Find the probability of getting exactly 6 girls in 8 births.
The probability of having exactly [tex]6[/tex] girls in [tex]8[/tex] birth is [tex]\boxed{\bf 0.10937}[/tex].
Further explanation:
Concept used:
The probability of an event [tex]E[/tex] is calculated as follows:
[tex]\boxed{P(E)=\dfrac{n(E)}{n(S)}}[/tex]
Here, [tex]n(E)[/tex] is the number of favorable outcomes in an event [tex]E[/tex] and [tex]n(S)[/tex] is the number of element in sample space [tex]S[/tex].
The probability of exactly [tex]r[/tex] success in [tex]n[/tex] trial is expressed as follows:
[tex]\boxed{P(F)=^{n}C_{r}p^{r}q^{n-r}}[/tex]
Here, [tex]r[/tex] is the probability of success in an event and [tex]q[/tex] is the probability of failure.
Calculation:
Consider [tex]A[/tex] as an event of having a girl in first birth and [tex]P(A)[/tex] as the probability of event [tex]A[/tex].
The probability of having a girl is [tex]P(A)=\frac{1}{2}[/tex].
Assume that [tex]A'[/tex] is the complement event of an event [tex]A[/tex] and [tex]P(A')[/tex] is the probability of complementary event [tex]A'[/tex].
The event is the event of not having a girl in the first birth.
The probability of event [tex]A'[/tex] is calculated as follows:
[tex]\boxed{P(A')=1-P(A)}[/tex] …… (1)
Substitute [tex]P(A)=\frac{1}{2}[/tex] in the equation (1) to obtain the probability of event [tex]A'[/tex].
[tex]\begin{aligned}P(A')&=1-\dfrac{1}{2}\\&=\dfrac{1}{2}\end{aligned}[/tex]
The probability of having exactly [tex]6[/tex] girls in [tex]8[/tex] birth is calculated as follows:
[tex]\begin{aligned}P(F&)=^{8}C_{6}\left(\dfrac{1}{2}\right)^{6}\left(\dfrac{1}{2}\right)^{8-6}\\&=\dfrac{8!}{6!\cdot 2!}\cdot (0.5)^{6}\cdot (0.5)^{2}\\&=28(0.5)^{8}\\&=0.10937\end{aligned}[/tex]
Thus, the probability of having exactly [tex]6[/tex] girls in [tex]8[/tex] birth is [tex]\boxed{\bf 0.10937}[/tex].
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Answer details:
Grade: Senior school
Subject: Mathematics
Chapter: Probability
Keywords: Probability, exact event, sample space, number of element, complement event, success, failure, favorable, trial, P(E)=n(E)/n(S), P(A')=1-P(A).
Final answer:
To find the probability of getting exactly 6 girls in 8 births, we use the binomial probability formula. In this case, the probability is approximately 0.01.
Explanation:
To find the probability of getting exactly 6 girls in 8 births, we can use the binomial probability formula:
P(x = 6) = C(n, x) * pˣ * (1-p)(n-x)
Where:
C(n, x) is the binomial coefficient, which represents the number of ways to choose x objects from a set of n objects.p is the probability of success (in this case, the probability of having a girl) in a single trial. n is the number of trials (in this case, the number of births).x is the desired number of successes (in this case, the desired number of girls).In this particular case, P(x = 6) = C(8, 6) * (0.5)⁶ * (0.5)(8-6) = 28 * 0.015625 * 0.015625 = 0.009765625, or approximately 0.01.
153 inches to 19 feet
5/6 ( 3/8 - x ) = 16
The value of x on solving the equation 5/6 (3/8 - x) = 16 is - 251 / 5.
What is the equation?In other terms, it is a mathematical statement stating that "this is equivalent to that." It appears to be a mathematical expression on the left, an equal sign in the center, and a mathematical expression on the right.
Given:
5/6 (3/8 - x) = 16
Solve the above equation as shown below,
Use the distributive property to solve the equation,
5 / 6 × 3 / 8 - 5 / 6 x = 16
15 / 48 - 5 / 6 x = 16
5 / 16 - 5 / 6 x = 16
5 / 6 x = 5 / 16 - 16
5 / 6x = -251 / 16
x = -251 / 16 × 6 / 5
x = - 251 / 5
Thus, the value of x is - 251 / 5.
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Kyle is six years older than Melissa. Nine years ago he was twice Melissa's age. How old is Kyle now?
Final answer:
Kyle is currently 21 years old. This was determined by setting up equations based on the information given and solving for Melissa's age first, which allowed us to find Kyle's age.
Explanation:
We are given that Kyle is six years older than Melissa. Also, nine years ago, he was twice her age. Let's represent Melissa's current age as M and Kyle's current age as K.
From the first piece of information, we can formulate the following equation:
1) K = M + 6
From the second piece of information, we get:
2) K - 9 = 2 * (M - 9)
Now, we substitute the expression from equation 1 into equation 2:
(M + 6) - 9 = 2 * (M - 9)
M - 3 = 2M - 18
After simplifying the equation, we find Melissa's current age:
M = 15
Using equation 1, we then calculate Kyle's current age:
K = 15 + 6
K = 21
Hence, Kyle is currently 21 years old.
The table shows the cost of a ski rental package for a given number of people. People Cost ($) 4 160 5 200 6 240 7 280 The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation.
The difference between the number of customers in line at the express checkout and the number in line at the superexpress checkout is x1 − x2. calculate the expected difference.
Solve the exponential equation. 2x = 1/2
Options: -1
-1/2
1
The exponential equation, 2ˣ = 1/2, has a value of -1.
What is an exponential equation?Exponential equations are equations in which variables occur as exponents.
Given is an exponential equation, 2ˣ = 1/2, we need to solve it,
2ˣ = 1/2
Taking ㏒ both the side,
㏒ 2ˣ = ㏒ 1/2
x ㏒ 2 = ㏒ 0.5
x = -0.301029996 / 0.301029996
x = -1
Hence, the exponential equation, 2ˣ = 1/2, has a value of -1.
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If ying zyiyu covered the first 200 miles of a trip going at 50 mph and the last hundred miles going at 40 mph, what was his average speed for the entire trip? Teacher told me it is not 45
The average speed of ying zyiyu is [tex]46.15\;\rm{mph}[/tex]
Average speed is the ratio of the total distance traveled by a body to the total time taken by the body to cover the total distance.
Here, ying zyiyu covered the first [tex]200\;\rm miles[/tex] of the trip at [tex]50\;\rm mph[/tex] so,
Total time taken by ying zyiyu to cover [tex]200\;\rm miles[/tex] is calculated as-
[tex]t_1=\dfrac{200}{50}\\t_1=4\;\rm hour[/tex]
Similarly, ying zyiyu covered the first [tex]100\;\rm miles[/tex] of the trip at [tex]40\;\rm mph[/tex] so,
Total time taken by ying zyiyu to cover [tex]100\;\rm miles[/tex] is calculated as-
[tex]t_2=\dfrac{100}{40}\\t_2=2.5\;\rm hour[/tex]
So, the total time taken by ying zyiyu to travel [tex]300\;\rm miles[/tex] is [tex]4+2.5=6.5\;\rm hours[/tex]
Now, the average spped is calculated as-
[tex]\rm{Average\;Speed}=\dfrac{Total\;Distance}{Total\;Time}\\\rm{Average\;Speed}=\dfrac{300}{6.5}\\\rm{Average\;Speed}=46.15\;\rm mph[/tex]
Hence, the average speed of ying zyiyu is [tex]46.15\;\rm{mph}[/tex].
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A rectangular box with a volume of 784 ft3 is to be constructed with a square base and top. the cost per square foot for the bottom is 15¢, for the top is 10¢, and for the sides is 1.5¢. what dimensions will minimize the cost
You make $0.75 for every newspaper you sell. How many newspapers do you have to sell to buy soccer cleats? (soccer cleats are $36.00)
Write an equation then solve
what is the unknown factor 9Xp= 45
To find the unknown factor in the equation 9Xp = 45, divide both sides by 9 to isolate X, resulting in Xp = 5. Therefore, the value of X is 5 when multiplied by the variable p.
To solve the equation 9Xp = 45, we need to find the value of an unknown variable X. The equation indicates that 9 times some number X equals 45. By dividing both sides of the equation by 9, we can isolate X to find its value.
Step 1: Write down the equation: 9Xp = 45.
Step 2: Divide both sides by 9: Xp = 45 ÷ 9.
Step 3: Simplify the right side: Xp = 5.
Therefore, the value of the variable X that makes the equation true when multiplied by p is 5.
A line passes through the point (-8,5) and has a slope of 3/2
Write an equation in slope-intercept form for this line.
To write the equation for this line in slope-intercept form, substitute the given values into the formula and solve for the y-intercept.
Explanation:To write an equation in slope-intercept form, we need to use the formula y = mx + b, where m is the slope and b is the y-intercept.
Given that the line passes through the point (-8,5) and has a slope of 3/2, we can substitute these values into the equation.
So, the equation of the line in slope-intercept form is y = (3/2)x + b. To find the y-intercept, we substitute the coordinates of the point (-8,5) into the equation and solve for b.
5 = (3/2)(-8) + b
5 = -12 + b
b = 17
Therefore, the equation in slope-intercept form is y = (3/2)x + 17.
Which of the following statements is not true about the function shown above?
A.
The function is increasing.
B.
The function has a y-intercept of (0, 6).
C.
The function has a constant rate of change of ‒2.
D.
The function is negative where x>3.
A store sold a total of 21,650 balls. It sold 11,795 baseballs. It sold 4,150 fewer basketballs than baseballs. The rest of the balls sold were footballs. How many footballs did the store sell?
Answer:
2210
Step-by-step explanation:
Given that a store sold a total of 21,650 balls.
No of baseballs sold =11795
There were baseballs, basketballs and footballs in the store
No of basketballs sold = 4150 fewer than baseballs = [tex]11795-4150\\=7645[/tex]
Total sales = [tex]21650[/tex]
Baseballs sold = [tex]11795\\[/tex]
Basketballs sold =[tex]7645[/tex]
No of footballs sold = [tex]21650-11795-7645\\=2210[/tex]
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Identify one characteristic of exponential growth.
Answer: Option 'd' is correct.
Step-by-step explanation:
Since we have given the exponential growth.
Properties of exponential growth are as follows:
1) The graph should pass through (0,1).
2) Domain of exponential growth function is the set of real numbers.
3) Range of exponential growth is greater than 0.
4) The graph is always increasing for the case of exponential growth.
Hence, Option 'd' is correct.
(d) estimate p(x < 1.5), i.e., the proportion of all thickness values less than 1.5. [hint: if you knew the values of μ and σ, you could calculate this probability. these values are not available, but they can be estimated.] (round your answer to four decimal places.)
To estimate p(x < 1.5), we can use the concept of probability. Given the information provided, we can assume a uniform distribution between 1.5 and 4. The shaded area in Figure 5.20 represents the shortest 30 percent of repair times. Therefore, we can estimate that p(x < 1.5) is approximately 0.30.
Explanation:To estimate p(x < 1.5), we can use the concept of probability. Given the information provided, we can assume a uniform distribution between 1.5 and 4. The shaded area in Figure 5.20 represents the shortest 30 percent of repair times. Since we want to estimate the proportion of values less than 1.5, we can estimate it as the shaded area to the left of 1.5. This shaded area is equivalent to the shortest 30 percent of repair times, which is 0.30. Therefore, we can estimate that p(x < 1.5) is approximately 0.30.
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The actual probability is 0.159
To estimate the probability P(X < 1.5) without knowing the exact values of the mean (μ) and standard deviation (σ), we can use the empirical rule (also known as the 68-95-99.7 rule). This rule states that for a normally distributed variable:
Approximately 68% of the data falls within 1 standard deviation (σ) of the mean (μ).
Approximately 95% of the data falls within 2 standard deviations (2σ) of the mean.
Approximately 99.7% of the data falls within 3 standard deviations (3σ) of the mean.
Since the exact values of μ and σ are not available, we can estimate them using the sample mean (X) and sample standard deviation (s) of the data.
In this case, let's assume we have a sample of thickness values {x1, x2, ..., xn}. The sample mean (X) is the average of all the sample values:
X = (∑xi) / n
The sample standard deviation (s) is the square root of the variance (s^2), which is the average of the squared deviations from the mean:
s^2 = ∑(xi - X)^2 / n
Once you have the estimated values of μ (approximately equal to X) and σ (approximately equal to s), you can use the empirical rule to estimate P(X < 1.5).
For example, if you estimate that μ = 2 and σ = 0.5, then:
P(X < 1.5) = P(X < μ - σ) ≈ P(X < 2 - 0.5) ≈ P(X < 1.5) ≈ 0.159
Remember that this is just an estimate, and the actual probability may be slightly different.
You want to install a 2 yd wide walk around a circular swimming pool. the diameter of the pool is 17 yd. what is the area of the walk? use 3.14 for π.
To find the area of the walk around a circular swimming pool with a given diameter and width, calculate the radius, add the walk width to it, and then compute the area of the walk using the area of a circle formula.
The area of the walk around the pool is:
Find the radius of the pool by dividing the diameter by 2. Radius = 17 yd / 2 = 8.5 yd.
Find the radius of the walk by adding 2 yards to the pool's radius. Walk's radius = 8.5 yd + 2 yd = 10.5 yd.
Calculate the area of the walk using the formula for the area of a circle: A = πr². Area = 3.14 x (10.5)² = 346.185 square yards.
What is the equation of the line that is parallel to the given line and passes through the point (–2, 2)?
y = x + 4
y = x +
y = –5x + 4
y = –5x +
we know that
If two lines are parallel, then their slopes are the same
Step 1
Find the slope of the given line
we know that
the formula to calculate the slope between two points is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]
in this problem we have
[tex](x1,y1)=(-5,-4)\\(x2,y2)=(0,-3)[/tex]
substitute in the formula
[tex]m=\frac{(-3+4)}{(0+5)}[/tex]
[tex]m=\frac{(1)}{(5)}[/tex]
[tex]m=\frac{1}{5}[/tex]
Step 2
Find the equation of the line
we know that
the equation of the line into point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{1}{5}[/tex]
[tex](x1,y1)=(-2,2)[/tex]
substitute
[tex]y-2=\frac{1}{5}(x+2)[/tex]
[tex]y=\frac{1}{5}x+\frac{2}{5}+2[/tex]
[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]
therefore
the answer is
[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]
A chicken soup recipe calls for 15 cups of chicken stock. How much is this in quarts?
I really need explanation for this Mean Value Theorem. Thanks
Write the decimal 2.06 as a mixed number.
The price of a new apple ipod has increased by 1/4. if the original price of the apple was $200, what is the price today? $150 $250 $200 $175 none of these
Answer: The price today = $250
Step-by-step explanation:
Given : The original price of apple was $200.
The price of a new apple ipod has increased by 1/4.
Then , the new price =(Original price) +([tex]\dfrac{1}{4}[/tex]) x (Original price)
= (Original price) ( [tex]1+\dfrac{1}{4}[/tex] )
[tex](\$200)(\dfrac{5}{4})=\$250[/tex]
Hence, the price of ipod today = $250
A pail holds
4 1/4
gallons of water. How much is this in cups?
A rectangular field is 0.4 kilometers long and 0.3 kilometers wide. What is the area of the field in square meters?
The area of the rectangular field is 120,000 square meters.
How do we find the area of the rectangular field?We shall multiply the length by its width, to find the area of the rectangular field.
We can calculate like this:
Area = Length x Width
Area = 0.4 kilometers x 0.3 kilometers
Next, we convert the measurements to square meters, recalling that 1 kilometer = 1000 meters:
Area = (0.4 km * 1000 m/km) x (0.3 km * 1000 m/km)
Area = (400 m) x (300 m)
Then, multiplying the values, we have:
Area = 120,000 square meters
Hence, the area of the rectangular field is 120,000 square meters.
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Write an equation for the following word problem. Use m for the number of monkeys and e for the number of elephants.
In a zoo, there are 5 times as many monkeys as there are elephants. How many monkeys are there? Thanks!
m = monkeys
e = elephants
there are 5 times as many monkeys as elephants so to find the number of monkeys the equation would be:
m = 5e
What is the percent increase from 250 to 900?
1. Write the percent change formula for an increase.
Percent Increase =
Amount of Increase
Original Amount
2. Substitute the known quantities for the amount of the increase and the original amount.
Percent Increase =
900 − 250
250
3. Subtract.
Percent Increase =
650
250
4. Express the ratio as a percent:
%
Answer:
260 %
Step-by-step explanation:
1) Since, the percentage formula is,
[tex]\text{Percent Increase}=\frac{\text{Amount of Increase}}{\text{Original Amount}}[/tex]
2) Given,
Original amount = 250,
New amount = 900
So, the amount of increase = New amount - Original amount = 900 - 250 = 650
By substituting the values,
[tex]\text{Percentage increase}=\frac{650}{250}[/tex]
3) Now, for expressing the ratio into percentage we need to multiply by 100,
[tex]\frac{650}{250}\times 100=\frac{65000}{250}= 260\%[/tex]
Marianna martinez sells copy paper to local schools. SHE EARNS A 13 PERCENT STRAIGHT COMMISSION ON ALL SALES. IN NOVEMBER HER SALES TOTALED $28,540. WHAT WAS HER COMMISSION?
Joaquin has $1,300 in the bank and has investments worth $4,000. He also has $7,000 worth of credit card debt. What is Joaquin's net worth? Select the best answer from the choices provided. $1,300 -$7,000 $5,300 -$1,700
Corey deposited $1,500 in a savings account that earns simple interest at 5.75%. What is the balance in his account at the beginning of the third quarter?
a. $1,556.78
b. $1,528.13
c. $1,543.13
d. $1,612.50
Peter can buy 5 juice bottles for $10 or 6 juice bottles for $12. How much do you think he would pay for 7 juice bottles? Why?