Kyle bought some boxes of donuts. There were 4 donuts in each box, and Kyle bought 76 donuts in all. Write an equation, that when solved, will tell how many boxes, b, of donuts Kyle bought?

So the expected value of the remainder when M is divided by 64 is approximately 0.2080.

To find the expected value of the remainder when M is divided by 64, we can find the probability that M is congruent to each possible remainder modulo 64 and then sum these probabilities multiplied by the corresponding remainders.

For a positive integer n, let P(n) denote the probability that a positive integer chosen from the set {1, 2, . . . , 100} is congruent to n modulo 64. Then

P(0) = P(64) = P(128) = ... = 1/100

P(1) = P(65) = P(129) = ... = 1/100

P(63) = P(127) = P(191) = ... = 1/100

Since the integers a, b, c, d, e, and f are chosen independently and uniformly at random from the set {1, 2, . . . , 100}, the probability that M is congruent to n modulo 64 is P(n)^6.

Therefore, the expected value of the remainder when M is divided by 64 is

E = 0 * P(0)^6 + 1 * P(1)^6 + 2 * P(2)^6 + ... + 63 * P(63)^6

= (0^6 + 1^6 + 2^6 + ... + 63^6) * P(0)^6

= (0 + 1 + 2 + ... + 63) * P(0)^6

= 2080 * (1/100)^6

= 0.2080

So the expected value of the remainder when M is divided by 64 is approximately 0.2080.

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For a positive integer n, let P(n) denote the probability that a positive integer chosen from the set {1, 2, . . . , 100} is congruent to n modulo 64. Then

P(0) = P(64) = P(128) = ... = 1/100

P(1) = P(65) = P(129) = ... = 1/100

P(63) = P(127) = P(191) = ... = 1/100

Since the integers a, b, c, d, e, and f are chosen independently and uniformly at random from the set {1, 2, . . . , 100}, the probability that M is congruent to n modulo 64 is P(n)^6.

Therefore, the expected value of the remainder when M is divided by 64 is

E = 0 * P(0)^6 + 1 * P(1)^6 + 2 * P(2)^6 + ... + 63 * P(63)^6

= (0^6 + 1^6 + 2^6 + ... + 63^6) * P(0)^6

= (0 + 1 + 2 + ... + 63) * P(0)^6

= 2080 * (1/100)^6

= 0.2080

Answer: No

Step-by-step explanation:

To determine whether the college graduate will have $200,000 saved in their retirement account after 25 years, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where A is the total amount of money in the account after the specified time, P is the initial amount of money deposited in the account, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years the money is invested.

In this case, the initial amount deposited each month is $150, the annual interest rate is 10%, the number of times the interest is compounded per year is 12 (once per month), and the number of years the money is invested is 25. Plugging these values into the formula above gives us:

A = $150 * (1 + 10%/12)^(12*25) = $150 * (1.0083)^300 = $150 * 3.4955 = $524.33

Since the goal is to have $200,000 saved in the account after 25 years, the college graduate will not have enough money in their account if they contribute $150 per month at 10% interest. In order to reach their goal, they would need to save more money each month or earn a higher interest rate on their contributions.

The solution of the differential equation is given by r = 5tan(t + c) where c is the constant of integration, determined by the initial condition (x, 5).

The given differential equation is dr sec21dt tant 1. This is a first order linear differential equation which can be solved using an integrating factor. The integrating factor is given by e^(integral(sec^2(t)dt)). The solution of the equation is given by

[tex]r = (integral(sec^2(t))) + c[/tex]

where c is the constant of integration

Let y = sec(2x)

dy/dt = 2tan(2x)sec(2x)

Now, substituting the given point, we get

5 = sec(2x)

⇒ 2x = arccosec(5)

⇒ x = arccosec(5)/2

Now, substituting this in the equation of the differentiable curve, we get

[tex]\int\limits^a_b {x} \, dx dy/dt = 2tan(arccosec(5))sec(arccosec(5))[/tex]

Hence, the solution of the differential equation passing through the given point is y = sec(2x) = sec(arccosec(5))

or r = sec(arccosec(5))

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A. The functions are given as follows:

B. The company from which the family should rent the truck is: Company Y.

There are two costs in the problem, given as follows:

The fixed costs for Company X are given as follows:

The variable cost is of 0.59 per mile, hence the function, considering a trip of m miles, is given as follows:

X(m) = 59.90 + 150 + 36 + 0.59m.

X(m) = 245.9 + 0.59m.

The fixed costs for Company Y are given as follows:

The variable cost is of 0.79 per mile, hence the function, considering a trip of m miles, is given as follows:

Y(m) = 39.90 + 52 + 0.79m

Y(m) = 91.9 + 0.79m.

The trip is of 750 miles, hence the costs are given as follows:

Due to the lower cost, Company Y should be chosen.

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Answer:

Step-by-step explanation:

There are 4 kings in a deck of playing cards.

There are 52 cards in a deck.

So the probability is 4 out of 52.

Which is 4/52,

Which can be reduced to 1/13.

4 divided by 4 = 1 and 52 divided by 4 =13.

The correct option is (d) i.e. the range of the relation is {-5, 0, 2, 4}.

What is Range ?

A function's range is a collection of all of its potential results, or alternatively, the collection of all conceivable representations of the domain's elements.

Given, {(2, -5), (1, 4), (-3, 0), (6, 2)}

Range is the result of a relation.

let say, X⇒ Y is a relation where X represents the domain and Y represents the range and both can be represented as ( X, Y).

So, all the values at the position of Y are called range of the given relation.

Hence, Range will be {-5, 0, 2, 4}.

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The solution is A = 37

The value of the equation A = 8a + 3b - 10 + c² is A = 37

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

A = 8a + 3b - 10 + c²

When the value of a = 2 , the value of b = 5 and the value of c = 4 ,

The equation A is given as

Substitute the value of a , b and c in the equation , we get

A = 8a + 3b - 10 + c²

A = 8 ( 2 ) + 3 ( 5 ) - 10 + 4²

A = 16 + 15 - 10 + 16

On simplifying the equation , we get

A = 31 + 6

The value of A = 37

Therefore , the value of A is 37

Hence , The value of the equation A = 8a + 3b - 10 + c² is A = 37

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The list of pairs of triangles are ∠A≅∠N, ∠B≅∠O, ∠C≅∠P for the given similar triangles.

Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry.

In Euclidean geometry, any three non-collinear points determine a distinct triangle and a distinct plane (i.e. a two-dimensional Euclidean space). To put it another way, every triangle has a plane that it is contained in, and there is only one plane that contains every triangle. If and only if all geometry is the Euclidean plane, all triangles are contained in a single plane; however, this is no longer true in higher-dimensional Euclidean spaces.

Given triangles are,

ΔABC and ΔNOP

And also given that they are similar triangles.

The pairs of the congruent angles are:

∠A≅∠N

∠B≅∠O

∠C≅∠P

Therefore, the list of pairs of triangles are ∠A≅∠N, ∠B≅∠O, ∠C≅∠P for the given similar triangles.

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The answer is option 3: approval ratings tended to fall as stock prices rose.

This means that when stock prices rose, the approval ratings of George Bush's presidency decreased. This can be interpreted as an indication that people were not satisfied with the performance of the stock market during the Bush presidency. This could be because the stock market was not performing as well as expected or because the people were not satisfied with the decisions made by the Bush presidency that impacted the stock market.

Whatever the reason, the negative correlation between the stock market performance and Bush's approval ratings shows that when stock prices rose, approval ratings tended to fall.

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Answer:

Step-by-step explanation:

To find the minimum number of daisies and lilies that Manuel must have watered, we need to find the least common multiple (LCM) of 11 and 12. The LCM of two numbers is the smallest positive integer that is a multiple of both numbers.

To find the LCM of 11 and 12, we can list the multiples of each number and find the smallest number that appears in both lists. The multiples of 11 are 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, etc. The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, etc.

We can see that the smallest number that appears in both lists is 11, which is the LCM of 11 and 12. Therefore, the minimum number of daisies and lilies that Manuel must have watered is 11. If he watered the same number of each flower, he must have watered at least 11 daisies and 11 lilies.

Answer:

To round a number to the nearest thousand, we first need to identify the thousands digit in the number. In this case, the thousands digit is 8, because 87388 is between 80000 and 90000.

To determine whether to round up or down, we need to look at the hundreds digit, which is 7 in this case. If the hundreds digit is 5 or greater, we round up. If the hundreds digit is less than 5, we round down. In this case, the hundreds digit is 7, which is greater than or equal to 5, so we need to round up.

To round up, we add 1000 to 87388, which gives us 88388. So, 87388 rounded to the nearest thousand is 88000.

Answer:

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

Out of 100 offices:

Remaining offices will be painted red:

Answer:

27 offices will be painted red.

Step-by-step explanation:

Yellow offices:

= 45% of 100 offices

= 0.45 × 100

= 45 yellow offices

Blue offices:

= 28% of 100 offices

= 0.28 × 100

= 28 blue offices

Red offices:

= Total number of offices - yellow offices - blue offices

= 100 - 45 - 28

= 55 - 28

= 27 red offices

Therefore, 27 offices will be painted red.

An equivalent fraction of 36/48 having denominator 6 could be 6/6 only.

A fraction represents a part of a number or any number of equal parts.

we are given a fraction as 36/48.

We can make equivalent fractions by multiplying or dividing both top and bottom by the same amount.

We have to only multiply or divide, never add or subtract, to get an equivalent fraction. Only divide when the top and bottom stay as whole numbers.

In this case we have a clue which is 48,

6 x 8 = 48

Then we would want to take the 6 and times it by the denominator which is 6

So 6 x 6 = 36

An equivalent fraction of 36/48 is 6/6.

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Answer:

8/33

p(d'c')

not having a cat=12/18

not a dog =4/11

12/18×4/11=8/33

Ans=8/33

She expects to have $2710591.78 when she retires at age 65 with the principal amount is 398100, the interest rate is 8%, time period is 24 and number of times interest applied is 3 by the concept of compound interest.

Interest that is paid on the principal and interest at regular periods is known as compound interest. The interest is calculated for the new principal at regular intervals after the interest that has already accumulated has been combined with the existing principal amount. The initial principal plus the interest that has accrued thus far are added together to form the new principal.

Interest on the principal + periodic compound = compound interest.

According to the question the principal amount is 398100, the interest rate is 8%, time period is 24 and number of times interest applied is 3.

Here the interest is compounded every 4 months

So, the formula of compound interest is as follows:

A=p (1+ [tex]\frac{r}{n}[/tex]) ∧ (n× t)

Where P is the principal balance, r is the interest rate, n is the number of times interest is compounded per year and t is the number of years.

Here the interest is compounded every 4 months hence the value of n is 12/4 which is equal too 3.

Insert the values of p, n, t, r in above equation,

A=398100(1+[tex]\frac{8}{300}[/tex]) ∧ (3×24)

A=398100× (1.027) ∧ (72)

A=398100×6.809

A=2710591.78

She expects to have amount $2710591.78 when she retires at age 65.

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The same cost of both of the plan of the gym will be in 5 visits. And plan B is better than Plan A as B is cheaper than A.

In mathematics, expression is the combining of variables with the application of operations and prescribed rules. It could take the shape of an equation, some numbers, etc.

We have,

plan A consists of :

Amount for monthly membership fee = $50

Cost per visit = $10

The expression of total fees would be:

50+10x,

where x is the number of times Jim visits the gym.

Plan B consists of :

Amount for monthly one time membership fee = $25

Cost per visit = 15

The expression of total fees would be:

25 + 15x,

where x is the number of times Jim visits the gym.

Here, x denotes the number of visits.

Let us suppose x = 1

Then, fees for plan A would be:

50 + 10 x1 = $60

Fees for plan B would be:

25 + 15 x1 = $40

To find the same cost in x number of visits:

We equate both the expressions.

50+10x = 25 + 15x

15x - 10x = 50 - 25

5x = 25

x = 5

That means, if Jim visits 5 times, the gym, then he would have the similar cost for both of the plans.

Hence, Plan B is better than Plan A as B is cheaper than A. The same cost of both of the gym will be in 5 visits.

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80% is her free throw shooting percentage.

Fractions are used to represent smaller pieces (or parts) of a whole. The parts might make up one thing, or more than one thing. Either way, altogether, they make up what's called a whole.

Given that, Jeremiah makes 4/5 of the free throw shots he attempts in basketball. Jeremiah likes to shoot free throws until he misses one. Let F be the number of shots it takes Jeremiah to miss his first free throw.

We can construct a fraction in which the numerator is how many shots she makes, and the denominator is how many shots she took overall.

We now have the following fraction:4/5

To convert this to a percentage, we want the denominator to be 20/20

= 4/5×20/20

= 80/100

= 0.8

Now multiply 0.8 with 100

= 0.8×100=80

Hence, 80% is her free throw shooting percentage.

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Answer:

Below

Step-by-step explanation:

16500 - 6800 = 9700 interest required to meet this situation in 14 years

6800 * i * 14  = 9700       where i = decimal interest

i = 9700/(6800*14) = .1018  = 10 .2 %

Answer: 6

Step-by-step explanation:

x=8-2

x=6

Rick's deposit in first 3 weeks is  $39  

1. Rick's deposit in the second week = 3  times($3)

                                                             = 3(3)

                                                             = 9

                                                             = [tex]3^{2}[/tex]

The exponential expression for Rick's 2nd week deposit = [tex]3^{2}[/tex]

Where,  Base  = 3

              Exponent = 2                                

2. Rick's deposit in 1st week = $3  

   Rick's deposit in 2nd week = 3 (3) = $9

   Rick's deposit in 3rd week =  3 (9) = $27  

   Rick's deposit in first 3 weeks = 3+9+27

                                                      = $39      

  Rick's deposit in all in the first 3 weeks is  $39  

3.   Rick's deposit for 15 weeks = [tex]3^{15}[/tex]

                                                    = $1,43,48,907.

We know, no. of weeks in a year = 52

Rick's deposit for 52 weeks ( 1 year ) = 52 times of 3

                                                             [tex]=3^{52}\\= 6.4610819e+24[/tex]

Since this is a huge number , Rick cannot keep up this savings plan for a year.

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Answer:

6 rows to 7 steal in each rows

Answer:

h = 6

Step-by-step explanation:

h is the short leg for AD in ΔADC: AD = 12

h is the long leg for DB in ΔCDB: DB = 3

Hence:

12/h = h/3

3 * 12/h = 3 * h/3  ==> isolate h by multiplying 3 on both sides

36/h = h

h * 36/h = h*h  ==> multiply by h on both sides to remove fractions

36 = h^2

h = [tex]\sqrt{36}[/tex]

h = 6

On solving the provided question, we can say that - the instantaneous rate of change of the function at the given value, by solving the equation  y = 11 - 5x, f'(1) = 3-8 = -5

A mathematical equation is a formula that uses the equals symbol (=) to link two expressions and represent their equivalence. A mathematical statement that demonstrates the equality of two mathematical expressions is an equation in algebra, in its most basic form. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

y = f(x) =

[tex]x^3 - 4x^2 + 7 \\at x =1[/tex]

f(x) = 3-4+7

= 6

F'(x) = [tex]3x^2 - 8x[/tex]

f'(1) = 3-8 = -5

equation = y - 6 = -5(x-1)

y = 11 - 5x

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The value of x is 7/3 and the value of y is -11/3 for the given equations.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the equations are 2x - 2y = 12 and -8x -y = -15. The value of x and y will be calculated as,

2x - 2y = 12

-8x - y = -15

Solve the above equation,

2x - 2(-8x + 15) = 12

2x + 16x - 30 = 12

18x = 42

x = 42 / 18

x = 7 / 3

The value of y is calculated as,

-8x - y = -15

y = ( -8 x 7 / 3 ) +15

y = (-56 + 45) /3

y = -11 / 3

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LCL would be 4 minutes and UCL would be 6 minutes if the company uses 2-sigma control limits instead.

The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means. The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.

Given

LCL = 3.5 minutes

UCL = 6.5 minutes

Mean = LCL + UCL/2

Mean = 3.5 + 6.5/2

Mean = 5

Standard deviation = UCL - LCL/6

Standard deviation = 6.5 - 3.5/6

Standard deviation = 0.5

LCL = 5 - 2(0.5)

LCL = 4

UCL = 5 + 2(0.5)

UCL = 6

LCL = 4 minutes and UCL = 6 minutes

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The equation that can be used to find b, when E and n are known is: b = (E - 12n) / 8.

This equation can be derived from the original equation of E=8b+12n. To solve for b, we can start by subtracting 12n from both sides of the equation to isolate b. We then divide both sides of the equation by 8 in order to solve for b.

The result is b = (E - 12n) / 8. This equation can be used to find the number of bracelets (b) when the total earnings (E) and the number of necklaces (n) are known.

We can rearrange the equation to solve for b.

E = 8b + 12n

Subtract 12n from both sides:

E - 12n = 8b

Divide both sides by 8:

(E - 12n)/8 = b

Therefore, the equation to find b, when E and n are known, is:

b = (E - 12n)/8

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An inequality that can represent the sum of a number and 11.5 is more than −4.5 is  b + 11.5 > −4.5 .

What is inequality?

In mathematics, a relationship between two expressions or values that are not equal to each other is called ‘inequality.’ So, a lack of balance results in inequality. For example, if you want to buy a new bicycle that costs 250 but you have 225. It is also an inequality as you are comparing two numbers that aren’t equal.

We use ‘=’ when two quantities are equal and when they are not equal we use the symbol ≠ to denote not equal. If two things are not equal, the first value can be either greater than (>) or lesser than (<) or greater than equal to (≥) or less than equal to (≤) the second value. So, as per the above example, 250 > 225.

Given :  the sum of a number and 11.5 is more than −4.5

Let us assume the number be "b"

according to question,

b + 11.5  is more than −4.

Thus, An inequality that can represent the sum of a number and 11.5 is more than −4.5 is  b + 11.5 > −4.5 .

Hence ,  b + 11.5 > −4.5 is the correct answer .

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Answer:

Step-by-step explanation:

thx for the points