the graph of g(x) is the graph of f (x)=x+9 reflected across the y axis.

which equation describes the function g?

1. g(x)=x-9
2. g(x)=-x-9
3. g(x)=-9x+9
4. g(x)=-x+9

Answers

Answer 1

Answer:

4. g(x)=-x+9

Step-by-step explanation:

The correct answer is actually g(x)=-x+9. Just took the text. XD

Answer 2

Answer-

[tex]g(x)=-x+9[/tex]

Solution-

The given function is,

[tex]f(x)=x+9[/tex]

Given that g(x) is the reflection of f(x) over y-axis.

The reflection of the point (x, y) across  the y-axis is the point (-x,y).

So, in case of reflection over y-axis the sign of only x-coordinate is changed and y-coordinate remains same.

So changing the sign of x in f(x) will yield its reflection over y-axis i.e g(x)

Therefore, g(x) is,

[tex]g(x)=-x+9[/tex]

The Graph Of G(x) Is The Graph Of F (x)=x+9 Reflected Across The Y Axis. Which Equation Describes The

Related Questions

Does anybody know a rule that will work for all of these?

Answers

y = something x plus or minus a number

going through each line it isn't a linear pattern ( they don't all have the same difference when subtracted or added together)

so now you play around with quadratic equations ( square roots, powers, etc.)


 and you will see that y = x^2 -5

PLEASE HELP ASAP!!/BRAINLIEST/5 STARS/HEART(THX)!

Jimmy is going to pack his backpack for a trip. His backpack is 60 cubic litres. He has a pile of equipment that takes up 43 cubic litres and then he has his sleeping bag that takes up 23 cubic litres. Let r be the amount of room left in his backpack. Which equation could you use to determine if he has enough room in his backpack.

A) r = 23 + 43
B) r = 23 + 43 + 60
C) 23 + 43 + r = 60
D) 23 + r = 60 + 43

Answers

To start, we know these facts:

His backpack is 60 cubic L
His equipment is 43 cubic L
His sleeping back is 23 cubic L
R = amount of room left.

The best formula to use is
C) 23 + 43 + R = 60

This is because we want to be able to solve for R in order to find how how much space he has left.

23 + 43 + R = 60
66+ R = 60
66-66 + R = 60-66
R = -6
He is over his amount by 6.

ANSWER:
C) 23 + 43 + R = 60

The equation for the given situation is 23 + 43 + r = 60. Therefore, option C is the correct answer.

Given that, Jimmy backpack is 60 cubic liters. He has a pile of equipment that takes up 43 cubic liters and then he has his sleeping bag that takes up 23 cubic liters.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let r be the amount of room left in his backpack.

Total space in backpack = A pile of equipment +  Sleeping bag + Room left

So, 60 = 43+23+r

The equation for the given situation is 23 + 43 + r = 60. Therefore, option C is the correct answer.

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Two consecutive numbers whose square differ by 25

Answers

Represent these numbers with x and y.  Their squares are x^2 and y^2, respectively.  The larger square is 25 more than the smaller square:

y^2 = x^2 + 25, assuming that y>x.  If x and y are consecutive, y exceeds x by 1:     x+1=y.

Square x+1 = y, obtaining x^2+2x+1.  Substitute your result (that is, your expression for y^2 in terms of x into the other equation:        
 
 x^2+2x+1 = x^2+25.  Then 2x+1=25; 2x=24; x=12, and y=13.

Check:  Is 13^2  25 units greater than 12^2?  Is 169 25 units greater than 144?  Yes.   So, the two consec. integers are 12 and 13.

x+4, -x+64. Use the expressions that represent the length and width of the game board to write an equation that models the area of the figure. Let y represent the area, and write your answer in the form y=ax²+bx+c, where a,b, and c are real numbers.

Answers

y=(x+4)(-x+64)
y=-x^2+68

Estimated the difference
645,908 + 335,297
_ - _ = _

Answers

My answer is in the attachment below. Please comment below any questions, comments, or concerns related to this answer.
Have a great day!

Over the last three evenings, Latoya received a total of 79 phone calls at the call center. The first evening, she received 6 fewer calls than the third evening. The second evening, she received 3 times as many calls as the third evening. How many phone calls did she receive each evening?

Answers

We need to represent the numbers of calls symbolically:

Third evening:      x calls
First eve:              x-6 calls
Second evening:  3x calls

Find x.  Add up these three numbers    x, x-6 and 3x and equate your sum to 79:

x+x-6+3x = 79.  Then 5x=79+6, or 5x = 85.  Thus, x = 17.

17 calls on the 3rd night, 
17-6 calls on the 1st night, and 
3(17) = 51 calls on the 2nd night.

Check!  Add together 17, 11 and 51.  Do these add up to 79?   Yes. 
The first evening she received 15.2 calls. The second night she received 42.6. The third evening she received 21.2

PLEASE HELP!
Yolanda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $57 and costs an additional $0.11 per mile driven. The second plan has an initial fee of $50 and costs an additional $0.13 per mile driven.

For what amount of driving do the two plans cost the same?
What is the cost when the two plans cost the same?

Answers

For the first plan, we can write it as 57+0.11m if m represents the miles driven due to that we have a base value of 57 but add $0.11 per mile . Similarly, for the second plan we can write 50+0.13m. Since we want them to be equal, we have 57+0.11m=50+0.13m. Subtracting 0.11m as well as 50 from both sides, we get 0.02m=7. Next, we can multiply both sides by 50 to get 350=the amount of miles needed for them to be the same. For the cost, we can plug 350 into either expression to get 57+0.11*350=95.5 dollars

If Sam has 6 different hats and 3 different scarves, how many different combinations could he wear

Answers

18

He can wear a different hat with one scarf so if that is multiplied by 6*3 you will get 18 different combinations that Sam can wear

If Sam has 6 different hats and 3 different scarves, the number of combinations he could wear is: 18 ways.

Given the following data:

Number of hats = 6 hats.Number of scarves = 3 scarves.

How to determine combinations.

In this exercise, the number of ways 6 different hats and 3 different scarves can be worn without any form of repetition should be calculated by using a combination.

Mathematically, combination is given by this formula:

[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]

Where:

n is the number of items.r is the number of times of choosing items.

For Sam's combination:

[tex]_hC_s = 6 \times 3[/tex]

Sam = 18 ways.

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What is the slope of the function

Answers

The slope of the function is 3
that would be 3.
hope this helps you.

Jasmine earns $36 for 4 hours of baby-sitting. She charges a constant hourly rate. Which table correctly shows the amount Jasmine earns baby-sitting for different numbers of hours?

Answers

I am pretty sure it is a because 2 is half of 4 and 18 is half of 36.

Answer:

A

Step-by-step explanation:


A chicken breast weighs 1.375 pounds on a digital scale. What is that same weight as a mixed number?

Answers

It’s 1 pound and 3/8 (three eighths). Also written as 1 1/3.

9.17/15.00
Is this a A+ or A or B or C

Answers

9.17/15 is very close to 9/15, or 3/5. 3/5 is the same as 60/100, which would be a D.
9.17/15.00 = 0.61, or about 61 percent.

That would likely earn a grade of D, unless the grading scale used is different from the usual 91-100, 81-90, 71-80, 61-70, 51-60.

Which linear system has a solution of
[tex]x = 2 \: and \: y = - 3[/tex]

Answers

bear in mind that, a "solution" so-called, or a zero, or a root, is really just an x-intercept of the graph, namely, where does the graph touch the x-axis?  that's a zero/root/solution/x-intercept.

now, about those two lads above, check the picture below.

notice, that, the horizontal line, by definition will never touch the x-axis, whilst the other one does, at x = 2.

What is a distributive property of 72 divided by 4

Answers

Answer:

[tex]\frac{72}{4}=18[/tex]

Step-by-step explanation:

To find : What is a distributive property of 72 divided by 4 ?

Solution :

The distributive property of division is given by,

[tex]\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}[/tex]

We have to divide 72 by 4,

So, Re-write 72 as 60+12.

Substitute,

[tex]\frac{72}{4}=\frac{60+12}{4}[/tex]

[tex]\frac{72}{4}=\frac{60}{4}+\frac{12}{4}[/tex]

[tex]\frac{72}{4}=15+3[/tex]

[tex]\frac{72}{4}=18[/tex]

Therefore, [tex]\frac{72}{4}=18[/tex]

Final answer:

While the distributive property is typically relevant for multiplication over addition or subtraction, you can apply it to division by first rewriting the division as multiplication by the reciprocal. For example, 72 divided by 4 can be rewritten as 72 times 1/4, and then distributed over a sum or difference.

Explanation:

The distributive property involves multiplication and addition or subtraction, not division. However, if we interpret your question in a bit different way, we can make use of the distributive property for division. To start, dividing 72 by 4 is the same as multiplying 72 by 1/4. So, we can rewrite it as follows:

72 * 1/4

The distributive property is applied when you multiply a number by a sum or a difference. For example, in case of [tex]72*1/4 = (40+32)*1/4[/tex], it would distribute as: [tex]40*1/4 + 32*1/4[/tex]. It gives us 10 + 8 = 18 which is the correct answer. This way, the distributive property can be used in division if the division is expressed as a multiplication.

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find the measure of <ghk <hki and <hkj show your work or wite and explanation

Answers

check the picture below.

Peter wants to borrow $3,000. He has two payment plans to choose from. Plan A is 4% interest over 6 years. Plan B is 5% interest over 4 years. Using the formula mc024-1.jpg for payment, m, which statement best compares the plans?
Plan A has a monthly payment of about $23 less and a total interest charge of $120 less than plan B.
Plan A has a monthly payment of about $23 less and a total interest charge of $120 more than plan B.
Plan A has a monthly payment of about $23 more and a total interest charge of $120 more than plan B.
Plan A has a monthly payment of about $23 more and a total interest charge of $120 less than plan B

Answers

To determine which payment plan is better for borrowing $3,000, Plan A or Plan B, one must calculate both the monthly payments and total interest charges using the given annual interest rates and compounding periods for each plan and compare the results accordingly.

Peter wants to borrow $3,000 and is considering two different payment plans. To compare these plans, we need to calculate the monthly payment and total interest charge for each.

Plan A has an annual interest rate of 4%, compounded monthly over 6 years (or 72 months). Using the formula for monthly payment (m), we can find the monthly payment for Plan A:

 m = P[r(1+r)^n] / [(1+r)^n-1]
Where:

P is the principal amount ($3,000)r is the monthly interest rate (annually 4%, monthly 0.04/12)n is the number of payments (6 years x 12 months/year = 72 months)

Similarly, Plan B has an annual interest rate of 5%, compounded monthly over 4 years (or 48 months). We use the same formula to calculate the monthly payment for Plan B.

After calculating m for both plans, we can also calculate the total interest paid by multiplying the monthly payment by the number of payments and subtracting the principal amount from the result for each plan. Then, we can compare the monthly payments and total interest charges between Plan A and Plan B.

Which expression is equivalent to (5x^3)(2x)^3?

A. 10x^6
B. 30x^6
C. 40x^6
D. 1000x^12

Answers

[tex]\bf (5x^3)(2x)^3\implies (5x^3)(2^3x^3)\implies (5x^3)(8x^3)\implies 5\cdot 8x^3x^3 \\\\\\ 40x^{3+3}\implies 40x^6[/tex]

Given the equation −4 Square root of x minus 3= 12, solve for x and identify if it is an extraneous solution

Answers

i believe ur answer is 12 and is extraneous

Answer:

[tex]x=\frac{225}{16}[/tex] is an extraneous solution.      

Step-by-step explanation:

Given : Equation [tex]-4\sqrt x-3=12[/tex]

To find : Solve for x and identify if it is an extraneous solution?

Solution :

Step 1 - Write the equation,

[tex]-4\sqrt x-3=12[/tex]

Step 2 - Add 3 both sides,

[tex]-4\sqrt x-3+3=12+3[/tex]

[tex]-4\sqrt x=15[/tex]

Step 3 - Squaring both sides,

[tex](-4\sqrt x)^2=(15)^2[/tex]

[tex]16x=225[/tex]

Step 4 - Divide both side by 16,

[tex]\frac{16}{16}x=\frac{225}{16}[/tex]

[tex]x=\frac{225}{16}[/tex]

For extraneous solution, Substitute the value of x back in the equation.

[tex] -4\sqrt (\frac{225}{16})-3=12[/tex]

[tex]-4\times\frac{15}{4}-3=12[/tex]

 [tex]-15-3=12[/tex]

[tex]-18\neq12[/tex]

The value of x does not satisfy the equation which means the value of x is an extraneous solution.

So, [tex]x=\frac{225}{16}[/tex] is an extraneous solution.

Parallelogram MNPQ was dilated to create parallelogram M'N'P'Q'.



Which statements are true about the parallelograms? Check all that apply.

The length of side MN is 2 units.
The length of side M'N' is 5 units.
The image is smaller than the pre-image.
Sides MQ and M'Q' both have the same slope, 1.
The scale factor is 2/5

Answers

Answer:

Options 1,2 and 4 are correct.

Step-by-step explanation:

We have been given a parallelogram MNPQ was dilated to create parallelogram  M'N'P'Q' and we asked to find out which of the given options are correct.

Let us see all the options one by one.

On using distance formula we can see that side MN is 2 units.

[tex]MN=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2} }[/tex]

[tex]MN=\sqrt{(4-2)^{2} +(-2-(-2))^{2} }[/tex]

[tex]MN=\sqrt{(2)^{2} } =2[/tex]

Therefore,option 1 is correct.

We can find the side M'N' by distance formula as we solved for side MN. After solving for M'N' we will get 5 units. Therefore, option 2 is also correct.

Now let us see third option. We can see that image M'N'P'Q' is bigger than pre-image MNPQ. Therefore, option 3 is false.

Now look at our option 4.

Since we know slope is rise (difference of y coordinates) over run (difference of x coordinates) . Upon looking at our image and pre-image we can see that as we increase our x coordinate by one unit our y coordinate also increase by one.

Therefore, option 4 is correct indeed.

Upon looking at our fifth option we can see that our image is bigger than our pre-image. If our image was dilated by factor of 2/5 it would have been smaller than our pre-image. We can see the scale factor is 5/2 instead of 2/5.

Therefore, our fifth option is false.

Considering the slopes and scale factor of the diagram given, the statements that are true about the parallelogram are: A, B, and D.

How to find Slope

Slope = vertical distance / horizontal distance = change in y / change in x.

How to find Scale Factor

Scale factor = length of image/corresponding length of pre-image.

Find the length of MN:

MN = |4 - 2| = 2 units (Option A is true).

Find M'N':

M'N' = |10 - 5| = 5 units (Option B is true).

MNPQ is the pre-image, while M'N'P'Q' is the image, therefore, the image is bigger than the pre-image. (Option C is NOT true).

Find Slope of MQ:

Slope = 1/1 = 1

Find Slope of M'Q':

Slope = 2/2 = 1 (Option D is true).

Find the scale factor:

Scale factor = dimension of image/dimension of pre-image = M'N'/MN

Scale factor = 5/2 (Option E is NOT true).

Therefore, considering the slopes and scale factor of the diagram given, the statements that are true about the parallelogram are: A, B, and D.

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Jed took 2 free throws in 5 seconds. Alex took 4 free throws in 12 seconds did the two shoot free throws at the same rate? Explain

Answers

2 free throws in 5 seconds....2/5 = 0.4 free throws per second
4 free trows in 12 seconds....4/12 = 0.3 free throws per second

no, they did not shoot their free throws at the same rate...because 2/5 does not equal 4/12

Jed and Alex do not shoot free throws at the same rate, Jed is faster by 0.5 seconds.

What is a unitary method?

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Jed took 2 free throws in 5 seconds.

∴ Jed can do 1 free throw in (5/2) = 2.5 seconds.

Alex took 4 free throws in 12 seconds.

∴ Alex can do 1 free throw in (12/4) = 3 seconds.

No, Jade and Alex do not shoot free throws at the same rate Jed is faster by 0.5 seconds.

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Ben earns $1500 each summer and puts the money in a savings account with a 6% simple interest rate. If he deposits the same amount each year, how much money will he have at the end of his third summer

$4770

$3250

$3175

$2850

Answers

he will have 4770 in his account 
I believe the answer is A. $ 4,770

The amount that Ben gets by the first year:

1,500 + (1,500 x 6%)  = 1590

The amount that Ben gets by the second year: 

(1590+1500)  + (3090 x 6%) = 3270.4

The amount that Ben gets by the third summer

(3270.4 + 1500 = $ 4770 

The interest rate is not calculated because the Bens till hasn't pass the rest of the year

The function g(x) = –x2 + 16x – 44 written in vertex form is g(x) = –(x – 8)2 + 20. Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = –x2 + 16x – 44?

Answers

It was moved up 20 units

Answer:

the graph of f(x) will be reflected over x axis, moved 8 units to the right and shifted 20 units up to get g(x)

Step-by-step explanation:

The function [tex]g(x) = -x^2 + 16x - 44[/tex] written in vertex form is [tex]g(x) = -(x - 8)^2 + 20[/tex]

The parent function is f(x)=x^2

Now we compare parent function f(x) and g(x)

In g(x), negative sign at first

f(x) ----> -f(x) , the graph is reflected across x axis

f(x)-----> f(x-h), the graph will be transformed h units to right

f(x)----> f(x) +k , the graph will be transformed k units up

[tex] g(x) = -(x - 8)^2 + 20[/tex], the graph of f(x) will be reflected over x axis, moved 8 units to the right and shifted 20 units up to get g(x)

Hannah travels 6 times as many minutes than Raoul does. Together, they travel 63 minutes. How many minutes does Hannah travel? Draw a model and wrote an equation to solve.

Answers

let h represent the # of minutes that Hannah travels and r the # of minutes that Raoul travels.  Then h + r = 63 min.     We are told that h=6r.

Then 6r + r = 63 min, so:

7r = 63 min, and    r=63 min  / 7   = 9 min.

Raoul travels for 9 minutes and Hannah travels for 6(9 minutes) = 54 minutes.

What is the solution of -8/2y-8=5/y+4 - 7y+8/y^2-16

Answers

Answer:

y = 8

Step-by-step explanation:

[tex]Domain:\\\\2y-8\neq0\ \wedge\ y+4\neq0\ \wedge\ y^2-16\neq0\\\\2y\neq8\ \wedge\ y\neq-4\ \wedge\ y^2\neq16\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq\pm\sqrt{16}\\\\y\neq4\ \wedge\ y\neq-4\ \wedge\ y\neq-4\ \wedge\ y\neq4\\\\\boxed{y\neq-4\ \wedge\ y\neq4}\\\\===========================[/tex]

[tex]\dfrac{-8}{2y-8}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-16}\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-4^2}\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{(y-4)(y+4)}\qquad\text{multiply both sides by (-2)}\\\\\dfrac{8}{y-4}=-\dfrac{10}{y+4}+\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{add}\ \dfrac{10}{y+4}\ \text{to both sides}\\\\\dfrac{8}{y-4}+\dfrac{10}{y+4}=\dfrac{14y+16}{(y-4)(y+4)}[/tex]

[tex]\dfrac{8(y+4)}{(y-4)(y+4)}+\dfrac{10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{8(y+4)+10(y-4)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{use the distributive property}\\\\\dfrac{8y+32+10y-40}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\qquad\text{combine like terms}\\\\\dfrac{(8y+10y)+(32-40)}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\\\\\dfrac{18y-8}{(y-4)(y+4)}=\dfrac{14y+16}{(y-4)(y+4)}\iff18y-8=14y+16\\\\18y-8=14y+16\qquad\text{subtract 14y from both sides}[/tex]

[tex]4y-8=16\qquad\text{add 8 to both sides}\\\\4y=24\qquad\text{divide both sides by 4}\\\\y=8\in D[/tex]

Answer:

6

Step-by-step explanation:

you drink one fourth of a pitcher of Kool-Aid your friend drinks 7/12 of the pitcher what fraction of the pitcher do you and your friend drink

Answers

1/4 is equal to 3/12 and 3/12 + 7/12 = 10/12 or 5/6
The Answer is 5/6. how you reach this answer is by finding the common denominator, which in this case is 12. So you multiply the numerator and the denominator by 3, which will become 3/12. You then add the two fractions and then simplify to get 5/6. Hope this helps.

Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink. What fraction of the bouquet is pink roses? There are 12 roses in a dozen.

Answers

Well, I know there are 12 roses. 
5 are white.
All you have to do is subtract 12 and 5. Once you do that you will have your answer!

Answer: 7/12 for pink roses.
Hope this helps! =) 

The requried fraction of the bouquet that is pink roses is 7/12, as of the given proportion.

If Angelica's bouquet of a dozen roses contains 5 white roses, then the remaining roses must be pink. Since there are 12 roses in a dozen, the number of pink roses in the bouquet would be 12 - 5 = 7.

To find the fraction of the bouquet that is pink roses, we divide the number of pink roses by the total number of roses:

Fraction of pink roses = Number of pink roses / Total number of roses

Fraction of pink roses = 7 / 12

Therefore, the fraction of the bouquet that is pink roses is 7/12.

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Janelle has 4 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 7mph and walks back at a speed of 3mph how long should she plan to spend walking back?

Answers

Final answer:

Janelle should plan to spend 3 hours walking back.

Explanation:

To find out how long Janelle should plan to spend walking back, we need to calculate the total time it takes her to run and walk. Since she runs at a speed of 7mph, she completes the distance of the race in 1 hour (4 miles / 7mph = 0.57 hours = 1 hour). Therefore, she spends 1 hour running and 3 hours left for walking. To find out the distance she walks back, we use the formula distance = speed x time. Since she walks at a speed of 3mph, the distance she walks back is 3mph x 3 hours = 9 miles.

In the circle graph above, you can see that 47% of the company's monthly income is used to pay the owner's personal salary. If the amount of the owners's personal salary was $2,176.10 this month, what was the company's total monthly income this month?

Answers

The answer to this question would be: $4630

In this question, 47% of the company income is used to pay owner's personal salary, which was $2,176.10
Then, to find the company total income the calculation would look like this:

owner's personal salary= 47% * total company income
$2,176.10= 0.47 * total company income
total company income= $2,176.10/ 0.47 = $4630

Final answer:

To find the total monthly income, set up a proportion using the percentage of the owner's salary with the given amount. Solve for the total income to find the answer.

Explanation:

In the circle graph above, the owner's personal salary represents 47% of the company's monthly income. This means that $2,176.10 is 47% of the total monthly income. To find the total income, you can set up a proportion: $2,176.10 is to 47% as X is to 100%. Solving this equation gives you the company's total monthly income as $4,635.

The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. the life of this bulb is normally distributed. what is the probability that a randomly selected bulb would last longer than 1150 hours?

Answers

For any normal random variable X with mean ÎĽ and standard deviation Ď , X ~ Normal( ÎĽ , Ď ), (note that in most textbooks and literature the notation is with the variance, i.e., X ~ Normal( ÎĽ , Ď² ). Most software denotes the normal with just the standard deviation.) You can translate into standard normal units by: Z = ( X - ÎĽ ) / Ď Moving from the standard normal back to the original distribuiton using: X = ÎĽ + Z * Ď Where Z ~ Normal( ÎĽ = 0, Ď = 1). You can then use the standard normal cdf tables to get probabilities. If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem. If a sample of size is is drawn from a population with mean ÎĽ and standard deviation Ď then the sample average xBar is normally distributed with mean ÎĽ and standard deviation Ď /âš(n) IYou can translate into standard normal units by: Z = ( X - ÎĽ ) / Ď Moving from the standard normal back to the original distribuiton using: X = ÎĽ + Z * Ď Where Z ~ Normal( ÎĽ = 0, Ď = 1). You can then use the standard normal cdf tables to get probabilities. If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem. If a sample of size is is drawn from a population with mean ÎĽ and standard deviation Ď then the sample average xBar is normally distributed with mean ÎĽ and standard deviation Ď /âš(n) IYou can translate into standard normal units by: Z = ( X - ÎĽ ) / Ď Moving from the standard normal back to the original distribuiton using: X = ÎĽ + Z * Ď Where Z ~ Normal( ÎĽ = 0, Ď = 1). You can then use the standard normal cdf tables to get probabilities. If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem. If a sample of size is is drawn from a population with mean ÎĽ and standard deviation Ď then the sample average xBar is normally distributed with mean ÎĽ and standard deviation Ď /âš(n) in You can translate into standard normal units by: Z = ( X - ÎĽ ) / Ď Moving from the standard normal back to the original distribuiton using: X = ÎĽ + Z * Ď Where Z ~ Normal( ÎĽ = 0, Ď = 1). You can then use the standard normal cdf tables to get probabilities. If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem. If a sample of size is is drawn from a population with mean ÎĽ and standard deviation Ď then the sample average xBar is normally distributed with mean ÎĽ and standard deviation Ď /âš(n) in this question we have X ~ Normal( ÎĽx = 1000 , Ďx² = 2500 ) X ~ Normal( ÎĽx = 1000 , Ďx = 50 ) Find P( X > 1150 ) P( ( X - ÎĽ ) / Ď > ( 1150 - 1000 ) / 50 ) = P( Z > 3 ) = P( Z < -3 ) = 0.001349898 Find P( X < 1100 ) P( ( X - ÎĽ ) / Ď < ( 1100 - 1000 ) / 50 ) = P( Z < 2 ) = 0.9772499

Which equation represents a line that passes through (–9, –3) and has a slope of –6?

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[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -9}}\quad ,&{{ -3}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -6 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-3)=-6[x-(-9)] \\\\\\ y+3=-6(x+9)\implies y+3=-6x-54\implies y=-6x-57[/tex]
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