An inlet pipe on a swimming pool can be used to fill the pool in 2020 hours. The drain pipe can be used to empty the pool in 2121 hours. If the pool is 2323 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool

The present value, or initial investment, needed to grow to $70,000 for the child's education at age 17 with continuous compounding at 6% is approximately $25,260.21.

To calculate the initial investment, or present value, needed to grow to $70,000 for the child's education at age 17 with continuous compounding at an interest rate of 6%, we can use the formula for continuous compound interest. The formula is:

PV = FV / e^(rt)

Where PV is the present value, FV is the future value, e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time period.

In this case, we have:

FV = $70,000

r = 6% or 0.06

t = 17 years

Using the formula, we can calculate the present value:

PV = 70000 / e^(0.06 * 17)

By plugging in the values into the formula and solving, we find:

PV ≈ 70000 / e^(1.02)

PV ≈ 70000 / 2.7696

PV ≈ 25260.21

Therefore, the initial investment, or present value, required to grow to $70,000 for the child's education at age 17 with continuous compounding at 6% is approximately $25,260.21.

Answer:

D) -3/2

Step-by-step explanation:

x intercept is when y = 0

(2x + 3)/(x + 4) = 0

2x + 3 = 0

x = -3/2

Answer:

$3.1

Step-by-step explanation:

7.75/2.5 = 3.1

Answer:3.1

Step-by-step explanation:

7.75/2.5=3.1

Answer:

Step-by-step explanation:

Given that the regression equation for a set of paired data is = -23.8 + 2x. The values of x run from 100 to 400.

A new data point, P(194, 364.2), is added to the set.

From the given we can write it as y = -23.8+2x

Put x=194 in the above equation we get,

[tex]y(194) = -23.8+2\times 194[/tex]

[tex]=-23.8+ 388[/tex]

= 364.2

Hence, point P(194,364.2) is on regression line and it is not outlier.

Answer:

d. x= 10^6.4

Step-by-step explanation:

[tex] log_{10}(x) = 6.4 \\ x = {10}^{6.4} \\ [/tex]

Answer:

Its is just 0

Step-by-step explanation:

Answer:

Then it would be on a line

Step-by-step explanation:

Answer:

10 13 3 12 2

Step-by-step explanation:

there is no true pattern, the numbers written out in letters are listed alphabetically in order

Answer:

Brian has $776 more account in his account than Chris.

Step-by-step explanation:

Compound interest Formula:

[tex]A=P(1+r)^t[/tex]

[tex]I[/tex]= A-P

A= Amount after t years

P= Initial amount

r= Rate of interest

t= Time in year

Given that,

Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years.

Here P = $10,000 , r= 4%=0.04, t=10 years

The amount in his account after 10 years is

[tex]A=10000(1+0.04)^{10}[/tex]

   =$14802.44

  ≈$14802

Five years after Brian's investment,Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years.

Here P = $10,000 , r= 7%=0.07, t=5 years

The amount in his account after 5 years is

[tex]A=10000(1+0.07)^{5}[/tex]

   =$14025.51

  ≈$14026

From the it is cleared that Brian has $(14802-14026)=$776 more account in his account than Chris.

Answer:

B) Brian has $766 more in his account than Chris

Step-by-step explanation:

Compound interest formula is [tex]A = P(1+r)^{2}[/tex]

P - principal amount

r - rate of interest

t - number of years

Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years

P = 10,000  

r= 4% = 0.04

t = 10

Plug in all the factors

[tex]Brian = 10000(1+0.04)^{10}= $14,802[/tex]

Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years.

P = 10,000  

r= 7% = 0.07

t =5

Plug in all the factors

[tex]Chris = 10000(1+.07)^{5 } = $14,026[/tex]

$14,802 - 14,026 = $776

Answer:

(6/5,0)

(0, 6/8)

Step-by-step explanation:

[tex]5x=6-8y[/tex]

when y = 0 x-intercept

when x = 0 y-intercept

Answer:

x-intercepts- (1.2,0)

y-intercepts- (0,0.75)

Step-by-step explanation:

Answer:

84 - if they can only have an appetiser and a main course

Step-by-step explanation:

We have 6 * 14 distinct combinations.

If we could also have 2 appetisers or 2 main courses, that brings us up to 316 combinations ([tex]6*14 + 6^2 + 14^2[/tex]) - this is not an options so we do not need to consider this.

Answer:

Cecilia=£3.20

Dave=£2.40

Step-by-step explanation:

-The sum of the ratios is:

[tex]\sum{Ratios}=4+3\\\\=7[/tex]

#To find out how much each pay, your multiply the individuals ratio divide by the sum of the ratios times the cost;

[tex]Cecilia=\frac{4}[7}\times 5.60\\\\=\£3.20\\\\Dave=Total- Cecilia's\\\\=5.60-3.20\\\\=\£2.40[/tex]

Hence,Cecilia pays £3.20 and Dave pays £2.40

Answer:

50(115-y) + 25y = 4125             [from eq2]

    5750 - 50y  + 25y = 4125           [distribute]

    5750 - 25y = 4125

     -25y = -1625

        y = 65             [divide both sides by (-25)]

There are 65 small boxes.

Put that value into either equation (now, which is easier?) to solve for x:

 x = 115 - y

 x = 115 - 65

 x = 50

 There are 50 large boxes.

- Mring0506

The required number of boxes that the truck contain is 55 small boxes and 65 large boxes.  

Given that, the large boxes weigh 45 pounds each, and the small boxes weigh 25 pounds each. There are 120 boxes in all, the truck is carrying a total of 4300 pounds.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Let the number of large boxes will be l and the number of small boxed be s,

According to the question,
l + s = 120
l = 120 - s - - - - - (2)
Again,
45l + 25s = 4300
put l in the above equation,
45[120 - s] + 25s = 4300
5400 - 45s + 25s = 4300
20s = 1100
s = 1100/20
s = 55
Now,
l = 120 - 55
l = 65

Thus, the required number of boxes that the truck contain is 55 small boxes and 65 large boxes.  

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Answer:

Step-by-step explanation:

2,3 and 5

Answer:2,3,5

Step-by-step explanation:

Answer: 135 days

Step-by-step explanation:

Since the amount of time it takes her to arrive is normally distributed, then according to the central limit theorem,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 21 minutes

σ = 3.5 minutes

the probability that her commute would be between 19 and 26 minutes is expressed as

P(19 ≤ x ≤ 26)

For (19 ≤ x),

z = (19 - 21)/3.5 = - 0.57

Looking at the normal distribution table, the probability corresponding to the z score is 0.28

For (x ≤ 26),

z = (26 - 21)/3.5 = 1.43

Looking at the normal distribution table, the probability corresponding to the z score is 0.92

Therefore,

P(19 ≤ x ≤ 26) = 0.92 - 28 = 0.64

The number of times that her commute would be between 19 and 26 minutes is

0.64 × 211 = 135 days

Answer:

135

Step-by-step explanation:

Answer:

by taking a survey

Step-by-step explanation:

Answer:$70

Step-by-step explanation: if there are 3 seeds in each pot, you start by dividing 42 by 3. This equals 14. This shows how many pots you will need to use up all of the seeds. So to find how much it will cost, you multiply the amount of pots by the cost of each pot. So 14 times 5, which equals 70.

Answer:

fylinh rhthkrjehtegjhgjebjbebkbkbkertgbgrbkrt

Answer:

  y = -3/4x +1

Step-by-step explanation:

Parallel lines have the same slope, so the slope of the line you want is -3/4. The point-slope form of the equation of a line is useful when you have this information:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -(-2) = -3/4(x -4)

If you want slope-intercept form, you can rearrange this ...

  y +2 = -3/4x +3

  y = -3/4x +1 . . . . . . subtract 2 from both sides

The options at the end of the question are not typed properly, the correct options are given below.

A. √[144/240(1−144/240)/240] + [131/234(1−131/234)/234]

B. 1.65√[144/240(1−144/240)/240] + [131/234(1−131/234)/234]

C. 1.96√[144/240(1−144/240)/240] + [131/234(1−131/234)/234]

D. √[275/474(1−275/474)/474] + [275/474(1−275/474)/474]

E. 1.65√[275/474(1−275/474)/474] + [275/474(1−275/474)/474]

Given Information:

Confidence interval = 90%

Sample size of adults over the age of 40 = n₁ = 240

Sample size of adults under the age of 40 = n₂ = 234

Number of adults over the age of 40 who would use an online dating service = 144

Number of adults under the age of 40 who would use an online dating service = 131

Required Information:

standard error = ?

Answer:

standard error = 0.075

Step-by-step explanation:

The population proportion of adults over the age of 40 who would use an online dating service is,

p₁ = 144/240

p₁ = 0.6

The population proportion of adults under the age of 40 who would use an online dating service is,

p₂ = 131/234

p₂ = 0.56

The Standard Error is  given by

SE = z*√(p₁(1 - p₁)/n₁ + p₂(1 - p₂)/n₂)

Where z is the corresponding z-score value for the 90% confidence level that is 1.65

SE = 1.65*√(0.6(1 - 0.6)/240 + 0.56(1 - 0.56)/234)

This is the equation corresponding to the correct option B given in the question.

SE = 1.65*0.0453

SE = 0.075

Therefore, 0.075 is the standard error for 90% confidence interval to estimate the difference between the population proportions of adults within each age group who would use an online dating service.

0.075 is the standard error for 90% confidence interval to estimate the difference between the population proportions of adults within each age group who would use an online dating service.

Given that,

Confidence interval = 90%

Sample size of adults over the age of 40 = n₁ = 240

Sample size of adults under the age of 40 = n₂ = 234

Number of adults over the age of 40 who would use an online dating service = 144

Number of adults under the age of 40 who would use an online dating service = 131

We have to determine,

The standard error  for a 90 percent confidence interval to estimate the difference between the population proportions of adults within each age group who would use an online dating service.

According to the question,

The population proportion of adults over the age of 40 who would use an online dating service is;

[tex]P_1 = \dfrac{140}{244} = 0.6[/tex]

 The population proportion of adults under the age of 40 who would use an online dating service is,

[tex]P_2 = \dfrac{131}{234} = 0.56[/tex]

Therefore, The Standard Error is given by,

[tex]Standard\ error = z \times \sqrt{\dfrac{p_1(1-p_1)}{n_1} + \dfrac{p_2 (1-p_2)}{n_2} } \\\\[/tex]

Putting all the values in the given formula,

[tex]= 1.65 \times \sqrt{\dfrac{0.16(1-0.16)}{240} + \dfrac{0.56(1-0.56)}{234} } \\\\\\= 1.65 \times \sqrt{\dfrac{0.16(0.84)}{240} + \dfrac{0.56 (0.44)}{234} } \\\\\\= 1.65 \times \sqrt{0.00056+0.0010}\\\\= 1.65 \times 0.0453\\\\= 0.075[/tex]

Hence,  0.075 is the standard error for 90% confidence interval to estimate the difference between the population proportions of adults within each age group who would use an online dating service.

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Given:

Given that the diameter of the circle is 10 kilometers.

We need to determine the area of the circle.

Radius of the circle:

The radius of the circle can be determined using the formula,

[tex]r=\frac{d}{2}[/tex]

Substituting d = 10, we get;

[tex]r=\frac{10}{2}[/tex]

[tex]r=5[/tex]

Thus, the radius of the circle is 5 kilometers.

Area of the circle:

The area of the circle can be determined using the formula,

[tex]A=\pi r^2[/tex]

Substituting r = 5, we get;

[tex]A=(3.14)(5)^2[/tex]

[tex]A=(3.14)(25)[/tex]

[tex]A=78.5[/tex]

Thus, the area of the circle is 78.5 square kilometers.

Determine the radius, which is 5 kilometers, before calculating the area of a circle with a diameter of 10 kilometers. Next, find the area, or roughly 78.54 km², using the formula Area = π × (radius)².

How to Calculate a Circle's Area

You can use the following formula to get the area of a circle with a given diameter:

π × (radius)² equals area.

Consequently, 78.54 km² is the approximate size of the circle with a diameter of 10 km.

The objective function in this scenario is minimizing the cost of shipping goods from the plant to the store.

The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation.

The most likely goal function, if we were to create a linear programme for this situation, would be to reduce the cost of shipping from the plants to the stores. This is important since it can become an expensive bottleneck.

Despite the fact that there are three factories and three stores, the costs will not be minimized if the same amount of goods are produced in each plant and carried to a specific store. In fact, the likelihood that each facility generates a distinct volume of items further exacerbates the issue.

Finding the optimal distribution of shipping commodities from each facility to each retailer is important as a result.

Hence, the objective function is minimizing the cost of shipping goods from the plant to the store.

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The options are missing in the question, which are as follow:

a. minimizing the quantity of goods distributed across the stores

b. minimizing the cost of shipping goods from the plant to the store

c. decreasing the cost of their raw material sourcing

d. increasing the number of goods manufactured at the plant

Answer:

84cm^2

Step-by-step explanation:

Area of a parallelogram is Base times Height

Area = BxH

plug in

B = 14

H = 6

Answer:

True

Step-by-step explanation:

That is the definition of a asymptote.  It is approached but will never get to the line.

Answer: True!

Step-by-step explanation:

An asymptote for a function f(x) is a straight line which is approached but never reached by f(x)

Answer:

This is nonlinear.

Step-by-step explanation:

Answer:

There  are two real solutions to this equation, representing the number of seconds elapsed between the dolphin exiting and reentering the water.

Step-by-step explanation:

The total of 280 makes no sense because it tries to combine unrelated measurements and counts, such as library dimensions with the count of items like bookshelves and computers. Dimensions and counts are separate numerical categories and should be considered independently.

The library dimensions, bookshelves, and computers are individual elements that depict various characteristics of the library. The sum provided i.e., 280, cannot portray any sensible information about the library because it mistakenly incorporates unrelated physical dimensions (length and width in feet) with the count of items (bookshelves and computers). This is like adding apples and oranges which, conceptually, makes no sense.

The dimensions of the library, the number of bookshelves, and the number of computers are distinct items that aren't inter-convertible or comparable as they belong to different quantitative categories. They should be considered independently to provide meaningful information about the library.

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Answer:

The base charge = $18.5 and surcharge for each pound is = $1.75

Step-by-step explanation:

Solution:

- Denote:

     Base charge = $x   ...... For for Weight ≤ 1 lbs

     Additional charge = $y / unit pounds

- We are given that the customer is billed $29.00 for shipping a 7​-pound package. We can express this statement in terms of "x" and "y".

- The 1-pound out of 7 pounds will be charged with $x and remaining 6 additional pounds of weight will be charged "$y" for each unit of weight.

                         $x + ( 7 - 1 )*$y = $29.00    .... Eq1

- Similarly for a receipt of $64.00 for a 27​-pound package. The 1-pound out of 27 pounds will be charged with $x and remaining 26 additional pounds of weight will be charged "$y" for each unit of weight.      

                         $x + ( 27 - 1 )*$y = $64.00   .... Eq2

- Now solve the two equations simultaneously by subtracting Eq1 from Eq2:

                        (26 - 6 )*$y = $(64 - 29)

                        20*$y = $35

                         y = 1.75

                        $x = 29 - 6*1.75

                        x = 18.5    

- The base charge = $18.5 and surcharge for each pound is = $1.75

Answer:

It i s 6

Step-by-step explanation:

Very six

Answer:

Step-by-step explanation:

Answer:

C) 250 feet

Step-by-step explanation:

Let the diameter of the circle be d feet.

[tex] \therefore \: C = \pi d \\ \therefore \: 250\pi = \pi d \\ d = \frac{250\pi}{\pi} \\ d = 250 \: ft[/tex]