The function y = x2 + 3 is a transformation of the function y = x2. How is the y-intercept of the function affected by the transformation?

The y-intercept of the graph of y = x2 is shifted down 3 units.
The y-intercept of the graph of y = x2 is shifted to the left 3 units.
The y-intercept of the graph of y = x2 is shifted to the right 3 units.
The y-intercept of the graph of y = x2 is shifted up 3 units.
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Answer on Edmentum is:

The y-intercept of the graph of y = x2 is shifted up 3 units.

Explanation:
The graph of a function in the form y = f(x) + k is the graph of f shifted up k units. The graph of y = x2 + 3 is the graph of y = x2 shifted 3 units up, so the y-intercept of the graph of y = x2 is shifted up 3 units.

Answers

Answer 1

The y-intercept of the graph of y = x2 is shifted up 3 units.

Exponential equation

The standard exponential equation is expressed as y = ab^x. Exponential equation is inverse of logarithmic equation.

Translation of coordinates

Translations is a transformation technique that changes the position of an object from one point on the plane to another.

Given the parent function f(x) = x^2

If the function is shifted 3 units up, the function g(x) is derived by adding 3 to the function f(x). The resulting function is given as;

g(x) = f(x) + 3

g(x) = x^2 + 3

Hence the equation of the new graph g(x) is expressed as g(x) = x^2 + 3

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Related Questions


After descending 8.25 feet, a bird is now
at a height of 16.5 feet. What was the initial
height of the bird?

Answers

24.75 feet was the initial height of the bird. We can use definitions and corresponding addition here:

The word descending is denoted as something or someone that moves or slopes downward. Our equation will look like so, with x representing the initial height of the bird:

x - 8.25 = 16.5 (or in other words, 16.50)

Now that we have our equation set up, we can use inverse operations to solve.

16.50 + 8.25 = 24.75

Since doing addition gave us a total of 24.75, we know that the initial height of the bird is 24.75 feet. To check our work, we can plug this number in for x:

24.75 - 8.25 = 16.50

When calculating, this equation is true. Therefore, the initial height of the bird is 24.75 feet. If you need extra help, do not hesitate to let me know and I will gladly assist you.


2.) A shop sells oranges at 6 for N100. A trader sells the same kind of oranges at 8 for N120.
Which price is cheaper, by how much per orange?

Answers

The cheaper price among this set of orange sales is the one done by trader B, who sells 8 for N120.

How is the cheaper price determined?

The cheaper price can be computed by finding out the price per unit.

Data and Calculations:

                               Price of Set     Unit Price

Sale of 6 oranges        N100           N16.67 (N100/6)

Sale of 8 oranges        N120           N15.00 (N120/8)

Thus, selling 8 oranges for N120 is cheaper than selling 6 oranges for N100, and N1.67.

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X is 30% of Y and Y is 45% of 600. What is the value of X?

Answers

Answer:

X = 81

Step-by-step explanation:

600 × 0.45 = 270

270 × 0.3 = 81

X = 81

The dialogue of a square is X units what is the area of the square in terms of X

Answers

The area of the square in terms of x unit is x²/ 2

Diagonal of a square

The expression for the diagonal of a square is written as'

d^2=s^2+s^2

Where

s² is the area of the squared² is the diagonal of the same square

But from the given question we have that the diagonal of the said square is 'x'

Now, let's substitute the values into the expression of the diagonal given above,

d^2=s^2+s^2

d² = s² + s²

We have,

x² = s² + s²

Collect and add like terms

x² = 2s²

But we know that s² represents the area of the square

So,

x² = 2 × area

Make 'area' subject of formula

Area = x²/ 2

Now, we can say that the area of the square in terms of x units is x²/2

Therefore, the area of the square in terms of x unit is x²/ 2

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kerri said that the quotient of 4.2/5 is about 8 tenths because 4.2/5 is close to 40 tenths /5 do you agree with Kerris reasoning?

Answers

Kerris reasoning that 4.2/5 is about 8 tenths because 4.2/5 is close to 40 tenths/5 is correct

How to interpret Kerris reasoning?

The quotient is given as:

4.2/5

Kerris reasoning is that

4.2/5 is approximately 0.8

We start by calculating the actual value of the quotient 4.2/5

Using a calculator, we have:

4.2/5 = 0.84

Approximate to the nearest tenth

4.2/5 = 0.8

This means that Kerris reasoning that 4.2/5 is about 8 tenths because 4.2/5 is close to 40 tenths/5 is correct

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the sum of three numbers is 3068.Two of the numbers are 1266 and 1755,find the third number

Answers

Answer:

47

Step-by-step explanation:

3068 - 1266 - 1755 = 47

Answer:

The third number is 47.

Step-by-step explanation:

The sum of three numbers is 3068 - this can be expressed mathematically as:

[tex]\displaystyle{x + y + z = 3068}[/tex]

Given that two of the numbers are 1266 and 1755 (in order) then substitute x = 1266 and y = 1755:

[tex]\displaystyle{1266 + 1755 + z = 3068}[/tex]

Find the third number - solve for z-variable:

[tex]\displaystyle{3021 + z = 3068}\\\\\displaystyle{z = 3068-3021}\\\\\displaystyle{z = 47}[/tex]

Therefore, the third number is 47.

Which of the LCM (40,120,150)?​

Answers

Answer:

2400

Step-by-step explanation:

40 = 2^3 * 5

120 = 2^5 * 5

150 = 2 * 3 * 5^2

LCM = 2^5 * 3 * 5^2

Solve for x

A. 4
B. 7
C. 1
D. 9

Answers

The value of x when the secants intersect is 4

How to find side when two secant intersect?

A secant of a circle is a line that connects two distinct points on a curve.

The secant touches two sides of the circumference of a circle.

Therefore, using secant rule,

4(x + 2 + 4) = 5(x - 1 + 5)

Hence,

4(x + 6) = 5(x + 4)

Hence, open the brackets

4x + 24 = 5x + 20

Therefore, subtract 4x from both sides

4x - 4x + 24 = 5x - 4x + 20

24 = x + 20

subtract 20 from both sides

24 - 20 = x + 20 - 20

x = 4

Therefore, the value of x is 4.

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The function f(x) is shown in the graph
f(a)
Which type of function describes ((x)?
© Exponential
O Logarithmic
O Rational
O Polynomial

Answers

Answer:

the function is an exponential funtion.

Step-by-step explanation:

learned it

A farmer finds there is a linear relationship between the number of bean stalks, n , she plants and the yield, y , each plant produces. When she plants 30 stalks, each plant yields 25 oz of beans. When she plants 32 stalks, each plant produces 24 oz of beans. Find a linear relationship in the form y=mn+b that gives the yield when n stalks are planted.

Answers

Answer:

  y = -1/2n +40

Step-by-step explanation:

We are given two ordered pairs (stalks, ounces) and asked for the slope-intercept form equation of the line through them.

Slope

The slope of the desired line can be found from the formula ...

  m = (y2 -y1)/(x2 -x1)

For the given points (30, 25) and (32, 24), the slope is ...

  m = (24 -25)/(32 -30) = -1/2

Y-intercept

The y-intercept of the desired line can be found from the formula ...

  b = y -mn

  b = 25 -(-1/2)(30) = 25 +15 = 40

Slope-intercept equation

The slope-intercept equation of a line is ...

  y = mn +b . . . . . line with slope m and y-intercept b

  y = -1/2n +40 . . . . . . line with slope -1/2 and y-intercept 40

The linear relationship between stalks (n) and yield (y) is ...

  y = -1/2n +40

How many workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days?

Answers

Considering the simple inverse rule of three, 12 workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days.

Inversely proportional relationship

Two variables are related when a change in one of them causes a change in the other.

Two variables have an inversely proportional relationship when an increase in one variable causes the other to decrease or, analogously, a decrease in one causes the other to increase.

In other words, two magnitudes are inversely proportional when as one increases, the other decreases in the same proportion, and as the first decreases, the second increases in the same proportion.

Simple inverse rule of three

The simple inverse rule of three is used when the problem deals with two inversely proportional magnitudes where the amount of one of a magnitude corresponding to a given amount of the other magnitude must be calculated.

To carry out an inverse rule of three, it must be taken into account that if for a value A of one magnitude, there is a value B of the other magnitude, while for a value of C of the first magnitude, the second magnitude is will correspond a value of X:

A → B

C → X

So: [tex]X=\frac{AxB}{C}[/tex]

Amount of workers needed

The number of people who perform a task is inversely proportional to the time it takes: a greater number of workers corresponds to less time to perform the task. Then:

9 days → 8 workers

6 days → amount of workers

So:[tex]amount of workers=\frac{9 daysx8 workers}{6 days}[/tex]

amount of workers= 12 workers

Finally, 12 workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days.

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Write a polynomial that has a GCF of 7m and another with a GCF of 2ab squared.

Answers

The polynomial that has a GCF of 7m is 14mn - 21m + 49m²n + 7mn²

The polynomial that has a GCF of 2ab² is 6a²b² - 8ab³ + 4a³b² + 2a³b³

Writing Polynomials

From the question, we are to write a polynomial that has a GCF of 7m

That is,

We are to write a polynomial that has a greatest common factor of 7m

Writing the polynomial

14mn - 21m + 49m²n + 7mn²

The  polynomial above has a greatest common factor of 7m. That is, 7m is the greatest factor that can divide each of the terms

We are to write a polynomial with a GCF of 2ab²

Writing the polynomial

6a²b² - 8ab³ + 4a³b² + 2a³b³

The polynomial above has a greatest common factor of 2ab². That is, 2ab² is the greatest factor that can divide each of the terms

Hence,

The polynomial that has a GCF of 7m is 14mn - 21m + 49m²n + 7mn²

The polynomial that has a GCF of 2ab² is 6a²b² - 8ab³ + 4a³b² + 2a³b³

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A. What are the coordinates of R’ if R (-2, 7) is dilated around the origin with k=3?
B. What are the coordinates of T’ if T (4,-1) is dilated by a scale factor of ½ with R as the center of the dilation?

Answers

A: The coordinates of the point R' are (- 6, 21).

B: The coordinates of the point T' are (1, 3).

How to generate new points by definition of dilation

In this question we must make use of rigid transformations to find the location of new points, rigid transformations are transformations used in geometric loci such that Euclidean distance is conserved. In this case, we need to use a kind of rigid transformation known as dilation, which is defined below:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]      (1)

Where:

O(x, y) - Center of dilationk - Dilation factorP(x, y) - Original pointP'(x, y) - Resulting point

Part A - If we know that O(x, y) = (0, 0), R(x, y) = (- 2, 7) and k = 3, then the coordinates of point R' are:

R'(x, y) = (0, 0) + 3 · [(- 2, 7) - (0, 0)]

R'(x, y) = (- 6, 21)

Part B - If we know that O(x, y) = (- 2, 7), T(x, y) = (4, - 1) and k = 1/2, then the coordinates of point T' are:

T'(x, y) = (- 2, 7) + (1 / 2) · [(4, - 1) - (- 2, 7)]

T'(x, y) = (- 2, 7) + (1 / 2) · (6, - 8)

T'(x, y) = (- 2, 7) + (3, - 4)

T'(x, y) = (1, 3)

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4. Find the value of x & y from the following equation 4x+5y=90, x+y=20 a. 10, 15 b. 10, 5 c. 10, 8 d. 10, 10​

Answers

Answer:

d. 10, 10

Step-by-step explanation:

4(10)+5(10) = 40 + 50 = 90

10 + 10 = 20

Hope this helps

An equation is formed of two equal expressions. In the two of the given equations, the value of x and y are 10 and 10, respectively. The correct option is D.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the two of the equation, which can be named as,

4x+5y=90   ...... equation 1

x+y=20   ............ equation 2

Solve the second equation for x,

x + y = 20

x = 20 - y ................ equation 3

In the first equation substitute the value of x from the third equation,

4x + 5y = 90

4(20 - y) + 5y = 90

Solving the equation for y,

80 - 4y + 5y = 90

y = 90 - 80

y = 10

Substitute the value of y in the second equation, to get the value of x,

x + y = 20

x + 10 = 20

x = 20 - 10

x = 10

Hence, In the two of the given equations, the value of x and y are 10 and 10, respectively.

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A car traveled at an average speed of 80 km/h for 5 hours. What was
the distance traveled?

Answers

Answer:

400 km

Step-by-step explanation:

Distance = rate times time

Distance = 80(5)

Distance = 400

What is the equation of the circle that has its center at -26,120 and passed through the origin

Answers

well, first off let's check those two points, we know it's centerd at (-26 , 120) and we also know it passes through (0 , 0), so the distance between those two points is its radius

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{-26}~,~\stackrel{y_2}{120})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{(~~-26 - 0~~)^2 + (~~120 - 0~~)^2} \implies r=\sqrt{(-26)^2 + (120 )^2} \\\\\\ r=\sqrt{( -26 )^2 + ( 120 )^2} \implies r=\sqrt{ 676 + 14400 } \implies r=\sqrt{ 15076 } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-26}{h}~~,~~\underset{120}{k})}\qquad \stackrel{radius}{\underset{\sqrt{15076}}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-26) ~~ )^2 ~~ + ~~ ( ~~ y-120 ~~ )^2~~ = ~~(\sqrt{15076})^2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (x+26)^2+(y-120)^2 = 15076~\hfill[/tex]

Pls need help 100 points and crown if right!!!
Marlene only has enough ingredients to make a 1/3

batch of cookies. For the smaller batch, she only needs 3/4

cup of sugar. How much sugar does the recipe for a full batch of cookies call for? Include all your work in your answer.

Answers

Answer:

[tex]\sf 2\dfrac{1}{4}\ cups \ of \ sugar[/tex]

Explanation:

Let the full batch be x

Here given:

3/4 cup of sugar required to make 1/3 batch of cookies

Build equation:

[tex]\sf \rightarrow \dfrac{1}{3}x = \dfrac{3}{4} \ cup \ of \ sugar[/tex]

Solve:

[tex]\sf \rightarrow x = \dfrac{3(3)}{1(4)}[/tex]

[tex]\sf \rightarrow x = \dfrac{9}{4}[/tex]

[tex]\rightarrow \sf x = 2\dfrac{1}{4}[/tex]

Answer:

2 2\3 cups of sugar.

Step-by-step explanation:

Donna has a $300 loan through the bank she is charged a simple rate The total interest she paid on the loan was $63 As a percentage what was the annual interest rate on her loan

Answers

The annual interest rate is 21%

How to determine the annual interest rate?

The given parameters are

Loan Amount, P = $300

Interest, I = $63

Number of years, T = 1

The annual interest rate is calculated as

I = PRT

Substitute the known values in the above equation

63 = 300 * R * 1

Evaluate the product

300R = 63

Divide through by 300

R = 21%

Hence, the annual interest rate is 21%

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cual es el valor x-3=11

Answers

x=14 espero qué esto ayude!

25(0.3x-4)-5(1.5x-6)+100·13/4

Answers

Answer:

255 (assuming x is the variable x)

340 (assuming x is the multiplication sign)

See explanation below.

Step-by-step explanation:

I assume that x is the variable x.

25(0.3x-4)-5(1.5x-6)+100·13/4 =

= 7.5x - 100 - 7.5x + 30 + 25 × 13

= -70 + 325

= 255

If my assumption above is incorrect, and x really means the multiplication sign, then we have this:

25(0.3×-4)-5(1.5×-6)+100·13/4 =

= 25(-1.2) - 5(-9) + 100(3.25)

= -30 + 45 + 325

= 340

find the domain of the function expressed by the formula:
y=1/x-7

Answers

The domain of the function is x  ≠ 7

How to determine the domain?

The function is given as:

y = 1/x - 7

Set the denominator not equal to 0

x - 7 ≠ 0

Add 7 to both sides

x  ≠ 7

Hence, the domain of the function is x  ≠ 7

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if im taking a 32 hour course and ive completed 73% of it how much time do i have left

Answers

Answer:

8.64 hours, so

8 hours, 38 mins, 24 seconds

Just find that 27% you have left, then find how much that 27% is in terms of time.

It might be wrong so double check it please.

Answer:

8.64 hours

which is 8hrs 38mins and 24secs

Step-by-step explanation:

If you've completed 73% then you have 27% left to go still. (100-73 = 27)

27% of 32

= .27×32

= 8.64 hours left

That is 8hrs and .64 of an hour .64×60=38.4 mins

which is 38 mins and .4 of a minute.

.4×60 = 24secs

Probably you will just round this answer.

Please help, need for math hw and cant figure it out

Answers

The standard form of the quadratic function f(x) = -3x^2 + 6x - 2 is f(x) = -3x^2 + 6x - 2

How to represent the quadratic function in standard form?

The quadratic function is given as

f(x) = -3x^2 + 6x - 2

The standard form of a quadratic function is represented as:

f(x) = ax^2 + bx + c

When both equations are compared, we can see that the function f(x) = -3x^2 + 6x - 2 is already in standard form

Where

a = -3

b = 6

c = -2

Hence, the standard form of the quadratic function f(x) = -3x^2 + 6x - 2 is f(x) = -3x^2 + 6x - 2

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i need help pls.............

Answers

Answer:

P = 6750n +7800rn ≤ 19r ≤ 31160n +620r ≤ 8110n = 19r = 8190,650 people

Step-by-step explanation:

This linear programming problem is described by an objective function and constraints on the variables. A graphical solution works well.

Objective function

The goal is to maximize the number of people exposed to the company's ad(s). The number of people reached is the sum of the products of the number of ads and the number reached per ad.

For n newspaper ads, we are told that 6750n people are reached.

For r radio ads, we are told that 7800r people are reached.

The total number of people reached is ...

  P = 6750n +7800r . . . . . . . the function we wish to maximize

Newspaper ads

We can run at most 19 newpaper ads:

  n ≤ 19

Radio ads

We can run at most 31 radio ads:

  r ≤ 31

Budget

The cost of n newspaper ads will be $160n.

The cost of r radio ads will be $620r.

We must stay within a budget for the ads, $8100:

  160n +620r ≤ 8110

Solution

The white area in the first quadrant of the attached graph represents the feasible solution space. (We reversed the inequality symbol in each inequality so the solution space would be white, not triple-shaded.) The corners of the solution space represent possible (n, r) pairs where the objective function might be maximized.

The solid red line on the graph shows the maximum value the objective function might have, and the (n, r) pairs that would give that maximum value. The value of the objective function increases the farther the line is from the origin. Drawing the line on the graph lets us readily identify the (n, r) coordinate pair that will place this line as far as possible from the origin, maximizing P. We find that to be (n, r) = (19, 8).

the number of newspaper ads to run is 19the number of radio ads to run is 8the group exposure is (6750)(19) +(7800)(8) = 190,650

Which of the following represents a quadratic function?
a. y = 3x - 2
b. y=6+5x + x²
c. x³10x = 21
d. y= 2² +4

Answers

Answer:

○ [tex]y = 6 + 5x + x^2[/tex]

Explanation:

What is a quadratic equation?

A quadratic equation is an algebraic equation where the highest power of [tex]x[/tex] is 2. The general form of a quadratic equation is as follows:

[tex]\boxed{ax^2 + bx + c = 0}[/tex],

where a, b, and c represent known constants, and [tex]x[/tex] is the unknown.

In this question, if you take a look at the second option, you will see that it is possible to rearrange the equation to make it look the general form:

[tex]y = 6 + 5x + x^2[/tex]

⇒ [tex]y = x^2 + 5x + 6[/tex]

Therefore, this equation is quadratic.

The other three options are not quadratic equations because none of them have an [tex]x^2[/tex]  term in them.

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

[tex]\leadsto[/tex] A quadratic equation is an algebraic equation of the second degree. The formula is:

[tex]\longrightarrow \sf{y = ax^2 + bx + c}[/tex]

This can also be written as:

[tex]\longrightarrow \sf{y = c + bx+ax^2}[/tex]

Comparing the equation above with each of the options, the equation that represents a quadratic function is:

[tex]\longrightarrow \sf{y=6+5 + x^2}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

◉ [tex] \large\bm{b. \: y=6+5x + x^2}[/tex]

832 x156 show your work​

Answers

Answer:

129792

Step-by-step explanation:

         156

     ×  832

    ----------

         312

      468

+  1248

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

  129792

At the beach, Nardia collected triple the number of seashells that Pierre did. Together, they collected 52 seashells. Which equations represents p, the number of seashells that Pierre collected.
3 p + p = 52
3 + p = 52
52 + p = 3 p
52 + p = 3

Answers

Answer:

A

Step-by-step explanation:

p = Pierre shells

Nardia shells = 3p

3p + p = 52

Answer:

a

Step-by-step explanation:

y+6=5(x-4)
wtirte the formula for f(x) in terms of x

Answers

The formula for f(x) in y + 6 = 5(x - 4) in terms of x is f(x) = 5(x - 4)- 6

What is a linear equation?

A linear equation is a equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

How to rewrite the formula?

A system of linear equations is a collection of at least two linear equations.

In this case, the linear function in the question is given as:

y + 6 = 5(x - 4)

Subtract 6 from both sides of the equation

y + 6 - 6 = 5(x - 4) - 6

Evaluate the difference in the above equation

y = 5(x - 4) - 6

Express the above equation as a function f(x)  i.e. we express y as a function of x

f(x) = 5(x - 4) - 6

Hence, the formula for f(x) in y + 6 = 5(x - 4) in terms of x is f(x) = 5(x - 4) - 6

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Twelve different video games showing drugs were observed. The duration times of drugs were​ recorded, with the times​ (seconds) listed below. Assume that these sample data are used with a 0.01 significance level in a test of the claim that the population mean is greater than 75 sec. If we want to construct a confidence interval to be used for testing that​ claim, what confidence level should be used for a confidence​ interval? If the confidence interval is found to be -34.1 sec < μ < 238.3 ​sec, what should we conclude about the​ claim?

88 15 537 53 0 52 197 40 182 0 2 59

1.) The confidence level should be _____%
2.) What should we conclude about the claim?
The given confidence interval __(contains / does not contain)___ the value of 75 sec, so there ___( is / is not )___ sufficient evidence to support the claim that the mean is greater than 75 sec.

_____________________________________________

NOTE: Please explain like I'm five. I'm not understanding why the confidence level should be anything but 90% and I don't know *why* we would conclude what we would conclude about this claim.

Answers

The answers to the questions are:

1. The confidence level is 99 percent.

2. We have to conclude that there is no sufficient evidence available to support this claim because the Confidence interval contains 75 sec.

How to solve for the confidence level

1. The confidence level here should be

1- 0.01 = 0.99

= 99 percent

Given that, 99% confidence interval for population mean (μ) is (-34.1 sec u< u < 264.1 ) seconds.

We are to test  the claim that the population mean is greater than 75 sec.

2.

The given confidence interval contains the value of 75 sec, so there is not sufficient evidence to support the claim that the mean is greater than 75 sec.

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Find the value of x.

Answers

Answer:

x = 106 degrees

Step-by-step explanation:

x + 104 + 40 + 110 = 360

x + 254 (No more 254)

- 254 (Again no more 254)

x = 106

Answer is 106

Step by step.

Using supplementary angle theory I was able to find three of the interior angles. The 4th interior angle was found by subtracting the three known angles from 360, finding the 4th angle is 74.

So again we use supplementary angle to find the value of x.
180 - 74 = 106
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