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Area of the circle is 78.5 sq. units.

Step-by-step explanation:

Circumference of the circle = 31.4 units

2 π r = 31.4 units

2 × 3.14 ×r = 31. 4 units

r = 31.4 / (2×3.14)

= 5 units.

Area of the  circle = π r² = 3.14 × 5 × 5 = 78.5 sq. units.

Answer: Yes a scalene triangle is a triangle with 3 sides that all have different lengths.

Answer:

Correct

Step-by-step explanation:

Scalene means it has no equal side.

Answer:

Scale Factor=2

Step-by-step explanation:

As the rectangle is enlarging from GHIJ to KLMN

then

Sacle Factor = Larger length / Smaller Length

Scale Factor = 5 cm / 2 cm = 2

Scale Factor = 20 cm / 10 cm = 2

Madison purchased 5 cans of soup and 7 frozen dinners.

Step-by-step explanation:

Given,

Quantity of sodium in each soup can = 500 mg

Quantity of sodium in each frozen dinner = 700 mg

Total quantity = 7400

Let,

Number of soup cans purchased = x

Number of frozen dinners purchased = y

According to given statement;

500x+700y=7400        Eqn 1

y = x+2        Eqn 2

Putting value of y from Eqn 2 in Eqn 1

[tex]500x+700(x+2)=7400\\500x+700x+1400=7400\\1200x=7400-1400\\1200x=6000[/tex]

Dividing both sides by 1200

[tex]\frac{1200x}{1200}=\frac{6000}{1200}\\x=5[/tex]

Putting x=5 in Eqn 2

[tex]y=5+2\\y=7[/tex]

Madison purchased 5 cans of soup and 7 frozen dinners.

Keywords: linear equation, substitution method

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Answer:

Madison purchased 5 cans of soup and 7 frozen dinners

Step-by-step explanation:

Answer:

81

Step-by-step explanation:

Step-by-step explanation:

[tex]2.41 \times {10}^{4} \\ = 2.41 \times 10000 \\ = 24100 \\ [/tex]

Answer:

c=36

Step-by-step explanation:

Answer:

The system has no solution

Step-by-step explanation:

we have

[tex]y=\frac{2}{3}x+7[/tex] ----> equation A

[tex]3y=2x-3[/tex]

Isolate the variable y

Divide by 3 both sides

[tex]y=\frac{2}{3}x-1[/tex] ------> equation B

Compare equation A and equation B

Both lines have the same slope and different y-intercept

so

Line A and Line B are parallel lines

The lines do not intersect

therefore

The system has no solution, because both lines are parallel

see the attached figure to better understand the problem

Answer:

4.875

Step-by-step explanation:

Answer:

Explanation:

1. Calculate the monthly interest owed during year 1

2. Calculate the monthly interest owed during year 2

3. Calculate the difference

Hence, the answer is the option c) $22.50

Answer:

42 and 58

Step-by-step explanation:

Let the two numbers be represented by A And B

A + B = 100

A = B + 16

Substitute B + 16 in place of A in equation 1

We have,

B + 16 + B = 100

It can also be written as

B + B + 16 = 100

2B + 16 = 100

Subtract 16 from both sides

2B + 16 - 16 = 100 - 16

2B = 84

Divide both sides by 2

2B/2 = 84/2

B = 42

Now substitute 42 for B in any of the equations to get A.

Using equation 1

A + B = 100

A + 42 = 100

Subtract 42 from both sides

A + 42 - 42 = 100 - 42

A = 58

Therefore the two numbers are 42 and 58

Answer: 3.14 *16.8*16.8*16.9=14977.3478

14977.3478= 14,977.35

Answer:185,422.61

Step-by-step explanation:8.25%/100=0.0825 but since it a sale tax you add a 1 so it would be 1.0825•35=37.88•89= 337.32•55=185,422.61

Answer:

no6666//7

Step-by-step explanation:

88../6

The sum of the 3 angles needs to be 180.

To find the third angle subtract to the known angles from 180.

180 - 48 - 71 = 61

The third angle is 61 degrees.

Final answer:

The proportional relationship between the number of rides and time is represented by the equation t = 3n where t is the total time in minutes and n is the number of rides.

Explanation:

Since it takes Esther 12 minutes to ride a roller coaster four times, we can find the time taken for one ride by dividing the total time by the number of rides.

Time for one ride = Total Time / Number of Rides = 12 minutes / 4 rides = 3 minutes per ride.

The proportional relationship between the number of rides (n) and the total amount of time (t) can be represented by the equation t = 3n. This indicates that for every ride, 3 minutes are added to the total time.

Answer:

raymond has about 38 cars left

Step-by-step explanation:

Because raymond started off with 57 cars and he got rid of( take away) 19 you must use subtraction. 57 - 19 =38

Step-by-step explanation:

2. The total number of calculators is 6 + 9 + 2 = 17.

When she hands out the first calculator, the probability that it is blue is 2/17.

When she hands out the second calculator, there is one less calculator total, so the probability that it is yellow is 9/16.

The probability of both is therefore:

P = 2/17 × 9/16

P = 9/136

3. There are 13 clubs in a standard deck of 52 cards.

The probability that the first card is clubs is 13/52 = 1/4.

Since you replace the card, there are still 52 cards in the deck.  So the probability that the second card is clubs is 13/52 = 1/4.

The probability that both cards are clubs is:

P = 1/4 × 1/4

P = 1/16

4. The total number of pieces of gum is 6 + 9 + 5 = 20.

When you pick the first piece, the probability that it is grape is 6/20.

When you pick the second piece, there's one less piece of gum, and one less grape flavor, so the probability is 5/19.

The probability that both pieces are grape is:

P = 6/20 × 5/19

P = 3/38

5. The total number of drinks is 6 + 3 + 4 = 13.

Since the coach replaces the first drink, the second selection will be independent of the first.  So the probability is still P = 6/13.

6. A die has six sides.  They are numbered 1 through 6.  Three of the numbers are even.  Each roll is independent, so the probability of a previous roll does not affect the probability of future rolls.

The probability that you get 3 even numbers, followed by a one, is:

P = (3/6) (3/6) (3/6) (1/6)

P = 1/48

***Important... Even though the question says 15m, the question owner says he meant to put 16m***

[tex]a^2+b^2=c^2\\\\16^2+30^2=34^2\\\\256+900=1156\\\\1156=1156[/tex]

True!

⭐ Answered by Hyperrspace (Ace) ⭐

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Answer:

The annual interest rate is 5.247%.

Step-by-step explanation:

Question

Claire deposited $2,500 into an account that accrues interest monthly. She made no additional deposits or withdrawals. After 2 years, Claire had $2,762.35 in the account. what is the annual interest rate of the account?

Subtract $2,500.00 from $2,762.35 and you get 262.35- the 2-year interest. To get the annual interest, divide 262.35 by 2, which equals 131.75. Then, divide 131.75 by 2,500 (original amount) and you get 0.05247. Lastly, multiply 0.05247 by 100 to get the answer (5.247%).

To find the annual interest rate, use the compound interest formula and set it equal to the final amount in the account. After performing the necessary computations, 'r' comes out to approximately 5%.

To find the annual interest rate of Claire's account, you'll need to use the compound interest formula: v(t) = p * (1 + r/n)^(nt), where:

Claire's account had $2,762.35 in it after 2 years. Therefore, you would set $2,762.35 equal to the formula and solve for 'r'.

Doing so yields $2,762.35 = $2,500 * (1 + r/12)^(12*2) which simplifies, after some mathematical computations, to an annual interest rate (r) of roughly 5%.

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Answer:

15/6

Step-by-step explanation:

if ax^2+bc+c=0 is given equation then slope of this equation will be

m=-a/b

Answer:

C. 8,624

Step-by-step explanation:

recall that the formula for circumference is

Circumference = 2πr  ( = given as 85 meters)

hence,

85 = 2πr

r = 85/(2π)

given h = 15m

volume of cylinder

= πr²h

= π (85/2π)² 15  (using calculator and assuming π = 3.14)

= 8628.58

Comparing with the choices, the closest choice (within rounding error) is C. 8,624

Answer:

no

Step-by-step explanation:

thirty percent of $28 is $8.4, so you would subtract the two leaving you with $19.6

2.5 sales tax of $19.6 is $0.49

Adding those two, the total comes to 20.09 which is just over budget

The amount of the book is more than $20. Then she does not have enough money.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Let 'x' be the markdown price. Then the equation is given as,

30% = [(28 - x) / 28] × 100

0.30 = [(28 - x) / 28]

8.4 = 28 - x

x = $19.6

Then the amount of book after tax is given as,

⇒ $19.6 x 1.025

⇒ $20.09

The amount of the book is more than $20. Then she does not have enough money.

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Answer:

The probe's final position is -143m

Step-by-step explanation:

Note that the words 'lowered' and 'below' mean subtract; while the word 'raised' means add. Thus, interpreting the statement to mathematical expression is done below.

[tex] - 90m + 50m - 138m + 35m[/tex]

[tex] = - 143m[/tex]

Therefore, the probe's final position is -143m. Hence, the sensor is 143m below the sea level.

Answer:

156

Step-by-step explanation:

13 × 12

13

×

12

=

26

130

=

156

Answer:

Step-by-step explanation:

m*n

m=13

n=12

13 * 12

156

The area of the metal frame surrounding a circular mirror can be calculated by figuring the expression 225x² - 9πx², which represents the area of the square minus the area of the circle.

The subject of this question is based in mathematics, specifically the area of geometry. The area of the metal frame surrounding the mirror can be found by calculating the difference between the area of the square frame and the area of the circular mirror.

The area of the square frame is given by the formula A = s² where 's' is the length of a side of the square. In this case, each side of the square is 15x so the area of the square frame would be (15x)² = 225x².

The area of the circular mirror is given by the formula A = πr² where 'r' is the radius of the circle. For this mirror, the radius is 3x, so the area of the mirror would be π*(3x)² = 9πx².

So, the area of the metal frame is the difference between the area of the square and the area of the circle. Thus, the area of the frame = 225x² - 9πx².

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Final answer:

To find the area of the metal frame, calculate the area of the square then subtract the area of the circle. The area of the frame is the difference between the square's area, (15x)², and the circle's area, π(3x)².

Explanation:

The question asks for the area of the metal frame surrounding a circular mirror with the mirror's radius being 3x and the frame's side length being 15x.

To find the area of the frame, first calculate the area of the square and then subtract the area of the circle (mirror). The area of the square is given by the formula A = side², so:

Next, calculate the area of the circle using the formula A = πr²:

Finally, subtract the mirror's area from the frame's area to find the area of the metal frame alone:

Answer: 9

Step-by-step explanation:

2x + 3 when x = 3

2(3) + 3

2 * 3 = 6

6 + 3 = 9

To evaluate the mathematical expression 2x + 3 for x = 3, substitute x = 3 into the equation to get 2(3) + 3 = 6 + 3, and then add the numbers to get 9.

To evaluate the expression 2x + 3 for x = 3, you would replace x with 3 in the expression, then follow the order of operations (PEMDAS/BODMAS) to solve the expression.

Here is the step-by-step breakdown:

So, when x = 3, the value of the expression 2x + 3 is 9.

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