Find the quadratic function y=​f(x) whose graph has a vertex ​(−3​,3​) and passes through the point ​(−6​,0). What is the function in standard form?

Answer:

Step-by-step explanation:

By the fundamental theorem of arithmetic given [tex]n\in \mathbb{N}_{\ge2}[/tex] there exists primes [tex]p_{i}[/tex] and integers [tex]\alpha_i[/tex] such that [tex]n[/tex] can be written as [tex]n=p_1^{\alpha_1}p_2^{\alpha_2}p_3^{\alpha_3}\cdots p_t^{\alpha_t}[/tex], now suppose that [tex]n[/tex]  is a non-perfect square, we are going to prove that there exists [tex]\alpha_i[/tex] such that is odd. By contradiction, suppose that [tex]\alpha_i[/tex] is even for all [tex]i[/tex], then writing [tex]\alpha_i=2\beta_i[/tex] for all [tex]i[/tex], we can write [tex]n=p_1^{\alpha_1}p_2^{\alpha_2}p_3^{\alpha_3}\cdots p_t^{\alpha_t}=  p_1^{2\beta_1}p_2^{2\beta_2}p_3^{2\beta_3}\cdots p_t^{2\beta_t}=(p_1^{\beta_1}p_2^{\beta_2}p_3^{\beta_3}\cdots p_t^{\beta_t})^2[/tex], thus we conclude that [tex]n[/tex] is perfect square, a contradiction, and then we conclude that there exists [tex]\alpha_i[/tex] such that is odd.

Answer:

The expected value is 5.

Step-by-step explanation:

As we can see, X=Y+Z. Then, by the linearity of the expected value operator, we have that

[tex]E(X)=E(Y)+E(Z).[/tex]

Observe that Y and Z have countable sets of outcomes (1,2,3,....) then,

[tex]E(X)=\sum^\infty_{n=1}nP(Y=n)[/tex],

[tex]E(Z)=\sum^\infty_{n=1}nP(Z=n)[/tex],

Then:

[tex]E(Y)=\sum^\infty_{n=1}nP(Y=n)=\sum^\infty_{n=1}n(\frac{1}{2} )^n=\\\\\sum^\infty_{m=1}\sum^\infty_{n=m}(\frac{1}{2} )^n=\sum^\infty_{m=1}(\frac{1}{2} )^{m-1}=\sum^\infty_{m=0}(\frac{1}{2} )^{m}=2.[/tex]

[tex]E(Z)=\sum^\infty_{n=1}nP(Z=n)=\frac{1}{3}\sum^\infty_{n=1}n(\frac{2}{3} )^{n-1}=\frac{1}{3}\sum^\infty_{m=1}\sum^\infty_{n=m}(\frac{2}{3} )^{n-1}[/tex]

Observe that, by the geometric series formula:

[tex]\sum^\infty_{n=m}(\frac{2}{3} )^{n-1}=\sum^\infty_{n=1}(\frac{2}{3} )^{n-1}-\sum^{m-1}_{n=1}(\frac{2}{3} )^{n-1}=3-\sum^{m-1}_{n=1}(\frac{2}{3} )^{n-1}=\\\\3-\sum^{m-2}_{n=0}(\frac{2}{3} )^{n}=3-\frac{1-(\frac{2}{3})^{m-1} }{1-\frac{2}{3}}=3(\frac{2}{3})^{m-1}[/tex]

Therefore

[tex]E(Z)=\frac{1}{3}\sum^\infty_{m=1}\sum^\infty_{n=m}(\frac{2}{3} )^{n-1}=\frac{1}{3}\sum^\infty_{m=1}3(\frac{2}{3})^{m-1} =\\\\ \sum^\infty_{m=1}(\frac{2}{3})^{m-1} = \sum^\infty_{m=0}(\frac{2}{3})^{m} =3.[/tex]

Finally, E(X)=E(Y)+E(Z)=2+3=5.

Using the binomial distribution, it is found that the expected value of the total number of tosses is of 5.

For each coin, there are only two possible outcomes, either it is heads, or it is tails. The outcome of a coin is independent of any other coin, hence the binomial distribution is used to solve this question.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected number of trials until q successes is:

[tex]E_s(X) = \frac{q}{p}[/tex]

For coin A, we obtain Heads with probability 1/2, hence:

[tex]E_{sA}(X) = \frac{1}{\frac{1}{2}} = 2[/tex]

For coin B, we obtain Heads with probability 1/3, hence:

[tex]E_{sB}(X) = \frac{1}{\frac{1}{3}} = 3[/tex]

2 + 3 = 5, hence, the expected value of the total number of tosses is of 5.

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Answer:

a. The radius of the navy pier wheel is 56% of the radius of the first ferris wheel

b. The radius of the first ferris wheel was 179% of the radius of the navy pier ferris wheel

c. The wheel was moving at 0.70 [tex]\frac{rad}{min}[/tex]

Step-by-step explanation:

Navy pier wheel circumference = Cn

First ferris wheel circumference = Cf

Cn = 0.56*Cf

a.

Circumference Perimeter = 2*π*Radius

Navy pier wheel radius = Rn

First ferris wheel radius = Rf

Cn = 0.56*Cf

2*π*Rn = 0,56*2*π*Rf        (equation 1)

dividing both sides by 2π

Rn = 0,56*Rf

b.

From equation 1

2*π*Rn = 0,56*2*π*Rf

dividing both sides by 2π

Rn = 0.56*Rf

dividing both sides by 0.56

Rf = [tex]\frac{1}{0.56}[/tex]*Rn

Rf = 1.79*Rn

c.

9 minutes / revolution

1 revolution = 2π radians

The wheel makes 2π radians in 9 minutes

Wheel velocity = [tex]\frac{2\pi }{9}  \frac{rad}{min}[/tex]

Wheel velocity = 0.70 [tex]\frac{rad}{min}[/tex]

Answer:

Option B. $0.70

Step-by-step explanation:

First day fine = $0.10

Second day fine (doubled or $0.30 which is lesser)

= $0.10 + $0.10           [$0.10 is lesser than $0.30]

= $0.20

Third day fine = $0.20 + $0.20           [ $0.20 is lesser than $0.30]

                      = $0.40

Fourth day fine = $0.40 + $0.30  = $0.70

[$0.30 is cheaper than doubling the amount $0.40 + $0.40]

Therefore, the total fine for a book on the fourth day is $0.70

Answer:

Security B is riskier than Security A.

Step-by-step explanation:

Security A and B have the same historical average annual return which is 7%, meaning that both of them have had the same results over the years.

However, the standard deviation of A is 3% and the standard deviation of B is 9%, therefore we can conclude that Security A is safer than Security B because a low standard deviation indicates that the annual returns tend to be close to the average (mean), while a high standard deviation indicates that the annual returns are spread out over a wider range of values.

For example:

Security A has this values over the years:

6, 7, 8, 7 where mean is 7.

Security B has this values over the years:

1, 13, 4, 12 where the mean is also 7.

But, A has a lower standard deviation and B a higher one, therefore, Security B is riskier.

Answer:

$12.5 per week

Step-by-step explanation:

(300)+12.5 +12.5+12.5+12.5=350

The rate of change in Michael's savings account per week is $12.50.

To find the rate of change in Michael's savings account per week, we need to determine how much the account balance increased per week. We can subtract the initial balance from the final balance and divide that by the number of weeks:

Rate of change per week = (Final balance - Initial balance) / Number of weeks

Using the given information, the rate of change per week is:

(350 - 300) / 4 = 50 / 4 = 12.5

Therefore, the rate of change in Michael's savings account per week is $12.50.

Answer:

Step-by-step explanation:

"Of" means "times"; "is" means "=". Write the English expression as a math expression and solve for "what".

  14 = 38% × what

  14/0.38 = what ≈ 36.84 . . . . . . divide by the coefficient of "what"

14 is 38% of 36.84

__

  92% × what = 110

  what = 110/0.92 ≈ 119.57 . . . . . divide by the coefficient of "what"

92% of 119.57 is 110.

Answer:

The answer is a point [tex](x,y) / x1\leq x\leq x2    ,  y1\leq y\leq y2[/tex]

Step-by-step explanation:

That happens because the points you have are in opposite corners, which means that they are the limits of the rectangle. so any point inside the rectangle is between that segment

Answer:

6 packs, 9 packs

Step-by-step explanation:

The ratio of mechanical pencil to free eraser is 2:4, or 1:2.

So that means, for every free eraser you get, you bought the double amount of pencils.

12 free erasers x 2 = 24 pencils

18 free erasers x 2 = 36 pencils

And a pack of pencils contains 4.

24/4 = 6 packs

36/4 = 9 packs

Answer:

6 packs and 9 packs

Step-by-step explanation:

Answer:

  0.062

Step-by-step explanation:

The numbers will decrease by 0.001 as you move the the left, so the list of numbers can be found as ...

  3rd number: 0.064

  2nd number: 0.064 -0.001 = 0.063

  1st number: 0.063 -0.001 = 0.062

Answer:

The coordinates of point B are (6,7).

Step-by-step explanation:

Given points are

Blue = A(-4,8)

Purple = M(1,7.5)

Green = B

It is given that point M is the midpoint of point A and B.

Let coordinates of points are (a,b).

Midpoint of two points is

[tex]Midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]

[tex]M=(\dfrac{-4+a}{2},\dfrac{8+b}{2})[/tex]

Coordinates of midpoint are (1,7.5).

[tex](1,7.5)=(\dfrac{-4+a}{2},\dfrac{8+b}{2})[/tex]

On comparing both sides we get

[tex]1=\dfrac{-4+a}{2}\Rightarrow 2=-4+a\Rightarrow a=6[/tex]

[tex]7.5=\dfrac{8+b}{2}\Rightarrow 15=8+b\Rightarrow b=7[/tex]

Therefore, the coordinates of point B are (6,7).

Answer:

  (x, y) = (-1, 3), (-3, 115), (2, 0)

Step-by-step explanation:

The first two test points are not roots. The last one is a root.

Answer:

  (x, y) = (5, -2)

Step-by-step explanation:

A graphing calculator provides a quick and easy way to find the solution.

_____

There are several other ways to solve these equations. Or you can estimate where the answer might be using logic like this:

The intercepts of the first equation are ...

So the graph of it will form a triangle with the axes in the 4th quadrant.

The intercepts of the second equation are ...

So the graph of it will form a triangle with the axes in the 1st quadrant. The x-intercept of this one is less than the x-intercept of the first equation, so the two lines must cross in the 4th quadrant.

The only 4th-quadrant answer choice is (5, -2).

Take the augmented matrix,

[tex]\left[\begin{array}{ccc|c}2&1&-3&-20\\1&2&1&-3\\1&-1&5&19\end{array}\right][/tex]

Swap the row 1 and row 2:

[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\2&1&-3&-20\\1&-1&5&19\end{array}\right][/tex]

Add -2(row 1) to row 2, and -1(row 1) to row 3:

[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&-3&4&22\end{array}\right][/tex]

Add -1(row 2) to row 3:

[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&0&9&36\end{array}\right][/tex]

Multiply through row 3 by 1/9:

[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&0&1&4\end{array}\right][/tex]

Add 5(row 3) to row 2:

[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&0&6\\0&0&1&4\end{array}\right][/tex]

Multiply through row 2 by -1/3:

[tex]\left[\begin{array}{ccc|c}1&2&1&-3\\0&1&0&-2\\0&0&1&4\end{array}\right][/tex]

Add -2(row 2) and -1(row 3) to row 1:

[tex]\left[\begin{array}{ccc|c}1&0&0&-3\\0&1&0&-2\\0&0&1&4\end{array}\right][/tex]

So we have [tex]\boxed{x=-3,y=-2,z=4}[/tex].

Answer:

1  0  0  -3

0  1  0  -2

0  0  1  4

  AND

(-3, -2, 4)

Step-by-step explanation:

I don't have a step-by-step explanation because I still don't understand this sh*t myself. The reason I know it's the right answer is because I just got a 30% on my quiz and it shows you the right answers after. Good luck in this class! You're gonna need it.

Answer:

Each share lost $20 in value over 4 days time

Step-by-step explanation:

$5 loss for 4 days

5 x 4 = 20

$20 loss in 4 days.

Answer:

17/26.

Step-by-step explanation:

Prob(Drawing a black card) = 26/52 = 1/2.

Prob(Drawing a card with a letter)

= Prob( Ace, King, Queen or Jack of  either Hearts or Diamonds)

= 8/52.

So the required probability = 26/52 + 8/52

= 34/52

= 17/26.

The profit is $496.30

a. The revenue function will be calculated thus:

R(x) = (1500 - 3x) × x

R(x) = 1500x - 3x²

b. The cost function will be:

C(x) = 8 × x = 8x

c. The profit function will be:

P(x) = Revenue - Cost

= 1500x - 3x² - (8x)

= 1500x - 3x² - 8x

Divide through by x

= (1500x - 3x² - 8x) / x

= 1500 - 3x - 8

1500 - 3x - 8 = 0

Collect like terms

3x = 1500 - 8.

3x = 1492

x = 1492/3

x = 496.3

The profit is $496.30

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Answer:

The answer to your question is: 2.65 x 10⁷ square miles

Step-by-step explanation:

Data

Southern ocean area =  7.85 x 10⁶ square miles

Difference between areas Indian ocean  = 1.865 x 10⁷ square miles

and the southern ocean

Process

a) To find the area of the Indian ocean we need to sum of the values of the area of the Southern ocean and the area of the difference between the Indian ocean and the southern ocean.

b)

      Area of the Indian Ocean = 1.865 x 10⁷ + 7.85 x 10⁶

                                                 = 2.65 x 10⁷ square miles

Answer:

The area of the Indian ocean is [tex]2.65\times 10^7[/tex]      

Step-by-step explanation:

Given : The area of the southern ocean is about [tex]7.85\times 10^6[/tex] square miles. The difference between the areas of the Indian ocean and the southern ocean is about [tex]1.865\times 10^7[/tex] square miles.

To find : Explain how to find the area of the Indian ocean. Then find the area.

Solution :

The area of the southern ocean is about [tex]7.85\times 10^6[/tex] square miles.

i.e. [tex]A_s=7.85\times 10^6[/tex]

The difference between the areas of the Indian ocean and the southern ocean is about [tex]1.865\times 10^7[/tex] square miles.

i.e. [tex]A_i-A_s=1.865\times 10^7[/tex]

Substitute the value of [tex]A_s[/tex]

[tex]A_i-7.85\times 10^6=1.865\times 10^7[/tex]

[tex]A_i=1.865\times 10^7+7.85\times 10^6[/tex]

[tex]A_i=1.865\times 10^7+0.785\times 10^7[/tex]

[tex]A_i=(1.865+0.785)\times 10^7[/tex]

[tex]A_i=2.65\times 10^7[/tex]

Therefore, The area of the Indian ocean is [tex]2.65\times 10^7[/tex]

9 (a - b) + 5 (2a - 2b)

mutiply the first bracket by 9

(9)(a)= 9a

(9)(-b)= -9b

mutiply the second bracket by 5

(5)(2a)=10a

(5)(-2b)= -10b

9a-9b+10a-10b

9a+10a-9b-10b ( combine like terms)

Answer : C. 19a - 19b

To simplify the expression 9(a - b) + 5(2a - 2b), we first distribute each term in the parentheses by the factor outside the parentheses and then gather like terms, getting 19a - 19b.

To solve this problem, we need to distribute each term in the parentheses by their respective factor outside the parentheses and then collect like terms.

Step 1: Distribute the terms

9(a - b) becomes 9a - 9b

5(2a - 2b) becomes 10a - 10b

Step 2: Collect like terms

9a + 10a = 19a

-9b - 10b = -19b

So, the expression 9(a - b) + 5(2a - 2b) simplifies to 19a - 19b, which is answer choice C.

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Answer:

Step-by-step explanation:

The shorter the term, the lower the amount of interest.

The lower the interest rate, the lower the amount of interest.

The loan that has both a shorter term and a lower interest rate will cost less in interest.

___

The total of payments for the 30-year loan is 396,232.87.

The total of payments for the 20-year loan is 290,013.55.

The amount saved by taking the shorter loan is the difference of these amounts: $106,219.32.

_____

You can use an amortization formula, spreadsheet, or a financial calculator to compute the payments for each loan. The total repayment amount is the product of the monthly payment and the number of them, 360 for the 30-year loan; 240 for the 20-year loan.

Answer:

  (5.5, -13.5)

Step-by-step explanation:

Midpoint M satisfies ...

  M = (S +T)/2

So ...

  2M = S + T

  2M -T = S

  2(5, -8) -(4.5, -2.5) = S = (10 -4.5, -16 +2.5)

  S = (5.5, -13.5)

Answer:

The correct answer is the second option.

Step-by-step explanation:

If X + R = S, then X = S - R. You need to subtract each pair:

-2 - 0 = -2

-8 - 3 = -11

0 - (-4) = 4

2 - 5 = -3

Answer:

B

Step-by-step explanation:

Edge2020

Answer:

Bob wins

Step-by-step explanation:

Think first in a simpler case. In a 2x2 matrix the determinant is zero if two columns or rows are proportional. So Alice writes the first number, then Bob write the same number in the same column but in the other row. Bob repeat the procedure after Alice's second number, and win.

If the matrix is nxn where n is even (like 2008) Bob will win following the previous procedure. Alice writes a number anywhere, Bob writes the same number in the same column in the above (or below) row.  Every time Alice write a number in the same row as her first one, Bob copy that number in the above (or below) row. Any other rows are not important, i.e, the determinant will be zero with any values in them.    

Answer:

here merchandise sell is $6000

correct option is A

Step-by-step explanation:

given data

salary = $300 + 10 % commission

paid = $900

to find out

merchandise sell

solution

we consider here sell is x

so paid will be                

paid = salary + 10% of x

so here put value

900 = 300 + 10% ×  x

900 - 300 = 10% ×  x

x = 600 / 10%                

x = 6000                  

so here merchandise sell is $6000

correct option is A

You would set up a ratio for the two known sides to equal the known side and x:

8/2 = 18/x

Cross multiply:

(2 * 18) = (8 * x)

Simplify:

36 = 8x

Solve for x by dividing both sides by 8:

x = 36/8

x = 4.5

To simplify the expression (-2)(-3)^2 - 2(2 - 5), you perform the calculations step by step. The final result is -12.

To simplify the expression (-2)(-3)^2 - 2(2 - 5), we perform the calculations step by step:

Therefore, the simplified expression is -12.

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Answer:

The answer is the function 3x+4y+5=0 is Slanted

Step-by-step explanation:

To be able to to know if this function is horizontal, vertical or slanted we should look at the gradient.

If the gradient is zero, then the line is horizontal.

If the gradient is infinite, then the line is vertical.

if not, then the line is slanted

We can look the gradient by the general form equation of a line:

y = mx + c

where y = dependent variable, x = independent variable, m = gradient, c = intercept.

With our equation, we can change things around to get the general form equation:

3x + 4y + 5 = 0

4y = 3x - 5

[tex]y = \frac{3}{4}x - \frac{5}{4}[/tex]

Where the gradient is 3/4

Therefore, as the gradient is a number other than zero or infinite, we know that this function is slanted.

Answer:

The answer to your question is: letter A

Step-by-step explanation:

data

Book = 100 pages

Zoey reads 1 page per minute

Now we solve it using rule of three

     1 page  ------------------  1 min

 100 pages ----------------   x

x = 100x1/1 = 100 min will take Zoey to read the book

   60 min  ------------------   1 hour

 100 min ---------------------   x

x = 100/60 = 10/6

and convert it to a mix fraction = 1 2/3    = 1 hour 40 minutes

Then, the answer is letter A

Answer:

A

Step-by-step explanation:

well since she reads 1 page per minute and there are 100 pages then that means it takes 100 minutes.

100 minutes= 1 2/3 hours which is in between 1 1/2 and 2 so the answer would be A

Answer:

The answer to your question is:

Step-by-step explanation: The third one is a factor

Factor

                                        5x³ − 135    

Find the prime factors of 135

             135   3

               45   3

                15    3                   Then 135 = 3³ x 5

                 5     5

                  1

                                   5x³  - 5(3)³

Factor   5    

                   5[  x³  - (3)³]

                   5 [  (x  - 3)(x² + 3x + 9)]

Answer:

5 [  (x  - 3)(x² + 3x + 9)]

Step-by-step explanation: