Consider the points below. P(2,0,2),Q(−2,1,4),R(6,2,6) (a) Find a nonzero vector orthogonal to the plane through the points P,Q, and R. (b) Find the area of the triangle PQR. x

a. The population of interest in this case is the general public of the United States who have knowledge about the criminal trial and its verdict. b. It is likely that the proportion of people unhappy with the verdict in the sample is similar to the proportion of individuals unhappy with the verdict in the population.

a. The population of interest in this case is the general public of the United States who have knowledge about the criminal trial and its verdict.

b. It is likely that the proportion of people unhappy with the verdict in the sample is similar to the proportion of individuals unhappy with the verdict in the population. This is because the television news program invited viewers to go to their website and indicate their opinion, which means that only a certain segment of the population who watched that particular news program and had access to the internet were able to participate in the poll. Additionally, people who feel strongly about the verdict may be more likely to participate in the poll, leading to potential bias in the sample. Therefore, it is important to acknowledge that the poll results may not be entirely representative of the entire population and should be interpreted with caution. In order to obtain a more accurate estimate of the proportion of people unhappy with the verdict in the population, a larger, more diverse and random sample should be used.

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RS = RT + TS = 24 cm

Let's plug our values into the equation above

24cm = 6x - 4 + 10cm

Combine like terms

24 cm = 6x + 6 cm

Subtract 6 cm from both sides

18 cm = 6x

Divide both sides by 6

3 = x

Plug 3 into the expression for RT

RT = 6(3) - 4 = 18 - 4 = 14 cm

Similarly, we know that TS = 10 cm and RS = 24 cm

24 cm - 10 cm = 14 cm

RT = 14 cm

14 cm = 6x - 4

Add 4 to both sides

18 cm = 6x

Divide both sides by 6

3 = x

Answer:

it's B

Step-by-step explanation:

(x + 5)^2 + (y - 2)^2 = 81

A. is not A

(1 + 5)^2 + (-4 - 2)^2

6^2 + -6^2

36 + (-36) = 0

B. is B

(-5 + 5)^2 + (11 - 2)^2

0^2 + 9^2

0 + 81 = 81

C. is not C

(-5 + 5)^2 + (2 - 2)^2

0^2 + 0^2

0 + 0 = 0

D. is not D

(-3 + 5)^2 + (-8 - 2)^2

2^2 + -10^2

4 + -100 = -98

Answer:

The 95% confidence interval for the population proportion of all persons who do not have any health insurance is (0.148, 0.192).

Here is the calculation:

Sample size = 800

Number of persons who do not have any health insurance = 120

Sample proportion = 120 / 800 = 0.15

Confidence level = 95%

Z-critical value for 95% confidence level = 1.96

Confidence interval = (sample proportion - Z-critical value * standard error of the sample proportion, sample proportion + Z-critical value * standard error of the sample proportion)

Standard error of the sample proportion = sqrt(sample proportion * (1 - sample proportion) / sample size)

Standard error of the sample proportion = sqrt(0.15 * (1 - 0.15) / 800) = 0.0128

Confidence interval = (0.15 - 1.96 * 0.0128, 0.15 + 1.96 * 0.0128)

Confidence interval = (0.148, 0.192)

Step-by-step explanation:

Step-by-step explanation:

step 1. U(-7, 2) -> U'(-2, -7)

step 2. V(-7, 7) -> V'(-7, -7)

step 3. W(-1, 6) -> W'(-6, -1)

Answer:

21

Step-by-step explanation:

Answer:

Step-by-step explanation:

Therefore, the MAP estimate of μ is simply the observed values x₁ and x₂.

To find the maximum a posteriori (MAP) estimate of the random variable μ, given two observations x₁ and x₂, we need to solve a system of two linear equations.

Let's denote μ₁ and μ₂ as the true values of the mean parameter μ corresponding to x₁ and x₂, respectively. We can write the two linear equations as follows:

x₊₁ = μ₁ + ε₁ ...(1)

x₂ = μ₂ + ε₂ ...(2)

where ε₁ and ε₂ are random noise terms.

Since the random variables ε₁ and ε₂ are independent standard normal random variables, we know that their means are zero, and their variances are both equal to 1.

Taking the MAP estimate means finding the values of μ₁ and μ₂ that maximize the posterior probability given the observed data. Assuming a flat prior distribution for μ, we can write the joint probability of x₁ and x₂ as:

P(x₁, x₂ | μ₁, μ₂) ∝ P(x₁ | μ₁) × P(x₂ | μ₂)

Since both x₁ and x₂ are normally distributed with mean μ₁ and μ₂, respectively, and variance 1, we can express the probabilities P(x₁ | μ₁) and P(x₂ | μ₂ as follows:

P(x₁ | μ₁) = (1/√(2π)) * exp(-(x₁ - μ₁)² / 2)

P(x₂ | μ₂) = (1/√(2π)) * exp(-(x₂ - μ₂)² / 2)

Taking the logarithm of the joint probability, we can simplify the calculations:

log[P(x₁, x₂ | μ₁ , μ₂)] ∝ -(x₁ - μ₁)² / 2 - (x₂ - μ₂)² / 2

To find the values of μ₁ and μ₂ that maximize this expression, we need to solve the following system of equations:

d/dμ1 log[P(x₁, x₂ | μ₁ , μ₂)] = 0

d/dμ2 log[P(x₁, x₂ | μ₁, μ₂)] = 0

Differentiating the above expression and setting the derivatives to zero, we have:

-(x₁ - μ₁) = 0 ...(3)

-(x₂ - μ₂) = 0 ...(4)

Simplifying equations (3) and (4), we obtain:

μ₁ = x₁

μ₂ = x₂

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Answer:

Step-by-step explanation:

Answer:

An horizontal line.

Step-by-step explanation:

Answer:

41.61730409 you have to use your calculator to get the answer

There is a 95% chance that the mean length of all term papers lies between confidence limits (11.58,17.82) for the given data:

14, 20, 25, 10, 16, 8, 15, 12, 18, 9

We assume the length of paper has an approximately normal distribution.

Sample size = 10

The sample mean for the given data = 14.7

The standard deviation for the given data = 5.04

Critical value is obtained from standard normal distribution at the level of significance 0.05.

The critical value is 1.96.

The 95% confidence interval for the mean length of all term papers is calculated as follows:

P(14.7 - (1.96 x (5.04/√10)) < µ < 14.7 + (1.96 x (5.04/√10))) = 0.95

P(11.58 < µ < 17.82) = 0.95

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The value of the probability of choosing a green lollipop and a purple lollipop is, 8 / 45

We have to given that;

One bag contains 3 red lollipops and 2 green lollipops.

And, The other bag contains four purple lollipops and five blue lollipops.

Hence, The probability of choosing a green lollipop is,

P₁ = 2 / 5

And, The probability of choosing a purple lollipop is,

P₂ = 4 / 9

Thus, The value of the probability of choosing a green lollipop and a purple lollipop is,

P = P₁ ×  P₂

P = 2/5 × 4/9

P = 8/45

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The scatter plot of the data in the table is:

And there we can see that the data is similar to a line. We can say that the two values are associated by a linear correlation.

Answer: 4x-9y=27 is this equation in standard form.

x/r - s = t

Add s to both sides.

x/r - s + s = s + t

x/r + 0 = s + t

x/r = s + t

Multiply both sides by r.

r(x/r) = r(s + t)

x = r(s + t)

Understand?

Answer:

x=tr/s

Step-by-step explanation:

x/r-s=t

x-s=t×r

x-s/s=tr/s

x=tr/s

Answer:

around 186 Words per minute

Step-by-step explanation:

I'm not exactly sure but you have to find out how much pages are on 1 page by dividing 90'000 by 325, which gets you 276. Then you times 81 by 276 to find out how much words jamie read, which gets you 22,356. then you will divide it by 120, which is 2 hours which gets you 186.

Answer:A

Step-by-step explanation:

The initial height is 12 feet.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

3 (x + 4)² + 12

The constant value = 12

The constant in the simplified form of the expression represents the initial height, in feet, of the ball.

So,

The initial height is 12 feet.

Thus,
Initial height = 12 feet.

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75% of the beads are green in color.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Chase ordered a set of beads

He received 4,000 beads in all.

3,000 of the beads were green.

We need to find the  percentage of the beads were green of 4000.

x/100×4000=3000

40x=3000

Divide both sides by 40

x=75%

Hence, 75% of the beads are green in color.

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Answer:

b

Step-by-step explanation:

Answer:

Hi! The answer to your question is B. 30 Trees

Step-by-step explanation:

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Hope this helps!!

- Brooklynn Deka

Without specific information about the data set, it is not possible to determine which equation is the best fit.

To determine the linear function equation that best fits the data set, we need more information about the data set itself. Without the data points or any other details, we cannot accurately determine which linear function equation is the best fit.

However, I can provide a general explanation of the four options:

y = -2x + 5: This is a linear equation with a negative slope of -2. It represents a line that decreases as x increases. The y-intercept is 5.

y = 2x + 5: This is a linear equation with a positive slope of 2. It represents a line that increases as x increases. The y-intercept is 5.

y = -1/2x + 5: This is a linear equation with a negative slope of -1/2. It represents a line that decreases at a slower rate as x increases. The y-intercept is 5.

y = 1/2x - 5: This is a linear equation with a positive slope of 1/2. It represents a line that increases at a slower rate as x increases. The y-intercept is -5.

Without specific information about the data set, it is not possible to determine which equation is the best fit. The best fit would depend on how well the equation aligns with the actual data points.

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Display ads sold on a cost per thousand impressions (CPM) basis often focus on reaching a large audience or maximizing brand exposure.

Cost per thousand impressions (CPM) is a common pricing model used in digital advertising, where advertisers pay for every one thousand times their ad is displayed to users.

In this model, the focus is on the number of impressions or views rather than the actual performance or engagement with the ad. As a result, display ads sold on a CPM basis often prioritize reaching a large audience and maximizing brand exposure.

By selecting a CPM pricing model, advertisers aim to increase their ad's visibility and generate brand awareness among a wide range of users.

They are interested in getting their message in front of as many people as possible, regardless of whether those users interact with the ad or take any specific action.

CPM-based display ads are commonly used for branding campaigns, where the primary goal is to create brand recognition, increase visibility, and establish a presence in the minds of potential customers.

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Answer:

Slope would equal 3.

slope= (y2-y1)/(x2-x1)

Plug in you get (8-2)/8-6)

Simplify (6)/(2)=3

Step-by-step explanation:

In this exercise we have to calculate the value of the water depth, so we have: d=5.5Cos(12t)+6

A periodic wave is a wave with a repeating continuous pattern that determines its wavelength and frequency

Putting together some information given in the statement we have:

Knowing that the formula will be given by an equation similar to:

\(d=acos(bt)+k\)

Where:

The amplitude difference is given by:

\(8.75-3.25=5.5\ m\)

The mean depth is:

\(k=\dfrac{(3.25+8.75)}{2}=6\ m\)

Then writing the equation with;

\(d=acos(bt)+k\\\\d=5.5cos(12t)+6\)

Hence the value of water depth will be d=5.5Cos(12t)+6

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In Triangle ABC which is an Isosceles triangle. AB = BC where mLB = 34° so mLA = 73°

Triangles that have at least two sides of equal length are said to be isosceles.

Sum of all angle of a traingle is 180°

So mLA + mLB +mLC = 180

2(mLA) + mLB = 180

2(mLA ) = 180 - 34

2(mLA ) = 146

mLA = 73°

An isosceles triangle has three angles, which, like other triangles, sum up to 180 degrees. The angles other than the apex angle among the three inner angles are identical in size. According to the isosceles triangle theorem, an isosceles triangle has equal-sized angles on either side of its equal sides. As a result, we have B = C in the isosceles triangle ABC where AB = AC.

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