Which of the four statements is true and also write a one-step inequality as an example of when you would "flip" the sign.

Answer:

3.8 months

Step-by-step explanation:

Question: Anthony invested $36,000 in an account paying an interest rate of 5.3% compounded

quarterly. Assuming no deposits or withdrawals are made, how long would it take, to

the nearest year, for the value of the account to reach $51,800?

First step! What is 5.3% of 36k?

1,908

Second Step! Divide

51,800/1,908= 27.1488469602

Third Step! Round

27.1488469602= 27.1

27.1 weeks.

7 weeks in a month.

12 months in a year.

27.1/7= 3.8

3.8 months

The number of years for the amount of compound interest to reach $51,800 is given by b = 7 years

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the number years be represented as b

where the amount after b years is = $ 51,800

The initial principal amount P = $ 36,000

The number of times the compound interest is applied = quarterly = 4

Now , the equation is

A = P ( 1 + r/n )ⁿᵇ

On solving for the number of years b , we get

b = ln ( A / P ) / n [ ln ( 1 + r/n ) ]

b = ln ( 51,800.00 / 36,000.00 ) / ( 4 × [ ln ( 1 + 0.053/4 ) ] )

On further simplification , we get

b = ln ( 51,800.00 / 36,000.00 ) / ( 4 × [ ln (1 + 0.01325 ) ] )

b = 6.911 years

On rounding to the nearest year , we get

b = 7 years

Therefore , the value of b is 7 years

Hence , the number of years is 7 years

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2x + 3x + 5x = 180

10x = 180

x = 18

2x = 36, 3x = 54, 5x = 90

They add up to 180 (definition of sum of angles of a triangle.)

Answer:

Step-by-step explanation:

5555

The red arcs mean those angles are the same.

When two angles are the same the corresponding sides are also the same.

5. X = 8

6. X = 11

7. 2x-16 = 8

Add 16 to both sides:

2x = 24

Divide both sides by 2:

X = 12

8. X + 19 = 8

Subtract 19 from both sides:

X = -11

Sim porque positivo não fecha

Answer:

Go down down and to the right

The interest rate is 29.43%

The given parameters are:

Amount, A = $470

Principal, P = $5425

The formula of rate is given as:

r= √A/P- 1

Substitute known values

r= √470/5425- 1

Evaluate the difference

r= √470/5424

Evaluate the quotient

r= √0.08665

Evaluate the exponent

r= 0.2943

Express as percentage

r = 29.43%

Hence, the interest rate is 29.43%

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Answer:

$55

Step-by-step explanation:

Let w = the no. of weeks

35 + 2.50w = amount you will have in the account after w weeks

115 - 7.5w = amount cousin will have in the account after w weeks

You need to set these expressions equal to each other.

35 + 2.50w = 115 - 7.5w     Multiply thru the equation

                                            by 10  to remove the fractions

350 + 25w = 1150 - 75w

100w = 800

w = 8 weeks

35 + 2.50w = 35 + 2.5(8) = 35 + 20 = $55

115 - 7.50w = 115 - 7.50(8) = 115 - 60 = $55

Answer:

1) A. 36

2) A. 10

3) B. 72

4) B. 42

5) A. 6

6) B. 90

7) C. less than

8) A. 22

9) D. 54

10) B. The diameter is two times the size of the radius.

Step-by-step explanation:

1) 12 x 3.14 = 36

2) 20/2 = 10

3) 12 x 2 x 3.14 = 72

4) 7 x 2 x 3.14 = 42

5) 36/3.14 = 12/2 = 6

6) 30 x 3.14 - 90

8) 11 x 2  =22

9) 9 x 2 x 3.14 = 54

Answer:

x = 24.7

Step-by-step explanation:

Here, we want to find the value of x

To do this, we are to use the appropriate trigonometric ratio

From what we have;

9 faces the angle given as it is the opposite, x is below and it is the adjacent

The trigonometric identity that links opposite to adjacent is the tan which is the ratio of former to latter

Thus, we have that;

tan 20 = 9/x

x = 9/tan 20

x = 24.7

Answer:

D) Slope: 1/8; y-intercept: 3

Step-by-step explanation:

An equation in the form y = mx + b has certain characteristics that help us determine the slope and y-intercept of the line easily.

The variable "m" gives us the slope of the line, while the variable "b" gives us the y-intercept of the line.

Taking y = 1/8x + 3, we can see that the m-value is 1/8 and the b-value is 3.

Therefore, the slope of this line is 1/8 and the y-intercept is 3.

The answer is D) Slope: 1/8; y-intercept: 3.

Answer:

x = 25

Step-by-step explanation:

One can use the Line Tangent to a Circle theorem to solve this problem. The Line Tangent to a Circle theorem states that when two non-parallel lines are tangent to a circle (the lines touch the circle at a single point), then the distance between the intersection point and the point of tangency is the same for both lines. This theorem does go by other names, but the actual theorem content is the same.

Using this one can form the equation;

BA = CA

Substitute,

2x + 3 = 53

Inverse operations,

2x + 3 = 53

     -3      -3

2x = 50

/2     /2

x = 25

Answer: 140

Step-by-step explanation:

Angle 4 and A are supplementary meaning they add to 180

Thus you can do 180-40 = 140 to get that angle A = 140.

Since the two lines are parallel, Angle A is congruent to Angle D. Then, since Angle D is opposite Angle 3, we know that that Angle 3 and Angle D are congruent.

Answer:

ok

Step-by-step explanation:

Answer:

huh????

Step-by-step explanation:

Answer:

2 to two too

Step-by-step explanation:

    thats how much i think

Answer:

4.31 as said

Step-by-step explanation:

Answer:

it could be 4.30 because when u divide those two the answer is 4.3057142857, and because the number in the hundreths place is just a 0 its probably just 4.30 i could be wrong sorry

Answer:

The answer is 120 feet.

Step-by-step explanation:

The area of the field (A) is:

A = w · l       (w - width, l - length)

It is known:

A = 12,000 ft²

l = w - 20

So, let's replace this in the formula for the area of the field:

12,000 = w · (w - 20)

12,000 = w² - 20

⇒ w² - 20w - 12,000 = 0

This is quadratic equation. Based on the quadratic formula:

ax² + bx + c = 0      ⇒  

In the equation w² - 20w - 12,000 = 0, a = 1, b = -20, c = -12000

Thus:

So, width w can be either

or

Since, the width cannot be a negative number, the width of the field is 120 feet.

The length of the field is 120 feet.

Option C is the correct answer.

A rectangle is a 2-D shape with length and width.

The length and width are different.

If the length and width are not different then it is a square.

The area of a rectangle is given as:

Area = Length x width

We have,

Let's start by using the given information to set up two equations:

Let x be the length of the field in feet.

Then, the width of the field is x - 20 feet.

The area of the field is given as 12,000 square feet:

x (x - 20) = 12,000

Expanding the left side of the equation, we get:

x² - 20x = 12,000

Bringing all the terms to one side, we get:

x² - 20x - 12,000 = 0

Now, we can solve this quadratic equation using factoring,

Completing the square, or the quadratic formula.

Here, we will use factoring:

x² - 20x - 12,000 = 0

(x - 120) (x + 100) = 0

The solutions are x = 120 and x = -100, but a negative length doesn't make sense, so we reject that solution.

Therefore,

The length of the field is 120 feet.

To check, we can substitute x = 120 into the equation for the width:

Width = x - 20 = 100 feet

Area = Length x Width

= 120 ft x 100 ft

= 12,000 sq ft

Thus,

The length of the field is 120 feet.

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Answer:

multiply the base and add the exponents

Answer:

You need to make the question again and include the chart.

Step-by-step explanation:

Answer:

The first hour is 14 euros and each hour after that is 2 euros.

Answer:

[tex]-13w-7[/tex]

Step-by-step explanation:

1) Remove parentheses.

[tex]-6w-8+1-7w[/tex]

2) collect like terms.

[tex](-6w-7w) +(-8+1)[/tex]

3) Simplify.

[tex]-13w-7[/tex]

Therefor, the answer is -13w - 7.

Answer:

c.

Step-by-step explanation:

5-7 = -2

2 - -3=5

-2/5

Answer:

P = 44

Step-by-step explanation:

perimeter of a square = 4a

where a = side lenght

equation:

⇒ 4a

solve by substituting 11 for a

⇒ 4a

⇒ 4 x 11

⇒44

Answer:

+9.2=7.6x

x+9.2=38x

______

5

Solution

=1.393939393

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Simplemente agregue usando la calculadora y debería obtener esta respuesta. ;)

3,100= 1,900 +84x

right since 84 months in 7 years

so 14.3% right?

Answer:

a) £600

b) £1400

Step-by-step explanation:

a)

original price = x

reduced price = £420

reduced price is 70% of original price

Since the discounted price, £420, is 70% of the original price, x, then

70% of x = 420

0.7x = 420

x = 420/0.7

x = 600

Answer: £600

b)

original price = x

discounted price = £840

discount percentage = 40%

The original price is x, and x is 100% of the original price since 100% is the whole amount. The discount is 40% of the original price. 100% - 40% = 60%. That means the discounted price is 60% of the original price.

60% of x = 840

0.6x = 840

x = 840/0.6

x = 1400

Answer: £1400

Answer:

3300

Step-by-step explanation:

Formula

Gross Salary = Basic + Commission

Givens

Basic = 3000

% = 12%

Solution

Gross = 3000 + 12/100 * 2500

Gross = 3000 + 30000/100

Gross = 3000 + 300

Gross = 3300