Answers
Answer:
a= 26
Step-by-step explanation:
180-130=50
total angle in triangle =180
4a+a+50=180
then proceed like norma algebra
Related Questions
A company that produces DVD drives has a 12% defective rate. Let X represent the number of defectives in a random sample of 55 of their drives.
Required:
a. What is the probability the sample will contain exactly 8 defective drives?
b. What is the probability the sample will contain more than 8 defective drives?
c. What is the probability the sample will contain less than 8 defective drives?
d. What is the expected number of defective drives in the sample?
Answers
Answer:
a) 0.1287 = 12.87% probability the sample will contain exactly 8 defective drives
b) 0.2092 = 20.92% probability the sample will contain more than 8 defective drives.
c) 0.6621 = 66.21% probability the sample will contain less than 8 defective drives.
d) The expected number of defective drives in the sample is 6.6
Step-by-step explanation:
For each DVD, there are only two possible outcomes. Either it is defective, or it is not. The probability of a DVD being defective is independent of any other DVD, which means that the binomial probability distribution is used 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.
A company that produces DVD drives has a 12% defective rate.
This means that [tex]p = 0.12[/tex]
Let X represent the number of defectives in a random sample of 55 of their drives.
This means that [tex]n = 55[/tex]
a. What is the probability the sample will contain exactly 8 defective drives?
This is [tex]P(X = 8)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{55,8}.(0.12)^{8}.(0.88)^{47} = 0.1287[/tex]
0.1287 = 12.87% probability the sample will contain exactly 8 defective drives.
b. What is the probability the sample will contain more than 8 defective drives?
This is:
[tex]P(X > 8) = 1 - P(X \leq 8)[/tex]
In which:
[tex]P(X \leq 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{55,0}.(0.12)^{0}.(0.88)^{55} = 0.0009[/tex]
[tex]P(X = 1) = C_{55,1}.(0.12)^{1}.(0.88)^{54} = 0.0066[/tex]
[tex]P(X = 2) = C_{55,2}.(0.12)^{2}.(0.88)^{53} = 0.0244[/tex]
[tex]P(X = 3) = C_{55,3}.(0.12)^{3}.(0.88)^{52} = 0.0588[/tex]
[tex]P(X = 4) = C_{55,4}.(0.12)^{4}.(0.88)^{51} = 0.1043[/tex]
[tex]P(X = 5) = C_{55,5}.(0.12)^{5}.(0.88)^{50} = 0.1450[/tex]
[tex]P(X = 6) = C_{55,8}.(0.12)^{6}.(0.88)^{49} = 0.1648[/tex]
[tex]P(X = 7) = C_{55,7}.(0.12)^{7}.(0.88)^{48} = 0.1573[/tex]
[tex]P(X = 8) = C_{55,8}.(0.12)^{8}.(0.88)^{47} = 0.1287[/tex]
So
[tex]P(X \leq 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.0009 + 0.0066 + 0.0244 + 0.0588 + 0.1043 + 0.1450 + 0.1648 + 0.1573 + 0.1287 = 0.7908[/tex]
[tex]P(X > 8) = 1 - P(X \leq 8) = 1 - 0.7908 = 0.2092[/tex]
0.2092 = 20.92% probability the sample will contain more than 8 defective drives.
c. What is the probability the sample will contain less than 8 defective drives?
This is:
[tex]P(X < 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)[/tex]
With the values we found in b.
[tex]P(X < 8) = 0.0009 + 0.0066 + 0.0244 + 0.0588 + 0.1043 + 0.1450 + 0.1648 + 0.1573 = 0.6621[/tex]
0.6621 = 66.21% probability the sample will contain less than 8 defective drives.
d. What is the expected number of defective drives in the sample?
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
In this question:
[tex]E(X) = 55(0.12) = 6.6[/tex]
The expected number of defective drives in the sample is 6.6
Teresita wanted to buy a dress for $50, but she decided to wait because she didn't have
enough money. A week later, the price had gone up 20%. Now she definitely had to wait to
buy it. A week later, she went back to the store, and the price had gone down 20% from the
last price. Teresita finally bought the dress. What did she pay for it?
Answers
Answer:
$48
Explanation:
> 50 x .20 = $10
$50 + $10= $60
-----------------------------
> 60 x .20 = $12
$60 - $12= $48
If a rope 36 feet long is cut into two pieces in such a way that one piece is twice as long as the other piece, how long must the long piece be? If a rope 36 feet long is cut into two pieces in such a way that one piece is twice as long as the other piece, how long must the long piece be
Answers
Answer:
24feet
Step-by-step explanation:
the first rope well give it letter X and the longer rope we'll give it 2x since it's twice then we add the two unknown numbers which must lead to a total of 36feet when we add the unknown digits we'll get 3x then simply the unknown digit with the total and u'll get 12 replace the X from the first letters with 12by multiplying
El valor de "x" que es solución de la ecuación 5x + 22 = 2x + 29 es:
Answers
Answer:
x =7/ 3
Step-by-step explanation:
5x+ 22= 2x+ 29
⇔5x - 2x= 29 - 22
⇔3x = 7
⇔x = 7/3
8x-5/6x
Find all real numbers for which the rational expression is undefined
Answers
9514 1404 393
Answer:
as written: noneperhaps intended: 0Step-by-step explanation:
The expression written here is interpreted according to the Order of Operations as ...
8x -(5/6)x
This reduces to (7 1/6)x, which is defined for all real numbers.
__
Maybe you intended the expression ...
(8x -5)/(6x)
This expression is undefined where its denominator is zero, at x = 0.
PLS HELP! What is the mistake made below in solving x2 – 12x + 10 = 0 using the completing the square method?
x2 – 12x + 10 = 0
x2 – 12x + (- 6)2 = - 10 + (- 6)2
x2 – 12x + 36 = 26
(x – 6)(x – 6) = 26
x – 6 = √26
x = 6 + √26
Answers
Answer:
Step-by-step explanation:
Everything is correct. But you forgot to add
x = 6 - square root of 26. The answer is
x = 6 + square root of 26 or
x = 6 - square root of 26
what is the answer I need help?
Answers
Answer:
8 1/8 units^3
Step-by-step explanation:
This figure is a rectangular prism, and the volume of a rectangular prism is given by the formula:
lwh
But since we have the area of the base snd the height of the figure, there is also one formula that we can use to find the volume:
bh
Which means area of base times the height.
USE THE FORMULA bh:
16 1/4 x 1/2
= 65/4 x 1/2
= 65/8
SIMPLIFIED: 8 1/8
Volume is measured in cubic units
SO YOUR ANSWER IS 8 1/8 units^3
❤❤❤PLEASE BE RIGHT AND CORRECT BEFORE ANSWERING
Answers
Answer:
y=-x+28
Step-by-step explanation:
The slope(rise/run) is -1, and because it starts at y=28, the answer is y=-x+28
Answer:
"C"
The slope is -2 !!! delta y = 20 delta x = 10
the y intercept is 28
Step-by-step explanation:
PLZ HELP- I NEED HELP IM A LIL SLOW
Answers
Answer:
7 and above
Step-by-step explanation:
Go and 7 draw a dot and a arrow to the right
Answer:
Step-by-step explanation:
in order for the parallelogram to be a rhombus, x=?
Answers
[tex]\\ \large\sf\longmapsto x + 15 = 2x - 40 \\ \\ \large\sf\longmapsto x - 2x = - 40 - 15 \\ \\ \large\sf\longmapsto - x = - 55\\ \large\sf\longmapsto x = 55[/tex]
The value of x is 55 degrees.
What is rhombus?A rhombus is a diamond-shaped quadrilateral that has all four sides equal
What are the properties of a rhombus?The properties of a rhombus are:
Opposite angles are equal.All sides are equal and, opposite sides are parallel to each other.Diagonals bisect each other perpendicularly.Sum of any two adjacent angles is 180°According to the given question.
We have a rhombus.
Since, we know that the diagonals of the rhombus bisect the angles.
Therefore,
[tex](x+15)^{o} = (2x-40)^{o}[/tex]
Solve, the above expression for x.
[tex]\implies x +15 = 2x -40\\\implies 15+40 = 2x -x \\\implies 55 = x \\0r\ x = 55^{o}[/tex]
Hence, the value of x is 55 degrees.
Find out more information about rhombus here:
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Suppose the bacteria population in a specimen increases at a rate proportional to the population at each moment. There were 100 bacteria 4 days ago and 100,000 bacteria 2 days ago. How many bacteria will there be by tomorrow
Answers
9514 1404 393
Answer:
about 3,160,000,000
Step-by-step explanation:
"Increases at a rate proportional to population" means the growth is exponential. It can be modeled by the equation ...
p = ab^t
We can find 'a' and 'b' using the given data points.
100 = ab^(-4) . . . . . . . population 4 days ago
100,000 = ab^(-2) . . . population 2 days ago
Dividing the second equation by the first, we find ...
1000 = b^2
b = 1000^(1/2)
Substituting for b in the first equation, we have ...
100 = a(1000^(1/2))^(-4) = a(1000^-2)
100,000,000 = a
Then the population model is ...
p = 100,000,000×1000^(t/2)
__
Tomorrow (t=1), the population will be ...
p = 100,000,000 × 1000^(1/2) ≈ 31.6 × 100,000,000
p ≈ 3,160,000,000 . . . . . bacteria by tomorrow
_____
Additional comment
We could write this as ...
p = 10^(8+1.5t)
Then for t=1, this is p = 10^(8+1.5) = 10^0.5 × 10^9 = 3.16×10^9
any equations that equal three?
Answers
A bucket contains 4 red balls that are numbered 1, 2, 3, 4. It also contains 6 black balls that are numbered 5, 6, 7, 8, 9, 10. Two balls are drawn from the bucket, one at a time, without replacement. Use this information to answer the following probability questions. Express answers as fractions, or round decimal answers to 4 decimal places. a. What is the probability that the first ball is even and the second ball is odd
Answers
The probability is 1/9
We want to find the probability that the first drawn ball is even, and the second is odd.
The probability of randomly drawing an even ball will be equal to the quotient between the number of balls with even numbers and the total number of balls in the bucket.
We have a total of 10 balls (4 red ones and 6 black ones)
and 5 of these have even numbers (2, 4, 6, 8, 10)
Then the probability of drawing a ball with an even number first is:
p = 5/10 = 1/5
now we want to get a ball with an odd number.
notice that we already got a ball with an even number and we did not replace it, so now there are 9 balls left in the bucket, 5 odd ones, and 4 even ones.
The probability of getting an odd ball is computed in the same way thana above, as the quotient between the number of balls with odd numbers (5) and the total number of balls in the bucket (9)
q = 5/9
The joint probability (the probability that these two events happen together) is equal to the product of the individual probabilities, so we will get:
P = p*q = (5/9)*(1/5) = 1/9
The probability is 1/9
If you want to learn more about this topic, you can read:
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The isosceles triangle and rectangle have the same perimeter find the value of x
Answers
Answer:
x=15
Step-by-step explanation:
x+2+x+2+2x-2=9+8+9+8
2x+4=34
2x=30
x=15
what is 88.92 x 21.33
Answers
Answer:
By multiplying 88.92 from 21.33 we get 1896.6636.
Hope it's helpfulAnswer:
1896.6636
Step-by-step explanation:
Hope this helps
Can someone help me with this?
Answers
Answer:
183.3 in^3
Step-by-step explanation:
Find the volume of the rectangular bottom
V = l*w*h
V = 5*5*6 =150 in^3
Find the volume of the triangular pyramid
V = 1/3 Bh where B is the area of the base and h is the height
V = 1/3 ( 5*5) * 4 = 100/3
Add the two volumes together
150 + 100/3
150 +33.3
183.3 in^3
how induction coil work
Answers
Answer:
Induction produces an electromagnetic field in a coil to transfer energy to a work piece to be heated. When the electrical current passes along a wire, a magnetic field is produced around that wire
Step-by-step explanation:
If my final is worth 15% of my mark and I'm at 70% right now what would I need to get on my final to get at least 75% overall
Answers
Answer:
Step-by-step explanation:
70*85/100 = 59.5 This is what you have right now.
You need 15.5 gross marks to get up to 75
As you can see, I'm sorry to say, you cannot do it.
Mind you, you would not miss by much. You could get about 74.5 if you got a hundred % on your final. This is just an estimate. I'm just trying to show you what you have to do to get near your goal. The 59.5 is accurate. So is the 15.5. Only your possible final grade is an estimate.
PLS PLS PLS HELP QUICKKKK
Find the value of x in each case
Answers
Answer:
KI and HE are parallel
So we apply the law of exterior angles ;
3X=X + 180– 2X
3X +X = 180
4X= 180
X= 180/4
X= 45
I hope I helped you^_^
simplified the expression y(y2 - y + 4)
Answers
Answer:
y^3 -y^2 +4y
Step-by-step explanation:
y(y2 - y + 4)
Distribute
y^3 -y^2 +4y
For the function F defined by F(x) = x2 – 2x + 4, find F(b+3).
Answers
Answer:
[tex]\displaystyle F(b + 3) = b^2 + 4b + 7[/tex]
Step-by-step explanation:
We are given the function:
[tex]\displaystlye F(x) = x^2 - 2x + 4[/tex]
And we want to find F(b + 3).
We can substitute:
[tex]\displaystyle F(b + 3) = (b + 3)^2 - 2(b+3) + 4[/tex]
Expand:
[tex]\displaystyle = (b^2 + 6b + 9) + (-2b -6) + 4[/tex]
Rearrange:
[tex]\displaystyle = (b^2) + (6b-2b) + (9 - 6 + 4)[/tex]
Combine like terms. Hence:
[tex]\displaystyle = b^2 +4b + 7[/tex]
In conclusion:
[tex]\displaystyle F(b + 3) = b^2 + 4b + 7[/tex]
A newsstand spends $600 a month on rent and electricity, and it spends $2
for each magazine that it sells. The newsstand charges $5 for each
magazine. If n is the number of magazines, which equation represents the
profit function of the newsstand?
O A. p = 2n + 600
B. p = 3n-600
O c. p = 600n + 3
O D. p = 5n-600
Answers
Answer: B. p = 3n-600
Step-by-step explanation:
Cost = 2n + 600Earned = 5nProfit(p) = Earned - Cost
p = 5n - (2n + 600) = 5n - 2n - 600 = 3n - 600
The equation representing the profit function of the newsstand is
p = 3n - 600
Option B is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The revenue generated by selling n magazines is 5n dollars.
The cost of selling n magazines is the sum of the cost of purchasing n magazines and the fixed cost of rent and electricity, which is $2n + $600.
Now,
The profit function can be represented by:
p = revenue - cost
= 5n - (2n + 600)
= 3n - 600
Thus,
The equation representing the profit function of the newsstand is
p = 3n - 600
Learn more about functions here:
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To mail an envelope first class the us pot charges 0.32 cents for the first ounce and 0.24 cents for each additional ounce. Use an inequality to find the maximum number of whole ounces that can be mailed for $7.98
Answers
Answer:
Not sure about the inequality, but maximum ounces is 31 ounces.
Might be.
[tex]7.98 \geqslant .24x + .32[/tex]
Solve the inequality
Answers
Answer:
hope this helps buddy, please mark the brainliest.
Step-by-step explanation:
Draw the line segment with endpoints (-5, 9) and (-1, -7) and find the value of y if x=-4;-2.5;-2;-1.5;0 plz answer asap
Answers
Answer:
5, - 1, - 3, - 5, - 11
Step-by-step explanation:
The equation of the line is y=-4x-11. The y values corresponding to x are 5, - 1, - 3, - 5, - 11
PLEASE HELP!!!!!!!!!!!!!!!! (answer in decimal!!!!!!!!)
Answers
9514 1404 393
Answer:
0.75
Step-by-step explanation:
You know that ...
P(S or T) = P(S) +P(T) -P(S and T)
When events are mutually exclusive, P(S and T) = 0. Then ...
P(S or T) = 5/8 + 1/8 = 6/8 = 3/4
P(S or T) = 0.75
Help!!????
Please!!!????
Answers
Answer:
true
mark me brainist if it comes out to be true
Answer:
The answer is TRUE.
Step-by-step explanation:
If f(x)=3x^2-x+6, evaluate f(-4)
Answers
Answer:
f(-4) = 58
Step-by-step explanation:
Let x = -4:
[tex]f(-4)=3(-4)^2-(-4)+6\\\\f(-4)=3(16)+4+6\\\\f(-4)=48+4+6\\\\f(-4)=58[/tex]
Simplify: [tex]\sqrt{36} - \sqrt{6} + \sqrt{126}[/tex]
Answers
Here’s the solution
Hope you understand it!!
A study examines the relationship between being a registered nurse (yes/no) and passing a cultural competency exam (yes/no) among a group of 987 randomly selected employees at your hospital. What test would be appropriate to determine if there is an association
Answers
Answer:
The appropriate test to determine if there is an association between being a registered nurse and passing a cultural competency exam among a group of 987 randomly selected hospital employees is a:
Chi-square Test.
Step-by-step explanation:
The Chi-Square Test uses either a diagram (like a scatter plot) or a hypothesis test to show the existence of an association between two variables or statistically demonstrate that a relationship exists between the two variables. Using the computed t-score, the significant association between two categorical variables can be measured and established.
