1. An amount ofP200,000is deposited for a period of 8 years. Compute the interest if it was made at a simple interest rate of18%. 2. Calculate the exact interest on an investment ofP2,000for a period from January 30 to September 15,2001 , if the rate of interest is10%. 3. A bank charges12%simple interest on aP300loan. How much will he repay if the loan is paid back in one lump sum after three years? 4. If you borrow money from your friend with simple interest of12%, find the present worth ofP20,000which is due at the end of nine months? 5. An engineer borrowed a sum of money under the following terms: P650,000 if paid in 90 days, orP600,000if paid in 30 days. What is the equivalent annual rate of simple interest? 6. Fifteen million pesos was invested in a software company on June 3,2009, at12%ordinary simple interest rate. Determine the date at which the investment would equal P19.5M. 7. A man invested part ofP20,000at18%and the rest at16%. The annual income from16%investment was P620 less than three times the annual income from18%investment. How much did he invest at18%? 8. What is the present worth ofP54,000due in five years if money is worth11%and is compounded semi - annually? 9. A bank offers1.2%per month. What is the effective interest rate if compounded monthly? 10. A commercial bank charges2%interest per month on the unpaid balance of loans made by its credit card subscribers. It claims that the annual interest applied is 12 (2\%)=24%. Is this true? 11. Compute the number of years whenP2,500is compounded toP5,800if invested at12%compounded quarterly. 12. A nominal interest of3%compounded continuously is given on the account. What is the accumulated amount ofP10,000after 10 years? 13. An amount ofP200,000is deposited for a period of 8 years. Compute the interest if a) it was made18%compounded bi - monthly; b) it was made at18%compounded continuously. 14. Two years ago,Ms.ABCdepositedP30,000in a fund that earns10%interest compounded semi - annually. If another deposit ofP20,000is made today, determine the accumulated amount in the fund after three years. 15. Three years ago, an engineer opened a savings account with an initial deposit of P200,000. He withdrew P50,000 three months later, and another P50,000 six months after the first withdrawal. Last year, he deposited P100,000 and withdrew P150,000 six months later. Find the account balance today if interest is10%compounded quarterly.

Answers

Answer 1

Simple Interest(SI) is calculated as $288,000 where principal is $200,000, interest rate is 18% and type is 8 year.

What is Simple Interest?

The Simple Interest (S.I.) formula is a way to figure out how much interest will pay on a given principle sum of money. It is the cost of borrowing that is computed using the original principle amount alone and a constant interest rate.

Formula of Simple Interest is,

[tex]SI = \frac{P*R*T}{100}\ or\ Simply\ write\ SI = P*R*T[/tex]

[tex]Where, P = Principal,\\R= Rate\ of\ Interest\\T = Time\ Period[/tex]

⇒  [tex]SI = \frac{20000*18*8}{100}\ or\ SI = 200000*0.18*8[/tex]

⇒ [tex]SI = \$\ 288000[/tex]

Simple Interest(SI) is calculated as $288,000 where principal is $200000, interest rate is 18% and type is 8 year.

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Answer 2

1. Simple Interest = 288000

2. Interest = 135

3. Total amount to be paid = $408

4. PV or present value = $18348.62

5. r = 51%

7. Amount invested in 18% is $3,685.714

8. 48 930.00.

9. EAR = 14.4%

10. 26.8% per year

12. ~P13439

13. SI = 288000

15.  the account balance today if interest is 10 % compounded quarterly.

How to calculate Simple interest?

1. Formula of simple interest is,

SI = P*R*T/100 or

Simply write SI = P*R*T

Where,

P = Principal

R = Rate of interest

T = Time period

SI = 20000*18*8/100 or

SI = 200000*0.18*8

SI = 288000

2. Interest = Principal*Interest

             rate*time

Principal = 2000

Interest rate = 10%

Time = January 30, 2001 to September 2001

Interest = 135

(2000*10%*243/360)

Assume 360 days in a year in days counting include the day counting start from and exclude the day counting ends on.

3. Total Interest 3 Years = 300*12%*3 = 108

Total Amount Repaid = 300 + 108 = $408

Total amount to be paid = 300+(300*12%*3)

=$408

4. Given , we need to find the present worth of $20,000 at 12% interest rate per year which is due at the end of 9 months.

Therefore, FV i.e , future value = $20,000

i = rate of interest per year = 12% = 0.12

t or Time =9 months = 9/12 year ( in terms of years)

We know , FV = PV + PV * r * t

=> 20000 = P + P * (0.12) * (9/12)

PV or present value = 18348.62 = $18348.62

5. FV = Principal (1 + rate of interest per period * number of interest period)

Equation-1:

650,000 = Principal (1 + rate of interest per period * 90 days / 360 days)

650,000 = Principal (1 + 0.25 rate of interest per period)

Principal = 650,000 / (1 + 0.25 rate of interest per period)

Equation-2:

600,000 = Principal (1 + rate of interest per period * 30 days / 360 days)

600,000 = Principal (1 + 0.08 rate of interest per period)

Principal = 600,000 / (1 + 0.08 rate of interest per period)

Equating the equations we get:

650,000 / (1 + 0.25r) = 600,000 / (1 + 0.08r)

650,000 (1 + 0.08r) = 600,000 (1 + 0.25r)

650,000 + 52,000r = 600,000 + 150,000r

50,000 = 98,000r

r = 51%

7. Annual return from 18% = 3 * (Annual return from 16%)

Let Investment made in 18% = K

Return from 16% = P620 is less than triple the yearly income from 18%, at P620.

(20,000 - K) * 16% = [3 * (K* 18%)] - 620

3,200 - 0.16K = 0.54 K - 620

2,580 = 0.70 K

K = $3,685.714

So, Amount invested in 18% is $3,685.714

9. EMR = effective monthly rate

EMR = EAR/12

12*EMR = EAR

EAR = 12*EMR

The EMR is given to be 1.2% = 0.012, so the EAR is,

EAR = 12*EMR

EAR = 12*(0.012)

EAR = 0.144

EAR = 14.4%

10. No.

It's [tex]1.02^{12}[/tex] =~ 1.268

26.8% per year

12. [tex]F=A(1+3\%)^{10}[/tex]

A = P10,000

[tex]F=10,000(1+3\%)^{10}[/tex]

~P13439

According to the final value formula of compound interest.

13. Formula of simple interest is,

SI = P*R*T/100 or

Simply write SI = P*R*T

Where,

P = Principal

R = Rate of interest

T = Time period

SI = 20000*18*8/100 or

SI = 200000*0.18*8

SI = 288000

15.

An engineer established a savings account three years ago with a P 200,000 opening deposit.

Three months later, he removed P50,000, and six months after that, P50,000 more.

He made an investment of P100,000 and a withdrawal of P150,000 six months later last year.

If interest is compounded quarterly at 10%, find the amount of the account right now.

The table has been attached.

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1. An Amount OfP200,000is Deposited For A Period Of 8 Years. Compute The Interest If It Was Made At A

Related Questions

Find the image of (3, -6) reflected across the y-axis.

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The image of the point after the reflection is (-3, -6).

How to determine the image of the point

To reflect a point across the y-axis, we simply negate its x-coordinate while keeping the y-coordinate the same.

Thus, the image of point (3, -6) reflected across the y-axis would be (-3, -6).

We can visualize this by drawing a line passing through the point (3, -6) and the y-axis.

The reflection of the point will be at the same distance from the y-axis but on the opposite side.

So, the reflection of the point (3, -6) across the y-axis is (-3, -6).

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Find the x- and y-intercepts of the parabola y=−10x2−16x−5

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The x-intercepts are approximately (-1.08, 0) and (-0.42, 0), and the y-intercept is (0, -5).

To find the x-intercepts of a parabola, we set y = 0 and solve for x. Similarly, to find the y-intercept, we set x = 0 and solve for y.

Setting y = 0 in the given equation, we get,

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jack bought 200 canned drinks to sell at his food and. the profit, y dollars, from the sale of the canned drinks as a function of the number of cans sold, x, is represented by the equation y=1.25x-100. How many cans must jack secc to recoup the cost of buying 200 canned drinks?

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To recoup the cost of buying 200 canned drinks, Jack needs to make a profit of zero, meaning that the revenue from selling the drinks needs to equal the cost of buying them.

Let's start by setting the profit equation equal to zero and solving for x:

0 = 1.25x - 100

1.25x = 100

x = 80

Therefore, Jack needs to sell 80 cans of drinks to recoup the cost of buying 200 canned drinks.

Step-by-step explanation:

express the sum of the angles of this triangle in two different ways ​

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X=60

Step-by-step explanation:

Firstly you must know that a triangle has 180° angle in it's all side.. so in this case you can say x+½x+(1,5)x= 180°

here x equal to 60°

this is a simple way to expres how can find the x angle

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Find the geometric mean of 8 and 32. The geometric mean is _

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Answer:

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Step-by-step explanation:

you add them and divide by how ever many you added

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One positive number is 5 more than another. The sum of their squares is 53. Then the larger number is 8.


Lets take x be the smaller number, then x + 5 = the larger number. Thus, we have the equation:
x2 + (x + 5)2 = 53
By Simplifying the equation, we get: 2x2 + 10x + 25 = 53
By Solving this quadratic equation, we get x = 3 and the larger number is 8.

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).

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I need help with this for math

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The answer of the given question based on finding the new coordinate of c is  (1, 5). and to determine if the image of Triangle ABC is similar or congruent to the original triangle is AB / A'B' = BC / B'C' = CA / C'A' = √(2).

What is Congruent triangles?

Congruent triangles are triangles that have the same shape and size. More specifically, if two triangles have exactly the same size and shape, then they are congruent triangles. This means that all the corresponding sides and angles of two triangles are equal. Congruent triangles can be thought of as being identical to each other, but they may be positioned and oriented differently in space.

To rotate a point 180° degrees counterclockwise about the origin, we can simply multiply its coordinates by the matrix:

[ -1  0 ]

[  0 -1 ]

So, the coordinates of the rotated point C would be:

[ -1  0 ]   [ 3 ]

[  0 -1 ]*[ 8 ] =[ -3 ]

           [  1 ]

we translate this point 4 units to the right and 4 units up by adding 4 to the x-coordinate and 4 to the y-coordinate:

[ -3 + 4 ]

[  1 + 4 ] = [ 1, 5 ]

Therefore, the new coordinates of point C are (1, 5).

To determine if the image of triangle ABC is similar or congruent to the original triangle, we can check if the ratios of the corresponding sides are the same. Let's calculate the lengths of the sides of the original triangle:

AB = √((8-3)² + (3-3)²) = 5

BC = √((3-8)² + (8-3)²) = 5*√(2)

CA = √((3-3)² + (3-8)²) = 5

Now, let's calculate the lengths of the sides of the image triangle, using the new coordinates:

A'B' = √((8-1)² + (3-5)²) = 5*√(2)

B'C' = √((1-1)² + (5-8)²) = 3

C'A' = √((1-8)² + (5-3)²) = 5*√(2)

We can see that the ratios of the corresponding sides are the same:

AB / A'B' = BC / B'C' = CA / C'A' = √(2)

Therefore, the image of triangle ABC is similar to the original triangle.

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Can someone please please help! Thank you so much! The picture is attached and I've written out the question! thank you!

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Answers

Answer:

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Step-by-step explanation:

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density = m/V = 534/60 = 8.9 g/cm^3

Create a stretch of 3 on function f(x) = 2x to make g(x) Group of answer choices

Answers

According to the given information, the function g(x) that represents a horizontal stretch of 3 on f(x) = 2x is [tex]\rm g(x) = \frac{2}{3}x$[/tex]. Thus, option A is correct.

What is functiοn?

A functiοn is a relatiοn between a set οf inputs and a set οf pοssible οutputs, with the prοperty that each input is related tο exactly οne οutput.

Tο create a hοrizοntal stretch οf 3 οn the functiοn f(x) = 2x, we can replace x in the functiοn with x/3, which will cause the οutput tο take three times the input value. This gives us the functiοn:

[tex]$$ g(x) = f\left(\frac{x}{3}\right) = 2\left(\frac{x}{3}\right) = \frac{2}{3}x $$[/tex]

Therefore, the function g(x) that represents a horizontal stretch of 3 on f(x) = 2x is [tex]g(x) = \frac{2}{3}x$.[/tex]

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Complete question:

Create a stretch of 3 on function f(x) = 2x to make g(x)

[Group of answer choices]

a. [tex]\rm g(x) = \tfrac{2}{3}x$[/tex]

b.  [tex]\rm g(x) = \tfrac{3}{2}x$[/tex]

c.  [tex]\rm g(x) = {2}x^3$[/tex]

d. [tex]$\rm g(x) = \sqrt[3]{{2}x} $[/tex]

Which expression is equivalent to (6−2 • 35)−2? HELP NOW

Answers

In response to the stated question, we can state that here  Hence, the linear equation (6 2 • 35) 2 equals 1/4096

What is a linear equation?

A linear equation is one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

We must do the following operations in the correct order to simplify the formula (62 • 35)2:

To start, we must multiply 2 by 35, which results in the number 70.

The result is -64 when we remove 70 from 6.

The final step is to raise the unfavorable integer -64 to the power of -2.

Hence, we can write:

[tex](6-2 * 35)-2 = (-64)^{-2}[/tex]

To make this statement easier to understand, keep in mind that taking the reciprocal of a number raised to a positive power is the same as raising it to a negative power. With those words:

[tex]a^-n = 1/a^n\\(-64)^-2 = 1/(-64)^2\\1/(-64)^2 = 1/4096[/tex]

Hence, the expression (6 2 • 35) 2 equals 1/4096.

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Assume that a procedure yields a binomial distribution with a trial repeated n times. Use

the binomial probability formula to find the probability of x successes given the

probability p of success on a single trial. Round to three decimal places.

n = 64, x = 3, p = 0. 04

0. 091

0. 139

0. 221

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Answers

The probability of 3 successes in 64 trials with a probability of 0.04 of success on a single trial is 0.375.

The probability of x successes in n trials with a probability p of success on a single trial can be calculated using the binomial probability formula. This formula is P(x successes) =[tex]nCx * (p^x) * (1-p)^(n-x)[/tex]. In this case, n = 64, x = 3, p = 0.04. Therefore, P(x successes) =[tex]64C3 * (0.04^3) * (1-0.04)^(64-3)[/tex]. Calculating this gives us P(x successes) = 0.375. Therefore, the probability of x successes in n trials with a probability p of success on a single trial is 0.375.

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X+y=9??? Can u give me a correct meaning of variable/s.

Answers

Answer:

In the equation X + y = 9, X and y are variables. Variables are used to represent unknown quantities or quantities that can vary. In this case, X and y represent two unknown numbers whose sum is equal to 9. We can use algebraic techniques to solve for either X or y, or both, depending on the situation. The values of X and y could represent anything, such as the number of apples and oranges in a basket, the length and width of a rectangle, or the ages of two people.

Question
Divide.

1582

Enter your answer as a mixed number in simplest form by filling in the boxes.

$$

Answers

Answer:

1582÷

Step-by-step explanation:

because u haven't told to divide wth any number

Answer:

Your question isn't complete. Kindly correct it.

How do you rewrite an equation into slope intercept form

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Answer: y=mx+b

Step-by-step explanation:

To change the equation into slope-intercept form, we write it in the form y=mx+b .

what is the exact value of tangent of 11 times pi over 12 question mark negative quantity of 2 minus radical 3 end quantity negative quantity of 2 plus radical 3 end quantity 2 minus radical 3

Answers

The exact value of tangent of 11 times pi over 12 is  [tex]-2+\sqrt{3}[/tex].

We have to find the exact value of [tex]tan\frac{11\pi}{12}[/tex]

[tex]tan\frac{11\pi}{12}=tan\frac{6\pi+5\pi}{12}[/tex]

[tex]tan\frac{11\pi}{12}=tan(\frac{6\pi}{12}+\frac{5\pi}{12})[/tex]

[tex]=tan(\frac{\pi}{2}+\frac{5\pi}{12})[/tex]

We have [tex]tan(\frac{\pi}{2}+x)=-cotx[/tex]

[tex]tan\frac{11\pi}{12}=-cot(\frac{5\pi}{12})[/tex]

[tex]tan\frac{11\pi}{12}=-cot(\frac{2\pi+3\pi}{12})[/tex]

[tex]tan\frac{11\pi}{12}=-cot(\frac{\pi}{6}+\frac{\pi}{4})[/tex]

We have identity [tex]cot(x+y)=\frac{cotxcoty-1}{coty+cotx}[/tex]

[tex]tan(\frac{\pi}{2}+x)= -\frac{cot\frac{\pi}{6}cot\frac{\pi}{4}-1}{cot\frac{\pi}{4}+ cot\frac{\pi}{6}}[/tex]

[tex]=\frac{-\sqrt{3}(1) - 1}{1+\sqrt{3}}[/tex]

Rationalize the denominator and simplify, we get:

[tex]=-2+\sqrt{3}[/tex]

Therefore, the exact value of  [tex]tan\frac{11\pi}{12}[/tex] is [tex]-2+\sqrt{3}[/tex].

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Complete question is:

Find the exact value of  [tex]tan\frac{11\pi}{12}[/tex] ?

A man of mass 60kg runs with a constant velocity. He has kinetic energy of 750j. Calculate his velocity

Answers

Answer:

the velocity of the man is 5 m/s.

Step-by-step explanation:

The kinetic energy of a moving object is given by the equation:

K.E. = 0.5 * m * v^2

where

K.E. is the kinetic energy

m is the mass of the object

v is the velocity of the object

In this problem, we are given that the man has a mass of 60 kg and a kinetic energy of 750 J.

So,

750 J = 0.5 * 60 kg * v^2

Solving for v:

v^2 = (2 * 750 J) / 60 kg

v^2 = 25 J/kg

v = sqrt(25 J/kg)

v = 5 m/s

Therefore, the velocity of the man is 5 m/s.

There were 5 choirs at the choir concert on Friday night. Each choir sang 5 songs.

Which shows how many songs the choirs sang in all?
A.
5 - 5
B.
5 × 5
C.
5 + 5
D.
5 × 6

Answers

The answer would be B. 5 x 5

A company makes flags for a holiday. For every 9 yards of red​ fabric, it uses 17 yards of blue fabric. This ratio is represented in the diagram. Explain how you would use the diagram to find the number of yards of blue fabric used when 63 yards of red fabric are used.

Answers

The company would use 19.5 yards of blue fabric when 63 yards of red fabric are used, according to the given ratio and diagram.

What are word problems?

Word problems are mathematical problems expressed in words, often used to apply mathematical concepts to real-life situations.

To find the number of yards of blue fabric used when 63 yards of red fabric are used, we can use the given ratio of 9 yards of red fabric to 17 yards of blue fabric.

To determine the number of units of red fabric needed for 63 yards divide the number of yards of red fabric by the scale factor for red fabric, which is 3. So, 63 yards ÷ 3 units per yard = 21 units of red fabric.

Use the ratio to determine the number of units of blue fabric needed. Since the ratio of red to blue fabric is 9:17.So, to find the number of units of blue fabric needed for 21 units of red fabric, we can multiply 21 by 17/9, which gives us 39 units of blue fabric.

So, 39 units of blue fabric ÷ 2 units per yard = 19.5 yards of blue fabric.

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What will be one-fifth of a complete angle in degrees

Answers

Answer:

72 degrees

Step-by-step explanation:

If a complete angle is 360 degrees, one-fifth of a complete angle would be:

360 ÷ 5 = 72

Therefore one-fifth of a complete angle is 72 degrees.

An angle measures 8° less than the measure of its complementary angle. What is the
measure of each angle?
and

Answers

An angle and its complementary angle add up to 90 degrees. Let's call one of the angles x. Then, the other angle (which is the complementary angle to x) is (90 - x).

According to the problem, x measures 8 degrees less than its complementary angle, so we can set up the equation:

x = (90 - x) - 8

Simplifying and solving for x, we get:

2x = 82

x = 41

Therefore, one of the angles measures 41 degrees, and the other angle (its complementary angle) measures:

90 - x = 90 - 41 = 49 degrees


If you have another question, please let me know!

HELPPP! Cari knows that it is a 45 mile drive from her house to the airport. She also knows that it is a 45 mile drive from her house to her grandparents house in the woods. How many miles is it directly from the airport to her grandparents house in the woods? Show your work.

Answers

Answer:

We can use the Pythagorean theorem to solve this problem. Let's assume that Cari's house is at point A, the airport is at point B, and her grandparents' house is at point C. We know that the distance from A to B is 45 miles and the distance from A to C is 45 miles. We want to find the distance from B to C, which we can call x.

We can form a right triangle with sides AB, AC, and BC. The distance we want to find, x, is the length of the hypotenuse of this triangle (side BC).

Using the Pythagorean theorem, we know that:

AB^2 + AC^2 = BC^2

Substituting in the values we know:

45^2 + 45^2 = x^2

Simplifying:

2025 + 2025 = x^2

4050 = x^2

Taking the square root of both sides:

x = sqrt(4050)

x is approximately equal to 63.64 miles (rounded to two decimal places).

Therefore, the direct distance from the airport to Cari's grandparents' house is approximately 63.64 miles.

A cylinder has a radius of 5 yards. Its volume is 1,177. 5 cubic yards. What is the height of the cylinder?

Answers

The height of the cylinder is 27 yards.

To find the height of a cylinder, we need to use the formula V = πr^2h, where V is the volume, π is the constant pi (3.14), r is the radius, and h is the height.

In this problem, we know the radius is 5 yards, and the volume is 1,177.5 cubic yards. We can rearrange the formula to calculate the height as h = V / (πr^2). Substituting the given values into the equation, we get: h = 1177.5 / (3.14 * 25) = 27 yards. Therefore, the height of the cylinder is 27 yards.

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The vertex of a parabola is (0, 0) and the focus is (1/8,0). What is the equation of the parabola?

Answers

if the vertex is at the origin, and the focus point horizontally to the right-side 1/8 units away from the vertex, well, that means is a horizontal parabola with a "p" value of +1/8, so

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\supset}\qquad \stackrel{p~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=0\\ k=0\\ p=\frac{1}{8} \end{cases}\implies 4(\frac{1}{8})(~~x-0~~) = (~~y-0~~)^2\implies \cfrac{1}{2}x=y^2\implies \boxed{x=2y^2}[/tex]

A piece of a plastic poll is shaped like a cylinder. The poll has a length of 15 feet. Which of the following is closest to the volume of the pole? 71 ft² 106 ft² 424 ft² 141 ft² A B C D​

Answers

Answer:

Since the pole is in the shape of a cylinder, its volume can be calculated using the formula V = πr²h, where r is the radius and h is the height (or length in this case). We are not given the radius, so we cannot calculate the exact volume. However, we can use an approximation assuming a reasonable radius.

Let's assume a radius of 1 foot. Then, the volume would be V ≈ π(1)²(15) = 15π ≈ 47.1 cubic feet.

The closest answer choice to this approximation is D) 141 ft². However, note that volume is measured in cubic units (feet cubed or ft³), not square units (feet squared or ft²). Therefore, none of the answer choices are in the correct units for the volume of a cylinder.

An arc of length 21 meters subtends a central angle of 287° in a
circle.
a) Find the circumference of the circle & area.

Answers

The circumference and area of the circle with the arc of length 21 meters and a central angle of 287° are 4.35 meters and 1.16 square meters.

An arc of length 21 meters subtends a central angle of 287° in a circle. The circumference of the circle and area are required to be determined.

Here is the solution:

Let us suppose that the radius of the circle is r. Thus, we can write:

r = (L/θ) r = (21/287)

Let us substitute the values of r in the formulae of the circumference of the circle and area of the circle.

Circumference of the circle:

C = 2πr

C = 2π (21/287)

C ≈ 4.35 meters

Area of the circle:

A = πr²

A = π (21/287)²

A ≈ 1.16 square meters

Therefore, the circumference of the circle is 4.35 meters and the area of the circle is 1.16 square meters.

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Solve from [0, 2pi)

cos x/2 = (sqrt(2))/2

Answers

Thus, cos x/2 = (sqrt(2))/2 has the solution for x =  4kx ± π/2 in the intervals  [0, 2pi).

Explain about the cosine function?

The ratio of the hypotenuse to the side adjacent to the acute angle together in right triangle is the cosine function, which is a trigonometric function.

This cosine function for only a specified range of angles is represented graphically by the cos graph. A trigonometric graph's horizontal axis is the angle, which is typically denoted by the symbol, and the y-axis is really the sine function of just that angle. The maximum and minimum values are 1 and 1.

There are amplitudes for both the sine and cosine functions. This is due to the scope limitations of each function. Both functions typically have an amplitude of 1, though this can vary depending on the way the function is constructed.

Given function:

cos x/2 = (sqrt(2))/2

OR,

cos x/2 = √2/2

cos x/2 = cos (2kx ± π/4) , k ∈ R (real number)

x/2 = 2kx ± π/4

x =  4kx ± π/2

Thus, cos x/2 = (sqrt(2))/2 has the solution for x =  4kx ± π/2 in the intervals  [0, 2pi).

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In the diagram, E is the midpoint of DF. What is the value of x?

Answers

Answer:

[tex]\large\boxed{\mathtt{x = 10}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked for the value of x.}[/tex]

[tex]\textsf{Because E is a Midpoint,} \ \overline{DE} \cong \ \overline{EF}.[/tex]

[tex]\textsf{Let's set them equal to each other.}[/tex]

[tex]\mathtt{45=3(x+5)}[/tex]

[tex]\large\underline{\textsf{Begin Solving:}}[/tex]

[tex]\mathtt{45= ( 3 \times x ) +(3 \times 5)}[/tex]

[tex]\mathtt{45= 3x+15}[/tex]

[tex]\large\underline{\textsf{Subtract 15 from Both Sides:}}[/tex]

[tex]\mathtt{3x=30}[/tex]

[tex]\large\underline{\textsf{Divide by 3:}}[/tex]

[tex]\large\boxed{\mathtt{x = 10}}[/tex]

Answer:

x = 10

Step-by-step explanation:

To find:-

The value of x.

Answer:-

We are here given that, E is the midpoint of DF. The value of DE is 45 and that of EF is 3(x+5) . We are interested in finding out the value of "x" .

According to Euclid's first axiom , Things which are half of the same thing are equal to one another. So here;

[tex]\sf:\implies DF = DF \\[/tex]

[tex]\sf:\implies \dfrac{DF}{2}=\dfrac{DF}{2} \\[/tex]

[tex]\sf:\implies DE = EF \\[/tex]

On substituting the respective values, we have;

[tex]\sf:\implies 45 = 3(x+5) \\[/tex]

[tex]\sf:\implies 45 = 3x + 15 \\[/tex]

[tex]\sf:\implies 3x = 45-15\\[/tex]

[tex]\sf:\implies 3x = 30 \\[/tex]

[tex]\sf:\implies x =\dfrac{30}{3}\\[/tex]

[tex]\sf:\implies \red{x = 10}\\[/tex]

Hence the value of x is 10 .

From a point 48 feet in front of a church, the angles of elevation to the base of the steeple and the top of the steeple are 40° and
49° 40',
respectively. find height of steeple

Answers

Answer: Let's call the height of the steeple "h". We can use the tangent function to set up an equation involving the angles of elevation:

tan(40°) = h / x

tan(49° 40') = (h + y) / x

where "x" is the distance from the point to the base of the steeple, and "y" is the height of the point above the ground.

We are given that the distance from the point to the church is 48 feet, so we can use the Pythagorean theorem to find the value of "y":

y^2 = x^2 - 48^2

We can substitute this expression for "y" into the second equation above:

tan(49° 40') = (h + √(x^2 - 48^2)) / x

We can now solve this equation for "h":

h = x tan(49° 40') - x √(1 + tan^2(49° 40')) + 48 tan(40°)

Plugging in the values for the angles and solving for "h", we get:

h ≈ 83.9 feet

Therefore, the height of the steeple is approximately 83.9 feet.

Step-by-step explanation:

4 Desiree, Marina, and Raúl each survey random samples of 60 students in their
school about whether they prefer to listen to music while completing homework.
They use the results to infer about what percent of students in the school prefer to
listen to music while completing homework. Based on the results of the three
surveys, what range of inferences is reasonable? Write your answers in the blanks.
Student Who
Gave Survey
Students Who Prefer to Listen to
Music While Completing Homework
48
39
42
Desiree
Marina
Raúl
39
48
From
% to
listen to music while completing homework.
% of the school population prefers to

Answers

Answer:

To calculate the range of inferences, we need to find the minimum and maximum percentages based on the results of the three surveys.

Desiree's survey found that 48 out of 60 students prefer to listen to music while completing homework, which is 80%.

Marina's survey found that 39 out of 60 students prefer to listen to music while completing homework, which is 65%.

Raúl's survey found that 42 out of 60 students prefer to listen to music while completing homework, which is 70%.

To find the minimum percentage, we can take the lowest value of the three surveys, which is 65%. To find the maximum percentage, we can take the highest value of the three surveys, which is 80%. Therefore, a reasonable range of inferences is:

From 65% to 80% of the school population prefers to listen to music while completing homework.

The value of my coins if I have p pennies, n nickels and twice as many quarters as pennies HELPPPPPPPPPP ASAPPWILL AWARD BRAINLIES~T

Answers

0.06p+0.05n

p=number of pennies
n=number of nickels
q=number of quarters
You know pennies are worth $0.01, nickels are worth $0.05, and quarters are worth $0.25.
You have twice as many quarters are pennies, so you have 2p quarters.
The value of your coins are: 0.01p+0.05n+0.25(2p)= 0.01p+0.05n+0.5p = 0.06p+0.05n where p is the number of pennies and n is the number of nickels.
Hope this helps!
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