Constructing parallel lines

What is the slope of the original line?


–1



What is the equation of the line that is parallel to the given line and passes through the given point?

If the base and height of the triangle that forms its base are 18 units and 12 units respectively then the height of the pyramid is 21 units.

The formula for the volume of a triangular pyramid is:

V = (1/3) * base area * height

We are given that the volume of the pyramid is 756 units^3, the base of the pyramid is a triangle with base length 18 units and height 12 units, so its area is:

A = (1/2) * base * height = (1/2) * 18 * 12 = 108 units^2

Substituting the given values into the formula for the volume of a pyramid, we get:

756 = (1/3) * 108 * h

Multiplying both sides by 3 and dividing by 108, we get:

h = 756 / 36 = 21

Therefore, the height of the pyramid is 21 units.

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Answer:

  0.13824

Step-by-step explanation:

You want the probability of exactly 4 successes in 6 trials if the probability of success in each trial is 0.4.

The probability of k successes in n trials with each having a probability of success of p is given by the formula ...

  P(k of n) = nCk·p^k·(1-p)^(n-k)

  P(4 of 6) = 6C4·0.4^4·0.6^2 = 15·0.0256·0.36 = 0.13824

The probability of exactly 4 successes is 0.13824.

__

Additional comment

The binomial coefficient nCk is computed as ...

  nCk = n!/(k!(n-k)!)

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The decision of whether or not to build pipelines to transport oil from Alberta to Texas or other parts of Canada is a complex one that involves multiple factors.

From a mathematical perspective, the debate over pipelines and oil sands can be analyzed in terms of supply and demand. On the other hand, opponents of pipelines argue that the supply of oil is finite and that the continued extraction and transportation of oil will have long-term negative consequences for the environment.

In addition to the economic and environmental factors, there are also geopolitical considerations to take into account. For example, some argue that building a pipeline to transport oil from Alberta to Texas would reduce Canada's reliance on foreign oil and would increase our energy independence.

However, others argue that building a pipeline would tie us more closely to the United States and would not necessarily benefit Canada in the long run.

Regardless of the decision that is ultimately made, it is clear that pipelines will continue to play a significant role in our energy infrastructure for many years to come.

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The equations that represent exponential growth are [tex]A = 20,000(1.08)^t[/tex], [tex]A = 40(3)^t,[/tex] [tex]P = 1700(1.07)^t[/tex] and the equations that represent exponential decay are [tex]A = 80(1/2)^t, A = 1600(0.8)^t,[/tex] and [tex]P = 1700(0.93)^t.[/tex]

The mathematical function used to calculate the exponential growth or decay of a given set of data is an exponential function. we can calculate changes in population, loan interest charges, bacterial growth, radioactive decay, or the spread of disease by using the exponential functions.

An exponential function is of the form:

[tex]f(x) = a ^x[/tex]

The function represents an exponential decay If b < 1

The function represents an exponential growth If b > 1

From the given data about equations, we have;

Exponential Growth is;

The equation with the values b < 1 is:

[tex]A = 20,000(1.08)^t[/tex]

[tex]A = 40(3)^t[/tex]

[tex]P = 1700(1.07)^t[/tex]

Exponential Decay is;

The equation with the values b > 1 is:

[tex]A = 80(1/2)^t[/tex]

[tex]A = 1600(0.8)^t[/tex]

[tex]P = 1700(0.93)^t[/tex]

Therefore, The equations that represent exponential growth are[tex]A = 20,000(1.08)^t[/tex], [tex]A = 40(3)^t[/tex], and[tex]P = 1700(1.07)^t[/tex]  the equations that represent exponential decay are [tex]A = 80(1/2)^t[/tex], [tex]A = 1600(0.8)^t\\[/tex], and [tex]P = 1700(0.93)^t.[/tex]

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The complete question is

Which equations represent exponential growth? which equations represent exponential decay? drag the choices into the boxes to complete the table

Answer:

Step-by-step explanation:

To determine if the table shows growth or decay, we can look at the coefficient of the exponential function y = 200(0.75)^t. The coefficient is 0.75, which is less than 1. This means that the value of the bike decreases over time, so the table shows decay.

To identify the annual percent increase or decrease in the value of the bike, we can compare the value of the bike after one year to its initial value. Plugging in t = 1 into the model, we get:

y = 200(0.75)^1

y = 150

So after one year, the value of the bike is $150. This represents a decrease of $50 from its initial value of $200. To find the percent decrease, we can use the formula:

percent decrease = (amount of decrease / initial value) x 100%

Plugging in the values, we get:

percent decrease = (50 / 200) x 100%

percent decrease = 25%

Therefore, the value of the bike decreases by 25% each year.

To estimate when the value of the bike will be $50, we can set y = 50 in the model and solve for t:

50 = 200(0.75)^t

0.25 = 0.75^t

log(0.25) = t log(0.75)

t = log(0.25) / log(0.75)

t ≈ 4.2

Therefore, the value of the bike will be $50 approximately 4.2 years after it was new.

Katie outscored approximately 1.39% of the students in her section.

If Katie received a z-score of 2.2, this means that her score was 2.2 standard deviations above the mean of the exam scores for her section.

We can use a standard normal distribution table or calculator to find the percentage of scores that fall above a z-score of 2.2.

Using a standard normal distribution table, we can find the proportion of scores that fall below a z-score of 2.2, and then subtract this from 1 to find the proportion of scores that fall above a z-score of 2.2.

The table value for a z-score of 2.2 is approximately 0.9861, which means that approximately 98.61% of the scores fall below a z-score of 2.2. Therefore, approximately:

1 - 0.9861 = 0.0139, or 1.39%

of the scores fall above a z-score of 2.2.

This means that Katie outscored approximately 1.39% of the students in her section.

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Answer: what do you need help with?

Step-by-step explanation:

Answer:

y = -3

x = 1

Step-by-step explanation:

To solve the system of equations using substitution, we need to isolate one variable in terms of the other in one of the equations and substitute this expression into the other equation. We can then solve for the remaining variable.

In this case, we are given two equations:6x - 9 = y

y = -3x

We can substitute the expression for y from the second equation into the first equation to get:

6x - 9 = -3x

Now we can solve for x:

6x + 3x = 9

9x = 9

x = 1

We can substitute this value of x back into one of the original equations to solve for y. Using the second equation, we have:

y = -3(1) = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

To verify the solution, we can substitute the values of x and y into the original equations and check if they are satisfied:

6x - 9 = y

6(1) - 9 = -3

-3 = -3

This equation is true, so x = 1 and y = -3 satisfy the first equation.

y = -3x

-3 = -3(1)

This equation is also true, so x = 1 and y = -3 satisfy the second equation.

Since x = 1 and y = -3 satisfy both equations, they are the solution to the system of equations using substitution.

The speed of the tugboat without the current is 35 miles per hour, and the speed of the current is 15 miles per hour.


Let t be the speed of the tugboat without the current and c be the speed of the current.
Upstream, the tugboat moves against the current, so its speed is (t - c).
Downstream, the tugboat moves with the current, so its speed is (t + c).
The upstream distance is 200 miles in 10 hours, so the upstream speed is 200/10 = 20 miles per hour.
The downstream distance is also 200 miles, but it takes 4 hours, so the downstream speed is 200/4 = 50 miles per hour.
Now, we have two equations with two variables:
  a. t - c = 20
  b. t + c = 50
Solve these equations simultaneously:
  a. Add the two equations to eliminate the variable c: 2t = 70
  b. Divide both sides by 2 to get t: t = 35 miles per hour
  c. Substitute the value of t back into one of the equations (e.g., t - c = 20): 35 - c = 20
  d. Solve for c: c = 15 miles per hour

Hence, The speed of the tugboat without the current is 35 miles per hour, and the speed of the current is 15 miles per hour.

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The expression representing the number of points Avery scored in terms of the number of points Jim scored is 2j - 10.

Let's assume that Jim scored 'j' points during the game. According to the given information, when Jim doubles his number of points and subtracts 10 from that number, the result is the same as the number of points Avery scored. Therefore, we can write an equation as follows:

2j - 10 = number of points scored by Avery

To find the expression representing the number of points Avery scored in terms of the number of points Jim scored, we simply solve the above equation for Avery's points:

number of points scored by Avery = 2j - 10

Therefore, the expression representing the number of points Avery scored in terms of the number of points Jim scored is 2j - 10.

In summary, Jim scored 'j' points during the game and when he doubles his number of points and subtracts 10 from that number, he gets the same result as the number of points Avery scored.

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At the grand opening, al's furniture store, there is offering spin wheel for discount. The probability that a customer gets a 10% or 20% discount is equals to the 0.75.

At the grand opening, al's furniture store, it offered a spin the wheel for a discount to its customers. The wheel is divided into 12 equal slices.

The percentage of discount awarded by 6 slices = 10%

The percentage of discount awarded by 3 slices = 20%

The percentage of discount awarded by 2 slices = 40%

The percentage of discount awarded by 1 slices

= 100%

We have to determine the probability that a customer gets a 10% or 20% discount. As we see all slices are independent to each other so events related to these also independent.

We have total 12 slices. Since, 6 slices awarded for 10% discount i.e. chances of getting 10% discount is equal = 6/12

Similarly, 3 slices awarded for 20% discount i.e. chances of getting 20% discount is 3/12.

Hence chances of getting 10% or 20% discount is

= P( X = 20%) + P( X= 10%)

= 6/12 + 3/12

= 1/2 + 1/4

= 0.50 + 0.25

= 0.75

Hence, required value is 0.75.

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The minimum value of the given function is 3 at x=-5.

By locating the vertex of the parabola that the function defines, we may determine the lowest or maximum value of G(x).

The x-coordinate of the vertex may be determined by using the formula x = -b/(2a), where a and b are the coefficients of the quadratic components in the function.

In this case, a = 3 and b = 30, so:

x = -b/(2a) = -30/(2*3) = -5

Now we can find the y-coordinate of the vertex by plugging in x = -5 into the function:

[tex]G(-5) = 3(-5)^2 + 30(-5) + 78 \\= 3(25) - 150 + 78 \\= 3(25) - 72 \\= 3(25 - 24) \\= 3(1) \\= 3[/tex]

Therefore, the minimum value of G(x) is 3 and there is no maximum value.

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Answer:

A = 81

Step-by-step explanation:

Using the formulas

A=a2

P=4a

Solving forA

A=1

16P2=1

16·362=81

Answer:

[tex]36 {r}^{4} {s}^{5}[/tex]

Perimeter of the square

one side has a length of 9r⁴s⁵

area is equal to 9r⁴s⁵ × 9r⁴s⁵

= 81r⁸s¹⁰

or 81r⁸s¹⁰cm²

The three equations are:

3x = 30.3

30.3 - x = 27.3

3x + 30.3 = 63.6

We have,

Equation 1:

3x = 30.3

Solving for x, we can divide both sides by 3:

x = 10.1

Equation 2:

30.3 - x = 27.3

Solving for x, we can subtract 27.3 from both sides:

x = 3

Equation 3:

3x + 30.3 = 63.6

Solving for x, we can first subtract 30.3 from both sides:

3x = 33.3

Then, we can divide both sides by 3:

x = 11.1

Thus,

The three equations are:

3x = 30.3

30.3 - x = 27.3

3x + 30.3 = 63.6

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The 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings is (3.36, 13.78).

To construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings, we can use a two-sample t-test with equal variances.

Let x₁ be the number of blocked intrusions per day before the change of firewall settings, and let x₂ be the number of blocked intrusions per day after the change of firewall settings. We have

x₂ = (56+47+49+37+38+60+50+43+43+59+50+56+54+58)/14 = 50.36

x₂ = (53+21+32+49+45+38+44+33+32+43+53+46+36+48+39+35+37+36+39+45)/20 = 40.95

s₁ = standard deviation of x₁ = 8.23

s₂ = standard deviation of x₂ = 8.98

The pooled standard deviation, sp, is given by

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

where n₁ and n₂ are the sample sizes. Since we assume equal variances, we use the formula for the pooled standard deviation. Substituting the values, we get:

sp = √(((14-1)8.23² + (20-1)8.98²)/(14+20-2)) = 8.63

The t-statistic for the difference between the means is given by

t = (x₁ - x₂) / (sp × √(1/n₁ + 1/n₂))

Substituting the values, we get

t = (50.36 - 40.95) / (8.63 × √(1/14 + 1/20)) = 2.28

We can use a t-distribution with degrees of freedom = n₁ + n₂ - 2 = 32 and a significance level of α = 0.05 to find the confidence interval. The confidence interval is given by

(x₂ - x₂) ± tsp√1/n₁ + 1/n₂)

Substituting the values, we get

(50.36 - 40.95) ± 2.0458.63√(1/14 + 1/20) = 8.57 ± 5.21

= (3.36, 13.78)

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The given question is incomplete, the complete question is:

The numbers of blocked intrusion attempts on each day during the first two weeks of the month were 56,47,49,37,38,60,50,43,43,59,50,56,54,58 After the change of firewall settings, the numbers of blocked intrusions during the next 20 days were 53,21,32,49,45,38,44,33,32,43,53,46,36,48,39,35,37,36,39,45. construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings (assume equal variances).

Total annual cost for Dave's car driving 6,000 miles last year is $2,250.00 with fixed cost of $1,250.00 plus variable cost of $1,000.00.

Based on the given information, we can use the formula for total cost

Total Cost = Fixed Cost + (Variable Cost per unit x Number of units)

In this case, we know the fixed cost is $1,250.00, and the variable cost per mile is $1,000.00 / 6,000 miles = $0.1667/mile. Therefore, we can calculate the total annual cost as

Total Cost = $1,250.00 + ($0.1667/mile x 6,000 miles)

Total Cost = $1,250.00 + $1,000.20

Total Cost = $2,250.20

So, Dave's total annual cost of driving his car for 6,000 miles is $2,250.20.

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--The given question is incomplete, the complete question is given

" Dave drove 6,000 miles in his car last year. The total of fixed costs was $1,250.00 and of variable costs was $1,000.00. What is the total annual cost?"--

Answer:

3 and a half would be greater than 3

Step-by-step explanation:

3 and a half would be 3.5 which is .5 more than just 3.

Chen’s parcel weighs 0.3 kg more than Megan’s parcel

When working with fractions and decimals, it is good to use only one unit for ease of solving.

We are given the weights as:

Weight of Chen’s Parcel = 1¹/₂ kg

Weight of Megan's Parcel = 1.2 kg

Now, let us convert the weight of Chen’s Parcel from fraction to decimal to get 1.5 kg

Thus:

Difference in weight = 1.5 kg - 1.2 kg

= 0.3 kg

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The circumference of circle be 60 in.

Give that,

Angle of sector = 60 degree

Arc length  = 10 inch

Arc length of circle = (Θ/360) x 2πr

Put the values

10 = (60/360)x2πr

⇒ r = 60/2π

Since circumference of circle = 2πr

Therefore,

circumference of the given circle = 2π x (60/2π)

                                                       = 60 in.

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both sides are equal, we can conclude that n = 150/29 is the correct solution.

What is an Equations?

Equations consist of two algebraic expressions separated by an equal (=) sign, representing the equality between the expressions on the left and right sides. Solving equations helps to find the value of a variable that represents an unknown quantity. If there is no "equal to" symbol, a statement cannot be considered an equation and is instead considered an expression.

(2n)/3 + 1 = (7n)/15 + 3 // subtract 1 from both sides

(2n)/3 = (7n)/15 + 2 // multiply both sides by 15 to eliminate fractions

10n = 3(7n)/5 + 30 // multiply both sides by 3

10n = 21n/5 + 30 // subtract 21n/5 from both sides

50n/5 - 21n/5 = 30 // simplify fractions

29n/5 = 30 // multiply both sides by 5/29

n = 150/29

To check the solution, we substitute n = 150/29 back into the original equation and see if both sides are equal:

(2n)/3 + 1 = (7n)/15 + 3

(2(150/29))/3 + 1 = (7(150/29))/15 + 3

100/29 + 1 = 70/29 + 3

129/29 = 129/29

Since both sides are equal, we can conclude that n = 150/29 is the correct solution.

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Answer:

$56,577.12

Step-by-step explanation:

To find the present value of the annuity, we can use the formula for the present value of an ordinary annuity, which is:

PV = PMT x [1 - (1 + r/n)^(-n*t)] / (r/n)

Where:

PV = present value

PMT = payment amount per compounding period

r = annual interest rate

n = number of compounding periods per year

t = total number of years

Plugging in the given values, we get:

PV = 2400 x [1 - (1 + 0.10/4)^(-4*3)] / (0.10/4)

PV = 2400 x [1 - (1.025)^(-12)] / (0.025)

PV = 2400 x [1 - 0.610355] / 0.025

PV = 2400 x 23.5742

PV = $56,577.12 (rounded to the nearest cent)

Therefore, the present value of the annuity is $56,577.12, assuming the interest is compounded quarterly and the annuity earns a 10% interest rate.

The cost of one watch is ₹4975. The answer we got was obtained by dividing the total amount for 36 watches by the number of watches

To find the price of one watch, we can divide the total fee of 36 watches by way of the quantity of number of watches:

Price of 1 watch = general cost of 36 watches / 36

We are given that the price of 36 watches is about ₹179100, so we can now do the replacement of this value in to the formulation:

Value of one watch Is = ₹179100 / 36

When we will Simplify this expression, we get:

Value of 1 watch = ₹4975

Therefore, the cost of one watch is ₹4975.

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Answer:

7.21x3.86/10.09

7 x 4 / 10

28 / 10

2.8

Answer: The answer is Q1: 2.3+34, Q2: 5.7+8.9.

Step-by-step explanation: Please give Brainlist.

Hope this helps!!!!

I can answer more questions if you like.

(Expert Answered)

Answer:

A. 25%

B. Candidate B

C. 60% of voters chose Candidate A and Candidate C

Step-by-step explanation:

Answer:

Step-by-step explanation:

If he puts smarty back

because it's an "and" multiply by the 2 possibilities

4/12 *4/12

=1/3 *1/3

=1/9

If does not put smarty back

4/12 *3/11

=1/3*3/11

=3/33

Answer: You have to add up the lengths.

Answer:

The answer to your problem is, 1,740 minutes

Step-by-step explanation:

The time period of 116 trainings solutions;

The time period of 1 weight training that we know is 15 minutes. Time period of 116 weight is 5 x 116 = 1,740

Thus the answer to your problem is, 1,740

Answer:1,740 minutes

Step-by-step:

I first saw that I need to take 15 minutes and x it be the 116 Practices.

So 15 x 116 is 1,740.

1,740 minutes is your answer.