Assuming a linear relationship, find the missing value in the table below.

The accumulated interest on the loan given, equals to $778.125.

Also known as compound interest, means the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

Amount payable equals to:

=  P(1+i/100)*n

= $5,000*(1 + 7.5%)^2

= $5,000 * 1.155625

= $5,778.125

The computation of the accumulated Interest goes as:

= Amount payable on loan - Loan Amount

= $5,778.125 - $5,000

= $778.125

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The shortest distance between Caroline's and Mattie's houses is 10 blocks .

In the question ,

it is given that,

Caroline leaves her house and walks 6 blocks ,

let the point where she starts be A , and the point where she ends be B .

So the distance AB = 6 blocks .

then she turns east and heads to 8 blocks to reach Mattie's house ,

let the point where she stops be C ,

So, the distance BC = 8 blocks ,

the shortest distance(AC) between Caroline and Mattie house can be calculated using the Pythagoras Theorem

AB + BC = AC

6 + 8 = AC

AC = 64 + 36

AC = 100

AC = 10

Therefore , The shortest distance between Caroline's and Mattie's houses is 10 blocks .

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The probability of getting 2 the same color is 9/11.

What is probability?

  According to the probability formula, the probability of an event occurring, or P(E), is equal to the proportion of positive outcomes to all outcomes. P(E) is defined mathematically as favorable outcomes divided by total outcomes. Mathematical branch known as probability deals with determining the possibility of an event occurring. Here using probability we can also calculate combination .

Here the total number of marbles are,

=>Total marbles = Blue + Red + Green

=>Total marbles = 5 + 4 + 3

=>Total marbles = 12

Then, Probability of a green = 3/12

=> Probability of not green = 1 - 3/12 = 9/12=3/4

To get exactly one green in two draws, we either get a green, not green, or a not green, green

=>First Draw Green, Second Draw Not Green

=> 1st draw: Probability of a green = 3/12

In 2nd draw: Probability of not green = 9/11 <-- 11 since we did not replace the first marble

To get the probability of the event, since each draw is independent, we multiply both probabilities

=> Probability of the event is (5/12) * (9/11) = 45/132

First Draw Not Green, Second Draw Not Green

=>1st draw: Probability of not a green = 9/12

=>2nd draw: Probability of not green = 7/11 <-- 11 since we did not replace the first marble

To get the probability of the event, since each draw is independent, we multiply both probabilities

=>Probability of the event is (9/12) * (7/11) = 63/132

To get the probability of exactly one green, we add both of the events:

First Draw Green, Second Draw Not Green + First Draw Not Green, Second Draw Not Green

=> 45/132 + 63/132 = 108/132=9/11.

Hence the probability of getting 2 the same color is 9/11.

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Answer:

21.7 mi/hr

Step-by-step explanation:

Weight of the bear is irrelevant

Unit rate = 65.1 mi / 3 hr =   21.7 mi /hr

Answer:

(d) 22

Step-by-step explanation:

1 to 4 difference is 3

4 to 10 difference is 6

10 to 22 difference is 12

22 to 46 difference is 24

46 to 94 difference is 48

so, you can see that the difference multiplies by 2 (3x2 = 6, 6x2 = 12, etc.)

thus the answer is d. 22

Answer:

x = 80

Step-by-step explanation:

This shape is a pentagon, and all of the angles in a pentagon always add up to 540. So, using this, we can create an equation, 3x + 300 = 540. we can then use the reverse order of operations to solve this, first subtracting 300 from both sides. this gets us the equation 3x = 240. We then divide 3 from both sides to get x alone and get x = 80.

Answer:

  x = 80°

Step-by-step explanation:

You want the value of x given a pentagon with two angles marked with expressions in x.

The sum of interior angles in an n-gon is 180° × (n -2). For the 5-sided figure shown, the sum of angles is 180° × 3 = 540°.

Using this value, we have ...

  (x +40°) +125° +(x +5°) +(x +50°) +80° = 540°

  3x +300° = 540° . . . . . . simplify

  x +100° = 180° . . . . . . . divide by 3

  x = 80° . . . . . . . . . . . . subtract 100°

The value of x is 80°.

Alex uses the Pythagorean distance method to calculate the distance between his home and his friend's home.

5² (a) + 3² (β). Can use any other formulas

Given

After leaving his house, Alex drives five miles to the east to reach the library. He leaves the library and drives three miles to a friend's home in the north.

Home would be, followed by the library and the homes of your friends.

By the Pythagoras theorem, we now have points a, b, and c.

House a2 plus library b2 equals friend's house c2.

He must utilize this formula to resolve the issue. √5² + 3².

√5² + 3².

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Answer:

x^2 - 9x + 18 = 0

Step-by-step explanation:

(x-3)(x-6) = 0

x^2 -6x - 3x + 18 = 0

x^2 - 9x + 18 = 0

Answer:

x² - 9x + 18 = 0

Step-by-step explanation:

given a quadratic with roots x = a and x = b then the factors are

(x - a) and (x - b) and the equation is the product of the factors

here roots are x = 3 and x = 6 then the factors are (x - 3) and (x - 6), then

(x - 3)(x - 6) = 0 ← expand factors using FOIL

x² - 9x + 18 = 0

According to the information, it can be established that both divers will be at 181.5 feet then after 9,075 minutes.

To find the time it took for both divers to be at the same depth, we must take into account the information provided by the question.

To solve this problem we must use the following mathematical operations. We must first find the time it takes for diver A to be at 181.5 ft.

20 * 9.075 = 181.5ft

Second, we must find the time it takes for diver B to be at the same depth.

As shown above, both divers are at 181.5 feet after 9,075 minutes.

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By using the distance formula, we can see that Luna's time in minutes is 120 minutes.

We know that she went a distance of 10 miles at a rate of 5 miles per hour.

Remember the linear relation:

distance = rate*time

Then if we define t as the time:

10 mi = (5mi/h)*t

(10 mi)/(5mi/h) = t

2 h = t

And we want the time in minutes, remember that:

1 hour = 60 min

Then:

2 hours = 2*(60 min) = 120 min

The correct option is the first one.

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The equation which is useful to find "n" number of weeks to reach our goal is 35n + 100 = 800.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

As per the given table,

Amount of money in 0 weeks = $100

Amount of money in 1st week = $135

In 2nd week = $170, in 3rd week = $205

So there is a $35 increment each week.

Let's say it takes "n" number of weeks to reach the goal.

So, 35n + 100 = 800

Hence the answer is The equation which is useful to find "n" number of weeks to reach our goal is 35n + 100 = 800".

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The answer is;

62.83

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now,

The first 6 prime numbers are  2, 3, 5, 7, 11 ,13

The square of 6 prime number

4, 9 ,25, 49 , 121 , 169

The mean difference of these number is

⇒ (4 + 9 + 25 + 49 + 121 + 169) / 6

⇒ 62.83

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Answer: 373 children and 213 adults

Step-by-step explanation:

Children can be represented by x and adults can be represented by y.

x+y=586

1.75x+2y= $1078.75

x=586-y <-- substitute into 1.75x+2y=1078.75.

1.75(586-y) +2y=1078.75

1025.5 - 1.75y+2y =1078.75

0.25y = 53.25

y=213 adults

x + 213 = 586

x= 373 children

Check:

1.75(373) +2(213)=1078.75

1078.75=1078.75

Option 3. The table that represents a direct variation function is Input x 4 6 8 Output y 6 9 12

Y = kx, where k is the constant proportionality, is the form of the direct variation equation. It is a two-variable linear equation. The direct variation graph is a straight line in a coordinate plane. The ratio of two directly varying quantities is a constant.

Y = kx is the given formula.

at that location,

y = 6

x = 4 as its value

It would provide us with

6 = 4k

4 divided

6 / 4 = 1.5

1.5 x 6 = 9

1.5 x 8 = 12

Thus, the third selection.

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Answer:

10/12

Step-by-step explanation:

36 divided by 3 is 12 so you would have to divide 30 by 3 to make it equivalent and you would get 10/12.

Hope this helped!

The range of a list or set is the difference between the smallest and largest numbers. To find the range, arrange all of the numbers in ascending order. Subtract (deduct) the lowest number from the highest. The answer provides the list's range.

The median is discovered by sorting all data points and selecting the one in the middle (or if there are two middle numbers, taking the mean of those two numbers)

In two simple steps, you can calculate the mean or average of a data set: Add up all of the values to find the sum. Subtract the sum from the total number of values in the data set.

The mode, median, and mean are the three main measures of central tendency. Each of these measures describes a different indication of the distribution's typical or central value.

The mean (average) and the median are the two most commonly used measures of the data's "center."

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Answer:

16

Step-by-step explanation:

(n-2)*180=total of the interior angles

(n-2)*180=157.5n

180n-360=157.5n

22.5n-360=0

22.5n=360

n=16

Answer:

to me it look like a reflection

Step-by-step explanation:

note in photo

In order to get a B in my class, I will need at least 230 points

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

But there's a direct way of doing that which is simply subtracting what we have from the total to get what is left.

The points needed = Total points required - points gotten.

Points needed = 350 - 120

Points needed = 230

I will need 230 points

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The relationship between the variables c and b is c = [tex]\frac{50}{3}b[/tex]

A variation is a relation between a set of values of one variable and a set of values of other variables. Direct variation. In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.

if c ∝ b

Then,

c = kb where k is a constant

When c = 50, b = 3

substituting into the equation above,

50 = 3k

k = 50/3

substitute k into the equation

c = [tex]\frac{50}{3}b[/tex]

In conclusion c is related to b by the equation c = [tex]\frac{50}{3}b[/tex]

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The greatest common factor of 96 and 144 is 48

Information given in the question

144

96

Greatest common factor can be found by listing the factors of the numbers required and choosing the common factors, the biggest number among them is the greatest common factor

listing the factors

144 =  1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.

96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96

the common factors = 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48,

the greatest among the factors is 48

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Answer:

$19.43

Step-by-step explanation:

when 5.5 pounds cost $14.74 then 1 pound costs $2.68

because 14.74 divided by 5.5 equals 2.68

To calculate the price of 7.25 you multiply the price for 1 pund by 7.25

7.25 * 2.68 = 19.43

The new length of the unstretched hanging-spring is 70 cm.

Hooke's law states that the spring's length change as a result of a compressive or tensile load is directly proportionate to the size of the force placed on the spring. Mathematically,

F = kx

Where;

K is the spring constant, while x represents the spring's length change.

As per the question-

L is the spring's uncompressed length: L = 0.5 m

Weight F1 linked to the spring: F1 = 100 N

First weight's effect on elongation x1: 60 - 50 = 10 = .01 m.

As per the Hooke's law;

F1 = Kx1

K = F1/X1

K = 100 / 0.1

K = 1000 N/m

Spring constant = 1000 N/m.

For the added 100-N block.

F = Kx2

x2 = F/K

x2 = 100 + 100 / 1000

x2 = 0.2m

x2 = 20 cm

L = 50 + 20 = 70 cm.

Thus, new length of the unstretched hanging-spring is 70 cm.

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y=2/3x+7 is equation in slope-intercept form of the line that passes through (6, 11). and (2, 25/3). ​

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given two points are (6, 11) and (2, 25/3). ​

m=25/3-11/2-6

=-8/3/-4

=8/12=2/3

Now we have to find y intercept by considering (6,11)

y=2/3x+c

11=2/3(6)+c

11=4+c

11-4=c

7=c

The slope intercept form of line is y=2/3x+7

Hence y=2/3x+7 is equation in slope-intercept form of the line that passes through (6, 11). and (2, 25/3). ​

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The ordered pair which is closest to a local minimum of the function f(x) is (2,0)

Given that,

A 6-row, 2-column table. The items in the first column, x, are negative 2, negative 1, 0, 1, and 3. The second column, f of x, contains the values -8, -3, -4, 1, 3 in the entries.

The system shows a table with values of x and its correspondent in a function f(x):

x        f(x)

2        -8

-1        -3

0        -3

1          4

2         1

3         3

f(x) is a local minimum of the function at x =2 and y=0 and the value of the function f(x) is -8. So, the ordered pair that lies closest to the function f(x)'s minimum is (2,0)

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The probability of the complement of this event occurring is  5/6.

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.

Sample space: {1,2,3,4,5,6}

Total number of outcomes=6

Complement of an Event: All outcomes that are NOT the event

In this case:

So, possible outcomes in the complement event:{1,2,4,5,6}

Number of possible outcomes=5

Formula:

Probability = (Number of possible outcomes)/(Total number of outcomes)

                  = 5/6

So, the probability of the complement of this event occurring is  5/6.

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The time it will take to fill the pool if the patch is off while Donnie is filling it, found using the combined filling rate is 6 days.

A flow rate is the fluid volume that passes a specified area within a unit of time.

The number days it takes to fill the pool = 2 days

The number of days it takes for the pool to drain = 3 days

The rate at which the pool fills = [tex]\dfrac{1}{2}[/tex] per day

The rate at which the pool drains = [tex]\dfrac{1}{3}[/tex] per day

The number of days it will take the pool to fill while the patch is off is found from the combined filling rate as follows;

The combined filling rate is [tex]\dfrac{1}{2} -\dfrac{1}{3} = \dfrac{3-2}{6} = \dfrac{1}{6}[/tex]

The combined filling rate can be taken as a combined flow rate.

The combined filling rate for filling the pool while the patch is off is [tex]\dfrac{1}{6}[/tex], which is a 6th of the pool is filled per day, therefore, it takes 6 days to fill the pool while the patch is off.

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Answer:

a) Slave labor was needed for the economy.

Step-by-step explanation:

Slave labor was needed for the economy of the southern states during the early 1800’s. Hence, the option (a) is correct.

Answer:

Step-by-step explanation: