Write 360 as a product of primes.
Use index notation when giving your answer

Answer:

6 is the ?

Step-by-step explanation:

The CPA selected the probability-proportional-to-size (PPS) sampling technique because it enables the selection of items in a population in proportion to the items' sizes. This technique yields a more accurate audit by precisely measuring the population of accounts receivable balances.

CPAs frequently employ the probability-proportional-to-size (PPS) sampling technique, also known as dollar-unit sampling, when examining the receivables balances of their clients. With this approach, it is possible to choose population members based on how big they are. The CPA can precisely gauge the population of accounts receivable amounts as a result, which is advantageous. A more accurate audit is made possible by the fact that the larger items in the population are more likely to be chosen than the smaller ones. Additionally, when the sample size grows, the audit's accuracy rises as well, which is another reason CPAs like to employ PPS sampling in their audits. This approach is advantageous because it ensures that the CPA is assessing the population of accounts receivable balances precisely and that the audit is carried out in a precise and trustworthy manner.

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If the teacher's crayon has a mass of 20 grams her bottle of glue is 65 grams more than the crayon the mass of the glue is 85 grams.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3, since each term after the first is found by adding 3 to the preceding term.

The nth term of an arithmetic sequence can be found using the formula:

an = a1 + (n-1)d

The mass of the glue is the sum of the mass of the crayon and the additional 65 grams.

So, the mass of the glue would be:

20 grams (mass of the crayon) + 65 grams (additional mass of the glue) = 85 grams.

Therefore, the mass of the glue is 85 grams.

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If we change an estimate with a 95% confidence interval to one with a 99% confidence interval, (A) we can expect the width of the confidence interval to widen.

We have a 5% probability of being incorrect with a 95% confidence interval.

We have a 10% probability of being incorrect with a 90% confidence interval.

A 95% confidence interval is narrower than a 99% confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).

We can anticipate an increase in the width of the confidence interval if we convert an estimate with a 95% confidence interval to one with a 99% confidence interval.

The 68-95-99.7 Rule states that 95% of values fall within two standard deviations of the mean, hence to calculate the 95% confidence interval, you add and subtract two standard deviations from the mean.

Therefore, if we change an estimate with a 95% confidence interval to one with a 99% confidence interval, (A) we can expect the width of the confidence interval to widen.

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Complete question:
If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the _____.

a. width of the confidence interval to increase

b. width of the confidence interval to decrease

c. width of the confidence interval to remain the same

d. sample size to increase

The magnitude of the force per unit length that each wire exerts on the other wire is 3 × 10⁻⁷ N/m.

Using Ampere's law, the force per unit length (F/L) between two parallel wires carrying currents I1 and I2 and separated by a distance d can be calculated as:

F/L = (μ0 ⨯ I1 ⨯ I2) / (2 ⨯ π ⨯ d)

Where μ0 is the permeability of free space (4π × 10⁻⁷ T⋅m/A),

I1 is the current in the first wire (4.00 A),

I2 is the current in the second wire (6.00 A), and d is the distance between the wires (0.400 m).

F/L = (4π × 10⁻⁷ T⋅m/A ⨯ 4.00 A ⨯ 6.00 A) / (2 ⨯ π ⨯ 0.400 m)

F/L = (24π × 10⁻⁷ T⋅m/A) / (0.800 m)

F/L = 3 × 10⁻⁷ ) T⋅m/A

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Answer:

glad it helps

Step-by-step explanation:

(4-5)- (13-18+2)

(-1)-13+18-2

= 2

Answer:

52

Step-by-step explanation: Just Multiply 4x13

Answer:

-$52

Step-by-step explanation:

-$13 * 4 = -$52

(i think it's negative because it ask for the change.)

There were 18 chickens in the field. Thus, the farmer saw 18 chickens and 12 pigs in the field.

Let x be the number of chickens and y be the number of pigs the farmer saw.

Then, we can write a system of equations:

x + y = 30 (since the total number of heads is 30)

2x + 4y = 84 (since chickens have 2 legs and pigs have 4 legs)

To solve for x and y, we can use the method of substitution.

Solving the first equation for x, we get: x = 30 - y

Substituting this into the second equation, we get: 2(30 - y) + 4y = 84

Simplifying, we get: 60 - 2y + 4y = 84 2y = 24 y = 12

So there were 12 pigs in the field.

To find the number of chickens, we can substitute this value back into either of the original equations.

Using the first equation, we get:

x + 12 = 30

x = 18

Therefore, there were 18 chickens in the field. Thus, the farmer saw 18 chickens and 12 pigs in the field.

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Answer: 2x^2

Step-by-step explanation:

    (x+5)

 x (2x - 9)

-----------------

X times 2x = 2x^2

I think is D

PLEASE MARK ME AS BRAINLIEST

Answer:

Part A-

Answer- f(x) is the profit made from selling 'x' number of salads.

Part B-

Question- Identify and interpret the key features of the function in the context of the situation you described in part A.

Answer-

End behavior- As 'x' approaches 25, f(x) approaches 20. As 'x' approaches 1, f(x) approaches 4.

Domain- 1, 4, 9, 16, 25

Range- 4, 8, 12, 16, 20

x and y- intercepts- None

Maximum- 20

Minimum- 4

Step-by-step explanation:

Mark as brainliest please :)

Answer:

the product of 46×58 is 2,668

Answer:

The product of 46 and 58 is 2,668.

Solution:

46

× 58

———

2,668

— based on my knowledge

We can see that the first component of the vector equation is always zero, so the parabola lies in the xz-plane.

Moreover, the second component is a quadratic function of t, which gives us a vertical parabola when plotted in the yz-plane. The third component is a linear function of t, so the curve extends infinitely in both directions. Therefore, we have a vertical parabola in the xz-plane.

This statement is referring to a specific vector-valued function, which we can write as:

f(t) = (0, t^2, ct)

where c is a constant.

The second component of this vector function is t^2, which is a quadratic function of t. When we plot this function in the yz-plane (i.e., we plot y = t^2 and z = 0), we get a vertical parabola that opens upward. This is because as t increases, the value of t^2 increases more and more quickly, causing the curve to curve upward.

The third component of the vector function is ct, which is a linear function of t. When we plot this function in the xz-plane (i.e., we plot x = 0 and z = ct), we get a straight line that extends infinitely in both directions. This is because as t increases or decreases, the value of ct increases or decreases proportionally, causing the line to extend infinitely in both directions.

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Withdrawls=$127.38, 38.26$

Total withdrawl:-

\(\\ \sf\longmapsto 127.38+38.26=165.64\)

Final balance=

\(\\ \sf\longmapsto 500-165.64+25=500-140.64=359.36\$\)

Their initial balance was =$500.00 so

They  With drawled =  $127.38, 38.26$

127+ 38.26=165.64

Deposit=25.00

so just add their deposit

165.64  and then subtract 500 and add 25 because they withdrew and then added money!

Final balance= 359.36

It will take 11 years for the canyon floor to have an elevation of −31 feet.

A mathematical statement known as an equation makes two expressions' values equal. It is a mathematical statement that says "this is equivalent to that," in other words. The left side appears to be a mathematical expression, the centre appears to be an equal sign, and the right side is another mathematical expression. The right side of the equation frequently has a value of zero.

Given,

The first step in this situation is to define the variables.

So, we have:

x: the age in years

y: height in feet

The equation used to model the issue is then written.

So, we have:

y = 1.5x - 14.5

Then, at a -31 foot elevation, we have:

-31 = 1.5x - 14.5

For years,

x = -16.5/1.5

x = 11

In 11 years it will take for the canyon floor to have an elevation of −31 feet.

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It's C.

Basically, when youre dividing something, the bases would stay the same but the exponents would change. For division, you'd have to substract the exponent of the denominator from the denominator (of like bases, of course)

In this case, it's 10^8-(-3).

The only reason it's not 10⁵ is because of the negative 3. If it were a positive 3, it would become 10⁵.

2.25 as a fraction is 9/4

Convert decimal into a fraction:

The first step to converting 2.25 to a fraction is to re-write 2.25 in the form p/q where p and q both are positive integers:

= 2.25/1

Multiply both numerator and denominator by 100 to remove a decimal point from the numerator:

= 2.25 x 100 / 1 x 100

= 225 / 100

Now the last step is to simplify the fraction by finding similar factors and cancelling them out:

= 225/100 = 9/4

so, the fraction form is  9/4

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Answer:

29

Step-by-step explanation:

69/2

Answer:

16

Step-by-step explanation:

x + 3= 9

x = 6

2x + 4= 2*6 + 4

2x + 4 = 12 + 4

2x + 4 =16

Charlies 16

hope it helps

Answer: he is 16

Step-by-step explanation:

Let x = Frank's age

2x+4+ = Charlie's age

x+3+ = Bob's age

9 = Bob's age

x+3=9

x=6

2x+4=2⋅6+4

2x+4=12+4

2x+4=16

Charlie is 16

One such vector is: w = (1/sqrt(2))<0, 0, 20> = <0, 0, 10sqrt(2)>. To find the vector in the direction of maximum rate of change,

we need to find the gradient of f(x, y) at the point (-1, 2) and then normalize it. The gradient of f(x, y) is given by: grad(f) = <2xy^3, 3x^2y^2> ,So, at the point (-1, 2),

we have: grad(f) = <−16, 12>, To normalize this vector, we need to divide it by its magnitude: ||grad(f)|| = sqrt((-16)^2 + 12^2) = 20 .

So, the vector in the direction of maximum rate of change is: v = (1/20)<−16, 12> = <-0.8, 0.6>, To find the vector in the direction of minimum rate of change, we can find the negative of the gradient and normalize it: grad(f) = <−16, 12>, ||grad(f)|| = 20.

So, the vector in the direction of minimum rate of change is: v = (1/20)<16, -12> = <0.8, -0.6>, Finally, to find a direction in which the rate of change is zero, we need to find a vector perpendicular to the gradient. One way to do this is to take the cross product of the gradient with any nonzero vector in the plane.

For example, we can take the vector <1, 0>: grad(f) = <−16, 12>, v = <1, 0>, u = v x grad(f) = <0, 0, 20>, So, any vector in the direction of u will have zero rate of change. One such vector is: w = (1/sqrt(2))<0, 0, 20> = <0, 0, 10sqrt(2)>.

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The compound interval for the given interval is (-∞, ∞).

A compound inequality is a combination of two inequalities that are combined by either using "and" or "or". The process of solving each of the inequalities in the compound inequalities is as same as that of a normal inequality but just while combining the solutions of both inequalities depends upon whether they are clubbed by using "and" or "or".

The given intervals are (-∞, -2] or [-3, ∞).

Now, the compound interval is (-∞, ∞)

Thus, the interval notation is -∞<x<∞

Therefore, the compound interval for the given interval is (-∞, ∞).

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Answer:

The third is correct.

Step-by-step explanation:

Preimage: A(2,3), B(5,6), C(8,6), D(8,3)

Image: A'(-2, 6); B'(-5,3); C'(-8,3); D'(-8,6)

Option 3.

                Translation              Rotation 180° Clockwise

                   (x, y-9)                              (-x,-y)

A(2,3)            (2,-6)                              A' (-2,-6)

B(5,6)            (5,-3)                              B' (-5,3)

C(8,6)            (8,-3)                              C' (-8,3)

D(8,3)            (8,-6)                               D' (-8,6)

Transformation involves changing the position of a shape.

The sequence of transformation is: (d) A translation rule by \(\mathbf{(x,y) \to (x, y - 9)}\) and then a 180 degrees clockwise rotation about the origin

The coordinates of the pre-image is:

\(\mathbf{A = (2,3)}\)

\(\mathbf{B = (5,6)}\)

\(\mathbf{C = (8,6)}\)

\(\mathbf{D = (8,3)}\)

Of the given sequence of transformations, option (d) is correct.

The proof is as follows.

First, translate ABCD by (x, y - 9)

So, we have:

\(\mathbf{(x,y) \to (x, y - 9)}\)

\(\mathbf{(2,3) \to (2, -6)}\)

\(\mathbf{(5,6) \to (5, -3)}\)

\(\mathbf{(8,6) \to (8, -3)}\)

\(\mathbf{(8,3) \to (8, -6)}\)

Next, rotate by 180 degrees.

The rule of this transformation is:

\(\mathbf{(x,y) \to (-x,-y)}\)

So, we have:

\(\mathbf{(2,-6) \to (-2,6)}\)

\(\mathbf{(5,-3) \to (-5,3)}\)

\(\mathbf{(8,-3) \to (-8,3)}\)

\(\mathbf{(8,-6) \to (-8,6)}\)

From the graph, the coordinates of the image are:

\(\mathbf{A" = (-2, 6)}\)

\(\mathbf{ B" = (-5,3)}\)

\(\mathbf{C" = (-8,3)}\)

\(\mathbf{D" = (-8,6)}\)

Hence, the sequence of transformation is:

(d) A translation rule by \(\mathbf{(x,y) \to (x, y - 9)}\) and then a 180 degrees clockwise rotation about the origin

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Answer:

what are the choices

Step-by-step explanation:

(a)The population of interest is the entire university community at Botho University. (b)The sample is the random sample of 200 members. (c)The average time spent in the library, which is 30 minutes, is a statistic because it is computed from the sample and represents a characteristic of the sample, not the entire population.

a) The population of interest in this case would be the entire university community at Botho University. It includes all members of the university community who could potentially spend time in the library.

b) The sample in this case is the random sample of 200 members that was taken from the university community. It represents a subset of the population of interest and is used to make inferences about the larger population.

c) In this case, 30 minutes is a statistic, not a parameter.

A statistic is a value calculated from a sample that describes some characteristic of the sample. In this case, the average time spent in the library, which is 30 minutes, was computed from the sample of 200 members. It represents the average time spent in the library by the sampled members.

On the other hand, a parameter is a value that describes a characteristic of the population. Since the average time spent in the library is based on the sample and not the entire population, it cannot be considered a parameter.

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No, the system is inconsistent.

Explanation:

1. Consistency in a system of linear equations means that there exists at least one solution that satisfies all the equations.

2. An augmented matrix is a matrix that represents the system of linear equations by arranging the coefficients and constants in a matrix form.

3. In the augmented matrix, the pivot columns are the columns that contain the leading non-zero entry in each row.

4. For a system of linear equations with a 3x5 augmented matrix, there can be at most 3 pivot columns since each row can have only one leading non-zero entry.

5. If the fifth column of the augmented matrix is not a pivot column, it means that there are only 4 pivot columns in total.

6. Having more variables than pivot columns implies that there are free variables that can take any value.

7. The presence of free variables leads to either no solution or an infinite number of solutions, depending on the specific values assigned to the free variables.

8. Since the system has more variables than pivot columns (4 instead of 5), it indicates the presence of free variables, resulting in either no solution or an infinite number of solutions.

9. Therefore, the system is not consistent.

In summary, the system is inconsistent because the fifth column of the augmented matrix is not a pivot column, indicating the presence of free variables and resulting in either no solution or an infinite number of solutions.

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Line 'b' is perpendicular to line 'a'. Then the slope of line 'b' is 5/4.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The points are given below.

(7, 10) and (2, 14)

The slope of the line 'a' is given as,

m = (14 - 10) / (2 - 7)

m = - 4 / 5

Line 'b' is perpendicular to line 'a'. Then the slope of the line 'b' is given as,

Slope = - 1 / m

Slope = - 1 / (-4/5)

Slope = 5/4

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Answer:

205,000

Step-by-step explanation:

(100,000*0.05) *21 +100,000

Answer:

Angle b=41.

Step-by-step explanation:

(2x+8) + (2x+8)=180...4x+16=180... subtract 16 from 180...4x=164 divide by 4 you get 41.

Answer:

The Real Answer is 82 721 x 912 Because of its high rotation

Step-by-step explanation:

Answer:

10^6

Step-by-step explanation:

Just multiply

Answer:

10^6

Step-by-step explanation:

just add one zero because there is only one zero in 10

The solution to the given differential equation is: x⁷ cos y = y + C

where C is the constant of integration

To solve the given differential equation:

\(\[7x^6\cos y dx - dy = 0\]\)

We can separate the variables and integrate both sides.

Separating variables, we can write the equation as:

\(\[7x^6\cos y dx = dy\]\)

Now, we can integrate both sides with respect to their respective variables:

\(\[\int 7x^6\cos y dx = \int dy\]\)

Integrating the left side:

\(\[\int 7x^6\cos y dx = 7 \int x^6 \cos y dx\]\)

To integrate \(\(x^6 \cos y\)\)with respect to x, we can use integration by parts.

Let's take u = x⁶ and \(\(dv = \cos y dx\)\).

Differentiating u with respect to \(\(x\) gives \(du = 6x^5 dx\).\)

Integrating dv with respect to x gives \(\(v = \int \cos y dx = \cos y \cdot x\).\)

Applying the integration by parts formula:

\(\[\int x^6 \cos y dx = u \cdot v - \int v \cdot du\]\)

Substituting the values:

\(\[\int x^6 \cos y dx = x^6 \cdot \cos y \cdot x - \int (\cos y \cdot x) \cdot (6x^5 dx)\]\)

Simplifying:

\(\[\int x^6 \cos y dx = x^7 \cos y - 6 \int x^6 \cos y dx\]\)

Moving the integral term to the left side:

\(\[7 \int x^6 \cos y dx = x^7 \cos y\]\)

Dividing both sides by 7:

\(\[\int x^6 \cos y dx = \frac{x^7 \cos y}{7}\]\)

Now, substituting this result back into our original equation:

\(\[7 \int x^6 \cos y dx = dy\]\)

\(\[\frac{7x^7 \cos y}{7} = dy\)

Simplifying:

x⁷ cos y = dy

Finally, the solution to the given differential equation is:

x⁷ cos y = y + C

where C is the constant of integration.

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