a factory produces 40,000 computer monitors per day. the manager of the factory claims that fewer than 940 defective computer monitors are produced each day. in a random sample of 200 computer monitors, there are 2 defective computer monitors. determine whether the manager's claim is likely to be true. explain.

S cannot be a basis for \(R^{n }\)

What is Matrix ?

A matrix is a rectangular array of numbers or symbols arranged in rows and columns. Matrices are commonly used in mathematics, physics, engineering, computer science, and other fields to represent systems of linear equations, transformations, and other mathematical objects and operations.

The statement "For each b in  \(R^{m }\), the equation Ax - b has a solution" is equivalent to the following statements:

A. The columns of A span \(R^{m }\)

B. Each b in \(R^{m }\) is a linear combination of the columns of A.

E. The matrix A has a pivot position in each column.

To explain why S cannot be a basis for  \(R^{n }\) , we can use the fact that a set of vectors S = {v1, ..., vk} is a basis for  \(R^{n }\) if and only if the matrix whose columns are the vectors in S is invertible. In this case, since k < n, the matrix whose columns are the vectors in S cannot be invertible because it has more columns than rows.

Therefore, S cannot be a basis for \(R^{n }\).

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Answer:

45 feet

Step-by-step explanation:

Set up Ratios

1/2 in/5 ft = 4 1/2 in/x

Solve for x by cross-multiplying:

\(\frac{1/2}{5}\) times \(\frac{4 1/2}{x}\)

4 1/2 times 5 = 22 1/2

1/2 times x = 1/2x

22 1/2 = 1/2x

45 = X

Therefore the actual length of the bus is 45 feet.

Hope it helps :)

Answer:

x = 13

Step-by-step explanation:

Inscribed Angle = 1/2 Intercepted Arc

30 = 1/2 (5x-5)

Multiply each side by 2

2*30 = 2* 1/2 ( 5x-5)

60 = 5x-5

Add 5 to each side

60+5 = 5x-5+5

65 = 5x

Divide each side by 5

65/5 = 5x/5

13 = x

Answer:

your answer is 70 min to mow 5 lawns

Step-by-step explanation:

Step 1

if it takes him 28 min to mow 2 lawns.

to mow 4 lawns, it would be 28+28 or 28x2=56

step 2

to figure out how long t would take to mow  5 lawns, you first have to figure out how much time was spent on 1 lawn.

which is: 28/2= 14

Step 3

now all you have to do it add

56+14

which gives you the answer

70

1) A nonagon is a polygon with nine sides.

To find the sum of the interior angles of a nonagon, we can use the formula:

aggregate of interior angles = (n - 2) × 180°

where n stands for the number of sides of the polygon.

Substituting n = 9 for a nonagon, we get:

sum of interior angles = (9 - 2) × 180° = 7 × 180°

Thus, the aggregate of the interior angles of a nonagon is:

sum of interior angles = 1260°

2)

To find the sum of the interior angles of a 17-gon, we can use the formula:

aggregate of interior angles = (n - 2) × 180°

where n stands for the number of sides of the polygon.

Substituting n = 17 for a 17-gon, we get:

sum of interior angles = (17 - 2) × 180° = 15 × 180°

Thus, the aggregate of the interior angles of a 17-gon is:

sum of interior angles = 2700°

3)
It is correct to state that a hexagon can be defined as a polygon with six sides.

To find the sum of the interior angles of a hexagon, we can use the formula:

aggregate of interior angles = (n - 2) × 180°

where n refers to the number of sides of the polygon.

Replacing n = 6 for a hexagon, we get:

sum of interior angles = (6 - 2) × 180° = 4 × 180°

Therefore, the sum of the interior angles of a hexagon is:

sum of interior angles = 720°

4)
To find the sum of the interior angles of a regular 20-gon, we can use the formula:

aggregate of interior angles = (n - 2) × 180°

where n refers to the number of sides of the polygon.

Substituting n = 20 for a 20-gon, we get:

sum of interior angles = (20 - 2) × 180 degrees = 18 × 180°

Thus, the sum of the interior angles of a regular 20-gon is:

sum of interior angles = 3,240°

5)
A regular octagon is a polygon with eight sides that are all congruent and eight angles that are all congruent.

To find the measure of each exterior angle of a regular octagon, we can use the formula:

dimensions of each exterior angle = 360° ÷ number of sides

For a regular octagon, the number of sides is 8. Replacing this value into the formula, we get:

measure of each exterior angle = 360° ÷ 8

Simplifying this expression, we get:

the dimensions of each exterior angle = 45°

Therefore, the dimensions of each exterior angle of a regular octagon is 45°.

6)

A regular 24-gon is a polygon with 24 sides that are all congruent and 24 angles that are all congruent.

To find the measure of each exterior angle of a regular 24-gon, we can use the formula:

mensuration of each exterior angle = 360° ÷ number of sides

For a regular 24-gon, the number of sides is 24. Replacing this value into the formula, we get:

measure of each exterior angle = 360° ÷ 24

Simplifying this expression, we get:

The measure of each exterior angle = 15°

Therefore, the measure of each exterior angle of a regular 24-gon is 15°

7)
The sum of the interior angles of any pentagon can be calculated using the formula:

Aggregate of interior angles = (n - 2) × 180°

where n refers the number of sides of the polygon.

For a pentagon, n = 5, so we have:

Aggregate of interior angles = (5 - 2) × 180° = 3 × 180° = 540°.

We can use this fact to set up an equation using the given expressions for the interior angles:

(5x + 2) + (7x - 11) + (13x - 31) + (8x - 19) + (10x - 3) = 540

Simplifying and solving for x, we get:

43x - 62 = 540

43x = 602

x = 14

Therefore, x = 14.

8)

The sum of the exterior angles of any polygon is always 360 degrees. Therefore, we can add the six exterior angles of the hexagon to get:

(11x-30) + 5x + 50 + (2x+60) + (6x-10) + 50 = 360

Simplifying and solving for x, we get:

24x + 120 = 360

24x = 240

x = 10

Therefore, x = 10.

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Answer:

1.6

Step-by-step explanation:

Answer:

1.6 degrees

Step-by-step explanation:

Answer:

A) 5÷9

Step-by-step explanation:

As, 5 is a whole number

And when the number ends with "ths" it is always the denominator

So here it is ninths so 9 will be in the denominator

Rounded to four decimal places, the p-value is 0.0844.

To determine the p-value for this hypothesis test, we need to follow these steps:

Step 1: State the null and alternative hypotheses.

Null hypothesis: The percentage of readers who own a laptop is 26%.

Alternative hypothesis: The percentage of readers who own a laptop is different from 26%.

Step 2: Determine the test statistic.

We can use a z-test for proportions since we have a large enough sample size and we know the population proportion. The formula for the test statistic is:

z = (p - p) / √(p(1-p) / n)

where p is the sample proportion, p is the hypothesized population proportion, and n is the sample size.

Using the given values, we have:

z = (0.17 - 0.26) / √(0.26(1-0.26) / 100)

z = -1.72

Step 3: Determine the p-value.

Since this is a two-tailed test, we need to find the area in both tails of the standard normal distribution that corresponds to a z-score of -1.72. Using a table or a calculator, we find that the area in the left tail is 0.0422 and the area in the right tail is also 0.0422.

Therefore, the p-value is the sum of the areas in both tails:

p-value = 0.0422 + 0.0422

p-value = 0.0844

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Answer:

18 cm each side

Step-by-step explanation:

Square has 4 sides. So, 72/4=18

18 cm each side

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The zeros are −4 and 5, because g(x)=−(x+4)(x−5).

Given the function  g(x)=−x^2+x+20

Factorize the expression

g(x) = -x^2 +5x - 4x + 20

g(x) = -x(x-5)-4(x-5)

g(x) = (-x-4)(x-5)

Equating the result to zero

x - 5 = 0

x = 5

Similarly, -x-4 = 0

-x = 4

x = -4

Hence the zeros are −4 and 5, because g(x)=−(x+4)(x−5)

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The arithmetic mean of two terms in an arithmetic sequence is 42 .

One term is 30 then other term is

42 = (x+30)/2

x=54

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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Answer:

2 nonreal solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the nature of the roots are determined by the discriminant

b² - 4ac

• if b² - 4ac > 0 then 2 real and irrational solutions

• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions

• if b² - 4ac = 0 then 2 real and equal solutions

• if b² - 4ac < 0 then no real solutions

5x² - 2x + 6 = 0 ← in standard form

with a = 5 , b = - 2 , c = 6

b² - 4ac

= (- 2)² - (4 × 5 × 6)

= 4 - 120

= - 116

since b² - 4ac < 0

then there are 2 nonreal solutions to the equation

In the given figure, for Angle X and Angle Y to be equal, line AB and CD should be parallel.

Therefore, the answer is CHOICE 2 : The lines are parallel.

The z test statistic needed for this hypothesis test is 0.75 .

Z test is a statistical test that is conducted on data that approximately follows a normal distribution. The z test can be performed on one sample, two samples, or on proportions for hypothesis testing. It checks if the means of two large samples are different or not when the population variance is known.

NOW,

sample proportion =  p = x / n = 0.23

Test statistics

z = ( p - p0 ) / \(\sqrt{ p0*(1-p0)}\) / n

= ( 0.23 - 0.20) /  \(\sqrt{ (0.20*0.80) / 100}\)

= 0.75

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There are 5 possibilities:

a. That particular ad scored 140 percent above comparable ads.

b. That particular ad scored 40 percent above comparable ads.

c. The percentage of respondents who read half or more of the written material in the ad was 40 percent.

d. The percentage of respondents who recalled seeing the ad was 40 percent.

e. That particular ad is capable of generating market share gains of 40 percent.

The purpose of the Starch Service is to report to what extent a client's magazine advertisements are seen and read. Using Starch, a client can compare the readership of current advertisements with past advertisements, or competitors advertisements. One use for the service is that it provides information as to how advertisements can be presented so that readership can be increased by the manipulation of various elements of magazine advertising included in the reports.

The answer is option (b): That particular ad scored 40 percent above comparable ads.

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the solutions of the equation in the interval [0, 2π) are π/4, 3π/4, 5π/4, 7π/4.

Squaring on both sides, we have 2cos2x = 1cos2x = 1/2

Let's recall the formula of cos 30°cos 30° = cos π/6 = √3/2cos 60°cos 60° = cos π/3 = 1/2cos 90° = cos π/2 = 0cos 120°cos 120° = cos 2π/3 = −1/2cos 150°cos 150° = cos 5π/6 = −√3/2

Now, the general solution of cos2x = 1/2 is given byx = nπ ± π/4where, n ∈ Z

The values of x in the interval [0, 2π) are: x = π/4, 7π/4x = 3π/4, 5π/4

Therefore, the solutions of the equation in the interval [0, 2π) are π/4, 3π/4, 5π/4, 7π/4.

The given equation is √2 cos 2x = 1.

Squaring on both sides, we get 2cos2x = 1.

Using the formula of cos2x, we have x = nπ ± π/4. Therefore, the general solution of cos2x = 1/2 is x = nπ ± π/4, where n ∈ Z.

The values of x in the interval [0, 2π) are x = π/4, 3π/4, 5π/4, 7π/4.

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Answer:

I would say about 13 minutes.

Step-by-step explanation:

9 4/5 KPH is about 6.1224489795918 Kilometers per minute

Multiply by 2 1/5 KPM

6.1224489795918 x 2 1/5 = 13.4693877551 Minutes

Answer: 13.469 or about 13.5 minutes

Step-by-step explanation:

Estimating part:

The first number can be rounded to 10, and second number to 2

You can set up a proportional equation

\(\frac{10 kilometers}{60 minutes} = \frac{2 kilometers}{x}\)

then cross multiply to get 10x=120, then divide to get x = 12 minutes

Exact answer:

I like making fractions into decimals to make it easier to see

The first number as a decimal is 9.8, and the second is 2.2

Set up another proportional equation

\(\frac{9.8 kilometers}{60 minutes} = \frac{2.2 kilometers}{x}\)

cross multiply to get 9.8x = 132

divide by 9.8 on both sides to get x = 13.5 minutes

By associative property the expression 53p+(16p+7p) is equivalent to the expression  53p+(16p+7p)

The given expression is 53p+(16p+7p)

Fifty three times of p plus sixteen times of p plus seven times of p

In the expression p is the variable and plus is the operator

We have to find the equivalent expression of the expression

Equivalent expression is the expression whose value is same as given expression and looks different

53p+(16p+7p)=  (53p+16p)+7p

By associate property  (53p+16p)+7p is equivalent to 53p+(16p+7p)

Hence, the expression 53p+(16p+7p) is equivalent to the expression  53p+(16p+7p) by associative property

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Answer:

The answer is 5 3/4

Step-by-step explanation:

13/4 = 3 1/4

3 1/4 + 2 2/4 = 5 3/4

Hope this helped you!

The decision for values of χ^2 obt close to 0 will depend on the level of significance and should be made in the context of the specific hypothesis being tested and the available evidence.

If the obtained value of chi-squared (χ^2 obt) is close to 0, it suggests that the observed data is not significantly different from the expected data. This means that the null hypothesis, which assumes that there is no significant difference between the observed and expected data, is likely to be accepted.

However, the decision whether to accept or reject the null hypothesis also depends on the level of significance (alpha) chosen for the test. If the level of significance is low, even a small difference between the observed and expected data can lead to the rejection of the null hypothesis. On the other hand, if the level of significance is high, a larger difference between the observed and expected data may be required to reject the null hypothesis.

Therefore, the decision for values of χ^2 obt close to 0 will depend on the level of significance and should be made in the context of the specific hypothesis being tested and the available evidence.

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When the values of χ 2 obt close to 0, the decision is likely to be that the null hypothesis cannot be rejected.

The chi-square test is a statistical test used to determine whether an observed distribution of categorical data varies significantly from an expected distribution. It is utilized to investigate the association between two or more categorical variables, and the test evaluates the likelihood of the observed frequencies of each category of data based on the expected frequency of that data.The Chi-Square DistributionThe chi-square distribution is a collection of distributions that are used to describe data that have a characteristic called degrees of freedom. The degrees of freedom are calculated using the number of categories minus 1 in the categorical variable being tested.

The distribution is always positive and right-skewed, with the majority of the distribution situated in the right tail. When the values of χ 2 obt close to 0, the decision is likely to be that the null hypothesis cannot be rejected.

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Answer:D

Step-by-step explanation:s aThe function is always increasing because wether the value of x increases or decreases, the value of f(x) is increasing as well

Answer: v = 40mm * 25mm * 2mm = 2000 mm^3 so, the weight is 2000 mm^3 * .0005oz/1mm^3 = 1oz

Step-by-step explanation:

Answer:

60/12= 5

5 feet

Answer:

5 feet

Step-by-step explanation:

Divide the length value (inches) by 12.

Answer:

x = 47.5

Step-by-step explanation:

5 times 5 = 25

9 times 5 = 45

45 divided by 2 = 22.5

25 + 22.5 = x

x = 47.5

a.The probability that a randomly selected watch will be in working condition for more than five years is approximately 6.68%. b.Approximately 93.32% of the watches will be in operating condition after the warranty period. c. The maximum life expectancy of the middle 95% of the watches is approxiamately 63.68 months. d.The range of the middle 95% of the watches is from 32.32 months to 63.68 months. The range represents 95% of the watches, it means that 5%.

a. To find the probability that a randomly selected watch will be in working condition for more than five years, we need to convert the time to the same unit as the distribution. Since the mean is given in years and the standard deviation is given in months,

we need to convert five years to months.

Mean = 4 years = 4 x 12 months = 48 months

Standard deviation = 8 months

To calculate the probability, we need to find the area under the normal distribution curve to the right of 60 months (5 years).

Using a standard normal distribution table or a calculator, we can find the z-score corresponding to 60 months:

z = (x - μ) / σ

z = (60 - 48) / 8 = 12 / 8 = 1.5

The probability can be found by looking up the z-score in the standard normal distribution table or using a calculator. From the table or calculator, we find that the probability is approximately 0.0668, or 6.68%.

b. The warranty period for Timely brand watches is three years. To find the percentage of watches that will be in operating condition after the warranty period, we need to find the probability that a randomly selected watch will last longer than three years.

We need to convert three years to months:

Warranty period = 3 years = 3 x 12 months = 36 months

We calculate the z-score:

z = (x - μ) / σ

z = (36 - 48) / 8 = -12 / 8 = -1.5

Using the standard normal distribution table or a calculator, we find the area to the left of -1.5 is approximately 0.0668. The probability that a randomly selected watch will not last longer than three years is approximately 0.0668.

To find the percentage of watches that will be in operating condition after the warranty period, we subtract this probability from 1 (since we want the complementary probability):

Percentage = 1 - 0.0668 = 0.9332 = 93.32%

c. The middle 95% of the watches represents the range within which 95% of the watches' life expectancy falls. To find the minimum and maximum life expectancy of this range, we need to determine the z-scores that correspond to the cumulative probability of 0.025 and 0.975.

For the minimum life expectancy (lower bound), we look up the z-score that corresponds to a cumulative probability of 0.025. This z-score is approximately -1.96.

z = -1.96

Using the z-score formula, we can find the corresponding value in months:

x = μ + (z x σ)

x = 48 + (-1.96 * 8) = 48 - 15.68 = 32.32

The minimum life expectancy of the middle 95% of the watches is approximately 32.32 months.

For the maximum life expectancy (upper bound), we look up the z-score that corresponds to a cumulative probability of 0.975. This z-score is also approximately 1.96.

z = 1.96

Using the z-score formula, we can find the corresponding value in months:

x = μ + (z x σ)

x = 48 + (1.96 x 8) = 48 + 15.68 = 63.68

d. Ninety-five percent of the watches refer to the range between the 2.5th and 97.5th percentiles. We already calculated the z-scores corresponding to these percentiles in part c: -1.96 and 1.96.

To find the range in months,

we convert the z-scores back:

\(x_{1}\)= μ +\(z_{1}\) x σ = 48 + (-1.96) x 8 = 32.32 months,

and \(x_{2}\)= μ + \(z_{2}\) x σ

= 48 + 1.96 x 8

= 63.68 months.

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Answer:

A

Step-by-step explanation:

Answer:

110

Step-by-step explanation:

Rate or proportion shows the relationship between the variation in the  number of two variables.

Given that the ratio of alternative songs to total songs is 9:14.

Total songs = 308

Since the to every 14 total songs, there is 9 alternative songs.

Thus,

Number of alternative songs = \(\frac{9}{14}\) x 308

                                                = 198

There are 198 alternative songs in the music library.

The number of songs that are NOT alternative songs = 308 - 198

                                                                                         = 110

Thus, there are 110 songs that are NOT alternative songs.

Answer: p = 39.99m + 0.05

Step-by-step explanation:

39.99 is your slope because it's the value that depends on the number of minutes while .05 is your y-intercept and it's just a one-time fee.

The proportion of people in each group that spends less than 21 minutes a day using the computer for leisure is 0.9871. The proportion of people in each group that spends more than 2 hours a day using the computer for leisure is 0.00002.

The proportion of people in each group that spends between 42 minutes and 126 minutes a day using the computer for leisure is 0.2531. The 28th percentile of people who spend time on the computer for leisure is 8.70. 72% of people spend more than 23.16 minutes per day on the computer for leisure.

a. Less than 21 minutes per day using a computer for leisure.Let X be the time spent on the computer for leisure.Using the exponential distribution formula:

P(X < 21) = 1 - eⁿ(n=-0.4*21)

= 0.9871

Therefore, the proportion of people in this group that spend less than 21 minutes a day using the computer for leisure is 0.9871.b. More than 2 hours.

Let X be the time spent on the computer for leisure.

Using the exponential distribution formula:

P(X > 120)

= eⁿ(n=-0.4*120)

= 0.00002

Therefore, the proportion of people in this group that spend more than 2 hours a day using the computer for leisure is 0.00002.c. Between 42 minutes and 126 minutes using a computer for leisure.

Let X be the time spent on the computer for leisure.Using the exponential distribution formula:P(42 < X < 126)

= eⁿ(n=-0.4*42) - eⁿ(n=-0.4*126)

= 0.2531

Therefore, the proportion of people in this group that spend between 42 minutes and 126 minutes a day using the computer for leisure is 0.2531.d. Find the 28th percentile.

Let X be the time spent on the computer for leisure

.Using the exponential distribution formula:P(X < p) = 0.28 gives e^(-0.4*p) = 0.28,

which gives p = 8.6982 rounded to 2 decimal places.

Seventy-two percent spend more than what amount of time?

Let X be the time spent on the computer for leisure.Using the exponential distribution formula:P(X > p) = 0.72 gives e^(-0.4*p) = 0.28, which gives p = 23.1551 rounded to 2 decimal places.

The proportion of people in each group that spends less than 21 minutes a day using the computer for leisure is 0.9871. The proportion of people in each group that spends more than 2 hours a day using the computer for leisure is 0.00002. The proportion of people in each group that spends between 42 minutes and 126 minutes a day using the computer for leisure is 0.2531. The 28th percentile of people who spend time on the computer for leisure is 8.70. 72% of people spend more than 23.16 minutes per day on the computer for leisure.

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