Rewrite the cylinder volume formula to solve for r.

The simplified polynomial for the area and perimeter of the rectangles are:

13). Area = 5x² + 40, Perimeter = 12x + 16

14). Area = x² + 10x + 12, Perimeter = 4x + 20

Area of rectangle = Length × Width

Perimeter of rectangle = 2(Length + Width)

13). Area of the rectangle = 5x × (x + 8)

Area of the rectangle = 5x² + 40

Perimeter of the rectangle = 2[5x + (x + 8)]

Perimeter of the rectangle = 2(6x + 8)

Perimeter of the rectangle = 12x + 16

12). Area of the rectangle = (x + 3)(x + 7)

Area of the rectangle = x² + 7x + 3x + 21

Area of the rectangle = x² + 10x + 21

Perimeter of the rectangle = 2[(x + 3) + (x + 7)]

Perimeter of the rectangle = 2(2x + 10)

Perimeter of the rectangle = 4x + 20.

Therefore, the simplified polynomial for the area and perimeter of the rectangles are:

13). Area = 5x² + 40, Perimeter = 12x + 16

14). Area = x² + 10x + 12, Perimeter = 4x + 20

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If (-8,3) lies on the circle and its Center is (-4,3) then, the radius of the circle is 4.

We know that the center of the circle is (-4, 3). Let's call the radius of the circle "r".

The distance between the center of the circle and the point (-8, 3) on the circle is equal to the radius "r".

Using the distance formula, we can find the distance between these two points;

d =√[(x2 - x1)² + (y2 - y1)²]

d = √[(-8 - (-4))² + (3 - 3)²]

d = √[(-8 + 4)² + 0²]

d = √[4²]

d = 4

Since the distance between the center of the circle and the point on the circle is equal to the radius, we have;

r = d = 4

Therefore, the radius of the circle is 4.

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a) Null: Mean = 20 days; Alt: Mean > 20 days. b) supported by t-value 6.708 > critical value at α=0.05. c) 95% confidence interval for mean patient discharge time is between 20.528 and 23.472 days, d) 99% confidence, a minimum sample size of 67 patients is required.

a) The null hypothesis is that the mean days for a patient to discharge is still 20 days, while the alternative hypothesis is that the mean days for a patient to discharge has increased and is now greater than 20 days.

Null hypothesis: 0:  = 20

Alternative hypothesis: 1:  > 20

b) We can use a one-sample t-test to test the hypothesis. We will use a significance level of 0.05.

The test statistic is given by:

t = (x - ) / (s / √n)

where x is the sample mean,  is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Here, x = 25,  = 20, s = 5, and n = 30. Plugging these values into the formula, we get:

t = (25 - 20) / (5 / √30) = 6.708

The degrees of freedom (df) for the t-distribution is n - 1 = 29. Using a t-table or calculator, the p-value for a one-tailed test with df = 29 and t = 6.708 is < 0.0001.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis. There is sufficient evidence to conclude that the mean days for a patient to discharge has increased.

c) To construct a 95% confidence interval for the mean days for a patient to discharge, we use the formula:

CI = x ± tα/2 * (s/√n)

where x is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the critical value for a t-distribution with df = n-1 and α = 0.05/2 = 0.025.

Here, x = 22, s = 5, and n = 40 (30 from the first sample + 10 from the second sample). The critical value for tα/2 with df = 39 is 2.022.

Plugging these values into the formula, we get:

CI = 22 ± 2.022 * (5/√40) = (20.528, 23.472)

Therefore, we can be 95% confident that the true mean days for a patient to discharge is between 20.528 and 23.472 days.

d) To find the minimum sample size required to estimate the mean days for a patient to discharge to within 2 days of error with a 99% confidence, we use the formula:

n = (zα/2 * s / E)²

where zα/2 is the critical value for a z-distribution with α = 0.01/2 = 0.005, s is the sample standard deviation (which we assume is the same as before, i.e., s = 5), and E is the desired margin of error (which is 2 days).

Plugging in the values, we get:

n = (2.576 * 5 / 2)² = 66.18

Therefore, the minimum sample size required is 67 patients.

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Answer: 14.5 kg

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The inverse function returns the original value for which a function gave the output.

This means if there is a function f(x) and at x = a, f(a) = k then f⁻¹(k) = a

This may be difficult to grasp with variables but essentially returning to the specific question
if f(3) = 17

then

f⁻¹(17) = 3

And that is the answer

Answer:

12 / min

720 / hr

17,280 / day

6,307,200 / yr

Now divide 1,000,000,000 by 6,307,200 (darn close to your 158!)

The solutions for the system of equations " 3x²-2y²+5=0 and 2x²-y²+2=0" are :

First Solution : x = 1, y = 2

Second Solution : x = 1, y = -2

Third Solution : x = -1, y = 2

Fourth Solution : x = -1 , y = 2.

In order to solve the system of equations 3x²-2y²+5=0 and 2x²-y²+2=0, we use substitution method;

From the second equation, we solve for y² in terms of x²:

The second equation is : 2x² - y² + 2 = 0;

We get, y² = 2x² + 2

Substitute this expression for y² into the first equation:

We get,

3x² - 2(2x² + 2) + 5 = 0

3x² - 4x² - 4 + 5 = 0

-x² + 1 = 0

x² = 1

We get, x = ±1

Substitute these values of x into the equation for y²:

y² = 2x² + 2

For x = 1, y² = 4,

Which means the solution set is (1,2) and (1,-2),

For x = -1, y² = 4

the solution set is (-1,2) and (-1,-2).

Therefore, the solutions to the system of equations are (1, 2), (1,-2), (-1,2) and (-1, 2).

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Answer: D

Step-by-step explanation:

The equation for a linear function is y = mx + b

We first need to find the slope of the object, we can see here than it perfectly lands on the point, (0, -3) and (6,0). We can use this formula to determine the slope:

(y2 - y1)/(x2 - x1)

Now let's plug in the numbers.

(0 + 3) / (6 - 0)

3/6

1/2

Now we know the slope is 1/2 and the y-intercept is -3, so let's make it into a slope-intercept form.

y = 1/2x - 3

There are exactly 250 blocks with exactly one face painted red.

What is cube ?

A cube is a three-dimensional solid shape with six square faces of equal size that meet at 90-degree angles. It is a special case of a rectangular prism, where all of the edges have the same length.

When the 10 x 10 x 10 cube is painted red on all faces, it means that all of the 1000 unit cubes inside the large cube are red.

When the cube is cut into ten 10 x 10 x 1 slices, each slice will contain 100 unit cubes. When each slice is cut into twenty-five 2 x 2 x 1 blocks, each block will contain 4 unit cubes.

Therefore, each 2 x 2 x 1 block will come from 4 unit cubes, and each unit cube will contribute to 4 different blocks.

To count the number of blocks with exactly one face painted red, we can focus on the blocks that have a red face on the bottom (or top) and three unpainted faces on the other sides. Each such block will correspond to one of the 100 unit cubes in a slice, and there are 10 slices, so there are 1000 such blocks in total.

However, each of these blocks has four unit cubes, so we need to divide by 4 to get the number of blocks. Therefore, the answer is:

1000 ÷ 4 = 250

Therefore, there are exactly 250 blocks with exactly one face painted red.

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The surface area of the cube is 384 mm².

A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.

Since there are six square that makes up a cube, to find the surface area of the cube, we find the area of one of the square and multiply by six

Where:

From the question,

Given:

Substitute this value into equation 1

Hence the right option is D. 384 mm².

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The value of the expression is -0.8

PEDMAS can be described as a mathematical acronym that is used for the representation of arithmetic operations on the basis of how they are to be carried out sequentially in an equation.

The alphabet represents different operations. They are;

From the information given, we have that;

0.6/(-0.9- -0.5 x -0.3)

Multiply the values

0.6/(-0.9 +0. 15)

add the values

0.6/0. 75

Now, divide the values

-0.8

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The probability that at most 1 call is received in 10 seconds is given as follows:

0.8557 = 85.57%.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are listed and explained as follows:

On average, a front desk operator receives 2 calls per 30 seconds, hence the mean for 10 seconds, which is one third of the time, is given as follows:

[tex]\mu = \frac{2}{3}[/tex]

The probability of at most one call is given as follows:

P(X <= 1) = P(X = 0) + P(X = 1)

Hence:

Hence:

P(X <= 1) = P(X = 0) + P(X = 1) = 0.5134 + 0.3423 = 0.8557 = 85.57%.

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Answer:

Step-by-step explanation:

V = πr²h

h = V/(πr²)

V = 42 gal

42 gal x 3.7854 l/gal = 158.987 l

158.987 l = 158,987 ml = 158,987 cm³

r = 18/2 = 9 in

9 in x 2.54 cm/in = 22.86 cm

h = (158987 cm³) / π(22.86 cm)² ≈ 96.82 cm

depending on how you round, the more precise answer is 96.8285 ≈ 96.83

The function is not defined for x > 5, as a result ƒ(7) does not exist.

The given piece-wise function is:

f(x) = {x - 2}²- 1

1

-x+1

x < 2

x = 2

2 < x ≤ 5

Step 2

f(x) = (x-2)² - 1

1

-x+1

x < 2

x = 2

2 < x ≤ 5

Note that the function is not defined for x > 5.

Step 3

Since the function is not defined for > 5, therefore ƒ(7) does not exist.

The function is not defined for x > 5, therefore ƒ(7) does not exist.

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Answer:

Larger number: 36

Smaller number: 13

(11) The value of expression 3/y + 2y/4 when y = 4 is [tex]2\frac{3}{4}[/tex].

Hence the correct option is (b).

(12) The value of expression 12/y + 3y/4 when y = 8 is [tex]7\frac{1}{2}[/tex].

Hence the correct option is (c).

(13) 2x/3 + 4 = 10 equation does x = 9.

Hence the correct option is (b).

(11) The given expression is,

3/y + 2y/4 = 3/y + y/2

Substituting the value of y = 4 we get,

3/4 + 4/2 = 3/4 + 2 = [tex]2\frac{3}{4}[/tex].

Hence the correct option is (b).

(12) The given expression is,

12/y + 3y/4

Substituting y = 8 in the given equation we get,

12/8 + (3*8)/4 = 3/2 + 6 = 1 + 1/2 + 6 = [tex]7\frac{1}{2}[/tex].

Hence the correct option is (c).

(13) Given the solution is x =9.

For first option: (2/3)*9 - 6 = 6 - 6 = 0

2x/3 - 6 = 12 does not satisfied by x = 9.

For second option: (2/3)*9 + 4 = 6 + 4 = 10

So, x = 9 satisfies 2x/3 + 4 = 10.

For third option: 3*9 - 12 = 27 - 12 = 15

So x = 9 does not satisfy 3x - 12 = 21.

For fourth option: 3*9 + 12 = 27 + 12 = 39

So x = 9 does not satisfy 3x + 12 = 19.

Hence the correct option is (b).

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The ratio of the surface area of Pyramid A to Pyramid B is: 36/49

We have the information from the question is:

Pyramid A and Pyramid B are similar.

The volume of Pyramid A is 648 [tex]m^3[/tex]

The volume of Pyramid B is 1029 [tex]m^3[/tex]

To find the ratio of the surface areas of Pyramid A to Pyramid B.

Now, As we know that:

If two solids are similar, then the ratio  of their volumes is equal to the cube

of the ratio of their corresponding linear measures.

[tex]\frac{Vol of A}{Vol of B} =(\frac{a}{b} )^3 =\frac{684}{1029}=\frac{216}{343}\\ \\ \frac{a}{b}=\frac{6}{7}[/tex]

If two solids are similar, then the n ratio of their surface areas is equal  to the square of the ratio of their  corresponding linear measures.

Surface area of A/ Surface area of B [tex]=(\frac{a}{b} )^2=\frac{36}{49}[/tex]

So, the ratio of the surface area of Pyramid A to Pyramid B is: 36/49

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there is no real number that can be raised to the third power to give a negative number, there are no real solutions to this equation. Therefore, there are no critical points of the function f(x) = x - 1/x² + 3.

what is critical points ?

In calculus, critical points are points on a function where its derivative is either zero or undefined. These points are important because they can indicate the location of maximum or minimum values of the function or points of inflection where the concavity of the function changes.

In the given question,

To find the critical points of the function f(x) = x - 1/x² + 3, we need to find the values of x where the derivative of the function is equal to zero or undefined.

First, we need to find the derivative of the function:

f'(x) = 1 + 2/x³

Next, we set the derivative equal to zero and solve for x:

1 + 2/x³ = 0

2/x³ = -1

x³ = -2

Since there is no real number that can be raised to the third power to give a negative number, there are no real solutions to this equation. Therefore, there are no critical points of the function f(x) = x - 1/x² + 3.

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Six types of costs are:

For assets attained in exchange for a deferred payment contract, the asset should be documented at its fair worth, which is the prevailing market rate. If establishing the fair value of the asset proves to be impracticable, the asset should be recorded based on the current value of upcoming payments due under the deferred payment agreement, stated using an apposite interest rate.

Generally, assets acquired in exchange of other non-monetary commodities should be appraised at their fair worth. If the truthful appraisal of the exchanged assets is uncertain, the assets should be noted down according to the seized amount of the items provided, including any received or paid cash during the transaction.

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The integer values that make the statement true are x = -3, -2, -1, 1, 2, 3

We have,

We can start by multiplying both sides of the inequality by -3x to get rid of the denominators:

-3/x < -x/3

Multiplying by -3x on both sides.

-9 < -x²

Rearranging.

x² < 9

Taking the square root of both sides.

|x| < 3

This means that x can take any integer value between -3 and 3, excluding 0.

Thus,

The integer values are x = -3, -2, -1, 1, 2, 3

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The value of m and n are 2√3 and 4√3/3 respectively.

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

There are special angles in trigonometry, examples are; 60° , 30° and 90°. This angles have exact values and can be calculated without using calculator.

Tan 60 = n/2

√3 = n/2

n = 2√3

cos 60 = 2/m

√3/2 = 2/m

m√3 = 4

m = 4/√3

= 4√3/3

Therefore the value of m and n are 2√3 and 4√3/3 respectively.

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Answer:

1213124

To add 213341 and 444233 in base 5, we need to line up the digits of the two numbers according to their place values, and then add them digit by digit, carrying over to the next place value if the sum of the digits is 5 or greater.

Here's how to do it:

 2   1   3   3   4   1

+ 4   4   4   2   3   3

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

 1   2   1   3   1   2   4

Therefore, the sum of 213341 and 444233 in base 5 is 1213124.

Therefore, the equation for that value x = 6, and m(A) = 90.

A mathematical equation expresses two things as being equal to one another, or as having the same value and worth. A specific equation that expresses a significant link between variables and numbers is called a formula.

The fact that the sum of a triangle's angles is 180 degrees must be used to determine the value of x. Angles J, A, and K in the triangle AJK allow us to write:

m(J) + m(A) + m(K) = 180

We can substitute the given angle measures into this equation:

(8x - 7) + m(A) + (x + 7) = 180

Simplifying this equation, we get:

9x + m(A) = 180 - 7 - 7

9x + m(A) = 166

We can use the same reasoning for triangle AJL:

m(J) + m(A) + m(L) = 180

Substituting the given angle measures, we get:

(8x - 7) + m(A) + (2x + 15) = 180

Simplifying this equation, we get:

10x + m(A) = 172

The two unknowns in our current set of equations are x and m(A). By removing the first equation from the second, we can find m(A):

10x + m(A) = 172

(9x + m(A) = 166)

x = 6

Now that we know x, we can substitute it into either equation to find m(A):

8x - 7 + m(A) + x + 7 = 180

15x + m(A) = 180

m(A) = 180 - 15x

Substituting x = 6, we get:

m(A) = 180 - 15(6) = 90

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The range, median and mode of the data-set are given as follows:

Considering the stem-and-leaf plot, the data-set is given as follows:

54, 55, 60, 66, 69, 72, 73, 74, 75, 75, 81, 82, 88, 89, 95, 96.

The range of a data-set is calculated as the difference between the highest value and the lowest value in the data-set, thus:

96 - 54 = 52.

The data-set has an even cardinality of 16, hence the median is calculated as the mean of the two middle elements as follows:

Median = (74 + 75)/2

Median = 74.5.

The mode of a data-set is the observation that appears the most times in the data-set, hence it is of 75, which is the only observation that appears twice in the data-set.

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Step-by-step explanation:

Answer

The price of 6 DVDs, including sales tax = $62.87

Sales tax = $2.99

Required:

The cost of one DVD.

Explanation:

Step 1: Price of 6 DVDs excluding sales tax.

The price of 6 DVDs excluding sales tax = $62.87 - $2.99 = $59.88

Step 2: Use the Unitary Method:

According to the question,

6 DVDs price = $59.88

1 DVD price excluding sales tax = $ 59.88/6

If an angle measure 125° then the angle measures a fraction of 25/72 of a full circle.

A circle is a two-dimensional geometric shape that is defined as the set of all points that are equidistant from a single point, called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle, passing through the center, is called the diameter. The circumference of a circle is the distance around the edge or perimeter of the circle. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π (pi) is a mathematical constant that represents the ratio of the circumference to the diameter of a circle, approximately equal to 3.14159.

A circle has 360 degrees. To find what fraction of a circle an angle measures, we can divide the angle by 360. In this case, the angle measures 125 degrees, so the fraction of a circle it turns can be calculated as:

125/360 = 0.347222222...

To simplify this fraction, we can multiply both the numerator and denominator by 2:

125/360 = (1252)/(3602) = 250/720

We can further simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 10:

250/720 = (2510)/(7210) = 25/72

Therefore, the angle measures a fraction of 25/72 of a full circle.

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