PLEASE HELP ASAP
A line that passes through the points (-1, -4) and (4, 2) is shown.
Which equation is the equation of the line that is perpendicular to the given line and passes through the point (-3, 7) ?

Answer:

x = 0 , x = 2

Step-by-step explanation:

3x² = 6x ( subtract 6x from both sides )

3x² - 6x = 0 ← factor out 3x from each term

3x(x - 2) = 0

equate each factor to zero and solve for x

3x = 0 ⇒ x = 0

x - 2 = 0 ( add 2 to both sides )

x = 2

solutions are x = 0 , x = 2

The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:

Simplify the numerator:

√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)

= √2m√5z√6

Simplify the denominator:

√(xy) = √(x) * √(y)

Combine the numerator and denominator:

√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)

Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

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Hello there I hope you are having a great day :) You Question A plumber can complete a job in 2 hours. If an apprentice helps, it takes only 1 1/3 hours. How long would it take the apprentice working alone?

(1 1/3) / 2 + (1 1/2) / a = 1

(4/3)a + (4/3)2 = 2a              multiply both sides by 2a

(4/3)2 = (2/3)a                      subtract (4/3)a from both sides

8/3 = 2a/3                            simplify

8 = 2a

4 = a

Hopefully that help you :)

The equations correctly set up the law of cosines to solve for x will be x² = 5² + 8² - 2 (5)·(8) cos 55°. Then the correct option is B.

The squared of the size of any solitary side of either a triangle is equal, by the cosine rule, to the total of the squares of the lengths of the other two sides, times by the cosine of something like the angle they are a part of.

Let the triangle ΔABC, then the cosine law is given as,

c² = a² + b² - 2 a·b cos C

From the graph, the measure of the length 'x' is calculated as,

x² = 5² + 8² - 2 (5)·(8) cos 55°

The equations correctly set up the law of cosines to solve for x will be x² = 5² + 8² - 2 (5)·(8) cos 55°. Then the correct option is B.

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Answer:

Because it is a regular polygon, the sum of all exterior angles is equal to 360 degrees (one revolution). If each side has an exterior angle of 40 degrees, we simply divide 360 by 40 to get 9.

Step-by-step explanation:

Hello!

surface area

= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)

= 160cm²

Answer:

4/5

Step-by-step explanation:

(i) The probability that it will take more than 10 minutes to serve a customer is approximately 0.1353.

(ii) The probability that a customer shall be free within 4 minutes is approximately 0.4866.

To solve this problem, we can use the exponential distribution formula. The exponential distribution is often used to model the time between events occurring at a constant average rate. In this case, we want to find the probability of specific service times.

Let's denote λ as the average number of customers served per hour. Given that 20 customers are served on average, we can determine λ by dividing the average number of customers by the time taken to serve them, which is 1 hour. Therefore, λ = 20 customers/hour.

Now, we can calculate the probability using the exponential distribution formula:

(i) To find the probability that it will take more than 10 minutes to serve a customer, we need to convert 10 minutes to hours, which is 10/60 = 1/6 hour. Let's call this value x.

The probability can be calculated as P(X > x) = 1 - P(X ≤ x), where X follows an exponential distribution with rate parameter λ.

P(X > 1/6) = 1 - P(X ≤ 1/6)

          = 1 - (1 - \(e^{(-\lambda x))\)     [Using the cumulative distribution function (CDF) of the exponential distribution]

          = \(e^(- \lambda x)\)

          = \(e^{(-20/6)\)

          ≈ 0.1353

(ii) To find the probability that a customer shall be free within 4 minutes, we convert 4 minutes to hours, which is 4/60 = 1/15 hour. Let's call this value y.

The probability can be calculated as P(X ≤ y), where X follows an exponential distribution with rate parameter λ.

P(X ≤ 1/15) = 1 - \(e^{(-\lambda y)\)

           = 1 - \(e^{(-20/15)\)

           ≈ 0.4866

Therefore, the probability that a customer shall be free within 4 minutes is approximately 0.4866.

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Answer:

2

Step-by-step explanation:

Parallel lines have the same slope. Hope this helps!

Answer: I know that DC is 12 and AD=8 the others i dont know.

Step-by-step explanation:

This is because opposite sides of a parallelogram are parallel and congruent. therefore AB and DC are equal/congruent.

The correct statement is;

False,  because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be  x = 2π/3 + 2nx and x = 4π/3 + 2nx.

Option D

From the information given, we have that;

All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx

There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx

Such that n is an integer.

This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.

The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.

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A rectangle and two semicircles make up this figure. The perimeter of this figure is 423.52m.

The complete length of a shape's boundary is referred to as the perimeter in geometry. The perimeter of a shape is determined by adding the lengths of all of its edges and sides. Linear measurements like centimeters, meters, inches, and feet are used to express its dimensions. The area around a form's edge is known as its perimeter. The perimeter of a shape is always calculated by summing the lengths of its sides.

Perimeter=2*1/2πd+2a

d=68, a=105

Perimeter = 2*1/2*3.14*68+2*105

423.52m

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Answer:

Because the absolute value of the test statistic is less than the positive critical value, there is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.

Step-by-step explanation:

The correlation​ matrix provided is:

Variables    Paper     Glass

  Paper           1         0.1853

 Glass        0.1853         1

Te hypothesis for the test is:

H₀: ρ = 0 vs. H₀: ρ ≠ 0

The test statistic is:

r = 0.1853 ≈ 0.185

As the alternate hypothesis does not specifies the direction of the test, the test is two tailed.

The critical value for the two-tailed test is:

\(r_{\alpha/2, (n-2)}=r_{0.05/2, (62-2)}=r_{0.05/2, 60}=0.250\)

The conclusion is:

Because the absolute value of the test statistic is less than the positive critical value, there is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.

The probability of a bone density test score being greater than 0.24 is 0.4052 or approximately 40.52%

we can use the standard normal distribution curve. This is a bell-shaped curve with a mean of zero and a standard deviation of one. The area under the curve represents the probability of a particular score occurring.

To find the probability of a bone density test score greater than 0.24, we need to find the area under the curve to the right of 0.24.

Using a standard normal distribution table or a calculator, we can find that the probability of a score being less than 0.24 is 0.5948. Therefore, the probability of a score being greater than 0.24 is:

P(score > 0.24) = 1 - P(score < 0.24)

= 1 - 0.5948

= 0.4052

So the probability of a bone density test score being greater than 0.24 is 0.4052 or approximately 40.52%.

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At a price of $3, the total revenue will be the greatest, and the company will sell 3 units at that price.

To find the total revenue at each price, we can multiply the price by the corresponding quantity.

Price        Quantity          Total Revenue

$6                0                      $0

$5                 1                       $5

$4                 2                       $8

$3                 3                        $9

$2                 4                         $8

$1                  5                          $5

To find the price at which total revenue is the greatest, we look for the highest value in the Total Revenue column.

In this case, the highest total revenue is $9, which occurs when the price is $3.

At a price of $3, the company will sell 3 units (as indicated in the Quantity column).

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Answer:

Step-by-step explanation:

At least 9 means more than 9 and includes 9

x ≥ 9     and    [9,  +∞)

At most 9 means numbers less than 9

x≤9       and  (-∞, 9]

more than 9 means bigger than 9 but not including 9

x > 9     and    (9,  +∞)

fewer than 9 means less than 9 but not including 9

x<9       and  (-∞, 9)

strictly between 7 and 9   means between 7 and 9 but not including

7<x<9      and    (7,9)       (This is the only one I'm unsure of.  Strictly, not sure if it includes or doesn't include, usually it just says include or doesn't include)

between 7 and 7 inclusive.   means it's just =7  There's no boundaries

x=7

no more than 7 means less than 7 and includes 7

x ≤ 7   and   (-∞, 7]

Answer:

5/7 meters

Step-by-step explanation:

Take the 5 meters and divide into 7 parts

5/7 = 5/7 meters

To find the length of each part, we can divide.

5 / 7 = 0.714...

We can just keep it as a fraction.

The answer is 5/7m

Best of Luck!

Step-by-step explanation:

∫ 9 arctan(1/x) dx

If u = 9 arctan(1/x), then:

du = 9 / (1 + (1/x)²) (-1/x²) dx

du = -9 dx (1/x²) / (1 + (1/x²))

du = -9 dx / (x² + 1)

If dv = dx, then v = x.

∫ u dv = uv − ∫ v du

= 9x arctan(1/x) − ∫ -9x dx / (x² + 1)

= 9x arctan(1/x) + 9/2 ∫ 2x dx / (x² + 1)

= 9x arctan(1/x) + 9/2 ln(x² + 1)

Evaluate from x=1 to x=√3.

[9√3 arctan(1/√3) + 9/2 ln(3 + 1)] − [9 arctan(1) + 9/2 ln(1 + 1)]

[9√3 (π/6) + 9/2 ln(4)] − [9 (π/4) + 9/2 ln(2)]

(3π√3)/2 + 9/2 ln(4) − (9π/4) − 9/2 ln(2)

(6π√3)/4 + 9 ln(2) − (9π/4) − 9/2 ln(2)

(6π√3 − 9π)/4 + 9/2 ln(2)

Answer:

\(9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)\)

Step-by-step explanation:

We are given the integral 9 arctan(1/x)dx on the interval x[ from 1 to √3 ].

Now let's say that u = arctan(1/x). The value of 'du' would be as follows:

du = - x / (1 + x²) * dx

If we apply integration by parts, v = 1, and of course u = arctan(1/x):

=> 9x arctan(1/x) − ∫ -9x dx / (x² + 1)

=> 9[x arctan(1/x) - ∫ - x / (1 + x²) * dx] on the interval x[ from 1 to √3 ]

Let's now simplify the expression ' ∫ - x / (1 + x²) * dx':

=> (Take the constant out, in this case constant = - 1), - ∫ x / (1 + x²) * dx

=> (Apply u-substitution, where u = 1 + x²), - ∫ 1/2u * du

=> (Take constant out again, in this case 1/2), - 1/2 ∫ 1/u * du

=> (Remember that 1/u * du = In( |u| )), - 1/2In( |u| )

=> (Substitute back 'u = 1 + x²), - 1/2In| 1 + x² |

So now we have the expression '9[x arctan(1/x) + 1/2In| 1 + x² |]' on the interval x[ from 1 to √3 ]. Let's further simplify this expression;

\(9\left[x\arctan \left(\frac{1}{x}\right)+\frac{1}{2}\ln \left|1+x^2\right|\right]^{\sqrt{3}}_1\\\\=> 9\left[\frac{1}{2}\left(2x\arctan \left(\frac{1}{x}\right)+\ln \left|1+x^2\right|\right)\right]^{\sqrt{3}}_1\)

Now computing the boundaries we have the following answer:

\(9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)\)

Answer:

STo solve for m in the equation -319.45 = m, we can isolate the variable m by adding 319.45 to both sides of the equation:

-319.45 + 319.45 = m + 319.45

This simplifies to:

0 = m + 319.45

Finally, we can subtract 319.45 from both sides to solve for m:

0 - 319.45 = m + 319.45 - 319.45

-319.45 = m

Therefore, the value of m is -319.45.tep-by-step explanation:

The missing value 'x' in the two-way relative frequency table is 0.36.

To convert the two-way table to a two-way relative frequency table, we need to calculate the relative frequencies for each category. Relative frequency is calculated by dividing the frequency of a particular category by the total count in that row or column.

Let's denote the missing value as 'x'. To find the value of 'x', we need to ensure that the sum of the relative frequencies in each row and each column adds up to 1.

First, let's calculate the relative frequencies for each category:

Likes hockey: The total count in this row is 12 + 18 = 30.

Relative frequency of "Likes hockey" = 12/30 = 0.4

Relative frequency of "Doesn't like hockey" = 18/30 = 0.6

Likes baseball: The total count in this column is 12 + 14 = 26.

Relative frequency of "Likes baseball" = 12/26 ≈ 0.4615

Relative frequency of "Doesn't like baseball" = 14/26 ≈ 0.5385

To ensure that the relative frequencies add up to 1, we can set up the following equations:

0.4 + x = 1 (sum of relative frequencies in the "Likes hockey" row)

0.4615 + 0.5385 + x = 1 (sum of relative frequencies in the "Likes baseball" column)

Simplifying the equations, we have:

x = 0.6 (1 - 0.4) = 0.6 * 0.6 = 0.36

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Angle WZY is 50 degrees, angle WZX is also 50 degrees, and angle XZW is 160 degrees.

What is the inscribed angle theorem?

The inscribed angle theorem, also known as the central angle theorem, states that an angle formed by two chords in a circle is half the measure of the arc they intersect, or subtend, inside the circle.

To find all other angles in the circle with quadrilateral WXYZ inscribed in it and WY going through the center Q:

Since WY goes through the center, angle WYZ and angle WXY are both right angles (90 degrees)

By the inscribed angle theorem, angle WZY is equal to half the measure of the arc WX.

Since angle XYZ is given as 50 degrees, the measure of the arc WX is 2 times 50 degrees, which is 100 degrees.

Therefore, angle WZY is 50 degrees.

By the same logic, angle WZX is also 50 degrees.

Since angles WYZ and WXY are right angles, angles XZY and WZX are also right angles.

Finally, we can find angle WZY + angle XYZ + angle XZW + angle WZX = 360 degrees (sum of angles in a quadrilateral), and we can solve for angle XZW which is 160 degrees.

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Answer: no

Step-by-step explanation:

because you can do what is known as the vertical line test to determine if it is a function you do that by plotting it and if it goes in a vertical line then it is a function

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

I guess it's False...Hope it helps you.

Answer:

true

Step-by-step explanation:

Answer: p = 0.13

Step-by-step explanation: Alice will receive, after the raise:

$48,000 + $6,400 = $54,400

When we add a percentage of raise to a number, we write:

x ( 1 + r )

where

x is the number we want to raise

r is the ratio we want to raise

So, for Alice's salary:

48,000(1 + r) = 54,400

1 + r = 1.13

r = 0.13

The $6,400 raise is 0.13, in nearest tenth percent "form" or 13% Alice's old salary percent.

Answer:

The perimeter is 57.2 cm and the area is 198.73 cm^2

Step-by-step explanation:

Step 1:  Determine the perimeter

\(Perimeter = 2(l + w)\)

\(Perimeter = 2(16.7\ cm + 11.9\ cm)\)

\(Perimeter = 2(28.6\ cm)\)

\(Perimeter = 57.2\ cm\)

Step 2:  Determine the area

\(Area = l * w\)

\(Area = 16.7\ cm * 11.9\ cm\)

\(Area = 198.73\ cm^2\)

Answer: The perimeter is 57.2 cm and the area is 198.73 cm^2

Answer:

The 1st option

Step-by-step explanation:

Because x can be anything that's not imaginary and y has to be below 2 always because of the negative value added before the 3. Also it's impossible to reverse the sign of the negative because negative x would only result in 3 becoming a fraction.

The value of the n is 1

In a direct variation, the relationship between two variables is of the form y = kx, where k is a constant of proportionality.

To find the constant of proportionality k in this problem, we can use the fact that the given points satisfy the equation for direct variation.

(2,18) is one of the given points, so we can substitute these values into the equation y = kx and solve for k:

18 = k(2)

k = 18/2

k = 9

Now that we have found the value of k, we can use it to find n when y = 9:

9 = 9n

n = 1

Therefore, the value of n is 1.

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