What is the ordered pair of C' after point C (1, 2) is rotated 90° clockwise?

A. C' (-1,2)

B. C (1, -2)

C. C (2,1)

D. C' (2, -1)

Answers

Answer 1

Answer:

D

Step-by-step explanation:

Under a clockwise rotation about the origin of 90°

a point (x, y ) → (y, - x ), thus

C(1, 2 ) → C'(2, - 1 ) → D

Answer 2

The image after the rotation is C' (2, -1), the correct option is D.

What is the image after the rotation?

Here we have the point (1, 2), and we have a rotation of 90° clockwise.

Notice that our point is on the first quadrant, then a rotation of 90° will leave us in the fourth quadrant.

The change that we will have is a permutation of the values, and the y-value must become negative, then the transformation gives:

(1, 2) ---> (2, -1)

The correct option is D.

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Related Questions

Cask’n’Cork wine shop has a markup rate of 15%. What price will the shop charge for a bottle of zinfandel wine that costs $12.48 wholesale?

Answers

Answer:$14.35

Step-by-step explanation:

The shop will charge $14.352 as markup price.

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Cask’n’Cork wine shop that has a markup rate of 15%. A bottle of zinfandel wine costs $12.48 wholesale.

Assume that the shop charges $x. Then, we can write -

x = 12.48 + 15% of 12.48

x = 12.48 + (15/100) x 12.48

x = 12.48 + (3/20) x 12.48

x = 12.48 + 1.872

x = 14.352

Therefore, the shop will charge $14.352 as markup price.

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Sergei estimated 149% of 67 by performing the following steps. Which statement is true?
(70)(150%)
- (70)(100% + 50%)
- (70)(100%) + (70)(50%)
- (70)(1)+ (70) )
- 70+35
- 105
The estimate is less than the actual answer because the percent and the number were both rounded down.
The estimate is less than the actual answer because the percent and the number were both rounded up.
The estimate is greater than the actual answer because the percent and the number were both rounded down.
The estimate is greater than the actual answer because the percent and the number were both rounded up.

Answers

Answer: Last option.

Step-by-step explanation:

In order to estimate the percent "n" of a number"x", you need easy numbers to work with, therefore you can round  "n" and "x" up or down; but it is important to remember that this estimation does not give you an exact value.

You can observe that Sergei's first step was to round 149% and 67 up, getting this result:

[tex]=105[/tex]

To verify if this estimate is less or greater than the actual answer, we can find the actual answer. This is:

[tex]\frac{67*149}{100}=99.83[/tex]

Therefore, we can conclude that the estimate is greater than the actual answer because the percent and the number were both rounded up.

Answer:

D

Step-by-step explanation:

I did it on Edgen 2020

A number q plus 8 is less than or equal to 15​

Answers

Answer:

q≤7

Step-by-step explanation:

q+8≤15

1) Subtract 8 from both sides:

q≤7

Answer:

[tex]\displaystyle 7 ≥ q; q + 8 ≤ 15[/tex]

Step-by-step explanation:

q + 8 ≤ 15

- 8 - 8

_______

[tex]\displaystyle q ≤ 7[/tex]

** The above answer is written in reverse, which is the exact same result.

I am joyous to assist you anytime.

Kyle gave 2/7 of his money to his wife and spent 3/5 of the remainder. If he had $300 left, how much money did he have at first?

Answers

Answer:

Kyle gave 2/7th  of his money to his wife and spent 3/5 of the remainder. If he had $300 left, the money had by Kyle at first is $1050

Solution:

Step 1:

Consider “x” as the money which Kyle had initially.  

From question, Kyle gave 2/7th of his money to his wife. So the remaining money left with Kyle is given as,

[tex]= 1 - \frac{2}{7}[/tex]

[tex]= \frac{7 - 2}{7} = \frac{5}{7}[/tex] ----- eqn 1

Now the remaining money left with Kyle is 5/7th.Given that Kyle spent 3/5 of the remaining money.  

Now the remaining money left with Kyle is given as  

[tex] = 1 - \frac{3}{5} = \frac{5 - 3}{5} = \frac{2}{5}[/tex]

Now kyle is left with $300, which is 2/5th of the initial money x .

We get equation as  

[tex]\frac{2}{5} x=300[/tex]

2x = 1500

x = 750

Now Kyle is left with 750$ which is 5/7th of the initial amount x.( by using eqn 1)

We get equation as

[tex]\frac{5}{7} x = 750[/tex]

5x = 5250

x = 1050

So the amount had by Kyle at first is $1050

Final answer:

Working backward from the $300 Kyle had after spending and giving some away, we find that the original amount of money was $1050, which is determined by reversing the operations he performed on his money.

Explanation:

To solve how much money Kyle had at first, we need to work backwards from the amount he had left ($300) after he spent some and gave some to his wife. First, we determine how much was left before he spent the 3/5 of the remainder.

Let's denote Kyle's initial amount of money as x. The equation representing what Kyle did with his money is

x - (2/7)x = Remaining Amount After Giving to Wife

Kyle then spends 3/5 of this remaining amount, and is left with $300, so we can represent this as:

(1 - 3/5)(Remaining Amount After Giving to Wife) = $300

Substituting the first equation into the second we get:

(1 - 3/5)(x - (2/7)x) = $300

Simplifying, we find that (2/5)(5/7)x = $300.

This simplifies down to:

(2/5)(5/7)x = (10/35)x = $300

Finally, solving for x, we multiply both sides by the reciprocal of (10/35),

x = $300 × (35/10)

x = $300 × 3.5

x = $1050

So, Kyle originally had $1050.

the lines below are parallel if the slope of the green line is -2 what is the slope of the red line

Answers

Answer:

-2

Step-by-step explanation:

Since they are parallel, they have the same slope. This will be true for any set of lines.

20/30 as a decimal rounded to the nearest tenth

Answers

Answer:

1.5

Step-by-step explanation:

Answer:

0.7

Step-by-step explanation:

30 cannot be multiplied to give a power of 10, so to find the decimal you have to divide: 2/3 = 2/3 + 2 ÷ 3

2 divided by 3 is 0.6666666... It is a recurring decimal.

However it is not practical to use recurring decimals in calculations, so the decimal is usually rounded off to 2 or 3 decimal places depending on the accuracy required for the answer.

the output of a function is 7 more than 3 times the input find the input when the output is -8​

Answers

Answer:

The input is -5 when the output is -8

Step-by-step explanation:

Let

y-----> the output

x ----> the input

we know that

The linear equation that represent this problem is

[tex]y=3x+7[/tex]

so

For y=-8

substitute in the equation and solve for x

[tex]-8=3x+7[/tex]

Subtract 7 both sides

[tex]-8-7=3x\\-15=3x[/tex]

Divide by 3 both sides

[tex]x=-5[/tex]

therefore

The input is -5 when the output is -8

find the slope of the line

Answers

Answer:

Undefined or No solution

Step-by-step explanation:

Because this line is a straight, vertical line, it means that the slope is undefined, or no solution. Any time you see a straight line going up and down, this will be true. However, if you see a horizonal line, this will not be true.

If K={(x, y) I x-y=5), is Set K a function?
Yes
No

Answers

Answer:

NO!

NO NUMBER VARIABLES CAN BE CALLED A FUNCTION

Markus receives dollar bills from his grandfather for on week. On the first day he received $1; on the second day he received $2, on third day he received $4, and on the fourth day he received $8. If this continues, how much money will Markus have by the end of the week?

Answers

Answer: $127

Step-by-step explanation:

5th day: 8 * 2 = 16

6th day: 16 * 2 = 32

7th day: 32 * 2 = 64

Then add all the money he got throughout the week,

1 + 2 + 4 + 8 + 16 + 32 + 64

= 127

A gas engine is 6% efficient. What portion of a 12 gallon tank of gas is wasted?

Answers

Answer:

282/25

Step-by-step explanation:

[tex]efficient \: = 12 \times \frac{6}{100} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{72}{100} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{18}{25 } \\ so \: \\ west \: = 12- \frac{18}{25} \\ \: \: \: \: \: \: \: \: \: \: \: \: = \frac{282}{25} \: \: gallon[/tex]

plzzzz...

mark it as a brilliant answer

The wasted portion of gallon tank will be "[tex]\frac{282}{25}[/tex]". A further solution is provided below.

Given:

Efficient percent = 6%Number of gallon = 12

Now,

The efficient portion will be:

= [tex]12\times \frac{6}{100}[/tex]

= [tex]\frac{72}{100}[/tex]

= [tex]\frac{18}{25}[/tex]

hence,

The wasted portion of gallon tank will be:

= [tex]12-\frac{18}{25}[/tex]

= [tex]\frac{282}{25} \ gallon[/tex]

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How many user must mike recruit in order for him to steam movies for free? The service costs $43.75 a month, but mikes rate is reduced by $1.25 for each new subscriber that he gets to sign up.

Answers

Answer:

35 subscribers

Step-by-step explanation:

Divide $43.75 by $1.25.

$43.75/$1.25 = 35

For each subscriber he gets, his service goes down by $1.25.

Since 35 * $1.25 = $43.75, for 35 new subscribers, his service will go down by $43.75.

He pays $43.75, so if the service goes down by $43.75, he will pay nothing since $43.75 - $43.75 = 0.

Answer: 35 subscribers

Follow below steps:

To determine how many users Mike must recruit for him to stream movies for free, we need to set up a simple algebraic equation. Mike's service costs $43.75 per month, and for each new subscriber he recruits, his rate is reduced by $1.25. Let's say the number of users Mike needs to recruit is represented by x.

The cost reduction for recruiting x users would be $1.25x. To get a free service, the total cost reduction must equal the monthly service cost of $43.75. Thus, the equation is $1.25x = $43.75.

To solve for x, we divide both sides by $1.25:

x = $43.75 / $1.25

x = 35

Therefore, Mike must recruit 35 new subscribers to stream movies for free.

2(4+2x) > 5x+5
Solve the inequality

Answers

Answer:

x < 3

Step-by-step explanation:

Apply distributive property on the left of the inequality to get rid of the parenthesis:

8+4x > 5x+5

subtract 4x from both sides to group all terms with x on the right:

8 > 5x-4x+5

8 > x +5

Now subtract 5 from both sides to collect all numerical terms on the left:

8 - 5 > x

3 > x

Therefore the solution to the inequality are of those real numbers strictly smaller than 3.

The inequality can be written as x < 3 or also as we had it initially: 3 > x

Notice that the opening of the angle symbol is always facing the number 3 , meaning that 3 is the larger of the two numerical objects that are compared.

I need urgent!!
The first people answer this question I give brainliest.

Directions:use the chart below to help answer the questions that follow

C.jeremy sister,Susie ,borrowed the money from their mom to pay for her order. The mother has agreed to deduct an equal amount of money from suzie allowance each week for the next five weeks to repay the loan . What is the weekly change in suzie allowance?

Numerical answer:

Explanation:


D. Jeremy grandparents want to change their order. They want to order three daisies and one geranium, instead of your daisies. How does this change affect the amount of their order? Explain how you arrived at your answer.


E. Jeremy approaches three people who do not want to buy any plants; however,they wish to donate some money for the fundraiser when Jeremy delivers the plants one week later. If the people promise to donate a total of $14.40, what will be the average cash donation?


F. Jeremy spends one week collecting orders.If 22 people purchase plants totaling $270,what is the average amount of Jeremy sale?

Numerical answer:

Explanation:

Answers

A) The total for the plants she buys is 8.50, so the change in her checking account would be -8.50, because they will take 8.50 out of her account when the check is cashed, the amount in her account is lowered.

B) Mr. Clark's total is 11.25. If he pays with a 20, subtract the plant total from 20:

20 - 11.25 = 8.75 is the amount of change Jeremy owes him.

The amount of money Jeremy collects would be that amount higher than what he needs.

C)  Suzie owed 2.50, divide the amount she borrowed by the number of weeks her mom is keeping money:

2.50 / 5 = 0.50

Her allowance will be 0.50 less than what she normally would get.

D) Grandparents original amount = $15.00

3 daises = 3 x 3.75 = 11.25

1 geranium = 2.25

Total for new order = 11.25 + 2.25 = 13.50

Difference = 15 - 13.50 = 1.50

The new order would be $1.50 less.

E) Divide the total amount of the donation by the number of people:

14.40 / 3 = $4.80

F) Divide total amount by total people:

270 / 22 = $12.27 average

Which scale would produce the largest scale drawing of an object when compared to the actual object?

A. 1 inch : 5 feet

B. 1 inch : 30 inches

C. 1 foot : 12 yards

D. 1 centimeter : 1 meter

Answers

Covert the ratios so they are all the same measurement type.

A. 5 feet = 5 x 12 = 60 inches.

The scale becomes 1:60

B. 1:30

C. 12 yards = 12 x 3 = 36 feet x 12 = 432 inches.

The scale is 12:432  = 1:36

D. 1 meter = 39.37 inches.

1 inch = 2.54 cm

39.37 x 2.54 = 99.99 inches

The scale converted to inches becomes 1 :100 inches.

The first number would be the size of the drawing, the second number is the size of the actual object

If you use all 4 scale factors for a real object that is 100 inches:

A would need 100/60 = 1.67 inches.

B would need 100/30 = 3.3 inches.

C would need 100/36 = 2.78 inches.

D would need 100/100 = 1 inch.

The larger scaled drawing would be B.

Answer:

Option B.

Step-by-step explanation:

We need to find which scale would produce the largest scale drawing of an object when compared to the actual object.

First of all cover all units in inches.

In option 1,

1 inch : 5 feet

We know that

1 feet = 12 inch → 5 feet = 60 inch

So the ratio in inches is 1:60. It means the scale factor is 60.

In option 2,

1 inch : 30 inches

So the ratio in inches is 1:30. It means the scale factor is 30.

In option 3,

1 foot : 12 yards

12 inches : 12 yards                     (1 feet = 12 inch)

1 inch : 1 yards

1 inch : 36 inch                     (1 yard = 36 inch)

So the ratio in inches is 1:36. It means the scale factor is 36.

In option 4,

1 centimeter : 1 meter

1 centimeter : 100 centimeter         (1 m = 100 cm)

1 inch : 100 inch

So the ratio in inches is 1:100. It means the scale factor is 100.

Option B has smallest scale factor, so it will produce the largest scale drawing of an object when compared to the actual object.

Therefore, the correct option is B.

Verbal expression for r+4

Answers

Answer:

a number increased by 4

Step-by-step explanation:

r = a number

increased by four = +4

four more than the number R

Step-by-step explanation: with the word than you would flip it to r+4

64.8 divided by 7 showing using long division

Answers

Answer:

9.257

Step-by-step explanation:

7 goes into 64 nine times with the remainder of 1. Bring the decimal point up and the 8 down. 7 goes into 18 two times with the remainder of 4. 7 goes into 40 5 times with the remainder of 5. 7 goes into 50 7 times. That equals 9.257.

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Final answer:

To divide 64.8 by 7 using long division, calculate how many times 7 can be subtracted from each part of the number 64.8 in sequence. This results in the final answer of 9.25.

Explanation:

To find 64.8 divided by 7 using long division, first write down 64.8 with a division bar over it and 7 on the left side of the bar. You would write:

7 | 64.8

Next, ask: How many times does 7 go into 64? This is 9 times since 7 times 9 is 63. Record the 9 above the line and record the product (63) below 64. Subtract 63 from 64 to get 1.

Bring down the 8 (from 64.8) to the right of the 1. Now you have 18. Ask how many times does 7 go into 18? This is 2 times. So you add the digit 2 next to 9 on top of the bar. 7 times 2 is 14.

Subtract 14 from 18 to get 4. As the decimal point should be straight up from where it is in the 64.8, record a decimal point.

Now, since there's no more numbers to bring down, you can add a 0 to 40. 7 goes into 40, 5 times. Therefore, we add 5 next to the 2 after the decimal point. So, 64.8 divided by 7 is 9.25.

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2 cubed minus 2 squared

Answers

Hello!

your answer is: 4

2 cubed is also written as: 2³

2 squared is also written as: 2²

so the re-written equation is: 2³ - 2²

To solve, simplify by doing the exponents.

2³ = 8

2² = 4

8 - 4 = 4

I hope this helps, and have a nice day!

What is the lcm of 24,36,and, 60?

Answers

Answer:  360

Step-by-step explanation:

LCM is least common multiple.  In other words, what number is divisible by 24, 36, and 60?

Factor each term.  See what they have in common and then multiply the common term by all of the leftovers.

                24                        36                         60

                 ∧                          ∧                           ∧

             12   2                    12  3                      12  5

                   

They all have a 12 in common.  The leftovers are 2, 3, & 5.

So, the LCM is 12 × 2 × 3 × 5   = 360

8-5b=-7 solve please

Answers

Answer:

Step-by-step explanation:

subtract 8

-5b=-15

divide negative 5

b=3

Answer the answer to your question is b=3

Which ordered pair is a solution of the equation? -3x-y=6

Answers

There are an infinite number of solutions, but some that work are (-2,0), (1,-3), and (0,-6)

The correct answer is (B) Only (-3, 3).

To determine which ordered pair is a solution of the equation, you need to substitute the values of \( x \) and \( y \) into the equation and see if it holds true. Let's check:

For option A: (-4, 4)
Substituting into the equation: \( -3(-4) - 4 - 6 = 12 - 4 - 6 = 2 \) which is not equal to 0, so it's not a solution.

For option B: (-3, 3)
Substituting into the equation: \( -3(-3) - 3 - 6 = 9 - 3 - 6 = 0 \) which is equal to 0, so it is a solution.

Thus, the correct answer is (B) Only (-3, 3).

Complete question :

Which ordered pair is a solution of the equation?

-3x-y-6

Choose 1 answer:

A Only (-4, 4)

B Only (-3, 3)

C Both (-4, 4) and (-3,3)

D Neither.

Solve a = 2x + 6xz for x

Answers

To solve the equation a = 2x + 6xz for x, isolate x on one side of the equation by following the steps: subtract 6xz from both sides, factor out x, and divide both sides by (2 + 6z).

To solve the equation a = 2x + 6xz for x, we need to isolate x on one side of the equation. Here are the steps:

Start with the equation: a = 2x + 6xz

Subtract 6xz from both sides: a - 6xz = 2x

Factor out x on the right side: a - 6xz = x(2 + 6z)

Divide both sides by (2 + 6z): (a - 6xz) / (2 + 6z) = x

Therefore, the solution for x is x = (a - 6xz) / (2 + 6z).

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How do you solve this?​

Answers

you call that 28x∉ then add√÷ um turn it around and come out  answer

A regular prism has two congruent rectangles as its bases. How can one base be transformed to carry onto the other?

One base must be translated to carry onto the other base


One base must be rotated to carry onto the other base


It is impossible to carry one base onto the other base


One base must be reflected to carry onto the other base

Answers

Answer:

One base must be translated to carry onto the other base

Step-by-step explanation:

A regular prism has two congruent rectangles as its bases. Since the bases of the prism are congruent and oriented the same way, neither reflection nor rotation will work to carry one base onto the other. It doesn't matter how many sides a geometric shape has.

Therefore the correct option is:

One base must be translated to carry onto the other base.

How many times dose 24 go into 1,392

Answers

Answer:

58

Step-by-step explanation:

1392/24=58

Answer: 24 goes into the number 1,392, 58 times

write an expression for the amount of money (in dollars) in n nickels

Answers

Answer:

m1.00 +n0.20

Step-by-step explanation:

20 times 5 equal one dollar

Final answer:

The amount of money in n nickels can be expressed as 5n.

Explanation:

The expression for the amount of money in n nickels can be written as 5n. Since each nickel is worth 5 cents, multiplying the number of nickels by 5 will give the amount in dollars. For example, if you have 3 nickels, the expression would be 5 x 3 = 15 dollars.

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a cheetah can run 27 m per second that means that a travels 27 m in 1 second at this rate how far can it travel in 8 Seconds​

Answers

Answer:

5.4 m/s2

Step-by-step explanation:

Answer: 216 meters per 8th second

Step-by-step explanation:

do 27 times 8 it will give you 216

12 less than m is no less than 132

Answers

The number will be "m = -120".

Let,

The number be "m".

According to the question,

The expression will be:

→         [tex]m-12=-132[/tex]

By adding "12" both sides of the expression, we get

→ [tex]m-12+12=-132+12[/tex]

→                 [tex]m = -120[/tex]

Thus the response above is right.

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Final answer:

To solve the given statement '12 less than m is no less than 132', we set up the inequality m - 12 ≥ 132. Adding 12 to both sides, we find that m ≥ 144.

Explanation:

Given the statement '12 less than m is no less than 132', we can set up an inequality to represent this relationship: m - 12 ≥ 132. To solve for m, we can add 12 to both sides of the inequality: m ≥ 132 + 12. Simplifying, we find that m ≥ 144. So, any value of m that is greater than or equal to 144 will satisfy the given statement.

Represent the following sentence as an algebraic expression, where "a number" is the letter x. number is decreased by 2.

Answers

Answer:

x-2

x decreased by 2 equals x-2.

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For which equation would x = 12 be a solution?

12 ÷ x > 12
12 - x ≥ 4
12x < 200

Answers

Answer:

12x < 200

Step-by-step explanation:

Substitute x = 12 into the left side of the inequality and compare with right side, that is

12 ÷ 12 = 1 < 12 ← not a solution

12 - 12 = 0 < 4 ← not a solution

12 × 12 = 144 < 200 ← this is a solution

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A nurse working in the intensive care unit (ICU) refers to the Institute for Healthcare Improvement (IHI) Ventilator Bundle prior to planning patient care. The nurse realizes nursing interventions outlined in the bundle will improve patients outcomes. Which of the following statement best describes how IHI-established nursing interventions should be included in each bundle?a) Nursing interventions found within the IHI bundles were selected based on the ability to provide optimal time management for the nurseb) Best practice derived from valid and reliable research studies guided nursing interventions being added to the IHI bundlesc) Nurse case managers serving as patient advocates recommended nursing interventions to be included in the IHI bundles based on patient preferenced) Hospitals, physicians, and nurses worked collaboratively to design patient care activities included in IHI bundles A company has determined that it must increase production of a certain line of goods by 112 times last years production. The new output will be 2885 items. What was last year's output? A companys total revenue from manufacturing and selling x units of their product is given by: y = 3x2 + 900x 5,000. How many units should be sold in order to maximize revenue, and what is the maximum revenue "Old Man Denman call all us together and stand on the steps and make he speech. 'You is free to go where you wants but I is beggin' yous to stay by me till us git the crops laid by.' The mens talk it over a-twixt theyselves and includes to stay. They says us might as well stay there as go somewhere else, and us got no money and no place to go." "My husband rents a little piece of land and us raise a corn crop and that's the way us do. Us raises our own victuals. I has chillen through the year(s) and they done scatter to the four winds. Some of them is dead." --Julia Francis Daniels Which of the following was probably true about Julia Francis Daniels? She and her husband left their former master's property to start a new life. She and her husband bought their own property from their former owner. She and her husband signed a farming contract with their former master. She and her husband agreed to supervise the workers and their children. Suppose that coin 1 hasprobability 0.7 of coming upheads, and coin 2 has probability 0.6of coming up heads. If thecoin flipped today comes up heads, thenwe select coin 1 to fliptomorrow, and if it comes up tails, thenwe select coin 2 to fliptomorrow. If the coin initially flipped isequally likely to be coin1 or coin 2, then what is the probabilitythat the coin flipped onthe 3rd day after the initial flip is coin1? In searching the bottom of a pool at night, a watchman shinesanarrow beam of light from his flashlight, 1.3 m above thewaterlevel, onto the surface of the water at a point 2.7 m from theedgeof the pool (Figure 23-50). Where does the spot of light hitthebottom of the pool, measured from the wall beneath his foot, ifthepool is 2.1 m deep? 1. Make a 100 mL volume of 100 mM acetic acid (HAC) HAC (glacial, 100%, 17.4 M, 1.05 g/ml, MW 60.05) ddh,0 ML add to 100 mL Measure 250 ml beaker. Add mL of ddH20 using a 100-ml graduated cylinder and transfer this volume to a ul of 100 mM HAC to the water. Mix with a stir bar. Calculate: (Round two decimal places for final answer) 3gallons (gal) =_____liters (L) 3. What happens and what results from an Earth's precession? Which of the following recommendations has been shown to improve blood lipid levels and reduce the risk for cardiovascular disease?a) maintaining fat intake to within 20-35% of total energyb) increasing saturated fat to at least 10% of total energyc) decreasing intake of dietary omega-3 fatty acids from cold-water fish, nuts, and canola oild) consuming the UL for vitamin B6, B12, and folate from supplements