Find the first three nonzero terms in the power series expansion for the product f(x)g(x).
f(x) = e^2x = [infinity]∑n=0 1/n! (2x)^n
g(x) = sin 5x = [infinity]∑k=0 (-1)^k/(2k+1)! (5x)^2k+1
The power series approximation of fx)g(x) to three nonzero terms is __________
(Type an expression that includes all terms up to order 3.)

Answers

Answer 1

Answer:

∑(-1)^k/(2k+1)! (5x)^2k+1

From k = 1 to 3.

= -196.5

Step-by-step explanation:

Given

∑(-1)^k/(2k+1)! (5x)^2k+1

From k = 0 to infinity

The expression that includes all terms up to order 3 is:

∑(-1)^k/(2k+1)! (5x)^2k+1

From k = 0 to 3.

= 0 + (-1/2 × 5³) + (1/6 × 10^5) + (-1/5040 × 15^5)

= -125/2 + 100000/6 - 759375/5040

= -62.5 + 16.67 - 150.67

= - 196.5


Related Questions

Avi's pet hamster Chubby loves to run in his hamster wheel. During one "race", Avi counts 100100100 rotations of the wheel. She wants to know how far Chubby ran, so she measures the diameter of the wheel and finds that it is 20 \text{ cm}20 cm20, start text, space, c, m, end text. How far did Chubby run? Round your answer to the nearest \text{cm}cmstart text, c, m, end text.

Answers

Answer:

63 cm

Step-by-step explanation:

If Chubby ran his wheel, which has a diameter of 20cm, we want to find its circumference - this will tell us how far Chubby has ran one one full rotation of the wheel.

The formula for the circumference of a circle is [tex]2\pi r[/tex], where r is the radius. We know the diameter is 20, which is double the radius, so the radius is [tex]20\div2=10[/tex] cm.

We can know substitute inside the formula:

[tex]2\cdot \pi \cdot10\\\\2\cdot 3.14 \cdot10\\\\ 6.28\cdot10\\\\62.8[/tex]

62.8 rounded to the nearest cm is 63.

Hope this helped!

Answer:

6280

Step-by-step explanation:

∠3 and ∠6 can be classified as:

Answers

Answer:

Alternate Interior Angles

Step-by-step explanation:

Since they are inside the parallel lines, Alternate Exterior Angles and any other similar theorems can be ruled out.

Since they are on opposite sides of each other, Corresponding Angles and any other similar theorems can be ruled out.

Since they are far apart from each other, Supplementary Angles, Adjacent Angles, Vertical Angles, and any other similar definitions can be ruled out.

Therefore, we are left with Alternate Interior Angles.

Answer:

angle 3 and angle 6 are

1) Alternate Angles

2) Interior Angles

Step-by-step explanation:

(see attached for reference)

please answer! I need these points for grade!

Answers

Answer:

∡NMO = 59°

Step-by-step explanation:

if MO bisect =>

=> ∡LMN = 2∡LMO =>

=> 5x - 22 = 2(x + 31)

5x - 22 = 2x + 62

5x - 2x = 62 + 22

3x = 84

x = 28°

∡LMO = ∡NMO => ∡NMO = x + 31

=> ∡NMO = 28 + 31 = 59°

Assume that a random sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level.

Answers

Answer:

Margin of Error = z∝/2 * Standard Error

Step-by-step explanation:

The formula for standard error is given by

SE = [tex]\sqrt{\frac{pq}{n} }[/tex]

Where p is the probability or proportion of success q=1-p and n is the number of trials or samples.

Now Margin of Error is given by

ME = z∝/2 * Standard Error

The confidence level is used to estimate the value of alpha.

For example 90% confidence means alpha= 1-0.9= 0.1 and alpha by 2 would be 0.05 . So the value for alpha by 2 would be 1.96

Which of the following points IS a solution to the system: y > - 3x + 4 / y > 2x / - y < 7 Selected answer is not correct.

Answers

Answer:

Solution : Third Option

Step-by-step explanation:

The first step here is to make all the signs uniform. As you can see the third inequality has a less than sign, which we can change to a greater than sign by dividing negative one on either side, making the inequality y > - 7.

[tex]\begin{bmatrix}y>-3x+4\\ y>2x\\ y>-7\end{bmatrix}[/tex]

Now take a look at the third option. Of course the y - coordinate, 3, is greater than - 7, so it meets the third requirement ( y > - 7 ). At the same time 3 > 1( 2 ) > 2, and hence it meets the second requirement as well. 3 > - 3( 1 ) + 4 > - 3 + 4 > 1, meeting the first requirement.

Therefore, the third option is a solution to the system.

Find the sum of the first 12 terms of the sequence 512, 256, 128, …

Answers

Answer: 1023.75 (a)

Step-by-step explanation:

The sequence is a Geometric progression with the common ratio of ¹/₂ and first term of 512.

a = 512, r = ¹/₂. To determine the ratio, just divide the second term by the first term.

Now to calculate the sum, we consider two formula here and select the one that is most appropriate,

(1)  a( rⁿ - 1 )/r - 1, when r is greater than 1

(2) a( 1 - rⁿ )/1 - rⁿ, when r is less than 1.

In this question, formula 2 shall be appropriate because r is less than 1.

so,

S₁₂      =  512( 1 - 0.5¹² )/1 - 0.5

             512( 1 - 2.44 ₓ 10⁻⁴ )/0.5

          = 512( 0,9998 )/0.5

          = 511.875/0.5

          = 1023.75

The answer is a

Write 4–6 sentences explaining why it is important to have precise definitions in mathematics.

Answers

Mathematics can be tricky so precise definitions are important. Without them there can be confusion which more often then not will generate a wrong answer. With clear precise definitions it is easier to understand the topic. Therefore, it is easier to get the correct answer.

wo independent samples have been selected, 100 observations from population 1 and 76 observations from population 2. The sample means have been calculated to be x⎯⎯⎯1=11.9 and x⎯⎯⎯2=12.9. From previous experience with these populations, it is known that the variances are σ21=27 and σ22=23. (a) Determine the rejection region for the test of

Answers

Answer:

[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]

Step-by-step explanation:

A test for the difference between two population means is to be performed.

As the population variances are known, the z-test will be used.

The hypothesis can be defined as follows:

H₀: μ₁ = μ₂ vs. Hₐ: μ₁ ≠ μ

Assume that the significance level of the test is, α = 0.05.

The critical region can be defined as follows:

The critical value of z for α = 0.05 is:

[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025} =-1.96\\\\z_{1-\alpha/2}=z_{1-0.05/2}=z_{0.975} =1.96[/tex]

Use a z-table.

[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]

You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the surface area of this box.

Answers

Answer:

20 by 20 by 20

Step-by-step explanation:

Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz ... 1

Given the volume V = xyz = 8000 ... 2

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x  + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.

The dimensions which minimize the surface area of this box is 20 *20* 20. This can be calculated by using surface area and volumes.

The calculation for total surface area:

Let the total surface of the rectangular box be expressed as:

S = 2xy + 2yz + 2xz

where,

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz .................(1)

Given:

Volume V = xyz = 8000 .............(2)

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x  + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since, Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20*20*20.

Find more information about Surface area here:

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The perimeter of a rectangular garden is 43.8 feet. It's length is 12.4t . What is it's width ?

Answers

Answer:5

Step-by-step explanation:

Complete each ordered pair so that it is a solution of the given linear equation.

x - 4y = 4; (_,3), (4,_)

Answers

Answer: (16,3)  and (4,0)

Step-by-step explanation:

Using the equation x-4y=4  is asking what is the value of x if the value of y is 3. So plot it into the equation and solve for x.

x-4(3)=4  multiply the left side

x - 12 = 4   add  12 to both sides

x= 16

You will now have the coordinates (16,3)  

In the second pair it gives the x coordinate which is 4 but we need to solve for y.  

4 - 4y=4  subtract 4 from both sides

-4        -4

 -4y = 0  Divide both sides by 4

    y = 0

The ordered pair will be (4,0)

Which expression is equivaleny to 0.7 + p + 0.86p?

A.1 + 1.56p
B.p + 1.56
C.2.56p
D. -0.84p

Answers

Answer:

None of the above.

1.86p + 0.7

Step-by-step explanation:

Step 1: Write expression

0.7 + p + 0.86p

Step 2: Combine like terms

0.7 + 1.86p

None of those answer choices are correct unless you wrote the problem incorrectly.

What fraction of a ton is a pound?

Answers

Answer:

There are 2000 pounds in a short ton. To convert short tons to pounds, multiply the ton value by 2000.

Answer:

5/100000 tons

Step-by-step explanation:

Use the gradient to find the directional derivative of the function at P in the direction of Q. g(x, y, z) = xye^z, P(2, 4, 0), Q(0, 0, 0)

Answers

Answer: Find answer in the attached files

Step-by-step explanation:

A teacher shares sweets among 8 students so they get 6 each. How many sweets would they each have got if there had been 12 students? ​

Answers

Answer:

4 sweets

Step-by-step explanation:

we know that there is a total of 48 sweets being handed out, and we can tell that this is an example of inverse proportion:

when one increases the other decreases

So, we multiply 8 * 6 to get 48, and then divide that by 12 to get 4 which is how many each student gets

for some constant k -> xy/z=k

Find the sum of all solutions to this equation : ((2x-4)/x+1)) * ((2x+8)/2) * ((2x-70)/(x+2)) =0

Answers

Answer:

x=0 or x=2 or x=−4 or x= (7)(2)

Step-by-step explanation:

|5x|=3 please help me

Answers

Answer: see below

Explanation:

|5x| = 3

5x = 3
x = 3/5

5x = -3
x = -3/5

x + y + z = -6 -2x – 2y – 2z = 12 5x + 5y + 5z = -30 find x y and z please

Answers

Answer:

  x = s, y = t, z = -6 -s -t

Step-by-step explanation:

These are dependent equations. For some values s and t, the solution is ...

  x = s, y = t, z = -6 -s -t

a function includes the points (4, -3) and (-9,4). what fraction in lowest terms represents the output value of this function for an input of zero

Answers

Answer:

  -11/13

Step-by-step explanation:

The equation of the line through these points can be written using the 2-point form of the equation of a line:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (4 -(-3))/(-9-4)/(x -4) -3

  y = (-7/13)x +28/13 -3

For x=0, the value of y is ...

  y = 28/13 -39/13 = -11/13

The output for an input of 0 is -11/13.

Jay is copying an angle. His work so far is shown below. Explain the importance of his next step, which is placing the point of the compass on L, opening the compass to N, and drawing an arc.


A. This ensures that when he draws another arc for angle Y, that it will be the right distance from point Z. <-- MY ANSWER


B. This arc is to make sure that both L and N are equidistant from M.


C. This arc makes sure that the distance from L to N is the same as the distance from Y to Z.


D. This way there will be two arcs drawn on both angles when he is done.

Answers

Answer:

  your answer is correct.

Step-by-step explanation:

For the purpose here, we'll call the missing point on the arc through Z point X.

Essentially, you want to make ΔXYZ ≅ ΔLMN by SSS. The construction so far ensures LM ≅ MN ≅ XY ≅ YZ. By copying the length LN to XZ, you ensure the congruence of the remaining sides of the triangles.

Then ∠XYZ ≅ ∠LMN because corresponding parts of congruent triangles are congruent.

In short, XZ needs to be the same distance as LN.

A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were made. At the end of an 8 year period, the balance in the account was $13231.30. What was the dollar amount of the initial deposit? Round your answer to the nearest dollar. Do not include a dollar sign ($) or comma in your answer.

Answers

Answer:

[tex]\large \boxed{\$10000.00}[/tex]

Step-by-step explanation:

We can use the formula for continuously compounded interest.

[tex]\begin{array}{rcl}A & = & Pe^{rt}\\13231.30& = & Pe^{0.035 \times 8}\\& = &Pe^{0.28}\\& = & P\times 1.3231298\\P & = &\dfrac{13231.30}{1.3231298}\\\\&=&\mathbf{10000.00}\\\end{array}\\\text{The initial deposit was $\large \boxed{\mathbf{\$10000.00}}$}[/tex]

A leaf blower was marked up 100% from an original cost of $152. If Eva bought the leaf blower and paid 7% sales tax, how much in total did she pay?

Answers

Answer:

$325.28

Step-by-step explanation:

152+152=304

304x1.07=325.28

Answer:

325.28

Step-by-step explanation:

increase the price by 100 %

152* 100%

152

Add this to the original price

152+152 = 304

Now find the sales tax

304 * 7%

304 * .07

21.28

Add this to the amount of the purchase price

304+21.28

325.28

A random sample of 1003 adult Americans was asked, "Do you pretty much think televisions are a necessity or a luxury you could do without?" Of the 1003 adults surveyed, 521 indicated that televisions are a luxury they could do without.

Requried:
a. Obtain a point estimate for the population proportion of adult Americans who believe that televisions are a luxury they could do without.
b. Verify that the requirements for constructing a confidence interval about p are satisfied.
c. Construct and interpret a 95% confidence interval for the population proportion of adult Americans who believe that televisions are a luxury they could do without.
d. Is it possible that a supermajority (more than 60%) of adult Americans believe that television is a luxury they could do without ? Is it likely?
e. Use the results of part (c) to construct a 95% confidence interval for the population proportion of adult Americans who believe that televisions are a necessity.

Answers

Answer:

a)0.519

b)requirements for constructing a confidence interval about p are satisfied.

c)0.488, and 0.550

d)yes this is because there is no possibility

that the true proportion is not captured in the confidence interval.

e)

0.450, 0.512

Step-by-step explanation:

a)The point estimate for the population proportion of adult Americans who believe that televisions are a luxury they could do without can be calculated as

521 of that adult that indicated that televisions are a luxury they could do without/1003 adults surveyed,

p = 521/1003

= 0.519.

b)

np(1-p)=1003×(0.519)×(1-0.519)

=250.39≥10 and the sample size is less than 5% of the population

therefore, requirements for constructing a confidence interval about p are satisfied.

c) we were given 95% confidence,

Then α=(1-0.95)

= 0.05

From the Z-tables,we can get the critical value is Z , which is (0.05/2) = Z (0.025) = 1.96

confidence interval can the be calculated using the formula below

- p ± Z*√ p (1 – p)/n

=0.519 ± 1.96√0.519×(1 – 0.519)/(1003)

= 0.519 ± 1.96×0.0158

0.519 ± 0.031

= 0.488, and 0.550

d) yes this is because there is no possibility

that the true proportion is not captured in the confidence interval.

e)the sample size can be calculated as

P=x/n

=(1003-521)/1003

=0.481

But we're given 95% confidence interval

Then

α=(1-0.95)=

0.05

From the Z-tables,we can get the critical value is Z , which is (0.05/2) = Z (0.025) = 1.96

Then convidence interval=

- p ± Z*√ p (1 – p)/n

=0.481 ± 1.96√0.481×(1 – 0.481)/(1003)

0.450, 0.512

12) A traffic control engineer reports that 75% of the vehicles passing through a checkpoint are from within the state. What is the probability that fewer than 4 of the next 9 vehicles are from out of state

Answers

Answer:

0.8343

Step-by-step explanation:

From the question, we have the following values:

Probability of vehicles that pass within the check point that are from within the state = 75% = 0.75

Probability of vehicles that pass within the check point that are from outsode the state = 100 - 75 = 25% = 0.25

P = 0.25

n = number of random variables = 9

The probability that fewer than 4 of the next 9 vehicles are from out of state is calculated as:

P < 4 = P ≤ 3

n = 9

P(x) = n!/(n - x)! x! × p^x × q^(n - x)

x = 3

p = 0.25

q = 0.75

P(x) = 9! /(9 - 3)! × 3! × 0.25^3 × 0.75^(9 - 3)

P(x) =0.8343

The probability that fewer than 4 (x<4) of the next 9 vehicles are from out of state is 0.83427.

Given information:

75% of the vehicles passing through a checkpoint are from within the state.

So, the probability that the vehicle is from within the state is 0.75.

The probability that the vehicle is from outside the state will be 1-0.75=0.25.

Now, let x be the random variable. So, the value of n=9. and x<4

It is required to calculate the probability that fewer than 4 of the next 9 vehicles are from out of state.

So, [tex]x< 4[/tex], p=0.25 and q=0.75.

So, the required probability can be calculated as,

[tex]P(x\le3) =\sum ^nC_x\times p^x \times q^{(n - x)}\\P(x\le3)=\sum\dfrac{n!}{(n - x)! x!} \times p^x \times q^{(n - x)}\\P(x\le3)= \dfrac{9!}{(9 - 3)! 3!} \times 0.25^3 \times 0.75^{(9 - 3)}+\dfrac{9!}{(9 - 2)! 2!} \times 0.25^2 \times 0.75^{(9 - 2)}+\dfrac{9!}{(9 - 1)! 1!} \times 0.25^1 \times 0.75^{(9 - 1)}+\dfrac{9!}{(9 - 0)! 0!} \times 0.25^0 \times 0.75^{(9 - 0)}\\P(x\le3)=0.83427[/tex]

Therefore, the probability that fewer than 4 of the next 9 vehicles are from out of state is 0.83427.

For more details, refer to the link:

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Y varies inversely with x. If Y=17 and k(The constant of variation) =76, what is x? Round to the nearest tenth if necessary.

Answers

Answer:

x ≈ 4.5

Step-by-step explanation:

Given y varies inversely with x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

Here k = 76 and y = 17 , thus

17 = [tex]\frac{76}{x}[/tex] ( multiply both sides by x )

17x = 76 ( divide both sides by 17 )

x ≈ 4.5 ( to the nearest tenth )

Which of the following best defines the midpoint of a segment? A. The point that splits a line segment into two equal parts. B. Any point on a line segment in between the two endpoints. C. When a line segment is split into equal thirds, a midpoint is any point in the middle third. D. Any point that is closer to one endpoint of the segment than the other.

Answers

Answer:

A. The point that splits a line segment into two equal parts.

Step-by-step explanation:

A. The point that splits a line segment into two equal parts.

Midpoint, as the word suggests, means the point which lies in the middle of something. The correct option is A.

What does a midpoint mean?

Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.

The statement that best describes the midpoint of a segment is the point that splits a line segment into two equal parts.

Learn more about Midpoint:

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32. Identify all real and non-real zeros of the function f(x) = x^3 + 5x^2 + 3x + 15.
options:

A. x = 0, −5, 1.7i, −1.7i

B. x = 0,−5, 1.7i

C. x = −5, 1.7i, −1.7i

D. x = 0,−3, −5

Answers

Answer:

x = -5 or x = i sqrt(3) or x = -i sqrt(3)

Step-by-step explanation:

Solve for x:

x^3 + 5 x^2 + 3 x + 15 = 0

The left hand side factors into a product with two terms:

(x + 5) (x^2 + 3) = 0

Split into two equations:

x + 5 = 0 or x^2 + 3 = 0

Subtract 5 from both sides:

x = -5 or x^2 + 3 = 0

x = (0 ± sqrt(0^2 - 4×3))/2 = ( ± sqrt(-12))/2:

x = -5 or x = sqrt(-12)/2 or x = (-sqrt(-12))/2

sqrt(-12) = sqrt(-1) sqrt(12) = i sqrt(12):

x = -5 or x = (i sqrt(12))/2 or x = (-i sqrt(12))/2

sqrt(12) = sqrt(4×3) = sqrt(2^2×3) = 2sqrt(3):

x = -5 or x = (i×2 sqrt(3))/2 or x = (-i×2 sqrt(3))/2

(2 i sqrt(3))/2 = i sqrt(3):

x = -5 or x = i sqrt(3) or x = (-2 i sqrt(3))/2

(2 (-i sqrt(3)))/2 = -i sqrt(3):

Answer: x = -5 or x = i sqrt(3) or x = -i sqrt(3)

Answer:

C. x = −5, 1.7i, −1.7i

Step-by-step explanation:

Quick answer:

C. x = −5, 1.7i, −1.7i

explanation:

C. is the only answer option that does NOT have 0 as a root, which is impossible, because there is a constant term, which means that all roots are non-zero. In other words, we cannot extract x as a factor.

Complete answer:

All odd degree polynomials have at least one real root.

By the real roots theorem, we know that

if there is a real root, it must be of the form [tex]\pm[/tex]p/q where q is any of the factors of the leading coefficient (1 in this case) and p is any factor of the constant term d (15 in this case).

Values of [tex]\pm[/tex]p/q are

On trial and error, using the factor theorem, we see that

f(-5) = 0, therefore -5 is a real root.  By long division, we have a quotient of x^2+3 = 0, which gives readily the remaining (complex) roots of +/- sqrt(5) i

The answer is {-5, +/- sqrt(5) i}, or again,

C. x = −5, 1.7i, −1.7i

what is 76.32 divided by 24.98 using compatible numbers to estimate each quotient?

Answers

Answer:

Approximately 3.05

Step-by-step explanation:

Using "compatible numbers" we can simply round these numbers to integer values.  Let's make 76.32 => 76 and 24.98 => 25

So from here let's do 76/25 to get 3 R 1/25

1/25 as a decimal is .04

So far, we have 3.04.  Going back to Look at our decimals, .32 and .98, there is a larger difference in our down rounding with the .32 than the up rounding from our .98.  So we should consider an extra value in our decimal.

Considering our whole number of 3.0, we can assume that our rounding will have an increase of about .01 or .015 in error.

Thus our number will be 3.04 + .01.

Making our quotient approximately 3.05.

Cheers.

What is the x-intercept?

Answers

Answer: x-intercept = -94, -74, and -54

Suppose we want to test the color distribution claim on the M&M’s website that a bag of plain M&M’s is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown. We select a sample of 400 plain M&M’s and found the following: Color Blue Orange Green Red Yellow Brown Frequency 30 48 55 66 70 131
Is there evidence to doubt the color distribution claimed by the website? Use =0.05

Answers

Answer:

Calculated χ² = 13.425

χ² (5,0.025) >14.45 and χ²(5,0.975) <1.24

The given data does not fall in the critical region so we accept H0 and conclude there is no evidence to doubt the color distribution claimed by the website.

Step-by-step explanation:

Color             Blue      Orange     Green    Red   Yellow    Brown

Frequency     30         48              55        66         70         131

Expected      40           40              40        80          80        120

H0:  The bag of plain M&Ms is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown

Ha: The color distribution is not equal to  the distribution stated in the null hypothesis.

Calculate chi square

χ² = (30-40)² /40 + (48-40)²/40 + (55-40)²/40 + (66-80)²/80 + (70-80)²/80 + (131-120)²/120

χ² = 2.5 + 1.6 + 5.625 + 2.45 + 1.25= 13.425

The critical region for χ²  for 5 degrees of freedom with ∝= 0.05 is

χ² (5,0.025) >14.45 and χ²(5,0.975) <1.24

The given data does not fall in the critical region so we accept H0 and conclude there is no evidence to doubt the color distribution claimed by the website.

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