2. Angela deposited $600 into an account paying a simple interest rate of 3.6% for 4.5 years. How
much interest did she earn? What was the balance of her account after the 4.5 years (assuming she made no deposits of withdrawals during the time)

Answer:

3 training sessions

Step-by-Step Explanation:

What we are going to have are two equations set equal to each other. Our variable is going to be the letter x. X represents the number of personal training sessions we would have to have at their current costs for the two equations to equal each other. Because we are only doing one month, the membership costs will stay constant.

For Silver Gym, membership is $40 and training sessions are 25$ per session. That "per session" tells you that this is where the variable goes. Your equation for a month at Silver Gym is 25x + 40.

Do the same for Fit Factor; $70 membership, $15 per session: 15x + 70.

Now let's set them equal to each other:

25x + 40 = 15x + 70

Next, we want to get variables on one side and constants on the other. I like to do variables on the left and constants on the right but, this is just personal preference -- we'll end up with the same answer regardless. To do this, we are going to subtract 15x from both sides, subtract 40 from both sides, and then simplify. So the above equation becomes:

25x - 15x + 40 - 40 = 15x - 15x + 70 - 40

Simplify by combining like terms. The 15x and - 15x cancel each other out, same with the 40 and - 40. Leaving us with:

10x = 30

Divide both sides to isolate your variable x and satisfy the division property of equality.

x = 30/10

x = 3

You would have to do 3 training sessions for the two gyms to be equal in cost.

The complex numbers corresponding to the given points in the complex plane are:

A: -2 + 3i

B: -1 - i

C: 3 - 4i

D: 4

What are complex numbers?

The complex number is the combination of a real number and an imaginary number. An example of a complex number is 4+3i. Here 4 is a real number and 3i is an imaginary number.

In the complex plane, the horizontal axis represents the real part of a complex number and the vertical axis represents the imaginary part. Using this information, we can identify the complex numbers corresponding to the given points:

A: [-2] + [3]i

This corresponds to the point (-2, 3) in the complex plane.

B: [-1] + [-1]i

This corresponds to the point (-1, -1) in the complex plane.

C: [3] + [-4]i

This corresponds to the point (3, -4) in the complex plane.

D: [4] + [0]i

This corresponds to the point (4, 0) in the complex plane.

Therefore, the complex numbers corresponding to the given points in the complex plane are:

A: -2 + 3i

B: -1 - i

C: 3 - 4i

D: 4

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Answer: Gold mining can contaminate drinking water and destroy pristine environments, endangering the health of people and ecosystems.

Thus the answer is d

Step-by-step explanation:

The ending balance is $5,480.

Given that,

Based on the above information, the calculation is as follows:

\(= \$4,000 \times (1 + 0.065)^5\)

= $5,480

Therefore, the ending balance is $5,480.

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Answer: Hi, the ending balance is 5,300

Step-by-step explanation:

I took the test and got an 100. Hope this helps!

Answer:

$5564.87

Step-by-step explanation:

We are to determine the difference between the future values of each investment

The formula for calculating future value:

FV = P (1 + r)^mn

FV = Future value  

P = Present value  

R = interest rate  

N = number of years

m = number of compounding

Madeline

P = Present value = 51,000

R = interest rate = 0.06125 / 365 = 0.000168

N = number of years = 13

m = number of compounding = 365

51,000 x (1.000168)^4745  = 113,070.20

Harper

51,000 x (1.004792)^156 = 107,505.33

Difference = 113,070.20 - 107,505.33 = $5,564.87

Answer:$5565 just took it

Step-by-step explanation:

Answer:

The answer is 81 hours....

Step-by-step explanation:

1000 - 352 = 648

648 ÷ 8 = 81

The drug has a half-life of 5 hours

Half-life is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential decay.

The formula is given as;

T1/2 = ln2 / λ

Where;

But λ = 15% = 0.15/hr

t1/2 = ln2 / 0.15

T1/2 = 0.693/0.15

T1/2 = 4.62 = 5 hours.

The half-life of the drug is 5 hours

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Answer:

Third option

Step-by-step explanation:

In order to find the answer to this question you must change the mixed number into a improper fraction and then multiply the numerators to the denominators.

\(7\times4\frac{5}{8}\)

Remember that all numbers have a invisible one as the denominator:

\(7=\frac{7}{1}\)

\(\frac{7}{1} \times4\frac{5}{8}\)

Turn the mixed number into a improper fraction:

\(8\times4=32+5=37\)

(Remember to keep the denominator the same)

\(=\frac{37}{8}\)

Now multiply:

\(7\times37=259\)

\(1\times8=8\)

\(=\frac{259}{8}\)

Turn the improper fraction into a mixed number:

\(\frac{259}{8} =32\frac{3}{8}\)

\(=32\frac{3}{8}\)

Hope this helps.

Answer:

1

Step-by-step explanation:

if the marbles are all the same there are no possible outcomes besides 1

The number of possible outcomes if she selects 2 marbles is 153.

Given that, Suzy randomly picks marbles from a bag containing 18 identical marbles.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.

So, number of possible outcomes if she selects 2 marbles is

18C2 = 18!/2!(18-2)!

= (18×17×16!)/(2!×16!)

= (18×17)/(2×1)

= 9×17

= 153

Therefore, the number of possible outcomes if she selects 2 marbles is 153.

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Answer:

47.5

Step-by-step explanation:

38/80x100%=47.5

Answer:

47.5%

Step-by-step explanation:

Before we get started in the fraction to percentage conversion, let's go over some very quick fraction basics. Remember that a numerator is the number above the fraction line, and the denominator is the number below the fraction line. We'll use this later in the tutorial.

When we are using percentages, what we are really saying is that the percentage is a fraction of 100. "Percent" means per hundred, and so 50% is the same as saying 50/100 or 5/10 in fraction form.

So, since our denominator in 38/80 is 80, we could adjust the fraction to make the denominator 100. To do that, we divide 100 by the denominator:

100 ÷ 80 = 1.25

ow we can see that our fraction is 47.5/100, which means that 38/80 as a percentage is 47.5%.

We can also work this out in a simpler way by first converting the fraction 38/80 to a decimal. To do that, we simply divide the numerator by the denominator:

38/80 = 0.475

Once we have the answer to that division, we can multiply the answer by 100 to make it a percentage:

0.475 x 100 = 47.5%

And there you have it! Two different ways to convert 38/80 to a percentage. Both are pretty straightforward and easy to do, but I personally prefer the convert to decimal method as it takes less steps.

I've seen a lot of students get confused whenever a question comes up about converting a fraction to a percentage, but if you follow the steps laid out here it should be simple. That said, you may still need a calculator for more complicated fractions (and you can always use our calculator in the form below).

If you want to practice, grab yourself a pen, a pad, and a calculator and try to convert a few fractions to a percentage yourself.

Hopefully this tutorial has helped you to understand how to convert a fraction to a percentage. You can now go forth and convert fractions to percentages as much as your little heart desires!

Answer: 7

Step-by-step explanation:

yarn = 4 1/5 = 21/5

measure of one piece = 3/5

no. of pieces of yarn = 21/5÷3/5

= 21/5×5/3

= 105/15 = 7

So the number of pieces of yarn cut will be 7

Answer:

7

Step-by-step explanation:

4.2' yarn

cut into 0.6' pieces

4.2/0.6 =7

Option(A) is the correct answer is A. 1,335 birds.

To calculate the number of birds that will be left after 20 years, we need to consider the annual decline rate of 2%.

We can use the formula for exponential decay:

N = N₀ * (1 - r/100)^t

Where:

N is the final number of birds after t years

N₀ is the initial number of birds (2,000 in this case)

r is the annual decline rate (2% or 0.02)

t is the number of years (20 in this case)

Plugging in the values, we get:

N = 2,000 * (1 - 0.02)^20

N = 2,000 * (0.98)^20

N ≈ 2,000 * 0.672749

N ≈ 1,345.498

Rounded to the nearest whole number, the number of birds that will be left after 20 years is 1,345.

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Answer:

\(Volume_B = 630in^3\)

Step-by-step explanation:

Given

\(Volume_A = 630in^3\)

Required

Determine \(Volume_B\)

Volume is calculated as thus:

\(Volume = Height * Area\)

From the question, we understand that both prisms have the same height and area;

This implies that

\(Volume_B = Volume_A\)

Substitute \(630in^3\) for \(Volume_A\)

\(Volume_B = 630in^3\)

Answer:

e.  630 in³

Step-by-step explanation:

ratio and proportion of volume with the same height:

vol A = 630

h = 21

Vol A = Vol B

   h            h

630 = Vol B

   21         21

Vol B = 630 (21)

               21

Vol B = 630 in³

Answer:

143

Step-by-step explanation:

Let's call the number we're trying to find "x".

According to the problem, we know that:

5/13 of x = 55

To solve for x, we can start by multiplying both sides by the reciprocal of 5/13, which is 13/5:

(13/5) * (5/13) * x = (13/5) * 55

Simplifying, we get:

x = 143

Therefore, the number we're looking for is 143.

Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.

To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.

4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.

To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8

Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8

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Answer:

3 9/10

Step-by-step explanation:

Find the common factor

8/10+3 1/10

3 9/10

(a) x² + y² + z² + 18(x - y + z) + 218 = 0

(b) (x + 9)² + (y - 9)² + 56 = 0

The general equation of a sphere of radius r and centered at C = (x₀, y₀, z₀) is given by;

(x - x₀)² + (y - y₀)² + (z - z₀)² = r²               ------------------(i)

From the question:

The sphere is centered at C = (x₀, y₀, z₀) = (-9, 9, -9) and has a radius r = 5.

Therefore, to get the equation of the sphere, substitute these values into equation (i) as follows;

(x - (-9))² + (y - 9)² + (z - (-9))² = 5²

(x + 9)² + (y - 9)² + (z + 9)² = 25      ------------------(ii)

Open the brackets and have the following:

(x + 9)² + (y - 9)² + (z + 9)² = 25

(x² + 18x + 81) + (y² - 18y + 81) + (z² + 18z + 81) = 25

x² + 18x + 81 + y² - 18y + 81 + z² + 18z + 81 = 25

x² + y² + z² + 18(x - y + z) + 243 = 25

x² + y² + z² + 18(x - y + z) + 218 = 0    [equation has already been normalized since the coefficient of x² is 1]

Therefore, the equation of the sphere centered at (-9,9, -9) with radius 5 is:

x² + y² + z² + 18(x - y + z) + 218 = 0

(2)  To get the equation when the sphere intersects a plane z = 0, we substitute z = 0 in equation (ii) as follows;

(x + 9)² + (y - 9)² + (0 + 9)² = 25

(x + 9)² + (y - 9)² + (9)² = 25

(x + 9)² + (y - 9)² + 81 = 25        [subtract 25 from both sides]

(x + 9)² + (y - 9)² + 81 - 25 = 25 - 25

(x + 9)² + (y - 9)² + 56 = 0

The equation is therefore, (x + 9)² + (y - 9)² + 56 = 0

To find the value of Az in the geometric sequence, we can use the given information. The geometric sequence is represented as follows: A3, 60, 160, 06 = 9.

From this, we can see that the third term (A3) is 60 and the common ratio (r) is 160/60.

To find Az, we need to determine the value of the nth term in the sequence. In this case, we are looking for the term with the value 9.

We can use the formula for the nth term of a geometric sequence:

An = A1 * r^(n-1)

In this formula, An represents the nth term, A1 is the first term, r is the common ratio, and n is the position of the term we are trying to find.

Since we know A3 and the common ratio, we can substitute these values into the formula:

60 =\(A1 * (160/60)^(3-1)\)

Simplifying this equation, we have:

\(60 = A1 * (8/3)^260 = A1 * (64/9)\)

To isolate A1, we divide both sides of the equation by (64/9):

A1 = 60 / (64/9)

Simplifying further, we have:

A1 = 540/64 = 67.5/8.

Therefore, the first term of the sequence (A1) is 67.5/8.

Now that we know A1 and the common ratio, we can find Az using the formula:

Az = A1 * r^(z-1)

Substituting the values, we have:

Az =\((67.5/8) * (160/60)^(z-1)\)

However, we now have the formula to calculate it once we know the position z in the sequence.

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Answer:

23 miles

Step-by-step explanation:

Answer:

6 months

Step-by-step explanation:

We can set up an equation based on his monthly savings to find out how long it will take for Hatif to reach $630 in his account.

Let's assume it takes Hatif "n" months to reach $630 in his account. Each month, he saves $80.

The equation representing the situation is:

$150 + $80n = $630

Now, let's solve for "n":

$80n = $630 - $150

$80n = $480

n = $480 / $80

n = 6

Therefore, it will take Hatif 6 months to reach $630 in his account.

The quadratic equation that fits each set of points (0.-8), (2, 0), and (-3, -5) is -3x² + 10x - 8 = 0

Quadratic equation:

Quadratic equation refers algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Given,

Here we have the set of points (0.-8), (2, 0), and (-3, -5).

Now, we have to find the quadratic equation for this points.

We know that the standard form of the quadratic equation is,

y = ax² +  bx + c

Here we have to use each point value in order to find the value of a, b and c to find the quadratic equation of the points,

First we have to take the point (0, -8) and apply it on the formula, then we get,

-8 = a(0)² +  b(0) + c

-8 = c

Now, use the point (2,0), then we get,

0 = a(2)² +  b(2) + c

0 = 4a + 2b + c --------------------(1)

Finally, take the point (-3, -5), then we get the equations,

-5 = a(-3)² +  b(-3) + c

-5 = 9a - 3b + c --------------------(2)

Now, apply the value of c as -8, then we get,

4a + 2b = 8 ----------------(3)

9a -3b = 3 -----------------(4)

Divide equation (4) by 3 and equation (3) by 2 on both sides then we get,

2a + b = 4

3a - b = 1

When we subtract these equation then we get the value of

a = -3

Then the value of b is

2(-3) + b = 4

b = 4 + 6

b = 10

Therefore, the quadratic equation is -3x² + 10x -8 = 0

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Answer:

ummm oop- haha

The equation for the situation is \(5x+6(0.95)=11.95\)

The solution to the equation is \(x=1.25\)

First, you must set up the equation.

\(5x+6(0.95)=11.95\)

Then, you must simplify the terms.

\(5x+5.7=11.95\)

Next, subtract 5.7 on both sides.

\(5x=6.25\)

Finally, divide 5 on both sides

\(x=1.25\)

The cost of each doughnut is $1.2 and the equation is 5(0.95) + 6x = 11.95 if the total cost of 5 doughnuts and 6 cookies at a bakery is $11.95.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The total cost of 5 doughnuts and 6 cookies at a bakery is $11.95.The cost of each cookie is $0.95.

The cost of 1 doughnut is x.

Total cost = $11.95

Total cost = 5(0.95) + 6x

11.95 = 5(0.95) + 6x

Or

5(0.95) + 6x = 11.95

After solving

x = $1.2

Thus, the cost of each doughnut is $1.2 and the equation is 5(0.95) + 6x = 11.95 if the total cost of 5 doughnuts and 6 cookies at a bakery is $11.95.

The options are:

6(0.95) + 5x = 11.95

5(0.95) - 6x = 11.95

5(0.95) + 6x = 11.95

5(0.95) + 6(11.95) = x

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Answer:

C. 37x + 35

Step-by-step explanation:

\(8(5x + 1) + 3(9 - x) \\ \\40x + 8 + 27 - 3x \\ 40x - 3x + 27 + 8 \\ 37x + 35\)

Answer:

  Draw perpendicular bisectors of two the sides

Step-by-step explanation:

The point that is the same distance from each of their houses is the point called the "circumcenter." It is the center of the circle that passes through the vertices of the triangle. Then each of the vertices is the same distance from the center.

The circumcenter is the intersection point of the perpendicular bisectors of the sides of the triangle. To find it, the group needs to draw perpendicular bisectors of two of the sides.

Answer:

The answer is C

Step-by-step explanation:

EDGE2020

Answer: 26.7

Step-by-step explanation:

Answer:

26.7

Step-by-step explanation:

Two steps for solving this equation that refer to the property of equality are:

6 = 9 - 3 (Symmetric property)

6 = 6 (Reflexive property)

The property of equality shows that the major operators for solving the unknown variables in an equation are addition, multiplication, division, and subtraction. In the solution below all of these are applied.

6 = -x - 15/5

We cross-multiply to get

30 = -x - 15

Collecting like terms

30 + 15 = -x

45 = -x

When we replace -x with 45, we will have:

6 = 45/5 - 3

6 = 9 - 3 (Symmetric property)

6 = 6 (Reflexive property)

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Answer:

The common ratio is 3

Step-by-step explanation:

if you divide the first number by the number following it, then the answer is three all the way down the line. So all you need to do to find the following term is to multiply the last number that you know by 3 and you get the number after that

Hope that was helpful :)ratio

Answer:

yes it is 3 I've been solving this for a few days and got 3

Answer:

31/15

Step-by-step explanation:

First, find the common multiplier of 20 and 12 (the lowest number that both fractions can be increased to). This is 60 (12 x 5 = 60, 20 x 3 = 60) and adjust the numerators accordingly: multiply 17 by five to get 85, and multiply 13 by three to get 39. Add them up to get 124/60, and then simplify - the answer will be 31/15! Hope this helps! Sorry if this was tough to understand, typing off my phone, so feel free to ask any questions :)

Answer:

0.720833

Step-by-step explanation:

First find the LCM of the two fractions

Then add the numerators together

form a single fraction

Lastly cancel the numerator and denominator if possible