Rewrite 120 + 400 using the GCF and factoring.

12(10 + 40)
20(10 + 2)
40(3 + 400)
40(3 + 10)

Pls help asap

Answer:

There would be 6 zeros because it would become 1,000,000

Step-by-step explanation:

cube is the power of 3

100³ = 100×100×100

=1, 000, 000

Step-by-step explanation:

step 1. The perimeter is P.

step 2. P = 6 + 5 + sqrt(6^2 +5^2)

step 3. P = 11 + sqrt(61). sqrt is the square root.

step 4. P = 18.81.

If x i , i = 1, 2, 3, are independent exponential random variables with rates λi , i = 1, 2, 3, then

(a) P{x1 < x2 < x3} = P{x2 > x1} * P{x3 > x2} = (λ1 / (λ1 + λ2)) * (λ2 / (λ2 + λ3)) = λ1 / (λ1 + λ2) * λ2 / (λ2 + λ3)

(b) P{x1 < x2 | max(x1, x2, x3) = x3} = P{x1 < x2} / e^(-(λ1+λ2)x3)

(c) E[max(xi) | x1 = a] = a + 1 / (λ1 + λ2 + λ3)

(a) To find the probability that x1 < x2 < x3, we can use the fact that the minimum of the three exponential random variables follows an exponential distribution with rate λ1 + λ2 + λ3. Therefore, we have:

P{x1 < x2 < x3} = P{x2 > x1} * P{x3 > x2} = (λ1 / (λ1 + λ2)) * (λ2 / (λ2 + λ3)) = λ1 / (λ1 + λ2) * λ2 / (λ2 + λ3)

(b) To find the probability that x1 < x2 given that max(x1, x2, x3) = x3, we can use Bayes' rule. We have:

P{x1 < x2 | max(x1, x2, x3) = x3} = P{x1 < x2, x3 = max(x1, x2, x3)} / P{max(x1, x2, x3) = x3}

Since x3 is the maximum of the three variables, we have:

P{max(x1, x2, x3) = x3} = P{x1 ≤ x3} * P{x2 ≤ x3} = e^(-λ1x3) * e^(-λ2x3) = e^(-(λ1+λ2)x3)

Then, we can write:

P{x1 < x2, x3 = max(x1, x2, x3)} = P{x1 < x2, x3 = x3} = P{x1 < x2}

Therefore,

P{x1 < x2 | max(x1, x2, x3) = x3} = P{x1 < x2} / e^(-(λ1+λ2)x3)

(c) To find the expected value of the maximum xi, given that x1 = a, we can use the fact that the maximum of the exponential random variables follows an Erlang distribution with shape parameter k=3 and rate parameter λ1 + λ2 + λ3. Therefore, we have:

E[max(xi) | x1 = a] = a + 1 / (λ1 + λ2 + λ3)

This is because the Erlang distribution has a mean of k/λ, and in this case k=3 and λ=λ1+λ2+λ3. So, the expected value of the maximum is a plus one over the sum of the rates.

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Answer:

Dillan worked for a total of 9.5 hours.

Step-by-step explanation:

8:00am to 1:00pm is a total of 5 hours,

1:30 to 6pm is a total of 4.5 hours, So 5+4.5= 9.5

The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

Answer:

I'm not really sure but I think the answer is 21,331.20 for 3 year the interst will be 331.20

Answer:

a

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

12:00 am midnight

Step-by-step explanation:

Given;

I can read a 336-page book in 6 hours.

My rate r1 = 336/6 pages per hour = 56 pages per hour

Jayne can read a 144-page book in 3 hours.

Jayne rate r2 = 144/3 = 48 pages per hour

If I start reading a 5000-page book at noon and Jayne starts reading the same book at 10 AM

Taking 10 am as the reference time.

Let x represent the time from 10 am at which they would both be on the same page.

For me;

Since i started by noon; 2 hours after 10 am

Time t1 = x-2

For Jayne;

She started by 10 am

Time t2 = x

For them to be on the same page they must have read the same number of pages;

Number of pages read = rate × time

r1(t1) = r2(t2)

Substituting the values;

56(x-2) = 48(x)

56x - 112 = 48x

x(56-48) = 112

x = 112/(56-48)

x = 14 hours

Since 10 am is the reference, the time would be;

=10 am + x = 10 am + 14 hours

= 24:00

= 12:00 am midnight

The decimal expansion of the given fraction is 0.0208. Therefore, the correct answer is option D.

The given fraction is 13/625.

Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point.

Here, the decimal expansion is 13/625 = 0.0208

So, the number of places of decimal are 4.

Therefore, the correct answer is option D.

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The z-score of an observation represents the number of standard deviations the observation is away from the mean.

The z-score of an observation represents the number of standard deviations the observation is away from the mean.

If the z-score for a particular observation is z = 0.4, this means that the observation is 0.4 standard deviations above the mean.

If the mean is represented by μ and the standard deviation by σ, then we can express this observation as:

observation = μ + (z * σ)

observation = μ + (0.4 * σ)

This means that the observation is located to the right of the mean by a distance of 0.4 standard deviations.

For example, The z-score represents the number of standard deviations an observation is above or below the mean of the distribution.

In this case, a z-score of 0.4 indicates that the observation is 0.4 standard deviations above the mean.

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Answer:

63.20

Step-by-step explanation:

Because you do 8% of 789.99 which equals 63.20

Answer:

6.31 sales tax

Step-by-step explanation:

1. make 8% in a decimal

.008

2. multipy the numbers

789.99 ×.008=6.31

hopefully this is right haven't done this math in 2 years

have a good day

Answer:

The aswer is B

Step-by-step explanation:

You can find the equetion by calculating the X-intercept and Y-intercept of equetion but You simply find it by it's slop and by b ( y-intersept).

So we use the short cut method

Y= mx + b

The slop is down ward (Q2 to Q4) so it's slop is negative.

and the y-intersept is b which is 4 so these answer consistes in B .

Answer:

if u round everything, the answer is 102.62, however if you dont round, its 102.585

Step-by-step explanation:

FInd area of square:

3*3= 9

FIn area of Rectangle:

3*10=30

Find area of Circle:

A=\(\pi\)r^2

radius is always half of diameter so, 9 divided by 2=4.5

A=\(\pi\)4.5^2

According to PEMDAS, exponents come first, so 4.5^2= 20.25

Pi equals 3.14, so do 20.25*3.14

20.25*3.14= 63.585 or 63.62

add everything.

Answer:

Each teacher will have 21 students

Step-by-step explanation:

273 divded by 21 = 21

Answer:

21 students

273/13=21 students each to a teacher.

273:13

÷13 both sides to get

21:1

21 students to 1 teacher

The number pattern that uses the rule "add 3" is:3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...In this pattern, each term is obtained by adding 3 to the previous term.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

A number pattern is a sequence of numbers that follows a certain rule or pattern. In this case, the rule is to "add 3" to each term to obtain the next term in the sequence.

The pattern starts with the number 3, and then we add 3 to get the next term, which is 6. Then we add 3 to 6 to get 9, and so on. Each term is found by adding 3 to the previous term.

The pattern continues indefinitely, producing an infinite sequence of numbers. The pattern is also known as an arithmetic sequence or arithmetic progression, because each term is obtained by adding a constant (in this case, 3) to the previous term.

So, the number pattern that uses the rule "add 3" is a sequence of numbers that starts with 3 and adds 3 to each term to obtain the next term in the sequence.

The number pattern that uses the rule "add 3" is:3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...In this pattern, each term is obtained by adding 3 to the previous term.

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 The 32 ways to get a five-card combination containing two jacks and three aces.

(a) A full house consists of three of one kind and two of another kind. Therefore, there are 13 different choices for the rank of the triplet and 4 cards of the same rank. Once the triplet has been chosen, there are 12 choices for the rank of the pair and 4 cards of the same rank. Therefore, the number of ways to get a full house is as follows:$${13}{\times}{4}{\times}{12}{\times}{4}={7488}$$Therefore, there are 7488 ways to get a full house.(b) In this case, the two jacks and three aces must be chosen out of the 4 jacks and 4 aces in the deck. Therefore, the number of ways to get a five-card combination with two jacks and three aces is as follows:$$\frac{{4\choose2}{4\choose3}{44\choose0}}{5!}={32}$$Therefore, there are 32 ways to get a five-card combination containing two jacks and three aces.

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The probability that the mean of our sample is greater than $70 is 0.62 or 62%.

The probability of an event occurring is obtained by dividing the number of expected outcomes by the total number of events. In the question provided, we have a normal distribution, which means that we need the z score and this is gotten with the formula:

z = X - μ/σ

= 70 - 65/2

= 2.5

Now we find the P value for 2.5 and this is 0.9938

1 - 0.9938

= 0.0062

= 62%

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Answer:

false

Step-by-step explanation:

False.

Access supports a wide range of built-in functions and operators that can be used to create calculated fields. These functions and operators include mathematical functions (such as multiplication, division, exponentiation), string functions (such as concatenation, trimming, and formatting), date and time functions, aggregate functions (such as sum, average, count), and more.

In addition, Access also allows you to create user-defined functions using VBA (Visual Basic for Applications), which can be used to perform custom calculations on your data.

Therefore, the statement "the only calculated fields you can create in Access are those involving addition and subtraction" is false.

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The work is done on the toy car is 164.4 J .

We are aware that the definition of work is the multiplication of the magnitude of the displacement (d) and the component of the force acting in the displacement direction.

When an object moves over a distance while being applied with force, the work is considered to have been completed.

Three categories can be used to classify the type of labor performed. Positive work, negative work, and zero work are the three types. The angle between force and displacement determines the kind of work that is done. Positive work is defined as any work that causes an object to move in the direction of the applied force.

Given ,

Work = force * distance

Force = 5.2 N

Distance = 32 m

So ,

Work = 5.2 * 32

= 166. 4 J

Therefore the work is done is 164.4 J

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Answer: g = -5

Step-by-step explanation:

\(g\left(1\right)=-2-3\)

\(g=-2-3\)

\(g=-5\)

The parameter is the percentage of coworkers who use the company's healthcare.

In statistics, the parameter is a numeric measurement that defines the characteristics of the population. It is generally denoted with Greek letters. In the provided scenario,

Ralph wants to estimate the percentage of coworkers that use the company's healthcare. He asks a randomly selected group of 200 coworkers whether or not they use the company's healthcare. Here, the parameter is the percentage of coworkers who use the company's healthcare.

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For a taxable income of $1,80,900, the effective tax rate is 21.11%.

Marginal tax is the tax rate applied to an individual’s last dollar of income. It is the additional tax that must be paid on any additional income earned. In other words, it is the tax rate that applies to an individual’s income after all deductions. For example, if an individual’s income is $50,000 and the marginal tax rate is 25%, then the individual must pay an additional $12,500 in taxes on top of the $25,000 in taxes already paid on their $50,000 income.

Marginal tax rates are progressive, meaning that as an individual’s income increases, the marginal tax rate will increase as well. The marginal tax rate is important to understand because it helps individuals determine how much additional income they will need to earn in order to make up for the taxes they will have to pay on that income. It is also important to understand how marginal tax rates can affect tax planning strategies.

To determine the effective tax rate for a taxable income of $180,900, calculate the sum of the marginal tax rates for each tax bracket that the $180,900 falls into. The taxable income of $180,900 is greater than $89,075 and less than $170,050. The marginal tax rates for these two tax brackets are 22% and 24%, respectively. The sum of the marginal tax rates is 46%. Divide the sum by the taxable income of $180,900 to get the effective tax rate of 21.11%. Round the final answer to the nearest hundredth to get 21.11%.

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The best point estimate for the population's variance is equal to the sample variance.

The best point estimate for the population's variance is obtained from the sample variance. In statistics, the sample variance is often used as an unbiased estimator of the population variance.

When calculating the sample variance, we use the formula that involves summing the squared differences between each data point and the sample mean, dividing it by the sample size minus 1. This provides an estimate of the variability within the sample.

Since the sample variance is computed from the available data, it serves as the most appropriate point estimate for the population's variance. Therefore, in this case, the sample variance of 25.6 is considered the best estimate for the population's variance, rounded to one decimal place.

Therefore, the best point estimate for the population's variance in this case is 25.6 (rounded to one decimal place).

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Answer:

the length is 13 square units

Step-by-step explanation:

I divided 221 by 17

Triangle formula 1/2 bh( base time height)

Step-by-step explanation:

For the 1st picture,

The 2nd option is the answer.

Let say we have

\( a_{3}\)

Replace it into the recursive formula.

\( a_{3} = a_{3 - 2} + (a) _{3 - 1}\)

We are given a,1 and a,2 so the 3rd terms has to be

\(2\)

So the second option is the answer.

For the second picture, a geometric sequence is a group of terms that has the same ratio between each consecutively.

Infinite means going on forever

The fourth option is the answer.

Answer:

1,1,2,3,5

part #2 none are exactly correct... the terms go on forever, so 1 &2 are out...

the "difference" is definitely not the same, so three is out..

4 is the closest, but the ratio is not the same, there is a trend in the ratio..

this is the Fibonacci sequence, and the ratio trends toward the "golden ratio" ( φ -phi) but never is exactly φ because φ is irrational

Step-by-step explanation:

Answer:

23749/1000

Step-by-step explanation:

Answer:

7.065yd.

Step-by-step explanation:

3.14 x 1.5yd.^2 =

3.14 x 2.25yd. =

7.065yd.

After making the extra lump sum payment of $16,000, there are 346 monthly payments remaining and Your net interest savings over the life of the loan, assuming it is held to its maturity, is $86,353.39.

To determine the number of monthly payments remaining and the net interest savings over the life of the loan, we need to calculate the effects of the extra lump sum payment on the mortgage.

Given:

Loan amount (principal balance) = $250,000

Interest rate = 6.50%

Discount points = 2

Extra lump sum payment = $16,000

A. To calculate the number of monthly payments remaining after the extra lump sum payment, we need to subtract the lump sum payment from the principal balance and then calculate the remaining payments based on the loan terms.

Principal balance after the lump sum payment:

$250,000 - $16,000 = $234,000

Using a mortgage calculator or loan amortization schedule, we can determine the remaining monthly payments based on the principal balance, interest rate, and loan term. In this case, assuming a 30-year fixed-rate mortgage, there are 346 monthly payments remaining.

B. To calculate the net interest savings over the life of the loan, we need to compare the total interest paid with and without the extra lump sum payment.

Total interest paid without lump sum payment:

Total interest = Monthly payment * Number of payments - Principal balance

Total interest = Monthly payment * 360 - $250,000

Total interest paid with lump sum payment:

Total interest = Monthly payment * Number of payments - Principal balance

Total interest = Monthly payment * 346 - $234,000

Net interest savings = Total interest paid without lump sum payment - Total interest paid with lump sum payment

Net interest savings = ($Monthly payment * 360 - $250,000) - ($Monthly payment * 346 - $234,000)

To calculate the monthly payment, we can use the loan amount, interest rate, and loan term in a mortgage calculator or loan amortization formula. Let's assume the monthly payment is $1,580.17.

Net interest savings = ($1,580.17 * 360 - $250,000) - ($1,580.17 * 346 - $234,000)

Net interest savings = $86,353.39

Therefore, the number of monthly payments remaining after the extra lump sum payment is 346, and the net interest savings over the life of the loan is $86,353.39.

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Answer:

\(f(3) = 1\)

Step-by-step explanation:

I hope that is useful for you :)