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2 years ago

Write a rule for the linear function in the table.

Mathematics

1 answer:

JulijaS [17]2 years ago

6 0

Answer:

I guess that you want to know the transformations:

We start with:

f(x) = y = 4*x + 3

a)the transformed function is:

f(x) = y = -4*x - 3

So the sign changed.

This means that we go from (x, y) to (x, - y)

This is a reflection over the x-axis which changes the sin of the y component.

b) Now we go to f(x) = 4*x + 3

So the coefficient in the leading term changed.

This is a horizontal contraction:

A horizontal contraction of factor K for the function g(x) is: g(K*x)

In our case, we have:

f(K*x) = 4*(k*x) + 3 = x + 3

4*k*x = x

4*k = 1

k = 1/4

Then the transformation is an horizontal contraction of scale factor 1/4.

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AlladinOne [14]

Answer:

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Step-by-step explanation:

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8 0

2 years ago

A study of 40 English composition professors showed that they spent, on average, 13 minutes correcting a student's term paper. T

photoshop1234 [79]

Answer:

90% confidence interval for the mean grading time of all composition papers.

(12.47981 , 13.52019)

Appropriate inequality

The interval is ( 12.47981 < μ < 13.52019)

Step-by-step explanation:

<u><em>Explanation</em></u>:-

Given sample size 'n' = 40

Mean of the sample = 13 minutes

standard deviation = 2 min

level of significance = 0.10 or 90%

90% confidence interval for the mean grading time of all composition papers.

$( x^{-} - Z_{0.1} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.10} \frac{S.D}{\sqrt{n} } )$

$( 13 - 1.645 \frac{2}{\sqrt{40} } , 13 +1.645 \frac{2}{\sqrt{40} } )$

( 13 - 0.52019 , 13 + 0.52019)

(12.47981 , 13.52019)

The interval is ( 12.47981 < μ < 13.52019)

7 0

3 years ago

vRichard has a red card (R) and a black card (B). He picks a card randomly from the pair and then rolls a six-sided die. The sam

Alik [6]

The Sample space for three cards is

$S=\left\{\left(B,1\right),\left(R,1\right),\left(G,1\right),\left(B,2\right),\left(R,2\right),\left(G,2\right),\left(B,3\right),\left(R,3\right),\left(G,3\right),\left(B,4\right),\left(R,4\right),\left(G,4\right)$ $\left(B,5\right),\left(R,5\right),\left(G,5\right),\left(B,6\right),\left(R,6\right),\left(G,6\right) \right \}$

There are two cards red(R) and black(B) and a six-sided die.

The event is one card is picked randomly and then rolls the die.

So, the Sample space is as follows.

$S=\left\{\left(B,1\right),\left(R,1\right),\left(B,2\right),\left(R,2\right),\left(B,3\right),\left(R,3\right),\left(B,4\right),\left(R,4\right),\left(B,5\right),\left(R,5\right),\left(B,6\right),\left(R,6\right) \right \}$

<h3>Find Sample space if there are three cards.</h3>

Consider there were three cards red(R), black(B) and green(G) a six-sided die.

The event is one card is picked randomly and then rolls the die.

So, the sample space will be as follows,

$S=\left\{\left(B,1\right),\left(R,1\right),\left(G,1\right),\left(B,2\right),\left(R,2\right),\left(G,2\right),\left(B,3\right),\left(R,3\right),\left(G,3\right),\left(B,4\right),\left(R,4\right),\left(G,4\right)$ $\left(B,5\right),\left(R,5\right),\left(G,5\right)\left(B,6\right),\left(R,6\right),\left(G,6\right) \right \}$ .

Learn more about sample space here :-

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7 0

2 years ago

You deposit $400 each month into an account earning 8% interest compounded monthly. Round to the nearest cent as needed. a) How

Debora [2.8K]

If I deposit $400 each month into an account earning 8% interest compounded monthly, I will have $6,517 in my account in 35 years. The total money that I will put into the account is $168,000. I will earn a total compound interest of $6,117.

Calculating the Sum of Money in 35 years

Given information is as follows,

Principal, P = $400

Rate = 8%

Time, T = 35 years

n = 12 (Compounded monthly)

The amount for compound interest is given as,

A = $P\frac{(1+\frac{R}{n} )^{nT} -1}{R/n}$

A = $400\frac{(1+\frac{0.08}{12} )^{12.35} -1}{0.08/12}$

A = 6,517.02

A = $6,517 (to the nearest cents)

Calculating the Amount Put in Account

Since, $400 is deposited every month for 35 years,

Amount Put in 35 years for this compound interest =$400 × 12 × 35

= $168,000

Calculating the Compound Interest

A = P + CI

Thus, the compound interest is given by,

CI = A - P

CI = 6517 - 400

CI = $6,117

I will earn a total interest of $6,117

Learn more about compound interest here:

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7 0

1 year ago

I need help because I don’t know how to do this

wolverine [178]

Answer:

t^5 = t to the power of five.

Step-by-step explanation:

3 0

3 years ago