Calculate the probability of winning: Roll a standard die and then flip a coin. You win if you toss “heads” and roll a 6. Round answer to two decimals places, for example if you answer is 0.624 round to 0.62
Answers
The probability of landing "heads" on a coin is 1/2, and the probability of rolling a 6 is 1/6.
Using the following given, the probability of winning therefore is
\(\begin{gathered} P(\text{Win})=P(\text{Heads})\cdot P(6) \\ P(\text{Win})=\frac{1}{2}\cdot\frac{1}{6} \\ P(\text{Win})=\frac{1}{12} \\ P(\text{Win})=0.083333 \end{gathered}\)Rounding to 2 decimal places, the probability of winning is 0.08.
Related Questions
UBL Bank currently has PKR 4600 million in transaction deposits on its balance sheet. The State Bank of Pakistan has currently set the reserve requirement at 10 percent of transaction deposits. If the State bank decreases the reserve requirement to 8 percent, reflect the result of this transaction on the balance sheet of UBL and effect of this change on its balance sheet
Answers
Answer:
UBL Bank
The result of this decrease in the reserve requirement in the balance sheet is reflected on the total amount of money created by UBL Bank increasing from PKR 46,000 million to PKR 57,500 million.
Step-by-step explanation:
Current transaction deposits on balance = PKR 4,600 million
Reserve requirement = 10 percent of transaction deposits
This implies that UBL Bank can create more money up to (4,600/0.1) million = PKR 46,000 million
If the State Bank of Pakistan decreases the reserve requirement to 8 percent, the money creation ability of UBL Bank will increase to (4,600/0.08) million = PKR 57,500 million
The effect of this change on its balance sheet is PKR 11,500 million. This implies that UBL Bank's ability to create money is increased by PKR 11,500 million.
In exercises 4-6, a survey reported that 235 of the 500 voters in a sample voted for candidate A and the rest voted for candidate B?
4. What percent of the voters in the sample voted for candidate A? What percent of the voters in the sample voted for candidate B?
5. What is the margin sampling error? Round your answer to the nearest tenth of a percent.
6. For each candidate, give an interval that is likely to contain the exact percent of all voters who voted for the candidate.
7. For #6, can you determine which candidate won? Explain.
Answers
4.
Total voters = 500
Number of voters that voted for candidate A = 235
Number of voters that voted for candidate B = 500 - 235 = 265
Percent of voters that voted for candidate A
= 235
500
× 100%
= 23500
500
= 47%
Percent of voters that voted for candidate B
= 265
500
× 100%
= 26500
500
= 53%
5.
Margin sample error = % of candidate B - 5 of candidate A
= 53% - 47%
= -/+ 6%
Margin sample error = + 6.0% or - 6.0%
6.
Candidate A interval
= 47 ± 0.5
= 46.5% or 47.5%
Candidate B interval
= 53±0.5
= 52.5% or 53.5%
7.
Candidate with the highest percentage win.
Therefore, candidate B won
To qualify as a contestant in a race, a runner has to be in the fastest 16% of all applicants. The running times are normally distributed, with a mean of 61 min and a standard deviation of 5 min. To the nearest minute, what is the qualifying time for the race? The qualifying time for the race is _____ min. (Round to the nearest minute as needed.)
Answers
We know that the running times are normally distributed and that the time of a runner to qualify has to be in the fastest 16%. From the properties of the normal distribution, we know that:
• Between one and two standards deviation of the mean we have approximately 13.5% of the data.
,• Between two and three standards deviations of the mean we have approximately 2.35% of the data.
,• Above three standards deviations of the mean we have 0.15%.
This means that above one standard deviation there are approximately 16% of the data. Then we just need to add one standard deviation to the mean to find the time a runner needs.
\(61+5=66\)Therefore, the running time to qualify is 66 min
Is the relation shown in
the table a function?
Explain.
Answers
The inputs 4 and 8 have more than one out, the relation is not a function.
Is the relation shown in the table a function?A relation is said to be a function if one input is mapped to one output.
that is, each x-value can only have one y-value.
From the table;
Input, output
4 ----- 1
8 ----- 3
4 ------5
8 ----- 4
4 is an input, it has an output of 1.
4 appeared again as input but this time has an output of 5.
This means one input has more than one output.
Also, 8 is an input, it has an output of 3.
8 appeared again as input but this time has an output of 4.
Which also means one input has more than one output.
Therefore, the relation is not a function.
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In a large population of students, 60% feel like they can do better in their math class. In a random sample of 5 students, what is the probability that at least 2 students feel like they can do better in their math class?
0.0870
0.2304
0.3174
0.6826
0.9130
Answers
The probability that at least 2 students feel like they can do better in their math class is E. 0.9130.
How to calculate the probabilityTo find the probability that at least 2 students feel like they can do better, we need to calculate P(X >= 2). This can be done using the cumulative distribution function (CDF) of the binomial distribution:
P(X >= 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)
Using the binomial probability formula, we can calculate:
P(X = 0) = (5 choose 0) * 0.6^0 * 0.4^5 = 0.01024
P(X = 1) = (5 choose 1) * 0.6^1 * 0.4^4 = 0.07680
Therefore,
P(X >= 2) = 1 - 0.01024 - 0.07680 = 0.91296
Rounding this to four decimal places, we get: 0.9130
Therefore, the answer is option E: 0.9130.
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A science teacher has 30 pounds of salt and 20 liters of water to use for a class experiment. Each of the 8 groups of students will receive an equal share of both the salt and the water. How much of the salt and water will each group get?
Answers
Answer:
3 3/4 lb salt2 1/3 L waterStep-by-step explanation:
Each group will get 1/8 of the total amount:
salt: (30 lb)/8 = 3 6/8 lb = 3 3/4 lb
water: (20 L)/8 = 2 4/8 L = 2 1/2 L
Each group will get 3 3/4 pounds of salt and 2 1/2 liters of water.
Mason goes to a store an buys an item that costs xx dollars. He has a coupon for 30% off, and then a 7% tax is added to the discounted price. Write an expression in terms of x that represents the total amount that Mason paid at the register.
Answers
THE TOTAL AMOUNT THAT MASON PAID IS 549
please help me thank you
Answers
Answer:
D) Perpendicular
Step-by-step explanation:
Red: 5y+4x=-30
Blue: y=5/4x-5
On the number line above, points A, B, C, and D are integers, and AB: BC: CD = 3:2:1. What is the length of AC?
Answers
Using proportions, it is found that the length of AC is of 15 units.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The ratios in this problem are given as follows:
\(\frac{AB}{BC} = \frac{3}{2}\).\(\frac{BC}{CD} = \frac{2}{1}\).\(\frac{AB}{CD} = \frac{3}{1}\).The entire length is of 18 units, AB is half of that, hence:
AB = 0.5 x 18 = 9 units.
BC is two thirds of the length from 6 to 15, hence:
BC = 2/3 x (15 - 6) = 6
Thus, the length of AC is:
AC = 9 + 6 = 15 units.
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Find the volume of the figure. For calculations involving , give both the exact value and an approximation to the nearest hundredth of a unit. Let d = 10 and h = 18.
________ ft3 ≈ _________ft3
Answers
Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.
Explain about the shape of cylinder:A cylinder is three-dimensional. It's not a flat thing. There are parallel circular bases in this shape. These bases have a curved face affixed to them. A cylinder in this instance has three faces. Along both end of a curved face, which rounds back to the face's origin, are two spherical bases.
Given that-
diameter d = 10 ftRadius r = 10/2 = 5 ftHeight h = 18 ftVolume of cylinder = πr²h
Volume of cylinder = 3.14 *5²*18
Volume of cylinder = 3.14*25*18
Volume of cylinder = 1413 ft³
Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.
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Which expression is represented on the number line?
Answers
Answer:
b
Step-by-step explanation:
because it is -2 four times and if you do -2 ×4 you get -8. hope thid helped
A right rectangular prism's edge lengths are 10.5 inches, 5 inches, and 2 inches. How many unit cubes with edge lengths of 0.5 inch can fit inside the prism?A)105 unit cubesB)210 unit cubes460 unit cubesD)840 unit cubes5)
Answers
Given
A right rectangular prism's edge lengths are 10.5 inches, 5 inches, and 2 inches.
To find how many unit cubes of edge length 0.5 inches can fit inside the prism.
Explanation:
It is given that, the volume of the rectangular prism is,
\(\begin{gathered} Volume=l\times b\times h \\ =10.5\times5\times2 \\ =105in^3 \end{gathered}\)Since the edge length of 0.5inch.
Then,
\(\begin{gathered} Volume\text{ of rectangular prism}=n\times Volume\text{ of a cube} \\ 105=n\times(0.5)^3 \\ n=\frac{105}{0.125} \\ n=840 \end{gathered}\)Hence, the number of cubes is 840 unit cubes.
The number of typos made by a student follows Poisson distribution with the rate of 1.5 typos per page. Assume that the numbers of typos on different pages are independent. (a) Find the probability that there are at most 2 typos on a page. (b) Find the probability that there are exactly 10 typos in a 5-page paper. (c) Find the probability that there are exactly 2 typos on each page in a 5-page paper. (d) Find the probability that there is at least one page with no typos in a 5-page paper. (e) Find the probability that there are exactly two pages with no typos in a 5-page paper.
Answers
Answer:
a) 0.8088 = 80.88% probability that there are at most 2 typos on a page.
b) 0.0858 = 8.58% probability that there are exactly 10 typos in a 5-page paper.
c) 0.001 = 0.1% probability that there are exactly 2 typos on each page in a 5-page paper.
d) 0.717 = 71.7% probability that there is at least one page with no typos in a 5-page paper.
e) 0.2334 = 23.34% probability that there are exactly two pages with no typos in a 5-page paper.
Step-by-step explanation:
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)
In which
x is the number of sucesses
e = 2.71828 is the Euler number
\(\mu\) is the mean in the given interval.
Binomial distribution:
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
The number of typos made by a student follows Poisson distribution with the rate of 1.5 typos per page.
This means that \(\mu = 1.5n\), in which n is the number of pages.
(a) Find the probability that there are at most 2 typos on a page.
One page, which means that \(\mu = 1.5\)
This is
\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\)
In which
\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)
\(P(X = 0) = \frac{e^{-1.5}*(1.5)^{0}}{(0)!} = 0.2231\)
\(P(X = 1) = \frac{e^{-1.5}*(1.5)^{1}}{(1)!} = 0.3347\)
\(P(X = 2) = \frac{e^{-1.5}*(1.5)^{2}}{(2)!} = 0.2510\)
\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2231 + 0.3347 + 0.2510 = 0.8088\)
0.8088 = 80.88% probability that there are at most 2 typos on a page.
(b) Find the probability that there are exactly 10 typos in a 5-page paper.
5 pages, which means that \(n = 5, \mu = 5(1.5) = 7.5\).
This is P(X = 10). So
\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)
\(P(X = 10) = \frac{e^{-7.5}*(7.5)^{10}}{(10)!} = 0.0858\)
0.0858 = 8.58% probability that there are exactly 10 typos in a 5-page paper.
(c) Find the probability that there are exactly 2 typos on each page in a 5-page paper.
Two typos on a page: 0.2510 probability.
Two typos on each of the 5 pages: (0.251)^5 = 0.001
0.001 = 0.1% probability that there are exactly 2 typos on each page in a 5-page paper.
(d) Find the probability that there is at least one page with no typos in a 5-page paper.
0.2231 probability that a page has no typo, so 1 - 0.2231 = 0.7769 probability that there is at least one typo in a page.
(0.7769)^5 = 0.283 probability that every page has at least one typo.
1 - 0.283 = 0.717 probability that there is at least one page with no typos in a 5-page paper.
(e) Find the probability that there are exactly two pages with no typos in a 5-page paper.
Here, we use the binomial distribution.
0.2231 probability that a page has no typo, so \(p = 0.02231\)
5 pages, so \(n = 5\)
We want P(X = 2). So
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 2) = C_{5,2}.(0.2231)^{2}.(0.7769)^{3} = 0.2334\)
0.2334 = 23.34% probability that there are exactly two pages with no typos in a 5-page paper.
Find the equation that can represent the situation if the sum of two numbers is 32. We also know that the greater number is 5 more than the smaller number. (5 points)
a
x + (x + 5) = 32
b
x − (x + 5) = 32
c
x(x + 5) = 32
d
x(x − 5) = 32
Answers
Answer:
A. x+(x+5)=32
Step-by-step explanation:
A hiking trail is shown as 14 cm on a map.
The scale is 1 : 150000
How far in km is it in real life?
Answers
Answer:
21km
Step-by-step explanation:
1km=100000cm
14x150000=2100000cm=21km
The distance in real life in kilometers by the given scale factor will be 21 kilometers.
What is the scale factor?You must specify the extent of the shape's enlargement when describing one.
The scale factor is the ratio of two dimensions such that one figure is large and another is small.
The scale factor is done due to the unpractical measurement of any figure.
As per the given,
Scale factor = 1 : 150000
It means 1 cm will convert to 150000 cm.
In real life = 14 x 150000 = 2100000 cm
2100000 cm = 21000 m = 21 kilometer
Hence "The distance in real life in kilometers by the given scale factor will be 21 kilometers".
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Abe is going to plant 54 oak trees and 27 pine trees. Abe would like to plant the trees in rows that all have the same number of trees and are made up of only one type of tree. What is the greatest number of trees Abe can have in each row?
HELP!
Answers
Answer:
9
Step-by-step explanation:
The GCF between 54 and 27 is nine.
The greatest common factor of 81 is 9
So 9 times 9 =81
The best answer would be 9 rows with 9 trees in each row
A car manufacturer determines that its profit P in pesos can be modeled by the function P (x)=x3+5x2+3x+1,where x represent the number of cars sold. what is the profit when x=10?
Answers
Answer:
1531 pesos
Step-by-step explanation:
The profit when x=10 is calculated as follows:
P(10) = 10^3 + 5(10^2) + 3(10) + 1 = 1000 + 500 + 30 + 1 = 1531 pesos.
Find the measure of the missing angle
Answers
Si tengo 10 melones y voy a repartir entre 15 niños cuánto le toca a cada uno
Answers
Answer:
0.66 melones por niño o 2/3
Step-by-step explanation:
10/15=2/3=0.66
a right triangle had side lengths d,e,and f as shown below. use these lengths to find sin x cos x and tan x
Answers
Cos X=D/F
Tan X= E/D
Using soh-cah-toa we know sin is opposite/ hypotenuse. Cos is adjacent/ hypotenuse. And tan is opposite/ adjacent
Please help- question below....thank you
Answers
The school cafeteria is thinking of introducing a vegetarian pizza to the menu. Which
sampling technique would you recommend to determine which of three possible
toppings should be used? Explain your recommendation. [C -2]
4.
Answers
I recommend use of simple random sampling to determine the three possible toppings to be used for the vegetarian pizza.
What is simple random sampling suitable?It is a sampling technique in which each member of the population has an equal chance of being selected for the sample. Here, the population would be students who regularly eat at the school cafeteria.
By using the sampling, we make sure that each student has an equal chance of being selected to taste test the different pizza toppings. This will help to eliminate bias and provide a representative sample of the population's preferences. They will provide feedback which will be used to determine which topping should be used for the vegetarian pizza.
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Mitch bought 4.6 feet of fabric. Each foot cost $3.50. How much did he spend in all on fabric?
Answers
Answer:
$16.10
Step-by-step explanation:
He spent $16.10 in total. Because 3.5 x 4.6 feet = 16.1
Answer:
$16.10
Step-by-step explanation:
3.50 x 4.6 = 14 + 2.10
Livia eats a chicken drumstick with 11 grams of protein. She also eats x cheese sticks, each with 7 grams of protein. The table shows y , the total number of grams of protein that Livia will consume if she eats x cheese sticks. Livia may eat only part of a cheese stick, so x may not always be a whole number.
A 2-column table with 4 rows. The first column is labeled x with entries 0, 2, 5, 7. The second column is labeled y with entries 11, 25, 46, 60.
What is the range of the function?
all real numbers
all real numbers greater than or equal to 0
all real numbers greater than or equal to 11
all integers greater than or equal to 11
Answers
The range of the function is (c) all real numbers greater than or equal to 11
How to determine the range?The table of values is given as:
x y
0 11
2 25
5 46
7 60
From the question, we understand that:
She eats 11 gram of protein from the chicken drumstick
This means that the minimum y value is 11
Also, we understand that:
x can take decimal numbers.
This means that y can take any decimal number above 11
Hence, the range of the function is (c) all real numbers greater than or equal to 11
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jul used one bag of flour. She baked two loaves of bread. Then she used the remaining flour to make 48 muffins. How much flour was in the bag when Makenzie began? Use the chart to help you solve the problem.
Recipe
Amount of flour needed
Bread
2 ¼ cups per loaf
Muffins
3 ¼ cups per 24 muffins
Pizza
1 ½ cups per pie
Answers
Answer:
momdhwdjwbdjwbdjwbdjwbdjwbd a amamamamamamama
Step-by-step explanation:
Select all of the statements that are true for the given function.
A.The function is concave down on (negative infinity, 3)
B. The function is concave up on (negative infinity, 3)
C.The function is concave up on (3, infinity)
D.There is a maximum value at (4, 0)
E. There is a minimum value at (4, 0)
F.The function is decreasing on (3,4)
G. The function is decreasing on (negative infinity, 1)
H. The function is Increasing on (negative infinity, -1)
Answers
The statements that are true about the function are
A. The function is concave down for the interval (-∞, 3)
B. The function has a maximum value at (4, 0)
F. The function is decreasing on the interval (3, 4)
G. The function is decreasing on the interval (-∞, 1)
How to find the statements that are true for the function.From the graph, we seee that the function is concave down for the interval (-∞, 3)From the graph, we see that the function has a maximum value at (4, 0) since the tangent at that point is zero and it is concave down.From the graph, we see that the function is negative on the interval (3, 4) . So, the function is decreasing on the interval (3, 4)From the graph, we see that the function is negative for x < 1. So, the function is decreasing on the interval (-∞, 1)So, the statements that are true about the function are
A. The function is concave down for the interval (-∞, 3)
B. The function has a maximum value at (4, 0)
F. The function is decreasing on the interval (3, 4)
G. The function is decreasing on the interval (-∞, 1)
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The position function
defined by:
s(x) = x³ - 3x²
changes direction at x=?
Answers
The given function changes its direction at x = 0.
What is a position function in calculus?
The position function (also known as a position equation) determines the location of an object at a given point in time. For example, the position function graph below tells you (in meters) where a car will be in the first few seconds after starting: A car's position function.
The given function is s(x) = x³ - 3x²
Let's draw a graph of it.
After drawing the graph we can see that the function changes its curve at the origin. i.e. at (0, 0)
Hence, the given function changes its direction at x = 0.
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How many degrees is 5pi/4 radians?
Answers
Answer: 225
Step-by-step explanation:
Create a ratio part/whole for radians = part/whole for degrees
\(\frac{\frac{5\pi }{4} }{2\pi } = \frac{x}{360}\) Keep change flip because you are dividing fractions for left side
\(\frac{5\pi }{4} (\frac{1}{2\pi }\)) = \(\frac{x}{360}\)
\(\frac{5}{8} (\frac{360}{1} ) =x\)
x = 225
A cereal box says that now it contains 20% more. Originally, it came with 20 ounces of cereal. How much cereal does the box come with now?
Answers
Answer:24ounces
Step-by-step explanation:
Multiply 20 ounces by .20 (The percent) then add your answer to the 20 ounces.
Joe wants to build a doll house for his daughter. He wants the doll house to look just like his house. His house is 29 feet wide and 32 feet tall at the highest point of the roof. If the dollhouse will be 2.5 feet wide, how many feet will its highest point be? (Round your answer to one decimal place.)
Answers
Answer:
3.5 feet
Step-by-step explanation:
The highest point of the dollhouse will be 2.76 feet.
What is proportion?A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio.
Given that,
The width of house = 29 feet.
And the height of the house = 32 feet.
Also, the width of dollhouse = 2.5 feet
Let the height of the doll is x feet.
To find the value of x,
Use proportion property,
29 / 32 = 2.5 / x
x = (32 × 2.5) / 29
x = 80 / 29
x = 2.758
the height of the doll is 2.76 feet.
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