Answer:
a) 0.3087 = 30.87% probability that exactly two iPhones will end up being serviced under warranty.
b) 0.4718 = 47.18% probability that at least two iPhones will end up being serviced under warranty
c) The expected number of iPhones in the family that require service is 1.5.
d) The standard deviation of the number of iPhones in the family that requires service is 1.0247.
Step-by-step explanation:
For each iPhone, there are only two possible outcomes. Either they have battery issues under warranty, or they do not. iPhones are independent. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Thirty percent of such iPhones will need battery service while under warranty.
This means that [tex]p = 0.3[/tex]
A family owns 5 iPhones produced within the time frame of potential faulty production.
This means that [tex]n = 5[/tex]
(a) What is the probability that exactly two iPhones will end up being serviced under warranty?
This is P(X = 2).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{5,2}.(0.3)^{2}.(0.7)^{3} = 0.3087[/tex]
0.3087 = 30.87% probability that exactly two iPhones will end up being serviced under warranty.
(b) What is the probability that at least two iPhones will end up being serviced under warranty?
This is:
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{5,2}.(0.3)^{2}.(0.7)^{3} = 0.3087[/tex]
[tex]P(X = 3) = C_{5,3}.(0.3)^{3}.(0.7)^{2} = 0.1323[/tex]
[tex]P(X = 4) = C_{5,4}.(0.3)^{4}.(0.7)^{1} = 0.0284[/tex]
[tex]P(X = 5) = C_{5,5}.(0.3)^{5}.(0.7)^{0} = 0.0024[/tex]
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.3087 + 0.1323 + 0.0284 + 0.0024 = 0.4718[/tex]
0.4718 = 47.18% probability that at least two iPhones will end up being serviced under warranty.
(c) What is the expected number of iPhones in the family that require service?
[tex]E(X) = np = 5*0.3 = 1.5[/tex]
The expected number of iPhones in the family that require service is 1.5.
(d) What is the standard deviation of the number of iPhones in the family that requires service?
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{5*0.3*0.7} = 1.0247[/tex]
The standard deviation of the number of iPhones in the family that requires service is 1.0247.
For each ordered pair determine if it is a solution to 7x+5y=9
(-4,-3)
(-3,6)
(5,0)
(2,-1)
The sum of three numbers is 83. The first number is 8 more than the second. The third number is 3 times the second. What are the numbers?
Answer:
23, 15 and 45
Step-by-step explanation:
a+b+c = 83
a = b + 8
c = 3*b
(b+8) + b + 3*b = 83
5*b + 8 = 83
5*b = 75
b = 15
a = b + 8 = 15 + 8 = 23
c = 3*b = 3*15 = 45
Verification
a+b+c = 23 + 15 + 45 = 83; correct
If a hummingbird hunted like an eagle, would its beak be useful?
Answer:
No
Step-by-step explanation:
hehe pls help i nneed it
Answer:
x = 32
Step-by-step explanation:
180 - 42 - 106 = x
x = 32
Graph the line with the equation y = – 1/5x-3
Answer:
Check image
Step-by-step explanation:
Can someone please help
Answer:
take 121 subtract it from 180 and you get 59 so angle d is 59°. and angle b is 154°
Need help with this bc I suck at math:(
Answer:
-45c
Step-by-step explanation:
Answer:
4c
Step-by-step explanation:
[tex]\frac{-60*c^{7} }{-15*c^{4}}[/tex]
Let's reduce the numbers and then we'll reduce exponents of c.
[tex]\frac{-60}{-15}=4[/tex]
Using exponent rules, we simply subtract the exponent from the top and the exponent from the bottom.
7 - 6 = 1
The exponent of c is 1, which is just c
Combining this, we get 4c
The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads. Which sentence most closely summarizes the data?
Answer:
About 80 necklaces have more than 28 beads.
Step-by-step explanation:
What slope is being shown in the equation:
y-9=-3(x+6)
¿cuál. es el. valor. nutricional total de la naranja ?
Answer:
Las naranjas aportan cantidades importantes de vitamina C y folatos. Tienen un contenido apreciable de tiamina, vitamina A, calcio, potasio yfibra y destacable contenido de carotenoides y flavonoides.
Step-by-step explanation:
Answer:
Las naranjas aportan cantidades importantes de vitamina C y folatos. Tienen un contenido apreciable de tiamina, vitamina A, calcio, potasio yfibra y destacable contenido de carotenoides y flavonoides.
Step-by-step explanation:
How does 39.54 compare to 39.4
Answer:
39.54 is greater than 39.4
Step-by-step explanation:
Answer:
39.54 is LESS than 39.4
Juan purchased a T-shirt for $18 plus sales tax. Sales tax is 4.5%. How much sales tax did Juan pay?
Answer:
$22.5%.....i think....not sure
Step-by-step explanation:
i've added $18 plus tax%.....not sure if its the answer
Answer: $5.63
Step-by-step explanation:
4.5% Divided By 100 To Get 0.045 Then I Multiplied That By $125 And Got 5.625 .. I Rounded It To $5.63
Ford provides an option of a sunroof and side air bag package for its Windstar model. This package costs$1400. Ford wants todetermine the percentage of Windstar buyers who would pay $1400 extra for the sunroof and side air bags. How many Windstar buyers must be surveyed if we want to be 95% confident that the sample percentage is within four percentage points of the true percentage for all Windstar buyers
Answer:
601 buyers must be surveyed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
How many Windstar buyers must be surveyed if we want to be 95% confident that the sample percentage is within four percentage points of the true percentage for all Windstar buyers?
We need to survey n buyers. n is found when [tex]M = 0.04[/tex]. We dont have an estimate for the proportion, so we use [tex]\pi = 0.5[/tex], which is when the largest sample will be needed.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.04}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2[/tex]
[tex]n = 600.3[/tex]
Rounding up
601 buyers must be surveyed.
I cut a pizza in half. Then I cut each half into 3 equal pieces and each piece into 2 equal slices. I sold 6 slices. What fraction of the pizza did I sell?
Answer:
6/12
Step-by-step explanation:
im pretty sure, i did it on a paper correct me if im wrong sorry if i am
The Gable Construction Corporation has placed bids for installing electronic message boards on two different highways.
Because of competition from other companies, Gable Construction Corporation officials estimate that the probability that
they will be awarded the Macon Expressway contract is 0.65 and the probability that they will be awarded the Seaview
Expressway contract is 0.43. Furthermore, the probability that they will be awarded both contracts is 0.22. What is the
probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway
Answer:
0.64 = 64% probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway
Step-by-step explanation:
We solve this question using these events as Venn sets.
I am going to say that:
Event A: Awarded the Macon Expressway.
Event B: Awarded the Seaview Expressway.
Probability that they will be awarded the Macon Expressway contract is 0.65
This means that [tex]P(A) = 0.65[/tex]
The probability that they will be awarded the Seaview Expressway contract is 0.43.
This means that [tex]P(B) = 0.43[/tex]
Furthermore, the probability that they will be awarded both contracts is 0.22.
This means that [tex]P(A \cap B) = 0.22[/tex]
What is the
Probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway?
Only A:
[tex]P(A) - P(A \cap B) = 0.65 - 0.22 = 0.43[/tex]
Only B:
[tex]P(B) - P(A \cap B) = 0.43 - 0.22 = 0.21[/tex]
Either
0.43 + 0.21 = 0.64
0.64 = 64% probability that they will be awarded the contract for either the Macon Expressway or the Seaview Expressway
What is 7 / 2 0 to 5
40÷ 1/25
1/3÷15
Change this mixed number into a improper fraction 3 5/9
11/15×3/44
1/8×32
54 1/2-42 3/4
3/4-1/2
15/16-7/16
Find the common denominator 3/5 and 7/9
Find the common denominator 3/9 and 1/4
Help please!!!
Which of the following are statistical questions? How many text messages did you send today? What are the ages of the students in Mark’s school? How many days are in a year? How many teeth does Fred have in his mouth? A. Only IV B. Only II C. Only III D. Only I
Answer:
Only 2
Step-by-step explanation:
Can someone help me ?!
Answer:
95
Step-by-step explanation:
3x + x = 380
4x = 380
x= 95
proof
3*95 = 285
Your share of 285 plus that of your friend shares of 95 will give you the total shares of 380
need help pleaseeee !!!
Answer:
A (0,8)
B (1,4)
C (2,2)
D (3,1)
A digital communication channel transmits bits of information, usually designated as 0 and 1. If a sender transmits a 0, he/she hopes the recipient receives a 0. If a sender transmits a 1, he/she hopes that the recipient receives a 1. Unfortunately, this is not always the case. Suppose on a certain transmission line, a transmitted 0 is received correctly 90% of the time (10% of the time a 1 is received), and a transmitted 1 is received correctly 74% of the time. (26% of the time a 0 is received.) It is known that on this transmission line, 80% of all bits transmitted are 0 bits. A randomly selected transmitted bit is examined. Say its value is X. The bit received is Y. a.What is the probability that X
Answer:
a) 0.80
b) 0.72
c) 0.02
Step-by-step explanation:
It is assumed that
X = Bit transmitted
Y = Bit received
[tex]X^{0}[/tex] = Transmissted bit is 0
[tex]X^{1}[/tex] = Transmissted bit is 1
[tex]Y^{0}[/tex] = Received bit is 0
[tex]Y^{1}[/tex] = Received bit is 1
As per the given condition
P [ [tex]Y^{0}[/tex] | [tex]X^{0}[/tex] ] = 90%
P [ [tex]Y^{0}[/tex] | [tex]X^{1}[/tex] ] = 100% - 90% = 10%
P [ [tex]Y^{1}[/tex] | [tex]X^{1}[/tex] ] = 74%
P [ [tex]Y^{0}[/tex] | [tex]X^{0}[/tex] ] = 100% - 74% = 26%
P [ Tramitted bits are 0 ] = 80%
Now calculate each situation
a)
As all the transmitted bits are o has possibilit of 80% then
P [ X = 0 ] = P [ [tex]X^{0}[/tex] ] = 80% = 0.80
b)
P [ X = 0, Y = 0 ] = P [ [tex]X^{0}[/tex] , [tex]Y^{0}[/tex] ] = P [ [tex]Y^{0}[/tex] | [tex]X^{0}[/tex] ] x P [ [tex]X^{0}[/tex] ] = 90% x 80% = 72% = 0.72
c)
P [ X = 1, Y = 0 ] = P [ [tex]X^{1}[/tex] , [tex]Y^{0}[/tex] ] = P [ [tex]Y^{0}[/tex] | [tex]X^{1}[/tex] ] x P [ [tex]X^{1}[/tex] ] = 10% x ( 100% - 80% ) = 10% x 20% = 2% = 0.02
Find the length below using the triangle given???asap
Answer:
PV = 8
VT = 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
in a 30-60-90° Δ, the ratio of sides, respectively, is 1: [tex]\sqrt{3}[/tex]: 2
if PT = 4 then PV is twice that, or 8
VT = PT·[tex]\sqrt{3}[/tex]
Look at the picture.
Thank u!
Answer:
option 2
Step-by-step explanation:
Step-by-step explanation:
option 2 is the right answer... I m sure , the formula is 1/2 × base× height...
You have 10 gallons of lemonade to sell. (1 gal $\approx$ 3785 cm3)
A conical paper cup is shown. Its height is 11 centimeters and the diameter of its base is 8 centimeters.
a. Each customer uses 1 paper cup. The cups are sold in packages of 50. How many packages should you buy?
b. How many cups will be left over if you sell 80% of the lemonade?
Answer:
Step-by-step explanation:
volume of cone cup = ⅓πr²h = ⅓π4²·11 ≅ 184.31 cm³
10 gal × 3,785 cm³/gal = 37,850 cm³
37,850 cm³ × (1 cone)/(184.31 cm³) ≅205.4 cones
Buy 5 packages (250 cones).
8 gal × 3,785 cm³/gal = 30,280 cm³
30,280 cm³ × (1 cone)/(184.31 cm³) ≅165 cones
250 - 165 = 85 cones left over
a). Number of packs of cups to be purchased = 5 packs
b). Number of cups remaining if 80% lemonade is sold = 85 cups
Volume of a cone: Volume of a cone is given by the expression,
[tex]V=\frac{1}{3}\pi r^2h[/tex]
Here, r = radius of the cone
h = Height of the cone
Given in the question,
Radius of the cone = [tex]\frac{8}{2}[/tex] = 4 cm Height of the cone = 11 cm Amount of lemonade = 10 gallonsa). Volume of one cone = [tex]\frac{1}{3}\pi (4)^2(11)[/tex]
= 184.307 cm³
Covert the gallons into cubic cm,
∵ 1 gallon = 3785 cm³
∴ 10 gallons = 37850 cm³
∵ 184.307 cm³ volume represents the number of cones = 1
∴ 1 cm³ will represent the voulume = [tex]\frac{1}{184.307}[/tex] cups
∴ 37850 cm³ will represent the volume = [tex]\frac{37850}{184.307}[/tex] cups
= 205.36 cups
≈ 205 cups
Therefoe, number of packs of cups to be bought = [tex]\frac{205}{50}[/tex]
= 5 packs
b). If 80% of the lemonade are sold, amount of lemonade sold = 10 × [tex]\frac{80}{100}[/tex]
= 8 gallons
Volume of 8 gallons lemonade in cm³ = 8 × 3785
= 30280 cm³
Therefore, number of cups to be used = [tex]\frac{30280}{184.307}[/tex] cups
= 164.29 cups
≈ 164 cups
Number of cups purchased = 250
And the number of cups remaining = 250 - 164
= 86 cups
Therefore, number of cups remaining are 86 cups.
Learn more about volume of the cone here,
https://brainly.com/question/14671146?referrer=searchResults
Estimate the square root to the nearest (a) integer and (b) tenth
105
a. nearest integer.
b. nearest tenth
Answer:
a. nearest integer: -10
b. nearest tenth: -10.2
Step-by-step explanation:
The estimated integers are a) 10 and b) 10.2
(a) To estimate the square root of 105 to the nearest integer, we can use a rough approximation.
The square root of 100 is 10, and the square root of 121 is 11. Since 105 is closer to 100 than it is to 121, we can estimate the square root of 105 to be approximately 10.
(b) To estimate the square root of 105 to the nearest tenth, we can use a calculator or perform some calculations.
The square root of 105 is approximately 10.246950766. Rounded to the nearest tenth, we get 10.2.
Hence the estimated integers are a) 10 and b) 10.2
Learn more about integers click;
https://brainly.com/question/490943
#SPJ2
How do I find the volume of a solid by rotating the region bounded by the given curves about a specified line?
Step-by-step explanation:
if a region is bounded by two curves y=f(x) and y=g(x) on an internal a,b where 0<g(x)< f(x) then the volume of the solid obtained by the rotating region about the Y-axis is expressed by the integral of the difference of two functions: v= 2πbfax(x)jdx
Add and Subtract Linear Expressions
1. Subtract m + 8 from 5m + 11.
Enter your answer in the box.
2. Add the two expressions.
−4.2x+3 and 2.5x−6
Enter your answer in the box.
Answer:
1. 4m + 3
2. -1.7x - 3
4 163-2 492
8. Find the product of:
a) 123 x 34
Answer:
4182
Step-by-step explanation:
Answer this correctly I’ll give brainalist + 10 points
Answer:
x = 43
Step-by-step explanation:
Since these angles are inside a right angle, we know their sums are complementary (they add up to 90°.)
x + x + 4 = 90
2x + 4 = 90 | Combine x's
2x = 86 | Subtract 4 from both sides
x = 43 | Divide both sides by 2
what is the area of a semicircle with a diameter of 8
Answer:
We'll use 3.14 as an approximation of pi. So, now we plug the values into the equation. A = 3.14 * 8^2/2.
Step-by-step explanation:
Answer:4
Step-by-step explanation: