A cylinder has a volume of 200 mm³ and a height of 17 mm.

a) The volume formula for a cylinder is V = r²h. Isolate for the variable r in this formula.


b) Using the equation where you isolated for r in part a, find the radius of the cylinder.
Round your answer to the nearest hundredth.

The altitudes of equal length, BE and CF gives AB = AC, from which we have;

From the given description, we have;

BE = CF

<CFB = <BEC = 90° All right angles are congruent

BC = BC by reflexive property of congruency

BC = The hypotenuse side of triangles ∆BFC and ∆CEB

Therefore;

∆BFC is congruent to ∆CEB by Right angle Hypotenuse Side, RHS, rule of congruency.

Therefore;

BF = CE by Corresponding Parts of Congruent Triangles are Congruent, CPCTC

Similarly, we have;

∆AEB is congruent to ∆AFC, by Side-Angle-Angle, SAA, rule of congruency

Which gives;

FA = AE by CPCTC

BF + FA = CE + AE, by substitution property of equality

BF + FA = AB

CE + AE = AC

Therefore;

Therefore;

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Using it's formula, the surface area of the figure is:

A. S=2332 m²

The surface area of a rectangular prism of dimensions l, w and h is given by:

S = 2(lw + lh + wh)

In this problem, the dimensions are:

35m, 9m, 16m

Hence the surface area of the rectangular prism is:

S = 2(35 x 9 + 35 x 16 + 16 x 9) = 2038 m².

The surface area of a cube of side length l is given by:

S = 6l².

In this problem, we have that l = 7 m, hence the surface area is:

S = 6 x 7² = 294 m².

The total surface area is the sum of the surface areas, hence:

T = 2038 m² + 294 m² = 2332 m².

Which means that option A is correct.

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Using the unit circle, the correct answer regarding the comparison of angles w and t is given by:

a. t > w.

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

From this, we get that the sine is represented by the vertical axis. As we advance into the second quadrant, as the angle increases, sine decreases. Hence, since sin w > sin t, we have that t > w and option a is correct.

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Answer:

[tex] {3}^{x} [/tex]

Step-by-step explanation:

[tex] {x}^{3} = 8[/tex]

[tex] {3}^{x} = 9[/tex]

Answer:

1/3

Step-by-step explanation:

The numbers are 1, 2, 3, 4, 5, and 6.

Both 3 and 6 are multiples of 3.

So, 2/6 is the probability since there is an equal change that the arrow will land on each section.

This simplifies to 1/3.

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Answer:

P (multiple of 3) =  [tex]\bf \frac{1}{3}[/tex]

Step-by-step explanation:

Numbers on the spinner, ξ = {1, 2, 3, 4, 5, 6}    (6 elements)

Multiples of 3 = {3, 6}   (2 elements)

P (multiple of 3) = no. of multiples of 3 / total no. of numbers on spinner

                          =  [tex]\frac{2}{6}[/tex]

                          =  [tex]\bf \frac{1}{3}[/tex]

The ship captain should be turned 129.49 so it's heading straight for Island B.

Given Island A is 160 miles from Island B and the captain of a ship travels 170 miles from Island A and then discovers that he is off course and 200 miles from island B.

So we gave it

a = 200 feet

b = 170 feet

c = 160 feet

We need to find angle C which goes directly to island B.

We apply the "cosine law":

[tex]\begin{aligned}\cos C&=\frac{a^2+b^2-c^2}{2ab}\\ &=\frac{(200)^2+(170)^2-(160)^2}{2\times 200\times 170}\\ &=\frac{40000+28900-25600}{68000}\\ &=\frac{43300}{68000}\\ &=0.636\end[/tex]

Now we multiply both sides by cos⁻¹, we get

cos⁻¹(cos C)= cos⁻¹(0.636)

C = 50.51

The interior angle is 50.51°

We need to find the outer angle to find the bearing the captain needs to turn

Applying the additional angle ruler:

The outside angle = 180 - 50.51 = 129.49°

Therefore, he must turn so as to head directly for Island B, where Island A is 160 miles from Island B and the captain is sailing 170 miles.

from Island A and then discovers that it is off-road and 200 miles away

Island B is 129.49.

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Any complex number [tex]z[/tex] can be written in polar/exponential form as

[tex]z = |z| e^{i\arg(z)} = |z| (\cos(\arg(z)) + i \sin(\arg(z)))[/tex]

In the complex plane, the given complex number belongs to the third quadrant since both its real and imaginary parts are negative. This means the argument must be between π and 3π/2, so the first two options are eliminated.

The difference between the remaining two options is the coefficient [tex]|z|[/tex]. We have

[tex]z = -2\sqrt3 - 6i \implies |z| = \sqrt{(-2\sqrt3)^2 + (-6)^2} = 4\sqrt3[/tex]

so (D) (the last option) is the correct choice.

The points are (7, 13/3).

Lets simplify the equation,

The equation of first line: y = 1/3 x + 2

the equation of second line: y= 4/3x - 5

Solve the system of equations by elimination,

Multiply equation A by -4 both sides

-4y = -4(1/3x +2)

-4y = -4/3x-8

After eliminating the equation we get,

y = 13/3

So now have to find x

13/3 = 1/3x + 2

Lets multiply above by 3
x = 13-6

x = 7.

Hence the points are (7, 13/3)

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Answer:

B

Step-by-step explanation:

What is the solution to the system of equations?

(7, 4)

(7, StartFraction 13 over 3 EndFraction)

(8, StartFraction 14 over 3 EndFraction)

(9, 7)

Using the law of sines, it is found that 1 triangle can be formed with the given conditions.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

Hence, for this problem, we have that the relation is:

[tex]\frac{\sin{64^\circ}}{10} = \frac{\sin{G}}{9}[/tex]

[tex]\sin{G} = 0.9\sin{64^\circ}[/tex]

[tex]\sin{G} = 0.8089[/tex]

[tex]G = \arcsin{0.8089}[/tex]

G = 54º

A triangle can have one angle of 64º and another of 54º, hence 1 triangle can be formed with the given conditions.

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Answer:

x = 10

Step-by-step explanation:

180 = 90 + 40 + (4x + 10)

180 = 130 + (4x + 10)

4x + 10 = 180 - 130

4x + 10 = 50

4x = 50 - 10

4x = 40

x = 40/4

x = 10

Answer:

x = 10

Step-by-step explanation:

An euclidean triangle is defined to have sum of all 3 interior angles equal to 180°.

In the given triangle, we know three measurement:

You may be wondering, where does 90° come from. The answer is you can find it by looking if a triangle has a little square symbol or not. If it does, the measurement will always be 90°.

Now since we know that sum of 3 interior angles must equal to 180° in euclidean triangle. Therefore, sum up three of measurement then set to 180°.

[tex]\displaystyle{90 + 4x+10 + 40= 180}[/tex]

Evaluate and solve for the x-variable:

[tex]\displaystyle{90 + 4x+10 + 40= 180}\\\\\displaystyle{4x+140 = 180}\\\\\displaystyle{4x=180-140}\\\\\displaystyle{4x=40}\\\\\displaystyle{x=10}[/tex]

Therefore, the value of x is 10

Based on the graph of the cupcakes done, we find that w(2) = 5.

Herein we have an application of linear equations to the production of cupcakes. In accordance with the graph, the horizontal axis is for the preparation time (x) and the vertical axis is for the quantity of cupcakes done (w). Based on the graph, we find that w(2) = 5.

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Answer:

200 yd²

Step-by-step explanation:

A = 17 yd

B  = 15 yd

C = 2 yd

D = 8 yd

b) Area of rectangle = length * width

 [tex]\sf Area \ of \ 2 \ triangle = 2* \dfrac{1}{2}* base * height = base* height\\\\[/tex]

Area of right triangular prism = Areas of two triangle +  area of the upper rectangle + area of middle rectangle + area of below rectangle

          = 8 * 15 +  17 * 2 + 15 *2 + 8*2

          = 120 + 34 + 30 + 16

          = 200 yd²

Answer:

option 3

Step-by-step explanation:

6x + 3x² - 4x ← collect like terms

= 6x - 4x + 3x²

= x(6 - 4) + 3x²

= x(2) + 3x²

= 2x + 3x²

Answer:

Option 3: [tex]2x+3x^{2}[/tex]

Step-by-step explanation:

Combine like terms: [tex]6x-4x=2x[/tex]

Put the equation together: [tex]2x+3x^{2}[/tex]

The correct answer option is Option 3: [tex]2x+3x^{2}[/tex].

Answer:

21

Step-by-step explanation:

Using alternate interior angles, we can conclude that angle C is equal to X (the 3rd, unmarked angle in the center triangle)

To find that 3rd angle, we can do 180 - 105 - 54. This is because all angles in a triangle must equal 180. Using this, we find that angle C is equal to 21. By the law, X must also equal 21.

Answer:

x is 21

Step-by-step explanation:

add 54 and 105, then subtract it by 180 and you get 21.

Answer: 7:4

Step-by-step explanation:

40 boys and girls 3:2 = 24 boys + 16 girls

4 boys are added  28 boys + 16 girls /4  = 7:4

Answer:

7:11

Step-by-step explanation:

We know the total number of students and the ratio of boys to girls.  The total for the ratio of boys and girls would be 5 (3+2).  Now we can set up proportions knowing these numbers.

b = 3

g =2

t =5

Let's find out how many actual boys there are by setting up a proportion

3/5 = b/40  

I will look at the denominators to find x.  5 times what gives me 40? (8).  So, I will multiple the top number (numerators).  Since I need to multiple the bottom number by 8 to get the number 40, I will now multiple the top number by 8 and get 24.

Now, I know how many actual boys and girls were in the original class.  There were 24 boys, 16 girls (40 - 24) and 40 total students.  

Now I will take this new information and apply it to the new situation.  Now I have 28 boys (24 + 4) and a new total 44.

The ratio of boys to girls would not be 28: 16 or 7:4

Answer:

x = 5, 1

Step-by-step explanation:

To solve for x, you must factor the equation. The factored equation will be: (x - 1) (x - 5) = 0. After factoring, isolate the two factored equations: (x - 1) = 0 and (x - 5) = 0. Then solve for x for both the equations which should get you to x = 5, 1.

Answer: -1/2

Step-by-step explanation:

The slope of a line tells you how steep the line is, and what direction it is going in. We can calculate the slope by seeing how much the line moves horizontally and vertically.

We can calculate the slope using [tex]\frac{rise}{run}[/tex], which is how much a point rises (goes up or down) and runs (goes left or right) to go to the next point.

Let's take two points on the graph: (-2, 0) and (0, -4). The rise will be the difference of the y-values, and the run will be the difference of the x-values.

[tex]\frac{-2-0}{0-(-4)}=\frac{-2}{4}=\frac{-1}{2}[/tex]

Hence, the slope of this line is [tex]\frac{-1}{2}[/tex]

Answer:

306 square meters

Step-by-step explanation:

The maximum area is when the length and width are the closest together.

70/2=35 we divide because there are 2 lengths and 2 widths in a rectangle

35/2=17.5, find the 2 closest integers, they are 17 and 18

17*18=306

Answer:

138

Step-by-step explanation:

There is 60 seconds in a minute, so if the heart beats 23 times in 10 seconds, it is 138 bpm.

23 * 6 = 138

Answer:

72°

Step-by-step explanation:

3x = 4x - 24 (alternate exterior angles theorem)

x = 24

So, angle RST measures 72°.

If three different orders are selected, find the probability that they are all from Restaurant B is; 0.026

Total orders both accurate and not accurate = 1131

Total orders from restaurant B (both accurate and not accurate) = 337

Probability of first order from B = 337/1131

Probability of second order from B = 336/1130

Probability of third order from B = 335/1129

Probability of the first three orders from B = 337/1131 × 336/1130 × 335/1129

Probability of the first three orders from B = 0.026

Complete question is;

Use the data in the following table , which lists drive - thru order accuracy at popular fast food chains Assume that orders are randomly selected from those included in the table Drive thru Restaurant A B C D Order Accurate 312 277 250 144 Order Not Accurate 32 60 37 19 If three different orders are selected , find the probability that they are all from restaurant A

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The linear and exponential equation that matches f(2) = 12 and f(4) = 48 are y = 18x - 24 and f(x) = 3(2)ˣ respectively

An equation is an expression that shows the relationship between two or more variables and numbers.

For the exponential function, when f(2) = 12:

12 = ab²       (1)

Also, at f(4) = 48:

48 = ab⁴   (2)

Hence:

a = 3, b = 2

f(x) = 3(2)ˣ

For the linear function using the points (2, 12) and (4, 48):

y - 12 = [(48 - 12) / (4 - 2)](x - 2)

y = 18x - 24

The linear and exponential equation that matches f(2) = 12 and f(4) = 48 are y = 18x - 24 and f(x) = 3(2)ˣ respectively

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The value of test statistic is Z =  -2.42.

According to the statement

we have given that the person in the US uses 123 gallons of water per day.

And conducted a survey of 40 randomly selected Americans and get a mean value is 113.03 gallons and a standard deviation of 25.99 gallons.

And we have to test the hypotheses with test statistic.

So,

Here we use the the z- test for one population =

Z = (sample mean - Claimed hypothesis mean)/ (standard deviation/(sample size)^1/2.)

Here the sample mean = 113.03

And claimed hypothesis mean = 123

Standard deviation = 25.99

Sample size = 40

Now put the values in the above written formula is

Z = (sample mean - Claimed hypothesis mean)/ (standard deviation/(sample size)^1/2.)

Z = 113.03 - 123 / (25.99/(40)^1/2)

Z = -9.97 / (25.99 / 6.32)

Z = -9.97 / 4.11

Z =  -2.42

So, The value of test statistic is Z =  -2.42.

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The probability of selecting 3 pencils from a box  of 5 red , 3 blue, 4 green pencils is 60/1320.

Given that box contains 5 red pencils, 3 blue pencils abd 4 green pencils.

We have to calculate the probability that 3 red pencils are selected from box. Probability is the likeliness of happening an event among all the events possible.It lies between 0 and 1. The formula of calculating probability is as under:

Probability = number of items/ total items.

Number of pencils in box=12

Number of red pencils=5

Number of blue pencils=3

Number of green pencils=4

Probability of randomly selecting 3 red pencils will be 5*4*3/12*11*10 if pencil is not replaced after drawn of pencil.

=60/1320

=1/22

Hence the probability that 3 red pencils are selected is 1/22.

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The resulting equation written in standard form is 16x² - 22x + 6 = 0.

Quadratic Equation in Standard Form: ax² + bx + c = 0

a, b and c are known values. a can't be 0.

"x" is the variable or unknown (we don't know it yet).

The "solutions" to the Quadratic Equation are where it is equal to zero.

They are also called "roots", or sometimes "zeros"

We can Factor the Quadratic (find what to multiply to make the Quadratic Equation)

Calculation for the given equation-

Now, y=-16x²+24x+6

Substitute, y = 12+2x in y = -16x²+24x+6.

=> 12+2x = -16x²+24x+6

=> 16x²-24x-6+12+2x = 0

=> 16x²-22x+6 = 0

Therefore, the quadratic equation given in the standard form is 16x²-22x+6 = 0.

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The complete question is-

The two equations are given below;

Y = 12 + 2x   linear equation

Y = -16x² + 24x + 6  quadratic equation

If you substitute 12 + 2x for y in the second equation how is the resulting equation written in standard form?

Answer:After dialation

A'=6,24

B'=12,12

C'=-12,6

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Answer:

correct answer is 110x + 29y = 333

Step-by-step explanation:

The statements that are true based on the midpoint given in the question include:

In geometry, the midpoint simply means the middle point of a line segment. The midpoint is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

Also, it should be noted that the midpoint bisects the segment.

In this case, m∠P + m∠Q + m∠R = 180°. This is because the sum of the angles in a triangle will be equal to 180°. Also, PT, QU, and RS intersect at the same point.

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Complete question:

Label the midpoint of PQ as point S, the midpoint of QR as point T, and the midpoint of RP as point U.

Next, draw PT, QU, and RS.

Which statements are true?

m∠Q = m∠R

The length of QU is half the length of RP.

m∠P + m∠Q + m∠R = 180°

QU ≅ RS

PT, QU, and RS intersect at the same point.

The sum of the lengths of QU and RS is equal to the length of PT.

Blank 1: Substitution property of equality

Blank 2: 50

Blank 3: Subtraction property of equality

The blank spaces in the task content can be filled with; Substitution property, 90° and subtraction property.

Since it follows from the vertical angles theorem that angle 1 = angle 4 as they are congruent.

Additionally, angles 1 and 2 are said to be complementary and hence, the sum of their measures is equal to 90°.

Finally, by virtue of the subtraction property of equality, the measure of angle 2 is; 90° - 40° = 50°.

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The required equation is 135 + 9x > 250.

The number of lawns Ed must mow is assumed to be x.

The amount Ed charges for each lawn he mows is $9.

Thus, the total amount Ed earns by mowing x lawns = $9x.

The savings which Ed has is $135.

Thus, the total amount Ed will have to spend can be written as the expression, $(135 + 9x).

The cost of the video game is given to be $250.

We are asked to write an equation, that can be used to find the number of lawns Ed mow, that is x so that the amount Ed has will be more than the amount he needs to buy the video game.

This can be shown as the equation:

Total amount Ed has > Cost of the video game,

or, 135 + 9x > 250.

Thus, the required equation is 135 + 9x > 250.

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