Solve for rrr.
Give an exact answer.
\dfrac12r-3=3\left(4-\dfrac32r\right)
2
1

r−3=3(4−
2
3

r)start fraction, 1, divided by, 2, end fraction, r, minus, 3, equals, 3, left parenthesis, 4, minus, start fraction, 3, divided by, 2, end fraction, r, right parenthesis
r =r=r, equals

Answers

Answer 1

The solution for r in the equation is r = 3

How to determine the solution for r in the equation?

From the question, we have the following parameters that can be used in our computation:

\dfrac12r-3=3\left(4-\dfrac32r\right)

Rewrite the above expression properly, as a fraction

So, we have the following representation

1/2r - 3 = 3(4 - 3/2r)

To start with, we need to open the brackets

So, we have the following representation

1/2r - 3 = 12 - 9/2r

Next, we multiply through by 2 to eliminate the fraction

This gives

r - 6 = 24 - 9r

Solving further, we collect the like terms

So, we have

r + 9r = 24 + 6

Evaluate the like terms

10r = 30

So, we have

r = 3 --- by dividing both sides by 10

Hence, the solution is 3

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Related Questions

g assuming a linear relationship between x and y, the larger r-square value is, the larger the absolute value of the coefficient of correlation

Answers

In the domain of finance, an R-Squared value above 0.7 is typically seen as indicating a high level of correlation, whereas one below 0.4 indicates a low level of correlation.

What is correlation?

A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.

The strength of the association is measured by the sample correlation coefficient, or r. The statistical significance of correlations is also examined.

For describing straightforward links between data, correlations are helpful. Consider a dataset of campgrounds in a park in the mountains as an illustration. You're interested in finding out if the height of the campsite—how high up the mountain it is—and the summer's typical high temperature are related.

Hence, In the domain of finance, an R-Squared value above 0.7 is typically seen as indicating a high level of correlation, whereas one below 0.4 indicates a low level of correlation.

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A perfect square has length n if its last n digits (in base 10) are the same and non-zero. What is the longest possible length? What is the smallest square achieving this length?

Answers

The longest possible length is 3 uints and the smallest square achieving this length is [tex]38^2[/tex] = 1444.

All squares end in the digit 0, 1, 4, 5, 6, or 9. A square ending in 11, 66, 55, 99 would be congruent to 3, 3, 2, 3 mod 4, but squares are congruent to 1 mod 4 or 0. So for a length > 1, the square should end in 4. For example, [tex]12^2[/tex] = 144.

A square ending in 4444 would be congruent to 12 mod 16, but squares are congruent to 0, 1 mod 16, 4 mod 16, or 9 mod 16. So, the maximum length should be 2 or 3.

If [tex]n^2[/tex] ends in 4, then n should end in 2 or 8. [tex](100a + 10b + 2) ^2[/tex]= 10000[tex]a^2[/tex] + 1000 (2ab) + 100 (4a + [tex]b^2[/tex]) + 10 (4b) + 4. So, if this ends in 44, then b = 6 or 1.

If b = 1, then 4a + [tex]b^2[/tex] is odd, so the square will not end in 444. If b = 6, then the square would be 1000k + (4a + 38) 100 + 44. This would end in 444 if we take, a= 9 or 4.

Thus the smallest numbers that end in  2 and whose square ends in 444 are 462 (square 213444) and 962 (square 925444).

[tex](100a + 10b + 8)^2[/tex] = 1000k + 100 ([tex]16a^2 + b^2[/tex]) + 10 (16b + 6) + 4.

Now, if this ends in 44, then b = 3 or 8.

let us take b=3, then [tex](100a + 38)^2[/tex] = 1000k + 100 (76a) + 1444, so this ends in 444 if a = 0. Hence, this should be the smallest solution.

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problem 1. (12 points) light bulbs of a certain type are advertised as having an average lifetime of 800 hours. the price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. a random sample of 50 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested, resulting in the accompanying output: variable n mean st. dev se of mean z p-value lifetime 50 738.44 38.20 5.40 -2.14 0.016 a) what conclusion would be appropriate for a significance level of .05? b) what about at a significance level of .01? c) which significance level would you recommend? why?

Answers

the test's finding at the 5% level of significance is that the true average longevity is not less than claimed.

The following is a definition of the test's hypothesis:

H0: The actual average lifetime, which is > 750 hours, is not less than what is stated

Ha! The actual average lifespan, at 750 hours, is less than what is advertised.

The examination is left-tailed.

Making a decision:

The null hypothesis is rejected if the test's p-value is less than the significance level (), and vice versa.

The test's p-value is calculated as,

0.016 as the p-value

(a)

The level of significance is 0.05.

The p-value is equal to 0.016/0.05.

The null hypothesis was rejected since the test's p-value was lower than the threshold for significance.

Consequently, the test's finding at the 5% level of significance is that the genuine average lifetime is shorter than

(b)

The level of significance is = 0.01.

The p-value is equal to 0.016 > = 0.01.

The null hypothesis could not be rejected since the p-value of the test was greater than the level of significance.

Therefore, the test's finding at the 5% level of significance is that the true average longevity is not less than claimed.

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What is the correct factorization of the following quadratic expression: x² - 7x - 60
a. (x-12) (x + 5)
b. (x+12) (x - 5)
c. (x-10) (x+6)
d. (x+10) (x-6)

Answers

a is the correct answer

What is the slope of a line perpendicular to the line whose equation is 6x+y=-5

Answers

Answer:

It would have a slope of a positive 6x

Step-by-step explanation:

Since the slope of the equation shown is -6x, we would just find the opposite which is -6x

what is the common ratio for this geometric sequence? 3,12,48,192

Answers

Answer: r=4

Step-by-step explanation:

12/3 = 4

48/3 = 4

192/48 = 4

You and a friend start running from the same location. Your distance d (in miles) after t minutes is d(t) = ⅕t. Your friend starts running 10 minutes after you. Your friend's distance f is given by the function f(t) = d(t - 10). Describe the transformation from the graph of d to the graph of f.

Answers

Answer: 23

Step-by-step explanation:

Answer: 23

Step-by-step explanation:

Matt's Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon,
the cafe sold 50 espressos in all, 24 of which were single-shot. What percentage of the
espressos were single-shot?

Answers

Answer: 48%

Step-by-step explanation:

scale up,

24/50=x/100

multiply 24/50 by 2 to get 100

so you get 48/100 which is 48%

Answer:

57 I think I'm not entirely sure

after constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. in order to correct this problem, you need to:

Answers

By using the concept of confidence interval, it can be concluded that-

To reduce confidence interval, it is needed to increase sample size.

Option c is correct

What is confidence interval?

Suppose there is an unknown parameter whose range of estimate is required. Confidence interval gives the range of estimate of this unknown parameter.

Formula for percentage confidence interval

[tex]\bar{x} \pm z_\frac{\alpha}{2} \times \frac{\sigma}{\sqrt{n}}[/tex]

We have to reduce the size of the confidence interval

Confidence interval has no effect on  mean, directly proportional to  standard deviation and inversely proportional to sample size

So to reduce confidence interval, it is needed to increase sample size.

Option c is correct

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Complete Question

After constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. in order to correct this problem, you need to:

Select one:

a. increase the population standard deviation

b. increase the level of confidence

c. increase the sample size

d. increase the sample mean

e. none of these would help

3 2/3 divided by 2/5

Answers

Answer:

9 1/6

Step-by-step explanation:

3 2/3 divided by 2/3

First convert 3 2/3 into a whole number

3 2/3 = 11/3

11/3 x 2/3 = 55/3

55/3 into a mixed number is 9 1/6

On a print-out of these slope fields, sketch for each three solution curves to the differential equations that generated them. Then complete the following statements: For the slope field in figure 1. a solution passing through the point (0.-1) has slope. For the slope field in figure 1. a solution passing through the point (-2.2) has slope. For the slope field in figure 2. a solution passing through the point (1.-3) has slope For the slope field in figure 2. a solution passing through the point (0.4) has a slope.

Answers

Therefore solution to this question is slope at (0,-1) is negative at (-2,2) is negative at (1,-3) is negative & (0,4) is also negative.

What is slope field?

A slope field, which displays the slope of a differential equation along specific vertical and horizontal axes of the x-y plane, can be used to estimate the tangent slope at a particular point on a curve, where the curve is one possible solution to the differential equation.

Here,

For figure 1 slope field=

[tex]\frac{dy}{dx}=\frac{-17x-2y}{y}[/tex]

For figure 2 slope field=

[tex]\frac{dy}{dx} = xy-3\\[/tex]

For figure 1 a solution passing through the point (0,-1)

therefore,

slope=

[tex]\frac{dy}{dx}=\frac{-17x-2y}{y}\\\frac{dy}{dx}=\frac{-17(0)-2(-1)}{-1}=-2[/tex]

so slope comes out to be negative

For figure 1 a solution passing through the point (-2,2)

[tex]\frac{dy}{dx}=\frac{-17x-2y}{y}\\\frac{dy}{dx}=\frac{-17(-2)-2(2)}{-1}=-30[/tex]

so slope comes out to be negative

For the slope field in figure 2. a solution passing through the point (1.-3)

[tex]\frac{dy}{dx} = xy-3\\\\\frac{dy}{dx}=(1*-3)-3=-6[/tex]

so slope comes out to be negative

[tex]\frac{dy}{dx} = xy-3\\\\\frac{dy}{dx}=(0*4)-3=-3[/tex]

so slope comes out to be negative.

Therefore solution to this question is slope at (0,-1) is negative at (-2,2) is negative at (1,-3) is negative & (0,4) is also negative.

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A customer leaves a tip of $3.00 on a $20 meal. At the same rate, what tip would they
leave for a $50 meal? What is the percentage the customer is leaving for a tip?

Answers

Answer: $7.5 tip

Step-by-step explanation:

divide 3 an 20 then get 0.15

then multiply 0.15 to 50 get 7.5

Tommy earned $62.40 in interest after 4 years on a principal of $400. His simple interest rate is 3.9%. Jane
earned $66.60 in interest after 3 years on a principal of $600. Her simple interest rate is 3.7%. Which bank would you rather
use, Tommy's or Jane's? Explain your reasoning.

Answers

Answer:

I would rather use Jane's bank because she earned more interest in a shorter amount of time. Jane's bank has a higher simple interest rate of 3.7%, which means she earned more money in a shorter amount of time than Tommy did with his 3.9% rate.

hi help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

a=3/4

Step-by-step explanation:

1) add 1/6 on both sides

-> 2/3a= 1/3+1/6

->2/3a = 1/2

2) isolate a by multiplying 3/2 on both sides

-> 2/3 x 3/2 a = 1/2 x 3/2

-> a=3/4

if you mix 3 ounces of blue paint and 2 ounces of yellow paint and decided to make 20 ounces how much of the yellow paint will there be?

Answers

8 ounce of yellow color required.

What is Ratio?

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two quantities of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol. As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

if you mix 3 ounces of blue paint and 2 ounces of yellow paint.

So, we have the composition ratio as 2:3

Then, to make 20 ounce paint 2/5 of the 20 ounces will be yellow paint, and the other 3/5 will be blue needed.

Thus, yellow = 2/5 x 20= 8 ounce

Blue= 3/5 x20 = 12 ounce

Hence, 8 ounce of yellow color required.

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Factorize a²+ b²-c²-d² - 2ab-2cd​

Answers

Answer:

(a-b+c+d)(a-b-c-d) answer of the following questoin

HELP…I SELECTED YES AND UHH YUP

Answers

Answer: 86.8 dollars per month

What are the next two numbers in this sequence? 0, 1, 3, 6, 10, ___, ___

A. 17, 25
B. 15, 21
C. 16, 23
D. 14, 19

Answers

Answer:

b

Step-by-step explanation:

your answer is b to be precise

the answer is b up by 5 then up by 6 the number rises by 1

Samuel has been planting young trees in her garden. The maple tree that is 125 centimeters tall is growing 3 centimeters per month, whereas the oak tree that is 83 centimeters tall is growing 10 centimeters per month. In a few months, the two trees will be the same height. What will that height be? How long will that take?

Answers

It will take 6 month to reach the same height for both maple tree and oak tree.

Explain the term rate of growth?

the country, region, or geographic area's yearly average rate of change in population size over a certain time period.

The given data is -

Present height of maple tree = 125 cmRate of growth = 3 centimeters per month.Present height of oak tree = 83 cmRate of growth of oak tree = 10 centimeters per month.

Let the number of months when both will have the same height be 'x'.

Thus,

For maple tree,the final height be-

125 + 3x

For oak tree,the final height be-

83 + 10x

Equating both

125 + 3x = 83 + 10x

7x = 125 - 83

7x = 42

x = 6 months

Thus, it will take 6 month to reach the same height for both maple tree and oak tree.

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a study of 20 worldwide financial institutions showed the correlation between their assets and pretax profit to be 0.86. 1. state the decision rule for 0.05 significance level: h0: rho ≤ 0; h1: rho > 0 (round your answer to 3 decimal places.) 2. compute the value of the test statistic. (round your answer to 2 decimal places.) 3. can we conclude that the correlation in the population is greater than zero? use the 0.05 significance level.

Answers

The decision rule is reject H(0) if t>1.714, test statistic t is 7.157 and Yes, we can conclude that the correlation in the population is greater than zero.

In the given question,

A study of 20 worldwide financial institutions showed the correlation between their assets and pretax profit to be 0.86.

n=20, r = 0.86

The decision rule for α=0.05 significance level:

H(0): P ≤ 0

H(1): P > 0

Degree of freedom(df) = n-2

Degree of freedom(df) = 20-2

Degree of freedom(df) = 18

This is the right tailed test using the t table.

Critical Value: [tex]t_{\alpha /2}[/tex], df = [tex]t_{\alpha /2}[/tex] = 1.714

(a) The decision rule is reject H(0) if t>1.714.

(b) Test statistic is t

t= r√(n−2)/√(1–r^2)

t= 0.86*√(20 -2)/√(1-(0.86)^2)

t= 0.86*√18/√(1-0.7396)

t= 0.86*4.243/√0.2604

t= 3.65/0.51

t= 7.157

Test statistic = 7.157

(c)  We have to conclude that the correlation in the population is greater than zero.

Yes, we can conclude that the correlation in the population is greater than zero.

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the telephone lines serving an airline reservation office are all busy about 60% of the time. a if you are calling this office, what is the probability that you will complete your call on the first try? the second try? the third try? b if you and a friend must both complete calls to this office, what is the probability that a total of four tries will be necessary for both of you to get through?

Answers

The probability that a total of four tries will be necessary for both of you to get through is 0.1728.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

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calculate 1001 base two +1011 base two​

Answers

Answer: 10100 base two

The odds in favor of Michael Jordan making a free throw were 21:4. Find the probability of Michael Jordan missing a free throw.

Give answer as a decimal rounded to the nearest hundredth.

Answers

The probability that he will miss is 25%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

The odds in favor of Michael Jordan making a free throw were 21:4.

Total number of throw is 21+4 = 25

The number of time he will miss is 4

So the probability that he will miss is 4/25 = 0.25

Hence, the probability that he will miss is 25%.

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ASAP!!

define: A formula to calculate Average Rate of Change over the interval, x [x1, x2].

Answers

divide the change in y-values by the change in x-values.

question the range for a list of measurements equals the greatest measurement minus the least measurement. the two lists of measurements, x and y , combined consist of 30 measurements with a range of 25. what is the range for the measurements in list x ? (1) the range for the 12 measurements in list y is 20. (2) list x consists of 18 measurements.

Answers

The statements are insufficient to answer the question.

What is measurement?

Measurement is the quantification of an object's or event's attributes for comparison with other objects or events. Measurement, in other words, is the process of determining how large or small a physical quantity is in comparison to a basic reference quantity of the same kind.

So we are given 2 lists, x and y and we are given the

1.  The total number of measurements is 30. x(n) + y(n) = 30.

2. Largest measurement - Smallest Measurement = 25

But we are not told the number of measurements in either x or y. We also don't know whether the largest of smallest measurement of the combined range belongs to x or y.

We need to find the largest measurement of x and the smallest measurement of x for our answer.

1)The range for the 12 measurements in list y is 20.

Okay so we know that y has 12 measurements, therefore x has 18. And we know the y(largest) - y(smallest) = 20 INSUFFICIENT

2) List x consists of 18 measurements.

We are told that x consists of 18 elements. We already figured this out in Statement 1 as well. It again does not tell us anything further. INSUFFICIENT DATA

Hence, the statements are insufficient to answer the question.

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an information technology company claims that a certain model of laptops have mean battery capacity of 5 hours. a consumer report firm wants to show that the actual mean is smaller than the company claims. what should be the null and alternative hypotheses?

Answers

The null and alternative hypotheses are-

Null hypothesis H₀; μ ≤ 9Alternative hypothesis Hₐ: μ > 9Explain the formulation of Hypotheses?

The null and alternate hypothesis must be formulated as two opposed and mutually excluding hypotheses for hypothesis testing.

This alternative hypothesis is a statement that contradicts the null and is the assertion that a sample research seeks to demonstrate. This null hypothesis can be accepted that represents the declaration of equality, the generally accepted presumption about the population.The intended relationship between the variables must be stated first. In order for researchers to determine whether such a hypothesis is true or untrue, it must also be able to be tested and falsified. Third, it must be consistent the with corpus of information already in existence. Last but not least, it should be said as briefly and simply as possible.

A specific laptop model's battery has a typical life of more than 9 hours, according to the claim.

For this assertion, we form:

Null hypothesis H₀; μ ≤ 9

Alternative hypothesis Hₐ: μ > 9

The assertion is represented by the alternative hypothesis in this right-tailed test.

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She was the first swimmer to cross the
between the two countries.

If you want your complaint to be addressed, you need to go through the appropriate
.

Answers

Answer:

Step-by-step explanation:

The word ‘channel’ has multiple meanings which can be discerned based on the context.

What is the thesaurus entry for the channel?

According to the thesaurus, as a noun, the word channel has two meanings. They are-

A pathway that contains water - here the channel is a strait or a small stream of water. The synonyms of the word, in this case, would be - avenue, carrier, route, and tunnel.

A means to achieve something- The synonyms, in this case, are the instrument, medium, and vehicle.

As a verb, the word channel means to direct or to convey something. Thus the synonyms would be to carry and to transmit.

How is ‘channel’ used in the contexts above?

In the sentences above the word, 'channel' is used as follows

She was the first swimmer to cross the channel between the two countries.- Here, the channel is a water body.

If you want your complaint to be addressed, you need to go through the appropriate channel.- Here, the channel is a medium or a route.

someone please help, thank you.

Answers

Step-by-step explanation:

it seems the questions 8., 9. and 10. demonstrate exactly what is the asked via variables in 11., 12. and 13.

you only need to apply the principles of equal angles of crossing lines again.

11.

to be parallel

50 + (x + 30) = 180

x + 80 = 180

x = 100.

12.

135 = 2y + 15

120 = 2y

y = 60

13.

70 = 4x - 10

4x = 80

x = 20

14.

yes, because

142 + 38 = 180°

15.

yes, because

112 + 68 = 180°

16.

no, because

146 + 44 = 190° <> 180°

17.

to be parallel, angle 1 = angle 2

88 = 2x

x = 44

18.

to be parallel, angle 1 = angle 3

88 = 2x + 10

2x = 78

x = 39

what is the answer for shrinking 6x-2(x-3)

Answers

Answer:

  4x +6

Step-by-step explanation:

You want the simplified form of 6x -2(x -3).

Simplify

Generally, the first step in simplifying an expression is elimination of parentheses. This is done using the distributive property.

  6x -2(x -3) = 6x -2x -2(-3) = 6x -2x +6

Then, like terms can be combined:

  6x -2x +6 = (6 -2)x +6 = 4x +6

The simplified expression is 4x +6.

__

Additional comment

We notice the terms have a common factor of 2, so we can use the distributive property to factor that out:

  = 2(2x +3)

This form may be useful in some circumstances, but is generally not considered to be the simplified form.

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What is the common difference between successive terms in the sequence? 0.36, 0.26, 0.16, 0.06, -0.04, -0.14, ...​

Answers

Answer:

0.36

0.26

0.16

0.06

the answers doesn't come in -

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Click on 'Surplus' and then click anywhere on the graph. Click and drag the endpoints of the triangle to show the total of consumer surplus and producer surplus at the original price and quantity. Next, use the tool 'Surplus2' in the graph on the right to identify the long-run surplus after the changes in market demand and supply. Use the same process as before to show the total of consumer surplus and producer surplus in long-run equilibrium. $120 $120 $100 o' $100 s , $ $80 Price Price $60 D 20 60 80 100 120 20 40 60 80 Quantity Quantity calculate the energy of a photon emitted when an electron in a hydrogen atom undergoes a transition from ???? how does your educational philosophy apply to your practice or beliefs of teaching (instructional models)? if the pressure reading of your pitot tube is 12.0 mm hg at a speed of 210 km/h, what will it be at 830 km/h at the same altitude? assume the density of air at sea level. what would be the most effective strategy to learn and retain a list of names of key historical figures for a week? for a year? Write a loop that inputs words until the user enters DONE. After each input, the program should number each entry and print in this format:#1: You entered _____When DONE is entered, the total number of words entered should be printed in this format:A total of __ words were entered.Sample RunPlease enter the next word: cat#1: You entered the word catPlease enter the next word: iguana#2: You entered the word iguanaPlease enter the next word: zebra#3: You entered the word zebraPlease enter the next word: dolphin#4: You entered the word dolphinPlease enter the next word: DONEA total of 4 words were entered. A nonrelativistic electron and a nonrelativistic proton have the same de Broglie wavelength. Which of the following statements about these particles are accurate? (There may be more than one correct choice.)A) Both particles have the same speed.B) The electron has more momentum than the proton.C) The electron has more kinetic energy than the proton.D) Both particles have the same kinetic energy.E) Both particles have the same momentum. According to the Declaration of Independence, what right do people have over government? you manage a blog that has a few contributing authors. what could you use to report the name of the author on each article page? I WILL OPEN MY ALT AND ANSWER AND GIVE YOU A BRINLIST OPEN IF YOU SHOWED YOUR WORK!!! OPEN THE IMAGE 34)on july 8, a fire destroyed the entire merchandise inventory on hand of larrenaga wholesale corporation. the following information is available: 243 divided by 15 and I need to show my work In snapdragons, the allele for red flower color (CR) is incompletely dominant to the allele for white flower color (CW). Snapdragons that are heterozygous for flower color have a pink phenotype.Which of the following crosses could yield all three flower color phenotypes (red, white, and pink) among the offspring?A. CROR CWCWC. CROW CROWB. CRCR CROWD. CROW CW CW