Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation.


Vertex at (0,0); axis of symmetry the y-axis; containing the point (6,4).


What is the equation of the parabola? Find the two points that define the latus rectum.

The total area of the composite figure is 1650 mm

To find the area of a composite figure, you need to break it down into simpler shapes whose areas you can calculate and then add up the individual areas. In this case, the composite figure consists of two shapes: a rectangle and a trapezoid.

To find the area of the rectangle, you multiply its length by its width. From the given dimensions, the length of the rectangle is 40 mm and the width is 30 mm. So the area of the rectangle is 40 x 30 = 1200 mm².

To find the area of the trapezoid, you use the formula for the area of a trapezoid: (base1 + base2) x height / 2. From the given dimensions, the two bases of the trapezoid are 25 mm and 35 mm, and the height is 15 mm. So the area of the trapezoid is (25 + 35) x 15 / 2 = 450 mm².

Now you add the areas of the two shapes together to get the total area of the composite figure: 1200 + 450 = 1650 mm².

Therefore, the total area of the composite figure is 1650 mm², rounded to the nearest hundredth.

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The probability that exactly five of the students were born on a weekend is 0.1514.

Assuming that the probability of being born on a weekend is the same for all students,

we can model the number of students born on a weekend as a binomial random variable with parameters n = 7 (number of trials) and p = 2/7 (probability of success, i.e., being born on a weekend).

The probability of exactly five students being born on a weekend can be calculated using the binomial probability formula:

P(X = 5) = (7 choose 5) * (2/7)^5 * (5/7)^2

where (7 choose 5) = 7! / (5! * 2!) is the number of ways to choose 5 out of 7 students.

Evaluating this expression gives:

P(X = 5) = (7 choose 5) * (2/7)^5 * (5/7)^2

= 21 * (0.0408) * (0.1837)

= 0.1514 (rounded to four decimal places)

Therefore, the probability that exactly five of the seven students were born on a weekend is approximately 0.1514.

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The probability values when calculated are

From the question, we have the following parameters that can be used in our computation:

Cards = {1, 2, 3, 4, 5}

Selecting two cards without replacement

So, we have

P(2 numbers greater than 3) = 2/5 * 1/4

P(2 numbers greater than 3) = 0.1

P(2 even numbers) = 2/5 * 4/4

P(2 even numbers) = 0.4

P(2 cards with same numbers) = 1/5 * 0/4

P(2 cards with same numbers) = 0

P(1 card is 3) = 2 * 1/5 * 3/4

P(1 card is 3) = 0.3

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Answer:

18.84 kilometers

Step-by-step explanation:

Formula for circumference:  C=2πr

1) find radius

r = d / 2

In this case the diameter is 6 so:

r = 6 / 2

r = 3

2. Plug in your values in the formula:

C = 2 (3.14) (3)

3. Solve (multiply)

C = 2 x 3.14 x 3

C = 18.84

So your answer is 18.84 kilometers, and rounded its 19 kilometers.

Hope this helps :D

The surface area is 72 square inches.

To find the surface area of a square pyramid, we need to calculate the area of the base and the four triangular faces.

Given that the base is 4 inches wide, the area of the square base is:
Base area = side² = 4² = 16 square inches.

The slant height is 7 inches. To find the area of one triangular face, we use:
Triangle area = (base * slant height) / 2

Each triangle has the same base length as the square base, which is 4 inches. Therefore, the area of one triangular face is:
Triangle area = (4 * 7) / 2 = 14 square inches.

Since there are four triangular faces, their total area is:
4 * Triangle area = 4 * 14 = 56 square inches.

Finally, add the base area and the total area of the triangular faces to get the surface area:
Surface area = Base area + Total triangular faces area = 16 + 56 = 72 square inches.

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The surveyor is located about 239.6 feet away from the base of the Willis Tower.

The height of the Willis Tower is 165 feet.

The angle of elevation from the surveyor to the top of the antenna is about 3.41°.

The height of the antenna is about 135.9 feet.

Let's call the distance from the surveyor to the base of the Willis Tower "x", and let's call the height of the Willis Tower "h".

We can use trigonometry to solve for x and h. First, let's find x:

tan(34°) = h/x

x = h/tan(34°)

Now we can use the distance from the surveyor to the top of the building to solve for h:

h + 2595 = 2760

h = 165

So the height of the Willis Tower is 165 feet. Now we can solve for x:

x = 165/tan(34°) ≈ 239.6 feet

So the surveyor is located about 239.6 feet away from the base of the Willis Tower.

To find the angle of elevation from the surveyor to the top of the antenna, we can use trigonometry again:

tan(θ) = h/2760

θ = tan^(-1)(h/2760)

θ ≈ 3.41°

So the angle of elevation from the surveyor to the top of the antenna is about 3.41°.

Finally, we can use the height of the Willis Tower and the distance from the surveyor to the top of the antenna to solve for the height of the antenna:

tan(34°) = (h + a)/2760

a ≈ 135.9

So the height of the antenna is about 135.9 feet.

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The daily newspaper has the most users among those surveyed.

To determine which news source has the most users, we need to compare the percentages of those who use each source.

According to the survey:

55% get news from local television station

60% get news from daily newspaper

40% get news from the internet

To compare these percentages, we can either convert them to fractions or decimals. Let's convert them to decimals:

55% = 0.55

60% = 0.60

40% = 0.40

Now we can compare them directly. We see that the source with the highest percentage is the daily newspaper, with 60% of those surveyed saying they get news from it. Therefore, the daily newspaper has the most users among the surveyed population.

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In one month, a total of 447 people stayed at the hotel.

In one month, a hotel had 382 adults and 65 children staying as guests.

To find out the total number of people who stayed at the hotel, we simply need to add the number of adults and children together.

In one month, a total of 447 people (382 adults and 65 children) stayed at the hotel.

Overall, this problem is a simple example of addition in action. By adding the number of adults and children together, we can determine the total number of people who stayed in the hotel.

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(a) We will use the "t" as test-statistics and the value of "t" is t = -0.87.

(b) We will use "z" as the test-statistics and the value of "z" is z = -0.77.

In statistics, a test statistic is a numerical summary of a sample that is used to make an inference about a population parameter. It is calculated from the sample data and is used to test a hypothesis or to make a decision about some characteristic of the population.

Part (a) : In this case, we do not know the "standard-deviation",

the case in which standard-deviation is un-known, "t" is used as a "test-statistics.

The Standard-error-of-mean (SE) is = s/√n = 0.5/√19 = 0.1148.

So, "t" = (mean - 2.5)/SE,

Substituting the values,

We get,

t = (2.4 - 2.5)/0.1148 = -0.87.

Part (b) : In this case, we know the "standard-deviation",

The case in which standard-deviation is known, "z" is used as a "test-statistics.

The Standard-error-of-mean (SE) is = s/√n = 0.45/√12 = 0.1299.

So, "z" = (mean - 2.5)/SE,

Substituting the values,

We get,

z = (2.4 - 2.5)/0.1299 = -0.77.

Therefore, the value of "z" is -0.77.

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The given question is incomplete, the complete question is

We want to conduct a hypothesis test of the claim that the population mean time it takes drivers to react following the application of brakes by the driver in front of them is more than 2.5 seconds. So, we choose a random sample of reaction time measurements. The sample has a mean of 2.4 seconds and a standard deviation of 0.5 seconds.

For each of the following sampling scenarios, choose an appropriate test statistic for our hypothesis test on the population mean. Then calculate that statistic. Round your answers to two decimal places.

(a) The sample has size 19, and it is from a non-normally distributed population with an unknown standard deviation.

Which test-statistic will you use z, t or It is unclear which test statistic to use.

(b) The sample has size 12,and it is from a normally distributed population with an known standard deviation of 0.45.

Which test-statistic will you use z, t or It is unclear which test statistic to use.

Answer:

It is not true since 9x - 3x = 6x and

3x(3) = 9x.

Answer:

Not true b/c

Step-by-step explanation:

9x-3x=6x

and3x(3)=9x

6x is not equal to 9x

The hire purchase price for the video recorder is 3,133.20.

To calculate the hire purchase price for the video recorder, follow these steps:

1. Calculate the initial deposit: 20% of the cash price (2,700) is (0.20 * 2,700) = 540.
2. Subtract the deposit from the cash price to get the outstanding balance: (2,700 - 540) = 2,160.
3. Calculate the interest for one year on the outstanding balance: 18% of 2,160 is (0.18 * 2,160) = 388.80.
4. Divide the interest by 12 to find the interest per month: (388.80 / 12) = 32.40.
5. Add the interest per month to the outstanding balance: (2,160 + 32.40 * 12) = 3,133.20.
6. The hire purchase price is 3,133.20, which is the total amount payable in 12 equal monthly instalments.

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Complete question:

A housewife purchased a videorecorder with a cash price of 8 2 700 under hire purchase terms She paid an initial deposit of 20% of the cash price and interest at 18% per annum on the outstanding balance is Charged. The Jamount payable is paid in 12 equal monththly instalments Calculate for the video recorder  The hire purchase price​

The terminal point (x, y, z) of vector v with the given initial point is (3, 0, 7).

To find the terminal point of vector v with initial point given, you can follow these steps:

Add the vector components to the coordinates of the initial point.

The vector v is given as (3, -6, 6) and the initial point is (0, 6, 1).

Add the x-components: 0 + 3 = 3

Add the y-components: 6 + (-6) = 0

Add the z-components: 1 + 6 = 7

The terminal point (x, y, z) of vector v with the given initial point is (3, 0, 7).

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Answer:

Approx 67.24%

Step-by-step explanation: If the Atlanta Hawks' free-throw percentage is 82%, the probability that a player will make one free throw is 0.82.

To find the probability that a player will make two free throws in a row, we can use the multiplication rule of probability which states that the probability of two independent events occurring together is the product of their individual probabilities.

Therefore, the probability of a player making two free throws in a row can be calculated as follows:

P(making two free throws in a row) = P(making first free throw) x P(making second free throw)

P(making two free throws in a row) = 0.82 x 0.82

P(making two free throws in a row) = 0.6724 or 67.24%

Therefore, the probability that a player for the Atlanta Hawks will make two free shots in a row is approximately 67.24%

The building is perfectly vertical and the observer is at a consistent height above the ground.

The method of indirect measurement can be used to estimate the height of a building by using similar triangles and the principles of proportionality. First, the distance from the base of the building to the observer and the distance from the ground to a known point on the building are measured. By maintaining the same angle of sight, the observer can move back until the top of the building is in their line of sight. At this point, a second pair of measurements is taken: the distance from the new location to the base of the building and the height of the visible portion of the building from the ground. By using the principles of proportionality between similar triangles, the height of the entire building can be estimated.

Specifically, the ratio of the height of the known point on the building to the distance from the observer to that point can be set equal to the ratio of the height of the entire building to the distance from the observer to the base of the building. This proportion can be solved algebraically to find the estimated height of the entire building.

B) What are some potential sources of error or inaccuracy in this method of estimation?

There are several potential sources of error or inaccuracy in this method of estimation. One major source of error is the assumption that the two triangles being compared are similar. If the angle of sight is not maintained exactly or if the ground is not perfectly level, the triangles may not be similar and the estimated height may be incorrect.

Additionally, the accuracy of the estimated height depends on the accuracy of the distance measurements. If the distances are not measured precisely, the estimated height will be proportionally less accurate.

Finally, this method assumes that the building is perfectly vertical and that the observer is at a consistent height above the ground. If the building is not perfectly vertical or the observer's height above the ground changes, this can also affect the accuracy of the estimated height.

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When i (x) = 3, the value of y is approximately -6.67. The equation relating i (x) and y in this inverse variation is xy = -20.

The given information states that the variables x and y vary inversely. To write an equation relating i (assuming it's x) and y, we first need to understand the concept of inverse variation.

In inverse variation, the product of the two variables remains constant. Mathematically, it can be represented as xy = k, where k is the constant of variation. We are given the values i (x) = 5 and y = -4. Using these values, we can find the constant of variation, k:

5 * -4 = k
k = -20

Now that we have the constant of variation, we can write the equation relating i (x) and y as:

xy = -20

Next, we want to find the value of y when i (x) = 3. We can use the equation we just derived to find the value of y:

3 * y = -20

Now, we can solve for y:

y = -20 / 3
y ≈ -6.67

So, when i (x) = 3, the value of y is approximately -6.67. The equation relating i (x) and y in this inverse variation is xy = -20.

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We can expect that approximately 525 people out of 1750 visitors to the museum would buy food at the cafeteria.

To find out how many people out of 1750 visitors to the Metropolitan Museum of Art would be expected to buy food at the cafeteria, follow these steps,
1. Determine the proportion of people who bought food in the random sample of 150 visitors: 45 people bought food, so the proportion is 45/150.
2. Simplify the proportion: 45/150 = 0.3 or 30%.
3. Apply this proportion to the total number of 1750 visitors: 1750 * 0.3 = 525.

So, based on the survey results, we can expect that approximately 525 people out of 1750 visitors to the museum would buy food at the cafeteria.

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The volume of the soccer ball to the nearest cubic inch is 125 cubic inches.

To find the volume of Sydney's soccer ball, we will use the formula for the volume of a sphere, which is V = (4/3)πr³, where V is the volume, r is the radius, and π is a constant (approximately 3.14).

First, we need to find the radius (r) of the soccer ball. Since the diameter is given as 6.2 inches, we can find the radius by dividing the diameter by 2: r = 6.2 / 2 = 3.1 inches.

Now we can plug the values into the volume formula:
V = (4/3)π(3.1)³
V ≈ (4/3)(3.14)(29.791)

Next, we calculate the volume:
V ≈ 124.72

Finally, we round the volume to the nearest cubic inch, which is approximately 125 cubic inches.

So, the volume of Sydney's soccer ball with a diameter of 6.2 inches is approximately 125 cubic inches when using π = 3.14.

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The equation of the circle in this problem is given as follows:

x² + y² = 49.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle. As this distance is of 7 units, it is then given as follows:

r = 7 -> r² = 49.

The center of the circle is at the origin, hence:

[tex](x_0, y_0) = (0,0)[/tex]

Thus the equation of the circle is given as follows:

x² + y² = 49.

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The coordinates of point M come out to be 4.8, 4.4

This case is solved by using the section formula which states that

The coordinate of point P that divides the line segment AB in the ratio of m:n where the coordinate of A is [tex]x_1,y_1[/tex] and the B is [tex]x_2,y_2[/tex] is described as

[tex]\frac{mx_2+nx_1}{m+n}[/tex],[tex]\frac{my_2+ny_1}{m+n}[/tex]

The line to be divided = PQ

Coordinates of P = (6,2)

Coordinates of Q = (3,8)

Ratio = 2:3

Thus, the coordinates of M = [tex]\frac{2*3+3*6}{2+3}[/tex],[tex]\frac{8*2+2*3}{2+3}[/tex]

= 24/5 , 22/5

= 4.8, 4.4

Point M with coordinates (4.8,4.4) lies on PQ and divides the segment so that the ratio of PM-MQ is 2-3

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The population in 4 year is 160 and in 6 year is 320.

The population is grows by a factor of 2 every two years.

We can use the following formula to get the rate of population growth every two years:

Growth factor: (population after n years / (population after (n-2) years) ^ 1/2

This formula can be used to determine the growth factor as follows:

Growth factor is equal to (40/10)*(1/2) = 2

This indicates that every two years, the population increases by a factor of 2.

Then, for 4 year the population

= 10 x 2⁴

= 10 x 16

= 160

For 6 year the population is

= 10 x 2⁶

= 10 x 32

= 320

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The value of x is 16.

Given,

The m line is parallel with the n line.

We need to find the value of x.

If two lines are parallel the corresponding angles are congruent.

Example:                              

                         [tex]\sf D[/tex] /

                          /

[tex]\sf A[/tex]<----------------[tex]\sf F[/tex]/----------------------->[tex]\sf B[/tex]

                      /

[tex]\sf C[/tex] <-----------[tex]\sf M[/tex]/------------------------------>[tex]\sf D[/tex]                    

                  /

            [tex]\sf E[/tex]  /

[tex]\sf AFD = CMF[/tex]

[tex]\sf AFM = CME[/tex]

From the figure, we see that

[tex]\sf 8x + 5 + 4x - 17 = 180[/tex]

[tex]\sf 12x - 12 = 180[/tex]

[tex]\sf 12x = 180 + 12[/tex]

[tex]\sf 12x = 192[/tex]

[tex]\sf x = \dfrac{192}{12}[/tex]

[tex]\sf x = 16[/tex]

Thus the value of x is 16.

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The explicit equation for the sequence 7, 10, 13, 16,... is an = 7 + 3n.

To find the explicit equation for the sequence 7, 10, 13, 16,..., we first need to identify the common difference.The common difference is the difference between any two consecutive terms in the sequence.

In this case, the common difference d is 10 - 7 = 3, 13 - 10 = 3, 16 - 13 = 3, and so on.

Next, we can use the formula for the nth term of an arithmetic sequence to find the explicit equation. The formula is:

an = a1 + (n - 1)d

where,

an = the nth term of the sequence

a1 = the first term of the sequence

d = the common difference

n = the number of the term we want to find

Since the sequence starts at x=0, we can rewrite the formula as: an = a0 + nd,

where a0 = 7 and d = 3.

Therefore, the explicit equation for the sequence is an = 7 + 3n

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Answer: y = 1.4

Step-by-step explanation:

if you write the equation it would be

-5y - 4 = -11

so first you would subtract 4 from -4 and -11 to cancel out the four.

so your equation would look like this -5y= -7

so now u would divide -5 by both sides to canceled out the -5

your equation should end up looking like

y=1.4

The roots of the given equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3[/tex]also satisfy the equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]

To find the roots of equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3,[/tex] we can substitute [tex]y = 2^(^x^-^2^)[/tex]to get:

[tex]y + 2^(^5^-^x^)^/^y = 3[/tex]

Multiplying both sides by y, we get:

[tex]y^2 + 2^(^5^-^x^) = 3y[/tex]

Substituting y = 2^(x-2), we get:

[tex]2^(^2^x^-^8^) + 2^(^5^-^x^) = 3 * 2^(^x^-^2^)[/tex]

Multiplying both sides by 2^8, we get:

[tex]4(2^x) + 32 = 768(2^(^2^-^x^))[/tex]

Simplifying, we get:

[tex]4(2^x) - 768(2^-^x) + 32 = 0[/tex]

Dividing both sides by 4, we get:

[tex]2^x - 192(2^-^x) + 8 = 0[/tex]

Multiplying both sides by [tex]2^x[/tex], we get:

[tex]4^x - 192 + 2^x = 0[/tex]

Adding 192 to both sides, we get:

[tex]4^x + 2^x - 192 = 0[/tex]

This is the same as the given equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]

Therefore, we have shown that the roots of the given equation [tex]2^(^x^-^2^) + 2^(^3^-^x^) = 3[/tex] also satisfy the equation [tex]4^(^x^) - 6*2^(^x^+^1^) + 32 = 0.[/tex]

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Answer:

(1/6)π(4^2) - (1/2)(2√3)(4)

= 8π/3 - 4√3 = about 1.4

To solve this problem, we need to use related rates. Let's start by drawing a diagram:

```
        /\
       /  \
      /    \
     /      \
    /        \
   /__________\
```

We know that the radius of the conical pile is always two times its height, so we can label the diagram as follows:

```
        /\
       /  \
      /    \
     /      \
    /        \
   /__________\
  /|    r=2h   \
 / |___________\
```

Now we need to find an equation that relates the height of the pile to its radius. We can use the formula for the volume of a cone:

```
V = (1/3)πr^2h
```

We want to solve for h in terms of r:

```
V = (1/3)πr^2h
3V/πr^2 = h
```

Now we can differentiate both sides of this equation with respect to time:

```
d/dt (3V/πr^2) = d/dt h
0 = (3/πr^2) dV/dt - (2/πr^3) dr/dt
```

We're given that the height is increasing at a rate of 2 cm/s when the pile is 11 cm high, so we know that:

```
dh/dt = 2 cm/s
h = 11 cm
```

We want to find the rate at which sand is leaving the bin, which is given by `dV/dt`. We can solve for this using the equation we derived:

```
0 = (3/πr^2) dV/dt - (2/πr^3) dr/dt
dV/dt = (2/3)πr^2 (dh/dt) / r
```

Now we just need to plug in the values we know:

```
dh/dt = 2 cm/s
h = 11 cm
r = 2h = 22 cm

dV/dt = (2/3)π(22)^2 (2) / 22
dV/dt = 264π/3
```

So the rate at which sand is leaving the bin when the pile is 11 cm high is `264π/3 cm^3/s`.

To solve this problem, we can use the relationship between the radius and height of the conical pile, as well as the given rate of height increase.

Since the radius (r) is always two times the height (h), we have r = 2h. The volume (V) of a cone is given by the formula V = (1/3)πr^2h. We can substitute r with 2h, so V = (1/3)π(2h)^2h.

Now, let's differentiate both sides with respect to time (t):

dV/dt = (1/3)π(8h^2)dh/dt

When the height is 11 cm, the rate of height increase (dh/dt) is 2 cm/s. We can substitute these values into the equation:

dV/dt = (1/3)π(8(11)^2)(2)

Solving for dV/dt:

dV/dt ≈ 2046.92 cm³/s

At that instant, the sand is leaving the bin at a rate of approximately 2046.92 cm³/s.

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a. The correlation between temperature and yield is 0.63, between stirring rate and yield is 0.05, and between temperature and stirring rate is -0.01.

b. The data suggest that increasing temperature causes yield to increase, but confounding variables cannot be ruled out.

c. The data do not provide strong evidence that increasing stirring rate causes yield to increase, and confounding variables cannot be ruled out.

a. To compute the correlation between temperature and yield, stirring rate and yield, and temperature and stirring rate, we can use the Pearson correlation coefficient.

The correlation between temperature and yield is 0.61, indicating a moderate positive correlation. The correlation between stirring rate and yield is 0.02, indicating a weak positive correlation. The correlation between temperature and stirring rate is -0.43, indicating a moderate negative correlation.

b. The correlation between temperature and yield suggests that increasing the temperature may lead to an increase in yield. However, we cannot conclude that this relationship is causal as there may be other factors (e.g., stirring rate) that are confounding the relationship. To establish a causal relationship, we would need to conduct a controlled experiment where we manipulate temperature while keeping other factors constant.

c. The correlation between stirring rate and yield is weak, and it is difficult to draw strong conclusions from this relationship. It is possible that the relationship is due to confounding factors such as temperature or other unmeasured variables. Further experimentation is needed to establish a causal relationship between stirring rate and yield.

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The point of intersection between the two given equations is (3, -2).

The problem is asking to find the point of intersection between the two given equations:

y = (1/3)x - 3 ............... (equation 1)

y = -x + 1 ............... (equation 2)

To solve for the intersection point, we can set the two equations equal to each other:

(1/3)x - 3 = -x + 1

Simplifying and solving for x:

(1/3)x + x = 1 + 3

(4/3)x = 4

x = 3

Now that we know x = 3, we can substitute it into either of the two original equations to find y:

Using equation 1: y = (1/3)x - 3 = (1/3)(3) - 3 = -2

Using equation 2: y = -x + 1 = -(3) + 1 = -2

Therefore, the intersection point is (3, -2).

To know more about intersection point, refer to the link below:

https://brainly.com/question/11632250#

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Answer:

Step-by-step explanation:

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