1 = Consider the functions f(x) = – 6x – 7 and g(x) = - = (x+7). (a) Find f(g(x)). (b) Find g(f(x)) (c) Determine whether the functions f and g are inverses of each other. (a) What is f(g(x))? f(g

Answer:

The value of x=17.

Step-by-step explanation:

3(x-1) = 4(x-5)

=3x-3=4x-20

Subtract both sides by 4x.

=3x-3-4x=4x-20-4x

= −x−3=−20

Add 3 to both sides.

=−x−3+3=−20+3

−x=−17

Divide both sides by -1.

−x/-1=−17/-1

x=17

In a straight line, like the one presented before you, there is 180 degrees. So that means 115 degrees + x is gonna equal 180.

So that means, x is gonna be 180 - 115. So x is 65 degrees

The minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ = 13.8 is 1268

Given: To find the minimum sample size, confidence level = 99%, standard deviation = 13.8, and one unit population mean. [Normally distributed]

Solving the given question:

We know that the formula for Margin of error is:

Margin of error = z-score * (standard deviation) / root (sample size)

E = z * σ / √(n), where

E = Margin of error

z = z-score

n = Sample size

σ = standard deviation

Therefore, sample size = ( z – score * standard deviation / margin of error)²

n = ( z * σ / E )²

First, calculate the z-score for the 99% confidence level.

From the normal distribution curve, the area under 99% confidence level is given as:

Area under 99% confidence level = (1 + confidence level) / 2 = (1 + 0.99) / 2 = 0.995

From the z-score table, we find the value of z with the corresponding area of 0.995

We find the value of the z-score corresponding to 0.995 is 2.58

Also given sample mean is one unit of the population. So the margin of error is 1

E = 1

And given Standard deviation = 13.8

σ = 13.8

Putting the values in the given formula of sample size n =

n = (2.58 * 13.8 / 1 )²

n = 1267.64

n = 1268

Hence the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ = 13.8 is 1268

Know more about “normal distribution” here: https://brainly.com/question/15103234

#SPJ4

Disclaimer: Determine the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and G = 13.8. Assume the population is normally distributed. A 99% confidence level requires a sample size of (Round up to the nearest whole number as needed )

Based on the table and equation given:Gymnastics is less expensive when the classes is 1.Ice-skating is less expensive when the classes is 3 or 4.

For 1 class, substitute x = 1 into y = 18x + 20:

y = 18(1) + 20

y = $38

For 2 class, substitute x = 2 into y = 18x + 20:

y = 18(2) + 20

y = $56

For 3 class, substitute x = 3 into y = 18x + 20:

y = 18(3) + 20

y = $74

For 4 class, substitute x = 4 into the equation y = 18x + 20:

y = 18(4) + 20

y = $92

From the above, we can conclude that, Gymnastics is less expensive when the classes is 1.

Ice-skating is less expensive when the classes is 3 or 4.

To learn more equation refer

https://brainly.com/question/29711868

#SPJ1

Answer: See explanation

Step-by-step explanation:

Number of tickets Elian won = e

Number of tickets Alberto won = A = e - 10

Therefore, Elian + Alberto ticket = 100

e + (e - 10) = 100

2e - 10 = 100

2e = 100 + 10

2e = 110.

e = 110/2

e = 55

Elina has 55 tickets

Alberto has 55-10 = 45 tickets

The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

To learn more about Accelation , refer:

https://brainly.com/question/10307723

#SPJ4

Answer:

7 and 1/2 or 15/2 (they are the same number just one is 15/2 is put into fraction form)

Step-by-step explanation:

Because 3 hours is half of 6 hours so 15x1/2=7 1/2 or 15/2

Hope this helps, pls consider giving a brainliest, aand have a good day

Figure R'S'T'U' is the image of Figure RSTU after a translation of 2 units left and 2 units down, and a reflection across the y-axis.

Examples of transformations are given as follows:

The rule applied for the translation is given as follows:

(x,y) -> (x - 2, y - 2).

Hence:

The rule applied for the reflection is of:

(x, y) -> (-x, y).

Hence the figure was reflected over the y-axis.

More can be learned about transformations in a figure at https://brainly.com/question/28687396

#SPJ1

The equation represents the total cost of turkey and amount is y= 3.25x.

We have,

The turkey costs $3. 25 per pound.

let x be the amount in pounds and y be the total cost in dollar.

Then, the relation between x and y

Total cost = 3.25 (amount in  poind)

y = 3.25 x

Thus, the required equation is y= 3.25x.

Learn more about Equation here:

https://brainly.com/question/29657983

#SPJ1

a a car accelerates, then maintains its speed before speeding up again

Answer:

XZ = 2.5 BD

Step-by-step explanation:

Comparing the two triangles,

\(\frac{BD}{BC}\) = \(\frac{XZ}{XY}\)

\(\frac{6}{8}\) = \(\frac{XZ}{20}\)

⇒ XZ = \(\frac{20*6}{8}\)

         = 15

XZ = 15

So that,

BD:XZ = 6:15

           = 1:2.5

Therefore, the relationship between BD and XZ is XZ = 2.5 BD.

The domain restrictions of the expression q²−7q−8/q²+3q−4 are q ≠ -4 and q ≠ 1. (option c)

The denominator of the expression is q²+3q−4. To determine the values that would make the denominator equal to zero, we can set it equal to zero and solve for q:

q² + 3q - 4 = 0

Now, we can factorize the quadratic equation:

(q + 4)(q - 1) = 0

To find the values of q, we set each factor equal to zero and solve for q:

q + 4 = 0 or q - 1 = 0

Solving these equations, we get:

q = -4 or q = 1

So, the values of q that would make the denominator equal to zero are q = -4 and q = 1. These are the values we need to exclude from the domain of the expression to avoid division by zero.

Therefore, the correct answer is option c) q ≠ 1 and q ≠ -4.

To know more about domain here

https://brainly.com/question/28599653

#SPJ4

Complete Question:

What are the domain restrictions of q²−7q−8/q²+3q−4?

a) q≠1 and q≠−8

b) q≠−1 and q≠4

c) q≠1 and q≠−4

d) q≠−1 and q≠8

Answer:

<UOX and <YOZ

Step-by-step explanation:

Adjacent angles are angles that share a common side and vertex. So, find the angles that share one side. In this case, the two sides of the angle <XOY are OX and YO. Remember when naming an angle that it should be one side, the vertex, the last side. So, the 2 adjacent angles are <UOX and <YOZ because they each share one common side and vertex.

Answer:

it will look like this let me know if I'm right and GOOD LUCK!

Step-by-step explanation:

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

Read more on inequality:

https://brainly.com/question/25275758

#SPJ1

Step-by-step explanation:

because angle A and C are similar, so

9x-8=28

9x=36

x=4

Answer: B.

Step-by-step explanation:

D. C. B.

100%

Answer:

When you flip over the the x-axis, the y-coordinate becomes the additive inverse. I.e. ; if I flipped over the x-axis, a (x,4) would become (x,-4). When you flip over the y-axis the x becomes the additive inverse. (x,4) will become (-x,4)

Step-by-step explanation:

If this helped you, you're welcome. If you have any questions, LMK.

Have a good day, and good luck! ⭐

The probability of a Type II error is represented by beta. Thus, the correct answer is option B.

Beta represents the probability of failing to reject the null hypothesis when it is false.

On the other hand, Type I error (alpha) represents the probability of rejecting the null hypothesis when it is true. A Type II error occurs when a false null hypothesis is not rejected. Hence, beta is the probability of making a Type II error.

The null hypothesis is rejected when the p-value is less than or equal to the level of significance, not exceeds it.

The p-value is the probability of obtaining a result as extreme as or more extreme than the observed result when the null hypothesis is true. If the p-value is less than the level of significance, the null hypothesis is rejected, and vice versa.

Hence, the statement "The null hypothesis is rejected when the p-value exceeds the level of significance" is false.

To know more about probability visit

https://brainly.com/question/13604758

#SPJ11

As a result of this definition, vertices are intersection of two lines that create an angle as well as the corners of polygons and polyhedra.\(f(x)=x^2-2x-10\)  general form to vertex form is y=[\((x-1)^{2}\)-9]

The intersection of two or more curves, lines, or edges is known as a vertex in geometry (plural: vertices or vertexes), which is frequently represented by the letters S, P, Q, or R. As a result of this definition, vertices are intersection of two lines that create an angle as well as the corners of polygons and polyhedra.

The point where two rays start or meet, where two line segments join or meet, where two lines intersect (cross), or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location is the vertex of an angle.

\(f(x)=x^2-2x-10\)

      = [\((x-1)^{2}\)-9]

Use the form, \(ax^{2} + bx+c\)

a=1

b=2

c=-10

Consider a vertex form of parabola,

\(a(x+d)^{2} + e\)

find the value of d, using the formula d=\(\frac{b}{2a}\)

d=\(\frac{2}{2*(-1)}\)

simplify the right side,

d= -1

find the value of e, using e= \(c-\frac{b^{2} }{4a}\)

e= \(-10\frac{2^{2} }{4*(-1)}\)

simplify the right side,

e= -9

substitute the value of a, d and e into vertex form.

y=  [\((x-1)^{2}\)-9]

To know more about vertex visit: https://brainly.com/question/12563262

#SPJ9

Answer:

Cubes in each layer: 6

Number Of Layers: 5

Volume: 30

Refer to the attachment for figure:

The height of the rectangle = 11 inches

What is rectangle?

A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Let x= height

Width becomes x+49

Diagonal BD=61 inches

By pythagoras theorem,

BD²=BC²+CD²

61²= (x+49)²+x²

3721=x²+98x+2401+x²

On simplification,

x²+49x-660=0

Find the factors

(x+60)(x-11)=0

x=-60, x=11

Consider positive value for height

height = 11 inches

To learn more about the rectangle from the given link

https://brainly.com/question/25292087

#SPJ4

Answer:

100

Step-by-step explanation:

it is 50 when he sees it in a horizontal line so double it to see how much it is if it where straight

Answer:

\(x\approx2.3153\)

Step-by-step explanation:

\(7e^{3x-5}=49\)

\(e^{3x-5}=7\)

\(3x-5=ln(7)\)

\(3x=ln(7)+5\)

\(x=\frac{ln(7)+5}{3}\)

\(x=2.315303383\)

\(x\approx2.3153\)

Answer:

D HOPE THIS HELPS YOU!!

ANSWER IS D

Step-by-step explanation:

Based on the given side lengths of 8, 11, and 12, none of them are equal. Therefore, we can classify the triangle as a Scalene Triangle.

To classify a triangle by its angles and sides, we can use the properties and definitions of different types of triangles. Let's analyze the given triangle with sides measuring 8, 11, and 12 and angles measuring 45 degrees, 65 degrees, and 70 degrees.

Classification by angles:

Acute Triangle: An acute triangle has all three angles less than 90 degrees.

Obtuse Triangle: An obtuse triangle has one angle greater than 90 degrees.

Right Triangle: A right triangle has one angle exactly 90 degrees.

Based on the given angles of 45 degrees, 65 degrees, and 70 degrees, none of them are greater than 90 degrees, so we can classify the triangle as an Acute Triangle.

Classification by sides:

Equilateral Triangle: An equilateral triangle has all three sides of equal length.

Isosceles Triangle: An isosceles triangle has two sides of equal length.

Scalene Triangle: A scalene triangle has all three sides of different lengths.

Based on the given side lengths of 8, 11, and 12, none of them are equal. Therefore, we can classify the triangle as a Scalene Triangle.

In summary, based on the given measurements, the triangle can be classified as an Acute Scalene Triangle. We determined this by comparing the angles to the definitions of acute, obtuse, and right triangles, and comparing the side lengths to the definitions of equilateral, isosceles, and scalene triangles.

for such more question on Scalene Triangle

https://brainly.com/question/1621576

#SPJ11

Answer:

79.2 km/hour

Step-by-step explanation:

1 m/sec= 3.6 km/hour 22m/sec= ? so just multiply 22 m/sec by 3.6 km/hour then the answer will be :- 79.2 km/hour