Create a Dataset Give a positive integer less than 100 as the last data value in each of the following datasets so that the resulting dataset satisfies the given condition (a) The mean of the numbers is substantially less than the median 51,52,53,54 (b) The mean of the numbers is substantially more than the median 2,3,4,5, (c) The mean and the median are equal. 2,3,4,5

The value of R(x) term is 36.

We are given that;

The equation x³ + 2x² - 72x - 28

Now,

We divide the first term, 8x, by the first term of d(x), which is x. This gives us 8, which is the third term of Q(x). We write 8 above the division bar and multiply it by d(x), which gives us 8x - 64. We subtract this from the new dividend, which gives us 36.

Since we cannot divide 36 by x-8 any further, we stop here and write 36 as the remainder R(x).

   x² + 10x + 8

  _______________

x-8 | x³ + 2x² - 72x - 28

    - (x³ - 8x²)

    -------------

        10x² - 72x

      - (10x² -80x)

      -------------

             8x -28

           - (8x -64)

           ----------

                36

Q(x) = x² + 10x + 8 and R(x) = 36.

Therefore, by the equation the answer will be R(x) = 36.

To learn more about equations :

brainly.com/question/16763389

#SPJ1

Answer:

lllllllllll

Step-by-step explanation:

Answer:

the third table

Step-by-step explanation:

Hope this helps and plz mark as brainliest!

Answer:

95,237,00

0989,000

955,700

132,200

Step-by-step explanation:

there are no really steps on this you just have to put the numbers in order from biggest to smallest

Answer:

D) As x increases, f(x) decreases; As x decreases, f(x) decreases

Step-by-step explanation:

To determine the end behavior of a function, it's worth noting the characteristics of the function.

As the function is clearly a parabola, given that the exponent is 2, this means that the function is even, which means as x increases, f(x) increases, and as x decreases, f(x) also increases. This is because for an even function, f(x)=-f(x). However, since the leading coefficient is negative, the parabola opens downwards, showing that as x increases, f(x) decreases, and as x decreases, f(x) decreases.

Therefore, D is correct. I've attached a graph to help you visualize what I've explained.

Answer:

the slope at x=3 is 24

for f(3+h)

Based on the given information, the operating characteristics of Willow Brook National Bank's drive-up teller window can be determined and the probability of customers having to wait for service can be calculated.

The arrival rate for the drive-up teller window is 0.5 customers per minute, while the service rate is 0.75 customers per minute. Since both arrival and service times follow exponential distributions, we can use the formulas for an M/M/1 queue to calculate the operating characteristics.

(a) The probability of having no customers in the system can be found using the formula P0 = 1 - (λ/μ), where λ is the arrival rate and μ is the service rate. Plugging in the values, P0 = 1 - (0.5/0.75) = 0.3333.

(b) The average number of customers waiting can be calculated using the formula Lq = (\(\lambda ^2\)) / (μ(μ - λ)). Plugging in the values,

Lq = (\(0.5^2\)) / (0.75(0.75 - 0.5)) = 0.6667.

(c) The average number of customers in the system is given by L = λ / (μ - λ). Plugging in the values, L = 0.5 / (0.75 - 0.5) = 1.

(d) The average waiting time for a customer can be calculated using the formula Wq = Lq / λ. Plugging in the values, Wq = 0.6667 / 0.5 = 1.3333 minutes.

(e) The average time a customer spends in the system is given by W = Wq + (1 / μ). Plugging in the values, W = 1.3333 + (1 / 0.75) = 2.6667 minutes.

(f) The probability that arriving customers will have to wait for service can be calculated using the formula Pw = λ / μ. Plugging in the values, Pw = 0.5 / 0.75 = 0.6667.

These calculations provide the operating characteristics of the drive-up teller window at Willow Brook National Bank.

Learn more about probability here:

https://brainly.com/question/31317254

#SPJ11

The metric unit from pounds to tons is 250 pounds = 0.125 tons

From the question, we have the following parameters that can be used in our computation:

250 pounds = how many tons

As a general rule, we have

1 pound = 0.0005 tons

Multiply both sides of the equation by 250

So, we have

250 * 1 pound = 0.0005 tons * 250

Evaluate the products

250 pounds = 0.125 tons

Hence, the conversion is 250 pounds = 0.125 tons

Read more about metric unit at

https://brainly.com/question/28234927

#SPJ1

Answer:

X=-4, y=-7

Step-by-step explanation:

6x-5y=11.     1st equation

y=7x+21    2nd equation

6x-5(7x+21)=11. Sub value of y in 2nd equation (7x+22) into 1st equation

6x-35x-105=11. Solve by distributative property

-29x-105=11.   Add x values

-29x=116.         add 105 to both sides

x=-4.                Solve for x

solve for y:

y=7x+21

y=7(-4)+21

y=-28+21

y=-7

check answer by substituting x and y into either equation

6x-5y=11

6(-4)-5(-7)=11

-24+35=11

11=11

Answer: 60 divided by 4

Step-by-step explanation:

Answer:

The average would be $15 for each shirt.

Step-by-step explanation:

divide the amount of money by the amount of shirts.

Answer:

A

Step-by-step explanation:

Khan gives you right answer and tells you what's wrong, but this site is for help so, all you need to do is use the destructive property.

12 x 2= 24 12 x 3 = 36 12 x -1 = -12

now you have the original expression, 24 + 36 - 12 (without the letters.)

Answer:

largest=2x+2

middle= x

smallest=x-4

Step-by-step explanation:

largest=2x+2

middle= x

smallest=x-4

The cost of the soil for each seedling is $0.35.

Division is an arithmetic operation that is the reverse of multiplication. It is used to find the number of times a quantity is contained within another quantity. Division can be represented using the division symbol (÷) or a fraction bar (/) and is performed by dividing the dividend by the divisor. The result of division is the quotient, which represents the number of times the divisor fits into the dividend. For example, if you have 8 apples and you divide them into 4 equal parts, each part would contain 2 apples. The expression 8 ÷ 4 = 2 represents this division, where 8 is the dividend, 4 is the divisor, and 2 is the quotient.

First, we need to find out how many seedlings Lara can plant with the bag of soil she bought. To do this, we divide the total amount of soil by the amount of soil required for each seedling:

16.25 cups of soil ÷ 1.25 cups of soil per seedling = 13 seedlings

Next, we divide the total cost of the soil by the number of seedlings to find the cost of the soil per seedling:

$4.55 ÷ 13 seedlings = $0.35 per seedling.

Therefore, the cost of the soil for each seedling is $0.35.

To know more about amount visit:

https://brainly.com/question/8082054

#SPJ1

We are given that{x = 4, y = 7, b = (5, 4, 8)}We have to check whether it satisfies the following quantified predicate or not.(∃ x. ∃ m. b[m] < x < y)

We have to prove whether this statement is true or false.Let us try to prove it as true. Let us choose an arbitrary value for x and m.

Let us choose m=1

Then, b[m]=4And, x=6

Therefore, 4<6<7, satisfies the predicate. Hence, the given statement is true.2) We are given that{x = 1, b = (2, 8, 9)}

We have to check whether it satisfies the following quantified predicate or not.(∀x. ∀k. 0 < k < 3 → x < b[k] )

We have to prove whether this statement is true or false.Let us try to prove it as false. For that, we have to find a counterexample. We have to disprove this statement.

That is if the statement is false, then the negation of this statement should be true, and that would mean the existence of a counterexample that satisfies the negation of the statement.

Therefore, (∃x. ∃k. 0 < k < 3 ∧ x ≥ b[k] )For k=1 and k=2, we get 2 values 8 and 9. Both of them are greater than or equal to x.So, the above statement holds true, which contradicts the initial statement.

Therefore, the given statement is false.3) We are given that{x = 0, b = (5, 3, 6)}

We have to check whether it satisfies the following quantified predicate or not.(∀x. ∀k. 0 < k < 3 ∧ x < b[k] )We have to prove whether this statement is true or false.Let us try to prove it as true.

Let us choose an arbitrary value for x and k.We have, 0< k <3 and x< b[k].

Let us choose k=2.

Then, b[k]=3

Therefore, the statement x<3 holds true.So, the above statement holds true for the given state.

Therefore, the given statement is true.

To know more about quantified predicate visit:

https://brainly.com/question/33355183

#SPJ11

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

a=t2−ba=t2-b

Answer: i think its 17

Step-by-step explanation:

Based on the calculation, it should be noted that the solution to the system of equations is x = 5.

To represent the costs (C) in dollars for x number of nights, we can use the equation:

C(x) = $500 (one-time preparation cost) + $10 (daily utility cost) * x (number of nights).

R(x) = $110 (rent per night) * x (number of nights).

Now, let's find the solution to the system of equations, which means finding the value of x where the costs equal the revenue:

C(x) = R(x)

Substitute the expressions for C(x) and R(x):

$500 + $10x = $110x.

To solve for x, we can move all the terms involving x to one side:

$110x - $10x   = $500.

Combine like terms:

$100x = $500.

Now, divide both sides by 100 to isolate x:

x = $500 / 100.

x = 5.

The solution to the system of equations is x = 5.

Learn more about equation

https://brainly.com/question/2972832

#SPJ1

Based on the information provided, the probability that Mitsugu has a quiz on Wednesday, Thursday,or Friday is 0.53 or 53%.

First, let's analyze the individual probabilities for these days:

Now, to find the total probability all we need to do is to add the partial probabilities previously given as it follows:

0.14 + 0.13 + 0.26 = 0.53

Finally, this number can be multiplied by 100 to find the probability in percentage:

0.53 x 100 = 53%

Learn more about probability in https://brainly.com/question/30034780

#SPJ1

Answer:

No estoy seguro, intenta preguntarle a tu profesor

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

-20

the counterclockwise circulation is also 0.Answer: The flux is 0. The circulation is 0.

Green's theorem is an important formula used in mathematics and physics to relate line integrals around a simple closed curve C to a double integral over the plane region D bounded by the curve C.

It states that for a vector field F in the plane, where F is continuously differentiable in a region containing D,

we have\($$\oint_C F\cdot dr = \iint_D \left(\frac{\partial F_2}{\partial x}-\frac{\partial F_1}{\partial y}\right)\,dx\,dy.$$

Here, F = (8x - 3y)i + (2y - 3x)j.\)

Therefore, \(F_1 = 8x - 3y and F_2 = 2y - 3x.\)

The curve C is a square with vertices at (0,0), (0,3), (3,3), and (3,0).

Let us first calculate the outward flux.

By Green's theorem,\($$\oint_C F\cdot dr = \iint_D \left(\frac{\partial F_2}{\partial x}-\frac{\partial F_1}{\partial y}\right)\,dx\,dy.$$$$\frac{\partial F_2}{\partial x}

= -3 \qquad \text{and} \qquad \frac{\partial F_1}{\partial y} = -3.$$\)

Thus,\($$\oint_C F\cdot dr = \iint_D (-3 + 3)\,dx\,dy = 0.$$\)

So, the outward flux is 0.

Next, let us calculate the counterclockwise circulation.

Again, by Green's theorem\(\(,$$\oint_C F\cdot dr = \iint_D \left(\frac{\partial F_2}{\partial x}-\frac{\partial F_1}\)

\({\partial y}\right)\,dx\,dy.$$$$\frac{\partial F_2}{\partial x} = -3 \qquad \text{and} \qquad \frac{\partial F_1}{\partial y} = -3.$$\)

Thus,\($$\oint_C F\cdot dr = \iint_D (-3 + 3)\,dx\,dy = 0.$$\)\)

To know more about counterclockwise visit:

brainly.com/question/3227295

#SPJ11

Answer:

Step-by-step explanation:

Assuming the question is x^2 + 6x = 27x, subtract 6x from both sides.       x^2 = 21x. Then, divide both sides by x and you get x= 0, 21

A small freezer costs $100,000 in cash and $139,360 by hire purchase.

Hire purchase refers to a payment system by which the purchaser of an item makes regular installment payments, which include finance charges.

Retailers require a downpayment or initial deposit to offer customers hire purchases.

The cash price of a small freezer = $100,000

Hire purchase costs:

Deposit (downpayment) = $62,560

Installment period = 24 months

Installment amount = $3,200

Total installment payments = $76,800 ($3,200 x 24)

The total cost under hire purchase = $139,360 ($62,560 + $76,800)

Learn more about hire purchases and downpayments at https://brainly.com/question/29699850.

#SPJ1

It can be brought on hire purchase by depositing $62,560 and 24 monthly installments of $3,200.

Answer:

X = 6

Step-by-step explanation:

First we need to get the x values on one side, and the numbers without the variable on the other:

Subtract 1.8x to the left side, and 4 to the right side.

Now we have 4x = 24.

24/4 = 6.

x= 6. :)

The mean of T is -10 and the standard deviation of T is √425 when X1 and X2 are independent.

To find the mean of T, we can use the properties of expected values. Since T = 11X1 - 2X2, the mean of T can be calculated as follows: E(T) = E(11X1) - E(2X2) = 11E(X1) - 2E(X2) = 11(10) - 2(20) = -10. To find the standard deviation of T, we need to consider the variances and covariance of X1 and X2. Since X1 and X2 are independent, the covariance between them is zero. Therefore, Var(T) = Var(11X1) + Var(-2X2) = 11^2Var(X1) + (-2)^2Var(X2) = 121(2^2) + 4(3^2) = 484 + 36 = 520. Thus, the standard deviation of T is √520, which simplifies to approximately √425. When X1 and X2 have a correlation of -0.76, the mean and standard deviation of T remain the same as in the case of independent variables. To calculate the probability P(T > 30) when X1 and X2 are independent, normally distributed variables, we need to convert T into a standard normal distribution. We can do this by subtracting the mean of T from 30 and dividing by the standard deviation of T. This gives us (30 - (-10))/√425, which simplifies to approximately 6.16.  We can then look up the corresponding probability from the standard normal distribution table or use statistical software to find P(T > 30). The probability will be the area under the standard normal curve to the right of 6.16.

Learn more about standard normal distribution here: brainly.com/question/32506784

#SPJ11

The matrix equation [4 5 40 - 9 - 5 27 1 - 7 32] can be written as a vector equation Ax = <40 27 32>

A matrix is a rectangular array of numbers, often denoted as Ax, where A is the matrix itself and x is the vector of numbers that make up the columns of the matrix.

In this problem, we are given the matrix equation 4 5 40 - 9 - 5 27 1 - 7 32 and asked to use the definition of Ax to write it as a vector equation.

To do this, we need to identify which numbers are in the matrix A and which numbers are in the vector x.

The numbers 4, 5, -9, -5, 1, and -7 represent the matrix A, while the numbers 40, 27, and 32 represent the vector x.

Therefore, the matrix equation can be written as Ax = 40 27 32.

To know more about matrix here.

https://brainly.com/question/28180105

#SPJ4

The equation of the plane is ax + by + cz + d = 0, where a = -1, b = -5, c = -5, and d = 11.

The equation of the plane that passes through points (1, 1, 1), (2, 0, 3), and (-1, 4, 2) can be found using the point-normal form of the equation of a plane.

To find the normal vector of the plane, we can take the cross product of two vectors formed by the given points. Let's call the vectors formed by (1, 1, 1) and (2, 0, 3) as vector A, and the vectors formed by (1, 1, 1) and (-1, 4, 2) as vector B.

Vector A = (2-1, 0-1, 3-1) = (1, -1, 2)
Vector B = (-1-1, 4-1, 2-1) = (-2, 3, 1)

Now, taking the cross product of A and B, we get the normal vector of the plane:
Normal vector = A x B = (1, -1, 2) x (-2, 3, 1) = (-1, -5, -5)

Using the normal vector and one of the given points (let's use (1, 1, 1)), we can write the equation of the plane as:
-1(x - 1) - 5(y - 1) - 5(z - 1) = 0

Simplifying the equation, we get:
-x - 5y - 5z + 11 = 0

So, the equation of the plane is ax + by + cz + d = 0, where a = -1, b = -5, c = -5, and d = 11.

To know more about equation refer here:

https://brainly.com/question/33722071

#SPJ11

Answer:

She should have divided the cost of the carton by the number of eggs to find the price per egg.