write equation from slope and 1 point. i need help on both questions please.

Answer:

A democratic country has a system of government in which the people have the power to participate in decision-making. ... In some democracies citizens help make decisions directly by voting on laws and policy proposals (direct democracy).

Below represents the proof that the quadrilateral QRST is a parallelogram

The coordinates are given as:

Q = (-1,-1)

R = (2,9)

S = (-4,5)

T = (-7,-5)

Calculate the length of each side using:

\(d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}\)

So, we have:

\(QR = \sqrt{(-1 - 2)^2 + (-1 -9)^2} = \sqrt{109}\)

\(RS = \sqrt{(-4 - 2)^2 + (5 - 9)^2} = \sqrt{52}\)

\(ST = \sqrt{(-7 + 4)^2 + (-5 - 5)^2} = \sqrt{109}\)

\(TQ = \sqrt{(-7 + 1)^2 + (-5 + 1)^2} = \sqrt{52}\)

The above computations show that opposite sides are equal.

Next, we determine the slope of each side using:

\(m = \frac{y_2 -y_1}{x_2 -x_1}\)

So, we have:

\(QR = \frac{9 + 1}{2 + 3} = \frac{10}3\)

\(RS = \frac{5-9}{-4 - 2} = \frac{2}3\)

\(ST = \frac{5+5}{-4 + 7} = \frac{10}3\)

\(TQ = \frac{-5+1}{-7 + 1} = \frac{2}3\)

The above computations show that opposite sides are parallel, because they have equal slope

Hence, the quadrilateral QRST is a parallelogram

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The correct expression is 300° - 840°. The expression that finds the measure of an angle that is coterminal with a 300° angle is  300° - 840°. (Option 2 )

The expression that finds the measure of an angle that is coterminal with a 300° angle is 300° - 360°k, where k is an integer.

To find an angle that is coterminal with 300°, we need to subtract a multiple of 360° from 300°. Since we want the angle to be less than 300°, we need to choose a negative value for k.

The only option given that is less than 300° is 300° - 840° = -540°. Therefore, the correct expression is 300° - 840°.

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Complete Question:

Which expression finds the measure of an angle that is coterminal with a 300° angle?

The equation to represent the time taken by piper to walk and skate is  x + 2x = 21. The correct option is (A).

A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.

Suppose the number of times piper walked be x.

Then, the number of times he skated is 2x.

Now, as the total time spent on walking and skating is 21 minutes, the equation can be written as,

Total time = Time for walking + time for skating

⇒ 21 = x + 2x

⇒ 3x = 21

⇒ x = 7

Thus, the solution of the equation is x = 7 which is equivalent to the time for walking in minutes.

Hence, the required equation is  x + 2x = 21 and its solution is 7.

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Answer:28

Step-by-step explanation: divide 420 by 15

Answer:

The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, and 72.

Answer:

8, 16, 24, 32, 40, 48, 56, 64, 72

Step-by-step explanation:

8, 16, 24, 32, 40, 48, 56, 64, 72

The null hypothesis (H₀): p > 0.58

and the alternative hypothesis (\(H_A\)) :  p = 0.58

Also there isn't sufficient evidence at the 0.01 level of significance, that is, at a 1% level of significance, to refute the publisher's claim

Let us assume that p defines the population proportion of the publishers who own a personal computer.

Now, to test the claim, 58 % of their readers own a personal computer. (ex. p = 0.58)

This is be an alternative hypothesis and the null hypothesis proportion should be, p > 0.58

Now for this scenario,

the null hypothesis is H₀: p > 0.58

and the alternative hypothesis is \(H_A\):  p = 0.58

The newsletter publisher reject the null hypothesis.

Thus, the alternative hypothesis was accepted.

So, we can draw the conclusion: There isn't sufficient evidence at the 0.01 level of significance, that is, at a 1% level of significance, to refute the publisher's claim.

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The complete question is:

A newsletter publisher believes that 58% of their readers own a personal computer. Is there sufficient evidence at the 0.01 level to refute the publisher's claim?

State the null and alternative hypotheses for the above scenario.

The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

A line process has three processing stages with the characteristics given below:

Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%

To determine the system capacity and the bottleneck stage and utilization of Stage 3:

The system capacity is calculated by the product of the processing capacity of each stage:

1 x 1 x 2 = 2 units per minute

The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:

Process time per unit = 1 + 2 + 3 = 6 minutes per unit

Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit

The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.

However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.

Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

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Answer:DDDDDD

Step-by-step explanation:

Answer:

Simplify the expression and it's 3a-4b+4c

Step-by-step explanation:

Answer:

Step-by-step explanation:

There are 3 blue, 5 red and the total of 8 marbles.

Two different colored marbles are:

Find the probability of each case:

Required probability is:

Answer:

15/28 is the probability of getting 2 that are different in colour.

Step-by-step explanation:

He is going to pick any marble, in second try, it must be a different colour marble.

total marble: 3 + 5 = 8 marbles

For blue marble:

In first try for blue marble: 3/8

second try for red marble: 5/7

probability then: 5/7 *  3/8 = 15/56 is the probability for blue marble.

For red marble:

In first try for red marble: 5/8

second try for blue marble: 3/7

probability then: 5/8 * 3/7 = 15/56

**

total probability of getting different in colour:

15/56 + 15/56

15/28  **

The constraint(s) to ensure that the ratio of 3 bedroom rentals to 2 bedroom rentals is no more than 4 to 1 is:

3X3 <= 4X2

This constraint states that the number of 3 bedroom rentals (X3) must be less than or equal to four times the number of 2 bedroom rentals (X2). This ensures that the ratio of 3 bedroom rentals to 2 bedroom rentals does not exceed 4 to 1.

For example, if there are 10 2 bedroom rentals (X2), the constraint would be:

3X3 <= 4(10)
3X3 <= 40

This means that the number of 3 bedroom rentals (X3) cannot exceed 40.

The constraint to ensure the ratio of 3 bedroom rentals to 2 bedroom rentals is no more than 4 to 1 is 3X3 <= 4X2.

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The probability that there will be no mutual best friendships is\([(n-1)/n]^{(2n)}\).

Given that there are n users in each group, A and B;

For a user in group A, the probability that this user selects someone who is not their mutual best friend is (n-1)/n

The probability that all users in group A choose someone who is not their mutual best friend is

For each user in group B;

the probability of not choosing their mutual best friend is (n-1)/n,

The probability that all users in group B choose someone who is not their mutual best friend is \([(n-1)/n]^{n}\)

The events of users in group A and users in group B choosing their mutual best friends are independent, therefore;

P(no mutual best friendships) = \([(n-1)/n]^n * [(n-1)/n]^n\)

P(no mutual best friendships) =\([(n-1)/n]^{(2n)}\)

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Answer:

Answer is A! 38 degrees

Step-by-step explanation:

opposite side is the same

The number of people died from aids in U.S. in 2005 are 2,30,68,96,671

Given, diseases tend to spread according to the exponential growth model.

In the early days of aids, the growth factor (i.e. common ratio; growth multiplier) was around 1.9.

In 1983, about 1700 people in the U.S. died of aids.

we have to find the number of people died from aids in 2005.

Let the exponential function, be

P(x) = AB^x

where, A is the initial population of people died of aids in U.S.

B is the growth factor of aids in U.S.

as, B = 1.9

In 1983, x = 0

P(0) = AB^0

1700 = A

Now, P(x) = 1700(1.9)^x

and the number of years from 1983 to 2005 are, 22 years

The number of people died from aids in 2005 be,

P(22) = 1700(1.9)^22

P(22) = 2,30,68,96,671

So, 2,30,68,96,671 people died from aids in 2005.

Hence, 2,30,68,96,671 people died from aids in 2005.

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Answer:

350 hours

Step-by-step explanation:

Answer:

There were 120 questions on the test.

Step-by-step explanation:

It is given that:

Number of questions answered = 54

Grade percent = 45%

Let,

x be the total number of questions

45% of x = 54

\(\frac{45}{100}x=54\\0.45x = 54\)

Dividing both sides by 0.45

\(\frac{0.45x}{0.45}=\frac{54}{0.45}\\x=120\)

Therefore,

There were 120 questions on the test.

Answer:

$30.00 to rent the van

.50 per mile x 150 miles

.50*150 = $75.00

30.00 + 75.00 = $105.00

you budgeted 100.00 you do not have enough money

Step-by-step explanation:

I hope that helps i already did this assignment and it was right :)

Answer:

ok so the answer is b

Step-by-step explanation: because if you divide the numbers and you get the answer you will have to add and there is your answer and please give me a 5 star.

Answer: We have to write two fractions that are equivalent to 1(a) and 1(b):

1(a) Equivalent fraction to 1(b):

Conclusion: The two fractions are Indeed the Equivalent!

Answer:

11.18

11.2

Step-by-step explanation:

hope it helps

Using the Binomial probability distribution,

The probability that exactly two customers in the sample will default on their payments is 0.31..

We have given that,

4% of total customers a mortgage company default on their payments .

The probability of success i.e number of customers default on their payments (p) = 4%

= 0.04

The probability of failure (q) = 1-p = 1-0.04 = 0.06

Total number of customers in sample (n) = 20

we have to find out the probability that exactly two customers in the sample will default on their payments.

Using the Binomial probability distribution,

P(X=x)= ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾

the required probability is P(X= 2 )

Now, P(X= 2) = ²⁰C₂(0.04)²(0.06)¹⁸

=> P(X=2) = 190 × 0.0016 × 1.0155 = 0.31

Hence, the required probability is 0.31

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The estimated answer of 40 is close to Keira's answer of 38.6. This suggests that her answer is reasonable.

One way Keira can check if her answer is reasonable is to use estimation.

She can round the numbers in the original division problem to the nearest multiples of 10, which makes the calculation easier, and check if the estimated answer is close to her actual answer. That is:

123.52 is approximately 120, and 3.2 is approximately 3. So the division problem becomes:

120 / 3 = 40

This estimated answer of 40 is close to Keira's answer of 38.6, which suggests that her answer is reasonable.

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Answer:

\(x = \frac{\sqrt 3}{ 3}\)

Step-by-step explanation:

Given

See attachment for complete question

First, we calculate the water pipe length (AC):

\(AC^2 = AB^2 + BC^2\)

\(AC^2 = 1^2 + x^2\)

\(AC^2 = 1 + x^2\)

\(AC = \sqrt{1 + x^2\)

The cost of laying across water is twice (2 times) laying on land.

So, the total cost (C) is:

\(C = 2 * \sqrt{1 + x^2} + 1 * (4 - x)\)

\(C = 2 \sqrt{1 + x^2} + (4 - x)\)

Differentiate

\(C' = \frac{2x}{\sqrt{1 + x^2}} - 1\)

To find the most economical cost, we simply minimize C' by equating C' to 0

\(C' = 0\)

\(\frac{2x}{ \sqrt{1 + x^2}}-1 = 0\\\)

\(\frac{2x}{ \sqrt{1 + x^2}}=1\)

Cross multiply

\(2x= \sqrt{1 + x^2}\)

Take square of both sides

\(4x^2 = 1+x^2\)

Collect like terms

\(4x^2 -x^2= 1\)

\(3x^2= 1\)

Solve for \(x^2\)

\(x^2 = \frac{1}{3}\)

Solve for x

\(x = \sqrt{\frac{1}{3}}\)

\(x = \frac{1}{\sqrt 3}\)

Rationalize:

\(x = \frac{1}{\sqrt 3} * \frac{\sqrt 3}{\sqrt 3}\)

\(x = \frac{\sqrt 3}{ 3}\)

Answer:

-3

Step-by-step explanation:

since it moves down by 3 units

The graph of a quadratic equation with a negative discriminant is a straight line.

What is discriminant?

This is because a negative discriminant means that the quadratic equation has no real solutions, and therefore the graph does not cross the x-axis. Instead, it either stays above or below the x-axis as a straight line.

The discriminant is a formula that is used to determine the nature of the roots of a quadratic equation. It is the expression under the square root symbol in the quadratic formula and is calculated as b²-4ac, where a, b, and c are coefficients of a quadratic equation in standard form. The discriminant can be used to determine whether the quadratic equation has real or complex roots, and whether the roots are rational or irrational. If the discriminant is positive, the quadratic equation has two real roots, if it is zero, the equation has one real root (a repeated root), and if it is negative, the equation has two complex (non-real) roots.

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Answer: To find the percentage of people with an IQ score less than 117, we need to calculate the z-score first. The z-score measures how many standard deviations an individual score is from the mean in a normal distribution.

The z-score formula is given by:

z = (x - μ) / σ

Where:

Let's calculate the z-score:

Now, we need to find the percentage of people with a z-score less than 1.1333. We can look up this value in the standard normal distribution table (also known as the Z-table) or use statistical software/tools.

Using the Z-table, we find that the percentage of people with a z-score less than 1.1333 is approximately 0.8708, or 87.08% (rounded to the nearest hundredth).

Therefore, approximately 87.1% of people have an IQ score less than 117.

Answer:

Step-by-step explanation:

When you reflect over the line y=-x, you flip the x and y coordinate and multiply them by negative one, so for example (2,3) would become (-3,-2) or (-1,7) would be (-7,1). Using this rule you can find the new point for each point in the figure. The point lying on (-2,1) would be reflected to (-1,2). The point on (-4,1) would move to (-1, 4). The point on (-4,-1) would be moved to (1,4). The point lying on (-3,-1) would be reflected onto (1,3). The point on (-3,-2) would be on (2,3). Lastly, the point on (-2,-2) would be reflected to (2,2). i hope this helped lol. :)