The radius of a circle is 14 feet. What is the area of the circle?

87.92 ft 2
615.44 ft 2
153.86 ft 2
1,230.44 ft 2

Andre's account after t years is [tex]V_h=538.45(1.025)^t[/tex] since is option C.

The Amount accumulated at the end of a interest year is the sum of the principla amount and the interest gained on the principal amount.

As Andres start the savings account after 3 years so, the equation representing the value of Andre's account after t years is-[tex]v_h=500(1.025)^{t-3}[/tex].

Also, the amount accumulated in the mean 3 years will be-

[tex]A=500(1.025)^3[/tex]

=$538.45

Hence, another way of writing the equation representing the value of Andre's account after t years is-[tex]V_h=538.45(1.025)^t[/tex]

As a result, option C is the correct answer.

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а. 5

b. 180(5-3)=540

,..,,..,.,.,

Answer:

508,000 in 11 years

Step-by-step explanation:

3.75% of 360,000 is 13500

So every year the population grows 13500 people

13500 * 11 = 148,500

148,500+360,000=508,000

So in 11 years the population would be 508,000

Using the z-distribution, it is found that the 99% confidence interval is (0.041, 0.2256), and it means that we are 99% sure that the population proportion is in this interval.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The other parameters are given by:

[tex]n = 90, \pi = \frac{12}{90} = 0.1333[/tex]

Then, the bounds of the interval are found as follows:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1333 - 2.575\sqrt{\frac{0.1333(0.8667)}{90}} = 0.041[/tex]

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1333 + 2.575\sqrt{\frac{0.1333(0.8667)}{90}} = 0.2256[/tex]

The 99% confidence interval is (0.041, 0.2256), and it means that we are 99% sure that the population proportion is in this interval.

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Answer:

44

Step-by-step explanation:

Lunch = 3 appetizers per guest

If there are 22 guests:  22 × 3 = 66 appetizers served

Dinner = 5 appetizers per guest

If there are 22 guests:  22 × 5 = 110 appetizers served

Difference = total dinner appetizers  - total lunch appetizers

                  = 110 - 66

                  = 44

Answer:

$1331 compounded annually after three years

Step-by-step explanation:

Given the following question:

1000 dollars invested (princpal)....
You invest that 1000 dollars for three years (time)....

Assuming it's compounded annually we need to substitute the values into the formula to calculate compound interest.

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
[tex]P=1000[/tex]
[tex]\frac{r}{n} =\frac{10}{100} =10\div100=0.1[/tex]
[tex]nt=(1)(3)[/tex]
[tex]A=1000(1+0.1)^{(1)(3)}[/tex]
[tex]1\times3=3[/tex]
[tex]A=1000(1+0.1)^{3}[/tex]
[tex]1+0.1=1.1[/tex]
[tex]1.1^3=1.1\times1.1\times1.1=1.331[/tex]
[tex]A=1000\times1.331[/tex]
[tex]1000\times1.331=1331[/tex]
[tex]=1331[/tex]

Which means after a intital investment of 1000 dollars you will have "1331 dollars" after three years compounded annually.

Hope this helps.

Answer:

See details below:

Step-by-step explanation:

We can start with the biggest factors and work our way down to see how arrive at 4 * 25.

In this case, the first part of the tree would be 50 * 2.

2 is prime, but 50 is not and thus must be factored.

Two possible factors of 50 are 2 and 25.

The 25 is not a prime number and must be factored further.

Two possible factors of 25 are 5 and 5.

Thus, the prime factorization of 100 is 2*2*5*5.

Then to simplify, we can combine the similar factors:  (2*2) * (5*5) = 4*25

I hope this makes sense

Answer:

0.02 seconds

Step-by-step explanation: A 70kg man jumps 1.00 meters down onto a concrete walkway. His downward motion stops in 0.02 seconds.

Answer:

1.25m

Step-by-step explanation:

v=u+gt

5=0+10t

5=10t

t=0.5s

s=ut+1/2gt^2

=0+(0.5×10×(0.5)^2)

=1.25m

When you reflect across the Y axis, the Y value remains the same and the x value becomes opposite.

Answer: (5,-3)

Answer:

36

Step-by-step explanation:

For the largest possible whole number length, this means it would have to be the longest side. Let's let this third side have a length of x.

By the triangle inequality theorem, 19+18>x, which means x<37.

So, the largest possible whole number length for the third side is 36.

Considering the volume of a cone, it is found that:

The volume of a cone of radius r and height h is given by:

[tex]V = \frac{\pi r^2h}{3}[/tex]

For cone 1, we have that V = 0.5 x 28.875 = 14.4375 in³ and r = 2.25 in(half the diameter), hence:

[tex]\frac{\pi (2.25)^2h}{3} = 14.4375[/tex]

[tex]h = \frac{14.4375 \times 3}{\pi \times (2.25)^2}[/tex]

[tex]h = 2.72[/tex]

For cone 2, we have that V = 28.875 in³ and r = 3 in, hence:

[tex]\frac{\pi (2.25)^2h}{3} = 28.875[/tex]

[tex]h = \frac{28.875 \times 3}{\pi \times (3)^2}[/tex]

[tex]h = 3.06[/tex]

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Answer:

the answer is (5g+4h)(5g-7h)

Step-by-step explanation:

25g^2-15gh-28h^2

=(25g^2+20gh)+(-35gh-28h^2)

=5g(5g+4h)-7h(5g+4h)

=(5g+4h)(5g-7h)

Step-by-step explanation:

[tex]volume = \pi {r}^{2}h[/tex]

[tex]695 = 3.14 \times {r}^{2} \times 11.5[/tex]

[tex] {r}^{2} = 19.2[/tex]

[tex]r = \sqrt{19.2} = 4.3[/tex]

Answer:

[tex]y=\frac{1}{2} x-8[/tex]

Step-by-step explanation:

The final answer is in the slope-intercept form, which is y=mx +c, where m is the slope and c is the y-intercept.

The slope of a perpendicular line is the negative reciprocal of the slope of the given line (the line it is perpendicular to). Thus, let's find the slope of the given line first.

Given line: y= -2x -9

The above equation is already in the slope-intercept from and thus, the slope is the coefficient of x.

Slope of given line= -2

The coefficient is the number that comes before a variable and it includes the positive or negative sign, which explains why the slope of the given line is -2 instead of 2.

Slope of perpendicular line= [tex]\frac{1}{2}[/tex]

Substitute the value of the slope into the equation:
[tex]y=\frac{1}{2} x+c[/tex]

To find the value of c, substitute a pair of coordiantes the line passes through.

When x= 8, y= -4,

[tex]-4=\frac{1}{2}(8)+c[/tex]

-4= 4 +c

c= -4 -4

c= -8

Thus, the equation of the perpendicular line is [tex]\bf{y=\frac{1}{2} x-8}[/tex].

What is reciprocal?

Answer:

the answer is 1323. i took the quiz on k12 and this was the answer

Step-by-step explanation:

hi

1323

bye (disco lovely_jinni #2028

Answer:

3rd

Step-by-step explanation:

Answer: graph 3

Step-by-step explanation:

Answer:

C) 390

Step-by-step explanation:

Area of Blue:

18 × 25 = 450 in

Area of White:

6 × 10 = 60 in

450 - 60 = 390

Therefore, 390 sq in is the correct answer.

Answer:

5/6

Step-by-step explanation:

it's a 15:18 ratio, just needs simplification

Answer:

(a)  144 ft

(b)  2 s

(c)  5 s

(d)  128 ft

Step-by-step explanation:

[tex]h(t) = -16t^2 + 64t + 80[/tex]

Part (a)

To find the turning point of the parabola:

1. differentiate the function:

[tex]\implies h'(t) = -32t + 64[/tex]

2. Set it to zero and solve for t:

[tex]\implies h'(t) =0[/tex]

[tex]\implies -32t + 64=0[/tex]

[tex]\implies 32t = 64[/tex]

[tex]\implies t=2[/tex]

3. Input found value of t back into the function and solve for h:

[tex]\implies h(2) = -16(2)^2 + 64(2) + 80=144[/tex]

Therefore, the maximum height reached by the ball is 144 ft

Part (b)

As found in part (a), the maximum height is reached when t = 2, so the ball reached its maximum height at 2 seconds.

Part (c)

The ball will hit the ground when h(t) = 0

1. Set the function to zero

[tex]\implies h(t)=0[/tex]

[tex]\implies -16t^2 + 64t + 80=0[/tex]

2. Solve for t:

Divide both sides by 16

[tex]\implies -t^2 + 4t + 5=0[/tex]

[tex]\implies t^2 - 4t - 5=0[/tex]

Factor:

[tex]\implies t^2 +t-5t - 5=0[/tex]

[tex]\implies t(t+1)-5(t+1)=0[/tex]

[tex]\implies (t+1)(t-5)=0[/tex]

Therefore:

[tex](t+1)=0 \implies t=-1[/tex]

[tex](t-5)=0 \implies t=5[/tex]

As time is positive, t = 5

So the ball will hit the ground at 5 seconds.

Part (d)

To find the height of the ball after 1 second, input t = 1 into the function and solve for h:

[tex]\implies h(1) = -16(1)^2 + 64(1) + 80=128[/tex]

Therefore, the height of the ball after 1 second is 128 ft

--------------------------------------------------------------------------------------

Parts (a) & (b) - alternative method

Rewrite the function in vertex form by completing the square.

Set the function to zero:

[tex]\implies-16t^2 + 64t + 80=0[/tex]

Subtract 144 from both sides:

[tex]\implies -16t^2+64t-64=-144[/tex]

Factor out -16:

[tex]\implies -16(t^2 - 4t +4)=-144[/tex]

Factor expression in brackets:

[tex]\implies -16(t-2)^2=-144[/tex]

Add 144 to both sides:

[tex]\implies -16(t-2)^2+144=0[/tex]

Therefore:

[tex]\implies h(t)=-16(t-2)^2+144[/tex]

The maximum height is the y-value of the vertex.

The vertex is (2, 144) so the maximum height is 144 ft.

The time the ball reached the max height is the x-value of vertex.

So the time then the ball reached the maximum height is 2 s

Answer:

82 degrees

Step-by-step explanation:

Reference Angle: the acute angle between the terminal arm/terminal side and the x-axis. The reference angle is always positive.

82 DEGREES

The value in the sequence closest to 300 is 310

Arithmetic sequence is a sequence where each term increases or decreases by addition or subtraction of a constant term

the first term a = 30

common difference, d = 40

which term is closest to 300 we solve like this

300 / 40 = 7.5 say 7

the 7th term, T7 is solved by

T7 = a + ( n - 1 ) d

T7 = 30 + ( 7 - 1 ) 40

T7 = 30 + 240

T7 = 270

checking for the 8th term to confirm the nearest

T8 = T7 + d = T7 + 40

T8 = 270 + 40

T8 = 310

therefore the 8th term is closest and the value is 310

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Answer:

susan is correct

Step-by-step explanation:

2+12+4+18+24+32=108

108 divided by 7=54

my reasoning is that the formula is add all and divide by how many numbers you added

Answer:

20π ft

Step-by-step explanation:

To find the circumference of the circle given its area, first find its radius.

[tex]\textcolor{steelblue}{\boxed{\text{Area of circle =}\pi {r}^{2} }}[/tex]

Substitute given area into the formula:

100π= πr²

Divide both sides by π:

100= r²

Square root both sides:

[tex]r = \sqrt{100} [/tex]

r= 10 ft

[tex]\textcolor{steelblue}{\boxed{\text{Circumference of circle = }2\pi {r}}}[/tex]

Since we have found the value of the radius, we can substitute r= 10 into the formula above to find the circumference.

Circumference of circle

= 2(π)(10)

= 20π ft

keeping in mind that in a rhombus all sides are equal, Check the picture below.

The perimeter of the rhombus is 60 cm if the lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively.

A rhombus is a two-dimensional shape with four straight, equal sides and parallels opposite pairs.

This form is similar to a diamond and is what you'd expect to see on a deck of cards to symbolize the diamond suit. Rhombuses can be found in a variety of settings in everyday life.

We have:

The length of the diagonals of the rhombus is 24 cm and 18 cm

As we know in the rhombus the diagonals intersect at the right angle so it makes a right-angle triangle.

So half of the right-angle 24 cm will be perpendicular to the right-angle triangle and half of the 18 cm will be the base of the right-angle triangle.

a = 24/2 = 12 cm

b = 18/2 = 9 cm

From the Pythagoras theorem the length of the hypotenuse:

[tex]c = \sqrt{12^2+9^2}[/tex]

c = 15 cm

Now the perimeter will be:

The perimeter of the rhombus = 4(15) = 60 cm

Thus, the perimeter of the rhombus is 60 cm if the lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively.

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Answer:

2 hours

Step-by-step explanation:

4.5 - 2.5 = 2

Hav ean amazing day!!

Please rate!!

Answer:

150

Step-by-step explanation:

since a circle is 360 degrees, add up all of the other degrees and then subtract from 360

Answer:

x = 26

Step-by-step explanation:

If Y= x - 12 and Y = 14

Then we input the value of y which gets us the equation of: 14 = x - 12

Now we add 12 on both sides to isolate the variable.

We ADDED 12 because we needed a way to cross out the - 12 on the right side. Now the equation would be 14+12 = x

Easily we can find that 26=x