If $100 is borrowed and the interest after 6 months is $8, what is the annual interest rate for a simple interest loan?

Answer:

1. 4√5

2. 3√5

3. √149

4. √58

Step-by-step explanation:

The Pythagorean theorem states "a^2 + b^2 = c^2",  where "a" and "b" are the legs, while "c" is the hypotenuse.

Knowing this, we can substitute each variable with given values on the triangles

1.  "4" and "8" are legs "a" and "b" and we need to find the hypotenuse "c"

4^2 + 8^2 = c^2

16 + 64 = c^2

80 = c^2

√80 = c

4√5 = c

2. "6" and "3" are legs "a" and "b" and we need to find the hypotenuse "c"

6^2 + 3^2= c^2

36 + 9 = c^2

45 = c^2

√45 = c

3√5 = c

3. "7" and "10" are legs "a" and "b" and we need to find the hypotenuse "c"

7^2 + 10^2 = c^2

49 + 100 = c^2

149 = c^2

√149 = c

4. "3" and "7" are legs "a" and "b" and we need to find hypotenuse "c"

3^2 + 7^2 = c^2

9 + 49 = c^2

58 = c^2

√58 = c

Answer: The answer is 11x+4y+13

Answer:

450 ducks

Step-by-step explanation:

75% can be rewritten as 75/100

75/100 of 600 can be rewritten as 75/100 * 600

Solve 75/100 = 0.75

0.75 * 600 = 450

The equation of the line is y = -4x -4.

We need to calculate the line which is parallel to y = -4x +3 and passes through the point (4, -20)

The given equation is y = -4x +3

Comparing this equation with the general equation of the line, y = mx +c, we get the slope of the equation is -4.

Now, When two lines are parallel to each other, their slopes are equal.

So, the slope of the required equation is -4.

Now, the equation of the line which passes through the points, [tex](x_{1} ,y_{1} )[/tex] and has slope m, is given by

[tex]y - y_{1} = m(x-x_{1} )[/tex]

Putting the values in the general equation, we get,

y - (-20) = -4(x - 4 )

y + 20 = -4x +16

y +4x = 16 -20 = -4

The equation of the line is y = -4x -4.

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By  calculating profit function to break even, the company needs to produce 23 units.

The amount received when a good or service is sold for a price is referred to as revenue. The cost of a product or service is the amount spent on its sale. Profit is defined as the difference between revenue and costs. A profit function is a relationship that shows the difference between the cost and revenue functions. The graph of a profit function can show the best combination of revenue and costs to produce the most profit. This is known as optimization.

Profit is defined as revenue less costs. This means that there is a profit function, P(x).

P(x) = R(x) - C(x)

Breaking even is the point at which revenue begins to exceed costs. It is thus the point at which P(x) = 0. Because these are all linear functions, you know that the business will be profitable after that point.

P(x) = 0

R(x) - C(x) = 0

R(x) = 24x

C(x) = 17x + 161

From the above equation,

R(x)=C(x)

24x=17x+161

7x=161

x=161/7

x=23

For the company to break even, 23 units must be produced.

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Answer:

45.47368421 (round as much as you need)

Step-by-step explanation:

We can model the equation using G(h) = -19h + 872, where -19 is the rate at which the bucket is emptying and 872 is the amount of gallons the bucket starts with.

Since gallons is the output, we would have 8 = -19h + 872 and we simply need to solve for h

[tex](8 = -19h+872)-872\\\frac{(-864=-19h)}{-19} \\h=45.47368421[/tex]

Tommy will pat bounce the ball 225 times in 405 seconds which was found using the given data.

Given: In 45 seconds, Tommy bounces a basketball 25 times.

Number of times he will pat bounce the ball in 405 seconds will be given as follows:

= (405 × 25)/45

=225

Therefore, Tommy will pat bounce the ball 225 times in 405 seconds which was found using the given data.

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Answer:$27

Step-by-step explanation:

$33.75/15 = $2.25 per book

12 books x $2.25/book =  $27

Answer:

$35.85

Multiply 2.39 * 15

Answer:tell me the math soulation first

Step-by-step explanation:

The area of the rectangle is 11/96 in²

In this question, we have the following parameters

Dimensions of rectangular area: 11/12 in x 1/8 in.

The area of a rectangle is the products of its dimensions

i.e. Area = products of dimensions

This implies that

Area = Length x Width

Substitute the known values in the above equation, so, we have the following representation

Area = 11/12 in x 1/8 in

Evaluate

Area = 11/96 in²

Hence, the rectangle area is 11/96 in²

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Answer:

√43

Step-by-step explanation:

Implement the Pythagorean formula to solve for sides of a right triangle: a^2 + b^2 = c^2, where "a" and "b" are the legs and "c" is the hypotenuse.

a = √6 and c = 49

√6^2 + b^2 = 49

6 + b^2 = 49

b^2 = 43

b = √43

Answer:

The square root of 43

Step-by-step explanation:

 I did this in class the other day

The value of the residual is 2.

We are given a fitted linear regression equation. The equation is given below.

ŷ = 6 - 2x

The x-value for the data points is 3, and the corresponding y-value is 2. We have to find the value of the residual.

We will substitute the given values in the equation of the regression line.

ŷ = 6 - 2x

ŷ = 6 - 2(3)

ŷ = 6 - 6

ŷ = 0

Thus, the predicted value of y in the given regression equation is 0. The actual value of y is 2. The residual is the difference between the actual and predicted values of y. Let the residual be denoted by the variable "r".

r = y - ŷ

r = 2 - 0

r = 2

Hence, the residual is 2.

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The amount that each student will have to raise on average in order to meet the goal would be $40

First, find the remaining amount that the members of the Westview Journalism Club are trying to raise:
= Amount to raise - Amount already raised

= 2, 100 - 1, 180

= $920

The amount that each student in the club will have to raise on average can be found as:

= Amount remaining to be raised / Number of students in the Westview Journalism Club

= 920 / 23

= $40

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The value of (18−42+2)21÷4⋅12 equal to -1386

Algebra is a branch of mathematics that assists in the representation of problems or situations through the use of mathematical expressions. In algebra, we use numbers with definite or fixed values such as 2, -1, 0.33, and so on. In algebra, an algebraic expression is composed of integer constants, variables, and the basic arithmetic operations of addition(+), subtraction(-), multiplication(), and division(/). 5x + 6 is an example of an algebraic expression. 5 and 6 are fixed numbers, while x is a variable.

Given that

(18−42+2)21÷4⋅12

Now we have to simplify the equation

(20-42)21/ 4 x 12

(-22)21/ 4 x 12

= (-462/4) x 12

= - 115.5 x 12

= - 1386

Therefore the value of  (18−42+2)21÷4⋅12 equals to -1386

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The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

The number of students who brought lunch on Thursday is 18 students.

The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

Number of students = 900

Number of students that brought lunch = 2% of 900

The number of students who brought lunch on Thursday.

= 2% of 900

= 2/100 x 900

2 x 9

= 18 students.

Thus,

The number of students who brought lunch on Thursday is 18 students.

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Answer:

depends on how you peel it

Step-by-step explanation:

if you peel it with one quick peel, you will have only one

if you do it with 2, you will have 2 peels an so on

The amount of peels will be greater in the bigger potato as compared to the smaller potato.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given data in the question,

There are two potatoes, a small one and a bigger one.

If you peel the bigger one, because of the bigger surface area, you will get more peels as compared to the smaller potato because the surface are is small, and you will get less number of peels.

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Considering the discrete probability distribution, it is found that:

a) The mean is of: 6.3

b)

The mean of the distribution is given by the sum of each outcome multiplied by it's probability, hence it is obtained as follows:

E(X) = 0.1 x 2 + 0.3 x 5 + 0.4 x 7 + 0.2 x 9 = 6.3.

The variance of the distribution is given by the sum of the difference squared between each observation and the mean, multiplied by it's probability, hence it is obtained as follows:

Var(X) = 0.1 x (2 - 6.3)² + 0.3 x (5 - 6.3)² + 0.4 x (7 - 6.3)² + 0.2 x (9 - 6.3)² = 4.01.

The standard deviation is the square root of the variance of the distribution, hence it is obtained as follows:

S(X) = sqrt(4.01) = 2.

We have that:

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The probability of drawing 2 Diamonds is 1/17.

The probability of drawing 1 diamond and 1 heart is 13/204.

How to find probability for a deck of cards?

According to the given question:

Since there are 52 cards, the probability of getting a diamond in the first draw is 13/52.

After the first card is drawn, there are just 12 diamonds left.

So, the probability of drawing the diamond now is 12/51.

The total probability is the product of two probabilities

So, P = 13/52 x 12/51 = 1/4 x 4/17

P = 1/17 ≈ 0.058

So the probability of drawing 2 Diamonds is 1/17.

Similarly, we know probability of getting a diamond in first is 13/52.

Also the probability of drawing a heart from 51 cards is 13/51.

The total probability P = 13/52 x 13/51

P = 1/4 x 13/51

P = 13/204 ≈ 0.063

So the probability of drawing 1 diamond and 1 heart is 13/204.

More likely outcome is the one whose probability is closer to unity. Since 13/204 > 1/17 that is 0.063 > 0.058 therefore drawing a heart and a diamond is a more likely outcome.

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The statements that are true according to the equation  h (x) = –3 |x – 1| + 4. are

The graph of the described function is attached

The vertex is marked (1, 4) in the graph

The y intercept is marked (0, 1) in the graph

Also from the equation, the y intercept is solved by

h (x) = –3 |x – 1| + 4

plugging the value of x

h (x) = –3 |0 – 1| + 4

h (x) = –3 |– 1| + 4

removing the modulus sign

h (x) = –3 * 1 + 4

h (x) = –3 + 4

h (x) = 1

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The cost of the tomatoes, in dollars per pound, using proportions, is of:

$0.86 per lb.

A proportion represents a fraction relative to a total amount, which is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in whichever context of a problem.

In this problem, the costs is obtained as follows:

Hence the cost in dollars per kg of the tomatoes is obtained as follows:

1.74 x 1.09 = $1.8966 per kg.

The relationship between kg and pounds is given as follows:

1 kg = 2.20 lb.

Hence the cost is written as follows:

$1.8966 per 2.20 lb.

The cost per pound of the tomatoes is of:

1.8966/2.20 = $0.86 per lb.

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Answer:

sada

Step-by-step explanation:

Please Add A Picture

Answer: 114

Step-by-step explanation:

firstly, convert meters to centimeters:

2.5m * 100cm in a meter = 250 cm

let the length of the first shelf equal x:

250 = x + (2x + 18) + (x - 12) + (x + 4)

combine like terms:

250 = 5x + ( 18 - 12 + 4) = 5x +10

subtract 10 from both sides:

240 = 5x, then solve for x

240/5 = x

x = 48 cm

the length of the second shelf was 2x + 18, so plug in 48 for x:

2(48) + 18 = 114

Answer:

114 [cm].

Step-by-step explanation:

1) if the length of the 1st shelf is 'x', then

2) the length of the 2d shelf is '2x+18', the 3d shelf is 'x-12' and the 4th shelf is 'x+4';

3) the sum of the all 4 shelves is 250 [cm], then it is possible to make up the equation:

x+(2x+18)+(x-12)+(x+4)=250;

4) the root of the equation above is x=48, then

5) the required length of the 2d shelf is 2*48+18=114 [cm].

The estimates for the number of transistors per IC, using an exponential function, are given as follows:

An exponential function has the general format presented as follows:

[tex]y = ab^\frac{x}{n}[/tex]

In which the parameters of the function are listed as follows:

By Moore's Law, the number of transistors per IC doubles every two years, hence the values of parameters b and n are both two, that is:

b = 2, n = 2.

We take 1972 as the reference year, when the amount was of 4000 transistors per IC, hence the value of parameter a is given as follows:

a = 4000.

Thus the equation is:

[tex]A(t) = 4000(2)^{\frac{t}{2}}[/tex]

Giving the number of transistors per IC in t years after the reference year of 1972.

2016 was 44 years after 1972, hence the estimate for the amount of transistors by IC was of:

[tex]A(44) = 4000(2)^{\frac{44}{2}} = 16,777,216,000[/tex]

2040 will be 68 years after 1972, hence the estimate for the amount of transistors by IC is of:

[tex]A(68) = 4000(2)^{\frac{68}{2}} = 6.87 \times 10^{13}[/tex]

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