Graph the line that passes through the points (3, -6) and (-6, -3) and determine
the equation of the line.

The depth of the water in the cone-shaped tank is increasing at a rate of approximately 1.385 meters per second.

To determine the rate at which the depth of the water is changing, we can use related rates. Let's denote the depth of the water as h(t), where t represents time. We are given that dh/dt (the rate of change of h with respect to time) is 12 m/sec, and we want to find dh/dt when h = 18 meters.

To solve this problem, we can use the volume formula for a cone, which is V = (1/3)πr^2h, where r is the base radius and h is the depth of the water. We can differentiate this equation with respect to time t, keeping in mind that r is a constant (since the base radius does not change).

By differentiating the volume formula with respect to t, we get dV/dt = (1/3)πr^2(dh/dt). Now we can substitute the given values: dV/dt = 12 m/sec, r = 26 meters, and h = 18 meters.

Solving for dh/dt, we have (1/3)π(26^2) (dh/dt) = 12 m/sec. Rearranging this equation and solving for dh/dt, we find that dh/dt is approximately 1.385 meters per second. Therefore, the depth of the water in the tank is increasing at a rate of about 1.385 meters per second.

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The ratio of the area of circle A to the area of circle B expressed in the common fraction is 4/9.

An arc is a portion of the circumference of a circle. The length of an arc is proportional to the radius of the circle and the measure of the angle formed by the arc and the center of the circle. The formula for the length of an arc is:

Arc Length = (Angle Measure / 360) x (Circumference)

In this problem, we are given that the arc of 55 degrees on circle A has the same length as the arc of 40 degrees on circle B. So we can set up the following equation:

(55/360) x (Circumference of A) = (40/360) x (Circumference of B)

We can simplify this equation by canceling out the common factor of 360:

(5/12) x (Circumference of A) = (2/9) x (Circumference of B)

Now we can use the fact that the circumference of a circle is equal to 2π times the radius:

(5/12) x (2π x radius of A) = (2/9) x (2π x radius of B)

We can cross-multiply and divide by 2π to find the ratio of the radii of the two circles:

(5/12) x (radius of A) = (2/9) x (radius of B)

radius of A / radius of B = (2/9) / (5/12) = 12/18 = 2/3

Since the ratio of the areas of two circles is equal to the square of the ratio of their radii, the ratio of the area of circle A to the area of circle B is:

Area of A / Area of B = (radius of A / radius of B)^2 = (2/3)^2 = 4/9

So the ratio of the area of circle A to the area of circle B is 4/9.

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Answer:

First one

Step-by-step explanation:

Answer:

\(13.69\pi\)

Step-by-step explanation:

here radius (r)=3.7

Step-by-step explanation:

Area of trapezoid

= 1/2 × 4 × [6 + (5+8)]

= 1/2 × 4 × 19

= 38 cm²

Answer:

2,134.57 or the bottom one

Step-by-step explanation:

I found the volume

Answer:

its D i did the Iready

Step-by-step explanation:

In a Stock Dividend Assets don't change, Liabilities don't change.

In a stock dividend scenario, where a company issues additional shares of its own stock to existing shareholders, the impact on the company's balance sheet is as follows:

Assets don't change, Liabilities don't change.

When a company declares a stock dividend, it is essentially distributing a portion of its retained earnings or accumulated profits to its shareholders in the form of additional shares. This means that the company is not receiving any new assets or incurring any new liabilities in the process.

From an accounting perspective, the value of the stock dividend is reflected in the equity section of the balance sheet. The retained earnings account decreases by the value of the dividend, while the common stock or additional paid-in capital account increases by the same value. This adjustment does not affect the company's assets or liabilities.

Therefore, the correct answer is: Assets don't change, Liabilities don't change.

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Answer: 1,176 miles

Step-by-step explanation:

490 / 5 = 98 miles

98 mph X 12 hours is 1,176

Answer:

c

a

Step-by-step explanation:

Answer:

5. is C which is 9.

6. is B which is 37.

Step-by-step explanation:

The first on is C. 9 because to find the interquartile range you need to subtract the upper quartile range by the lower quartile range. The upper is 16 and the lower is 7 so you do 16-7 which is 9.

The last question is B. 37 because the lower quartile range is first line in the box plot which is 37.

Answer:

corresponding angles are congurent

Step-by-step explanation:

Answer:

Corresponding angles are congruent

Explanation:

If you line the triangles up on top of each other, they should be the same and you should not see any angles or lines from triangle 1 away from triangle 2

X and Y are not independent.

P(Y > 2X) = 3/16.

Marginal pdf of X = 12x(1-x)² for 0 < x < 1

(a) To determine if X and Y are independent, we need to check if the joint pdf can be factored into the product of the marginal pdfs:

f(x,y) = 24xy if 0 < x, 0 < y, x + y < 1, and zero otherwise.

Marginal pdf of X can be calculated by integrating the joint pdf over the all possible values of y:

f(x) = ∫ f(x,y) dy from 0 to 1-x

= ∫ 24xy dy from 0 to 1-x

= 12x(1-x)² for 0 < x < 1

Similarly, the marginal pdf of Y can be found by integrating the joint pdf over all possible values of x:

f(y) = ∫ f(x,y) dx from 0 to 1-y

= ∫ 24xy dx from 0 to 1-y

= 12y(1-y)² for 0 < y < 1

To check for independence, we need to verify if f(x,y) = f(x)f(y) for all x and y. However, if we multiply the marginal pdfs, we get:

f(x)f(y) = 144xy(1-x)²(1-y)² for 0 < x < 1 and 0 < y < 1

This is not the same as the joint pdf, so X and Y are not independent.

(b) To find P(Y > 2X), we need to integrate the joint pdf over the region where Y > 2X:

P(Y > 2X) = ∫∫ f(x,y) dA over the region where Y > 2X

= ∫∫ 24xy dA over the region where Y > 2X

= ∫∫ 24xy dxdy over the region where 0 < y < 2x and x+y < 1

= ∫[0,1/2] ∫[y/2,1-y] 24xy dxdy

= 3/16

Therefore, P(Y > 2X) = 3/16.

(c) The marginal pdf of X is given by:

f(x) = ∫ f(x,y) dy from 0 to 1-x

= ∫ 24xy dy from 0 to 1-x

= 12x(1-x)² for 0 < x < 1

Same result we get in part (a).

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X and Y are not independent.

P(Y > 2X) = 3/16.

Marginal pdf of X = 12x(1-x)² for 0 < x < 1

(a) To determine if X and Y are independent, we need to check if the joint pdf can be factored into the product of the marginal pdfs:

f(x,y) = 24xy if 0 < x, 0 < y, x + y < 1, and zero otherwise.

Marginal pdf of X can be calculated by integrating the joint pdf over the all possible values of y:

f(x) = ∫ f(x,y) dy from 0 to 1-x

= ∫ 24xy dy from 0 to 1-x

= 12x(1-x)² for 0 < x < 1

Similarly, the marginal pdf of Y can be found by integrating the joint pdf over all possible values of x:

f(y) = ∫ f(x,y) dx from 0 to 1-y

= ∫ 24xy dx from 0 to 1-y

= 12y(1-y)² for 0 < y < 1

To check for independence, we need to verify if f(x,y) = f(x)f(y) for all x and y. However, if we multiply the marginal pdfs, we get:

f(x)f(y) = 144xy(1-x)²(1-y)² for 0 < x < 1 and 0 < y < 1

This is not the same as the joint pdf, so X and Y are not independent.

(b) To find P(Y > 2X), we need to integrate the joint pdf over the region where Y > 2X:

P(Y > 2X) = ∫∫ f(x,y) dA over the region where Y > 2X

= ∫∫ 24xy dA over the region where Y > 2X

= ∫∫ 24xy dxdy over the region where 0 < y < 2x and x+y < 1

= ∫[0,1/2] ∫[y/2,1-y] 24xy dxdy

= 3/16

Therefore, P(Y > 2X) = 3/16.

(c) The marginal pdf of X is given by:

f(x) = ∫ f(x,y) dy from 0 to 1-x

= ∫ 24xy dy from 0 to 1-x

= 12x(1-x)² for 0 < x < 1

Same result we get in part (a).

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The value of  integral sin (x^2+y^2)dA is 2π(cos(9) - cos(64)).

To evaluate this integral using polar coordinates, we first need to express the region R in terms of polar coordinates. In polar coordinates, the equation of a circle with radius r is given by r^2 = x^2 + y^2. So, the region R can be expressed as 3 < or = r < or = 8.

Now, we can express the integral in polar coordinates:

∫∫R sin (x^2+y^2)dA = ∫θ=0 to 2π ∫r=3 to 8 sin (r^2) r dr dθ

We integrate first with respect to r, then with respect to θ:

∫θ=0 to 2π ∫r=3 to 8 sin (r^2) r dr dθ

= ∫θ=0 to 2π [-cos(64) + cos(9)] dθ

= 2π(cos(9) - cos(64))

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Answer:

One Twelfth (1/12) of a Mile per Day

Step-by-step explanation:

If Eliza has 3 days to build this fence, you can divide the total length of the fence (1/4 mile) into 3 sperate sections for each day. Dividing 1/4 by 3 gets you. 1/12 of a mile will be built each day.

Answer:

5

Step-by-step explanation:

5-[2-(-4)-6]

Work from the inside out

5-[2+(4)-6]

5-[6-6]

5 - 0

5

Answer:

1 3/4 gallons

Step-by-step explanation:

Answer:

Point Form:

( 0 , 3 )

Equation Form:

x = 0 , y = 3

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Let x be the tax rate. Hence, we can write

then, we must move 350 to the righ hand side, it reads

and now, we must convert the rate in decimal form to percentage form.

The relation between these form is

Therefore, we have

then, the answer in percentage is 8%.

Answer:

There should be 6 blue bags.

Step-by-step explanation:

Answer:

15a

Step-by-step explanation:

Multiply  

3

by  

5

=

15

a

The problem here is a related rates problem. There are two things that we must determine here to arrive at the answer. First, we need to obtain an equation that represents the distance between the tips of the hands of the watch.

Then we need to find the rate of change of that distance or dx/dt when the time is 1 o'clock. So let us first obtain an equation that represents the distance between the tips of the hands of the watch. We will use the Pythagorean Theorem to find this equation, which states that: a² + b² = c².

The distance between the tips of the hands of the watch can be represented by the hypotenuse of the right triangle formed by the two hands of the watch, so we can use this equation to get the value of the distance between the tips of the hands:Distance² = 6² + 5²Distance² = 61Distance = √61We can now find dx/dt using the equation: Distance² = 6² + 5²Distance² = 61Distance = √61 Differentiating both sides of the equation with respect to t, we have:2Distance(d Distance/dt) = 0 + 0 + 0dDistance/dt = (-2Distance/distance) (dh/dt) + (2Distance/distance) (dm/dt)where h is the hour hand, and m is the minute hand. Let h = 5mm, and m = 6mm at one o'clock. Then we can substitute to find dx/dt at 1 o'clock: Distance = √61dh/dt = 0 (since the hour hand does not move)dm/dt = 6π radians/hour d Distance/dt = (-2(√61)/(√61)) (5) + (2(√61)/(√61)) (6π)≈ 3.85 mm/hour

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Natalie will choose 7 and 8 as the yellow-shaded region corresponds to Natalie's possible choices.

Even though it appears complex, 3-dimensional trilateration is a straightforward mathematical process that underlies GPS. It's critical to have a fundamental understanding of 2-D Trilateration, which is necessary to completely comprehend 3-D Trilateration. Similar principles apply to three-dimensional trilateration, however, spheres rather than circles are used. Here is how the Global Positioning System uses 3-D trilateration to pinpoint an object's precise location. When the first satellite sends a signal, the GPS receiver measures the distance between the two. Say the distance between the receiver and the satellite is 20 000 miles. This implies that the receiver might be located anywhere on the 20 000 km diameter green sphere's surface and in any direction.

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using standard z value, 20% of sandwiches are less than 10.58 inches.

In the given question,

Subway sells foot long sandwiches that have a mean of 11 inches and a standard deviation of 0.5 inches.

20% of sandwiches are less than...............inches.

The cumulative standardized normal distribution table indicates a z value of -0.84 for 20%.

From the question we know that

Mean(μ) = 11 inches

Standard Deviation(σ) = 0.5 inches

We have to find less than of 20% of sandwiches for z value of -0.84

P(ƶ<z) = 20%

We can write it as

P(ƶ<-0.84) = 20/100

P(ƶ<-0.84) = 0.20

Since z = -0.84

X-μ/σ = -0.84

Now putting the value

X-11/0.5 = -0.84

Multiply by 0.5 on both side

X-11/0.5 *0.5= -0.84*0.5

X-11= -0.42

Add 11 on both side

X-11+11= -0.42+11

X = 10.58

Hence, 20% of sandwiches are less than 10.58 inches.

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Right question is here

Subway sells foot long sandwiches that have a mean of 11 inches and a standard deviation of 0.5 inches. 20% of sandwiches are less than ................. inches. (The cumulative standardized normal distribution table indicates a z value of -.84 for 20%)

(a) 11.500

(b) 11.42

(c) 10.58

(d) cannot be determined from the information given

The probability that no more than 13 of the tickets have popcorn coupons is 0.1114.

It is a binomial distribution "DISCRETE probability distribution that encapsulates the likelihood that a value will take one of two independent values when a particular set of conditions is met. The assumptions for the binomial distribution are that each trial has a single possible outcome, each trial has an equal chance of success, and each trial is independent of the others or mutually exclusive ".

Let X the random variable of interest, on this case we now that:

X ∼ Binom( n = 18, p = 0.97)

The probability mass function for the Binomial distribution is given as:

P( X ) = ( ₙCₓ )(p)ˣ( 1 - p )ⁿ⁻ˣ

Where (ₙCₓ) means combinatory and it's given by this formula:

ₙCₓ = n! / ( n - x )! x!

And we want to find this probability:

P( X = 13 )

And using the probability mass function we got:

P( X = 13 ) = ₁₈C₁₃ ( 0.597 )¹³ ( 1 - 0.597 )¹⁸⁻¹³

P( X = 13 ) = 8568 × 0.00122367561 × 0.01062980336

P( X = 13 ) = 0.11144766975

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Answer:

An elevator can hold up to about 2000 pounds of weight.The combined weight of everyone currently in the elevator is 1980 pounds. Write an inequality showing the possible amount of weight that can be added to the elevator. S can be your variable hope this helps.

Answer:

f(x) = 9(x + 5)2 - 6 (-5,-6)

f(x) = 6(x + 9)2 - 5 (-9,-5)

f(x) = 9(x - 5)2 + 6 (5,6)

f(x) = 6(x - 5)2 - 9. (5,-9)

f(x) = 5(x - 6) +9. (6,9)

Step-by-step explanation:

To find the vertex: for the x-coordinate, take the "h" in the parentheses (x + h) and reverse its sign. For the y-coordinate, use the "k" term as-is.

The coordinates of the vertex of the equations are:

The vertex form of the quadratic function is given as:

y = a(x -h)^2 + k

Where:

Vertex = (h,k)

Using the above highlight, the coordinates of the vertex of the equations would be:

f(x) = 9(x + 5)^2 - 6

Vertex = (-5,-6)

f(x) = 6(x + 9)^2 - 5

Vertex = (-9,-5)

f(x) = 9(x - 5)2 + 6

Vertex =(5,6)

f(x) = 6(x - 5)^2 - 9

Vertex = (5,-9)

f(x) = 5(x - 6) +9

Vertex = (6,9)

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The polynomial with the 3rd -degree binomial with the constant term 8 is x³ - 8 and 5x³ - 8.

Given that,

A binomial of third degree with constant term of 8.

We have to find a polynomial with the conditions.

We know that,

Binomial is nothing but a polynomial which has 2 terms in it.

And one term should be a constant and that is number 8.

The degree means the degree of the polynomial which has the greatest degree that means power of the variable.

And the degree of the binomial that means power of variable should be 3.

The binomial equation are-

x³ - 8 and 5x³ - 8

Therefore, the polynomial with the 3rd -degree binomial with the constant term 8 is x³ - 8 and 5x³ - 8.

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The question is incomplete the complete question is -

Find a 3rd -degree binomial with a constant term of 8.