For what value of b will the polynomial P(x) = 4x^3 - 3x^2 + bx + 6 have the same remainder when it is divided by x - 1 and by x +3?

You can use the following formula:

A = (b*h)/2

Where:

b = Base = 12cm

h = Height = 6cm

So:

A = (12*6)/2 = 72/2 = 36cm²7

Answer:

The hourly rate is better between 1 and 8 hours.

Step-by-step explanation:

There are two options

A fixed amount of $1560.

Or an hourly rate of $180 the hour.

So for the first option, the cost equation as a function of time, t, is:

f(t) = $1560

(it does not depend on t)

While for the second option, the equation would be:

g(t) = $180*t

First, we want to answer:

We can expect that for smaller values of t the second option is better but let's see that:

or what lengths of time would the hourly rate be less​ expensive?

Then we need to solve:

f(t) = g(t)

for t, this is:

$1560 = $180*t

$1560/$180 = t = 8.66

So, for t = 8.66, the cost is the same in both options.

For t < 8.66

(between 1 and 8 hours) the second option is better. (here the hourly rate is better)

for t > 8.66

(9 hours or more) is better the first option, as the hourly (here the flat fee is better)

If you have access to the information on the back of Ken's bank statement, you can calculate his revised statement balance by adding any credits and subtracting any debits from the previous statement balance.

Reconciling a bank account involves comparing the transactions in your own financial records with those listed on your bank statement. The goal is to ensure that the account balance in your financial records matches the balance reported by the bank.

To reconcile a bank account, you typically start with the ending balance on the previous bank statement, which becomes the beginning balance on the current statement. You then compare this balance with the transactions listed on the current statement, adding any credits (such as deposits or interest payments) and subtracting any debits (such as withdrawals or fees).

The resulting balance should match the ending balance listed on the current bank statement. If it does not match, then there may be errors or discrepancies in the account that need to be investigated. This can involve reviewing bank records, receipts, and other financial documents to identify any errors or missing transactions.

Reconciling your bank account on a regular basis is important for ensuring the accuracy of your financial records and identifying any issues or errors in a timely manner. It can also help you identify areas where you may be overspending or where you can save money by reducing fees or optimizing your financial habits.

Whether or not Ken's account reconciles depends on whether the calculated revised statement balance matches the bank's reported statement balance. If they match, then the account is reconciled. If they do not match, then there may be discrepancies in the account that need to be investigated and resolved.

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The amount to be paid is more on credit card 2 is more, it must be paid first.

Card 1:

Current balance = $8,312.69

Annual percentage rate APR = 24.16%

Credit limit = $10,000.

Used amount = $10,000 - $8,312.69

Used amount = 1687.31

A = P\((1 + r/n)^{nt}\)

P = $1687.31

r = 24.16% = 0.2416

Take n = 1 and time = 1 year.

A =  1687.31*\((1 + 0.2416/n)^{1*1}\)

A = 1687.31 * 1.2416

A = $2094.96

For Card 2:

Current balance = $1,180.34

APR = 21.15%

Credit limit = $75,00

Used amount = $75,00 - $1,180.34

Used amount = $6319.66

A = 6319.66*\((1 + 0.2115/n)^{1*1}\)

A = 6319.66 * 1.2115

A = $7656.26

As the amount to be paid is more on credit card 2 is more, it must be paid first.

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0.94 is the probability that the HR director will select an employee who is not a multiple of 13.

The probability that the HR director will select an employee who is not a multiple of 13 is the number of employees who are not multiples of 13 divided by the total number of employees.

There are 50 employees in total, and there are 50/13 = 3 employees who are multiples of 13.

So the number of employees who are not multiples of 13 is 50 - 3 = 47.

Thus, the probability that the HR director will select an employee who is not a multiple of 13 is 47/50.

Simplifying this fraction, we find that the answer is 47/50 = 94/100 i.e. 0.94 is the probability that the HR director will select an employee who is not a multiple of 13.

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The administration's willingness to pay to save a student's statistics life is no more than option c) $100,000.

To estimate the administration's willingness to pay to save a student's statistical life, we need to calculate the cost per statistical life saved. Currently, the probability of a student dying from the plague is 1/3,000. If the rats are eradicated, this probability is reduced to zero. The cost of eradicating the rats is $1,000,000. To calculate the cost per statistical life saved, we divide the cost by the number of statistical lives saved.

The number of statistical lives saved is the product of the number of students on campus (30,000) and the reduction in probability (1/3,000).
Cost per statistical life saved = $1,000,000 / (30,000 * (1/3,000))
                         = $1,000,000 / (30,000 * 1/3,000)
                         = $1,000,000 / 10
                         = $100,000
Therefore, the correct answer is option c) $100,000.

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If an auditorium has 20 rows of seats. there are 20 seats in the first row, 21 seats in the second row, 22 seats in the third row, and so on. then,  there are 39 seats present in the 17th row.

The given data is as follows:

Number of rows of seats = 20

Number of seats in the first row = 20

Number of seats in the second row = 21

Number of seats in the third row = 22 and so on.

Let's calculate the common difference between the seats,

common difference = 21-20 = 1 or 22-21 = 1

Therefore common difference = 1

Then the number of the seats in 17th row will be

The number of the seats = 20 + (20 - 1)* 1

The number of the seats= 39 seats.

Therefore, there are a total of 39 seats present in the 17th row.

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Step-by-step explanation:

step by step by solutions are given

check it

hope you like the answer

Answer: B

Step-by-step explanation:

203.95-11.95=192

192/4=48

One ticket cost 48 dollars, and the service fee is $11.95. Therefore, c=11.95+48t

Answer:

79/120

Step-by-step explanation:

Answer:

79/120

Step-by-step explanation:

You make all the answers to have the same denomination and then add them.

(a) The intersection of two subspaces U and V in R^n is always a subspace of R^n.

(b) The union of two subspaces U and V in R^n may not be a subspace of R^n, and a counterexample can be provided.

(a) To prove that the intersection of two subspaces U and V in R^n is a subspace of R^n, we need to show that it satisfies the three properties of a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector.

Let x and y be two vectors in the intersection of U and V. Since x and y are in both U and V, they belong to U + V. Therefore, x + y is in U + V, and by definition, it is also in the intersection of U and V. Similarly, for any scalar c, cx is in U and V, and thus in their intersection. Finally, the zero vector is in both U and V, and therefore it is in their intersection.

(b) To demonstrate that the union of two subspaces U and V in R^n may not be a subspace of R^n, consider the following example: Let U be the x-axis and V be the y-axis in R^2. Both U and V are subspaces of R^2. However, their union is the set of all points in R^2, which includes vectors that do not lie on either the x-axis or the y-axis. For example, the vector (1, 1) is not in either U or V, but it is in their union. Since the union contains vectors that are not closed under addition or scalar multiplication, it fails to be a subspace of R^2.

In conclusion, the intersection of two subspaces U and V in R^n is always a subspace of R^n, while the union of two subspaces U and V in R^n may not be a subspace of R^n, as shown by the counterexample of the x-axis and y-axis in R^2.

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Answer:

#1) Write a function to model population growth. Use a graph to predict when the population will reach 20, 000.

Answer: In this case what you have to do is use an exponential growth equation. In short the correct function that will model this population growth of 14% each year is P(t) = 350(1.14)^t and the population will reach 20,000 in about 31 years.

I hope it helps,

Step-by-step explanation:

plz mark brainlyest

Answer:

{-8, 2, 4, 6}

Step-by-step explanation:

If you want only the "inputs," they are {-8, 2, 4, 6}.  The corresponding outputs are {-6, -3, 2, 5}.

The volume of the region bounded by the given surfaces is 181.46 units³.

The volume of the region bounded by z = 168 – y, z = y, y = x², and y = 84 – x² is calculated as follows;

The intersection points between the surfaces y = x² and y = 84 - x².

x² = 84 - x²

2x² = 84

x² = 42

x = √42

The intersection points between the surfaces z = 168 - y and z = y

168 - y = y

2y = 168

y = 84

x: -√42 to √42

y: x² to 84 - x²

z: y to 168 - y

The volume V is given by the triple integral as;

V = ∫[x² to 84 - x²] ∫[y to 168 - y] ∫[y to 168 - y] dz dy dx

V = ∫[x² to 84 - x²] ∫[y to 168 - y] (168 - 2y) dy dx

V = ∫[x² to 84 - x²] (168y - y²) dy dx

Simplify the integral function further as follows;

V = ∫[(168y - y²) from y to 168 - y] dx

V = ∫[(168(168 - y) - (168 - y)²) - (168y - y²)] dx

V = ∫[(168(168 - y) - (168 - y)²) - (168y - y²)] dx

V = ∫[(168 - y)(168 - y) - (168 - y)² + y²] dx

V = ∫[(168 - y)² - (168 - y)² + y²] dx

V = ∫[y²] dx

V = ∫[x²] dx

V = ∫[√42 to -√42] x² dx

The volume of the region is calculated as;

V = [x³/3] from √42 to -√42

V = [(√42)³/3 -  (-√42)³/3]

V = 90.73 + 90.73

V = 181.46 units³

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Therefore, the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM is approximately 0.1755, rounded to four decimal places.

To calculate the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM, we need to use the Poisson distribution formula. The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space. In this case, the mean (λ) is given as 5. The formula for the Poisson distribution is:

P(X = k) = (e*(-λ) * λ\(^k\)) / k!

Where:

P(X = k) is the probability of getting exactly k calls

e is the base of the natural logarithm (approximately 2.71828)

λ is the mean number of calls (given as 5)

k is the number of calls (in this case, 4)

k! is the factorial of k

Let's calculate the probability using the formula:

P(X = 4) = (e*(-5) * 5⁴) / 4!

P(X = 4) ≈ 0.1755

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Answer:

Step-by-step explanation:

Let the number of cans be x

5% of x is 61, solve the equation below for x:

In the given formula we have variables:

If we have to solve it for P then it should be called 'Principal' or 'Loan amount'.

If we have to solve it for n then it should be called 'Number of payments' or 'Number of installments'.

Since n is the power of a number we need logarithm to solve it for n.

Answer:

"Principal (loan amount)"

"Term of the loan (in months)" or "Number of monthly payments"

Logarithms

Step-by-step explanation:

Monthly Payment Formula

\(M=\dfrac{Pr\left(1+r\right)^n}{\left(1+r\right)^n-1}\)

where:

If we solve for P, the name of the formula is "Principal (loan amount)".

If we solve for n, the name of the formula is "Term of the loan (in months)" or "Number of monthly payments".

When solving for n, we need to use logarithms:

\(\boxed{\begin{aligned}M&=\frac{Pr\left(1+r\right)^n}{\left(1+r\right)^n-1}\\\\M(\left(1+r\right)^n-1)&=Pr\left(1+r\right)^n\\\\\frac{\left(1+r\right)^n-1}{\left(1+r\right)^n}&=\frac{Pr}{M}\\\\1-\frac{1}{\left(r+1\right)^n}&=\frac{Pr}{M}\\\\\frac{1}{\left(r+1\right)^n}&=1-\frac{Pr}{M}\\\\\left(r+1\right)^{-n}&=1-\frac{Pr}{M}\\\\\ln \left(r+1\right)^{-n}&=\ln \left(1-\frac{Pr}{M}\right)\\\\-n\ln(r+1)&=\ln\left(1-\frac{Pr}{M}\right)\\\\n&=\frac{-\ln\left(1-\frac{Pr}{M}\right)}{\ln(r+1)}\end{aligned}}\)

Answer: A function is a relation between domain and range such that each value in the domain corresponds to only one value in the range. Relations that are not functions violate this definition. They feature at least one value in the domain that corresponds to two or more values in the range.

Step-by-step explanation:

Answer:

The answer to your question is given in the attached photo.

Step-by-step explanation:

To determine the answer to the question,

First, we shall determine the value 3A.

This is obtained by multiplying matrix A by 3 as shown in the attached photo.

Next, we shall carry out the operation 3A – B as shown in the attached photo.

Answer:

Amount set aside for food = 0.12 × 4,000

Step-by-step explanation:

His net pay = $4,000

His budget

Food = 12% of his budget

Assume $4,000 is his budget

Then,

Food = 12% of $4,000

= 12/100 × 4,000

= $480

The Equation is

Amount set aside for food = 0.12 × 4,000

The equation would be set up as follows:

\(\begin{aligned} \rm {Amount \: for \: food \: pay} &= \dfrac{12 \times 4000}{100}\\&= \$\:480 \end{aligned}\)

Given that:

Amount of net pay is $4,000

Percentage of budget used for food is 12%

To calculate the amount towards food, we'll take out 12% of amount of net pay which is $4,000.

It would be written symbolically as:

\(\begin{aligned} \rm {Amount \: for \: food \: pay} &= \dfrac{12 \times 4000}{100}\\&= \$\:480 \end{aligned}\)

Thus, amount for food pay is in total $ 480, and is calculated by above equation.

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A hypothesis is a statement regarding a characteristic of one or more populations. The null hypothesis is a statement of no change, no effect, or no difference. The alternative hypothesis is a statement we are trying to find evidence to support.

Generally, the null hypothesis expresses that there is no change, no difference, no effect, and in another way, no relationship between the independent and dependent variables. Because we are hypothesizing that nothing is happening, then it is called the null hypothesis.

The null and alternative hypothesis are two conflicting claims which researchers weigh evidence for and against using a statistical test. Null hypothesis (H0) means there is no effect in the population. Meanwhile, alternative hypothesis (Ha or H1) means there is an effect in the population.

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The equation of the number of pages is y = 40 + 10x and for 9 days, you read 130 pages

From the question, we have

Initial number of pages = 40

Rate per day = 10 pages per day

The equation of the number of pages is then represented as

y = Initial number of pages + Rate per day x Number of days

Substitute the known values in the above equation, so, we have the following representation

y = 40 +10 * x

Evaluate

y = 40 + 10x

For 9 days, we have

x = 10

This gives

y = 40 +10 * 9

Evaluate

y = 130

Hence, the number of pages is 130

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Answer:

w= -4

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

w is -4

Step-by-step explanation:

\(4w = 2w - 8\)

make w the subject:

\(4w - 2w = - 8 \\ 2w = - 8\)

divide all sides by 2:

\( \frac{2w}{2} = \frac{ - 8}{2} \\ \\ w = - 4\)

The optimal solution using the two-phase simplex method for the given linear programming problem, we first need to convert it into standard form by introducing slack and surplus variables.

The problem can be rewritten as follows: Minimize Z = 2x1 + 3x2
subject to: 2x1 + 4x2 + s1 = 4
-x1 - 3x2 - s2 = -36
x1 + x2 = 10
x1, x2, s1, s2 ≥ 0

In the first phase of the simplex method, we introduce artificial variables and solve the problem to obtain an initial feasible solution. The initial tableau is constructed with the objective row as [0, 0, -M, -M, 0] and the constraint rows corresponding to the coefficients of the variables and artificial variables. Here, M represents a large positive number.

Next, we perform the simplex iterations to improve the solution. At each iteration, we pivot to select the entering and leaving variables until the optimal solution is reached. The iterations involve calculating the ratios of the right-hand side to the pivot column elements and selecting the minimum ratio as the pivot row.

In the second phase, we remove the artificial variables and proceed with the simplex iterations using the revised tableau. The iterations continue until the optimal solution is obtained, and the objective function value is minimized.

Unfortunately, I cannot generate the detailed steps and iterations of the two-phase simplex method in this text-based format. It requires a series of calculations and tabular representation. However, by following the steps of the two-phase simplex method, including initializing the tableau, performing simplex iterations, and removing the artificial variables in the second phase, you can find the optimal solution for the given problem.

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g(x) = x^2 - 3

f(x) = x^3+7x^2-x

Start with the g(x) function. Replace every x with f(x)

g(x) = x^2 - 3

g(f(x)) = ( f(x) )^2 - 3

Then replace the f(x) on the right side with x^3+7x^2-x

g(f(x)) = (x^3+7x^2-x)^2 - 3

The highest term inside the parenthesis is x^3. Squaring this leads to (x^3)^2 = x^(3*2) = x^6

So the highest exponent found in g(f(x)) is 6, meaning the degree of is 6

Answer:

The shape is a kite and x=26

Step-by-step explanation:

The shape is a kite because the two adjacent sides at the right match and the two sides on the left match

To find x:

125+125=250

360-250=110

(3x-11)+(2x-9)=110

Combine like terms: 5x-20=110

Add 20 to both sides: 5x-20+20=110+20

5x=130

Divide both sides by 5: 5x/5=130/5

x=26

Answer:

The maximum number of people that can be in the Trumpington marching band is 940 people

Step-by-step explanation:

The number of members = 20·n

The number per row = 26

The number left = 4

Therefore, we have;

If there are x rows of 26, we have;

26 × x = 20·n - 4

We have;

26 × x < 996

26 × x < 20·n

20·n < 996 therefore, 20·n ≤ 980

We check that 980/26 = 37  and some fractions

26 × 37 = 962 which will leave a remainder of 2

Therefore, we note that for 26 to have a remainder of 4, the last digit of the factor x must be 6 so has to get the last digit of the product 26 × x to be 6 while the digit of the product 20×n  is 0 which will live 4 members out to get to the next 10 as follows;

26 × 36 = 936 while 20 × 47 = 940

We get 940 - 936 = 4 members

Therefore, the maximum number of people that can be in the Trumpington marching band = 940.

i. The crude death rate is approximately 10.53 deaths per 1,000 population.

ii. The cause-specific mortality rate for lung cancer is approximately 0.5 deaths per 1,000 population.

iii. The proportional mortality rate for lung cancer is approximately 0.47%.

Explanation:

i. Crude Death Rate:

The crude death rate is calculated by dividing the total number of deaths from all causes by the population and then multiplying by a constant factor (usually 1,000 or 100,000) to obtain the rate per 1,000 or 100,000 population.

Given:

Total number of deaths from all causes = 2,106

Population = 200,000

Crude Death Rate = (Total number of deaths from all causes / Population) * 1,000

Crude Death Rate = (2,106 / 200,000) * 1,000

Crude Death Rate = 10.53 deaths per 1,000 population

ii. Cause-Specific Mortality Rate:

The cause-specific mortality rate is calculated by dividing the number of deaths from a specific cause by the population and then multiplying by a constant factor (usually 1,000 or 100,000) to obtain the rate per 1,000 or 100,000 population.

Given:

Cases of cancer among both men and women = 100

Population = 200,000

Cause-Specific Mortality Rate = (Cases of cancer / Population) * 1,000

Cause-Specific Mortality Rate = (100 / 200,000) * 1,000

Cause-Specific Mortality Rate = 0.5 deaths per 1,000 population

iii. Proportional Mortality Rate:

The proportional mortality rate is calculated by dividing the total number of deaths from a specific cause by the total number of deaths from all causes and then multiplying by 100 to obtain the percentage.

Given:

Total number of deaths from lung cancer = 10

Total number of deaths from all causes = 2,106

Proportional Mortality Rate = (Total number of deaths from lung cancer / Total number of deaths from all causes) * 100

Proportional Mortality Rate = (10 / 2,106) * 100

Proportional Mortality Rate ≈ 0.47%

Therefore:

i. The crude death rate is approximately 10.53 deaths per 1,000 population.

ii. The cause-specific mortality rate for lung cancer is approximately 0.5 deaths per 1,000 population.

iii. The proportional mortality rate for lung cancer is approximately 0.47%.

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