Finding Angle Measures When Parallel Lines Are Cut By a Transversal

After 14.39 years the principle amount will reach to 13500 dollars.

What is compound interest?

Compound interest, also known as interest on principal and interest, is the practicize of adding interest to the principal amount of a loan or deposit.

Given: 5100 dollars is placed in an account with an annual interest rate of 7%.

Principle amount (P) = 5100 dollars.

Rate of interest = 7% = 0.07

Total amount (A) = 13500 dollars.

Here the interest is compounded annually, so we can use the compound interest formula,

[tex]A = (1+r)^t[/tex]

Plug the values in the formula

[tex]13500 = 5100(1+0.07)^t\\2.6471 = (1+0.07)^t[/tex]

Taking log on both sides,

[tex]log(2.6471) = log(1.07)^t\\log(2.6471) = t log(1.07)\\t = 14.39[/tex]

Hence, after 14.39 years the principle amount will reach to $13500.

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Answer:

The correct answer would be: 18.1

Step-by-step explanation:

Answer:

the C(X) pattern is +4? i need more context but i can give u that much

Step-by-step explanation:

The behavior of f(x) from given options is option (4) up on the left, up on the right.

A function f(x) 's end behavior is how the graph of the function f(x) behaves as x gets closer to positive or negative infinity. The functions degree or the polynomial degree and leading coefficient of a given function will determine the end behavior of the function.

Here we have

f(x) = 3x³² + 8x² - 22x + 43

Here

polynomial degree of f(x) is 32

And leading coefficient is 3  

Therefore,

The leading term of the given function is 3x³²

As the given polynomial has an even degree (32) and positive leading coefficient (3) then the graph will open upwards on both left and right.

Therefore,

The behavior of f(x) from given options is option (4) up on the left, up on the right.

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5725 is the height of the mountain prior to construction, represented by the variable h.

Two or more expressions with an Equal sign is called as Equation.

Given,

The mountain that contains Mount Rushmore is approximately 5,675 feet high.

The height of the mountain is 622.5 feet less than 1.1 times its height before construction began.

1.1h – 622.5 = 5,675 is the equation to find the height of the mountain prior to construction, represented by the variable h

1.1h – 622.5 = 5,675

We need to find the value of h

Add 622.5 on both the sides

1.1h=5675+622.5

1.1h=6297.5

Divide both sides by 1.1

h=6297.5/1.1

h=5725

Hence 5725 is the height of the mountain prior to construction, represented by the variable h.

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Answer:

$6.30

Step-by-step explanation:

The state sales tax rate in North Carolina is 4.5% estimate the state sales tax on a model of the wright brothers’ airplane that costs $139.99.

You are asked to estimate meaning $139.99 should be rounded to $140. Because 4.5% = 0.045

sales tax (estimated):

0.045 * $140 = $6.30

CHECK:

Exact amount is:

0.045 * 139.99 = $6.29955

The The temperature at midnight is -5.6°C.

What is the short definition of temperature?

It should be noted that there are 8 hours between midnight and 6 am.

Therefore, the equation will be:

x + (0.65 × 8) = -0.1

x + 5.5 = - 0.1

x = -0.1 - 5.5

x = - 5.6

The temperature at midnight is -5.6°C.

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Answer: x≤12

Step-by-step explanation: the room holds a max of 12 people, so the number of people will be less than or equal to 12

The number of schedules that are possible, considering each case and the Fundamental Counting Theorem, is given as follows:

a) No restrictions: 3,628,800.

b) Last two games against the same team: 362,880.

The Fundamental Counting Principle states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the factorials as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Teams play each other only once during the season, hence, if there are no restrictions, the parameters are given as follows:

[tex]n_1 = 10, n_2 = 9, \cdots, n_{10} = 1[/tex]

Hence the number of schedules is:

N = 10! = 10 x 9 x 8 x ... x 1 = 3,628,800.

If the last game is fixed, then the remaining games are an arrangements from 9 games, and thus the number of schedules is:

N = 9! = 362,880.

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Answer:

-42,000

Step-by-step explanation:

10-³ would be -30, so

2.0 x -30 = -600

10² would be 20, so

3.5 x 20 = 70

Multiply the two

-600 X 70 = -42,000

Answer:

22.287

Explanation:

This is because 15 is a whole number.

It is also 15.000

37.287

-15.000[tex]\\[/tex]

22.287

Answer:

12x-6

Step-by-step explanation:

(3x+4)+(9x-10)

= 3x+4+9x-10

=3x+9x+4-10

=12x-6

ANSWER IS 12X-6

Using Midsegment theorem, the value of x and y are 17 and 2 respectively and the length of DF is 20 units.

The Midsegment theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.

Therefore, DH is midsegment of  triangle DEF.

Hence, let's find x

1 / 2 (28) = x - 3

14 = x - 3

add 3 to both sides of the equation

14 = x - 3

14 + 3 = x - 3 + 3

x = 17

Let's find the length DF as follows:

DF = y + 8 + x - 7

Recall x = 17

Therefore,

DF = y + 8 + 17 - 7

DF = y + 8 + 10

DF = y + 18

y+ 8 = 10

y = 2

Hence,

DF = 2 + 18

DF = 20 units

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Explanation:

0.4 = 4/10 = 2/5

The original slope as a fraction is 2/5

Flip the fraction to get 5/2, then flip the sign to get -5/2 which is the perpendicular slope

The orginal slope 2/5 and perpendicular slope -5/2 multiply to -1. This is true of any pair of perpendicular lines where neither line is vertical nor horizontal.

Rephrased another way: -5/2 is the negative reciprocal of 2/5.

The confidence interval for the population mean difference is between -33.2 and + 33.2

You have a 5% probability of being incorrect with such a 95% confidence interval. You have such a 10% probability of becoming incorrect with a 90% confidence interval. In contrast to a 95 % confidence interval, a 99 per cent confidence interval would be larger (plus or minus 4.5 per cent as opposed to 3 per cent, for example).

The answer in this situation would be +/-(2 * 16.6) from the mean, or -33.2 and +33.2 points from the sample mean because the 95% confidence interval is equal to two standard deviations on either side of the mean. This would result in an answer of A.

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Your question is incomplete, but probably the full question was:

A teacher wants to compare the mean geology scores of two different classes. She is testing the null hypothesis that there is no difference in the population mean scores of the two classes. The difference of the sample means is 51.4. If the standard deviation of the distribution of the difference of sample means is 16.66, what is the 95% confidence interval for the population mean difference?

A)between -33.2 and + 33.2

B)between -49.9 and +49.9

C)between -102.8 and +102.8

D)between -154.2 and +154.2

The size of the F-ratio value would increase as the numerator of the F-ratio (MS Between) increased and The size of the F-ratio value would increase as the numerator of the F-ratio (MSBetween) increased.

Given that,

The F ratio can be defined as,

F =Mean Sum of Squares of between treatments / Mean Sum of Squares of within treatments

F =MS Between /MS within

Increase the difference between the sample means.

As the difference between the sample means increases, between treatments has larger effect

(MS known ) . This affects the numerator of F-ratio.

Hence, As numerator of F-ratio ( MS Between ) increases, the size of the F-ratio value would increase.

Increase the size of sample variances.

As the size of sample variance increases, with treatments has larger effect ( MS within ). This

affects the denominator of F-ratio.

Hence, As the denominator of F-ratio (MS Within ) increases. The size of F-ratio will decrease.

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Answer:

Step-by-step explanation:

y=X-2

The value of (5 - 6b)² when it is expanded is 25 -60b + 36b² (third option).

The square of a number is the value derived when a number is multiplied by itself. Multiplication is the mathematical operation that is used to determine the product of two or more numbers. The sign that is used to represent multiplication is x.

The square of a number is denoted by the power 2. For example, the square of 2, 2² is 4 (2 x 2).

Thus, (5 - 6b)² is the same as (5 - 6b) x (5 - 6b).

When multiplied, the expression becomes:

(5 - 6b) x (5 - 6b)

When multiplied, the expression becomes: 25 - 30b - 30b + 36b²

Add similar terms together: 25 -60b + 36b²

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The inequality can be simplified to:

-7 < x < 3

And the graph can be seen in the image at the end.

Here we have the inequality:

|x + 2| + 1 > 6

To solve this, we need to isolate the variable x, so if we first subtract 1 we get:

|x + 2| +1 - 1 > 6 - 1

|x + 2| > 5

The absolute value part can be decomposed into two.

-5 < x + 2 < 5

Now we can subtract 2 in all the inequality, so we get:

-5 - 2 < x + 2 - 2 < 5 - 2

-7 < x < 3

The graph of this can be seen below

Answer:

1.102, 1.12, 1.1212, 1.2

Step-by-step explanation:

Answer:

1 ) 1.102

2 ) 1.12  

3 ) 1.1212

4 ) 1.2

Hope this helps! :)

Answer:

  600 ft by 1200 ft

Step-by-step explanation:

You want the dimensions of the largest rectangular area that can be enclosed on three sides with 2400 feet of fencing.

Let x represent the dimension of the field that is parallel to the river, and y the dimension out from the river. The sum of the three side lengths is ...

  x + 2y = 2400

Solving for y gives ...

  y = (2400 -x)/2

The area is the product of the two dimensions:

  A = xy = x(2400 -x)/2

We observe that this is the factored form of a quadratic with zeros at x=0 and x=2400. Its leading coefficient is negative, so the graph opens downward, and the vertex is the point where area is a maximum.

The vertex is located on the line of symmetry at the x-value that is halfway between the zeros:

  x = (0 +2400)/2 = 1200

  y = (2400 -x)/2 = (2400 -1200)/2 = 600

The dimensions of the field that has the largest area are 600 ft by 1200 ft.

__

Additional comment

As we observed here, the side parallel to the "river" will use 1/2 of the fencing, and the remaining two sides will each use 1/4 of the fencing. This is the general solution to such a fencing problem.

Answer:

6.68

Step-by-step explanation:

[tex]20.16+20.78+12.53 = 53.47[/tex]

[tex]53.47 \div 8 = 6.68375[/tex]

The mean of samples of 100 IQ scores taken out from this population will have a distribution with mean M=104 and standard deviation s=3.5.  

We know the population mean and standard deviation, that has a bell-shaped distribution:

μ= 107

σ=35

The sampling distribution, the distribution of the mean of samples of size n out of this population, will have the same mean as the population mean.

μ (m) = μ =107

The standard deviation will be related to the population standard deviation and the sample size as:

σ (m)= σ/[tex]\sqrt{N}[/tex]

         = 35/10=3.5

Then, the mean of samples of 100 IQ scores taken out from this population will have a distribution with mean M=104 and standard deviation s=3.5.

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The answer is [tex]3A+3B=\left[\begin{array}{ccc}-6&-21\\18&3\end{array}\right][/tex]

To solve the given expression, we have to first know about matrix addition and scalar multiplication.

Matrix addition is possible only when both matrices have equal dimensions. Scalar multiplication is the multiplication of a real number and a matrix. Each element of the matrix is multiplied by a scalar value in scalar multiplication.

To solve the given problem, first, substitute the value of A and B in the formula,

[tex]3A+3B=3\left[\begin{array}{cc}-4&-3\\6&1\end{array}\right] +3\left[\begin{array}{cc}2&-4\\0&0\end{array}\right][/tex]

Using scalar multiplication, multiply the real number and the matrix. So we get,

[tex]\begin{aligned}3A+3B&=\left[\begin{array}{ccc}3(-4)&3(-3)\\3(6)&3(1)\end{array}\right] +\left[\begin{array}{ccc}3(2)&3(-4)\\3(0)&3(0)\end{array}\right]\\&=\left[\begin{array}{ccc}-12&-9\\18&3\end{array}\right] +\left[\begin{array}{ccc}6&-12\\0&0\end{array}\right]\end{aligned}[/tex]

To add two matrices with the same dimension, add their corresponding element. So we get,

[tex]\begin{aligned}3A+3B&=\left[\begin{array}{ccc}-12+6&-9-12\\18+0&3+0\end{array}\right] \\&=\left[\begin{array}{ccc}-6&-21\\18&3\end{array}\right]\end{aligned}[/tex]

Therefore, the answer is [tex]3A+3B=\left[\begin{array}{ccc}-6&-21\\18&3\end{array}\right][/tex]

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2w + 10 = 26 can you use to find w, the number of weeks the driving classes last the driving test will last for 8 weeks.

A linear equation is an algebraic equation of the form y = mx + b. involving only a constant and a first-order ( linear ) term, where m is the slope and b is the y - intercept.

If w is the number of weeks,

The equation to represent this equation is to be 2w + 10 = 26

2w = 26 - 10

2w = 16

w =  [tex]\frac{16}{2}[/tex]

w = 8

Hence the driving test will last for 8 weeks.

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Answer: 20

Step-by-step explanation:

5 boxes with 10, 10, 10, 10, and 10 donuts in each box.

She gives one box away, so that is 50-10=40

Then she gives 2 boxes away, which is 40-20=20, so she has 20 donuts left to share with her classmates.

Answer: 20

Step-by-step explanation:

5 x 10 = 50 Donuts

50 Donuts - 10       for the Bus driver

40 Donuts - 20      for the school principal

=20

She can share 20 Donuts with her classmates.

The average rate of change of the function g(n) from n = 1 to n = 5 is 0.2 inches.

We are given;

A researcher is following the growth of a particular type of flower. She writes the given equation to show the height of the flower g(n), in inches, after n days.

g(n) = 10(1.02)^n

which is an exponential function.

We need to find the average rate of change of the function g(n) from n = 1 to n = 5.

We know that the average rate of change = slope of the function.

The slope of the function is given by:

Slope = Change in y-coordinate / change in x-coordinate

We have,

g(n) = 10(1.02)^n;

for n = 1; g(n) = 10(1.02)^1 = 10 * 1.02 = 10.2

for n = 5; g(n) = 10(1.02)^5 = 10 * 1.1 = 11

Put the values in the slope formula;

slope = 11 - 10.2 / 5 - 1 = 0.8 / 4 = 0.2

Thus, the average rate of change of the function g(n) from n = 1 to n = 5 is 0.2 inches.

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a. False, the slope of f(x) will be steeper than m(x).

b. False, the y-intercept of m(x) will be equal to f(x).

What is a slope?

Slope and slant both refer to an incline away from a reference surface or line that is generally straight. The definition of slope is "a vertical inclination in an oblique direction" Here, the land abruptly slopes either upward or downhill.

Here, we have

f(x) = x and m(x) = 3/5f(x)

a.  m₁ = slope of f(x) = x is 1

     m₂ = slope of m(x) = 3/5f(x) is 3/5

    m₁ >  m₂

f(x) = x is more steeper than m(x) = 3/5f(x).

b.  a₁ = intercept of f(x) = x is 0.

    b₁ = intercept of m(x) = 3/5f(x) is 0.

The y-intercept of m(x) will be equal to f(x).

Hence, a. False, the slope of f(x) will be steeper than m(x).

b. False, the y-intercept of m(x) will be equal to f(x).

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