A bank wishes to estimate the mean balances owed by customers holding Mastercard. The population standard deviation is estimated to be $300. If a 98% confidence interval is used and the maximum allowable error is $80, how many cardholders should be sampled?
A. 76
B. 85
C. 86
D. 77

Given:

The functions are:

[tex]p(x)=\dfrac{1}{x+1}[/tex]

[tex]q(x)=\dfrac{1}{x-1}[/tex]

To find:

The rational expression for [tex]p(x)-q(x)[/tex].

Solution:

We have,

[tex]p(x)=\dfrac{1}{x+1}[/tex]

[tex]q(x)=\dfrac{1}{x-1}[/tex]

Now,

[tex]p(x)-q(x)=\dfrac{1}{x+1}-\dfrac{1}{x-1}[/tex]

[tex]p(x)-q(x)=\dfrac{(x-1)-(x+1)}{(x+1)(x-1)}[/tex]

[tex]p(x)-q(x)=\dfrac{x-1-x-1}{x^2-1^2}[/tex]             [tex][\because a^2-b^2=(a-b)(a+b)][/tex]

[tex]p(x)-q(x)=\dfrac{-2}{x^2-1}[/tex]

Therefore, the required rational expression for [tex]p(x)-q(x)[/tex] is [tex]\dfrac{-2}{x^2-1}[/tex].

Answer:

a) Because this asks about the radius and height, I assume that we are talking about a cylinder shape.

Remember that for a cylinder of radius R and height H the volume is:

V = pi*R^2*H

And the surface will be:

S = 2*pi*R*H + pi*R^2

where pi = 3.14

Here we know that the volume is 1000cm^3, then:

1000cm^3 = pi*R^2*H

We can rewrite this as:

(1000cm^3)/pi = R^2*H

Now we can isolate H to get:

H = (1000cm^3)/(pi*R^2)

Replacing that in the surface equation, we get:

S = 2*pi*R*H + pi*R^2

S = 2*pi*R*(1000cm^3)/(pi*R^2) + pi*R^2

S = 2*(1000cm^3)/R + pi*R^2

So we want to minimize this.

Then we need to find the zeros of S'

S' = dS/dR = -(2000cm^3)/R^2 + 2*pi*R = 0

So we want to find R such that:

2*pi*R = (2000cm^3)/R^2

2*pi*R^3 = 2000cm^3

R^3 = (2000cm^3/2*3.14)

R = ∛(2000cm^3/2*3.14) = 6.83 cm

The radius that minimizes the surface is R = 6.83 cm

With the equation:

H = (1000cm^3)/(pi*R^2)

We can find the height:

H = (1000cm^3)/(3.14*(6.83 cm)^2) =  6.83 cm

(so the height is equal to the radius)

b) The surface equation is:

S = 2*pi*R*H + pi*R^2

replacing the values of H and R we get:

S = 2*3.14*(6.83 cm)*(6.83 cm) + 3.14*(6.83 cm)^2 = 439.43 cm^2

c) Because if we pack cylinders, there is a lot of space between the cylinders, so when you store it, there will be a lot of space that is not used and that can't be used for other things.

Similarly for transport problems, for that dead space, you would need more trucks to transport your ice cream packages.

Answer:

The number of positive real zeros is 2 or 0

Step-by-step explanation:

Given

[tex]f(x)=x^5+3x^2-4x+2[/tex]

Required

Number of positive real zeros

Using Descartes rule of signs;

We write out the signs in front of each term;

Sign = + + - +

Count the number of times the sign alternate; i.e. from positive to negative and from negative to positive

From positive to negative, we have: 1 (i.e. + - )

From negative to positive, we have: 1 (i.e. - +)

Add up the count

[tex]count = 1+1[/tex]

[tex]count = 2[/tex]

Hence, the number of positive real zeros is 2 or 0

Answer:

8 ounces of tomato paste for each cup of water.

Step-by-step explanation:

Just divide 48 / 6 to get 8 oz of tomato paste per cup of water.

Hope this helps!

Work Shown:

48 oz of tomato paste = 6 cups of water

48/6 oz of tomato paste = 6/6 cups of water

8 oz of tomato paste = 1 cup of water

In short, we divide both values by 6 so that the "6 cups" becomes "1 cup". We can say the unit rate is 8 oz of tomato paste per cup of water.

Here, we want to find the interest rate and principal

The interest rate, r = 6% and the principal, P = Rs 65,000

Compound interest:

A = P(1 + r/n)^t

Simple interest :

I = P * r * t

Simple interest for 2 years = Rs 7800

Simple interest for 1 year = Rs 7800 / 2

= Rs 3900

Compound interest for 2 years = Rs 8034

Compound interest for the second year = Rs 8034 - Rs 3900

= Rs 4134

Interest on Rs 3900 = Rs 4134 - Rs 3900

= Rs 234

Therefore,

Interest rate, r = 234/3900 × 100

= 0.06 × 100

r = 6%

Recall,

Simple interest :

I = P * r * t

Then,

P = I / r * t

= 3900 / 6% * 1

= 3900 / 0.06

= 65,000

P = Rs 65,000

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Answer:

12

Step-by-step explanation:

Find the LCM (Least Common Multiple) of the three numbers.

We could multiply 3 x 4 x 6 to get 72, but there is a smaller multiple, 12.

6 x 2 = 12

4 x 3 = 12

3 x 4 = 12

Hope this helps!

Answer:

Yes, it is rational number.

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

Answer:

an arithmetic sequence

Step-by-step explanation:

an arithmetic series is wrong also heres an example i found of an arithmetic sequence

The terms in the given sequence represents an arithmetic sequence.

Arithmetic sequence is a sequence of numbers where the numbers are arranged ion a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.

Given sequence of numbers is,

-8, -4, 0, 4, 8, 12, ......

We have to find which sequence does it represent.

This is not a series since they are not represented as the sum.

If the sequence is a geometric sequence, then the ratio of consecutive numbers will be same.

If it is arithmetic sequence, then the difference of consecutive numbers will be same.

Here, ratio is not same.

Difference are same.

-4 - -8 = 4, 0 - -4 = 4, 4 - 0 = 4, 8 - 4 = 4, ........

Common difference is 4.

Hence it is an arithmetic sequence.

Learn more about arithmetic Sequence here :

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Answer: 14 seed packs

Step-by-step explanation:

You'd divide the 9 tomatoes by the 6 seed packs that were necessary to grow them, resulting in 1.5 tomatoes per seed pack. Divide 21 by this 1.5 to find the number of seed packs needed to grow 21 tomatoes, which would be 14.

Answer:

Hello,

Answer A StartFraction x cubed + 2 x squared Over 3 EndFraction cm3

Step-by-step explanation:

[tex]V=x^2*\dfrac{x+2}{3} \\\\\boxed{V=\dfrac{x^3+2x^2}{3} }\\[/tex]

the third of the sum of the cube of x and double of the square of x ( cm³)

The Volume of pyramid with a square base of side x cm and height of (x + 2) cm is (x³ + 2x²) / 3

Volume is the amount of space occupied by a three dimensional shape or object.

Area of the square base = x * x = x² cm²

Volume of pyramid = (1/3) * area of base * height = (1/3) * x² * (x + 2)

Volume of pyramid = (x³ + 2x²) / 3

The Volume of pyramid with a square base of side x cm and height of (x + 2) cm is (x³ + 2x²) / 3

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Answer:

12

Step-by-step explanation:

113.04=3.14 x 3^2 x h/3

Answer:

The Hong Kong dollar equivalent of K70 is HK $ 94.71.

Step-by-step explanation:

Given the exchange rate as K1: HK $ 1,353, to calculate Hong Kong dollar equivalent of K70 the following calculation must be performed:

1,353 x 70 = X

94.71 = X

Therefore, the Hong Kong dollar equivalent of K70 is HK $ 94.71.

Answer:

x=3

Step-by-step explanation:

The ratios need to be the same

AB             CB

---------- = ----------

AD             ED

3           x

-----  = ---------

3+9       12

3           x

-----  = ---------

12          12

X must equal 3

Answer:

82991 employees

Step-by-step explanation:

One way to solve this would be to solve for 1% of the company's employees and use that value to solve for 100% (100%=the whole part, or the total). We know that

28300 = 34.1%

If we divide a number by itself, it turns into 1. Dividing both sides by 34.1, we get

829.912 = 1%

Then, we know that anything multiplied by 1 is equal to itself. We want to figure out 100%, or the whole part, so we can multiply both sides by 100 to get

100% = 82991

Answer:

P(z > -1.76) = 1 - P(z < -1.76) = 1 - 0.0392 = 0.960

Answer:

8

Step-by-step explanation:

To determine the common difference, take the second term and subtract the first term

11-3 = 8

Check with the other terms in the sequence

19-11= 8

27-19 = 8

35-27=8

The common difference is 8

Answer:

C. 8

Step-by-step explanation:

There is a common difference between them and that’s 8.

3 + 8 = 11

11 + 8 = 19

19 + 8 = 27

27 + 8 = 35

Answer:

[tex](a)\ \frac{dP}{dt} = kP + r[/tex]

[tex](b)\ \frac{dP}{dt} = kP - r[/tex]

Step-by-step explanation:

Given

[tex]\frac{dP}{dt} = kP[/tex]

Solving (a): Differential equation for immigration where [tex]r > 0[/tex]

We have:

[tex]\frac{dP}{dt} = kP[/tex]

Make dP the subject

[tex]dP =kP \cdot dt[/tex]

From the question, we understand that: [tex]r > 0[/tex]. This means that

[tex]dP =kP \cdot dt + r \cdot dt[/tex] --- i.e. the population will increase with time

Divide both sides by dt

[tex]\frac{dP}{dt} = kP + r[/tex]

Solving (b): Differential equation for emigration where [tex]r > 0[/tex]

We have:

[tex]\frac{dP}{dt} = kP[/tex]

Make dP the subject

[tex]dP =kP \cdot dt[/tex]

From the question, we understand that: [tex]r > 0[/tex]. This means that

[tex]dP =kP \cdot dt - r \cdot dt[/tex] --- i.e. the population will decrease with time

Divide both sides by dt

[tex]\frac{dP}{dt} = kP - r[/tex]

Answer:

4x-5=4x-5

Step-by-step explanation:

Answer:

3 sqrt(3) =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj / hyp

cos 30 = x/6

6 cos 30 = x

6 ( sqrt(3)/2) = x

3 sqrt(3) =x

Answer:

the answer is B

Step-by-step explanation:

[tex] {{ (- 2)}^{3}}^{5 \div 3} = { ( - 2)}^{5} = - 32[/tex]

write -8 form of 2 on up and complete other steps

Given:

There is a 65% chance you will make a free throw.

To find:

The percent of the time you will miss.

Solution:

If p is the percent of success and q is the percent of failure, then

[tex]p+q=100\%[/tex]

[tex]q=100\%-p[/tex]         ...(i)

It is given that there is a 65% chance you will make a free throw. It means the percent of success is 65%. We need to find the percent of the time you will miss.  It means we have to find the percent of failure.

Substituting p=65% in (i), we get

[tex]q=100\%-65\%[/tex]

[tex]q=35\%[/tex]

Therefore, there is a 35% chance you will miss the free throw.

Answer:

a

Step-by-step explanation:

The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is

[tex]\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt[/tex]

In this case, we have

x(t) = exp(t ) + exp(-t )   ==>   dx/dt = exp(t ) - exp(-t )

y(t) = 5 - 2t   ==>   dy/dt = -2

and [a, b] = [0, 2]. The length of the curve is then

[tex]\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt[/tex]

[tex]=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}[/tex]

The exact length of the curve when the parametric equations are x = f(t) and y = g(t) is given below.

[tex]e^2 -\dfrac{1}{e^2 }[/tex]

It is the reverse of differentiation.

The parametric equations are given below.

[tex]\rm x=e^t+e^{-t}, \ \ 0\leq t\leq 2\\\\y=5-2t, \ \ \ \ \ 0\leq t\leq 2[/tex]

Then the arc length of the curve will be given as

[tex]\int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}[/tex]

Then we have

[tex]\rm \dfrac{dx}{dt} = e^t-e^{-t}\\\\ \dfrac{dy}{dt} = -2[/tex]

Then

[tex]\rightarrow \int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}\ \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t-e^{-t})^2 + (-2)^2} \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t+e^{-t})^2} \ dt\\\\\rightarrow \int _0^2 (e^t+e^{-t}) \ dt\\\\\rightarrow (e^2-e^{-2}) \\\\\rightarrow e^2 - \dfrac{1}{e^2}[/tex]

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Answer:

[tex]5 {x}^{2} + 21 + 5x[/tex]

Step-by-step explanation:

TOTAL AMOUNT earned = Tim money + Melina money

[tex]5 {x}^{2} - 4x + 8 + (9x + 13)[/tex]

[tex] = 5 {x}^{2} - 4x + 8 + 9x + 13[/tex]

[tex] = 5 {x}^{2} + 21 + 5x[/tex]

Complete Question:

A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x) = -0.001x² + 3x - 1800.

a. What is his maximum profit per day?

b. How many cans must be sold in order to obtain the maximum profit?

Answer:

a. $450

b. 1500 cans

Step-by-step explanation:

Given the following quadratic function;

P(x) = -0.001x² + 3x - 1800  ......equation 1

a. To find his maximum profit per day;

Since P(x) is a quadratic equation, P(x) would be maximum when [tex] x = \frac {-b}{2a} [/tex]

Note : the standard form of a quadratic equation is ax² + bx + c = 0  ......equation 2

Comparing eqn 1 and eqn 2, we have;

a = -0.001, b = 3 and c = -1800

Now, we determine the maximum profit;

[tex] x = \frac {-b}{2a} [/tex]

Substituting the values, we have;

[tex] x = \frac {-3}{2*(-0.001)} [/tex]

Cancelling out the negative signs, we have;

[tex] x = \frac {3}{2*0.001} [/tex]

[tex] x = \frac {3}{0.002} [/tex]

x at maximum = 1500

Substituting the value of "x" into equation 1;

P(1500) = -0.001 * 1500² + 3(1500) - 1800

P(1500) = -0.001 * 2250000 + 4500 - 1800

P(1500) = -2250 + 2700

P(1500) = $450

b. Therefore, the soft-drink vendor must sell 1500 cans in order to obtain the maximum profit.

10(3+5)^2

10(8)^2

10(64)

=640

Answer:

B is the correct answer of your question.

I HOPE I HELP YOU....

Answer:

The travel time that separates the top 2.5% of the travel times from the rest is of 91.76 seconds.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 80 seconds and a standard deviation of 6 seconds.

This means that [tex]\mu = 80, \sigma = 6[/tex]

What travel time separates the top 2.5% of the travel times from the rest?

This is the 100 - 2.5 = 97.5th percentile, which is X when Z has a p-value of 0.975, so X when Z = 1.96.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.96 = \frac{X - 80}{6}[/tex]

[tex]X - 80 = 6*1.96[/tex]

[tex]X = 91.76[/tex]

The travel time that separates the top 2.5% of the travel times from the rest is of 91.76 seconds.

Answer:

25.61 feet

Step-by-step explanation:

First, we can draw a picture (see attached picture). With the wall representing the rightmost line, and the ground representing the bottom line, the ladder (the hypotenuse) forms a 80 degree angle with the ground and the wall and ground form a 90 degree angle.

Without solving for other angles, we know one angle and the hypotenuse, and want to find the opposite side of the angle.

One formula that encompasses this is sin(x) = opposite/hypotenuse, with x being 80 degrees and the hypotenuse being 26 feet. We thus have

sin(80°) = opposite / 26 feet

multiply both sides by 26 feet

sin(80°) * 26 feet = opposite

= 25.61 feet as the height of the wall the ladder reaches

The height of the wall does the ladder reach to the nearest hundredth of the foot is 25.61 feet.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.

Josue leans a 26 feet ladder against a wall so that it forms an angle of 80° with the ground.

The condition is shown in the diagram.

Then the height of the wall will be

[tex]\rm \dfrac{h }{26 } = sin 80 \\\\h \ \ = 26 \times sin 80\\\\h \ \ = 25.61 \ ft[/tex]

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