What is the following sum in simplest form? StartRoot 8 EndRoot 3 StartRoot 2 EndRoot StartRoot 32 EndRoot 3 StartRoot 8 EndRoot 3 StartRoot 2 EndRoot 5 StartRoot 42 EndRoot 9 StartRoot 2 EndRoot 5 StartRoot 2 EndRoot StartRoot 32 EndRoot.

A graph of the line that passes through the two points (-3/2, -3/2) and (3/2, 3/2) is shown in the image attached below.

In Mathematics and Geometry, the slope of any straight line can be calculated by using this mathematical equation (expression);

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

From the information provided above, we have the following data points located on the line:

Points on the x-coordinate = (-3/2, 3/2).

Points on the y-coordinate = (-3/2, 3/2).

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (3/2 + 3/2)/(3/2 + 3/2)

Slope (m) = 3/3 = 1

At point (-3/2, -3/2), an equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

Where:

y - (-3/2) = 1(x - (-3/2))

y + 1.5 = x + 1.5

y = x

Next, we would use an online graphing calculator to plot the linear equation as shown in the graph attached below.

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Simplify implies to reduce a mathematical expression to it lowest form. The 4th root of the given question is 6x.

Simplification is a process which requires showing a given equation in its most simple form. Such that it can not be simplified further i.e complete simplification.

To simplify the given question completely, convert all the terms to the power of 4. Because we are to simplify the 4th root of the given expression.

So that,

\(\sqrt[4]{1296x^{2} }\)  =  \(\sqrt[4]{(6^{4})(x^{4}) }\)

              = \(((6^{4})*(x^{4}) ^{\frac{1}{4} }\)

expand as follows;

\(((6^{4})*(x^{4}) ^{\frac{1}{4} }\) = \((6)^{\frac{4}{4} } (x)^{\frac{4}{4} }\)

                    = 6*x

                    = 6x

Therefore, the simplified form of the given question is 6x.

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Answer:

what do you need help with?

Step-by-step explanation:

❤️

In the standard (x, y) coordinate plane, lines p and q intersect at the point (1, 3), while lines p and r intersect at the point (2, 5).

In the given scenario, lines p and q intersect at the point (1, 3) and lines p and r intersect at the point (2, 5). Each point of intersection represents a solution that satisfies both equations of the respective lines.

The equations of lines p and q can be determined using the point-slope form or any other form of linear equation representation. Similarly, the equations of lines p and r can be determined to find their intersection point.

The coordinates (1, 3) and (2, 5) indicate the precise locations where the lines p and q, and p and r intersect, respectively, on the coordinate plane.

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The stretch of an exponential decay function is y = 2(1/5)ˣ

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

The list of exponential functions

An exponential function is represented as

y = abˣ

Where

In this case, the exponential function is a decay function

This means that

The value of b is less than 1

An example of this is, from the list of option is

y = 2(1/5)ˣ

Hence, the exponential decay function is y = 2(1/5)ˣ

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Complete question

Which is a stretch of an exponential decay function?

Of(x) = -(5)ˣ

Of(x) = 5(2)ˣ

O fix) = 2(1/5)ˣ

The volume of the right prism include the following: 8,640 in³.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

Next, we would determine the area of the triangle at the base of the right prism as follows:

Base area = 1/2 × ( 36 × 12)

Base area = 1/2 × 432

Base area = 216 in².

Now, we can calculate the the volume of this right prism:

Volume = base area × height

Volume = 216 × 40

Volume = 8,640 in³.

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The approximate probability that greater than 99 out of 160 students will pass their college placement exams is 0.2831.

To approximate the probability using the normal distribution, we can use the concept of the binomial distribution approximation to the normal distribution. In this case, we have a large sample size (160 students) and a probability of success (passing the exam) that is not extremely small or large (64%).

To calculate the probability that greater than 99 out of 160 students will pass the exam, we can use the normal approximation to the binomial distribution. The mean of the binomial distribution is given by μ = n * p, and the standard deviation is given by σ = sqrt(n * p * (1 - p)), where n is the sample size and p is the probability of success.

In this case, n = 160 and p = 0.64.

Therefore, the mean is μ = 160 * 0.64 = 102.4,

and the standard deviation is σ = sqrt(160 * 0.64 * (1 - 0.64)) ≈ 5.1055.

Now, we can calculate the probability using the normal distribution. We want to find the probability of having more than 99 students pass the exam out of 160, which is equivalent to finding the probability that the number of successes is greater than 99.

We can standardize the value using the z-score formula: z = (x - μ) / σ, where x is the desired number of successes. In this case, x = 99.5 (to account for continuity correction, as we're dealing with a discrete distribution).

z = (99.5 - 102.4) / 5.1055 ≈ -0.565

Using a standard normal distribution table or a calculator, we can find the probability corresponding to the z-score of -0.565, which is the probability of having more than 99 students pass the exam.

Looking up the z-score of -0.565 in the standard normal distribution table, we find that the probability is approximately 0.2831.

Rounding the answer to four decimal places, the approximate probability that greater than 99 out of 160 students will pass their college placement exams is 0.2831.

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Answer:

x=y-3/5

Step-by-step explanation:

y=5x+3

y-3=5x

y-3/5=x

x=y-3/5

The change in the nominal exchange rate, in Canada's perspective, is a depreciation of the Canadian dollar by 2.76%.

Nominal exchange rate is the price of one currency in terms of another currency. It represents the number of units of one currency that can be purchased with a single unit of another currency. In Canada's perspective, a change in nominal exchange rate means the value of the Canadian dollar in US dollars. So, to calculate the change in nominal exchange rate from Canada's perspective.

Nominal Exchange Rate = Real Exchange Rate x (1 + Inflation of Canada) / (1 + Inflation of US) Given, Real Exchange Rate of Canada

= 4.9% Inflation of Canada

= 8.5% Inflation of US

= 3.8%  Nominal Exchange Rate

= 4.9% x (1 + 8.5%) / (1 + 3.8%) Nominal Exchange Rate

= 4.9% x 1.085 / 1.038 Nominal Exchange Rate

= 5.3099 / 1.038 Nominal Exchange Rate

= 5.11 (rounded to two decimal places)

This means that if there were no inflation, the nominal exchange rate from Canada's perspective would have been 5.11 Canadian dollars per US dollar. But due to inflation, the Canadian dollar depreciated by 2.76% (calculated as (5.11 - 4.97) / 5.11 x 100%). Therefore, the change in the nominal exchange rate, in Canada's perspective, is a depreciation of the Canadian dollar by 2.76%.

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The answer is D! counter clockwise 180-degree rotation

Answer:

w=120°

x=45°

y=30°

Step-by-step explanation:

AT=PR, AR=PT

Therefore, y=30°

y+45°=x+30°

x=45°

In triangle:

y+30°+w=180°

w=120°

Hope it helps! :)

Answer:

8.5% tax rate

Step-by-step explanation:

17/200= 0.085 = 8.5%

Answer:

a slope is a number that describes both the direction and the steepness of the line.

Step-by-step explanation:

B ⨯ A = {(a,1), (a,2), (a,3), (b,1), (b,2), (b,3)}.

A ⨯ B = {(1,a), (1,b), (2,a), (2,b), (3,a), (3,b)}.

When A and B have the same cardinality, the sets B ⨯ A and A ⨯ B have the same number of elements, and therefore the same cardinality.

We have,

a)

B ⨯ A is the Cartesian product of B and A, which is the set of all ordered pairs (b, a) where b is an element of B and a is an element of A.

Therefore,

B ⨯ A = {(a,1), (a,2), (a,3), (b,1), (b,2), (b,3)}.

b)

A ⨯ B is the Cartesian product of A and B, which is the set of all ordered pairs (a,b) where a is an element of A and b is an element of B.

Therefore,

A ⨯ B = {(1,a), (1,b), (2,a), (2,b), (3,a), (3,b)}.

c)

The cardinality of a set is the number of elements in that set.

We can prove that |B ⨯ A| = |A ⨯ B| by showing that they have the same number of elements.

Let n be the number of elements in A, and let m be the number of elements in B.

|B ⨯ A| = m × n because for each element in B, there are n elements in A that can be paired with it.

|A ⨯ B| = n × m because for each element in A, there are m elements in B that can be paired with it.

Since multiplication is commutative, m × n = n × m.

So,

|B ⨯ A| = |A ⨯ B|.

The statement "B ⨯ A ≠ A ⨯ B" is not always true, but when it is, it means that A and B have different cardinalities.

In this case, |B ⨯ A| ≠ |A ⨯ B| because the order in which we take the Cartesian product matters.

However, when A and B have the same cardinality, the sets B ⨯ A and A ⨯ B have the same number of elements, and therefore the same cardinality.

Thus,

B ⨯ A = {(a,1), (a,2), (a,3), (b,1), (b,2), (b,3)}.

A ⨯ B = {(1,a), (1,b), (2,a), (2,b), (3,a), (3,b)}.

When A and B have the same cardinality, the sets B ⨯ A and A ⨯ B have the same number of elements, and therefore the same cardinality.

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Answer:

96 baceballs

Step-by-step explanation:

Hope this helps!

The given function f(x) = x² + x + 6 has a minimum value. Using the formula x = -b/2a, we find the x-coordinate of the minimum point as -1/2. Substituting this value back into the function, we get a y-coordinate of 5.75. Therefore, the parabola has a minimum value of 5.75. The correct answer is D.

The given function is f(x) = x² + x + 6. We can determine the maximum or minimum value of a parabola by analyzing its quadratic term (x²) coefficient.

In this case, the coefficient of the quadratic term is positive (1), indicating that the parabola opens upwards and has a minimum value.

To find the x-coordinate of the minimum point, we can use the formula x = -b/2a, where a is the coefficient of the quadratic term and b is the coefficient of the linear term.

For our function f(x), a = 1 and b = 1, so the x-coordinate of the minimum point is x = -1/(2*1) = -1/2.

Substituting this value back into the function, we can find the y-coordinate of the minimum point: f(-1/2) = (-1/2)² + (-1/2) + 6 = 1/4 - 1/2 + 6 = 5.75.

Therefore, the parabola modeled by function f has a minimum value of 5.75. Hence, the correct answer is D.

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The correct question would be as

Select the correct answer.

Consider function f.

f(x) = x² = x + 6

Which statement is true about the parabola modeled by function f?

A. The parabola has a maximum value of 0.5.

B. The parabola has a maximum value of 5.75.

C. The parabola has a minimum value of 0.5.

D. The parabola has a minimum value of 5.75.

610 students must be randomly selected to estimate the mean weekly earnings of students at one college.

We have to find our α level, that is the subtraction of 1 by the confidence interval divided by 2.

So: α = (1 - 0.95)/2

      α = 0.025

Now, we have to find z in the Z-table as such z has a p-value of 1 - α .

so, Z = 1.96

Now, find the margin of error M as such,

M = z(σ/√n)

In which  is the standard deviation of the population and n is the size of the sample.

The population standard deviation is known to be $63.

This means that σ = 63

ample mean within $5 of the population mean

This is n for which M = 5.

So, M = z(σ/√n)

5 = 1.96(63/√n)

2.55 = (63/√n)

√n = 24.70

n = 610.4

n ≈ 610

Therefore, 610 students must be randomly selected to estimate the mean weekly earnings of students at one college.

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Answer:

64

Step-by-step explanation:

320/5 = 64

Answer:

Your answer is 64 beats pm

Step-by-step explanation:

320 divided by 5= 64

The graph that represents the situation is required.

What is graph?

A graph is a structure that resembles a set of items in discrete mathematics, more especially in graph theory, in which certain pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Graphs are a popular tool for graphically illuminating data connections. A graph serves the objective of presenting facts that are either too many or complex to be fully expressed in the text while taking up less room.

Here the  X- axis denotes the number of hours and

Y- axis denotes the pounds of ice.

The given ordered pair is

\(\left(\frac{1}{2}, 1 \frac{1}{2}\right)=(0.5,1.5)\)

At zero hours the ice produced will be zero so, the third and fourth options are incorrect.

The only graph where the line passes through (0.5,1.5).

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Answer:

(h • g)(n) = 4n^2 + 2

Step-by-step explanation:

What we simply have to do here is to place g(n) into h(n)

Hence, we replace the n value in h(n) by the totality of g(n)

Thus, we have that

(2n)^2 + 2

= 4n^2 + 2

Answer:

you dont he never will

Step-by-step explanation:

he left

got milk

forgot about you

never came back

Answer:

He will neva come back

Step-by-step explanation:

Have a good day!

The balance after 10 years based on an interest rate of  5.25% will be $461.25.

The interest rate of the account can be calculated by using the formula I = P × R × T, where I is the interest amount, P is the original principal amount, R is the annual interest rate, and T is the time in years.

Using this formula, we can calculate the interest rate as follows:

I = 422 - 401 = 21

P = 401

T = 1

R = I / (P × T) = 21 / (401 × 1) = 0.0525

Therefore, the interest rate of the account is 5.25%.

To calculate the balance after 10 years, we can use the formula A = P(1 + rt), where A is the final amount (balance after 10 years), P is the original principal amount, r is the interest rate, and t is the number of years.

Using this formula, we can calculate the balance after 10 years as follows: A = 401(1 + 0.0525 × 10) = 461.25

Therefore, the balance after 10 years will be $461.25.

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The period of function is approximately 0.6465 days, which means that the pattern of daylight hours repeats approximately every 0.6465 days, or about every 15.55 hours.

A periodic function is a function that repeats its values in a regular pattern over a specified interval or set of input values.

More specifically, a function f(x) is said to be periodic with period P if, for all values of x in the domain of f(x), we have:

f(x + P) = f(x)

The period of a periodic function is the distance along the x-axis between two consecutive peaks or troughs of the graph of the function. For the given function f(x)=2.95sin(2π365x)+12.21, the coefficient of x in the argument of the sine function is 2π365, which represents the frequency of the oscillation.

The period P of a sine function with frequency f is given by:

P = 1/f

Therefore, for the given function, the period is:

P = 1/f = 1/(2π365) ≈ 0.00177 years

However, since the function is modeling the number of hours of daylight, it is more convenient to express the period in terms of days. One year has 365 days, so we can convert the period to days by multiplying it by 365:

P = 0.00177 × 365 ≈ 0.6465 days

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No, the determinant of a matrix can only be calculated for square matrices. A square matrix has an equal number of rows and columns, while a non-square matrix has a different number of rows and columns.

The determinant is a mathematical property that is defined for square matrices only. It is a scalar value that represents certain characteristics of the matrix. To calculate the determinant of a square matrix, you can use various methods such as expansion by minors, cofactor expansion, or using the properties of determinants.

For example, let's consider a 3x2 non-square matrix:

```

A = [[1, 2],

    [3, 4],

    [5, 6]]

```

Since A is a non-square matrix, we cannot calculate its determinant.

the determinant is a concept applicable only to square matrices. Non-square matrices do not have a determinant.

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The probability that the sample mean is between 1300 and 1400 is approximately 1.34%.

We can use the Central Limit Theorem and the standard normal distribution to calculate the probability that the sample mean is between 1300 and 1400. The Central Limit Theorem states that as the sample size increases, the distribution of the sample means will approach a normal distribution, regardless of the distribution of the population.

Since we have a sample of 80 observations, we can assume that the sample mean follows a normal distribution with a mean of 1460 (the population mean) and a standard deviation of:

Standard deviation of the sample mean

= population standard deviation ÷ \(\sqrt {sample size\)

\(= 270 \div \sqrt{80} = 27\)

So the standard deviation of the sample mean is 27.

We can now standardize the interval between 1300 and 1400 by subtracting the mean and dividing it by the standard deviation of the sample mean.

\(Z_1\) = (1300 - 1460) / 27 = -2.59

\(Z_2\) = (1400 - 1460) / 27 = -2.22

We need to find the area under the standard normal distribution curve between Z1 and Z2.

Using a standard normal table or a calculator with the standard normal distribution function, we can find the probability that a random variable from the standard normal distribution is between -2.59 and -2.22. This probability is approximately 0.0134 or 1.34%.

Therefore, the probability that the sample mean is between 1300 and 1400 is approximately 1.34%.

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Answer:

For an nth term U(n) = a + (n - 1)d

n = number of terms

a = first term

d = common difference

a = 5

d = 2 - 5 = - 3

U(n) = 5 + (n -1)-3

= 5 - 3n + 3

= 8 - 3n

The formula for the sequence is 8 - 3n

Hope this helps