The solutions are given below:-
Part (a),
X₁ + X₂ have distribution Bi(n₁+n₂, p)
Part (b),
P(X ₁+ X₂ = 1 | X₂ = 0) = np(1-p)ⁿ¹⁻¹
P(X₁+X₂ = 1| X₂ = 1) = (1-p)ⁿ¹
P(X₁ + X₂ = 1) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹
What is binomial distribution?Since both variables are independent but they have the same probability parameter, you can interpret that as if the experiment that models each try in both variables is the same.
When you sum both random variables together, what you obtain as a result is the total amount of success in n₁+n₂ tries of the same experiment, thus X₁+X₂have distribution Bi(n₁ + n₂, p).
b)
Note that, if X₂ = k, then X₁ +X₂ = 1 is equivalent to X₁ = 1-k. Since X1 and X₂ are independent, then P(X₁ +X₂ = 1| X₂ = K) = P(X1=1-k|X₂=k) = P(X₁ = 1-k).
If k = 0, then this probability is equal to P(X₁ = 1) = np(1-p)ⁿ¹⁻¹
If k = 1, then it is equal to P(X₁ = 0) = (1-p)ⁿ¹
Thus,
P(X₁+X₂ = 1) = P(X₁+X₂ = 1| X₂ = 1) * P(X₂=1) + P(X₁+X₂ = 1| X₂ = 0) * P(X₂ = 0) = (1-p)ⁿ¹ * np(1-p)ⁿ²⁻¹+ (1-p)ⁿ²*np(1-p)ⁿ¹-¹.
The complete question is given below.
Let X1 and X2 be two random variables following Binomial distribution Bin(n1,p) and Bin(n2,p), respectively. Assume that X1 and X2 are independent.
(a) The mgf of binomial distribution Bin(n, p) is (1 − p + pet)n. Use this fact to obtain the distribution of X1 + X2.
(b) Find the probability P(X1 + X2 = 1|X2 = k) for k = 0 and 1. Then use the law of total probability to find P (X1 + X2 = 1)
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Find the surface area if the pyramid
Answer: [tex]533 yd^{2}[/tex]
Step-by-step explanation:
The surface area of the base is:
(20 x 17.3) / 2
= 346 / 2
= 173
The surface area of one of the three identical triangles is:
(20 x 12) / 2
= 240 / 2
= 120
So in total, your answer would be one base plus three of those identical triangles:
173 + (3 x 120)
= [tex]533 yd^{2}[/tex]
plot the numbers -1.5 3/2, 3/2 and-4/3 on the number line.
Answer: -1.5, -4/3, 3/2, 3/2
Step-by-step explanation:
First, convert the numbers to decimals or fractions.
-1.5
3/2 = 1.5
3/2 = 1.5
-4/3 = -1.3
Therefore, on a number line, the numbers would be in the following order:
-1.5, -4/3, 3/2, 3/2
To obatin the graph of y=(x-8)^2 shifts the graph of y=x^2
To obatin the graph of y=(x-8)^2 shifts the graph of y=x^2 8 units right
How to determine the transformationFrom the question, we have the following parameters that can be used in our computation:
y=(x-8)^2
y = x^2
In the above equations, we can see that
The value of 8 is subtracted from x in y = x^2 to get y = (x - 8)^2
This represents a right translation by 8 units
Hence, the translation is 8 units to the right
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wat factor of 26 is between 4 and 26
Answer:
13
Step-by-step explanation:
cos 13 x 2 = 26
13 is a factor that is more than 4 and less then 26
The factor of the number 26 that is between 4 and 26 is 13. Factors are the numbers that can divide into a number without leaving a remainder. In this case, the factors of 26 are 1, 2, 13, and 26.
Explanation:In mathematics, a factor of a number is a number that divides into another number without leaving a remainder. In the case of the number 26, its factors include 1, 2, 13, and 26. The factor of 26 that is between 4 and 26 is 13.
To find this, you can go through the factors of 26 one by one. The factors are found by dividing 26 by all the numbers up to 26, and the numbers that give a remainder of 0 are the factors. In this case, 1, 2, 13, and 26 divide evenly into 26, and so are the factors of 26. Of these, only 13 lies between 4 and 26.
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If f(x)=2x-10 and the domain of f(x) is the set of untethers from -1 to 3 which values are elements of the range of f(x) Select all that apply
Answer:The range is all number greater than -10, so the values that are elements of the range of f(x) are c) -9, d) -6, and e) -2
Step-by-step explanation:
Please help me thank you
All the correct points lie on line f (x) = - 3x - 5 are (3, - 14)
What is Coordinates?A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
We have to given that;
The equation of line is,
⇒ f (x) = - 3x - 5
Now, All the correct points that lie on line are satisfy the line.
For point (5, - 21);
⇒ f (x) = - 3x - 5
⇒ - 21 = - 3 × 5 - 5
⇒ - 21 = - 15 - 5
⇒ - 21 ≠ - 20
For point (3, - 14);
⇒ f (x) = - 3x - 5
⇒ - 14 = - 3 × 3 - 5
⇒ - 14 = - 9 - 5
⇒ - 14 = - 14
For point (0, - 6);
⇒ f (x) = - 3x - 5
⇒ - 6 = - 3 × 0 - 5
⇒ - 6 = - 0 - 5
⇒ - 6 ≠ - 5
For point (-5, 8);
⇒ f (x) = - 3x - 5
⇒ 8 = - 3 × - 5 - 5
⇒ 8 = 15 - 5
⇒ 8 ≠ 10
For point (-3, 5);
⇒ f (x) = - 3x - 5
⇒ 5 = - 3 × - 3 - 5
⇒ - 5 = 9 - 5
⇒ - 5 ≠ 4
Thus, Point (3, - 14) lie on the line.
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Two plants that are pure bred are crossed. One is short and one is tall, Tall is dominant. What are the expected phenotypes for the offspring?
A. All tall
B. All short
C. Half short, half tall
D. All medium height
The expected phenotypes for the offspring is All tall.
What is Phenotype?Mendel came to the conclusion that some features predominated over other inherited traits when he noticed that a heterozygote offspring might exhibit the same phenotype as the parent homozygote. However, the connection between genotype and phenotype is rarely as straightforward as Mendel's descriptions of dominant and recessive patterns.
Given:
One is short and one is tall, Tall is dominant.
When two plants that are tall and short are crossed. They would all produce tall plants as a result, T.
The first crossing produced these children.
As a result of their parents' TT and SS genes, they all now have TS genes.
There will be some towering and some short off springs when these off springs are crossed. TS and TS will cross at this location. Given that they are all genetically tall and short.
So, The ratio of tall to short children they would have according to Mendel is 3:1.
Hence, almost All are tall.
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K
A recipe for soup calls for 4 tablespoons of lemon juice and cup of olive oil. The given recipe serves 2 people, but a cook wants to make a larger batch that serves 20.
a) How many cups of lemon juice will the chef need for the larger batch?
b) How many pints of olive oil will the che need for the larger batch?
a) The chef needed
cups of lemon juice for the larger batch.
(Type a whole number, proper fraction, or a mixed number.)
Answer: A) 2 and a half B) 5 pints
Step-by-step explanation:
in 1 cup there are 16 table spoons.
a) 4tbsp (2 servings) times 10 (to reach 20 servings) =40 tbsp
40/16 =2.5
ANSWER A= 2 and a half cups of lemon juice.
in 1 pint there are 2 cups.
b)
1 cup = 1/2 a pint,
1/2 pint (2 servings) times 10 (to reach 20 servings) = 5 pints
ANSWER B= 5 pints of olive oil
This is a Algebra probolem
Answer:
B=B1B2B3/B1B2+B2B3+B1B3
Step-by-step explanation:
B1 B2 B3=B2B3B+B1B3B+B1B2B
B2B3B+BB1B3B+B1B2B=B1B2B3
(B2B3+B1B3+B1B2)B=B1B2B3
B=B1B2B3/B2B3+B1B3+B1B2
B=B1B2B3/B1B2+B2B3+B1B3
The quotient of a number and two increased by 2 is 9. What is the number
Answer:
x = 3.5
Step-by-step explanation:
x/2 + 2 = 9
x/2 = 7
x = 3.5
Find the difference 800-699
Answer: The answer is 101
You are getting on a plane to visit family 1200 miles away. The plane you are boarding will travel on
average 500 miles per hour. How long will the trip take you?
Answer:
Step-by-step explanation:
2 hrs 12 mins
Naomi had a total of 168 apps on her phone. She recognized that 25% of the apps were games. How many game apps did Naomi have on her phone? 42 43 57 84
Answer: 42
Step-by-step explanation: 165 x .25 = 42
Answer:
42
Step-by-step explanation:
If Naomi has 168 apps, then 100% is equal to 168 (since that's all her apps)
If 25% of these apps are games, then 25% is equal to x
If we multiply the number of total apps by the percentage of games, we'll find the total number of game apps
First change the percentage into a decimal:
25% = 0.25
Then multiply:
168 * 0.25 = x
Simplify:
x = 42
Another way you can do this is by realizing that 0.25 is equal to 1/4. If 168 is multiplied by 1/4, then that means the resulting equation is:
168/4 = x
x results in the same answer as the previous way:
x = 42
If a family borrows $12,843 for an addition to their home, and the loan is to be paid off in monthly payments over a period of 5 years, how much should each payment be? (Interest has been included in the total amount borrowed.)
The monthly payments over a period of 5 years is $214.05.
What is fixed rate mortgage?A fixed-rate mortgage is a home loan option with a specific interest rate for the entire term of the loan. Essentially, the interest rate on the mortgage will not change over the lifetime of the loan and the borrower's interest and principal payments will remain the same each month.
Given that, a family borrows $12,843 for an addition to their home.
The loan is to be paid off in monthly payments over a period of 5 years
We know that, 5 years = 60 months
Now, monthly payment = Total money/Number of months
= 12,843/60
= $214.05
Therefore, the monthly payments over a period of 5 years is $214.05.
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Given: f(x) = 2/3x-4 and g(x) = x + 1
Four statements about this system are written
below.
I.f(4) = g(4)
II.When x = 12, f(x) = g(x).
III. The graphs of f(x) and g(x) intersect at
(12,4).
IV. The graphs of f(x) and g(x) intersect at
(4, 12).
Which statement(s) are true?
A. II, only
C. I and IV
B. IV, only
D. II and III
The statements that are true about the two given functions intersections are; D. II and III
How to find the points of intersection of functions?The functions we are working with are;
f(x) = ²/₃x - 4
g(x) = ¹/₄x + 1
I) f(4) = ²/₃(4) - 4 = -4/3
g(4) = ¹/₄(4) + 1 = 2
II) f(12) = ²/₃(12) - 4
f(12) = 4
g(12) = ¹/₄(12) + 1
g(12) = 4
III) The coordinates of their intersection is; 12, 4
IV) This is incorrect
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What is the volume of the composite figure shown below? 15 mm 13 mm 15 mm 3 mm 12 mm O 1,008mm^3 O 2,412mm^3 O 2,880mm^3 O 3,465mm^3
The volume of the composite figure is: 2,412 millimeters cubed.
How to find the Volume of the composite figure?
Dimension of top rectangular prism:
Volume of top rectangular prism = 13× 12× 12
Volume of top rectangular prism = 1872 mm³
Dimension of bottom rectangular prism:
Volume of bottom rectangular prism = 15× 12× 3
Volume of bottom rectangular prism = 540 mm³
Volume of the composite figure = 1872 + 540
Volume of the composite figure = 2412 mm³
Therefore the volume of the composite figure is 2412 mm³.
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PLS HELP!! Write an equation for the function graphed above
y=
The trigonometric function equation obtained for the graph is y = 4 sec (πx) - 2.
What is trigonometric function?
Simply put, trigonometric functions also referred to as circular functions are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle.
The upper waver have a value of y = 2 and the lower waves have a value of y = -6.
Add the points and divide by 2 -
[2 + (-6)] / 2
(2 - 6) / 2
-4 / 2
-2
Therefore, the midline is y = -2.
The vertical asymptotes are drawn and they intersect the midline at certain points.
Then the sinusoidal function is drawn using the intersection point.
There is one period of sinusoidal function that is starting from x = 0 and goes upto x = 2.
This pattern tells that the function is of cosine.
Then the graph will be of trigonometric function secant .
The value of C = -2 , A = 4, D = 0
Here C is the midline value, A is the points above and below the midline, D is the horizontal shift and 2π/B is the period.
Now, 2π/B = 2
2B = 2π
B = π
Now, use the formula -
y = A cos (B(x - D)) + C
y = 4 cos (π(x - 0)) - 2
y = 4 cos (πx) - 2
y = 4 sec (πx) - 2
Now plot the graph for the obtained function.
The graph is same as given in the question.
Therefore, the function is y = 4 sec (πx) - 2.
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Write an equation for the following points. (1, 100) (2, 50) (4, 25), (5, 20)
The equation of line is y = -50x + 150
What is Slope?
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Points:(1, 100) (2, 50) (4, 25), (5, 20)
so, the slope is
= (50-100)/ (2-1)
= -50 /1
= -50
using slope intercept form
y - 100 = m (x- 1)
y- 100 = -50(x-1)
y- 100 = -50x + 50
y = -50x + 50 + 100
y = -50x + 150
Hence, the equation of line is y = -50x + 150.
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Solve. Show work.
log3 5 + log3 x = log3 35
Answer:
X=7
Step-by-step explanation:
To solve this equation, we need to use the logarithmic properties. First, we can use the property loga(bx) = x loga(b) to rewrite the equation:
log3(5) + log3(x) = log3(35)
This can be rewritten as:
log3(5x) = log3(35)
Using the property loga(b) = c, we can re-write the equation as:
x = 35/5
Now, we can calculate the value of 35/5:
35/5 = 7
Therefore, the solution to the equation is x = 7.
1. Pemba attempted 25 free throws. She made 12 of them and missed 13.
Show her free-throw results as a fraction. Explain why a fraction is a
useful way to show these statistics.
She made 12 out of 25 free throws, so in fraction it is expressed as 12/25. A fraction is useful here to show how many of her throws are successful compared to all the attempted throws.
A fraction is defined to be a part of a whole. It can also be defined as a numerical quantity that's not an integer. The parts of a whole or collection of things can be represented by a fraction. For instance, to cut a pie in half means we cut the pie so that there will be 2 halves of the pie.
A common fraction has two parts, which are the numerator and the denominator. The number above the line is the numerator, while the number under the line is the denominator. The numerator represents the parts and the denominator represents a whole collection.
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Josh rode his bike 11.4 miles. Claire rode her bike 6.8 miles. Which explains how mental math can be used to find how much farther Josh rode than Claire?
A. Round 11.4 to 11. Round 6.8 to 7. Then subtract 7 from 11 to get 4. Josh rode 4 miles farther than Claire.
B. Add 0.2 to 6.8 to get 7. Subtract 7 from 11.4 to get 4.4. Then add 0.2 to 4.4 to get 4.6. Josh rode 4.6 miles farther than Claire.
C. Subtract 0.4 from 0.8 to get 0.4. Subtract 6 from 11 to get 5. Then add 0.4 to 5 to get 5.4. Josh rode 5.4 miles farther than Claire.
D. Round 11.4 to 11. Round 6.8 to 7. Then subtract 7 from 11 to get 4. Then add 0.4 and 0.8 to 4 to get 5.2. Josh rode 5.2 miles farther than Claire.
The statement that explains how mental math can be used to find how much farther Josh rode than Claire is that to round 11.4 to 11. Round 6.8 to 7. Then subtract 7 from 11 to get 4. Josh rode 4 miles farther than Claire. That is option A.
What is the use of mental maths?The use of metal maths is simply the calculation of a given mathematical problem without the use of an aid such as electronic devices.
The number of miles covered by Josh = 11.4 miles
The number of miles covered by Claire = 6.8 miles
To use mental maths, the values are rounded up to the nearest whole number and the difference between the two are gotten.
That is;
11.4 = 11
6.8 = 7
Therefore the difference in the distance between the two individuals = 11-7 = 4 miles.
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Please help and thank you in advance
Answer:
A. y = -3x + 2
Step-by-step explanation:
Slope of a line perpendicular to another line is the negative reciprocal of the slope of the other line.
1/3 → -3/1
Pat and Rich drove to the beach
last weekend. It took them twice as
long to get back as it did to drive
there. If they spent 9 hours traveling
to and from the beach, how long
did it take them to drive each way?
The total time that it took Pat and Rich to get to the beach is given as 3 hours.
How to solve for the total timeLet's call the time it took Pat and Rich to drive to the beach "t".
Since it took them twice as long to get back, it took them 2t to get back.
The total time they spent traveling was 9 hours, so we can set up an equation:
t + 2t = 9
Combining like terms:
3t = 9
Finally, dividing both sides by 3:
t = 3
So it took them 3 hours to drive to the beach, and 6 hours to drive back.
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Work out the following sheet
x = 112 degrees.
A full triangle is 180 degrees total so do 180 - (39 + 29) = 112.
y = 220 degrees.
The sum of exterior angles are 360 degrees so 360 - 140 = 220.
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Describe each translation in words T(x,y) (x+4,y+9)
The translation means that the x coordinate is moving 4 units to the right and the y coordinate is moving9 units to the right.
What is translation?A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions. The shape just shifts from one place to another, therefore there is no change in the shape.
The translation is T(x,y) (x+4,y+9).
The translation means that the x coordinate is moving 4 units to the right and the y coordinate is moving9 units to the right.
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On the unit circle the radius of the circle is 1, which means x=
Answer:
In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
Step-by-step explanation:
5 What is the solution for y in the following system of equations?
7x + 2y = 8
-
7x+6y= -88
Answer:
working on a answer one second
Step-by-step explanation:
Two companies, Apple and Samsung, have recently conducted aggressive advertising campaigns to maintain and possibly increase their respective shares of the market for mobile phones. Before the advertising campaigns began, the market share of Apple was 45%, whereas Samsung had 40% of the market. Other competitors accounted for the remaining 15%. To determine whether these market shares changed after the advertising campaigns, a marketing analyst solicited the preferences of a random sample of 200 customers of mobile phones. His finding is as follows. Mobile phone brands Number of customers preferred the brand Apple 102 Samsung 82 Others 16 Can the analyst infer at the 5% significance level that customer preferences have changed from their levels before the advertising campaigns were launched?
The degrees of freedom for this test are (3 - 1) = 2. With a 5% significance level and 2 degrees of freedom, the critical value for a chi-squared distribution is 5.991.
How solve the problem?
To determine whether customer preferences have changed, the analyst can conduct a hypothesis test. The null hypothesis is that customer preferences have not changed, and the alternative hypothesis is that customer preferences have changed.
The test statistic used to test this hypothesis is a chi-squared statistic. The formula for the chi-squared statistic is:
X² = ∑((O - E)² / E)
where O is the observed frequency, and E is the expected frequency based on the null hypothesis.
The expected frequency for Apple is 200 * 0.45 = 90, for Samsung is 200 * 0.40 = 80, and for others is 200 * 0.15 = 30.
Calculating the chi-squared statistic:
X² = ∑((102 - 90)² / 90) + ((82 - 80)² / 80) + ((16 - 30)² / 30) = (12² / 90) + (2² / 80) + (14² / 30) = 144 / 90 + 4 / 80 + 196 / 30 = 2.56 + 0.05 + 6.53 = 9.14
The degrees of freedom for this test are (3 - 1) = 2. With a 5% significance level and 2 degrees of freedom, the critical value for a chi-squared distribution is 5.991.
Since 9.14 > 5.991, the analyst can reject the null hypothesis and conclude that customer preferences have changed from their levels before the advertising campaigns were launched.
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explain a drop of 200 feet
Answer:-200
Step-by-step explanation:
determine whether each statement about Jordan's fruit cups is true or false?
The solution of the Jordan's system is 3/2 and -1.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
y = 2x² + 3..............(1)
y – x = 6
y= 6 +x ..............(2)
Put the value from (2) in equation (1) we get
y = 2x² + 3
6+ x = 2x² + 3
2x² + 3 -6 -x = 0
2x² - x - 3 = 0
2x² -3x + 2x -3= 0
x( 2x-3) +1 (2x-3)= 0
(2x- 3)(x+1)= 0
x= 3/2, -1.
Hence, the value is 3/2, -1.
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The Question you have attaches seems to incomplete/ inappropriate.
the complete question is
Jordan is solving this system of equations: y = 2x2 + 3 and y – x = 6. Which statements are true about Jordan’s system? Check all that apply.