the formula for the nth term of an arithmetic sequence can be found using the formula a subscript n baseline

Answer:

b = 3

Step-by-step explanation:

We already know that x = 2, so just plug it back into the equation to solve for the variable b.

\(b(2(2)+6)=30\)

\(b(4+6)=30\)

\(10b=30\)

\(b=3\)

We can check this by plugging it back in:

\(3(2(2)+6)=30\)

\(3(10)=30\)

\(30=30\)

This is the correct solution :)

\(\left(\dfrac{3^8}{3^5} \right)^3\\\\\\=\left(3^{8-5}\right)^3\\\\=(3^3)^3\\\\=(3)^{3\cdot 3}\\\\=3^9\)

Answer:

The GCF is 6 and the lowest term is 2/5

Step-by-step explanation:

GCF is the greatest common factor. The highest number both of the numbers can be divided by.

12 can be divided by 6 and so can 30. This number can not go any higher so 6 is the GCF

Now divide the denominator and numerator by 6.

So:

12/6 = 2

30/6 = 5

Put it together

2/5

Reduced using the GCF, 12/30 is 2/5

Answer:

Step-by-step explanation:

area of side triangles=2(1/2×6×4)=24 units²

area of 3 rectangles=6×7+2(5×7)==42+70=112 units²

or=(6+5+5)×7=16×7=112 units²

Total surface area=24+112=136 units²

An engineer is designing a fuel tank in the shape of a cylinder, the approximate radius of the cylinder is 8.2 inches.

Volume:

V = πr²h

Height:

h = 2r

V = πr²h

V= πr²(2r)

V= 2πr³

And we know that the volume must be 3,500 in³, now we can replace that and solve for R, we will get:

V= πr²h

3500 = 3.14 x 2 x (r)³

r = 8.2 inch

The cylinder's approximate radius must be 8.2 inches.

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterised as an infinitely curved surface.

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For equation (1), y' = xy + y, we can see that it is a linear differential equation since it is a first-order equation and the terms involving y and its derivatives have a power of 1.

For equation (2), y' = y^2(22+y^2), we can see that it is a Bernoulli differential equation since it is a first-order equation and the terms involving y and its derivatives have a power of 2.

To find the general solution of equation (2), we can use the following steps:

Divide both sides by y^2 to obtain y^(-2)y' = 22+y^2.

Substitute u = y^(-1) to obtain u' = -22u - 1.

Solve for u using separation of variables to obtain u = Ce^(-22x) - (x+D), where C and D are constants.

Substitute back y^(-1) for u to obtain the general solution y = (Cx+D)/(1-22xy), where C and D are constants.

Therefore, the general solution of equation (2) is y = (Cx+D)/(1-22xy), which is a rational function.

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Answer:

a = 4

Step-by-step explanation:

Ez, I did it where 6a - 3a which is just 3a and added the 21 to the other side. So now it is 12 = 3a which is simply 4.

Answer:

A, C

Step-by-step explanation:

7^6 is equal to:

7^8/7^2

(7²)³

Answer:

A, C

Step-by-step explanation:

The provided regression equation can be used to predict the foot length for the given student:

Foot length = 5.00 + 0.51(Height)

Substituting the student's height of 73 inches into the equation, we get:

Foot length = 5.00 + 0.51(73) = 41.83 cm

Therefore, the predicted foot length for this student is 41.83 cm.

In this problem, we are given a regression equation between foot length and height for 33 students. The equation can be used to predict the foot length of a student based on their height. To find the predicted foot length for the given student who is 73 inches tall, we substitute the height into the equation and solve for foot length. The predicted foot length is obtained as 41.83 cm, which is rounded to two decimal places.

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Answer:

5

Step-by-step explanation:

Answer:

Manny.

Step-by-step explanation:

Because they split cleaning on Thursday and Manny finished first, then on Friday Manny will clean more stalls because they are faster.

Answer:

You can make 7.5 gifts presents (or just 7)

Step-by-step explanation:

First I calculated the area of 1 box, which is 80 inches squared. Then I just divided the 600 square inches with the 80 inches. 600/80= 7.5. Therefore, you can make 7 presents (since you cannot wrap half of a present (0.5))

Hope this helps !

Complete question is;

Shelby's family has a cell phone data plan that provides each family member with 5 gigabytes of data. Which ratios correctly relate to the number of family members to the number of gigabytes of data? Select all that apply

A) 1 to 10

B) 2 to 5

C) 2 to 10

D) 3 to 15

Answer:

Option C & D are correct.

Step-by-step explanation:

We are told that there is a cell phone data plan that provides each family member with 5 gigabytes of data.

This means that 1 family member gets 5 gigabytes of data.

Thus, ratio of family members to gigabytes of data will be at least;

1 : 5

In option A, we have ratio 1 to 10. This is wrong because it means 1 family member gets 10 gigabytes which doesn't follow with the 5 gigabytes provided.

In option B, we have ratio 2 to 5. This is wrong because it means 2 family members are sharing 5 gigabytes whereas the question says each family member gets 5 gigabytes.

In option C, we have ratio 2 to 10. This is correct because it means 2 family members share 10 gigabytes equally which means each has 10/2 = 5 gigabytes.

In option D, we have ratio 3 to 15. This is correct because it means 3 family members share 15 gigabytes equally which means each has 15/3 = 5 gigabytes.

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

Answer:

Jim is 12 years old. Anna is 3 times older than Jim. Calculate Anna’s age using multiplication.

Step-by-step explanation:

The problem above is solved by using multiplication and the solution to the problem is 36.

you multiply 12 * 3 and you get 36.

hope that helps!

The slope of the regression line is 0.0138. - If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent underwater. (Correct) - If the depth of the dive is decreased by one meter, it subtracts 0.0138 minutes from the time spent underwater. (Incorrect) - If the depth of the dive is increased by 0.0138 meter, it adds approximately 0.001 minute (or 0.06 seconds) to the time spent underwater. (Incorrect)

Step 1:

The slope of the regression line is 0.0138.

Step 2:

The slope of 0.0138 in this context indicates that for every additional meter in depth, the penguin spends an additional 0.0138 minutes (or approximately 0.83 seconds) underwater. In other words, as the penguin dives deeper, it tends to stay underwater for a slightly longer duration.

To address the provided options:

- The first option, "If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent underwater," is correct based on the given slope value. Increasing the depth by one meter corresponds to adding 0.0138 minutes to the dive duration.

- The second option, "If the depth of the dive is decreased by one meter, it adds 0.0138 minutes to the time spent underwater," is incorrect. According to the slope, decreasing the depth by one meter would actually result in a decrease of 0.0138 minutes in the dive duration.

- The third option, "If the depth of the dive is increased by 0.0138 meter, it adds one minute to the time spent underwater," is incorrect. The slope indicates that for an increase of 0.0138 minutes (or approximately 0.83 seconds) in dive duration, the depth would need to increase by one meter.

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The complete question is:

A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled The relation of dive duration (DD) to depth (D). Duration DD is measured in minutes and depth D is in meters. The report then says, The regression equation for this bird is: DD = 2.69 + 0.0138D.

Step 1:

What is the slope of the regression line?

Step 2:

Explain in speci?c language what this slope says about this penguin's dives.

If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.

If the depth of the dive is decreased by one meter, it adds 0.0138 minutes to the time spent under water.

If the depth of the dive is increased by 0.0138 meter, it adds one minute to the time spent under water.

Answer:

SA=64

V=28

Step-by-step explanation:

formula for SA: 2(lw+hw+lh)

formula for volume: l*w*h

where

l-(length)=2

w-(width)=2

h-(height)=7

lets solve for SA first:

2(2*2+2*7+2*7)

2(4+14+14)

2(32)

64

SA=64

now lets solve 4 volume

v=lwh

v=2*2*7

v=28

Answer:

D

Step-by-step explanation:

Somehting bknbye3uehnfhnjun Español uno, como sulfhídrica

Answer:

a. sin 300 = -∛3/2, cos 300 = 1/2

b. sin -225 = √2/2, cos -225 = √2/2

c. sin 5π/6 = 1/2, cos 5π/6 = -3√2

d. sin -4π/3 = √3/2, cos -4π/3 = -1/2

Step-by-step explanation:

See unit circle

In public opinion polling, a sample as small as about 1,500 people can faithfully represent the "universe" of Americans.

The size of a sample needed for accurate representation of a larger population, known as the "universe," depends on several factors, including the desired level of confidence and margin of error. While larger sample sizes generally provide more precise estimates, they also require more resources and time. Statistically, a sample size of around 1,500 is often considered sufficient for accurately representing the opinions and characteristics of the larger American population.

The principle behind this is known as the "law of large numbers" and the "central limit theorem." These statistical concepts suggest that as the sample size increases, the sample's distribution becomes closer to the population's distribution. By using appropriate sampling techniques, such as random sampling, stratified sampling, or quota sampling, pollsters aim to select a diverse and representative subset of the population. Through statistical analysis, they can estimate the views and preferences of the larger population based on the responses collected from the sample. A well-designed and properly conducted survey with a sample size of around 1,500 individuals can provide reliable insights into the opinions and attitudes of Americans as a whole.

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Based on the given frequency distribution in the histogram, the shape of the distribution of water bills can be described as skewed right. Option C

In a skewed right distribution, the tail of the distribution extends to the right side, indicating that there are some higher values or outliers on that end.

In this case, we can observe that there are more residents with higher water bills (e.g., 13 residents with bills in the range of 200 to 225) compared to the lower bills (e.g., 1 resident with a bill in the range of 100 to 125). This indicates a right-skewed pattern.

Therefore, the correct answer is "skewed right."

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The method to solve a proportion is given below.

We are given that;

A proportion

Now,

A proportion is an equation that shows that two ratios are equal. For example, if we have a ratio of 2:3 and another ratio of 4:6, we can write a proportion as 2/3 = 4/6. To solve a proportion, we can use cross-multiplication, which means multiplying the cross terms and setting them equal. For example, to solve for x in the proportion x/5 = 3/10, we can cross-multiply as follows:

x/5 = 3/10

x * 10 = 5 * 3

10x = 15

x = 15/10

x = 1.5

So, x = 1.5 is the solution of the proportion. We can check our answer by plugging it back into the original proportion and simplifying:

1.5/5 = 3/10

0.3 = 0.3

Therefore, by proportion answer will be given above.

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Answer:

\( {a}^{6} {b}^{2} \)

solution

\( {a}^{3} \times b \times {a}^{3} \times b \\ = {a}^{3 + 3} \times {b}^{1 + 1} \\ = {a}^{6} {b}^{2} \)

hope this helps...

Good luck on your assignment..

Answer:

\(a^{6}b^{2}\)

Step-by-step explanation:

\(a^3 \times b \times a^3 \times b\)

If there are no exponents written, then the exponent is 1.

\(a^3 \times b^1 \times a^3 \times b^1\)

When multiplying two powers that have the same base, you can add the exponents.

\(a^{3+3} \times b^{1+1}\)

\(a^{6} \times b^{2}\)

The result for the evaluation of the given definite integral is 24, under the condition that the given definite integral is  \(I = \int\limits^4_0 { (|x^{2} -4| - x^{2} )} \, dx\)  .
The provided definite integral  \(I = \int\limits^4_0 { (|x^{2} -4| - x^{2} )} \, dx\)can be split into two integrals by using integration by parts

\(I = \int\limits^4_0 { (|x^{2} -4| - x^{2} )} \, dx = \int\limits^2_0 {(4-x^{2} )} \, dx - \int\limits^4_2 {(x^{2} -4)} \, dx\)

Hence, the first integral \(\int\limits^2_0 {(4-x^{2} )} \, dx\) is

\(\int\limits^2_0 {(4-x^{2} )} \, dx\) \(= [4x - (1/3)x^{3} ]\)
= [8/3]

Then, the second integral \(\int\limits^4_2 {(x^{2} -4)} \, dx\) is

\(\int\limits^4_2 {(x^{2} -4)} \, dx\)  = [-x³/3 + 4x]
= [-64/3]

Now,
I = [8/3] - [-64/3]
= [72/3]
= 24.
The result for the evaluation of the given definite integral is 24, under  the condition that the given definite integral is \(I = \int\limits^4_0 { (|x^{2} -4| - x^{2} )} \, dx\)

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ANSWER:

4th option:

STEP-BY-STEP EXPLANATION:

We have the following function:

We can see that the parent function of this function is:

Therefore, the function has a given behavior in the graph of the 4th option:

it has gone up 4 lines and left -2 making it go for a (4,-2)

The correct answer is: No, neither method shows that factors are necessary or sufficient.

The methods of agreement and difference are both used in causal inference to analyze the relationship between factors and outcomes. However, neither method alone can determine whether factors are necessary or sufficient conditions.

The method of agreement examines cases where the outcome occurs and compares the presence or absence of different factors. If a factor is consistently present in all cases where the outcome occurs, it suggests that the factor may be related to the outcome. However, this method does not provide information about whether the factor is necessary or sufficient.

On the other hand, the method of difference compares cases where the outcome occurs and cases where it does not, identifying factors that are present in the former but absent in the latter. This method helps identify factors that are associated with the outcome, but it also does not establish whether the factors are necessary or sufficient conditions.

To determine whether a factor is necessary or sufficient, additional evidence and reasoning are required. Additional experiments, data analysis, or theoretical considerations are needed to establish the causal relationship and determine the nature of the factor's influence on the outcome. Hence, "No, neither method shows that factors are necessary or sufficient" is the correct option.

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