The probability that a randomly selected jury of 12 people is all male is 2.1 × 10⁻⁵.
What is the probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
An order does not matter so it is a Combination.
There are 16 men and we are going to choose 12 --> ₁₆C₁₂
There are 30 people and we are going to choose 12 --> ₃₀C₁₂
₁₆C₁₂ / ₃₀C₁₂
[tex]= \frac{16!}{(16 - 12)!} \div \frac{30!}{(30 - 12)!}[/tex]
= 0.00002104211
= 2.1 × 10⁻⁵
Hence, the probability that a randomly selected jury of 12 people is all male is 2.1 × 10⁻⁵.
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Which fraction is equivalent ?
Answer:
Option A
Step-by-step explanation:
→ Simplify all the options
a. 5/6 and b is 2/3
The following inequalities form a system. y is greater than or equal to two-thirds times x plus 1 y is less than negative one-fourth times x plus 2 Which ordered pair is included in the solution to this system? (−6, 3.5) (−6, −3) (−4, 3) (−4, 4)
The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given phrase,
y is greater than or equal to two-thirds times x plus 1 ⇒ y ≥ (2/3)x + 1
y is less than negative one-fourth times x plus 2 ⇒ y < (-1/4)x + 2
Substitute, point (−6, −3)
-3 ≥ (2/3)(-6) + 1
-3 ≥ -3
Substitute in second inequality,
-3 < (-1/4)(-6) + 2
-3 < 7/2
Hence "The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality".
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what value of aa would indicate no association between gender and voting pattern for the people in the sample?
The value of ' a 'indicating no association between gender and voting pattern for the people in the sample is 500.
What is sample?A sample is a result of a random experiment. We sample a random variable when we select a specific value from among its possible possibilities. A exact value is that of a sample. The potential values and likelihood of each are determined by the random variable's probability distribution. They should be picked at random from a broader group or population in order to assist you understand more about the population as a whole. Samples are employed in statistical testing when population sizes are too big for all prospective participants or observations to be included in the test.
Here,
Considering Split ticket,
a + b = 600 ---(1)
Considering No Split ticket,
c + d = 400 ---(2)
Considering Men,
a + c = 800 ---(3)
Considering Women,
b + d = 200 ---(4)
Applying (1) - (4),
a + b - b - d= 600 - 200
a - d = 400 ---- (5)
Applying (2) - (4),
c + d - b - d = 400- 200
c - b = 200 ----(6)
a - c = 200 --- (7)
Applying (3) + (7)
2a = 1000
a = 500
For those in the sample, the value of "a" showing there is no correlation between gender and voting behavior is 500.
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the diameter of a tree was 14 in. during the following year, the circumference increased 4 in. about how much did the tree's diameter increase? about how much did the tree's cross-section area change?
The diameter of the tree increased by 0.27in. (approximately) and the change in tree's cross section area is 27.5 in.².
As given in the question,
Diameter of the tree 'd' = 14in.
Radius = 7in.
Circumference of the tree = πd
= 3.14 × 14
= 43.96 in.
New circumference increased by 4 in. = 43.96 + 4
= 47.96in.
New diameter = 47.96 / 3.14
= 15.27 in. (approximately)
New Radius ≈ 7.6 in.
Increase in diameter= 15.27 - 15
= 0.27 in.
Area of cross section original tree = 3.14 × 7²
= 153.9 in.²
New area of cross section original tree = 3.14 × 7.6²
= 181.4 in.²
Change in area = 181.4 - 153.9
= 27.5 in.² ( approximately)
Therefore, increase in diameter is 0.27in. and change in cross - section area is 27.5 in.²
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The value of a brand new car is $ 40 , 000 $40,000 and the value depreciates 19% every year. Write a function to represent the value of the car after t t years, where the quarterly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per quarter, to the nearest hundredth of a percent
Answer:
Function: V(t) = 40,000(0.81^(4t))
Quarterly rate of change: -19.00%
what is the probability of rolling a die ten times and obtaining odd digits on eight or less of the rolls?
The probability of rolling a die 10 times and obtaining odd digit 8 or less of the rolls is 529/512 = 1.033
Let us call, getting an odd no. on a roll of die, Success.
The, clearly, the probability p of Success is 3/6 = 1/2.
Hence, q = 1 −p = 1/2
If, X = x denotes the no. of success in n trials, then, X is a
Binomial Random Variable, with parameters
n = 10, and, p = 1/2.
Binomial Random Variable:
This is a specific type of discrete random variable. A binomial random variable counts how often a particular event occurs in a fixed number of tries or trials. For a variable to be a binomial random variable, ALL of the following conditions must be met:
There are a fixed number of trials (a fixed sample size).On each trial, the event of interest either occurs or does not.The probability of occurrence (or not) is the same on each trial.Trials are independent of one another.Then, the Probability of x success out of n trials, i.e.,
P (X = x), is,
P (X = x) = p(x) =ⁿCₓ pˣ , qⁿ⁻ˣ, x = 0,1,2, ........, n
In our case,
P (X = x) = ¹⁰Cₓ (1/2)ˣ (1/2)¹⁰⁻ˣ ,x = 0,1,2,..., 10, i.e.,
P (X = x) = p(x) = ¹⁰Cₓ (1/2)¹⁰ = ¹⁰Cₓ /1024, x = 0, 1, ..., 10.
Hence,
The Required Probability = P( X< 8),
⇒ P (X = 0)+ P( X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) +P(X = 6) + P(X= 7) + P(X =8)
⇒ 1/1024 ( 1 + 10 + 45 + 120 +210 + 252 + 210 + 120 +90)
⇒ 1/1024 ×1058
⇒ 529 / 512
⇒ 1.033
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Help help help help help I will give 20 points
Answer:
Step-by-step explanation:
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A gas station is open 365 day a year, 24 hours a day. The store owner estimates that they served 40,000 cups of coffee last year. This quantity can also be expressed asfunctionsequation editorcups of coffee per hour (round to the nearest whole cup). This is a ? reasonable not reasonable estimate.
The quantity can also be expressed as a function equation in cups of coffee per hour is; f(x) = 5x
How to Solve function word problems?
We are told that a gas station is open for the 365 days of the year and 24 hours each day.
Thus,
Total number of hours in the year = 365 * 24 = 8760 hours
Now, the number of cups they served for the year = 40000 cups
Now, the rate of cups per hour = 40000/8760 = 4.566 ≈ 5 cups per hour
The quantity can also be expressed as a function equation in cups of coffee per hour; f(x) = 5x
where;
x is the number of hours
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What type of variable is required to construct a confidence interval for a population proportion?.
The type of variable required is Qualitative with two possible outcomes.
What is a confidence interval?
An estimate level of uncertainty is expressed by a range of values known as a confidence interval.
Keeping in mind, the z-score and other data's decimal places should be preserved when generating the confidence interval upper and lower bounds. The responses will be accurate and round-off errors will be prevented.
Also, the confidence interval boundaries are expressed in percentages. The maximum value of 0.8740, for instance, is 87.4% in decimal notation.
Make sure to specify the confidence level, the percentage of the population that the confidence interval actually captures, and the bounds expressed in percentages when expressing the meaning of the confidence interval.
Hence, the type of variable required to construct a confidence interval for a population proportion is Qualitative with 2 possible outcomes.
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suppose that a random sample of 25 measurements is selected from a population with mean 70 and standard deviation 10. what is the mean and standard deviation of the sampling distribution of the sample mean?
The mean and standard deviation of the sampling distribution is 70 and 2 respectively.
Given a random sample of 25 measurements means
n = 25.
Population with mean(µ) 70 means
µ = 70.
Population with standard deviation(σ) 10 means
σ = 10.
mean of sampling distribution is itself same as mean of population
so mean of sampling distribution is 70.
standard deviation of sampling distribution is
σ/[tex]\sqrt{n}[/tex].
put the value of σ= 10 and n =25.
10/[tex]\sqrt{25}[/tex] = 10/5 = 2
So mean of sampling distribution is 70 and standard deviation of sampling distribution is 2.
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the base of a right triangle is 6 and the perpendicular height is 8, what is the length of a hypotenuse
The length of hypotenuse is 10. It can be obtained by using Pythagorean Theorem.
What is Pythagorean theorem?
It is a theorem which gives the relationship between the length of base, perpendicular height, and hypotonus. This relationship is valid only for a right angled triangle.
The length of hypotenuse is given by the following formula:
[tex]h=\sqrt{b^2+p^2}[/tex]
Here, h is the length of hypotenuse, b is the length of base, and p is the length of perpendicular.
Substitute 6 for b and 8 for p in the above equation.
[tex]h=\sqrt{6^2+8^2}\\=\sqrt{36+64}[/tex]
Now, take the square root of 100.
[tex]h=\sqrt{100}\\=10[/tex]
Hence, the length of hypotenuse is 10.
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y+5-1/3x=7 find y and then x to find the corresponding values
Answer:
y+5-1/3x=7 find y and then x to find the corresponding values
y = 5 - 1/3x + 7
y = 5 - 1/3(x) + 7
y = 5 - (1/3)x + 7
y = (5 - 1/3x) + 7
y = (5 + 7) - (1/3)x
y = 12 - (1/3)x
For y = 12,
12 - (1/3)x = 12
(1/3)x = 0
x = 0
Therefore, when y = 12, x = 0.
Simplify the expression to a polynomial in standard form: (x-1)(3x^2+7x+5) (x−1)(3x 2 +7x+5)
The standard form for the given expression is 3x³ - 3x² - 2x - 5.
How to write a polynomial in standard form?A polynomial can be written in standard form by writing its terms in descending order of their powers and the constant terms comes at the end.
The given polynomial is (x - 1)(3x² + 7x + 5).
It can be written in standard form as follows,
(x - 1)(3x² + 7x + 5)
= x(3x² + 7x + 5) - 1(3x² + 7x + 5)
= 3x³ + 7x² + 5x - 3x² - 7x - 5
= 3x³ - 3x² - 2x - 5
Hence, the given expression can be written in standard form as,
3x³ - 3x² - 2x - 5
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Need help asap now please!!!!!!!!
Answer:
C. 150
Step-by-step explanation:
Divide 1,350 by 9, which gives you 150 (with no remainders)
Answer:
150
Step-by-step explanation:
1350 divided by 9
the mean score of 888 players in a basketball game was 14.514.514, point, 5 points. if the highest individual score is removed, the mean score of the remaining 777 players becomes 121212 points. what was the highest score?
The highest score is 32 points.
Given,
Mean score of 8 players =14.5
After removing highest score then,
Mean score of 7 players =12
let
the sum of all score be 'x'
highest score be 'y'
At first,
[tex]Mean=\frac{sum\ of\ all\ scores}{total\ number\ of\ scores}\\\\14.5=\frac{x}{8}\\\\x=116[/tex]
after removing the highest score, mean will be
[tex]Mean=\frac{sum\ of\ all\ scores-highest\ score}{number\ of\ scores}\\\\12=\frac{x-y}{7}\\\\x-y=84[/tex]
substituting 'x'
[tex]116-y=84\\\\116-84=y\\\\y=32[/tex]
Thus, the highest score is 32 points.
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a sample of 1600 computer chips revealed that 42% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature claimed that above 39% do not fail in the first 1000 hours of their use. is there sufficient evidence at the 0.10 level to support the company's claim? state the null and alternative hypotheses for the above scenario.
Reject this null hypothesis because the p-value (0.0523) is lower than the significance level (0.10) in this case.
Explain the term Null hypothesis?The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data or measured phenomena for any given single observed variable.Let p represent the fraction of the population.
Taking into account the provided data, we have
Null hypothesis: H0 : p ≤ 0.35.
Alternative hypothesis: H1 : p > 0.35, the test is a right-tailed test since the alternative is right-tailed;
For the stated question-
n = 1000; p' = 0.42.
Test statistics for this sample proportion:
z = (p' - p) / √p(1 - p)/n
Put the values-
z = (0.42' - 0.39) / √0.39(1 - 0.39)/1000
z = 1.94
P-value for this right tailed test is;
P(z > 1.94) = 0.0523
Therefore reject this null hypothesis because the p-value (0.0523) is lower than the significance level (0.10) in this case.
We draw the conclusion that we have enough data to back up the company's claim at the 0.10 level.
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in a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. if 10 boys and 14 girls are competing, how many different ways could the six medals possibly be given out?
answer: 72 or 1572480 depends on how you do the math
according to a recent survey 85 percent of high school students own a personal media player. what is the probability that 6 out of 10 random highschool students own a personal media player
The probability is 0.04.
Define probability sampling.
The sampling probability of an element or member of the population in statistics, in the theory relating to sampling from finite populations, is its likelihood of being included in the sample during the drawing of a single sample.
Probability sampling refers to the selection of a sample from a population when this selection is based on the principle of randomization, that is, random selection or chance. When compared to non-probability sampling, probability sampling is more difficult, time-consuming, and typically more expensive.
Solution Explained:
Given,
x = 7, n = 10, p = 0.85 and q = 0.15
Using the formula,
P(X=6) = [tex]_{n}C_{x} (0.85)^{n} (0.15)^{x}[/tex]
= [tex]_{10}C_{6} (0.85)^{6} (0.15)^{4}[/tex]
= 210(0.377)(0.0005)
= 0.04
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Data Island is a beautiful beach resort. It has been a premier touristic destination for over 80 years, and the earliest holiday homes have been built just a few steps away from the beach itself. You work for a real estate agency that sells and rents holiday homes in Data Islands. Recently, one of the interns working on the Data Science Team presents you a report. According to the linear regression model they have run, the price of a house is proportional to its age. But this does not make any sense: after all, newer houses should be worth more.
1. Comment the regression output, noticing that the Sig. column is reporting the p-value of the coefficient. What can you tell about the sign of Age’s slope?
2. Why do you think the model forecasts an higher price for old holiday homes? Think carefully about all the information you have concerning Data Island.
3. Assuming that more data and variables are available, what would you suggest your intern to do to fix their report?
A lovely beach resort is Data Island. Since it first became a popular tourist destination more than 80 years ago, the earliest vacation homes have been constructed just a few steps from the beach. You are a real estate agent for a company that deals in vacation rentals and sales in the Data Islands. A report was recently presented to you by one of the interns on the data science team. The age of a house affects its price, according to the linear regression model they have ran. But this is absurd because newer homes ought to be more valuable.
1. As the coefficient of Age is positive, so the older the house, the more price it is. Sig. (or p-value) = 0.000 which implies that the co-efficient of Age is significant.
2. This may be that the people who live there are reluctant to sell it, so they quote a higher price or the size of old houses are large or they may be located at prime location.
3. We would ask new interns to consider other independent variables for the regression equation like size of house, location, etc.
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samantha is considering job offers from two companies. company a offered her a starting salary of $48,000 with a $2100 raise at the end of each year. company b offered her a starting salary of $48,000 with a 3.7% raise at the end of each year.
Let f(t) represent Rosa's salary at Company A, t years after accepting a position at Company A, and let g(t) represent Rosa's salary at Company B t years after accepting a position at Company B.
Complete the table of values below:
t f(t) g(t)
0 50000 50000
1
2
3
The value of f(t) are 48000, 52200, 54300, 56400, and g(t) are 48000, 49776, 51617.71, and 53527.56.
She was given a starting wage of $48,000 from Company A, with annual raises of $2100.
The formula for Company A is
f(t) = 48000 + 2100t
She was given a starting wage of $48,000 from Company B, with an annual rise of 3.7%.
The formula for Company B is
g(t) = 48000 × [tex](1 + 0.037)^t[/tex]
The value of f(t) and g(t),
t ------- f(t) ------- g(t)
0 ----- 48000 ----- 48000
1 ------ 52200 ----- 49776
2 ----- 54300 ----- 51617.71
3 ----- 56400 ----- 53527.56
The graphical representation of both the linear equations of company A and company B.
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The dimensions of a box have been doubled. How many times greater is the volume of the box?
8, 6, 4, or 2
Answer:
The volume increases 8-fold or by 700%.
Step-by-step explanation:
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at a deli counter, there are 9 sandwiches with meat and 10 vegetarian sandwiches. dante is at the counter buying sandwiches for a picnic. in how many ways can he choose 9 sandwiches if 8 or more must be vegetarian sandwiches?
There are two different ways in which he can choose 9 sandwitches. It can be solve by the concept of permutation and combination.
What is permutation and combination?
A permutation is an arrangement of several items taken one at a time or all at once in a specific order.
Combinations are based entirely on grouping. Combinations can be used to determine how many different groups that can be created from the available items.
Since all vegitarian sandwiches looks like same and all sandwitches with meat looks like same hence, their order will not affect the number of choice.
If 8 sandwitches are vegitarian then 1 sandwitch must be with meat. So that total sandwithches becomes 9.
If all 9 sindwitches are vegetarian then there is no option to choose another sandwitch. Because he can choose only 9 sandwitches.
Hence, there are two different ways in which he can choose 9 sandwitches.
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x + 2y = -6
6x +2y =4
Step-by-step explanation:
um, I'm going to use elimination method to solve this simultaneous equation
x+2y=-6.......... equation 1
6x+2y=4........ equation 2
subtract equation 2 from equation 1
-5x = -10
x = -10/-5
x=2
substitute x=2 in equation 1
therefore equation 1 becomes
2+2y=-6
2y=-6-2
2y=-8
y=-8/2
y=-4
C. If this is Thursday, then I do not go to church.
Converse:
Inverse:
Contrapositive:
I need help trying to find the area of this triangle please help.
Answer:
28 ft²
Step-by-step explanation:
You want the area of a triangle with a base of 7' and a height of 8'.
Area formulaThe formula for the area of a triangle is ...
A = 1/2bh
where b is the base of the triangle, and h is the height perpendicular to the base.
Here, it is convenient to use the side marked 7' as the base of the triangle. The distance marked 8' is the perpendicular distance from the base to the top of the triangle. So, the area is ...
A = 1/2(7 ft)(8 ft) = 28 ft²
The area of the triangle is 28 square feet.
__
Additional comment
As you can see, the vertex opposite the base does not need to lie above the base segment. All that matters is the perpendicular distance from that vertex to the base line.
You make a total of 16 two-point and three-point shots in a basketball game. You score a total of 35 points. Which system can be used to find the number p of two-point shots and the number q of three-point shots you make? Responses p+q=35 2p+3q=16 p plus q is equal to 35, , 2 p plus 3 q is equal to 16, p+q=16
2p+3q=16 and p+q=35 are system of equations used to find the number p of two-point shots and the number q of three-point shots you make
What is Equation?Two or more expressions with an Equal sign is called as Equation.
We need to find the number p of two-point shots and the number q of three-point shots you make.
a total of 16 two-point and three-point shots in a basketball game.
2p+3q=16
Total score is of 35 points.
p+q=35
These two equations 2p+3q=16 and p+q=35 can be used to find the number p of two-point shots and the number q of three-point shots you make.
Hence, 2p+3q=16 and p+q=35 are system of equations used to find the number p of two-point shots and the number q of three-point shots you make
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one sample has n = 8 scores and m = 2. a second sample has n = 4 and m = 8. if the two samples are combined, then what is the mean for the combined sample?
The combined sample mean for sample one, whose size equals 8 scores and mean equals 2, and for sample second, whose size equals 4 scores and mean equals 8, is 4..
A combined sample mean is calculated by taking the mean of each group and combining (adding) the results of each average.
We have given that,
For First sample :
Sample size ,n₁ = 8 scores
sample mean, m₁ or X₁-bar = 2
Sample 2 :
Sample size, n₂ = 4
sample mean , m₂ or X₂-bar = 8
Combined sample mean is given by,
M or X-bar =( n₁× x₁-bar + n₂ × x₂-bar)/(n₁+n₂)
plug all the known values in above formula
=> M = (8×2 + 4×8 )/12
=> M = 48/12 = 4
Hence, combined sample mean is 4 .
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Which of the following options have the same value as 60% and 94?
A: 0.06⋅94
B: 0.6⋅94
C: 5/3⋅94
D: 60⋅94
E: 60/100⋅94
Answer:
0.6 x 94
Step-by-step explanation:
You can convert 60% into a decimal, by moving the decimal place twice to the left, and it will still be the same. So, we have 0.60. Then, usually the term "and" means addition, but that is not in one of the answers, so I suppose they mean multiplication. So, we can set up this equation:
0.6 x 94
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Find the values of the variables in each parallelogram
Adjacent angles of a parallelogram are supplementary.
[tex]x+2x=180 \\ \\ 3x=180 \\ \\ x=\boxed{60}[/tex]
dominic has a family history of hypertension. according to the chronic disease risk reduction intakes (cdrr) for sodium, dominic should lower or maintain his sodium intake to below mg/day to reduce his risk of chronic disease, including hypertension
Dominic should lower or maintain his sodium intake to below 2,300 mg/day.
Chronic disease :The Chronic Disease Risk Reduction (CDRR) consumption of 2,300 mg/day was recently developed due to connections between high sodium intake and the risk of hypertension. It is anticipated that sodium intake below this level will lower the risk of chronic diseases.
Adults may be at risk for chronic diseases if their sodium intake exceeds their CDRR intake. The population's cardiovascular health may be improved by efforts to reduce sodium consumption. Among healthy individuals, lowering daily sodium intake to CDRR is anticipated to lower the risk of developing chronic diseases, primarily by lowering blood pressure.
Hence, sodium intake to below 2,300 mg/day can reduce his risk of chronic disease.
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