if after 40 month amount of 2375 is received by 15/2% interest rate, how much is principal ?​

Based on the information given the variance of their​ weights is 119.9200 kg².

What is variance?

The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other. This symbol is frequently used to represent variation: σ².

Main body:

n=sample size=10

Standard deviation=10.9508 kg

Using this formula

Variance=(Standard deviation)²

Let plug in the formula

Variance=(10.9508 kg)²

Variance= 119.9200 kg²

Hence the variance of their​ weights is 119.9200 kg².

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Solution to the fraction  (-7 + 3) x 3² + ⅖ x (-1.1 - 3.9) = -38

Fractions are expressed in mathematics as a number value that defines a part of a whole or group of objects

To simplify the fraction into a simple form the following steps are followed;

Evaluate (-7 + 3) x 3² + ⅖ x (-1.1 - 3.9)

(-7 + 3) x 9 + ⅖ x (-1.1 - 3.9)

Add the numbers

(-4) x 9 + ⅖ x (-1.1 - 3.9)

Evaluate the exponent

(-4) x 9 + ⅖ x (-5)

Multiply the number

-36 + ⅖ x (-5)

-36 -10/5

Subtract the number from each other

-36 -10/5

=-36-2

Answer = -38

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The probability that the selections are both boys is 7/10

The given parameters in the question are

Seventh grade

Boys = 7

Girls = 3

Eight grade

Boys = 4

Girls = 4

The probability of selecting a boy is calculated as

P(Boy) = Number of boys/Number of students

So, we  have

Seventh grade

Boys = 7

Girls = 3

P(boy) = 7/10

Eight grade

Boys = 4

Girls = 4

P(boy) = 4/8

The probability that the selections are both boys is

P = P(boy) * P(boy)

So, we have

P = 7/10 * 4/8

Evaluate

P = 7/20

Hence, the probability is 7/20

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The answer to the questions from 4 through 12 are below:

4. z³ + 5z + 3z² + 1 - 4 - 2z²

= z³ + 5z² + 5z + - 3

5. Perimeter of the square = Addition of all the sides

= (2d - 3) + (3c) + (2d - 3) + (3c)

= 2d - 3 + 3c + 2d - 3 + 3c

= 4d + 6c - 6

6. Perimeter of the triangle = Addition of all the sides

= (4a - 2b) + (9a - 4) + (7a + 3)

= 4a - 2b + 9a - 4 + 7a + 3

= 20a - 2b - 1

7. Perimeter of a square = 4 × side length

= 4 × 10x

= 40x

8. Perimeter of a rectangle = 2(length + width)

= 2{(2x + 7) + (3x + 8y)}

= 2(2x + 7 + 3x + 8y)

= 2(5x + 8y + 7)

= 10x + 16y + 14

Simplify the following

9. 3a + a² + 5(a - 2)

= 3a + a² + 5a - 10

= a² + 8a - 10

10. 8(v + w) + 7(v + 2w)

= 8v + 8w + 7v + 14w

= 15v + 22w

11. 4c² + 6(c + c²) - 2c

= 4c² + 6c + 6c² - 2c

= 10c² + 4c

12. z³ + 5(z + 3) + 4(2 - 2z²)

= z³ + 5z + 15 + 8 - 8z²

= z³ - 8z² + 5z + 23

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The proportional equation between y and x^2 is:

y = 3*x^2

We know that y is directly proportional to x^2, then we can write:

y = k*x^2

Where k is the constant of proportionality.

We also know that when x = 10, the value of y is 300, replacing that in the above equation we get:

300 = k*(10)^2

Now we can solve this for k:

300 = k*100

300/100 = k

3 = k

Then the equation is:

y = 3*x^2

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The number of adult tickets were sold is 130 tickets.

Given,

In the question:

Total tickets were sold for the school play is 390 tickets.

The number of student tickets sold was two times number of adult tickets sold.

To find the how many adult tickets were sold?

Now, According to the question:

Based on the given conditions:

Let the number of adult tickets be x.

Formulate the condition:

x × (1 + 2) = 390

x × 3 = 390

Simplify

x = 390/3

x = 130

Hence, The number of adult tickets were sold is 130 tickets.

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Answer:

-5/4

Step-by-step explanation:

slope

[tex]\frac{y2-y1}{x2-x1}\\\\ \frac{2-(-3)}{-4-0}=\frac{5}{-4}\\ \\slope = \frac{-5}{4}[/tex]

The answer to the inequality is  -55 < 49. That is -55 is less than 49.

What is inequality?

This refers to the relationship between two values that are not equal. It can be represented with the following symbols; < less than,> greater than, ≥ greater than or equal to,≤ less than or equal to, and  ≠ not equal to.

The given equation States that;

5(11 − ) < + 49

5*11- < +  49

-55  < +49

Therefore, -55 is less than 49.

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how long does it take Peter to clean a room by himself is[tex]t = \frac{95+-5\sqrt{493} }{2}[/tex]
What does "rate" mean mathematically?

A rate is a unique ratio where the two words are expressed in several units.

Let Peter take time to clean 1 room be = t
Let Parker take time to clean 1 room be = t+15
Total Time taken by both to clean to room T= 110
Equation for total time taken to clean 2 room by both
[tex]\frac{1}{t} +\frac{1}{t+15} =\frac{2}{T}[/tex]

[tex]\frac{1}{t} +\frac{1}{t+15} =\frac{2}{110}[/tex]
By taking LCM

[tex]\frac{2t+15}{t^{2}+15} =\frac{1}{55}[/tex]
By cross multiplication in above equation

[tex]110t+825=t^{2} +15t[/tex]
[tex]t^{2}-95t-825=0[/tex]

Hence the answer is   [tex]t = \frac{95+-5\sqrt{493} }{2}[/tex]

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Answer:

C

Step-by-step explanation:

6/9 simplified is 2/3

Hope this helps

Dilation entails altering a figure's size.

Because the is larger than, Isaiah's assertion is untrue.

Although dilation is not a hard transformation, the angles of the figures it dilates remain unchanged.

The aforementioned claim suggests that,

The dimensions of and should be equal.

However, it is evident that;

are not equivalent.

In reality

greater than

Therefore, Isaiah's assertion is false.

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The equation of the linear function is y=8x+(-8).

What do you mean by equation?

A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation. Take the example of 3x + 5 = 15. Equations can be of several sorts, including linear, quadratic, cubic, and others.

According to data in the given question,

We have points (0,-8) and (1,0), thus

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\=\frac{(0-(-8))}{1-0} \\=8[/tex]

Then

y=8x+b

Points (0,-8) means that when x=0, y=-8 and we use this to find b,

y=8x+b

-8=8(0)+b

-8=0+b

b=-8

So, y=8x+(-8)

Therefore, the equation of the linear function is y=8x+(-8).

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5 is the difference between the two numbers 12 and 7.

Given,

In the question;

The difference between 3 times a number and 7 is 5.

Write and solve an equation to determine the number.

Now, According to the question:

Let's assume the unknown number to be x,

so three time the number would be 3x.

The difference between 3 times a number (3x) with 7 is 5, so we can write it as:

3x - 7 = 5

Now we can solve this equation to the find x (the unknown number).

3x = 5 + 7

3x = 12

x = 12/3

x = 4

Therefore 3x= 12

So, 5 is the difference between the two numbers 12 and 7.

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Answer:

[tex]\frac{11}{221}\approx{0.0498}\approx{4.98\%}[/tex]

Step-by-step explanation:

Two cards are drawn randomly from a well-shuffled deck of cards without replacement. Find the probability of getting both face cards in succession.

In a deck of 52 cards, there are three face cards (J, Q, and K) in each of four suits (clubs, diamonds, hearts, and spades). That means there are 12 face cards in total (J♣, Q♣, K♣, J♦, Q♦, K♦, J♥, Q♥, K♥, J♠, Q♠, K♠).

The probability of drawing a face card the first time, then, is 12 out of 52.

There is now one less face card in the deck, as well as one less card in the deck. Therefore, the probability of drawing a face card a second time is 11 out of 51.

The probability, then, of drawing two face cards in succession is:

[tex]\frac{12}{52}\times{\frac{11}{51}}=\frac{132}{2652}=\frac{11}{221}\approx{0.0498}\approx{4.98\%}[/tex]

Answer:

521 mm2

Step-by-step explanation:

Formulas:

area of circle= 3.14 x radius x radius

area of semicircle = 0.5 x 3.14 x radius x radius

diameter of circle= 20mm

radius=0.5x20mm=10mm

area of trapezium= 0.5 x (base+base) x height

Working:

area of semicircle= 0.5 x 3.14 x 10mm x 10mm = 157mm2

area of trapezium = 0.5 x (20mm+32mm) x 14mm = 364mm2

total area of figure= 157mm2 + 364mm2 =521mm2

Based on the given equation and the given value of (), the value of 5() from the equation is 490

If

() = 94 + 2 + 2

The equation can be solved by substituting the value of () into 5()

Substituting is the method of inserting the known value of a variable into an equation to solve for the value of the equation.

Then,

(5)()

= 5(94 + 2 + 2)

= 5(98)

= 490

So therefore, the value of 5() is given by 490.

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Answer:

E and X

Step-by-step explanation:

look for the 6 then behind it

Answer:

X and E

Step-by-step explanation:

"axes" is the plural of axis. The x-axis is the flat line marked with numbers and arrows at the ends. Its labelled x on the right side.

The y-axis is the up-and-down line marked with numbers and arrows at the ends, labelled y at the top.

The origin is where the two axes cross.

Points J, E, X and P are all on the axes. But X and E are 5 units from the origin (where the lines cross) J and P are 9 units from the origin.

2, 6 and 10 were labelled on the axes, but each tick mark is an evenly spaced amount. So the 5 was unlabelled, but it is understood to be 5. See image.

Answer:

x-int=-40

y-int=15

Step-by-step explanation:

we have points 0,15 and -40,0 on the line.

It is as easy as the y-int being 15 and the x-int being -40!

the y-int will always be= (0,#)

the x-int will always be (#,0)

The distance of all the side of ΔABC and ΔA'B'C' are equal which makes them congruent triangles.

What is congruent triangles?

When all 3 corresponding sides and every one 3 corresponding angles area unit equal in size, 2 triangles area unit aforementioned to be congruent.

Main Body:

First let us find the co-ordinates of both the triangles.

A= (3,5)

B = (-2, 3)

C= (-4,-1)

A' =(10,-5)

B'= (5, -3)

C' =(3,1)

Distance between two points =  d=√((x₂ – x₁)² + (y₂ – y₁)²).

In ΔABC

Distance of side AB =  √((3 –(-2) )² + (5 –3 )²)

                                 = √5² +2²

                                 = √29

Distance of side BC = √((-2-(-4) )²+ (3 -(-1 )²)

                                 = √20

Distance of side CA = √((3-(-4) )² + (5-(-1) )²)

                                 = √7² + 6²

                                 = √85

Distance of side A'B' = √((10 -5)² + (-5-(-3))²

                                   = √(5² +2²)

                                   = √29

Distance of side B'C' = √ ((5-3)² + (-3 -1)² )

                                  = √ (2)² +4²

                                  = √20

Distance of side C'A' = √((10-3)² + ( -5-1)²)\

                                   = √(7)² + 6²

                                   = √85

This shows each side of ΔABC is equal to side of ΔA'B'C'.

hence the triangles are congruent.

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The required change in height of the missile is 16100 feet.

Given that,
A missile was fired from a submarine from 200 feet below sea level. If the missile reached a height of 15900 feet before exploding, the change in the altitude of the missile is to be determined.

Change in defined as when the object is in one state but after a certain period of time, the state of the object changes is called change of the state.

here,
The height attained by the missile above sea level is 15900 feet.
The height attained by the missile below the seal level is 200 feet.
Change in height = 15900- (-200) = 15900 + 200 = 16100.

Thus, the required a change in height of the missile is 16100 feet.

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The equations that represent the proportional relationships between the variables are as follows:

     Problem                   Variables to use          Equation

1. Tyler swimming         Time / Distance          D = 1.25t

2. Factory production   Total quantity, Q,         Q = 3s + 8p

                                      and Sparkling / Plain

3. Paint mixture            Blue / White Paints  6q = 1.5b + 5w

An equation models a mathematical statement in which two or more expressions (involving numbers, variables, and operands combined) are equated using the equation symbol (=).

Speed = 5 m/4s

= 1.25 m/s (5/4)

Swimming equation: D = 1.25t

Where D = distance and t = time spent.

Given the speed and time, we can find the swimming distance covered by Tyler.

Bottles of sparkling water = 3

Bottles of plain water = 8

Ratio = 3:8

Production equation, Q = 3s + 8p

Where Q = total quantity, s = sparkling water, and p = plain water

Blue paint = 1 ½ quarts

White paint = 5 quarts

Ratio = 1.5:5

Production equation, 6q = 1.5b + 5w

Where 6q = 6 quarts, b = blue paint, and w = white paint

Thus, using the equations, we can use the known variables to find the unknown variables.

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The total change in yards where the team started is 3x

The given parameters in the question are:

Yards per play = unknown

Number of plays = 3 consecutive plays

Represent the yards per play with x

So, we have

Yards per play = x

The total change in yards is the amount of yard per play multiplied by the number of plays

This is represented as

Total change = Yards per play * Number of plays

Substitute the known values in the above equation So, we have the following equation

Total change = x * 3

Evaluate

Total change = 3x

Hence, the total change is 36 yards

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Answer: Yes

Step-by-step explanation:

Because if you keep going it will reach 86, since it's added by 4, so 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86.

The addition of w, 9 and 4 is (w+13).

According to the question,

We have the following information:

We need to add w, 9 and 4.

We already know that a variable can only be added or subtracted from the terms having the same variables. For example, 8x can only be added to 5x but not 5y.

So, in this case, w is the variable and it can not be added to any other term because the other two are whole numbers.

Now, the whole numbers can be easily added.

So, we have the following expression:

w+9+4

w+13

Hence, the addition of w, 9 and 4 is (w+13).

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Answer:

B; 14 cents/1 ounce

Step-by-step explanation:

So you were given the information that there is 140 cents per 10 ounces. Now, we have to get that into a unit rate, which is a number over 1. It would have to be B because the info. was cents/ounces and typically money is over amount.

So you do 140/10

That equals out to 14/1

So it is 14 cents/1 ounce.

Hope this helps!!! :)