f(x) = 3x + a & g(x) = b-5x
Given that gf(1) = 2 and g-1(7) = 1, find the value of “a” and the value of “b”

Answer:

10 + 10 + 10 = 10 x 3

                   = 30

Answer:

- The center line is at 16.5 ounces.

- The standard deviation of the sample mean = 0.112 ounce.

- The UCL = 16.836 ounces.

- The LCL = 16.154 ounces.

Step-by-step explanation:

The Central limit theorem allows us to write for a random sample extracted from a normal population distribution with each variable independent of one another that

Mean of sampling distribution (μₓ) is approximately equal to the population mean (μ).

μₓ = μ = 16.5 ounces

And the standard deviation of the sampling distribution is given as

σₓ = (σ/√N)

where σ = population standard deviation = 0.25 ounce

N = Sample size = 5

σₓ = (0.25/√5) = 0.1118033989 = 0.112 ounce

Now using the 3 sigma limit rule that 99.5% of the distribution lies within 3 standard deviations of the mean, the entire distribution lies within

(μₓ ± 3σₓ)

= 16.5 ± (3×0.112)

= 16.5 ± (0.336)

= (16.154, 16.836)

Hope this Helps!!!

Answer:

Step-by-step explanation:

Set up an equation:

7x + 10x + 13x = 100000 and solve for x:

30x = 100000 so

x = 3333.33

Anna gets 7(3333.33) = 23333.31

Louise gets 10(3333.33) = 33333.33

Lacey gets 13(3333.33) = 43333.29

Answer:

B (48)

Step-by-step explanation:

One particular property of medians is the 2/3 ratio. Basically, the centroid separates the median into two line segments, and the longer line segment is 2/3 of the median length. So, 72 x 2/3 is 48.

Answer:1.7 x 10 ^ -5

Step-by-step explanation:

Answer:1.7 x 10-5

hope this helps

Answer:

14.6 % increase

Step-by-step explanation:

44 divided by 30 = 1.46

To decimal = 14.6 percent

I think

9514 1404 393

Answer:

  0

Step-by-step explanation:

In week 44, Natasha's gross salary comes to 93,500, so she already exceeds the 90,000 limit on social security taxable income.

Natasha pays no social security tax in week 45.

Answer:

A

Step-by-step explanation:

Answer:

xbxbkzkdkdjd

Step-by-step explanation:

bz va yJnzz

Answer:0.03125

Step-by-step explanation:

GOO*OOGLE

Step-by-step explanation:

(1/2)^5   = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 =   1/32

Answer:

0.9544 = 95.44% probability of the resulting sample proportion being within .04 of the true proportion

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

20% of the residents in a certain state support an increase in the property tax. Sample of 400.

This means that \(p = 0.2, n = 400\)

Mean and standard deviation:

Mean \(\mu = p = 0.2\)

Standard deviation \(s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.2*0.8}{400}} = 0.02\)

How likely is the resulting sample proportion to be within .04 of the true proportion (i.e., between .16 and .24)?

This is the pvalue of Z when X = 0.24 subtracted by the pvalue of Z when X = 0.16. So

X = 0.24

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.24 - 0.2}{0.02}\)

\(Z = 2\)

\(Z = 2\) has a pvalue of 0.9772

X = 0.16

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.16 - 0.2}{0.02}\)

\(Z = -2\)

\(Z = -2\) has a pvalue of 0.0228

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability of the resulting sample proportion being within .04 of the true proportion

Answer:

2/8 because each 1/4 0f the 8 slices is equal to 2/8 by multipliction or you can say 1/4 of 8

Answer:

2/8

Step-by-step explanation:

1/4

times everything by 2 as 8 / 4 = 2

2/8

Answer: y = -2x - 4

Step-by-step explanation:

This question asks that you give your answer in slope-intercept form, which is written as y = mx + b, where m is the slope, and b is the y-intercept.

In order to write an equation for this line in slope-intercept form, you need to find the slope and the y-intercept. You can find the slope by selecting any two clear points on the graph and finding the [change in y] ÷ [change in x].

For example, I’ll use (-3, 2) and (-2, 0):

Change in y: 2 - 0 = 2

Change in x: -3 - (-2) = -1

Change in y ÷ Change in x = 2 ÷ (-1) = -2

So, the slope, m, is -2. Finding b, or the y-intercept is a lot more straightforward; you just find where the line intercepts the y-axis, or when x = 0. Looking at the graph, we can see that the y-intercept is -4, so b = -4.

Now, we can put these together in an equation.

y = mx + b, where m = -2 and b = -4

y = -2x -4

Answer:

9

Step-by-step explanation:

5x-3= 2x+24

5x=2x+27

3x=27

X=9

Answer: A.  9

Step-by-step explanation:

The diagonal is bisected by the other diagonal.  So the 2 parts of the diagonal are equal

5x - 3 =  2x + 24                 >Bring like terms to 1 side

3x = 27                                >Divide both sides by 3

x = 9

The median of the given data set is 26.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

Given the data set, we need to find the median.

So, let's arrange the numbers from smallest to largest in order to find the median.

\(\sf 15,20,22,26,28,35,36.\)

\(\text{Median}=\sf 26\)

Therefore, the median of the data set is 26.

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Answer:

3.LOOK AND  CHOOSE THE CORRECT SENTENCES

(1 Punto)

Does Daniela Works every day?

Do Daniela Work every day?

Does Daniela Work every day?

Did Daniela Work every day?

4.LOOK AND  CHOOSE THE CORRECT SENTENCES

(1 Punto)

Margarita don't brushes her car

Margarita doesn't brush her car

Margarita doesn't brushes her car

Margarita didn´t brush her car

5.LOOK AND  CHOOSE THE CORRECT SENTENCES

(1 Punto)

Do Camilo and Diana dances in the class?

Do Camilo and Diana dance in the class

Does Camilo and Diana dance in the class?

Do Camilo and Diana dance in the class?

6.LOOK AND CHOOSE THE CORRECT SENTENCES

(1 Punto)

You don't read a book

You don't reads a book

You doesn't read a book

7.LOOK AND CHOOSE THE CORRECT SENTENCES  

INTERROGATIVE  

____ he ___ better than you?

(1 Punto)

Does- plays

Does- play

Do- play

Do . plays

8.LOOK AND CHOOSE THE CORRECT SENTENCES  

NEGATIVE

It  ___ snow in summer.

(1 Punto)

doesn't

don't

9.LOOK AND CHOOSE THE CORRECT SENTENCES  

AFFIRMATIVE  

My cousin _____ English very well.

(1 Punto)

Speak

Speaking

Speaks

10.LOOK AND CHOOSE THE CORRECT SENTENCES  

AFFIRMATIVE  

We _____  our bikes

(1 Punto)

Wash

Washes

Washing

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Step-by-step explanation:

The amount that she owes after she factors in interest will be $33,455.64.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Rita necessities to apply for a line of credit for another vehicle. Her advance is $25,000. The financing cost on the advance is 6% and is accumulated yearly. She intends to take care of the advance in 5 years.

Then the amount is given as,

A = $25,000 x (1 + 0.06)⁵

A = $25,000 x (1.06)⁵

A = $25,000 x 1.3382

A = $33,455.64

The amount that she owes after she factors in interest will be $33,455.64.

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Answer:

Domain: x \(\geq\) -5

Range: y \(\geq\) -3

Step-by-step explanation:

The domain is all the possible inputs or x value.  x will be greater than -5.

The range is all of the possible outputs or y value.   y will be greater than -3

Answer:

Domain:  [-5, ∞)

Range:  [-3, ∞)

Step-by-step explanation:

The given graph shows a continuous curve with a closed circle at the left endpoint (-5, -3) and an arrow at the right endpoint.

A closed circle indicates the value is included in the interval.

An arrow shows that the function continues indefinitely in that direction.

The domain of a function is the set of all possible input values (x-values).

As the leftmost x-value of the curve is x = -5, and it continues indefinitely in the positive direction, the domain of the  graphed function is:

The range of a function is the set of all possible output values (y-values).

From observation, it appears that the minimum y-value of the curve is y = -3. The curve continues indefinitely in the positive direction in quadrant I. Therefore, the range of the graphed function is:

Answer:

X = -5 and Y = -15

Step-by-step explanation:

Hope this helps!

Answer:

y=-8x+2

Step-by-step explanation:

The reason that is the answer is because the slope-intercept form is y=mx+b where m is the slope and b is the y-intercept so y=mx+b would be y=-8x+2

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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The statement about the given set {motorboat, ferry} ⊂ {ferry, tug boat, motorboat, canoe} is; True

We are given the following statement about sets as;

{motorboat, ferry} ⊂ {ferry, tug boat, motorboat, canoe}

Now, the symbol ⊂ simply means "a subset". A subset is defined as a set whose elements are all members of another set.

Looking at the original set {ferry, tug boat, motorboat, canoe}, we can see that motorboat and ferry are both members of the original set and as such they can both form a subset of the original set. Thus, the given statement is correct.

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Answer: 4.35 × 10⁵

435,000 = 4.35 × 10⁵

Plz mark brainleist:)

Answer:

4.35 x 10 to the 5th power

Step-by-step explanation:

Answer:

\(x= 30/7\)

Step-by-step explanation:

\(2/3 x = -1/2 x + 5\)

\(2/3x+1/2x = + 5\)

\(7/6x=5\)

\(x=5 \times 6/7\)

\(x= 30/7\)

9514 1404 393

Answer:

  P(M&P) = 0.05

Step-by-step explanation:

P(M+P) = P(M&P') +P(P&M') +P(M&P)

0.64 = 0.38 +0.21 +P(M&P)

P(M&P) = 0.64 -0.59 = 0.05

The probability the customer will select both items is 0.05.

_____

Additional comment

Inside parentheses, & = "and"; + = "or".

Answer:

Step-by-step explanation:

(10^2-6^2) gives the hypotenuse of the smaller triangle therefore we get 8 units for that side.looking for the value of x

(8^2-3^2)=x^2

(64-9)=x^2

55=x^2

X=√55

The quantity which represents the 0.031 in the given formula of compound interest, the value represents the annual compound interest rate 3.1%, So option A is correct

A loan or deposit amount is subject to compound interest as interest. In everyday life, it is the most prevalent idea. Both the principal and the interest accrued over time affect the compound interest for a given amount. Between compound and simple interest, this is the primary distinction.

\(A = P[1 + r/n]^{nt}\)

Where,

A = compound interest

P = Principle Amount

r  =  Interest rate

n = number of period for which interest is calculated

t = time

Given that,

A equal to 2,400 plus quantity 1 plus 0.031 over 4 end quantity all raised to the power of 4 times t

\(A = 2400[1 + 0.031/4]^{4}\)

So, here we can see that r is equal to 0.031

It represents the annual compound interest rate of the compound interest

Hence, it is a annual compound interest which has value of 3.1%

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True, the surface area of the cylinder is 100units²

The surface area of a three-dimensional object is the sum of the area of all the outer surfaces, it is also measured in square units.

The surface area of a cylinder is expressed as;

SA = 2πrh + 2πr²

where 2πr² is the area of the bases

2πrh = lateral area

75 = 2 × 3.14 × 6 × r

r = 75/37.68

r = 1.99 unit

base area = 2 × 3.14 × 1.99²

= 25 units ( nearest whole number)

The surface area = 75+25

= 100units²

Therefore the surface area of the cylinder to nearest whole number is 100units².

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