There are 8 ounces in a cup, 2 cups in a pint, 2 pints in a quart, and 4 quarts in a gallon.
1 L≈ 0.26 gallons
7 KL= cups

Answers

Answer 1
Since 1 L / 0.26 gallons (the slash is being used like a ratio, more like an equals sign, not a division symbol), and we’re trying to find kL / cups, we have to first change L to kL.
Since there are 1000 L in a kL, we have to multiply 0.26 gallons by 1000 to get gallons in a kL. 0.26 x 1000 = 260
Now we have to change gallons to cups. Since there are 16 cups in a gallon (2 x 2 x 4), you have to multiply 260 by 16 to get cups in a gallon. 260 x 16 = 4160.
That means there are 4160 cups in a kL, using those conversion factors.

Related Questions

Find the average rate of change for the function over the given interval y=x^2+9x between x=3 and x=7.

Answers

Answer:

average rate of change = 19

Step-by-step explanation:

the average rate of change of f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

here [ a, b ] = [ 3, 7 ] and y = f(x) , then

f(b) = f(7) = 7² + 9(7) = 49 + 63 = 112

f(a) = f(3) = 3² + 9(3) = 9 + 27 = 36

then

average rate of change = [tex]\frac{112-36}{7-3}[/tex] = [tex]\frac{76}{4}[/tex] = 19

Royal Co. receives a dividend of $4.88 per share. Today the closing price of the stock is $59.95. The current stock yield to the nearest tenth of a percent is: 8.1% 8.0% 8.2% 8.3% None of these

Answers

Receiving $4.88 dividend out of the closing stock price of $59.95, means that the stock yield is 8.1%

Dividend is defined as a distribution of payment by a company to its shareholders that is originated from the company's profit and is payable to the shareholders every quarter in a given year, while stock yield is defined as an income generated by the stock being held by the shareholders.

To determine the percentage of stock yield, we will need to divide the closing price of the stock which is $59.95 with the amount of dividend distributed for each stock held which is $4.88, and the calculation is as follows:

59.95/4.88×100%=8.1%

Therefore the stock yield is 8.1%

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When conducting a hypothesis test for a given sample size, if the probability of a Type I error decreases, then the _____________.
a. probability of incorrectly accepting the null hypothesis decreases
b. probability of Type II error decreases
c. probability of incorrectly accepting the null hypothesis increases
d. probability of incorrectly rejecting the null hypothesis increases

Answers

The probability of a Type I error is the probability of incorrectly rejecting the null hypothesis. When the probability of a Type I error decreases, the probability of a Type II error, It decreases the likelihood of choosing the null hypothesis wrongly.

When conducting a hypothesis test for a given sample size, a Type I error is the probability of incorrectly rejecting the null hypothesis. This means that the null hypothesis is true, but the hypothesis test incorrectly rejects it. A Type II error is the probability of incorrectly accepting the null hypothesis. This means that the null hypothesis is false, but the hypothesis test incorrectly accepts it. When the probability of a Type I error decreases, it means that the hypothesis test is more accurate in correctly rejecting the null hypothesis when it is false. This in turn means that the probability of a Type II error also decreases, as the test is more accurate in correctly accepting the null hypothesis when it is true. In other words, when the probability of a Type I error decreases, the probability of a Type II error decreases as well.

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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!

Question 9

Answers

The Spaceship Earth at Epcot Center takes on a spherical shape, so we will use the formula for the volume of a sphere.

Volume of a sphere:

V=4/3•π•r^3, where r=radius

We are given the circumference of the sphere, so we will need to solve for the radius to use the formula. Since a sphere has a circle base, meaning the cross-section resembles a circle, we will use circle formulas to find the radius.

Circumference formula:

C=2•π•r

We are given that the circumference equals 518.1ft, so we can input it into the formula and solve for the radius or “r:”

(518.1)=2•π•r

Divide both sides by 2•π:

82.458=r

So, the radius is approximately 82.458ft. Now that we have “r,” we can use the volume of a sphere formula:

V=4/3•π•(82.458)^3

Simplify with PEMDAS:

V=4/3•π•560,658.474

V=[4(π•560,658.474)]/3

V=2,348,480.72412ft^3

So, the answer choice is c.) because it is the closest

Find the distance between (6,-2) and (1,2)

Answers

Answer: [tex]\displaystyle d=\sqrt{41} \approx 6.4[/tex]

Step-by-step explanation:

     We will use the distance formula to help us solve (see attached). Let (6, -2) be point one and (1, 2) be point two.

[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]

[tex]\displaystyle d=\sqrt{(1-6)^2 +(2--2)^2}[/tex]

[tex]\displaystyle d=\sqrt{(-5)^2 +(4)^2}[/tex]

[tex]\displaystyle d=\sqrt{25 +16}[/tex]

[tex]\displaystyle d=\sqrt{41} \approx 6.4[/tex]

41 is a prime number, so this is the simplest radical form.

Which angles are consecutive interior angles?

Answers

By using the properties of angle, it can be concluded that

[tex]\angle QPS[/tex] and [tex]\angle TSP[/tex] are consecutive interior angle

What is angle?

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

[tex]\angle QPS[/tex] and [tex]\angle TSU[/tex] are not consecutive interior angle as [tex]\angle PST[/tex] falls in between

[tex]\angle QPS[/tex] and [tex]\angle RSU[/tex] are not consecutive interior angle as [tex]\angle RSU[/tex] is an exterior angle

[tex]\angle QPS[/tex] and [tex]\angle TSP[/tex] are consecutive interior angle

[tex]\angle QPS[/tex] and [tex]\angle OPN[/tex] are not consecutive interior angle as [tex]\angle OPN[/tex] is an exterior angle

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Does y = x2 + 1 represent a linear or nonlinear function? Explain.

Answers

Answer: the function is nonlinear

Step-by-step explanation:

y = x2 + 1 is a nonlinear equation because for it to be an linear question it must be the following

Linear:

2x-1=y 

y=2x-1

nonlinear

y = x2 + 1 

Linear equations are a constant slope ( straight line )  and nonlinear equations has a slope that varies between points so y = x2 + 1 is an non-linear equation because it has an slope that varies between points.

two events, a and b are independent if and only if . recall that a reorganization of the multiplication rule will yield . suppose for some events a and b, . which of the following statements is true of a and b? select an answer and submit. for keyboard navigation, use the up/down arrow keys to select an answer. a events a and b are independent since and . b events a and b are not independent, but they are mutually exclusive since . c events a and b are independent since ; however . d events a and b are not independent since and .

Answers

Option- A is correct that is event a and b are independent when consider some events a and b rearranging the multiplication rule will result in.

Given that,

If and only if, two events, a and b, are independent. Remember that rearranging the multiplication rule will result in. Consider some events a and b.

We have to find which of the following claims about a and b is true.

We know that,

We have if the occurrence of event A has no bearing on the probability that event B will also occur, then the two events A and B are said to be independent.

P(A and B) = P(A) P(B) can be used to numerically describe the probability of two separate events.

As a result, we can draw the conclusion that two events, a and b, are independent if and only if they are.

Therefore, Option- A is correct that is event a and b are independent when consider some events a and b rearranging the multiplication rule will result in.

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A manufacturer of floor mops would like her product to last 700 hours, on the average. She hopes the mean number of hours is not a lot less than 700 (people will not continue to buy her product) or a lot more than 700 (people would seldom have to buy the product). However, the manufacturer has reason to believe the mean may have changed. A random sample of 48 items shows that sample mean = 675 and sample standard deviation = 77 hours. Use the significance level α=.05. What is the appropriate test to perform? Regarding the hypothesis testing in question 1, what is the rejection region? Regarding the hypothesis testing in question 1, what is the p-value of the test? Round your answer to four decimal places Regarding the hypothesis testing in question 1, what is your conlusion?

Answers

The appropriate test to perform is one sample t test

The rejection reason is t statistic less than -2.012 or t statistic more than -2.012

The p value of the test is 0.0292

Firstly,

       As the population standard deviation is unknown and the sample size is more than 30, it is appropriate to use one sample t test for this hypothesis testing

Testing if the mean is changed from 700 levels or not

Null and alternate hypothesis are 700

Degree of freedom,

                       n-1

                      = 48-1

                      = 47

Using alpha level 0.05 and t critical table, we found the following two critical values

t critical values= -2.012 and 2.012

So, the rejection reason is t statistic less than -2.012 or t statistic more than -2.012

Now,

        Population means = 700 hours

        Sample mean = 675 hours

        n = 48

So,

Test statistic= (mean-alternate hypothesis)/(s/√n)

                     = (675-700)/ (77/√48)

                     =-25/11.1140

                     = -2.249

Degree of freedom = n-1

                                  = 48-1  

                                  = 47

With t distribution table for -2.249 and 47 degrees of freedom obtain p value of 0.0292

So, pvalue= 0.0292

Reject null hypothesis since the p value is less than alpha level

So, we conclude that the mean has changed from 700 hours

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You can spend at most $8 on potatoes and carrots for a stew. Potatoes cost $2 per pound,
and carrots cost $1 per pound. Write an inequality that represents the amounts of potatoes
and carrots you can buy. Let x = pounds of potatoes and let y = pounds of carrots.

Answers

Answer:

[tex]2x + y \leq 8[/tex]

Step-by-step explanation:

since potatoes cost $2 they are represented as 2x

Carrots cost $1 and are simply y

You randomly observe purchases at a candy store and record the weight of each bag of candy
with 100 different customers. You find the proportion of weights greater than 2 pounds. Is
investigating this sample proportion the same as investigating the sampling distribution of the
proportion?

Answers

Answer:

OptionB)

Step-by-step explanation:

→→When you are talking about sample proportion You are considering a Single ,set of same kind of Data,Like body weight of  Students in a class, from which you are taking out samples for Observation.

For example, A colony is being studied whether each human in that colony is healthy or not by checking their body mass index.

→→When we are investigating or considering Sampling Distribution we consider two different sets or kinds of Data set Possessing Similar Characteristics because we have to compare these two sets of Data.

For example , Take two colonies A and B , Check their honesty by observing how many floors they have made in their Plot.Whether they care or don't care about their Surrounding or Mother Earth by looking, if number of floors exceeds than 2 i.e ground floor and first floor , it means Dishonest , if maximum number of floor =2 ,it means honest.

Find the volume of the composite solid (STEP BY STEP PLEASE) 25 POINTS

Answers

Answer:

  2268π ft³ ≈ 7125 ft³

Step-by-step explanation:

You want the volume of a 22 ft long cylinder capped by a hemisphere 9 ft in radius.

Cylinder

The formula for the volume of a cylinder of radius r and height h is ...

  V = πr²h

Hemisphere

The formula for the volume of a hemisphere of radius r is ...

  V = 2/3πr³

Total volume

The sum of the volumes of the two figures is ...

  Vtotal = πr²h +2/3πr³ = πr²(h +2/3r)

Using the given values for height and radius, we find the volume to be ...

  Vtotal = π(9 ft)²(22 ft + 2/3(9 ft)) = π(9 ft)²(28 ft)

  Vtotal = 2268π ft³ ≈ 7125 ft³

The volume of the composite is about 7125 cubic feet.

Question 2
What is the length of DE? (number only)

Answers

The length of DE is 6.3

Similar triangles are triangles that have a similar appearance but differ in size.

Two triangles are similar if their angles are the same (corresponding angles) and their sides have the same ratio or proportion (corresponding sides)

If two triangles are similar, it means that their corresponding angle pairs are all equal.All triangle corresponding sides are proportional.

The " ~ " symbol is used to represent similarity.

According to the question,

In ΔABC and ΔDBE,

(1) ∠B = ∠B (common)

(2) ∠ACB = ∠DEB (opposite sides are equal)

(2) ∠CAB = ∠ECB

Therefore , ΔABC ~ ΔDBE

By using similar triangle property

The ratio of correspond sides are equal ,

AB/BD = BC/BE = AC/DE

=> 2/1 = AC/DE

=> 12.6 / DE = 2/1

=> DE =  12.6/2

=> DE = 6.3

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1. Gordon estimates that the ramp will be 6 inches tall when it is 60 inches
long. Explain the error that he made and correct the error.

Answers

Answer:

it's 0.25 for the first one

use a proof by contraposition to show that for integers m and n if m n is even then m is even or n is even

Answers

The contrapositive is true

Proving a contraposition involves proving that the contrapositive of a statement is true. The opposite of "if m n is even then m is even or n is even" is "if m is not even and n is not even then m n is not even".

To prove this statement by a proof by contrast, first assume that m is not even and neither is n. This means that both m and n are odd.

Since m and n are odd, m n is also odd. This can be expressed as:

If m and n are odd, we can write m as;

2k + 1 and n as 2l + 1 for integers k and l.

Then mn = (2k + 1)(2l + 1) = 4kl + 2k + 2l + 1 = 2(2kl + k + l) + 1,

which is odd. Therefore, m n is not even if m is not even and n is not even.

It turns out that the opposite of the original statement is true, so the original statement must also be true. Therefore, if m n is even, then we can say that   that m is even or n is even using a proof by contrast.

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hroughout the 2016 presidential election primaries, millennials (those aged 20 to 36 years) consistently supported senator bernie sanders over secretary hillary clinton. according to the 2016 gallup poll of 1,754 millennials, 55% had a favorable opinion of sanders compared with hillary clinton (38%). calculate the 90% confidence interval for both reported percentages. step-by-step calculation for hillary clinton (4 points)

Answers

The range of 90% confidence will be: (0.5305,0.5695)

What is percentage?

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Given,

Sample percentage equals 0.55

z = 1.645 for 90% confidence.

Therefore, the range of 90% confidence will be:

(0.5305,0.5695)

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researcher is using a Kruskal-Wallis test to evaluate the difference between three treatment conditions using a sample of n-8 in each treatment. What value of H is necessary to conclude that there is a significant difference among the treatments using a 05 Select one O a. H25.99 Ob. H2 347 c H2 1.96 O d. H 2080

Answers

C. H2 1,96

To establish whether there is a significant difference between treatments using the Kruskal-Wallis test, the calculated value of H should be compared to the critical values ​​in the table of H values. The critical value of H to use depends on the significance level chosen for the test (0.05 in this case).

Using a significance level of 0.05, the critical value of H for a sample size of n-8 for each treatment is approximately H2 1.96. That is, if the calculated H value is greater than 1.96, we can conclude that there is a significant difference between the treatments.

Hence, the correct answer in this case is c. H2 1,96

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2. Use the product rule (and chain rule) to find the derivative of the following
(a) y = x²(3x + 4)²
(b) y = (1+x²) (2 - x²³)³
(c) y = (2+√)(x+3)²
(d) y = (2x² + 1)(x5 +3)4

Answers

The derivative of the following are:

(a) 36x³ + 72x² + 32x

(b) 2x(2-x²³)³ - 69x²²(2-x²³)(1+x²)

(c) -1/2√x(x+3)² + 2(x+3)(2+√x)

(d) 4x(x⁵+3)⁴ + 20x⁴(2x²+1)(x⁵+3)³

What is a derivative?

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.

Here, we have

Given

(a) y = x²(3x + 4)²

Derivative with respect to x and we get

dy/dx = 2x(3x + 4)² + x²(18x + 24)

dy/dx = 36x³ + 72x² + 32x

(b) y = (1+x²) (2 - x²³)³

Derivative with respect to x and we get

dy/dx = 2x(2 - x²³)³ + (1+x²)(-23x²²)3(2 - x²³)²

dy/dx = 2x(2-x²³)³ - 69x²²(2-x²³)(1+x²)

(c) y = (2+√x)(x+3)²

Derivative with respect to x and we get

dy/dx = -1/2√x(x+3)² + (2+√x)2(x+3)

dy/dx = -1/2√x(x+3)² + 2(x+3)(2+√x)

(d) y = (2x² + 1)(x⁵ +3)⁴

Derivative with respect to x and we get

dy/dx = 4x(x⁵ +3)⁴ +  (2x² + 1)4(x⁵ +3)³(5x⁴)

dy/dx = 4x(x⁵+3)⁴ + 20x⁴(2x²+1)(x⁵+3)³

Hence, the derivative of the following are:

(a) 36x³ + 72x² + 32x

(b) 2x(2-x²³)³ - 69x²²(2-x²³)(1+x²)

(c) -1/2√x(x+3)² + 2(x+3)(2+√x)

(d) 4x(x⁵+3)⁴ + 20x⁴(2x²+1)(x⁵+3)³

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h is a trigonometric function of the form h(x)=acos(bxc)+d. Below is the graph of h(x) The function has a maximum point at (3,6) and a minimum point at (6.5,-9) find the formula for h(x). Give an exact expression.
h(x)=
*from klan academy*
Please Help URGENT

Answers

The exact expression for the cosine function is given as follows:

h(x) = 7.5cos(2π/7(x + 0.5)) - 1.5.

How to define the cosine function?

The definition of the cosine function is given as follows:

h(x) = acos(b(x - c)) + d.

The parameters of the function are given as follows:

a: amplitude.b: The period is of 2π/B.c: phase shift.d: vertical shift.

The difference between the maximum value and the minimum value is of 6 - (-9) = 15, hence the amplitude is obtained as follows:

a = 15/2 = 7.5.

From the graph given at the end of the answer, the period is of 7 units, hence:

2π/b = 7

7b = 2π

b = 2π/7.

The minimum value should be at x = 0, however it is at x = -0.5, hence the phase shift is given as follows:

c = -0.5.

Considering the amplitude of 7.5, without vertical shift the function would oscillate between -7.5 and 7.5, however is oscillates between -9 and 6, hence the vertical shift is given as follows:

d = -1.5.

Thus the function is defined as follows:

h(x) = 7.5cos(2π/7(x + 0.5)) - 1.5.

Missing Information

The graph of the function is given by the image shown at the end of the answer.

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Determine whether the rule represents an exponential function. Explain why or why not.
Y=-2•x^7 WILL MARK BRAINLIEST

A. Since the independent variable X is not the exponent, y=-2•x^7 does not represent an exponential function.

B. Since the independent variable X is not the base, y=-2•x^7 does not represent an exponential function.

C. Since the independent variable x is the base, y=-2•x^7 does represent an exponential function.

D. Since the independent variable X is the exponent, y=-2•x^7 represents an exponential function.

Answers

The equation y = - 2 · x⁷ is not an exponential function because the independent variable x is the base of the formula instead of being its exponent. (Correct choice: A)

Does a given expression represent an exponential function?

In this problem we need to determine whether the equation y = - 2 · x⁷ represent an exponential function or not. Exponential functions are expressions of the form:

y = b · aˣ

Where:

a, b - Real coefficients. (b - Value when x = 0, a - Base)x - Independent variable.y - Dependent variable.

By direct comparison we notice that the given equation is not an exponential function as the independent variable x is not the exponent of the expression and it is the base instead. The expression y = - 2 · x⁷ is a power function, not an exponential function.

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Please help I’m going to fail i need help please

Answers

The volume of the figure can be calculated by adding the volumes of the two rectangular prisms. The first rectangular prism has dimensions 12 in x 10 in x 2 in, so its volume is 12102 = 240 in^3. The second rectangular prism has dimensions 10 in x 7 in x 21 in, so its volume is 10721 = 1540 in^3. The total volume of the figure is 240 in^3 + 1540 in^3 = 1780 in^3.

these statements are the congruence statements for right triangles: ha, ll, la, and hl. you will need to use them for congruence statements. match the abbreviation to its description. for right triangles: 1. a hypotenuse and a leg define congruence. hl 2. a hypotenuse and an acute angle define congruence. la 3. a leg and an acute angle define congruence. ll 4. two legs define congruence. ha

Answers

Answer:

HA:A hypotenuse and an acute angle define congruence

HL:A hypotenuse and a leg define congruence

LL: Two legs define congruence

LA:A leg and an acute angle define congruence

Step-by-step explanation:

HA theorem:

                     When hypotenuse and one acute angle of a triangle is congruent to hypotenuse and one acute angle of a other triangle, then the triangles are congruent

HL theorem:

                     When hypotenuse and one leg of a triangle is congruent to hypotenuse and one leg of other triangle, then the triangles are congruent

LL theorem:

                    When two legs of a triangle is congruent to the two legs of other triangle, then the triangles are congruent

LA theorem:

                    When one leg and one acute angle of a triangle is congruent to one leg and one acute angle of other triangle, then the triangle are congruent

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Travis, Jessica , and robin are collecting donations for the school band. Travis wants to collect 20% more than jessica and robin wants to collect 35% more than travis. If the students meet there goals and Travis collects $43 how much money did they collect in all

Answers

They collected $134.45 and we can find this using percentage.

Travis = $43

Jessica = 43 - (43 × 20%) = $34.4

Robin = 43 + (43 × 35%) = $58.05

Percentage (%):

In maths percentage is the value of ratio that shows the fraction of 100.percent means per 100.It does not have any units.Percentage is denoted by %It is also known as per cent.In order to find percent, we use the formula (original number/ another number) multiply by 100.It has a variety of uses in mathematics.Percentage increase and decrease can be calculated by computing the difference between the two values and comparing to the initial value.

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determine the number of n digit numbers with all digits even, such that 2 and 4 each occur a nonzero, odd number of times.

Answers

According to the question asked the number of digits with all digits even can be found as:

aₙ = 6ⁿ + 2.3ⁿ + 1(n≥0)

Given:

let the number be aₙ.

The number aₙ equals the number of n permutations at the multiset S

where S = { ∞ 2, ∞ 4, ∞ 6, ∞, 8, ∞ 10} on which 2 and 4 occurs

a non zero even number at times.

The exponential generating function have a₀, a₁, a₂,....aₙ

f'(x) = (1+x²/2! + x⁴/4!+...)ⁿ

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Diana averages 6 mph walking
to school. Averaging 35 mph on
the way back home by car, she
takes } hour less time.
How far is the school
from her home?

Answers

If Diana averages 6 mph walking to school. The distance from  the school to her home is 5.4 miles.

What is distance?

Distance can be defined as how far an object is from another object.

Formula for Distance

Distance = Speed × Time

Solving for t (time) to walk to school

6t = 35 (t-.75)              

6t = 35t - 26.25

Collect like terms

29t= 26.25

Divide both side by  29t

t = 26.25/29

t=  .9

t=54 minutes

Solving for Distance (d)

d = 6× .9

d = 5.4 miles

Therefore the distance is 5.4 miles.

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The complete question is:

Diane averages 6 mph walking to school. Averaging 35 mph on the way back home by car, she takes 3/4 hour less time. How far is the school from her home?

Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.]
f(x) = 7(1 − x)−2
f(x) =
[infinity] sum.gif
n = 0
Find the associated radius of convergence R.
R =

Answers

The radius of convergence R of the given function f(x) = (-1)^n(1 - x)² be,

R = 1/2.

Given, a function f(x)

f(x) = (-1)^n(1 - x)²

we have to find the radius of convergence R of the given function,

first will find the (n+1)th term of the given function

as, an = (-1)^n(1 - x)²

then an+1 = (-1)^(n+1)(1 - x)²

to find the radius of convergence, we will find

lim x->∞ an+1/an

lim x->∞ ((-1)^(n+1)(1 - x)²)/((-1)^n(1 - x)²)

On solving the limits, we get

lim x->∞ an+1/an = 2x

then R = 1/2

as, -1/2 < x < 1/2

so, the radius of the convergence be, 1/2

Hence, the radius of the convergence be, 1/2

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A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. Suppose that in February 2012, a sample of 1,000 adults showed 410 indicating that their financial security was more than fair. In February 2010, a sample of 1,100 adults showed 385 indicating that their financial security was more than fair.
(a)
State the hypotheses that can be used to test for a significant difference between the population proportions for the two years. (Let p1 = population proportion saying financial security more than fair in 2012 and p2 = population proportion saying financial security more than fair in 2010.)
H0: p1 − p2 = 0
Ha: p1 − p2 ≠ 0
H0: p1 − p2 > 0
Ha: p1 − p2 ≤ 0
H0: p1 − p2 ≠ 0
Ha: p1 − p2 = 0
H0: p1 − p2 ≥ 0
Ha: p1 − p2 < 0
H0: p1 − p2 ≤ 0
Ha: p1 − p2 > 0

Answers

The hypotheses that can be used to test for a significant difference between the population proportions for the two years is H0 :- P1 = P2

How to calculate the hypotheses?

In math, the process of calculating the hypotheses is to select a statistic based on a sample of fixed size, calculate the value of the statistic for the sample and then reject the null hypothesis if and only if the statistic falls in the critical region.

Here we know that certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. Suppose that in February 2012, a sample of 1,000 adults showed 410 indicating that their financial security was more than fair. In February 2010, a sample of 1,100 adults showed 385 indicating that their financial security was more than fair.

And we need to find the hypotheses that can be used to test for a significant difference between the population proportions for the two years.

Here let us consider P1 refers population proportion saying financial security more than fair in 2012 and P2 refers population proportion saying financial security more than fair in 2010.

As per the definition of the hypotheses, the resulting hypotheses is written as,

=> H0 :- P1 = P2

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assume that the heights of of adult males in a certain region are normally distributed. the heights (in inches) of 20 randomly selected adult males from this region are listed below: 70 72 71 70 69 73 69 68 70 71 67 71 70 74 69 68 71 71 71 72 use this sample data and a .05 significance level to test the claim that the variance of all heights in this region is less than 6.25.

Answers

The sample variance is 2.976 , which means it's lesser than 6.25. We calculate this using the standard method.

Given:

Sample data is 0.05

The sample size is 20.

And ,

The hypotheses are:

H0: sigma^2 = 6.25 (>=)

Ha: sigma^2 < 6.25

The critical value is 10.117. If the test statistic is less than this value, we'll reject the null hypothesis. We Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. For a mnemonic device, remember—when the p-value is low, the null must go.

The test statistic is:

2.976 * 19 / 6.25 = 9.047.

So we reject the null hypothesis. The variance is not 6.25, which means it is lesser then 6.25

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Q3. (b)
The length of human pregnancies from conception to birth approximate a normal
distribution with a mean of 266 days and a standard deviation of 16 days.
(i). What percentage of all pregnancies will last less than 240 days?.
Soln.

Answers

Answer:

5.2%

Step-by-step explanation:

Solve for w: -3(-9w + 6) – 5w = 4(w – 6) – 8

Answers

Step-by-step explanation:

27w - 18 - 5w = 4w - 24 - 8

22w - 18 = 4w - 32

18w = -14

w = -14/18

w = -7/9

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