If you shift the quadratic parent function, Flx) =x, down 9 units, what is the equation of the new function?​

9514 1404 393

Answer:

  2nd quadrant

Step-by-step explanation:

Reversing the signs of both coordinates reflects the point across the origin. The quadrant diagonally opposite quadrant 4 is quadrant 2.

_____

You recall that quadrants are numbered 1 to 4 counterclockwise, starting from upper right.

Answer:

Principal = Rs 2000

Time = 4 years

Interest = Rs 400

Now, Interest= Principal×Rate×Time/100

400= 2000×R×4/100

R= 400×100/2000×4

Step-by-step explanation:

Hope it is helpful....

Answer:

68 inches

Step-by-step explanation:

16+16+18+18

To put along the outside edge of the 18 inches wide and 16 inches tall board, 68 inches of ribbon is required. The length of the ribbon required is the same as the perimeter of the classroom board.

A perimeter of a rectangle is double the sum of the breadth and length of that rectangle.

It is given that the width of the classroom board is 18 inches and its height is 16 inches.

The shape of the board is a rectangle.

Therefore, it can be assumed that a rectangle with a length of 16 inches and a width of 18 inches is given.

K wants to put the ribbon along the outside edge of the board. To find the inches of ribbon required for the task, it is sufficient to find the perimeter of the board.

The perimeter of the boards can be calculated as follows:

Perimeter = 2 × (length + width)

                 = 2 × (16 + 18)

                 = 2 × 34

                 = 68 inches

Hence, 68 inches of ribbon is required to be put along the outside edge of the board.

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Answer:

Step-by-step explanation:

I believe the correct answer from the choices listed above is option D. The expression that could be used to determine the average rate at which the object falls during the first 3 seconds of its fall would be  (h(3)-h(0))/3. Average rate can be calculated by the general formula:

Average rate = (change in y-axis) / (change in x-axis)

In this case,

Average rate = (change in height) / (change in time)

Answer: 14.25 or 14 1/4

Step-by-step explanation:

15 3/4 = 15.75

1 1/2 = 1.5

15.75 - 1.5 = 14.25

14.25 = 14 1/4

Answer:

A. ^3√5 is the answer.

Step-by-step explanation:

5^( 1 / 3 ) = ^3√5

The probability that you have to wait an additional six minutes or more is 0.01800; 310.056

X is an exponential random variable with probability density function,

f(x) = λe − λx, x>0

The required probability that you have to wait for more than 5 minutes is give,

P (X>5) = ∞∫5 λe − λx

dx = λ(e − λx − λ) ∞5

= e − 5λn as,

So, the probability is e − 5λ

That probability that you have to wait for additional five minutes or more given that you have already waited for 10 minutes will be, = e − 5λ

So, the probability is e−5λ because exponential distribution is memory-less which means that it does not consider the past events happened.

therefore, the probability that you have to wait an additional six minutes or more is 0.01800; 310.056

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Answer:

$315

Step-by-step explanation:

You are going to want to use the simple interest formula for this. The one below is modified for solving the interest earned.

I = interest amount

P = principal amount

r = interest rate (decimal form)

t = time

Now we can plug in the values into the equation:

This means that Rachel earned $315 worth of interest in the 15 year period.

Answer: $315

Step-by-step explanation:

Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

Answer:

2

Step-by-step explanation:

Answer:

Answer B

Step-by-step explanation:

Answer:

$40/5

Step-by-step explanation:

If you're trying to figure out the cost of each class divide the amount of money you pay in all ($40 dollars) by 5. Once you do that you should get 8, so $8 per class.

Answer:

79.5

Step-by-step explanation:

35 correct = 35x2.5=87.5

32 wrong = 32x-0.25=-8

no. of pts = 87.5+(-8) = 79.5

The slope of the line shown in the graph is __2/3__

and the y-intercept of the line is __6___

The general linear equation is written as follows:

y = ax + b

Where a is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is y = 6, then we can write the line as:

y = ax + 6

The line also passes through the point (-9, 0), replacing these values in the line we will get:

0 = a*-9 + 6

9a = 6

a = 6/9

a = 2/3

That is the slope.

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Answer:

\(x=-2, x=\frac{4}{3}, x = 3\)

Step-by-step explanation:

First, factor it.

\((x+2)(3x-4)(x-3)=0\)

Use the Zero Factor Principle and equate them each to 0.

\(x+2=0\\x=-2\\\\3x-4=0\\x=\frac{4}{3}\\\\x-3=0\\x=3\)

This is how you find the roots of \(3x^3-7x^2-14x+24\).

(a) Boris performed better on the aptitude test, since its z-score was higher.

(b) Callie performed better on the knowledge test.

(c) The z-score for the aptitude test was still higher than the z-score for the knowledge test, so Boris performed better on the aptitude test.

(a) To determine which test Boris performed better on, we need to compare his z-scores for the knowledge test and the aptitude test.

For the knowledge test, his z-score is calculated as:

z = (55 - 60) / 3 = -1.67

For the aptitude test, his z-score is:

z = (106 - 110) / 6.8 = -0.59

Since the z-score for the aptitude test is higher than the z-score for the knowledge test, Boris performed better on the aptitude test.

(b) To determine which test Callie performed better on, we need to compare her z-scores for the knowledge test and the aptitude test.

For the knowledge test, her z-score is:

z = (67 - 60) / 3 = 2.33

For the aptitude test, her z-score is:

z = (119 - 110) / 6.8 = 1.32

Since the z-score for the knowledge test is higher than the z-score for the aptitude test, Callie performed better on the knowledge test.

(c) Boris' z-score on the logic test (-0.43) is unrelated to his performance on the knowledge and aptitude tests, so it does not change the answer to which test he performed better on. The z-score for the aptitude test was still higher than the z-score for the knowledge test, so Boris performed better on the aptitude test.

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Answer:7.25 feet

Step-by-step explanation:

6.25+6.5=12.75

20-12.75=7.25

The number of  children bought meal tickets =  700

The number of adult  bought meal tickets = 950

A linear equation is one that can be written as display style a 1x 1+ldots +a nx n+b=0, where x 1, ldots, x n are the variables and display style b, a 1, ldots, a n are the coefficients, which are frequently real integers.

Let x and y be the quantity of kid and adult tickets sold, respectively. 1650 tickets were sold in total, as far as we know.

x + y = 1650

x = 1650 - y

At $12 for adults and $4 for children, the total revenue from tickets is $14200. There are

4x + 12y = 14200

substituting the value of x in the equation:

4(1650 - y) + 12y = 14200

6600 - 4y + 12y = 14200

6600 + 8y = 14200

8y = 14200 - 6600 = 7600

y = 7600 / 8

= 950 adult tickets

x = 1650 - 950

= 700 children tickets

The number of  children bought meal tickets =  700

The number of adult  bought meal tickets = 950

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Answer:

multiplication......

Step-by-step explanation:

The volume of the toy can be expressed as (1/2)(L - l) cubic inches.

To find the volume of the toy, we need to calculate the volume of the larger wooden triangular prism and subtract the volume of the removed triangular prism.

The volume of a triangular prism is given by the formula:

Volume = (1/2) * base * height * length

For the larger wooden triangular prism:

Base length = 1 inch

Height = 1 inch

Length = length of the prism (let's assume it to be L)

So, the volume of the larger wooden triangular prism is:

V1 = (1/2) * 1 * 1 * L = (1/2)L

For the removed triangular prism:

Base length = 1 inch

Height = 1 inch

Length = length of the removed prism (let's assume it to be l)

So, the volume of the removed triangular prism is:

V2 = (1/2) * 1 * 1 * l = (1/2)l

Finally, the volume of the toy is obtained by subtracting V2 from V1:

Volume of the toy = V1 - V2 = (1/2)L - (1/2)l = (1/2)(L - l)

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The volume of the toy is given as 68

Volume of the wooden prism =

3 * 3 * 8

= 72

The volume of the triangular prism

= 1/2 x 1 / 1 x 8

= 4

If the triangular prism removed from the center has the same base and height (for simplicity, assume it's also 1 inch by 1 inch and the length l2 of it), the volume of this smaller prism is:

The volume of the toy =

72 - 4

= 68 inches

The volume of the toty is 68 inches

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Answer:

y=12

Step-by-step explanation:

y is inversely proportional to x

y=k/x

k is a constant of proportionality

k=yx

y1x1=y2x2

8(9)=y2(6)

y2=8(9)/6

y2=12

Step-by-step explanation:

there is no diagram here.

I assume that the race track is a rectangle in the middle and two half-circles at the left and right ends, and that the length of the rectangle is D = 2R. which makes the rectangle actually a square, as the width is the diameter of the (half-)circles, which is also 2R.

Sonic ran the track 5 times in 10 seconds with a speed of 321 m/s.

that means he ran 10×321 m in 10 seconds = 3210 m.

so, 5 times the track is 3210 m, which means that the track itself is 3210/5 = 642 m long.

and based on the assumptions above the track consists of 2 times the length of the rectangle (or square), and the full circumference of a circle with radius R (2 half-circles make one full circle).

we know the formula for the circumference of a circle :

2×pi×radius

so, we have then

642 = 2×2R + 2×pi×R = R×(4 + 2×pi)

R = 642 / (4 + 2×pi) = 62.43201701...

and when using the requested "cut-off" pi = 3.14, we get

R = 642 / (4 + 2×3.14) = 62.45136187...

and that is rounded 62.5

so, the second answer option is correct.

Answer:

3, 4, 27

Step-by-step explanation:

1) Area scale factor = 9

Length scale factor = 3 because √9

2) 12/3 = 4

3) 3³ = 27

Penetration equation is given by  B(x) = B₀ * exp(-x / λ).

To determine the magnetic field penetration (B(x)) inside a superconducting plate, we need to consider the penetration equation. The penetration equation is written as:

B(x) = B₀ * exp(-x / λ),

where B₀ is the magnetic field at the surface of the superconducting plate, x is the distance from the surface, and λ is the penetration depth.

(a) To show that B(x) inside a superconducting plate perpendicular to the axis and of thickness d is given by this equation, we can follow these steps:

Step 1: Assume that the magnetic field is perpendicular to the surface of the superconducting plate (i.e., along the axis).

Step 2: When x = 0 (i.e., at the surface of the plate), the magnetic field is B₀:

B(0) = B₀ * exp(-0 / λ) = B₀ * exp(0) = B₀.

Step 3: As x increases and penetrates inside the superconducting plate, the magnetic field decreases due to the exp(-x / λ) term in the penetration equation.

Step 4: At the other surface of the plate (i.e., at x = d, where d is the thickness of the plate), the magnetic field will be:

B(d) = B₀ * exp(-d / λ).

Thus, we have shown that the magnetic field penetration (B(x)) inside a superconducting plate perpendicular to the axis and of thickness d is given by the penetration equation B(x) = B₀ * exp(-x / λ).

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The number of  hours it would take 6 pipes to fill 1/4 of the lake is 4.5 hours

Given that

It takes 4 of the pipes 12 hours to fill the lake.

This means that

Rate = 12 hours/4 pipes

So, we have

Rate = 3 hours/ pipe

For 6 pipes to fill 1/4 of the lake. we have

Time = 3 hours *6 * 1/4

Evalaute

Time = 4.5 hours

Hence, the time taken is 4.5 hours

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Math SAT scores explain about 98.7% of the variation in the total SAT scores.

In statistics, correlation or dependence exists as any statistical relationship, whether causal or not, between two random variables or bivariate data.

A correlation exists as a statistical measure (expressed as a number) that defines the size and direction of a relationship between two or more variables. A correlation between variables, however, does not automatically mean that the change in one variable exists as the cause of the change in the values of the other variable.

Since r² exists = (0.9935)² = 0.9870, we interpret r² as 98.7% of the variation in the y variable exists explained by the x variable.

In context, math SAT score explains about 98.7% of the variation in total SAT score.

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Answer:

c = 25 * 5^t

Step-by-step explanation:

c = 25 * 5^t

This equation best suits N on the scale as it follows the pattern of the number of colonies being 5 times the previous year.

The simplified form of the expression -6w + (–8.3) + 1.5+ (–7w) is -13w - 6.8.

Given the expression in the question;

-6w + (–8.3) + 1.5+ (–7w)

To simplify, first remove the parenthesis

Note that;

-6w + × - 8.3 + 1.5 + × - 7w

-6w - 8.3 + 1.5 - 7w

Next collect and add like terms

-6w - 7w - 8.3 + 1.5

Add -6w and -7w

-13w - 8.3 + 1.5

Add -8.3 and 1.5

-13w - 6.8

Therefore, -13w - 6.8 is the simplified form.

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Answer:

632.4

Step-by-step explanation:

You have to add all the numbers then dived it by ten. Hope this helps all mark me brainlest plzzzz

The interest earned by Mrs Grey over the 7 years is R5670. The cost of the television set 5 years ago was R20,600.

4.1.1 To calculate the interest earned by Mrs Grey over 7 years, we use the formula for simple interest: Interest = Principal x Rate x Time. Mrs Grey's principal is R18,000 and the rate is 4.5% per annum. The time is 7 years. Using the formula, we can calculate the interest as follows:

Interest = R18,000 x 0.045 x 7 = R5670. Therefore, Mrs Grey has earned R5670 in interest over the 7 years.

4.1.2 To calculate the cost of the television set 5 years ago, we need to account for the inflation rate. The cost of the television set now is R27,660. The average rate of inflation over the last 5 years is 6.7% per annum. We can use the formula for compound interest to calculate the original cost of the television set:

Cost 5 years ago = Cost now / (1 + Inflation rate)^Time

Cost 5 years ago = R27,660 / (1 + 0.067)^5 = R20,600. Therefore, the cost of the television set 5 years ago was R20,600.

4.1.3 To determine the rate of simple interest Mrs Grey should have invested her money at 7 years ago, we can use the formula for interest: Interest = Principal x Rate x Time. We know the principal is R18,000, the time is 7 years, and the interest earned is R5670. Rearranging the formula, we can solve for the rate:

Rate = Interest / (Principal x Time)

Rate = R5670 / (R18,000 x 7) ≈ 0.0448 or 4.48% per annum. Therefore, Mrs Grey should have invested her money at a rate of approximately 4.48% per annum to have earned enough interest to purchase the television set using only her original investment and the interest earned over the 7 years.

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