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Use a factor tree to find the prime factorization of 125. Write the prime factorization using exponents.
A. 3 to the power of 5 • 1
B. 5 to the power of 3
C. 5 • 25
D. 5 to the power of 5

The above answer is correct! The correct response is A.

Just got it right on edge 2020, hope this helps!! Good luck, and have a great day! :)

The solution is, Using a half-angle identity we get the exact value of

sin 3pi/8 is ±√[(2 + √2) / 4].

Here, we have,

The half angle formula of sin in trigonometry is

sin A/2 = ±√[(1 - cos A) / 2].

If 0 < x < π/2 , then cos x > 0.

now, we have,

sin 3pi/8

here, A/2 = 3pi/8  so, A = 3pi/4 = 6π/8

applying this  half angle formula of sin in trigonometry

we get,

sin 3π/8 = ±√[(1 - cos 6π/8) / 2]

              = ±√[(1 + 1/√2) / 2]

              = ±√[(2 + √2) / 4]

so, we get,

sin 3π/8 = ±√[(2 + √2) / 4]

Hence, The solution is, Using a half-angle identity we get the exact value of sin 3pi/8 is ±√[(2 + √2) / 4].

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Answer:

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

There are various combinations of coins.

In total there are:

Answer:

64

Step-by-step explanation:

3.2*20=64

Answer:

Multiplying 20 by 320% is the same thing as multiplying 20 by 3.2, or 20(3.2)=64. Hope this helped!

Step-by-step explanation:

Answer:

x^3+7x^2-50x-336 or (x-7)(x+6)(x+8)

Step-by-step explanation:

Factor each equation.

x^2-x-42= (x-7)(x+6)

x^2+x-56= (x-7)(x+8)

The common factor is (x-7), therefore the other factors of the expressions must multiply to find the common factor.

(x-7)(x+6)(x+8)=x^3+7x^2-50x-336.

The surface area of the base ball to the nearest whole number is 26 in²

A sphere is defined as the set of all points in three-dimensional Euclidean space that are located at a distance.

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of a sphere is expressed as;

SA = 4πr²

where r is the radius and it's calculated as;

C = 2πr

9 = 2πr

r = 4.5/π =

SA = 4 π × (4.5/π)²

SA = 81/π

SA = 26 in²( nearest whole number)

Therefore the surface area of the sphere is 26 in²

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Answer:

Let us set up a ratio to find the relationship between side lengths of the two triangles.

25:10

5:2

We can divide both sides by two, but there's no need as the smaller triangle has multiples of two.

So, if XZ is 6, let's place it into the ratio and find what "x" is.

5(3) : 2(3)

15 : 6

x = 15

The linear function is given as follows:

\(y = \sqrt{x} + 4\)

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The y-intercept is of 4, hence the parameter b is given as follows:

b = 4.

The line is inclined to 60° with the positive direction of X-axis, hence the slope m is given as follows:

m = tan(60º)

\(m = \sqrt{3}\)

Thus the function is given as follows:

\(y = \sqrt{x} + 4\)

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The length of the radius is 34.39 feet

The given parameters are:

Circumference, C = 216 feet

The circumference is calculated as:

C = 2pi r

So, we have

2 * 3.14 * r = 216

This gives

6.28 * r = 216

Divide by 6.28

r = 34.39

Hence, the length of the radius is 34.39 feet

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Answer:

To graph the line with slope -1 passing through the point (-2,4), we can use the point-slope form of the equation of a line, which is:

where m is the slope of the line, and (x1, y1) is the given point on the line. Substituting the given values, we get:

Simplifying this equation, we get:

Now we can graph this line by plotting the given point (-2,4), and then using the slope of -1 to find one or more additional points on the line. We can do this by starting at the given point and then moving one unit down (since the slope is negative) and one unit to the right (since the slope is -1). This gives us the point (-1,3). We can then connect these two points to graph the line.

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Answer:

Ashley is 7 years old.

and its step by step

Answer: linear



Step-by-step explanation:

-Hope this helps :D

Answer:to what

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

12 - 10 = 2 - 9 = -7

1 ) 3a + b - 4b + 5a

= Solution,

= 3a + 5a +b - 4b

= 8a - 3b

2 ) x + 10x + 2y - 8

= Solution,

= x + 10x + 2y - 8

= 11x + 2y - 8

3 ) 10x² - 4 - 2x²+ x ²

= Solution,

= 10x² - 2x² + x ² - 4

= 9 x² - 4

4 ) 3b + a - b + 2a

= Solution,

= 3b - b + a + 2a

= 2b + 3a

5 ) 6y³ - y³- 2x² + x²

= Solution,

= 6y³ - y³ - 2x² + x²

= 5y³ - x²

6 ) -2y + 2 + 3y + 1

= Solution,

= - 2y + 3y +2 +1

= y + 3

7 ) 1 + 3x + 4x²- 5x + 8

= Solution,

= 1 + 8 + 3x - 5x + 4x²

= 9 - 2x + 4x²

8 ) 12 x + 3y + 6x + y

= Solution,

= 12x + 6x + 3y + y

= 18x + 4y

9 ) - 4a³ + 1 + a³ + 7a²

= Solution,

= -4a³ + a³ + 1 + 7a²

= 3a³ + 1 + 7a²

10 ) -2 + 35b - 8b - 2b

= Solution,

= -2 + 27b - 2b

= -2 + 25b

11) - 2b + 3ab + a + 9ab

= Solution,

=- 2b + 3ab + 9ab + a

= - 2b + 12ab + a

12 ) - x³ + 2x + 2x³ - x + x²

= Solution,

= - x³ + 2x³ + 2x - x + x²

= x³ + x + x²

~Eveloyane~

Using the hypergeometric distribution, it is found that the probabilities are given as follows:

a) 0.2059 = 20.59%.

b) 0.5294 = 52.94%.

c) 0.2647 = 26.47%.

The formula is:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem, the parameters are as follows: N = 17, k = 8, n = 2.

Item a:

This probbility is P(X = 2), hence:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 2) = h(2,17,2,2) = \frac{C_{8,2}C_{9,0}}{C_{17,2}} = 0.2059\)

Item b:

This probbility is P(X = 1), hence:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 1) = h(1,17,2,2) = \frac{C_{8,1}C_{9,1}}{C_{17,2}} = 0.5294\)

Item c:

This probbility is P(X = 0), hence:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 0) = h(0,17,2,2) = \frac{C_{8,0}C_{9,2}}{C_{17,2}} = 0.2647\)

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Answer:

10*9*4=360

Step-by-step explanation:

Volume = Length * Width * Height

To Find :

How many gallons of a 80​% antifreeze solution must be mixed with 100 gallons of 20​% antifreeze to get a mixture that is 70​% antifreeze.

Solution :

Let, x gallons of 80​% antifreeze solution is required :

So,

\((x \times 80) + ( 100 \times 20 ) = (x + 100 )\times 70\\\\8x + 200 = 7( x + 100)\\\\x = 500\)

Therefore, 500 gallons of 80% antifreeze solution is required.

Answer:

A) The reasonable domain is limited to positive whole numbers.

Step-by-step explanation:

got it right

The expression that represents the perimeter of the rectangle is 30h - 2

The dimensions of the rectangle are given as:

Length = 7h + 3

Width = 8h - 4

The perimeter of the rectangle is given as:

P = 2 * (Length + Width)

Substitute the known values in the above equation

P =2 * (7h + 3 + 8h - 4)

Evaluate the like terms

P = 2 * (15h - 1)

Evaluate the product

P = 30h - 2

Hence, the expression that represents the perimeter of the rectangle is 30h - 2

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Answer:

36

Step-by-step explanation:

1/2 × b× h

= 1/2 × 9×8

= 9×4

= 36 sq. in

Answer:

Width = 20 inches and Length = 32 inches

Area of rectangle = 640 feet²

Step-by-step explanation:

Perimeter of rectangle = 104 feet

Let width of rectangle = x

Length of rectangle = x+12

We need to find area of rectangle.

First we need to find value of x

The formula used to calculate perimeter of rectangle is: \(Perimeter= 2(Length+Width)\)

Putting values and finding x

\(Perimeter= 2(Length+Width)\\104 = 2(x+12+x)\\104=2(2x+12)\\104=4x+24\\4x=104-24\\4x=80\\x=\frac{80}{4}\\x=20\)

So, Value of x= 20

So, Width x= 20 inches

Length = x+12 = 20+12 = 32 inches

So, Width = 20 inches and Length = 32 inches

Now finding Area

The formula used is: \(Area=Length\times Width\)

Putting values and finding area

\(Area=Length\times Width\\Area=20\times 32\\Area=640 \ feet^2\)

Area of rectangle = 640 feet²

The required sine function is

y = 2 sin (3π/4 (x) + 3

For given function,

A sine function that has a midline of 3, an amplitude of 2 and a period of 3pi/4

A = 2

T = 3π/4

Since we know

The values of all trigonometric functions depending on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.

In this case, the midline is 3

⇒ D = 3

Using the generalized equation of sine function,

y = A sin (B (x + C)) + D

y = 2 sin (3π/4 (x + 0) + 3

y = 2 sin (3π/4 (x) + 3

Therefore, the required sine function is

y = 2 sin (3π/4 (x) + 3

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The angle that is supplementary to <DEA is DEC

To determine the angle that is supplementary to <DEA , we need to consider the following;

From the information given, we have that;

<DEA is supplementary to <DEC that is sum of angles on a straight line.

Then,

<DEA + <DEC = 180 degrees

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Answer:8z+5

Step-by-step explanation: Add 3z to 5z  which equals 8z and do 9-4 which equals 5 .Lastly add together.

The amount (present value at age 60) that Sandro would neet in his retirement savings account in order to have a monthly income of $1,500 until he is 90 years old, compounded at 4.5% monthly is $296,041.74.

The present value is computed using an online fiance calculator that discounts the future withdrawals (monthly income) for a 360-months period.

End of withdrawal period = 90 years old

Beginning of withdrawal period = 60 years old

The number of years between 60 and 90 = 30 years

N (# of periods) = 360 months (30 years x 12)

I/Y (Interest per year) = 4.5%

PMT (Periodic Payment) = $-1,500

FV (Future Value) = $0

Results:

Present Value (PV) = $296,041.74

Sum of all periodic payments = $540,000 ($1,500 x 360 months)

Total Interest = $243,958.26

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Answer:

12%

Step-by-step explanation:

each shares 12% because 100-28=72

72÷6=12%

1. Initial prediction for the data set with smaller Mean Absolute Deviation was Period A. Prediction was wrong.

2. The Mean Absolute Deviation for Period A is 1.8 and Period B, 1.1

This means that period B has a smaller Mean absolute deviation.

We start by finding the mean for each set;

Period A: Mean = (1×92 + 1×94 + 3×95 + 1×96 + 2×97 + 1×99 + 1×100)/10

= 960/10

= 96

Period B: Mean = (1×94 + 3×95 + 1×96 + 4×97 + 1×98)/10

= 961/10

= 96.1

Period A:

Mean Absolute Deviation = ((92-96) + (94-96) + 3(95-96) + (96-96) + 2(97-96) + (99-96) + (100-96))/10

Mean Absolute Deviation = (4 + 2 + 3 + 0 + 2 + 3 + 4)/10

Mean Absolute Deviation = 1.8

Period B:

Mean Absolute Deviation = ((94-96.1) + 3(95-96.1) + (96-96.1) + 4(97-96.1) + (98-96.1))/10

Mean Absolute Deviation = (2.1 + 3.3 + 0.1 + 3.6 + 1.9)/10

Mean Absolute Deviation = 1.1

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