A business owes $8000 on a loan. Every month, the business pays 12 of the amount remaining on the loan.

How much will the business pay in the sixth month?

Final answer:

The Converse of the Base Angles Theorem states that if two angles of a triangle are congruent, then the triangle is isosceles.

Explanation:

In geometry, the theorem that can prove a triangle to be isosceles is the Converse of the Base Angles Theorem. It states that if two angles of a triangle are congruent, then the triangle is isosceles. In other words, if the two base angles of a triangle are equal, then the triangle is isosceles. For example, if angles A and B in triangle ABC are congruent (angle A = angle B), then triangle ABC is isosceles.

Final answer:

The expression 3x² signifies a quadratically powered variable (x) that is multiplied by the coefficient 3, commonly seen in algebraic equations.

Explanation:

The expression 3x² represents a mathematical formula where the variable x is squared (multiplied by itself) and then multiplied by 3. The squaring of a variable is a fundamental concept in algebra that symbolizes a number raised to the power of 2.

The coefficient 3 in this case indicates that the square of x is being tripled. Therefore, if x is 2, x² would be 4, and 3x² would be 12. This type of expression is essential in solving quadratic equations and appears frequently in various mathematical contexts.

Answer:2/10

Step-by-step explanation: 10 students, 2 of them forgot their lunch. So 2/10 of the students will be chosen by the teacher

Answer:

A:  x ≥  -1

its rightc bc

Reuben's driving rate is 72 miles per hour. At this same rate, it would take him 13 hours to drive 936 miles.

To determine how long it would take Reuben to drive 936 miles at the same rate, we first need to find his driving rate. Reuben drove 576 miles in 8 hours. To find his rate, we divide the distance by the time:

Rate = Distance / Time

Rate = 576 miles / 8 hours = 72 miles/hour

Next, we use this rate to find out how long it will take him to drive 936 miles:

Time = Distance / Rate

Time = 936 miles / 72 miles/hour = 13 hours

Thus, it would take Reuben 13 hours to drive 936 miles at the same rate.

find the slope of the line given:

y = mx+b

y = -3x/2 -7/2

slope = -3/2

the slope of the perpendicular line is the negative reciprocal

 so answer is 2/3

When two events are dependent, this means that one event cannot occur without the other, or simply put the two events are connected to each other in one way or the other.

When two events are independent, this means that the two events can occur separately, with one event having no effect on the occurrence of the other.

Therefore the dependent and independent events are as follows:

Independent event:

 c. rolling a die twice

The outcome of the first die does not affect the outcome of the second die, hence independent.

Dependent event:

d. drawing one card from a standard​ deck, not replacing​ it, and then selecting another card

By the act of not replacing the drawn card, we are changing the probability of selecting another card, hence dependent.

The probability of rolling a number greater than 4 on a six-sided die is 1/3 or 0.33 or 33%. This is obtained by dividing the number of favourable outcomes (2, i.e., 5 and 6) by the total number of outcomes (6).

The subject of the question is the probability in mathematics, specifically related to an experiment involving rolling a six-sided die. To answer your question, a six-sided die has numbers from 1 to 6. But you are asking about throwing a number greater than 4. There are only two outcomes that are greater than 4, the numbers 5 and 6. Therefore, the possible favorable outcomes are 2.

The total outcomes (since it's a six-sided standard die) are 6. Probability is calculated by dividing the number of favorable outcomes by the total number of outcomes. In this case, it will be 2/6 = 1/3 which is approximately 0.33 or 33%.

This means, if you roll the die, on an average, you can expect to roll a number greater than 4 about 33 times if you roll it 100 times.

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To calculate the overall percentage reduction on the price of the radio, we need to calculate the final price after both discounts. The first discount of 20% off reduces the price by 20/100 = 0.2. The second discount of 25% off reduces the price by 25/100 = 0.25. The overall percentage reduction is 40%.

To find the overall percentage reduction on the price of the radio, we need to calculate the final price after both discounts. The first discount of 20% off reduces the price by 20/100 = 0.2. So, the price after the first discount is 1 - 0.2 = 0.8 times the original price. The second discount of 25% off reduces the price by 25/100 = 0.25. So, the final price after both discounts is 0.8 * (1 - 0.25) = 0.8 * 0.75 = 0.6 times the original price.

To calculate the overall percentage reduction, we can subtract the final price from the original price, divide by the original price, and multiply by 100. The overall percentage reduction is ((1 - 0.6) / 1) * 100 = 40%.

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7000 = 3624*(1+0.21)^x

7000 = 3624 *1.021^x

7000/3624 = 1.021^x

875/453 = 1.021^x

xlog(1.021 = log(875/453

x = 31.677

 31 years 9 months

Answer:

Option A is the answer.

Step-by-step explanation:

p = 3624.40

r = 2.1% or 0.021

n = 1

t = ?

A = 7000

Compound interest formula is :

[tex]A=p(1+\frac{r}{n})^{nt}[/tex]

Substituting the values in formula:

[tex]7000=3624.40(1+\frac{0.021}{1})^{t}[/tex]

=> [tex]\frac{7000}{3624.40} =(1.021)^{t}[/tex]

=> [tex]1.93135=(1.021)^{t}[/tex]

[tex]t=\frac{log1.93135}{log1.021}[/tex]

=> t = 31.670 years.

Closest to option A.

The pair of triangles that are congruent by ASA is figure C

Two triangles can be judged to be congruent using the ASA (Angle-Side-Angle) criterion. For triangles to satisfy ASA congruency:

Put otherwise, the ASA criterion determines that two triangles are congruent if two of their angles and the included side are congruent, respectively. For this criterion, the angles and sides' order matters.

Based on the explanations, hence the pair of triangles that are congruent by ASA is figure C

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The height of the triangle is 14 cm.

To find the height of the triangle, we can use the formula for the area of a triangle: Area = 1/2 * base * height. In this case, the base is 6 cm and the area is 42 cm^2. By rearranging the formula, we can solve for the height: Height = 2 * Area / Base. Plugging in the values, we get Height = 2 * 42 cm^2 / 6 cm = 14 cm.

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There are 150 nickels and 125 dimes in the box.

Let x = the number of nickels in the box

Let y = the number of dimes in the box

Firstly, we have to convert value of nickels and dimes into cents.

Value of 1 nickel = 5 cents

Value of 1 dime = 10 cents

Value of 1 dollar = 100 cents

Thus, the equation (1) (in cents) can be written as:

x + 2y = 400             Equation (1)

If my nickels were dimes and dimes were quarters:

A quarter is worth 25 cents.

Thus, the equation (2) (in cents) can be written as:

5x+10y =2000

5(x+2y)= 2000

x+2y = 2000/5

2x + 5y = 925             Equation (2)

Multiply Equation (1) by "2", we get:

10x +25y= 4625

5(2x+5y)=4625

2x+5y=4625/5

2x + 4y = 800        Equation (1)

Subtraction Equation (1) from Equation (2):

2x +5y-2x -4y=925-800

y= 125

2x + 5y = 925

2x + 5 × 125 = 925

2x + 625 = 925

2x = 925 - 625

2x = 300

x = 150

There are 150 nickels and 125 dimes in the box.

Here, we can check it by putting the value of x and y in Equation (1):

5x + 10y = 2000

5× 150 + 10 × 125 = 2000

750 + 1250 = 2000

2000 = 2000

There are 150 nickels and 125 dimes in the box.

Answer: Hourly wage

Step-by-step explanation:

The term "hourly wage" describes the gross pay that is calculated based on the number of hours an employee has worked.

The hourly wage is the amount of money that is earned by a employee for every hour worked or it is the amount of money paid by employer for every hour worked.

Here, the gross pay is calculated by multiplying the hourly wage to the number of hours worked.

Answer:

Option B is correct.

Step-by-step explanation:

Important state labor laws and safety regulations came about as a result of the 1911 - Triangle shirtwaist factory fire

The Triangle shirtwaist factory fire was one of the worst industrial disasters during that time. Many people died due to a fire breakout in the factory. They could not escape the building and died due to smoke inhalation or burns.

After this incident, a Committee on Public Safety was formed that led to a legislation requiring labor laws and improved factory safety standards.

An expression is defined as a set of numbers, variables, and mathematical operations. The given expression 7t · s · 3rt, when simplified will be equal to 21rst². The correct option is C.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression 7t · s · 3rt can be written as,

7t · s · 3rt

= 7 × t × s × 3 × r × t

= 21rst²

Hence, the given expression 7t · s · 3rt, when simplified will be equal to 21rst².

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Answer:

x=0

Step-by-step explanation:

Proposition 1) If a ● b = 0, then a = 0 or b = 0

Proposition 2) 3x = 0

=>  3 = 0 or x = 0

Given that 3 ≠ 0, x must be equal to 0.

Conclusion: x = 0