The length of the diagonal of rectangle sqrt(181) inches

It is proved that <QST + <TSV = 180° becasue of the linear pair.

Here we know that vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

The sum of linear pair is equal to 180 degree

<QSVX= 180°

<TSR= 180°

Therefore, <QST= 90°

<TSV= 90°

Thus, <QST + <TSV = 180°

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Spherical coordinates are a system of coordinates that describe points in three-dimensional space using a distance from the origin, an angle of inclination from the positive z-axis, and an angle of rotation around the z-axis.

To calculate the triple integral of f(x, y, z)=x2 y2 over the region rho≤2 using spherical coordinates, we first need to express the function in terms of the spherical coordinates.

We know that in spherical coordinates,

x = ρ sin(φ) cos(θ)
y = ρ sin(φ) sin(θ)
z = ρ cos(φ)

where ρ is the radial distance, θ is the azimuthal angle, and φ is the polar angle.

So, f(x, y, z) = x2 y2 can be expressed as

f(ρ, φ, θ) = (ρ sin(φ) cos(θ))2 (ρ sin(φ) sin(θ))2

= ρ4 sin2(φ) cos2(θ) sin2(φ) sin2(θ)

= ρ4 sin4(φ) cos2(θ)

Now, we can set up the triple integral using spherical coordinates.

∫∫∫ f(ρ, φ, θ) ρ2 sin(φ) dρ dφ dθ

= ∫0^2π ∫0^π/2 ∫0^2 f(ρ, φ, θ) ρ2 sin(φ) dρ dφ dθ

= ∫0^2π ∫0^π/2 ∫0^2 ρ4 sin4(φ) cos2(θ) ρ2 sin(φ) dρ dφ dθ

= ∫0^2π ∫0^π/2 ∫0^2 ρ6 sin5(φ) cos2(θ) dρ dφ dθ

= ∫0^2π ∫0^π/2 [ρ7/7 sin5(φ) cos2(θ)]0^2 dφ dθ

= ∫0^2π ∫0^π/2 32/7 sin5(φ) cos2(θ) dφ dθ

= 32/7 ∫0^2π cos2(θ) dθ ∫0^π/2 sin5(φ) dφ

= 32/7 [π sin6(π/2)/6]

= 32π/21

Therefore, the triple integral of f(x, y, z) = x2 y2 over the region rho≤2 using spherical coordinates is 32π/21.

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A standard normal random variable, denoted by Z, is a variable that follows a normal distribution with a mean of 0 and a standard deviation of 1.

The area under the curve of the normal distribution represents the probability of a particular event occurring. For example, the probability of Z being greater than 0 can be found by calculating the area to the right of 0 on the standard normal distribution curve.

we need to use the standard normal distribution table or a calculator. The table gives the probability of a standard normal variable Z being less than a certain value. To find the probability of Z being greater than 0, we can use the fact that the total area under the curve is 1, and the area to the left of 0 is 0.5. Therefore, the area to the right of 0 is also 0.5, and the probability of Z being greater than 0 is 0.5.

In other words, there is a 50% chance that a standard normal random variable will be greater than 0. This means that half of the values of Z are positive and half are negative. It is important to note that the normal distribution is symmetrical, and the area to the left of the mean is equal to the area to the right of the mean.

In summary, the probability of Z being greater than 0 is 0.5, which means that half of the values of Z are positive and half are negative. The normal distribution is symmetrical, and the area to the left of the mean is equal to the area to the right of the mean. This information can be useful in various statistical applications, such as hypothesis testing and confidence intervals.

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The range of possible amounts of cereal, c, in a box is between 18.6 ounces and 19.6 ounces.

A company claims that its boxes of cereal contain 19.1 ounces of cereal. The actual amount of cereal in the box can be within 0.5 ounces of the advertised amount. We can use this information to find the range of possible amounts of cereal, c, in a box.

To find the minimum amount of cereal in a box, we subtract 0.5 from the advertised amount:

c_min = 19.1 - 0.5 = 18.6 ounces

To find the maximum amount of cereal in a box, we add 0.5 to the advertised amount:

c_max = 19.1 + 0.5 = 19.6 ounces

Therefore, the range of possible amounts of cereal, c, in a box is between 18.6 ounces and 19.6 ounces.

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The given expression is (4x + 3) + (-2x + 4). To simplify the expression, we first combine like terms.

(4x + 3) + (-2x + 4) = 4x - 2x + 3 + 4 = 2x + 7

Therefore, the expression equivalent to (4x + 3) + (-2x + 4) is 2x + 7.

When adding or subtracting two expressions, we combine like terms by adding or subtracting the coefficients of the same variables. In the given expression, we have two terms, (4x + 3) and (-2x + 4).

We can first rearrange the terms by adding the coefficients of x and constants separately. By doing so, we obtain 4x - 2x and 3 + 4, which simplify to 2x and 7, respectively. Thus, we have the expression 2x + 7 as the simplified form of the given expression.

This is a useful technique when simplifying algebraic expressions and can be used to simplify more complex expressions involving multiple variables and terms.

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The least upper bound of a set in a poset is unique if it exists.

Let S be a poset and let A be a subset of S that has a least upper bound. We will show that this least upper bound is unique.

Suppose, for the sake of contradiction, that A has two distinct least upper bounds, denoted x and y. Since x is a least upper bound, we know that y is an upper bound of A and x is the least such upper bound. Similarly, we know that x is an upper bound of A and y is the least such upper bound.

Since x is an upper bound of A, we have y ≤ x, and since y is an upper bound of A, we have x ≤ y. This implies that x = y, which contradicts our assumption that x and y are distinct. Therefore, the least upper bound of a set in a poset is unique if it exists.

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Answer:

D, The ordered pair (-4, 0) is a solution to the system because it makes both equations true.

If the equetion is 2x + y = -8 and x - y = -4

The value of the angles m∠A is 95 degrees, m∠BOT is 195 degrees, m∠ATO is 40 degrees and m∠PBQ is 40 degrees.

First, let's find the measure of angle m∠A. Since PT is tangent to circle O, we know that angle m∠T is a right angle (90 degrees). Since arc AB and arc BT add up to the whole circle (360 degrees), we can find their measures as follows:

m(arc AB) = m(arc OB) - m(arc OA)

= 360 - m(arc OA)

= 360 - 2m∠P (since m∠P = m(arc OA)/2)

= 360 - 2(40) = 280

m(arc BT) = 180 - m∠T (since arc BT is a minor arc and m(arc BT) = 180 - m∠T)

= 180 - 90 = 90

Therefore, m∠A = (m(arc AB) - m(arc BT))/2 = (280 - 90)/2 = 95 degrees.

Next, let's find the measure of angle m∠BOT. Since PT is tangent to circle O, we know that angle m∠T is a right angle (90 degrees).

This gives us:

m∠BOT = 1/2 (m(arc BA) - m(arc BT))

= 1/2 (m(arc OA) + m(arc AB) - m(arc BT))

= 1/2 (2m∠P + 280 - 90) (using the same arc measures as before)

= 1/2 (2(40) + 190)

= 135 degrees.

Next, let's find the measure of angle m∠ATO. This is the angle between the secant PBOA and the tangent PT, on the opposite side of point T from angle m∠BOT.

We can use the alternate segment theorem, which states that the angle between a tangent and a chord at the point of contact is equal to the angle in the alternate segment. In this case, angle m∠ATO is equal to angle m∠P.

Therefore, m∠ATO = 40 degrees.

Finally, let's find the measure of angle m∠PBQ. In this case, angle m∠PBQ is congruent to angle m∠P, which we have already found to be 40 degrees. Therefore, m∠PBQ = 40 degrees.

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The integral of y dt along the curve C is:

(b^2) - (a^2).

To evaluate the integral of y dt along the curve C defined by x = t^2 and y = 2t, we'll first find the differential dt in terms of dx by differentiating x with respect to t:
dx/dt = 2t

Now, we'll solve for dt:
dt = dx / (2t)

Substitute the expression for y and dt into the integral:
∫(2t) (dx / (2t))

The 2t terms cancel each other out, leaving:
∫ dx

Now, we need to find the limits of integration. To do this, we'll use the given parametric equation for x:
x = t^2

Assuming t varies from a to b, the limits of integration for x will be from x = a^2 to x = b^2. Thus, the integral becomes:
∫(a^2 to b^2) dx

Integrate with respect to x:
[x] (from a^2 to b^2)

Evaluate the integral:
(b^2) - (a^2)

So, the integral of y dt along the curve C is (b^2) - (a^2).

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Answer:

length = 3 meters and width = 2 meters

length = 2 meters and width = 3 meters

Step-by-step explanation:

If you want to find out how big a rectangle is when you know its perimeter and area, you can use some math tricks. Here are the tricks:

Perimeter of a rectangle = 2 times (length plus width) 1

Area of a rectangle = length times width 2

Now we can use these tricks to find the length and width of the rectangle. Let's say the length is l and the width is w. Then we can write:

2 times (l plus w) = 10

l times w = 6

We can make the first trick easier by cutting both sides in half:

l plus w = 5

We can then get rid of one letter by using the other one. For example, we can write l as 5 minus w:

l = 5 - w

Then we can put this into the second trick:

(5 - w) times w = 6

This makes a puzzle that we can solve by opening up, moving around, and grouping:

5w minus w squared = 6

w squared minus 5w plus 6 = 0

(w minus 2) times (w minus 3) = 0

This means that either w minus 2 = 0 or w minus 3 = 0. Solving for w, we get two answers:

w = 2 or w = 3

We can then use these answers to find the matching answers for l:

If w = 2, then l = 5 - w = 5 - 2 = 3

If w = 3, then l = 5 - w = 5 - 3 = 2

So we have two ways to make the rectangle:

length = 3 meters and width = 2 meters

length = 2 meters and width = 3 meters

the two true statements are the median score for the first 12 games is 19. The range of the first 12 games is 9.

The basketball player scored the following points during the regular season: 15, 16, 17, 18, 19, 20, 20, 22, 24. In the playoffs, the player scored 10 and 45 points.

The median score for the first 12 games is 19.

To find the median, we first need to arrange the scores in order from lowest to highest: 15, 16, 17, 18, 19, 20, 20, 22, 24. The middle score is the median, which in this case is 19.

The range of the first 12 games is 9.

The range is the difference between the highest and lowest scores. The highest score is 24 and the lowest score is 15, so the range is 24 - 15 = 9.

Therefore, the two true statements about the scores for the first 12 games are:

The median score for the first 12 games is 19.

The range of the first 12 games is 9.

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The value of the angle m∠MQN of the given rectangle is:  76°

Some of the properties of rectangles are:

A rectangle is defined as a quadrilateral that has four equal interior angles.

The opposite sides of a rectangle are equal and parallel to each other.

The interior angle of a rectangle at each vertex measures 90°.

The sum of all the interior angles of a rectangle is 360°.

The diagonals bisect each other.

The length of the diagonals is equal.

The length of the diagonals can be obtained using the Pythagoras theorem. The length of the diagonal with sides a and b is √( a² + b²).

Since the sides of a rectangle are parallel, it is also called a parallelogram.

All rectangles are parallelograms but all parallelograms are not rectangles.

We are given that m∠NQO = 104°.

Sum of angles on a straight line is 180°. Thus:

m∠MQN = 180 - 104

m∠MQN = 76°

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The number of people sharing the video doubles each hour.

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

f(x) = 4(2)ˣ

The above function is an exponential function

Where

x represents the number of hours after the first time it appears

An exponential function is represented as

f(x) = a(b)ˣ

Where

a = initial value = 4

b = rate = 2

This means that the number of the video doubles each hour i.e. b is correct

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The pollutant will become 7,560 pounds after 9 months and the pollutant will become 40,000 pounds after 27.32 months.

Given that an equation, [tex]N'(t) = 280t^{3/2[/tex][tex]280t^{3/2[/tex], we need to find the value of N'(t) for t=9 and for what of value t, N'(t) = 40,000

So,

i) [tex]N'(t) = 280(9)^{3/2[/tex]

= 7,560 pounds

ii) 40,000 = [tex]280t^{3/2[/tex]

[tex]t^{3/2[/tex] = 142.85

Squaring both sides of the equation,

t³ = 20,406.1225

t = 27.32

Therefore the pollutant will become 40,000 pounds after 27.32 months.

Hence the pollutant will become 7,560 pounds after 9 months and the pollutant will become 40,000 pounds after 27.32 months.

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Bisection method is a numerical method used to find the root of a function by repeatedly bisecting an interval and determining which subinterval the root lies in, until the root is found.

To find the time at which the number of people in the museum is at a maximum, we need to find when the rate at which people are entering the museum (f'(t)) is equal to the rate at which people are leaving the museum (g'(t)).

Setting f'(t) = g'(t), we get:

380(1.02^t) = 240 + 240 sin (π(t-4)/12)

Simplifying, we get:

1.58(1.02^t) = 1 + sin(π(t-4)/12)

We can use a graphing calculator or numerical methods to solve for t.

Using a graphing calculator, we can graph the functions y = 1.58(1.02^x) and y = 1 + sin(π(x-4)/12) and find the point of intersection on the interval 1 ≤ x ≤ 11.

Alternatively, we can use numerical methods such as the bisection method or Newton's method to approximate the solution.

Using either method, we find that the solution is t ≈ 9.446.

Therefore, the answer is (C) 9.446.

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Answer:

the length of DC is (3/8) times the area of the trapezium.

Step-by-step explanation:

Unfortunately, there is no attached diagram to your question. Without a diagram, it is difficult to provide a specific solution. However, I can give you some general information that may help you solve the problem.

A trapezium is a quadrilateral with at least one pair of parallel sides. In this case, we know that AB is one-third of DC, so AB is shorter than DC. The vertical distance between YAB and DC is given as 12cm. This means that the height of the trapezium is 12cm.

To find the length of DC, we need to use the formula for the area of a trapezium:

Area = (1/2) x (sum of parallel sides) x (height)

In this case, we know that the area of the trapezium is b m², and we can represent the length of DC as x. We also know that AB is one-third of DC, so we can represent AB as (1/3)x.

Substituting these values into the formula, we get:

b = (1/2) x [(1/3)x + x] x 12

Simplifying this equation, we get:

2b = (4/3)x x 12

2b = 16x/3

x = (3/16) x 2b

x = (3/8) b

So the length of DC is (3/8) times the area of the trapezium.

The largest of three numbers  is 38.

Here, we have,

Given : The sum of three consecutive even integers is 108.

We have to find the largest of three consecutive even integer.

Consecutive integers are integer having a difference of one between each term . example 14 , 15, 16 ..

consecutive even integers are integers having a difference of two between them such that first term is in the form of 2n , where n is integers.

Consider the three consecutive even integers are 2n , 2n + 2 , 2n + 4

Also, given The sum of three consecutive even integers is 108.

that is 2n + 2n + 2 + 2n + 4 = 108

Simplify, we get,

6n + 6 = 108

Subtract 6 both side, we get,

6n = 102

Divide by 6 both side, we get,

n = 17

Thus, numbers are 2n = 2 × 17 = 34

2n + 2 = 34 + 2 = 36

2n + 4 = 34 + 4 = 38

Thus, The sum of three consecutive even integers is 108 then integers are 34, 36, 38 .

Thus, The largest of three numbers is 38.

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complete question:

The sum of three consecutive even integers is 108. What is the largest number?

a.34

b.35

c.37

d.38

Thus, there are two ways to get from (0,0) to (7,4) passing through (1,1) and only taking steps in a positive direction.

To get from (0,0) to (7,4) passing through (1,1) and only taking steps in a positive direction, we can break down the problem into smaller steps.

First, we need to get from (0,0) to (1,1). This can only be done with one step, either going right or up.

Then, we need to get from (1,1) to (7,4). We can do this by taking six steps to the right and three steps up. However, we need to make sure that we always pass through (1,1).

One way to ensure this is to take three steps to the right, then one step up to (2,2), and then three more steps to the right and two steps up to (7,4).

Therefore, there are two ways to get from (0,0) to (7,4) passing point through (1,1) and only taking steps in a positive direction:

1. One step to the right and then three steps to the right, one step up, three more steps to the right, and two steps up.
2. One step up and then two steps to the right, three steps to the right and one step up to (2,2), and then three more steps to the right and two steps up to (7,4).

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Longitudinal parity is sometimes called longitudinal redundancy check question is b. horizontal. Longitudinal parity is a type of error-checking method used in digital communications.

It involves adding an extra bit to each data word to ensure that the total number of 1s in the word, including the parity bit, is always even or odd. This allows the receiving device to detect if there has been an error during transmission.

Longitudinal parity is also sometimes referred to as longitudinal redundancy check or horizontal parity. In conclusion, the correct term to fill in the blank in your question would be "horizontal".

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The value of y is given as follows:

y = 12.

The value of x is obtained applying the angle bisection theorem, which divides an angle into two angles of equal measure, hence the opposite segments also have equal length.

The segments for this problem, along with their lengths, are given as follows:

Hence the value of y is obtained as follows:

5y - 18 = 3y + 6

2y = 24

y = 12.

(due to the angle bisection theorem, both segments have equal length, hence we equal their lengths to obtain the variable y).

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If the Porters also had a ($2,840) long-term capital loss, their investment interest expense deduction would be $5,160.

To calculate their investment interest expense deduction, we first need to determine their adjusted gross income (AGI). Their AGI is calculated by subtracting the investment expenses ($3,800) and the long-term capital loss ($2,840) from their total income, which is $186,000 + $5,020 = $191,020 - $3,800 - $2,840 = $184,380.

Next, we need to calculate their investment interest expense limitation. This is equal to their investment income, which is $5,020. Since their investment interest expense ($6,000) is greater than their investment income, their investment interest expense deduction is limited to the excess of investment interest expense over investment income, which is $6,000 - $5,020 = $980.

Finally, we need to adjust their investment interest expense deduction for the long-term capital loss. Since the Porters have a long-term capital loss, they can only deduct investment interest expense up to the amount of net investment income after taking into account the long-term capital loss. Their net investment income is $5,020 - $2,840 = $2,180. Therefore, their investment interest expense deduction is limited to $2,180, which is less than the amount of investment interest expense they incurred. Thus, their investment interest expense deduction is $2,180, plus the amount of investment interest expense they could not deduct due to the limitation, which is $980. Therefore, their total investment interest expense deduction is $3,160.

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The distance from the bottom of the building to the point where the ladder is touching the building for Triangle 2 is 14 feet. Option D.

Since Triangle 1 and Triangle 2 are similar right triangles formed by a ladder leaning against a building, their corresponding sides are proportional.

In Triangle 1, the distance along the ground from the bottom of the ladder to the building is 8 feet, and the distance from the bottom of the building to the point where the ladder is touching the building is 16 feet. Let's label this side as x.

In Triangle 2, the corresponding side along the ground from the bottom of the ladder to the building is 7 feet, and the corresponding side from the bottom of the building to the point where the ladder is touching the building is unknown. Let's label this side as y.

Since the triangles are similar, we can set up the following proportion based on the corresponding sides:

x / 8 = y / 7

To solve for y, we can cross-multiply and then divide:

7x = 8y

y = (7x) / 8

Now, substitute the given value for x from Triangle 1 into the equation:

y = (7 * 16) / 8

y = 14 Option D is correct.

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A fact is a statement that is considered to be true based on evidence or experience. It starts with a relationship, which expresses a connection or correlation between two or more entities, and is followed by a list of arguments.

The arguments of a fact can be variables, which represent unknown values, or simple values, such as numbers or strings. In some cases, a fact can have a structure similar to that of a rule, which defines a set of conditions that must be satisfied for the fact to be true. However, unlike a rule, a fact is not conditional and is considered to be true at all times.

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The confidence interval 0.333 < p < 0.777 can be expressed in the form p +- E as 0.555 +- 0.222.

The confidence interval 0.333 < p < 0.777 gives a range of possible values for the true population proportion, p, with a certain level of confidence. To express this interval in the form p +- E, we need to find the midpoint of the interval, which is (0.333 + 0.777)/2 = 0.555. This midpoint represents the best estimate of the true population proportion based on the sample data.

To find the margin of error, E, we need to calculate half of the width of the confidence interval, which is (0.777 - 0.333)/2 = 0.222. The margin of error represents the maximum amount by which the sample proportion may differ from the true population proportion.

Therefore, the confidence interval 0.333 < p < 0.777 can be expressed in the form p +- E as 0.555 +- 0.222.

A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. In this case, the confidence interval 0.333 < p < 0.777 gives a range of possible values for the true population proportion, p, with 95% confidence. This means that if we were to repeat the sampling process many times and construct a confidence interval each time, about 95% of the intervals would contain the true population proportion.

To express the confidence interval in the form p +- E, we need to find the midpoint of the interval, which is (0.333 + 0.777)/2 = 0.555. This midpoint represents the best estimate of the true population proportion based on the sample data.

The margin of error, E, represents the maximum amount by which the sample proportion may differ from the true population proportion. To find the margin of error, we need to calculate half of the width of the confidence interval, which is (0.777 - 0.333)/2 = 0.222. This means that the sample proportion could vary by up to 0.222 in either direction from the midpoint of the interval.

Therefore, the confidence interval 0.333 < p < 0.777 can be expressed in the form p +- E as 0.555 +- 0.222. This means that we are 95% confident that the true population proportion falls within the range of 0.333 to 0.777, with the best estimate of the true population proportion being 0.555 and a margin of error of 0.222.

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The absolute value function that matches the graph is given as follows:

y = |x|

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The vertex of the function in this problem is at the origin, hence:

(h,k) = (0,0).

The leading coefficient is of a = 1, as when x = 1, y = 1.

Hence the absolute value function that matches the graph is given as follows:

y = |x|

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Jim can paint 1/2 of a house in one hour, which means he can paint 1/12 of a house in 10 minutes. Jane can paint a whole house in 1/5 hour, which means she can paint 1/5 of a house in 1 minute.

When Jane joins Jim after 10 minutes, Jim has already painted 1/12 of a house. Together, they paint 1/12 + 1/5 of a house in one minute.

To find out how long it will take them to paint one whole house together, we can set up the equation:

1/12 + 1/5 = x/1

Where x is the amount of time it takes them to paint one whole house together.

Combining the fractions on the left side, we get:

(5 + 12)/60 = x

Simplifying, we get:

17/60 = x

Therefore, it will take Jim and Jane 17/60 of an hour, or approximately 17 minutes and 0.3 seconds, to complete one whole house together.\

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(a) The ratio of the areas, A2/A1, is (4π[tex]r^{2}[/tex])/π[tex]r^{2}[/tex] = 16.
(b) The ratio of the volumes, V2/V1, is (4/3)π[tex]4r^{3}[/tex] / (4/3)π[tex]r^{3}[/tex] = 64.

(a) Given that the radius of sphere 2 is four times the radius of sphere 1, let's denote their radii as r1 and r2 = 4r1. The surface areas A1 and A2 can be calculated as follows:

A1 = 4πr1^2
A2 = 4π(4r1)^2 = 4π(16r1^2) = 64πr1^2

To find the ratio A2/A1:

A2/A1 = (64πr1^2) / (4πr1^2) = 64/4 = 16

So, the ratio of the areas is 16:1.

(b) Similarly, let's calculate the volumes V1 and V2:

V1 = (4/3)πr1^3
V2 = (4/3)π(4r1)^3 = (4/3)π(64r1^3) = 64(4/3)πr1^3

To find the ratio V2/V1:

V2/V1 = (64(4/3)πr1^3) / ((4/3)πr1^3) = 64

So, the ratio of the volumes is 64:1.

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Brady sees 1101 lunches included a fruit or a vegetable.

To find out how many lunches included a fruit or a vegetable, we need to add the number of lunches that included a fruit to the number of lunches that included a vegetable, and then subtract the number of lunches that included both a fruit and a vegetable (since we don't want to count these twice).

So, lunches that included a fruit or a vegetable = (lunches with fruit) + (lunches with vegetable) - (lunches with both fruit and vegetable)

lunches that included a fruit or a vegetable = 866 + 468 - 233

lunches that included a fruit or a vegetable = 1101

Therefore, 1101 lunches included a fruit or a vegetable.

Learn more about vegetable here

https://brainly.com/question/29781793

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