What value of y will make the equation true? √34 × √y =34

The median and quartiles fall in the middle age classes.

The median is the middle value in a set of data, meaning that half of the data falls below the median and half falls above it. The quartiles divide the data into four equal parts, with the first quartile (Q1) being the 25th percentile, the second quartile (Q2) being the median or 50th percentile, and the third quartile (Q3) being the 75th percentile.

In terms of age classes, the median and quartiles would fall in the middle age classes. For example, if the age classes were 0-10, 11-20, 21-30, 31-40, 41-50, 51-60, 61-70, 71-80, and 81-90, the median and quartiles would fall in the 21-30, 31-40, and 41-50 age classes.

It is important to note that the specific age classes that the median and quartiles fall in will depend on the distribution of the data. However, they will always fall in the middle age classes, as they represent the middle values of the data set.

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Answer:

D should be the anwser if i did my math correctly!

if you look at the part where the first part connects with the second part:

y = 5 if x < - 2

y = -2x + 1 if  -2 ≤ x < 1

we don't have a discontinuity there, so there shouldn't be a dot.

When we graph over intervals like (a, b) or [a, b] or something like that, we use dots to define the end of the intervals, and to denote that the function ends abruptly or we have a jump.

In this case, you can see that between the end and the second part and the beginning of the third part there is a jump, so the use of dots is correct there, but if you look at the part where the first part connects with the second part:

y = 5 if x < - 2

y = -2x + 1 if  -2 ≤ x < 1

we don't have a discontinuity there, so there shouldn't be a dot.

That is the only error with the graph.

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a. There is a negative externality present in the description and cost function.

b. Firm 1 produces 10 units of output (x), while Firm 2 produces 70 units of output (y). The profit for Firm 1 is $190, and the profit for Firm 2 is $1,800.

c. If both firms are merged, the joint output is 80 units (x + y), and the joint profit is $1,990.

d. Yes, the government can apply a tax/subsidy to improve efficiency.

a. The negative externality arises from the cost function of Firm 2, which includes a term (-10x) dependent on Firm 1's output. This indicates a cost imposed on Firm 2 due to Firm 1's production level.

b. To maximize their profits independently, Firm 1 sets its output level (x) where marginal cost equals the competitive price, resulting in x = 10. Firm 2 sets its output level (y) where marginal cost equals the competitive price, considering Firm 1's output level, leading to y = 70. The profit for each firm is calculated using the given cost functions and competitive prices.

c. When the firms are merged into one business, their individual outputs (x and y) are combined, resulting in a joint output of 80 units. The joint profit is the sum of the individual profits obtained by calculating the revenue and costs for the merged business. In this case, the joint profit is $1,990, which is higher than the combined profit of the individual firms.

d. To address the negative externality, the government can impose a per-unit tax on Firm 1's output equal to the external cost imposed on Firm 2. The tax revenue can then be used to subsidize Firm 2's production. This mechanism helps internalize the externality and improve efficiency by aligning private costs with social costs.

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Firm 1 produces output x with a cost function c₁(x) = x² + 10. Firm 2 produces output y with a cost function c2(y, x) = y² - 10x. Both firms face competitive product markets. The competitive price of x is $20 and the competitive price of y is $40.

a. Is there any externality in the description? If yes, positive or negative? Briefly explain.

b. Suppose both firms make independent decisions. How much do they each produce? Profit?

c. What are the output if both firms are merged into one business? How large is the joint profit? Is there any incentive for the shareholders to merge the businesses?

d. Is it possible for a government to apply tax/subsidy (with balanced budget) to improve the efficiency of the two firms when they operate independently? Briefly describe how such a program would work.

To calculate the height of the tree that would leave a 35 cm space from a 250 cm tall ceiling, subtract the desired space from the total height. Hence, the tree should be 215 centimeters tall.

The calculation involves understanding and using the concepts of height and ceiling space. When you want a tree to leave a certain amount of space from the ceiling, you have to subtract that desired space from the total height of the room. So, if your ceiling is 250 centimeters high and you desire a space of 35 centimeters to be left, the tree's height should be calculated as follows:

So, in this scenario, the tree must be 215 centimeters tall to fit perfectly under your ceiling with 35 centimeters of space left.

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For mileages greater than 55 miles, Company A will charge less than Company B. For mileages less than or equal to 55 miles, Company B will charge less than Company A.

To determine at what mileages Company A will be cheaper than Company B, we can set up an inequality by equating the total cost for each company and solving for m.

Let's assume that Frank drives m miles in total.

For Company A, the cost is a fixed $108, regardless of the number of miles driven.

For Company B, the cost will depend on the number of miles driven. The initial fee is $75, and then there is an additional charge of $0.60 for each mile driven. So the total cost for Company B is:

Total Cost for Company B = $75 + ($0.60/mile) × m

= $75 + $0.60m

To find out when Company A is cheaper than Company B, we need to set up an inequality where the total cost for Company A is less than the total cost for Company B:

$108 < $75 + $0.60m

Subtracting $75 from both sides:

$33 < $0.60m

Dividing both sides by $0.60:

m > 55

Therefore, for mileages greater than 55 miles, Company A will charge less than Company B. For mileages less than or equal to 55 miles, Company B will charge less than Company A.

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Answer: 140,000

............................

The radius of the circumscribed circle of ABC is 5.8.

What is the radius of a circle?

A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary usage, it also refers to the length of such line segments. The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."

Here, we have

Given: A(-5,-4), B(3,-4), C(-1,6)

The midpoint of AB = M(-1,-4)

CM = 6-(-4) = 10

CM ⊥ AB

AC = √[-5-(-1)]²+(-4-6)²

AC = 2√29 = BC = a

SinA = CM/AC = 5/√29

BC/SinA = 2R = 58/5 = 5.8

Hence, the radius of the circumscribed circle of ABC is 5.8.

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The integral that represents the volume of the solid generated by rotating the region enclosed by the curves x = y^2 and y = 2^(1/2)x about the y-axis is:

∫(0 to 2) π(4y^2 - y^4) dy.

Therefore, the correct option is ∫(0 to 2) π(4y^2 - y^4) dy.

An integral is a mathematical concept that represents the accumulation or sum of infinitesimal quantities over a certain interval or region. It is a fundamental tool in calculus and is used to determine the total value, area, volume, or other quantities associated with a function or a geometric shape.

The process of finding integrals is called integration. There are various methods for evaluating integrals, such as using basic integration rules, integration by substitution, integration by parts, and more advanced techniques.

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Answer:

Step-by-step explanation:

Area of a circle = πr²

where

r is the radius

From the question

r = 14 m

π = 3.14

The area of the circle is

A = 3.14 × ( 14 ) ²

= 3.14 × 196

= 615.44

We have the final answer as

Hope this helps you

Answer:

x = 0.447

Step-by-step explanation:

You need to use your graphing calculator for this.

In y=, put 13(0.25)^x in Y1 and put 7 in y2. Using 2nd trace, find the intersections.

The answer I got was x = 0.447.

Answer:

256 miles

Step-by-step explanation:

The Pythagoras theorem is a² = b² + c² where a is the hypotenuse or longest side

To find the shorter side, the equation is rearranged so c² = a² - b² (whether it is b or c doesn't matter)

so √377² - 277² = 255.7342371

Answer to number 22

Answer: 256 miles

Answer:

$50,000

Step-by-step explanation:

The computation of the amount received after paying off the mortgage is shown below

= Value of the house - mortgage amount

= $150,000 - $100,000

= $50,000

By deducting the mortgage amount from the value of the house we can get the amount received and the same is shown in the computation part

Since in the question it is given that the Rosetta sells her house and paid off mortgage so only these two items are considered and others are to be ignored

Answer:

B.) $50,000

Step-by-step explanation:

Because I said so aaaandddd because its correct the work don't lie.

the slope of the line is 8 and equation line is y = 8x.

What is the slope of line?

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.

We know that formula two find the slope of the line joining two points which is

slope m = 24-16 / 3-2

m = 8/1 = 8

y = 8x

Hence the slope of the line is 8 and equation line is y = 8x.

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Step-by-step explanation:

left to right.

the smallest numbers are on the left, the largest in the right.

all the numbers in the line are sorted.

so, going from left to right the numbers get continuously larger (no exception), and when going from right to left, they get continuously smaller.

remember that the negative numbers are smaller than the positive numbers. so, the negative numbers (if there are any in your case) are on the left side.

and negative numbers get smaller by "seemingly increasing" : -1 is larger than -2 and so on.

so, the range of the negative numbers starts on the left side with the "largest" negative number (but when you think about it, it IS the smallest number) and their absolute value gets smaller until they reach 0, and then the positive numbers start from small to large.

this also asked to fractions and mixed fraction numbers :

e.g. -2 1/2 is smaller than -2 and larger than -3.

because it is -2 + -1/2 = -2 - 1/2 = -2 1/2.

in that sense it is the same principle as with positive numbers :

2 1/2 = 2 + 1/2

-2 1/2 = -2 - 1/2

The spherical coordinate system is the most suitable system of coordinates to describe the spherical shell between two concentric spheres centered at (4,1,2).

A system of coordinates is a set of numbers used to describe the position of a point in space. There are different types of coordinate systems, each with its own advantages and disadvantages.

The spherical shell is the region of space between two spheres with the same center, but different radii. In this case, the center of both spheres is at (4,1,2) and the inner sphere has a radius of 7 while the outer sphere has a radius of 13.

One of the most commonly used coordinate systems for describing spheres is the spherical coordinate system.

To use this system of coordinates to describe the spherical shell, we first need to determine the radial distance for each point in the shell. This distance is between 7 and 13, since the shell lies between the inner and outer spheres.

Therefore, to describe a point in the spherical shell using spherical coordinates, we use the radial distance, polar angle, and azimuthal angle. These coordinates can then be used to plot the spherical shell and understand its geometry and properties.

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Answer:

the mean of A and C is 10

Step-by-step explanation:

Given;

mean of A and B = 20

mean of B and C = 24

mean of A, B and C = 18

\(\frac{A + B}{2} = 20\\\\A+ B = 40 ---- (1)\\\\\frac{B + C}{2} = 24\\\\B+ C = 48----(2)\\\\\frac{A+ B+ C}{3} = 18\\\\A+ B+ C= 54---(3)\\\\From (1); \ A = 40 - B\\\\From(2); \ C = 48 - B\\\\\Substitute \ the \ values \ of \ A \ and \ C \ into \ (3)\\\\(40-B) + B + (48-B) = 54\\\\simplify;\\\\(40 + 48) + (B-B-B)= 54\\\\88 -B = 54\\\\-B = 54-88\\\\-B = -34\\\\B = 34\)

Recall; A = 40 - B

           A = 40 - 34

           A = 6

Also, C = 48 - B

        C = 48 - 34

       C = 14

Therefore, the mean of A and C is calculated as;

\(= \frac{A + C}{2} \\\\= \frac{6 + 14}{2} \\\\= 10\)

Answer:

10

Step-by-step explanation:

just add the to together.

Answer:

Step-by-step explanation:10

There were total 276 guests in the wedding that Joy organised.

Given,

fraction of the guest that chose beef = 1/3

fraction of the guest that chose chicken = 5/12

fraction of the guest that chose vegetarian = 1  - 1/3 - 5/12 = 1/4

we are asked to find the total number of guests in the wedding:

guests that chose vegetarian = 1/4

guests that chose vegetarian = 69

1/4 of the guest = 69

4/4 of the guest = 69 x 4 = 276

Hence there are total 276 guests in the wedding.

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Answer:

Rational

Step-by-step explanation

It can only be irrational if it repeated, but this one doesn't so it is rational.

Hope that helped

Answer:

30 miles

Step-by-step explanation:

50/5= 10X3=30

Answer:

7.3%

Step-by-step explanation:

Cost for 50 glasses = ₹1500 -----> Cost Price (C.P)

Cost per glass = 1500/50 = ₹30

Here, 4 glasses break. So, she now has

50-4 = 46 glasses

She sold 46 glasses for ₹35 each,

Money earned = 46x35 = ₹1610 -----> Selling Price (S.P)

Since S.P > C.P,

she made a profit = 1610-1500 = ₹110

Profit% = Profit/Cost Price x 100

= 110/1500 x 100

= 7.3%

Answer:

12

Step-by-step explanation:

16/4=4

4+8=12

There are 10 x 9 x 8 x 3 ways that the swimmers could finish the race so that first place wins a trophy and second place wins a certificate. This is equivalent to 2,160 ways.  

a) There are ten swimmers, so there are ten different ways that the first place could be won. Once that swimmer has been decided, there are nine remaining ways to win second place.

Once second place has been decided, there are eight remaining ways to win third place, and so on. Therefore, there are 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 ways to finish the meet.

This is equivalent to 10! ways to finish the meet. This number is approximately 3,628,800 ways.

b) Once the top four have been decided, there are 6 remaining swimmers. Since order doesn't matter, the number of ways to choose 6 people from 6 is 1. There is only one way to choose all six. Therefore, there is only one way to choose the remaining six people to compete.

c) Once again, there are 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 ways to finish the meet. This is equivalent to 10! ways to finish the meet. There are 10 ways to choose first place, and once first place has been decided, there are 9 ways to choose second place.

Therefore, there are 10 x 9 ways that the first and second places could finish. Once the first and second places have been decided, there are eight remaining ways to win third place.

Since there are only three people left, there are only three possible ways that the remaining three swimmers could finish the race.

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Answer:

Step-by-step explanation:

Jenna will complete remaining distance in 6 hours.

Since we know that . Let us find the rate at which Jenna traveled 100 miles.

Remaining distance is 400-100=300.

Now let us find the time Jenna will take to travel 300 miles.

Therefore, Jenna took 6 hours to complete remaining distance.

The range of this function can be represented using the interval [-1,1]. However, if we have a function h(x) = x^3, we know that the output values can take on any real number, so the range of this function can be represented using the interval (-∞, ∞).

Interval notation is a shorthand way of representing a range of numbers using brackets and parentheses. For example, the interval [0,1] represents all real numbers between 0 and 1, including 0 and 1 themselves. The interval (0,1) represents all real numbers between 0 and 1, excluding 0 and 1 themselves.

To represent the domain of a function using interval notation, we consider the set of all input values for which the function is defined. For example, if we have a function f(x) = x^2, we know that this function is defined for all real numbers. Therefore, the domain of this function can be represented using the interval (-∞, ∞).

To represent the range of a function using interval notation, we consider the set of all output values that the function can take. This can be a bit trickier, as some functions may take on a continuous range of values, while others may only take on a finite set of values. For example, if we have a function g(x) = sin(x), we know that the output values will always be between -1 and 1. Therefore, the range of this function can be represented using the interval [-1,1]. However, if we have a function h(x) = x^3, we know that the output values can take on any real number, so the range of this function can be represented using the interval (-∞,∞).

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Complete Question:

Fill in the blanks. (Enter the range in interval notation.) Function Alternative Notation Domain Range y = y = cos-1 x -1 < x< 1