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The graph of the function after transformation is attached below.

The connection between several systems is defined by coordinate transformations, which offer formulas for the coordinates in one system in terms of the coordinates in another system.

The graph of the transformed function is attached below. The red graph indicates the parent function f(x) = x² and the blue graph indicated the graph of transformation g(x) = x² - 2

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The proportion of slots who meet these specifications is 15.86%.

We are given that the width in inches of slots cut by a milling machine follows approximately the N(0.97,0.001) distribution.

Also, the specifications allow slot widths between 0.9698 and 0.9702

Let X = width in inches of slots cut by a milling machine

The z-score probability distribution for normal distribution is given by;

Z =  (X - μ) /σ  ~ N(0,1)

where, μ = population mean width = 0.97

           σ  = standard deviation = 0.001

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the specifications allow slot widths between 0.9698 and 0.9702 is given by = P(0.9698 < X < 0.9702)

=  P(0.9698 < X < 0.9702)  = P(X < 0.9702) - P(X  0.9698)

P(X < 0.9702) = P  [(X - μ) /σ < [tex]\frac{0.9702 - 0.97}{0.001}[/tex]] = P (Z < 0.2) =

P(X ≤0.9698) = P [(X - μ) /σ ≤  [tex]\frac{0.9698 - 0.97}{0.001}[/tex] ] = P (Z ≤ -0.2) = 1-  P(Z < 0.2)

                                                                                  = 1 - 5793 = 0.4207

So, in the z table the P(Z  x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.2 in the z table which has an area of 0.5793.

Therefore,  P(0.9698 < X < 0.9702) = 0.5793 - 0.4207 = 0.1586

Hence, the proportion of slots who meet these specifications is 15.86%.

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Answer:

(a - b)/(a + b).

Step-by-step explanation:

a²-ab-ac+bc / a² +ab-ac-bc

= a(a - b) - c(a - b) / a(a + b) - c(a + b)

= (a - c)(a - b) / (a - c)(a + b)

The (a - c) is common to top and bottom, so

= (a - b)/(a + b).

The solution of the equation 2.54-x+12= 21-42.5x+7 is x = 0.324

The equation is

2.54-x+12 = 21-42.5x+7

Rearrange the terms are do the suitable arithmetic operation in the equation

2.54-x+12= 21-42.5x+7

-x+12+2.54 = -42.5x+7+21

Add the like terms together

-x+14.54 = -42.5x+28

Here we have to rearrange the term and make the all the like terms in each sides

Move 14.54 to the right hand side and move -42.5x to the left hand side

Then the equation will become

-x+42.5x = 28-14.54

41.5x = 13.46

x = 13.46/41.5

x = 0.324

Hence, the solution of the equation 2.54-x+12= 21-42.5x+7 is x = 0.324

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Answer:

Communitive Property

Step-by-step explanation:

a * b = b * a

In your case,

(-a / b) * (-c / d) = (-c / d) * (-a / b)

brainly pls :)

Answer:

Answer:

Communitive Property

Step-by-step explanation:

a * b = b * a

In your case,

(-a / b) * (-c / d) = (-c / d) * (-a / b)

Step-by-step explanation:

Answer: No.

Step-by-step explanation:

3 x 5 = 15,

but 10 x 5 = 50.

In order for the ratios to be equivalent, they would have to be written like this:

3/10 = 15/50

Therefore, it is not equivalent.

Hope this helps!

The slope of the line is 2 , the correct option is (A).

Slope of the line is defined as the change in y coordinate with respect to the change in x coordinate of the line , the slope of the line is denoted by "m" .

The slope of the line passing through the two points (a,b) and (c,d) is given by m = (d-b)/(c-a) .

In the question ,

a line is given

let us name the points as M and N ,

the named graphed is shown below,

Assuming the cube in the graph be of 1 unit each.

So , the coordinates of M and N from the graph is

M = (1,1) and N= (-1,-3),

So the slope of the line passing through the points (1,1) and (-1,-3) is

slope = (-3-1)/(-1-1)

= -4/-2

= 2.

Therefore , the slope of the line is 2 , the correct option is (A).

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Answer:

- 3b + 21

Step-by-step explanation:

- 3(b - 7) ← multiply each term in the parenthesis by - 3

= - 3b + 21

Answer:

-3(b-7) = -3b + 21

If Stacy works alone, it will take her 11 hours 40 minutes to paint the doghouse.

If Diego works alone, it will take him 5 hours 40 minutes to paint the doghouse.

given data

Diego and Stacy can paint a doghouse in 5 hours

Diego works twice as fast as Stacy

Let x be the number of hours it would take Diego to paint the doghouse and y be the number

Putting the given information mathematically

Diego and Stacy can paint a doghouse in 5 hours

Diego works twice as fast as Stacy

x + y = 5hours

Since x = 2y

2y + y = 5

3y = 5

y = 5/3

y = 1 1/3

from x = 2y

x = 2 * 5/3

x = 10/3

x = 3 1/3

1/3 hours is a fraction of hours. we convert it to minutes by multiplying by 60

= 1/3 * 60

= 20 minutes

Therefore it will take Diego 3 hours 20 minutes and Stacy 1 hour 20 minutes for them to complete a 5 hours work

If Diego works alone

Diego alone = 5 hours + Stacy's hours * 1/2

since Diego is twice faster than Stacy then Stacy's time will be halved

Diego alone = 5 hours + 80 minutes * 1/2

Diego alone = 5 hours + 40 minutes

Diego alone = 5 hours 40 minutes

if Stacy works alone

Stacy alone =  5 hours + Diego's hours * 2

Stacy alone =  5 hours + 3 hours 20 minutes * 2

Stacy alone =  5 hours + 6 hours 40 minutes

Stacy alone = 11 hours 40 minutes

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Answer:6+2w=h

The height of the tree will be 32 inches on week 13

Step-by-step explanation:

ok

The side of the triangle is 15 inches.

The perimeter of an equilateral triangle is 17 inches more than the perimeter of a square, and the side of the triangle is 8 inches longer than the side of the square.

Hence,

let

perimeter of the square = x inches

perimeter of an equilateral triangle = x + 17

Let

side of the square = y

side of the triangle = 8 + y

Therefore,

Perimeter of the square

x = y + y + y + y

x = 4y

Perimeter of the triangle

x + 17 = 8 + y + 8 + y + 8 + y

x + 17 = 24 + 3y

x - 3y = 7

Combine the equation,

x = 4y

x - 3y = 7

Therefore,

4y - 3y = 7

y = 7

x = 4(7)

x = 28

Therefore,

side of the triangle = 8 + y = 8 + 7 = 15 inches

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The equation of an ellipse with center, (h, k) that is elongated in the x-direction is: (x - h)²/a² + (y - k)²/b² = 1.

In aspects of locus, an ellipse is the collection of every point on an XY-plane with whom the distance from 2 fixed points (called foci) adds up to the a constant value.

The standard form of equation of ellipse with centres (h, k) that is elongated in the x-direction is given as;

(x - h)²/a² + (y - k)²/b² = 1

Now, when the centre of the ellipse coincides with the origin of coordinates axis, the becomes;

x²/a² + y²/b² = 1

Thus, the equation of ellipse of obtained.

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Answer:

The new company’s train is C. 15.2 miles faster.

Step-by-step explanation:

Train A: 228/3 = 76 miles per hour

Train B: 228/2.5 = 91.2 miles per hour

91.2 - 76 = 15.2

Answer:

Step-by-step explanation:

the angle C is the opposite angle to that of 85 degrees, therefore congruent, we subtract 85 x 2 ° from the sum of the angles (360 °, is a round angle) and find the sum of the other two angles, always opposite and increasing, divide by two and we have the value of the angle B

C = 85°

B = [360 - (85 * 2)] : 2

B = (360 - 170) : 2

B = 190 : 2

B = 95°

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

check

85 + 85 + 95 + 95 = 360°

the answer is good

Answer:

A) 30 x ? = ? + 25 = ?.

B) 30 x 4 = 120.  120 + 25 = 145.

Answer: The answer is $145 to rent the skis for four hours.

Answer:

-52

Step-by-step explanation:

I hope this helps!

Answer: -52

Step-by-step explanation: Using PEMDAS

(2x3)+4-62

6+4-62

10-62

= -52

[tex]__________________________[/tex]

Refer to the attachment for the answer

Answer:

The constant of proportionality is $1.80

y = 1.80x

Step-by-step explanation:

The constant of proportionality is $1.80

An equation that relates the total cost, y, and the number of lemons, x, is

y = 1.80x

where,

y =Total cost

x = number of lemon

When x = 4

y = 1.80x

y = 1.80(4)

y = 7.2

y = $7.2

When y = $4.20

y = 1.80x

4.20 = 1.80x

x = 4.20 / 1.80

x = 2 1/3

x = 2 1/3

When y = $9.00

y = 1.80x

9.00 = 1.80x

x = 9.00 / 1.80

x = 5

x = 5

When x = 18

y = 1.80x

y = 1.80 × 18

y = 32.4

y = $32.4

The table of values indicates a proportional relationship between the number of gallons of gas and the number of miles driven, therefore;

A proportional relationship is one in which one variable, y, can be obtained from another variable, x, by multiplying x by a factor.

Please find attached a table showing the number of gallons of gas and the miles driven obtained from a similar question online

Let x represent the number of gallons of gas and let f(x) represent the number of miles driven

The difference between the consecutive terms of the first three values in the number of gallons and miles driven are each equal to 2 and 62 respectively

4 - 2 = 2 - 0 = 2

124 - 62 = 62 - 0 = 62

Therefore, given that the first difference is constant, the first three points have a linear relation, which gives;

Slope of the line = 62/2 = 31

Intercept = 0

Therefore;

f(x) = 31•x

Checking the fourth point, gives;

x = 10

f(10) = 31 × 10 = 310

The relationship between the miles driven, f(x), and the number of gallons is therefore a proportional relationship, which is presented as follows;

f(x) = 31•x

Therefore, if the number of gallons of gas, x, is known, the number of miles driven, f(x), can be found using the equation;

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Answer: a) $171          b) $729

Step-by-step explanation:

a) 0.19 * $900 = $171

b) net pay = the money one earns after all deductions

$900 (what she earned) - $171 (taxes she had to pay) = $729

Answer: A is not equivalent to the other 2

Step-by-step explanation:

A. 15j+30

B. 5(3j-6) = 15j-30

C 3(5j-10) = 15j-30

multiply the stuff inside paranthesis for the last 2

So a is the outsider

Answer : Transitive Property

If that's not correct, try Symmetric or substitution cause I know it's not reflexive

Answer:

- 8

Step-by-step explanation:

the coefficient is the numeric value, including the sign, in front of the variable.

4a - 8b + c

the coefficient of b is - 8

In my opinion, Report 1 is more persuasive than Report 2 due to the fact that the margin of error in Report 1 is narrower than in Report 2.

This is further explained below.

Generally,  we consider report one and report two

For Report

at 98% confidence interval = $64.35 to $83.59

Therefore, the Margin of error

M.E= $83.59 - $64.35

M.E = $19.24

For Report 2:

95% confidence interval = $58.37 to $71.93

Margin of error

M.E= $71.93 - $58.37

M.E= $13.56

Since Report 1 has a smaller margin of error than Report 2, I find Report 1 to be more convincing.

In conclusion, A report with a lower margin of error, in my opinion, is often more credible than one with a bigger one.

This is because more exact data indicates a report with a reduced margin of error.

To put it another way, information in a report with a lower margin of error is more likely to be correct than information in a report with a higher margin of error.

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Answer:

D) 116

Step-by-step explanation:

Supplementary angles add up to 180°

 ∠CDE + ∠FDE = 180

3x + 10 + 6x + 8 = 180

3x + 6x + 10 + 8 = 180

Combine like terms,

              9x + 18 = 180

Subtract 18 from both sides,

                    9x  = 180 - 18

                    9x = 162

Divide both sides by 9

                     x = 162 ÷ 9

                    [tex]\sf \boxed{\bf x = 18}[/tex]

∠FDE = 6x + 8

         = 6*18 + 8

         = 108 + 8

         = 116°

5N² is expressed as a product of prime factors in index form as  [tex]5^{5} * 3^{2} * x^{10}[/tex] .

In the expression of a number as the product of its prime factors, known as prime factor index form, each prime factor is only mentioned once, either as itself or, if necessary, to a required power.

Given:

N is a number that is expressed as a product of its prime factors in index form.

N = [tex]3x * 5x^{2} * x^{3}[/tex]

We have to express 5N² as a product of prime factors in index form.

5N² = 5([tex]3x * 5x^{2} * x^{3}[/tex])²

       = [tex]5 * 9x^{2} *5^{4} x^{2} *x^{6}[/tex]

       = [tex]5 * (5^{2}x)^{2}* (3x )^{2} *x^{6}[/tex]

( using exponential properties  [tex]a^{m} *a^{n} = a^{m+n} and (a^{m} )^{n} = a^{mn}[/tex])

    = [tex]5^{5} * 3^{2} * x^{10}[/tex]

The prime factors of 5N² are 5,3 and x respectively.

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Answer:

Shark 4

Step-by-step explanation:

It has the lowest value

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-4)}}} \implies \cfrac{-6}{8 +4}\implies {\Large \begin{array}{llll} -\cfrac{1}{2} \end{array}}[/tex]