A cylinder has a radius of 10ft and a height of 11.4ft. What is the approximate volume of the cylinder? Use 3.14 for pi.

Answer:

7 + 55\(\sqrt{11}\)

Step-by-step explanation:

term one is 7

so term 2 is 7 + \(\sqrt{11}\)

and term 3 is 7 + 2\(\sqrt{11}\)

common pattern here: 7 + (n-1)\(\sqrt{11}\)

when n = 56

7 + 55\(\sqrt{11}\)

The interest accrued in the first four years is $1.69 and a half years is $0.21.

What is interest rate?

The amount that the lender charges the borrower above and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

Given:

Jeff took out a 15 year unsubsidized loan for $9.800 to attend four years of college.

The rate is 4.3%.

We have to find the interest accrued in the first four-and-a-half years.

First to find the interest for first four years.

p = $9.800,  r  = 4.3% = 0.043,  t = 4

⇒ I = P x r x t

   I = 9.800 x 0.043 x 4

   I = 1.6856

   I = $1.69

Now to find the interest for a half years.

p = $9.800 ,  r = 4.3% = 0.043,  t = 1/2

I = p x r x t

I = 9.800 x 0.043 x 1/2

I = 0.2107

I = $0.21

Hence, the interest accrued in the first four years is $1.69 and a half years is $0.21.

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Answer:

6x2-10x-4

Step-by-step explanation:

hx=(2x-4)(3x+1)

hx=2x(3x+1)-4(3x+1)

hx=6x2+2x-12x-4

hx=6x2-10x-4

The solution to the system of equations using elimination method is:

x = 5 and y = 3

To solve the system of equations by elimination method, we need to eliminate one of the variables by adding or subtracting the two equations.

In this case, we can eliminate y by adding the two equations together:

3x - y + 2x + y = 12 + 13

Simplifying the left side and the right side, we get:

5x = 25

Dividing both sides by 5, we get:

x = 5

Now that we know x, we can substitute it into one of the original equations to find y. Let's use the second equation:

2x + y = 13

2(5) + y = 13

Simplifying, we get:

10 + y = 13

Subtracting 10 from both sides, we get:

y = 3

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The complete question is below:

solve by elimination method

3x - y = 12

2x + y = 13

The height is 114.83 ft and the distance of the ø if someone is observing below is 84.8.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that at a given point of 67.7ft at the ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees.

The base will be calculated as:-

tan(38.6) = P / B

tan(38.6) = 67.7 / B

B = 67.7 / tan(38.6)

B = 54.8 ft

The height will be calculated as:-

Cos(42.4) = B / H

H = 84.8 / Cos(42.4)

H = 114.83 ft

Therefore, If someone were to look down from above, they would be 114.83 feet from the object and 84.8 feet away.

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Answer:

1.4oz

Step-by-step explanation:

You subtract the weight of the box and the bars with the empty box. Then divide the answer you got from that, with 12 and you get your answer.

The weight of each cereal bar is 1.4 oz.

"It is a statement which consists of equal symbol between two mathematical expressions."

For given example,

Let 'x' be the weight of single cereal bar.

A box contains 12 cereal bars.

The empty box weighs 1.75 oz.

The box and the bars weigh 18.55 oz.

This means the the total weight of the box is:

total weight = weight of the empty box + weight of 12 cereal bars

So, we get an equation,

⇒ 18.55 = 1.75 + ('x' × 12)

We solve above equation to find the weight of each cereal bar.

⇒ 18.55 = 1.75 + 12x

⇒ 12x = 16.8

⇒ x = (16.8)/12

⇒ x = 1.4 oz.

Therefore, the weight of each cereal bar is 1.4 oz.

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The correct place to the decimal is after 4 digits, that is 4431.5

Decimals are the numbers, having two parts, a whole number part and a fractional part separated by a point that point is called the decimal. For example, 7.5 is a decimal number.

Given that, Mary says the digits in the quotient of 381.109÷0.86 are 44315.

but she doesn't know where to place the decimal point.

The division is 381.109/0.86

Placing the decimals in numerator and removing from denominator,

Since, in the denominator the decimal is two digits before, so multiply numerator and denominator by 100,

38110.9/86

According to rule, put the decimal point in the answer at the same place it is at in the dividend,

38110.9/86 = 4431.5

Hence, she should put decimal before digit 5.

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Answer:

54 cm

Step-by-step explanation: 1/2b x h

1/2(18) x 6

9 x 6=54

Answer:

30

Step-by-step explanation:

(n+8)=2(7+8)=2(15)=30

Answer:

30

Step-by-step explanation:

9514 1404 393

Answer:

  21.6 years

Step-by-step explanation:

The first statement tells you the account balance can be modeled by ...

  A = 440(2)^(t/8) . . . . . where t is in years

We want to find t when A = 2860

  2860 = 440(2^(t/8))

  6.5 = 2^(t/8) . . . . . . . . . . divide by 440

  log(6.5) = (t/8)log(2) . . . . take logarithms

  t = 8·log(6.5)/log(2) ≈ 21.604 . . . . . . divide by the coefficient of t; evaluate

It would take about 21.6 years for the value to reach $2,860.

Answer:squares area is. 24

Step-by-step explanation:

6×4 = 24

Answer:

That is the simplest answer I'm pretty sure

Step-by-step explanation:

Answer:

it cannot be simplified further

Answer:

Step-by-step explanation:

Answer:

n = 9 / 2 or 4.5

Step-by-step explanation:

2/3 = 3/N

cross multiply

2 x n = 2n

3 x 3 = 9

2n = 9

divided both sides by 2

2n / 2 = 9 / 2

n = 9 / 2

Answer:

The x-coordinate is the solution to x - 4 = 0, which is x = 4 and the y-coordinate is 3 so the answer is (4, 3).

Answer:

74.44

Step-by-step explanation:

\(P(10)=0.018(10)^3-0.294(10)^2+3.065(10)+55.190 \\ \\ =74.44\)

The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

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Answer:

I got 4,000,000 on the calculator

Step-by-step explanation:

Answer:

400,000

Step-by-step explanation:

2 x 5 = 10

10 x 8 = 80

80 x 100 = 8,000

8,000 x 500 = 400,000

Answer:

Step-by-step explanation:

If he earns $48 dollars in 3 hours, you need to divide 48 by 3 to work out how much he makes per hour. and 48/3 = 16. So he makes $16 dollars an hour.

Answer:

16$

Step-by-step explanation:

You would have to divide the number of hours he worked for three days by the days he worked in order to find out what he would earn per hour.

This means the answer is 16 dollars per hour.

The solution to the given inequality in interval notation is: -6 ≤ v ≤ 3

In this exercise, you're required to determine all the values of v that simultaneously satisfy given inequality. First of all, we would have to eliminate the fraction on the left-hand side of the inequality by adding using an appropriate lowest common denominator of 3 as follows:

(2 × |4v + 6|)/3 - 2/1 ≤ 10

[(2 × |4v + 6|) - (3)2]/3 ≤ 10

[(2 × |4v + 6|) - 6]/3 ≤ 10

Cross-multiplying, we have:

(2 × |4v + 6|) - 6 ≤ 10 × 3

(2 × |4v + 6|) - 6 ≤ 30

Adding 6 to both sides, we have:

(2 × |4v + 6|) - 6 + 6 ≤ 30 + 6

(2 × |4v + 6|) ≤ 36

Dividing both sides by 2, we have:

(2 × |4v + 6|)/2 ≤ 36/2

|4v + 6| ≤ 18

Evaluating the absolute value function, we have:

4v + 6 ≤ ±18

For the positive interval, we have:

4v ≤ 18 - 6

4v ≤ 12

v ≤ 12/4

v ≤ 3.

For the negative interval, we have:

4v ≥ -18 - 6

4v ≥ -24

v ≥ -24/4

v ≥ -6

Lastly, we would express the solution as an interval notation as follows:

-6 ≤ v ≤ 3

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Question:

Solution:

Consider the following equation:

To isolate the variable, we must have the variable x on one side of the given equation. To achieve this, we can subtract to both sides of the equation 2x:

this is equivalent to:

this is equivalent to:

then, we can conclude that the correct answer is:

SUBTRACT 2X FROM BOTH SIDES

The obtained answers for the given line segments are as follows:

9. The value of the line segment \(\overline {DE}\) = 43; Where \(\overline { DF}\) = 61 and \(\overline {EF}\)

10. The value of x is 6; Where \(\overline {DE}\) = 4x - 1, \(\overline {EF}\) = 9, and \(\overline { DF}\) = 9x - 22

11. The value of line segment \(\overline {EF}\) = 32; Where  \(\overline { DF}\) = 78, \(\overline {DE}\) = 5x - 9, and \(\overline {EF}\) = 2x + 10

12. The value of line segment \(\overline { DF}\) = 57; Where \(\overline {DE}\)  = 4x + 10 \(\overline {EF}\) = 2x - 1, and \(\overline { DF}\) = 9x - 15.

The calculation for the required values is as follows:

9. Finding \(\overline{DE}\):

It is given that,

\(\overline{DF}\) = 61; \(\overline{EF}\) = 18

From the figure, we can write

\(\overline{DF} = \overline{DE} + \overline{EF}\)

On substituting the given values,

61 = \(\overline{DE}\) + 18

⇒ \(\overline{DE}\) = 61 - 18

∴ \(\overline{DE}\) = 43

10. Finding x:

It is given that,

\(\overline {DE}\) = 4x - 1, \(\overline {EF}\) = 9, and \(\overline { DF}\) = 9x - 22

From the figure we have

\(\overline{DF} = \overline{DE} + \overline{EF}\)

On substituting,

(9x - 22) = (4x - 1) + 9

⇒ 9x - 22 = 4x - 1 + 9

⇒ 9x - 4x = 8 + 22

⇒ 5x = 30

∴ x = 6

11. Finding \(\overline{EF}\):

It is given that,

\(\overline { DF}\) = 78, \(\overline {DE}\) = 5x - 9, and \(\overline {EF}\) = 2x + 10

From the figure we have

\(\overline{DF} = \overline{DE} + \overline{EF}\)

On substituting,

78 = (5x - 9) + (2x + 10)

⇒ 78 = 5x - 9 + 2x + 10

⇒ 7x + 1 = 78

⇒ 7x = 78 - 1

⇒ 7x = 77

∴ x = 11

On substituting x = 11 in \(\overline {EF}\) = 2x + 10; we get

\(\overline {EF}\) = 2(11) + 10

      = 22 + 10

      = 32

Therefore, the value of the line segment \(\overline {EF}\) is 32.

12. Finding \(\overline {DF}\):

It is given that,

\(\overline {DE}\)  = 4x + 10 \(\overline {EF}\) = 2x - 1, and \(\overline { DF}\) = 9x - 15

From the figure we have

\(\overline{DF} = \overline{DE} + \overline{EF}\)

On substituting,

(9x - 15) = (4x + 10) + (2x - 1)

⇒ 9x - 15 = 4x + 10 + 2x - 1

⇒ 9x - 15 = 6x + 9

⇒ 9x - 6x = 9 + 15

⇒ 3x = 24

∴ x = 8

On substituting x = 8 in \(\overline { DF}\) = 9x - 15; we get

\(\overline { DF}\) = 9(8) - 15

      = 72 - 15

      = 57

Therefore, the value of the line segment \(\overline { DF}\) is 57.

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Answer:

4.5 hours

Step-by-step explanation:

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Answer:

Basically You are asking how many hours we need to reach 7:00, if we are at 2:30, so: we need 4hours, to reach 6:30, and and extra 30minutes to reach 7:00pm. The answer is 4hours and 30minutes.

Answer:I’m pretty sure it would be A!

Step-by-step explanation:

Answer:

Should be A

Step-by-step explanation:

But it all depends on the mirror

Answer:

true

Step-by-step explanation:

type 1 and type 2 are not independent of each other - as one increases, the other decreases

The recursive relation of the data distribution a(n) = a ( n - 1 ) x n - ( n - 1 ).

A sequence of values is defined by a mathematical equation termed as a recursive relation, also known as recursive relation. It derives current value(s) through specified initial value(s) and previous value dependent rule(s). In essence, it generates numeric sequences.

Note that every individual unit can be derived by multiplying the preceding one with a rising integer, and subsequently subtracting a descending integer:

1 x 1 - 0 = 1

1 x 2 - 1 = 1

1 x 3 - 2 = 5

5 x 4 - 3 = 17

17 x  5 - 4 = 71

71 x 6 - 5 = 247

We can deduce the relation of a(n) = a ( n - 1 ) x n - ( n - 1 ).

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Answer:

27

Step-by-step explanation:

4^3 is 4*4*4 which is 64

3/4^3 is 3/4*3/4*3/4 which is 27/64

then divide 64 ÷ 27/64

you can cross cancel 64 and get 27.

Answer: 66%

Step-by-step explanation: To convert a fraction to a percentage, divide the top number by the bottom number. For example, \(\frac{1}{4}\) is 25% because if divide them, (1÷4=0.25) then we get 25%. So, for this problem, we solve 2÷3, which equals 0.66, or 66%.

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The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.

To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).

In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.

Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:

2n = 60

Solving this equation, we find:

n = 60/2 = 30

Thus, the value of n is 30.

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