which expression is equivalent to 5^4 x (5^-3)

A. 5^1
B. 5^2
C. (1/5)^1
D. (1/5)^2

Answer:

r = - 189

Step-by-step explanation:

Given

- 13 = \(\frac{r}{9}\) + 8 ( subtract 8 from both sides )

- 21 = \(\frac{r}{9}\) ( multiply both sides by 9 )

- 189 = r

Answer: r= -189

Step-by-step explanation:

An approach of assigning probabilities which assumes that all outcomes of the experiment are equally likely is referred to as the "equally likely" or "classical" probability approach

The equally likely or classical probability approach assumes that each possible outcome of an experiment is equally likely to occur. This approach is based on the principle of symmetry and assumes that there is no inherent bias or preference towards any particular outcome

This approach is used for situations where there is no inherent bias or preference towards any particular outcome, and each outcome is considered equally likely to occur.

Therefore, the approach is classical probability approach

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Given the numbers:

Let's arrange the numbers from the least to the greatest without the use of a calculator.

Now, let's first simplify each term.

We have:

Therefore, arranging the numbers from the least to the greatest, we have:

Answer:

n=-3.1

Step-by-step explanation:

To solve this, first subtract 3 from both sides of the equation to get 2n=-6.2. Next, divide both sides of the equation by 2 n order to get the final answer of n=-3.1

Step by step answer:

Both triangles are isosceles.

For the right triangle:

69+69=138

180-138=42

For the right angle:

The 42 degrees meets at a right angle.

90-42=48

For the left triangle:

180-48=132

132÷2=66

x=66°

Answer:

see explanation

Step-by-step explanation:

to find the pre- image coordinates use the opposite vector to translate the image coordinates.

the opposite vector to (4, - 3 ) is (- 4, 3 ) , then

(- 1, 3 ) → (- 1 - 4, 3 + 3 ) → (- 5, 6 )

(3, - 4 ) → (3 - 4, - 4 + 3 ) → (- 1, - 1 )

(4, 0 ) → (4 - 4, 0 + 3 ) → (0, 3 )

Answer:

(3, - 4 ) → (3 - 4, - 4 + 3 ) → (- 1, - 1 )

(4, 0 ) → (4 - 4, 0 + 3 ) → (0, 3 )

Step-by-step explanation:

to find the pre- image coordinates use the opposite vector to translate the image coordinates.

the opposite vector to (4, - 3 ) is (- 4, 3 ) , then

(- 1, 3 ) → (- 1 - 4, 3 + 3 ) → (- 5, 6 )

(3, - 4 ) → (3 - 4, - 4 + 3 ) → (- 1, - 1 )

(4, 0 ) → (4 - 4, 0 + 3 ) → (0, 3 )

Hence, the correct answers are (3, - 4 ) → (3 - 4, - 4 + 3 ) → (- 1, - 1 ),

(4, 0 ) → (4 - 4, 0 + 3 ) → (0, 3 )

Answer:

-3/4

Step-by-step explanation:

If you take two points, the rise is 3. Also, the change in y is 4. Since the line is going downwards from left to right, it has to be negative.  

a) The rate at which the top of the ladder is sliding down the wall when the bottom of the ladder is 5 m from the wall is -0.1 m/s.

b) The rate of change of the angle between the ground and the ladder when the bottom of the ladder is 5 m from the wall is -25/676 rad/s.

c) The rate of change of the area of the triangle bounded by the ladder, the building, and the ground, when the bottom of the ladder is 5 m from the wall is 3.5 m^2/s.

a) To find the rate at which the top of the ladder is sliding down the wall, we start by expressing the length of the ladder, z, in terms of the distances x and y using the equation z^2 = x^2 + y^2.

By differentiating this equation with respect to time, we obtain 2z(dz/dt) = 2x(dx/dt) + 2y(dy/dt), where dz/dt represents the rate of change of z, dx/dt is the rate at which x is changing, and dy/dt is the rate at which y is changing.

Given that dx/dt = 0.6 m/s, x = 5 m, and z = 13 m, we can substitute these values into the equation and simplify to find 13(dz/dt) = 3 + y(dy/dt).

To isolate dy/dt, we differentiate equation (1) with respect to t, resulting in dy/dt = [2z(dz/dt) - 2x(dx/dt)] / (2y).

Substituting the given values and dz/dt = 0.6, we find dy/dt = (13/12)(dz/dt) - (1/2). Plugging in dz/dt = 0.6, we obtain dy/dt = (13/12) * 0.6 - 0.5 = -0.1 m/s. The negative sign indicates that the top of the ladder is sliding down the wall.

b)

This can be determined by differentiating the equation involving the tangent of the angle and applying the chain rule.

To find the rate of change of the angle, θ, between the ground and the ladder, we start with the equation tan θ = y/x. By differentiating both sides with respect to t,

we get sec^2θ(dθ/dt) = (1/x)dy/dt,

where dθ/dt represents the rate of change of θ.

Substituting x = 5, y = 12, and dy/dt = -0.1, we find sec^2θ = 25/169.

Taking the square root of both sides, we get secθ = 13/5.

To find dθ/dt, we have (dθ/dt) = [(1/x)dy/dt] / sec^2θ = (5/169)(-0.1) / (169/25) = -25/676 rad/s.

c)

This can be determined by differentiating the equation for the area of the triangle.

The area of the triangle, A, can be expressed as A = (1/2)xy. By differentiating with respect to t, we find dA/dt = (1/2)[x(dy/dt) + y(dx/dt)], where dA/dt represents the rate of change of the area.

Substituting the given values and calculating, we find

dA/dt = (1/2)[5*(-0.1) + 12*0.6] = 3.5 m^2/s.

Thus, the rate of change of the triangle's area is 3.5 m^2/s.

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Answer:

3

Step-by-step explanation:

2 times 1 is 2 and then multiply 1/2 by 2 and you'll get 1 then add those two numbers together and you will get 3.  Note: The best way to do these types of things in multiplication is to split the numbers up among the decimal places so if you did 15 times 4 then an easy way to do it would be to split the 15 with 10 and 5 so then multiply the 10 by 4 and you get 40 now do the same to the 5 and you get 20 so now add those two numbers together and you get 60(This has nothing to do with the answer i just want to help make it easier for future problems such as this).

Answer:

3

Step-by-step explanation:

[Given]

2 * \(1\frac{1}{2}\)

[Make improper fractions and solve by multiplying across]

\(\frac{2}{1}*\frac{3}{2} =\frac{6}{2}=3\)

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

1/8

Step-by-step explanation:

50/100 * 25/100

1/2 * 1/4 = 1/8

Based on the given conditions, Jane has $31, Kevin has $25, and Hans has $50 in their wallets.

Let's solve the problem step by step.

First, let's assume that Jane has X dollars in her wallet. Since Kevin has $6 less than Jane, Kevin would have X - $6 dollars in his wallet.

Next, we're given that Hans has 2 times what Kevin has. So, Hans would have 2 * (X - $6) dollars in his wallet.

According to the information given, the total amount of money they have in their wallets is $106. We can write this as an equation:

X + (X - $6) + 2 * (X - $6) = $106

Simplifying the equation:

4X - $18 = $106

4X = $124

X = $31

Now we know that Jane has $31 in her wallet.

Substituting this value into the previous calculations, we find that Kevin has $31 - $6 = $25 and Hans has 2 * ($25) = $50.

To find the total amount they have, we sum up their individual amounts:

Jane: $31

Kevin: $25

Hans: $50

Adding these amounts together, we get $31 + $25 + $50 = $106, which matches the total amount stated in the problem.

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The complete question is:

Jane, kevin and hans have a total of $106 in their wallets. kevin has $6 less than Jane. hans has 2 times what kevin has. how much do they have in their wallets?

Answer:The answer is (√229)/6

Step-by-step explanation: i dont know

Answer:

\((\)√\(\frac{229}{6}\)\()\)

Step-by-step explanation:

Easy.

Answer:

16.5 :)

Step-by-step explanation:

hope this helps !!

The values of the given expression having exponent with negative fractional base i.e. \(-2^{(3/2)^2}\\\) is evaluated out to be 16/9.

First, we need to simplify the expression inside the parentheses using the rule that says "exponents with negative fractional base can be rewritten as a fraction with positive numerator."

\(-2^{(3/2)^2}\) = (-2)² × (2/3)²

Now, we can simplify the expression  further by solving the exponent of (-2)² and (2/3)²:

(-2)² × (2/3)² = 4 × 4/9 = 16/9

Therefore, the value of the given expression \(-2^{(3/2)^2}\\\)  is 16/9.

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The question is :

What is the value of the expression \(-2^{(3/2)^2}\) ?

To determine the mean, variance, and standard deviation of the distribution representing the number of credit cards people own, we can use the formulas for these statistical measures. The mean represents the average number of credit cards, the variance measures the spread or variability of the data, and the standard deviation is the square root of the variance

To calculate the mean, we multiply each value of X by its corresponding probability P(x) and sum the results. The variance is calculated by finding the squared difference between each value of X and the mean, multiplying it by the corresponding probability, and summing the results. The standard deviation is the square root of the variance. By performing these calculations, we can determine if the mean is indeed three credit cards and assess the accuracy of the Vice President's claim.

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If a first time homebuyer is given the choice of two loans: loan a: 390,000, 15 year-fixed, 4 discount points. The amount the hole buyer save in total by choosing loan is:  b) 11,427.

To compare the total cost of each loan, we need to calculate the total payments made over the life of the loan.

For loan A, the monthly payment is $3,509.71 and the loan term is 15 years, so the total payments would be:

Total payments = monthly payment x number of months

Total payments = $3,509.71 x (15 x 12)

Total payments = $631 747.8

However, loan A also has a 4-point discount, which means the borrower paid 4% of the loan amount upfront to reduce the interest rate.

Discount points = loan amount x discount rate

Discount points = $390,000 x 0.04

Discount points = $15,600

To calculate the total cost of loan A, we need to add the discount points to the total payments:

Total cost of loan A = total payments + discount points

Total cost of loan A = $631 747.80 + $15,600

Total cost of loan A = $647,347.80

For loan B, the monthly payment is $3,659.86 and the loan term is 15 years, so the total payments would be:

Total payments = monthly payment x number of months

Total payments = $3,659.86 x (15 x 12)

Total payments = $658,774.5

To calculate the total cost of loan B, we simply add the total payments:

Total cost of loan B = total payments

Total cost of loan B =  $658,774.5

Therefore, the total amount saved by choosing loan A over loan B is:

Savings = total cost of loan B - total cost of loan A

Savings = $658,774.5 - $647,347.80

Savings = $11,427

Therefore, the answer is option b) $11,427.

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The given telescoping series ∑n=1 to infinity (4n^4 - 4(n-1)^4) diverges. The given telescoping series diverges, and no finite sum can be assigned to it.

To determine the sum of the telescoping series, let's expand the terms and simplify the expression.

Expanding (n-1)^4 gives us n^4 - 4n^3 + 6n^2 - 4n + 1. Subtracting this from 4n^4 gives us 4n^4 - (n^4 - 4n^3 + 6n^2 - 4n + 1) = 3n^4 + 4n^3 - 6n^2 + 4n - 1.

Now, we can rewrite the series as ∑n=1 to infinity (3n^4 + 4n^3 - 6n^2 + 4n - 1).

Upon inspection, we notice that the terms do not cancel each other out, and there are no common patterns that would allow us to simplify the series or find a closed form.

The series will continue to increase without bound as n approaches infinity. Therefore, the given telescoping series diverges, and no finite sum can be assigned to it.

Hence, the sum of the telescoping series is ∅ (empty set), indicating that it diverges.

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Therefore, The correct change to Badri's table is to switch "indirect" to "direct" and "direct" to "indirect" in the second column. The relationship between distance and the electric force is direct, while for mass it is indirect.

Explanation: The table created by Badri has an error in the second column where the relationship to the strength of electric force for distance is listed as indirect and for mass is listed as direct. This is incorrect as the relationship for distance is actually direct and for mass is indirect. Therefore, the correct change to the table would be to switch "indirect" to "direct" and "direct" to "indirect" in the second column.

Therefore, The correct change to Badri's table is to switch "indirect" to "direct" and "direct" to "indirect" in the second column. The relationship between distance and the electric force is direct, while for mass it is indirect.

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Answer: 4 exercises

Step-by-step explanation:

If we completed 87.5% of the math exercises before dinner, then we have completed 0.875 × total number of exercises.

Let "\(x\)" be the total number of exercises.

\(0.875x = 28\)

Solving for \(x\), we get:

\(\boxed{\begin{minipage}{4 cm}\text{\LARGE 0.875x = 28 } \\\\\\ \large $\Rightarrow$ $\frac{0.875x}{0.875}$ = $\frac{28}{0.875}$\\\\$\Rightarrow$x = 32\end{minipage}}\)

Therefore, the total number of exercises is 32.

We completed 28 exercises before dinner, so we have:  32 - 28 = 4 exercises left to do after dinner.

________________________________________________________

An exponential function. The explanation involves solving the differential equation f'(x) = kf(x) using separation of variables, and the long answer includes a more detailed derivation of the general solution.

If f(x) is a function whose derivative is a constant multiple of itself, then we can write this as:
f'(x) = kf(x)
where k is a constant. This is a first-order homogeneous differential equation, which has the general solution:
f(x) = Ce^(kx)
where C is a constant of integration. This is an exponential function.

To see why an exponential function is the solution to the differential equation f'(x) = kf(x), we can use the technique of separation of variables. We can write:
f'(x)/f(x) = k
Now we can integrate both sides with respect to x:
∫ f'(x)/f(x) dx = ∫ k dx
ln|f(x)| = kx + C
where C is another constant of integration. Solving for f(x), we get:
f(x) = Ce^(kx)
as before.
This means that any function of the form Ce^(kx) satisfies the differential equation f'(x) = kf(x), where k is a constant. This includes functions like 2e^(3x), 0.5e^(0.2x), and so on.

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p(x)= (x-4)²-(x-6)². ... 4X - 20 = 0 => X = 20/4 => X= 5.

Number of rooms left excluding a quarter of 140 is: 105 rooms.

A quarter is one-fourth. A quarter of a number is therefore, one-fourth of that number or 1/4 part of the number.

Therefore, number of rooms cleaned = 1/4(140) = 35.

A quarter of the 140 rooms is: 35.

Number of rooms left for cleaning in the afternoon = 140 - 35

Number of rooms left for cleaning in the afternoon = 105 rooms.

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using exponents, On simplifying the equation, we get =4m+8.

The PEMDAS order of operations must be followed when you want to simplify a mathematical equation without using parenthesis (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). There are no parenthesis in the expression, so you may start looking for exponents. If it does, first make that simpler.

Work simplification is to develop better work processes that boost output while cutting waste and costs.

Simplifying an expression is the same as solving a mathematical issue. When you simplify an equation, you essentially try to write it as simply as you can. There shouldn't be any more multiplication, dividing, adding, or deleting to be done when the process is finished.

Given equation,

m-(8-3m)

=m-8+3m

=4m+8

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Answer: b

Step-by-step explanation:

Answer:

A: the solution set includes all values of x greater than -8 and less than 9

Step-by-step explanation:

In order to figure out what the solution set is, we have to isolate the x in the middle of the inequality. To do that, we have to subtract each aspect of the inequality by 8, which is the constant in the middle (just like we would do to isolate a variable in an equation):

\(0-8 < 8+x-8 < 17-8\\-8 < x < 9\)

Now that we have simplified the inequality, we see that x has to be greater than -8 and less than 9. So, the solution set includes all values of x greater than -8 and less than 9. In other words, the answer is A

Answer:10

Step-by-step explanation:Multiply 10*10

The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.

First, we take the derivative of the equation with respect to x:

2x/a^2 = -2y/b^2 * dy/dx

Simplifying, we get:

dy/dx = -b^2*x/a^2*y

Now, we set this equal to -1/b^2:

-b^2*x/a^2*y = -1/b^2

Cross-multiplying and simplifying, we get:

x/a^2*y = 1/b^2

Finally, we can rearrange this equation to get:

y = b^2*x/a^2

This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

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Statements that are true:
- The survey was conducted on a random sample of American adults.
- The sample size is large enough to conduct a hypothesis test.
- The sampling distribution can be assumed to be approximately normally distributed due to the large sample size.

To determine whether conditions are met for conducting a hypothesis test, we need to consider the following factors:

1. Random sampling: The survey should be based on a random sample of the population. In this case, the survey was conducted among 500 randomly selected American adults, which satisfies this condition.

2. Sample size: The sample size should be large enough to make the results more reliable. With 500 participants, the sample size is reasonably large.

3. Normality: The sampling distribution should be approximately normally distributed. Given the large sample size, we can apply the Central Limit Theorem, which states that the sampling distribution of the proportion will be approximately normally distributed.

Based on these conditions, we can conclude that it is appropriate to conduct a hypothesis test for the given situation.

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