A cell phone manufacturer would like to estimate the mean difference in battery lifespan for a phone in full-power
versus power-saver mode. they randomly select eight phones and determine the battery lifespan, in hours, for each
phone using each power mode. the data are displayed in the table.
phone
full power
low power
1
8.25
14
2
8
15.5
3
8.5
13.5
4
8.5
14.25
5
8.25
15.25
6
9
13.75
7
8.5
14.5
8
8.25
15
what is the mean difference (low - full) and the standard deviation of the differences?
did=5.875. si=0.899
dir = 5.875. dift = 0.961
*dit = 6,063, sdir=0.899
ditt = 6,063, 5#=0.961

There are 1,443,600 ways to draw three names for first, second, and third prize from a pool of 112 people.

To determine the number of ways to draw three names for first, second, and third prize from a pool of 112 people, we can use the permutation formula.

The number of permutations of n objects taken r at a time is given by:

P(n, r) = n! / (n - r)!

where n! represents the factorial of n (the product of all positive integers up to n).

For this problem, we want to find the number of ways to draw three names out of 112, without replacement and with regard to the order in which they are drawn (i.e., the first name drawn is for first prize, the second name drawn is for second prize, and the third name drawn is for third prize). Therefore, we can use the permutation formula to obtain:

P(112, 3) = 112! / (112 - 3)!

= 112! / 109!

= 112 x 111 x 110

= 1,443,600

Therefore, there are 1,443,600 ways to draw three names for first, second, and third prize from a pool of 112 people.

To know more about prize refer here

https://brainly.com/question/27682388#

#SPJ11

The graph that best represents  the solution to the following pair of equations
y = 2x − 17

y = −2x + 3

Is option B.

Since y equals both of the expressions the expressions equal each other

2x - 17 = -2x + 3

Now you solve it algebraically

Add 2x to both sides

4x - 17 = 3

Add 17 to both sides

4x = 20

Divide both sides by 4

x = 5

Now you x into one of the original equations to get y

y = 2(5) - 17

Multiply

y = 10 - 17

Subtract

y = -7

Now you are looking for lines where they intersect at point (5, -7), which is Option (B)

Learn more about Graph at:

https://brainly.com/question/25184007

#SPJ1

Full Question:

Although part of your question is missing, you might be referring to this full question:

Which graph best represents the solution to the following pair of equations?

y = 2x − 17

y = −2x + 3

The cross product of a = 8, 0, −2 and b = 0, 9, 0 is 18, 0, 72.

The cross product of two vectors a and b is given by:

a × b = |a| |b| sinθ n

where |a| and |b| are the magnitudes of vectors a and b, θ is the angle between them, and n is a unit vector perpendicular to both a and b in the direction given by the right-hand rule.

Given a = 8, 0, −2 and b = 0, 9, 0, we have:

|a| = √(8² + 0² + (-2)²) = √68 = 2√17

|b| = √(0² + 9² + 0²) = 3√2

The angle between a and b is 90 degrees since they are perpendicular.

So, sinθ = sin(90°) = 1

A unit vector n in the direction of a × b can be found by:

n = (a × b) / |a × b|

where |a × b| is the magnitude of a × b.

Now, we can find a × b:

a × b = |a| |b| sinθ n

= (2√17)(3√2)(1) n

= 6√34 n

To find n, we first need to find a × b in component form:

a × b = (a₂b₃ - a₃b₂)i - (a₁b₃ - a₃b₁)j + (a₁b₂ - a₂b₁)k

= (-18)i - (-16)j + 0k

= -18i + 16j

The magnitude of a × b is:

|a × b| = √((-18)² + 16²) = 2√170

Therefore, a unit vector n in the direction of a × b is:

n = (a × b) / |a × b|

= (-18i + 16j) / (2√170)

= (-9/√170)i + (8/√170)j

Thus, we have:

a × b = 6√34 (-9/√170)i + 6√34 (8/√170)j

= -54/17 i + 48/17 j

To know more about cross product,

https://brainly.com/question/31199280

#SPJ11

The slant height of the cone is approximately 4.09 cm and the height is approximately 3.

let the radius of the cone be 'r', the slant height be 's', and the height be 'h'. then, we have:

total surface area of the cone = πrs + πr² = 24πlateral surface area of the cone = πrs = 15π

we can use the second equation to express 'r' in terms of 's':

πrs = 15π

rs = 15r = 15/s

substituting this value of 'r' in the first equation, we get:

π(15/s)s + π(15/s)² = 24π

simplifying and solving for 's', we get:

s² = h² + r² = (15/2π)² + (15/s)²

to find the slant height 's', we can solve this equation using the given values of total surface area and lateral surface area:

24π = πrs + πr² = πs(15/s) + π(225/s²)

24 = 15/s + 225/s²²²⁵s + 15s² = 360

s² + (15/225)s - 24 = 0s² + 0.0667s - 24 = 0

solving for 's' using the quadratic formula, we get:

s = 4.09 cm (approx.)

to find the height 'h', we can use the equation:

h = √(s² - r²)

substituting the values of 's' and 'r' that we just found, we get:

h = √(4.09² - (15/2π)²) ≈ 3.16 cm 16 cm.

Learn more about slant here:

 https://brainly.com/question/4627780

#SPJ11

The correct statement is: There is no significant difference between means.

There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value of a given data set. Pythagorean means consist of arithmetic mean, geometric mean, and harmonic mean

If the error bars overlap, but do not contain the mean of the other group, it means that there is no significant difference between the means. Overlapping error bars indicate that the means are within the range of uncertainty, and there is not enough evidence to conclude that the means are significantly different from each other.

Know more about means here:

https://brainly.com/question/31101410

#SPJ11

The algorithm described in your question is an example of a divide and conquer algorithm. It solves problems of size n by dividing them into four subproblems of size n-4, recursively solving each subproblem, and then combining the solutions in constant time. This approach can be useful when solving problems that can be broken down into smaller, similar subproblems.

The divide and conquer strategy is often used in computer science, especially in the design and analysis of algorithms. It is used in various areas such as sorting, searching, and optimization problems. The key idea behind this approach is to break down a problem into smaller subproblems that can be solved more easily. The solutions to the subproblems are then combined to find the solution to the original problem.

Overall, the algorithm you mentioned seems like an efficient way to solve problems of size n, as long as the size of n is sufficiently large to justify the recursive division into subproblems.

To know more about algorithm visit:

https://brainly.com/question/28724722

#SPJ11

If you know that p = .7, then the value of q is 0.3 (option b)

If you know that p = .7, the value of q can be calculated using the complement rule of probability, which states that the probability of an event occurring is equal to one minus the probability of that event not occurring. In other words, q is equal to one minus p.

Therefore, q = 1 - p = 1 - 0.7 = 0.3.

It is important to note that the sum of p and q should always equal one, as there are only two possible outcomes in a given event. In this case, the sum of p and q is 0.7 + 0.3 = 1, which confirms that the values are correct.

Hence the correct option is (b).

To know more about probability here

https://brainly.com/question/11234923

#SPJ4

A tax rate of $0.0711 per $1,000 of assessed valuation in decimal form can be calculated as follows. First, divide the tax rate by 1,000 to determine the rate per dollar: $0.0711 / 1,000 = $0.0000711.

This represents the decimal equivalent of the tax rate per dollar. To express it as a percentage, multiply the decimal value by 100: $0.0000711 * 100 = 0.00711%.

Therefore, a tax rate of $0.0711 per $1,000 of assessed valuation is equal to 0.00711% in decimal form.

To know more about tax rate, visit:

https://brainly.com/question/30629449

#SPJ11

The value of df for a test with four categories and a sample of any size is 3.

The degrees of freedom (df) for a chi-square test for goodness of fit is calculated as (number of categories - 1) since one category can be determined from the frequencies of the other categories.

In this case, there are four categories, so the degrees of freedom would be (4 - 1) = 3.

Know more about degrees of freedom here:

https://brainly.com/question/31424137

#SPJ11

Answer:

Neil Armstrong and Buzz Aldrin

Step-by-step explanation:

Fifty years after Neil Armstrong, Buzz Aldrin and Michael Collins became etched in history, the Apollo 11 mission remains an iconic moment in broadcasting. It's estimated that between 600-650 million people tuned in around the world to Armstrong and Aldrin's broadcast from the lunar surface on July 20, 1969.

A total of 3 comparisons are required to find 42 using binary search in this particular array.

In binary search, the number of comparisons required to find a target value depends on the size of the array and the position of the target value within the array.

In this case, we have an array with 13 elements. In the first comparison, we compare the target value (42) with the middle element of the array.

The first comparison: 42 is compared with the middle element 8.

Since 42 is greater than 8, we can eliminate the first half of the array and continue the search in the second half. Now we have an array with 6 elements.

The second comparison: 42 is compared with the middle element 21.

Since 42 is greater than 21, we can again eliminate the first half of the remaining array and continue the search in the second half. Now we have an array with 3 elements.

The third comparison: 42 is compared with the middle element 42.

We have found the target value in the third comparison.

Know more about binary search here:

https://brainly.com/question/31605257

#SPJ11

To determine the addition and multiplication tables for the congruence-class ring F[x]/(p(x)), we first need to find the congruence-class representatives for the polynomials modulo p(x). In this case, we have F = Z3 and p(x) = [tex]x^{2}[/tex] + 1.

The congruence-class representatives for F[x]/(p(x)) are given by the polynomials of degree at most 1: 0, 1, 2, x, x + 1, x + 2. These representatives will be used to construct the addition and multiplication tables.

Addition table:

+  |  0   1   2   x  x+1 x+2

---------------------------

0  |  0   1   2   x  x+1 x+2

1  |  1   2   x  x+1 x+2  0

2  |  2   x  x+1 x+2  0   1

x  |  x  x+1 x+2  0   1   2

x+1| x+1 x+2  0   1   2   x

x+2| x+2  0   1   2   x  x+1

Multiplication table:

*  |  0   1   2   x  x+1 x+2

---------------------------

0  |  0   0   0   0   0   0

1  |  0   1   2   x  x+1 x+2

2  |  0   2   1  x+2 x+1  x

x  |  0   x  x+2 x+1  2   1

x+1|  0 x+1 x+1  2   1  x+2

x+2|  0 x+2  x  1  x+2 x+1

To determine if F[x]/(p(x)) is a field, we need to check if every non-zero element in the ring has a multiplicative inverse. In this case, we can see that the element x does not have a multiplicative inverse since it is not possible to find a polynomial y(x) such that x * y(x) ≡ 1 (mod p(x)). Therefore, F[x]/(p(x)) is not a field for F = Z3 and p(x) = [tex]x^{2}[/tex] + 1.

To learn more about tables here:

https://brainly.com/question/30846163

#SPJ4

Integrating ∫ dx gives us:

∫ln(3x) dx = x ln(3x) - x + C

Integration by parts is a technique used to evaluate integrals of products of functions. It is based on the product rule of differentiation. The formula for integration by parts is:

∫ u dv = uv - ∫ v du

To evaluate the integral ∫ln(3x) dx, we can use integration by parts. Let's assume u = ln(3x) and dv = dx. Then, we can find du and v as follows:

u = ln(3x)
dv = dx

To find du, we differentiate u with respect to x:
du/dx = 1/x

To find v, we integrate dv with respect to x:
v = ∫ dx = x

Now, we can use the integration by parts formula:

∫ u dv = uv - ∫ v du

Applying the formula:

∫ln(3x) dx = x ln(3x) - ∫ x (1/x) dx

Simplifying further:

∫ln(3x) dx = x ln(3x) - ∫ dx

Integrating ∫ dx gives us:

∫ln(3x) dx = x ln(3x) - x + C

where C is the constant of integration.

Read more about integration by parts at :

https://brainly.com/question/27746495

#SPJ4

the function y = cos(-8it) = cos(8it) satisfies the differential equation y′′ - 64y = 0 for k = -8i.To find the negative values of k for which the function y = cos(kt) satisfies the differential equation y′′ - 64y = 0,

We first find the first and second derivatives of y with respect to t:

y' = -ksin(kt)

y'' = -k^2cos(kt)

Substituting these into the differential equation, we get:

-k^2cos(kt) - 64cos(kt) = 0

Dividing both sides by cos(kt), we get:

-k^2 - 64 = 0

Solving for k, we get:

k = ±8i

Since we are looking for negative values of k, the answer is:

k = -8i

Therefore, the function y = cos(-8it) = cos(8it) satisfies the differential equation y′′ - 64y = 0 for k = -8i.

to learn more about derivatives click here:brainly.com/question/30365299

#SPJ11

The mean height of the sunflowers is,

⇒ 112.5

We have to given that;

The table shows information about the heights, in cm, of 48 sunflowers in a garden center.

Here, Mean for height of sunflower are,

(90 + 100) / 2 = 95

(100 + 110) / 2 = 105

(110 + 120) / 2 = 115

(120 + 130) / 2 = 125

(130 + 140) / 2 = 135

Hence, WE can formulate;

The mean height of the sunflowers is,

⇒ (95 × 8 + 105 × 12 + 115 × 15 + 125 × 10 + 135 × 3) / 48

⇒ (760 + 1260 + 1725 + 1250 + 405)/ 48

⇒ 5400 / 48

⇒ 112.5

Therefore, The mean height of the sunflowers is,

⇒ 112.5

Learn more about the addition visit:

https://brainly.com/question/25421984

#SPJ1

To find the slope of the tangent to the curve at the point (2, -8), we need to find the derivative of the function p(x) and evaluate it at x = 2.

(a) p(x) = x^3 - 8x

p'(x) = 3x^2 - 8

p'(2) = 3(2)^2 - 8 = 4

So the slope of the tangent to the curve at the point (2, -8) is 4.

(b) The instantaneous rate of change of the function is the same as the derivative of the function. So the instantaneous rate of change of p(x) at x = 2 is p'(2) = 4.

To know more about derivative refer here

https://brainly.com/question/30365299#

#SPJ11

The number of different ways that 11 books can be arranged on a bookshelf is 39,916,800.

To determine the number of ways the 11 books can be arranged on a bookshelf, we can use the formula for permutation, which is given by:

P(n,r) = n!/(n-r)!

Where n is the total number of items and r is the number of items selected. In this case, we have 11 books and we want to arrange them all, so r = 11.

Therefore, the number of different ways the 11 books can be arranged on a bookshelf is:

P(11,11) = 11!/(11-11)! = 11! = 39,916,800.

This means that there are 39,916,800 different possible ways to arrange the 11 books on the bookshelf.

Visit here to learn more about permutation:

brainly.com/question/1216161

#SPJ11

The prοbability that a randοmly selected dοughnut cοntains mοre than 20 grams οf sugar is apprοximately 0.8413 (rοunded tο fοur decimal places).

Standardizing refers tο the prοcess οf transfοrming data values intο standardized units, typically in the fοrm οf z-scοres. When we standardize a variable, we subtract the mean οf the variable frοm each data pοint and then divide the result by the standard deviatiοn.

Tο find the prοbability that a randοmly selected dοughnut cοntains mοre than 20 grams οf sugar, we need tο calculate the area under the nοrmal distributiοn curve tο the right οf 20 grams.

Let's denοte the mean as μ = 26 grams and the standard deviatiοn as σ = 6 grams. We want tο find P(X > 20), where X represents the amοunt οf sugar in a randοmly selected dοughnut.

Tο calculate this prοbability, we need tο standardize the value οf 20 grams using the z-scοre fοrmula:

z = (X - μ) / σ

z = (20 - 26) / 6

z = -1

Nοw, we need tο find the prοbability οf Z being greater than -1. We can use a standard nοrmal distributiοn table οr a statistical calculatοr tο find this prοbability.

Using a standard nοrmal distributiοn table, we find that the prοbability οf Z being greater than -1 is apprοximately 0.8413.

Therefοre, the prοbability that a randοmly selected dοughnut cοntains mοre than 20 grams οf sugar is apprοximately 0.8413 (rοunded tο fοur decimal places).

To know more about probability visit:

https://brainly.com/question/31425759

#SPJ4

The simplified value of the expression is 9

Evaluate equation in the bracket first, obtain the quotient of the values in bracket

(3⁴ / 3⁰)² = (81/1)²

Taking the square of the quotient value obtained

(3⁴ / 3⁰)² = 6561

Multiply the value obtained by [tex]3^{-6}[/tex]

Now we have ;

[tex]3^{-6}[/tex] × 6561 = 0.00137174211 × 6561

0.00137174211 × 6561 = 9

The simplified value of the expression obtained using the BODMAS approach will be 9

Learn more on BODMAS ; https://brainly.com/question/29626868

#SPJ1

The measure of angle ADC, based on the definition of similar triangles is determined as: 80 degrees.

Two triangles are similar to each other if their corresponding pairs of angles have angle measure that are equal or congruent to each other.

In the image shown above, side ED and side CB are parallel to each other, thus, this means that angle ADE and angle ABC are corresponding angles. Since corresponding angles are equal to each other, therefore, measure of angle ADC and measure of angle ABC are equal.

Thus, we have:

m<ADC = 80 degrees.

Learn more about Similar Triangles on:

https://brainly.com/question/14285697

#SPJ1

A valid categorical syllogism with two universal premises cannot conclude with a universal statement, but must conclude with a particular statement.

A categorical syllogism is a deductive argument consisting of three categorical propositions that contain a total of three terms, each of which appears twice in the argument. The three terms are called the major term, the minor term, and the middle term. The middle term is the term that appears in both premises but not in the conclusion, while the major term and minor term are the terms that appear in the conclusion.

In a valid categorical syllogism with two universal premises, both the major term and minor term are distributed in both premises. This means that the conclusion can only contain a term that is not distributed in either premise, which is a particular term (i.e., a statement that refers to some but not all of the members of a category).

For example, consider the following categorical syllogism:

All dogs are mammals.

All mammals are animals.

Therefore, all dogs are animals.

In this syllogism, both the major term ("animals") and minor term ("dogs") are distributed in both premises, so the conclusion can only contain an undistributed term, which is a particular term ("some dogs are animals").

Therefore, a valid categorical syllogism with two universal premises cannot conclude with a universal statement, but must conclude with a particular statement.

To learn more about syllogism

https://brainly.com/question/1558469

#SPJ11

Step-by-step explanation:

integral from 0 to 2pi of cos3x

(sin3x)/3 from 0 to 2 pi

sin 6pi /3 - sin 0 /3 = 0

As x approaches positive infinity (∞), f(x) approaches positive infinity (∞).

As x approaches negative infinity (-∞), f(x) approaches negative infinity (-∞).

When x approaches 8 from the left (x → 8-), f(x) approaches negative infinity (-∞).

When x approaches 8 from the right (x → 8+), f(x) approaches positive infinity (∞).

To determine the corresponding behavior of f(x) for different behaviors of x, let's examine each scenario:

When x approaches positive infinity (∞):

As x becomes larger and larger, the behavior of f(x) can be determined by looking at the highest power term, which is x^3 in this case. Since x^3 grows faster than x and (x - 8), the dominant term is x^3. Therefore, as x approaches positive infinity, f(x) also approaches positive infinity (∞).

When x approaches negative infinity (-∞):

Similar to the previous case, as x becomes more negative and approaches negative infinity, the dominant term is still x^3. Hence, f(x) also approaches negative infinity (-∞).

When x approaches 8 from the left (x → 8-):

When x approaches 8 from the left side, meaning slightly smaller values than 8, the term (x - 8) approaches 0 from the negative side. Thus, f(x) approaches negative infinity (-∞).

When x approaches 8 from the right (x → 8+):

Similarly, when x approaches 8 from the right side, slightly greater values than 8, the term (x - 8) approaches 0 from the positive side. Therefore, f(x) approaches positive infinity (∞).

In summary:

As x approaches positive infinity (∞), f(x) approaches positive infinity (∞).

As x approaches negative infinity (-∞), f(x) approaches negative infinity (-∞).

When x approaches 8 from the left (x → 8-), f(x) approaches negative infinity (-∞).

When x approaches 8 from the right (x → 8+), f(x) approaches positive infinity (∞).

To know more about positive infinity refer here:

https://brainly.com/question/27954028

#SPJ11

The first term that appears in both sequences is 58.

To find the first term that appears in both sequences, we can generate the terms of each sequence until we find a match.

Sequence 1: Multiply by 3 starting from 10

Starting from 10, the sequence would be: 10, 30, 90, 270, 810, ...

Sequence 2: Subtract 7 starting from 58

Starting from 58, the sequence would be: 58, 51, 44, 37, 30, ...

By comparing the terms of both sequences, we can see that the number 58 is the first term that appears in both sequences. After the first term, the sequences diverge and no longer have matching terms.

Therefore, the answer is 58, which is the first term that appears in both the "multiply by 3 starting from 10" sequence and the "subtract 7 starting from 58" sequence.

Rounding up to the nearest integer, the required sample size is 29179.

To determine the sample size needed to achieve a margin of error within ±1.5% in estimating a population proportion with 99% confidence, we can use the formula:

n = (Z² * p * (1 - p)) / E²

where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (99% confidence corresponds to a Z-score of approximately 2.576)

p = estimated or assumed population proportion (since we don't have an initial estimate, we can assume p = 0.5 to get the maximum sample size)

E = desired margin of error (±1.5% = 0.015)

Plugging in the values:

n = (2.576² * 0.5 * (1 - 0.5)) / 0.015²

n = (6.635776 * 0.25) / 0.000225

n ≈ 29178.227

Know more about sample size here:

https://brainly.com/question/30885988

#SPJ11

Answer:

The football team members

Step-by-step explanation:

The substitution method means that we need to isolate one variable in one equation and replace that in other equation. While by graphing, we need to graph all the equations and find the intercept points.

A system of equations is a group of two equations or more that must be solved at the same time.

Generally, we should have the same number of variables than equations.

Now let's define the two methods:

Substitution: In this method we need to isolate one of the variables in one of the equations, and then replace that in other of the equations. In that way, you can reduce the number of equations (and variables) by 1.

Graphing: To solve by graphing we need to graph all the equations on the same coordinate axis and then find the points where the graphs intercept, these points are the solutions of the system.

Learn more about systems of equations at:

https://brainly.com/question/13729904

#SPJ1

The standard error of the estimate is 0.36.

The standard error of the estimate (SEE) can be calculated as:

SEE = sqrt(SSR / (n - k))

where SSR is the sum of squared residuals, n is the sample size (number of observations), and k is the number of explanatory variables (excluding the intercept).

In this case, SSR = 4.75, SST = 7.62, n = 100, and k = 4. Therefore, we have:

SEE = sqrt(4.75 / (100 - 4))

SEE = sqrt(4.75 / 96)

SEE ≈ 0.49

Rounding to 2 decimal places, the standard error of the estimate is approximately 0.49.

Learn more about standard error of the estimate:

https://brainly.com/question/30850097

#SPJ11

The distance from the vertex to the focus is :

8 feet

The spotlight has a parabolic cross-section with an opening width of 4 ft and a depth of 2 ft at the vertex. To find the distance from the vertex to the focus, we can use the equation for a parabola in the form y = (1/4f)x^2, where f is the distance to the focus.

Since the parabola is 4 ft wide at the opening, the value of x is 2 ft (half of the width). The depth at the vertex, which is the value of y, is 2 ft. Substituting these values into the equation, we get:

2 = (1/4f)(2^2)

2 = (1/4f)(4)

Now, we solve for f:

8 = f

So, the focus is 8 ft away from the vertex.

To learn more about parabola visit : https://brainly.com/question/4061870

#SPJ11

15 people out of 200 households used both brands of soap.

Since it is given that 80 households use neither Brand A nor Brand B, then:

= 200 - 80

= 120 must use Brand A, Brand B, or both.

It is also given that 60 households use only Brand A and that three times as many households use Brand B exclusively as use both brands.

If x is the number of households that use both Brand A and Brand B, then 3x use Brand B alone.

All the sections in the circles can be added up and set equal to 120 and then the equation can be solved for x:

60 + x + 3x = 120

60+4x = 120

4x = 120 - 60

4x = 60

x = 15.

Read more about Probability

brainly.com/question/24756209

#SPJ1