Two numbers have a sum of 49, and 4 TIMES the first number MINUS the second number is EQUAL to 141. What are the two numbers?

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!

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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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.

the answer is A because 1 is the same as 78

The opposite sides are parallel.

Their angle measures add to 360°

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]

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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Answer:

$360

Step-by-step explanation:

Find 3% of 500 = 15

Multiply 15 by 24 = 360

Answer:

-84

Step-by-step explanation:

Since m=-4, we can plug -4 into the expression and use PEMDAS

7(m - 8)

7((-4)-8)

7(-12)

-84

Answer:

C. and D.

Step-by-step explanation:

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

Answer:

Did this help?

Step-by-step explanation:

Answer:

2/5x7

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

Step-by-step explanation:

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

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 :)

Answer:

2×2×5×7=20×7=140

2×3×6×7=36×7=252

252+140=392

Answer:

y = -2x + 3

Step-by-step explanation:

If you do rise/run, you recognize that the slope of the line is -6/3, which = -2. You can also see that the y-intercept of the line is at 3.

The equation of a line is represented by y=mx+b, with m being the slope and b being the y-intercept value.

Just plug in -2 as m and 3 as b in y=mx + b, and you will get your answer.

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

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

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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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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Step-by-step explanation:

Nsjssjsjsjshsnmsksjnsnsns

Answer:

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

Answer:

It's exponential

Step-by-step explanation:

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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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