Answer:
D
Step-by-step explanation:
Firstly, we need to know the number of total possible results. We can do this by placing the first die in horizontal band and the second die in vertical band.
The total number of results would be 36 results.
Now, to get the number of 8s
The possible sums that can give 8 is 2 and 6, 2and 5 and 3 with 4 and 4.
All are possible two times asides the 4 and 4 that could only show one time.
This means as we can have 2 and 6 we can also have 6 and 2
The total number of expected results is thus: 5/36
Final answer:
The probability of rolling a sum of 8 with two number cubes is 5/36.
Explanation:
To find the probability of rolling a sum of 8 with two number cubes, we need to look at all the possible combinations that result in an 8.
The number cubes (dice) each have faces numbered from 1 to 6.
We can roll a (2,6), (6,2), (3,5), (5,3), (4,4) to get a sum of 8.
This gives us a total of 5 favorable outcomes.
Since each die has 6 faces, the number of possible outcomes when rolling two dice is 6 x 6, which equals 36.
To get the probability of the sum being 8, we divide the number of favorable outcomes (5) by the total number of possible outcomes (36).
This calculation gives us the probability 5/36.
Myriah wants to use dimensional analysis to find out how many centimeters (cm) are in 1.4 meters (m). Which of these equalities will be useful for this calculation?
Answer:
Option (4) is the answer.
Step-by-step explanation:
The given question is without options ; here is the complete question.
Myriah wants to use dimensional analysis to find out how many centimeters (cm) are in 1.4 meters (m). Which of these equalities will be useful for this calculation?
2.54 cm = 1 in.
1 m = 39.37 in.
1 cm = 10 mm
100 cm = 1 m
During the dimensional analysis Myriah wants to convert the dimension from meter to centimeter.
Option (1), In this option given equality is to convert centimeter to inch. which is not required.
Option (2), In this option equality is to convert meter to inch which is not required.
Option (3) the equality given will convert cm to mm, which is not required.
Option (4) equality given in this option will convert meter to centimeter which is the required equality.
Therefore, Option (4) will be the answer.
A.J. has 20 jobs that she must do in sequence, with the times required to do each of these jobs being independent random variables with mean 50 minutes and standard deviation 10 minutes. M.J. has 20 jobs that he must do in sequence, with the times required to do each of these jobs being independent independent random variables with mean 52 minutes and standard deviation 15 minutes.
(a) Find the probability that A.J. finishes in less than 900 minutes.
(b) Find the probability that M.J. finishes in less than 900 minutes.
(c) Find the probability that A.J. finishes before M.J.
Final answer:
To find the probability that A.J. and M.J. finish their jobs within a certain time, we need to calculate the z-score for the given values and use a standard normal distribution table or a calculator to find the probability.
Explanation:
(a) To find the probability that A.J. finishes in less than 900 minutes, we need to calculate the z-score (standard score) for the value 900 using the formula: z = (x - mean) / standard deviation. In this case, x = 900, mean = 50 minutes, and standard deviation = 10 minutes. Once we have the z-score, we can use a standard normal distribution table or a calculator to find the probability.
(b) To find the probability that M.J. finishes in less than 900 minutes, we use a similar process as in part (a), but with different mean and standard deviation values. In this case, x = 900, mean = 52 minutes, and standard deviation = 15 minutes.
(c) To find the probability that A.J. finishes before M.J., we can compare the means of the two distributions. Since A.J.'s mean is lower than M.J.'s mean, the probability of A.J. finishing before M.J. is higher.
A researcher for an airline interviews all of the passengers on five randomly selected flights.
Identify which sampling technique is used.
a. Stratified.
b. Convenience.
c. Cluster.
d. Random
Answer
Cluster sampling. See explanation below.
Step-by-step explanation:
For this case they not use random sampling since we are selecting people from flights. Because we select just 5 random flights.
Is not stratified sampling since we don't have strata clearly defined on this case, and other important thing is that in order to apply this method we need homogeneous strata groups and that's not satisfied on this case.
Is not convenience sampling because they NOT use a non probability method in order to select the people from the flights.
So then the only possible method is cluster sampling since we have clusters clearly defined (Passengers from the airlines), and we satisfy the condition of homogeneous characteristics on the clusters and an equal chance of being a part of the sample, since we are selecting RANDOMLY, the 5 flights to take the information.
Which of the following inequalities matches the graph below?
(A) The correct inequality is not listed.
(B) 5x + y ≥ 1
(C) 5x + y ≤ 1
(D) 5x − y ≥ 1
Answer:
The answer to your question is letter A
Step-by-step explanation:
Process
1.- Find two points of the line
A (1, 4) B ( -1, 5)
2.- Find the slope of the line
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
[tex]m = \frac{-5 - 4}{-1 - 1}[/tex]
[tex]m = \frac{-9}{-2} = \frac{9}{2}[/tex]
3.- Find the equation of the line
y - y1 = m(x - x1)
y - 4 = 9/2(x - 1)
2y - 8 = 9x - 9
9x - 2y = - 9 + 8
9x - 2y = - 1
4.- Convert the equation to a inequality,
9x - 2y ≤ -1
What is the area of the shaded portion of the circle?
(5π – 11.6) ft2
(5π – 5.8) ft2
(25π – 11.6) ft2
(25π – 5.8) ft2
Answer:
The first option is the correct one, the area of the shaded portion of the circle is
[/tex](5 \pi -11.6)ft^2[/tex]
Step-by-step explanation:
Let us first consider the triangle + the shadow.
The full area of the circle is the radius squared times pi, so
A=[tex](5 ft)^2 \cdot \pi \\25 ft^2 \cdot \pi[/tex]
Since [tex]\frac{72^{\circ}}{360^{\circ}}=\frac{1}{5}[/tex], the area of the triangle + the shaded area is one fifth of the area of the whole circle, thus
[tex]A_1=\frac{1}{5}25 ft^2 \cdot \pi\\ =5 ft^2 \cdot \pi[/tex]
If we want to know the area of the shaded part of the circle, we must subtract the area of the triangle from [tex]A_1[/tex].
The area of the triangle is given by
[tex]A_{triangle}=\frac{1}{2}\cdot (2.9+2.9)ft \cdot 4 ft\\= 11.6 ft^2[/tex]
Thus the area of the shaded portion of the circle is
[tex]A_1-A_{triangle}=5 \pi ft^2-11.6ft^2\\= (5 \pi -11.6)ft^2[/tex]
Answer:
A
Step-by-step explanation: i did the test and review
Which Of the following represnt the range of the function y=-1/2(x+10)^2+14?
1) y>=-5 2)y>=10 3) y<=7 4) y<=14, Explain plz
Answer:
The answer is option is (4) y ≤ 14
Step-by-step explanation:
The given function, y = - 0.5[tex](x + 10)^{2} + 14[/tex]
We have to find the range of this function. If we take the first part of the function alone we can see that it is always negative or zero. So the maximum value of the function is 14.
This happens when we make the first part zero and for that we put x = -10.
So the maximum value of the function occurs at x = -10 and that value is y = 14.
Hence the range is y ≤ 14.
The answer is option is (4) y ≤ 14
Drag each tile to the correct location on the table. Each tile can be used more than once, but not all tiles will be used.
Choose the justification for each step in the solution to the given equation.
Answer:
The answer to your question is below
Step-by-step explanation:
1) Given
2) Subtraction property of equality (because we are subtracting the same quantity on both sides).
3) Simplification
4) Subtraction property of equality ( because we are subtracting the same quantity on both sides).
5) Simplification
6) Multiplication property of equality (because we are multiplying the same quantity on both sides).
7) Simplification
A researcher interested in language development obtains a sample of 25 three-year-old girls and a sample of 25 three-year-old boys. Each child is given a vocabulary test and the researcher computes the mean score for each sample. The difference between the two sample means is an example of a
a. statistic
b. variable
c. constant
d. parameter
Answer:
(a) statistic
Step-by-step explanation:
The researcher conducted the research using sample space of 25 three-year-old girls and 25 three-year-old boys. This sample space is subjected to test with an expected outcome. The test allows the research to perform analysis on the event base on data he has collected. The collection, analysis and interpretation of data is called statistics.
In the Parallelogram below, x = ?
Answer:
12
Step-by-step explanation:
3x + 7 = 5x - 17
5x - 3x = 7 + 17
2x = 24
x = 12
Which explicit rule represents the following arithmetic sequence: 7, 11, 15, 19, 23,...
1. an=3+4n
2. an=7+4n
3. an= 4+7n
4. an=7x4^n-1
｡☆✼★ ━━━━━━━━━━━━━━ ☾
The correct option would be A. an = 3 + 4n
You may test my substituting values in:
3 + 4(1) = 7
3 + 4(2) = 11
etc
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Answer:
a
Step-by-step explanation:
Liam uses 2 quarts of yellow paint and adds 3 1/4 Jars of blue paint.Evan uses 1/2 quarts of yellow paint and adds 5 1/2 of red paint.They end up with the same volume of paint.write an equation to show it.
Answer:
2 + (13/4)x = 1/2 + (11/2)y
Step-by-step explanation:
Let each jar of paint used by Liam be x
Let each jar of paint used by Evan be y.
Liam uses 2 quarts of yellow paints and adds 3 1/4 jars of blue paint. so we have
2 + 3 1/4x
= 2 + (13/4)x
Since Evan also uses 1/2 quarts of yellow paints and add 5 1/2 jar of red paint, we have
1/2 + 5 1/2y
= 1/2 + (11/2)y
Since they end up with the same volume of paint, we have
2 + (13/4)x = 1/2 + (11/2)y
Final answer:
The equation to show that Liam and Evan end up with the same volume of paint, considering all quantities are in quarts, is 2 + 3.25 = 0.5 + 5.5.
Explanation:
To solve the problem where Liam and Evan end up with the same volume of paint, we can write an equation that sets the total volume of paint used by each person equal to each other. Since Liam uses 2 quarts of yellow paint and adds 3 1/4 (which is equivalent to 3.25) jars of blue paint and Evan uses 1/2 quart of yellow paint and adds 5 1/2 (equal to 5.5) jars of red paint, the equation comparing their total amounts of paint in quarts can be written as:
2 + 3.25 = 0.5 + 5.5
Before writing this equation, we need to ensure that both expressions represent quantities in the same unit. We confirm that all the amounts are given in quarts, so there is no need to convert units in this case. The equation illustrates that the total volume of paint used by Liam and Evan is equal.
Last year, a bakery sold w loaves of bread. This year, the bakery sold three more than twice the number of loaves of bread sold last year. If next year the bakery plans on selling twice the number of loaves of bread sold this year, how many loaves of bread does the bakery expect to sell next year?
Answer:
Bakery will sell [tex]4w+6[/tex] loaves of bread next year.
Step-by-step explanation:
Given:
Number of loaves of bread sold last year = 'w'
Now Given:
This year, the bakery sold three more than twice the number of loaves of bread sold last year.
Framing in equation form we get
Number of loaves of bread sold this year = [tex]2w+3[/tex]
Also Given:
next year the bakery plans on selling twice the number of loaves of bread sold this year.
framing in equation form we get;
Number of loaves of bread bakery will sell next year = [tex]2(2w+3) = 4w+6[/tex]
Hence Bakery will sell [tex]4w+6[/tex] loaves of bread next year.
The bakery expects to sell 4w + 6 loaves of bread next year.
Let's break down the problem step by step:
1. Number of loaves sold this year:
- Last year, the bakery sold w loaves of bread.
- This year, the bakery sold three more than twice the number of loaves sold last year.
- Therefore, the number of loaves sold this year is:
[tex]\[ 2w + 3 \][/tex]
2. Number of loaves expected to be sold next year:
- Next year, the bakery plans to sell twice the number of loaves sold this year.
- Therefore, the number of loaves expected to be sold next year is:
[tex]\[ 2 \times (2w + 3) \][/tex]
3. Simplify the expression:
- Distribute the 2 in the expression:
[tex]\[ 2 \times (2w + 3) = 2 \times 2w + 2 \times 3 = 4w + 6 \][/tex]
Therefore, the bakery expects to sell 4w + 6 loaves of bread next year.
One line of text on a page uses about 4/15 of an inch. There are 0.5-inch margins at the top and bottom of a page. Write and solve an inequality to find the number of lines that can be typed on a page that is 17 inches long.
Answer:
60 lines can be typed in the page
Step-by-step explanation:
Given:
Length of the page = 17 inches
Length of the margin = 0.5-inch
length of one line = 4/15
To Find:
The number of lines that can be typed on a page
Solution:
Let the number of line that can be typed be n
then
n <= [tex]n \leq \frac{\text { total length of the page}-\text {top margin} - \text{ bottom margin}}{\text{size of each line }}[/tex]
the top and bottom margins are 0.5 inches each
so we will be having
=> [tex]n \leq \frac{17 -0.5-0.5}{\frac{4}{15}}[/tex]
=>[tex]n \leq \frac{16}{\frac{4}{15}}[/tex]
=>[tex]n \leq \frac{16\times 15}{4}[/tex]
=>[tex]n \leq\frac{240}{4}[/tex]
=> [tex]n \leq 60[/tex]
Inez bought a package of wrapping paper and 4 bows. If she wrapped 4 identical gifts with the cost of the paper and bow, how much did it cost to wrap each gift
Answer: [tex]\$1.99[/tex]
Step-by-step explanation:
The missing figure is attached.
For this exercise you need to analize the information provided.
You can observe in the picture attached that the cost of a package of wrapping paper is $3.76 and each bow costs $1.05.
Since Inez bought 1 package of wrapping paper and 4 bows, you get that the total amount of money she spent was:
[tex]Total=\$3.76+4(\$1.05)\\\\Total=\$7.96[/tex]
According to the data given in the exercise, Inez wrapped 4 identical gifts. So, let be "x" the cost for wrapping each gift.
This is:
[tex]x=\frac{\$7.96}{4}\\\\x=\$1.99[/tex]
1.99
Step-by-step explanation:
You go out to eat and your bill comes to $123. The GST is 5% and you leave a 15%
tip. How much would it cost altogether?
Final answer:
The total cost, including a 5% GST and a 15% tip on a bill of $123, would be $147.60, calculated by adding the GST and the tip amount to the original bill.
Explanation:
To calculate the total cost of the meal including tax and tip, we add both the Goods and Services Tax (GST) and the tip percentage to the original bill amount.
Calculate the GST by converting the percentage to a decimal and multiply by the bill amount: 0.05 × $123 = $6.15.Add the GST to the original bill: $123 + $6.15 = $129.15.Calculate the tip amount: Convert 15% to a decimal and multiply by the original bill amount: 0.15 × $123 = $18.45.Add the tip to the subtotal: $129.15 + $18.45 = $147.60.The total cost, including a 5% GST and a 15% tip on a bill of $123, would be $147.60.
An investor just purchased a rectangular 2-acre retail lot for $250 a frontage foot. If she paid $100,000 total, what was the depth of the lot?
a. 400’ b. 250 c. 871’ d. 218’
Answer:
[tex] Depth = \frac{Area}{# frontage feet}= \frac{87120 ft^2}{400}=217.8 \approx 218[/tex]
So for this case the best answer would be:
d. 218’
Step-by-step explanation:
Previous concepts
Foot front : "Is a foot measured along the front of a piece of property".
Solution to the problem
For this case we need to begin finding the number of frontage feet, with the following formula:
[tex]Frontage fronts=\frac{Amount paid}{Unitary price}[/tex]
And for this case if we replace the values given we got:
[tex]Frontage fronts=\frac{100000}{250}=400 fromtage foot[/tex]
Now we need to convert the area to square feet. And we know that:
[tex] 1 acre= 43560 ft^2[/tex]
And converting we got: [tex]2 acre *\frac{43560 ft^2}{1 acre}=87120 ft^2[/tex]
Now we can divide the total area by the total of frontage feer and we got:
[tex] Depth = \frac{Area}{# frontage feet}= \frac{87120 ft^2}{400}=217.8 \approx 218[/tex]
So for this case the best answer would be:
d. 218’
An aircraft carrier made a trip. The trip there took 5 hours and the trip back took 6 hours. It averaged 3 mph faster on the trip there then on the return trip. Find the aircraft carriers speed on the outbound trip.
Answer: The outbound trip is 18 miles per hour
Step-by-step explanation:
Let x represent the speed of the plane.
An aircraft carrier made a trip. Let us assume that this trip was outbound. The trip there took 5 hours.
Distance = speed × time. Therefore
Distance = 5x
The trip back took 6 hours. It averaged 3 mph faster on the trip there then on the return trip. This means that the speed on the trip back is x - 3 mph.
Distance = 6(x-3) = 6x - 18
Since the distance is the same,
5x = 6x - 18
6x - 5x = 18
x = 18
The speed on return or inbound trip would be 18 - 3 = 15 mph
Need help with please show me how to get the answer
Answer:
? = 47°
Step-by-step explanation:
The angle marked B at the intersection of the secants is half the difference of the arcs they intercept.
∠B = (DE -AC)/2 = (142° -48°)/2 = 47°
The unknown angle is 47°.
A pair of boots and a pair of tennis shoes cost $196.12. The difference in their cost is $44.38. Determine the cost of each type of footwear Write and solve using system of equations
Answer: A pair of boots costs $120.25. A pair of tennis shoes costs $75.87✔️
Step-by-step explanation:
Let B the cost of a pair of boots and let T the cost of a pair of tennis shoes.
Then we know:
A pair of boots and a pair of tennis shoes cost $196.12:
B + T = $196.12 } Equation 1
We also know:
The difference in their cost is $44.38:
B - T = $44.38 } Equation 2
From the equation 1 we know T:
T = $196.12 - B
Now we can substitute this value in equation 2:
B - ($196.12 - B) = $44.38
B - $196.12 + B = $44.38
2B = $44.38 + $196.12 = $240.5
B = $240.5/2 = $120.25◄cost of a pair of boots
Since we know the value of T from the equation 1:
T = $196.12 - B = $196.12 - $120.25 = $75.87◄cost of a pair of tennis shoes
Answer: A pair of boots costs $120.25. A pair of tennis shoes costs $75.87✔️
VerifyWe can substitute these values in equations 1 and 2 and check the results:
B + T = $196.12 } Equation 1
$120.25 + $75.87 = 196.12 ✔️check!
B - T = $44.38 } Equation 2
$120.25 - $75.87 = $44.38 ✔️check!
Spymore
The cost of a pair of boots is $120.25 and the cost of a pair of tennis shoes is $75.87.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, a pair of boots and a pair of tennis shoes cost $196.12.
Let the cost of a pair of boots be b and the cost of a pair of tennis shoes be t.
Now, b+t=196.12 --------(I)
The difference in their cost is $44.38.
b-t=44.38 --------(II)
Add equation (I) and (II), we get
b+t+b-t=196.12+44.38
2b=240.5
b=240.5/2
b=$120.25
Substitute b=$120.25 in equation (I), we get
b+t=196.12
t=196.12-120.25
t=$75.87
Therefore, the cost of a pair of boots is $120.25 and the cost of a pair of tennis shoes is $75.87.
To learn more about the linear system of an equations visit:
https://brainly.com/question/27664510.
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A set of observations on a variable measured at successive points in time or over successive periods of time constitute aa. geometric series.
b. time invariant set.c. time series.
d. logarithmic series.
Answer:
time series
Step-by-step explanation:
A time series is a sequence of observations on a variable measured at successive points in time or over successive periods of time.
In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The mean response was 5.9 with a standard deviation of 2.2.
(a) What response represents the 92nd percentile?
(b) What response represents the 62nd percentile?
(c) What response represents the first quartile?
Answer:
a) A response of 8.9 represents the 92nd percentile.
b) A response of 6.6 represents the 62nd percentile.
c) A response of 4.4 represents the first quartile.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 5.9
Standard Deviation, σ = 2.2
We assume that the distribution of response is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) We have to find the value of x such that the probability is 0.92
P(X < x)
[tex]P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.92[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z<1.405) = 0.92[/tex]
[tex]\displaystyle\frac{x - 5.9}{2.2} = 1.405\\x = 8.991 \approx 8.9[/tex]
A response of 8.9 represents the 92nd percentile.
b) We have to find the value of x such that the probability is 0.62
P(X < x)
[tex]P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.62[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z<0.305) = 0.92[/tex]
[tex]\displaystyle\frac{x - 5.9}{2.2} = 0.305\\x = 6.571 \approx 6.6[/tex]
A response of 6.6 represents the 62nd percentile.
c) We have to find the value of x such that the probability is 0.25
P(X < x)
[tex]P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.25[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z<0.305) = -0.674[/tex]
[tex]\displaystyle\frac{x - 5.9}{2.2} = -0.674\\x = 4.4172 \approx 4.4[/tex]
A response of 4.4 represents the first quartile.
After collecting eggs from his chickens, Dale puts the eggs into cartons to sell. Dale fills 151515 cartons and has 777 eggs left over. Each carton holds 121212 eggs. How many eggs did Dale collect?
Answer:
187 eggs
Step-by-step explanation:
Correct Question:
After collecting eggs from his chickens, Dale puts the eggs into cartons to sell. Dale fills 15 cartons and has 7 eggs left over. Each carton holds 12 eggs. How many eggs did Dale collect?
Dale filled up each carton with 12 eggs (that's the full capacity.
Dale filled up 15 full cartons.
So, the eggs he collected in carton:
15 * 12 = 180 eggs
He still had 7 left over, so total number of eggs that Dale collected is:
180 + 7 = 187 eggs
Hector spent $36.75 for 2 dvds that cost the same amount.The sales tax was $2.15.Hector also used a coupon for $1.00 of his purchase. How much did each dvd cost.
Answer:
Each DVD cost for Hector at $17.80.
Step-by-step explanation:
Total Money Spent = $36.75
Number of DVD to buy = 2
Sales tax = $2.15
Amount of Coupon to be used = $1.00
We need to find the cost of each DVD.
Let the Cost of each DVD be 'x'.
Now We can say that Total Money spent on DVD's is equal to Number of DVD to buy multiplied by Cost of each DVD plus Sales Tax minus Amount Coupon used.
Framing in equation form we get;
[tex]2x+2.15-1=36.75[/tex]
Solving the equation to find the value of x we get;
[tex]2x+1.15=36.75\\\\2x=36.75-1.15\\\\2x= 35.6\\\\x=\frac{35.6}{2}= \$17.8[/tex]
Hence Each DVD cost for Hector at $17.80.
Solve the equation by factoring: x^2 + 13x = -42
Answer:
-6 and -7 are the roots
Step-by-step explanation:
The quadratic equation given is:
[tex]x^{2}+13x=-42\\Taking\ -42\ to\ left\ hand\ side\ we\ get\\x^{2} +13x+42=0[/tex]
We can factorise the equation as:
[tex]x^{2}+6x+7x+42=0\\(x^{2}+6x)+(7x+42)=0\\[/tex]
Taking x common from the first bracket and 7 common from the second bracket we get:
[tex]x(x+6)+7(x+6)[/tex]
Taking (x+6) common from both terms we get:
[tex](x+6)(x+7)=0[/tex]
x= -6 or x=-7
Hence -6 and -7 are the roots of the given quadratic equation.
How many ways can you choose 4 cookies from a cookie jar containing 25 cookies of all the same type?
Answer:
Only one.
Step-by-step explanation:
Given that there are 25 cookie of the same type in a cookie jar.
We have to select 4 cookies from these 25.
Since they are all the same type, they are identical.
The question is
How many ways can you choose 4 cookies from a cookie jar containing 25 cookies of all the same type?
There is no difference if we take any four cookies from these 25.
Hence no of different ways = 1
Only one is the answer.
Answer:
Step-by-step explanation:
25 P4=25×24×23×22=303600
3 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a red card?
Answer: [tex]\dfrac{15}{17}[/tex]
Step-by-step explanation:
Total number of cards in a deck = 52
Number of red cards = 26
Number of cards not red =
Number of ways to draw not red cards = [tex]^{26}C_3[/tex]
Total ways to draw 3 cards = [tex]^{52}C_3[/tex]
The probability that none of three cards are red = [tex]\dfrac{^{26}C_3}{^{52}C_3}[/tex]
[tex]=\dfrac{\dfrac{26!}{3!(26-3)!}}{\dfrac{52!}{3!(52-3)!}}[/tex] [∵ [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]]
[tex]=\dfrac{\dfrac{26\times25\times24\times23!}{(23)!}}{\dfrac{52\times51\times50\times49!}{3!(49)!}}=\dfrac{2}{17}[/tex]
Now , the probability that at least one of the cards drawn is a red card = 1- Probability that none cards are red
[tex]=1-\dfrac{2}{17}=\dfrac{17-2}{17}=\dfrac{15}{17}[/tex]
Hence, the required probability = [tex]\dfrac{15}{17}[/tex]
A mixture weighing 600kg has two ingredients: sand, cement and stones. There is twice as much cement as sand and three times as much stones as sand. How much cement in the mixture?
Answer:
Step-by-step explanation:
All the masses here are based on the main mass of the sand. So we will call sand "x". If there is two times as much cement as sand, then cement is 2x; if there is three times as much stone as sand, then stone is 3x. All of these added together equal a mass of 600 kg:
x + 2x + 3x = 600 so
6x = 600 and
x = 100 kg
There are 100 kg of sand. That means that there is 200 kg of cement and 300 kg of stone
Answer:
200 kg
Step-by-step explanation:
Total weight of the mixture = 600kg
Let the weight of the cement in the mixture be x kg.
According to the problem statement, there is twice as much cement as sand, therefore the weight of sand relative to cement will be 1/2, i.e.
sand weight = 1/2x =0.5x
Similarly, weight of stone will be three times as much as sand.
Meaning, stone weight = 3*0.5x=1.5x
Total weight of all the components will be
cement weight + sand weight + stone weight =
x + 0.5x + 1.5x = 3x
But 3x = 600,
x = 600/3= 200 kg
A fast-food restaurant runs a promotion in which certain food items come with game pieces. According to the restaurant, 1 in 4 game pieces is a winner. If Jeff gets 4 game pieces, what is the probability that he wins exactly 1 prize?
(a) 0.25
(b) 1.00
(c) (41)(0.25)1(0.75)3
(d) (41)(0.25)3(0.75)1
(e) (0.75)3(0.25)1
Answer:
(c) [tex]\left\ ({{4} \atop {1}} )\right.[/tex] [tex]0.25^{1} 0.75^{3}[/tex]
Step-by-step explanation:
As given in the statement, we have:
Out of 4 games pieces, 1 is winner.
Probability to win =p= [tex]\frac{1}{4}[/tex]
Jeff has game pieces = n = sample size = 4
As we need to find the probability that he wins exactly 1 prize, we will use binomial probability here :
[tex]P (X = k) = \left\ ({{n} \atop {k}} )\right. p^{k} (1-p)^{n-k} \\[/tex]
Evaluating at k=1, (k=1 as we need to find probability for exactly 1 prize won)
put n = 4, p =[tex]\frac{1}{4}[/tex]
P (X = 1) =[tex]\left\ ({{4} \atop {1}} )\right. 0.25^{1} (1-0.25)^{4-1}[/tex]
P =[tex]\left\ ({{4} \atop {1}} )\right. 0.25^{1} (0.75)^{3}[/tex]
Which is the probability that he wins exactly 1 prize and is option c.
Probability (Jeff wins 1 price in 4 game pieces) = C] [tex](4 c 1)(0.25)^1(0.75)^3[/tex]
Important Information : Probability (Winning a price) = 1 / 4 = 0.25
Probability (Not winning price) = 1 - Pr (Winning Price) = 1 - 0.25 = 0.75
Using Binomial Probability : Pr (X = r) = [tex]N c r . P^r . Q^(n-r)[/tex] .
Here N = number of trials (4 game pieces here) , P = Probability of Success (of winning price = 0.25) , R = Number of Success (1 price) , Q = Probability of failure (of not winning price = 0.75) ,
So, Probability = [tex]4 c 1 (0.25)^1 (0.75)^3[/tex]
To learn more about Probability, refer https://brainly.com/question/13609688?referrer=searchResults
A boy thinks he has discovered a way to drink extra orange juice without alerting his parents. For every cup of orange juice he takes from a container of orange juice, he pours one cup of water back into the container. If he completes this process three times on the same container of juice, the resulting mixture will be exactly 50% water and 50% juice. How many cups of orange juice were originally in the container. (P.S ITS NOT 6)
Answer:
x=4.8473 cups
Step-by-step explanation:
Concentration of Liquids
It measures the amount of substance present in a mixture, often expressed as %. If there is an volume x of a substance in a total volume mix of y, the concentration is given by
[tex]\displaystyle C=\frac{x}{y}[/tex]
It we take a sample of that mixture, we must consider that we are getting only the substance, but all the mixture (assumed it has been uniformly mixed). For example, if we take a glass of liquid from a 80% mixture of juice, the glass will also have a 80% of juice.
Let's solve the problem sequentially. At first, let's assume all the container is full of x cups of juice. Its concentration is 100%. Now let's take 1 cup of pure juice and replace it by 1 cup of pure water. The new amount of juice in the container is
x-1 cups of juice.
The new concentration is
[tex]\displaystyle \frac{x-1}{x}[/tex]
The boy takes a second cup of liquid, but this time it's not pure juice, it has a mixture of juice and water with a concentration computed above. Now the amount of juice is
[tex]\displaystyle x-1-\frac{x-1}{x}[/tex] cups of juice.
Simplifying, the cups of juice are
[tex]\displaystyle \frac{\left (x-1\right)^2}{x}[/tex]
The new concentration is
[tex]\displaystyle \frac{\left (x-1\right)^2}{x^2}[/tex]
For the third time, we now have
[tex]\displaystyle \frac{\left (x-1\right)^2}{x}-\frac{\left (x-1\right)^2}{x^2}[/tex] cups of juice.
Simplifying, the final amount of juice is
[tex]\displaystyle \frac{\left (x-1\right)^3}{x^2}[/tex]
And the final concentration is
[tex]\displaystyle \frac{\left (x-1\right)^3}{x^3}[/tex]
According to the conditions of the question, this must be equal to 50% (0.5)
[tex]\displaystyle \frac{\left (x-1\right)^3}{x^3}=0.5[/tex]
Taking cubic roots
[tex]\displaystyle \sqrt[3]{\frac{\left (x-1\right)^3}{x^3}}=\sqrt[3]{0.5}[/tex]
[tex]\displaystyle \frac{\left (x-1\right)}{x}=\sqrt[3]{0.5}[/tex]
Operating and joining like terms
[tex]\displaystyle x-\sqrt[3]{0.5}\ x=1[/tex]
Solving for x
[tex]\displaystyle x=\frac{1}{1-\sqrt[3]{0.5}}[/tex]
[tex]x=4.8473\ cups[/tex]
Let's test our result
Final concentration:
[tex]\displaystyle \frac{\left (4.8473-1\right)^3}{4.8473^3}=0.5[/tex]
A manufacturing process produces a critical part of average length 120 millimeters, with a standard deviation of 3 millimeters. All parts deviating by more than 5 millimeters from the mean must be rejected. What percentage of the parts must be rejected, on average? Assume a normal distribution.
Answer:
9.692%
Step-by-step explanation:
We have been given that a manufacturing process produces a critical part of average length 120 millimeters, with a standard deviation of 3 millimeters. All parts deviating by more than 5 millimeters from the mean must be rejected.
5 millimeters below mean would be [tex]115[/tex] and 5 millimeters above mean would be [tex]125[/tex].
Corresponding z values for 115 and 125 would be:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{115-120}{3}[/tex]
[tex]z=\frac{-5}{3}[/tex]
[tex]z=-\frac{5}{3}[/tex]
[tex]z=\frac{125-120}{3}[/tex]
[tex]z=\frac{5}{3}[/tex]
Now, we need to find [tex]P(z<-\frac{5}{3})+P(z>\frac{5}{3})[/tex] using normal distribution table.
[tex]P(z<-\frac{5}{3})+P(z>\frac{5}{3})=P(z<-1.66)+P(z>1.66)[/tex]
We know that [tex]P(z>1.66)=1-P(z<1.66)[/tex].
[tex]P(z>1.66)=1-0.95154 [/tex]
[tex]P(z>1.66)=0.04846[/tex]
[tex]P(z<-\frac{5}{3})+P(z>\frac{5}{3})=0.04846+0.04846[/tex]
[tex]P(z<-\frac{5}{3})+P(z>\frac{5}{3})=0.09692[/tex]
Now, we need to convert 0.09692 into percentage as:
[tex]0.09692\times 100\%=9.692\%[/tex]
Therefore, 9.692% of parts must be rejected on average.
About 0% of the parts would be rejected, on average.
Z scoreThe z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (x - μ) / σ
where μ is the mean, x = raw score and σ is the standard deviation.
Given μ = 120, σ = 3. For z > 5:
P(z > 5) = 1 - P(z < -38.3) = 1 - 1 = 1 = 0%
About 0% of the parts would be rejected, on average.
Find out more on Z score at: https://brainly.com/question/25638875