Answer:
a. [tex]P(x\le 3) = 0.9957[/tex] and [tex]P(x < 3) = 0.965[/tex]
b. [tex]P(X \ge 4) = 0.0043[/tex]
c. [tex]P(1 \le x \le 3)= 0.5313[/tex]
d. [tex]E(x) = 0.75[/tex] and [tex]\sigma(x)= 0.8441[/tex]
e. [tex]P(0) = 0.0769[/tex]
Step-by-step explanation:
Given
X ~ Bin(15, 0.05)
This implies that:
[tex]n = 15[/tex]
[tex]p =0.05[/tex]
A binomial distribution is represented as:
[tex]P(x) = ^nC_x\ p^x\ (1- p)^{n-x}[/tex]
Solving (a):
(i)
[tex]P(x\le 3)[/tex]
This is solved as:
[tex]P(x\le 3) = P(0) + P(1) + P(2) + P(3)[/tex]
[tex]P(0) = ^{15}C_0\ * 0.05^0\ (1- 0.05)^{15-0} = 1 * 1 * 0.95^{15} = 0.4633[/tex]
[tex]P(1) = ^{15}C_1\ * 0.05^1\ (1- 0.05)^{15-1} = 15 * 0.05 * 0.95^{14} = 0.3658[/tex]
[tex]P(2) = ^{15}C_2\ * 0.05^2\ (1- 0.05)^{15-2} = 105 * 0.05^2 * 0.95^{13} = 0.1348[/tex]
[tex]P(3) = ^{15}C_3\ * 0.05^3\ (1- 0.05)^{15-3} = 455 * 0.05^3 * 0.95^{12} = 0.0307[/tex]
So:
[tex]P(x\le 3) = 0.4644 + 0.3658 + 0.1348 + 0.0307[/tex]
[tex]P(x\le 3) = 0.9957[/tex]
(ii)
[tex]P(x < 3) = P(0) + P(1) + P(2)[/tex]
[tex]P(x < 3) = 0.4644 + 0.3658 + 0.1348[/tex]
[tex]P(x < 3) = 0.965[/tex]
Solving (b):
[tex]P(X \ge 4)[/tex]
This is represented as:
[tex]P(x \le 3) + P(X \ge 4) = 1[/tex]
[tex]P(X \ge 4) = 1 - P(x \le 3)[/tex]
[tex]P(X \ge 4) = 1 - 0.9957[/tex]
[tex]P(X \ge 4) = 0.0043[/tex]
Solving (c):
[tex]P(1 \le x \le 3)[/tex]
This is represented as:
[tex]P(1 \le x \le 3) =P(1) + P(2) + P(3)[/tex]
[tex]P(1 \le x \le 3) = P(1) + P(2) + P(3)[/tex]
[tex]P(1 \le x \le 3)= 0.3658 + 0.1348 + 0.0307[/tex]
[tex]P(1 \le x \le 3)= 0.5313[/tex]
Solving (d): E(x) and Sigma(x)
[tex]E(x) = n * p[/tex]
[tex]E(x) = 15 * 0.05[/tex]
[tex]E(x) = 0.75[/tex]
[tex]\sigma(x)= \sqrt{E(x)* (1-p)}[/tex]
[tex]\sigma(x)= \sqrt{0.75* (1 - 0.05)}[/tex]
[tex]\sigma(x)= \sqrt{0.7125}[/tex]
[tex]\sigma(x)= 0.8441[/tex]
Solving (e):
Calculate P(0) when n= 50
Using: [tex]P(x) = ^nC_x\ p^x\ (1- p)^{n-x}[/tex]
[tex]P(0) = ^{50}C_0 * 0.05^0 * (1- 0.05)^{50-0}[/tex]
[tex]P(0) = 1 * 1 * (0.95)^{50}[/tex]
[tex]P(0) = 1 * 1 * 0.0769[/tex]
[tex]P(0) = 0.0769[/tex]
A car uses 8 gallons of gasoline to travel 192 miles. How many gallons are used to go 144 miles? *
Answer:
6 gallons
Step-by-step explanation:
You can find this using the ration method.
If, 8 gallons : 192 miles
x gallons : 144 miles
We must find the value of x, which is the number of gallons used to travel 144 miles.
Cross multiply the ratios.
192 x = 8 × 144
192 x = 1152
x = 1152 ÷ 192
x = 6
∴ It takes 6 gallons to travel 144 miles.
Find the solutions of the quadratic equation –9x2 + 49 = 0.
Answer:
x=49/18
Step-by-step explanation:
Which of the following is true about the mass of an object? (10 points)
It is equal to its weight.
It is proportional to its weight.
It is always more than its weight.
It changes at different locations.
Step-by-step explanation:
The correct answer is
It is proportional to its weight.
Hope it will help :)❤
Step-by-step explanation:
mass is proportional to the weight of the object
w = mg
A coin is flipped 20 times. It lands on Tails 12 times. What is the experimental probability of landing on Tails?
0.2
0.4
0.5
0.6
Answer:
0.6
Step-by-step explanation:
Answer:
0.2 I think
Step-by-step explanation:
What are the answers to 9 and 10?
Answer:
9. A. AC
10. D. 3
Step-by-step explanation:
:)
In a study of incentives used by companies to retain mature workers by The Conference Board, it was reported that 41% use flexible work arrangements. Suppose that of those companies that do not use flexible work arrangements, 30% give time off for volunteerism. In addition, suppose that of those companies that use flexible work arrangements, 50% give time off for volunteerism. If a company is randomly selected, determine the following probabilities:
a. The company uses flexible work arrangements or gives time off for volunteerism.
b. The company uses flexible work arrangements and does not give time off for volunteerism.
c. Given that the company does not give time off for volunteerism, the company uses flexible work arrangements.
d. The company does not use flexible work arrangements given that the company does give time off for volunteerism.
e. The company does not use flexible work arrangements or the company does not give time off for volunteerism.
Answer:
a) 0.587 = 58.7% probability that the company uses flexible work arrangements or gives time off for volunteerism.
b) 0.205 = 20.5% probability that the company uses flexible work arrangements and does not give time off for volunteerism.
c) 0.3317 = 33.17% probability that the company uses flexible work arrangements.
d) 0.4634 = 46.34% probability that the company does not use flexible work arrangements given that the company does give time off for volunteerism.
e) 0.795 = 79.5% probability that the company does not use flexible work arrangements or the company does not give time off for volunteerism.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
a. The company uses flexible work arrangements or gives time off for volunteerism.
41% use flexible work arrangements.
Of the 100-41 = 59% that do not use flexible work arrangments, 30% give time off for volunteerism. So
[tex]p = 0.41 + 0.59*0.3 = 0.587[/tex]
0.587 = 58.7% probability that the company uses flexible work arrangements or gives time off for volunteerism.
b. The company uses flexible work arrangements and does not give time off for volunteerism.
41% use flexible work arrangements. Of those, 100 - 50 = 50% do not give time off for volunteerism. So
[tex]p = 0.41*0.5 = 0.205[/tex]
0.205 = 20.5% probability that the company uses flexible work arrangements and does not give time off for volunteerism.
c. Given that the company does not give time off for volunteerism, the company uses flexible work arrangements.
Here, we use conditional probability.
Event A: Does not give time off for volunteerism
Event B: Uses flexible work arrangments.
0.205 = 20.5% probability that the company uses flexible work arrangements and does not give time off for volunteerism.
This means that [tex]P(A \cap B) = 0.205[/tex]
Probability that the company does not give time off for volunteerism:
0.205(uses flexible work arrangments).
100 - 30 = 70% of 59%. So
[tex]P(A) = 0.205 + 0.7*0.59 = 0.618[/tex]
The desired probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.205}{0.618} = 0.3317[/tex]
0.3317 = 33.17% probability that the company uses flexible work arrangements.
d. The company does not use flexible work arrangements given that the company does give time off for volunteerism.
Again conditional probability.
Event A: Gives time off for volunteerism
Event B: Does not use flexible work arrangements.
Probability of giving time off for volunteerism:
50% of 41%(have flexible work arrangements).
30% of 59%(don't have flexible work arrangements).
So
[tex]P(A) = 0.5*0.41 + 0.3*0.59 = 0.382[/tex]
Gives time off for volunteerism and does not use flexible work arrangements.
30% of 59%. So
[tex]P(A \cap B) = 0.3*0.59 = 0.177[/tex]
The desired probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.177}{0.382} = 0.4634[/tex]
0.4634 = 46.34% probability that the company does not use flexible work arrangements given that the company does give time off for volunteerism.
e. The company does not use flexible work arrangements or the company does not give time off for volunteerism.
Does not use flexible work arrangments: 59%
Dont give time off for volunteerism(70% already in the 59%, so we dont add) and 50% of 41%.
[tex]p = 0.59 + 0.5*0.41 = 0.795[/tex]
0.795 = 79.5% probability that the company does not use flexible work arrangements or the company does not give time off for volunteerism.
This scatter plot shows a relationship between
the outdoor temperature and number of cusomers
in an ice cream store. Which best describes the
relationship between the variables?
Help please, stuck on this one!
Answer:
AFCE = 30
P+Q = 11
Step-by-step explanation:
From the picture, you can see the figure can be decomposed into two identical large triangles with area 20, and 4 identical longer ones, that have to cover the remaining area 40, thus 10 each.
From that you can count the area.
Second puzzle is just trial and error.
Why is the product of a rational number and an irrational number irrational? because the product is always a non-terminating, non-repeating decimal because the product is always a fraction because the product is always a negative number because the product is always a repeating or a terminating decimal
Answer:
Because the product is always a non-terminating, non-repeating decimal.
The product of a rational number and an irrational number will always be an irrational number. Then the correct option is A.
What is a rational number?If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.
The product of a rational number and an irrational number will always be an irrational number.
Because the product is always a non-terminating, non-repeating decimal number.
Then the correct option is A.
More about the rational number link is given below.
https://brainly.com/question/9466779
#SPJ2
Find the values of x and y. Write your answer in simplest form.
Answer:
x=30°
y=30°
Step-by-step explanation:
x= 180-150=30°
y)
180=30 + 90 + z
z +120 = 180
z= 60
90-60=y
y=30
30°
use the distributive property to write the following expressions in expanded form 8(a+3b)
Answer:
8a + 24b
Step-by-step explanation:
'distributive' is just like sharing across
Answer:
8a + 20b + 4b
Step-by-step explanation:
Distributing it would be 8a+24b so expanding it would equal: 8a+20b+4b
After a few hours, a colony of bacteria that doubles every hour has 8000 bacteria. After n more hours, there will be T more bacteria as given by the equation
T = 8000(2)". Find the number of bacteria that will be present in 4 hours?
Answer:
T= 16000(2)
=36 000
T=36 000(2)
=72 000 in 4 hours
Help please quickly!!!!!!1
Answer:
[tex]9[/tex]
Step-by-step explanation:
As per the problem, the given triangle is a right triangle. This is signified by the box around one of its angles, this box states that the angle it is surrounding is a right angle.
Since it is a right triangle, one can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that; ([tex]a^2 + b^2 = c^2[/tex]), where ([tex]a[/tex]) and ([tex]b[/tex]) are the legs of the right triangle, or the sides adjacent to the right angle. ([tex]c[/tex]) is the hypotenuse or the side opposite the right angle.
Substitute in the given values and solve, note that ([tex]a[/tex]) represents the unknown leg (side).
[tex]a^2 + b^2 = c^2\\\\a^2 + (\sqrt{19})^2 = (100)^2\\\\a^2 + 19 = 100[/tex]
Inverse operations,
[tex]a^2 + 19 = 100\\-19\\\\a^2 = 81\\\\a = \sqrt{81}\\\\a = 9[/tex]
asking for a friend but what is 1/3 ÷ 4? (ill mark you)
Answer:
Answer is 1/12
Step-by-step explanation:
It is the same as 1/3 x 1/4. Hence, giving us 1/12 as answer.
please solve the 5 questions for 5 brainlist and 5 star mark and 17 points
Answer:
1) 27
2) 2/5
3) 1
4) 1.5 lbs
Step-by-step explanation:
1) First, 8505/315 = 27
2)I don't really have an explanation for this one-
3) 2/3 = 6/9. 6/9 + 3/9 = 1
4) 4/8 x 3 = 1.5
1. 2
8,505 ÷ 315 = 27
2. 2 ÷ 5
Fractions are division problems so it would be 2 divided by 5
3. 9/9 or 1
Make them have the same denominator
2/3 + 3/9 = 6/9 + 3/9 = 9/9 = 1
4. 1 ½
4/8 simplified is ½ so you should do ½ x 3 = 1 ½
5. The baker needs 750 more grams
Multiply 2.5 by 1000, which is 2500
That’s how many grams the baker needs, now you need to do 2500 - 1750
Which is 750 grams
Sorry that this took a while, but I am happy to help you!!
pls help I have to turn it in by Monday morning and it’s 1am or I fail
Answer:
w=36
f=12
k=13
Step-by-step explanation:
Answer:
5f=60 f=60/5 f= 12 check: 12× 5 =60The insurance company has determined that in any one year, the probability that George will have a car accident is 0.05 and that if he has an accident, the probability that he will be hospitalized is 0.40.
Find the probability that George will have an accident but not be hospitalized. Write your answer in decimal form.
PLS ANSWER QUICKLY AND PLS ANSWER CORRECTLY TEST WORTH 20 PERCENT OF MY GRADE
Answer:
b just tool the test
Step-by-step explanation:
- Jared rides his bicycle 6 miles in 3/5 of an hour. At this rate, how many miles
could he ride in 3 hours?
Answer:
30 miles
Step-by-step explanation:
3 hours = 180 minutes
3/5 of an hour = 36 minutes
180/36 = 5
5 times 6 = 30
I hope this helps :)
a) List the differences between Linear and Exponential Functions.
Answer:
What is the difference between linear and exponential functions? Linear functions change at a constant rate per unit interval. An exponential function changes by a common ratio over equal intervals.
Urgent! Math! Consider jkl below
Answer:
Correct, Incorrect, Incorrect, Correct
Step-by-step explanation:
sin is opposite over hypotenuse
tan is opposite over adjacent
25°
y
X120°
y = [? ]
Answer:
95
Step-by-step explanation:
ur welcome
brainliest plz
In AMNO, m = 720 cm, n = 160 cm and o=870 cm. Find the measure of 20 to the
nearest degree.
The measure of angle O from the triangle MNO is 156.92°.
What is cosine rule?In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.
The formula for the cosine rule is c=√(a²+b²-2ab cosC)
Given that, in triangle MNO, m = 720 cm, n = 160 cm and o=870 cm.
Now, 870=√(720²+160²-2×720×160 cosO)
870²=720²+160²-2×720×160 cosO
756900=544000-230400 cosO
212900=-230400 cosO
cosO= -212900/230400
cosO= -0.92
∠O=156.92°
Therefore, the measure of angle O from the triangle MNO is 156.92°.
Learn more about the cosine rule here:
https://brainly.com/question/26952873.
#SPJ1
Answer:
158
Step-by-step explanation:
I DONT WANT HOW TO DO IT JUST THE ANSWER- DO BOTH
Answer:
a) 1200
b) 450
c) 380
d) 560
Step-by-step explanation:
What are the values of m and 0 in the diagram below?
Answer:
The correct answer ishope it helps
My Pool party has 3839 girls and 2638 boys. How many People Altogether?
Answer:
6477
Step-by-step explanation:
wow, u got a big party there
Answer:
dangggg but 6477
Step-by-step explanation:
cashews cost $1.74 per pound. walnuts cost $1.92 per pound. how much will 3 1/3 pounds of cashews and 2 5/8 pounds of walnuts cost in all?
Answer:
6.09+3.84=9.93 is the desired answer
Step-by-step explanation:
Cashews total cost step by step
1.74×3.5
Multiply 1.74 and 3.5 to get 6.09.
6.09
Peanuts total cost step by step
1.92×2
Multiply 1.92 and 2 to get 3.84.
3.84
HELP PLZ................
Find the equation of the straight line that passes through these pairs of points -4 ,2 and 1,7
Answer:
Y=x+6
Step-by-step explanation:
to find out the slope you use the equation y2-y1/x2-x1. When you plug in the coordinates it will look like 7-2/1-(-4) and this is equal to 5/5 which can be simplified to 1. So the slope is 1! Now to find the y intercept you have to do b=y1-m*x1! If you plug into the coordinate it will be b=2−(1)⋅(−4) which is equal to 6. Then to construct out equation of the line it will be y=mx+b so now we plug in the slope and the y intercept so that the equation would be y=x+6
Malachy was thinking of a number. Malachy divides by 2, then adds 9 to get an answer of 4. What was the original number?
Answer:
The number is -10
Step-by-step explanation:
I will answer this while I read through the question.
Let the number be x
Divide by 2
[tex]\frac{x}{2}[/tex]
Add 9 to it
[tex]\frac{x}{2} + 9[/tex]
It gives 4
[tex]\frac{x}{2} + 9 = 4[/tex]
Now, we solve for x
Collect Like Terms
[tex]\frac{x}{2} = 4-9[/tex]
[tex]\frac{x}{2} = -5[/tex]
Make x the subject
[tex]x = -5 *2[/tex]
[tex]x = -10[/tex]