at 2 p.m., two cars leave eagle river, wi, one headed east and one headed west. if the car traveling east averages 55 mph and the car traveling west averages 40 mph, when will the cars be 237.5 miles apart?

The correct option regarding whether the two functions are inverse functions is given as follows:

B. No, because the composition does not result in an answer of x.

Two functions are inverses of each other if the composition of these two function has a result of x.

From the image given at the end of the answer, the two functions in this problem are defined as follows:

Their composition is given as follows:

[tex](G \circ F)(x) = G(\sqrt{x} + 4)[/tex]

[tex](G \circ F)(x) = (\sqrt{x} + 4)^2 - 4[/tex]

[tex](G \circ F)(x) = x + 8\sqrt{x} + 16 - 4[/tex]

[tex](G \circ F)(x) = x + 8\sqrt{x} + 12[/tex]

The composition does not result in x, hence the two functions are not inverses and the correct statement is given by statement B.

The problem is given by the image shown at the end of the answer.

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Answer:

x =4 & y = -7

Step-by-step explanation:

this is the right answer

Answer:

B

Step-by-step explanation:

5.21 x 10^19 + 3.149 x 10^17

10^17(5.21 x 10^2 + 3.149)

10^17(521 + 3.149)

10^17(524.149)

5.24149 x 10^17 x 10^2

5.24149 x 10^(17+2)

5.24149 x 10^19

Answer: b. 5.24149 × 1019

Step-by-step explanation: I took the test

The solution is

a) The compound interest for the second period is $ 2.01 and the amount after the second period is $ 404.01

b) The compound interest for the first period is $ 114.125 and the amount is $ 18,374.125

The compound interest for the second period is $ 114.83828125 and the amount after second period is $ 18,488.96

What is Compound Interest?

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

a)

Let the principal be P = amount after first period =  $ 402

Now , the rate of interest r = 6 %

The compound interest is calculated by compounding monthly

Now , the interest for the second period = ( PRT / 100 x 12 )

Substituting the values in the equation , we get

The interest for the second period = ( 402 x 6 x 1 ) / 1200

The interest for the second period = $ 2.01

The amount after the second period = amount after first period +  interest for the second period

The amount after the second period = 402 + 2.01

The amount after the second period = $ 404.01

b)

Let the principal be P = $ 18260

The rate of interest r = 2.5 %

The compound interest is calculated by compounding quarterly

Now , the interest for the first period = ( PRT / 4 x 100 )

Substituting the values in the equation , we get

The interest for the first period = ( 18260 x 2.5 ) / 400

The interest for the first period = 45650 / 400

The interest for the first period = $ 114.125

The amount for the first period = 18260 + 114.125

The amount for the first period = $ 18,374.125

Now , the principal for the second period = interest + amount of first period

The principal for the second period = $ 18,374.125

The rate of interest = 2.5 %

The interest for the second period = ( PRT / 4 x 100 )

Substituting the values in the equation , we get

The interest for the second period = ( 18374.125 x 2.5 ) / 400

The interest for the second period = 45935.3125 / 400

The interest for the second period = $ 114.83828125

The amount for the second period = 18,374.125+ 114.84

The amount for the second period = $ 18,488.96

Hence , the amount and interest is calculated

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Using a mean and standard deviation as inputs, the following formula can be used to get the percentile of a normal distribution:

Percentile Value is equal to z +.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.

While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.

The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation.

Standard deviation may be written as SD.

A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance.

Though in algebra, it is simpler

According to our question-

a. 157 is less then 161

b. n>173, n be a real number.

Hence, Using a mean and standard deviation as inputs, the following formula can be used to get the percentile of a normal distribution: Percentile Value is equal to z +.

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The solution to the products of exponents is as follows;

1) -24a³b⁷

2) 15a⁵b¹⁵

3) -10d⁴ + 17sd² - 6s²

4) 6x³ - 33x² + 45x - 6

5) 21x⁷y¹¹

6) 8y⁴ + 25y³ + 60y² + 10y + 7

7) 20s³ + 50s² + 32s + 6

The Product of Powers Property of exponents states that when we multiply two powers with the same base, we add the exponents.

1) (3a²b⁴) * (-8ab³)

= -24a³b⁷

2) (3a²b⁷) * (5a³b⁸)

= 15a⁵b¹⁵

3) (-2d² + s)(5d² - 6s)

Expanding the bracket to get;

(-10d⁴ + 5sd² + 12sd² - 6s²)

= -10d⁴ + 17sd² - 6s²

4) (3x - 6) * (2x² - 7x + 1)

= 6x³ - 33x² + 45x - 6

5) (7x²y³) * (3x⁵y⁸)

= 21x⁷y¹¹

6) (y² + 3y + 7) * (8y² + y + 1)

= 8y⁴ + 25y³ + 60y² + 10y + 7

7) (4s + 2) * (5s² + 10s + 3)

= 20s³ + 50s² + 32s + 6

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The answer is that the the equation for a cosecant function with vertical asymptotes found at x equals pi over 4 plus pi over 4 times n comma such that n is an integer is 2 coscec 4x.

Cosecant is one of the trigonometric ratios . It is calculated as the ratio of the hypotenuse to the perpendicular of a right triangle. It is also calculated as the reciprocal of the sine function.

Now, here if the vertical asymptotes is x = pi/4 + pi/4 (n).

This is not defined when n=0.

so, when x= pi/4,

sin 4x = sin x = 0

which means w =0 .

and we get the equation for cosecant function  to be f(x)= 2 cosec 4x since cosec x = 1/ sin x.

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Answer:

7.7

Step-by-step explanation:

I got this by subtracting 13.3 - 5.6

Answer: g(f(-2))=-96

Step-by-step explanation:

[tex]Given: \ f(x)=e^{6x}\ \ \ \ g(x)=8ln(x)\ \ \ \ g(f(-2))=?\\\\f(-2)=e^{6*(-2)}\\\\f(-2)=e^{-12}\\\\Hence,\\\\g(f(-2))=8ln(e^{-12})\\\\g(f(-2))=8*(-12)\\\\g(f(-2))=-96[/tex]

Answer:

-96

Step-by-step explanation:

Given:

[tex]\begin{cases}f(x)=e^{6x}\\ g(x)=8 \ln (x) \end{cases}[/tex]

To find g[f(-2)], substitute x = -2 into the function f(x):

[tex]\implies f(-2)=e^{6 \times -2}=e^{-12}[/tex]

Then substitute the function f(-2) in place of the x in function g(x):

[tex]\implies g[f(-2)]=8 \ln \left(e^{-12}\right)[/tex]

[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\begin{aligned}\implies g[f(-2)]&=-12\cdot 8 \ln \left(e\right)\\&=-96 \ln \left(e\right)\end{aligned}[/tex]

Apply the log law:  ln(e) = 1

[tex]\begin{aligned}\implies g[f(-2)]&=-96 \ln \left(e\right)\\&=-96(1)\\&=-96\end{aligned}[/tex]

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

As one calculation:

[tex]\begin{aligned}g[f(-2)]&=8 \ln \left(e^{6 \times -2}\right)\\& = 8 \ln \left(e^{-12}\right)\\& = -12 \cdot 8 \ln \left(e\right)\\& = -96(1)\\& = -96\end{aligned}[/tex]

Answer:

D. -6 < x ≤ -3

Step-by-step explanation:

21 ≤ -3(x − 4) < 30

21/3 ≤ -3(x − 4)/3 < 30/3

7 ≤ -(x − 4) < 10

7 ≤ -x - (-4) < 10

7 ≤ -x + 4 < 10

7 - 4 ≤ -x + 4 - 4 < 10 - 4

3 ≤ -x < 6

(3 ≤ -x < 6)/(-1)

-3 >= x > -6   ==> when dividing by a negative number, switch the inequality          

                           sign

-6 < x ≤ -3 ==> D

There will be 40% chance that the team will win.

Odds, are given as (chances for success) : (chances against success) or vice versa.

If odds are stated as an A to B chance of winning then the probability of winning is given as P(winning) = A / (A + B) while the probability of losing is given as P(Losing) = B / (A + B).

For 2 to 3 odds for winning:

P(winning) = 2/2+3

                 = 2/5

                 = 0.4

⇒ The percent chance of winning is 40.

Therefore, 40% is the required answer.

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(a) The probability of either A or B occurring is 0.81.

(b) The probability that neither A nor B will happen is 0.19.

In the given question,

P(A)=0.39 P(A) = 0.39 and P(B)=0.42. P(B) = 0.42

(a) We have to find the probability of either A or B occurring.

P(A)=0.39

P(B)=0.42.

Since, events A and B are mutually exclusive

P(A and B) = 0

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.39 + 0.42 - 0

P(A or B) = 0.81

Probability of either A or B occurring is = 0.81

(b) Now we have to find the probability that neither A nor B will happen.

P(A or B) = 0.81

Probability that neither A nor B will happen = 1 - P(A or B)

Probability that neither A nor B will happen = 1 - 0.81

Probability that neither A nor B will happen = 0.19

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The right question is:

The events A and B are mutually exclusive. Suppose P(A)=0.39 P(A) = 0.39 and P(B)=0.42. P(B) = 0.42.

(a) What is the probability of either A or B occurring? (Round your answer to 2 decimal places.)

(b) What is the probability that neither A nor B will happen? (Round your answer to 2 decimal places.)

Answer:

1. Scalene Triangle

2. 135 degrees

3. 80 degrees

I don't have much time for the rest, i'm sryyyyy

I hope i could helppp :3

As per the sign system of the Cartesian plane coordinates of A' will be (x,-y).

The cartesian plane is defined in mathematics as a two-dimensional coordinate plane formed by the intersection of the x- and y-axes. The origin is the point where the x- and y-axes intersect perpendicularly.

Quadrant one (QI) is the top right fourth of the coordinate plane, where all coordinates are positive. Quadrant two (QII) is the coordinate plane's top left fourth. Quadrant three (QIII) is the fourth from the bottom left. Quadrant four (QIV) is the fourth from the bottom right.

Given:

The direction of rotation = clockwise, (from the first quadrant to forth quadrant then third quadrant, and so on)

Angle of rotation = 90° about the origin

According to the question, let's take our start point as A(x, y)

So, A( x, y) will lie in the first quadrant.

After 90° rotation about the origin A' will lies in fourth quadrant.

As per the sign system of the Cartesian plane coordinates of A' will be (x,-y).

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After evaluation, we can conclude that the expression (E) 8/2 * 2/12 is equivalent to the given expresion 16/24.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

It's possible to multiply, divide, add, or subtract with this mathematical operation.

You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.

So, we have the expression:

16/24

We need to find the equivalent expression from the options as follows:

So, let's take option (E) as it seems the answer and evaluation is:

8/2 * 2/12 (Be LHS)

Now, multiply:

8/2 * 2/12 = 16/24

16/24 = 16/24

Therefore, after evaluation, we can conclude that the expression (E) 8/2 * 2/12 is equivalent to the given expression 16/24.

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Answer:

D. 7

Step-by-step explanation:

[tex] \frac{ \sqrt{196} }{\sqrt{4} } \\ [/tex]

[tex] \frac{14}{2} [/tex]

=7

The value of y is 10. The measure m∠ C and m∠ D are 40° and 76° respectively.

What is external angle?

The angle created when a transversal cuts one of two lines and is located outside of the line. It describes the angle between a side of a polygon and an expanded adjacent side.

The measure of an external angle of a triangle is equal to the sum of opposite interior angles.

∠DEF is an exterior angle. The opposite interior angles of ∠DEF are m∠ C and m∠ D

Therefore,

m∠ C + m∠ D = ∠DEF

4y° + (7y + 6)° = 116°

Add like terms

11y + 6 = 116

Subtract 6 from both sides:

11y = 110

Divide both sides by 11:

y = 10

Putting y = 10 in  m∠ C = 4y° and m∠ D =  (7y + 6)°

m∠ C = 40°

m∠ D = 76°

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Answer:

-8x+25x+5-7=3x-9

or ,17x -2=-9+2

or, -14x=-7

or, x=-7/-14

x=1/2

Answer:

-8x +25x +5-7=3x-9

17x-2 = 3x-9

17x-3x=9+2

14x =11

x= 14/11

Answer:

B. 7−10; 11−14; 15−18; 19−22

Step-by-step explanation:

Answer:

The first answer on the bottom goes with the picture on top.

The second answer on the bottom goes with the table on the bottom.

Step-by-step explanation:

It is just asking you to list the x values and the y value.  The x values are the domains and the y values are the ranges.  That's it.

Distributive property of real numbers illustrated by the equation. -2(x 4)=-2x-8

The equation -2(x 4)=-2x-8 is an example of the distributive property of real numbers. This property states that when a number is multiplied by a group of numbers that are being added together, the number can be distributed to each of the terms in the group. To rewrite this equation as -2x + (-2)(-4) = -2x - 8, the number -2 is allocated to each of the terms in the group (x and -4) in this equation.Simplifying further, we get -2x - 8 = -2x - 8.

-2(x 4) = -2x - 8

Distribute -2 to each term in the group

-2x + (-2)(-4) = -2x - 8

Simplify

-2x - 8 = -2x – 8

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The python program code is written to find the area of the shape.

The size of a region on a planar or curved surface is expressed mathematically as area. The term "surface area" refers to the area of an open surface or the perimeter of a three-dimensional object, whereas "plane area" refers to the area of a shape or planar lamina.

The program is given as:

print('Please, enter sides lengths:')

# Getting sides lengths

a, b, c, d, e = map(float, (input('A = '), input('B = '), input('C = '), input('D = '), input('E = ')))

# Finding a rectangle area

rect_area = a * b

# Finding a triangle area

triang_height = (c**2 - (a / 2)**2)**0.5

triang_area = 0.5 * a * triang_height

# Sum area

area = rect_area + triang_area

print('Total room area: %f' % area)

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Answer:

  30°

Step-by-step explanation:

You want the angle of elevation to a point 2900 feet up that is 5800 feet distant on a straight line.

The sine of the angle is the ratio of the height to the straight-line distance.

  sin(θ) = h/d = 2900/5800 = 1/2

  θ = arcsin(1/2) = 30°

The angle of elevation is 30° from the base to the top.

Answer: When doing a problem like this I always draw an example so I can see it. If you do that you see a right triangle with the hypothenuse, 2500 feet, is the distance from the top to the base. The opposite side is 1250 feet. Then remember  sine= o/h, (opposite side over hypothenuse). So divide 1250/2500 and you get .5  Now take your calculator and use "inv" or sin-1 button to get the answer of the angle. x = 30

sinθ 1250/2500 = 1/2; θ = sin-1(1/2) = 30°

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]x^{2} +2x+16=0\\x^{2} +2x+1-1+16=0\\(x^{2} +2x+1)-1+16=0\\(x+1)^{2} +15=0\\(x+1)^{2}=-15[/tex]

The solution does not exist because all numbers squared are greater than zero.

Answer:

B=20

C = 40  

These are the answers

Spanish is a Romance language of the Indo-European language family that emerged from the Iberian peninsula's colloquial Latin. It is now a worldwide language with around 500 million native speakers, primarily in the Americas and Spain. Twenty nations have Spanish as their official language.

These numbers in Spanish are:

1. 49: cuarenta y nueve

2. 97: noventa y siete

3. 113: ciento trece

4. 632: seiscientos treinta y dos

5. 1.781: mil setecientos ochenta y uno

6. 3.558: tres mil quinientos cincuenta y ocho

7. 1.006.015: un millon seis mil quince

8. 67.224.370: sesenta y siete millones doscientos veinte y cuatro mil trescientos setenta

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Answer:

49: cuarenta y nueve

2. 97: noventa y siete

3. 113: ciento trece

4. 632: seiscientos treinta y dos

5. 1.781: mil setecientos ochenta y uno

6. 3.558: tres mil quinientos cincuenta y ocho

7. 1.006.015: un millon seis mil quince

8. 67.224.370: sesenta y siete millones doscientos veinte y cuatro mil trescientos setenta

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

We are told that line AC divides angle BAE in half or "bisects" it. We are also told that line AD divides angle CAE in half as well. Lastly we are giving the value of angle DAE which is 36.

Since line DA split angle CAE in half and we have half of the value, that means that the measure of angle CAE is 36 times 2 which is 72.

72 happens to be our answer for angle BAC because angle BAC is half of the largest angle BAE, which was divided in two by line AC.

Hope this helps!

The function rule that could be represented by the graph is given as follows:

y = 2x³ + x - 3.

The first step in defining the function is looking at it's y-intercept, which is the value of y when the graph of the function crosses the y-axis.

This value is of -3, hence the function can be defined as follows:

f(x) = ax^n + x - 3.

Then we look at the behavior of the function. It has an inflection point, as it is concave down and then it becomes concave up, hence:

Thus:

f(x) = ax³ + x - 3.

Then we look at the x-intercept, meaning that when x = 1, y = 0, this the leading coefficient is obtained as follows:

0 = a + 1 - 3

a = 2.

Thus the function is defined as follows:

y = 2x³ + x - 3.

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