Answer:
[tex]E(X_n)=\frac{2(n-1)}{27}[/tex]
[tex]E(y)=\frac{14}{9}[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size n=9
Number of Green [tex]g=4[/tex]
Number of yellow [tex]y=4[/tex]
Number of white [tex]w=4[/tex]
Probability of Green Followed by yellow P(GY) ball
[tex]P(GY)=\frac{4}{9}*\frac{3}{9}[/tex]
[tex]P(GY)=\frac{4}{27}[/tex]
Generally the equations for when n is even is mathematically given by
[tex]Probability of success P(S)=\frac{4}{27}[/tex]
[tex]Probability of Failure P(F)=\frac{27-4}{27}[/tex]
[tex]Probability of Failure P(F)=\frac{23}{27}[/tex]
Therefore
[tex]E(X_n)=\frac{n}{2}*P[/tex]
[tex]E(X_n)=\frac{n}{2}*\frac{4}{27}[/tex]
[tex]E(X_n)=\frac{2n}{27}[/tex]
Generally the equations for when n is odd is mathematically given by
[tex]\frac{n-1}{2}[/tex]
[tex]E(X_n)=\frac{n-1}{2}*\frac{4}{27}[/tex]
[tex]E(X_n)=\frac{2(n-1)}{27}[/tex]
b)
Probability of drawing white ball
[tex]P(w)=\frac{2}{9}[/tex]
Therefore
[tex]E(w)=\frac{1}{p}[/tex]
[tex]E(w)=\frac{1}{\frac{2}{9}}[/tex]
[tex]E(w)=\frac{9}{2}[/tex]
Therefore
[tex]E(y)=[E(w)-1]\frac{4}{9}[/tex]
[tex]E(y)=[\frac{9}{2}-1]\frac{4}{9}[/tex]
[tex]E(y)=\frac{14}{9}[/tex]
Find each product.
1. 2x(x^2-6x+3)
2. 2a^2(5b^2 + 3ab + 6a + 1)
Given:
The expressions are:
[tex]2x(x^2-6x+3)[/tex]
[tex]2a^2(5b^2+3ab+6a+1)[/tex]
To find:
The product of each expression.
Solution:
According to the distributive property of multiplication over addition, we get
[tex]a(b+c)=ab+ac[/tex]
The first expression is:
[tex]2x(x^2-6x+3)[/tex]
Using distributive property of multiplication over addition, we get
[tex]2x(x^2-6x+3)=(2x)(x^2)+(2x)(-6x)+(2x)(3)[/tex]
[tex]2x(x^2-6x+3)=2x^3-12x^2+6x[/tex]
Therefore, the product of [tex]2x(x^2-6x+3)[/tex] is [tex]2x^3-12x^2+6x[/tex].
The second expression is:
[tex]2a^2(5b^2+3ab+6a+1)[/tex]
Using distributive property of multiplication over addition, we get
[tex]2a^2(5b^2+3ab+6a+1)=(2a^2)(5b^2)+(2a^2)(3ab)+(2a^2)(6a)+(2a^2)(1)[/tex]
[tex]2a^2(5b^2+3ab+6a+1)=10a^2b^2+6a^3b+12a^3+2a^2[/tex]
Therefore, the product of [tex]2a^2(5b^2+3ab+6a+1)[/tex] is [tex]10a^2b^2+6a^3b+12a^3+2a^2[/tex].
The two lines below intersect as shown what the value of x (2x+29) (9x-13)
Given:
Two lines intersect each other.
Consider the below figure attached with this question.
To find:
The value of x.
Solution:
If two lines intersect each other then the vertically opposite angles are congruent and their measures are equal.
In the given figure, the measures of two vertically opposite angles are (2x+29)° and (9x-13)°.
[tex]2x+29=9x-13[/tex]
[tex]2x-9x=-29-13[/tex]
[tex]-7x=-42[/tex]
Divide both sides by -7.
[tex]x=\dfrac{-42}{-7}[/tex]
[tex]x=6[/tex]
Therefore, the value of x is 6.
Mr. Catone noticed that many of the students in his classes had been born in
another country. He randomly chose 16 students and found that 7 of them
had been born in another country. If Mr. Catone's sample is representative,
which of the following is closest to the number of his 144 students who were
born in another country?
o
A. 54
Option A
B. 63
O
C. 72
D. 112
O
Item #3050
Please help me with this!!!!! I don't get it
Answer:
y = -1/7
Step-by-step explanation:
Mathematically, the distance between two points on a coordinate plane can be calculated using the formula;
d = √(x2-x1)^2 + (y2-y1)^2
for the first two points;
(5,y) and (1,4) ; we have
d = √(5-1)^2 + (y-4)^2
d = √(y-4)^2 + 16
For the other two;
(5,y) and (10,-3)
We have ;
d = √(5-10)^2 + (y + 3)^2
d = √(y+ 3)^2 + 25
from the question, these two distances are equal
all we have to do here is to equate the two distances
So we have it that;
(y-4)^2 + 16 = (y + 3)^2 + 25
y^2 -8y + 16 + 16 = y^2 + 6y + 9 + 25
-8y + 32 = 6y + 34
-8y -6y = 34-32
-14y = 2
y = -2/14
y = -1/7
Can someone help please
Answer:
geometric
common ratio 2/3
Step-by-step explanation:
We know that the sequence is not arithmetic
3-2 =1
2-4/3 = 6/3 -4/3 = 2/3
The common difference is not the same
Now check geometric
The common ratio:
Take the second term over the first term
2/3
Now take the third term over the second term
4/3 ÷ 2
4/3 * 1/2 = 2/3
The common ratio is the same so the sequence is geometric with a common ratio of 2/3
Math help please urgent
Answer:
THREE AND SIX OR FOUR AND FIVE
Step-by-step explanation:
They're just opposite ends !
Step-by-step explanation:
Alternate Interior Angles: 3 and 6
Alternate Exterior Angles: 2 and 7
Jessie borrowed $1800 from the bank at a rate of 7.5% simple interest per year. Over the course of 4 years, how much interest did he pay?
22 dividido en 3 es?
Answer:
Step-by-step explanation:
7.3
Answer:
7.3
Step-by-step explanation:
22/3 = 22/3
(Decimal: 7.333333)
find the percent increase is admission to the amusement park is raised from $70 to $80.
Answer:
14.286% increase
Step-by-step explanation:
Since the admission to the amusement park increased by $10 we need to find what percentage of $70 equals $10.
We can find this percentage by multiplying 10 (the difference in money) by 100 (a hundred percent), and dividing that by 70 (the initial cost)
[tex]10*100/70=14.286[/tex]
12. The local regional transit authority of a large city was interested in determining the mean
commuting time for workers who drive to work. They selected a random sample of 125
workers who drive to work and asked them how long they spent commuting to work in
minutes). A 95% confidence interval was constructed and reported as (27.74, 30.06).
(a) Show that the conditions for calculating a confidence interval for a mean are satisfied.
(b) Interpret the interval in the context of this problem.
1. We conclude that the conditions for calculating a confidence interval for a mean are satisfied.
2. Since interval was constructed and is reported, we assume that distribution of the sample mean is normal.
Do the conditions for a mean confidence interval calculation hold?Let x be the sample mean
Let s be the sample standard deviation
Let n be the sample size
Let α be the significance level
Let Z be the standard normal distribution value.
To determine if conditions for calculating confidence interval for a mean are met, we have to check the followings:
1. Random sampling:
The sample of 125 workers was selected randomly.
2. Independence:
We assume that each worker's commuting time is independent of each other.
3. Sample size:
n = 125 > 30. This satisfies the condition for the central limit theorem to apply.
4. Normality:
The 95% confidence interval was constructed using the formula x ± Zα/2(s/√n).
Since interval was constructed and is reported, we can assume that the distribution of the sample mean is approximately normal. Therefore, we can conclude that the conditions for calculating a confidence interval for a mean are satisfied.
Read more about confidence interval
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I need to find the sum of the interior angel
pls telll/pls tell pls tell pls tell
Answer: 2
Step-by-step explanation:
Given
The polynomial is [tex]x^4+x^3-2x^2+x+1[/tex] is divided by [tex]x-1[/tex]
According to the remainder theroem
[tex]\Rightarrow x-1=0\\\Rightarrow x=1[/tex]
Put [tex]x=1[/tex] in the polynomial to get the remainder
[tex]\Rightarrow 1+1-2+1+1\\\Rightarrow 2[/tex]
So, we get the remainder 2.
Students at a local high school travel to school by car, bus, and bicycle. 1/5 of the 825 students Tavel by car, 48% of the students travel by bus, 0.08 of the students travel by bicycle. The remaining students travel to school by walking. How many students walk to the local high school?
Answer:
198 students walk to the local high school
Step-by-step explanation:
Total number students = 825
1/5 of the students travel by car
48% of the students travel by bus
0.08 of the students travel by bicycle
To find the number of students who wal to school we have to find the exact number of students who travel to school by car, bus and bicycle and subtract the result from the total number of students
Students who travel by car = 1/5×825
= 165 students
Students who travel by bus = 48% × 825
= 48/100 × 825
= 12/25 × 825
= 396 students
Students who travel by bicycle = 0.08 × 825
= 66
So now we add the results fo the equations above and subtract it from the total number of students to get the number of students that walk to school
Students that walk to school = 825 - (165 + 396 + 66)
= 825 - 627
= 198 students
Therefore 198 students walk to the local high-school
which veal represents the functions ?
A. graph A only
B. graph D only
C. graph B and graph D
D. graph C and graph D
hola quien habla español bueno ya no Adios :)
Answer:
C.(B and D
Step-by-step explanation:
9.2\times 10^{-3}-1.3\times 10^{-3}
9.2×10
−3
−1.3×10
−3
Answer:
73
Step-by-step explanation:
9.2 x 10 - 3 - 1.3 x 10 - 3
92 -3 - 13- 3
73 is the answer if that the question
Answer:
[tex](9.2 \times {10}^{ - 3}) - (1.3 \times {10}^{ - 3} ) \\ \\ = { \tt{(9.2 - 1.3) \times {10}^{ - 3} }} \\ \\ = { \tt{7.9 \times {10}^{ - 3} }}[/tex]
On a set of blueprints, the length of a building is 16 inches. The actual building is 85 1/3 feet long. Which of the following is the correct scale?
1:64
1:5
1:32
1:12
Answer:
1 : 64
Step-by-step explanation:
We require the dimensions to be the same units
1 foot = 12 inches , then
85 [tex]\frac{1}{3}[/tex] feet = [tex]\frac{256}{3}[/tex] × 12 = 256 × 4 = 1024 inches
Scale is then
16 in : 1024 in ( divide both parts by 16 )
= 1 : 64
Help someone plsss!!!!!!!!!!
Answer:
150 degrees.
Step-by-step explanation:
We know, 1 Hour angles = 15 Degrees
So, 10 hour walking = 10*15 = 150 degrees
Hope this will help. Please mark me brainliest.
Calculate the measure of angle P:
Answer:
122.3 degrees
Step-by-step explanation:
To get the measure, we use the appropriate method
The method we are going to use here is the cosine rule
We have the general form as;
a^2 = b^2 + c^2 -2bc Cos A
where a = 25
b = 9 and c = 19
Substituting these values;
25^2 = 9^2 + 19^2 - 2(9)(19) Cos A
183 = -342 cos A
cos A = -183/342
cos A = -0.54
A = arc cos -0.54
A = 57.65 ( since cosine is negative in the second quadrant, then the value will be 180 - 57.65
= 122.35
Please give real answers with an explaination. 50 points + 5-star rated. No Docs/No Files/No Links only answer with explaination.
Answer:
x = 135°
Step-by-step explanation:
4 sides and the diagonal are the same.
Therefore, it is square with each interior angle = 90°
The diagonal bisects the interior angle to 45° , 45°
x + 45° = 180° [ straight line angle ]
x = 180 - 45 = 135°
Ridas father is 4 times old as rida. After 5 years father will be three times as old as rida.Find their present ages
Answer:
Rida is 10 years old and her father is 40 years old.
Step-by-step explanation:
Given:
Present age
Present age of Rida = x
Present age of Rida's father = 4x
Age after 5 years
Age of Radi after 5 years = x + 5
Age of Radi's father after 5 years = 3(x + 5)
What To Find:
The present age of Rida and Rida's father.
Solution:
According to the statement the equation will be,
⇒ 4x + 5 = 3(x + 5)
Remove and solve the brackets,
⇒ 4x + 5 = 3x + 15
Take numbers to RHS and variable to LHS,
⇒ 4x - 3x = 15 - 5
Subtract 3x from 4x and 5 from 15,
⇒ x = 10
Now substitute the values of Rida's age and Rida's father's age,
Rida's age = x = 10 years
Rida's father's age = 4x = 4(10) = 40 years
What is The answer , what goes in the QR
may be QR also equal to 34
find the area of the irregular figure. 2in. 5in. 2in. 4in. 4in. 3in. 3in.
The shape can be split into 3 separate shapes:
On the left side a square 3 x 3 = 9 square inches.
The middle rectangle that is 2 x 5 = 10 square inches
The bottom rectangle which is 4 x 4 = 16 square inches
Total area = 9 + 10 + 16 = 35 square inches
A particular strain of bacterium has 20 bacteria in generation 1 and triples in
population every generation. The explicit formula for the number of bacteria
in generation n is:
a(n) = 20-3(n-1)
How many bacteria are in generation 9?
A. 480
B. 131,220
C. 6561
D. 393,660
evaluate the expression 4(n+5)-8 when n =1/4 and m=0.5
Answer:
17
Step-by-step explanation:
Given
4(n + 5) - 8m ← substitute n = 0.25, m = 0.5 into the expression
= 4(0.25 + 5) - 8(0.5)
= 4(5.25) - 4
= 21 - 4
= 17
A table tennis ball has a radius of 2 cm. There are 3 table tennis balls stacked on top of one another in a cylinder that has the same diameter as the table tennis balls. The table tennis balls reach the top and bottom of the cylinder. How much volume is left inside the cylinder when the container is full?
Answer:
Volume left = 16π cm³ or 50.265 cm³
Step-by-step explanation:
Let's first find the surface area of the tennis ball.
S.A = (4/3)πr³
Radius of a ball = 2 cm
Thus;
S.A = (4/3)π(2)³
S.A = 32π/3
Since there are 3 radius balls that will make the cylinder full, then;
Surface area of 3 balls = 3 × 32π/3 = 32π
Now, formula for volume of cylinder is;
V = πr²h
r = 2 cm
h = 4 × 3 = 12 (since diameter of tennis ball is 4 cm)
Thus;
V = π × 2² × 12
V = 48π
Thus;
Volume left = Volume of cylinder - surface area of 3 balls = 48π - 32π = 16π cm³ or 50.265 cm³
The graph shown below represents the rate at which water drains from a tank once the drain is opened which statement correctly describes the graph
A. The water is draining at constant rate of 1/2 gallon per minute, and the tank contained exactly 14 gallons when the drain opened
B. The water is draining at a constant rate of 2 gallons per minute,and the tank contained exactly 14 gallons when the drain was opened
C. The water is draining at a constant rate of 5 gallons per minute, and the tank contained exactly 14 gallons when the drain was opened
D.the water is draining at a constant rate of 14 gallons per minute, and the tank contained exactly 1/2 gallon when the drain was opened
Answer:
A
Step-by-step explanation:
The slope is -1/2 and the y-intercept is 14
Please help me with these questions
Answer:
A. <EKH and <EKF
B. <EKH and <FKG
C. <HKJ and <GKJ
Step-by-step explanation:
A. A linear pair are two adjacent angles that forms a straight line that equals 180°.
<EKH and <EKF is a linear pair
B. A pair of vertical angles are opposite angles formed when two straight lines intersect. They share a common vertex.
<EKH and <FKG
C. Adjacent angles share a common vertex and a common side. The pair of adjacent angles that are not a linear pair will not form a straight line.
<HKJ and <GKJ are adjacent angles that share the same vertex (<K) and the same side (KJ). However they do not form a straight line. Therefore, <HKJ and <GKJ are a pair of adjacent angles that are not a linear pair.
Ranking brainliest if correct
Answer:
Hello! answer: 18
Step-by-step explanation:
AC = 27 DF = 9 those are both the bottom sides of the triangles so we can find AB with this info so... 27 ÷ 9 = 3 DE = 6 6 × 3 = 18 therefore AB = 18 hope that helps!
help please hurryyyy!!! help pls hurry
Answer:
3 is 18
4 is 14
5 is 10
6 is 6
I hope this helps
help me with this mathematics
Answer: B
Step-by-step explanation: 65/100 = 65%
