Marcy has a picture frame that is 18 by 24 inches. If she has another frame congruent to the first one, and
one of its sides is 24 inches long, determine the length of the other side.

A racecar driver goes around in circles on a racetrack.

The driver that goes around in circles is a racecar driver on a circular racetrack.

In motorsport events like stock car racing or Formula 1, drivers often compete on oval or circular tracks where they make continuous laps around the circuit.

These tracks are specifically designed to allow drivers to navigate the curves and maintain a circular path throughout the race.

The nature of circular tracks requires drivers to master the art of maintaining speed and control while making consistent and precise turns.

They need to find the optimal racing line, which is the most efficient path around the track, to maximize their speed and minimize the time taken to complete each lap.

The driver's skill and strategy play a crucial role in their success on circular tracks.

In addition to professional racing, drivers in amusement park rides such as go-karts or bumper cars also go around in circles as they maneuver the vehicles on circular tracks.

These attractions provide a fun and thrilling experience for participants as they navigate the circular path, often competing with others to reach the finish line or engage in friendly collisions.

Overall, drivers who go around in circles are typically found in racing events or amusement park attractions that involve circular tracks. Their ability to handle the curves and maintain control is essential for their performance and enjoyment of the activity.

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Answer:

2.6 kilometers

Step-by-step explanation:

To find the circumference of a circle, we can use the formula:

Circumference = π * diameter

Given that the diameter of the volcanic crater is 840 meters, we can substitute this value into the formula:

Circumference = π * 840

Using the approximate value of π as 3.14159, we can calculate the circumference:

Circumference = 3.14159 * 840

Circumference ≈ 2643.1796 meters

To convert the circumference to kilometers, we divide the value by 1000:

Circumference in kilometers = 2643.1796 / 1000

Circumference ≈ 2.6432 kilometers

Therefore, the circumference of the rim of the volcanic crater is approximately 2.6 kilometers (rounded to 1 decimal place).

Answer:

m(arc)DC = 120°

Step-by-step explanation:

m<B = 60°

m(arc)DC = 2m<C = 2 × 60° = 120°

To determine whether the series ∑(n=1 to ∞) 1/(n+2) is convergent or divergent, we can use the Integral Test. By evaluating the integral ∫(1/(x+2)) dx from 1 to ∞, we find that the integral converges. Therefore, the given series is also convergent.

The Integral Test states that if f(x) is a continuous, positive, and decreasing function on the interval [1, ∞) and if the series ∑(n=1 to ∞) f(n) is represented by the integral ∫(f(x)) dx from 1 to ∞, then the series and integral either both converge or both diverge.

In this case, the series is ∑(n=1 to ∞) 1/(n+2). To apply the Integral Test, we evaluate the integral ∫(1/(x+2)) dx from 1 to ∞. The integral is given by:

∫(1/(x+2)) dx = ln|x+2| + C

To find the value of the integral from 1 to ∞, we evaluate ln|x+2| at the limits of integration:

ln|∞+2| - ln|1+2| = ln(∞) - ln(3)

Since ln(∞) is infinity and ln(3) is a finite value, the integral evaluates to infinity.

Since the integral diverges, by the Integral Test, the series ∑(n=1 to ∞) 1/(n+2) also diverges.

Therefore, the given series is divergent.

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To show that (A^-1) = A for A = [[3, 7], [-a, -1]], we can find the inverse of matrix A and then compare it to matrix A itself.

The formula for finding the inverse of a 2x2 matrix A = [[a, b], [c, d]], where D = ad - bc ≠ 0, is: A^-1 = (1/D) * [[d, -b], [-c, a]], where D is the determinant of matrix A.
For the given matrix A = [[3, 7], [-a, -1]], we can compute the determinant: D = (3 * -1) - (7 * -a) = -3 + 7a. Since D ≠ 0 (assuming a ≠ 0), we can proceed to find the inverse: A^-1 = (1/D) * [[-1, -7], [a, 3]].

Comparing A^-1 to A, we see that they are not equal. Therefore, the statement (A^-1) = A is not true for the given matrix A. A step-by-step approach to determine whether the given matrix A is equal to its inverse (A^-1). It begins by stating the formula for finding the inverse of a 2x2 matrix and then applies it to the given matrix A. By computing the determinant and finding the inverse, it is demonstrated that the inverse of A is not equal to A, indicating that the statement (A^-1) = A is false.

The explanation highlights the key calculations and concepts involved in determining the validity of the statement.

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To price the derivative using the two-period binomial model, we need to calculate the expected payoff of the derivative using the risk-neutral probabilities.

The possible outcomes for the two-period binomial model are H and T,  there are four possible states of the world: HH, HT, TH, and TT.

To calculate the expected payoff we need to calculate the probability of each state occurring. The probability of HH occurring is pp=0.60.6=0.36, the probability of HT and TH occurring is pq+qp=0.60.4+0.40.6=0.48, and the probability of TT occurring is qq=0.40.4=0.16.

Next, we can calculate the expected payoff in HH and TT states, the derivative pays off 1, and in the HT and TH states, the derivative pays off 0. The expected payoff of the derivative in the HH and TT states is 10.36=0.36, and the expected payoff in the HT and TH states is 00.48=0.

We need to discount the expected payoffs back to time 0 using the risk-neutral probabilities.

The probability of that state occurring multiplied by the discount factor, which is 1/(1+r), where r is the risk-free interest rate.

Since this is a risk-neutral model, the risk-free interest rate is equal to 1. Therefore, the risk-neutral probability of each state occurring is

HH: 0.36/(1+1) = 0.18

HT/TH: 0.48/(1+1) = 0.24

TT: 0.16/(1+1) = 0.08

Finally, we can calculate the price of the derivative

Price = 0.181 + 0.240 + 0.240 + 0.081 = 0.26

Therefore, the price of the derivative is 0.26.

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The total number of seeds that Josiah would plant would be = nR×S

To determine the total number of seeds that Josiah will plant will be to add the seeds in the total number of rooms he planted.

Let each row be represented as = nR

Where n represents the number of rows planted by him.

Let the seed be represented as = S

The total number of seeds he planted = nR×S

Therefore, the total number of seeds that was planted Josiah would be = nR×S.

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Becca made a total of 24 rolls and 12 biscuits.

Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.

Becca made 2 trays of rolls and biscuits, with 12 rolls and 6 biscuits in each tray. To find the total number of rolls and biscuits, we need to multiply the number of rolls and biscuits per tray by the number of trays, and then add them together:

Total rolls = 2 trays × 12 rolls per tray = 24 rolls

Total biscuits = 2 trays × 6 biscuits per tray = 12 biscuits

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Answer:

just check if the y coordinate for each center is equal to 0

Step-by-step explanation:

30

Given the expression for the instantaneous voltage expressed as:

Given the following parameter:

θ = 30⁰

Substitute the given parameter into the formula to have:

Therefore the instantaneous voltage when θ = 30⁰ is 30.

To prove that the function f ◦ g is surjective, we need to show that for every element c in the codomain of f ◦ g, there exists an element a in the domain of g such that (f ◦ g)(a) = c.

Let's assume c is an arbitrary element in the codomain of f ◦ g. Since f is surjective, there exists an element b in the domain of f such that f(b) = c. Since g is surjective, there exists an element a in the domain of g such that g(a) = b.

Now, let's consider (f ◦ g)(a). By the definition of function composition, (f ◦ g)(a) = f(g(a)). Since g(a) = b, we can substitute it in the expression: (f ◦ g)(a) = f(b) = c.

Therefore, for every element c in the codomain of f ◦ g, we have found an element a in the domain of g such that (f ◦ g)(a) = c. This proves that the function f ◦ g is surjective.

In conclusion, if g : a → b and f : b → c are both surjective functions, then the function f ◦ g is also surjective.

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For the given inequality 14 - 3f > 2 the option that comes out be correct is

f < 4 i.e option 2.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.The majority of the time, size comparisons between two numbers on the number line are made.

Here, "Less than" and "Greater than" have new meanings.

Less-than sign is the symbol for such phrase.

14 - 3f > 2

adding 3f on both sides:

14 - 3f + 3f > 2 + 3f

14 > 2 + 3f

subtracting 2 on both sides:

14 - 2 > 2 + 3f - 2

12 > 3f

dividing 3 on both sides:

(12)/3 > (3f)/3

4 > f

which means f < 4

Therefore, option 2 is correct.

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Answer:

8 minutes!

Step-by-step explanation:

Zero point Twenty five miles takes two minutes

So how many minutes will it take her to run two miles?

One mile takes her four minutes you need to multiply it by two for the other mile so the answer is 8

Answer:

8 minutes

Step-by-step explanation:

The game to be fair, the player should win 60.

In order to determine the fair winnings for this game, we need to calculate the probability of winning and then set it equal to the cost of playing the game.
Step 1: Calculate the probability of winning.
There are two scenarios for winning:
1. First roll is even, and the second roll matches the first.
2. The probability of rolling an even number on a six-sided die is 3/6 or 1/2, since there are three even numbers (2, 4, and 6).
Step 2: Calculate the probability of the second roll matching the first roll.
Since there are 6 sides to the die, the probability of the second roll matching the first is 1/6.
Step 3: Calculate the combined probability of both events.
To find the combined probability of both events, multiply the probabilities: (1/2) × (1/6) = 1/12. So the probability of winning is 1/12.
Step 4: Set up an equation to determine fair winnings.
Let x be the fair winnings for the game. The cost of playing the game is $5. In order for the game to be fair, the expected value (probability of winning multiplied by the winnings) should equal the cost of playing the game:
(1/12) × x = 5
Step 5: Solve the equation for x.
To solve for x, multiply both sides of the equation by 12:
x = 5 × 12
x = 60
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Answer:

80% of HCl used is 0.75 of a liter

40% or HCl used is 0.25 of a liter.

Step-by-step explanation:

Comment

You need a total of 1 liter which has a concentration of 70%.

Let x be the concentration of the 80%  HCl

Let 1-x be the concentration of the 40% HCl

Solution

(1 - x)*40/100 + x*80/100 = 70/100 * 1           Multiply by 100

40*(1-x) + 80x = 70                                         Remove the brackets (left)

40 - 40x + 80x = 70                                       Combine

40 + 40x = 70                                                 Subtract 40  from both sides

40-40 + 40x = 70 - 40                                    Combine

40x = 30                                                          Divide by 30

x = 30/40

Answer

x = 0.75 of a liter

1-x = 0.25 of a liter.

The equation of the set of all points equidistant from A and B is:
\(√[(x - 2.5)^2 + (y - 3.5)^2 + (z - 0)^2] = √[22.5]\)

To find the equation of the set of all points equidistant from points A(-1, 6, 2) and B(6, 1, -2), we can use the midpoint formula. The midpoint of AB is the point equidistant from both A and B.

Midpoint coordinates:
\(x-coordinate = (-1 + 6) / 2 = 2.5\\y-coordinate = (6 + 1) / 2 = 3.5\\z-coordinate = (2 - 2) / 2 = 0\)

Therefore, the midpoint is \(M(2.5, 3.5, 0).\)

Now, we can find the distance from the midpoint M to A or B using the distance formula.

Let's use the distance from M to A as an example.

Distance from M to A:
\(√[(2.5 - (-1))^2 + (3.5 - 6)^2 + (0 - 2)^2]\\√[3.5^2 + (-2.5)^2 + (-2)^2]\\√[12.25 + 6.25 + 4]\\√[22.5]\)

The distance from M to A is \(√[22.5].\)

Therefore, the equation of the set of all points equidistant from A and B is:
\(√[(x - 2.5)^2 + (y - 3.5)^2 + (z - 0)^2] = √[22.5]\)

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Answer:

k = -50

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

0.8k - 20 = -60

Step 2: Solve for k

Answer:

k = - 50

Step-by-step explanation:

0.8 k - 20 = - 60

Add 20 to each side

0.8 k - 20 + 20 = - 60 + 20

0.8 k = - 40

divide each side by 0.8

0.8 k / 0.8 = -40 / 0.8

k = - 50

a) An equation to show the relationship between the number of gallons of gasoline and the distance driven is r = 25 mpg.

b) The total distance to be traveled using 6.3 gallons is 157.5 miles.

c) If the car is driven 14,000 miles in one year, the gallons of gasoline used would be 560 gallons.

d) If the gasoline costs $4.10 per gallons, the total cost of purchasing gasoline for the year is $2,296.

e) The miles per gallon is 25 mpg.

f) The gasoline cost per mile is $0.164.

Miles per gallon (MPG) shows the distance traveled by a vehicle, measured in miles, per gallon of gasoline.

The mpg is used to assess a vehicle's fuel efficiency.

a) The volume of the car's gas tank = 17 gallons

The distance on a single tank of gas = 425 miles

Let r = the rate of gasoline consumption per mile

An equation to show the relationship between the number of gallons of gasoline and the distance driven = 425/17 = 25 mpg

b) The number of gallons of gas in the tank = 6.3 gallons

The total distance to be traveled using 6.3 gallons = 157.5 miles (6.3 x 25)

c) If the car is driven 14,000 miles in one year, the gallons of gasoline used would be = 560 gallons (14,000/25).

d) The cost of gasoline per gallon = $4.10

The total cost of purchasing gasoline for the year = $2,296 ($4.10 x 560)

e) The miles per gallon = 25 mpg (14,000/560).

f) The gasoline cost per mile = $0.164 (560 x $4.10)/14,000

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Answer:

A

Step-by-step explanation:

Answer:  

x^{2} + x - 4 or  A

Step-by-step explanation:

correct on edge 2023

Answer:

Slope=−  2.000  = 0.857  =−0.429

x−intercept=  3 /49  =16.33333

y−intercept=  7 /49  =7

Hope this helps! Please mark Brainliest!

Answer:

its c

Step-by-step explanation:

to took it

Answer:

B

Step-by-step explanation:

Answer:

87.8

Step-by-step explanation:

I assume you know how to do this so I didn't show any steps. Have a nice night. :)

Answer

Quiz: Measures of Center

I got one wrong, so use at discretion

Step-by-step explanation: I took the test

1. 87.8

2. 6,060

3. 36

4. 312

5. 4.41 and 45.6

6. no mode

7. 0.236

8. 1,136

9. no mode

10. 33,745

After solving the equation the linear equation is x = 27/5 , y = 7/5.

What do you mean by linear equation?

Equations with the highest degree of 1 are called linear equations. This means that the exponent of the variable in the linear equation is greater than 1. The graph of a linear equation is always a straight line.

A linear equation is an algebraic equation in which each term has exponent 1, and the graph of this equation is always a straight line. For this reason, it is called a "linear equation".

Given system of equation:

7x - 7y = 28 ..........(1)

2x - 7y = 1 .............(2)

Solve this system of linear equation. Find the value of 7y from equation (1) and substitute in equation(2)

7x - 7y = 28

7x - 28 =7y .............(3)

Substitute this value in equation (2)

2x - (7x - 28) = 1

2x - 7x + 28 = 1

-5x + 28 = 1

5x = 28 - 1

5x = 27

x = 27/5

Substitute this value in equation (3)

7y = 7(27/5) - 28

7y = 189/5 - 28

7y = 49/5

y = 7/5

Therefore, x = 27/5 , y = 7/5

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Answer:

1/a + 1/c = 2/b

Step-by-step explanation:

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

We may build up a proportion and solve for the scale model radius of Neptune using the ratio between the radii of the two planets and the known scale model radius of the Earth. The scale model of Neptune that is produced has a radius of around 9.7 cm.

We may take advantage of the fact that the ratio between the two planets' radii and the ratio between their respective scale model radii is the same. Let's name the Neptune scale model radius "r" Then, we may set up the ratio shown below:

Neptune's radius is equal to the product of Earth's radius and its scale model.

With the provided values, we may simplify and obtain:

24620 km / 6370 km equals 2.5 cm / r

We obtain the following when solving for "r":

r = (24620 km * 2.5 cm) / (6370 km)

r ≈ 9.7 cm

Therefore, a scale model of Neptune would have to be drawn with a radius of approximately 9.7 cm.

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To determine whether the variable is qualitative or quantitative, the reasoning for the following question will be:

a) qualitative, State of residence describes an attribute or characteristic, making the variable qualitative. Because the state of residence can be determined through measurement or counting, the variable is qualitative.

b) quantitative, The state of residence serves as a description of an attribute or characteristic, so the variable is quantitative. Since determining the state of residence requires measuring or counting, the variable is quantitative.

c) qualitative, Your variable will be quantitative if it is something like, say, your age or salary, which is typically something that can be discovered by counting or using mary-screw analysis. However, in this case, the state of residence is obviously a qualitative factor.

d) qualitative, If your variable is something like, say, your age or salary, or if it's something that is typically discovered by counting or Mary, then these kinds of variables are quantitative. But in this case, the state of residence is categorically important for this question.

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Answer:

a) the largest y-intercept is 1

b) 13.5

c) y=x-3

d) 8

Step-by-step explanation:

the question was worded very strangely and I will answer the way I precieved it.

for question d, I simply considered the question to be asking what is X when y is 17 and since the equation of that line is 2x-1

Each girl on the basketball team averages 136/12 = 11.33 points.The average number of points each girl scores, we first need to calculate the total number of points scored by the team.

Since the team average is 136 points, the total points scored by the team would be 136 x 12 = 1632 points.There are 8 boys on the team, and each boy averages 12 points. Therefore, the total points scored by the boys would be 8 x 12 = 96 points. To find the total points scored by the girls, we subtract the total points scored by the boys from the total team points: 1632 - 96 = 1536 points.

Since there are 4 girls on the team, we divide the total points scored by the girls (1536) by the number of girls (4) to find the average points scored by each girl: 1536/4 = 384 points. Therefore, each girl on the team averages 384/12 = 11.33 points.

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Given:

The equation is:

\(y+2=6(x+6)\)

To find:

The given equation in the form of \(Ax+By=C\), where A, B, C are integers.

Solution:

We have,

\(y+2=6(x+6)\)

It can be rewritten as:

\(y+2=6x+36\)

\(y-6x=36-2\)

\(-6x+y=34\)

The above equation is in the form of \(Ax+By=C\), where \(A=-6,B=1\) and \(C=34\).

Therefore, the requires equation is \(-6x+y=34\).

Answer:

A.

Step-by-step explanation: