Is the sequence {81, 27, 9, 3, 1, …} arithmetic or geometric?

Answers

Answer 1

Answer:

Geometric

Step-by-step explanation:

That is a geometric sequence, because the each number divided into 3. As we know if the pattern are multiply or divided it will be geometric, if it is sum or subtract will be arithmetic.

hope this helps

if u have question let me know in comments

Answer 2

The given sequence is geometric. The common ratio of the geometric sequence is 1/3.

What is geometric progression?

A geometric progression (G.P.) is a sort of sequence in which each successive term is obtained by multiplying the prior term by a set number known as a common ratio.

This progression is also known as a pattern-following geometric sequence of integers.

The given sequence in the problem is;

81, 27, 9, 3, 1, …

Due to the fact that each number is split into three, that sequence is geometric. The pattern will be geometric if it is multiplied or divided, and arithmetic if it is the result of addition or subtraction.

The common ratio of the sequence is found as;

[tex]\rm r = \frac{27}{81} =\frac{9}{27} =\frac{3}{9} =\frac{1}{3} =\frac{1}{3}[/tex]

The common ratio of successive terms is equal.

Hence, the given sequence is geometric.

To learn more about the geometric progression, refer to https://brainly.com/question/14320920.

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Related Questions

Solve this and I’ll give u 5 stars and brainleist

Answers

Answer:

notice: temperature rises quickly at sunrise, and drops before sunsetwonder: whether this location is shaded by mountains later in the day

Step-by-step explanation:

notice

The temperature starts off below zero in the early morning and stays cold until the sun comes up. Then it warms rapidly to an above zero temperature that peaks in early afternoon. Once the sun gets lower, the temperature starts cooling off again. (The daily temperature range of 25-27 degrees is pretty typical for partly-cloudy sky conditions and stable weather.)

wonder

We wonder if this isn't a location that is on the east- or north-side of a mountain, or in a mountain valley, where the sun hits it early and is shaded later in the day. (The topo map attached seems to show it is in such a location.)

Plzz help i really need help..

Answers

Answer:

D. neither.

Step-by-step explanation:

A function is when one x-value only has one corrisponding y-value.

The answer it's D. Neither

Test the claim that the proportion of people who own cats is significantly different than 80% at the 0.2 significance level. The null and alternative hypothesis would be:______.
A. H0 : μ = 0.8 H 1 : μ ≠ 0.8
B. H0 : p ≤ 0.8 H 1 : p > 0.8
C. H0 : p = 0.8 H 1 : p ≠ 0.8
D. H0 : μ ≤ 0.8 H 1 : μ > 0.8
E. H0 : p ≥ 0.8 H 1 : p < 0.8
F. H0 : μ ≥ 0.8 H 1 : μ < 0.8
The test is:_____.
a. left-tailed
b. right-tailed
c. two-tailed
Based on a sample of 200 people, 79% owned cats.
The test statistic is:______.
The p-value is:_____.
Based on this we:_____.
A. Fail to reject the null hypothesis.
B. Reject the null hypothesis.

Answers

Answer:

C. H0 : p = 0.8 H 1 : p ≠ 0.8

The test is:_____.

c. two-tailed

The test statistic is:______p ± z (base alpha by 2) [tex]\sqrt{\frac{pq}{n} }[/tex]

The p-value is:_____. 0.09887

Based on this we:_____.

B. Reject the null hypothesis.

Step-by-step explanation:

We formulate null and alternative hypotheses as  proportion of people who own cats is significantly different than 80%.

H0 : p = 0.8 H 1 : p ≠ 0.8

The alternative hypothesis H1 is that the 80% of the  proportion is different and null hypothesis is , it is same.

For a two tailed test for significance level = 0.2 we have critical value  ± 1.28.

We have alpha equal to 0.2  for a two tailed test . We divided alpha with 2 to get the answer for a two tailed test. When divided by two it gives 0.1 and the corresponding value is ± 1.28

The test statistic is

p ± z (base alpha by 2) [tex]\sqrt{\frac{pq}{n} }[/tex]

Where p = 0.8 , q = 1-p= 1-0.8= 0.2

n= 200

Putting the values

0.8 ± 1.28 [tex]\sqrt{\frac{0.8*0.2}{200} }[/tex]

0.8 ± 0.03620

0.8362, 0.7638

As the calculated value of z lies within the critical region  we reject the null hypothesis.

I cant seem to get the second one right...

Answers

Rx=1 means to reflect the given point on the line of x= 1

The mapping for the reflection on line x is x = k

(-2,7) = (-2(1) - -2,7) = (4,7)

The missing value is 7

A helicopter is at a cruising height of 1,200 feet. Suppose the angle of depression to the landing pad is 15°, which is located on top of a building that is 64 feet high. If the helicopter continues at the current cruising height, how far does the helicopter need to travel to be directly above the landing pad? Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the answer rounded to the nearest foot.

Answers

Answer:

we have a right triangle and to get the internal angle of the right triangle formed at the helicopter we subtract 62 degrees from 90 which equals 28 degrees

we now use the cosine to find the distance (d) from the helicopter

cosine 28 = 85/d

d = 85 / cosine 28 = 85 / 0.8829 = 96.2736 = 96 feet

Help please anyone. Thank You

Answers

Answer:

A) 144 yd²

Step-by-step explanation:

Base= 8x8=64

Side = 1/2*8*5=20

64+20+20+20+20=144 yd²

Answer:

168 sq yds

Step-by-step explanation:

5x8/2x2=40

8x8/2x2=64

8x8=64

40+64+64=168

A sandman earns a commission of 26%. One week he had sales of $24400. Find the commission for the week.

Answers

Answer:

6344

Step-by-step explanation:

Find 26% of 24400

24400 * 26%

24400 * .26

6344

HELP ASAP ROCKY!!! will get branliest.​

Answers

Answer:

Hey there!

The slope is -1/3, because the rise over run is -1/3.

Let me know if this helps :)

solve this equation 4log√x - log 3x =log x^2​

Answers

Answer:

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

Step-by-step explanation:

*Move terms to the left and set equal to zero:

4㏒(√x) - ㏒(3x) - ㏒(x²) = 0

*simplify each term:

㏒(x²) - ㏒(3x) - ㏒(x²)

㏒(x²÷x²) -㏒(3x)

㏒(x²÷x² / 3x)

*cancel common factor x²:

㏒([tex]\frac{1}{3x}[/tex])

*rewrite to solve for x :

10⁰ = [tex]\frac{1}{3x}[/tex]

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

1 · x = [tex]\frac{1}{3x}[/tex] · x

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

*that would be our answer, however, the convention is to exclude the "1" in front of variables so we are left with:

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

The length of the longest side of a triangle is 5 inches more than twice the length of the shortest
side, and the length of the middle side is 2 inches more than the length of the shortest side. The
perimeter of the triangle is 235 inches. So the shortest side is inches long. Type in your
numerical answer only; do not type any words or letters with your answer.

Answers

Answer:

Length of shortest side: 57

Length of medium side:59

Length of long side: 119

Step-by-step explanation:

Which algebraic expression means “three more than a number squared”? 2 n + 3 2 n minus 3 n squared + 3 n squared minus 3

Answers

the answer is n^2+3 or n squared + 3

when it says “three more” it’s implying + 3. When it says “a number squared”, we can use a variable (n) to represent any number and then square it making it n^2.

al we have to do is combine both parts to get n^2+3

The algebraic expression that means "three more than a number squared" is n² + 3, where n is the number.

What is the algebraic expression?

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The statement is given in the question, as follows:

“three more than a number squared”

The expression n² represents the square of the number, and the expression + 3 represents the addition of three more to the square of the number.

So, n² + 3 represents the value of the square of the number plus three.

Thus, the algebraic expression that represents "three more than a number squared" is n² + 3.

Learn more about the algebraic expression here :

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Find the measure of ∠BEF
Please HELP ASAP

Answers

Answer:

100°

Step-by-step explanation:

We know that angles EFD and AEF are the same as they are alternate interior angles.

We also can note that BEF and AEF are supplementary, meaning their angle lengths will add up to 180°.

So we can create an equation:

(2x + 60) + (3x + 20) = 180

Combine like terms:

5x + 80 = 180

Subtract 80 from both sides

5x = 100

Divide both sides by 5

x = 20.

Now we can use this to find the measure of BEF.

[tex]2\cdot20 + 60[/tex]

[tex]40 + 60 = 100[/tex]

Hope this helped!

Answer:

BEF = 100

Step-by-step explanation:

The angles are same side interior angles and same side interior angles add to 180 degrees

2x+60 + 3x+20 = 180

Combine like terms

5x+80 = 180

Subtract 80

5x = 100

Divide by 5

5x/5 = 100/5

x = 20

We want BEF

BEF = 2x+60

      = 2x+60

      = 2*20 +60

     = 40+60

     = 100

Suppose that two.integers from the set of 8 integrs {1,2,3....8} are chosen at random. Find the probability that i. both numbers match. ii. Sun of the two numbers picked is less than 4?

Answers

Answer: a) 0.003

b) 0.125

c) 0.047

Step-by-step explanation:

We have a set of 8 numbers {1,2,...,8}

Let's analyze each case:

a) 5 and 8 are picked. The probability here is:

In the first selection, we have two possible picks (we can pick 5 or 8), so we have two possible outcomes out of 8 total outcomes,  the probability for the first selection is:

P = 2/8 = 1/4.

Now, if one of those numbers was picked in the first selection, only one outcome is possible in this second selection, (if before we picked a 5, here we only can pick an 8, or if in the first selection we picked an 8, here we only can pick a 5.)

the probability is:

P = 1/8

The joint probability is equal to the product of the individual probabilities, so here we have:

P = (1/4)*(1/8) = 1/32 = 0.003

b) The numbers match (we draw two sixes, for example) :

In the first selection, we can have any outcome (the only requirement is that in the second selection we pick the same outcome), so the probability is:

P = 8/8 = 1

in the second selection, we can have only one outcome, so here the probability is:

P = 1/8

The joint probability is p = 1/8  = 0.125

c) The sum is smaller than 4:

The combinations are:

1 - 1  , 1 - 2  and 2 - 1

We have 3 combinations, and the total number of possible combinations is:

8 options for the first number and 8 options for the second selection:

8*8  = 64

The probability is equal to the number of outcomes that satisfy the sentence (3) divided by the total number of outcomes (64):

P = 3/64 = 0.047

A table has five bowls. None of the quantities in the bowls are prime, though the last two bowls are empty. Two of the quantities are squares, and when added to the remaining number, the sum is 21. What are the amounts in the first three bowls?

Answers

Since two of the quantities are squares and the sum of all of three is equal 21, then the possible values of those two quantities are: 1,4,9,16

Let's consider each possibility

1 and 4

21-1-4=16, but 16 is also square and there can be only two square so NO

1 and 9

21-1-9=11, but 11 is prime, so NO

1 and 16

21-1-16=4... 4 is a square ,so NO

4 and 9

21-4-9=8 , 8 is not prime and not a square, so YES

4 and 16

21-4-16=1, but 1 is a square ,so NO

9 and 16

9+16=25>21 so.. NO

Therefore, the amounts in the first three bowls are 4,8,9.

Find the sum of 1 + 3/2 + 9/4 + …, if it exists. This is infinite series notation. The answer is NOT 4.75.

Answers

Answer:

D

Step-by-step explanation:

First, this looks like a geometric series. To determine whether or not it is, find the common ratio. To do this, we can divide the second term and the first term, and then divide the third term and the second term. If they equal to same, then this is indeed a geometric series.

[tex](3/2)/(1)=3/2\\(9/4)/(3/2)=(9/4)(2/3)=18/12=3/2[/tex]

Therefore, this is indeed a geometric series with a common ratio of 3/2.

With just this, we can stop. This is because since the common ratio is greater than one, each subsequent value is going to be bigger than the previous one. Because of this, the series will not converge. Therefore, the series has no sum.

To see this more clearly, imagine a few more terms:

1, 1.5, 2.25, 3.375, 5.0625...

Each subsequent term will just increase. The sum will not converge.

Answer:

No Sum --- it doesn't exist.

Step-by-step explanation:

The partial sums get arbitrarily large--the go to infinity.

The geometric series you are trying to sum has common ratio = 3/2.

The sum of the infinite series exists only when |common ratio| < 1.

The formula for the partial sum of n terms is (r^(n+1) - 1) / (r - 1) = (1.5^(n+1) - 1) / 0.5, or in decimals instead of fraction.. i.e. 1 + 1.5 + 2.25 + 5.0525 + 25.628 + 656.840..... therefore It would take a long time but you'd be adding up forever and goes to infinity.

which operation should you perform first when evaluating the expression 3²+ 2​

Answers

Answer:

You should calculate 3² first.

Step-by-step explanation:

In PEMDAS, E (which stands for exponents) comes before A (which stands for addition) so therefore you should calculate 3² first.

Answer: Exponents is done first (evaluate [tex]3^2[/tex] first)

Explanation:

The acronym PEMDAS helps determine the order of operations

P = parenthesis

E = exponents

M = multiplication

D = division

A = addition

S = subtraction

With the expression [tex]3^2+2[/tex] we have two operations going on here: exponents and addition.

Since exponents comes before addition (E comes before A in PEMDAS), this means we evaluate [tex]3^2[/tex] first, then add later.

Please help me I’ve been struggling

Answers

Answer:

147cm³

Step-by-step explanation:

Bottom rectangular prism: 3x4x6=72

Top rectangular prism: 5x5x3=75

72+75=147cm³

The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). If q(t) = 4t³ – 1, what is p(t)?

Answers

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]q(t) = 4t^3-1\\\\(qop)(t)=q(p(t))=4\left( p(t) \right) ^3-1=4t-21\\\\p(t)^3=\dfrac{4t-21+1}{4}=\dfrac{4(t-5)}{4}=t-5\\\\p(t)=\sqrt[3]{t-5}[/tex]

Cheers.

Taking into account the definition of composite function, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].

What is composite function

The composite function is one that is obtained through an operation called composition of functions, which consists of evaluating the same value of the independent variable (x) in two or more functions successively.

In other words, a composite function is generally a function that is written inside another function. The composition of a function is done by substituting a function into another function.

Solving a composite function means finding the composition of two functions.

Function p(t)

The expression of the composite function (qp)(t) is read "p composite with q". This means that you should do the following compound function: q[p(t)].

The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). And q(t)=4t³ – 1. Then:

s(t)= q[p(t)]

4t -21= 4[p(t)]³ – 1

Solving:

4t -21 +1= 4[p(t)]³

4t -20 = 4[p(t)]³

(4t -20)÷ 4 = [p(t)]³

4t÷4 -20÷ 4 = [p(t)]³

t -5 = [p(t)]³

[tex]\sqrt[3]{t-5}=p(t)[/tex]

Finally, the function p(t) is [tex]\sqrt[3]{t-5}[/tex].

Learn more about composite function:

https://brainly.com/question/10687170

https://brainly.com/question/12396459

https://brainly.com/question/17227038

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The company charges $5 per sq ft, AND has a minimum charge of 3 sq ft per order (meaning if a customer orders something SMALLER than 3 sq ft they still are charged as if they ordered 3 sq ft, never less - but if they order something larger than 3 sq ft they just pay regularly by the sq ft). What would you charge someone who orders a piece of glass 12in X 12in

Answers

Answer:

15 dollars

Step-by-step explanation:

12 inches = 1 ft

so 12 inch by 12 inches  is 1 ft * 1 ft

1 ft* 1 ft

1 ft^2

This is smaller than 3 ft^2 so they will get charged for 3 ft^2

3 ft^2 = 3 ft^2 * $5 / ft^2 = 15 dollars

Determine whether the statement (p∧(p⟶q))⟶q is a tautology one time by using truth table and the other time without using truth table

Answers

It is.........................................................

One way to prove this without a truth table is to use a conditional proof. We assume the portion p ^ (p --> q). If that's true, then so is p and p-->q

Using p and p-->q, the modus ponens rule allows us to derive q. It says that if p is true and p --> q, then q must be true as well.

Since we arrive at q, we have found the conclusion we're after. The assumption (p ^ (p-->q)) leads to q, and therefore the entire statement (p ^ (p-->q)) --> q is true for any combination of p,q.

(3.5x10^8)x(4.0x10^-12)=

Answers

Answer:

Below

Step-by-step explanation:

● (3.5× 10^8) × (4×10^(-12))

● (3.5×4) × (10^8 × 10^(-12) )

● 14 × 10^ (-12+8)

● 14 × 10^(-4)

● 14/10^4

What Number is equivalent to 4^3
A. 7
B. 12
O C. 64
D. 81

Answers

Answer:

C

Step-by-step explanation:

4³ means 4 multiplied by itself 3 times, that is

4 × 4 × 4

= 16 × 4

= 64 → C

Suppose that 67.2% of all adults with type 2 diabetes also suffer from hypertension. After developing a new drug to treat type 2 diabetes, a team of researchers at a pharmaceutical company wanted to know if their drug had any impact on the incidence of hypertension for diabetics who took their drug. The researchers selected a random sample of 500 participants who had been taking their drug as part of a recent large-scale clinical trial and found that 317 suffered from hypertension.
The researchers want to use a one‑sample z ‑test for a population proportion to see if the proportion of type
2 diabetics who have hypertension while taking their new drug, p, is different from the proportion of all type
2 diabetics who have hypertension. They decide to use a significance level of ???? = 0.05.
A. Determine the p value for this test.
B. Determine the value of the z test statistic.

Answers

Answer: A. p-value = 0.04

              B. z = - 1.77

Step-by-step explanation: To calculate z test statistic or z-score for a population proportion, first find the proportion (p-hat):

[tex]p_{hat}[/tex] = [tex]\frac{317}{500}[/tex] = 0.634

Then determine the standard deviation:

[tex]\sigma = \sqrt{\frac{p_{hat}(1-p_{hat})}{n} }[/tex]

[tex]\sigma = \sqrt{\frac{0.634(0.366)}{500} }[/tex]

[tex]\sigma = \sqrt{0.00046 }[/tex]

[tex]\sigma[/tex] = 0.0215

Calculating z-score:

[tex]z=\frac{p_{hat}-p}{\sigma}[/tex]

[tex]z=\frac{0.634-0.672}{0.0215}[/tex]

[tex]z=-1.77[/tex]

Z-test for the population proportion is z = - 1.77

P-value is the probability describing the data if null hypothesis is true, i.e.:

P(z< -1.77)

Using z-score table, the probability is:

P(z< -1.77) = 0.04

p-value = 0.04

P-value for this test is p-value = 0.04.

2 less than five times a number.

Answers

Answer:

X will be the number.  

5 times that number X is 5X

2 less than 5 times the number is 5X - 2

Hope this helps! Plz mark brainliest! (づ ̄3 ̄)づ╭❤~

Answer

5x + 2

Step-by-step explanation:

5x + 2 or 5x - 2

Find the value of x.
A. 3
B. 9
C. 0
D. 12

Answers

Answer:

x=3

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

3x(x+1) = 4x(x)

Divide each side by x

3x(x+1)/x = 4x(x)/x

3(x+1) = 4x

Distribute

3x+3 = 4x

Subtract 3x

3x+3-3x= 4x-3x

3 =x

Answer:

x = 3

Step-by-step explanation:

0 is a rediculas answer 9 and 12 are to big.

The lines are supposed to have a simular length:

3(3) + 4 = 13

4(3) + 3 = 15

These are the best answers that fit.

which expression have a value of 2/3
A: 8+(24 divided by 12) X 4
B:8+24 divided by (12X4)
C: 8+24 divided 12X4
D: (8+24) divided (12X4)

Answers

B is the correct answer!
32 / 48 =2/3

A coin is flipped eight times where each flip comes up either heads or tails. How many possible outcomes a) are there in total

Answers

Answer:

256 outcomes.

Step-by-step explanation:

Each time you flip the coin you have two possible outcomes, it can either come up with heads or tails.

You're going to flip the coin eight times so the first time you can have 2 possible outcomes, the second time you have 2 possible outcomes, the third time you have 2 possible outcomes, etc.

Since you are going to do this eight times you are going to multiply each of the outcomes, so you will have:

Possible outcomes = 2×2×2×2×2×2×2×2= 256

Thus, there are 256 different outcomes in total.


What is the volume of a cube with a side length of
of a unit?

Answers

It’s d times it three times length width height

find the unknown angles

Answers

Answer:

y=135

x=45

Step-by-step explanation:

x= 45

It is an isosceles so

180-90=90

90/2= 45  

y=135

angles on a straight line add up to 180 so

180-45=135

Hope this helps!

The number of times a player has golfed in one's lifetime is compared to the number of strokes it takes the player to complete 18 holes. The correlation coefficient relating the two variables is -0.26. Which best describes the strength of the correlation and what is true about the causation between the variables?

Answers

Answer: It is a weak negative correlation and it is not likely causal.

Step-by-step explanation:

Given: The number of times a player has golfed in one's lifetime is compared to the number of strokes it takes the player to complete 18 holes. The correlation coefficient relating the two variables is -0.26.

Variables : "number of times a player has golfed in one's lifetime" and "number of strokes it takes the player to complete 18 holes".

Since -0.26 is more closer to 0 as compared to 1 , so it describes a weak negative correlation.

Also, it is not likely causal as number of times a player has golfed in one's lifetime not cause number of strokes it takes the player to complete 18 holes.

Answer: B) It is a weak negative correlation, and it is likely casual

Correct on edge 2020!

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A circle has (2,1). Find the coordinates of the endpoint of a diameter if one endpoint is(7,1) plz hurry thank you! What physical traits were favored in the peppered moth AFTER the Industrial Revolution? 10TIME REMAINING51:54Which statement best describes Grendel's perspective?ng, swords whonking,and doors of the meadhallEs reared and fell overbats in a fire, menng speeches, dying or, sneaking offe driven back, sometimesdown, sometimes they'dand make his people giveHe enjoys watching the violent men kill one another.O He admires the powerful weapons and strong men.O He wishes to be part of the excitement somehow.He feels disgusted by the wasteful natul of war.5.not in a way I could What is the verb?A. Wouldn't giveB. BreakC. Would give What is topographic Map? what are the challenges faced by the role of climate on crop production? Sunita bought a 10 kg box of grapes from the market. She gave 3 1/2 kg of her grapes to her friend Reena and 2 1/4 kg to Anita. How many kilograms of grapes were left with her? GRANTING BRAINLIEST!! Suppose that an areas rate of groundwater recharge exceeds its rate of groundwater discharge. What can you conclude about the areas groundwater supply? - Write a sentence stating your conclusion about the groundwater supply - Write a sentence supporting your conclusion Is the statement [x]=[x+1] true for all real numbers McConnel corporation has bonds on the market with 16.5 years to maturity, a YTM of 7.7 percent, a par value of 1000 and current price of 1065. The bonds make semiannual payment and have a par value of $1,000.Required:What must the coupon rate be on these bonds? An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola.Beverage Sample Size Sample Mean Sample SDStrawberry Drink 10 537 22Cola 10 559 17Required:a. Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value.b. State the relevant hypotheses. c. Compute the test statistic value and find the P-value.d. State the conclusion in the problem context.e. What assumptions are necessary for your analysis?1. The distributions of compression strengths are approximately normal.2. The distributions of compression strengths have equal means. 3. The distributions of compression strengths are the same.4. The distributions of compression strengths have equal variances. Amber lives in New York, "the city that never sleeps," so she feels she has a great deal of freedom and choice. However, sociologists argue that this freedom prevents city dwellers from developing intimate personal relationships or community, a situation that is often referred to as Group of answer choices A man spends 880$ a month. Out of this, 26% goes to his rent. Find how much is his rent. Need Help ASAP drivers education name at least four things you can do to make your vehicle more visible to other drivers as you are driving The function of the external structures of the female reproductive system include:Select one:a. Enables the sperm to enter the bodyb. Protects the internal organsc. Both A & Bd. None of the Above Question 13 (5 points)If you take in fewer calories than you need, you have what kind of energy balance? BRAINLIST RIGHT ANSWERPeople who try to cover the cloven hoof of empire with thepetticoats of "Expansion" are as careless of the dictionaryas of the constitution. The Philippines do not meanexpansion. It does not expand the fire of freedom to pourwater on it. ... Expansion is enlargement in kind. If the ex-Spanish colonies applied for admission to this republic andwe accepted them, that would be expansion.-Charles F. Lummis, editorial in the Land of SunshineWhat does the opinion in this excerpt represent?O A. Concern regarding an entanglement in foreign affairs during theCuban RevolutionB. Debate regarding U.S. aims and territorial gains in the Spanish-American WarC. Contention regarding the abandonment of neutrality during WorldWarO D. Fear regarding the spread of Socialism as a result of the Russian Dena uses 7.4 pints of white paint and blue paint to paint her bedroom walls. 2/5 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use yo paint her bedroom walls Nimisha wants to draw a wheel like the one shown. Each shaded part of the wheel should be one-third of each unshaded part. What should be the degree measure of the angle formed at the center by each shaded part?