As $n$ ranges over the positive integers, what is the maximum possible value that the greatest common divisor of $13n 8$ and $5n 3$ can take

When two players A and B alternately flip a fair coin, the probability  E(T) is 4. (A tosses the coin first, then B tosses the coin, then A, then B and so on).

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty.

Two players, A and B, turn a fair coin in succession (A tosses the coin first, then B tosses the coin, then A, then B and so on). The order of the heads and tails is noted. If there is a head followed by a tail, the game is done, and the person who throws the tail wins (HT sub-sequence).

We must ascertain the game's estimated duration. Allow T coin tosses for the game to proceed. Find E (T).

[tex]E(T) = first instance of HT in seriesE(T) =0.5×(1+2)+0.5×(1+E(T))\\0.5×E(T)=0.5×4\\E(T) =4[/tex]

As a result, when two players A and B alternately flip a fair coin, The E(T) is 4. (A tosses the coin first, then B tosses the coin, then A, then B and so on).

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The interest generated in Pauls savings account is $4.68

The amount generated in Larissa's savings account is $5015.80

Compound interest is interest that builds up over a certain length of time on both principal and interest. The principle is also used to account for the interest that has accrued on a principal over time. Furthermore, the cumulative principal value is used to calculate interest for the subsequent time period. The new way of calculating interest now utilized in all international financial and commercial operations is known as compound interest. When we look at the compound interest values that have built over various time periods, the power of compounding is clearly apparent.

The interest that is paid on both principle and interest and is compounded on a regular basis is known as compound interest. The interest is calculated for the new principal at regular intervals when the accumulated interest and the current principal are combined. The initial principal plus the interest that has already accrued make up the new principal.

The initial principal(p) of Paul is $1000

rate(r) is 5.5%

Number of days(t) = 20th March to 20th April = 31 days = 31/365 years

So the Amount generated =[tex]p * (1 + \frac{r}{365})\x^{365*t}[/tex]

⇒ A = [tex]1000* (1 + \frac{5.5}{100*365})\x^{31} = 1000*1.00468 = 1004.68[/tex]

The interest generated = 1004.68 - 1000 = $4.68

Similarly for Larissa

time = 24th Feb to 17th March = 21 days = 21/365 years

So the Amount generated =[tex]p * (1 + \frac{r}{365})\x^{365*t}[/tex]

⇒ A = [tex]5000* (1 + \frac{5.5}{100*365})\x^{21} = 5000*1.00317 = 5015.80[/tex]

The amount generated is $5015.80

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maybe try not

Step-by-step explanation:

Answer:

it would be 6 miles a day

Step-by-step explanation:

do to 41.2 miles in 1 week and a 4 mile start plus six more days it would be 6x6=36+4=40

Answer:

Step-by-step explanation:

+1=2

Answer: 112 degrees

Step-by-step explanation:

Since the two lines are parallel and the line that intersects them is a transversal, 180 - 68 = x

Solving 180 - 68,

you can find that x = 112 degrees :>

Answer: a measure of an x angle is the longest line on the graph so that how u know

Step-by-step explanation:

Answer: The two problems aren't related

Step-by-step explanation:

The first problem has a 3 and a 9 but no 2, but the second problem does,  which shows that these two problems are not related. Also, if you simplify the first one, you will get 27 [tex]\sqrt[4]{3}[/tex], which is not related to the second problem

The average speed so far is 226.4 miles per hour.

Time taken: 3 hours 49 minutes + 6 hours 27 minutes

= 10 hours 16 minutes

Total distance: 163 miles + 411 miles

= 574 miles

Average speed: 574 miles / (10 hours 16 minutes)

= 226.4 miles per hour

To calculate the average speed of the Copeland family's trip so far, we need to know the total distance they have traveled and the total time they have spent traveling. We can calculate this by adding the distance driven by Mr. Copeland (163 miles) and the distance driven by Mrs. Copeland (411 miles) to get a total distance of 574 miles. Then, we can add the time taken by Mr. Copeland (3 hours 49 minutes) and the time taken by Mrs. Copeland (6 hours 27 minutes) to get a total time of 10 hours 16 minutes. We can then divide the total distance (574 miles) by the total time (10 hours 16 minutes) to get an average speed of 226.4 miles per hour.

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The algorithm completes in an acceptable amount of time because it will draw n forms in around n2 steps.

A mathematical algorithm is a process that describes a series of steps that can be used to accomplish a mathematical computation. A typical illustration of a mathematical algorithm would be the step-by-step process used in long division. A set of instructions called an algorithm is used to solve a problem or complete a task. An algorithm is a set of instructions that spells out how to carry out a task. An algorithm can be thought of as a series of detailed instructions that result in a predictable pattern in a set of numbers or in lines of code.

given

Which of the following best describes the algorithm for drawing n forms, where n is a very big number  based on the numbers in the table.

Because it will take around n2 steps to draw n forms, the algorithm completes in a fair length of time.

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Answer:

Yes, they are similar by SSS

Answer:

Step-by-step explanation:

1/13 x 18

of= multiply

18x1=18

13x1=13

18/13

As a PROPER FRACTION, it is 1 5/13

Answer: 18/13

Step-by-step explanation:

You have to multiply the fractions.

The table formed using equivalent ratios.

16 : 128

5 : 40.

3 sticks of butter -----> 24 cookies.

Let the number of cookies made for other stick of butter be 'y'.

Then, number cookies for the 16  sticks of butter

3/24 = 16/ y

y = 16*24 / 3

y = 128 cookies.

Again, number cookies for the 5 sticks of butter

3/24 = 5/ y

y = 5*24 / 3

y = 40 cookies.

Thus, number of cookies made by 5 sticks of buter are 40.

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Step-by-step explanation:

one way of simply calculating this is by using basic percentage calculations.

So because 90% of bacteria was left after every hour, one could use the intial number we were given to find out the next bacteria count. You could work it out by :

so in the 1hr the bacteria count was 90.

so you continue working it out for each hr

then work it out until u hve calculated for 5hrs, so the answers for each hr will be 90, 81, 72.9, 65.61, 59.049

then add them up and it will give you 368.559 bacteria count. When rounded off it will be 369.

thats how i would hve tackled it

The bacteria count after 5 hours was found to be 59.

For this case we have a function of the form:

y = A × ([tex]b^{x}[/tex]) <  br/ >

Where,

A - the initial amount of bacteria

b - decrease rate

x - time in hours

Substituting values we have in the above form, we get:

y = 100 × [tex](0.90)^{x}[/tex] <  br/ >

Then after 5 hours we have the equation,

y = 100 × [tex](0.90)^{x}[/tex] <  br/ > <  br/ > y = 59.049 <  br/ >

Rounding to the nearest whole number the equation becomes,

y = 59 <  br/ >

Therefore, the bacterium count after 5 hours was found to be 59.

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Answer:

Step-by-step explanation:

Assuming the interest rate remains constant throughout the 10-year period, Rajesh will have enough money in the account to cover all of the required loan payments. The total amount of money he will withdraw over the 10-year period will be $30,000 (250 x 12 months x 10 years). At the end of the 10-year period, he will have $50,847.90 in the account, which is more than enough to cover the required loan payments.

Rates of birth and death within that group dictate the rate at which world's population would double.

200 years

500 million people became 1 billion people around the world in 200 years, or until 1825. The second doubling, from 1 billion to 2 billion in 1930, only took 100 years. The subsequent doubling, from 4 billion to 6 billion by 1975, only took 45 years. The first billion people on earth were present in the year 1830; the second billion were present in the years 1830 to 1930; and the third billion were present in the year 1990, which happened 60 years later.

The world's population increased to 500 million to one billion people in 200 years, starting in 1825.

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The perimeter of the picture is 20f-8 inches.

Sides of the picture = 5f-4

Inches added to the picture = 2

The perimeter of a two-dimensional form, like a square or a rectangle, is the space surrounding its edge. It is frequently employed to gauge a parcel of land's dimensions or the width of a fence.

Since two inches are added, therefore after framing the side length becomes-

5f-4+2

= 5f-2

The perimeter of the square is given as

= side x 4 or 4s

Therefore, the perimeter of the framed picture will be given as -

= 4(5f-2)

= 20f - 8

The perimeter can also be found by adding the side length four times. This can be noted as -

5f-2 + 5f-2 + 5f-2 + 5f-2

= 20f - 8

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Answer:

Step-by-step explanation:

4 m/s squared

The probability that the mean systolic blood pressure of 23 women is between 119 and 122 mm Hg is 0.0579.

The Central Limit Theorem states that the distribution of the mean of a large sample (n>30) taken from a population with a finite mean and standard deviation will be approximately normal.

Since we are given that systolic blood pressures are normally distributed and we have n = 23>30, we can assume that the mean systolic blood pressure of 23 women will be approximately normally distributed with a mean of 114.8 mm Hg and a standard deviation of 13.1/[tex]\sqrt{23}[/tex] = 2.731 mm Hg.

To find the probability that the mean systolic blood pressure of 23 women is between 119 and 122 mm Hg, we can standardize the problem and use the standard normal distribution table.

We can standardize the problem by finding the number of standard deviations away from the mean of the lower and upper bounds of the range.

z_lower = (119 - 114.8) / 2.731) = 1.537

z_upper = (122 - 114.8) / 2.731) = 2.636

Now we can use the standard normal distribution table to find the probability that a standard normal variable is between z_lower and z_upper.

P(z_lower < Z < z_upper) = P(Z ≤ 2.636) - P(Z < 1.537) = 0.9958 - 0.9379 = 0.0579

Therefore, the probability that the mean systolic blood pressure of 23 women is between 119 and 122 mm Hg is 0.0579.

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The complete question is -

For women aged​ 18-24, systolic blood pressures are normally distributed with a mean of 114.8 mm Hg and a standard deviation of 13.1 mm Hg. If 23 women aged​ 18-24 are randomly​ selected, find the probability that their mean systolic blood pressure is between 119 and 122 mm Hg. Round to four decimal places.

The number of positive integers less than 1000 that are neither 7-nice nor 8-nice is 749.

N = (ke1 + 1)(ke2 + 1)· · ·(kei + 1).

This means we must have N ≡ 1 (mod k).

Yes, choose a = 2^N−1/k so that

a^k = 2^N−1

, which has N divisors.

So, we need to find the number of integers that are neither 1 mod 7

nor 1 mod 8.

We can use the principle of inclusion and exclusion.

There are [999/7]= 143 integers that are 1 mod 7.

There are [999/8]= 125 integers that are 1 mod 8.

There are [999/56 ]= 18 integers that are 1 mod 56.

By PIE, the answer is 999 − 143 − 125 + 18 = 749.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common way to represent the set of integers in mathematical terms.

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Answer:

money. you need to know how to count your money so nobody cheat you out of it

Answer:

4/7

Step-by-step explanation:

=> The simplest form of

56

:

98

56:98 is

4

:

7.

4:7.

Step-by-step explanation:

Given ratio -

56

:

98

56:98

We have to reduce it to its simplest form,

For that, we have to find the GCD of the numerator as well as the denominator:

So, the GCD for

56

56 and

98

98 is

14.

14.

Now, divide both the numerator and denominator by the GCD:

=

>

56

÷

14

98

÷

14

=>

98÷14

56÷14

=

>

4

7

=>

7

4

Hence, the simplest form is

4

:

7.

4:7.

Answer:

1000/39

Step-by-step explanation:

Answer:

They both type at the same rate.

Step-by-step explanation:

Ms. Leah's unit rate

186/3 = 62  She can type 62 words in 1 minute

Mr. Thomas's unit rate:

310/5 = 62  He can type 62 words in 1 minute.

Answer:

y = x + 11

Step-by-step explanation:

the equation of a straight line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 14 ) and (x₂, y₂ ) = (9, 20 )

m = [tex]\frac{20-14}{9-3}[/tex] = [tex]\frac{6}{6}[/tex] = 1 , then

y = x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 14 )

14 = 3 + c ⇒ c = 14 - 3 = 11

y = x + 11 ← equation of line

A line passes through points (3,14) and (9,20), linear function rule in terms of x and y for this line is y = x + 11

A linear function in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the point values from the problem, we get:m = (20 - 14) / (9 - 3) = 6/6 = 1

The y-intercept  be found by plugging in any one of the point values and the slope into the equation y = mx + b and solving for b. Using the point (3,14), we get:

14 = 1*3 + b

b = 11So the linear function in terms of x and y is:

y = x + 11

A linear function is a type of mathematical function that, when graphed, defines a straight line. It is defined by the equation y = mx + b, where x and y are variables, m is the line's slope, and b is the y-intercept (the point where the line crosses the y-axis). The slope (m) of the line represents its steepness, and the y-intercept (b) represents the point at which the line intersects the y-axis.

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The rate of increase of the volume of the cube is 0.8 cubic inches per second.

Let x denote the edge of the cube at any given instant.

The total surface area of the cube

= 6x^2

The given condition is: 6x^2 = 150

=> x^2 = 25

=> x = 5

Now, the rate of increase of the edge of the cube is 0.2 inches/second.

Therefore, the rate of increase of the volume of the cube = rate of increase of the edge * rate of increase of the edge * rate of increase of the edge

=> 0.2 * 0.2 * 0.2

= 0.008 inches^3/second

= 0.8 cubic inches/second

The rate of increase of the volume of the cube is 0.8 cubic inches per second, which is calculated by multiplying the rate of increase of the edge (0.2 inches/second) three times.

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By means of ratio properties, the simplified form of ratio 1.5 : 20 is equivalent to ratio 3 : 40.

Ratios are relationships between two real numbers of the form a : b, the simplification of ratios can be done by using the following ratio property:

Simplification property for ratios

a : b ← (a · c) : (b · c)

Where a, b, c are real numbers.

The purpose of ratio simplification is to eliminate any decimal number in a ratio. If we know that a = 1.5, b = 20 and c = 2, then the simplified form of the ratio is:

1.5 : 20 → (1.5 · 2) : (20 · 2)

(1.5 · 2) : (20 · 2) = 3 : 40

By ratio properties, ratio 3 : 40 is the simplified form of ratio 1.5 : 20.

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Yes, the equation Y = 2/3x represents a proportional relationship.

If one variable is always equal to a constant multiplied by the other variable(quantity), then we can say that those variables are in a proportional relationship.

In the direct relationship between two quantities, if one quantity increases, the other quantity also increases and vice-versa.

For example, if each square foot of carpet costs $1.50, then the cost of the carpet is proportional to the number of square feet. The direct proportion relationship is written as y ∝ x.

y = kx where k is the constant of proportionality.

The constant of proportionality is 2/3. It tells us that for every 1 unit increase in x, Y increases by 2/3 units.

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Answer:

To find the percent markup, we can use the following formula:

Markup = (selling price - cost price) / cost price * 100

We know that the department store buys 100 shirts at a cost of $1,200 and sells them at a selling price of $20 each.

Markup = ($20 - $12) / $12 * 100

Markup = $8 / $12 * 100

Markup = 2/3 * 100

Markup = 67%

So the percent markup is 67%.

Answer:

i don't know br

Step-by-step explanation:

Sorry but this is like college stuff:(

The true statement is t = 2 years.

What is simple interest?

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

Here, we have

Given: suppose you deposited $400 in a saving account 2 years ago.

The simple interest rate is 2.5%. The interest you earned in those 2 years is $18.40.

We have to find the true statement.

We concluded that

I = 2.5%

P = $400

t = 2 years

Hence, the true statement is t = 2 years.

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The graph of the function at each interval represent

(1) - increasing, (2) - decreasing, and (3) - decreasing.

What is graph of the function?

The set of ordered pairs where f(x) = y is displayed as the graph of a function in mathematics. These pairs are the Cartesian coordinates of points in two-dimensional space and, in the typical case where x and f(x) are real numbers, they form a subset of this plane.

Let the graph of the function is given.

We have to find What does the graph of the function at each interval represent.

As we can see that there are three intervals of the graph are shown (1), (2), and (3).

We can see that in the first interval (1) the graph is increasing.

And in the second (2) and third interval (3) the graph of the function is decreasing.

Hence, the graph of the function at each interval represent

(1) - increasing, (2) - decreasing, and (3) - decreasing.

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