The volume of a cylinder is 480pie cm3. The height of the cylinder is 30 cm. What is the radius of the
cylinder?
The radius of the cylinder is
cm. (Simplify your answer.)

Answer:

π/6 , 7π/6

Step-by-step explanation:

3sinx = sinx + 1 ⇒ 2sinx = 1 ⇒ sinx = 1/2

At which value(s) of x does sinx equal 1/2?

x = arcsin(1/2) at π/6 and 5π/6

[tex]~~~~~\sin 30^{\circ} = \dfrac{\text{Perpendicular}}{\text{Hypotenuse} }\\\\\\\implies \dfrac 12 = \dfrac{8}x\\\\\\\implies x = 8\cdot2\\\\\\\implies x = 16 ~ \text{cm.}[/tex]

Answer:

first choice

Step-by-step explanation:

First, observe the axis.

The graph has labeled:

vertical axe as h (hight) and

horizontal axe as t (time).

Second, observe on the graph that the object is dropped from the height 120 feet because at the point t = 0 (when the drop did not start yet) the height is h = 120.

→We can eliminate the last choice that said "object is dropped from -16 feet"

Third, the equations for the hight of the object after t seconds are when the object is dropped from 120 feet are:

h(t) = -16t² + 120

if t= 0 then hight should be 120

h(t) = -16·0² + 120 = 120 ✅

and

h(t) = -16t² - 120

if t= 0 then hight should be 120

h(t) = -16·0² - 120 = - 120 ❌

→Eliminate the second choice that said at t=0 , h(t) = -120

→The first choice is the correct one

Answer:

-10 + 28i

Step-by-step explanation:

Multiply the binomials ↓

1*5+3i+(5i*5)+(5i*3i)

Simplify ↓

5+3i+25i+15i²

Combine like terms ↓

5+28i+15i²

Now, since i is the square root of -1, i² (i times i) is equal to -1 ↓

5+28i-15

28i-15+5

28i-10

hope helpful ~

Answer:

Q1: 6

Med: 11

Q3: 13

Box plot: Place the far left line on 2 and the far right line on 14 to represent the minmum and maximum. For the box, drag the middle line inside to 11, keep the left side of the box on six and drag the right side to 13. It should look like the picture below when you're done.

Step-by-step explanation:

hope this helps!

Answer:

1100/7

Step-by-step explanation:

Because, this is half circle then if we need the length of it we will use the circumference (2 x pie x r) x 1/2

To convert any given angle from the measure of degrees to radians, the value has to be multiplied by π/180.

hope it helps...!!!

Answer:

there are 2pi radians in a circle

there are also 360 radians in a circle

let r = radians and d = degrees

2*pi*r=360*d

2pi/360*radians = degrees

(pi/180)*radians = degrees

Answer:

The two events are independent

Step-by-step explanation:

Since the king was placed back in the deck and the deck was re-shuffled,

the drawing of a king does not effect the probability of subsequently drawing a queen.

The probability of picking the queen is independent of the probability of picking the king.

pick a card from a shuffled pack and draw a king. You put it back in the pack, shuffle, and then pick another card. This time you draw a queen. How are the two events of picking a king and picking a queen related to be justified

Probability can be defined as the ratio of favorable outcomes to the total number of events.

There is a 52-card deck.
Pick a card from a shuffled pack and draw a king. You put it back in the pack, shuffle,
Probability can be given as for the draw of the king,
p = 1/52

Put it back in the pack, shuffle, and then pick another card. This time you draw a queen.
Probability can be given as for the draw of the queen,
p = 1/52

Since both probabilities is the same it implies the probability of one event is independent of the other.

Thus, the probability of picking the queen is independent of the probability of picking the king.

Learn more about probability here:

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Answer:

A Rectangle should fit all these rules.

Answer:

C number of binders because the teacher would have to order binders depending on how many students there are.

Step-by-step explanation:

Answer:

Summary:

The solution to 2.5 - 1.2x < 6.5 - 3.2x lies in the interval (-∞, 2).

Answer:

452.16

Step-by-step explanation:

di is twice the radius and to get area you need radius so 24/2=12

now insert 12 into the formula 12^2*3.14 now use pemdas

12^2=144

144*3.14

452.16

Answer:

Area of circle = 452.16

Step-by-step explanation:

Conversion of diameter into radius,

→ r = 24/2

→ [ r = 12 ]

Formula we use,

→ Area = π × r²

Now the area of circle will be,

→ π × r²

→ 3.14 × (12)²

→ 3.14 × 144

→ 452.16

Hence, area of circle is 452.16.

Answer:

a=13m

Step-by-step explanation:

that's it in the picture

Answer:

[tex]\sf a=\boxed{13}\:cm[/tex]

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

[tex]\implies \sf \sin(31^{\circ})=\dfrac{a}{25}[/tex]

[tex]\implies \sf a=25\sin(31^{\circ})[/tex]

[tex]\implies \sf a=12.87595187...\:cm[/tex]

Therefore, a = 13 cm (to the nearest whole number)

The two equations that could be used to determine the number of pictures (x) and songs (y) is x + y = 16  and 650x + 2200y = 18150

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

Let x represent the number of pictures and y represent the number of songs, hence:

x + y = 16    (1)

And:

650x + 2200y = 18150    (2)

The two equations that could be used to determine the number of pictures (x) and songs (y) is x + y = 16  and 650x + 2200y = 18150

Find out more on equation at: https://brainly.com/question/2972832

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Answer:

5

19

Step-by-step explanation:

Is the correct answer to the probability

Answer:

First, evaluate 3^3

3^3 means three times itself three times.

[tex]3 * 3 * 3 = 27[/tex]

[tex]\sqrt{27} = 5.19[/tex]

Next, square root eight.

[tex]\sqrt{8} = 2.82[/tex]

Now, divide the two numbers.

[tex]5.19 / 2.82 = 1.84[/tex] if needed, include full form: 1.840425531914894

(3n)³ = 27

= 27√8 = 2.82

= 27√8 = 2.82√27 = 5.19

5.19/2.82 = 1.84

Here is your answer buddy..

Answer:

[tex]\displaystyle \large{f^{-1}(7)=5}[/tex]

Step-by-step explanation:

Given:

[tex]\displaystyle \large{f(x)=2x-3}[/tex]

To find:

[tex]\displaystyle \large{f^{-1}(7)}[/tex]

Inverse Function Definition:

Notation Definition (Example - Exponential Function and Logarithm are Inverse to each other.)

[tex]\displaystyle \large{f(x) = \{(x,y) \in \mathbb{R} \times \mathbb{R^{+}} \ | \ y=a^x, a\neq 1, a > 0 \}}\\\displaystyle \large{f^{-1}(x) = \{(x,y) \in \mathbb{R^{+}} \times \mathbb{R} \ | \ y=\log_a x, a\neq 1, a > 0 \}}[/tex]

Notice that both functions have swapped domain and range. Domain is set of all x-values while range is set of all y-values.

Inverse Property:

Back to the question, first, we have to find an inverse of linear function. We can do by swapping x and y [f(x)] variables.

[tex]\displaystyle \large{f(x)=2x-3 \to x=2f(x)-3}[/tex]

Solve for f(x):

[tex]\displaystyle \large{x=2f(x)-3}\\\displaystyle \large{x+3=2f(x)}\\\displaystyle \large{f(x)=\dfrac{x+3}{2}}\\\therefore \displaystyle \large{f^{-1}(x)=\dfrac{x+3}{2}}[/tex]

Therefore, the inverse is (x+3)/2. Next, we find [tex]\displaystyle \large{f^{-1}(7)}[/tex] which we can do by simply substituting x = 7 in the inverse.

[tex]\displaystyle \large{f^{-1}(7)=\dfrac{7+3}{2}}\\\displaystyle \large{f^{-1}(7)=\dfrac{10}{2}}\\\displaystyle \large{f^{-1}(7)=5}[/tex]

Therefore, the answer is 5.

Answer:

Option B is the answer

am not really sure though

Answer:

2.5

Step-by-step explanation:

i am not absolutely sure but according to me it is right

ANSWER:

2.45

Expalnation:

If you add/subtract 0.75 to the corrct side, you'll get 2.45.

3.2-2.45=0.75

2.45-1.7=0.75

Hence, this is the corrct answer.

Answer:

1. C(d)=0.69x+25.95

2. C(d)=0.69(57)+25.95

[0.69 times 57 is 39.33]

=  65.28 dollars

3. 136.3 miles

Step-by-step explanation:

For the first question....

Since this is a function, we have to start with C(d). Even if you drive 0 miles, you still have to pay $25.95 just for renting the truck, so that is constant. For every mile you drive, you pay $0.69. Since we don't know how far anyone is going to drive, we will put 'x' as the amount of miles driven. The number of miles driven (x) multiplied by 0.69 will be the cost of that. The final function would be C(d)=0.69x+25.95.

For the second question....

We know the general function now, so driving 57 miles would mean substituting "x" for 57, and doing the multiplication (if necessary), 0.69 times 57 equals 39.33 (the dollar amount for driving 57 miles, not including the starting fee of 25.95)

Doing the math, you can get $65.28 (39.33+25.95).

For the third question...

If we have a budget, we know that C(d) is the amount of money spent, so we'll substitute the budget (120) for that. We'll solve the equation for x from there, and should get 136.3 miles (rounded to the nearest hundredth).

Hope this helps!

The linear model for the daily cost is C(x) = $1378 + $1.83(x).

The cost of producing 267 widgets is $1,866.61

Fixed cost is the cost the remains constant with the number of widgets produced. Variable cost increases with  the number of widgets produced. Daily cost is the sum of fixed cost and variable cost.

Fixed cost = fixed cost + (variable cost x number of widgets)

C(x) = $1378 + $1.83(x).

C(x) = $1378 + $1.83(267) = $1,866.61

To learn more about fixed cost, please check: https://brainly.com/question/25879561

Answer:

I believe 20. is (0,0)

Step-by-step explanation:

Sorry if I'm mistaken, I don't know number 18. though. I'm terribly sorry. I hope you figure it out soon and you have an amazing day! ^^ <3

There are 2 tangent lines that pass through the point

[tex]y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2[/tex]

and

[tex]y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2[/tex]

Explanation:

Given:

[tex]y=\frac{x}{x+1}[/tex]

The point-slope form of the equation of a line tells us that the form of the tangent lines must be:

[tex]y=m(x-1)+2[/tex] [tex][1][/tex]

For the lines to be tangent to the curve, we must substitute the first derivative of the curve for [tex]m[/tex]:

[tex]\frac{dy}{dx} =\frac{d(x)}{dx}(x+1)-x^\frac{d(x+1)}{dx} \\ \\[/tex]

[tex]\frac{dy}{dx} =\frac{x+1-x}{(x+1)^2}[/tex]

[tex]\frac{dy}{dx}= \frac{1}{(x+1)^2}[/tex]

[tex]m=\frac{1}{(x+1)^2}[/tex] [tex][2][/tex]

Substitute equation [2] into equation [1]:

[tex]y=\frac{x-1}{(x+1)^2}+2[/tex] [tex][1.1][/tex]

Because the line must touch the curve, we may substitute [tex]y=\frac{x}{x+1}:[/tex]

[tex]\frac{x}{x+1}=\frac{x-1}{(x+1)^2}+2[/tex]

Solve for x:

[tex]x(x+1)=(x-1)+2(x+1)^2[/tex]

[tex]x^2+x=x-1+2x^2+4x+2[/tex]

[tex]x^2+4x+1[/tex]

[tex]x\frac{-4±\sqrt{4^2-4(1)(1)} }{2(1)}[/tex]

[tex]x=-2[/tex] ± [tex]\sqrt{3}[/tex]

[tex]x=-2[/tex] ± [tex]\sqrt{3}[/tex] [tex]and[/tex] [tex]x=-2-\sqrt{3}[/tex]

There are 2 tangent lines.

[tex]y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2[/tex]

and

[tex]y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2[/tex]

Answer:

152 in^2

Step-by-step explanation:

If you take the left side and consider it a whole rectangle, you can calculate the area of that triangle to be 80. Using the same method, you can find the area of the rectangle of the right to be 72. Then add them together.

80 + 72 = 152 in^2

Answer:

It should be D

Step-by-step explanation:

I think it’s D since that’s what I got

Answer:

300 lbs

Step-by-step explanation:

We know that Larry bench pressed 200 lbs last week, and that he is supposed to increase by 15%. We know that any number times one is that same numbers. That means a number that is increaseing has to be greater than 1. So, we have to convert 15% into a decimal. That is 0.15. That plus one is 1.15. Now we just have to multiply 1.15 with 200. We get 300.

Answer:

Emily, use the circle formula to solve this (x−a)^2 + (y−b)^2 = r^2

Step-by-step explanation:

where  a  and b are the center off sets in the x and y directions , repspectively.  

(x - 5)² + (y + 2)² =81/4

So you now know,  the center is at   (x,y) = ( 5, 2)

and the radius is   [tex]\sqrt{\frac{81}{4} }[/tex]  ,  why is is square rooted ?  you ask.

because in our formula above it's   r^2  .. so we need to square root it to find it's value.

[tex]\frac{\sqrt{81} }{\sqrt{4} }[/tex]  =  [tex]\frac{9}{2}[/tex]  =  4.5  rounded to two decimals    4.50 but not necessary

Answer:

  D.  F(G(H(x))) depends on G(H(x))

Step-by-step explanation:

A function depends on its argument (the stuff in parentheses after the function name). The argument of function F in F(G(H(x))) is G(H(x)).

  F(G(H(x))) depends on G(H(x))

__

Answer choices A and C do not make any statement about the given composition. Answer choice B shows a composition (H(G(x))) that has no relation to the argument of function F.

Answer:  D.  F(G(H(x))) depends on G(H(x))

Step-by-step explanation:

Answer:

[tex] {4x}^{2} - 20x + 25[/tex]

Step-by-step explanation:

[tex] {(2x - 5)}^{2} = {(2x)}^{2} - 2(2x)(5) + {5}^{2} = 4 {x}^{2} - 20x + 25[/tex]