4. If you are given that plq and p || r,
what can you conclude about lines q and r?
State the theorem that justifies that conclusion.

The component form of the sum of u and v with direction angles is u + v = (10√2 - 50)i + 10√2 j.

We are given the magnitudes and direction angles of vectors u and v. We need to find the component form of their sum.

Let's first convert the given magnitudes and direction angles to their corresponding components. For vector u:

|u| = 20, θu = 45°

The x-component of u is given by:

ux = |u| cos(θu) = 20 cos(45°) = 10√2

The y-component of u is given by:

uy = |u| sin(θu) = 20 sin(45°) = 10√2

Therefore, the component form of vector u is:

u = 10√2 i + 10√2 j

Similarly, for vector v:

|v| = 50, θv = 180°

The x-component of v is given by:

vx = |v| cos(θv) = -50 cos(180°) = -50

The y-component of v is given by:

vy = |v| sin(θv) = 50 sin(180°) = 0

Therefore, the component form of vector v is:

v = -50 i + 0 j

The component form of the sum of u and v is given by the sum of their x- and y-components:

u + v = (10√2 - 50) i + (10√2 + 0) j

Simplifying, we get:

u + v = (10√2 - 50) i + 10√2 j

Therefore, the component form of the sum of u and v is:

u + v = (10√2 - 50) i + 10√2 j

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The question is -

Find the component form of the sum of u and v with the given magnitudes and direction angles θu and θv.

| | u | | = 20 , θu = 45° | | v | | = 50 , θv = 180°.

The percentage that each expense has out of the total budgeted amount of $45,000  have been computed, where insurance has 8.00%, Utilities 7.00% and so on.

What is a percentage?

In this case, percentage refers to proportion of each expense from the total budgeted expense of $45,000, which means that in order to total budgeted expense of $45,000, which means that in order to compute the percentage of total budgeted for each expense category, we divide the expense by the total budgeted expense

Insurance=$3600/$45,000=8.00%

Utilities=$3150/$45,000=7.00%

Clothing=$2700/$45000=6.00%

Transportation=$1350/$45000=3.00%

Entertainment=$5400/$45000=12.00%

Savings=$4050/$45000=9.00%

Taxes=$7200/$45000=16.00%

Food=$7650/$45000=17.00%

Housing=$9900/$45000=22.00%

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Answer:

38/3 in fraction form

Step-by-step explanation:

calculate exponents: 3^3 = 27

2/3 + 27 - 5/6 * 18

multiply and divide (left to right): 5/6 * 18 = 15

2/3 +27 - 15

add and subtract (left to right): 2/3 + 27 - 15 = 38/3

38/3

converted improper fraction to mixed number

12 2/3

Answer:

1. y2-y1/x2-x2

2.y=mx+b

3.Ax+By=C

Step-by-step explanation:

Using the P-value method of testing hypotheses with a significance level of 0.05, the sample provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

To test the claim that the mean score of job applicants from the university is greater than 160, we will perform a one-sample t-test using the P-value method. The null hypothesis (H0) assumes that the mean score is equal to 160, while the alternative hypothesis (Ha) assumes that the mean score is greater than 160.

First, we calculate the test statistic, which is the t-value. The formula for the t-value is:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values, we have:

t = (183 - 160) / (12 /   √(25))

  = 23 / (12 / 5)

  = 23 * (5 / 12)

  ≈ 9.58

Next, we find the P-value associated with the test statistic. The P-value represents the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. Since the alternative hypothesis is one-sided (greater than 160), we calculate the P-value by finding the probability of the t-distribution with 24 degrees of freedom being greater than the calculated t-value.

Consulting statistical tables or using software, we find that the P-value is very small (less than 0.0001).

Since the P-value (less than 0.0001) is less than the significance level (0.05), we reject the null hypothesis. This provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.

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Nonnegative integer solutions of the equation 21 + x2 + x3 + 24 + 25 + 6 = 30, we can simplify it to x^2 + x^3 = -16, which doesn't have any nonnegative integer solutions. Therefore, there are no solutions to this equation.
   

For the second part of the question, solutions that satisfy for every i € {1,2,3,4,5,6}, w is positive and even. As there are no solutions to the given equation, there are also no solutions that satisfy this condition. Therefore, the answer to this question is also zero. there are no nonnegative integer solutions for the given equation and no solutions that satisfy the condition for even and positive w.

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e) The test statistic and P-value for the chi-square test of homogeneity would be -1.75 and 0.004, respectively.

A chi-square test of homogeneity is a useful tool for comparing two or more categorical variables. In this case, the two variables are smoking (smokers and non-smokers) and alcohol consumption (those who had consumed alcohol in the past week and those who hadn't).

The chi-square statistic is calculated by finding the difference between the observed and expected frequencies of the two groups and squaring it. The expected frequencies are found by multiplying the sample size by the overall probability of success (in this case, drinking alcohol).

The P-value is then calculated based on the chi-square statistic and the degrees of freedom (in this case, one). In this case, the chi-square statistic is -1.75 and the P-value is 0.004.

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The length of the rectangle whose area is 7 units larger than its perimeter is 13 units.

The area of a rectangle is the product of its length and width.

The perimeter of a rectangle is the sum of the lengths of all the sides.

Given, Area of a rectangle is 7 units larger than its perimeter.

Assuming the length of the rectangle to be 'l' and the width to be 'w',

and the width is 3 units.

∴ (l×w) = 2(l + w) + 7.

(l×3) = 2(l + 3) + 7.

3l = 2l + 6 + 7.

l = 13 units.

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Step-by-step explanation:

SA=ph+2A, that is, perimeter × height+ twice area

p=21+20+29=70cm

h=22cm

70×22=1540cm

A=1/2 ×20×21=210×2=420

1540+420=1960cm2

Answer:

if an angle measures more than 90 degrees, then the angle is obtuse

The value of cos B in the fraction is 12/37.

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.

Given:

A right-angled triangle.

The trigonometric identity:

Cos B = Adjacent leg of the triangle/ Hypotenuse of the triangle

Cos B = 12/37

Therefore, Cos B = 12/37.

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\( \large{ \tt{❁ \: S \: O \: L \: U \: T \: I \: O \: N \: ❁}}\)

\( \large{ \tt{❇ \: FIND \: SP \: WITHOUT \: VAT \: / \: SP\: ❇}}\)

\( \large{ \tt{❃ \: SP \: with \: VAT= SP + VAT\% \: of \: SP}}\)

\( \large{ \tt{⇢ \: 4068 = SP + 13\% \: of \: SP}}\)

\( \large{ \tt{⇢ \: 4068 = SP + \frac{13}{100} \: sp}}\)

\( \large{ \tt{⇢ \: 4068 = \frac{100 \: \: SP + 13 \: SP}{100} }}\)

\( \large{ \tt{⇢ \: 4068 = \frac{113 \: SP}{100} }}\)

\( \large{ \tt{⇢ \: 113 \: SP = 406800}}\)

\( \large{ \tt{⇢ \: SP = \frac{406800}{113} }}\)

\( \large{ \tt{⇢ \: SP = 3600}}\)

\( \large{ \tt{✽ \: NOW , \: FIND \: THE \: MP \:✽ }}\)

\( \large {\tt{❃ \: SP = MP - dis\% \: of \: MP}}\)

\( \large{ \tt{⇾ \: 3600 = x - 10\% \: of \: x}}\)

\( \large{ \tt{⇾ \: 3600 = x - \frac{10}{100} } \: x}\)

\( \large{ \tt{⇾ \: 3600 = \frac{100x - 10x}{100} }}\)

\( \large{ \tt{⇾ \: 3600 = \frac{90x}{100} }}\)

\( \large{ \tt{⇾ \: 90x = 360000}}\)

\( \large{ \tt{⇾ \: x = \frac{360000}{90} }}\)

\( \large{ \tt{⇾ \: x = Rs \: 4000}}\)

\( \large{ \boxed{ \boxed{ \tt{☂ \: OUR \: FINAL \: ANSWER : \boxed {\tt {\: Rs \: 4000}}}}}}\)

If the shape is made up of one half-circle attached to an equilateral triangle with side lengths 20 inches then, the perimeter of the shape is 91.4 inches.

To find the perimeter of the shape, we need to know the length of the curved boundary (the circumference of the half-circle) and the length of the straight boundary (the perimeter of the equilateral triangle).

The radius of the half-circle is half the length of the side of the equilateral triangle, which is 10 inches. Therefore, the circumference of the half-circle is:

C = πr = π(10) = 31.4 inches.

The perimeter of the equilateral triangle is 3 times the length of one side, which is 20 inches. Therefore, the perimeter of the triangle is:

P = 3s = 3(20) = 60 inches

Finally, the perimeter of the entire shape is the sum of the lengths of the curved and straight boundaries:

Perimeter = C + P = 31.4 + 60 = 91.4 inches.

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Complete Question

This shape is made up of one half-circle attached to a square with side lengths 11 inches. Find the perimeter of the shape.

You can use 3.14 as an approximation for π. help i don't know it.

Answer: 25%

Step-by-step explanation: The total number of city council is 80 and 20/80 is 1/4

Among all unbiased estimators which are weighted averages of Y₁, ..., Yₙ, the sample mean as an estimator of population mean is an estimator with lower sampling variances.

The sample mean is known to be an unbiased estimator of the population mean.

Which means that on average, it provides an estimate that is equal to the true population mean.

However, when considering estimators that are weighted averages of the observations.

The sample mean tends to have lower sampling variances compared to other unbiased estimators.

Lower sampling variance is desirable because it indicates less variability in the estimates obtained from different samples.

A lower sampling variance implies that the sample mean is likely to be closer to the population mean, providing a more precise estimate.

Therefore, among unbiased estimators that are weighted averages, sample mean stands out as having a lower sampling variance.

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The circumcenter of the parallelogram with vertices (-2,-4), (-4,4), (2,12), and (4,4) is located at points (0, 4).

What is the circumcenter of a parallelogram?

The circumcenter of a parallelogram is the center of its circumcircle, which is the circle that passes through all four vertices of the parallelogram.

To find the circumcenter of the parallelogram with vertices (-2,-4), (-4,4), (2,12), and (4,4),

you can find the midpoint of each diagonal and then find the midpoint of the line segment connecting the midpoints.

The circumcenter is then located at this midpoint.

The midpoint of the diagonal (-2,-4) and (2,12) can be found as:

( (-2 + 2)/2 , (-4 + 12)/2 ) = (0, 4)

The midpoint of the diagonal (-4,4) and (4,4) can be found as:

( (-4 + 4)/2 , (4 + 4)/2 ) = (0, 4)

The midpoint of the line segment connecting the midpoints of the diagonals can be found as:

( (0 + 0)/2 , (4 + 4)/2 ) = (0, 4)

Hence, the circumcenter of the parallelogram with vertices (-2,-4), (-4,4), (2,12), and (4,4) is located at points (0, 4).

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False. The expected cell frequency in statistical analysis, specifically in the context of contingency tables and chi-square tests, is not based on the researcher's opinion. Instead, it is determined through mathematical calculations and statistical assumptions.

In contingency tables, the expected cell frequency refers to the expected number of observations that would fall into a particular cell if the null hypothesis of independence is true (i.e., if there is no relationship between the variables being studied). The expected cell frequency is calculated based on the marginal totals (row totals and column totals) and the overall sample size.

The expected cell frequency is computed using statistical formulas and is not influenced by the researcher's opinion or subjective judgment. It is a crucial component in determining whether the observed frequencies in the cells significantly deviate from what would be expected under the null hypothesis.

By comparing the observed cell frequencies with the expected cell frequencies, statistical tests like the chi-square test can assess the association or independence between categorical variables in a data set.

Thus, the statement "the expected cell frequency is based on the researcher's opinion" is false. The expected cell frequency is derived through statistical calculations and is not subject to the researcher's subjective input.

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Answer:

c. non-linear and increasing

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Equation:

\(9 /\frac{3}{4}\) \(=x\)

\(12=x\)

Check!

\(12(\frac{3}{4} )=9\)

Therefore, the greatest number of file boxes that can be stacked is 12.

The probabilities do you need in order to calculate p(getting a on 2 or fewer spins):

-p(0 successes)

-p(1 success)

-p(2 successes)

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.

Here,

What odds are required to determine p(getting a on two or fewer spins):

-p(0 successes)

-p(1 triumph)

-p (2 successes)

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The answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.

In this scenario, P(Z ≤ b) represents the cumulative probability of a standard normal distribution up to the value of b. To find the corresponding value of b, we need to find the z-score that corresponds to a cumulative probability of 0.0311.

By looking up the z-table or using a statistical calculator, we can find that the z-score corresponding to a cumulative probability of 0.0311 is approximately -1.865.

Therefore, the answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.

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The angle between the planes −x+3y+3z=5 and −5x+5y+5z=1 is approximately θ = 45.57 degrees.

To find the angle between two planes, we can use the dot product of their normal vectors. The normal vectors of the planes can be obtained by extracting the coefficients of x, y, and z terms from their respective equations.

For the first plane −x+3y+3z=5, the normal vector is [−1, 3, 3]. Similarly, for the second plane −5x+5y+5z=1, the normal vector is [−5, 5, 5].

We can calculate the dot product of the two normal vectors by multiplying their corresponding components and summing them up: (−1)(−5) + (3)(5) + (3)(5) = 5 + 15 + 15 = 35.

The magnitude of the first normal vector is √(\((-1)^2\) + \(3^2\) + \(3^2\)) = √(1 + 9 + 9) = √19.

The magnitude of the second normal vector is √(\((-5)^2 + 5^2 + 5^2\)) = √(25 + 25 + 25) = √75 = 5√3.

Now, we can find the cosine of the angle between the planes using the dot product and the magnitudes of the normal vectors: cos(θ) = (dot product) / (magnitude of first normal vector * magnitude of second normal vector) = 35 / (√19 * 5√3) = 7 / (√19 * √3) = (7√3) / √(19 * 3) = (7√3) / √57.

To convert this result to degrees, we can use the inverse cosine function: θ = arccos((7√3) / √57) ≈ 45.57 degrees.

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Answer:

I believe echolocation

Answer:

echolocation

Step-by-step explanation:

Answer:

3408cm²

Step-by-step explanation:

n (number of observations per region): n = 18, Degrees of freedom: df = 34, Point estimate for the southern part of the county: x1 = 155.056, Point estimate for the northern part of the county: x2 = 168.889

analyze the data related to the mean home prices in the northern and southern parts of the county. Here's a summary of the relevant values:

n (number of observations per region): n = 18

Degrees of freedom: df = 34

Point estimate for the southern part of the county: x1 = 155.056

Point estimate for the northern part of the county: x2 = 168.889

In this case, the real estate agent wants to test if the mean home price in the northern part of the county is higher than the southern part. The given data provides t Stat (1.949) and the t Critical one-tail value (2.441).

To determine whether the claim is true or not, we need to compare the t Stat and the t Critical one-tail values. The claim is supported if the t Stat is greater than the t Critical one-tail value.

In this case, the t Stat (1.949) is less than the t Critical one-tail value (2.441). Therefore, we cannot support the claim that the mean home price in the northern part of the county is significantly higher than the mean price in the southern part at the given 99% confidence level.

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Answer:

88059595400 hectares

Step-by-step explanation:

Convert 340 million square miles into hectares.

1 square mile = 258.99881 hectares

340,000,000 square miles = 88059595400 hectares

The forest is 88059595400 hectares.

Answer:

\(8.80597(10^{10})\) hectares

Step-by-step explanation:

This is unit conversion:

\(340,000,000miles(\frac{258.999 hectares}{1 mile} )\)

We then multiply, with our units miles canceling out and leaving us with hectares:

\(8.80597(10^{10})\) hectares

or

88059700000 hectares

Area of the shaded part to one decimal place is 15.0 cm²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.e.t.c

The area of the shaded part = area of sector - ( area of triangle + area of small sector)

area of big sector = 90/360 × 22/7 × 49

= 1/4 × 22 × 7

= 38.5 cm²

Area of small sector = 1/3 of big sector

= 38.5/3 = 12.83

The base of the triangle =

cos 60 = x/7

x = 7 × 1/2

x = 3.5 cm

sin60 = y/7

y = 0.866 × 7

y = 6.1 cm

area of triangle = 1/2 × 3.5 × 6.1

= 10.68 cm²

Area of the shaded part = 38.5 -( 10.68+12.83)

= 38.5 - 23.51

= 14.99

= 15.0 cm²( 1dp)

therefore the area of the shaded part to one decimal place e.is 15cm²

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Answer:

a) 5y - 25

Step-by-step explanation:

Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)