The ratio of the height of two similar cylinders is 4:1. What is the ratio of their volumes?

Answer:

Step-by-step explanation:

length=sqare root of(12^2+12^2-2*12*12*cos(75))=14.6

The length of a chord whose central angle is 75° in a circle with a radius of 12 inches is 14.6 inches.

A circle is the set of all points in the plane that are a fixed distance (the radius) from a fixed point (the center)

A central angle is an angle with endpoints and located on a circle's circumference and vertex located at the circle's center

[tex]cos A = \frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex], where a, b ,c are the sides opposite to ∠A, ∠B, ∠C respectively.

In triangle, let ∠A = 75°.

∴ We can write, [tex]cos 75 = \frac{b^{2}+c^{2}-a^{2}}{2bc}[/tex].

So,  we can write,

(cos 75)(2 x 12 x 12) = (12)² + (12)² - a²

⇒ a = 14.6

∴ the length of the chord is 14.6 inches.

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Answer:

75 in^2

Step-by-step explanation:

L = 3W here.  Also, P = 2W + 2L = 40 in here.  Subbing 3W for L, we get

                                    2W + 2(3W) = 40, or

                                     2W + 6W = 40, or 8W = 40.  Thus, W = 5 in and L = 15 in

and the area is W*L, or 5(15) in^2, or 75 in^2

The width of the rectangle is 5 inches and the length is 15 inches. Therefore, the area of this rectangle is 75 square inches.

Let's indicate the width of the rectangle as 'w'. Given the length is three times the width, it would be represented as '3w'. The perimeter of any rectangle is calculated as 2*(length + width). Therefore, 2*(w + 3w) = 40. Solving this, we get 'w' as 5 inches and, therefore, the length as 15 inches.

The area of a rectangle is calculated by multiplying the length and width. Therefore, the area of this rectangle would be length * width = 15*5 = 75 square inches.

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For this case we have that the rug is rectangular.

By definition, the perimeter of a rectangle is given by:[tex]P = 2a + 2b = 2 (a + b)[/tex]

Where:

a, b: Represent the sides of the rectangle

Substituting according to the data we have:

[tex]P = 2 (5 + 3)[/tex]

Thus, the correct expression is option B.

Answer:

Option B

Answer:

[tex]\frac{3}{11}=\frac{21}{y}[/tex]

Step-by-step explanation:

3 boys     ->   8 girls     -> 11 students

21 boys   ->   _____     ->  y students

This information is lined up for you to solve for your number of students, y:

Looking vertically you could say the proportion is:

[tex]\frac{3}{21}=\frac{11}{y}[/tex]

Looking horizontally you could say the proportion is:

[tex]\frac{3}{11}=\frac{21}{y}[/tex]

There are other ways to write this but this last one I wrote answers your question.

Answer:

[tex]\large\boxed{\dfrac{5}{11}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ P(A\ \cup\ B)=P(A)+P(B)-P(A\ \cap\ B).\\\\\text{We have:}\\\\P(A)=\dfrac{4}{11},\ P(B)=\dfrac{3}{11},\ P(A\ \cup\ B)=\dfrac{2}{11}.\\\\\text{Substitute:}\\\\\dfrac{2}{11}=\dfrac{4}{11}+\dfrac{3}{11}-P(A\ \cap\ B)\\\\\dfrac{2}{11}=\dfrac{7}{11}-P(A\ \cap\ B)\qquad\text{subtract}\ \dfrac{7}{11}\ \text{from both sides}\\\\-\dfrac{5}{11}=-P(A\ \cap\ B)\qquad\text{change the signs}\\\\P(A\ \cap\ B)=\dfrac{5}{11}[/tex]

Answer:

Step-by-step explanation:

[tex]\bf ~\hspace{10em}\textit{Double Angle Identities}\\\\ sin(2\theta)=2sin(\theta)cos(\theta) ~\hfill cos(2\theta)= \begin{cases} cos^2(\theta)-sin^2(\theta)\\ 1-2sin^2(\theta)\\ \boxed{\bf 2cos^2(\theta)-1} \end{cases} \\\\\\ tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}[/tex]

well, take a peek at the cos(2θ) identities.

Answer:

1/4

Step-by-step explanation:

y varies directly as x means you should translate this as y=kx.

y varies indirectly as x means you should translate this as y=k/x.

Anyways we had directly, so the equation is of the form y=kx for any point (x,y) where k is the constant.

We are given y=kx and that this equation should satisfy (x,y)=(8,2).

So let's plug in 8 for x and 2 for y giving us

2=k*8

Divide both sides by 8:

2/8=k

Simplify:

1/4=k

So k is a constant, that constant, the never changing number, for the point (x,y) is 1/4.

That means the equation is y=1/4 *x. The 1/4 is the constant of variation, also called the constant of proportionality.

The constant of variation, in this case, is found to be 1/4 using the formula y = kx.

The constant of variation in this case is 1/4.

Given that y varies directly as x and y = 2 when x = 8, we can use the formula y = kx to find the constant of variation.

By substituting the values y = 2 and x = 8 into the formula, we get 2 = k * 8, which simplifies to k = 1/4.

In the system of equations, x represents the number of tickets of Level 1 seats while y represents the number of tickets of Level 2 seats.

Given to us,

system of equations,

Equation 1, 150x + 250y = 125,000,

Equation 2,  x + y = 50,000,

Total number of seats = 50,000 seats,

Total number of sales = $125,000,

Level 1 tickets price = $150,

Level 2 tickets price = $250,

Let us assume, Number of tickets of Level 1 is [tex]\bold x[/tex], and, Number of tickets of Level 2 is [tex]\bold y[/tex],

Total sales = (Number of tickets of Level 1 x Level 1 tickets price ) + (Number of  tickets of Level 2 x Level 2 tickets price )

125,000 = ([tex]\bold x[/tex] x 150) + ([tex]\bold y[/tex] x 250)

125,000 = 150x + 250y

Now,

Total number of seats = Number of tickets of Level 1 + Number of tickets of Level 2

50,000 = x + y

Therefore, In the system of equations, x represents the number of tickets of Level 1 seats while y represents the number of tickets of Level 2 seats.

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The variables x and y represent the number of Level 1 and Level 2 tickets sold, respectively. These variables show how many of each type of ticket were sold at their respective prices ($150 and $250) to achieve a total sale of $125,000.

The problem presents a linear system of equations that models the pricing of tickets sold at a concert.

The equations are:

In this system:

Therefore, these equations together show the total number of tickets sold and the total revenue from these tickets.

Answer:

American Bison

Step-by-step explanation:

First find out how many feet the bison runs in an hour.

To find that out you have to multiply 3520 by 60 minutes because there are 60 minutes in an hour.

So 3520*60 = 211,200 feet

Then you have to convert 211,200 feet into miles and since there are 5,280 feet in an a mile you have to divide.

So 211,200 divided by 5,280 = 40

So the American Bison runs 40 miles per hour which is faster than the White Tailed Deer who only runs 30 miles per hour.

So the answer is the American Bison.

Answer:

[tex]y-\frac{3}{2}=\frac{-13}{3}(x-\frac{1}{2})[/tex] point-slope form

[tex]13x+3y=11[/tex] (standard form)

Let me know if you prefer another form.

Step-by-step explanation:

The slope of a line can be found using [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] provided you are given two points on the line.

We are.

Now you can use that formula.  But I really love to just line up the points vertically then subtract them vertically then put 2nd difference over 1st difference.

 (4/5  ,  1/5)

-( 1/2  ,  3/2)

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

3/10          -13/10

2nd/1st = [tex]\frac{\frac{-13}{10}}{\frac{3}{10}}=\frac{-13}{3}[/tex] is our slope.

So the following is point-slope form for a linear equaiton:

[tex]y-y_1=m(x-x_1) \text{ where } m \text{ is slope and } (x_1,y_1) \text{ is a point on the line }[/tex]    

Plug in a point [tex](x_1,y_1)=(\frac{1}{2},\frac{3}{2}) \text{ and } m=\frac{-13}{3}[/tex].

This gives:

[tex]y-\frac{3}{2}=\frac{-13}{3}(x-\frac{1}{2})[/tex]

I'm going to distribute:

[tex]y-\frac{3}{2}=\frac{-13}{3}x-\frac{-13}{6}[/tex]

Now I don't like these fractions so I'm going to multiply both sides by the least common multiply of 2,3, and 6 which is 6:

[tex]6y-9=-26x+13[/tex]

Add 26x on both sides:

[tex]26x+6y-9=13[/tex]

Add 9 on both sides:

[tex]26x+6y=22[/tex] This is actually standard form of a line.

It can be simplified though.

Divide both sides by 2:

[tex]13x+3y=11[/tex] (standard form)

Answer:

[tex]\large\boxed{y=-\dfrac{13}{3}x+\dfrac{11}{3}}-\bold{slope\ intercept\ form}\\\boxed{13x+3y=11}-\bold{standard\ form}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have two points

[tex]\left(\dfrac{4}{5},\ \dfrac{1}{5}\right),\ \left(\dfrac{1}{2},\ \dfrac{3}{2}\right)[/tex]

Convert fractions to the decimals

(divide the numerator by the denominator) :

[tex]\dfrac{4}{5}=0.8,\ \dfrac{1}{5}=0.2,\ \dfrac{1}{2}=0.5,\ \dfrac{3}{2}=1.5[/tex]

[tex]\left(\dfrac{4}{5},\ \dfrac{1}{5}\right)=(0.8,\ 0.2)\\\\\left(\dfrac{1}{2},\ \dfrac{3}{2}\right)=(0.5,\ 1.5)[/tex]

Calculate the slope:

[tex]m=\dfrac{1.5-0.2}{0.5-0.8}=\dfrac{1.3}{-0.3}=-\dfrac{13}{3}[/tex]

Put the value of slope and the coordinates of the first point to the equation of a line:

[tex]0.2=-\dfrac{13}{3}(0.8)+b[/tex]      multiply both sides by 3

[tex]0.6=(-13)(0.8)+3b[/tex]

[tex]0.6=-10.4+3b[/tex]           add 10.4 to both sides

[tex]11=3b[/tex]           divide both sides by 3

[tex]\dfrac{11}{3}=b\to b=\dfrac{11}{3}[/tex]

Finally:

[tex]y=-\dfrac{13}{3}x+\dfrac{11}{3}[/tex] - slope-intercept form

Convert to the standard form (Ax + By = C):

[tex]y=-\dfrac{13}{3}x+\dfrac{11}{3}[/tex]      multiply both sides by 3

[tex]3y=-13x+11[/tex]          add 13x to both sides

[tex]13x+3y=11[/tex] - standard form

Answer:

-6

Step-by-step explanation:

[tex]m^2-36=0[/tex]

Adding 36 on both sides gives:

[tex]m^2=36[/tex]

Square rooting both sides:

[tex]m=\pm \sqrt{36}[/tex]

[tex]m=\pm 6[/tex]

So if square -6 , you will get 36 just like when you square 6.

That is [tex](-6)^2=6^2=36[/tex]

Answer:

-6

Step-by-step explanation:

If one solution to the problem m²-36=0 is 6, the other solution is -6.

(m + 6) • (m - 6)  = 0

Any solution of term = 0 solves product = 0 as well.

m+6 = 0  

m = -6

m-6 = 0

m = 6

Answer:

Height of light post = 33 feet

Step-by-step explanation:

We will use the trigonometric ratios to find the height of light post

The given scenario forms a right angled triangle with the right angle with the light post.

The distance between light post and the person is the base.

So, base = b = 40 feet

The height of light post will be the perpendicular

So,

Perpendicular = p = x

Angle = 35°

So,

tan (angle) = p/b

tan 35° = p/40

0.7002 =p/40

0.7002*40 = p

p = 28 feet

Since the persons eye level is 5 feet from the ground, 5 feet will be added to perpendicular for actual height of light post.

Height of light post = 28+5 = 33 feet ..

Answer: 123.5 in^2

Step-by-step explanation: The formula for the area of a trapezoid is a+b/2 x h. In other words, base 1 plus base 2 divided by 2, and multiplied by the height. Plug in the numbers. The equation is:

6+7/2 x 19 = 123.5.

Since you are finding the area, the answer would be in inches squared. The answer is 123.5 in^2.

Answer:

A) 0.0194

B) 1.94%

C) $ 170,000

Step-by-step explanation:

Value of house in 1992 = P = $ 120,000

Value of house in 2007 = S = $ 160,000

Time difference from 1992 to 2007 = 15 years

Part A)

The formula of compound interest is:

[tex]S=P(1+r)^{t}[/tex]

P is the original amount i.e. $ 120,000

t is the time in years which is 15 years

S is the amount after t years which is $ 160,000

r is the annual growth rate

Using the values, we get:

[tex]160000=120000(1+r)^{15}\\\\\frac{160000}{120000}=(1+r)^{15}\\\\ \frac{4}{3}=(1+r)^{15}\\\\(\frac{4}{3} )^{\frac{1}{15}}=1+r\\\\ r=(\frac{4}{3} )^{\frac{1}{15}}-1\\\\ r=0.0194[/tex]

Thus, the annual growth rate is 0.0194

Part B)

In order to convert a decimal to percentage, simply multiply the decimal by 100.

So, 0.0194 in percentage would be 1.94%

Part C)

We have to find the value of house in 2010 i.e. after 18 years. So t =18

Using the values in the formula, we get:

[tex]S=120000(1+0.0194)^{18}\\\\ S=169584[/tex]

Rounded to nearest thousand dollars, the value of the house would be $ 170,000

Answer:

it is 11 degrees and i did the doom quiz and passt so yeah bye peace

[tex]g(f(x))=3x+2+5=3x+7[/tex]

Answer:

See below in bold.

Step-by-step explanation:

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

= 5x - 9.

(g - h)(x) = 4x - 4 - (x - 5)  ( Note we put the x - 5 in parentheses)

= 4x - 4 - x + 5

=  3x + 1.

(g.h)(x) = (4x - 4)(x - 5)

so (g.h)(1) = (4(1) - 4)(1 - 5)

= 0 * -4

= 0.

The product of the functions will be (g·h)(x) = 4x² – 24x + 20. At x = 1, the product of the functions is zero.

A statement, principle, or policy that creates the link between two variables is known as a function.

The functions are given below.

g(x) = 4x – 4

h(x) = x – 5

Then the sum of the functions will be

(g + h)(x) = (4x – 4) + (x – 5)

(g + h)(x) = 4x – 4 + x – 5

(g + h)(x) = 5x – 9

Then the difference in the functions will be

(g – h)(x) = (4x – 4) – (x – 5)

(g – h)(x) = 4x – 4 – x + 5

(g – h)(x) = 3x + 1

Then the product of the functions will be

(g·h)(x) = (4x – 4)(x – 5)

(g·h)(x) = 4x² – 4x – 20x + 20

(g·h)(x) = 4x² – 24x + 20

At x = 1, then we have

(g·h)(x) = 4(1)² – 24(1) + 20

(g·h)(x) = 4 - 24 + 20

(g·h)(x) = 0

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Answer:

W (-1, 4) ---> W' (-4, -1)

X (-1, 2)  ---> X' (-2, -1)

Y (2, 2)  ---> Y' (-2, 2)

Z (2, 4)  ---> Z' (-4, 2)

Step-by-step explanation:

We are given the graph with a rectangular figure WXYZ and we are to find the coordinates of its vertices W'X'Y'Z' after the transformation of 90° rotation.

We know that, the rule for 90° rotation of a point (x, y) gives (-y, x).

So,

W (-1, 4) ---> W' (-4, -1)

X (-1, 2)  ---> X' (-2, -1)

Y (2, 2)  ---> Y' (-2, 2)

Z (2, 4)  ---> Z' (-4, 2)

Answer

W'

✔(-4,1)

X'

✔ (-2, -1)

Y'

✔ (-2, 2)

✔Z'(–4, 2)

Step-by-step explanation:

Look at the picture

To solve for the amount of pure silver in the alloy mixture, use the alloy mixture equation in algebra. After setting up and solving the equation, we find that roughly 22.83 ounces of pure silver are used to produce the desired alloy,

This problem can be solved using the alloy mixture equation, which is used to determine how to create a desired mixture by blending two substances of different concentrations. Let's denote the amount of pure silver used as 'x'. So, the equation can be set up as follows:

($30.48 × x + $21.35 × 52) / (x + 52) = $24.76.

After multiplying through by (x + 52) and doing algebra, you will find that x (ounces of pure silver) equals approximately 22.83 ounces.

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Answer:

- 90

Step-by-step explanation:

These are the terms of an arithmetic sequence with n th term

[tex]a_{n}[/tex] = a + (n - 1)d

where a is the first term and d the common difference

d = 6 - 9 = 3 - 6 = - 3 and a = 9, hence

[tex]a_{34}[/tex] = 9 - 3 × 33 = 9 - 99 = - 90

The [tex]a_{34}[/tex] is -90 in the given sequence.

The given sequence is 9,6,3,......

We are asked to find the [tex]34^{th}[/tex] term in the sequence which is denoted by  [tex]a_{34}[/tex].

We first need to know what type of sequence is given in the question.

A sequence where the difference between the consecutive terms is always the same.

The formula used to find the value of the required term is given by:

[tex]a_n = a + (n-1)d[/tex]

Where a = first term, n = the term value and d = common difference.

The given sequence is 9,6,3,.....

We see that the given sequence is an arithmetic sequence.

6 - 9 = -3 and 3 - 6 = -3

so,

d = -3.

Here a = 9.

And we need to find the value in the sequence at n = 34.

substituting a,d, and n values in  [tex]a_n = a + (n-1)d[/tex].

We get,

[tex]a_{34} = 9 + ( 34 - 1 ) (-3)\\a_{34} = 9 + 33(-3)\\a_{34} = 9 - 99\\a_{34} = -90[/tex]

Thus, the [tex]a_{34}[/tex] is -90 in the given sequence.

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Answer:

34

Step-by-step explanation:

You can use the distance formula to find the distance between any two points in the coordinate plane.

For this problem, you can use a simpler method since both points have the same x-coordinate. Two points than have the same x-coordinate are on the same vertical line. The distance between them is the absolute value of the difference between the y-coordinates.

distance = |-12 - 22| = |-34| = 34

Answer:

34

Step-by-step explanation:

By the distance formula:

[tex]D = \sqrt{[-4-(-4)]^2 + (22-(-12))^2} = \sqrt{34^2} = |34| = 34[/tex]

Answer:

[tex]7\sqrt{2}[/tex]

Step-by-step explanation:

We start by factoring 98 and look for a perfect square:

98=7*7*2 = [tex]7^{2} *2[/tex]

This allow us to simplify the radical:

[tex]\sqrt{98} = \sqrt{7^{2}*2 }[/tex]

Finally we have:

[tex]\sqrt{7^{2}*2 } =7\sqrt{2}[/tex]

Answer:

32.49

Step-by-step explanation:

First you must set up the probably and plug in the variables into the formula. Sthe formula would turn into the equation: C=30.99 (c for cost) + .5 [r for tax] (30.99) c for cost. Then you will solve the equation:

1. C= 30.99+.5(30.99)

2. C= 30.99+ 1.50

3. C= 32.49

Answer:

The total cost of the shoes is $32.5395.

Step-by-step explanation:

The equation that you must use is [tex]C=p+p\times r[/tex]. Keep in mind that percentage number is the number divided by 100 in real numbers. For example, 5% equals 0.05. So, instead of using the term 5%, you must use 0.05.

Now, let's replace the variables in the equation with the data that the problem gives.

[tex]C=p+p\times r[/tex]

[tex]C=(30.99)+(30.99)\times (0.05)[/tex]

[tex]C=30.99+1.5495[/tex]

The term $1.5495 refers to the tax that must be paid for the shoes. The total cost is the sum of the price and the tax.

[tex]C=32.5395[/tex]

Thus, the total cost of the shoes is $32.5395.

Answer:

B and C

Step-by-step explanation:

There are 3 conditions for the difference of squares.

The correct answer is B and C

Final answer:

Binomials that are a difference of squares have the form a² - b² and can be factored into (a + b)(a - b), where both terms are perfect squares. Examples include x² - 9 and 4y² - 25.

Explanation:

To determine which binomials are a difference of squares, we look for expressions in the form of a2 - b2. A difference of squares can be factored into (a + b)(a - b), where a and b are any expressions. It is essential that both terms be perfect squares and that they are subtracted from one another.

For example, x2 - 9 is a difference of squares as it can be factored into (x + 3)(x - 3), where both x2 and 9 are perfect squares. Another example could be 4y2 - 25, which factors to (2y + 5)(2y - 5). Keep in mind that if the sign is not subtraction, or if either term is not a perfect square, the binomial does not represent a difference of squares. The correct choice of examples, factoring process, and the nature of perfect squares are essential to identify differences of squares accurately.

(gºf) means solve f(x) first, then use that for g(x)

In the equation for f(x) replace x with -3:

f(x) = x +4 = -3 +4 = 1

Now replace the x in the equation for g(x) with 1

g(x) = x = 1

Answer:

7 pieces

Step-by-step explanation:

Stock that must be available at the beginning of each month = 26 yards

Since,

1 yard = 36 inches

26 yards = 26 x 36 = 936 inches

This means 936 inches of fabric must be available at beginning of each month.

Current Inventory:

4 pieces that are each 22 1/2 (or 22.5) inches long. So total length of these fabrics =  4 x 22.5 = 90 inches

3 pieces that each 33 inches long. So total length of these fabrics = 3 x 33 = 99 inches

Therefore, the total length of current inventory = 90 + 99 = 189 inches.

Length of fabric needed more:

Length of fabric that must be bought more = 936 - 189 = 747 inches

It is given that the fabric must be bought in pieces are the 3 yards long. 3 yards is equal to 108 inches.

So,  I have to buy pieces that are each 108 inches long and I need to complete 747 inches in total.

Therefore, the number of pieces that I need to buy = [tex]\frac{747}{108}=6.9[/tex]

Since, the pieces cannot be bought in fraction, I need to buy 7 complete pieces to replenish my stock.

You need to purchase 7 pieces of 3-yard fabric.

To determine how many pieces of fabric you need to buy, follow these steps:

Therefore, you need to purchase 7 pieces of fabric to replenish your stock.

Answer:

length = 11

width = 6

Step-by-step explanation:

The area of a rectangle is defined by the following formula:

[tex]A=lw[/tex]

The question content tells us this:

[tex]l=3w-7\\A=66[/tex]

If we plug these into our formula, we can find the dimensions.

[tex]66=w(3w-7)\\66=3w^2-7w\\[/tex]

Once we factor this out, we find that [tex]w=6[/tex] and [tex]w=-\frac{11}{3}[/tex]

Since a side length can't be a negative, our width is 6.

[tex]66=6l\\11=l[/tex]