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What is 75% of the area of a circle with a circumference of 10 units? Round the solution to the nearest square unit.

75% of the area of the circle is 6 square units.

Step-by-step explanation:

Given:

Circumference of a circle = 10 units

Now we have to find the radius of the circle, then we have to find the area of the circle.

Circumference of a circle = 2*π*r            [π = 3.14]

2*3.14*r = 10

6.28r = 10

Dividing both side by 6.28, we get

r = 10/6.28

r = 1.59

Now let’s find the area of the circle.

The area of the circle = π*r^2

= 3.14*1.59*1.59

The area of the circle = 7.94, which is 100 %

Now we have to find the 75% of the area of the circle.

75% = 0.75

75% of the area of the circle = 0.75*7.94

= 5.95

To round off to the nearest whole number, we get 6 square units.

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The table shows conversions of common units of length. Unit of Length Customary System Units Metric System Units 1 inch 2.54 centimeters 1 foot 0.3048 meters 1 mile 1.61 kilometers How many miles are equivalent to 800 meters? Round answer to the nearest hundredth. 0.50 miles 1.29 miles 2.62 miles 4.97 miles

The table shows conversions of common units of length. Unit of Length Customary System Units Metric System Units 1 inch 2.54 centimeters 1 foot 0.3048 meters 1 mile 1.61 kilometers How many miles are equivalent to 800 meters? Round answer to the nearest hundredth. 0.50 miles 1.29 miles 2.62 miles 4.97 miles

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Please help meee!!!! A circle has its center at (1, 4) and a radius of 2 units. What is the equation of the circle? (x − 1)2 + (y − 4)2 = 4 (x + 2)2 + (y + 4)2 = 2 (x + 1)2 + (y − 4)2 = 4 (x − 1)2 + (y − 4)2 = 2

A.

Step-by-step explanation:

We have been given that a circle has its center at (1, 4) and a radius of 2 units. We are asked to write the equation of the given circle.

Since we know that the center-radius form of circle equation is:

, where (h,k) is the center of circle and r is radius of circle.

Upon substituting our given values in above format we will get,

Therefore, the equation of our given circle is and option A is the correct choice.

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The side of a square measures (3x − 6) units. Part A: What is the expression that represents the area of the square? Show your work to receive full credit. (4 points) Part B: What are the degree and classification of the expression obtained in Part A? (3 points) Part C: How does Part A demonstrate the closure property for polynomials? (3 points)

A. The area of a square is given as:

A = s^2

Where s is a measure of a side of a square. s = (2 x – 5) therefore,

A = (2 x – 5)^2

Expanding,

A = 4 x^2 – 20 x + 25

B. The degree of a polynomial is the highest exponent of the variable x, in this case 2. Therefore the expression obtained in part A is of 2nd degree.

Furthermore, polynomials are classified according to the number of terms in the expression. There are 3 terms in the expression therefore it is classified as a trinomial.

C. The closure property demonstrates that during multiplication or division, the coefficients and power of the variables are affected while during multiplication or division, only the coefficients are affected while the power remain the same.

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The graph of f(x) = |x| is reflected across the x-axis and translated to the right 6 units. Which statement about the domain and range of each function is correct? Both the domain and range of the transformed function are the same as those of the parent function. Neither the domain nor the range of the transformed function are the same as those of the parent function. The range but not the domain of the transformed function is the same as that of the parent function. The domain but not the range of the transformed function is the same as that of the parent function.

D. The domain but not the range of the transformed function is the same as that of the parent function.

Step-by-step explanation:

We are given,

The function is reflected across x-axis, which gives .

And then the function is translated to the right by 6 units, which gives .

Thus, the transformed function is

So, from the graph shown below, we get,

Domain of both the functions f(x) and g(x) is set of all real numbers.

Range of f(x) is .

But, Range of g(x) is .

Hence, the correct option is,

D. The domain but not the range of the transformed function is the same as that of the parent function.

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Use a translation rule to describe the translation of x that is 1 units to the left and 6 units up A. T<-1,6>(x) B. T<-1,-6>(x) C. T<1,6>(x) D. T<1,-6>(x)

Use a translation rule to describe the translation of x that is 1 units to the left and 6 units up A. T(x) B. T(x) C. T(x) D. T(x)

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Frank corporation manufacturers a single product that has a selling price of \$20.00 per unit. fixed expenses total \$45,000 per year, and the company must sell 5,000 units to break even. if the company has a target profit of \$13,500, sales in units must be:

Frank corporation manufactures a single product that has a selling price of \$20.00 per unit. fixed expenses total \$45,000 per year, and the company must sell 5,000 units to break even. if the company has a target profit of \$13,500, sales in units must be:

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If the area of circle p is 1,600 units squared, in units what is the diameter?

Answer:  The correct option is (C). 10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

Step-by-step explanation:  Given that the segment AB has point A located at (8, 9). The distance from A to B is 10 units.

We are to select the correct option that could be used to calculate the coordinates for point B.

Let, (x, y) be the co-ordinates of point B.

According to distance formula, the distance between two points (a, b) and (c, d) is given by

Therefore, the distance between the points A(8, 9) and B(x, y) is given by

Since, distance between A and B is 10 units, so

d = 10.

Therefore,

Thus, the correct statement is

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared.

Option (C) is correct.

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Optimization problem:A manufacturer determines that x employees on a certain production line will produce y units per month where . To obtain the maximum monthly production, how many employees should be assigned to the production line?**It is NOT sufficient to find an answer that you think is a max or a min without testing for relative extrema. You MUST test relative extrema at all times by using either the first or second derivative test even if you only have one critical value/point.

Cal problem!

given production
P(x)=75x^2-0.2x^4

To find relative extrema, we need to find P'(x) and solve for P'(x)=0.

P'(x)=150x-0.8x^3    [by the power rule]

Setting P'(x)=0 and solve for extrema.
150x-0.8x^3=0  =>
x(150-0.8x^2)=0 =>
0.8x(187.5-x^2)=0
0.8x(5sqrt(15/2)-x)(5sqrt(15/2)+x)=0
=>
x={0,+5sqrt(15/2), -5sqrt(15/2)}   by the zero product rule.
[note: eqation P'(x)=0 can also be solved by the quadratic formula]

Reject negative root because we cannot hire negative persons.

So possible extrema are x={0,5sqrt(15/2)}

To find out which are relative maxima, we use the second derivative test.  Calculate P”(x), again by the power rule,
P”(x)=-1.6x
For a relative maximum, P”(x)<0, so
P”(0)=0  which is not <0  [in fact, it is an inflection point]
P”(5sqrt(15/2))=-8sqrt(15/2) < 0, therefore x=5sqrt(15/2) is a relative maximum.

However, 5sqrt(15/2)=13.693 persons, which is impossible, so we hire either 13 or 14, but which one?

Let’s go back to P(x) and find that
P(13)=6962.8
P(14)=7016.8

So we say that assigning 14 employees will give a maximum output.

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WILL GIVE BRAINLIEST!A rhombus has coordinates A(-6, 3), B(-4, 4), C(-2, 3), and D(-4, 2). What are the coordinates of rhombus A′B′C′D′ after a 90° counterclockwise rotation about the origin followed by a translation 3 units to the left and 2 units down? A′(-6, -8), B′(-7, -6), C′(-6, -4), D′(-5, -6) A′(6, -8), B′(7, -6), C′(6, -4), D′(5, -6) A′(-6, 8), B′(-7, 6), C′(-6, 4), D′(-5, 6) A′(6, 8), B′(7, 6), C′(6, 4), D′(5, 6)

C. Yes, because the population values appear to be normally distributed.

Step-by-step explanation:

Given is a graph which shows the distribution of values of a population

The graph has the following characteristics

i) Bell shaped

ii) symmerical about mid vertical line

iii) Unimodal with mode = median =mean

iv) As x deviates more from the mean probability is decreasing and also curve approaches asymptotically the x axis

Hence we find that the curve is a distribution of normal

Option C is right

C. Yes, because the population values appear to be normally distributed.

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Write an equation of an ellipse in standard form with the center at the origin and a height of 4 units and width of 5 units.

The standard form of equation of an ellipse is in the
form:

[(x – h)^2] / a^2 + [(y – k)^2] / b^2 = 1

Where, h and k are the center points, and a and b are one
half the length of the major and minor axis.

Since height is 4 units and width is 5 units, therefore:

a = 5 / 2 = 2.5

b = 4 / 2 = 2

and h = k = 0 (at the origin)

The standard equation then becomes:

x^2 / (2.5)^2 + y^2 / 2^2 = 1

x^2 / 6.25 + y^2 / 4 =1

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Which statement is true the graph of y=log(x-4) is the graph of y=log(x) translated 4 units down

The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

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Then length of a rectangle is 5 units longet than its width. which if the following represents its area in square units?5xx (5-x)x (x-5)x (x+5)2x+2 (x+5)

Then length of a rectangle is 5 units longet than its width. which if the following represents its area in square units?5xx (5-x)x (x-5)x (x+5)2x+2 (x+5)

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If g(x)=4×2-16 were shifter 5 units to the right and 2 down, what would the new equation be?

Answer:  The correct option is (C). 10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

Step-by-step explanation:  Given that the segment AB has point A located at (8, 9). The distance from A to B is 10 units.

We are to select the correct option that could be used to calculate the coordinates for point B.

Let, (x, y) be the co-ordinates of point B.

According to distance formula, the distance between two points (a, b) and (c, d) is given by

Therefore, the distance between the points A(8, 9) and B(x, y) is given by

Since, distance between A and B is 10 units, so

d = 10.

Therefore,

Thus, the correct statement is

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared.

Option (C) is correct.

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If a = 4 units and b = 3 units, the length of the diagonal of the outside square rounded to the nearest tenth is

Answer:  The correct option is (C). 10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

Step-by-step explanation:  Given that the segment AB has point A located at (8, 9). The distance from A to B is 10 units.

We are to select the correct option that could be used to calculate the coordinates for point B.

Let, (x, y) be the co-ordinates of point B.

According to distance formula, the distance between two points (a, b) and (c, d) is given by

Therefore, the distance between the points A(8, 9) and B(x, y) is given by

Since, distance between A and B is 10 units, so

d = 10.

Therefore,

Thus, the correct statement is

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared.

Option (C) is correct.

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What is the number of square units in the area of the triangle whose vertices are points (2,0), (6,0), (8,5)

What is the number of square units in the area of the triangle whose vertices are points (2,0), (6,0), (8,5)

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In a right triangle, the length of one leg is 6 units. The length of the other leg is 8 units. What is the length of the hypotenuse (hint: use Pythagorean Theorem)?

The triangle ABC is similar to triangle LMP. The order here is very important. The letters correspond to one another
A corresponds to L (first letters of each sequence)
B corresponds to M (second letters of each sequence)
C corresponds to P (third letters of each sequence)

In a similar fashion, the segments also correspond to one another.
AB corresponds to LM (first two letters of each sequence)
AC corresponds to LP (first and last letters of each sequence)
BC corresponds to MP (last two letters of each sequence)

————————————

AB corresponds to LM. AB is 4 units long. LM is 2 units long. So AB is twice as long as LM. This ratio (of 2:1) will be applied to every paired corresponding value.

Also, the right angle is at angle M for triangle LMP. The right angle will be at angle B for triangle ABC (since B corresponds to M). The answer will have an x coordinate of 7. So the answer is either choice B or choice C.

If we move 4 units down from point B, we land on (7,-10). That isn’t listed as an answer choice. Let’s try moving 4 units up from point B. We land on (7,-2). This is an answer choice

So the final answer is choice C) (7,-2)

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A right triangle has one leg that is 12 units long and a hypotenuse that is 15 units long. Find the length of the other leg

Answer:  The correct option is (C). 10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

Step-by-step explanation:  Given that the segment AB has point A located at (8, 9). The distance from A to B is 10 units.

We are to select the correct option that could be used to calculate the coordinates for point B.

Let, (x, y) be the co-ordinates of point B.

According to distance formula, the distance between two points (a, b) and (c, d) is given by

Therefore, the distance between the points A(8, 9) and B(x, y) is given by

Since, distance between A and B is 10 units, so

d = 10.

Therefore,

Thus, the correct statement is

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared.

Option (C) is correct.

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What is the length of DC ? 2 units 3 units 6 units 9 units

What is the length of DC ? 2 units 3 units 6 units 9 units

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Use the triangle midsegment theorem to solve for x. What is AX? 2 units 4 units 6 units 8 units

The triangle ABC is similar to triangle LMP. The order here is very important. The letters correspond to one another
A corresponds to L (first letters of each sequence)
B corresponds to M (second letters of each sequence)
C corresponds to P (third letters of each sequence)

In a similar fashion, the segments also correspond to one another.
AB corresponds to LM (first two letters of each sequence)
AC corresponds to LP (first and last letters of each sequence)
BC corresponds to MP (last two letters of each sequence)

————————————

AB corresponds to LM. AB is 4 units long. LM is 2 units long. So AB is twice as long as LM. This ratio (of 2:1) will be applied to every paired corresponding value.

Also, the right angle is at angle M for triangle LMP. The right angle will be at angle B for triangle ABC (since B corresponds to M). The answer will have an x coordinate of 7. So the answer is either choice B or choice C.

If we move 4 units down from point B, we land on (7,-10). That isn’t listed as an answer choice. Let’s try moving 4 units up from point B. We land on (7,-2). This is an answer choice

So the final answer is choice C) (7,-2)

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A recatangle's length is 2 units more than twice its width.It's area is 40 square units.The equation w(2w+2)=40 can be used to find w,the width of the rectangle.What is the width of the rectangle?

A recatangle’s length is 2 units more than twice its width.It’s area is 40 square units.The equation w(2w+2)=40 can be used to find w,the width of the rectangle.What is the width of the rectangle?

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The four steps necessary to complete a cost of production report in a process cost system are 1. allocate costs to transferred and partially completed units 2. determine the units to be assigned costs 3. determine the cost per equivalent unit 4. calculate equivalent units of production the correct ordering of the steps is 2, 3, 4, 1 2, 4, 3, 1 4, 2, 3, 1 2, 3, 1, 4

127=7 (mod n) means when 127 is divided by n, the division leaves a remainder of 7.

The statement is equivalent to
120=0 (mod n), meaning that n divides 120.

All divisors of 120 will satisfy the statement because 120 divided by a divisor (factor) will leave a remainder of 0.

Factors of 120 are:
n={1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}, |n|=16.
You can count how many such values of n there are, and try to check that each one satisfies 127=7 mod n.

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Department w had 2,400 units, one-third completed at the beginning of the period; 16,000 units were transferred to department x from department w during the period; and 1,800 units were one-half completed at the end of the period. assume the completion ratios apply to direct materials and conversion costs. what is the equivalent units of production used to compute unit conversion cost on the cost of production report for department w? assume the company uses fifo.

The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.

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If CX = 5 units, then DZ = __units.

If CX = 5 units, then DZ = __units.

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Using the side-splitter theorem, Daniel wrote a proportion for the segments formed by line segment DE. What is EC? 2 units 2.4 units 3 units 3.75 units

The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is – 1.

So, from that basic knowledge you can analyze each option:

a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.

So, the right choices are a, c and g.