Suppose you have an experiment where you toss a fair coin 3 time you didn't count the number of heads observe over those 3 tosses use this experiment to address each of the falling question round solution to 3 destiny places
Answers
a) In order to complete the table for the probability distribution for the variable X:
X = the number of heads observed when you flip a coin three times,
b) we create a list of all the possible outcomes. We use the notation: H = heads, T = tails.
The possible outcomes after tossing the coin three times are:
[tex]HHH,HHT,HTH,THH,TTT,TTH,THT,HTT[/tex]From the list above we see that we have 8 equiprobable events. Now, we classify the events according to the number of Heads included.
- Events with x = #H = 0: TTT
- Events with x = #H = 1: HTT, THT, TTH
- Events with x = #H = 2: HHT, HTH, THH
- Events with x = #H = 3: HHH
Using the data above we compute the probabilities for each x, we simply compute the quotient between the number of outcomes of each case by N = 8 (the total number of possible outcomes):
[tex]\begin{gathered} P\mleft(x=0\mright)=\frac{1}{8}=0.125 \\ P(x=1)=\frac{3}{8}=0.375 \\ P(x=2)=\frac{3}{8}=0.375 \\ P(x=3)=\frac{1}{8}=0.125 \end{gathered}[/tex]c) Shape of the probability disribution. The probability distribution of x is: Symmetric.
d) Using the data above, we can compute the mean number of heads for the distribution:
[tex]\begin{gathered} E(x)=\sum ^3_{n=0}x_n\cdot P(x_n_{}) \\ E(x)=0\cdot P(x=0)+1\cdot P(x=1)+2\cdot P(x=2)+3\cdot P(x=3) \\ E(x)=0+1\cdot0.375+2\cdot0.375+3\cdot0.125 \\ E(x)=\frac{3}{2}=1.5 \end{gathered}[/tex]So the mean number of heads for this distribution is 1.5
Related Questions
Two-digit natural numbers are formed, with replacement, from the digits 0 through 9.
How many numbers are greater than 64?
Answers
There are 35 natural numbers that are greater than 64.
Natural numbers:
Natural number are the numbers that start from 1 and end at infinity. In other words, they are counting numbers and they do not include 0 or any negative values.
Given,
Two-digit natural numbers are formed, with replacement, from the digits 0 through 9.
Here we need to find the numbers that satisfied the given condition and that is also greater than 64.
We know that, two digit natural numbers range from 10 to 99.
Since there are replacement take place, then each number formed from 10 to 99 is valid in this exercise.
Now, we have to move on to the other thing that is, those number are greater than 64,
Then we have to calculate it as,
=> 99-64 = 35 are greater than 64.
And those number are 65,66,67,68,69,...,98,99.
Finally, we have identified that there are 35 number are greater than 64.
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what is the least common multiple of 62 and 31?
Answers
Answer:
there is none so it would be 62
Step-by-step explanation:
Can u help me answer question 24 BTW this is lesson 6 the distributive property 24. 5(2x+7) = __________
Answers
We have the following:
[tex]5\mleft(2x+7\mright)=_{}[/tex]We apply the distributive property that tells us that the multiplication of a number by a sum is equal to the sum of the multiplications of said number by each of the addends.
Therefore:
[tex]5(2x+7)=_{}10x+35[/tex]
Which of the following are true?
A.-2.7<- 4.6
B.-7.3 1.2
C.-5.2 - 2.9
D. 4.7 3.4
O A and D
O B and C
OC and D
O A and B
Answers
Answer:
B and C are correct
Step-by-step explanation:
I need to find the inequality 5-12x<29
Answers
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x > −2
Interval Notation:
(−2, ∞)
X is greater than -2
Can someone help me with this geometry question? My instructor said I was wrong?
Answers
If 7 ballpoint pens cost $9.66, how much will 12 pens cost? (100 points)
Answers
Answer:
16.56
Step-by-step explanation:
9.66/7
=1.38 each
1.38x12=16.56
Answer:
16.56
Step-by-step explanation:
Cal made the graph at right. Use the graph to write a problem involving fractions.
Answers
We need to come up with a question involving the graph.
Very simple!
We can ask how much time in a day Cal spends for different activities.
We can say:
According to the graph, how much time of the day does Cal spend studying and sleeping?
answering this question:
[tex]\begin{gathered} \frac{1}{8}+\frac{1}{3} \\ =\frac{3(1)+8(1)}{3\times8} \\ =\frac{3+8}{24} \\ =\frac{11}{24} \end{gathered}[/tex]Which of the following graphs shows the preimage P(x)=|x| and the image I(x)=1/2⋅P(x)?
Answers
Given,
The expression for function P(x) is | x |.
The expression for function I(x) is | x |/2.
Required:
The graph of the function.
The graph of the function is,
The function P(x) is represented by black line.
The function I(x) is represented by Red line.
Hence, option A is correct.
Write an phrase that would translate into the following mathematical expression: 8z- 2 ?
Answers
The mathematical expression 8z - 2 can be phrased as:
The difference between 8 times the variable z and 2.
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Any mathematical object has a symbol, and that symbol is called a variable. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.
Consider the mathematical expression,
8z - 2
The expression can be defined as 2 less than the product of 8 and variable z.
The expression can also be rephrased as:
The difference between 8 times the variable z and 2.
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Pythagorean TheoremFor the following right triangle, find the side length x. Round your answer to the nearest hundredth.18Х11
Answers
Solution
For this case we can use the Pythagoras theorem and we have:
[tex]18^2=11^2+x^2[/tex]And solving for x we got:
[tex]x=\sqrt[]{18^2-11^2}=\sqrt[]{324-121}=\sqrt[]{203}=14.25[/tex]Then the answer is:
14.25
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 40 pounds each, and the small boxes weigh 25 pounds each. There are 135 boxes in all. If the truck is carrying a total of 4350 pounds in boxes, how many of each type of box is it carrying?
Number of large boxes:
Number of small boxes:
Answers
Number of large boxes will be 65.
Number of small boxes will be 70.
What is mathematical expression?
Expression in math is defined as the collection of the numbers, variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The large boxes weigh 40 pounds each, and the small boxes weigh 25 pounds each.
There are 135 boxes in all.
If the truck is carrying a total of 4350 pounds in boxes.
Let number of large boxes = x
Number of small boxes = y
Since, There are 135 boxes in all.
So, We get;
x + y = 135 ... (i)
And, The large boxes weigh 40 pounds each, and the small boxes weigh 25 pounds each and the truck is carrying a total of 4350 pounds in boxes.
So, we can formulate;
40x + 25y = 4350 ... (ii)
Solve equation (i) and (ii) as;
Multiply 40 by (i) and subtract by (ii) we get;
40x + 40y - 40x - 25y = 5,400 - 4,350
15y = 1,050
y = 70
And, x + y = 135
x + 70 = 135
x = 135 - 70
x = 65
Thus, Number of large boxes will be 65.
Number of small boxes will be 70.
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).5,4, 16/5... Find the 7th term.
Answers
In order to find the 7th of the sequence, first let's find the common ratio of the sequence.
To do so, let's divide one term by the term before:
[tex]q=\frac{4}{5}[/tex]Now, we can use the following formula to find the 7th term:
[tex]a_n=a_1\cdot q^{n-1}[/tex]For n = 7, we have:
[tex]\begin{gathered} a_7=5\cdot(\frac{4}{5})^6 \\ a_7=1.311 \end{gathered}[/tex]The greatest common factor of 36 and 60 is 12. Explain what this means.
Answers
For 12 to be the GCF (Greatest common factor) between 36 and 60, means that the greatest number that can divide both 36 and 60 at the same time is 12.
Solve Each system of equations.
-r + t = 5
-2r+t=4
Answers
Solve equations
-(1) + 6 = 5
5= 5
-2(1) + 6 = 4
4=4
_________
Step by step
We have two equations
-r + t = 5 to t = r + 5 when put in y intercept form for easy math
t = r + 5
-2r + t = 4
To solve, substitute the t value from the first equation for t in the second
-2r + (r + 5) = 4
Combine like terms
-1r + 5 = 4
Subtract 5 from both sides to solve for r
-1r + 5 - 5 = 4 - 5
Combine
-1r = -1
Divide both sides by -1 to solve for r
-1/-1 r = -1/-1
r = 1
Now substitute the r value into one of the equations to solve for t
(-1)(1) + t = 5
-1 + t = 5
Subtract (-1) from both sides to solve for
t = 6
Graph in the attachment
Which expression is equivalent to 10x – 6?
Answers
Answer:
1. -6 + 10x
Step-by-step explanation:
The expression 10x – 6 is the same as adding -6 to 10x, or 10x + -6. Since addition equations can be rearranged, 10x + -6 can also be written as -6 + 10x.
Answer:
[tex] \sf{ \large{ - 6 + 10x}}[/tex]
Step-by-step explanation:
10x - 6
note: there is a plus sign at 10x
+10x - 6
so when you switch it will be like this
-6 + 10x
Solve the following inequality for n. Write your answer in the simplest form.9n + 4 ≤ 6n - 6
Answers
Given,
The expression is,
[tex]9n+4\le6n-6[/tex]Substracting 4 from both sides then,
[tex]\begin{gathered} 9n+4-4\le6n-6-4 \\ 9n\le6n-10 \end{gathered}[/tex]Substracting 6n from both sides then,
[tex]\begin{gathered} 9n\le6n-10 \\ 9n-6n\le6n-6n-10 \\ 3n\le-10 \end{gathered}[/tex]Multiplying both sides by 1/3 then,
[tex]\begin{gathered} 3n\le-10 \\ 3n\times\frac{1}{3}\le-10\times\frac{1}{3} \\ n\le-\frac{10}{3} \end{gathered}[/tex]Hence, the solution for n is n<= (-10/3).
If M is a centroid of triangle WOR and YR =16, what is the length of WR
Answers
If M is a centroid of triangle WOR and YR =16, the length of WR
side will be WR = 48.
What is the triangle's centroid?The centroid of the thing represents its center. A triangle's centroid is the point at which its three medians intersect. It can also be described as the point at which the three medians intersect.The median is a line that connects the midpoints of two sides and the opposite vertex of a triangle. A triangle is a two-dimensional shape with three sides. The three angles add up to 180 degrees.The centroid of a triangle divides the triangle's medians in a 2: 1 ratio.The ratio of the two sides will be given here as:
WY/ YR = 2/1
Determine the value of YR to determine the value of WR.
WY/16 = 2/1
WY = 32
WR will have the following value:
WR = WY+ YR
WR = 32+ 16
WR = 48
As a result, the value of the side WR is 48.
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use nPr formula 11P0=
Answers
we know that
the formula is equal to
P(n,r) = n! / (n-r)!
we have that
nPr = n!/(n-r)!
we have
11P0
so
n=11
r=0
= 11!/(11-0)!
=11!/11!
=1
answer is 1Can someone explain to me how to find the answers
Answers
Part a: The missing length = 28 units.
Part b: The missing length = 25 units, for the given similar triangle.
What is termed as the similarity of the triangle?If two triangles' corresponding angles seem to be congruent and their corresponding sides are proportional, they are said to be similar. In other phrases, similar triangles have the same shape but may or may not be the same size. The triangles have been congruent if their side lengths are also of equal length.Part a: For the similar triangles.
Let the unknown value be x.
The, using the similarity of the triangle,
63/x = 27/12
x = (63×12)/27
x = 28 units.
The missing length is 28 units.
Part b: For the similar triangles.
Let the unknown value be x.
The, using the similarity of the triangle,
21/15 = (10 + x)/x
21x = 150 - 15x
6x = 150
x = 25
The missing length is 25 units.
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what is the probability that Glenn will get a yellow marble
Answers
The bag has 5 marbles
3 yellow marbles
2 red marbles
"Glen chooses a marble first and then Kris chooses one" You have to determine the probability of Kris choosing a yellow marble if Glen chooses a yellow one first.
1. First you have to determine the probability that Glen choose a yellow marble first.
To do so, you have to calculate the quotient between the number of yellow marbles on the bag and the total number of marbles on the bag:
[tex]\begin{gathered} P(Y_1)=\frac{nº\text{yellow}}{\text{total}} \\ P(Y_1)=\frac{3}{5} \end{gathered}[/tex]2. and 3.
After Glen takes the first yellow marble from the bag, the total number of marbles is reduced by one and so is the number of yellow marbles on the bag, so:
New total: 4 marbles
Number of yellow marbles: 2
4.
To determine the probability of Kris choosing a yellow marble, you have to use the data on the remaining marbles on the bag. And calculate the quotient between the remaining number of yellow marbles and the remaining number of marbles:
[tex]\begin{gathered} P(Y_2)=\frac{2}{4} \\ P(Y_2)=\frac{1}{2} \end{gathered}[/tex]If f(x) = 4x - 1 and g(x)=2x-4, what is (fog)(x)?
Answers
The value of the composite function (f o g)(x) is 8x - 17
How to evaluate the function?The definition of the functions are given as
f(x) = 4x - 1
g(x) = 2x - 4
The composite function definition is given as
(f o g)(x)
This composite function is calculated using the following composite function formula
(f o g)(x)= f(g(x))
Substitute the known values in the above equation
So, we have the following equation
(f o g)(x) = 4(g(x)) - 1
So, we have the following equation
(f o g)(x) = 4(2x - 4) - 1
Open the brackets
(f o g)(x) = 8x - 16 - 1
Evaluate
(f o g)(x) = 8x - 17
Hence, the composite function is (f o g)(x) = 8x - 17
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Write the number in standard notation.5.8 × 10−3
Answers
0.0058
Explanation:The given scientific notation is:
[tex]5.8\times10^{-3}[/tex]This can also be written as:
[tex]\begin{gathered} 5.8\times\frac{1}{1000} \\ \\ =\frac{5.8}{1000} \\ \\ =0.0058 \end{gathered}[/tex]Therefore 5.8 x 10^-3 in standard form is 0.0058
A laptop computer consumes about 40 watts of electricity per hour when operating. At $0.20 per kilowatt-hour, how much does a laptop cost to operate for 10 hours?A )8 centsB )800 centsC )40 centsD) 200 cents
Answers
A) 8 cents
Explanation
Step 1
find the rate
[tex]\begin{gathered} \text{rate}=\text{ 40 }\frac{\text{w}}{h} \\ \end{gathered}[/tex]cost
[tex]\begin{gathered} \text{ Cost= 0.20 per 1000 wats hour} \\ \end{gathered}[/tex]hence
total cost = time*rate*consume
[tex]\begin{gathered} \text{ Total cost = 10 hours}\cdot40\frac{w}{h}\cdot0.2\frac{\text{ \$}}{1000\text{ w}} \\ \text{ Total cost =}0.08\text{ dollars} \end{gathered}[/tex]now, to convert from dollars to cents, multply by 100
[tex]\text{ Total cost =}0.08\text{ dollars}\cdot(\frac{100\text{ cents}}{1\text{ dollar}})=8\text{ cents}[/tex]I hope this helps you
This graph shows how fast the international space station travels in orbit around Earth What is the meaning of the point with an x-coordinate of 3?A. In 1 second, the space station travels 3 miles B. In 3 seconds, the space station travels 3 miles in 15 miles.C. The space station travels 3 miles in 15 seconds D. It takes the space st 3 seconds to go 5 miles.
Answers
From the graph, x coordinate 3 mean it takes 3 seconds to travels 15 miles.
Option B is the correct answer.
Higher Order Thinking Veronica needs to buy 13 pounds of cheese. When the clerk places some cheese in a container and weighs it, the scale shows 1 pounds. The container weighs pound. How many more pounds of cheese should be added to the scale to get the amount that Veronica needs? Explain how you solved the problem.
Answers
After calculating some basic arithmetic we have come to find that, 12 pounds of more cheese should be added to the scale to get the amount that Veronica needs which 23 pounds.
What is arithmetic?Using the four operations, arithmetic is a branch of mathematics that deals with the characteristics of numbers.
Division, multiplication, and subtraction are the four operations. The rules for each operation are very detailed.
As an illustration of arithmetic, one of the rules of addition and subtraction is that addition increases the overall value of a number while subtraction decreases the overall value of a number.
Veronica needs to buy 13 pounds of cheese
Cheese in a container weighs = 1 pounds
Mass of cheese clerk needs to add = 13 - 1
= 12 pounds
(as 1 pound is already there)
Thus, 12 pounds of more cheese should be added to the scale to get the amount that Veronica needs which 23 pounds.
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Bismuth-210 has a half-life of about 6 days. After 21 days, how many milligrams of a1,220 mg sample will remain? Round answer to the nearest tenth place. If answerdoes not have tenths place use a zero so that it does.
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Bismuth-210 has a half-life of about 6 days.
After 21 days, how many milligrams of a 1,220 mg sample will remain?
Round answer to the nearest tenth place.
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} We\text{ have that:} \\ 0.5\text{ = e}^{-6k} \\ Taking\text{ In of both sides, we have that:} \\ ln\text{ 0.5 = -6k} \\ That\text{ means that:} \\ k\text{ =}\frac{-ln\text{ 0. 5}}{6} \end{gathered}[/tex][tex]Let\text{ the number to remain, A=1220e}^{-(-\frac{ln0.5}{6})(21)}[/tex][tex]\begin{gathered} 107.83378\text{ mg} \\ \approx\text{ 107. 8 mg \lparen to the nearest tenth\rparen} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]107.\text{ 8 mg \lparen to the nearest tenth\rparen}[/tex]need help with this problem.
Answers
[tex]\cfrac{6^3\cdot 15^3}{(7^0)^3}\implies \cfrac{(6\cdot 15)^3}{(1)^3}\implies \cfrac{90^3}{1}\implies 729000[/tex]
What is the variable being tested in an experiment?0 A.response variableO B. placeboO C.control variableOD.explanatory variable
Answers
Given
Variables
Find
Which variable being tested in an experiment
Explanation
The dependent variable is the variable that is being measured or tested in an experiment
response variable is often referred as dependent variable.
Final Answer
hence , the correct option is A.
4. A fruit stand sells boxes of apples. Each box weighs the same amount. The table shows the number of boxes and the total number of pounds. AppIGN Number of Boxes Tocal Number of Pounds И. 7 8 72 10 Which of the following correctly describes the relationship in the table? A. Number of boxes + 4 = total number of pounds B. Number of boxes x 9 + total number of pounds C. Number of boxes - 9 total number of pounds D. Number of boxes x 6 = total number of pounds
Answers
From the table it can be observed if we multiply the number of boxes by 9, then it gives total number of pounds for the corresponding number of boxes.
As 4 multiply by 9 is 36, which is total number of pounds for 4 boxes. In similar manner total number of pounds can be obtained for different number of boxes.
So answer is,
[tex]\text{ Number of boxes}\times9=\text{ total number of pounds}[/tex]Option B is correct.
