25 points plus brainliest

Answer:

The value of x is 7 if the equation can be reduced to (x + 9)³ = 4096 after applying the properties of the integer exponent option (C) 7 is correct.

What is an integer exponent?

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

The equation is:

After solving:

(x + 9)³ = 4096

x + 9 = ∛4096

x + 9 = 16

x = 7

Thus, the value of x is 7 if the equation can be reduced to (x + 9)³ = 4096 after applying the properties of the integer exponent option (C) 7 is correct.

Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, if the mean of the first data set is x, then the sum of the values in the first data set is 13x (since there are 13 classmates), and the sum of the values in the second data set is also 13x (since none of the values have changed). Therefore, the mean of the second data set will also be x, and the change in the means will be zero.

Answer:

1 2/6

Step-by-step explanation:

3 1/2 - 2 and 6 inches

change 6 to 1/6

3 1/2 = 3/6

2 1/6 = 1/6

-

_____

1 2/6

The number of the small seats is 30 while the number of the big seats is 94.

We know that from the question, Vicky is an airline attendant. Last week, she worked on flights on 3 small jets and 5 large jets, which could seat a total of 560 passengers. The week before, she was assigned to flights on 5 small jets and 2 large jets, which could seat a total of 338 passengers.

Now;

Let the number of small seats be x and the number of large seats be y

It follows that;

3x + 5y = 560 ----- (1)

5x + 2y = 338 ------(2)

If you multiply (1) by 5 and (2) by 3 we have;

15x + 25y = 2800 ------ (3)

15x + 6y = 1014 -----------(4)

        19 y = 1786

y = 1786/19

= 94

Substitute y = 94 into (1)

3x + 5(94) = 560

x = 560 -  5(94)/3

x = 30

Learn more about simultaneous equations:https://brainly.com/question/16763389

#SPJ1

You should pay approximately $10,117.09 initially to secure the annuity and receive annual payments of $1500 over the 9-year period.

To find the cost of the annuity, we need to calculate the present value of the future payments. The present value represents the current worth of future cash flows, taking into account the interest earned or charged over time. In this case, we'll calculate the present value of the $1500 payments using compound interest.

The formula to calculate the present value of an annuity is:

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

Where:

PV is the present value of the annuity (the amount you should pay initially)

PMT is the payment amount received annually ($1500 in this case)

r is the interest rate per period (6.28% or 0.0628)

n is the total number of periods (9 years)

Let's substitute the values into the formula:

PV = $1500 × [1 - (1 + 0.0628)⁻⁹] / 0.0628

Calculating this expression:

PV = $1500 × [1 - 1.0628⁻⁹] / 0.0628

PV = $1500 × [1 - 0.575255] / 0.0628

PV = $1500 × 0.424745 / 0.0628

PV ≈ $10117.09

To know more about compound interest here

https://brainly.com/question/29335425

#SPJ4

The ball is approximately 50 meters from the ground after about 5.477 seconds.

To find the approximate time it takes for the ball to reach a height of 50 meters, we need to solve the quadratic equation \(f(x) = -5x^2 + 200 = 50\).

Let's set f(x) equal to 50 and solve for x:

\(-5x^2 + 200 = 50\)

Rearranging the equation, we have:

\(-5x^2 = 50 - 200\\-5x^2 = -150\)

Dividing both sides by -5:

\(x^2 = 30\)

Taking the square root of both sides:

x = ±√30

Since we are looking for the time in seconds, we only consider the positive value of x:

x ≈ √30

Using a calculator, we find that the square root of 30 is approximately 5.477.

Please note that this is an approximate value since the quadratic model provides an approximation of the ball's height and does not account for factors such as air resistance.

For more such questions on quadratic equation

https://brainly.com/question/30164833

#SPJ8

Answer:

option A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

a. The Miquels’ monthly housing cost is the sum of their expenses: $396.80 + $34.15 + $139.40 + $44.75 + $51.20 + $29.75 + $63.84 + $18.50 = $778.39.

b. The Federal Housing Administration (FHA) recommends that housing expenses should not exceed 31% of a household’s monthly gross income. For the Miquels, this would be 0.31 * $2,478.60 = $768.37.

c. No, their monthly housing cost of $778.39 is not within the FHA recommendation of $768.37.

Answer:

-6 47/20

Step-by-step explanation:

A second linearly independent solution of y₂ is \(-\frac{1}{6x^3}\)

The general Equation is y" + P(x)y' + q(x)y = 0 ...............(i)

where P(x), Q(x) are continues in the internal I ≤ R.

If y₁(x) is a solution of equation 1 in I then y₁(x) ≠ 0.

Then y₂(x) = y₁(x)\(\int{\frac{e^{-\intP(x)dx}}{(y_{1}x)^2}}dx\) is another solution.

The differential equation is x²y" + xy' – 9y = 0 where x > 0.

As y₁(x) = x³ is one solution of differential equation.

Divide throughout by (x²) to given differential equation.

1/x² (x²y" + xy' – 9y = 0)

y" + (y'/x) – (9/x²)y = 0 ................(ii)

By comparing equation (i) & (ii) we get:

p(x)=1/x , q(x)= –are continuous for x>0

So, another solution,

y₂(x) = y₁(x)\(\int{\frac{e^{-\intP(x)dx}}{(y_{1}x)^2}}dx\)

Now putting the values of P(x) And Q(x)

y₂(x) = \(x^3\int\limits {\frac{e^{\int(1/x)dx} }{(x^3)^2}} \, dx\)

y₂(x) = \(x^3\int\limits {\frac{\frac{1}{x} }{x^6} }} \, dx\)

y₂(x) = \(x^3\int\limits {\frac{1}{x^7} }} \, dx\)

y₂(x) = \(x^3\int\limits {x^-7} } \, dx\)

y₂(x) = \(x^3\left[\frac{x^{-7+1}}{-7+1}\right]\)

y₂(x) = \(-\frac{1}{6}(x^3\times x^{-6})\)

y₂(x) = \(-\frac{1}{6x^3}\)

So, the answer of this question is \(-\frac{1}{6x^3}\).

To learn more about Differential equation link is here:

brainly.com/question/14620493

#SPJ4

1. The variability of the data tends to increase when using a repeated measures design. Disagree.

The repeated measures design involves collecting data from the same participants under different conditions or time points. This design reduces the variability caused by individual differences, as each participant serves as their own control. Therefore, the variability of the data tends to decrease rather than increase.

2. The cost of the study will tend to decrease when using a repeated measures design. Agree.

In a repeated measures design, data is collected from the same participants multiple times, reducing the need to recruit a large number of participants compared to independent group designs. This reduction in participant recruitment and associated costs can lead to a decrease in the overall cost of the study.

3. The number of participants will tend to increase when using a repeated measures design. Disagree.

A repeated measures design typically requires a smaller number of participants compared to independent group designs. In repeated measures, the same participants are measured multiple times, providing more statistical power and efficiency. Therefore, the number of participants needed may decrease compared to other designs.

4. The time it takes to run a study will tend to decrease when running a repeated measures design. Agree.

Since repeated measures involve collecting data from the same participants multiple times, the time required to run the study can be reduced. Researchers do not need to recruit and coordinate with new participants for each condition or time point, leading to a more efficient data collection process.

To know more about repeated measures designs refer here:

https://brainly.com/question/28902435?#

#SPJ11

Answer:192

Step-by-step explanation:

Calculate the area l*w or s*s

Divide the two areas to get the number of 1*1 from 1 plywood then multiply by their number which is 6 here

4*8=32/1=32*6=192

Answer:

About 33 years.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Simple Interest Rate Formula: \(\displaystyle A = P(1 + r)^t\)

Logarithm Property 1: \(\displaystyle log(a^x) = xloga\)

Step-by-step explanation:

Step 1: Define

Identify

P = 5000

r = 5% = 0.05

A = 25000

t = unknown

Step 2: Solve for t

Answer:

x=10

Step-by-step explanation:

5x-4=46

+4. +4

5x=50

x=10

Answer:

x = 10

Step-by-step explanation:

5x = 46 + 4 = 50

x = 50 / 5 = 10

x = 10

hope u find this helpful :)

Answer:

N + 3 = -5

n= -8

N-4=9

n=13

4+N=10

n=6

-10+N=3

n=13

N-10=1

n=11

-11+n=-12

n=-1

N+19=20

n=1

15+N=-10

n=-25

N-6=-12

n=-6

N+4=16

n=12

Step-by-step explanation:

The given equation is a solution of the differential equation y' + 2y = 2 e^x and it is a non-autonomous differential equation.

We can verify that the function y = 2/3 e^x + e^(-2x) if it is a solution of the differential equation y' + 2y = 2 e^x.

Let us substitute the function y = 2/3 e^x + e^(-2x)  into the left side of this differential equation which gives,

LHS: y' + 2y = [2/3 e^x + e^(-2x)]/dx + 2 [2/3 e^x + e^(-2x)]

⇒ 2/3 e^x - 2e^(-2x) + 4/3 e^x + 2 e^(-2x)

⇒ (2+4)/3 e^x = 2 e^x = RHS

Thus, LHS is equal to RHS which means that y = 2/3 e^x + e^(-2x)  is a solution of the differential equation y' + 2y = 2 e^x.

In this differential equation, the rate of change of y depends on y as well as on x. So, this is a non-autonomous differential equation.

The given question is inappropriate. The complete question is 'Is y = 2/3 e^x + e^(-2x) is a solution of the differential equation y' + 2y = 2 e^x?'

To know more about differential equations:

https://brainly.com/question/19131859

#SPJ4

Answer:Here is the algebraic solution: T is the tens digit O is the ones digit T+O = 14 So

Step-by-step explanation:O = 14 - T <---- this is the first equation

The original number is 10*T + O

If the digits are reversed the original number is increased by 18.

The number if the digits are reversed is:

10*O + T = 10*T + O + 18

10*(14-T) + T = 10*T + (14-T) + 18 <--- substitutes O with 14-T per first equation above in bold

140 - 10T + T = 10T + 14 - T + 18 <--- distributive left side

140 - 9T = 9T + 32

140 = 9T + 9T + 32

140 - 32 = 9T + 9T

108 = 18T

108/18 = T

T= 6

THe tens digit is 6.

The ones digit must be 8.

Reversing 86 - 68 = 18

The original number is 68.

A person who does not ignore a sunk cost increases the probability of making irrational decisions. This is because they are more likely to continue investing time, money, or effort into a project or situation that is not yielding positive results.

When we refer to a "sunk cost," we mean a cost that has already been incurred and cannot be recovered. Ignoring a sunk cost means not taking it into consideration when making decisions about the future. By not ignoring a sunk cost, individuals may feel a psychological attachment to their past investment, leading them to continue investing in something that may not be beneficial.

This can result in irrational decision-making and potentially wasting additional resources. For example, imagine a person who has spent a significant amount of money on a gym membership but rarely goes to the gym. Instead of accepting the fact that the money is already spent and may not be recouped.

They may feel compelled to continue paying for the membership in the hopes of eventually utilizing it. This decision is influenced by their failure to ignore the sunk cost and assess the situation rationally.

To know more about Cost visit.

https://brainly.com/question/14566816

#SPJ11

The expression for the extended stage is (LW - 216) / (12 - W)

A rectangle is a 2-D shape with length and width.

The length and width are different.

If the length and width are not different then it is a square.

The area of a rectangle is given as:

Area = Length x width

We have,

Rectangular stage.

Length = L

Width = W

New area = 216 + 12x

Now,

Assume,

The length has been extended.

So,

The new dimensions.

Length = (L + x)

Width = W

Area = (L + x) W

Area = LW + xW ______(2)

Now,

From (1) and (2),

216 + 12x = LW + xW

Solve for x.

216 + 12x = LW + xW

12x - xW = LW - 216

x ( 12 - W ) = LW - 216

x = (LW - 216) / (12 - W)

Thus,

The expression for the extended stage is  x = (LW - 216) / (12 - W)

Where L and W are the length and width.

Learn more about rectangles here:

https://brainly.com/question/15019502

#SPJ1

State, AAA rated and High tech firm bonds have maturity of 10years, 5years and 3 years respectively.

Bond is a financial instrument that represents a debt obligation. When you purchase a bond, you are essentially lending money to the issuer (which can be a government, corporation, or other entity) in exchange for regular interest payments and the repayment of the principal amount at a specified future date, known as the maturity date.

1. Maturity of Each Bond Group:

- State bonds: The state bonds have a maturity of 10 years.

- AAA rated bonds: The AAA rated bonds have a maturity of 5 years.

- High tech firm bonds: The high tech firm bonds have a maturity of 3 years.

2. Coupon Rates:

- State bonds: The state bonds have a 5% coupon rate.

- AAA rated bonds: The AAA rated bonds have a 6.5% coupon rate.

- High tech firm bonds: The coupon rate is not provided for the high tech firm bonds.

3. Par Values:

- State bonds: The par value of each state bond is not mentioned.

- AAA rated bonds: The par value of each AAA rated bond is not mentioned.

- High tech firm bonds: The par value of each high tech firm bond is $500.

4. Municipal Bonds:

Based on the given information, there is no mention of Sylvester purchasing any municipal bonds. Therefore, none of Sylvester's new investments are municipal bonds.

5. Corporate Bonds:

- High tech firm bonds: The high tech firm bonds are issued by a high tech firm, which indicates that they are corporate bonds.

6. Standard & Poor's Consultation:

From the information provided, there is no specific indication as to which bond purchase Sylvester consulted Standard & Poor's for.

Learn more about bonds here:

https://brainly.com/question/26712131

#SPJ1

If a cone is sliced by a vertical plane that passes through the vertex, the resulting cross section will be a triangle.

The vertical plane cuts through the cone at its highest point, which is also the point where the two sides of the cone meet (i.e. the vertex). As the plane cuts through the cone, it intersects with the sloping sides of the cone at different angles, creating a triangular shape.

The resulting cross section will have the same base as the original cone, which is a circle. However, the height of the cross section will be shorter than the height of the original cone, since the vertical plane has removed a portion of the cone.

Overall, the resulting cross section will be a triangle with a circular base, which is often referred to as a frustum. This shape is commonly used in architecture and engineering, as it allows for tapered structures such as pillars and columns to be created.

Learn more about cross section here: https://brainly.com/question/16881438

#SPJ11

The probability that the next customer will pay the debit card is 37% if the 34 customers paid cash, 26 customers used a debit card, and 11 customers used a credit.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

We have:

Total number of customers = 34+26+11 = 71

Total number of customers who used debit card as payment method = 26

The probability that the next customer will pay debit card:

= 26/71

= 0.3661%

= 36.61% ≈ 37%

Thus, the probability that the next customer will pay the debit card is 37% if the 34 customers paid cash, 26 customers used a debit card, and 11 customers used a credit.

Learn more about the probability here:

brainly.com/question/11234923

#SPJ1

Answer:

It depends how you were taught. You could say it's 11 (eleven) or 2.

Answer:

I think 2 lol

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

If 20 cups are used on the first recipe then 4 are used on the second, the way to find the answer is to divide 20 by 4. 20 divided by 4 will get 5. Now we have to divide the 10 cups of flour by 5 which in the end will get 2.

Answer:

B

Step-by-step explanation:

4^3 matches 4×4×4

5^2 matches 5×5

The Equilibrium Points are: (0,0).

Stability of Equilibrium Points: Inconclusive.

Outcome from Various Initial Points:

Equilibrium Points: The equilibrium points are the points where the system comes to rest, indicated by dx/dt = 0 and dy/dt = 0. Solving the equations dx/dt = 5x and dy/dt = -5y, we find x = 0 and y = 0. Therefore, the equilibrium points are (0,0).

Stability of Equilibrium Points: The stability of the equilibrium points can be determined using linearization. The Jacobian matrix J(x,y) is given as J(x,y) = [5 0; 0 -5]. For the equilibrium point (0,0), we have J(0,0) = [0 0; 0 0]. The eigenvalues of the Jacobian matrix are both zero, indicating that they lie on the imaginary axis. From this analysis, we cannot conclude anything about the stability of the equilibrium point (0,0).

Outcome of the System from Various Initial Points:

Case 1: When x(0) > 0 and y(0) > 0:

Both dx/dt and dy/dt are positive, causing the solution curve to move upwards and to the right. The trajectory approaches the equilibrium point (0,0) as t approaches infinity.

Case 2: When x(0) < 0 and y(0) < 0:

Both dx/dt and dy/dt are negative, causing the solution curve to move downwards and to the left. The trajectory approaches the equilibrium point (0,0) as t approaches infinity.

Case 3: When x(0) > 0 and y(0) < 0:

dx/dt is positive and dy/dt is negative. The solution curve moves upwards and to the left. The trajectory does not approach the equilibrium point (0,0) as t approaches infinity.

Case 4: When x(0) < 0 and y(0) > 0:

dx/dt is negative and dy/dt is positive. The solution curve moves downwards and to the right. The trajectory does not approach the equilibrium point (0,0) as t approaches infinity.

Please note that the stability analysis for the equilibrium point (0,0) is inconclusive, as the eigenvalues are both zero.

Learn more about equilibrium points

https://brainly.com/question/1527528

#SPJ11

The constant of proportionality of the graph is 5/4

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

The graph

On the graph, we have the following coordinates

(x, y) = (4, 5)

The constant of proportionality is then calculated as

k = y/x

So, we have

k = 5/4

Hence, the result is 5/4

Read more about constant of proportionality at

https://brainly.com/question/14374943

#SPJ1

Answer:

Step-by-step explanation:

Hope this helps u!!

Answer: 913%

Step-by-step explanation:

Based on the concept of payday loans, Barbara's annual percentage rate is 9.125%

The Annual Percentage Rate (APR) is a term that is used to describe the cost paid each year to borrow money, such as fees, expressed as a percentage.

In this case, to get the annual percentage rate (APR) on Barbara's loan calculate the effective interest rate for the 8-day period and then annualize it.

Given that Barbara borrowed $75 and was charged a fee of $15 for an 8-day term the total amount she needs to repay is $75 + $15 = $90.

To calculate the effective interest rate we can use the following formula:

Effective Interest Rate = (Total Interest / Principal) * (365 / Loan Term)

Total Interest = $15 (fee)

Principal = $75 (loan amount)

Loan Term = 8 days

Substituting the values into the formula:

Effective Interest Rate = (15 / 75) * (365 / 8)

Effective Interest Rate = 0.2 * 45.625

Effective Interest Rate = 9.125%

Therefore, APR = Effective Interest Rate * Compounding Frequency

APR = 9.125% * 1

APR = 9.125%

Hence, in this case, it is concluded the approximate annual percentage rate (APR) on Barbara's loan is around 9.125%.

Learn more about Annual Percentage Rate here: https://brainly.com/question/30774234

#SPJ6

The general solution to the system x' = Ax, where A is the given matrix, can be expressed as x(t) = Ce^(At), where C is a constant matrix and e^(At) is the matrix exponential of At. This solution represents a linear combination of exponential functions, where each component of x(t) is determined by the corresponding component of C and the matrix exponential of At.

To find the general solution to the system x' = Ax, we can express the solution in terms of the matrix exponential. The matrix exponential of At, denoted as e^(At), is defined as the power series expansion of the exponential function applied to the matrix At. It can be computed using various techniques, such as diagonalization, Jordan decomposition, or power series.

The general solution to the system x' = Ax can then be written as x(t) = Ce^(At), where C is a constant matrix. This solution represents a linear combination of exponential functions, where each component of x(t) is determined by the corresponding component of C and the matrix exponential of At.

The matrix exponential e^(At) has properties that are analogous to those of the scalar exponential function. It satisfies the initial condition e^(A * 0) = I, where I is the identity matrix, and it can be used to find solutions for different initial conditions by appropriately choosing the constant matrix C.

Learn more about Matrix here: brainly.com/question/29000721

#SPJ11