Using the binomial distribution, it is found that there is a 0.8202 = 82.02% probability that the shipment will make it through the control check.
For each article, there are only two possible outcomes, either it meets the specifications, or it does not. The probability of an article meeting the specifications is independent of any other article, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
10 articles are picked, hence [tex]n = 10[/tex].85% of the articles meets all specifications, hence [tex]p = 0.85[/tex]The probability is:
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{10,8}.(0.85)^{8}.(0.15)^{2} = 0.2759[/tex]
[tex]P(X = 9) = C_{10,9}.(0.85)^{9}.(0.15)^{1} = 0.3474[/tex]
[tex]P(X = 10) = C_{10,10}.(0.85)^{10}.(0.15)^{0} = 0.1969[/tex]
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.2759 + 0.3474 + 0.1969 = 0.8202[/tex]
0.8202 = 82.02% probability that the shipment will make it through the control check.
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24. Solve for x: 3x - 2(x - 4) = 5(2x + 4) -3
x=-1
3x-2x+8=10x+20-3
x+8=10x+17
-9x=9
x=-1
Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
[tex]x-2\left(x-4\right)=5\left(2x+4\right)-3[/tex]
[tex]-2\left(x-4\right)\\\mathrm{Distribute}\\-2x+8[/tex]
[tex]3x-2x+8=5\left(2x+4\right)-3[/tex]
[tex]\mathrm{Combine\: like\: terms}[/tex]
[tex]x+8=5\left(2x+4\right)-3[/tex]
[tex]\left(2x+4\right)-3\\\mathrm{Distribute}\\10x+20-3\\10x+17[/tex]
[tex]x+8=10x+17[/tex]
[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]
[tex]x+8-8=10x+17-8[/tex]
[tex]x=10x+9[/tex]
[tex]\mathrm{Subtract\:}10x\mathrm{\:from\:both\:sides}[/tex]
[tex]x-10x=10x+9-10x[/tex]
[tex]-9x=9[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-9[/tex]
[tex]\frac{-9x}{-9}=\frac{9}{-9}[/tex]
[tex]\bold{x=-1}[/tex]
How do I verify: tan(x)+cot(x)=(2)/sin(2x)?
I always get stuck after writing out (sin^2x+cos^2x)/sin(x)cos(x)
[tex]sin^2(\theta)+cos^2(\theta)=1\qquad \qquad sin(2\theta)=2sin(\theta)cos(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]tan(x)+cot(x)=\cfrac{2}{sin(2x)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doing the left-hand-side}}{\cfrac{sin(x)}{cos(x)}+\cfrac{cos(x)}{sin(x)}\implies \cfrac{sin^2(x)+cos^2(x)}{\underset{\textit{using this LCD}}{sin(x)cos(x)}}} \implies \cfrac{1}{sin(x)cos(x)}[/tex]
now, let's recall that anything times 1 is just itself, namely 5*1 =5, 1,000,000 * 1 = 1,000,000, "meow" * 1 = "meow" and so on, so we can write anything as time 1.
let's recall something else, that same/same = 1, so
[tex]\cfrac{cheese}{cheese}\implies \cfrac{spaghetti}{spaghetti}\implies \cfrac{horse}{horse}\implies \cfrac{butter}{butter}\implies \cfrac{25^7}{25^7}=1[/tex]
therefore
[tex]\cfrac{1}{sin(x)cos(x)}\cdot \cfrac{2}{2}\implies \cfrac{2}{2sin(x)cos(x)}\implies \cfrac{2}{sin(2x)}[/tex]
QUESTION 19 PLEASE HELP ME ASAP
Answer:
changes over time
Step-by-step explanation: its going up not staying at one spot
40x^-4 y^6
________
10x^-5 y^5
Answer:
[tex]4xy[/tex]
Step-by-step explanation:[tex](40/10) *(x^-^4/x^-^5) * (y^6/y^5) \\=4*x*y=4xy[/tex]
Someone help please
It is 4pi/7, or b. Just want to help ;)
130 is what percent of 70?
Answer:
91%
Step-by-step explanation:
hopes this helps
Answer:
185.71%
Step-by-step explanation:
130 / 70 = 1.857142857
(1.857142857)(100) = 185.71%
Pls help ASAP
Give the domain and range
Answer:
D: {-2, 0, 2}
R: {-1, 1, 3
Jose left the airport and traveled toward the mountains. Kayla left 2.1 hours later traveling 35 mph faster in an effort to catch up to him. After 1.2 hours Kayla finally caught up. Find Jose's speed.
========================================================
Explanation:
x = Jose's speed in mph
x+35 = Kayla's speed since she drives 35 mph faster than Jose
Jose gets a 2.1 hour head start and it takes Kayla 1.2 hours to reach him. So this means Jose has been driving for 2.1+1.2 = 3.3 hours when Kayla reaches him. The distance he travels is
distance = rate*time
d = r*t
d = x*3.3
d = 3.3x
while Kayla's distance equation is
d = r*t
d = (x+35)*1.2
d = 1.2x+42
Since Kayla meets up with Jose at the 1.2 hour mark, this means the two distances they travel is the same. Set their distance expressions equal to one another. Solve for x.
3.3x = 1.2x+42
3.3x-1.2x = 42
2.1x = 42
x = 42/(2.1)
x = 20
Jose's speed is 20 mph, while Kayla's speed is x+35 = 20+35 = 55 mph.
Jose's fairly slow speed is probably due to a number of factors such as heavy traffic, icy roads, or poor visibility. Kayla probably got a bit of a break with more favorable conditions.
Since Jose travels at 20 mph and does so for 3.3 hours, he travels d = r*t = 20*3.3 = 66 miles. Kayla travels d = r*t = 55*1.2 = 66 miles as well. We get the same number each time to help confirm the answer.
3. What is the exact area of triangle ABC? Use special right triangles to help find the base of the triangle. Show your work.
The exact area of triangle ABC is 93.51 cm².
The given parameters;
Height of the triangle, h = 18 cmThe base of the triangle is calculated by using trigonometry ratio as follows;
[tex]tan (30) = \frac{b}{18} \\\\[/tex]
where;
b is the base of the triangle ABC[tex]b = 18 \times tan(30)\\\\b = 10.39 \ cm[/tex]
The area of the triangle ABC with the calculated base and given height is calculated as follows;
[tex]A = \frac{1}{2} \times base \times height\\\\A = \frac{1}{2} \times 10.39 \times 18\\\\A = 93.51 \ cm^2[/tex]
Thus, the exact area of triangle ABC is 93.51 cm².
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A triangle has sides measuring 7 centimeters and 13 centimeters that form an angle measuring 44°. Which of these is CLOSEST to the length of the third side of the triangle? A) 8.1 centimeters B) 8.7 centimeters C) 9.3 centimeters D) 9.9 centimeters
Answer:
9.3 centimeters
Step-by-step explanation:
HELP!!!! I need help
Answer:
1 Tenths = 10 Hundredths
10.74 - 10.60 = 0.14
0.14 = 14 hundredths
Thus, you need 10 ones, 6 tenths and 14 hundredths to make 10.74.
Help again please ?? I have 5 more that needs to be answer also ..
Which of the following word phrases describe the expression y + 3?
A.three less than y
B.the sum of y and 3
C.the product of y and 3
D.three more than y
find the difderence of 3/4 and 1/28
Answer:
5/7
Step-by-step explanation:
3/4-1/28
21/28-1/28
20/28
simplify
5/7
Find (fog)(x) and the domain
Answer:
(fog)(x) = 2sqrt(x) + 3
Domain: {x | x ∈ R, x>=0}
Step-by-step explanation:
(fog)(x) = f(g(x))
let f(a) = f(g(x))
f(a) = 2a+3 = 2(g(x)) + 3 = 2sqrt(x) + 3
To find domain, pick most restricting domain of the functions that make up the compound function.
A rectangular garden is 35m long and 25m broad. find the perimeter of the rectangular garden. find the length of wire required to fence with 2 round.
Answer:
The perimeter is the distance all round,
Step-by-step explanation:
perimeter of a rectangle is gotten by the formula
P=2(L+W)
2(35+25)=120m
The wire covers the distance all round
so we use 120m×2=240m
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MATH
BOARD
Model the product on the grid. Record the product.
1. 3 X 13 =
2. 5 >
Find the product.
Using the grid model, the product of 3 and 13 is 39
Product refers to the result of multiplying two or more numbers or quantities together. It is a fundamental operation in arithmetic and algebra. When multiplying two numbers, the product is obtained by adding together a number of copies of one of the numbers, equal to the value of the other number.
Given, two numbers 3 and 9, and a grid.
To determine the product of 3 and 13 just count all the grids covered in 3 rows up to 13 columns or adding 3 for 13 times will result in 39.
Count the grids covered in a red box attached in the image below.
3+3+3+3+3+3+3+3+3+3+3+3+3=39
So, the product of 3 and 13 is 39.
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2 and 5/6 divided by 1 and 2/3 find the solution and write it in simplest form
Thanks for the help!!!!
Answer:
1 7/10
Step-by-step explanation:
= 17/6 ÷ 5/3
= 17 x 3
= 6 x 5
= 51/30
= 1 7/10
Convert the following fraction to a decimal.
Divide using polynomial long division.
2. (x² + 7x +44) = (x +4)
Answer:
the answer is given in the photo below
Lucy borrowed $73,250 to purchase a home. The bank offered her an APR of 3.15% for a term length of 20 years. Excel calculates the monthly payment to be $411.77. If she were to pay only the minimum payment for the lifetime of the loan, how much will Lucy be paying in interest?
Amount Lucy will be paying in interest will be $38,596.2
Using the compound amount formula to get the amount after she will pay back after 20 years expressed as:
[tex]A =P(1+\frac{r}{n} )^{nt}[/tex]
A is the amount after 20 yearsr is the rate = 3.15% = 0.0315time in years = 20 yearsn is the compounding time = 12 (monthly)P is the amount borrowed = $73,250Substitute the parameters into the formula;
[tex]A=73,250(1+\frac{0.0315}{12} )^{20(12)}\\A= $73,250 (1.8761)\\A= \$137,421.49[/tex]
If Excel calculates the monthly payment to be $411.77, the amount paid for 20 years will be $411.77 * 240months = $98,824.8
Amount Lucy will be paying interest will be $137,421- $98,824.8 = $38,596.2
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-2 1/5 - 1 3/10 help!!
Share £30 in the ratio 1:5 between Tim and Sam
The graph of the function f is shown below
Find f(0)
Answer:
2
Step-by-step explanation:
Write that down before Katie deletes it. There is no work to show, only read the graph.
Miguel buys eggs and apples at the store.
• He pays a total of $56.97.
• He pays a total of $6.17 for the eggs.
• He buys 8 bags of apples that each cost the same amount.
.
Write and solve an equation which can be used to determine x, how much each bag
of apples costs.
The cost of each bag of apple is $6.35
Let the cost of a bag of apple be xIf Miguel buys eggs and apples at the store.
• He pays a total of $56.97.
• He pays a total of $6.17 for the eggs.
• He buys 8 bags of apples that each cost the same amount
The correct equation that represents the statement will be given as:
6.17 + 8x = 56.97Make x the subject of the formula
8x = 56.97 - 6.17
8x = 50.8
x = 50.8/8
x = 6.35
Hence the cost of each bag of apple is $6.35
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-6 = 1/4w -1/2 solve for w
Help help help math math math
Answer:
180 - 17 - 14 =149
180 - 149 = 31*
Step-by-step explanation:
Answer: 180 - 17 - 14 =149180 - 149 = 31*
Step-by-step explanation: it’s right
Which equation matches the graph?
Answer:
i think 4x+3y = -24 is answer
The triangles shown bellow must be congruent?
True or False?
Which of these is a ratio table?
A
1
2.
3
o ono
WON
B.
5
6
7
A
1
2
3
chAUD
B
4
5
7
WN
B
A
1
2
3
COA
4
9
А
1
2
3
B
2.
4
6
ANUD
INI
Answer:
The last one
Step-by-step explanation:
A ratio table means that each number in the first column is multiplied by the same number to get the answer in the 2nd column