3** and then decreases rapidly into **quadrant 4**. It crosses the **y-axis** at (0, -2).

Hence, option **C **is correct.

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What is the GIM of a strip mall with annual income of $547,500 and a value of $6,345,000?

### Answers

**Answer:**

11.6

**Step-by-step explanation:**

GIM means Gross Income Multiplier and it is a method used for valuating a property or an investment. **It is expressed mathematically as the ratio of the property's value/sales price and its gross annual income.**

GIM = Value of an investment/Gross annual income.

Given the annual income = $547,500 and Value = $6,345,000;

GIM = $6,345,000/$547,500

GIM = 11.589

**GIM ≈ 11.6**

**Hence, the Gross Income Multiplier of the strip mall is approximately 11.6.**

GIM has no units.

Use completing the square to solve the equation x^2+16x=-44.

### Answers

Rewrite the equation

x^2+16x=-44

Complete the square on the left hand side and add the answer to the right side to balance it

(16/2)^2=(8)^2=64

x^2+16x+64=-44+64

Simplify the equation

(x+8)^2=20

Find the roots of both sides

x+8=4.5 to nearest tenth

x=4.5-8

x=-3.5

Hope it helps

we need to **add **64 on both sides and required equation is x=-8±2√5-8

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

The given equation is x²+16x=-44

Now we need to make the **coefficient **of x variable half and to square it.

(16/2)²=8²=64

Now **add** 64 on both the sides

x²+16x+64=-44+64

x²+16x+64=20

(x+8)²=20

x+8=±√20

x+8=±2√5

Now **subtract **8 on both sides

x=-8±2√5-8

Hence, we need to add 64 on both sides and required **equation **is x=-8±2√5-8

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An ice sculpture is melting at a constant rate. It's weight changes -1 4/5 pounds every hour. What is the total change in weight of the sculpture after 3 1/2 hours?

### Answers

**Answer:**

It will decrease by 6 3/10 lbs in the 3 1/2 hours

**Step-by-step explanation:**

The rate is -1 4/5 lbs per hour

The time is 3 1/2 hours

Multiply to find the weight change

-1 4/5 * 3 1/2

Change to improper fractions

- ( 5*1 +4) /5 * ( 2* 3+1)/2

- 9/5 * 7/2

-63/10

Changing back to a mixed number

-6 3/10

It will decrease by 6 3/10 lbs in the 3 1/2 hours

**Answer:**

-6 3/10 pounds

**Step-by-step explanation:**

The weight of ice sculpture changes -1 4/5 pounds every 1 hour.

In 3 1/2 hours, multiply the time with the weight.

-1 4/5 × 3 1/2

Multiply.

-9/5 × 7/2

-63/10 = -6 3/10

Solve the system using multiplication for the linear combination method. 6x – 3y = 3 –2x + 6y = 14 What is the solution to the system

### Answers

**Answer:**

work is shown and pictured

Correct Answer would be

D: (2,3)

Fill in the blank. A _______ variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure.

### Answers

**Answer:**

Random variable

**Step-by-step explanation:**

**The reason it is a random variable is because a, the definition fits, and b you can use context clues as well, such as 'determined by chance' which is another example of random! So, the answer is random, because random variables are determined by chance. Hope this helped.**

**Answer:**

"A **random** variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure."

**A random variable is distinct on the off chance that it takes on a countable number of quantities.**

The total cost of a sweater and a jacket was $71.55 If the price of the sweater was $3.19 less than the jacket, what was the price of the sweater? Express your answer as a simplified fraction or a decimal rounded to two places.

### Answers

Answer: $34.18

Step-by-step explanation:

Let the cost of the Jacket = $x and

The cost of the sweater. = $y

Now total price. = $71.55.

So, $x + $y. = $71.55 -- 1

From the second statements, the price of the sweater was $3.19 less than the price of the jacket. Transforming that into equation

y = ( x - $3.19 )

Now substitute for y in the equation (1) above.

x + ( x - 3.19 ) = 71.55

Now solve the equation

x + x - 3.19 = 71.55

2x - 3.19. = 71.55

2x = 71.55 + 3.19

2x. = 74.74

x = 74.74/2

= $37.37. cost of the jacket

Now to determine the cost of the sweater,

$71.55 - $37.37 = $34.18

The cost of the sweater = $34.18.

The tee for the sixth hole on a golf course is 400 yards from the tee. On that hole, Marsha hooked her ball to the left, as sketched below. Find the distance between Marsha’s ball and the hole to the nearest tenth of a yard. Answer any time! :D

### Answers

**Answer:**

181.8 yd

**Step-by-step explanation:**

The law of cosines is good for this. It tells you for triangle sides 'a' and 'b' and included angle C, the length of 'c' is given by ...

c^2 = a^2 +b^2 -2ab·cos(C)

For the given geometry, this is ...

c^2 = 400^2 +240^2 -2(400)(240)cos(16°) ≈ 33,037.75

c ≈ √33037.75 ≈**181.8 . . . yards**

**Marsha's ball is about 181.8 yards from the hole**.

**Answer:**

181.8 yds

**Step-by-step explanation:**

I got it correct on founders edtell

The four-member math team at Pecanridge Middle School is chosen from the math club, which has three girls and five boys. How many different teams made up of two girls and two boys could be chosen?

### Answers

**Answer:**

[tex]Total\ Selection = 30\ ways[/tex]

**Step-by-step explanation:**

**Given**

Girls = 3

Boys = 5

**Required**

How many ways can 2 boys and girls be chosen?

The keyword in the question is **chosen;**

This implies **combination **and will be calculated as thus;

[tex]Selection =\ ^nC_r = \frac{n!}{(n-r)!r!}[/tex]

**For Boys;**

n = 5 and r = 2

[tex]Selection =\ ^5C_2[/tex]

[tex]Selection = \frac{5!}{(5-2)!2!}[/tex]

[tex]Selection = \frac{5!}{3!2!}[/tex]

[tex]Selection = \frac{5 * 4 * 3!}{3!*2 * 1}[/tex]

[tex]Selection = \frac{20}{2}[/tex]

[tex]Selection = 10[/tex]

**For Girls;**

n = 3 and r = 2

[tex]Selection =\ ^3C_2[/tex]

[tex]Selection = \frac{3!}{(3-2)!2!}[/tex]

[tex]Selection = \frac{3!}{1!2!}[/tex]

[tex]Selection = \frac{3 * 2!}{1 *2!}[/tex]

[tex]Selection = \frac{3}{1}[/tex]

[tex]Selection = 3[/tex]

**Total Selection is calculated as thus;**

[tex]Total\ Selection = Boys\ Selection * Girls\ Selection[/tex]

[tex]Total\ Selection = 10 * 3[/tex]

[tex]Total\ Selection = 30\ ways[/tex]

Find a formula for an for the arithmetic sequence.

### Answers

Answer:

a(n)= a(n+1)+4

Step-by-step explanation:

The first terms of this sequence are: 4,0, -4, -8, -12

Let 4 be a0 and 0 a1.

● a1-a0 = 0-4

●a1-a0 = -4

●a1 = -4+a0

So this relation links the first term with the second one.

replace 1 in a1 with n.

0 in a0 will be n-1

● an = -4+a(n-1)

Add one in n

● a(n+1) = a(n)-4

● a(n) = a(n+1)+4

What is the value of x? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

### Answers

**Answer:**

10.2 m

**Step-by-step explanation:**

180 - 81 - 30 = 69

law of sines

x /sin 30 = 19/sin 69

x = 10.2

The summer has ended and it’s time to drain the swimming pool. 20 minutes after pulling the plug, there is still 45 000L of water in the pool. The pool is empty after 70 minutes. Calculate the rate that the water is draining out of the pool. (Hint: remember this line is sloping down to the right) (3 marks) Rate=0-45000/70-20 Rate = (0 - 45000) / 70-20 Rate = -45000 / 50 Rate=-900/minute b)Calculate how much water was in the pool initially (at time 0). (2 marks)

### Answers

**Answer:**

there were **63,000L of water** initially in the pool

**Step-by-step explanation:**

do 900L times the first 20 minutes to find out how much water was drained during the first 20 minutes and you get 18,000L drained

then, add 18,000L plus the rest of the 45,000L of water drained from the pool to get 63,000L of water intially in the pool

A manufacturer makes plastic wrap used in food packaging and aims to have a minimum breaking strength of 0.5 kg. If the mean breaking strength of a sample drops below a critical value, the production process is halted and the machinery is inspected. Which of the following is a Type 1 error in context?

A) Halting the production process when too many rubber bands break.

B) Halting the production process when the true breaking strength is below the desired level.

C) Halting the production process when the true breaking strength is within specifications.

D) Allowing the production process to continue when the true breaking strength is below specifications.

E) Allowing the production process to continue when the true breaking strength is within specifications

### Answers

Answer:

Option D

Step-by-step explanation:

A type I error occurs when you reject the null hypothesis when it is actually true.

The null hypothesis in this case is minimum breaking strength is less than or equal to 0.5.

A type one error would be allowing the production process to continue when the true breaking strength is below specifications.

Rolling a 6-sided die and counting the number of each outcome that occurs is a bionomial random variable. True or False? Which option gives the most accurate response?

### Answers

**Answer:**

False.

**Step-by-step explanation:**

This is NOT an example of a binomial random variable, because a binomial random variable can only have TWO possible outcomes: success or failure. In the case of rolling a die, there are SIX possible outcomes: 1, 2, 3, 4, 5, or 6.

So, rolling a 6-sided die and counting the number of each outcome that occurs is NOT a binomial random variable.

Hope this helps!

The given **statement **"Rolling a 6-sided die and **counting **the number of **each **outcome that occurs" is **false.**

What is Binomial distribution?

A **common **discrete distribution is used in statistics, as **opposed **to a continuous distribution is called a **Binomial **distribution. It is given by the formula,

P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)

Where,

x is the number of **successes** needed,

n is the number of trials or sample size,

p is the **probability** of a single success, and

q is the probability of a single **failure**.

The given **statement** "Rolling a 6-sided die and counting the number of each outcome that occurs" is not an **example **of the binomial random variable. This is because the **binomial **random variable can only have two possible **outcomes**, which is not true in the **case **of a die that had **six faces **and six outcomes** **for each through.

Although if the probability is needed to be **calculated **for the same digit occurring or not it can be **calculated** using the binomial random **variable.**

Hence, The given **statement **"Rolling a 6-sided die and counting the number of each outcome that occurs" is **false.**

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A heating pad takes 3,030 Watts during each time it is turned on. If you only use it for 34 minutes, how much CO2 was created? Round to 1 decimal.

### Answers

**Answer:**

1.7kW/hr

**Step-by-step explanation:**

Using the formula for calculating the energy used up during the process;

Energy used up = Amount of CO₂ created.

Energy used up in the process = Power * Time.

**Given Parameters:**

Power = 3,030Watts

Converting to Kilowatts, power = 3030/1000 kW

**Power (in kW) = 3.03kW**

Time taken = 34 minutes

Converting to hour;

Since 60 minutes = 1hr

34minutes = (34/60)hr

**34minutes = (17/30)hr**

**Required:**

Energy used up = 3.03 * 17/30

Energy used up = 51.51/30

**Energy used up = 1.717 kW/hr**

**Hence, amount of CO₂ created in kW/hr is 1.7 kW/hr to 1 decimal place.**

There are 3 times as many novels as comic books in a bookstore.If there are 2480 books altogether, how many comic books are there in the bookstore.

### Answers

**Answer:**

there are 620 comic books

**Step-by-step explanation:**

let number of comic books be x

total books=3x+x

2480=4x

2480/4=x

620=x

**Answer:**

**6****2****0**

**Step-by-step explanation:**

**Let**** ****comic**** ****books ****be**** ****'**** ****X ****'**

**Let**** ****Novels**** **** ****be**** ****'**** ****3****x**** ****'**

**Now****,**** ****finding ****the**** ****value ****of**** ****X **

**According ****to**** ****Question,**

**[tex]3x + x = 2480[/tex]**

**Collect**** ****like**** ****terms**

**[tex]4x = 2480[/tex]**

**Divide**** ****both**** ****sides**** ****of**** ****the**** ****equation ****by ****4**

**[tex] \frac{4x}{4} = \frac{2480}{4} [/tex]**

**Calculate**

**[tex]x = 620[/tex]**

**Thus****,**** ****There**** ****are**** ****6****2****0**** ****comic**** ****books**** ****in**** ****the**** ****book**** ****store****.**

**Hope**** ****this**** ****helps.****.****.**

**Best**** ****regards****!****!**

Kara Danvers (Supergirl) has always relied on her strength to win fights. But what happens when she meets an alien just as strong? Her sister is training her to be a more technical fighter so that Supergirl can meet any challenge. The data below record the significant strikes during randomly selected training sessions 6 months apart. Is Kara showing improvement in her fighting?

### Answers

**Answer:**

The answer is below

**Step-by-step explanation:**

The corresponding data are missing, which are the following:

Strikes (pre):

29

32

44

34

19

Strikes (post):

51

45

68

92

64

We have to say the difference between the post-pre values of the strike. The d will be the average of the differences between the post and pre values. If Kara is to show improvement, her post-workout attacks should be more than the pre-workout values. Let m be the population mean of the difference:

H0: m = 0 the mean difference in Strikes between post and pre is zero.

H0: m>0, the mean difference in strikes between post and pre is more than zero.

High Fructose Corn Syrup (HFCS) is a sweetener in food products that is linked to obesity and type II diabetes. The mean annual consumption in the United States in 2008 of HFCS was 60 lbs with a standard deviation of 20 lbs. Assume the population follows a Normal Distribution.

a. Find the probability a randomly selected American consumes more than 50 lbs of HFCS per year.

b. Find the probability a randomly selected American consumes between 30 and 90 lbs of HFCS per year.

c. Find the 80th percentile of annual consumption of HFCS.

d. In a sample of 40 Americans how many would you expect to consume more than 50 pounds of HFCS per year.

e. Between what two numbers would you expect to contain 95% of Americans HFCS annual consumption?

f. Find the quartile and Interquartile range for this population.

g. A teenager who loves soda consumes 105 lbs of HFCS per year. Is this result unusual?

### Answers

**Answer:**

Explained below.

**Step-by-step explanation:**

* X* = annual consumption in the United States in 2008 of HFCS

[tex]X\sim N(60, 20^{2})[/tex]

(**a**)

Find the probability a randomly selected American consumes more than 50 lbs of HFCS per year.

[tex]P(X>50)=P(\frac{X-\mu}{\sigma}>\frac{50-60}{20})=P(Z>-0.50)=P(Z<0.50)=0.6915[/tex]

**P (X > 50) = 0.6915**.

(**b**)

Find the probability a randomly selected American consumes between 30 and 90 lbs of HFCS per year.

[tex]P(30<X<90)=P(\frac{30-60}{20}<\frac{X-\mu}{\sigma}<\frac{90-60}{20})\\\\=P(-1.5<Z<1.5)\\\\=0.93319-0.06681\\\\=0.86638\\\\\approx 0.8664[/tex]

**P (30 < X < 90) = 0.8664**.

(**c**)

Find the 80th percentile of annual consumption of HFCS.

P (X < x) = 0.80

⇒ P (Z < z) = 0.80

⇒ *z* = 0.84

[tex]z=\frac{x-\mu}{\sigma}\\\\0.84=\frac{x-60}{20}\\\\x=60+(20\times 0.84}\\\\x=76.8[/tex]

**80th percentile = 76.8**.

(**d**)

In a sample of 40 Americans how many would you expect to consume more than 50 pounds of HFCS per year.

P (X > 50) = 0.6915

Number of American who consume more than 50 lbs = 40 × 0.6915

= 27.66

≈ 28

**Expected number = 28**.

(**e**)

Between what two numbers would you expect to contain 95% of Americans HFCS annual consumption?

According to the Empirical rule, 95% of the normally distributed data lies within 2 standard deviations of mean.

[tex]P(\mu-2\sigma<X<\mu+2\sigma)=0.95\\\\P(60-2\cdot20<X<60+2\cdot20)=0.95\\\\P(20<X<100)=0.95[/tex]

**Range = 20 < X < 100**.

(**f**)

Find the quartile and Interquartile range for this population.

**1st quartile: Q₁**

P (X < Q₁) = 0.25

⇒ P (Z < z) = 0.25

⇒ *z* = -0.67

[tex]z=\frac{Q_{1}-\mu}{\sigma}\\\\-0.67=\frac{Q_{1}-60}{20}\\\\Q_{1}=60-(20\times 0.67)\\\\Q_{1}=46.6[/tex]

**3rd quartile: Q₃**

P (X < Q₃) = 0.75

⇒ P (Z < z) = 0.75

⇒ *z* = 0.67

[tex]z=\frac{Q_{3}-\mu}{\sigma}\\\\0.67=\frac{Q_{3}-60}{20}\\\\Q_{3}=60+(20\times 0.67)\\\\Q_{3}=73.4[/tex]

**Inter quartile range:**

[tex]IQR=Q_{3}-Q_{1}=73.4-46.6=26.8[/tex]

(**g**)

Compute the *z*-score for *x* = 105 lbs as follows:

[tex]z=\frac{Q_{3}-\mu}{\sigma}\\\\z=\frac{105-60}{20}\\\\z=2.25[/tex]

*Z*-scores greater than +2.00 or less than -2.00 are considered as unusual.

Thus, the result **unusual.**

27) Jake tells a joke to 3 people and each of those people tells the joke to 3 more people,

and so on. How many people will hear the joke in the 4th round of jokes told? How

many people will hear the joke in total after the fourth round?

### Answers

**Answer:**

15

**Step-by-step explanation:**

**Answer:**

12 people heard the joke?

**Step-by-step explanation:**

Using traditional methods, it takes 9.5 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 15 students and observed that they had a mean of 10.0 hours with a standard deviation of 1.6. A level of significance of 0.1 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.

### Answers

Answer:

Step-by-step explanation:

Null hypothesis: u = 9.5hrs

Alternative: u =/ 9.5hrs

Using the t test

t = x-u/sd/√n

Where x is 10hrs, u is 9.5, sd is 1.6 and n is 15

t = 10-9.5 / (1.6/√15)

t = 0.5 / (0.4131)

t = 1.21

In order to make a conclusion, we have to find the p value at a significance level lot 0.1. The p value is 0.2263 which is greater than 0.1. This, we will fail to reject the null hypothesis and conclude that there is not enough statistical evidence to prove that the technique performs differently than the traditional method.

100 POINTS!!! NEED HELP ASAP The question is the first picture and the second question is the answers to choose. Thank you!

### Answers

**Answer:**

4, 3, 5, 8, 7, 6, 1, 2

**Step-by-step explanation:**

Let’s label the options with numbers.

Solve the percentages:

1) 442/(442+267) = 62.4%

2) 701/(701+187) = 78.9%

3) 267/(267+442)= 37.7%

4) 187/(187+701) = 21.1%

5) 442/(442+701) = 39.4%

6) 701/(442+701) = 61.3%

7) 267/(187+267) = 58.8%

8) 187/(187+267) = 41.2%

Arrange from least to greatest.

4, 3, 5, 8, 7, 6, 1, 2

An account is opened with an initial deposit of $100 and earns 3.0% interest compounded monthly. What will the account be worth in 25 years? Round your answer to the nearest dollar.

### Answers

**Answer:**

A = $211.50

A = P + I where

P (principal) = $100.00

I (interest) = $111.50

**Step-by-step explanation:**

**$209.37** will the account be worth in 25 years.

What is compound interest?

**Compound Interest** is defined as** interest** **earn** on** interest**.

[tex]A = P(1 + \frac{r}{100})^{t}[/tex]

P= $100

r = 3%

t=25 years

substitute the values in formula,

[tex]A = 100(1 + \frac{3}{100})^{25}[/tex]

[tex]A = 100(1 + 0.03)^{25}[/tex]

[tex]A = 100(1.03)^{25}[/tex]

[tex]A=100(2.0937)[/tex]

[tex]A=209.37[/tex]

Hence, **$209.37** will the account be worth in** 25 years**.

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Need Answers ASAP!!!! (due today)

### Answers

**Answer:**

**1.**

**a. 20 m²**: barn door is 5m x 4m

**b. 468 m²**:surface area of barn

i. left and right barn walls: 2(15 x 7) = 210

ii. back wall: 7 x 8 = 56

iii. front wall: (7 x 8) - 20* = 36

*20 for the barn door

iv. front of roof: (4 x 4) / 2 = 8 x 2* = 16

*I split the triangle into 2 smaller triangles

v. sides of roof: 2(5 x 15) = 150

**2.**

**a. 15 m²**: silo door is 3m x 5m

**b. 244.18 m²**: surface area of silo

i. SA(silo)=2πrh+2πr²

ii. SA(silo) = 2π(2.5)(14) + 2π(2.5)²

iii. SA(silo) = 259.18

iv. SA(silo - door) = 259.18 - 15

v. SA(silo - door) = 244.18

**3.**

**a. 712.18 m²**: total surface area painted red

i. add both surface areas: 468 + 244.18 = 712.18 m²

hope this helps :)

The length of a rectangle is 4yd longer than its width. If the perimeter of the rectangle is 36yd, find its area

### Answers

**Answer:**

[tex] \boxed{\sf Area \ of \ the \ rectangle = 91 \ yd^{2}} [/tex]

**Give****n****:**

Length of the rectangle = 4 yd longer than its width

Perimeter of the rectangle = 36 yd

**To**** ****Fin****d****:**

Area of the rectangle

**Step-by-step explanation:**

Let the width of the rectangle be 'w' yd

So,

Length of the rectangle = (w + 4) yd

[tex] \therefore \\ \sf \implies Perimeter \: of \: the \: rectangle = 2(Length + Width) \\ \\ \sf \implies 36 = 2((4 + w) + w) \\ \\ \sf \implies 36 = 2(4 + w + w) \\ \\ \sf \implies 36 = 2(4 + 2w) \\ \\ \sf 36 =2(2w+4) \: is \: equivalent \: to \: 2(2w + 4) = 36: \\ \sf \implies 2(2w + 4) = 36 \\ \\ \sf Divide \: both \: sides \: of \: 2 (2w + 4) = 36 \: by \: 2: \\ \sf \implies 2w + 4 = 18 \\ \\ \sf Subtract \: 4 \: from \: both \: sides: \\ \sf \implies 2w = 14 \\ \\ \sf Divide \: both \: sides \: of \: 2w = 14 \: by \: 2: \\ \sf \implies w = 7[/tex]

So,

Width of the rectangle = 7 yd

Length of the rectangle = (7 + 4) yd

= 13 yd

[tex] \therefore \\ \sf Area \ of \ the \ rectangle = Length \times Width \\ \\ \sf = 7 \times 13 \\ \\ \sf = 91 \: {yd}^{2} [/tex]

The population of fruit flies in a laboratory grows geometrically and is checked everyday at noon. If the population began with 80 fruit flies and reached 125 in two days, what is the population after 4 days?

### Answers

**Answer:**

[tex]\boxed{195}[/tex]

**Step-by-step explanation:**

The fruit flies grows geometrically.

[tex]125=80k^2[/tex]

Find the value of k.

[tex]\sqrt{\frac{125}{80} } =k[/tex]

[tex]1.25=k[/tex]

[tex]P=80(1.25)^t[/tex]

[tex]t[/tex] is number of days.

[tex]P=80(1.25)^4[/tex]

[tex]P=195[/tex]

Which algebraic expression represents the phrase "six less than a number"?

SERE

6x - X

X-6

6- X

X - 6x

### Answers

**Answer:**

The answer is option B.

**Step-by-step explanation:**

six less than a number is written as

x - 6

Hope this helps you

Rotation

The triangle DEF with vertices D (-4, 4), E (-1, 2), F (-3, 1). Graph the figure and its image after a 90 ° clockwise rotation about its origin.

### Answers

**Answer:**

**Step-by-step explanation:**

The vertices of the already rotated triangle are:

D '(4, 4)

E '(1, 3)

F '(2, 1)

**Answer:**

D '(4, 4)

E '(1, 3)

F '(2, 1)

**Step-by-step explanation:**