The diameter D of a sphere is 12.4 m. Calculate the sphere's surface area A.
Use the value 3.14 for , and round your answer to the nearest tenth.

After simplifying i^61 we get the answer is i

Define Complex number

Every complex number may be represented in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element labelled i sometimes known as the imaginary unit, and satisfying the equation i² = 1.

We have the given expression : i ^ 61

Rewrite it,

i ^ 61 as (i^4)^15 * i

we know, i² = -1

so, i ^ 4 = i² * i² = -1 * -1 = 1

so, put i ^ 4 value,

⇒1^15 * i

power 1 to the 15 is 1,

⇒1 * i

⇒ i

Hence, the answer is ' i '

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Option a is correct using algebric formulas.

(x + y)³ = x³ + y³ +3xy( x + y )

(x + y + z)² = x² + y² + z² + 2( xy + yz + zx )

So breaking it into

(( x + y )³)² = (x³ + y³ +3xy( x + y ))²

(x³ + y³ +3xy( x + y ))² = x^6 + y^6 + 9x²y²(x² + y² + 2xy) + 2( x³y³ + 3xy^4( x + y ) + 3x^4y( x + y) )

x^6 + y^6 + 9x²y²(x² + y² + 2xy) + 2( x³y³ + 3xy^4( x + y ) + 3x^4y( x + y) )

So after rearranging the terms

we get  (x + y)^6 as

x6 + 6x5y + 15x4y2 + 20x³y3 + 15x²y4 + 6xy5+y6

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The volume of gasoline in the tank as a function of time can be determined as,

The time taken to fill the tank can be determined as,

Thus, the requried domain is,

The range of the function can be determined as,

Thus, the above expressions gives the required domain and range of the function.

As per the angle sum property, the value of x is 125°

Angle sum property:

According to the angle sum property, the sum of interior angles of a triangle is 180°.

Given,

In the given diagram, PQR and SQT are straight line.

Now we need to find the value of x.

As per the angle sum property, we know that the sum of all the angles of the triangle is 180 degrees.

While we equate the given values within this property, we get.

x° + 55° = 180°

x° = 180° - 55°

x° = 125°

Therefore, the value of x is 125°.

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Answer:

16°F

Step-by-step explanation:

The temperature is −4°F. What will the temperature be if the temperature rises 20°F?

-4 + 20 = 16

so:

16°F

We have to replace the values in the equation

Since the square of a negative number is a positive number, (-4)^2 = +16

Answer:

A

Step-by-step explanation:

It is given that lines k and p are parallel. You also know that angles 2 and 3 are equal because of vertical angles. Due to the parallel lines, you can say that angles 1 and 2 are equal because they are corresponding angles (same-side).

These two angles are not alternate interior angles because angle 1 is exterior and on the same side as angle 2. The third option would not make sense because you are trying to prove two angles are equal, not that lines are parallel.

The conservationist expects to be in the lake would be; 142 trouts.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given, that determine the number of trout in a lake, a conservationist catches 200 trout, tags them, and throws them back into the lake.  

We have to find conservationists who expect to be in the lake.

Now, initially, trout count = 200

Then, again 56 trouts caught then, trout count = 200 + 56

But 14 of them are tagged that means; they are part of 200 trouts so we should not count again in 56 trouts.

So, trout count = 200 + 56 – 14  = 142.

Hence, the conservationist expects would be; 142 trouts.

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The standardized measure of the degree to which the independent variable caused a change in the dependent variable is a standard change.

A dependent variable is what is determined in an experiment or test and is the one that is influenced throughout the experiment. The dependent variable is affected by the independent variable.

In mathematical modeling, statistical modeling, and experimental sciences, dependent and independent variables are variables. Dependent variables are so named because their values are explored in an experiment under the assumption or requirement that they are dependent, by some law or rule, on the values of other variables.

In conclusion, the standard change illustrates the change.

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Answer:

Option 1. This is a vertical pair of angles because they are two nonadjacent (not next to each other) angles formed by intersecting lines. The sides of one angle are the opposite rays to the sides of the other angle. (Angle 5=Angle 7)

Option 2 and 4 are wrong as the angles are not created by a set of parallel lines and a transversal.

Option 3 is wrong as the angles are not adjacent.

Option 5 is wrong as the angles do not have a sum of 90°.

Answer:

The answer is C

Step-by-step explanation:

If you substitute every x value for 5, you know that every equation can have 5 as an answer but C.

A. 3x+2=4x-3

Isolate the x(s) and combine like terms

3x+2-2=4x-3-2

3x=4x-5

3x-4x=4x-4x-5

-x=-5

-x(-1)=-5(-1)

x=5

Therefore A is a solution

B. (x+2)(x-5)=0

Substitution--Substitute every x for a 5

(7)(0)=0

anything multiplied by 0 will be 0

B. Is a solution because it is true.

C. 4x+2=15

Isolating the x(s) and combine like terms

4x+2-2=15-2

4x=13

4x÷4=13÷4

x=3.25

C is not a solution because x should equal to 5 but in this equation x can only be equal to 3.25. C is wrong.

We know our answer so we don't have to keep solving the rest of the equations.

But I'll just do D

D. 3x-10=x

Isolate the x(s) and combine like terms

3x-x-10=x-x

2x-10=0

2x=10

2x÷2=10÷2

x=5

D is a solution.

Data:

• Monthly budget: $15

• Price of a package of ramen: $1.48

• Price of a music download: $1.15

Procedure:

Answer: 10.1

Women are paid approximately 80 percent of what men are paid.

Multiple studies have been carried out to discuss the income inequality prevailing in United States. Pay inequity has been found as a corollary of the income inequality.

The women and men has different pay levels for the same work at certain work places. Income inequality is considered as an injustice and to put forward this issue may organizations are trying.

Hence according to multiple studies, including those by the American association of university women and the pew research center, on average, women are paid approximately 80 percent of what men are paid.

We can see the appreciable difference in the pay levels of women and men prevailing.

As a result several laws has been passed recently to have a solution for this injustice.

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The probability that exactly 10 customers will use the atm during the next noon lunch hour is 0.0948

From the question, we have the following parameters:

Average number of customers = 12

Number of customers = 10

The above parameters means that:

x = 10

λ = 12

The probability of a Poisson distribution is represented as

P(x) = λˣe⁻λ/x!

This gives

P(x = 12) = 10¹² * e⁻¹⁰/12!

Evaluate

P(x = 12) = 10¹² * e⁻¹⁰/479001600

Solving further, we have

P(x = 12) = 0.0948

Hence, the probability is 0.0948

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Answer:

4:2 and 14:7

Step-by-step explanation:

The ratios equivalent to 8:4 would be:

4:2

14:7

5:10 wouldn't be equivalent because if you simplify that, it is 1/2 and if you simplify 8/4, it is 2. 1/2 and 2 are not the same.

:D

Answer:

They are all equivalent except for 5:10

Step-by-step explanation:

You can write ratios as fractions

[tex]\frac{8}4}[/tex]   [tex]\frac{4}{2}[/tex]  [tex]\frac{14}{7}[/tex]   [tex]\frac{5}{10}[/tex]  If I simplify each fraction, I can see that they all equal 2 expect for the the last one.

2   2   2   1/2

The location of the center of dilation in the figure and the image formed following the dilation is the point N

The scale factor of the dilation is 0.5

A dilation transformation resizes an object such that the lengths of the sides of the image (the object formed) following the dilation of the original image has sides that are a constant multiple of the side lengths of the original object.

The center of dilation is a reference and fixed point, such that the center of is in the same location relative to the preimage and the image.

The location or point shared by both the figure LMNO and the image of LMNO formed following the dilation, which is figure L'M'N'O' is the point N.

Therefore;

The scale factor of the dilation is found using the definition of a scale factor, which is the ratio of the scale of a new figure to the scale of an original figure, therefore:

[tex]The \ scale \ factor,\, s.f. = \mathrm{\dfrac{Length \ of \ the \ sides \ of \ L'M'N'O'}{Length \ of \ the \ sides \ of \ LMNO}}[/tex]

MN = 6 units

LO = 6 units

ML = ON = √(6² + 2²) = 2·√(10)

M'N' = L'O' = 3 units

M'L' = O'N' = √(3² + 1²) = √(10)

Which gives:

[tex]s.f. = \dfrac{M'L'}{ML} =\dfrac{\sqrt{10} }{2 \cdot \sqrt{10} } = \dfrac{1}{2}=0.5[/tex]

The scale factor of the dilation is, s.f. = 0.5

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Answer:The boat is traveling at a rate of 3 ft/s.

Step-by-step explanation:

Answer:

a. Yes

Step-by-step explanation:

If you plug in the ordered pairs, the -5 is x and 16 is y.

The equation would look like this:

16=30x-14

Add 14 on both sides

14+16=30

30=30x

divide by 30 on both sides

1=1

a. Yess

Answer:

I believe so

Step-by-step explanation:

When writing a repeating decimal as fraction , the fraction do not always have only 9’s or 9’s and 0’s as digits in the denominator .

Repeating Decimal is a decimal in which after certain point a particular digit  or sequence of digit repeats itself infinitely  .

For Example : 0.66666666...    

When in a fraction the numerator is divided by the denominator , it is not at all necessary that the denominator will always have 9’s or 9’s and 0’s .

We can understand more with the help of an example .

example : 1/3 = 0.3333... is a repeating decimal , which does not have a 9 , 0 in the denominator .

(ii) 5/3 = 1.666666.... is a repeating decimal , which does not have a 9 , 0 in the denominator .

Therefore , When writing a repeating decimal as fraction , the fraction do not always have only 9’s or 9’s and 0’s as digits in the denominator .

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It is to be noted that the absolute expression that shows how far the student's score is from the average is given as: "| x - 74| (Option C)

The student obtained a score of x% based on the question. As a result, x% might be larger or lower than the average score of 74%.

To establish how distant the student's score is from the average, we must subtract the student's score from the average score; i.e. (x - 74)

This difference, however, might be negative: as a result, the absolute value of (x - 78) must be calculated, yielding |x - 74|.

As a result, the phrase that may be used to assess how distant the student's score is from the average is as follows: |x - 74| which is the same as option c - An Absolute expression.

Absolute expressions are or modulus of a real number x, abbreviated |x| in mathematics, is the non-negative value of x regardless of its sign.

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Answer:

a: 120 = 2x + 40

80 = 2x

x = 40

b: (3x + 10) + (x-30) = 180

4x - 20 = 180

4x = 200

x = 50

c: 105 = 2x - 11

116 = 2x

58 = x

d: 8y + 36 = 14y - 24

-6y = -60

y = 10

64 = 48 + x

16 = x

y = 10, x = 16

e: 75 + (2x - 5) = 180

70 + 2x = 180

2x = 110

x = 55

2(55) - 5 =y

y = 105

f: (2x + 8) + (3x + 17) = 180

5x + 25 = 180

x = 31

3(31) + 17 = 5y + 15

110 = 5y + 15

95 = 5y

y = 19, x = 31

The equation used to find the amount of time Emmet answers phone calls is t +25= 45

An equation is an expression that shows the relationship between two or more numbers and variables.

The amount of time Emmet answers phone calls = 20

She spends delivering flowers to patient's room= 25 minutes

She spends meetings volunteering at the hospital=  45

Let t be the amount of time Emmet answers phone calls in the hospital

Hence the equation used to calculate the amount of time spent on calls;

t + 25= 45

Now collect the like terms;

t= 45-25

t= 20

Hence, The equation used to find the amount of time Emmet answers phone calls is t +25= 45

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The car stops after moving for 20 seconds

From the question, the function is given as

v(t) = 0.5t^2 - 14t + 80

When the car comes to a stop, the vehicle is 0

This is represented as

v(t) = 0

So, we have

0.5t^2 - 14t + 80 = 0

Expand the equation

0.5t^2 - 10t - 4t + 80 = 0

Factorize the equation

0.5t(t - 20) - 4(t - 20) = 0

So, we have

(0.5t - 4)(t - 20) = 0

Solve for t

t = 8 and t  = 20

20 is greater than 8

Hence, the car comes to a stop at 20 seconds

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Given:

a.) A person had 14,000 infested in two accounts.

b.) One paying 9% simple interest.

c.) One paying 10% simple interest.

Let,

x = the amount invested at 9% simple interest

y = the amount invested at 10% simple interest

1.) We know the total amount of money invested is $14,000. We get,

x + y = 14,000

2.) We know that the total interest for the year for the two accounts is $1432. We get,

0.09*x + 0.1*y = 1,339

Let's equate the two equations,

x = 14,000 - y (Substitute for x)

0.09*(14,000 - y) + 0.1*y = 1,339

1,260 - 0.09y + 0.1y = 1,339

0.1y - 0.09y = 1,339 - 1,260

0.01y = 79

0.01y/0.01 = 79/0.01

y = 7,900

Therefore, $7,900 was invested at the rate of 10% simple interest.

Let's determine x, substituting y = 7,900 in x + y = 14,000.

x + y = 14,000

x + 7,900 = 14,000

x = 14,000 - 7,900

x = 6,100

Therefore, $6,100 was invested at the rate of 9% simple interest.

Answer:

There are 25 5's in 125.

Step-by-step explanation:

5 can go in 125 25 times.

(unless you are talking about literally-- there is one 5 in 125)

Answer:

22

Step-by-step explanation:

When 2 to the power of hundred is divided by 5 it show s remainder of 1

2 to the 100th power is solved as follows

2 ^ 100 = 1.2676506 * 10^30

This is solved using a calculator and the solution means that

2 * 2 * 2 * 2 * 2 * 2 * 2 * 2...............2   (2 multiplying itself till the number of 2's are up to 100)

This gives the value = 1.2676506 * 10^30

Division of the  2^100, by 5

2^100 / 5

2^1 / 5 remainder =2

2^2 / 5 remainder = 4

2^3 / 5 remainder = 3

2^4 / 5 remainder = 1

2^5 / 5 remainder = 2

2^6 / 5 remainder = 4

2^7 / 5 remainder = 3

2^8 / 5 remainder = 1

2^9 / 5 remainder = 2

2^10 / 5 remainder = 4

2^11 / 5 remainder = 3

It can be seen that it generates a pattern which is

The pattern counts in 4's. If we follow the pattern and count to 2^30

= 100 / 4

= 25 ⇒ this is a multiple of 4 and multiples of 4 goes with remainder 1

This is to say

2^97 / 5 remainder = 2

2^98 / 5 remainder = 4

2^99 / 5 remainder = 3

2^100 / 5 remainder = 1

Hence 2^100 divided by 5 will give a remainder of 1

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