A couple is starting a family and decides to have four children. Assume that the probability of having a boy or have a girl are equal. a) Find a probability model for the number of girls the couple has. b) Find the probability that the couple has at least one girl. c) What is the probability that the couple has exactly one boy or exactly one girl
Answers
Answer:
0.9375 ; 0.5
Step-by-step explanation:
Given that :
p = 0.5
Probability model for the Number of girls the couple has :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
P(x = 0) = 4C0 * 0.5^0 * 0.5^4 = 0.0625
P(x = 1) = 4C1 * 0.5^1 * 0.5^3 = 0.25
P(x = 2) = 4C2 * 0.5^2 * 0.5^2 = 0.375
P(x = 3) = 4C3 * 0.5^3 * 0.5^1 = 0.25
P(x = 4) = 4C4 * 0.5^4 * 0.5^0 = 0.0625
Probability of having atleast one girl
Number of trials, n = 4
P(x ≥ 1) = p(x = 1) + p(x = 2) + p(x = 3) + p(x = 4)
Using the relation :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
Using calculator ;
P(x ≥ 1) = 0.9375
Probability of having exactly one boy or exactly one girl
1 boy 3 girls OR 1 girl 3 boys
P(x = 1)
P(x =x) = nCx * p^x * (1 - p)^(n - x)
P(x = 1) = 4C1 * 0.5^1 * 0.5^3
P(x = 1) = 4 * 0.5 * 0.125
P(x = 1) = 0.25
The probability of having one girl, 3 boys and vice versa is 0. 25
Hence, Probability of having exactly one boy or exactly one girl
0.25 + 0.25 = 0.5
Related Questions
The graph of y=x^2 is shown in the figure. What is the average rate if change of this function over the interval -1
Answers
Answer:
The average rate of change of the function h(x) over the interval between 2 points (a , h(a)) and (b ,h(b)) is the
slope of the secant line
connecting the points.
It is found using.
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∣
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2
h
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b
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−
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b
−
a
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−−−−−−−−−−−−−−−−
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h
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This means that the average of all the slopes of tangents between (2 ,9) and (0 ,-1) is 5
4. If a salesperson receives a base pay of $800 per month and a 5% commission on sales, what is the regression equation relating monthly sales and income for this person?
Answers
The regression equation relating monthly sales and income for a salesperson who receives a base pay of $800 per month and a 5% commission on sales, expressed as Y = a + bxY
Step 1: Identify the regression equation which has the form of Y = a + bx, where
Y is the dependent variable,
x is the independent variable,
a is the constant, and
b is the slope of the line.
In this case, the monthly income received by the salesperson is dependent on the amount of sales, which is the independent variable.
Therefore, the equation can be expressed as:
Y = a + bx, where
Y = monthly income and
x = sales.
Step 2: Find the value of a, the constant term in the regression equation. a represents the value of Y when x = 0.
In this case, the value of a is equal to the base pay of $800 because this amount is received regardless of the amount of sales.
Therefore, a = 800.
Step 3: Find the value of b, the slope of the regression line.
The slope of the line represents the change in Y for each unit increase in x.
Since the salesperson receives a 5% commission on sales, this means that for each dollar of sales, they receive an additional 5 cents of income.
Therefore, the value of b is equal to 0.05.
Hence, the regression equation relating monthly sales and income for this person can be expressed as:
Y = a + bxY
= 800 + 0.05x
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Please say the answer as fast possible with working. It would be so kind if you sended this early
Answers
Answer: 2. 2
3. 110,121,132
4.22,110
5.4.5
Step-by-step explanation:
2. 20-12=8, 8divided by 4=2
3. 363 divided by 3=121(this is the avg of the consecutive multiples so one multiple must be 11 above and another 11 below
4.66 divided by 3=22, 22x 2 and 22 x 5
5.2 x2=4, 13-4=9, 9 divided by 2 is 4.5
Solve the given differential equation by undetermined coefficients. y(4) + 2y'' + y = (x − 5)^2
y(x)=
Answers
The particular solution to the given differential equation is:
y_p(x) = (x − 5)^2
To solve the given differential equation by the method of undetermined coefficients, we assume that the particular solution has the form:
y_p(x) = A(x − 5)^2 + B(x − 5) + C
where A, B, and C are constants to be determined.
We can now proceed to find the values of A, B, and C by substituting the assumed form of the particular solution into the differential equation.
First, let's find the derivatives of y_p(x):
y_p'(x) = 2A(x − 5) + B
y_p''(x) = 2A
Now, substitute these derivatives and y_p(x) into the differential equation:
2A + 2(2A) + A(x − 5)^2 + B(x − 5) + C = (x − 5)^2
Simplifying the equation, we get:
4A + A(x − 5)^2 + B(x − 5) + C = (x − 5)^2
Comparing the coefficients of like terms on both sides, we have:
4A = 0 (coefficients of x^0 terms)
B = 0 (coefficients of x^1 terms)
A = 1 (coefficients of x^2 terms)
C = 0 (coefficients of x^0 terms)
Therefore, the values of A, B, and C are:
A = 1
B = 0
C = 0
Substituting these values back into the assumed form of the particular solution, we have:
y_p(x) = (x − 5)^2
Thus, the particular solution to the given differential equation is:
y_p(x) = (x − 5)^2
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Tamar's house is greater than 472 and less than 500 which number can be on Tamar's house?
Answers
490
472 <490<500
it fits the criteria
Tim sells two types of pizza. He charges $10 for a cheese pizza and $15 for a pepperoni pizza. Yesterday he sold 64 pizzas in all. For every cheese pizza he sells 3 pepperoni pizzas. How much money did he make selling pizzas yesterday?
Answers
Answer:$880
Step-by-step explanation:
1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3 1/3
4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64
55 55 55 55 55 55 55 55 55 55 55 55 55 55 55 55
so to explain 1 cheese pizza to 3 pepperonis(1/3) that is 4 pizzas together, and we do that until 64. If pepperoni pizza is 15 each, we time that by 3 which is 45, plus the 10 for cheese pizza which makes it 55. we do 55 dollars until we equal the 64 pizzas, which is 16 together. so 55 x 16=880 dollars selling pizza
You buy 10 pounds of bird seed at Store A for $11.50. Your friend buys 15 pounds of bird seed at Store B for $19.50. How much less would you spend buying 20 pounds of bird seed at the store with the better deal?
Answers
Answer:
Step-by-step explanation:
$11.50/10 = $1.15 per pound
$19.50/15 = $1.30 per pound
$1.15 * 20= $23
$1.30 * 20 =$26
$26- $23 = $3
answer: $3
it is fair to say that the ucr is: group of answer choices a mutually exclusive measure not a truly reliable measure an exhaustive measure all of the above
Answers
The UCR (Uniform Crime Reporting) is B. not a truly reliable measure.
The UCR is a program established by the FBI in 1930 to collect and analyze crime statistics from law enforcement agencies across the United States. Although it provides useful data and insights into crime trends, it is not without its limitations. One significant issue with the UCR is that it relies on voluntary reporting from law enforcement agencies, meaning that some areas may not provide complete or accurate data. This can lead to an underrepresentation of certain crimes or inconsistencies in reporting across jurisdictions.
Another limitation is that the UCR only includes reported crimes, excluding any unreported criminal activity. This means that the data does not necessarily provide a comprehensive picture of all crimes occurring in a given area. Additionally, the UCR uses a hierarchy rule, meaning that if multiple crimes are committed during a single incident, only the most severe crime is counted. This can result in an undercounting of less severe but still significant crimes.
In summary, although the UCR provides valuable information on crime trends and patterns, it is not a truly reliable measure due to its reliance on voluntary reporting, exclusion of unreported crimes, and hierarchy rule. Therefore, the correct option is B.
The question was incomplete, Find the full content below:
it is fair to say that the ucr is: group of answer choices
A. A mutually exclusive measure
B. Not a truly reliable measure
C. An exhaustive measure
D. All of the above
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Solve on the interval [0, 2pi):3 sec x - 2 = 13 sec x =3secx= 1cos = -1Is it 0?
Answers
3 sec x - 2 = 1
Add 2 to both sides
3 sec x = 1+ 2
3 sec x = 3
divide both sides by 3
sec x = 3/3
sec x = 1
\(\begin{gathered} \text{ sec x = 1} \\ x=sec^{-1}1 \\ x\text{ = 0 } \\ \text{and also, the interval is \lbrack{}0, 2}\pi\rbrack \\ x\text{ = 2}\pi \\ \text{The answer is x = 0 and x = 2}\pi \end{gathered}\)x3 - 7x,
f(x) = 8,
2x + 3,
x < -3
- 3 < x < 3
x > 3
Answers
Answer:
I did the math and I believe that answer is : -12x4-5x
Step-by-step explanation:
23, f(x) = 4x- 25, f(x) = x2-3x + 10 26. 27. f(x) 3x2 29, f(x) = 2x3-5x2 + 4x-1 30. f(x) = x3-3x2 31, f(x)--2x3-8x2 + 6x + 36 28, f(x) = x3-x2-x + 1 For each function use the leading coefficient test to determine whether y → oo or y →-oo as x → oo. 33, y=2x3-x2 + 9 35. y =-3x4 + 5 34. y=-3x + 7 36, y = 6x4-5x2-1 38, y = 5x-7x4 37. y=x-3x3 For each function use the leading coefficient test to determine whether y → or y →
If p(x) = x^2 – 1 and q(x) = 5(x-1), which expression is equivalent to (p – q)(x)?
Answers
Answer:
x² - 5x + 4
Step-by-step explanation:
note (p - q)(x) = p(x) - q(x) , thus
p(x) - q(x)
=x² - 1 - 5(x - 1) ← distribute parenthesis
= x² - 1 - 5x + 5 ← collect like terms
= x² - 5x + 4
Answer:
x^2 - 5x - 6
Find the Slope and Y-intercept of each line
Answers
Slope of graph is -4 and y- intercept is -8.
What is slope of graph?
In math, slope is employed to explain the gradient and direction of lines.
Main Body:
The slope of a line is the ratio of rise to run. Hence, here are the steps to find slope from a graph.
Select any two random points on the graph of the line (preferably with integer coordinates).Label them as A and B (in any order).Calculate the "rise" from A to B. While going vertically from A to B, if we have to go"up", then the rise is positive;
"down", then the rise is negative.
Calculate the "run" from A to B. While going horizontally from A to B, if we have to go"right", then the run is positive;
"left", then the run is negative.
Now, use the formula: slope = rise/run.hence slope of graph = -8/2 = 4.
And y intercept is point cutting y-axis , so it is -8.
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who owns iods? as part of the pew internet and american life project, researchers surveyed a random sample of 800 teens and a separate random sample of 400 young adults. for the teens, 79% said that they own an ipod or mp3 player. for the young adults, this figure was 67%. do the data give convincing evidence of a difference in the proportions of all teens and young adults who would say that they own an ipood or mp3 player?
Answers
Based on the survey data, we can conclude that a higher proportion of teenagers own an iPod or MP3 player compared to young adults.
To determine if the difference is significant, we need to conduct a hypothesis test. We can begin by stating the null hypothesis as "there is no significant difference in the proportion of all teens and young adults who would say they own an iPod or MP3 player."
We can also state the alternative hypothesis as "there is a significant difference in the proportion of all teens and young adults who would say they own an iPod or MP3 player."
Next, we need to determine the test statistic and calculate the p-value to determine if the difference in the proportions is statistically significant. Assuming that the data follows a normal distribution, we can use a two-sample z-test to test our hypothesis.
Using a significance level of 0.05, we find that the test statistic is 3.07, and the p-value is 0.002. Since the p-value is less than the significance level, we can reject the null hypothesis and conclude that there is convincing evidence of a difference in the proportions of all teens and young adults who would say they own an iPod or MP3 player.
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Which of the following can be used to show that these triangles are congruent?
Answers
The hidden information is that angleACB is equal to angle DCE
Brainliest pls!
The total cost for 10 pairs of headphones, including shipping was $125. The shipping charge was $15. What was the cost of each pair of headphones? Write and an equation and find the solution.
Answers
Answer:
y=15+12.5xStep-by-step explanation:
given data
chipping charge= $15
cost of 10 pair= $125
le the cost of 1 pair be x
given that 10 pairs cost $125
then 1 would cost x
cross multiply we have
10x=$125
x= 125/10
x=$12.5
therefore the equation for the solution is
let y be the total cost
y=15+12.5x
find the total surface area of this cone
Answers
Step-by-step explanation:
your answer is 113 0.97 inch square
hope it helps
Answer: the answer is 360
Step-by-step explanation:
i am also an Acellus user and this is what worked for me
Harmon’s Jewelry Store receives a shipment of 500 jewelry pieces, but 15 pieces are damaged. At this rate, if Mrs. Harmon places an order for 5,500 jewelry pieces, how many should she expect to be damaged?
Answers
Answer:
She should expect 165 jewelry pieces to be damaged.
Step-by-step explanation:
5,500/500 = 11
11 x 15 = 165
Solve for y .−5y−8(−7y+4)=−7−9(2−y)
asap
Answers
Answer:
y = 7/50
Step-by-step explanation:
-5y + 56y - 32 = -7 - 18 + y
50y = -25 + 32
50y = 7
y = 7/50
Answer:
\( \frac{1}{2} \)
Step-by-step explanation:
Open the bracket
\( - 5y + 56y - 32 = 7 - 18 + 9y\)Collect the like terms
\(51y - 9y = - 11 + 32\)
\(42y = 21\)
Divide both sides by 42
\(y = \frac{21}{42} \)
\(y = \frac{1}{2} \)
The 4-It wall shown here slands 28 ft from the building. Find the length of the shortest straight bearn that will reach to the side of the building from the ground outside the wall. Bcom 2 Building 1'
Answers
The length of the shortest straight is approximately 28.01 ft.
What is the right triangle?
A right triangle is" a type of triangle that has one angle measuring 90 degrees (a right angle). The other two angles in a right triangle are acute angles, meaning they are less than 90 degrees".
To find the length of the shortest straight beam,we can use the Pythagorean theorem.
Let's denote the length of the beam as L and a right triangle formed by the beam, the wall, and the ground. The wall is 28 ft tall, and the distance from the wall to the building is 1 ft.
Using the Pythagorean theorem,
\(L^2 = (28 ft)^2 + (1 ft)^2\)
Simplifying the equation:
\(L^2 = 784 ft^2 + 1 ft^2\\ L^2 = 785 ft^2\)
\(L = \sqrt{785}ft\)
Calculating the value of L:
L ≈ 28.01 ft
Therefore, the length of the shortest straight beam is approximately 28.01 ft.
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Steven's mother asked him to buy 750 grams of sugar. at the supermarket, he finds that the sugar packages give the weight in kilograms. what is the amount of sugar in kilograms that steven needs to buy? a. 0.075 kg b. 0.75 kg c. 75 kg d. 750 kg e. 750,000 kg
Answers
Answer:
b. 0.75 kg
Step-by-step explanation:
1 kilogram is 1000 grams
A company has $36,000 to hire a mathematician and his or her secretary. Out of respect for the mathematician's training, the mathematician will be paid $8000 more than the secretary. How much will each be paid
Answers
The money paid to the secretary is $14000 and the money paid to mathematician is $22000.
What is an equation?A mathematical statement that establishes the equality of two mathematical expressions is the called an equation.
Total money available for hiring = $36000
Let the money given to secretary = X
Money given to the mathematician = X + 8000
X + (X + 8000) = 36000
2X = 28000
X = 14000
Money given to secretary is $14000.
Money given to the mathematician is $22000.
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Help pls and ty! What is the area of this trapezoid?
Enter your answer in the box.
__ units2
Answers
Answer:
88 units^2
Step-by-step explanation:
The area of a trapezoid is equal to \(\frac{a+b}{2}h\), where a and b are the top and bottom of the trapezoid and h is height.
We can see that a (top) equals 17, and b (bottom) equals 5 + 17 + 5 = 27. Then, the height of the trapezoid is 4.
\(\frac{17+27}{2} * 4\) \(\frac{44}{2} * 4\) \(22 * 4\) \(88\)Therefore, the answer is 88 units^2.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
as we can see on the picture, the trapezoid has two parallel sides or "bases", one above is 17 units long the other below is 5+17+5 = 27 units long, and we also know its height is 4, so
\(\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h=height\\ a,b=\stackrel{parallel~sides}{bases}\\[-0.5em] \hrulefill\\ a=17\\ b=27\\ h=4 \end{cases}\implies \begin{array}{llll} A=\cfrac{4(17+27)}{2}\\\\ A=2(17+27)\\\\ A=2(44)\implies A=88 \end{array}\)
An angle measures 48.4° less than the measure of its supplementary angle. What is the measure of each angle?
Answers
Answer:
65.8° and 114.2°
Step-by-step explanation:
Suplementary angles sum 180°
then:
a + b = 180° eq 1
a = b - 48.4 eq 2
replacing the value of eq 2 in eq 1:
(b-48.4) + b = 180°
2b - 48.4 = 180°
2b = 180 + 48.4
2b = 228.4
b = 114.2°
from the eq. 1
a = b - 48.4
a = 114.2 - 48.4
a = 65.8°
Check:
114.2° + 65.8° = 180°
Add (1.3t3 + 0.4t2 – 24t) + (8 – 18t + 0.6t2)
For each term in the second polynomial, enter the letter showing where that term should be placed to add the polynomials vertically.
1.3t3 + 0.4t2 + (–24t)
+ A. B. C. D
= 0.6t2
= 0t3
= 8
= –18t
Answers
On adding the given polynomials, 1.3t³+0.4t²-24t and 8-8t+0.6t² we will get 1.3t³+t²-32t+8
What is a polynomial?A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
For example of a polynomial of a single indeterminate x is x² − 4x + 7.
Given that, two polynomials, 1.3t³+0.4t²-24t and 8-8t+0.6t², we need to add them,
= (1.3t³+0.4t²-24t) + (8-8t+0.6t²)
= 1.3t³+0.4t²-24t + 8-8t+0.6t²
= 1.3t³+t²-32t+8
Hence, on adding the given polynomials, 1.3t³+0.4t²-24t and 8-8t+0.6t² we will get 1.3t³+t²-32t+8
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Answer:
b = 0.6t2
a = 0t3
d = 8
c = –18t
Step-by-step explanation:
If v = 5i - 4j and w = xi + 5j, find all numbers x for which || v + w|| = 2. Select the correct choice and fill in any answer boxes in your choice below. A. x = B. There is no solution
Answers
The number x for which || v + w|| = 2 is -1.
To solve for x, we need to calculate the vector sum of v and w, which is given by (5i - 4j) + (xi + 5j) = (5 + x)i + j. Next, we need to find the magnitude of this vector, which is given by ||v + w|| = √((5 + x)² + 1²).
Setting ||v + w|| equal to 2 and solving for x, we get:
√((5 + x)² + 1²) = 2
Squaring both sides, we get:
(5 + x)² + 1² = 4
Simplifying, we get:
x² + 10x + 20 = 0
Using the quadratic formula, we get:
x = (-10 ± √60)/2
x ≈ -8.66 or x ≈ -1.34
Since ||v + w|| cannot be negative, we take the positive root, x ≈ -1, as our final answer.
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a newspaper took a random sample of 1000 registered voters and found that 550 would vote for the green party candidate for governor. is this evidence that more than 1/2 of the entire voting population would vote for the green party candidate? to answer this question, you will have to test the hypothesis versus . assume a type i error rate of . what is the associated standard score for this hypothesis test?
Answers
The associated standard score for this hypothesis test is 3.16. There is is evidence that more than 1/2 of the entire voting population would vote for the green party candidate for governor.
To determine whether the random sample of 1000 registered voters showing 550 votes for the Green Party candidate is evidence that more than half of the entire voting population would vote for the Green Party candidate, we will conduct a hypothesis test with the null hypothesis H0: p ≤ 0.5 and the alternative hypothesis Ha: p > 0.5. We will assume a Type I error rate of 0.05.
The steps to determine the standard score are as follows:1: Calculate the sample proportion (p):
p = 550/1000 = 0.55
2: Calculate the standard error (SE):
SE = sqrt[(p * (1 - p))/n] = sqrt[(0.55 * 0.45)/1000] ≈ 0.0158
3: Calculate the z-score (standard score) for the hypothesis test:
z = (p - p₀) / SE = (0.55 - 0.5) / 0.0158 ≈ 3.16
4. From the p-value table, the p-value is 0.00078885
The associated p-value for this z-score is extremely small (less than 0.001), which means we can reject the null hypothesis H0: p ≤ 0.5 and conclude that there is evidence to support the alternative hypothesis Ha: p > 0.5.
The associated standard score is approximately 3.16. Therefore, this is evidence that more than 1/2 of the entire voting population would vote for the green party candidate.
Note: The question is incomplete. The complete question probably is: a newspaper took a random sample of 1000 registered voters and found that 550 would vote for the green party candidate for governor. Is this evidence that more than 1/2 of the entire voting population would vote for the green party candidate? to answer this question, you will have to test the hypothesis H0: p ≤ 0.5 versus Ha: p > 0.5. assume a type i error rate of 0.05. What is the associated standard score for this hypothesis test?
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Add parentheses to make true3 + 4 × 2 = 1472 ÷ 12 - 6 = 12
Answers
We want to find where to put the parentheses on each expression to make the expression true.
First, we identify the symbols +, x, / and - to identify the pairs of numbers. For example, in the expression
\(3+4\cdot2\)we have two symbols (+, *).
Now, this would give us two pairs of expression where we can put the parentheses. That is, one possibility per symbol. So we have
\((3+4)\)and
\((4\cdot2)\)Now, let us try the first choice. Remember that first we have to evaluate what is inside the parentheses. This would give us
\((3+4)\cdot2=7\cdot2=14\)which coincides to the value we wanted.
In the second case, we have the following symbols / and -
This would give us two pairs for grouping, namely
\((72/12)\)and
\((12\text{ -6)}\)as before, we will first evaluet the first option
\((\frac{72}{12})\text{ - 6=6 -6 =0}\)If we try the second option, we woud get
\(\frac{72}{(12\text{ -6)}}=\frac{72}{6}=12\)which would give us the correct value.
how many sides does a regular polygon have if each of its interior angles is 170
Answers
Answer:
Step-by-step explanation:
What is the slope of a line perpendicular to the line whose equation is
x - 5y = -10. Fully reduce your answer
Answers
Answer:
The slope or incline is -5
Step-by-step explanation:
rewrite to get the form
y = ...
x - 5y = -10
- 5y = -10 -x
divide left and right if the = sign by -5 gives:
(-5/-5)y = (-1/-5)x + (-10/-5)
y = 1/5x +2
So the incline is 1/5
a perpendicular line has an incline of -1 *5/1 = -5
The slope or incline is -5
Yesterday, of the coffee shop's customers ordered flavored coffee. of the
orders were for chocolate flavored coffee. What part of the coffee shop's
customers ordered chocolate flavored coffee?
67
56
14