Lily goes to gym once every 8 days. Ann goes once every 12 days and Taylor comes once every 16 days. This Wednesday all of them were in the gym. How many days after this Wednesday will all of them meet at the gym again and what day of the week will it be?

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]

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

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:

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:

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:

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:

x = 19cm

Step-by-step explanation:

use pythagorean theorem:

a² - c² = b²

10² - 22² = b²

100 - 484 = b²

384 = b²

√384 = b

19cm = b or x

Answer:

30.8cm

Step-by-step explanation:

i am from connexus 8th grd pre algrabra

unit 5 lesson 3

1. 1:2

2. C. yes they are similar they have porportional side lengths and = ange measures

3. x = 4.5m

4. x = 30.8cm

5. x = 6 m

i hope this helps! = ) <3

Answer:

The MAD of set 1 is 5 less than the MAD of set 2.

Step-by-step explanation:

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:

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:

you know 25% is one fourth of 100%, aka the whole number, so just multiply the 25% of the number times 4 to get the whole number

Answer:

r = 129.1 %

Step-by-step explanation:

Using the compounding formula:

A = P (1 + r/t)^nt

$12, 543 = $7178 (1 + r/12)^12(7)

-7178

$5365 = (1 + r/12)^84

[tex]\sqrt[84]{5365}[/tex] = [tex]\sqrt[84]{(1 +\frac{r}{12})^{84}}[/tex]

1.107642572 = 1 + r/12

(0.108 = r/12) (12)

r = 1.2917 = 129.1 %

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.

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.

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:

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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:

Step-by-step explanation:

If a +  3b =  7, subtract 3b from both sides of the equation

       -3b  = -3b       then you get

   a = 7-3b        now plug this into the other equation: 3a-2b=8

3(7-3b) -  2b = 8

21 - 9b  - 2b = 8

21 - 11b = 8           add 11 b to both sides

   + 11b    +11b

21 = 8 + 11b          subtract 8 from both sides

-8    -8

13 = 11b

What is 4a+b?

4(7-3b) + b =

(28 - 12b) + b =

28-11b   (from above 13=11b)

28 - 13 = 15

Answer: ( C ) The perimeter of the rectangle is (10x+18) Units

Step-by-step explanation: This is the right answer because I just checked and I did the math

Answer:

it is c i had the same problem

Step-by-step explanation:

Answer:

algorithm

Step-by-step explanation:

It sounds like algorithm.

The mathematical terms that originated from the Arabic mathematician, al-Khwarizmi, are ""algorithm"" and ""algebra.""

Al-Khwarizmi was a Persian mathematician and astronomer who lived in the 8th and 9th centuries. His works were instrumental in the development of algebra and the use of Hindu-Arabic numerals. The term ""algorithm"" is derived from a Latinization of his name, Algoritmi, and originally referred to the numerical methods he described in his treatise on arithmetic.

The word ""algebra"" comes from the Arabic word ""al-jabr,"" which appears in the title of his book ""Kitab al-Jabr wa-l-Muqabala"" (The Compendious Book on Calculation by Completion and Balancing). This book laid the foundations for algebra as a branch of mathematics, and the terms he introduced are still in use today to describe mathematical procedures and the study of equations and algebraic structures.

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:

20.8%

Step-by-step explanation:

To find the final probability, two separate events must be done and the final propagation is the multiplication of these, like this:

First event:

Probability of black socks on Monday:

Total pair of socks: 1 + 3 + 5 = 9

Number of black socks on Monday: 3

Thus:

3/9 = 1/3

Second event:

Probability of white socks on Tuesday:

Total pair of socks: 8

Number of white socks on Tuesday: 5

Thus:

5/8

Final probability:

1/3 * 5/8 = 5/24

P = 0.208

So the probability would be 20.8%

The probability of black socks on Monday = 1/3

The probability of white socks on Tuesday = 5/8

To find the final probability, two separate events must be done and the final propagation is the multiplication of these, like this:

First event:

Probability of black socks on Monday:

Total pair of socks: 1 + 3 + 5 = 9

Number of black socks on Monday: 3

Thus:

Probability will be: 3/9 = 1/3

Second event:

Probability of white socks on Tuesday:

Total pair of socks: 8

Number of white socks on Tuesday: 5

Thus:

Probability will be: 5/8

Final probability:

1/3 * 5/8 = 5/24

P = 0.208

So, the probability would be 20.8%.

Find more information about Probability here:

brainly.com/question/24756209

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:

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:

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:

Step-by-step explanation:

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:

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:

1 at (2.5, 2.5)

Step-by-step explanation:

you can try graphing it on desmo