The area of the base of a cylinder is 48 square inches and its height is 14 inches. A cone has the same area for its base and the same height. What is the volume of the cone?

Trigonometry

[tex]Sine\frac{Opposite}{Hypotenuse} Cos\frac{Adjacent}{Hypotenuse} Tan\frac{Adjacent}{Opposite} \\S\frac{O}{H} C\frac{A}{H} T\frac{A}{O}[/tex]

Depending on which angle you use, decides which formula you use.

We'll use the top right angle.

9 is the adjacent.

x is the opposite.

So you need to use

[tex]Tan\frac{Adjacent}{Opposite} \\Tan45\frac{9}{x} \\x = \frac{9}{Tan45} \\x = 9[/tex]

If you solve y, you can check this is correct by doing pythagoras' theorem.

[tex]Cos\frac{Adjacent}{Hypotenuse} \\Cos45\frac{9}{y} \\y = \frac{9}{cos45} \\y = 9\sqrt{2}[/tex]

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

Answer:

50%

Step-by-step explanation:

you need to figure out what percent ok AK is BG

so we know that AK is 20 units long 10-(-10)=20

and BG is 10 units long 8-(-2)=10

so then you can solve with a proportion

10/20 = x/100

cross multiply that out

20x=1000

divide by 20

x= 50

50%

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Your answer is (C) !

The correct equation to find the amount of time they spent swimming laps is:

[tex]c. \( \frac{1}{2} \times 1 \frac{1}{2} \)[/tex]

To find the amount of time Paul and Krystal spent swimming laps, we need to determine what half of 1 1/2 hours is. This can be calculated by multiplying 1 1/2 by 1/2.

Let's look at the options:

a. [tex]\( 1 \frac{1}{2} - \frac{1}{2} \):[/tex] This would subtract 1/2 hour from 1 1/2 hours, which is not what we need.

b. [tex]\( 1 \frac{1}{2} \div \frac{1}{2} \):[/tex]This would divide 1 1/2 hours by 1/2, which is not what we need.

c. [tex]\( \frac{1}{2} \times 1 \frac{1}{2} \):[/tex]This is the correct operation, as it multiplies 1 1/2 hours by 1/2 to find half of the time.

d.[tex]\( \frac{1}{2} + 1 \frac{1}{2} \):[/tex] This would add 1/2 hour to 1 1/2 hours, which is not what we need.

So, the correct equation to find the amount of time they spent swimming laps is:

[tex]c. \( \frac{1}{2} \times 1 \frac{1}{2} \)[/tex]

Let's calculate it:

[tex]\[\frac{1}{2} \times 1 \frac{1}{2} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4} \text{ hours}\][/tex]

Therefore, Paul and Krystal spent [tex]\( \frac{3}{4} \)[/tex] hours (or 45 minutes) swimming laps.

Explanation:

The first determinant is that of the matrix of coefficients:

[tex]|A|=\left|\begin{array}{cc}5&2\\-3&-5\end{array}\right|=(5)(-5)-(-3)(2)=-19[/tex]

The second determinant is the same as the above but with the constants substituted for the x-coefficients.

[tex]|A_x|=\left|\begin{array}{cc}14&2\\3&-5\end{array}\right|=(14)(-5)-(3)(2) =-76[/tex]

The third determinant is the same as the first but with the constants substituted for the y-coefficients.

[tex]|A_y|=\left|\begin{array}{cc}5&14\\-3&3\end{array}\right|=(5)(3)-(-3)(14)=57[/tex]

_____

The solution to the system of equations is then ...

[tex]x=\dfrac{|A_x|}{|A|}=\dfrac{-76}{-19} =4\\\\y=\dfrac{|A_y|}{|A|}=\dfrac{57}{-19} =-3[/tex]

ANSWER

8π ft

EXPLANATION

The circumference of a circle is calculated using the formula C=πd.

Where d=8 is the diameter of the circle.

We substitute d=8 into the formula to obtain,

C=8π ft.

Because we are looking for the exact circumference, we leave the answer in terms of π.

Answer:

The correct answer is,

circumference = 8π feet

Step-by-step explanation:

Formula:-

Circumference of a circle = 2πr

Or circumference = πd

Where 'r' is the radius of circle and 'd' is the diameter of circle

It is given that, diameter of circle is 8 feet

To find the circumference

Here d= 8 feet

Circumference = πd = π * 8 = 8π feet

Answer:

  17.  37 2/7

  20.  3.4

Step-by-step explanation:

17.  The scale factor of the smaller triangle PQR to the larger triangle LMN is given by the ratio of corresponding sides:

  RP : NL = 18 : 28 = 9 : 14

The perimeter of LMN is the sum of the lengths of its sides:

  16 + 14 + 28 = 58

So, the perimeter of PQR is ...

  (9/14)×58 = 261/7 = 37 2/7 . . . . units

__

20. By the same reasoning as above, the sides of triangle RQP are 25/40 = 5/8 of those of triangle MNP. Then ...

  RQ = (5/8)·MN

  5x -2 = (5/8)·24 = 15 . . . . substitute the measures shown

  5x = 17 . . . . . add 2

  x = 17/5 = 3.4 . . . . . . divide by 5

The value of x is 3.4.

Answer:

The least number of pizza make deal 1 better than deal 2 is 4

The cost of deal 1 is $53.99 and the cost of deal 2 is $60

The cost per pizza of deal 1 is $5.399

The better deal is deal 1

Step-by-step explanation:

* Deal 1 becomes better if it costs less than deal 2

- Assume that the number of pizza are n

* Deal 1:

∵ The cost of one large pizza = $8.99 for first 1 and = $5 for each

   additional one

∵ They ordered n large pizza

∴ The cost = 8.99 + 5(n - 1)

- Multiply the bracket by 5

∴ The cost = 8.99 + 5n - 5

- Add like terms

∴ The cost = 3.99 + 5n

∴ The cost of deal 1 = 3.99 + 5n

* Deal 2:

∵ The cost of any large pizza is $6

∵ They ordered n large pizza

∴ The cost = 6 × n = 6n

∴ The cost of deal 2 = 6n

- We need Deal 1 better than deal 2

- Then, put the cost of deal 1 < the cost of deal 2

∵ 3.99 + 5n < 6n

- Subtract 5n from both sides

∴ 3.99 < n

∴ n > 3.99

∴ n = 4

* The least number of pizza make deal 1 better than deal 2 is 4

∵ n = 10

∴ The cost of deal 1 = 3.99 + 5(10) = 53.99

∴ The cost of deal 2 = 6(10) = 60

* The cost of deal 1 is $53.99 and the cost of deal 2 is $60

∵ The cost per one pizza = total cost ÷ the number of pizza

∴ The cost per pizza of deal 1 = 53.99 ÷ 10 = 5.399

* The cost per pizza of deal 1 is $5.399

∵ The unit price of deal 1 is $5.399

∵ The unit price of deal 2 is $6

∵ $5.399 < $6

∴ The unit rate of deal 1 is less than the unit price of deal 2

* The better deal is deal 1

Deal #1 becomes a better deal at 4 pizzas. The cost of 10 pizzas for Deal #1 is $43.99, and for Deal #2 is $60.00. The cost per pizza in Deal #1 is $8.99 for the first pizza and $5 for each additional pizza. Deal #1 is the better deal when ordering 4 or more pizzas because the cost per pizza decreases as more pizzas are added to the order.

To determine at what number of pizzas Deal #1 becomes a better deal than Deal #2, we need to compare the total cost of pizzas under each deal.

For Deal #1, the cost structure is as follows:

The first pizza costs $8.99.

Each additional large pizza on the same order costs $5.

For Deal #2, the cost is a flat rate of $6.00 per large pizza.

Let's first find out at what point the total cost of pizzas under Deal #1 equals the total cost under Deal #2. We'll denote the number of additional pizzas (after the first one) as 'n'.

The total cost for Deal #1 can be expressed as:

[tex]\[ C_1 = 8.99 + 5n \][/tex]

The total cost for Deal #2 is:

[tex]\[ C_2 = 6(n + 1) \][/tex]

We set [tex]\( C_1 \) equal to \( C_2 \)[/tex]  to find the break-even point:

[tex]\[ 8.99 + 5n = 6(n + 1) \][/tex]

[tex]\[ 8.99 + 5n = 6n + 6 \][/tex]

[tex]\[ 8.99 - 6 = 6n - 5n \][/tex]

[tex]\[ 2.99 = n \][/tex]

Now let's calculate the cost of 10 pizzas for each deal:

For Deal #1:

[tex]\[ C_{10} = 8.99 + 5(10 - 1) \][/tex]

[tex]\[ C_{10} = 8.99 + 5 \times 9 \][/tex]

[tex]\[ C_{10} = 8.99 + 45 \][/tex]

[tex]\[ C_{10} = \$43.99 \][/tex]

For Deal #2:

[tex]\[ C_{20} = 6 \times 10 \][/tex]

[tex]\[ C_{20} = \$60.00 \][/tex]

The cost per pizza in Deal #1 is $8.99 for the first pizza and $5 for each additional pizza. As the number of pizzas increases, the average cost per pizza decreases.

ANSWER

D) 4n

EXPLANATION

You can observe the following pattern from the table.

For the first term, we have,

[tex]1\to 4(1)[/tex]

For the second term, we have,

[tex]2\to 4(2) = 8[/tex]

For the third term, we have,

[tex]3\to 4(3) = 12[/tex]

For the fourth term,

[tex]4\to 4(4) = 16[/tex]

For the nth term, we will have,

[tex]n\to 4(n)[/tex]

The correct choice is D.

Answer:

Yo ________ en el mar.

A. nadó

b. nadé

c. nadamos

Step-by-step explanation:

The new price is $15.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Original Price: $20.

Discount Rate: 25%.

The discount amount,

= 25% of 20

= 5

The price,

= 20 - 5 = $15

Therefore, $15 is the new price.

To learn more about the percentage;

https://brainly.com/question/24159063

#SPJ2

Answer:

The dimensions ⇒ 3 × 4

Step-by-step explanation:

* Any matrix has two dimensions

- Raw and column

- The dimensions very important in the operations on matrices

- We called the number of raw m and the number of column n

- We must write the number of raw before the number of column

- m × n is the dimensions of the matrix

* Example : If the dimension of a matrix is 2 × 3, that

  means the matrix has 2 raw and 3 column

* Now lets look to our problem

∵  It has 3 raw and 4 column

∴ Its dimensions is 3 × 4

Answer:

Size of matrix = 3 × 4

Step-by-step explanation:

We are given the following matrix and we are to determine its dimensions:

[tex] \left [ \begin {array}{cccc} 1&-3&8&4\\7&5&3&0\\9&6&-2&-1 \end { array } \right ] [/tex]

We know that the dimension of a matrix is written in the form:

rows × columns

Here we have 3 rows and 4 columns. Therefore, the size of this matrix is 3 × 4.

Answer:

260 cm

Step-by-step explanation:

formula for finding volume:

l x w x h = v

l=length   w=width    h=height    v=volume

[tex]10\frac{2}{5}[/tex] × 3 × [tex]8\frac{1}{3}[/tex]

[tex]10\frac{2}{5}[/tex] = [tex]\frac{52}{5}[/tex]

how did i do that?

cross multiply the whole number and the denominator together and add the product by the numerator.

[tex]8\frac{1}{3}[/tex] = [tex]\frac{25}{3}[/tex]

so, [tex]\frac{52}{5}[/tex] × [tex]\frac{25}{3}[/tex] × [tex]\frac{3}{1}[/tex]

cross simplify(dont have to do it just makes everything easier)

and you get:

[tex]\frac{52}{1}[/tex] × [tex]\frac{5}{1}[/tex] × [tex]\frac{1}{1}[/tex]

and you get [tex]\frac{260}{1}[/tex]

[tex]\frac{260}{1}[/tex] = 260 cm

plz give me a brainliesttttt

Answer:

Step-by-step explanation:

52/5 x 3/1 x 25/3= 3900/15= 260 cm^3

Answer:

Message instructor about this question

Step-by-step explanation:

The question does not provide the appropriate information for a suitable answer. The equation tells you height above sea level, but the question asks when the height above ground level will be zero. No information is given as to where ground level is in relation to sea level.

The best choice is "Message instructor about this question." Ask the instructor where ground level is in relation to sea level.

___

In any event, the equation can be made somewhat simpler by factoring -16 ouf of it. Then you get ...

h(t) = -16(t^2 -7t -18) = -16(t -9)(t +2)

For h(t) = 0, solutions are ...

0 = -16(t -9)(t +2)

A product will be zero only when at least one of the factors is zero.

t = 9 or -2 . . . . . values that make the factors zero

The rocket comes back to sea level 9 seconds after launch.

___

If the rocket is launched from ground level (288 ft), then we want to find t when ...

h(t) = 288 = -16t^2 +112t +288

Subtracting 288 and factoring out -16, we get ...

0 = -16(t^2 -7t) = -16t(t -7)

Solutions are ...

t = 0 or t = 7

It is no surprise that the rocket is at ground level at t=0, since we have assumed that is where it is launched from. The other solution, t=7, tells us the rocket returns to gruond level 7 seconds after launch.

_____

Possible solutions are ...

9 seconds if "ground level" means "sea level."

7 seconds if "ground level" means "launch height."

... something else if "ground level" is not one of these

Answer:

a = 102.05

b = 393.76

B = 93°

Step-by-step explanation:

The law of sines tells you ...

a/sin(A) = b/sin(B) = c/sin(C)

Since the sum of angles in a triangle is 180°, angle B must be ...

B = 180° -72° -15° = 93°

and the unknown sides must be ...

a = c/sin(C)·sin(A) = 375·sin(15°)/sin(72°) ≈ 102.05192

B = 93°

b = 375·sin(93°)/sin(72°) ≈ 393.75796

_____

The rounding requirement got cut out of your picture, so we can't help you with that.

Answer: -13

j(5)=11

k(5)=24

11-24=-13

7 inches best 7 x 2 = 14 / 2 = 7 inches

Answer:

See below.

Step-by-step explanation:

15 - -5

= 15 - 1(-5)

= 15 + 5

= 20.

Answer:

15--5

add the negatives so its positive.

15+5=20

Step-by-step explanation:

Answer:

[tex](-3, \frac{9}{5})[/tex]

Step-by-step explanation:

We have the equation [tex]2x + 5y-3 = 0[/tex].

The ordered pairs of this equation have the form [tex](x_0, y_0)[/tex]

Where x is the independent variable and y is the dependent variabe.

That is, the points belonging to the line [tex]2x + 5y-3 = 0[/tex] have the form [tex](x_0, f (x_0))[/tex]

For [tex]y = f(x)[/tex].

So, we need to find [tex]f(x_0)[/tex] for x_0 = -3.

Then we substitute x = -3 into the equation and clear the value of y.

[tex]2(-3) + 5y -3 = 0[/tex]

[tex]-6 + 5y = 3\\\\5y = 9\\\\y = \frac{9}{5}[/tex].

Then the ordered pair is:

[tex](-3, \frac{9}{5})[/tex]

Answer:

[tex]\large\boxed{A.\ 0}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}ax+by=c\\dx+ey=f\end{array}\right\\\\D=\left|\begin{array}{ccc}a&b\\d&e\end{array}\right|=ae-bd\\\\D_x=\left|\begin{array}{ccc}c&b\\f&e\end{array}\right|=ce-fb\\\\D_y=\left|\begin{array}{ccc}a&c\\d&f\end{array}\right|=fa-cd\\\\\text{If}\ D\neq 0\ \text{then the system of equations has one solution}\ x=\dfrac{D_x}{D}\ and\ y=\dfrac{D_y}{D}\\\\\text{If}\ D=0\ \text{and}\ D_x=0\ \text{and}\ D_y=0\ \text{then the system of equations has}\\\text{infinitely many solutions.}\\\\\text{If}\ D=0\ \text{and}\ D_x\neq0\ \text{or}\ D_y\neq0\ \text{then the system of equations has}\\\text{no solutions.}[/tex]

[tex]\text{We have}\\\\\left\{\begin{array}{ccc}3x+4y=12\\x-6y=-18\end{array}\right\\\\D=\left|\begin{array}{ccc}3&4\\1&-6\end{array}\right|=(3)(-6)+(1)(4)=-18+4=-14\\\\D_x=\left|\begin{array}{ccc}12&4\\-18&-6\end{array}\right|=(12)(-6)-(-18)(4)=-72+72=0\\\\x=\dfrac{D_x}{D}\to x=\dfrac{0}{-14}=0[/tex]

Using Cramer's Rule, the value of x in the given system of linear equations is approximately -5.09.

To solve the system of linear equations using Cramer's Rule, we need to find the determinants of the coefficient matrix and the matrices obtained by replacing the corresponding column of the coefficient matrix with the constant matrix. Let's find the determinants:

Determinant of the coefficient matrix = |3 -4| = (3)(-6) - (4)(1) = -18 - 4 = -22

Determinant of the matrix obtained by replacing the x column = |-18 -4| = (-18)(-6) - (-4)(1) = 108 - (-4) = 112

Now, using Cramer's Rule:

x = Determinant of the matrix obtained by replacing the x column / Determinant of the coefficient matrix

x = 112 / -22 = -5.09

Therefore, the value of x in the given system of linear equations is approximately -5.09.

Answer:

Step-by-step explanation:

The difference between double the first purchase and the second purchase is $7 and 2 pounds of jelly beans. Hence a pound of jelly beans is $3.50.

  (4t +8j) -2(2t +3j) = (33) -2(13) . . . . . let t and j represent pounds of trail mix and jelly beans, respectively

  2j = 7 . . . . . . . . . . simplify

  j = 7/2 = 3.50

Using that value in the first purchase, we get ...

  2t +3(3.50) = 13

  2t = 13 -10.50

  t = 2.50/2 = 1.25

A pound of trail mix is $1.25.

45.00x +17.99 = 422.99 (Setup Equation)

45.00x = 405 (Subtract 17.99 from both sides)

x = 9 (Divide both sides by 45.00)

Answer:

9

Step-by-step explanation:

First, you write out the equation. We don't know how many tickets Eva bought, so it can be represented by x. Each ticket costs 45 dollars. The amount of tickets times 45 plus the fee will equal 422.99, so the equation will look like this:

45x + 17.99 = 422.99

Subtract 17.99 from both sides:

45x = 405

Divide 45 on both sides:

x = 9

Eva bought 9 tickets

hope this helps :)

Answer:   [tex]\bold{\dfrac{41}{80}}[/tex]

Step-by-step explanation:

[tex]\dfrac{puppies}{total}+\dfrac{kittens}{total}+\dfrac{unicorns}{total}\\\\\\=\dfrac{15}{80}+\dfrac{16}{80}+\dfrac{10}{80}\\\\\\=\large\boxed{\dfrac{41}{80}}[/tex]

the general term for the sequence m, -m, m, -m, . . . is

The correct option is (A).

The given sequence is: m, -m, m, -m, ...

Let's analyze the pattern:

1. For n = 1, the term is m.

2. For n = 2, the term is -m.

3. For n = 3, the term is m.

4. For n = 4, the term is -m.

5. And so on...

From the pattern, we can see that the sign alternates between positive and negative, and the term alternates between m and -m. This suggests that we can use [tex](-1)^(n-1)[/tex] to control the sign alternation and m to control the alternation between m and -m.

Now, let's check the options one by one:

A. [tex]m(-1)^(n-1)[/tex]

  Substituting n = 1, we get[tex]m * (-1)^(1-1) = m * (-1)^0 = m * 1 = m[/tex]

  Substituting n = 2, we get [tex]m * (-1)^(2-1) = m * (-1)^1 = m * -1 = -m[/tex]

  This matches our sequence. So, Option A seems correct.

B.[tex](-m)^n[/tex]

  This doesn't match our sequence because it would give us [tex](-m)^1 = -m,[/tex][tex](-m)^2 = m^2, (-m)^3 = -m^3[/tex], and so on, which doesn't alternate between m and -m.

C.[tex](-1)m^(n + 1)[/tex]

  Substituting n = 1, we get [tex](-1)m^(1 + 1) = (-1)m^2 = -m^2[/tex]

  Substituting n = 2, we get [tex](-1)m^(2 + 1) = (-1)m^3 = -m^3[/tex]

  This doesn't match our sequence because it doesn't alternate between m and -m.

D.[tex](-1)m^(n - 1)[/tex]

  Substituting n = 1, we get [tex](-1)m^(1 - 1) = (-1)m^0 = -1[/tex]

  Substituting n = 2, we get[tex](-1)m^(2 - 1) = (-1)m^1 = -m[/tex]

  This also doesn't match our sequence because it doesn't alternate between m and -m.

So, the correct answer is Option A:[tex]m(-1)^(n-1).[/tex]

Answer:

1/4 of the pan

Step-by-step explanation:

1/3 of 3/4 = 1/4

b. 0.9 million dollars

Answer:

Option a

Step-by-step explanation:

Given that in the first week of its release, the latest video game sold $4.5 million dollars in games.

[tex]P_t=P_0e^{-0.4t}[/tex]

To find out the predicted game sales to the nearest $0.1 million for the fifth week of this game’s release we have to substitute t =5

P0 = initial sales of games = 4.5 million

Thus substitute to get

[tex]P(5) =4.5 e^{-0.4*5} =0.609[/tex] million

Hence when rounded off to 0.1 million we have

0.6 million dollars

Option a

Answer:

they became "roamin' numerals"

Step-by-step explanation:

Answer:

1.85 gallons

Step-by-step explanation:

1 gallon = 3.785 liters

(7 liters)/(3.785 liters/gallon) = 1.85 gallons

Answer:

1.8492

Step-by-step explanation:

for an approximate result, divide the volume value by 3.785

Answer:

a) ±5

b) ±9

Step-by-step explanation:

In each case, the expression on the left is the square of the expression you're asked to find the value of. Then the value of your expression is the square root of the constant on the right. That square root can be either positive or negative.

___

a) a^2 +2ab +b^2 = (a +b)^2 = 25

(a +b) = ±√25 = ±5

___

b) a^2 -8ab +16b^2 = (a -4b)^2 = 81

(a -4b) = ±√81 = ±9

Answer:

The new points would be (-7, -1), (-3, -2) and (-8, 1). The angle would not change

Step-by-step explanation:

When you rotate points by 180 degrees, you simply change the sign on the ordered pairs. This will give you the new points.

Also, spinning the points will not change the angle between them. Therefore it stays the same.

Answer:

False. He is not correct.

Step-by-step explanation:

To find the percent increase subtract  the old time from the new time then divide that number by the old time. 25-20=5. 5/20=.25. There was a 25% increase in time worked. Evan worked 125% of the original time but only worked 25% more time.

Answer:

Correct Answer 7/10

Step-by-step explanation: