a. The probability of all girls in a family with four children is 1/16 or 0.0625.
b. The probability of all girls given there is at least one girl is 1/15 or 0.0667.
c. The probability of having at least one boy and one girl in a family with four children is 15/16 or 0.9375.
a. To calculate the probability of all girls, we need to consider the possible outcomes of each child being a girl. Since each child has an independent probability of being a girl or a boy, the probability of all girls is (1/2) * (1/2) * (1/2) * (1/2) = 1/16 or 0.0625.
b. Given that there is at least one girl, we have three remaining children. The probability of all girls among the three remaining children is (1/2) * (1/2) * (1/2) = 1/8. Therefore, the probability of all girls given there is at least one girl is 1/8 divided by the probability of having at least one girl, which is 1 - (1/2)⁴ = 15/16, resulting in a probability of 1/15 or approximately 0.0667.
c. The probability of having at least one boy and one girl can be calculated by subtracting the probability of having all boys from the total probability space. The probability of having all boys is (1/2)⁴ = 1/16. Therefore, the probability of having at least one boy and one girl is 1 - 1/16 = 15/16 or approximately 0.9375. This probability accounts for all possible combinations of boys and girls in a family with four children, excluding the scenario of having all boys.
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If the perimeter of a rectangle is 24 cm and one dimension is 10 cm, what is the area?
Answer:
40
Step-by-step explanation:
Answer:
24-10-10=4
4/2=2
10*2=20
20Step-by-step explanation:
If p(x)= 2^x, what is the value of p(3) - p(2)?
Answer:
4
Step-by-step explanation:
p(3) = 2³ = 8
p(2) = 2² = 4
8-4 = 4
PLEASE HELP ME ASAP I SWEAR IT WOULD BE A BIG HELP.
Jethro has sat 5 tests.
Each test was marked out of 100 and Jethro's mean mark for the 5 tests is 74
Jethro has to sit one more test that is also to be marked out of 100
Jethro wants his mean mark for all 6 tests to be at least 77
Work out the least mark that Jethro needs to get for the last test.
This paper will discuss the mathematics involved in determining the least mark that Jethro needs to get for the last test in order to end up with a mean mark of 77 over all 6 tests.
Jethro has sat 5 tests and each test was marked out of 100. Therefore, Jethro’s marks for the 5 tests can be represented by x1, x2, x3, x4, and x5. Jethro’s mean mark for the 5 tests is 74, which can be represented by the mathematical equation: (x1 + x2 + x3 + x4 + x5) / 5 = 74.
Jethro needs to sit one more test that is also marked out of 100 and he wants his mean mark for all 6 tests to be at least 77. Therefore, the least mark that Jethro needs to get for the last test can be found by rearranging the equation to: (x1 + x2 + x3 + x4 + x5 + x6) / 6 = 77. This can be written in its simplified form as: 6x6 = 77(x1 + x2 + x3 + x4 + x5).
In order to find the least mark that Jethro needs to get for the last test, x6, the other terms must be known. Since Jethro has already sat the 5 tests the marks for these tests are known, so they can be added together. This results in: x6 = 77(x1 + x2 + x3 + x4 + x5) / 6. Therefore, Jethro needs to get a mark of at least 77.6 (rounded to the nearest tenth) on the last test in order to end up with a mean mark of 77.
Dubnium-262 has a half-life of 34 s. How long will it take for 500.0 grams to
decay to just 1.0 g? *
Answer:
the time taken for the radioactive element to decay to 1 g is 304.8 s.
Step-by-step explanation:
Given;
half-life of the given Dubnium = 34 s
initial mass of the given Dubnium, m₀ = 500 grams
final mass of the element, mf = 1 g
The time taken for the radioactive element to decay to its final mass is calculated as follows;
[tex]1 = 500 (0.5)^{\frac{t}{34}} \\\\\frac{1}{500} = (0.5)^{\frac{t}{34}}\\\\log(\frac{1}{500}) = log [(0.5)^{\frac{t}{34}}]\\\\log(\frac{1}{500}) = \frac{t}{34} log(0.5)\\\\-2.699 = \frac{t}{34} (-0.301)\\\\t = \frac{2.699 \times 34}{0.301} \\\\t = 304.8 \ s[/tex]
Therefore, the time taken for the radioactive element to decay to 1 g is 304.8 s.
The time required to decay 500 grams to 1 gram is 304.8 seconds and this can be determined by using the given data.
Given :
Dubnium-262 has a half-life of 34 s.
Final mass = 1 gram
Initial mass = 500 gram
Time taken by a radioactive element to decay is:
[tex]1 = 500(0.5)^{\frac{t}{34}}[/tex]
Simplify the above equation.
[tex]\rm \dfrac{1}{500} = (0.5)^{\frac{t }{34}}[/tex]
Now, take the log on both sides in the above equation.
[tex]\rm log(0.002 ) = \dfrac{t}{34}\times log(0.5)[/tex]
[tex]\rm \dfrac{log(0.002)}{log(0.5)} \times 34 = t[/tex]
t = 304.8 sec
So, the time required to decay 500 grams to 1 gram is 304.8 seconds.
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Stop and Shop sells 6 cases of Pepsi for $21.60. What is the constant of proportionality?
Answer: $3.60 per case
Step-by-step explanation: $21.60 divided by 6 = 3.60
Prove the following is equivalent: n* (n-1 C 2) = nC2 * (n − 2) .
The equivalence of the expressions n × ([tex]{}^{(n-1)}C_2[/tex]) and [tex]{}^nC_2[/tex] × (n − 2) has been proven mathematically.
To prove the equivalence of the expressions n × ([tex]{}^{(n-1)}C_2[/tex]) and [tex]^{n}C_2[/tex] × (n − 2), we can demonstrate that they yield the same result.
First, let's simplify each expression:
n × ([tex]{}^{(n-1)}C_2[/tex]) = n × [(n-1)! / 2!(n-1-2)!]
= n × [(n-1)! / 2!(n-3)!]
= n × [(n-1)(n-2) / 2]
= n × (n² - 3n + 2) / 2
= (n³ - 3n² + 2n) / 2
[tex]{}^nC_2[/tex] × (n − 2) = [n! / 2!(n-2)!] × (n-2)
= [n! / 2!(n-2)!] × (n-2)
= [(n)(n-1)(n-2)! / 2!(n-2)!] × (n-2)
= [(n)(n-1)] / 2
= (n² - n) / 2
By comparing the two simplified expressions, we can see that (n³ - 3n² + 2n) / 2 is equal to (n² - n) / 2.
Hence, we have proven that n × ([tex]{}^{(n-1)}C_2[/tex]) is equivalent to [tex]{}^nC_2[/tex] × (n − 2).
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Find the mean of the following probability distribution? Round your answer to one decimal.
x 0,1,2,3,4
P(x) 0.0017, 0.3421, 0.065, 0.4106, 0.1806
mean = ___
The mean of the given probability distribution is 2.4.
To find the mean of a probability distribution, we multiply each value of x by its corresponding probability and then sum them up. Using the provided data:
x: 0, 1, 2, 3, 4
P(x): 0.0017, 0.3421, 0.065, 0.4106, 0.1806
mean = 0(0.0017) + 1(0.3421) + 2(0.065) + 3(0.4106) + 4(0.1806)
= 0 + 0.3421 + 0.13 + 1.2318 + 0.7224
= 2.4263
Therefore, the mean of the given probability distribution is approximately 2.4 (rounded to one decimal place).
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Please help me finish this i will give brainlest :) to the first person.
Answer: 8
Step-by-step explanation:
64 ÷[4* 27 (-5^2
-5 times -5 =25
27-25=2
4*2=8
64 divided by 8= 8
8 is your answer
What is your dream career and why ?
Answer:
Step-by-step explanation:
Professional dancers cause I’ve danced since I was 3 and I’ve always wanted to do it. And I wanna model on the side
Answer:
Detective/Forensics scientist
Step-by-step explanation:
I want to be a detective/ forensic scientist because I am interested in science and investigating.
Type the correct answer in each box. If necessary, use / for the fraction bar(s).
Find the solution for this system of equations.
12x + 15y = 34
-6x + 5y = 3
Answer:
x=5/6 and y=8/5
(5/6 , 8/5)
Step-by-step explanation:
You can use the elimination method! The point of this method is to add or subtract one equation from the other, multiplying them by constants if necessary, to cancel out one variable so you can solve for the other. Then, you can plug the value you got for your solution into either equation to solve for the other. I'll demonstrate.
Look at the two equations and the coefficients of both variables. You have 12x and -6x -- 6*2=12, so this is perfect. (You could also eliminate the y because 5*3=15, but I'll show you by eliminating the x instead.)
Here's what that looks like:
(-6x+1y=3)2
-12x+10y=6
So we just multiplied the second equation by 2 on both sides. Let's see how that helps us.
12x+15y=34
-12x+10y=6
If we add the two equations now, x will be canceled out and we can solve for y.
12x+15y=34
+(-12x+10y=6)
___________
0x+25y=40
25y=40
0x=0, so we can get rid of the x. Now, we need to solve for y.
25y=40
y=40/25
You probably know how to simplify fractions, so divide both the numerator and the denominator by 5 to get y=8/5.
Now you can use this value in either equation and solve for x. I'll use the first. (This is called substitution.)
12x+15(8/5)=34
12x+3(8)=34 <-- What I did here is cancel out the 5 in the denominator with 15 to leave 3, because 5*3=15.
12x+24=34
12x=10
x=10/12
x=5/6 (Divide the numerator and denominator by 2.)
You can write your answer as a point, too. (5/6 , 8/5)
The average American consumes 81 liters of alcohol per year. Does the average college student consume more alcohol per year? A researcher surveyed 10 randomly selected college students and found that they averaged 97.7 liters of alcohol consumed per year with a standard deviation of 23 liters. What can be concluded at the the α = 0.01 level of significance?
The α = 0.01 level of significance, we can conclude that the average alcohol consumption of college students is significantly higher than that of the average American population.
To determine if the average alcohol consumption of college students is significantly different from the average consumption of the average American, we can conduct a hypothesis test.
Let's set up the hypotheses:
Null hypothesis (H0): The average alcohol consumption of college students is equal to the average American consumption. (μ = 81)
Alternative hypothesis (H1): The average alcohol consumption of college students is greater than the average American consumption. (μ > 81)
We can use a one-sample t-test to analyze the data. Since we don't have information about the population standard deviation, we'll use the t-distribution and the sample standard deviation instead.
Given that the sample mean (x) of the 10 randomly selected college students is 97.7 liters and the sample standard deviation (s) is 23 liters, we can calculate the t-statistic using the following formula:
t = (x - μ) / (s / √n)
Where:
x = sample mean
μ = population mean
s = sample standard deviation
n = sample size
Plugging in the values, we get:
t = (97.7 - 81) / (23 / √10)
Calculating this expression gives us the t-value.
However, we also need to determine the critical value for the test based on the significance level (α = 0.01) and the degrees of freedom = n - 1.
Since we have 10 randomly selected college students = 10 - 1 = 9.
To find the critical value, we can consult the t-distribution table. With α = 0.01 and df = 9, the critical t-value is approximately 2.821.
Comparing the calculated t-value to the critical t-value, we can draw a conclusion. If the calculated t-value is greater than the critical t-value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
Now let's calculate the t-value:
t = (97.7 - 81) / (23 / √10)
≈ 16.700
Since the calculated t-value (16.700) is much greater than the critical t-value (2.821), we can reject the null hypothesis.
Therefore, based on the given data and the α = 0.01 level of significance, we can conclude that the average alcohol consumption of college students is significantly higher than that of the average American population.
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The mean score in a physics test is 75% with the standard deviation 6.5%. Suppose that the scores in the test are approximately normally distributed. What is the probability that a randomly selected student scores more than 82%? Round your answer for 4 decimal places.
__________
The probability that a randomly selected student scores more than 82% on the physics test, we can use the standard normal distribution and the given mean and standard deviation.
The z-score formula is given by z = (x - μ) / σ, where z represents the z-score, x is the observed value, μ is the mean, and σ is the standard deviation. In this case, the observed value is 82%, the mean is 75%, and the standard deviation is 6.5%. Plugging these values into the formula, we calculate the z-score as z = (0.82 - 0.75) / 0.065 = 1.0769.
Next, we need to find the area to the left of the z-score in the standard normal distribution table or using a calculator. The area to the left of 1.0769 corresponds to the probability of scoring less than 82%. Let's assume this area is P(z < 1.0769).
The probability of scoring more than 82%, we subtract P(z < 1.0769) from 1: P(z > 1.0769) = 1 - P(z < 1.0769).
Using a standard normal table or a calculator, we can find P(z < 1.0769) to determine the probability.
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Which figure can be formed from the net?
Answer:
#1 is the answere
Step-by-step explanation:
Check the sides
Should i trust the links people say "Their is an imagine in this link that contains the answer" usually these links are from sus profiles. So should i use it or no?
Answer:
no don't ever click on links okay.
Step-by-step explanation:
Martina runs 6 miles in 50 minutes. At the same rate, how many miles would she run in 35 minutes?
Answer:
4.2 miles
Step-by-step explanation:
Martina runs 6 miles in 50 minutes, we have to find the rate at which she is running. Put it in a fraction [tex]\frac{6}{50}[/tex] or she runs 6 miles every 50 minutes. When we divide we get that she is running, 0.12 miles evrey minute. The question askes us how far Matina will run in 35 minutes, so we multiply 0.12 by 35, and we get that she will run 4.2 miles.
A person visits the store and picks up five kg vegetables for did he buy?
£6.25. Which vegetable
Tomato - £1.50 per kg Carrot - £1.75 per kg Cabbage - £2 per kg Beetroot - £1.25 per kg
what steps do i take to prove this? i have a few more
Answer:
They are opposite angles. If you rotate the figure SQM 180 degrees counter clockwise, they will be the exact same triangle and therefore the exact same measure.
Step-by-step explanation:
MARKING BRAINLIEST TO FIRST PERSON WHO IS CORRECT!
I need help with #13
Answer:
True
False
False
Step-by-step explanation:
Suppose you invest $188.00 in an account earning 2.80% APR. When will you have one million dollars in the account? Round your answer to two decimal places, i.e. 5.45
Answer: You will have one million dollars in the account after approximately 84.89 years.
APR is a yearly percentage rate that reflects the actual cost of borrowing on loans and investments. The APR is the rate of interest that must be charged on the balance of a savings account to attain a certain goal in the specified time period. The formula for compound interest is used in this case. The formula for compound interest is:A=P(1+r/n)^(nt)Where: A = amount P = principal (initial amount) r = annual interest rate (as a decimal) n = number of times interest is compounded per year t = number of years In this scenario: A = $1,000,000P = $188.00r = 0.028n = 1 (compounded once per year)t = unknown. Now let's solve for t:1,000,000 = 188(1 + 0.028/1)^(1t)ln (5,319.15) = t ln (1.028) ln (5,319.15) = 0.028t84.89 years = t Therefore, it will take approximately 84.89 years to reach one million dollars in the account.
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Hello!
What's Eri's teddys name?
Answer:
Werid I don’t know
Step-by-step explanation:
What is the value of x in the equation below?
12 – 2(x-1)=6
Factor 9z^2 - 6x +1.
pls will mark you brainiest
Answer:
It is not factorable
Step-by-step explanation:
The expression is not factorable with rational numbers.
Answer:
This is not factorable.
Step-by-step explanation:
This is not factorable.
Rewrite the expression in the form x^n
Answer:
[tex]x^{\frac{5}{3} }[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} *\frac{5}{2} \\\\\frac{5}{3}[/tex]
A recent stocktake measured the price of BBQs at a large hardware store. From the stocktake, it was determined that the price was normally distributed with a mean of 500 dollars and a standard deviation of 50 dollars. Twenty per cent of the BBQs would cost more than what price? Select from the answers below.
575.5
542
526
459
The price at which twenty percent of the BBQs would cost more is $542 and it follows a normal distribution.
In this case, we are given that the price of BBQs at a large hardware store follows a normal distribution with a mean of $500 and a standard deviation of $50. We want to find the price at which twenty percent of the BBQs would cost more.
To solve this problem, we need to find the value, denoted as x, for which 20% of the BBQs are priced higher. This can be done by finding the z-score corresponding to the 20th percentile and then converting it back to the original scale.
The z-score is calculated using the formula:
z = (x - μ) / σ,
where μ is the mean and σ is the standard deviation.
To find the z-score corresponding to the 20th percentile, we can use a standard normal distribution table or a statistical calculator. The z-score corresponding to the 20th percentile is approximately -0.84.
Now we can use the z-score to find the corresponding value in the original scale:
-0.84 = (x - 500) / 50.
Solving for x, we get:
-0.84 * 50 = x - 500,
-42 = x - 500,
x = 500 - 42,
x = 458.
So, twenty percent of the BBQs would cost more than $458. However, since we need to choose from the given options, the closest price to $458 is $459.
Therefore, the answer is $459.
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Please Help 8th Grade math!!!!!!! only anwser 9
it's 40.00 beacuase justo subtract
9514 1404 393
Answer:
Chris's gym charges more
Step-by-step explanation:
The difference between 2 rentals and 1 rental at Chris's gym is ...
$55.50 -52.75 = $2.75 . . . . cost of court rental at Chris's gym
This $2.75 cost at Chris's gym is higher than the corresponding $2.00 cost at Tyrell's gym.
Chris's gym charges more to reserve the basketball courts.
Based on meteorological records the probability that it will snow in a certain town on January 1st is 0.185. Find the probability that in a given year it will not snow on January 1st in that town rack Dic 0.815 0.227 ack Die 5.405 1.185 ack Die
The probability that it will not snow on January 1st in that town in a given year is 0.815.
Based on the meteorological records, A probability forecast includes a numerical expression of uncertainty about the quantity or event being forecast. Ideally, all elements (temperature, wind, precipitation, etc.)
The probability that it will not snow in a certain town on January 1st in a given year is 0.815. Here's how to arrive at the answer:Given that the probability of snowing on January 1st in that town is 0.185. Then, the probability of not snowing on January 1st is 1 - 0.185 = 0.815.
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The given information probability of it not snowing on January 1st of a given year in that town is 0.815.
Therefore, the probability of it not snowing on January 1st of a given year in that town is 0.815.
Here's how to solve the problem: Given: The probability of it snowing on January 1st of a given year in that town is 0.185. The complement of the probability of it snowing on January 1st is the probability of it not snowing on January 1st of a given year in that town, which is:
P(not snowing on January 1st) = 1 - P(snowing on January 1st)
P(not snowing on January 1st) = 1 - 0.185
P(not snowing on January 1st) = 0.815
Therefore, the probability of it not snowing on January 1st of a given year in that town is 0.815.
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In the lexicographic ordering of the permutations of the set {A,B,C,D,E,F,G,H} , what is the next permutation after GAEDBHFC? (Assume the usual alphabetic order of letters.)
a. HAEFBDCG b. GAEDCBFH c. DEHBFGCA d. None of the other answers is correct. e. FDAEGBCH
In the lexicographic ordering of the permutations of the set {A,B,C,D,E,F,G,H} , the next permutation after GAEDBHFC will be GAEDBHFD.
What is lexicographic ordering?
Lexicographic ordering or dictionary ordering is a way of ordering elements based on their alphabetical or numerical values.
To find the next permutation in the lexicographic ordering, we need to find the smallest possible permutation that is greater than GAEDBHFC by considering the order of the letters.
Let's analyze the given permutation:
GAEDBHFC
To find the next permutation, we start from right to left and look for the first occurrence of a letter that can be replaced by a greater letter. In this case, the first such occurrence is "C" (after "H").
Next, we need to find the smallest letter that is greater than "C" from the remaining letters. From the letters {C, D, E, F, G, H}, the smallest greater letter than "C" is "D".
Now, we swap "C" with "D":
GAEDBHFD
After swapping, we need to sort the remaining letters in ascending order to obtain the smallest permutation. The remaining letters are {B, E, F, G, H}. Sorting them gives:
GAEDBHFD
Therefore, the next permutation after GAEDBHFC is GAEDBHFD.
The correct answer is:
b. GAEDBHFD
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Find the potential function f for the field F.
F = -1/x i+1/y j-1/z k
The potential function for the given field is f = ln |y| - ln |z| - ln |x| + C, where C is a constant of integration.
Given field is F = (-1/x) i+ (1/y) j- (1/z) k
The potential function f is given by
∂f/∂x = -1/x .........(1)∂f/∂y = 1/y .........(2)∂f/∂z = -1/z .........(3)
Using the equation (1)
we get
f = -ln |x| + C1
Using the equation (2)
we get
f = ln |y| + C2
Using equation (3) we get
f = -ln |z| + C3
On adding the above three equations we get
f = ln |y| - ln |z| - ln |x| + C
where C = C1 + C2 + C3 is a constant of integration.
Therefore, the potential function for the given field is f = ln |y| - ln |z| - ln |x| + C, where C is a constant of integration.
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answer easy question quick
Answer:
Step-by-step explanation:
a) 9.80- 98/10
b) 7.3- 73/10
a) 7/100- 0.07
b) 82/10- 8.2
Hope this helps
Fraction:
a) 98/100
b) 73/10
Decimal:
a) 0.07
b) 8.2
Hey I'm Chloe Can you Help Me, I will give Brainlest, Thank you :)
Stefan sells Jin a bicycle for $104 and a helmet for $17. The total cost for Jin is 110 % of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Answer:
Stefan spent 108.9$ and made 12.1$
Step-by-step explanation:
Hey I'm Aiden I can help you, I will take Brainlest, Your welcome :)
take 10% of 121 and subtract it from 121 and you get the price he paid and made