The pmf of X = the number of children in the family is
1/4 + 3/8 + 3/8 =1
It is given that,
a family decides to have children until it has three children of the same gender i.e. BBB or GGG.
X can take the values {3,4,5}
and we know that
P(X = 3) + P(X = 4) + P(X = 5) = 1
We will find each term one by one,
P(X = 3) = ([tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex])*2
= [tex]\frac{1}{8}[/tex] * 2
P(X = 3) = [tex]\frac{1}{4}[/tex]
P(X = 4) = ([tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex])*6
= ([tex]\frac{1}{16}[/tex]) * 6
P(X =4) = [tex]\frac{3}{8}[/tex]
P(X = 5) = ([tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex])*12
= ([tex]\frac{1}{32}[/tex])* 12
P(X = 5) = [tex]\frac{3}{8}[/tex]
Therefore the pmf equation implies,
[tex]\frac{1}{4} + \frac{3}{8} + \frac{3}{8}[/tex] = [tex]\frac{32}{32}[/tex] = 1.
The probability mass function (pmf) is also called a probbility function or frequency which characterizes the distribution of a discrete random variable. It is a function over the sample space of a discrete random variable X which gives the probability that X is equal to a certain value.
To know more about probability here
https://brainly.com/question/28812653
#SPJ4
a radioactive substance decays exponentially. a scientist begins with 110 milligrams of a radioactive substance. after 22 hours, 55 mg of the substance remains. how many milligrams will remain after 32 hours?
A radioactive substance will have a decay of A ≈ 31.1936 mg after 32 hours.
Radioactive decay (additionally referred to as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the manner with the aid of using which an volatile atomic nucleus loses electricity with the aid of using radiation. A fabric containing volatile nuclei is taken into consideration radioactive.
Every atom seeks to be as strong as possible. In the case of radioactive decay, instability happens whilst there's an imbalance withinside the quantity of protons and neutrons withinside the atomic nucleus. Basically, there's an excessive amount of electricity withinside the nucleus to preserve all of the nucleons together.
Initial Radioactive substance, A₂ = 110 mg Remains substance, A = 55 mg time, t = 22 hours
Here, radioactive substance decay. exponentially.
[tex]a=a_{0}e^{at} \\\\55=110*e^{22k} \\\\\frac{55}{110} = e^{22k} \\\\ \\e^{22k} =\frac{1}{2}[/tex]
Taking lo both side, we get ln (1/2) = lne²²K
ln (1/2) = k*22
[tex]k=\frac{ln(1/2)}{22}[/tex]
K = -0.03150669
Substance remains after 32 hours,
t=32 hr
[tex]A=110*e^{( (-0.03150669))*32} \\A=110*e^{(-1.2602676)} \\\\[/tex]
A = 110x 0.283578131
A = 31.19359441
A ≈ 31.1936 mg
Learn more about radioactive substance visit: brainly.com/question/29122789
#SPJ4
Consider matrix A
135
3 5
A =
2
8 -1 3
What matrix results from -8*4?
A?
Answer:
[tex]\begin{pmatrix}24&-40&-16\\ -64&8&-24\end{pmatrix}[/tex]
Step-by-step explanation:
Each element of the matrix is multiplied by -8
given cos(-x) = 3/4 and tanx= √7/3, find sin(-x)
The trigonometric function sin(-x) is -√7/4 when cos(-x) = 3/4 and tanx= √7/3
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
cos(-x) =cosx= 3/4
and tanx=
We need to find sin(-x)
tank is ratio of sinx and cosx
We know that tanx=sinx/cosx
√7/3=sinx/3/4
Apply cross multiplication
sinx=√7/3.3/4
sinx=√7/4
sin(-x)=-sinx=-√7/4
Hence, Trigonometric function sin(-x) is -√7/4 when cos(-x) = 3/4 and tanx= √7/3
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ1
Need Urgent help please. Let y = f(x) be a cubic polynomial with leading coefficient a = 2 and f(-2) = f(1) = f(2) = 0. find the factored form of f.
Answer:
-2
Step-by-step explanation:
8283’a
Research Study: We want to figure out what characteristics of boys are most attractive to high-school girls. High-school girls were randomly assigned three groups to hear about a guy with trendy clothes, a nice car, or a confident attitude. There were 9 girls in each group. They gave ratings on a scale from 1 to 10, with 1 being "not interested" and 10 being "very interested."
Question: Is there a significant difference between the attractiveness ratings given by the three groups of girls?
What is the factor?
What are the levels of the factor?
Step 1: State Hypotheses
Null:
Research:
Step 2: Determine Comparison Distribution
What is the distribution shape and degrees of freedom for the comparison distribution?
Step 3: Set the Criteria for a Decision
Alpha = .05
dfB =
dfW=
Critical value:
Is the rejection region placed in the upper or lower tail? How do you know?
Step 3: Compute the Test Statistic
Trendy Clothes
Nice Car
Confident Attitude
8
6
10
6
7
9
9
8
10
6
6
10
8
4
8
6
5
9
7
5
10
6
6
9
6
8
8
Step 5: Make a Decision
Reject/Fail to Reject the null?
What does this mean (be sure to talk about significance)?
Test statistic Z= 0.13008 < 1.96 at 0.10 level of significance.
The null hypothesis is accepted.
There is no significant difference between the attractiveness ratings given by the three groups of girls.
Surveyed two random samples of 390 men and 360 women who were tested.
first sample percentage,
p1 = 360 ÷ 390 = 0.9230
second sample percentage,
p2 = 47 ÷ 52 = 0.9030
There is no change, according to the null hypothesis the percentage of males who have positive tests is significantly from the percentage of women who have positive tests.
Different Hypotheses:
There is a discrepancy in the percentage of schoolgirls who heard about a male with stylish clothes, a great automobile, or a confident demeanor across the three groups that were randomly allocated.
Z = (p1 - p2) ÷ √(PQ((1 ÷ n1) + (1 ÷ n2)))
where
p = (n1p1 + n2p2) ÷ n1 + n2
p = 0.920
Z = (0.9230 - 0.9030) ÷ √(0.9230((1 ÷ 390) + (1 ÷ 52)))
Test statistic Z = 0.13008
Level of significance = 0.10
The critical value Z₀.₁₀ = 1.645
Test statistic Z=0.13008 < 1.645 at 0.1 level of significance
The null hypothesis is accepted.
Learn more about the Null hypothesis at
https://brainly.com/question/16945299?referrer=searchResults
#SPJ4
golden rectangles are rectangles for which the ratio of the width w to the length l is equal to the ratio of l to l 1 w. the ratio of the length to the width for these rectangles is called the golden ratio. find the value of the golden ratio using a rectangle with a width of 1 unit
golden rectangles are rectangles for which the ratio of the width w to the length l is equal to the ratio of l to l 1 w. The value of this golden ratio = 1/2 (1 + √5) = 1.618
Ratio:
Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion. We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Students occasionally struggle to understand the difference between ratio and proportion.
To learn more about ratio visit:
brainly.com/question/13419413
#SPJ4
a rhombus has side lengths of 10 and a diagonal measuring 12. what is the length of the other diagonal?
When the other diagonal is 12 inches long and the side is 10 inches long, the diagonal is 16 inches long.
What is rhombus?A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths. A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposing sides of a parallelogram are equal. A quadrilateral with four equal sides that has the shape of a diamond is called a rhombus. In everyday life, rhombus-shaped objects can be seen.
Here,
The length of side=10 inch
The length of diagonal= 12 inch
Let the length of diagonal be x.
6²+(x/2)²=10²
(x/2)²=64
x/2=8
x=16 inch
The length of diagonal is 16 inch when other diagonal measure 12 inch and side measures 10 inch.
To know more about rhombus,
https://brainly.com/question/27870968
#SPJ4
A function has a constant halving time. What type of function does this represent?.
An exponential decay function is one that has a constant time of halving.
What is function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.
Here,
The function which has a constant halving time is in the following form,
A(t)=A₀(¹/²)^(t/h)
Where: A₀ is the initial amount
h is the half life time or the halving time.
t is the time
A(t) the amount that remains at time t
The previous function represents an Exponential decay function.
To know more about function,
https://brainly.com/question/28193995
#SPJ4
Which of these tables (if any) represent a proportional relationship?
Answer: none of them
Step-by-step explanation:
they are not equal and dont look right i dont think im sorry if i get it wrong
Convert to standard form:
[tex]y = \frac{5}{12}x - \frac{1}{2}[/tex]
Show work please
Answer: x=12y+6/5
Let's solve for x.
y=5/12x − 1/2
Step 1: Flip the equation.
5/12x + −1/2 =y
Step 2: Add 1/2 to both sides.
5/12x + −1/2 + 1/2 = y + 1/2
5/12x = y + 1/2
Step 3: Divide both sides by 5/12.
5/12x 5/12 = y + 1/2/5/12
x=12y + 6/5
How do I solve this equation 1 3/4÷3
Answer:
1 3/4 * 3
we turn 1 3/4 to improper fraction:
7/4
so,
7/4 * 3 = 21/4 or 5 1/4
Step-by-step explanation:
at a resturant, diners are given the choice of 4 appetizers, 5 entrees, 3 deserts, and 2 wines. how many different dinners can be assembles?
Total number of ways in which dinner can be assembled will be 120.
What is restaurant?
A restaurant is a place of business where customers can order and receive food and drinks. Meals are typically prepared and consumed on the premises, but many eateries also provide take-out and delivery options.
A commercial space where customers can buy food or drinks.
There are 4 different types of appetizers, so there are 4 ways to choose one of them, which comes out to 4C1 = 4.
Similarly, there are 3 ways to choose desserts and 5 ways to choose an entrees.
2 methods for selecting wines are also included.
As a result, there are
5 x 4 x 3 x 2 = 120 different ways to assemble dinner in total.
Hence, total number of ways in which dinner can be assembled will be 120.
To know more about restaurant, click on the link
https://brainly.com/question/18439537
#SPJ4
The mean number of years Americans work before retiring is 34. Which of the following will be a Type I error? (A) We conclude that the mean is 34 years when it really is not 34 years. (B) We conclude that the mean is 34 years when it really is 34 years. (C) We conclude that the mean is not 34 years when it really is 34 years. (D) We conclude that the mean is not 34 years when it really is not 34 years.
The error of type I is Despite the fact that the median age is 34, we get to the conclusion that it is not. The appropriate response to this question is option C.
A Type I error is rejecting the null hypothesis when it is actually true. It involves making inferences from statistically significant outcomes even though they might have happened by chance or for other reasons.
The probability of error will depend on the significance level (alpha or) that you choose. In order to determine the statistical likelihood of receiving your results, you established that number at the outset of your investigation (p-value).
The usual level of significance is 0.05 or 5%. The likelihood that the null hypothesis is true is only
For more information on type I error kindly visit to
https://brainly.com/question/17438496
#SPJ4
a two-factor anova is conducted and the data are plotted. the chart shows two parallel lines separated by a distance of 9 points. the lines represent factor a and the x axis of the chart represents the levels of factor b. how should you interpret these results?
The correct option is, there is a main effect for Factor A but there is no interaction.
What is two factor anova?
The mean of a quantitative The mean of a quantitative variable is estimated using a two-way ANOVA in relation to the levels of two categorical variables.
Two-way analysis of variance is an extension of one-way analysis of variance in statistics that looks at the impact of two different categorical independent variables on a single continuous dependent variable.
The parallel lines indicates no interaction effect.
For the above problem option 'a' is correct.
There is a main effect for Factor A but there is no interaction
Hence, the correct option is, there is a main effect for Factor A but there is no interaction.
To know more about two-facto anova, click on the link
https://brainly.com/question/14637579
#SPJ4
Complete question:
A two-factor ANOVA is conducted and the data are plotted. The chart shows two parallel lines separated by a distance of 9 points. The lines represent Factor A and the x axis of the chart represents the levels of Factor B. How should you interpret these results?
Select one:
a. There is a main effect for Factor A but there is no interaction
b. There is a main effect for Factor A and there is also an interaction effect
c. There is a main effect for Factor B and there is an interaction effect
d. There is no interaction effect and no main effects
If f(x) = 3x³ + 5x² - 4, then what is the remainder when f(x) is divided by
x-1?
Please answer number 2 I think I answer is A but please explain how you got your answer.
what is the probability you get this question right if you pick a random answer? a.20% b. 80% c. 25% d. 20% e. 50%
Answer: 80%
Step-by-step explanation:
select the most appropriate response. what does it mean when sample results are not statistically significant?
The sample results would be somewhat expected if the null hypothesis were true.
The correct option is (b).
Given,
In the question:
The complete question is this:
Select the most appropriate response.
What does it mean when sample results are not statistically significant?
The null hypothesis is true The sample results would be somewhat expected if the null hypothesis were true.The null hypothesis is wrongThe sample results would be unexpected if the null hypothesis were true.The question is based on MCQ's
Now, According to the question:
What does it mean when sample results are not statistically significant?
It means The sample results would be somewhat expected if the null hypothesis were true.
Learn more about Null Hypothesis at:
https://brainly.com/question/28920252
#SPJ4
the national center for health statistics has found that there is a 0.41% chance that an american citizen will die from falling. what is the probability that you will not die from a fall? (round to the nearest hundredth of a percent)
If there is a 0.41% chance that an American citizen will die from falling, then the probability that you will not die from a fall is 99.59%
The chances of an American citizen will die from falling = 0.41%
The probability is the ratio of number of favorable outcomes to the total number of outcomes
The equation will be
The probability = Number of favorable outcomes / Total number of outcomes
The probability that you will not die from a fall = 1 - The chances of an American citizen will die from falling
Substitute the values in the equation
The probability that you will not die from a fall = 1 - 0.41
= 99.59%
Therefore, the probability that you will not die from a fall is 99.59%
Learn more about probability here
brainly.com/question/11234923
#SPJ4
Which fraction equals a repeating decimal?
A: 18/81
B: 11/88
C: 1/5
D: 5/8
Answer:
A: 18/81
Step-by-step explanation:
A: 18/81 = 0.222222222.....
B: 11/88 = 0.125
C: 1/5 = 0.2
D 5/8 = 0.625
Could you please give me brainiest for this? I just need 1 more to get to the next level. Thanks!
i need help on this! i did the first part though
Answer:
Winning jump = 5.474
Her best jump = 4.76
Step-by-step explanation:
4.25×1.12=4.76
4.76×1.15=5.474
when constructing a confidence interval for a population mean from a sample of size 10, the number of degrees of freedom for the critical value is
the Degree of freedom is 9.
What is confidence interval?
A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.
We have given,
Sample size =n=10
Degree of freedom =n-1=10-1=9
Hence the Degree of freedom is 9
Learn more about confidence interval, by the following link.
https://brainly.com/question/17097944
#SPJ4
question a 15-foot ladder is leaning against a wall. the top of the ladder is sliding down the wall at a rate of 2 ft/sec. how fast is the bottom of the ladder moving when it is 12 feet away from the wall?
Speed the top of the ladder is sliding down = 1.6ft/sec when it is 12 feet away from the wall
15-foot ladder is leaning against a wall.
the top of the ladder is sliding down the wall at a rate of 2 ft/sec.
how fast is the bottom of the ladder moving when it is 12 feet away
Using equivalent proportion
15 ft -------------------2ft/sec
12 ft-------------------X ft/sec
Hence X = (12 x 2) ÷ 15 =1.6 ft/sec
learn more about of rating here
https://brainly.com/question/15401968
#SPJ4
A line passes through (9,-1) the point and has a slope of 2/3.
Write an equation in slope-intercept form for this line.
Answer:
y = 2/3 x - 7
Step-by-step explanation:
y = mx + b
y = 2/3 x + b
-1 = 2/3 × 9 + b
-1 = 6 + b
b = -7
y = 2/3 x - 7
Answer:
y = 2x-17
Step-by-step explanation:
We have a point and a slope, we can write the equation in point slope form and then convert to slope intercept form
y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point
y-1 = 2(x-9)
Distribute
y-1=2x-18
Add 1 to each side
y-1+1 = 2x-18+1
y = 2x-17
This is slope intercept form
Step-by-step explanation:
a stock had returns of 10.00%%.3.00% and -7.00% over the past 3 years.what is the mean ofthe stock's returns over the past 3 years minus the sample standard deviation of the stock'sreturns from the past 3 years?
The mean of the stock's returns over the past 3 years minus the sample standard deviation of the stock's returns from the past 3 years is -6.54
What is the standard deviation?
A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
Standard deviation It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.
Mean :
Mean = [10+3 + (-7) ] / 3 = 2
sample standard deviation :
subtract the mean from each data element.
10- 2 = 8
3-2 = 1
-7 - 2 = -9
Square those numbers.
8² = 64
1² = 1
(-9)² = 81
Add those
64+1+81 = 146
Divide by (number of elements -1 = 3 -1 = 2)
146/2 = 73
Take square root
8.54
So, the sample standard deviation = 8.54
The mean of the stock's returns over the past 3 years minus the sample standard deviation of the stock's returns from the past 3 years
= 2 - 8.54
= -6.54
To learn more about the standard deviation from the given link
https://brainly.com/question/12402189
#SPJ4
the population of a town increased from 3600 in 2005 to 5650 in 2011. find the absolute and relative (percent) increase.
Absolute increase in population will be 2050
And percentage increase will be 56.94 %
We have given population in 2005 is 3600
And population in 2011 is 5650
So absolute increase in population = 5650-3600 = 2050
We have to find the percentage increase in population
So relative percentage increase in population will be 2050/3600 *100 = 56.94 %
So population will increase by 60 %
learn more about of population here
https://brainly.com/question/14348251
#SPJ4
I NEED HELP!! IM RUNNING OUT OF TIME!!!
Domain and range of G?
G = {( -8, 7 ), ( -9, 0 ), ( 3, 7 )}
Write answers as set notation
For the given set G = {(-8, 7), (-9, 0), (3, 7)}, domain is {-8, -9, 3} and range is {7, 0, 7}.
What is domain?Domain is the values of all inputs, In a function f(x), the set of all values of x is called domain
The given set is,
G = {( -8, 7 ), ( -9, 0 ), ( 3, 7 )}
Since, domain is the set of all values of x,
And range is the set of all values of y
In the given set,
Domain = {-8, -9, 3}
Range = {7, 0, 7}
The domain is {-8, -9, 3} and range is {7, 0, 7}.
To know more about Domain on:
https://brainly.com/question/13113489
#SPJ1
the screenshot is the work that i need help with
Answer:
Step-by-step explanation:
if the speed of the river is s, write an expression for the time it takes to travel 5 kilometers upstream and an expression for the time to travel 10 kilometers downstream
The time taken to travel upstream will be t = 5/(s - r) and the time taken to travel downstream will be equal to t = 10/(s + r).
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given information in the question,
Speed of boat in still water = s
Distance to travel upstream = 5 km and,
Distance to travel downstream = 10 km
Then, the time taken to travel upstream,
t = d/s
t = 5/(s - r)
And, the time is taken to travel downstream.
t = d/s
t = 10/(s + r)
To know more about arithmetic operations:
https://brainly.com/question/13585407
#SPJ1
The value of y varies exponentially with respect to x and the 1-unit growth factor is 1.7. Which of the following is the best explanation for the meaning of this growth factor?
Whenever x changes by 1, the value of y becomes 1.7 units larger than its previous value.
Whenever x changes by 1, the value of y becomes 11.7 times as large as its previous value.
Whenever x changes by 1.7, the value of y doubles its previous value.
Whenever x changes by 1.7, the value of y becomes 1 unit larger than its previous value.
Whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value
We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.
Given that,
With respect to x, the value of y varies exponentially, and the 1-unit growth factor is 1.7.
We have to find which of the following best describes the significance of this growth factor.
We know that,
The required expression for y with respect to x is
y=(1.7)ˣ------>equation(1)
1.7=1- unit growth factor.
When ever x changes by 1.
x=x-1----->equation(2)
Putting equation (2) in (1)
y'=1.7ˣ⁺¹
y'=1.7ˣ×1.7----->equation(3)
Here [ y is new value after increase]
Taking ratio of (3) and (1)
y'/y= (1.7)ˣ×(1.7)/(1.7)ˣ
y'=(1.7)y
Therefore, We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.
To learn more about value visit: https://brainly.com/question/14170328
#SPJ4