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Part 1
Find the amount in the account for the given​ principal, interest​ rate, time, and compounding period.
P​$​, r​%, t ​years; compounded quarterly

Answer:

Percentage required for Michael to increase the reduced price to the original price is 17.647 %

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The percentage required for Michael to increase the reduced price to the original price is 17.647 %

What is the Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data,

Let the price of an item be = $ 100

Now, the price of the item has been reduced by 15 % by Michael

So, the new price of the item is

Reduced Price = 100 - 15% of 100

                        = 100 - ( 15/100 ) x 100

                        = 100 - 15

                         = $ 85

So, the reduced price is $ 85

Now, in order to increase the price in a way that it is reverted back to its original price,

Let the percentage required = x %

The original price = x % of the Reduced Price

Substituting the values, we get

Original price = x % of Reduced Price

100 = ( x/100 ) × 85

Multiply by 100 on both sides, and we get

85x = 10000

x = 117.647 %

So, the increase in percentage is 117.647 - 100 = 17.647 %

Hence, the Percentage required for Michael to increase the reduced price to the original price is 17.647 %

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Answer:

2827.43

I think this should be correct

Answer:

\(706.5\)

Step-by-step explanation:

The circumference can be rearranged to solve for r, or radius

C= 2πr ⇒ r=C/2π

\(\frac{94.2}{(2)(3.14)}=15\)

r=15

A= πr²

\(A=(3.14)(15)^{2}\)

\(A=(3.14)(225)\)

\(A=706.5\)

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The following data shows the daily production of cell phones. 7, 10, 12, 15, 18, 19, 20. Mean The formula for finding the mean is: mean = (sum of observations) / (number of observations).

Therefore, the mean for the daily production of cell phones is: Mean = (7+10+12+15+18+19+20) / 7

= 101 / 7

Mean = 14.43

Variance The formula for finding the variance is: Variance = (sum of the squares of the deviations) / (number of observations - 1) Where the deviation of each observation from the mean is: deviation = observation - mean First, calculate the deviation for each observation:7 - 14.43

= -7.4310 - 14.43

= -4.4312 - 14.43

= -2.4315 - 14.43

= 0.5718 - 14.43

= 3.5719 - 14.43

= 4.5720 - 14.43

= 5.57

Now, square each of these deviations: 56.25, 19.62, 5.91, 0.33, 12.75, 20.9, 30.96 The sum of these squares of deviations is: 56.25 + 19.62 + 5.91 + 0.33 + 12.75 + 20.9 + 30.96

= 147.72

Therefore, the variance for the daily production of cell phones is: Variance = 147.72 / (7-1) = 24.62 Standard deviation ) Mean = 14.43b) Variance per Day = 24.62c) Standard Deviation = 4.96

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The equation (1), which is equivalent to p'(x) = -3p(x), has exactly three distinct real solutions.

Let p(x) = (x - a)(x - b)(x - c)(x - d). Then p(x) = 0 has exactly four distinct real solutions, namely a, b, c, and d.

Taking the logarithmic derivative of p(x), we get:

p'(x)/p(x) = 1/(x - a) + 1/(x - b) + 1/(x - c) + 1/(x - d)

Multiplying both sides by p(x), we obtain:

p'(x) = p(x) / (x - a) + p(x) / (x - b) + p(x) / (x - c) + p(x) / (x - d)

Simplifying, we get:

p'(x) = (x - b)(x - c)(x - d) + (x - a)(x - c)(x - d) + (x - a)(x - b)(x - d) + (x - a)(x - b)(x - c)

Therefore, the equation (1) can be written as p'(x) = -3p(x).

By Rolle's theorem, between any two distinct real roots of p(x) (i.e., a, b, c, and d), there must be at least one real root of p'(x). Since p(x) has four distinct real roots, p'(x) must have at least three distinct real roots.

Moreover, since p(x) has degree 4, it can have at most four distinct real roots. Therefore, p'(x) = 0 can have at most four distinct real roots. Since we know that p'(x) has at least three distinct real roots, it follows that p'(x) = 0 has exactly three distinct real roots.

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Answer:

<ABC=90

Step-by-step explanation:

right angles are always equal to 90

The required factors of the given expression x³ - 6x² - x + 30 is (x - 5)(x + 2)(x -3).

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

Here,

Gien expression,
= x³ - 6x² - x + 30
= (x - 5)(x + 2)(x -3)

Thus, the required factors of the given expression x³ - 6x² - x + 30 is (x - 5)(x + 2)(x -3).

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Answer:

34*2.3 =65

Step-by-step explanation:

Big boxes have 1/4 of 20 gigabytes of ram will be 5 gigabytes.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Big boxes have 1/4 of 20 gigabytes of ram.

Then the multiplication of the numbers 1/4 and 20 will be given by putting a cross sign between them. Then we have

⇒ (1/4) x 20

⇒ 20 / 4

⇒ 5 gigabytes

Big boxes have 1/4 of 20 gigabytes of ram will be 5 gigabytes.

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Answer:

4

Step-by-step explanation:

We use 1/2base times height to find the area and since we already have an area we just do 24= 6h then we divide 6 on both sides and height equals 4

Answer: 6 inches

Step 1: Subtract 12 because 12 iches is the base.

24 - 12 = 2

Step 2: Divide 12 by 2 because triangles have two equal sides.

12 ÷ 2 = 6

Answer = 6

Answer:

The purpose of the vertical line test is to determine if the function is in fact a function. (Option C)

Explanation:

Once a vertical line is drawn to every part of the function and it only hit one point on the graph, then it is a function. For example,

If the vertical line hits two points or more on the graph, then the graph is not a function. For example, a circle is not a function.

Given the following data set:

[13,13,13,15,15,16,16,17,17]​

Let's determine the median.

Step 1: Arrange the data points from smallest to largest.

The set is already arranged in ascending order.

[13,13,13,15,15,16,16,17,17]​

Step 2:

a.) If the number of data points is odd, the median is the middle data point in the list.

b.) If the number of data points is even, the median is the average of the two middle data points in the list.

There are 9 data in the set, it is odd. The middle data is the 5th data.

[13,13,13,15,15,16,16,17,17]​

The 5th data is 15.

Therefore, the median of the given set of data is 15.

Answer:

-3

Step-by-step explanation:

The parametric equations of the line of intersection between the planes x - y + z = 0 and x + 2y + 3z = 6 are x = 2t + 6, y = t, and z = -t - 6.



To find the parametric equations of the line of intersection between two planes, we need to determine a point on the line and find its direction vector.

First, we solve the system of equations formed by the two planes: x - y + z = 0 and x + 2y + 3z = 6. By eliminating x, we get -3y - 2z = -6.Setting y = t and z = s as parameters, we can express the point on the line as (x, y, z) = (2t + 6, t, s).Now, substituting these values into the first equation, we obtain 2t + 6 - t + s = 0, which simplifies to t + s = -6.

Therefore, the parametric equations for the line of intersection are:

x = 2t + 6

y = t

z = -t - 6, where t and s are parameters.

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Given the series 2, 4, 7, 11, 16, the next number in the series is 22.

Note that series usually have an underlying pattern. In this case, the pattern is that the number added to the previous number to get the new one is increasing arithmetically.

that is

1 +1  = 2
2 + 2 = 4
3 + 4 = 7
4 + 7 = 11
5 + 11 = 16


As you can see , aded 1, then 2, then 3 and so on. Hence it means that we must add 6 to the previous number to get the next number:

That is


6 + 16 = 22

Hence, 22 is the next number in the series.

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-3,4. i adding this cause this answer needs atleast 20 characters

Answer:The 99% confidence interval is

To find the 99% confidence interval for the mean systolic blood pressure (SBP) level, we use the formula:

CONFIDENCE INTERVAL = Mean ± Z * (Standard Deviation / √n)

Where:

Mean is the sample mean of SBP

Z is the Z-score corresponding to the desired confidence level

Standard Deviation is the population standard deviation

Explanation:

Given that the sample size is 13 and the standard deviation is 10, we need to calculate the sample mean and the Z-score for the 99% confidence level.

First, we calculate the sample mean:

Mean = (129 + 134 + 142 + 114 + 120 + 116 + 133 + 142 + 138 + 148 + 129 + 133 + 140) / 13

= 1724 / 13

≈ 132.62

Next, we need to determine the Z-score for a 99% confidence level. The Z-score can be found using a Z-table or a statistical calculator. For a 99% confidence level, the Z-score is approximately 2.576.

Now, we can calculate the confidence interval:

Confidence Interval = 132.62 ± 2.576 * (10 / √13)

132.62 ± 2.576 * (10 / 3.6056)

≈ 132.62 ± 2.576 * 2.771

≈ 132.62 ± 7.147

Therefore, the 99% confidence interval for the mean SBP level is approximately (125.47, 139.77).

Answer:

This is gebber gabber but yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

7.49+6.21= 13.70

The right answer is provided by: Taking into account the hypothesis tested and the p-value of the test.

There is enough proof to conclude that using drugs X and Y results in different mean cholesterol levels.

What theories are being tested?

If there is no difference in the cholesterol levels, then the null hypothesis is tested, which is:

H₀:Hₓ-H

It is determined whether there is a difference at the alternative hypothesis, so:

H₀:Hₓ-H≠0

The p-value of 0.003 0.01 leads us to reject the null hypothesis and determine that there was a difference, hence the following is the right response:

There is enough proof to conclude that using drugs X and Y results in different mean cholesterol levels.

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Answer:

It is linear since it is a straight line.

Answer:

B

Step-by-step explanation:

y = 6/x is not  an example of a linear function

Option B is correct

A linear function can be written in the form ax + by = c

Let us consider the options given and see which of them cannot be expressed in the form ax + by + c

For y  =   9  -  2x

This can also be expressed as

-2x + y  =  9

For y  =  x/2  +  9

This can also be expressed as:

x  -  2y  =  - 18

For y  =  5/6 x - 8

This can also be expressed as:

-5x  +  6y  =  -48

Only y = 6/x cannot be expressed in the form ax + by = c. Therefore, y  = 6/x is not an example of a linear function

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The solution to the linear system is x₁ = 0, x₂ = -5/4, and x₃ = 3/2.

We start with the augmented matrix:

[1 2 3 | 2]

[-1 2 5 | 5]

[2 1 3 | 9]

First, we eliminate the variable x₁ from the second and third equations by adding the first equation to them:

[1 2 3 | 2]

[0 4 8 | 7]

[0 -3 -3 | 5]

Next, we eliminate the variable x₂ from the third equation by adding 3/4 times the second equation to it:

[1 2 3 | 2]

[0 4 8 | 7]

[0 0 3 | 18/4]

Now, we have the system in row echelon form. We can perform backward substitution to find the values of the variables. Starting from the last equation, we have:

3x₃ = 18/4 -> x₃ = 18/4 / 3 = 3/2

Substituting this value back into the second equation, we have:

4x₂ + 8(3/2) = 7 -> 4x₂ + 12 = 7 -> x₂ = -5/4

Finally, substituting the values of x₂ and x₃ into the first equation, we have:

x₁ + 2(-5/4) + 3(3/2) = 2 -> x₁ - 5/2 + 9/2 = 2 -> x₁ = 0

Therefore, the solution to the linear system is x₁ = 0, x₂ = -5/4, and x₃ = 3/2.

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Answer:

y = x + 5

Step-by-step explanation:

The output (y) is five more than the input (x)

and this is expressed symbolically as

y = x + 5

The statement that the integral of entire functions is always zero is false.

An entire function is a complex function that is defined on the whole complex plane and is complex differentiable everywhere. Entire functions can have non-zero integrals over certain regions in the complex plane.

For example, the integral of the entire function f(z) = e^z over a square contour of side length 1 centered at the origin is non-zero. In fact, using Cauchy's integral theorem, we can evaluate this integral as follows:

∫(C) e^z dz = 0

where C is the square contour of side length 1 centered at the origin. However, if we consider the square contour of side length 2 centered at the origin, then the integral of f(z) = e^z over this contour is non-zero.

Therefore, the statement that the integral of entire functions is always zero is false.

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The product of 8759 x 2391 x 2391 x 7759 is 388,895,526,171,961.

To find the product of 8759 x 2391 x 2391 x 7759, we can use the associative property of multiplication. This property states that the way in which we group the factors does not affect the result of the multiplication.

So, we can group the factors in pairs and multiply each pair together before multiplying the products. Let's start with 8759 x 7759 and then multiply the products of 2391 x 2391.

8759 x 7759 = 67,907,881
2391 x 2391 = 5,716,881

Now, we can multiply these two products together to get the final result.

67,907,881 x 5,716,881 = 388,895,526,171,961

Therefore, the product of 8759 x 2391 x 2391 x 7759 is 388,895,526,171,961.

Using the associative property of multiplication can make it easier to find the product of a large number of factors. By grouping the factors in pairs and multiplying each pair together, we can simplify the problem and make it more manageable.

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Answer:48

Step-by-step explanation:

Based on the number of data lying in different ranges, we can say that the correct option is option B.

58, 70, 73, 75, 78, 84, 86, 88, 95, 102, 119, 123, 124, 141, 170, 203

A histogram is an approximate representation of the distribution of numerical data.

Number of data in the 40-60 range=1

Number of data in the 60-80 range=4

Number of data in the 80-100 range=4

Number of data in the 100-120 range=2

Number of data in the 120-140 range=2

Number of data in the 140-160 range=1

Number of data in the 160-180 range=1

Number of data in the 180-200 range=0

Number of data in the 200-220 range=1

Based on the number of data lying in different ranges, we can say that the correct histogram shown is in option B.

Thus, based on the number of data lying in different ranges, we can say that the correct option is option B.

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