The report "The New Food Fights: U.S. Public Divides Over Food Science" states that younger adults are more likely to see foods with genetically modified ingredients as being bad for their health than older adults. This statement is based on a representative sample of 178 adult Americans aged 18 to 29 and a representative sample of 427 adult Americans aged 50 to 64. Of those in the 18 to 29 age group, 48% said they believed these foods were bad for their health, while only 3% of those in the 50 to 64 age group believed this.
(a) Are the sample sizes large enough to use the large-sample confidence interval to estimate the difference in the population proportions? Yes Y Let - 0.48 and p =0.38, -178 and 1 = 427, where the 1 subscript indicates the age 18-29 group and the 2 subscript indicates the age 50-64 group. Since 654 n (1-P) = 92.56 - 162.26 and 2(1-2) 264.74 are all at least 10, the sample sizes are large enough to use the large-sample confidence interval
(b) Estimate the difference in the proportion of adult Americans aged 18 to 29 who believe the foods made with genetically modified ingredients are bad for their health and the corresponding proportion for adult Americans aged 50 to 64. Use a 90% confidence interval. (Use Pi - P2. Use a table or technology. Round your answers to four decimal places.) (0.02545 x 0.17083 x )
(c) Is zero in the confidence interval? Yes No What does this suggest about the difference in the two population proportions?

Answer:

{2.3, 5.0, 7.5, 10.0, 12.5} Option b

Step-by-step explanation:

Domain is the input values and the range is the output values. The y values.

Answer:

b

Step-by-step explanation:

Answer:

letter D

:)

Step-by-step explanation:

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

If y and x have a proportional relationship, then we can write an equation of the form y = kx, where k is a constant of proportionality.

To find the value of k, we can use the given values of y and x:

y = kx

24 = k(12)

k = 2

Now that we know k, we can use the equation to find the value of y when x=16:

y = kx

y = 2(16)

y = 32

Therefore, when x=16, y=32.

The measure of Angle C is approximately 26°.

A, B, C are vertices of a triangle, where AB = 8 cm, BC = 6 cm. To determine the measure of angle C, we need to use the cosine rule.

The cosine rule states that the square of one side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides and the cosine of the angle between them.

Mathematically, we can represent it as follows:a² = b² + c² - 2bc cos(A)where a is the side opposite to angle A, b is the side opposite to angle B, c is the side opposite to angle C.

In this case, we have AB = c = 8 cm, BC = a = 6 cm, and AC = b. We need to find the measure of angle C, which is represented as cos(C).

Using the cosine rule, we can write the equation as follows:$$\begin{aligned} b^2 &= c^2 + a^2 - 2ca\cos(C) \\ \Right arrow b^2 &= 8^2 + 6^2 - 2 \times 8 \times 6 \cos(C) \\ \Right arrow b^2 &= 64 + 36 - 96 \cos(C) \\ \Right arrow b^2 &= 100 - 96 \cos(C) \end{aligned}$$We know that b is a positive length. Hence, b² > 0 or 100 - 96 cos(C) > 0. Solving for cos(C),  

we get: cos(C) < 100/96cos(C) < 1.0417Using a calculator, we can determine the inverse cosine of 1.0417 as:cos⁻¹(1.0417) = 0.4569 radians = 26.201° (rounded to the nearest degree)

Therefore, the measure of angle C is approximately 26°.

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Answer:

C. No correlation

Step-by-step explanation:

From the given scatter plot, it has no correlation. Therefore, option C is the correct answer.

Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.

Correlations in a scatter plot:

Therefore, option C is the correct answer.

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Answer:

it means the middle of the points

Step-by-step explanation:

Answer:

The midpoint is halfway between the two end points, halfway between the two x values

Step-by-step explanation:

Complete question :

The American Automobile Association (AAA) reports that of car accidents, 56% are caused by aggressive driving. If 3 accidents are chosen at random, find the probability for the following. Please round the final answers to 2 or 3 decimal places.

None are caused by aggressive driving.

At least 1 is caused by aggressve driving

Answer:

P(none caused by aggressive driving ) = 0.085184

P(atleast one caused by aggressive drive) = 0.914816

Step-by-step explanation:

Given:

Percentage accidents caused by aggressive driving = 56%

Hence,

Probability that an accident is caused by aggressive driving : p(aggressive) = 0.56

p(not aggressive) = 1 - p(aggressive)

p(not aggressive) = 1 - 0.56 = 0.44

A.) If 3 accidents are chosen at random ; probability that none is caused by aggressive driving :

Independent probability :

1st accident * 2nd accident * 3rd accident

P(not aggressive) * p(not aggressive) * p(not aggressive)

0.44 * 0.44 * 0.44 = 0.085184

B.) probability that atleast one is caused by aggressive driving :

Probability that atleast 1 is caused by aggressive driving = (1 - probability that none is caused by aggressive driving)

= 1 - 0.085184 = 0.914816

Answer: w=−xy+x/y

Step-by-step explanation:

Let's solve for w.

w=

x

y

−x

Step 1: Multiply both sides by y.

wy=−xy+x

Step 2: Divide both sides by y.

wy

y

=

−xy+x

y

w=

−xy+x

y

Answer:

$240

Step-by-step explanation:

The new price of the video game system is 300*1/5, which is $60. Since we want the money saved, we do 300-60, which is 240

Answer:

Step-by-step explanation:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144,233,377,610,987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, ... Can you figure out the next few numbers?

Answer:

b) Inductive

Step-by-step explanation:

It is correct to say that this is an example of inductive reasoning, because the reasoning is based on a situational perception and not on actual logic. Sarah based her reasoning on a premise that if she and her brothers have brown hair, then if she had another brother, he would also have brown hair.

Answer:

15

Step-by-step explanation:

A÷B= H (Area divided by base equals height)

315÷21= 15

Answer:

height = 15

Step-by-step explanation:

Area of a parallelogram: Base * height

Plug in the values we know.

21 * height = 315

Divide both sides by 21

height = 15

Question 24 :

P594.65 : 35 days

P594.65/7 : 35/7 days

P84.95 : 5 days

⇒ A. P84.95

Question 25 :

88.75 + 85.5 + 90.5 + 87.25 / 4

352/4

88

⇒ B. 88

Question 26 :

I = P × r × t

I = 580.00 × 0.065 × 1

I = P37.70

⇒ B. P37.70

Considering the definition of distance between two points, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

The distance between two points is equal to the length of the segment that joins them. Therefore, to determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of said squares.

In other words, the distance between two points in space is the magnitude of the vector formed by said points.

So, given the coordinates of two distinct points (x1, y1) and (x2, y2), the distance between two points is the square root of the sum of the squares of the difference of the coordinates of the points:

distance= \(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)

In this case, you know:

Replacing in the definition of distance:

distance= \(\sqrt{(5-(-2))^{2} +(-4-1)^{2} }\)

distance= \(\sqrt{(5+2)^{2} +(-5)^{2} }\)

distance= \(\sqrt{7^{2} +(-5)^{2} }\)

distance= \(\sqrt{49+25 }\)

distance= √74= 8.6023

Finally, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.

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Answer:

48,236.7

Step-by-step explanation:

40,000 + 8,000 + 200 + 30 + 6 + 7/10

7/10 can also be written .7

Answer:

true

Step-by-step explanation:

got it right in my lesson

Step-by-step explanation:

The equation being

D = -65m

They provides us with m

We can plug it in to find out the value of D

The first one is 0

D = -65(0) = 0m

The second is 1

D = -65(1) = -65m

And the last one is 2

D = -65(2) = -130m

Answer:

We failed to reject H₀

Z > -1.645

-1.84 > -1.645

We failed to reject H₀

p > α

0.03 > 0.01

We do not have significant evidence at a 1% significance level to claim that less than 40% of U.S. cell phone owners use their phones for most of their online browsing.

Step-by-step explanation:

Set up hypotheses:

Null hypotheses = H₀: p = 0.40

Alternate hypotheses = H₁: p < 0.40

Determine the level of significance and Z-score:

Given level of significance = 1% = 0.01

Since it is a lower tailed test,

Z-score = -2.33 (lower tailed)

Determine type of test:

Since the alternate hypothesis states that less than 40% of U.S. cell phone owners use their phone for most of their online browsing, therefore we will use a lower tailed test.

Select the test statistic:  

Since the sample size is quite large (n > 30) therefore, we will use Z-distribution.

Set up decision rule:

Since it is a lower tailed test, using a Z statistic at a significance level of 1%

We Reject H₀ if Z < -1.645

We Reject H₀ if p ≤ α

Compute the test statistic:

\($ Z = \frac{\hat{p} - p}{ \sqrt{\frac{p(1-p)}{n} }} $\)

\($ Z = \frac{0.31 - 0.40}{ \sqrt{\frac{0.40(1-0.40)}{100} }} $\)

\($ Z = \frac{- 0.09}{ 0.048989 } $\)

\(Z = - 1.84\)

From the z-table, the p-value corresponding to the test statistic -1.84 is

p = 0.03288

Conclusion:

We failed to reject H₀

Z > -1.645

-1.84 > -1.645

We failed to reject H₀

p >  α

0.03 > 0.01

We do not have significant evidence at a 1% significance level to claim that less than 40% of U.S. cell phone owners use their phones for most of their online browsing.

Therefore , the solution of the given problem of function comes out to be g(x) (-1)ⁿ (n+2)!/n! (9ⁿ⁻²) xⁿ.

On the midterm exam, there will be a variety of questions on each topic, including questions about both made-up and actual locations as well as numerical variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.

Here,

With x = 0, we can use the formula for the geometric series to represent the function g(x) = 1/(9+x)3 as a power series:

=> 1 / (1 - t) =∑ (n = 0 to n) t

where |t|  1 and t is some integer.

In this instance, we have:

=>  g(x) = 1/(9+x)³ = \((1/9)^{3}\) \((1+(-x/9))^{-3}\)

So, using the above calculation and the value of t = -x/9, we can write:

=>  G(x) = (1/9)3 n(x/9) (n=0 to infinite)

If we condense this phrase, we get:

=>  (n=0 to infinite) = g(x) \((-1)^{n}\) (n+2)!/n! (\(9^{n-2}\)) \(x^{n}\)

Thus, the power series expansion for g(x) with the origin at x = 0 is as follows:

=> (n=0 to infinite) = g(x) (-1)ⁿ (n+2)!/n! (9ⁿ⁻²) xⁿ

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Answer:

1/4

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

You're trying to figure out how many more hours he needs to work in order to have worked for 240 hours.

Answer:

Step-by-step explanation:

208

Crew because 23>8 23 is larger than 8

Magnitude=A great size, or extent of something

Answer: A

In looking for solutions in the graph of y=f(x) where f(x) = 0, you're looking for the x-intercepts.  The catch is that you only want the x-value of the intercepts.

The intercepts are (-4,0) and (7,0), so the solutions are -4 and 7.

The hundredth term of the given sequence is 388.

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given that, we need to find the 100th term in the sequence an= 4n-12,

Put n = 100,

a₁₀₀ = 4 x 100 - 12

= 400 -12

= 388

Hence the hundredth term of the given sequence is 388.

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Answer:

Tommy has 12 slices

Step-by-step explanation:

1. You have 4 cakes, and it says to cut it into thirds.

2. So, each cake gets cut into three pieces.

3a. Now you have 12 pieces (or slices!) of cake.

3b. From cutting the cakes into three pieces, you could also just multiply the 4 cakes by 3 (the number of slices), and you would get 12, the answer.

Answer:

I'm pretty sure the answer is B

Step-by-step explanation:

Hope this helped :) Sorry if its wrong

Answer:

b

Step-by-step explanation:

I like to think of it as this:

If the circle is filled, it is \(\leq or \geq \\\) (more)

If not, it's < or >

The arrow points in the direction the line is going.

In this graph, the line is going to the left. So is the symbol.