Directions-Graph the following slope intercept equation

The coordinates of all four vertices of quadrilateral BPQF, we can use the shoelace formula to find its area. The shoelace formula states that the area of a polygon with vertices (x1, y1), (x2,

A triangle is a closed, two-dimensional geometric shape that has three sides and three angles. It is one of the basic shapes in geometry and can be formed by connecting three non-collinear points. Triangles can be classified based on their side lengths and angles.

To solve this problem, we can use the fact that the area of a triangle is equal to half the product of its base and height. Let's first find the length of the sides of the square.

Since the area of the square is 1320 square centimeters, we can find its side length by taking the square root of 1320:

√(1320) ≈ 36.32

So the side length of the square is approximately 36.32 cm.

Next, let's find the coordinates of points E and F. Since E is the midpoint of AB, its coordinates are:

E = ((0+36)/2, (36+0)/2) = (18, 18)

Similarly, since F is a quarter point of BC close to point B, its coordinates are:

F = (36, (3/4)36) = (36, 27)

Now let's find the equation of line CE. Since we know two points on the line (C and E), we can use the point-slope form of a linear equation to find its equation:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is one of the points on the line. We can find the slope of the line by taking the difference in y-coordinates and dividing by the difference in x-coordinates:

m = (0 - 36)/(36 - 18) = -2

Using the point-slope form with point C, we get:

y - 0 = -2(x - 36)

y = -2x + 72

Similarly, the equation of line DB can be found using points D and B:

m = (0 - 36)/(0 - 18) = 2

y - 0 = 2(x - 0)

y = 2x

Finally, we can find the coordinates of point P by solving the system of equations:

y = -2x + 72

y = 2x

Setting the two expressions for y equal to each other, we get:

-2x + 72 = 2x

4x = 72

x = 18

Substituting x = 18 into either equation, we get:

y = 2x = 36

So the coordinates of point P are (18, 36). To find the coordinates of point Q, we can use the fact that it lies on line DF. Since we know two points on the line (D and F), we can again use the point-slope form of a linear equation:

m = (27 - 0)/(36 - 0) = 3/4

y - 0 = (3/4)(x - 0)

y = (3/4)x

To find the intersection point of lines DF and CE, we need to solve the system of equations:

y = (3/4)x

y = -2x + 72

Setting the two expressions for y equal to each other, we get:

(3/4)x = -2x + 72

(11/4)x = 72

x = 64/11

Substituting x = 64/11 into either equation, we get:

y = (3/4)(64/11) ≈ 14.73

So the coordinates of point Q are (64/11, 14.73).

Hence, Now that we have the coordinates of all four vertices of quadrilateral BPQF, we can use the shoelace formula to find its area. The shoelace formula states that the area of a polygon with vertices (x1, y1), (x2,

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1.) The probability that the sample mean will be greater than 48 minutes is 0.9332.

2.) The probability of the sample mean being between 44 and 49 minutes is 0.6687.

3.) The z-score of 10 indicates that the sample mean of 65 minutes is 10 standard deviations above the population mean.

To solve this problem, we can use the Central Limit Theorem (CLT), which states that the distribution of sample means tends to be approximately normally distributed, regardless of the shape of the original population, when the sample size is large enough.

1.) Probability of sample mean > 48 minutes:

To calculate this probability, we need to standardize the sample mean using the formula: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, the population mean (μ) is 45 minutes, the population standard deviation (σ) is 12 minutes, and the sample size (n) is 36. We want to find the probability of the sample mean being greater than 48 minutes.

Calculating the z-score:

z = (48 - 45) / (12 / √36) = 3 / 2 = 1.5

Using a standard normal distribution table or calculator, we find that the probability corresponding to a z-score of 1.5 is approximately 0.9332. Therefore, the probability that the sample mean will be greater than 48 minutes is approximately 0.9332.

2.) Probability of sample mean between 44 and 49 minutes:

To calculate this probability, we need to find the z-scores for both 44 and 49 minutes and then calculate the area between those z-scores.

Calculating the z-scores:

For 44 minutes:

z1 = (44 - 45) / (12 / √36) = -1 / 2 = -0.5

For 49 minutes:

z2 = (49 - 45) / (12 / √36) = 4 / 2 = 2

Using the standard normal distribution table or calculator, we find the probabilities corresponding to z1 and z2:

P(z < -0.5) ≈ 0.3085

P(z < 2) ≈ 0.9772

The probability of the sample mean being between 44 and 49 minutes is approximately P(-0.5 < z < 2) = P(z < 2) - P(z < -0.5) ≈ 0.9772 - 0.3085 = 0.6687.

3.)Conclusion from 100 samples with a mean of 65 minutes:

If 100 samples were collected, and the sample mean was 65 minutes, we would need to assess whether this value is significantly different from the population mean of 45 minutes.

To make this assessment, we can calculate the z-score for the sample mean of 65 minutes:

z = (65 - 45) / (12 / √36) = 20 / 2 = 10

The z-score of 10 indicates that the sample mean of 65 minutes is 10 standard deviations above the population mean. This is an extremely large deviation, suggesting that the sample mean of 65 minutes is highly unlikely to occur by chance.

Given this, we can conclude that the sample mean of 65 minutes is significantly different from the population mean. It may indicate that there is a systematic difference in the delivery times between the sample and the population, possibly due to factors such as increased demand, traffic, or other external variables

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Answer:

Put the 4 at the beggining at line then always at +20 to it

Step-by-step explanation:

3+2/x=1

(3x+2)/×=1

3x+2=x

2=-2×

x= -1

Answer:

14 in

Step-by-step explanation:

the formula for the circumference of a circle is

2×pi×r

or (because the diameter is 2×r)

pi×d

with r being the radius and d being the diameter.

44 = pi×d

d = 44/pi = 14.00563499... in ≈ 14 in

Answer:

3rd number = 30

2nd number = 7

1st number = 15

Step-by-step explanation:

(T) total of three numbers = 52

let 3rd number = 2 x

let 2nd number = x - 8

let 1st number = x

T = 1st + 2nd + 3rd

52 = 2x + (x - 8) + x

52 + 8 = 4x

60 = 4x

x = 60 / 4

x = 15

therefore,

let 3rd number = 2 (15) = 30

let 2nd number = 15 - 8 = 7

let 1st number = 15

Answer:

3rd = 30

2nd  = 7

1st  = 15

Step-by-step explanation:

(T) total = 52

3rd  = 2 x

2nd = x - 8

1st = x

T = 1st + 2nd + 3rd

52 = 2x + (x - 8) + x

52 + 8 = 4x

60 = 4x

x = 15

so

3rd = 2 (15) = 30

2nd  = 15 - 8 = 7

1st  = 15

Answer:

0.1

Step-by-step explanation:

For a density curve, total area = 1

Probability lies in between 0 and 1

The Area of rectangle :

Area = Length * width

Length = 0 - 10 = 10

Area = 1

Hence,

Area = Length * width

1 = 10 * w

1 = 10w

w = 1 /10

w = 0.1

Answer:

2.16•x is up ur function

21. 6 feet in 10 minutes

Step-by-step explanation:

when u multiply by ten u move the decimal to the right one place

Answer:

this is what u need .........

Answer:

it's 48

Step-by-step explanation:

you must do 480×10÷100

Answer:

The probability that it will rain in atleast two consecutive days will be 0.167936.

Step-by-step explanation:

Since it rains on 40% of the days, then the probability of it raining on each day is

This follows a binomial distribution

Since it's a five-day tour and they want to know the probability that rain falls in atleast TWO CONSECUTIVE days then we have to consider 2 days as one, as we do in combination problems, so that they are always together before we use in our binomial probability density function.

Our Probability Density Function is given as

\(P(X) = \binom{n}{x} p^x \times q^{n-x}\)

Where p is probability of raining and q = 1 - p is probability of not raining.

Our n is 4 since we are considering two days as one.

We are looking the P(X≥2) = 1 – P(X<2) = 1 – [P(X = 0) + P(X = 1).

\(P(X = 0) = \binom{4}{0} 0.4^0 \times 0.6^4 = 0.1296\)

\(P(X = 1) = \binom{4}{1} 0.4^1 \times 0.6^3 = 4\times 0.4 \times 0.216 = 0.3456\)

Therefore P(X≥2) = 1 – (0.1296 + 0.3456) = 0.5248.

Remember we combined two consecutive days that it will rain as one, their probabilities will be:

2! x 0.4 x 0.4 = 0.32

Therefore, the probability that it will rain in atleast two consecutive days will be

0.32 x 0.5248 = 0.167936

Answer:

undefined

Step-by-step explanation:

division by zero is undefined

Division Property of zero

For any nonzero real number a

The quotient of "a" and 0 is undefined. That is a/0 is undefined

Answer:

5

Step-by-step explanation:

because it is the right answer

Answer:

8 weeks

Step-by-step explanation:

265-30 = 240

240/30(per week)=8

Answer is 8 weeks

Answer:

x = -175

Step-by-step explanation:

Step 1: Define

h(x) = -25

h(x) = 1/5x + 10

Step 2: Substitute and Evaluate

-25 = 1/5x + 10

-35 = 1/5x

x = -175

The area of the triangle with the given vertices is 11.5 square units.

The area of a triangle can be calculated using the coordinates of its vertices using the following formula.

To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:

A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2

Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:

A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2

A = (0 - 4 + 27)/2

A = 23/2

A = 11.5

Therefore, the area of the triangle with the given vertices is 11.5 square units.

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Answer: yes

Step-by-step explanation: they have to be past 0 to start

Answer:

y = -7x -7

explanation:

y - y₁ = m ( x - x₁ )

y - -7 = -7 ( x - 0 )

y + 7 = -7x

y = -7x -7

Or using the formula:

y = mx + b

y = -7x - 7

using this formula, if only passes y-axis, we can find equation without doing any work.

Answer:

6110

Step-by-step explanation:

The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and

he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle.  It is defined as the length of the opposite side divided by the length of the hypotenuse

The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360

2∅  2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720

sin 2∅ = sin0 = 0; Sin90=1;  sin180=0; sin240= -0.8660; sin270 = -1;

Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397

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We have the following system:

Each one of those equations represents a line, and their interception is the solution for this system(if the lines are parallel, there's no solution, and if they are the same line, infinite solutions).

We can calculate their interception, by making a substitution. Using the value for 'y' from the first equation in the second equation, we get the following:

Using our 'x' value in any of those equations, we get our interception.

The solution for this system is

To plot those lines, you just need two points of each line. Since (4,4) is the interception, it belongs to both lines, then, we just need an extra point from each one. An easy point to calculate is the y-intercept.

Calculating the y-intercept for the first line:

y-intercept = (0,-8)

Calculating the x-intercept for the second line:

y-intercept = (0,5)

To plot, you just mark the y-intercept and drag to the point (4,4).

The graphs looks like this:

Answer:

Number 2

Step-by-step explanation:

The solution to the inequality 6x - 6 < -30 is x < -4, and it is graphically represented as a closed circle at -4 and shading to the left of -4 on the number line.

To solve the inequality 6x - 6 < -30, we can follow these steps:

Step 1: Add 6 to both sides of the inequality to isolate the variable:

6x - 6 + 6 < -30 + 6

6x < -24

Step 2: Divide both sides of the inequality by 6 to solve for x:

(6x)/6 < (-24)/6

x < -4

The solution to the inequality is x < -4. This means that any value of x less than -4 will satisfy the inequality.

To graph the solution on the number line, we represent -4 as a closed circle (since it is not included in the solution) and shade the region to the left of -4 to indicate all values less than -4.

On the number line, mark a point at -4 with a closed circle:

<--------●-----------------

Then, shade the region to the left of -4:

<--------●================

The shaded region represents the solution to the inequality x < -4.

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Recall that the standard form of the line is of the form

where A,B and C are constants. What is most important is that in standard form, the numbers A,B,C are integers. This means that they cannot be fractions nor decimal numbers.

Starting from the equation y=-1.5x+4, Malcolm did right by adding 1.5x on both sides

so we have 1.5x+y=4. However, 1.5 is a decimal number. So he needs to multiply the whole equation by 2, so he does not have any more decimals on the standard form. That is

so the standard form is

Answer:

2 : 3

Step-by-step explanation:

A disc has a diameter of 21 cm while a mini disc has a diameter of 14cm. Write the ratio of the mini disc diameter to the disc diameter.

Answer: Let the diameter of the mini disc be \(d_1\) while the diameter of the disc be \(d_2\). To get the ratio of the mini disc diameter to the disc diameter, we just simply have to divide the diameter of the mini disc by the diameter of the disc and then represent the fraction in ratio form. The ratio of the disc diameters is given by:

Ratio of the mini disc diameter to the disc diameter = Diameter of mini disc / diameter of disc

Ratio of the mini disc diameter to the disc diameter = \(\frac{14}{21}=\frac{2}{3}\)

Ratio of the mini disc diameter to the disc diameter = 2 : 3

Answer:

The slope of Zane is 18.50/2 = 9.25

Subtract both slopes to find the true statement.

10.5 - 9.25 = 1.25

The correct statement is:

Abrielle earns $1.25 more than Zane.

Answer:

what the person on the top said. Their right.

Answer:

the agency makes 17370 and the agent makes 5211.

Step-by-step explanation:

The term "isometric" has the Greek roots "isos," which means "same," and "metron," which means "measure." The definition of an isometric transformation is one in which the original figure and its transformed equivalent have the same shape, size, and orientation.

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Answer: 16.3 cm

Step-by-step explanation:

2.5 meters = 98.4252 inches.

(Round to 98.4)

98.4 - 11.5 = 86.9

(keep subtracting till you can't subtract 11.5 anymore w/o getting a negative number)

6.4 in = 16.3 cm (multiply the length value by 2.54)

16.3 cm left over.

Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.

To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:

A = \(Pe^(^r^t^)\)

where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.

In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:

640 = \(Pe^(^0^.^0^3^5^*^9^)\)

640 = Pe^0.315

P =\(640/e^0^.^3^1^5\)

P = 432.43

Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.

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