If the graph of f(x)=x^2, how will the graph be affected if it is changed to f(x)=1/3x^2?

Answer: so there are 666 multiples of 3 between 2 and 2000.

Step-by-step explanation:

the smallest number = 3 which is 3*1. The largest number is = 1998 = 3*666

multiples of 3 between {2,2000} = 666-1+1 = 666

Answer:

Both ways are correct

If you multiply the cost by 8% and add, you will still get 108% as your total.

Answer:

Both ways are correct

Step-by-step explanation:

Father's way is ( 40 × 0.08 ) + 40 = $43.2

Mothers way is 40 × 1.08 = $43.2

Answer:

The sample mean that will cut off the upper 95% of all samples of size 20 taken from the population is of 1963.2 pounds.

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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

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

The average breaking strength of a certain brand of steel cable is 2000 pounds, with a standard deviation of 100 pounds.

This means that [tex]\mu = 2000, \sigma = 100[/tex]

A sample of 20 cables is selected and tested.

This means that [tex]n = 20, s = \frac{100}{\sqrt{20}} = 22.361[/tex]

Find the sample mean that will cut off the upper 95% of all samples of size 20 taken from the population.

This is the 100 - 95 = 5th percentile, which is X when Z has a p-value of 0.05, so X when Z = -1.645. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]-1.645 = \frac{X - 2000}{22.361}[/tex]

[tex]X - 2000 = -1.645*22.361[/tex]

[tex]X = 1963.2[/tex]

The sample mean that will cut off the upper 95% of all samples of size 20 taken from the population is of 1963.2 pounds.

Answer:

they sold 64hotdogs and 128 sodas

Step-by-step explanation:

2x+x=192 3x=192 x=64

Answer: hello from the question the volume of tank = 6000 gallons while the value in the Torricelli's equation = 5000 hence I resolved your question using the Torricelli's law equation

answer:

1) a) -180  gallons/minute ,

  b)  -160 gallons/minute

  c)  -120 gallons/minute

  d) 0

2) The water is flowing out fastest when t = 5 min

3) The water is flowing out slowest after t = 20 mins

Step-by-step explanation:

Volume of tank = 5000 gallons

Time to drain = 50 minutes

Volume of water remaining after t minutes by Torricelli's law

V = 5000 ( 1 - [tex]\frac{1}{50}t[/tex] )^2 ----- ( 1 )

1) Determine the rate at which water is draining from the tank

First step : differentiate equation 1 using the chain rule to determine the rate at which water is draining from the tank

V' = [tex]-10000[ ( 1 - \frac{1}{50}t ) (\frac{1}{50}) ][/tex]

a) After t = 5minutes

V' = - 10000[ ( 1 - 0.1 ) * ( 0.02 ) ]

   = -180  gallons/minute

b) After t = 10 minutes

V' = - 10000[ ( 1 - 0.2 ) * ( 0.02 ) ]

   = - 160 gallons/minute

c) After t = 20 minutes

V' = - 10000 [ ( 1 - 0.4 ) * ( 0.02 ) ]

   = -120 gallons/minute

d) After t = 50 minutes

V' = - 10000 [ ( 1 - 1 ) * ( 0.02 ) ]

   = 0 gallons/minute

2) The water is flowing out fastest when t = 5 min

3) The water is flowing out slowest after t = 20 mins  because no water flows out after 50 minutes

Answer:

See pic below.

Step-by-step explanation:

The opposite of 5 is -5.

Answer:

Option B.

Step-by-step explanation:

We can see that we have an asymptote at x = 2

Remember that in a rational function, the asymptote is at the x-value such that the denominator is equal to zero.

So, the denominator is something like:

(x + a)

we have that the denominator is zero when x = 2

Then:

(2 + a) = 0

solving that for a, we get:

a = -2

Then the denominator of the rational function is:

(x - 2)

For the given options, the only one with this denominator is option B, then the correct option is B.

Answer:

B. f(x) = 1/x-2

Step-by-step explanation:

Math is ez bro.

Answer:

3/8

Step-by-step explanation:

The value of 37.5% reduced to the lowest terms is 15/40.

A fraction is written in the form p/q, where q ≠ 0. Fractions are of two types they are proper fractions and improper fractions. Fractions can also be converted into percentages by multiplying them by 100.

We know e can convert percentages into decimals and fractions by dividing the percentage value by hundred.

Given we have to convert 37.5% as a fraction which is,

= 37.5/100.

= 375/1000.

= 75/200.

= 15/40.

learn more about percentages here :

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Step-by-step explanation:

xx is the Roman number of 20

Answer:

Hello,

|FD|=15

Step-by-step explanation:

Since the triangles are similar, the bissects are also.

k*35=21 ==> k=21/35

k*25=|FD|

|FD|=(21/35)*25=15

Answer:

The answer is "Principal of marginal analysis".

Step-by-step explanation:

To determine unless the benefits of even an aggressive resource would outweigh its costs, and therefore increase utility, individuals and businesses can use a valuation model to compare the risks versus the benefits of more activities, like whether to create or consuming more. It's the amount during which net value is greater than or equal to marginal cost that's the optimal quantity in this situation. The amount where the marginal social cost curve and consumer surplus line connect.

Answer:

(D)

Step-by-step explanation:

i think dat is an open ended question

Answer:

Step-by-step explanation:

x = 0, 1/5

Answer:

multiply the numerator together and denominator together

Answer:

za/2: Divide the confidence level by two, and look that area up in the z-table: .95 / 2 = 0.475. ...

E (margin of error): Divide the given width by 2. 6% / 2. ...

: use the given percentage. 41% = 0.41. ...

: subtract. from 1.

Answer:

[tex]9\sqrt{3}[/tex]

Step-by-step explanation:

This is a 30-60-90 triangle.

It's good to remember this. The side length opposite to the 60 degree angle is always the base multiplied by [tex]\sqrt{3}[/tex]

Answer:

9√3.

Step-by-step explanation:

tan 60 = √3

So w/9 =√3

w = 9√3

Answer:

30 degrees

Step-by-step explanation:

Use the Tan formula.

Given:

The graph of a function is given.

To find:

The point that is the relative maxima on the interval x = –1 and x = 2 in the graph.

Solution:

Relative maxima: It is the maximum point of a function over a short interval.

From the given graph it is clear that the graph of the function over the interval x = –1 and x = 2 has a relative maxima at (0,0).

Clearly, (0,0) is represented by point a.

So, the point a is the relative maxima on the interval x = –1 and x = 2 in the graph.

Therefore, the correct option is A.

Answer:

By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

What percentage of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean?

By the Empirical Rule, approximately 68% of the bulbs have lifetimes that lie within 1 standard deviation to either side of the mean.

Answer:

The p-value of the test is 0.0007 < 0.01, which means that the class demonstrates that the percentage was higher in Owensboro, KY.

The possible proportion of patrons that do borrow books from the Owensboro Library is 0.82.

Step-by-step explanation:

For Americans using library services, the American Library Association claims that at most 67% of patrons borrow books. Test if the proportion is higher in Owensboro, KY.

At the null hypothesis, we test if the proportion is of at most 0.67, that is:

[tex]H_0: p \leq 0.67[/tex]

At the alternative hypothesis, we test if the proportion is of more than 0.67, that is:

[tex]H_1: p > 0.67[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.67 is tested at the null hypothesis:

This means that [tex]\mu = 0.67, \sigma = \sqrt{0.67*0.33}[/tex]

The class randomly selected 100 patrons and found that 82 borrowed books.

This means that [tex]n = 100, X = \frac{82}{100} = 0.82[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.82 - 0.67}{\frac{\sqrt{0.67*0.33}}{\sqrt{100}}}[/tex]

[tex]z = 3.19[/tex]

P-value of the test and decision:

The p-value of the test is the probability of a finding a sample proportion of 0.82 or above, which is 1 subtracted by the p-value of z = 3.19.

Looking at the z-table, z = 3.19 has a p-value of 0.9993.

1 - 0.9993 = 0.0007

The p-value of the test is 0.0007 < 0.01, which means that the class demonstrates that the percentage was higher in Owensboro, KY.

What is the possible proportion of patrons that do borrow books from the Owensboro Library?

The sample proportion of 0.82.

Answer:

the answer to your question is 7.8 (E)

The  distance from point N to LM is 7.8, 8.1 and 8.4 unit.

Perpendicular lines are those that cross at a straight angle to one another. Examples include the opposite sides of a rectangle and the steps of a straight staircase. the icon used to represent two parallel lines.

Perpendicular lines are two separate lines that cross one other at a right angle, or a 90° angle.

Given:

In ΔNOM

The Perpendicular distance is 7.8 unit

and, Hypotenuse distance id 8.1 unit

Now, In ΔNOL

The Perpendicular distance is 7.8 unit

and, Hypotenuse distance id 8.4 unit

Learn more about perpendicular here:

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Answer:

MD = 2

SS = 18

SAMPLE VARIANCE = 2.25

STANDARD ERROR = 0.5

Step-by-step explanation:

Given :

A 8 7

B 7 5

C 6 6

D 7 6

E 9 7

F 8 5

G 5 4

H 9 4

I 7 4

Difference, d = Before - After

______ d

A 8 7 __ 1

B 7 5 __ 2

C 6 6 __ 0

D 7 6 __ 1

E 9 7 __ 2

F 8 5 __ 3

G 5 4 __ 1

H 9 4 __5

I 7 4 ___3

The mean of difference, MD ;

MD = Σd/ n = (1+2+0+1+2+3+1+5+3) / 9 = 18 / 9 = 2

The sum of square, SS ;

(1 - 2)^2 + (2 - 2)^2 + (0 - 2)^2 + (1 - 2)^2 + (2 - 2)^2 + (3 - 2)^2 + (1 - 2)^2 + (5 - 2)^2 + (3 - 2)^2 = 18

Sample variance, S² = SS/(N-1) = 18 / (9 - 1) = 18 / 8 = 2.25

Sample standard deviation, S = √Variance = √2.25 = 1.5

Standard Error, S.E = S / √n = 1.5 / √9 = 0.5

Test statistic : MD / S.E = 2 / 0.5 = 4

We test at α = 0.05 since no α - value is stated in the question.

Critical value at 0.05, df = 8 ;

Critical value = 2.306

Since; Test statistic > Critical value, then result is significant at α = 0.05

Answer:

The null hypothesis is [tex]H_0: \sigma = 0.3[/tex]

The alternative hypothesis is [tex]H_1: \sigma \neq 0.3[/tex]

Step-by-step explanation:

Test if the tar content of filtered​ 100-mm cigarettes has a standard deviation different from 0.30 ​mg.

At the null hypothesis, we test if the standard deviation is of 0.3, that is:

[tex]H_0: \sigma = 0.3[/tex]

At the alternative hypothesis, we test if the standard deviation is different of 0.3, that is:

[tex]H_1: \sigma \neq 0.3[/tex]

Answer:

-1/3x+3 = x-1

Step-by-step explanation:

The solution is (3,-2)

Check and see if the point solves the equation

-1/3x+3 = x-1

-1/3(3) +3 = 3-1

-1+3 = 3-1

2=2 yes

Answer:

C

Step-by-step explanation:

Answer:

✔ positive

✔ 1

✔ closely

✔ increases

ED2021

9514 1404 393

Answer:

  x = √2

Step-by-step explanation:

A graph indicates the only solution is near x=√2.

__

Square both sides, separate the radical and do it again.

  [tex]\displaystyle(2-x)\sqrt{\frac{x+2}{x-1}}=\sqrt{x}+\sqrt{3x-4}\qquad\text{given}\\\\(2-x)^2\cdot\frac{x+2}{x-1}=x+(3x-4)+2\sqrt{x(3x-4)}\qquad\text{square}\\\\\frac{(2-x)^2(x+2)}{x-1}-4x+4=2\sqrt{x(3x-4)}\qquad\text{isolate radical}\\\\\left(\frac{(2-x)^2(x+2)-4(x-1)^2}{x-1}\right)^2=x(3x-4)\qquad\text{square}\\\\(x^3-6x^2+4x+4)^2=4(x-1)^2(3x^2-4x)\qquad\text{multiply by $(x-1)^2$}[/tex]

Now, we can put this polynomial equation into standard form and factor it.

  [tex]x^6 -12x^5+32x^4-76x^2+48x+16=0\\\\(x-2)^2(x^2-2)(x^2-8x-2)=0\qquad\text{factor it}\\\\x\in \{2,\pm\sqrt{2},4\pm3\sqrt{2}\}[/tex]

The original equation requires that we restrict the domain of possible solutions. In order for the radicals to be non-negative, we must have x ≥ 4/3. In order for the left side of the equation to be non-negative, we must have x ≤ 2. So, the only potential solutions will be in the interval [4/3, 2].

The only values in the above list that match this requirement are {√2, 2}. We know that the right side of the equation cannot be zero, so the value x=2 is also an extraneous solution.

The only solution is x = √2.

_____

Additional comment

For solving higher-degree polynomials, I like to use a graphing calculator to help me find the roots. The second attachment shows the roots of the 6th-degree polynomial. They can help us factor the equation. (There are also various machine solvers available that will show factors and roots.)

Answer:

The point estimate for the population proportion of people who performed volunteer work in the past year is 0.396.

Step-by-step explanation:

Point estimate of a proportion:

Proportion is the number of desired outcomes divided by the number of total outcomes.

518 out of 1309 people performed volunteer work:

This means that:

[tex]p = \frac{518}{1309} = 0.396[/tex]

The point estimate for the population proportion of people who performed volunteer work in the past year is 0.396.

Answer:

101 is the answer of the question

Answer:

101 degrees

Step-by-step explanation:

First you add all the percentages

39 + 28 + 30 + 3 = 100%

To find the number of degrees of basketball you multiply 28% by 360 because it’s a circle.

28/100 * 360 = 10,080/100 = 100.8 ~ 101

Answer:

x > 8

Step-by-step explanation:

You can start y multiplying both sides by 4 to cancel out the division by 4:

x/4 > 2

*4      *4

x > 8

Answer:

x > 8

Step-by-step explanation:

x/4 > 2

=> x > 2 × 4

=> x > 8