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The circumference of a circle with a radius of 9 millimeters is approximately 56.54867 mm, or 57 mm when rounded to two significant figures.

The circumference of a circle can be calculated using the formula C = 2πr, where π (pi) is approximately 3.14159 and r is the radius of the circle. Given that the radius of the circle is 9 millimeters, we can plug this value into the formula to find the circumference.

C = 2 × 3.14159 × 9 mm

After calculating, the circumference (C) is 56.54867 mm. However, if we keep the significant figures consistent with the given radius, the circumference is approximately 57 mm.

The circumference of the circle with a radius of 9 millimeters is approximately 56.55 millimeters, calculated using the formula [tex]\(C = 2 \pi r\)[/tex].

The circumference (C) of a circle is calculated using the formula [tex]\(C = 2 \pi r\)[/tex], where r is the radius of the circle. Given that the radius (r) is 9 millimeters, substitute this value into the formula:

[tex]\[ C = 2 \pi \times 9 \][/tex]

Using an approximate value for [tex]\(\pi\)[/tex], which is 3.14159, the calculation is:

[tex]\[ C \approx 2 \times 3.14159 \times 9 \][/tex]

[tex]\[ C \approx 56.54867 \][/tex]

Therefore, the circumference of the circle with a radius of 9 millimeters is approximately 56.55 millimeters.

Answer:

10

Step-by-step explanation:

You can use process of elimination for this question

Since one of the chord is drawn in and part on the radius is connected to it, that "part" radius bisects the chord

Therefore, the chord is 16 units long

Then the diameter must be even longer

The only option that works for the radius is 10 as the diameter would be 20

If the radius was 5, the diameter would be 10 which is less than the chord

If the radius was 6, the diameter would be 12 which is less than the chord

Answer:

[tex] ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

And replacing we got:

[tex] ME= 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}= 0.0432[/tex]

And replacing into the confidence interval formula we got:

[tex]0.37 - 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}=0.327[/tex]

[tex]0.37 + 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}=0.413[/tex]

And the 95% confidence interval would be given (0.327;0.413).

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

The confidence interval would be given by this formula

[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

Assuming a 95% of confidence. For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.

[tex]z_{\alpha/2}=1.96[/tex]

The margin of error would be:

[tex] ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

And replacing we got:

[tex] ME= 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}= 0.0432[/tex]

And replacing into the confidence interval formula we got:

[tex]0.37 - 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}=0.327[/tex]

[tex]0.37 + 1.96 *\sqrt{\frac{0.37 (1-0.37)}{480}}=0.413[/tex]

And the 95% confidence interval would be given (0.327;0.413).

Answer:

The tank can hold 4110.26 gallons of water.

Step-by-step explanation:

In order to solve this question we need to compute the volume of this tank, the volume is given by:

V = (area of the base)*height

Since the base is circullar, it is given by:

area of the base = pi*r^2

So we have:

V = height*pi*r^2

The radius of circle is the diameter divided by 2, so in this case r = 10/2 = 5 ft. We can now use the values on the equations:

V = 7*3.14*(5)^2 = 549.5 ft^3

Since each cubic foot holds 7.48 gallons of water the volume in gallons is:

V = 549.5*7.48 = 4110.26 gallons

The tank can hold 4110.26 gallons of water.

To find the number of gallons a cylindrical tank can hold, calculate the volume in cubic feet using the formula V = πr^2h, where the diameter is 10 feet (radius is 5 feet) and the height is 7 feet, then multiply the volume by 7.48 gallons per cubic foot.

To calculate the number of gallons a cylindrical tank can hold, we first need to find the volume of the cylinder in cubic feet and then convert that volume to gallons. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.

Since the diameter of the tank is given as 10 feet, the radius (r) would be half of that, which is 5 feet. The height (h) is given as 7 feet. Plugging these values into the formula, we get:

V = π(5)^2(7) = π(25)(7) = π(175) cubic feet.

Using the conversion factor 7.48 gallons per cubic foot, we can find the total gallons the tank holds:

Gallons = Cubic feet × 7.48 gallons/cubic foot

Gallons = π(175) × 7.48 gallons/cubic foot

We thus calculate the total volume in gallons.

Answer:

Step-by-step explanation:

Answer:

1.6

Step-by-step explanation:

[tex] \tan \: A = \frac{4}{5} \\ \\ \cot \: A = \frac{1}{ \tan \: A } = \frac{1}{ \frac{4}{5} } = \frac{5}{4} \\ \\ csc\: A = \sqrt{1 + {cot}^{2}\: A} \\ = \sqrt{1 + { \bigg( \frac{5}{4} \bigg)}^{2} } \\ = \sqrt{1 + \frac{25}{16} } \\ = \sqrt{\frac{16 + 25}{16} } \\ = \sqrt{\frac{41}{16}} \\ = \frac{ \sqrt{41} }{4} \\ = \frac{6.40312424}{4} \\ = 1.60078106 \\ \therefore \: csc \: A =1.6[/tex]

Answer:

56.7% to one decimal place

Step-by-step explanation:

30 students

13 are boys

30-13=17

17 are girls

As a decimal 0.5667

As a percentage 56.67%

56.7% to one decimal place

Answer:

Gregoire is correct; the diameter is a chord that passes through the center of the sphere.

Step-by-step explanation:

A sphere is a geometrical shape formed from a circle. Some of its parts are: diameter, center, radius circumference, etc.

The center of a sphere is a point at its middle. The diameter is a straight line, e.g a chord, that is drawn from one point on the circumference of a sphere to another point and passes through its center. While radius is a line that is from the center of the sphere to a point on its circumference.

A diameter is twice of a radius, so that:

                            Radius = [tex]\frac{Diameter}{2}[/tex]

⇒                        Diameter = 2 × Radius

Therefore with respect to the question, Gregoire is correct because a diameter is a chord that passes through the center of the sphere.

Answer:

a

Step-by-step explanation:

Answer:

y = 5[tex]e^{tan(x)}[/tex]

Step-by-step explanation:

work in picture below

Answer:

4x^3 + 41x^2 +51x + 54

Step-by-step explanation:

This is a polynomial distribution

(x + 9 )(4x^2 + 5x + 6) We start by multiplying every term with x

4x^3 + 5x^2 + 6x there is plus sign between (x+9) so we put plus and start multiplying every term by 9

4x^3 + 5x^2 + 6x + 36x^2 + 45x + 54

4x^3 + 41x^2 +51x + 54

Answer:

Step-by-step explanation:

Suppose m = 2 + 6i, and |m+n|=3√10,

The modulus sign means m+n can either be positive or negative as shown.

If it is positive:.2+6i+n = 3√10

n = 3√10-(2+6i)

n = 3√10-2-18√10i

n = (-2+3√10)+√10i

b) Example of the complex number is given as (-2+3√10)+√10i. This is a complex number because it contains the real part and the imaginary part.

Answer:

7 inches

Step-by-step explanation:

Height : Diameter

14 : 6

H : 3

H/14 = 3/6

H = 14 × 3/6

H = 7

Answer:

7 inches

Step-by-step explanation:

Answer:

x^2 - 81

Step-by-step explanation:

There is a formula called the difference of squares, which is

(a+b)(a-b) = a^2 - b^2

Answer: 9x²-81x

Step-by-step explanation:

1. Reorder the terms like this: (9x)• (x-9)

2. Remove unnecessary Parentheses like this: 9x•(x-9)

3. Distribute 9x through the Parentheses like this:

9x would become 9x² (because I combined 9x and 9x which become 9x²)

(x-9) would become -81x (so if you need further explanation I took the (x-9) and made it -9x then multiplied it by the 9x because of distributive property.)

The solution: 9x²-81x

Answer:

Santiago earns 8.7 $ from each sold shirt

Step-by-step explanation:

1). 45 % of 6 is = 6 * 0.45 = 2.7 $

2). 6 $ + 45 % of 6 = 6 + 2.7 = 8.7 $ - Answer

Answer:

Use the value for the variable to solve for the other unknowns.  Substitute the value for the variable into the expression for the number of seats on the middle level.  Substitute the value for the variable into the expression for the number of seats on the lower level.

Answer:

limit is 2.

Step-by-step explanation:

f(x) = 10x + 2  for x< 0   ,

f(x) = |2 - x|  for x>=0

get x close to 0

lim  10x + 2  x-->0-  = 2

lim  |2 - x|   x-->0+ =  2

Answer:

Length = 12yards

Width = 14yards

Sum = 26yards

Step-by-step explanation:

Let assume the play ground is rectangular in form.

Area of a rectangle = length × width

Given area of the playground = 168yd²

If the width of the playground is 2yd longer than its length, then:

W = L+2

Substituting W = L+2 into the formula above we have:

A = L × (L+2)

A = L²+2L

168 = L²+2L

L²+2L-168 = 0

L²+14L-12L-168 = 0

L(L+14)-12(L+14) = 0

(L-12)(L+14) = 0

L-12 = 0 and L+14 =0

L = 12 and -14

Taking the positive length, L = 12yards

If Length = 12yards

W = L+2

W = 12+2

Width = 14yards

Sum of the length and width will be:

L+W= 12+14

= 26yards

Answer:

The length  of playground is 12 yd

The width of playground is 14 yd

The sum of the length and width of playground is 26 yd

Step-by-step explanation:

The area, A of the playground is given as 168 yd²

The formula for the area of the playground is given as follows;

Area, A of playground = Length, L × Width, W

The Width =  length  + 2 yd or W  = L + 2

Therefore, A = L × (L + 2)

A = L² + 2·L

Where we have A = 168 yd², we have the area equation presented as follows

168 = L² + 2·L or

L² + 2·L - 168 = 0

Factorizing the above equation gives

L = 12 or L = -14 we note that the appropriate solution is L = 12 yd

Therefore W = L + 2 = 12 + 2 = 14 yd

The length  of playground = 12 yd

The width of playground = 14 yd

The sum of the length and width of playground = 12 + 14 = 26 yd.

Answer:

Ruby pays a dollar every 12 messages.

Step-by-step explanation:

It costs Ruby $4 to send 48 text messages. To find the unit rate, you would divide 48 by 4. So the result would lead to 12 messages per dollar.

Answer:

54mm

Step-by-step explanation:

50, 50, 52,53, 54, 55, 55, 55, 57

If we are looking for when they would be the same at a given time:

First, we need to set them to each other:

50 + 10x = 25 + 15x

Move them around and then get this:

25 = 5x

Divide by 5 from both sides

5 = x

Answer: m<D = 80º

Step-by-step explanation:

Since we know triangle ABC is congruent to triangle EDC, the angle 60º can be know for angle ACB. Triangles have a interior total of 180, so 40+60 is 100. Subtract 100 from 180 to get your angle of B. Since the triangles are similar we know that B=D so D=80º

Answer: 1 1/4

Step-by-step explanation:

Solving the fraction parts

3/8 + 7/8 = 10/8

Reducing the fraction part, 10/8

10/8= 5/4

Simplifying the fraction part, 5/4

5/4= 1 1/4

Answer:

10/8

Step-by-step explanation:

You add 7/8 + 3/8 and that equals 10/8

I hope that's helpful

Answer:

B.- There is no vertical asymptote at x=0

E.- There is a removable discontinuity at x= -a

Step-by-step explanation:

Answer:

The above answers are correct! The correct options are B and E!

Step-by-step explanation:

Hope this helped confirm :)

Have a great day!

Answer:

The answer to your question is  77/500    

Step-by-step explanation:

Data

decimal number = 0.154

fraction number = ?

Process

To convert a decimal number into a fraction, express the decimal number without the zero and the decimal point (this number will be the numerator) and write as a denominator a number one plus as many zeros after this number as numbers there are after the decimal point of the numerator.

Example

              0.154 has three number after the decimal point then we write 1000

                             154/1000 =

Simplify

                              77/500            

Answer:

5/6

Step-by-step explanation:

Rise over run

y2-y1 / x2-x1

30-15 / 36-18

Hope this helps!

Answer:

He should be very confident

Step-by-step explanation:

He should be very confident because he has a 7 out of 8 chance of getting a small medium or large prize and he has a 1 out of 8chance of getting nothing

The probability that the box selected will win the prize is A = 7/8 = 87.5 %

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that the box selected will win the prize be A

Now , the total number of boxes = 8

The box which has a big prize = 1

The number of boxes which have medium prize = 3

The number of boxes which have small prizes = 3

So , the total number of boxes with prize = 7 boxes

And , probability that the box selected will win the prize A = total number of boxes with prize / total number of boxes

On simplifying , we get

The probability that the box selected will win the prize A = 7 / 8

The probability that the box selected will win the prize A = 0.875

Hence , the probability is 7/8

To learn more about probability click :

https://brainly.com/question/17089724

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Answer:

the radius

Step-by-step explanation:

4/3*pi*r squared

Answer:

C

Step-by-step explanation:

In order to be a function, all of the graphs need to pass the vertical line test

Vertical line test- Only one point per vertical line, if there are more than one, it is not a function

C is the only one that has more than one point at a vertical line

The answer is c. If there are 2 points in a vertical line, it is not a function.

The theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots is 0.28

Explanation:

School students = 40

Total people = 130

Total contestant spot = 9

Probability of 3 contestant from school = ?

The number of combinations of 3 of the 40 students getting a spot = ⁴⁰C₃

The number of combinations of the other audience members filling the other 6 spots = ⁹⁰C₆

The number of 9 contestants with 3 students in them = ⁴⁰C₃ X ⁹⁰C₆

The total number of possible 9 contestants from the audience = ¹³⁰C₉

Probability of the group of contestants having 3 students = [tex]\frac{^4^0C_3 X ^9^0C_6}{^1^3^0C_9}[/tex]

Solving the equation further we get:

Probability of the group of contestants having 3 students = 0.28