what is the smallest possible perimeter for a rectangle whose area is 16 in2?

Answers

Answer 1

Answer: 4in

Step-by-step explanation:


Related Questions

help please might give brainliest answer

Answers

ms alvarez and ms saundres bc if u divide 150 by 25 it equals 6 and 162 by 27 also equals 6

Use a Riemann sum with 4 rectangles of equal width to approximate the area between y=3x^(2)+1 and the x-axis on the interval -1,5. Use the left -hand endpoint of each subinterval.

Answers

The approximate area between y=3x^(2)+1 and the x-axis on the interval -1 to 5 is 136.6875.

We can approximate the area between y=3x^(2)+1 and the x-axis on the interval -1 to 5 using a Riemann sum with 4 rectangles of equal width. The left-hand endpoint of each subinterval will be used.

The width of each rectangle is the length of the interval (5-(-1)) divided by the number of rectangles (4). Therefore, the width of each rectangle is

(5-(-1))/4 = 6/4 = 1.5.

Since we are using the left-hand endpoint of each subinterval, the x-values of the left-hand endpoints of the rectangles are

-1, -1+1.5

-1+1.5+1.5

-1+1.5+1.5+1.5 = -1+4.5=3.5

The height of each rectangle is determined by the value of y at the corresponding x-value.

Therefore, the heights of the rectangles are

3(-1)^2+1=2

3(-1+1.5)^2+1=7.125

3(3.5)^2+1=35.125

3(3.5+1.5)^2+1=46.875

The area of each rectangle is the product of its width and height, so the areas of the rectangles are

2*1.5=3

7.125*1.5=10.6875

35.125*1.5=52.6875

46.875*1.5=70.3125.

Therefore, the approximate area between y=3x^(2)+1 and the x-axis on the interval -1 to 5 is 136.6875.

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Can 3,8,15 make a triangle

Answers

Answer is NO!

hope this helps! Have an amazing and blessed day! :)

Answer: yes

Step-by-step explanation:

how to evaluate 8.1p plus 7.9r when p=6 and r=7

Answers

The value of the expression  8.1p plus 7.9r when p=6 and r=7 will be 103.9.

What is an expression?

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

An expression is a mathematical proof of the equality of two mathematical expressions.

8.1p + 7.9r = 8.1(6) + 7.9(7)

⇒ 103.9

Hence "The value of the expression  8.1p plus 7.9r when p=6 and r=7 will be 103.9".

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Doug buys a pumpkin every year. The first time he bought a pumpkin, at year 0, it cost $2.60. He notices the price is getting more expensive, at a rate of 7% per year.

Doug sketches a graph of the situation.

Which statements are true?

Select each correct answer.



Responses

The graph has an x-intercept and a y-intercept.
The graph has an , x, -intercept and a , y, -intercept.

The graph increases from left to right.
The graph increases from left to right.

The point ​ (0, 2.60) ​is on the graph.
The point , ​, , begin ordered pair 0 comma 2.60 end ordered pair, , ​, is on the graph.

The graph has a y-intercept only.
The graph has a , y, -intercept only.

The graph decreases from left to right.
The graph decreases from left to right.

The point (2.60, 0) is on the graph.

Answers

The correct statements regarding the graph of the exponential function y = 2.60(1.07)^x are given as follows:

The graph increases from left to right.The point (0, 2.60) ​is on the graph.The graph has a y-intercept only.

What is the definition of the exponential function?

The definition of an increasing exponential function is given as follows:

y = a(1 + r)^t.

In which the parameters are given as follows:

a is the y-intercept of the exponential function, representing the initial value.r is the growth rate of the exponential function.

In the context of this problem, the values of these parameters are given as follows:

a = 2.6, r = 0.07.

Hence the function is given as follows:

y = 2.6(1.07)^x.

The features of the function are given as follows:

y-intercept at point (0, 2.6).Increasing, as the term elevated to x has an absolute value greater than 1.No x-intercepts, as the horizontal asymptote of the graph is at x = 0.

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Select all of the choices that are equal to (-5)-(-12)

Answers

Answer:

7 {No choices are given}

Step-by-step explanation:

Given problem,

→ (-5) - (-12)

Let's solve the problem,

→ (-5) - (-12)

→ (-5) + 12

→ (-5 + 12) = 7

Thus, the answer is 7.

Students at a high school are asked to evaluate their experience in the class at the end of each school year. The courses are evaluated on a 1-4 scale - with 4 being the best experience possible. In the History Department, the courses typically are evaluated at 10% 1's, 15% 2's, 34% 3's, and 41% 4's. Mr. Goodman sets a goal to outscore these numbers. At the end of the year he takes a random sample of his evaluations and finds 11 1's, 14 2's, 47 3's, and 53 4's. At the 0.05 level of significance, can Mr. Goodman claim that his evaluations are significantly different than the History Department's?

Answers

It cannot be concluded that there is a statistically significant difference between Mr. Goodman’s evaluations and the History Department’s

H₀: There is no difference in Mr. Goodman’s evaluations and the History Department’s

H: there is a significant difference between Mr. Goodman’s evaluations and the History Department’s

Applying chi-square test

relative  observed Expected residual Chi-square

1's 0.100 11.000 12.500 -0.42 0.180

2's 0.150 14.000 18.750 -1.10 1.203

3's 0.340 47.000 42.500 0.69 0.476

4's 0.410 53.000 51.250 0.24 0.060

total 1.000 125 125   1.9196

test statistic  X²=1.9196

p-value =0.5893

Hence it cannot be concluded that there is a statistically significant difference between Mr. Goodman’s evaluations and the History Department’s as we fail to reject the null hypothesis.

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PLEASE ANSWER
ANSWER!!!!!!!
This scatter plot shows the number of magazines checked out and the number of books checked out.

Choose the statement that is best supported by the data in the scatter plot.
The data shows a negative linear association between the number of magazines checked out and the number of books checked out.
The data shows a negative linear association between the number of magazines checked out and the number of books checked out.

The data shows a positive linear association between the number of magazines checked out and the number of books checked out.
The data shows a positive linear association between the number of magazines checked out and the number of books checked out.

The data shows a non-linear association between the number of magazines checked out and the number of books checked out.
The data shows a non-linear association between the number of magazines checked out and the number of books checked out.

The data shows no apparent association between the number of magazines checked out and the number of books checked out.

Answers

The data shows a negative linear association between the number of magazines checked out and the number of books checked out.

What is Graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Scatter plots are used to plot data points on a horizontal and a vertical axis in the attempt to show how much one variable is affected by another.

If one variable tends to increase as the other decreases, the association is negative.

By observing the scaterplot we understand that the value is decreasing as the other value is increasing.

Hence, The data shows a negative linear association between the number of magazines checked out and the number of books checked out.

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the mean water temperature downstream from a discharge pipe at a power plant cooling tower should be no more than 100°f. assume the water temperature is approximately normally distributed with standard deviation of 2°f. the water temperature is measured on nine randomly chosen days, and the sample average of those nine temperatures is found to be 98°f. (a) is there sufficient evidence in the sample data to support the claim that the mean water temperature is not acceptable at α

Answers

A) Yes , there is there sufficient evidence in the sample data to support the claim that the mean water temperature is not acceptable at α.

Hypothesis test for the given  population mean :

The claim is that the mean water temperature is significantly below 100 °F.

Then, the null and alternative hypothesis are:

H0 : Ц = 100

H1 : Ц < 100

The significance level is 0.05.

The sample has a size n=9.

The sample mean is M=98.

The standard deviation : σ=2

Standard error = 0.667

Z = -3

Therefore,  P-value (0.001) is smaller than the significance level (0.05)

The null hypothesis is rejected.

The hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error is known as null hypothesis.

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PLEASE HELP WITH THIS PICTURE IM STUCK

Answers

Answer:

A. The plane will travel 1180 miles in 10 hours

B. The plane is traveling at a rate of 118 miles per hour

Step-by-step explanation:

Step 1: Divide 590 by 5 to get how many miles it travels in 1 hour

    1. 590/5 = 118 miles per hour

Step 2: Multiply 118 by 10 to get how many miles it travels in 10 hours

    2. 118 ∙ 10 = 1180 miles per 10 hours

license plates in a country far away consist of 2 letters followed by 4 digits (0-9). if the only restriction is that plates can not have the same digit 4 consecutive times, how many plates are possible? (so sw-4444) is not allowed by (sw-4443) is

Answers

As per the given probability, there are 6760000 number of plates number are possible.

Probability:

In math, probability means the possibility of favorable outcome.

Given,

License plates in a country far away consist of 2 letters followed by 4 digits (0-9). if the only restriction is that plates can not have the same digit 4 consecutive times,

Here we need to find how many plates are possible.

Here we have given that, A license plate composed of 2 letters followed by 4 digits.

The first step is considering the letters in the plate.

Here we know that, the plate consists of 2 letters.

And in alphabets, we have 26 letters which start from A to Z.

Therefore, we can choose 2 letters from 26 letters in 26² ways.

Now, we considering the digits in the plate.

Here the plate consists of 4 digits.

And we have 10 digits which starts from 0 to 9.

Now we can choose 4 digits from 10 digits in 10⁴ ways.

Therefore, the number of possible plates is

=> 26² × 10⁴

=> 676 x 10000

=> 6760000

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Two quantities vary inversely. If the value of the first is 15 when the value of the second is 18, find the value of the second quantity when the first is 10. 8 1/3 12 27.

Answers

Using the inverse proportion formula, the value of the second quantity y in the question is (D) 27.

What is inverse proportion?

One kind of proportionality relationship is inverse proportion.

If two quantities are inversely related, one will increase while the other will decrease.

Building a wall would be an example of an inverse proportion in action.

On the other hand, in indirect or inverse proportion, if one quantity rises, the other one falls, and vice versa.

So, the value of the second quantity will be:

The formula for inverse proportion:

y = k/x ...(1)

Pur x = 15 and y = 18 in (1) as follows:

15 = k/15

× 15 on both sides:

15 × 15 = k/15 × 15

k = 270

Now, obtain y as follows using the same process:

Let, x = 10 and k = 270:

y = k/x

y = 270/10

y = 27

Therefore, using the inverse proportion formula, the value of the second quantity y in the question is (D) 27.

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Complete question:
Two quantities vary inversely. If the value of the first is 15 when the value of the second is 18, find the value of the second quantity when the first is 10.

a. 8

b. 1/3

c. 12

d. 27.

Answer:

27

Step-by-step explanation:

odyssey

a racecar travels around an oval track. let d represent the distance driven by the racecar (in meters) from the starting line, and let t represent the number of seconds since the racecar left the starting line. the function f , defined by the formula f ( t )

Answers

Race car track I don’t know

Determine the range of the following graph

Answers

Answer: R: yE[-8,7]

Step-by-step explanation:

Shera is building a cabinet. She is making wooden braces for the corners of the cabinet. Find the surface area of each brace.

Answers

The surface area of each brace of the cabinet is 30 square inches

What is the surface area of each brace?

length = 3 inWidth = 3 inHeight = 1 in

Surface area of the first brace = 2 (lh +wh + lw )

= 2{(3×1) + (3 × 1) + (3 × 3)}

= 2(3 + 3 + 9)

= 2(15)

= 30 square inches

Surface area of the second brace = 2 (lh +wh + lw)

= 2{(3×1) + (3 × 1) + (3 × 3)}

= 2(3 + 3 + 9)

= 2(15)

= 30 square inches

Total surface area of the cabinet = Surface area of the first brace + Surface area of the second brace

= 30 square inches + 30 square inches

= 60 square inches

Consequently, the total surface area of the cabinet is 60 square inches

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WILL GIVE BRAINLEST! AND 20 POINTS!

Answers

Answer:

i need the points

Step-by-step explanation:

idek

Answer: Choice B.

The relationship is not proportional. The number of water bottles that are thrown away Increases from month to month than the number of water bottles that are recycled.

Choose the expression that is equivalent to 8-^10/(8^4)(8^0)

1/8^14

8^14

- 1/8^14

- 8^14

Answers

The expression 1/8¹⁴ is equivalent to 8⁻¹⁰ / (8⁴)(8⁰). The 1st option is the answer

How to determine the expression that is equivalent to 8⁻¹⁰ / (8⁴)(8⁰)?

Index ( plural indices) is the power or exponent which is raised to a number or a variable e.g in number 3⁵, 5 is the index of 3.

Given: the expression 8⁻¹⁰ / (8⁴)(8⁰)

8⁻¹⁰ / (8⁴)(8⁰) can be written as:

8⁻¹⁰ / (8⁴)(8⁰) = 8⁻¹⁰ / (8⁴)(1)          (Note: 8⁰ = 1)

                     = 8⁻¹⁰ / 8⁴               (Note:  1/8⁴ = 8⁻⁴  )

                     =  8⁻¹⁰ × 8⁻⁴

                     = 8⁻¹⁰ ⁺ ⁻⁴

                     = 8⁻¹⁴

                    = 1/8¹⁴

Thus, 1/8¹⁴ is the equivalent to 8⁻¹⁰ / (8⁴)(8⁰)

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In parallelogram wxyz, what is cy? 11 ft 15 ft 21 ft 23 ft

Answers

The CY in the given Parallelogram WXYZ is 15 ft.

A parallelogram is defined as, "A geometrical figure whose sides are parallel to each other. "
In the given Parallelogram WXYZ, the length of the sides is not given. Although, the length of the two diagonal sides is given which are CY and CW with a variable x. The following are the values of these two diagonals:
CY = (2x -  7) ft                  .....(1)
CW = (x + 4) ft                   ......(2)

In this given question, we need to find the value of CY. So, we can find the value of CY by finding the value of variable x.

To find the value of x, we follow the theorem:
"In the parallelogram, The diagonals bisect each other"
We get that,
CY = CW                       ......(3)
By putting the value equation (1) and (2) in equation (3), we get
2x - 7 = x + 4                    ......(1)
By subtracting 'x' and adding '7' on both sides of the equation.
x = 11,
So we get,

x = 11.
By putting the value of 'x' in equation (1), we get:

CY  = 2(11) - 7 =  11 - 7
CY = 4.

Hence, the value of CY is 4.

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At breakfat diner a cup of coffee cot$2. 75 and a muffin i $3. 25. What i the ale tax on the two item if the rate i 7. 5%?

Answers

The sales tax on both muffin and cup of coffee at breakfast dinner is $0.45.

Define the term sale tax?The government levies a consumption tax known as a sales tax on the purchase of merchandise and services. At the point of purchase, a standard sales tax is imposed, collected by the shop, and paid to the government. You must also pay sales tax, which is calculated as a percentage of both the selling price of the items and services you buy.

As the stated question-

A muffin was $3.25 and A cup of coffee cost $2.75 7. 5% is the rate at the breakfast eatery.

Thus,

Total cost = $3.25 + $2.75

Total cost = $6.00

Sales tax = 7.5% of $6.00

Sales tax = 7.5 x 6.00 / 100

Sales tax = $0.45

Thus, the sales tax on both muffin and cup of coffee at breakfast dinner is $0.45.

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The correct question is-

At breakfast diner a cup of coffee cost $2. 75 and a muffin s $3. 25. What is the sale tax on the two item if the rate is 7. 5%?

FILL IN THE BLANK. Fill in the blank: A data analyst uses _____ to decide which data is relevant to their analysis and which data types and variables are appropriate.

Answers

Answer:

statistical methods

Step-by-step explanation:

Data analyst uses to "Database organization" to decide which data is relevant to their analysis and which data types and variables are appropriate.

What is database organization ?

A database is a structured information collection that is often kept electronically in a computer system. Typically, a database management system is in charge of managing a database (DBMS).

It is a system, frequently abbreviated to just database, is the collective term for the data, the DBMS, and the applications that are connected to it.

The most popular forms of databases, today usually describe their data in rows and columns in a collection of tables to facilitate processing and data querying.

Also the information may then be accessed, managed, changed, updated, regulated, and organized with ease. SQL is a structured query language that is used by the majority of databases to write and query data.

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with is 1+1 i want to see if dis work

Answers

Answer:

1,999,999,999,999,999,999,999,999,999,999,999$

naaaaaaa

1+1 = 0

Step-by-step explanation:

lol your answer is 2

1 + 1 = 2.

Add 1 and 1 together to get 2.

You were expecting a joke answer, weren’t ya? XD

Suppose the mean gmat score is 550 with a standard deviation of 100. Hayden takes the gmat and is told his z-score is 2. 5. Interpret the meaning of a z-score in this context.

Answers

a 2.5 z score is that, Hayden's score is 2.5 standard deviations below the 550

z-scores are used to describe normal distributions

The interpretation of a 2.5 z score is that, Hayden's score is 2.5 standard deviations below the 550

How to interpret the z-scores

The z-score is given as:

z = 2.5

The mean and the standard deviation are:

Mean = 550

Standard deviation = 100

A z-score is the number of standard deviations above or below the mean.

Hence, a 2.5 z score is that, Hayden's score is 2.5 standard deviations below the 550

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9c-18c-11c=-20 solve for c

Answers

Answer:

C = 1

Step-by-step explanation

Answer:

c = 1

Step-by-step explanation:

9c - 18c - 11c = - 20

Combine like terms.

- 20c = - 20

Divide both sides by -20.

c = 1

In baseball each time a player attempts to hit the ball it is recorded the ratio of his compared to the total Tems is there a batting average each player on the team wants to have the highest batting average to help their team the most for the season so far Jenna has hit the ball 12 times Outta 15 attempts thought I said the 19 out of 10 times which player has a ratio that means you have a better batting average?

Answers

The answer is: A) Tasha, because she has the lowest ratio since 0.75 < 0.8

Explain:

i did the test

Answer:

Step-by-step explanation:the answer is a

The box plots show the math scores of students in two different classes. Based on the box plots, which statement is correct?
A. The median score of Class A is greater than the median score of Class B.
B. The lower quartile of Class A is greater than the lower quartile of Class B.
C. The upper quartile of Class A is greater than the upper quartile of Class B.
D. The maximum score of Class A is greater than the maximum score of Class B.

Answers

Based on the box plots, the statement which is correct is that: A. The median score of Class A is greater than the median score of Class B.

What is a box and whisker plot?

In Mathematics, a box plot is also referred to as box and whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Additionally, the five-number summary of any box plot (box and whisker plot) include the following:

MinimumFirst quartileMedianThird quartileMaximum

By critically observing the box plot (box and whisker plot) which represent the math scores of students in in two different classes, we can reasonably and logically deduce the following median scores;

Median score of class A = 80

Median score of class B = 75

Therefore, a median score of 80 in Class A is greater than the median score of 75 in Class B.

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in a family with 7 ​children, excluding multiple​ births, what is the probability of having 3 boys and 4 girls

Answers

The probability having of 3 boys and 4 girls is 33 or 0.33

what is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

solution:

Assuming 50/50 chance on boy/girl we see following outcome:

(1/2^7).

Since there is only one way you can have 3 girls, followed by 4 boys.

If you would tell the boys apart, and the girls, for instance by their names, the probability would be:

6 * (1/2)^3 *(1/2)^4 * 24.

6 Times because the girls would then have 6 orders of having been born.

24  Times because then the boys would have 24 orders of having been born.

Therefore, The probability of 3 boys and 4 girls is 33 or 0.33

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A researcher is attempting to determine which ethnic group is more likely to go to the movies at a movie theatre. The dependent variable is metric. Which of the following tests is most appropriate?
analysis of variance

Answers

The correct answer is analysis of variance.

Given that,

Which ethnic group visits movie theaters most frequently That is the question being asked by a researcher. Metric is the dependent variable.

To find :  Which of the following tests is most appropriate

What is ANOVA ?

Analysis of variance (ANOVA) is a statistical technique for examining variations in means. It consists of a number of statistical models and the estimating techniques they require. The statistician Ronald Fisher is credited with creating the ANOVA. According to the law of total variance, which is the foundation of ANOVA, the observed variance in a given variable is divided into components that can be attributed to various causes of variation. ANOVA generalizes the t-test beyond two means by offering a straightforward statistical test for the equality of two or more population means. In other words, the ANOVA is employed to compare two or more means.

Therefore, the correct answer is analysis of variance.

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Find the real solution(s) of the equation. Round your answer to the nearest hundredth. 12x^4 = 78​

Answers

Answer:

x = 4√104/2

Step-by-step explanation:

Find:
11/3÷2/3
the question is five and

Answers

Answer:11/2Step-by-step explanation:KCF (Keep Change Flip):

We keep the first number 11/3, change ÷ to ×, and flip 2/3 to 3/2:

11/3 x 3/2 = 33/6

Simplify:

33/6 ÷ 3/3 = 11/2

Solution:11/2

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

suppose that you have 440 feet of rope and want to use it to make a rectangle. what dimensions should you make your rectangle if you want to enclose the maximum possible area?

Answers

The maximum possible area is 110 x 110 feet

What is area ?

Area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

The term "area" refers to the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its width.

440/4 = 110 x 110 feet

the biggest area is with a square.  A square has 1/4  dimensions for each side. with 1/4 of the total perimeter. 1/4 of 440 is 110 feet.

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an infant is brought to the emergency department with poor skin turgor, weight loss, lethargy, and tachycardia. this is suggestive of: group of answer choices dehydration calcium excess overhydration sodium excess what is the most important reason for starting intravenous infusions in the upper extremities rather than the lower extremities of adults? determine the area under the standard normal curve that lies to the right of the z-score 0.11 and to the left of the z-score 0.41. How do parents have kids Select all the inequalities that can be solved using only the Addition Property of Inequality. A. w 4 > 10 B. 12 20x C. 7y/10 5.5 D. 3.25 < x 9.75 E. z 1/2 9.8 the nurse is monitoring a patient who sustained an open fracture of the left hip. what type of shock should the nurse be aware can occur with this type of injury? what is the term for an observable phenomenon in nature that is widely supported with empirical evidence; it tells us something happens, but not the why or how? massachusetts state supreme court decision in 1842 which declared that there was nothing inherently illegal in workers organizing a union or a strike the numbers 1447, 1005, and 1231 have something in common: each is a 4-digit number beginning with 1 that has exactly two identical digits. how many such numbers are there? When using the indirect method, adding a decrease in prepaid insurance to net income eliminates the effect of recording insurance expense that ______. a. moves water and solutes from the renal tubules into the peritubular capillaries b. is called secretion c. is called reabsorption d. occurs as water and solutes move from the glomerulus to the glomerular capsule. I have $270 and 10 but I need $395 and 44, how much more money do I need? Everyone is exposed regularly to ionizing radiation found in the soil, water, and air and from cosmic rays. In fact, 80% of the ionizing radiation people are exposed to comes from naturally occurring sources. Ionizing radiation can cause double-strand breaks in the DNA. Often, the DNA breaks have missing nucleotides at the broken ends. What type of repair would likely be used, and what would be the result of repairing this type of damage?A. Nonhomologous end joining would be used and would lead to properly repaired DNA.B. Direct repair would be used to join the DNA, but errors would still remain.C. Nonhomologous end joining would be used to join the DNA, but errors would still remain.D. Direct repair would be used and would lead to properly repaired DNA.C the dispensing of controlled substances has divided patients, doctors, pharmacists and law enforcement agencies as they strive to create a balance between treating legitimate chronic pain and keeping powerful pain meds out of the hands of abusers. a recent convention discussed the development of a viable strategy for pain medications. 100 points please help 4. Governments sometimes try to manipulate exchange rates in order to:a. O make their exports cheaperb. O increase interdependencec. O overcome trade restrictionsd. O make their exports more expensive poindexter is funded by a group of wealthy investors for the sole purpose of providing funding for individuals and small firms that are trying to convert their new ideas into viable products. what is this type of funding called? a beam of monochromatic light with a wavelength of 580 nm in air travels into water. what is the wavelength of the light in water? give your answer in nanometers which joint is highlighted? which joint is highlighted? sternoclavicular sternal end acromioclavicular acromion Light is refracted through a diamond. If the angle of incidence is 30, and the angle of refraction is 12, what is the index of refraction?.