In the derivation of the formula for the volume of a cone, the volume of the cone is calculated to be times the volume of the pyramid that it fits inside. Which expression represents the volume of the cone that is times the volume of the pyramid that it fits inside? (2r2h) (4r2h)

Answer:

The Correct answer:

$799.06

Final answer:

To find out how much Andy will have in his account after 10 years with a 4.8% interest compounded continuously, we use the formula A = Pe^{rt}. Substituting the values, we find that the amount will be approximately $808.85.

Explanation:

To calculate how much Andy will have in his account in 10 years with an initial investment of $500 at a 4.8% interest rate compounded continuously, we use the formula for continuous compounding, which is A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), and t is the time in years.

Using the given values:

P = $500

r = 4.8% or 0.048

 t = 10 years

Let's compute the final amount:

A = 500 * e^0.048 * 10

Now we calculate the exponent:

e^0.48 (approximately 1.6177)

And then the final amount:

A = 500 * 1.6177 ≈ $808.85

After 10 years, the amount in Andy's account, compounded continuously at a rate of 4.8%, will be approximately $808.85.

Answer:

A) The solution set is (6,-8).

Step-by-step explanation:

3x - y = 26

-3x       - 3x        Subtract 3x from both sides

-y = -3x + 26     Divide both sides by -1

y = 3x - 26

Now plug this into 7x + 8y = -22 to solve for x

7x + 8(3x - 26) = -22        Distribute

7x + 24x - 208 = -22       Combine like terms

31x - 208 = -22

     + 208    + 208            Add 208 to both sides

31x = 186                           Divide both sides by 31

x  = 6

Plug this into y = 3x - 26 to solve for y

y = 3(6) - 26           Multiply

y = 18 - 26              Subtract

y = -8

If this answer is correct, please make me Brainliest!

Final answer:

The system of equations is solved using the substitution method, resulting in x = 6 and y = -8. Hence, the correct choice is the ordered pair (6, -8).

Explanation:

To solve the system of equations by the substitution method, let's start by solving the second equation for y:

3x - y = 26
=> y = 3x - 26.

Now, substitute this expression for y into the first equation:

7x + 8(3x - 26) = -22
=> 7x + 24x - 208 = -22
=> 31x = 186
=> x = 6.

Now, substitute x back into the expression we found for y:

y = 3(6) - 26
=> y = 18 - 26
=> y = -8.

The solution to the system is the ordered pair (6, -8), which means the correct choice is:

O A. The solution set is { (6, -8) } (Type an ordered pair.)

Answer:

ok The circumference of a circle is 2πr or πD if diameter is given.

The answer is 25.13 cm

Step-by-step explanation:

Now method 1:

C=2πr

So finding for radius in this equation=diameter/2

8/2=4 cm

So now 2 × 22/7 × 4

176/7=25.13 cm

OR

C=πD

22/7 × 8

176/7=25.13 cm

Answer:

S={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}

Step-by-step explanation:

As can be seen in the Sample Tree attached, the eight elements in the sample space whose outcomes are all the possible head-tail sequences obtained in the three tosses are:

S={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}

When tossing a coin three times, there are 8 possible outcomes listed as HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. These elements represent all possible head-tail sequences for three coin tosses.

When a coin is tossed three times, each outcome is a sequence of heads (H) and tails (T). Since there are two possible outcomes for each toss, the total number of possible sequences is 23 = 8. Let's list these sequences using set-roster notation.

The sample space is:

These elements cover all possible outcomes where each toss can either result in heads or tails.

Answer:

Square

Step-by-step explanation:

If its 4 sided and two measures are 90 degrees then that means the other two must be 90 degrees. That means its a square or a rectangle. Now since the 4 sides arent all the same and two sides being 6 and two sides being 5, you can rule out it being a square.

Answer:

False.

Step-by-step explanation:

All the sides of an equilateral triangle are equal.

None of the sides of a scalene triangle are equal to each other.

Therefore, an equilateral triangle is not similar to a scalene triangle.

Answer:

52 square feet

Step-by-step explanation:

We are given that

Length,l=6 feet

Width,b=[tex]1\frac{1}{3}=\frac{4}{3}[/tex] feet

Depth,h=3 feet

Area of all painted sides  except bottom=[tex]lb+2(bh+hl)[/tex]

Using the formula

Area of all painted sides  except bottom=[tex]6\times \frac{4}{3}+2(\frac{4}{3}\times 3+3\times 6)[/tex]

Area of all painted sides  except bottom=[tex]8+2(4+18)[/tex]

Area of all painted sides  except bottom=[tex]8+44[/tex]

Area of all painted sides  except bottom=52 square feet

Answer:

k=8192

Step-by-step explanation:

The number of teams,t remaining after each round, r, can be expressed as:

[tex]t=65,536(\frac{1}{2})^r[/tex]

First, we determine the round,r at which there will be 8 teams left.

[tex]t=65,536(\frac{1}{2})^r\\8=65536*0.5^r\\0.5^r=8 \div 65536\\2^{-1r}=2^{-13}\\-r=-13\\r=13[/tex]

Using this value of r

[tex]If \: r=\frac{Log\frac{1}{k}}{Log\frac{1}{2}} \\Since\: r=13\\13=\frac{Log\frac{1}{k}}{Log\frac{1}{2}}\\$Cross Multiply$\\Log\frac{1}{k}=13 X Log 0.5\\ $Using a Log b=Log $b^{a}\\Log\frac{1}{k}= Log 0.5^{13}\\\frac{1}{k}=0.5^{13}\\\frac{1}{k}=\frac{1}{8192}\\k=8192[/tex]

Answer:

The correct option is;

C. Sediment carried in the slowly moving water is deposited.

Step-by-step explanation:

Here we note that the drainage rate of the water is slow and the plane of the drainage is given as level ground.

Therefore, there would less mass transport of sedimentary materials from the region and the level planes with slow drainage would favor the deposition of sediments along the level plane

From the above, the correct option is C.

Answer:

C

Step-by-step explanation:

Answer:

1 at (2.5, 2.5)

Step-by-step explanation:

you can try graphing it on desmo

Answer:

-80 orchestra seats

-200 main seats

- 120 balcony seats

Step-by-step explanation:

Let x b number of orchestra seats

Let y be number of main seats

Let z be number of balcony seats.

Thus, we have the following equations;

For all seats sold;

70x + 45y + 35y = 18,800 - - - - eq1

For half of orchestra sold;

70•½•x + 45y + 35y = 16,000 - - eq2

For total seats;

x + y + z = 400 - - - - eq3

Solving eq1, eq2 and eq3 simultaneously, we have;

x = 80

y = 200

z = 120

Thus, we have;

-80 orchestra seats

-200 main seats

- 120 balcony seats

Answer:

D: C = 4π

Step-by-step explanation:

The formula for circumference is C = 2πr

The diameter is 4 which means the radius is 2.

Plug the value of r into the formula.

C = 2π2

C = 4π

D: C = 4π

The extraneous solution of the logarithmic problem log₃( 18x³) -log(2x) = log₃144 is -4.

A log function is a way to find how much a number must be raised in order to get the desired number.

[tex]a^c = b[/tex] can be written as,

log[tex]_a[/tex]b = c

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

Solving the function using the basic logarithmic value, we get,

log₃( 18x³) -log(2x) = log₃144

log₃ (18x³/2x) = log₃144

log(9x²) = log₃144

Take antilog.

9x² = 144

x = ±4

If we solve further we will get that the value of x can be either -4 or 4, if take the value of x as -4, in the beginning then you will get log₃(18(-4)³) as the log of negative value which is impossible.

Hence, x=-4 is an extraneous solution for the given expression log₃( 18x³) -log(2x) = log₃144.

Learn more about Logarithms:

brainly.com/question/7302008

#SPJ5

The slopes are the only thing we care about when it comes to determining if the lines are parallel or perpendicular. The y intercepts do not affect the answer, so we can ignore them entirely.

The slopes of the two given equations are -4/5 and -5/4. Note how they are both negative. This means that we do not have perpendicular lines. One slope must be positive and the other negative, for perpendicular lines to form.

Another way to see it: the two slopes must multiply to -1 to have perpendicular lines form. We see that (-4/5)*(-5/4) = 1 instead.

Yet another way to see it: The term "opposite reciprocals" means we flip the fraction and we flip the sign (from positive to negative). The reciprocal part happens, but the sign change does not happen.

The lines are not parallel because the slopes would have to be equal for that to happen.

Answer:

Step-by-step explanation:

Answer:

y = 3x - 1

Step-by-step explanation:

The slope of this line is 3x and the y-intercept is -1.

I graphed the equation and the point along with the new equation below.

If this answer is correct, please make me Brainliest!

Answer:

The correct answer is the solution of the system of equations are w = 10 and m = -8. The answer is not at all reasonable.

Step-by-step explanation:

The two system of equations are m + 2w = 12 and m + 3w = 22 where m and w represent the number of men and women working in an office.

We subtract both the sides with each other in order to solve the system of equation.

⇒ m + 3w - m - 2w = 22 - 12

⇒ w = 10.

⇒ m = -8.

The values of w and m are not reasonable at all. Since m and w represent the number of men and women in an office, they cannot be less than zero.

Answer:

5 miles

Step-by-step explanation:

In the diagram, the distance between the lighthouse is |AB|=c.

Using Cosine Rule,

c²=a²+b²-2abCos C

=7²+4²-2(4)(7)Cos 45°

=49+16-56cos45°

=25.40

c=√25.40=5.04 miles

The distance between the lighthouses is approximately 5 miles.

Answer:

The distance between the two lighthouse is 5miles

Step-by-step explanation:

Since the shape of the sketch is a right angled triangle we use SOHCAHTOA to solve. An image showing the step by step working is attached.

Answer:

The answer would be B) -2 1/8

Step-by-step explanation: i just took the test and i got that right

Answer:

B) -2⅛

Step-by-step explanation:

All other options are irrational

............................

Answer:

A = 41+B

A = 55

Step-by-step explanation:

A be the amount (in dollars) that Kala earns in a week

B = books sold

Kala earns 41 dollars each week working part-time at a bookstore. This does not depend on selling any books

She earns 1 dollar for each book sold

A = 41+B*1

A = 41+B

Let B = 14

A = 41+14

A = 55

Answer:

Equation: A = 41 + B

Amount Kala earns if she sells 14 books: 55 dollars

Step-by-step explanation:

A = 41 + B

B = 14

A = 41 + 14

A = 55

Answer: there would be 9 chipmunks after 5 years.

Step-by-step explanation:

An initial population of 7 chipmunks in Mary's yard increases by 6% each year. It means that the population is increasing in an exponential rate.

The function that models the situation is expressed as

f(x) = ab^x

Where

a represents the initial population of chipmunks

b represent the rate of growth

x represent the number of years

From the information given,

a = 7

b = 1 + 6% = 1 + 6/100 = 1.06

x = 5 years

After 5 years,

f(5) = 7 × 1.06^5

f(5) = 9

Answer:

( C ) "none above"

Step-by-step explanation:

first you start by combining like terms

-2y-8+4y-2y-8+4y

-8+2y-2y-8+4y

-16+4y or 4y-16 would be the max simplification!

hope that helps  

The television station can show 1 full 45-second commercial during the 13/12 minutes of advertising time allocated each hour.

The question involves calculating how many 45-second commercials can be shown during the 13/12 minutes of advertising time allocated by a television station each hour. To solve this, we first need to convert the minutes to seconds and then divide by the length of one commercial.

13/12 minutes is equal to 13/12 × 60 seconds, which gives us 65 seconds of advertising time per hour. One commercial is 45 seconds long. Therefore, the number of 45-second commercials that can be shown is 65 divided by 45.

Divide the total advertising seconds by the duration of one commercial: 65 / 45 = approximately 1.44.

Since we cannot show a fraction of a commercial, the television station can show 1 full 45-second commercial per hour.

Answer:

1/3 or 3/6 they are the same thing

Step-by-step explanation:

Answer:

The probability of rolling an odd number is 5/6

Step-by-step explanation:

probability: desired/all

Let's find the possible outcomes of rolling odd.

1,3,5 are all odd. We have 3 outcomes.

Now find the possible outcome of a power of 2.

2 is

2

1

, 4 is

2

2

. We have 2 DIFFERENT outcomes.

(If these outcomes overlapped, we would have to subtract to get unique outcomes. In this case, these outcomes are different)

Now, we find the total number of possible outcomes.

A dice has 6 different outcomes.

Now add up the desired outcomes,

3 + 2 = 5

and so the probability is

5/6

Answer:

D

Step-by-step explanation:

The outcomes of events. A and B are dependent on each other.

The question relates to probability in Mathematics, specifically the probability of selecting a red (event A) or a mystery novel (event B) from Chloe's bookshelf. Both probabilities are 7/10 as 7 out of 10 books are red or mysteries. The probability of both A and B occurring simultaneously is 5/10, as 5 out of 10 of the books are red mysteries.

The subject of this question is the calculation of probabilities in Mathematics. Here we have two events: event A, defined as selecting a red book, and event B, defined as selecting a mystery novel. Considering Chloe's bookshelf, she has 7 red books out of a total of 10, meaning that the probability of event A is 7/10. In addition, she has 7 mystery novels out of a total of 10 books, meaning that the probability of event B is 7/10 also.

It can be said that both events A and B are independent, because the colour of the book does not affect what genre it is. Also, it's worth mentioning that the likelihood of both A and B occurring, meaning the selection of a red mystery novel is (5/10) as 5 out of 10 books are red and mysteries.

https://brainly.com/question/22962752

#SPJ2

Answer:

Cathy is asked to find the length of AC. She could use the Pythagorean Theorem and AC^2 = 3^2 + 2^2. What other formula could she use?

A) (0 + 3)^2 - (1 + 3)^2

B) (0 + 1)^2 - (3 + 3)^2

C) (0 - 3)^2 + (1 - 3)^2

D) (0 - 1)^2 + (3 - 3)^2

Option C is the right choice.

Step-by-step explanation:

Given:

Cathy have used Pythagoras formula to find the hypotenuse.

Hypotenuse of the right angled triangle = AC

We know that:

In right angled triangle:

Hypotenuse square (h)^2 = Square of one side (p)^ + Square of another sides (b)^

⇒ [tex]h^2=p^2+b^2[/tex]

In Cathy's calculation:

⇒ [tex]AC^2=3^2+2^2[/tex]

⇒ [tex]AC^2=9+4[/tex]

⇒ [tex]AC^2=13[/tex]

We have to look for another equation.

Lets see the options individually.

A. [tex]AC^2=(0 + 3)^2 - (1 + 3)^2= 9-16 = 7[/tex]

B. [tex]AC^2=(0 + 1)^2 - (3 + 3)^2=1-0 =1[/tex]

C. [tex]AC^2=(0 - 3)^2 + (1 - 3)^2 =9+4=13[/tex]

D. [tex]AC^2=(0 - 1)^2 + (3 - 3)^2=1+0 =1[/tex]

So,

The other formula Cathy can use is, C i.e. (0 - 3)^2 + (1 - 3)^2 .

Option C is the right choice.

The correct answer is option  C) (0 - 3) + (1 - 3)

If AC is the hypotenuse, and the lengths of the other two sides are 3 and 2, then AC = 3 + 2.

 However, Cathy can also use the distance formula, which is derived from the Pythagorean Theorem. The distance formula calculates the distance between two points in a coordinate plane. If we have two points (x1, y1) and (x2, y2), the distance d between these points is given by:

d = (x2 - x1) + (y2 - y1)

Given that one endpoint of AC, let's call it A, is at (0, 3) and the other endpoint, let's call it C, is at (1, -3), we can apply the distance formula to find AC:

AC = (1 - 0) + (-3 - 3)

AC = (1) + (-6)

AC = 1 + 36

AC = 37

Therefore, the length of AC is the square root of 37, which is 37.

Let's evaluate the other options to see why they are incorrect:

A) (0 + 3) - (1 + 3): This formula would calculate the difference between the squares of the distances from the origin to two points, which does not correspond to the distance between two points.

B) (0 + 1) - (3 + 3): Similar to option A, this formula calculates the difference between the squares of the distances from the origin to two points, which is not the correct application of the Pythagorean Theorem for finding the distance between two points.

D) (0 - 1) + (3 - 3): This formula incorrectly calculates the distance by subtracting the y-coordinates instead of the x-coordinates and does not account for the difference in x-coordinates properly.

Thus, the correct formula to use, other than the direct application of the Pythagorean Theorem, is the distance formula, which in this case is option C) (0 - 3) + (1 - 3).

Step-by-step explanation:

The total number of students = 100

Let A represents calculus and B represents French

The no of students taking calculus = 32

The no of students taking French = 29

The no of students taking calculus and french = 13

the probability that the student is taking Calculus or French = ?

P (AUB) = P(A) + P(B) - P(A∩B)

= [tex]\frac{32}{100}[/tex] + [tex]\frac{29}{100}[/tex] - [tex]\frac{13}{100}[/tex]

= [tex]\frac{48}{100}[/tex]

Reducing to lowest fraction,  it becomes [tex]\frac{12}{25}[/tex]

The probability that the student is taking Calculus or French =  [tex]\frac{12}{25}[/tex]

The probability that a randomly selected student is taking Calculus or French is 12/25.

To find the probability that a randomly picked student is taking either Calculus or French, we use the principles of set theory, specifically the formula for the union of two sets:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Here,
A = Students taking Calculus = 32
B = Students taking French = 29
A ∩ B = Students taking both Calculus and French = 13
Total students = 100

The formulas for the probabilities are:
P(A) = 32/100
P(B) = 29/100
P(A ∩ B) = 13/100

Now substitute these values into the union formula:

P(Calculus or French) = 32/100 + 29/100 - 13/100 = 48/100 = 12/25

Therefore, the probability that a randomly picked student is taking either Calculus or French is 12/25.