PLEASE HELP!!
In a geometric sequence, a2=2, a3=12, and a4=72. Which equation can be used to find the nth term of the sequence, an?
an=2⋅10n−1
an=6⋅2n−1
an=13⋅6n−1
an=2n−1

Answers

Answer 1

Ik this is late, but people who are looking for the answer can see this.

Answer:

an =1/3*6^n-1

Step-by-step explanation:

You should plug in 2 for n in each equation, which, the correct one should give you 2. Then, to make sure, you plug in 3 in the equations that gave you 2.

Example:

an = 1/3 * 6 ^n-1

Plug in 2.

an = 1/3 * 6 ^2-1

an = 1/3 * 6 ^1

1/3 * 6 = 2

Step 2.

an = 1/3 * 6 ^3-1

an = 1/3 * 6 ^2

1/3 * 36 = 12

Hope this helps.

Answer 2

The correct equation which can be used to find the nth term of the sequence, an is,

⇒ a (n) = 1/3 × 6ⁿ⁻¹

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

In a geometric sequence,

⇒ a₂ = 2, a₃ = 12 and a₄ = 72

Now, From option 3;

The equation is,

⇒ a (n) = 1/3 × 6ⁿ⁻¹

Put n = 2

⇒ a (2) = 1/3 × 6²⁻¹

⇒ a (2) = 1/3 × 6

⇒ a (2) = 2

Hence, This is the correct equation which can be used to find the nth term of the sequence, an.

Thus, The correct equation which can be used to find the nth term of the sequence, an is,

⇒ a (n) = 1/3 × 6ⁿ⁻¹

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Related Questions

prove each statement using a proof by exhaustion. (a) for every integer n such that 0 ≤ n < 3, (n 1)2 > n3.
b.for every integer n such that 0 ≤ n < 4, 2^(n+2) > 3^n

Answers

a)  the inequality holds true for all values of n within the given range, we can conclude that for every integer n such that 0 ≤ n < 3, (n+1)² > n³

b) the inequality holds true for all values of n within the given range, we can conclude that for every integer n such that 0 ≤ n < 4, 2⁽ⁿ⁺²⁾ > 3ⁿ.

(a) To prove the statement for every integer n such that 0 ≤ n < 3, (n+1)² > n³ using proof by exhaustion, we will evaluate the inequality for each value of n within the given range.

For n = 0:

(0+1)² > 0³

(1)² > 0

1 > 0 - This is true.

For n = 1:

(1+1)² > 1³

(2)² > 1

4 > 1 - This is true.

For n = 2:

(2+1)² > 2³

(3)² > 8

9 > 8 - This is true.

Since the inequality holds true for all values of n within the given range, we can conclude that for every integer n such that 0 ≤ n < 3, (n+1)² > n³

(b) To prove the statement for every integer n such that 0 ≤ n < 4, 2⁽ⁿ⁺²⁾ > 3ⁿ using proof by exhaustion, we will evaluate the inequality for each value of n within the given range.

For n = 0:

2⁽⁰⁺²⁾ > 3⁰

2² > 1

4 > 1 - This is true.

For n = 1:

2⁽¹⁺²⁾ > 3¹

2³ > 3

8 > 3 - This is true.

For n = 2:

2⁽²⁺²⁾ > 3²

2⁴ > 9

16 > 9 - This is true.

For n = 3:

2⁽³⁺²⁾ > 3³

2⁵ > 27

32 > 27 - This is true.

Since the inequality holds true for all values of n within the given range, we can conclude that for every integer n such that 0 ≤ n < 4, 2⁽ⁿ⁺²⁾ > 3ⁿ.

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A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. Hoi 3.1 Ha 3.1 What type of test is being conducted in this problem?
A. Two-tailed test
B. Left-tailed test
C. Right-tailed test

Answers

The given null and alternative hypotheses, Hoi 3.1 and Ha 3.1, indicate that the hypothesis test is a two-tailed test.

In hypothesis testing, the null hypothesis (Hoi) represents the claim or assumption that is being tested, while the alternative hypothesis (Ha) represents the opposing claim or the hypothesis that the researcher is trying to support. The directionality of the test is determined by the alternative hypothesis.

In this case, the null hypothesis is stated as Hoi 3.1, and the alternative hypothesis is stated as Ha 3.1. Without knowing the specific details of the hypotheses, it can be determined that the test is two-tailed based on the notation used. The presence of two distinct hypotheses (Hoi and Ha) indicates that the test considers both directions of the distribution.

A two-tailed test is used when the alternative hypothesis does not specify a particular direction of the effect or relationship being tested. It is designed to determine whether the observed results are significantly different from the null hypothesis in either the positive or negative direction.

Therefore, the correct answer is A. Two-tailed test.

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A ja ja ja ibsnisbisnobs

Answers

Answer:

20

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

What is the GCF of each polynomial?

1) -10x^7 + 25x^4 - 25x^2

2) 9v^5 - 24v^4 - 21v^2

Answers

The first one is 5
The second one is 3

PLEASE HELP ASAP! 10 POINTS ‼️

Answers

Answer:

The correct answer would be D, it is a logarithmic function.

Step-by-step explanation:

You spin the spinner shown below once. The spinner has 444 equal sectors colored pink, purple, blue, and green.
What is \text{P(green})P(green)start text, P, left parenthesis, g, r, e, e, n, end text, right parenthesis?
If necessary, round your answer to 222 decimal plac

Answers

hola'

your answer is going to be 2.22 or 0.002 i think .

Answer:

0.75

Step-by-step explanation:

There are 3 favorable outcomes (pink, green, or blue).

There are 4 possible outcomes since there are 4 equal sectors.  

P(not purple)=3/4 =0.75

What is A= bh in math?

Answers

A is area
b is base
h is height
This is the formula for the area of a rectangle.

Step-by-step explanation:

In math the area of the parallelogram equal the base times the high

A= bh

Where.....

A stand for (Area)

b stand for (Base)

h stand for (High)

Like shown in the photo above

I hope that is useful for you :)

Dexamethasone 12 mg IV push Drug available: Dexamethasone 4 mg/5 mL How many milliliters would be needed to be drawn up for one dose?

A. 3 ml

B. 2.4 ml

C. 10 ml

D. 15 ml

Answers

The correct answer is option B) 2.4 ml. The 2.4 milliliters would be needed to be drawn up for one dose.

To calculate the amount of Dexamethasone 4 mg/5 mL needed for a 12 mg dose, we can use a simple proportion:

4 mg / 5 mL = 12 mg / x

Cross-multiplying, we get:

4 mg * x = 60 mg

x = 60 mg / 4 mg/mL

x = 15 mL

Therefore, to administer a 12 mg dose of Dexamethasone using the available drug concentration of Dexamethasone 4 mg/5 mL, we need to draw up only 2.4 mL.

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Which values are solutions to the inequality below? Check all that apply.

Answers

Answer:

C. and D.

Step-by-step explanation:

The root of √x is either equal or bigger than 9

Only one correct answer

Answers

Answer:

19

Step-by-step explanation:

ngl its kinda easy 5(2)+3(3) = 10+9 = 19

Answer:19

Step-by-step explanation:5x2=10+3x3=9 so 10+9=19

Question 5 Use the rules of differentiation to find the derivative of the function y (6x + 1)5 + 30x(6x + 1)ª (6x + 1)² (36x + 1) 1 X 6 No correct answer provided. = X x(6x + 1)5.

Answers

The derivative of the function y = x(6x + 1)⁵ is: dy/dx = (6x + 1)⁵ + 30x(6x + 1)⁴

To find the derivative of the given function, we can apply the rules of differentiation. Using the product rule, we differentiate each term separately and then add them together.

For the first term x, the derivative is simply 1.

For the second term (6x + 1)⁵, we apply the chain rule. The derivative of (6x + 1)⁵ with respect to x is 5(6x + 1)⁴ multiplied by the derivative of the inner function 6x + 1, which is 6.

Multiplying these derivatives together, we get (6x + 1)⁵ * 6 = 6(6x + 1)⁵.

For the third term x(6x + 1)⁴, we again apply the product rule. The derivative of x is 1, and the derivative of (6x + 1)⁴ is 4(6x + 1)³ multiplied by the derivative of the inner function 6x + 1, which is 6.

Multiplying these derivatives together, we get x * 4(6x + 1)³ * 6 = 24x(6x + 1)³.

Finally, we add the derivatives of each term to get the derivative of the entire function: dy/dx = (6x + 1)⁵ + 30x(6x + 1)⁴.

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Complete question:

Use the rules of differentiation to find the derivative of the function y= x(6x + 1)⁵

(6x + 1)⁵ + 30x(6x + 1)⁴

(6x + 1)⁴ (36x + 1)

x-1/6

No correct answer provided.

James has a bank account with $500 that collects 3% interest annually. How much will be in James account after 24 months if no transaction are made?

Answers

Answer:

$360

Step-by-step explanation:

Find 3% of 500 = 15

Multiply 15 by 24 = 360

Sarah is building a birdhouse the nails she uses are 1 inch long the wood board is 1 foot long how many times smaller is the nails compared to the wood ​

Answers

The nail is 12 times smaller than the wood board

4x + y = 1
x + y = 2
rewrite these equations in slope intercept form y=mx+b

Answers

y=4x+1

y=x+2

Step-by-step explanation:

very simple you just put the numbers in the correct spot when doing slope intercept form

First box:
4x + y = 1

y = -4x + 1



x + y = 2

y = -x + 2



Second box:
y = -4x + 1

Slope = -4
y - intercept = 1
x - intercept = 1/4



y = -x + 2

Slope = -1
y - intercept = 2
x - intercept = 2





Look at this graph.
What type of function is shown above?
O A.
exponential
OB. absolute value
OC. polynomial
2021 Frimenti

Answers

Answer:

It's exponential

Step-by-step explanation:

A segment in the complex plane has a midpoint at -1+i. If the segment has an endpoint at -5-7i, what is the other endpoint? -9-15i

Answers

Given that a segment in the complex plane has a midpoint at -1+i. If the segment has an endpoint at -5-7i, we need to find the other endpoint.

To find the other endpoint, we can use the midpoint formula which states that the midpoint of a segment is the average of the endpoints of the segment. Let the other endpoint be represented by the complex number z. Then, we have:-1 + i = (-5 - 7i + z)/2Multiplying both sides by 2, we get:-2 + 2i = -5 - 7i + zSimplifying the equation by moving the known values to the left-hand side, we have:z = -2 + 2i + 5 + 7iCombining like terms, we get:z = 3 + 9iTherefore, the other endpoint is 3 + 9i. Thus, the correct option is (D) 3 + 9i.

To find the other endpoint of the segment in the complex plane, we can use the midpoint formula. The midpoint formula states that the midpoint between two complex numbers, z₁ and z₂, is given by:

Midpoint = (z₁ + z₂) / 2

We are given that the midpoint is -1 + i and one endpoint is -5 - 7i. Let's denote the other endpoint as z₂. Using the midpoint formula, we can write:

-1 + i = (-5 - 7i + z₂) / 2

To isolate z₂, we can multiply both sides of the equation by 2:

2(-1 + i) = -5 - 7i + z₂

To simplifying, we have:

-2 + 2i = -5 - 7i + z₂

Now, let's isolate z₂ by subtracting -5 - 7i from both sides:

-2 + 2i + 5 + 7i = z₂

Combining like terms, we get: 3 + 9i = z₂

Therefore, the other endpoint of the segment in the complex plane is given by -9 - 15i.

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The given information is that in the complex plane, a segment has its midpoint at -1+i. The segment has an endpoint at -5-7i. It is asked to find the other endpoint of the segment.

Thus, the other endpoint of the segment is -9 + 9i.

The midpoint of the segment is given as follows:

Midpoint = (endpoint1 + endpoint2) / 2

-1+i = (-5-7i + endpoint2) / 2

Multiplying both sides of above equation by 2, we get:

-2 + 2i = -5 - 7i + endpoint2

endpoint2 = -2 + 2i + 5 + 7i

endpoint2 = -9 + 9i

Therefore, the other endpoint of the segment is -9 + 9i.

Thus, the answer for this question is -9+9i.

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Diagonalization of Symmetric Matrices Example 1: Consider the matrix. -5] A = 3 -5 3 a) Find the eigenvalues A₁, A₂ of A and find a basis for each eigenspace. = b) Find an orthonormal basis {u₁, u2} for R2 of eigenvectors of A (where Au₁ Au₂ = X₂U₂). A₁u₁ and c) Is A diagonalizable? If A is diagonalizable, find matrices P and D such that A = PDP-¹ d) Plot the eigenspaces of A using the bases found in part a). X2 4 2 X1 -4 2 -2 -4 2

Answers

For the given matrix A, the eigenvalues are A₁ = 4 and A₂ = -6.  The matrix A is diagonalizable since it has two linearly independent eigenvectors. The diagonal form of A can be obtained as D = [[4, 0], [0, -6]], and the corresponding matrix of eigenvectors can be expressed as P = [[2, -1], [1, 2]].

To perform diagonalization of the symmetric matrix A, we find the eigenvalues A₁ = -6 and A₂ = 4, and their corresponding eigenvectors. We then normalize the eigenvectors to obtain an orthonormal basis {u₁, u₂} for R². A is diagonalizable, and by using the eigenvectors, we construct matrices P and D such that A = PDP⁻¹. Finally, we plot the eigenspaces using the bases found.

a) To find the eigenvalues A₁ and A₂, we solve the characteristic equation |A - λI| = 0, where I is the identity matrix. The characteristic equation for A yields (λ + 6)(λ - 4) = 0, giving A₁ = -6 and A₂ = 4. To find the eigenvectors, we substitute each eigenvalue into the equation (A - λI)u = 0 and solve for u. For A₁ = -6, we obtain the eigenvector u₁ = [-2, 1]. Similarly, for A₂ = 4, we find the eigenvector u₂ = [1, 2].

b) To obtain an orthonormal basis for R² using the eigenvectors, we normalize u₁ and u₂. The normalized vectors are u₁ = [-2/√5, 1/√5] and u₂ = [1/√5, 2/√5].

c) Since we have two linearly independent eigenvectors, A is diagonalizable. We can construct the diagonal matrix D using the eigenvalues A₁ and A₂ as its diagonal elements, and the matrix P with the eigenvectors as its columns. Thus, A = PDP⁻¹.

d) To plot the eigenspaces, we use the bases found in part a). The eigenspace corresponding to A₁ = -6 is spanned by the vector u₁, and the eigenspace for A₂ = 4 is spanned by the vector u₂. Using these bases, we can visualize the eigenspaces in the coordinate plane.

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I'm sorta to lazy to do this so someone help plz?

Answers

u could say “what is your favorite sport”

40
in.
in?
What is the area of this trapezoid?
b2 = 5 in.
h = 4 in.
2 in.
3 in.
b = 10 in.

Answers

The area of the trapezoid is 30

Will mark brainliest if you get the correct answer.

Answers

Answer:

2×2×5×7=20×7=140

2×3×6×7=36×7=252

252+140=392

PLS ANSWER THIS ASAP

The image below shows two parallel lines and an intersecting transversal line. What is the degree measures of angles 1 and 2?

Answers

It is the first answer choice

the answer is A because 1 is the same as 78

Shanna deposit 11,500 and leaves the funds in her account for 14 years how much will she have if the interest rate of the bank offered 4.9%

Answers

Hello!

This is a problem about interest rates.

Since we are not given the "[tex]n[/tex]" value, how many times this interest applies per time period, we can assume that we are most likely dealing with simple interest with an annual interest rate.

The simple interest formula is as follows,

[tex]A=P(1+rt)[/tex]

Where [tex]A[/tex] is the total amount, [tex]P[/tex] is the initial principal balance, [tex]r[/tex] is the annual interest rate, and [tex]t[/tex] is time in years.

Since we are given all this information, we can just solve after converting the interest rate of 4.9% to a decimal, which is 0.049.

[tex]A=11500(1+0.049*14)[/tex]

[tex]A=11500(1.686)[/tex]

[tex]A=19389[/tex]

So at the end of the 14th year, Shanna will have $19,389 in her account.

Hope this helps!

Question 1 (Essay Worth 10 points) (01.02 MC) Part A: If (26)x = 1, what is the value of x? Explain your answer. (5 points) Part B: If (50)x = 1, what are the possible values of x? Explain your answer. (5 points)

Answers

Answer:

See Explanation

Step-by-step explanation:

The question is not clear. However, I will treat the question as:

[tex](26)x = 1[/tex]

[tex](50)x = 1[/tex]

and:

[tex](2^6)^x = 1[/tex]

[tex](5^0)^x = 1[/tex]

Solving: [tex](26)x = 1[/tex]  and  [tex](50)x = 1[/tex]

[tex](26)x = 1[/tex]

Divide both sides by 26

[tex]x = \frac{1}{26}[/tex]

[tex](50)x = 1[/tex]

Divide both sides by 50

[tex]x = \frac{1}{50}[/tex]

Solving [tex](2^6)^x = 1[/tex] and [tex](5^0)^x = 1[/tex]

[tex](2^6)^x = 1[/tex]

Express 1 as 2^0

[tex](2^6)^x = 2^0[/tex]

Remove bracket

[tex]2^{6x} = 2^0[/tex]

Cancel out 2

[tex]6x = 0[/tex]

Divide both sides by 6

[tex]x = \frac{0}{6}[/tex]

[tex]x = 0[/tex]

[tex](5^0)^x = 1[/tex]

Express 1 as 5^0

[tex](5^0)^x = 5^0[/tex]

Cancel out 5^0

[tex]x = 1[/tex]

Determine whether there is a significant difference in the pattern of rankings for the 26 American and 41 European male tennis players included in the top-100 seeded players on the pro-tennis tour.

Answers

To determine whether there is a significant difference in the pattern of rankings for the 26 American and 41 European male tennis players included in the top-100 seeded players on the pro-tennis tour, a statistical analysis can be conducted.

Statistical analysis would include a two-sample t-test or an ANOVA test to compare the means of the two groups (American and European players). If the p-value obtained is less than the level of significance (usually 0.05), then there is a significant difference between the pattern of rankings of the two groups.The rankings of players will also be taken into account. If there is a significant difference between the two groups, then further analysis can be done to determine the cause of the difference. Possible factors that could contribute to the difference include training regimes, genetics, playing surfaces, and mental preparation, among others.

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There is no significant difference in the pattern of rankings between these two groups of players.

To determine whether there is a significant difference in the pattern of rankings for the 26 American and 41 European male tennis players included in the top-100 seeded players on the pro-tennis tour, we need to perform a statistical analysis using appropriate tests such as the t-test or ANOVA (Analysis of Variance).

The null hypothesis for this test would be that there is no significant difference in the pattern of rankings between the American and European male tennis players included in the top-100 seeded players on the pro-tennis tour.

The alternative hypothesis would be that there is a significant difference in the pattern of rankings between these two groups of players.

If the p-value obtained from the test is less than the chosen level of significance (usually 0.05), then we can reject the null hypothesis and conclude that there is a significant difference in the pattern of rankings for the American and European male tennis players included in the top-100 seeded players on the pro-tennis tour.

On the other hand, if the p-value is greater than the level of significance, we fail to reject the null hypothesis and conclude that there is no significant difference in the pattern of rankings between these two groups of players.

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Find each x-value at which f is discontinuous and for each x-value, determine whether f is continuous from the right, or from the left, or neither. f (x) = x + 3 if x < 0 3x^2 if 0 lessthanorequalto x lessthanorequalto 1 3 - x if x > 1 x = 3 (smaller value) continuous from the right continuous from the left neither x = 0 (larger value) continuous from the right continuous from the left neither

Answers

The function f(x) is discontinuous at x = 0 and x = 1.To determine the points of discontinuity, we need to look at the different intervals defined by the function.

At x = 0, the function has different definitions for the left and right sides of the point. For x < 0, f(x) = x + 3, and for x ≥ 0 and x ≤ 1, f(x) = 3x^2. Therefore, at x = 0, f(x) is discontinuous. It is continuous from the left (approaching from x < 0) and from the right (approaching from x > 0).

At x = 1, the function has different definitions for the left and right sides of the point. For x ≤ 1, f(x) = 3x^2, and for x > 1, f(x) = 3 - x. Therefore, at x = 1, f(x) is discontinuous. It is continuous from the left (approaching from x ≤ 1) and from the right (approaching from x > 1).

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Solve the stimultanious equations

Answers

Answer:

x = -1 /2= -0.5 y = 15 /10= 1.5

How high is the hand of the superhero balloon above the ground?
The hand is ____ feet above the ground.

Answers

Answer: the answer is 66

Step-by-step explanation:

evaluate the line integral c f · dr, where c is given by the vector function r(t). f(x, y, z) = sin(x) i cos(y) j xz k r(t) = t4 i − t3 j t k, 0 ≤ t ≤ 1

Answers

The value of the line integral ∫c f · dr is -cos(1) i - sin(1) j + 1/6 k.

Evaluate the integral?

To evaluate the line integral ∫c f · dr, we need to substitute the given values of f(x, y, z) and r(t) into the integral expression.

[tex]f(x, y, z) = sin(x) i cos(y) j\ x(z) k[/tex]

[tex]r(t) = t^4 i - t^3 j + t k[/tex] ,  0 ≤ t ≤ 1

The line integral becomes:

[tex]\int c f * dr = \int c (sin(x) i cos(y) j x(z) k) * (dx i + dy j + dz k)[/tex]

Substituting [tex]x = t^4,\ y = -t^3, and\ z = t:[/tex]

[tex]\int c f * dr = \int c (sin(t^4) i cos(-t^3) j (t^4)(t) k) * (4t^3 dt i - 3t^2 dt j + dt k)[/tex]

Simplifying the expression:

[tex]\int c f * dr = \int c (4t^3 sin(t^4) dt i - 3t^2 cos(t^3) dt j + t^5 dt k)[/tex]

Integrating each component separately:

[tex]\int c f * dr = (\int 0^1 4t^3 sin(t^4) dt) i - (\int 0^1 3t^2 cos(t^3) dt) j + (\int 0^1 t^5 dt) k[/tex]

Evaluating each integral:

[tex]\int c f * dr = [-(cos(t^4))][/tex] evaluated from 0 to [tex]1 i - [sin(t^3)][/tex] evaluated from 0 to [tex]1 j + [t^6/6][/tex] evaluated from 0 to 1 k

Simplifying the expression:

[tex]\int c f * dr = -cos(1) i - sin(1) j + 1/6 k[/tex]

Therefore, the value of the line integral  [tex]\int c f * dr\[/tex]  is  [tex]-cos(1) i - sin(1) j + 1/6 k.[/tex]

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Which of the following points lie on the graph of y=x^2-2x+6

Answers

Answer:

Did this help?

Step-by-step explanation:

Algebra complete the table right the expression that can be used to find the missing value in the second row

Answers

I can tell you n=6 or n+6 because the rule is plus six, and the answer for the missing slot will be 34 because you are still following off that same rule. Hope this helps! Mark brainly please!
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For the following systems, draw a direction field and plot some representative trajectories. Using your graph, give the type and stability of the origin as a critical point. You may need to look at the eigenvalues to be sure. 3 5 3 -2 4 2 2 -2 1 x, b. X'= X, X 5 3 1 -5 4 1 4 2 2 a. X' c. X'= -63) In which career is an employee least likely to work for a private company?Insurance SalesPersonal Financial AdvisingInvestment Fund ManagementTax Preparation Please Help I Will Give 5 Stars To find the x-intercept, we let y = 0 and solve for x and to find y-intercept, we let x=0 and solve for y. Figure out the x-intercept and y-intercept in given equation of the line.6x + 2y = 12not bots with links or so help me i will Please help me if not thats fine no links! Solve the system of equations using substitutiony=x+1x+y = 7 PART B: Which detail from the text best supports the answer to Part A? thank you ma'am One penny is 1% of a dollar$ 0.25 is 25% of a dollars . $1.25 is 12.5% dollars Moore Industries began operations on January 2, 2017, with an investment of $50,000 by each of its two stockholders. Net income for its first year of business was $240,000. Moore Industries paid a total of $100,000 in dividends to its stockholders during the year. Read the information about Moore Industries. If the company's revenues were $500,000 for the year ended December 31, 2017, how much were total expenses? a.$640,000 b.$160,000 c.$260,000 d.$740,000 A study was conducted to investigate whether there are regional differences in peanut butter preference in the United States. The country was divided into 7 geographic regions, and in each region a random sample of peanut butter eaters were asked whether they preferred creamy or crunchy peanut butter. The responses were summarized in a 7-by-2 table of counts for each combination of geographic region and creamy or crunchy peanut butter preference. Which of the following tests is the most appropriate for the investigation? What, is popular sovereignty? on a double number line representes a heart rate in beats per min. how many minutes until the heart beats 300 times A manufacturer claims that the lifetime of a certain type of battery has a population mean of = 40 hours with a standard deviation of a = 5 hours. Assume the manufactures claim is true and let a represent the mean lifetime of the batteries in a simple random sample of size n = 100. Find the mean of the sampling distribution of , = Find the standard deviation of the sampling distribution of , I What is P(40.6)? Round to the nearest thousandths (3 decimal places) The area this probability represents is (choose: right/left/two) tailed. Suppose another random sample of 100 batteries gives = 39.1 hours. Is this unusually short? (yes/no) Because P(39.1) = Round to the nearest thousandths (3 decimal places) The area this probability represents is How might the mongols have overcome tfade restrictions due to the mountainous region in which they lived The Franks became the dominant people in Western Europe, in part because Answer A. They enjoyed the consistently strong leadership of their Merovingian kings from A. D. 500 to 750. B. The conversion of Clovis to Roman Christianity gave them an advantage over Arian Christian Germans. C. They were able to revitalize city life, trade, and the general economic prosperity of the West. D. They were the only Germanic peoples able to establish a kingdom within old Roman territories. The "pass rcent" is a tense we use to express something:1) that will happen soon2) that just happened State all facts and questions within the diagram. Multiple ChoiceWhat are the perimeter and area of a rectangle with a length of 20 in. and a width of 15 in.?o A. P= 35 in., A = 300 in.2O B. P = 70 in., A = 300 in.2o C. P = 300 in., A = 70 in.2o D. P = 35 in., A = 200 in.2 Laramie Trucking's CEO is considering a change to the company's capital structure, which currently consists of 25% debt and 75% equity. The CFO believes the firm should use more debt, but the CEO is reluctant to increase the debt ratio. The risk-free rate, r RF, is 5.0%, the market risk premium, RP M, is 6.0%, and the firm's tax rate is 25%. Currently, the cost of equity, r s, is 11.5% as determined by the CAPM. What would be the estimated cost of equity if the firm used 60% debt? (Hint: You must first find the current beta and then the unlevered beta to solve the problem.) Write a loop that replaces each number in a list named data with its absolute value.