A study1 conducted in July 2015 examines smartphone ownership by US adults. A random sample of 2001 people were surveyed, and the study shows that 688 of the 989 men own a smartphone and 671 of the 1012 women own a smartphone. We want to test whether the survey results provide evidence of a difference in the proportion owning a smartphone between men and women.

Let group 1 be US men and let group 2 be US women.

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1Anderson M, "The Demographics of Device Ownership," pewresearch.org, October 29, 2015.

(a) State the null and alternative hypotheses. Your answer should be an expression composed of symbols: =,≠,<,>,μ,μ1,μ2,p,p1,p2,rho,p^,p^1,p^2,r.

H0: vs Ha:Edit

(b) Give the notation for the sample statistic.

p1-p2

p^1-p^2

μ1-μ2

x-1-x-2

rho1-rho2

r1-r2

(c) Give the value for the sample statistic.

Value: Enter your answer in accordance to the question statement the absolute tolerance is +/-0.003

(d) In the sample, which group has higher smartphone ownership: men or women?

Women

Men

(e) Use StatKey or other technology to find the p-value.

Round your answer to three decimal places.

p-value = Enter your answer in accordance to the question statement the absolute tolerance is +/-0.03

Answer:d= -1/8

Step-by-step explanation: hope this helps!

Answer:

d = 31/8 or 3 and 7/8

Step-by-step explanation:

1/2(2d - 3/4) + 2/5 = 4d/5

Distribute the 1/2 to the numbers in the parentheses

d - 3/8 + 2/5 = 4d/5

Combin the 3/8 and 2/5 by finding a common denominator

d - 31/40 = 4d/5

Multiply the 5 to cancel it out

5d - 31/8 = 4d

Move the 5d over

-31/8 = -d

Divide by -1 to make the -d positive

d = 31/8 or 3 7/8

The correct answer is e. You reject the null hypothesis that ρ is 0. Rejecting the null hypothesis indicates that there is a statistically significant correlation between the variables. This implies that changes in one variable (x) are associated with changes in the other variable (y), and the relationship is not due to random chance.

The significance of the correlation coefficient is determined by conducting a hypothesis test, typically using a t-test or an F-test. The test compares the observed correlation coefficient (r) with the expected value of zero under the null hypothesis. If the calculated test statistic exceeds the critical value at a chosen significance level (e.g., 0.05), the null hypothesis is rejected, indicating a significant correlation.

It is important to note that a significant correlation does not imply causation (option a). It simply suggests a strong statistical association between the variables, indicating that they tend to vary together.

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Answer:

0.125

Step-by-step explanation:

Becuase math

Your answer would be 1/x^2 -6

Answer: Answer:the person entering the room is 10 years oldStep-by-step explanation:x / 5 = 40x = 40 * 5x = 200so the total of all the ages of 5 people

Step-by-step explanation:

Answer:

bottom one

Step-by-step explanation:

x+3y>6  and y>2x+4

Compared with the beam, the large cube has the same volume but a smaller surface area.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

Given that, there are two sets of eight blocks, each with an edge measurement of 1 cm. Two blocks are placed on top of two other blocks to form a big cube. You assemble the second set into a 1-by-8-block straight beam.

Since the volume is the same.

The surface area of a cube,

=6a²

=6(2)²

=6×4

=24 cm²

The surface area of a beam,

=1 × 8

=8 cm²

Thus, compared with the beam, the large cube has the same volume but a smaller surface area.

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Answer:

The correct answer is D.

Step-by-step explanation:

According to the Pythagorean Theorem, the legs of a right triangle squared and added together is equivalent to the hypotenuse squared. To solve for x, you can use any of the two right triangles. Each of the bottom legs of the right triangles is 9 units since the two right triangles are congruent, so now we apply the Pythagorean Theorem to solve for x. \(x^2+9^2=19^2\) ⇒ \(x^2+81 = 361\) ⇒ \(x^2 = 280\) ⇒ \(x = \sqrt{280}\) ⇒ \(x = \sqrt{4 * 70}\) ⇒ \(x = \sqrt{4} * \sqrt{70}\) ⇒ \(x = 2\sqrt{70}\).

Answer:

There is no separation (distance) between the first y-intercept (6) and the second (6).

Step-by-step explanation:

We'll assume that the table shows points on a straight line.

If we go from x = 2 to x = 8 (an increase of 6), the corresponding y values go from y =2 to y = -10 (a decrease of 12).  Thus, the slope of the line represented by the table is

m = rise / run = -12/6, or m = -2.

We need to find the equation of the line represented by the table, so that we can know the y-intercept.  Start with y = mx + b and substitute -2 for m:

y = -2x + b.  We arbitrarily choose an ordered pair from the table, such as (11, -16).  Here we substitute 11 for x and -16 for y:

-16 = -2(11) + b, or

-16 = -22 + b, which yields b = 6.

This is the same y-intercept as the '6' in the given f(x) = -2x + 6.  So:  There is no separation (distance) between the first y-intercept (6) and the second (6).

Step-by-step explanation:

A= πr^2

A = 8^2×π=64π= 201.06 ft^2

The number of nickels are 8.5 which was calculated by using the given data.

Word problems frequently involve mathematical modelling issues in which data and knowledge about a specific system are provided and a learner is asked to construct a model.

Given: A boy has three more nickels than dimes.

Let, x = number of dimes

Number of nickels = x + 3

He would have spent a quarter of his money if he had spent three nickels and three dimes.

x + 3 + 3x = 25

4x = 25 - 3

x =22/4

x = 5.5  

So, number of dimes = 5.5

number of nickels = x + 3 = 5.5 + 3 =8.5

Therefore, the number of nickels are 8.5 which was calculated by using the given data.

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Answer:

420 hg = __4200000___ cg

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

took the test

Answer:

Option C is the correct answer

\( x = 34 \\y=17\sqrt3\)

Step-by-step explanation:

\( \sin \: 30 \degree = \frac{17}{x} \\ \\ \frac{1}{2} = \frac{17}{x} \\ \\ x = 17 \times 2 \\ \\ x = 34 \\ \\ \tan \: 30 \degree = \frac{17}{y} \\ \\ \frac{1}{ \sqrt{3} } = \frac{17}{y} \\ \\ y = 17 \sqrt{3} \)

(a) In trade equilibrium, the consumption point for the Home consumer can be shown on a graph where wheat is on the x-axis.

(b) If the world relative price increases above 2/3, the Foreign consumer's utility will decrease compared to the benchmark trade equilibrium with a world price of 2/3.

a, Since the relative price of wheat to cloth is 2/3, the Home consumer's consumption point will lie on a budget line with a slope of -2/3. The specific coordinates of the consumption point cannot be determined without additional information about preferences and the Home consumer's budget constraint.

To show that an increase in the relative price of wheat from 2/3 raises Home's utility, we need to consider the concept of substitution effect. When the relative price of wheat increases, it becomes relatively more expensive compared to cloth. The Home consumer will respond by consuming less wheat and more cloth, moving along the budget line to a new consumption point. This movement is driven by the substitution effect, where the consumer substitutes away from the now relatively more expensive wheat towards the relatively cheaper cloth. Since the Home consumer's preferences and utility are not known, the specific utility level cannot be quantified, but it can be concluded that the utility increases due to the substitution effect.

b.  In the benchmark equilibrium, the Foreign consumer maximizes utility given the initial relative price. If the relative price increases, it means that wheat becomes relatively more expensive compared to cloth in the world market.

As a result, the Foreign consumer will have to consume less wheat and more cloth in order to remain on the same budget line. This movement along the budget line leads to a decrease in utility because the consumer has to give up some desired wheat consumption to obtain more cloth. The magnitude of the utility decrease depends on the specific preferences and utility function of the Foreign consumer, but it can be concluded that the utility will be lower when the relative price of wheat increases above 2/3 in the world market.

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The solution to the given differential equation is: x⁷ cos y = y + C

where C is the constant of integration

To solve the given differential equation:

\(\[7x^6\cos y dx - dy = 0\]\)

We can separate the variables and integrate both sides.

Separating variables, we can write the equation as:

\(\[7x^6\cos y dx = dy\]\)

Now, we can integrate both sides with respect to their respective variables:

\(\[\int 7x^6\cos y dx = \int dy\]\)

Integrating the left side:

\(\[\int 7x^6\cos y dx = 7 \int x^6 \cos y dx\]\)

To integrate \(\(x^6 \cos y\)\)with respect to x, we can use integration by parts.

Let's take u = x⁶ and \(\(dv = \cos y dx\)\).

Differentiating u with respect to \(\(x\) gives \(du = 6x^5 dx\).\)

Integrating dv with respect to x gives \(\(v = \int \cos y dx = \cos y \cdot x\).\)

Applying the integration by parts formula:

\(\[\int x^6 \cos y dx = u \cdot v - \int v \cdot du\]\)

Substituting the values:

\(\[\int x^6 \cos y dx = x^6 \cdot \cos y \cdot x - \int (\cos y \cdot x) \cdot (6x^5 dx)\]\)

Simplifying:

\(\[\int x^6 \cos y dx = x^7 \cos y - 6 \int x^6 \cos y dx\]\)

Moving the integral term to the left side:

\(\[7 \int x^6 \cos y dx = x^7 \cos y\]\)

Dividing both sides by 7:

\(\[\int x^6 \cos y dx = \frac{x^7 \cos y}{7}\]\)

Now, substituting this result back into our original equation:

\(\[7 \int x^6 \cos y dx = dy\]\)

\(\[\frac{7x^7 \cos y}{7} = dy\)

Simplifying:

x⁷ cos y = dy

Finally, the solution to the given differential equation is:

x⁷ cos y = y + C

where C is the constant of integration.

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a) The vertex-form definition of the quadratic function is given as follows: y = 1/3(x - 3)² + 5.

b) The rider's minimum height above the ground is of: 5 meters,

c) The horizontal distance is given as follows: x = 0 m and x = 6 m.

The quadratic function in the context of this problem is defined as follows:

y = x²/3- 2x + 8.

In which:

The coefficients are given as follows:

a = 1/3, b = -2, c = 8.

The x-coordinate of the vertex is given as follows:

x = -b/2a = -(-2)/(2/3) = 3.

Hence the y-coordinate of the vertex is given as follows:

y = (3)²/3 - 2(3) + 8 = 5 meters.

Hence the vertex-form definition of the equation is given as follows:

y = 1/3(x - 3)² + 5.

As the function is concave up, the minimum height is of 5 meters.

For the horizontal distance at a height of 8m, we have that:

x²/3 - 2x + 8 = 8

x²/3 - 2x = 0

x(x/3 - 2) = 0.

Hence:

x = 0 m and x = 6 m.

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Answer:

The missing dimension, radius = 6.00 m

Step-by-step explanation:

We are given the following things:

Height of cylinder, \(h\)  = 15 m

Radius of cylinder, \(r = z\) m (Labelled as \(z\))

Volume of cylinder, \(V = 1696.5\ m^{3}\)

Please refer to the image attached for the dimensions of cylinder as given.

We know that the volume of a cylinder can be given as:

\(V = \pi r^{2} h\)

Where \(r\) is the radius of cylinder

\(h\) is the height of cylinder

Putting the values of \(V, r \text{ and } h\):

\(1696.5 = \pi z^{2} \times 15\\\Rightarrow z^{2} = 36.01\\\Rightarrow z = 6.00\ m\)

Hence, The missing dimension, radius = 6.00 m

Answer:

1) 20

2) -10

Step-by-step explanation:

1) 2x + 3y² =

2(4) + 3(-2)² =

8 +3(4)=

8 + 12 =

20

2) -5(x + y) =

-5(4 + -2) =

-5(2) =

-10

Answer:

we just need to put the values of x,y,z to

x = 4

y = -2

z = 7

1) 2x + 3\(y^{2}\)

  2(4) + 3(\(-2^{2}\))

  8 + 3 (4)

  8 + 12

 = 20

2) -5(x+y)

   -5 (4 + (-2))

   -5 (4 -2)

   -5 (2)

    = -10

Therefore, the probability mass function of N is:

\(P(N=3) = p*(1-p)\\P(N=4) = p*p*(1-p) + (1-p)*(1-p)*p\\P(N=5) = p*p*p*(1-p) + (1-p)*(1-p)*(1-p)*p + 2*p*(1-p)*p*(1-p)\\P(N=6) = p*p*p*p*(1-p) + (1-p)*(1-p)*(1-p)*(1-p) + 3*p*p*(1-p)*(1-p) + \    \ \ \  2*p*(1-p)*p*p*(1-p) + 2*p*p*(1-p)*p*(1-p) \\\)

And so on, for larger values of N.

To find the probability mass function of N, we need to consider the two cases mentioned in the question.

Case 1: A sequence of events followed by an odd.
For this case, the probability of rolling an even number on the first roll is p. The probability of rolling the same even number on the second roll is also p. The probability of rolling an odd number on the third roll is (1-p) because the even numbers have been exhausted. So, the probability of this specific sequence of rolls occurring is p*p*(1-p).

Case 2: A sequence of odds followed by an even.
For this case, the probability of rolling an odd number on the first roll is 1-p. The probability of rolling the same odd number on the second roll is also 1-p. The probability of rolling an even number on the third roll is p because the odd numbers have been exhausted. So, the probability of this specific sequence of rolls occurring is (1-p)*(1-p)*p.

We can then find N's overall probability mass function by adding the probabilities of all possible sequences that lead to observing both an even and an odd number.

The smallest value in support of N must be 3, since it takes at least 3 rolls to observe both an even and an odd number.

Therefore, the probability mass function of N is:

\(P(N=3) = p*(1-p)\\P(N=4) = p*p*(1-p) + (1-p)*(1-p)*p\\P(N=5) = p*p*p*(1-p) + (1-p)*(1-p)*(1-p)*p + 2*p*(1-p)*p*(1-p)\\P(N=6) = p*p*p*p*(1-p) + (1-p)*(1-p)*(1-p)*(1-p) + 3*p*p*(1-p)*(1-p) + \    \ \ \  2*p*(1-p)*p*p*(1-p) + 2*p*p*(1-p)*p*(1-p) \\\)

And so on, for larger values of N.

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Answer:

The answer is 48

Step-by-step explanation:

Have a nice day

a² + b² = c²

50² + 51² = c²

2500 + 2601 = c²

5101 = c²

√5101 ≈ 71.42 cm.

Answer: Area of the rectangle = 102.5 cm²  Round to 103 cm²

Step-by-step explanation:

The diagonal is the hypotenuse, c So subtract the square on the base (length) to find the altitude (height).

a² + b² = c²

a² + 50² = 51²

a² = 51² - 50²

a² = 2601 -2500

a² = 101  take the square root of both sides

a = √101

a = 10.04987562  Round to 10.05

Area = LW

Area = 50 × 10.05

Area = 102.5 cm²  Round to 103 cm²

The gradient vector field of function f(x,y) is given as follows:

grad(f(x,y)) = (1 + 9xy)e^(9xy) i + 9x²e^(9xy) j.

The gradient vector field of a function

Suppose that  a function defined as follows:

f(x,y).

The gradient function is defined considering the partial derivatives of function f(x,y), as follows:

grad(f(x,y)) = fx(x,y) i + fy(x,y) j.

The gradient of a function is a vector field. It is obtained by applying the vector operator V to the scalar function f(x, y). Such a vector field is called a gradient (or conservative) vector field.

In which:

fx(x,y) is the partial derivative of f relative to variable x.

fy(x,y) is the partial derivative of f relative to variable y.

The function in this problem is defined as follows:

f(x,y) = xe^(9xy).

The partial derivative relative to x  as follows:

fx(x,y) = e^(9xy) + 9xye^(9xy) = (1 + 9xy)e^(9xy).

The partial derivative relative to y  as follows:

fy(x,y) = 9x²e^(9xy).

Hence the gradient vector field of the function is defined as follows:

grad(f(x,y)) = (1 + 9xy)e^(9xy) i + 9x²e^(9xy) j.

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Answer:

Step-by-step explanation:

Sorry I can't explain how it is done. It is very difficult to explain on paper.

The given problem can be solved by using Malus Law. According to Malus Law, the intensity of the light transmitted through a polarizing sheet is equal to the product of the intensity of incident light.

The square of the cosine of the angle between the polarizing axis and the transmission axis. Let the intensity of the incident light be I. Then the intensity of light transmitted through the first polarizing sheet is I. 1) Intensity of light transmitted through the second polarizing sheet is Icos²(24º)

2) Intensity of light transmitted through the third polarizing sheet is Icos²(9º)3) The percentage of light transmitted through the third polarizing sheet relative to the first one is:T = [Icos²(9º)] / [I] = cos²(9º)×100% = 92.24% ≈ 92%Thus, the percentage of light transmitted through the third polarizing sheet relative to the first one is approximately 92%.

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Answer:

add the lengths of each side of the shape. If there are units, include units in your final result.

Step-by-step explanation:

add the lengths of each side of the shape. If there are units, include units in your final result.

Answer:

add up all of the sides. hope this helps!

Step-by-step explanation:

Perimeter is a one-dimensional measurement that represents the distance around a closed geometric figure or shape (no gaps). To find perimeter, add the lengths of each side of the shape. If there are units, include units in your final result.