Given m||n, find the value of x.
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170
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Answer:
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               \(\hookrightarrow \text{In other words: } x + 59+ 84 + x + 51=180\)

              \(x + 59 + 84 + x + 51= 180\\2x + 194=180\\2x = -14\\x = -7\)

              m∠A = x + 51 = -7 + 51 = 44

Answer: 44

Hope that helps!

Answer: They are all symmetry :)

Step-by-step explanation:

Divide all the shapes with a straight line

The scenario that could be modeled by the graph is:

A. The number of pounds of apples, y, minus two times the number of pounds of oranges, x, is at most 5.

A linear function is defined as a function in the form of f(x) = mx + bc where 'm' and 'c' are real numbers.

It represents the line's slope-intercept form, which is written as y = mx + c.

This is because a linear function represents a line, i.e., its graph is a line. Here,

'm' is the slope of the line

'c' is the y-intercept of the line

'x' is the independent variable

'y' (or f(x)) is the dependent variable

Looking at the options, the fact that option A has 5, and x is minus two times, 5/2= 2.5, and that is where the second arrowhead is pointing to on the x axis, it means option A is correct.

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Answer:

Step-by-step explanation:

change in x (horizontal) = 4 - 1 = 3

Change in y (vertical)  = 9 - 3 = 6

Slope = change in x / change in y

slope = 3 / 6 = 1/2

Answer:

The speed on motorboat is 20 mph

Step-by-step explanation:

here, we want to find the speed on the motorboat

if he has a speed of x mph on the motor boat, his speed on the ski will be (x + 10) mph

The total hours is 4 hours

Mathematically; speed = distance/time

Time on ski is 27/x+ 10

Time on motor boat is 62/x

The addition of both is 4

Thus;

27/(x + 10) + 62/x = 4

27(x) + 62(x + 10) = 4(x)(x + 10)

27x + 62x + 620 = 4(x^2 + 10x)

89x + 620 = 4x^2 + 40x

4x^2 -49x-620 = 0

using the quadratic formula;

{-b ± √(b^2-4ac)}/2a

where a = 4, b = -49 and c = -620

= 49 ± √(-49)^2-4(4)(-620)/8

So we have

49+ 111/8 or 49-111/8

Speed cannot be negative

(49 + 111)/8

= 20 mph

Answer:

y = -5/4x +1

Step-by-step explanation:

The slope-intercept form of a line is given by

y = mx + b  where m is the slope and b is the y intercept

We are given the slope and a point on the line

y = -5/4 x + b

We can substitute the point for x and y and solve for b

-9 = -5/4(8)+b

-9 = -10+b

Add 10 to each side

-9+10=-10+10+b

1 = b

The slope intercept form of the equation is

y = -5/4x +1

Answer:

k= -14

Step-by-step explanation:

\(\boxed{slope = \frac{y1 - y2}{x1 - x2} }\)

\( \frac{5}{3} = \frac{7 - (3 - k)}{k + 3 - ( - 5)} \)

\( \frac{5}{3} = \frac{7 - 3 + k}{k + 3 + 5} \)

\( \frac{5}{3} = \frac{4 + k}{k + 8} \)

Cross multiply:

3(4 +k)= 5(k +8)

Expand:

12 +3k= 5k +40

Bring k terms to one side, constant to the other:

5k -3k= 12 -40

Simplify:

2k= -28

Divide both sides by 2:

k= -14

15.50 x 20 = $310

31 x 8 = $248

310 + 248 = $558

Her total pay for the week is $558.

Hope you got a good grade!!! :)

-8

f(x) is y, in which x is the independent variable

when x = 5, y = -8

This is the answer to your problem

The mean time between requests is estimated to be 22.366 microseconds with a standard error of 2.248 microseconds.

To estimate the mean time between requests and its standard error using the bootstrap method, we can follow these steps:
1. Compute the sample mean of the given data. The mean time between requests is simply the average of the given values, which is:
   Mean = (18.77 + 28.81 + 11.87 + 15.92 + 23.2 + 21.12 + 22.79 + 39.99 + 21.86 + 15.33) / 10 = 22.366 microseconds
2. Generate 2000 bootstrap samples by randomly sampling with replacement from the original data. Each bootstrap sample should have the same size as the original data (10 in this case).
3. For each bootstrap sample, compute the mean time between requests.

4. Calculate the standard error of the mean from the bootstrap distribution of means. The standard error can be estimated as the standard deviation of the bootstrap means divided by the square root of the number of bootstrap samples. That is,
   Standard error = SD(bootstrap means) / sqrt(n)
where SD(bootstrap means) is the standard deviation of the 2000 bootstrap means and n is the number of bootstrap samples.
Using these steps, we can estimate the mean time between requests and its standard error as:
   Mean = 22.366 microseconds
   Standard error = 2.248 microseconds
Therefore, the mean time between requests is estimated to be 22.366 microseconds with a standard error of 2.248 microseconds.

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The equation in spherical coordinates is a) 3sin²ϕ - 2sinϕcosθ/ρ - 3cos²ϕ = 0

b) 2sinφcosθ + 4sinφsinθ + 5cosφ = 1/ρ

a) The equation in Cartesian coordinates is 3x² - 2x + 3y² - 3z² = 0. To convert to spherical coordinates, we use the following substitutions:

x = ρsinϕcosθ

y = ρsinϕsinθ

z = ρcosϕ

Substituting these values into the Cartesian equation gives:

3(ρsinϕcosθ)² - 2(ρsinϕcosθ) + 3(ρsinϕsinθ)² - 3(ρcosϕ)² = 0

3ρ²sin²ϕcos²θ - 2ρsinϕcosθ + 3ρ²sin²ϕsin²θ - 3ρ²cos²ϕ = 0

3ρ²sin²ϕ(cos²θ + sin²θ) - 2ρsinϕcosθ - 3ρ²cos²ϕ = 0

3ρ²sin²ϕ - 2ρsinϕcosθ - 3ρ²cos²ϕ = 0

Simplifying and dividing by ρ² gives:

3sin²ϕ - 2sinϕcosθ/ρ - 3cos²ϕ = 0

(b) The equation in rectangular coordinates is 2x + 4y + 5z = 1. To write it in spherical coordinates, we use the same conversion formulas as before:

2(ρsinφcosθ) + 4(ρsinφsinθ) + 5(ρcosφ) = 1

Simplifying and dividing by ρ, we get:

2sinφcosθ + 4sinφsinθ + 5cosφ = 1/ρ

This is the equation in spherical coordinates.

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The value of the probability of selecting gray marble is,

⇒ 4 / 9

We have to given that;

A bag contains 3 black, 2 white marbles, and 4 gray marbles.

And,  A marble Is replaced before picking a second marble.

Hence, We get;

Total marbles = 3 + 2 + 4

                      = 9

And, Number of gray marbles = 4

Thus, The value of the probability of selecting gray marble is,

⇒ 4 / 9

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A = 2π ∫ [3, 5] √((5 - x)(1 + (1/4) * (5 - x)^(-1))) dx. This integral can be evaluated using standard techniques, such as substitution or expanding the exon.

To find the exact area of the surface obtained by rotating the curve y = √(5 - x) about the x-axis over the interval 3 ≤ x ≤ 5, we can use the formula for the surface area of revolution. The second paragraph will provide a step-by-step explanation of the calculation.

The formula for the surface area of revolution about the x-axis is given by: A = 2π ∫ [a, b] y * √(1 + (dy/dx)²) dx,

where a and b are the limits of integration.

In this case, the limits of integration are 3 and 5, as given in the problem statement.

First, we need to calculate dy/dx, the derivative of y with respect to x. Taking the derivative of y = √(5 - x), we have:

dy/dx = (-1/2) * (5 - x)^(-1/2) * (-1) = (1/2) * (5 - x)^(-1/2).

Now we substitute the values into the formula for surface area:

A = 2π ∫ [3, 5] √(5 - x) * √(1 + ((1/2) * (5 - x)^(-1/2))²) dx.

Simplifying the expression inside the integral, we have:

A = 2π ∫ [3, 5] √(5 - x) * √(1 + (1/4) * (5 - x)^(-1)) dx.

Next, we can combine the square roots:

A = 2π ∫ [3, 5] √((5 - x)(1 + (1/4) * (5 - x)^(-1))) dx.

This integral can be evaluated using standard techniques, such as substitution or expanding the exon. Apressifter performing the integration, we will have the exact value of the surface area of the rotated curve about the x-axis over the given interval.

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The relation between logarithmic function and exponential function is they both are inverse of each other.

As given in the question,

Relation between logarithmic function and exponential function is given by:

Therefore, relation between the logarithmic function and the exponential function is  that both are inverse of each other.

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Answer:

Below

Step-by-step explanation:

When it reaches the ground h = 0

h =     0 = -16t^2+676

            16t^2 = 676

             t^2 = 42.25       t = 6.5 s

The article red was titled "sense of emotion of dog and cat to humans"

To visualize the differences in feeling between Dogs and cats towards people, I would think of a dog swaying its tail and hopping up with fervor upon seeing its owner, whereas a cat may approach its owner more calmly and gradually with a loose tail.

I might picture the puppy gasping and looking for physical fondness, whereas the cat may lean toward to be petted or rubbed under the chin.

Dogs show enthusiasm and affection towards owners, while cats exhibit different behaviors. Dogs show excitement through body language like wagging tails, jumping, seeking affection, and vocalizing.

Pets express joy and eagerness to be around humans, with cats being more reserved towards humans. Although affectionate, cats express emotions subtly such as calm body posture and soft chirping.

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The area of the mean for a unformly distribution is gievn below

Given that a is the minimum or lowest value and b is the maximum or highest value

From the question given,

a= 0; b=4.1

The mean of this distribution is as shown below

Hence the mean of this distribution is 2.05

The standard deviation of the uniformly distribution is given by the formula below:

The standard deviation is as shown below:

Hence, the standard deviation is 1.1836 to the nearest 4 decimal place

The probability of exactly 2.6 is 0. This is because the probability of finding an exact number of a uniform distribution is 0

c. The probability that the round off error for a jumper's distance is exactly 2.6 is

P(x = 2.6) = 0

The probability that the round off error for the distance that a long jumper has jumped is

between 0.7 and 1.2 mm P(0.7 <3 <1.2) is as shown below:

between 0.7 and 1.2 mm P(0.7 <3 <1.2) is 0.1220 correct to four decimal place

The probability that the jump's round off error is greater than 2.72 is P(x > 2.72). This can be solved as shown below

e. Hence, the probability that the jump's round off error is greater than 2.72 is P(x > 2.72) = 0.3366

P(x > 1.7 x > 0.7) is as shown below:

f. Hence, P(x > 1.7 / x > 0.7) = 0.7059 correct to 4 decimal place

The 43rd percentile is

g. Hence, the 43rd percile is 1.763

The minimum for the upper quarter is as shown below

h. Hence, the minimum for the upper quarter is 3.075

Answer:

y = x + 6

x = 1

y = ¼(x - 5) + 3

Step-by-step explanation:

Vetices are;

A(1,5), B(5,3) and C(-3, -2)

Thus;

Median of AB is; D = (1 + 5)/2, (5 + 3)/2

D = (3, 4)

Median of BC is; E = (5 + (-3))/2, (3 + (-2))/2

E = (1, 0.5)

Median of AC is; F ; (-3 + 1)/2, (-2 + 5)/2

F = (-1, 1.5)

Thus, the median lines will be;

CD, AE & BF.

Thus;

Equation of CD is;

(y - (-3))/(x - (-2)) = (-2 - 4))/(-3 - 3)

(y + 4)/(x + 2) = -6/-6

y - 4 = 1(x + 2)

y = 4 + x + 2

y = x + 6

Equation of AE;

(y - 5)/(x - 1) = (0.5 - 5)/(1 - 1)

(y - 5)/(x - 1) = -4.5/0

Cross multiply to get;

0(y - 5) = -4.5(x - 1)

-4.5x = -4.5

x = 1

Equation of BF;

(y - 3)/(x - 5) = (1.5 - 3)/(-1 - 5)

(y - 3)/(x - 5) = -1.5/-6

(y - 3)/(x - 5) = 1/4

y - 3 = ¼(x - 5)

y = ¼(x - 5) + 3

Answer:

a) 2x² - 32 = 2(x-4)(x+4)

e) 3x² - 75 y² = 3(x-5y)(x+5y)

i) (x+5)² - 16 = (x+1)(x+9)

j) (x-4)² - 9 = (x-7)(x-1)

m) (3x+5)² - x² = (2x+5)(4x+5)

Step-by-step explanation:

Basically first you expand the expression into terms and then you refactor again.

In thsi question, the confidence coefficient when the level of significance is 0.03 is C. 0.9700.

In statistics, the confidence coefficient is the complement of the level of significance (α) used in hypothesis testing. The confidence coefficient represents the confidence level or the degree of certainty associated with a confidence interval.

The level of significance, denoted by α, is the probability of rejecting the null hypothesis when it is true. It is typically chosen before conducting a statistical test and determines the critical value or the cutoff point for decision-making.

To find the confidence coefficient, we subtract the level of significance from 1. In this case, the level of significance is 0.03. Subtracting 0.03 from 1 gives us a confidence coefficient of 0.97, which can be written as 0.9700 when rounded to four decimal places.

Therefore, the correct answer is C. 0.9700, which represents the confidence coefficient when the level of significance is 0.03.

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The length of the object if the volume is 217 cm³ is; 19.91cm

The volume of a rectangular prism is given by the formula;

Hence, since Volume = 217cm³, width = 2.8cm and height = 5cm.

Therefore;

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Answer:

So, the correct answer is (30.104, 32.896).

Step-by-step explanation:

To find the 95% confidence interval for the mean number of pounds of trash per person per week, we can use the following formula:

CI = X + Zα/2 * (σ/√n)

σ = population standard deviation = 7.8 pounds

n = sample size = 120

Plugging in the values, we get:

CI = 31.5 ± 1.96 \times(7.8/√120)

CI = 31.5 ± 1.96 \times 0.711

CI = 31.5 ± 1.39

Therefore, the 95% confidence interval for the mean number of pounds of trash per person per week is (30.11, 32.89).

So, the correct answer is (30.104, 32.896).

The top of the 17-foot ladder is sliding down the wall at a rate of -16/7.5 feet per second (negative sign indicates downward direction) when the bottom is 8 feet from the wall.

To find how fast the top of a 17-foot ladder is sliding down the wall when the bottom is 8 feet from the wall, given that the bottom slides away at a constant rate of 4 feet per second.

First, let's set up the problem using the given information. Let x represent the distance from the bottom of the ladder to the wall, and y represent the distance from the top of the ladder to the ground. According to the Pythagorean theorem, we have:

\(x^2 + y^2 = L^2\), where L is the length of the ladder, 17 feet in this case.

Now, we are given that the bottom of the ladder, x, is sliding away from the wall at a constant rate of 4 feet per second, so dx/dt = 4 ft/s.

Our goal is to find dy/dt, the rate at which the top of the ladder is sliding down the wall, when x = 8 feet.

First, differentiate both sides of the Pythagorean equation with respect to time t:

2x(dx/dt) + 2y(dy/dt) = 0

When x = 8 feet, we can find y by plugging the value into the Pythagorean equation:

\(8^2 + y^2 = 17^2\)
\(y^2 = 289 - 64\)
\(y^2 = 225\)
y = 15

Now, plug the values x = 8, y = 15, and dx/dt = 4 into the differentiated equation:

2(8)(4) + 2(15)(dy/dt) = 0

Simplify and solve for dy/dt:

64 + 30(dy/dt) = 0
dy/dt = -64 / 30
dy/dt = -16 / 7.5

Therefore, the top of the 17-foot ladder is sliding down the wall at a rate of -16/7.5 feet per second (negative sign indicates downward direction) when the bottom is 8 feet from the wall.

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The probability that Cynthia's morning porridge will be just right is 15%.

Probability is defined as the likeliness of an event to happen. It can be determined by dividing the total number of the desired outcome by the total number of samples.

The sum of the probabilities in a probability distribution is always 1.

If there are three outcomes: too cold, just right, and too hot, then the sum of their probabilities is equal to 1 or 100%.

P(too cold) + P(just right) + P(too hot) = 100%

35% + P(just right) + 50% = 100%

P(just right) = 100 - (35 + 50)

P(just right) = 100 - 85

P(just right) = 15%

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The difference between the highest score and the lowest score: Lowest score = 51Highest score = 93Range = Highest score - Lowest score= 93 - 51= 42.0 . Therefore, the range for the sample of students is 42.0. In statistical mathematics, the range is the difference between the highest and lowest values.

To calculate the range of the sample of students with the given test scores, we need to first sort the scores in ascending or descending order. Then, we find the difference between the highest score and the lowest score.

The given test scores for 8 randomly chosen students in a statistics class are:[51, 93, 93, 80, 70, 76, 64, 79]To find the range of these scores, we need to find the difference between the highest score and the lowest score: Lowest score = 51Highest score = 93Range = Highest score - Lowest score= 93 - 51= 42.0

Therefore, the range for the sample of students is 42.0.

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Answer:101

Step-by-step explanation:

The fourth and fifth intermediate quotients when converting 219 to binary are 13 and 6, respectively.

To convert a decimal number to binary, we divide the decimal number successively by 2, and note the remainder at each step. The binary number is obtained by writing these remainders in reverse order.

219 / 2 = 109 remainder 1 --> 1st remainder

109 / 2 = 54 remainder 1 --> 2nd remainder

54 / 2 = 27 remainder 0 --> 3rd remainder

27 / 2 = 13 remainder 1 --> 4th remainder

13 / 2 = 6 remainder 1  --> 5th remainder

6 / 2 = 3 remainder 0 --> 6th remainder

3 / 2 = 1 remainder 1 --> 7th remainder

1 / 2 = 0 remainder 1 --> 8th remainder

The binary number is obtained by writing these remainders in reverse order: 11011011.

219 / 2 = 109 remainder 1

109 / 2 = 54 remainder 1

54 / 2 = 27 remainder 0

27 / 2 = 13 remainder 1--> fourth intermediate quotient

The fifth intermediate quotient is obtained when we divide 219 by 2 five times:

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The average rate of change of f(x) = -3x² + 1 over each of the given intervals are; -18, 6 nd 38

We are given the function;

f(x) = -3x² + 1

(a) From 2 to 4;

f(2) = -3(2)² + 1

f(2) = -12 + 1

f(2) = -11  (2, -11)

f(4) = -3(4)² + 1

f(4) = -47  (4, -47)

Slope = (-47 - (-11))/(4 - 2)

Slope = -36/2

Slope = -18

(B) From -2 to 0;

f(-2) = -3(-2)² + 1

f(2) = -12 + 1

f(2) = -11  (-2, -11)

f(4) = -3(0)² + 1

f(4) = 1  (0, 1)

Slope = (1 - (-11))/(0 - (-2))

Slope = 12/2

Slope = 6

(C) From 2 to 5;

f(2) = -3(2)² + 1

f(2) = -12 + 1

f(2) = -11  (2, -11)

f(5) = -3(5)² + 1

f(5) = -74  (0, -74)

Slope = ((-74) - 2)/(0 - 2)

Slope = -76/-2

Slope = 38

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If you take the test and get a positive result, the probability that you have tetrachromacy is approximately 0.3571 or 35.71%.

To determine the probability that you have tetrachromacy given a positive test result, we can use Bayes' theorem. Let's define the following probabilities:

P(T) = Probability of having tetrachromacy (10% or 0.1)

P(¬T) = Probability of not having tetrachromacy (90% or 0.9)

P(Pos|T) = Probability of a positive test result given tetrachromacy (true positive rate, 70% or 0.7)

P(Pos|¬T) = Probability of a positive test result given no tetrachromacy (false positive rate, 14% or 0.14)

We want to find P(T|Pos), the probability of having tetrachromacy given a positive test result.

According to Bayes' theorem:

P(T|Pos) = (P(Pos|T) * P(T)) / P(Pos)

To find P(Pos), the probability of a positive test result, we can use the law of total probability:

P(Pos) = P(Pos|T) * P(T) + P(Pos|¬T) * P(¬T)

Plugging in the values:

P(Pos) = (0.7 * 0.1) + (0.14 * 0.9)

= 0.07 + 0.126

= 0.196

Now we can calculate P(T|Pos):

P(T|Pos) = (P(Pos|T) * P(T)) / P(Pos)

= (0.7 * 0.1) / 0.196

= 0.07 / 0.196

≈ 0.3571

Therefore, if you take the test and get a positive result, the probability that you have tetrachromacy is approximately 0.3571 or 35.71%.

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