find the average of the numbers 11, 20, 13, and 16

Answer:

72

Step-by-step explanation:

Given that the second term of the sequence is 5, and that we are to multiply the previous term by 3 and subtract 4, we can use that as a recursive formula to find the other terms of the sequence.

The first term of the sequence is:

5*3-4 = 11

The third term of the sequence is:

53-4=11

113-4=29

The fourth term of the sequence is:

53-4=11

113-4=29

29*3-4=83

The difference between the first and fourth terms of the sequence is:

83-11 = 72

So the difference between the first and fourth terms of the sequence is 72.

Answer:

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The distance is 710000 km and the first spaceship has travelled 110000 km in the first hour.

The remainder of the distance is reducing by:

Time to travel before they meet:

Add the first hour to this to get total travel time of 4 hours.

Answer:

the answer is 0

Step-by-step explanation:

because the question you asked has no digits other than 0

Hope it helps.

If you have any query, feel free to ask.

Answer:

-1 ≤ x ≤ 5

Step-by-step explanation:

-1 ≤ x ≤ 5 is the answer

The value of x that is not in the domain of the function is given as follows:

x = -2.

The domain of a function is the set that contains all the possible input values for the function.

The function in this problem is defined as follows:

H(x) = (x + 2)/(x² + 4x + 4).

The function is a fractional function, meaning that the denominator cannot assume a value of zero.

Hence the values of x that are not in the domain of the function are obtained as follows:

x² + 4x + 4 = 0

(x + 2)² = 0

x + 2 = 0

x = -2.

Hence the value of x = -2 does not belong to the domain of the function H(x), as it would make the denominator assume a value of zero.

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Answer:

m∠10 = 41°

Step-by-step explanation:

If ∠9 and ∠10 are complementary. Then ∠7 and ∠8 are complementary as well. Complementary angles meameansns they sum up to 90 degrees.

m∠7 + m∠8 = 90

m∠7 + 41 = 90

m∠7 = 90 - 41 = 49°

Given that m∠7 ≅ m∠9. So m∠9 = 49° and m∠10 = 41°.

1234 in. set A and 1234 in set B and 1234 in set C so the answer is (1234)

The value of the set ( A ∩ C )' = A' ∪ C' = { 4 , 5 , 6 , 7 , 8 }

The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.

Given data ,

Let the universal set be represented as U

The value of U = { 1, 2, 3, 4, 5, 6, 7, 8 }

Let the value of set A = { 1 , 2 , 3 , 4 }

Let the value of set C = { 1 , 2 , 3 , 6 , 8 }

Now , the equation of set is  ( A ∩ C )'

The value of ( A ∩ C )' = A' ∪ C'

Substituting the values in the equation , we get

A' = U - A

A' = { 1, 2, 3, 4, 5, 6, 7, 8 } - { 1 , 2 , 3 , 4 }

A' = { 5 , 6 , 7 , 8 }

And ,

C' = U - C

C' = { 1, 2, 3, 4, 5, 6, 7, 8 } - { 1 , 2 , 3 , 6 , 8 }

C' = { 4 , 5 , 7 }

So , ( A ∩ C )' = A' ∪ C'

Substituting the values in the equation , we get

( A ∩ C )' = { 4 , 5 , 6 , 7 , 8 }

Hence , the set ( A ∩ C )' is { 4 , 5 , 6 , 7 , 8 }

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The amount invested in the two different bank accounts which has a simple interest of $ 560 is $ 2000 and $ 4000 respectively

Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.

Simple Interest = ( Principal Amount x Rate x Time Period ) / 100

Given data ,

Let the simple interest be represented as SI

The value of SI = $ 560

Now , the total amount A = $ 6000

Let the first bank account be A

Let the second bank account be B

The amount invested in the bank account A be = P

The amount invested in the bank account B be = ( 6000 - P )

The rate of interest of bank account A = 8 %

The rate of interest of bank account B = 10 %

Now ,

The SI of bank account A = ( Principal Amount x Rate x Time Period ) / 100

Substituting the values in the equation , we get

The SI of bank account A = ( P x 8 x 1 ) / 100

The SI of bank account A = 8P/100

And ,

The SI of bank account A = ( Principal Amount x Rate x Time Period ) / 100

Substituting the values in the equation , we get

The SI of bank account A = [ ( 6000 - P ) x 10 x 1 ] / 100

The SI of bank account A = ( 60000 - 10P ) /100

And , the total SI = $ 560

So ,

8P/100 +  ( 60000 - 10P ) /100 = 560

Multiply by 100 on both sides of the equation , we get

8P + 60000 - 10P = 56000

On simplifying the equation , we get

-2P = -4000

Divide by -2 on both sides of the equation , we get

P = $ 4000

So , the amount invested in bank account A = $ 4000

And , the amount invested in bank account B = $ 2000

Hence , the amount invested is $ 4000 and $ 2000 respectively

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Answer:(1,0) which is the second one in the picture

Step-by-step explanation:The vertex is in (1,0).

If Mrs. Sharma spends 17/25 parts of her earnings on her children's education, then she is spending (17/25) x 100 = 68% of her earnings on her children's education.

If the number of children is the same, she spends 68%/number of children on her daughter education.

If she spends 68% of her earnings on her children's education, then she is saving 100 - 68 = 32% of her earnings.

So, she spends 68% on her daughter education and she saves 32% of her earning.

Answer:

The compound interest formula is A = P(1 + r/n)^(nt) where A is the final amount, P is the principal (initial deposit), r is the annual interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = 2750, r = 0.035, n = 4 (because interest is compounded quarterly) and t = 7 (because we are trying to find the balance after 7 years).

So the formula becomes:

A = 2750(1 + 0.035/4)^(4*7)

By plugging the number into the formula we can find the final amount after 7 years

A = $3,974.23

So the amount of money in the account at the end of 7 years is $3,974.23, rounded to the nearest hundredth.

Answer:

Step-by-step explanation:

Answer:

The Graph is Below

Step-by-step explanation:

Explanation:

The TI-84 calculator is fairly powerful and can handle things like this, but it's not needed to be honest. Any calculator will do.

"csc" is shorthand for "cosecant". It's the reciprocal of sine.

csc = 1/sin

Recall that

sin = opposite/hypotenuse

which means

csc = 1/sin = hypotenuse/opposite

What we'll need are the hypotenuse and opposite sides. Plot the points (0,0) and (-20,21). Draw a segment between them. This forms the hypotenuse of the right triangle shown below. This triangle is in the quadrant Q2 in the upper left corner. The hypotenuse 29 is found using the pythagorean theorem a^2+b^2 = c^2.

Use a = 20 and b = 21 to find c = 29.

According to that diagram, we can then say:

csc = hypotenuse/opposite = 29/21

[tex]\cfrac{1}{4}x+1=32\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4\left( \cfrac{1}{4}x+1 \right)=4(32)}\implies x+4=128\implies x=124[/tex]

The exponential equation that models the function of Maureen's car is 26,525 (0.92)

a = 26,525 and b = 0.92

Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of  3 main parts

a = the starting value

b = the base function

x = the exponents

Considering the problem,

the starting = $26,525

the base = depreciation

the exponents = x

A year ago hence x = 1

$24,403 = $26,525(b)¹

b = 24,403 / 26,525

b = 0.92

hence we can say that a = 26,525 and b = 0.92

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The numerator of the rational expression will be 6.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 1 / b + 5 / b = x / b.

The expression will be solved as below,

E = (1/b) + (5/b)

E = ( 1 + 5 ) / b

E = 6 / b

Hence, the numerator will be equal to 6.

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Answer:

In order to find the values of k and m in a parallelogram, you would need to have additional information such as the coordinates of the points that make up the parallelogram and the formulas or equations that relate k and m to these points.

Here is one way to find the values of k and m in a parallelogram:

Label the four vertices of the parallelogram as A, B, C, and D with the opposite sides parallel to each other.

Find the slope of the line segment AB by using the formula (y2-y1)/(x2-x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Let the slope of AB be represented by k.

Find the slope of the line segment AD by using the same formula and let it be represented by m.

The values of k and m are now found.

Please note that, this method is only applicable if the Parallelogram is not degenerate i.e, it is not a rectangle or a line.

It is also important to keep in mind that different formulas or equations may be used depending on the specific context of the problem. It is also important to check that the slopes of opposite sides are equal.

Step-by-step explanation:

Therefore , the solution of the given problem of interest comes out to be

A = $3,130.37  is the amount after 15 years.

Simple interest is calculated by dividing the principal by the borrowing cost, the remaining time, and other elements. The simple return formula in marketing is principal + interest plus hours. Utilizing this method is the simplest way to calculate interest. As a percentage of the principle sum is the most frequent way to calculate income. For instance, he will only pay his portion of the 100% cost if he borrows $100 from a friend and agrees to pay the loan back with 5% interest.. You have to pay interest on money you borrow, and you have to charge interest on money you lend.

Here,

Given :  

a ) the equation that can be formed is

2500x - 1.5y = 30

b)

Using compound formula :

=> Then solve the equation for A

A = P(1 + r/n)nt

A = 2,500.00(1 + 0.015/12)(12)(15)

A = 2,500.00(1 + 0.00125)(180)

A = $3,130.37

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Answer:

Step-by-step explanation:

No, the entire population of Turks and Caicos would not be able to fit on the football field. The total area of the football field is 6,480 square yards, which is equivalent to 13,728 square feet. Since each person takes up 2 square feet, this means that only 6,864 people could fit on the field. Therefore, the population of Turks and Caicos is more than double the amount of people that could fit on the football field.

The value of a is 18.43°

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Given that, cos2a=4/5

cos 2a = 4/5

2a = cos⁻¹(4/5)

2a = 36.86°

a = 18.43°

Hence, the value of a is 18.43°

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The value of angle X Is 85° ( nearest degree)

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

the law of sines is used to solve the triangle, when we know two angles and one side or two angles and one included side. It means that the law of sines can be used when we have ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) criteria.

therefore x/sin X = z/sinZ

89/sinX = 84/sin 70

89sin70 = 84sin X

= 89× 0.94 = 84sinX

=83.66 = 84sin X

sin X = 83.66/84

sinX = 0.996

X = sin^-1 0.996

X = 85° ( nearest degree)

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Answer:

according to BODMAS RULE

first step is to open the bracket , and solve

-82 - 6x - 12=  14x + 2 -6x -12

-82=14x + 2

-84 = 14x

x= -6

Answer:

Step-by-step explanation:

The number 11 belongs to the set of natural numbers. Natural numbers are the set of all positive whole numbers, including 0, and the number 11 is a positive whole number.

Answer: the estimated maintenance cost of cars when the age of cars is 12 years is 16.5 ( in 100 birr)

Step-by-step explanation:

To obtain the regression equation for costs related to age of cars, we can use the method of least squares. This method involves finding the line of best fit that minimizes the sum of the squared differences between the predicted values and the actual values.

The equation for a linear regression line is:

y = a + bx

where a is the y-intercept and b is the slope of the line.

To find the slope of the line (b), we can use the formula:

b = (n(∑xy) - (∑x)(∑y)) / (n(∑x^2) - (∑x)^2)

To find the y-intercept (a), we can use the formula:

a = (∑y - b(∑x)) / n

Given the data provided, we can calculate the following values:

∑x = 142

∑y = 150

∑xy = 2430

∑x^2 = 10304

n = 8

By substituting these values into the formulas for b and a, we can find the slope and y-intercept of the line:

b = (8(2430) - 142(150)) / (8(10304) - 142^2) = 0.5

a = (150 - 0.5(142)) / 8 = 13.5

Therefore, the regression equation for the costs related to age of cars is:

y = 13.5 + 0.5x

To estimate the maintenance cost of cars when the age of cars is 12 years, we can substitute x = 12 into the equation and solve for y:

y = 13.5 + 0.5(12) = 16.5

So the estimated maintenance cost of cars when the age of cars is 12 years is 16.5 ( in 100 birr)

No, 4 hundreds is not 10 times as much as 4 thousandths.

Numbers in the tens are numbers that are multiples of 10, such as 10, 20, 30, 40, etc.

4 hundreds is equal to 4 × 100 = 400.

4 thousandths is equal 4/1000 = 0.004

To compare their magnitudes, we can divide 0.4 by 0.004:

400 ÷ 0.004 = 100000

So 4 hundreds (400) is significantly larger than 4 thousandths (0.004).

Therefore, 4 hundreds is 100000 times as much as 4 thousandths.

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The percentage discount that Cyprian was allowed altogether was 8.21%.

The percentage discount is a portion of the sales price that reduces the amount the purchaser or customer pays for their purchase.

Percentages are ratios of a value or variable compared to another or the whole matter.

We express Percentages as the quotients of the division operations multiplied by 100.

In this situation, the overall percentage discount is worked out step by step as follows:

Discount on goods worth Sh. 800 = 11%

= Sh. 88 (Sh. 800 x 11%)

Discount on goods worth Sh. 17,000 = 8.6%

= Sh. 1,462

The total value of goods = Sh. 17,800 (Sh. 800 + Sh. 17,000)

Percentage discount = 8.21% (Sh. 1,462/Sh. 17,800 x 100)

Thus, overall, the total discount based on the full value of goods Cyprian bought was 8.21%.

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each of the lap is of length 6617.6 miles.

What are Distance and velocity?

a velocity is a unit of measurement for the Distance an object travels in a

the predetermined period of time. Here is a word equation that illustrates the

connection between space, speed, and time: velocity is calculated by

dividing the total Distance traveled by the journey time.

Diane and Douglas both drive at an average rate of 50 miles per hour. So if they travel for the same time they will end up covering the same distance as well.

As we know velocity = rate of change of displacement or

She drove a total distance of 86,028.8 yd on a race track.

He drove 13 laps where each lap was the same lefty.

each lap is 86028.8/13 = 6617.6

Hence each of the lap is of length 6617.6 miles.

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