The transformations to the parent function of a quadratic equation are given below. Write an equation of the new function in vertex form.

translated 3 units down ___


reflected over the x-axis, then translated 5 units left ___

Answer:

20%

Step-by-step explanation:

8 -> pizzas

12 -> hamburgers

14 -> pastas

6 -> steaks

40 = 8 + 12 + 14 + 6 -> total dishes

so the probability become from actual cases on total cases

so (8 / 40)

8/40 = 1/5 = 20/100 = 20%

Answer:

6 months

Step-by-step explanation:

We can set up an equation based on his monthly savings to find out how long it will take for Hatif to reach $630 in his account.

Let's assume it takes Hatif "n" months to reach $630 in his account. Each month, he saves $80.

The equation representing the situation is:

$150 + $80n = $630

Now, let's solve for "n":

$80n = $630 - $150

$80n = $480

n = $480 / $80

n = 6

Therefore, it will take Hatif 6 months to reach $630 in his account.

The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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Answer:

400

Step-by-step explanation:

25 times the length is 1000 m.

Let length = L

25L = 1000

L = 40

10 times the perimeter is 1000 m.

Let the perimeter = P

10P = 1000

P = 100

perimeter = 2L + 2W

2(40) + 2W = 100

80 + 2W = 100

2W = 20

W = 10

The length is 40 m, and the width is 10 m.

A = LW

A = 40 m * 10 m

A = 400 m^2

Answer:

Table could be first x = 2, y = 4, then x = 4, y = 8. It is proportional because both (x,y) values equal 1/2. The equation is x = 1/2y. Last, the table could be the same, or you could do first, x = 6, y = 12, then x = 12, y = 24, because they still equal 1/2.

Step-by-step explanation:

Answer:

The function f(x) to model U. S. cell phone usage over the time period of 2010 to 2016 can be expressed as f(x) = 43 * (1.23^x), where x is the number of years since 2010. Part b: The estimated cell phone usage in 2013 can be calculated by substituting x = 3 into the function f(x) = 43 * (1.23^x). This yields an estimated cell phone usage of 68.4 million in 2013, which can be rounded to the nearest ten thousand to 68 million.

Step-by-step explanation:

The 98% confidence interval for the true mean statistics anxiety score (μ) is approximately (39.037, 39.763).

To calculate the 98% confidence interval for the true mean statistics anxiety score (μ) for all undergraduate students in the U.S., we can use the formula:

Confidence interval = sample mean ± (critical value * standard error)

First, we need to find the critical value associated with a 98% confidence level. Since we are assuming a normal distribution, we can use the Z-table or a statistical software to find this value. For a 98% confidence level, the critical value is approximately 2.33.

Next, we calculate the standard error (SE) using the formula:

SE = standard deviation / √sample size

In this case, the standard deviation is 0.9 and the sample size is 33. Plugging these values into the formula, we get: SE = 0.9 / √33 ≈ 0.156

Now, we can calculate the confidence interval:Confidence interval = 39.4 ± (2.33 * 0.156)

Simplifying the expression:Confidence interval ≈ 39.4 ± 0.363

This gives us the interval (39.037, 39.763). This means we are 98% confident that the true mean statistics anxiety score for all undergraduate students in the U.S. falls within this interval.

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Answer:

9

Step-by-step explanation:

1. To find how 3x+10=16, we must subtract 10 from both sides.

                           -10  -10

2. now we have 3x=6, we divide 3 from both sides

                           3    3

3. we end with x=2.

Now we know x=2, we plug in 2 into our second equation.

1. 4(2)+1 we multiply 4 times 2.

2. we are then left with 8+1, which equals 9.

The volume of the given pyramid is  64 cubic inches.

The volume of the pyramid is the product of one-third of the height and square of the base side length.

The volume of Pyramid A =  (1/3)(side²)(height)

The volume of a square pyramid is equal to one-third of the product of the base’s area and the pyramid’s height. The formula is:

V = (1/3) × a² × h

where a is the length of the square base, and h is the height (or altitude).

We are given that;

h = 3 inch, a = 8 inch, and hypotenuse = 5 inch,

Now, we can plug in the values into the formula and get:

V = (1/3) × 8² × 3

V = (1/3) × 64 × 3

V= (64 x 3)/3

V = 64 inch³

Therefore, by the given data the volume of the pyramid will be 64 cubic inches.

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Answer:

6.24 x \(10^{-7}\)

Step-by-step explanation:

0.000000624 in scientific notation is 6.24 x \(10^{-7}\)

Answer:

Step-by-step explanation:

The resulting number is in scientific notation. In this case, the number is 6.24 * 10^-7.

An inequality for the number of tickets the theater club needs to sell is 10x+8y ≤ 800 and need to sell at the door to reach its goal is 48.

Given:

Tickets to a play cost $10 at the door and $8 in advance. The theater club wants to raise at least $800 from the sale of the tickets from the play. Write and graph an inequality for the number of tickets the theater club needs to sell. If the club sells 40 tickets in advance.

Use x to represent the number of tickets sold at the door and y to represent the number of tickets sold in advance.

Standard form:

10x + 8y ≤ 800

Slope intercept form:

y < (-5/4)x + 100

Slope: -5/4

y-intercept: 100

Tickets sell at the door to reach its goal is:

10x + 8*40 = 800

10x + 320 = 800

10x = 800 - 320

10x = 480

divide by 10 on both sides

x = 480/10

x = 48

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The Experimental probability and the theoretical probabilities are 0.2 and 0.3 respectively.

If the spinner is fair, then each color must have the same probability,

this means that the probability for each color is the number of times that the color (in this case blue) is in the spinner divided by the total amount of colors in the spinner, then the theoretical probability for each color is:

Pt = 1/5 = 0.20

The experimental probability can be found by dividing the number of times that the spinner landed on a given color (in this case for blue we have 15 times) divided by the total number of spins ( 50)

Pe = 15/50 = 0.30

Therefore, the Experimental probability and the theoretical probabilities are 0.2 and 0.3 respectively

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Complete question:

A spinner has 5 equal-sized sections with different colors. You spin the spinner 50 times. The results are shown in the table. Find the theoretical and experimental probabilities of spinning blue.

Red Green Blue Yellow Orange

8           11      15       9          7

The theoretical probability is

The experimental probability is

Given function:

This is a transformation of the

b)

It was first reflected in the x-axis:

Then translated right by 4 units:

So the applicable choices are:

c)

See the attached with all transformations f(x) → h(x) → g(x).

Answer:

\(\textsf{a)} \quad f(x)=x^3\)

b)   4. horizontal shift of 4 units right

     2. reflection in the x-axis

c)  See attachment.

Step-by-step explanation:

Given function:

\(g(x)=-(x-4)^3\)

The parent function is:

\(f(x)=x^3\)

To transform the parent function f(x) to g(x):

1.  Horizontal shift of 4 units right:

\(\implies f(x-4) = (x-4)^3\)

2.  Reflection in the x-axis:

\(\implies -f(x-4) = -(x-4)^3\)

To sketch the graph of g(x):

Answer:

answer: 15, 28, 20, 36, 21, 18

Answer:

a). Point A

b). 90°

c). Anticlockwise

Step-by-step explanation:

As it's clear from the picture attached,

Triangle XYZ has been rotated about a point A to form an image X'Y'Z'.

Angle of rotation is 90° about a point A.

a). Point which is the center of the rotation → point A.

b). Angle of rotation → 90°

c). Direction of rotation → Anticlockwise

Answer:

255.5 miles

Step-by-step explanation:

146 miles - 2 hours

x miles - 3.5 hours

Cross multiply

2x = 146 x 3.5

2x = 511

Divide both sides by 2

x = 511/2

x = 255.5 miles

Answer:

255.5 Miles

Step-by-step explanation:

2 Hours= 146

1 Hour= 73

Half an hour=36.5

3.5 hours= 255.5

Answer:

width= 14

Step-by-step explanation:

Play around with numbers, i used 4, then 6, then 5 for the length. 5 is correct, do 5*2=10+4=14; 14*2+5*2= 28+10= 38

Therefore, the width of the rectangle is 14.

Answer:

w = 5

l = 14

Step-by-step explanation:

We have to use system of equations here.

Let w be the width and l be the length

l=2w+4

w=l(1/2)-4

The equation is going to look like this

l+w+l+2 = 38

2l+2w = 38

Now, I will substitute l with what I said was equal to l above

2(2w+4)+2w = 38

Distribute:

4w+8+2w = 38

Combine like terms

6w+8=38

Same to both sides, subtract 8 on both sides

6w=30

Divide each side by 6

w=5

We know the width is 5, and now using the width, we can find the length, so we do 5*2+4 which is 14. Then we can plug that in:

2w+2l

2(5)+2(14)

10+28=38

Please let me know if you have any questions

{(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range that defines the correct relation. The correct option is D.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

When one magnitude depends on another, the relationship between them is known as a mathematical function. So long as they are uniquely and solely connected.

Every mathematical function is the relationship between an element of group A and an element of group B. Consequently, the following algebraic expression can be used to represent this function:

Therefore, the {(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range that defines the correct relation. The correct option is D.

The complete question is given below,

Which relation describes a function? What makes it a function?

A) {(-2,3),(-2,5),(-6,7)} Each member of the range is unique.

B) {(2,3),(3,3),(3,4)} Each member of the domain and range is positive.

C) {(2,3),(3,3),(3,4)} Each member of the domain and range is a real number.

D) {(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range.

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Answer:

(3x-4) by (3x+2) or (-3x+4) by (-3x-2)

Step-by-step explanation:

To factor 9x^2-6x-8 we want to find the factors of 9 and the factors of -8 that when multiplied in sequence and then added give us -6.

factors of -8:

-8 & 1

8  & -1

-4  & 2

4  & -2

you might also want to remember that these can be flipped, so if you have -8 & 1 you can also have 1 &-8.

factors of 9:

9  &  1

-9  & -1

3  &  3

-3  &  -3

So now we just need to find numbers where

a & b are factors of 9 and c & d are factors of -8 and a*c+b*d=-6,

if that is the case then (ax+c)*(bx+d)=9x^2-6x-8

guess: 3 & 3 and -4 & 2

3*(-4) + 3*2=-12 +6 = -6

so one factoring is (3x-4)*(3x+2)

This means that one of the possible dimensions of the blanket is (3x-4) by (3x+2)

guess: -3 & -3 and 4 & -2

(-3)*4+(-3)*(-2)= -12+6 = -6

so another factoring is (-3x+4)*(-3x-2)

So you could also have a blanket with dimensions (-3x+4) by (-3x-2) but this might not make sense to do because, if you input positive numbers for x you will get negative dimensions which in the real world don't exist for a knitted blanket.

p.s sorry for the late response.

Answer:

The answer is 32

Step-by-step explanation:

The formula for finding the area of a trapezoid is:

         ((base 1 + base 2)/ 2 )* h

Now all you have to do is substitute the numbers in.

Note: bases will always be the ones like 12 and 4 in this case. We have just named then 1 and 2.

Answer:

32 square units

Step-by-step explanation:

\(\displaystyle A=\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(12+4)(4)=\frac{1}{2}(16)(4)=\frac{1}{2}(64)=32\)

Note that \(b_1\) and \(b_2\) are the lengths of each base of the trapezoid, so it doesn't matter which is which.

The complete order of the inverse function of the function f(x) = x + 5 is:

1. y = x + 5

2. x = y + 5

3. x - 5 = y

4. y = x - 5

The function is given as:

f(x) = x + 5

The opposite of the function f(x) = x + 5 is the inverse of the function.

So, we have:

f(x) = x + 5

Express f(x) as y

y = x + 5

Swap the positions of x and y

x = y + 5

Make x the subject of the formula

x - 5 = y

Rewrite as:

y = x - 5

Hence, the inverse function of the function f(x) = x + 5 is y = x - 5

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Answer: D

Step-by-step explanation:

Therefore, the probability that there will be at most 71 visitors at this national park in one weekend is 0.9887.

The Poisson distribution is a probability distribution that describes the probability of a certain number of independent events occurring within a fixed interval of time or space, given that the events occur at a constant average rate and are randomly distributed throughout the interval.

Given that the number of visitors at a national park in one weekend follows a Poisson distribution with a mean of 55.

We need to find the probability that there will be at most 71 visitors in one weekend, that is, P(X ≤ 71).

We can use the cumulative distribution function (CDF) of the Poisson distribution to calculate this probability:

P(X ≤ 71) = F(71) = Σ(k=0 to 71) [e^(-λ) * λ^k / k!]

Where λ is the mean of the Poisson distribution, which is 55 in this case.

Using a calculator or software, we can compute this probability to be:

P(X ≤ 71) = F(71) = 0.9887 (rounded to 4 decimal places)

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Answer:

Probability that there will be at most 71 visitors in one weekend, Assuming variable follows poisson distribution is 0.9887

Probability:

Probability means occurence of an event in respect of another event .

suppose a coin is tossed one time , the probability of getting heads is 1/2

Poisson distribution:

Poisson distribution is also called discrete probability distribution which helps to find the probability of an event happening a certain number of times (k) within a given interval of time. The Poisson distribution has only one parameter, λ (lambda), which is also  the mean number of events.

According to the information:

Given: No. of visitors follows a poisson distribution with a mean of 55

To calculate the probability that there will be at most 71 visitors λλλλin one weekend , cumulative distribution is used:

P[X≤71]=F[71]=∑[k=0 to 71][\(e^{λ}\)*\(λ^{k}\)/k!]

After calculating P[X≤71] = F[71] = 0.9887

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Answer:

-17

Step-by-step explanation:

x+7=-10

x=-10-7

x=-17

Answer:

-10+x= -7

Step-by-step explanation:

Are you on k12?

Answer:

Step-by-step explanation:

the triangles are proportional

9/81=1/3

140-x/x=1/3

3(140-x)=x

420-3x=x

4x=420

x=420/4 = 105

Answer:

2.321428571%

Step-by-step explanation:

Given in the question,

P=$350

T=4years

I=$32.50

We know that

I=PTR/100

32.50=350*4*R/100

R=32.50*100/350*4

R=2.321428571%

So, the rate of interest is 2.321428571%