Find the components of PQ, P= (-7,-4), Q = (5, -8). (Use symbolic notation and fractions where needed. Give your answer as the point's coordinates in the form (*.*). (*, *)...)) PQ Let R=(3,-4). Find the point P such that PR has components (3,0). Find the unit vector in the direction opposite to v= = (-1,4). Find the vector of length 2 making an angle of 60° with the x-axis. Find the components and length of the following vectors: -li + 5j Components: { Length: li - 4j Components: { Length: -5i + 5j Components: { Length: -li +2j Components: { Length:

Answer:

y = 10

Step-by-step explanation:

If y varies directly with x, and y=20 when x=-2, the best way to find y when x=-1 is to divide 20/-2, which equals -10.

Now cancel out -1 by dividing it by 1, and do the same with -10 by dividing it by 1 also. This equals 10, and that's your answer. Check the table I made below representing the problem. It should make it easier understand.

Answer:

12-157.5  13-6ft

Step-by-step explanation:

the first one just look up 65% of 450 and minus the number you get by 450

the second one do the butterfly method

\(\frac{5}{12} \frac{x}{14.4} \\\)

the heights on top and shadows on bottom

12x=72

x=6

Answer:

-1/3

Step-by-step explanation:

Rewrite as y = ax + b then inspect a

-y - (1/3)x = 0

y = (-1/3)x

so slope is -1/3

Answer:

7/24

Step-by-step explanation:

two minuses make a +,

meaning this equation is basically

-1/12+3/8

find a common denominator by LCM.

8,16,24,32

12,24,36,48

they share 24

denominator is 24

12*2 is 24, -1*2 = -2. 8*3 = 24 so we do 3*3 = 9

-2+9/24

7/24

Answer:

\(f'(x)=1+\ln x\)

Step-by-step explanation:

\(f'(x)\) is notation for the first derivative of \(f(x)\).

Recall the product rule:

\((f\cdot g)'=f'\cdot g+g'\cdot f\)

Therefore, we have:

\(\displaystyle \frac{d}{dx}(x\ln x)=\frac{d}{dx}(x)\cdot \ln(x)+\frac{d}{dx}(\ln x)\cdot x\)

Note that:

\(\displaystyle \frac{d}{dx}(x)=1,\\\\\frac{d}{dx}(\ln x)=\frac{1}{x}\)

Simplify:

\(\displaystyle \frac{d}{dx}(x\ln x)=1\cdot \ln x+\frac{1}{x}\cdot x, \\\\\frac{d}{dx}(x\ln x)= \ln x+1=\boxed{1+\ln x}\)

The derivative is:

\( \bold{f(x) \: = \: x \: \times \: (In(x))}\)

\( \bold{f'(x) \: = \: \frac{d}{dx} (x \: \times \: In(x))}\)

\( \bold{f'(x) \: = \: \frac{d}{dx} (x) \: \times \: In(x) \: + \: x \: \times \: \frac{d}{dx} (In(x))}\)

\( \bold{f'(x) \: = \: 1In(x) \: + \: x \: \times \frac{1}{x} }\)

\( \bold{f'(x) \: = \: In(x) \: + \: x \: \times \: \frac{1}{x} }\)

\( \boxed{ \bold{f'(x) \: = \: In(x) \: + \: 1}}\)

The equation of variation is xy = k.

The required values are given below.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

y inversely varies as x.

That means, y ∝ 1/x.

So, y = kx, where k constant of variation.

Then, x × y = k

When y = 8, x = 3.

k = 3 × 8 = 24

So, the equation of variation is xy = 24.

When x = 6,

6y = 24

⇒ y = 4

When y = 9, x = 6.

k = 6 × 9 = 54

So, the equation of variation is xy = 54.

When y = 4,

4x = 54

⇒ x = 27/2

When y = 1.5, x = 14.

k = 1.5 × 14 = 21

So, the equation of variation is xy = 21.

When x = 9,

9y = 21

⇒ y = 7/3

When y = 20, x = 10.

k = 20 × 10 = 200

So, the equation of variation is xy = 200.

When y = 25,

25x = 200

⇒ x = 8

Therefore, the values are given above.

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So first you’ll have to find the total or the sum of collected.

$90+$60= $150

Because you’re finding the percent of the total collected by girl scouts, divide the amount collected from the girl scouts by the total.

$90/$150= .6

Multiply that by 100 to get %60.

The height of the steeple is 12.66 feet.

To find the height of the steeple, we will use the concept of angle of elevation. Angle of elevation is the angle between the horizontal line and the line of sight when we look up at an object.

Let's denote the height of the church as h1 and the height of the steeple as h2. Then, the total height of the church and the steeple is h1 + h2.

Using the concept of angle of elevation, we can write the following equations:

tan(35°) = h1/50 tan(47°40') = (h1 + h2)/50

Solving the first equation for h1, we get:

h1 = 50 * tan(35°) = 35.08 feet

Substituting the value of h1 into the second equation and solving for h2, we get:

50 * tan(47°40') = 35.08 + h2

h2 = 50 * tan(47°40') - 35.08

= 47.74 - 35.08 = 12.66 feet

Therefore, the height of the steeple is 12.66 feet.

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Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, if the mean of the first data set is x, then the sum of the values in the first data set is 13x (since there are 13 classmates), and the sum of the values in the second data set is also 13x (since none of the values have changed). Therefore, the mean of the second data set will also be x, and the change in the means will be zero.

Answer:

Part 1: x = -2

Part 2: x = 56

Step-by-step explanation:

Part 1:

12x + 9 = -15

Given that-

12x + 9 = -15

12x + 9 - 9 = -15 -9                >> Subtract 9 to both sides

12x = -24

12x/12 = -24/12                    >> Divide both sides by 12

x = -2

Check Answer:

12(-2) + 9 = -15                 >> 12 × -2 = -24

-24 + 9 = -15                   >> -24 + 9 = -15

-15 = -15                        >> Correct

Part 2:

x/7 - 4 = 4

Given that-

x/7 - 4 = 4

x/7 - 4 + 4 = 4 + 4                 >> Add 4 to both sides

x/7 = 8                

7x/7 = 8 × 7                             >> Multiply both sides by 7

x = 56

Check Answer-

Substitute x in the equation the check.

56/7 - 4 = 4              >> 56/7 = 8

8 - 4 = 4                  >> 8 - 4 = 4

4 = 4                        >> Correct

RevyBreeze

The probability of NOT drawing a face card from a standard deck of 52 cards is 10 over 13.

First determine the total number of face cards and non-face cards in a standard deck of 52 cards.                                   In a standard deck, there are 12 face cards (3 face cards per suit: Jack, Queen, and King, and 4 suits: Hearts, Diamonds, Clubs, and Spades). This means there are 52 - 12 = 40 non-face cards.

Now, we'll calculate the probability of NOT drawing a face card:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Probability of NOT drawing a face card = (Number of non-face cards) / (Total number of cards)
Probability = 40 / 52

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (4):
Probability = (40/4) / (52/4)
Probability = 10 / 13

So, the probability of NOT drawing a face card from a standard deck of 52 cards is 10/13. Your answer: 10 over 13.

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Answer:

48 yards

Step-by-step explanation:

Use the Pythagorean theorem:

\( {a}^{2} = {52}^{2} - {20}^{2} = 2704 - 400 = 2304\)

\(a > 0\)

\(a = \sqrt{2304} = 48 \: yd\)

Answer:

a

Step-by-step explanation:

2 angles. 1 sude

a. The variance in the advertisement time for the 30-minute TV show is 0.67 minutes squared. The probability that the amount of time spent on advertisement for the 30-minute TV show is greater than 10 minutes is 0.67.

a. To calculate the variance in the advertisement time, we can use the formula for the variance of a uniform distribution. The formula for variance is (b - a)^2 / 12, where 'a' is the minimum value and 'b' is the maximum value. In this case, the minimum value is 8 minutes and the maximum value is 12 minutes. Plugging these values into the formula, we get (12 - 8)^2 / 12 = 16 / 12 = 0.67 minutes squared.

b. To find the probability that the amount of time spent on advertisement is greater than 10 minutes, we need to calculate the proportion of the distribution that lies above 10 minutes. Since the distribution is uniform, this proportion is equal to (b - 10) / (b - a), where 'a' and 'b' are the minimum and maximum values, respectively. Plugging in the values, we get (12 - 10) / (12 - 8) = 2 / 4 = 0.5.

The variance in the advertisement time for the 30-minute TV show is 0.67 minutes squared. The probability that the amount of time spent on advertisement for the 30-minute TV show is greater than 10 minutes is 0.5.

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Answer:

point-slope form, standard form, and slope-intercept form

Step-by-step explanation:

The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.

Here is an image with each form

Data from a random sample must be satisfied in order to construct a confidence interval about a population mean.

What is population mean?

There are various mean types in mathematics, particularly in statistics. Each mean helps to summarize a certain set of data, frequently to help determine the overall significance of a specific data set.

A group characteristic is averaged out to create the population mean. The group may consist of a person, an object, or a thing, such as "everyone who lives in the United States."

Data from a random sample is required in order to create a confidence interval estimate for an unknown population mean.

Following are the steps for creating and interpreting the confidence interval: Utilizing the sample data, determine the sample mean x - x bar.

Do not forget that in this part, we have the population standard deviation σ.

Therefore, data from a random sample must be satisfied in order to construct a confidence interval about a population mean.

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the 95% confidence interval for the difference in the true mean tooth damage for the two types of cereal eaters is (-1.167, 3.587).

Margin of error (MOE) is a statistical term that refers to the amount of random sampling error that is expected to be present in a survey or experiment. It is the range of values above and below the point estimate of a population parameter that is likely to contain the true value of the parameter with a certain level of confidence.

Based on the summary data provided,

we can use a two-sample t-test to construct an approximate 95% confidence interval for the difference in the true mean tooth damage for the two types of cereal eaters.

The sample mean tooth damage for sweetened-cereal lovers = 6.41 with a sample size of 15, and the sample mean tooth damage for unsweetened-cereal lovers is 5.20 with a sample size of 10. The pooled sample standard deviation is calculated as follows:

sₐ = √(((n1-1)×s₁² + (n2-1)×s₂²) / (n₁+ n₂ - 2))

= √(((15-1)×3.59² + (10-1)×1.81²) / (15 + 10 - 2))

= 2.715

Using the formula for the standard error of the difference between two means, we can calculate the margin of error for a 95% confidence interval as:

ME = t (d f ) × sₐ × √(1/n₁ + 1/n₂)

= 2.262× 2.715 ×√(1/15 + 1/10)

= 2.377

Therefore, the approximate 95% confidence interval for the difference in the true mean tooth damage for the two types of cereal eaters is:

(6.41 - 5.20) ± ME

= 1.21 ± 2.377

= (-1.167, 3.587)

So, the answer is (6.41-5.20) ± 2.377, or (-1.167, 3.587), which is the third option.

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Answer:

The equation is:

8x + 4 = 68

and the solution is:

x = 8

Step-by-step explanation:

The equation is:

8 time x and 4 is 68

8x+4 = 68

Solve:

8x + 4 - 4 =  68 - 4

8x + 0 = 64

8x = 64

x = 64/8

x = 8

Check:

8*8 + 4 = 68

Answer:

27 ounces of blueberry juice. 40 ounces of soy milk. 13 ounces of banana flavoring.

Step by Step:

4 + 1.3 = 5.3, This is how much of the smoothie is made up of the soy milk and banana flavoring, 5.3 ounces.

So to find the amount of blueberry juice in the smoothie you have to subtract 8-5.3. This finds the remaining part of the smoothie, which is the blueberry juice. 8-5.3 = 2.7

2.7 ounces of blueberry juice in each smoothie.

Now you have to multiply every ingredient by 10, since there are 10 smoothies.

4 * 10 = 40

1.3 * 10 = 13

2.7 * 10 = 27

You need 40 ounces of soymilk, 13 ounces of banana flavoring, and 27 ounces of blueberry juice to make 10, 8-ounce smoothies.

do you have a picture or problem sentance that goes with that

Answer:

£450

Step-by-step explanation:

using the formula C = 12×m.p + d

£8000 = 12m.p + £2600

collecting like terms, £8000 - £2600 = 12m.p

£5400 = 12m.p

dividing by coefficient of m.p,

£5400/12 = 12m.p/12

when you divide,

£450 = m.p

hence, m.p = £450

An expression showing the effect doubling the radius has on the cone's volume is 4πr²h/3.

In Mathematics and Geometry, the volume of a cone can be calculated by using this formula:

Volume of cone, V = 1/3 × πr²h

Where:

When the radius of this cone is doubled, we have the following:

Radius, r = 2r

By substituting the given parameters into the formula for the volume of a cone, we have the following;

Volume of cone, V =  1/3 × π × (2r)² × h

Volume of cone, V =  1/3 × π × 4r²h

Volume of cone, V = 4πr²h/3.

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Answer: 157.1

Step-by-step explanation:

Null space is defined as the set of vectors 'x' in Rn that are solutions to the matrix equation A*x = 0. False: The set of all vectors of the form 1 x y where x and y range over all real numbers is a subspace of R3. True: The set of all vectors of the form 0 x y where x and y range over all real numbers is not a subspace of R3.

1) False Null space can consist of zero vector only. A null space is defined as the set of vectors 'x' in R^n that are solutions to the matrix equation A*x = 0.

2) True The number of columns can never be less than the number of rows of the matrix in order for a null space to exist, hence a 4x3 matrix may have the null space of only the zero vector.

3) True The set of all vectors of the form 1 x y where x and y range over all real numbers, is a subspace of R^3. This set contains zero vector because for x=0 and y=0, we get the vector as [0,0,0]. Hence it is a subspace of R^3.

4) False The set of all vectors of the form 0 x y where x and y range over all real numbers, is not a subspace of R^3 as it doesn't contain zero vector. To have a subspace of R^3, it should contain a zero vector.

So, the correct options are:1) False2) True3) True4) False

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x = 6

Step-by-step explanation:

\(2x + 11 - 5x = 5 - 6x\)

Collect like terms and simplify

\( - 2x - 5x + 6x = 5 - 11 \\ - x = - 6\)

Divide through by -1 to reverse the inequality

\(x = 6\)

The volume of the solid obtained by rotating the region bounded by y = 5x and y = 5x about y = 5 is 0.

To find the volume of the solid obtained by rotating the region bounded by the curves y = 5x and y = 5x about the line y = 5, we can use the method of cylindrical shells.

Let's first sketch the two curves y = 5x and y = 5 on the xy-plane. These two lines intersect at the origin (0, 0) and at (1, 5).

The region bounded by these curves is a triangle with vertices at (0, 0), (1, 5), and the origin.

Now, we want to rotate this triangular region about the line y = 5. This will create a cylindrical shell with an inner radius of 5 - y and an outer radius of 5 - y (since we are rotating about the line y = 5). The height of the cylindrical shell will be the x-coordinate of the points on the curves (y = 5x or y = 5x) as they sweep around the rotation axis.

The volume of the cylindrical shell can be expressed as:

dV = 2π * (outer radius) * (height) * (thickness)

Now, we need to find the outer radius and height in terms of y (since we are integrating with respect to y).

The outer radius is 5 - y (distance from y = 5 to y = 5x or y = 5x).

The height is the x-coordinate of the points on the curves, which can be expressed as x = y/5 for y = 5x and x = y/5 for y = 5x.

So, the volume of the solid obtained by rotating the region bounded by y = 5x and y = 5x about y = 5 can be expressed as:

v = ∫[from y = 0 to y = 5] 2π * (5 - y) * (y/5 - y/5) dy

v = ∫[from y = 0 to y = 5] 2π * (5 - y) * 0 dy

v = ∫[from y = 0 to y = 5] 0 dy

v = 0

Therefore, the volume of the solid obtained by rotating the region bounded by y = 5x and y = 5x about y = 5 is 0.

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Using the hypergeometric distribution, it is found that there is a 0.1515 = 15.15% probability that you pick at least 3 green balls.

The balls are chosen without replacement, hence the hypergeometric distribution is used.

The formula is:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The probability that you pick at least 3 green balls is:

\(P(X \geq 3) = P(X = 3) + P(X = 4)\)

Hence:

\(P(X = 3) = h(3,12,4,5) = \frac{C_{5,3}C_{7,1}}{C_{12,4}} = 0.1414\)

\(P(X = 4) = h(4,12,4,5) = \frac{C_{5,4}C_{7,0}}{C_{12,4}} = 0.0101\)

Then:

\(P(X \geq 3) = P(X = 3) + P(X = 4) = 0.1414 + 0.0101 = 0.1515\)

0.1515 = 15.15% probability that you pick at least 3 green balls.

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Answer:

-4.84

Step-by-step explanation:

the -4.84 is closest to the positive side of a number line. meaning -4.84 is greater

Answer:

-4.84

Step-by-step explanation:

Becuase the smaller the minus number the greater Becuase its the reverse of positive numbers

In the analysis of variance procedure (ANOVA), "factor" refers to the independent variable, which is manipulated in order to observe its effect on the dependent variable.

In the analysis of variance procedure (ANOVA), factor refers to:
b. the independent variable

In ANOVA, a factor is an independent variable that is manipulated or controlled to investigate its effect on the dependent variable. Different levels of a factor represent the variations in the independent variable being tested. The different levels of a treatment are often created by manipulating the factor.
In contrast, independent variables are not considered dependent on other variables in various experiments. [a] In this sense, some of the independent variables are time, area, density, size, flows, and some results before the affinity analysis (such as population size) to predict future outcomes (dependent variables).

In both cases it is always a variable whose variable is examined through a different input, statistically also called a regressor. Any variable in an experiment that can be assigned a value without assigning a value to another variable is called an independent variable.

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