math test , if 9 = 90 , 8 = 72 , 7 = 56 , 6 = 42 , 3 = ?

Answer:

Step-by-step explanation:

THE ANSWER TO YOUR QUESTION IS C.

Answer:

1)  The functions are not inverses.

\(\textsf{2)} \quad g^{-1}(n)=&\dfrac{3}{8}n-\dfrac{7}{8}\)

\(\textsf{3)} \quad g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\)

Step-by-step explanation:

The inverse composition rule states that if two functions are inverses of each other, then their compositions result in the identity function.

Given functions:

\(g(x) = 4 + \dfrac{7}{2}x \qquad \qquad f(x) = 5 - \dfrac{4}{5}x\)

Find g(f(x)) and f(g(x)):

\(\begin{aligned} g(f(x))&=4+\dfrac{7}{2}f(x)\\\\&=4+\dfrac{7}{2}\left(5 - \dfrac{4}{5}x\right)\\\\&=4+\dfrac{35}{2}-\dfrac{14}{5}x\\\\&=\dfrac{43}{2}-\dfrac{14}{5}x\\\\\end{aligned}\)                 \(\begin{aligned} f(g(x))&=5 - \dfrac{4}{5}g(x)\\\\&=5 - \dfrac{4}{5}\left(4 + \dfrac{7}{2}x \right)\\\\&=5-\dfrac{16}{5}-\dfrac{14}{5}x\\\\&=\dfrac{9}{5}-\dfrac{14}{5}x\end{aligned}\)

As g(f(x)) or f(g(x)) is not equal to x, then f and g cannot be inverses.

\(\hrulefill\)

To find the inverse of a function, swap the dependent and independent variables, and solve for the new dependent variable.

Calculate the inverse of g(n):

\(\begin{aligned}y &= \dfrac{8}{3}n + \dfrac{7}{3}\\\\n &= \dfrac{8}{3}y + \dfrac{7}{3}\\\\3n &= 8y + 7\\\\3n-7 &= 8y\\\\y&=\dfrac{3}{8}n-\dfrac{7}{8}\\\\g^{-1}(n)&=\dfrac{3}{8}n-\dfrac{7}{8}\end{aligned}\)

Calculate the inverse of g(x):

\(\begin{aligned}y &= 1-2x^3\\\\x &= 1-2y^3\\\\x -1&=-2y^3\\\\2y^3&=1-x\\\\y^3&=\dfrac{1}{2}-\dfrac{1}{2}x\\\\y&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\\end{aligned}\)

Answer:

1.

If the composition of two functions is the identity function, then the two functions are inverses. In other words, if f(g(x)) = x and g(f(x)) = x, then f and g are inverses.

For\(\bold{g(x) = 4 + \frac{7}{2}x\: and \:f(x) = 5 -\frac{4}{5}x}\), we have:

\(f(g(x)) = 5 - \frac{4}{5}(4 + \frac{7}{2}x)\\ =5 - \frac{4}{5}(\frac{8+7x}{2})\\=5 - \frac{2}{5}(8+7x)\\=\frac{25-16-14x}{5}\\=\frac{9-14x}{5}\)

\(g(f(x)) = 4 + (\frac{7}{5})(5 - \frac{4}{5}x) \\=4 + (\frac{7}{5})(\frac{25-4x}{5})\\=4+ \frac{175-28x}{25}\\=\frac{100+175-28x}{25}\\=\frac{175-28x}{25}\)

As you can see, f(g(x)) does not equal x, and g(f(x)) does not equal x. Therefore, g(x) and f(x) are not inverses.

Sure, here are the inverses of the functions you provided:

2. g(n) = (8/3)n + 7/3

we can swap the roles of x and y and solve for y to find the inverse of g(n). In other words, we can write the equation as y = (8/3)n + 7/3 and solve for n.

y = (8/3)n + 7/3

n =3/8*( y-7/3)

Therefore, the inverse of g(n) is:

\(g^{-1}(n) = \frac{3}{8}(n - \frac{7}{3})=\frac{3}{8}*\frac{3n-7}{3}=\boxed{\frac{3n-7}{8}}\)

3. g(x) = 1 - 2x^3

We can use the method of substitution to find the inverse of g(x). We can substitute y for g(x) and solve for x.

\(y = 1 - 2x^3\\2x^3 = 1 - y\\x = \sqrt[3]{\frac{1 - y}{2}}\)

Therefore, the inverse of g(x) is:

\(g^{-1}(x) =\boxed{ \sqrt[3]{\frac{1 - x}{2}}}\)

Answer:

But the 2lbs.

Step-by-step explanation:

Divide $9.19 by 2 and you get 4.595 which would be the cheapest option out of the 3 because the 1lb is $7.05 and the 3lb is $5.13.

You're welcome.

Answer:

141.5 in

Step-by-step explanation

AB // CD // EF

12 / 15 = 21 / y        (By the property of 3 parallel lines and its transversals)

y = (15*21) / 12 = 26.25

CD // EF // GH

21 / y = x / 10       21 / 26.25 = x / 10

x = (21*10) / 26.25

x = 8

perimeter of ABHG = (y-14) +15 + y + 10 + (5x-3) + x + 21 + 12 = 141.5

The area of the composite figure whose vertices have the  (2,-2), (2,1), (4,2), (6,2), (4,-1) coordinates is 6 square units

We first need to plot all the given points A  (2,-2), B (2,1), C (4,2), D (6,2)and E (4,-1) which is coordinate geometry

After joining the Points which is a pentagon and it can be divided in two shapes one is triangle CDE and a quadrilateral ABCE

Using the distance formula

BC = \(\sqrt{(y2-y1)^{2}+(x2-x1)^{2} }\) = \(\sqrt{(2-1)^{2} + (4-2^{2} }\) = √5

Since BC = AE and BC ll AE , we can say ABCE is a parallelogram

area of a parallelogram = base × Altitude

                                      = 2 × 2= 4

Area of triangle CDE where CD is perpendicular and CE is the base

                        = 1/2 ( 2×2)

                        = 1/2 (4)

                         = 2 square units

So the area of ABCDE = Area of ABCE + area of CDE

                                     = 4 square units + 2 square units

                                      = 6 square units

Hence, the area of the composite figure whose vertices have the  (2,-2), (2,1), (4,2), (6,2), (4,-1)coordinates is 6 square units

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Answer:

x = 3

Step-by-step explanation:

By inscribed angle theorem:

\(m\angle FGE = \frac{1}{2} \times m(\widehat{EF}) \\ \\ \implies \: (31x + 3) \degree = \frac{1}{2} \times 192 \degree \\ \\ \implies \: (31x + 3) \degree = 96 \degree \\ \\ \implies \: 31x + 3 = 96 \\ \\ \implies \: 31x = 96 - 3 \\ \\ \implies \: 31x = 93 \\ \\ \implies \: x = \frac{93}{31} \\ \\ \implies \: x = 3\)

So the new coordinates of point C are (1, 2), and the image of Triangle ABC is congruent to the original triangle.

A triangle is a closed, two-dimensional geometric figure with three straight sides and three angles. It is one of the basic shapes in geometry and can be classified based on the length of its sides or the size of its angles. A triangle with all sides of equal length is called an equilateral triangle, while a triangle with two sides of equal length is called an isosceles triangle. A triangle with no sides of equal length is called a scalene triangle. Triangles can also be classified based on the size of their angles, with an acute triangle having all angles less than 90 degrees, a right triangle having one angle equal to 90 degrees, and an obtuse triangle having one angle greater than 90 degrees.

Here,

To find the new coordinates of point C after the rotation and translation, we need to perform each transformation separately and then combine them.

Rotation:

To rotate a point 180° counterclockwise about the origin, we switch the sign of both coordinates. Therefore, the new coordinates of point C after the rotation are (-3, -2).

Translation:

To translate a point to the right 4 and up 4, we add 4 to the x-coordinate and 4 to the y-coordinate. Therefore, the new coordinates of point C after the translation are (1, 2).

To determine if the image of Triangle ABC is similar or congruent to the original triangle, we need to compare the corresponding sides and angles of both triangles.

Since we performed a rotation of 180°, all the angles in the image triangle are congruent to the corresponding angles in the original triangle. Additionally, since we performed a translation, the sides of the image triangle are congruent to the corresponding sides of the original triangle. Therefore, the image triangle is congruent to the original triangle.

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Answer: a = 3

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

this is for the 20 characters thing

Answer: Nonlinear; power of x is greater than 1 (Bottom right corner)

Explanation:

The equation y = x^2 - 1 is known as a quadratic since the largest exponent here is 2. This equation cannot be written in slope intercept form y = mx+b, so that's why it's not linear. You can also graph y = x^2-1 to get a curved parabola. The graph must be a straight line if you want a linear equation.

Answer:

  y = {-1/2x +7 for x < 6; 1/2x +1 for x ≥ 6}

Step-by-step explanation:

You want y = 1/2|x -6| +4 written as a piecewise function.

The absolute value function changes its definition when its argument is negative:

  y = |x|   ⇒   y = -x for x < 0, and y = x for x ≥ 0

This means our piecewise function will have one definition for (x-6) < 0 and another for (x -6) ≥ 0.

The argument is negated in this domain, so we have ...

  y = -1/2(x -6) +4

  y = -1/2x +3 +4

  y = -1/2x +7

The absolute value function is an identity function in this domain:

  y = 1/2(x -6) +4

  y = 1/2x -3 +4

  y = 1/2x +1

Combining these descriptions into one, we have ...

  \(\boxed{y=\begin{cases}-\dfrac{1}{2}x+7&\text{for }x < 6\\\\\dfrac{1}{2}x+1&\text{for }x\ge6\end{cases}}\)

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The per-unit reactance of the transformer is 0.0444 pu.

To calculate the per-unit reactance of the transformer, we need to use the following formula:

Xpu = X / (Vbas\(e^2\) / Sbase)

where X is the reactance in ohms, Vbase is the base voltage in volts, and Sbase is the base power in volt-amperes.

In this case, the rated power of the transformer is 5 kVA, and the rated voltage on the high side is 400V. Therefore, the base power and base voltage are:

Sbase = 5 kVA

Vbase = 400V

The reactance of the transformer referred to the low voltage side is given as 2Ω. To convert this to per-unit, we substitute the values in the formula:

Xpu = 2Ω / (300\(V^2\) / 5 kVA)

Xpu = 0.0444 pu

Therefore, the per-unit reactance of the transformer is 0.0444 pu.

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Chris' gross pay for the week after selling computer equipment worth $17,000 is $2,600.

The gross pay is the addition of the base pay and the sales commission.

The sales commission is graduated and computed as follows:

Chris' base pay = $300

Sales Commissions:

First $5,000 = 10%

Above $5,000 = 15%

Last week's sales = $17,000

10% Commission = $500 ($5,000 x 10%)

15% Commission = $1,800 ($17,000 - $5,000 x 15%)

Total Commission = $2,300

Gross pay = Base Pay + Commission

= $2,600 ($300 + $2,300)

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A 95% confidence interval that the true proportion of pennies more than 10 years old in the piggy bank is between 0.392 and 0.588.

What is confidence interval ?

A confidence interval is a statistical range that provides an estimate of the likely range of values for a population parameter (such as a mean, proportion, or standard deviation) based on a sample of data. It is calculated using a specific level of confidence, which represents the probability that the true population parameter falls within the calculated range.

Confidence intervals are typically expressed as a range of values with a margin of error or standard error. The margin of error represents the amount of random variation that is expected due to sampling error, while the standard error reflects the variability of the sample data.

According to the question:

To calculate the 95% confidence interval for the proportion of pennies that are more than 10 years old, we can use the formula:

\(CI = p \± z\sqrt{p(1-p)/n}\)

where:

CI is the confidence interval

p is the sample proportion (number of pennies more than 10 years old divided by the total number of pennies)

z is the critical value from the standard normal distribution for the desired level of confidence (in this case, 95%, which corresponds to a z-value of 1.96)

n is the sample size (100 pennies in this case)

Substituting the given values, we get:

p = 49/100 = 0.49

z = 1.96

n = 100

Plugging these values into the formula, we get:

\(CI = 0.49 \± 1.96\sqrt{0.49(1-0.49)/100}\)

Simplifying and solving for the upper and lower bounds of the confidence interval, we get:

CI = 0.49 ± 0.098

CI = (0.392, 0.588)

Therefore, we can say with 95% confidence that the true proportion of pennies more than 10 years old in the piggy bank is between 0.392 and 0.588.

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The given graph representing function is a relation.

For the given question,

For every singles value of 'x' there is value on y. Thus, no domain element is repeating for the graph.

Thus, the graph shows the relation of the function.

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Answer:

B-10.5 miles

Step-by-step explanation:

SANA PO MAKATULONG

PAKIFOLLOW PO

Answer:

0

Step-by-step explanation:

(2m)/(2m+3)-(2m)/(2m-3)=1

Simplifying the left hand first

(2m)/(2m+3)-(2m)/(2m-3) = {2m(2m-3) - 2m(2m+3)}/(4m²-9)

(4m²-6m-4m²-6m)/(4m²-9) = (-12m) / (4m²-9)

Now this equates to 1

(-12m) / (4m²-9) = 1

-12m =  4m²-9

4m²+ 12m -9 =0 ⇒⇒⇒ This is a quadratic equation that has 2 real solutions.

4m²+ 12m -9 =0

m² + 3m + (3/2)²= 9/4 + 9/4

(m + 3/2)² = 18/4

m = √18/2 - 3/2 or m = -√18/2 - 3/ = 0.621 = -3.621

So we can say that the equation has NO extraneous solutions.

Answer = 0

(I'm pretty sure it's correct)

Answer:

26 meters

Step-by-step explanation:

To solve the perimeter you need to know the formula which is 6 + 7 x 2 and you get 26 meters

The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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The probability of flipping heads, spinning an odd number, and then flipping tails is 1/8.

The probability of flipping heads, spinning an odd number, and then flipping tails is given by the product of the individual probabilities of each event.

The probability of flipping heads is 1/2,

the probability of spinning an odd number is 2/4 or 1/2, and

the probability of flipping tails is 1/2.

So, the probability of flipping heads, spinning an odd number, and then flipping tails is:

1/2 * 1/2 * 1/2 = 1/8

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The line segment XY is tangent to circle Z by using the Pythagorean theorem to find the radius of the circle, and the formula for the distance between a point and a line to find the distance between the center of the circle and the line.

Now let's look at the information given in the problem. We are given the length of line segment XY, which is 3.6 units. We are also given the lengths of two line segments that connect the endpoints of XY to the center of the circle Z: YZ, which is 1.8 units, and ZX, which is 2.7 units.

To determine if XY is tangent to circle Z, we need to check if it is possible for a circle with center Z and radius r to pass through points X and Y. If it is not possible, then XY must be tangent to the circle.

In this case, we can use the lengths of YZ and ZX as the legs of the right triangle, and r as the hypotenuse. We can set up the following equation:

r² = YZ² + ZX²

Substituting the given values, we get:

r² = 1.8² + 2.7²

r² = 7.29

r = √7.29

r ≈ 2.7

Now that we know the radius of circle Z, we can check if it is possible for it to pass through points X and Y. To do this, we need to find the distance between the center of the circle and the line XY. If this distance is equal to the radius of the circle, then XY is tangent to the circle.

To find the distance between the center of the circle and the line XY, we can use the formula for the distance between a point and a line. This formula is:

distance = |Ax + By + C| / √(A² + B²)

where A, B, and C are constants that depend on the equation of the line, and x and y are the coordinates of any point on the line.

In this case, we can use the equation of line XY, which is:

y = 0

Substituting this into the formula, we get:

distance = |A(0) + B(1) + C| / √(A² + B²)

distance = |B| / √(B²)

distance = 1 / √1

distance = 1

Since the distance between the center of circle Z and line XY is 1 unit, and the radius of circle Z is also 1 unit, we can conclude that XY is tangent to circle Z.

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Answer:

Question No 1

The range of rainfall for the highland storms is 44 mm

Question No 2

The range of rainfall for the lowland storms is 30 mm

Step-by-step explanation:

Question 1

What is the range of rainfall for the highland storms?

2 46 8 10 12 14 16 18 20 22 24 26 28 30 32

First we arrange data in ascending order.

2 8 10 12 14 16 18 20 22 24 26 28 30 32 46

Now we have to find range. The formula used is: \(Range=Maximum\:Value-Minimum\:Value\)

In the given data set:

Maximum Value = 46

Minimum Value = 2

Finding range by putting values in the formula:

\(Range=Maximum\:Value-Minimum\:Value\\Range=46-2\\Range=44\)

So, the range of rainfall for the highland storms is 44 mm

Question 2

What is the range of rainfall for the lowland storms?

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

First we arrange data in ascending order.

The data is already arranged in ascending order

Now we have to find range. The formula used is: \(Range=Maximum\:Value-Minimum\:Value\)

In the given data set:

Maximum Value = 32

Minimum Value = 2

Finding range by putting values in the formula:

\(Range=Maximum\:Value-Minimum\:Value\\Range=32-2\\Range=30\)

So, the range of rainfall for the lowland storms is 30 mm

Answer:

sorry im late

Step-by-step explanation:

the highland storms is 30 and the lowland is 26 right 2020edge

On solving the provided question, we can say that the probability of the red die rolling is 16.67% probability = 0.1667

A branch of mathematics called probability theory determines the chance that an event will occur or that a statement is true. A probability is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or likelihood that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain event relative to all possible outcomes.

red die, there are 3 numbers greater than 3 out of 6 numbers

Probability (A) = 3/6 = 1/2.

green die, there are 2 numbers less than 3 out of 6 numbers

Probability (B) = 2/6 = 1/3.

events are independent

P(A and B) = \(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667\)\(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667.\)

16.67% probability = 0.1667

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1)

Surface area of rectangular prism:

SA = 2( hw + lw + lh )

h= height of prism .

w = width of prism .

l = length of prism .

Substitute the values,

h= 4m

w=1.2 m

l= 13.4 m

SA = 2(4*1.2 + 13.4*1.2 + 13.4*4)

SA = 148.96 m²

2)

Surface area of triangular prism:

SA = (S1 +S2 + S3)L + bh

h= height of prism .

b = base of prism .

S1 , S2 , S3 = sides of triangle .

Substitute the values,

SA = (3+ 4 + 0.5)4 + 0.5*3

SA = 31.5 in²

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Answer:

599, 123.72 but am not really sure from that answer

Answer:

599,000

Hope this is also a correct answer...

Answer:

5. Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The required order from least to greatest is √3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

An arrangement of numbers in which the numbers are arranged from smallest to greatest numbers is called ascending order.

Given that, some numbers, 3√2, √3 − 1, √19 + 1, 6, 2√10 ÷ 5 and √14.

We need to order them from least to greatest,

3√2 = 4.24

√3 − 1 = 0.73

√19 + 1 = 5.35

6

2√10 ÷ 5 = 1.26

√14 = 3.74

The order from least to greatest is :-

0.73, 1.26, 3.74, 4.24, 5.35 and 6

i.e.

√3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

Hence, the required order from least to greatest is √3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6

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Answer:

Step-by-step explanation:

If f(x)=x²+4 then (fof⁻¹)(x)=(f⁻¹of)(x)=x is proved

A relation is a function if it has only One y-value for each x-value.

Composite functions are when the output of one function is used as the input of another.

If f(x)=x²+4

Then we have to prove f⁻¹of(x)=f⁻¹(f(x)

Let us consider fof⁻¹(x)

f(f⁻¹(x))

x

So (fof⁻¹(x))=x

Now f⁻¹of(x)=f⁻¹(f(x)

=x

Hence, If f(x)=x²+4 then (fof⁻¹)(x)=(f⁻¹of)(x)=x is proved

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Answer:

Step-by-step explanation:

y = 3x is an example of such an equation.

Answer:

D for Khan Academy. :p

Hope it helps :)

Step-by-step explanation: