a bag contains five batteries, all the same size and equally likely to be selected. Each battery is a different brand. If you select three batteries at random, use the counting principle to determine how many points will be in the sample space if the batteries are selected with replacement and without replacement?

Answers

Answer 1
Final answer:

When selecting three batteries at random with replacement, there are 125 points in the sample space. When selecting three batteries at random without replacement, there are 60 points in the sample space.

Explanation:

To determine the number of points in the sample space when selecting three batteries at random with replacement, we use the counting principle. Since there are 5 batteries, each with an equal likelihood of being selected, and we are selecting three batteries, we can calculate the number of points in the sample space as follows:

Number of points = Number of possible outcomes for the first battery * Number of possible outcomes for the second battery * Number of possible outcomes for the third battery

Since there are 5 batteries, the number of possible outcomes for each battery is 5. Therefore,

Number of points = 5 * 5 * 5 = 125

So, there are 125 points in the sample space when selecting three batteries at random with replacement.

When selecting three batteries at random without replacement, the number of points in the sample space will be different. We can calculate it using a similar approach, but taking into account that once a battery is selected, it is removed from the bag and cannot be selected again. Therefore, for the first battery, there are 5 possible outcomes. For the second battery, there will be 4 possible outcomes since one battery has already been selected. For the third battery, there will be 3 possible outcomes. Therefore,

Number of points = 5 * 4 * 3 = 60

So, there are 60 points in the sample space when selecting three batteries at random without replacement.

Answer 2
Final answer:

The number of possible outcomes for selecting three batteries with replacement is 125. For selecting three batteries without replacement, the total is 60. The counting principle multiplies the number of options for each choice to calculate the sample space.

Explanation:

When selecting three batteries from a bag containing five different brands at random, the number of points in the sample space can be determined using the counting principle. The sample space represents all possible outcomes of an experiment.

a. Sampling with replacement

When batteries are selected with replacement, after each selection, the chosen battery is put back into the bag, making it available for the next selection. Thus, for each pick of the three batteries, there are five choices. The total number of points in the sample space for selecting three batteries with replacement is therefore 5 × 5 × 5 = 125.

b. Sampling without replacement

When batteries are selected without replacement, the chosen battery is not put back in the bag, which means the options decrease with each selection. The first pick has five choices, the second pick will have four (since one battery is already picked), and the third pick will have three. The total number of points in the sample space for selecting three batteries without replacement is therefore 5 × 4 × 3 = 60.


Related Questions

Heights of men on a baseball team have a Bell shaped distribution with a mean of 172cm and a standard deviation of 8cm. Using the empirical rule, what is the approximate percentage of the men between the following values? a. 156cm and 188cm b. 164cm and 180cm

Answers

I believe the correct answer is B. rate 5 if this helped! 

a used car priced at$5000.00 . The salesperson then offered a discount of $250.00.

What is the percent discount?

Answers

95% discount. You find this out by subtracting 250 from 5000 to get 4750 and then doing 4750 divided by 5000 to get .95 and then multiply by 100 to get 95%
The percent discount is the percent of the original that is subtracted (discounted).

250 / 5000 = 5%

Pamela's age is two times Jiri's age. The sum of their ages is
33
. What is Jiri's age?

Answers

let x is Jiri's age
2x is Pamela's age

x + 2x = 33
3x =33
x = 33/3
x =11
Answer: Jiri's age is 11
Jiri's age is 11 because x + 2x is 3x... 3x =33 and then when you divide it, you get 11

hi there i could really use the help with this question please

Answers

you can rise up the ticket amount to 6$ instead of 5$

a pail holds 2 3/4 gallons of water how much is this in cups

Answers

1 gallon is 16 cups

we have 11/4 cups which multiplied by 16 gives us 44 cups

A conical cup is made from a circular piece of paper with radius 6 cm by cutting out a sector and joining the edges as shown below. Suppose θ = 5π/3.

Answers

The [tex]r[/tex], [tex]h[/tex], and 6 cm form a right triangle, so you find [tex]h[/tex] with the Pythagorean Theorem.

[tex]r^{2}+h^{2}=6^{2}[/tex]
We have [tex]r=5[/tex], so
[tex]5^{2}+h^{2}=6^{2}[/tex]
[tex]\rightarrow 25+h^{2}=36[/tex]
[tex]\rightarrow h^{2}=11[/tex]
[tex]\rightarrow h=\sqrt{11}[/tex]

Answer:

(a) 10π cm

(b) r = 5 cm

(c) h = √11 cm

Step-by-step explanation:

(a) The surface of the opening the cup is circular in shape and a sector is cut from circle is calculate by formula,

C = r × θ

here, r = 6 cm

and θ = [tex]\frac{5\pi}{3}[/tex]

⇒ [tex]C = 6 \times \frac{5\pi}{3} = 10\pi[/tex]

(b) For finding the radius of the cup,

As the circumference of the circle is 10π

and we know that area of cone is calculate by formula, 2πr

⇒ 2πr = 10π

⇒ r = 5 cm

(c) In cone we know slant height(l) = 6 cm

Radius = 5 cm

Thus, using Pythagoras theorem,

l² = h² + r²

⇒ h² = l² - r²

⇒ h² = 36 - 25

⇒ h = √11 cm

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. xy = 9, x = 0, y = 9, y = 11

Answers

When integrating using shells, the first step is to plot the graph. I personally plotted it with the x and y axis switched, because it aids me in picturing the graph. The integral ranges from 9 to 11, since those are the limits from the two lines y = 9 and y = 11. The reason that these are the limits is because it is rotating around the x, not the y.
[tex] \int\limits^{11}_{9}[/tex]
Now that you have the limits of the integral, you have to find what goes inside it. 
Because you are integrating using shells, you need to remember to include the [tex]2\pi y[/tex] Again, there is a y here instead of an x, because you are rotating around the x axis. Then you just need to input the function f(y). If you look at the graph that you (hopefully) plotted, you can see that this function ranges between the y axis and the curve [tex]f(y) = \frac{9}{y}[/tex]. Put together the pieces, and you have the integral
[tex] \int\limits^{11}_{9} {2 \pi y*f(y)} \, dy [/tex]
After substituting in [tex]f(y) = \frac{9}{y}[/tex], you get 
[tex] \int\limits^{11}_{9} {2 \pi y*\frac{9}{y}} \, dy [/tex]
Simplified, this is [tex] 18\pi\int\limits^{11}_{9} \, dy [/tex]
Integrating, we get [tex] 18\pi * 2[/tex]

Therefore, the solution is [tex] 36 \pi [/tex]

Note: I didn't spend very much time reviewing these integrals, so I may be incorrect. 
Final answer:

The volume of the solid obtained by rotating the region bounded by the curves about the x-axis is found using cylindrical shells, resulting in a total volume of 36π cubic units.

Explanation:

To find the volume of the solid obtained by rotating the region bounded by the curves xy = 9, x = 0, y = 9, and y = 11 about the x-axis, we will utilize the method of cylindrical shells. The curves define a region in the xy-plane which, when rotated about the x-axis, forms a solid with varying radii. To apply the method, we first need to express the variable x in terms of y from xy = 9 to obtain x = 9/y.

Next, the volume of a representative cylindrical shell with thickness dy and height x = 9/y is given by the circumference of the shell (2πy) times the height (9/y) times the thickness (dy). This leads to the volume element dV = 2πy(9/y)dy = 18πdy. Integrating this volume element with respect to y between the limits 9 and 11 yields the total volume.

Using the integral calculus, the volume V is:
V = ∫911 18π dy = 18π [y]∫911 = 18π(11 - 9) = 36π cubic units.

Thus, the volume of the cylinder is 36π cubic units.

The digits 2 comma 3 comma 4 comma 5 comma and 2, 3, 4, 5, and 6 are randomly arranged to form a​ three-digit number. ​ (Digits are not​ repeated.) Find the probability that the number is even and greater than 600.

Answers

There are total of 5 digits, of which we arrange 3 of them.
Therefore using permutations we can find total possible 3-number combinations.
5P3 = 5*4*3 = 60

To be greater than 600 means first digit must be 6. (1 possibility)
A number is even only if last digit is even, 2 or 4.  (2 possibilities)
The 2nd digit then can only be 3,5, (2 or 4).    (3 possibilities)
The total possible even 3-digit numbers greater than 600 is product of each digit's possibilities.
---> 1*3*2 = 6

Therefore probability is 6/60 = 1/10.

Your neighbor had to drop the selling price of her home from $180,000 to $165,000. What percent did the price get lowered? Round to nearest tenth

Answers

You could do 165,000 divided by 180,000. This is 165000/180000, and that will give you the percentage that 165000 is of 180000 in decimal form, which is 0.9167.
Then we round to the nearest tenth, which is 0.92
0.92 as a percentage is 92%.
100% - 92% = 8%
The price of the home dropped by 8%.

What divided by 2 equals -12

Answers

The answer would be -6
-24 divided by 2= -12

The product of two positive numbers is 120. One number is 7 more than the other. Determine the two numbers

Answers

xy= 120
x= 7+y

(7+y)(y) = 120
y^2 + 7y - 120 = 0
(y + 15) (y - 8) = 0

Since we are finding two positive numbers,
If y= 8 then x= 15

The two numbers are 8 and 15

One numer is 17 more than another number the sum of the two numbers is 25 find the numbers

Answers

uh i think it's 18 and 7?

s(t)=9t-4, find S(4)

Answers

for this problem, you need to substitute 4 in for your variable t. the original equation is S(t) and the one you need is S(4) -- in other words, evaluate this equation when t = 4.

S(4) = 9(4) - 4
S(4) = 36 - 4
S(4) = 32 is your answer.
Final answer:

To calculate S(4), substitute the value of t with 4 into the function S(t), which results in S(4) = 9(4) - 4, giving the final answer of 32.

Explanation:

To find S(4), we need to substitute the value of t with 4 in the function S(t) = 9t - 4. This is a simple evaluation of a function for a given input.

Step-by-step calculation:

Write down the function: S(t) = 9t - 4Substitute t with 4: S(4) = 9(4) - 4Multiply 9 by 4: S(4) = 36 - 4Subtract 4 from 36: S(4) = 32

Therefore, S(4) is 32.

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Which problem could be solved with the expression 4*(4+2)

A - Danny ran 4 miles in the morning and 2 miles in the afternoon. He did this for 4 days. How many miles did he run?
B - Bobby sold 4 baseball cards on Monday. He then sold 2 more on Tuesday. He sold the same amount for 2 weeks. How many did he sell?
C - Suzanne makes wooden dolls. She made 2 in the morning and 2 in the afternoon. She did this for 4 days. How many dolls did she make?


A Danny's Problem
B Bobby's Problem
C Suzanne's Problem

Answers

The answer is A.

He ran for six (6) miles every day. 4 in the morning and 2 at night = 6 per day.

He did this for four (4) days. The way to figure this would be to go 6 * 4. This equals 24 miles.

Go back a few steps (punny!).

So days multiplied by how many miles he ran a day which is calculated by miles in morning added to miles at night.

days*(miles per morning + miles per night)

days=4
miles per morning=4
miles per night = 2

4 * (4+2)

Calculating this out....

4 * (4+2)

(4+2 = 6)

4 * 6 = 24.

So A is the answer.

the production line where you work can assemble 5 amplifiers every 30 minutes at this rate how long should it take the line to assemble 125 amplifiers

Answers

See this question as Ratio.

Amplifiers  :   Time Taken in minutes
    
      5          :          30
   
     5x= 125
       x= 25

       so

5*25 : 30*25

125 : 750


750 minutes.
 12 hours 30 minutes.

The time taken to assemble 125 amplifiers is required.

Time taken to assemble 125 amplifiers is 750 minutes or 12 hours and 30 minutes.

Time taken to assemble 5 amplifiers is 30 minutes

[tex]5\ \text{amplifiers}=30\ \text{minutes}[/tex]

So,

[tex]1\ \text{amplifier}=\dfrac{30}{5}=6\ \text{minutes}[/tex]

[tex]125\ \text{amplifiers}=125\times 6=750\ \text{minutes}=\dfrac{750}{60}=12.5\ \text{hours}[/tex]

So, time taken to assemble 125 amplifiers is 750 minutes or 12 hours and 30 minutes.

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A theater can seat 273 people. The number of rows is 8 less than the number of seats in each row. How many rows of seats are there?

Answers

r * s = 273
r = s - 8.....s = r + 8

r(r + 8) = 273
r^2 + 8r = 273
r^2 + 8r - 273 = 0
(r - 13)(r + 21) = 0

r - 13 = 0
r = 13

r + 21 = 0
r = -21.....extraneous solution...not ur answer

r = 13
s = r + 8 = 13 + 8 = 21

so there are 13 rows.....each row containing 21 seats



The life span of a certain insect in days is uniformly distributed over the interval (20,36). What is the probability the insect will live 24 days or less? Possible Answers a) .24 b) .25 c) .20 d) .75

Answers

Answer:

  b)  0.25

Step-by-step explanation:

The required probability is ...

  (24 -20)/(36 -20) = 4/16 = 1/4 = 0.25

_____

Comment on the attached graph

The red line is the probability distribution function (pdf) for this uniform distribution. The green line is the cumulative distribution function (cdf) for this uniform distribution. It is the integral of the pdf.

The probability of interest is the value of the cdf at x=24. That value is 0.25, meaning the area under the pdf curve to the left of x=24 is 1/4 of the total area under the pdf curve. That proportion is what is calculated above.

Suppose that, from measurements in a microscope, you determine that a certain bacterium covers an area of 1.50μm2. Convert this to square meters.
Express your answer in square meters.

Answers

Convert 1.50μm2 to m2 I do unit conversion by fractions. Set up an identity relating the two units: 1μm=10−6m Divide both sides by the unit you want to get rid of: 10−6m1μm=1 Now we can use that fraction to convert any micrometers we see into meters by multiplying. The value of the fraction is 1, so we don't affect the equation's truth at all, just the units. As we are converting square micrometers to square meters, we will have to multiply by the conversion fraction twice. The units will cancel properly if we set up the equation correctly, and there won't be any question about whether we divided when we should have multiplied, or vice versa. 1.50μm2∗10−6m1μm∗10−6m1μmObserve that the units cancel the way we want:1.50μm2∗10−6m1μm∗10−6m1μm=1.50∗10−6∗10−6m2

A tree is 2 1/2 feet tall. How tall will it be in 3 years if it grows 1/4 foot each year? Which method will NOT give the correct number of feet?

Answers

Since the answers are not given, I will give an explanation myself. Multiplying three years by the number of feet per year (1/4 foot), but not adding it to the original height (2 1/2 feet), will give you the WRONG answer. 

a recipe for 2 dozen corn muffins calls for 3 cups of flour. The number of muffins varies directly with the amount of flours you use. find the direct variation equation for the relationship between the number of cups of flours and the number of muffins

Answers

Hope this helps you out

Select the option for "?" that continues the pattern in each question.

(1.) 3, -6, 12, 4, 20, ?

(2.) 7, 16, 8, 27, 9, ?

(3.) 2, 7, 26, 101, 400, ?

(4.) 7, 21, 8, 72, 9, ?

Answers

1. 13
2. 9 or 38 not really sure
3.1595
4.. 810


The length of the base of a triangle is twice its height. If the area of the triangle is 64 square​ kilometers, find the height.

Answers

Area of a triangle = base x height / 2
64 = base x height / 2
(multiply 2 on both sides)
128 = base x height 
then if base= 16 and height = 8 then 16 x 8 = 128
thus the base is 16 which is twice the height:8
Final answer:

To find the height of the triangle with an area of 64 square kilometers and a base twice its height, we use the area formula: A = (1/2) × base × height, which leads us to determine that the height is 8 kilometers.

Explanation:

The question given involves finding the height of a triangle when the area is known and the relation between the base and height is given. Since the base is twice the height (b = 2h), and we know the formula for the area of a triangle is A = (1/2) × base × height, we can substitute the known area and the base-height relationship into this formula to solve for the height.

The area (A) is given as 64 square kilometers, which leads to the equation:

A = (1/2) × b × h = (1/2) × (2h) × h = h²,

Therefore, with A = 64 km², we obtain:

64 = h².

Taking the square root of both sides gives us the height (h):

h = √64 km = 8 km.

So the height of the triangle is 8 kilometers.

the function f(x) varies directly with x and f(x)=250 when x=50
what is f(x) when x=5
10
15
25
50

Answers

The answer is 25.  f(x)=5*5=25

The function f(x) varies directly with x and f(x) is 250 when x is 50, so

f(x) is 25 when x=5

What does the statement y varies directly as x describe?

the function f(x) varies directly with x and

f(x)=250 when x=50

when x=5  f(x) = 5*5 = 25

Some textbooks will say "y varies directly as x," "y varies proportionally as x," or "y is directly proportional to x" to describe direct variation. This implies that the ratio between them always remains the same and that as x increases, y increases, and as x drops, y decreases.The direct variation equation can also be written as x = y / k. This indicates that the relationship between x and y is direct, with the constant of proportionality being equal to 1 / k.If x varies in direct proportion to y, the equation of variation is written as X times Y = K.

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can you simplify 3/r + 7/r+3

Answers

Combine the fractions by finding a common denominator. 
10r+9/r(r+3)

Jim wants to build a rectangular parking lot along a busy street but only has 2,200 feet of fencing available. If no fencing is required along the street, find the maximum area of the parking lot.

Answers

The perimeter of the parking :
2 W + L = 2,200 ( there is no fence along the street )
L = 2200 - 2 W
The area of the parking is:
A = W  x L = W ( 2,200 - 2 W ) = 2,200 W - 2 W²
A` = 2,200 - 4 W
2,200 - 4 W = 0
4 W = 2,200
W = 2,200 : 4 = 550 ft
L = 2,200 - 1,100 = 1,100 ft
The maximum area is:
A max = 1,100 x 550 = 605,000 ft² 
Final answer:

The problem is an optimization problem in mathematics where one must use algebra and calculus to maximize the area of a rectangular parking lot with a given amount of fencing along three sides. By setting up a function for the area in terms of width and differentiating, the maximum area can be found.

Explanation:

The problem presented involves finding the maximum area of a rectangular parking lot given a certain amount of fencing, when one side of the rectangle requires no fencing. This is a classic optimization problem in mathematics which involves the use of algebra and calculus. By setting up a function for the area of the rectangle in terms of one variable and differentiating to find the maximum value, we can determine the solution.

Lets assume that the length of the lot that is along the busy street doesn't require fencing, and let the width of the lot be w and the length be l. Since fencing is only required for three sides, and we have 2,200 feet of fencing, the perimeter equation is 2w + l = 2,200. Solving for l, we get l = 2,200 - 2w. The area A of the parking lot will be given by the equation A = w * l. Substituting the expression for l into the area equation, we get A = w(2,200 - 2w) or A = 2,200w - 2w^2. To find the maximum area, we take the derivative of A with respect to w, set it to zero, and solve for w. Once the width is found, we can find the length using the perimeter equation and thus calculate the maximum area of the lot.

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What is 14.7 times 11.361 showing your work ?

Answers

Answer: Hello mate!

this multiplication can be hard because of the numbers after the decimal point. You could use the next trick.

14.7*10 = 147 and 11.361*1000 = 11361

now you could do the multiplication without concerning about the decimals, and afther that divide it back by 10*1000.

and [tex]14.7*11.361 = \frac{147}{10}*\frac{11361}{1000} = \frac{147*11361}{10*1000}  = \frac{147*11361}{10000} = \frac{1670067}{10000}[/tex]

now you need to divide by 10000, that is equivalent to move the decimal point by 4 ) places to the left.

1670067/10000 = 167.0067

A hardware store sells 35% fewer lawnmowers in july than in april. If 39 were sold in july, how many were sold in april/

Answers

.35 *39 is 13.6
39-13 is 26
26 is the answer

Answer: 0.65a = 39

Step-by-step explanation:

jay simplified the expression 3 x (3 +12 / 3) -4. for his first step ,he added 3 + 12 to get 15. what was jay's error? find the correct answer

Answers

you should be dividing 12/3

Jay's error was in the order of operations. The correct result is 17.

Jay's error lies in how he interpreted the expression. According to the order of operations (PEMDAS/BODMAS), multiplication and division should be performed before addition and subtraction.

So, the correct first step is to perform the division [tex]\( \frac{12}{3} = 4 \)[/tex]and then add 3 to the result, not add 3 and 12 together first.

The correct first step:

[tex]\[ 3 \times (3 + \frac{12}{3}) - 4 \][/tex]

[tex]\[ = 3 \times (3 + 4) - 4 \][/tex]

[tex]\[ = 3 \times 7 - 4 \][/tex]

= 21 - 4

= 17

Therefore, Jay's error was in the order of operations. The correct result is 17.

What type of simple machine is the crescent wrench

Answers

The crescent wrench is a type of lever, a simple machine that amplifies force to provide greater torque on fasteners with less input effort.

The crescent wrench is a type of simple machine, specifically it is a form of a lever. When you use a crescent wrench, you apply force to the handle, which then applies force to the object you are turning. The pivot point, or fulcrum, is the adjustable jaw which grips the nut or bolt. This allows the user to exert a greater torque on the fastener with less force than would be needed if just using one's hands.

Like other levers, the crescent wrench allows for a mechanical advantage, which is the ratio of output to input forces for any simple machine. By lengthening the handle of the wrench (the effort arm), we achieve a greater mechanical advantage, and thus, can apply more torque to the bolt or nut we are trying to turn.

the Lynch family bought a house for 75,300 .a few years later ,they sold the house for 80,250 how much greater was selling price than the purchase price

Answers

The answer would be 4950 because if you subtract 80250 to 75300 you get 4950
4950 because 80250-75,300=4950

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