Answer:
10% to decimal is equal to 0.1.
Therefore 20 x 0.1 = 2
Step-by-step explanation:
Each window is independently probable for having minor defects. The expected number of window frames having minor defects = 2.
Other figures are:
Standard deviation for the number of windows frames to have minor defects in this random sample of 20 window frames = 1.34 approx.P(Exactly 2 windows will need minor adjustment) = 0.285 approx.P(More than 3 windows will need minor adjustment) = 0.1329 approx.How to find that a given condition can be modeled by binomial distribution?Binomial distributions consists of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
The expected value and variance of X are:
[tex]E(X) = np[/tex][tex]Var(X) = np(1-p)[/tex]For the considered case, we can assume that each window is independent of each other for having defects or being perfect.
Each window can be having defects (call it success) or no defects(call it failure).
Then, we can take:
X = number of windows out of 20 windows being perfect (no defect).
Then we get:
Success = window having defectn = 20p = 10% = 0.10 (as given in the problem)[tex]X \sim B(n=20,p=0.1)[/tex]Evaluating each sub parts one by one:
Case a: How many window frames would you expect to have minor defects?Expect number of defective windows = E(X) = np = 20 × 0.1 = 2
Case b: Calculate the standard deviation for the number of window frames to have minor defects in this random sample of 20 window frames.Standard deviation is the positive root of variance.
Standard deviation of number of windows (out of 20 windows of sample) having defects = [tex]\sqrt{Var(X)} = \sqrt{np(1-p)} = \sqrt{2(0.9)} \approx 1.34[/tex]
Case c: Calculate the probability that exactly 2 window frames will need minor adjustment.P(X = 2) = [tex]^{20}C_2(0.1)^2(0.9)^{18} \approx 0.285[/tex]
Case d: What is the probability that more than 3 window frames will need minor adjustments?P(X > 3) = 1 - P(X ≤ 3)
[tex]P(X > 3) = 1 -[ P(X = 0) + P(X = 1) +P(X= 2)+ P(X = 3)]\\\\P(X > 3) = 1- [^{20}C_0(0.1)^0(0.9)^{20} +^{20}C_1(0.1)^1(0.9)^{19} +\\\: \:\: ^{20}C_2(0.1)^2(0.9)^{18} +^{20}C_3(0.1)^3(0.9)^{17} ]\\\\P(X > 3) \approx 1-[ 0.1216 + 0.2702 + 0.2852 + 0.1901]=1-0.8671=0.1329 \\\\P(X > 3) \approx 0.1329[/tex]
Thus, the needed figures are:
Expected number of window frames having minor defects = 2Standard deviation for the number of windows frames to have minor defects in this random sample of 20 window frames = 1.34 approx.P(Exactly 2 windows will need minor adjustment) = 0.285 approx.P(More than 3 windows will need minor adjustment) = 0.1329 approx.Learn more about binomial distribution here:
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please help
every package of a certain caculator also includes 4 batteries. select all equations that represent the relationship between the number of packages and the number of batteries
a.) p = 4b
b.) b = 4p
c.) p=1/4b
d.)b= 1/4p
Answer:
c
Step-by-step explanation:
A baker makes apple tarts and apple pies each day. Each tart, t, requires 1 apple, and each pie, p, requires 8 apples. The baker receives a shipment of 184 apples every day. If the baker makes no more than 40 tarts per day, which system of inequalities can be used to find the possible number of pies and tarts the baker can make?
Answer: t<40
8p+<184
Step-by-step explanation:
The inequalities representing the given condition will be [tex]t\leq40[/tex] and [tex]8p+t\leq184[/tex].
Given information:
A baker makes apple tarts and apple pies each day.
The baker receives a shipment of 184 apples every day.
A tart requires 1 apple and a pie requires 8 apples.
Let t be the number of tarts made each day and p be the number of pies made each day.
The baker makes no more than 40 tarts per day. So, the condition can be written as,
[tex]t\leq40[/tex]
And the condition for each day apple delivery can be written as,
[tex]8p+t\leq184[/tex]
Therefore, the inequalities representing the given condition will be [tex]t\leq40[/tex] and [tex]8p+t\leq184[/tex].
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The Baltic Sea is almost completely surrounded by countries in Europe. The average depth of the Baltic Sea is 52 meters below the surface. The deepest point in the Baltic Sea is 407 meters lower than this.
What is the deepest point in the Baltic Sea relative to the surface?
Answer:
-459
Step-by-step explanation:
-52 - 407 = -552 + (-407) = -459
Please solve with explanation (10 points)
Answer:
Question (a)
[tex]x^2-a^2-bx-ab=0[/tex]
Write in standard form [tex]ax^2+bx+c=0[/tex]:
[tex]\implies x^2-bx-(a^2+ab)=0[/tex]
Therefore,
[tex]a=1[/tex][tex]b=-b[/tex][tex]c=-(a^2+ab)[/tex]Using quadratic formula:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\implies x=\dfrac{b\pm\sqrt{(-b)^2+4(1)(a^2+ab)} }{2(1)}[/tex]
[tex]\implies x=\dfrac{b\pm\sqrt{b^2+4a^2+4ab} }{2}[/tex]
[tex]\implies x=\dfrac{b\pm\sqrt{(b+2a)^2} }{2}[/tex]
[tex]\implies x=\dfrac{b \pm (b+2a)} {2}[/tex]
[tex]\implies x=\dfrac{2b+2a} {2}=b+a[/tex]
[tex]\implies x=\dfrac{-2a} {2}=-a[/tex]
Question (b)
[tex]6x^2-15ax=2bx-5ab[/tex]
Write in standard form [tex]ax^2+bx+c=0[/tex]:
[tex]\implies 6x^2-15ax-2bx+5ab=0[/tex]
[tex]\implies 6x^2-(15a+2b)x+5ab=0[/tex]
Therefore,
[tex]a=6[/tex][tex]b=-(15a+2b)[/tex][tex]c=5ab[/tex]Using quadratic formula:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\implies x=\dfrac{(15a+2b)\pm\sqrt{(-15a-2b)^2-4(6)(5ab)} }{2(6)}[/tex]
[tex]\implies x=\dfrac{(15a+2b)\pm\sqrt{225a^2+60ab+4b^2-120ab} }{12}[/tex]
[tex]\implies x=\dfrac{(15a+2b)\pm\sqrt{225a^2-60ab+4b^2} }{12}[/tex]
[tex]\implies x=\dfrac{(15a+2b)\pm\sqrt{(15a-2b)^2} }{12}[/tex]
[tex]\implies x=\dfrac{(15a+2b) \pm (15a-2b) }{12}[/tex]
[tex]\implies x=\dfrac{30a }{12}=\dfrac52a[/tex]
[tex]\implies x=\dfrac{4b}{12}=\dfrac13b[/tex]
Question (c)
[tex]\dfrac{x^2}{x-1}=\dfrac{a^2}{2a-4}[/tex]
Cross multiply:
[tex]x^2(2a-4)=a^2(x-1)[/tex]
Write in standard form [tex]ax^2+bx+c=0[/tex]:
[tex](2a-4)x^2-a^2x+a^2=0[/tex]
Therefore,
[tex]a=(2a-4)[/tex][tex]b=-a^2[/tex][tex]c=a^2[/tex]Using quadratic formula:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\implies x=\dfrac{a^2\pm\sqrt{(-a^2)^2-4(2a-4)(a^2)} }{2(2a-4)}[/tex]
[tex]\implies x=\dfrac{a^2\pm\sqrt{a^4-8a^3+16a^2} }{4a-8}[/tex]
[tex]\implies x=\dfrac{a^2\pm\sqrt{a^2(a-4)^2} }{4a-8}[/tex]
[tex]\implies x=\dfrac{a^2\pm a(a-4)}{4a-8}[/tex]
[tex]\implies x=\dfrac{a^2\pm (a^2-4a)}{4a-8}[/tex]
[tex]\implies x=\dfrac{2a^2-4a}{4a-8}=\dfrac{2a(a-2)}{4(a-2)}=\dfrac12a \ \ \ (a\neq 2)[/tex]
[tex]\implies x=\dfrac{4a}{4a-8}=\dfrac{a}{a-2} \ \ \ \ (a\neq 2)[/tex]
Find the value of x?
Answer:
x=25
All triangles must equal 180
95+35=130
What is the first step in solving In(x - 1) = In6 - Inx for x?
Answer:
x=3
Step-by-step explanation:
In(x-1) = In(6) - In(x)
In(x-1) + In(x) = In(6)
In((x-1)x) = In(6)
In(x^2-x) = In(6)
x^2-x=6
x^2-x-6=0
x^2+2x-3x-6=0
x(x+2)-3(x+2)=0
(x-3)(x+2)=0
x=3 because x=-2 need to be cancel out
Trevor folded a corner of a rectangular piece of paper to form a pentagon, as shown below. What is the area of the shaded pentagon? A. 84.5 square inches B. 75.5 square inches c. 39.5 square inches D. 35 square inches.
PLEASE HELP I WILL GIVE BRAINLIEST.
Answer:
B. 75.5 square inches
Step-by-step explanation:
Area (pentagon) = Area (rectangle) - Area (triangle)
= length x width - 1/2 x breadth x height
= 10 x 8 - 1/2 x 3 x 3
= 80 - 4.5
= 75.5 square inches
Solution :-
B. 75.5 square inches
Answer:
B) 75.5 in²
Step-by-step explanation:
Area of rectangle = width × length
⇒ area of rectangle = 8 × 10 = 80 in²
Area of triangle = 1/2 × base × height
⇒ area of triangle = 1/2 × 3 × 3 = 4.5 in²
Area of pentagon = area of rectangle - area of triangle
= 80 - 4.5
= 75.5 in²
Solve the following compound inequality: 4x + 8 15
Answer:
4x - 8 = 15
4x = 15 + 8
4x = 23 (divide both sides by 4 to get x)
4x/4 = 23/4
x = 5.75
Step-by-step explanation:
x = 5.75!!!!!
Help help math math math math
Answer:
(-2, -2)
Step-by-step explanation:
Firstly you can substitute the y= -6x -14 Directly into the other equation having one equation that looks like this 8x+3(-6x-14)= -22 then solve for X and substitute in the y equation you also get the y value
Answer:
(-2, -2)
Step-by-step explanation:
Determine the value of x circles
Which number is divisible by both 3 and 9?
OA) 21,369
OB) 27.621
OC) 27,629
OD) 36,663
Answer: A) 21,369
Step-by-step explanation: since 21,369 can be divided by 3 and = a whole number then it's divisible and also it's divided without a remainder / it's compatible so, 21,369/3= 7,123 which makes (A) your correct answer
Find the value of xx, yy, and zz in the parallelogram below.
Answer:
Step-by-step explanation:
Opposite sides of a parallelogram are congruent, so:
[tex]8x+3=19 \longrightarrow x=2[/tex]
[tex]27=-y-5 \longrightarrow y=-32[/tex]
g - 32 = 52
a) obtain a formula for g
b) Solve for g
Answer:
a) obtain a formula for g
=> g - 32 = 52
=> g = 52 + 32
b) Solve for g
=> 52 + 32
=> g = 84
Answer:
a) obtain a formula for g
Calculate the sum of first n natural numbers as sumtotal= n*(n+1)/2.
Create a variable sum to store the sum of array elements.
Traverse the array from start to end.
Update the value of sum as sum = sum + array[i]
Print the missing number as SumTotal – sum.
b) Solve for g
g = 84
Hope it helps!!!Brainliest pls!!!
Find g'(x) given that g(x) = x^3 cos(πx)
Answer:
[tex]3x^2 cos (\pi x)-\pi x ^3sin(\pi x)[/tex]
Step-by-step explanation:
Product rule, noticing that the second function is composed.[tex]g'(x) = (3x^2)\cdot cos(\pi x) + (x^3) \cdot [-\pi sin(\pi x)] = 3x^2 cos (\pi x)-\pi x ^3sin(\pi x)[/tex]
Hello!
We can use the product rule to differentiate this function.
Let g(x) = f(x) · h(x).
Recall the following:
[tex]\frac{dy}{dx} f(x) * h(x) = f'(x)h(x) + h'(x)f(x)[/tex]
In this instance, let:
[tex]f(x) = x^3\\\\h(x) = cos(\pi x)[/tex]
Differentiate each.
f(x):
Use the product rule:
[tex]\frac{dy}{dx}x^n = nx^{n-1}\\\\f'(x) = 3x^{3-1} = 3x^2[/tex]
h(x):
Use the chain rule.
[tex]h'(x) = \pi (1) * -sin(\pi x) = -\pi sin(\pi x)[/tex]
Now, we can use the above product rule.
[tex]g'(x) = 3x^2 * cos(\pi x) + (-\pi sin(\pi x) * x^3)\\\\\boxed{g'(x) = 3x^2cos(\pi x) - \pi x^3 sin(\pi x)}[/tex]
Lotto Texas offers multi-million dollar jackpots with drawings every Wednesday and Saturday. Lach $1 ticket allows the player to pick 6
numbers from 54. To win the jackpot, all 6 numbers must match (in any order)
How many different lottery tickets could be sold?
How many ways are there to win the jackpot? I
How many ways are there to match 5 of 6 numbers?
How many ways are there to match 3 of 6 numbers?
How many ways are there to match 4 of 6 numbers?
The computation of the probability from the jackpots drawings of Lotto Texas shows that the number of different lottery tickets that could be sold is 25827165.
How to calculate the probability?The number of different lottery tickets that could be sold will be:
= 54C6
= 54! / (54-6)!6!
= 54! / 48!6!
= 25827165
The number of ways that are there to match 5 of 6 numbers will be:
= 6C5 × (54 - 6)C1
= 6 × 48
= 288
The number of ways that are there to match 3 of 6 numbers will be:
= 6C3 × (54 - 6)C3
= 20 × 17296
= 345920
The number of ways that are there to match 4 of 6 numbers will be:
= 6C4 × (54 - 6)C2
= 15 × 1128
= 16920
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$641.29 is what percent of $986,60?
I need this ASAP
Answer:
65%
Step-by-step explanation:
You start by dividing 641.29 by 986.60 (641.29/986.60). This gets you .65, which as a percentage is 65%
Solve the equation. Check your solution using substitution.
{45.28 = 19.83 + z}
Group of answer choices
z=25.45
z=65.11
z=897.9
z=2.28
Answer:
z=25.45
because {45.28=19.83+25.45}
{45.28=45.28}
Here is a prism. Its face is made from 6 identical squares
with side length 2 cm.
12 cm
2 cm
Diagram not drawn to scale
Work out the volume of the prism.
State the unit of your answer.
The volume of the prism that its faces is made from 6 identical squares is 48 cm³.
Volume of a square prismA square prism is a 3-dimensional cuboid where the base and top are equal squares.
v = a²hwhere
a = side length
h = height
Therefore,
a = 2 cm
h = 12 cm
Therefore,
v = a²h
v = 2² × 12
v = 4 × 12
v = 48 cm³
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Answer:
288cm (cubed)
Step-by-step explanation:
4*2=8*12=96
6*2=12*12=144
2*2=4*12=48
144+96+48=288
What are the coordinates of your new IMAGE A’B’C’?
A’=____
B’=____
C’=____
Answer:
Sensor Calibration
Convert between coordinate systems of every sensor, image, vehicle and global coordinate axis system. So data from a sensor can be mapped globally.
Calibration of a camera helps to convert a pixel in an image to
Computer Vision
Step-by-step explanation:
From a group of six people, two individuals are to be selected at random. How many selections are possible?
Answer:
15
Step-by-step explanation:
The radii of two similar cones are 27:125. What is the ratio of their areas?
Answer:
729 : 15,625
Step-by-step explanation:
the ratio of their areas is 27² : 125² = 729 : 15,625
23 divided by 8 I need help
Answer:
2.875
Step-by-step explanation:
Answer:
2.875
Step-by-step explanation:
its not a whole number its a fraction or decimal but i gave u the decimal
What is the equation in slope intercept form of a line that is perpendicular to y = 1/4x - 1 and passing through the point (4, 1)?
1. y = 4x + 17
2. y = 4x - 1
3. y = 4x + 17
4. y = 1/4x + 17
How many lateral faces does a triangular pyramid have?
one
two
three
four
Answer:
three
Step-by-step explanation:
The lateral faces are any faces besides the base.
In summary, we will count how many sides there are in a triangular pyramid, and subtract one for the base.
-> A triangular pyramid has four sides / faces
-> A triangular pyramid has three lateral faces
Answer: 3
Step-by-step explanation: i did the quiz
please help me asap
Answer:
The second option: Waxing crescent - first quarter; Waning gibbous - third quarter
PLEASE HELP PLEASE PLEASEEEE TY
Answer: 120
Step-by-step explanation: To find the volume of these two combined, we must use V = s*s*s. 4 * 10 * 2 = 80, and 2 * 5 * 4 = 40, and since we are combining this together for an added volume (since it is a tower), it is 120 inches cubed.
One year, the population of a city was 354,000. Several years later it was 414,180. Find the percent increase.
well, from 354000 to 414180, their difference is 414180 - 354000 = 60180.
if we take 354000 to be the 100%, what is 60180 off of it in percentage?
[tex]\begin{array}{ccll}amount&\%\\\cline{1-2}354000&100\\60180&x\end{array}\implies \cfrac{354000}{60180}=\cfrac{100}{x}\implies \cfrac{100}{17}=\cfrac{100}{x}\\\\\\100x=1700\implies x=\cfrac{1700}{100}\implies x=17[/tex]
The percent increase in the population is 17%.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, the population of the city increased from 354000 to 414180.
The amount of increase is:
414180 - 354000
= 60180
The percent increase is given by:
(60180/354000) × 100%
= 17%
Hence, the percent increase in the population is 17%.
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The scale of the drawing was 1 centimeters:4 meters.What is the ratio of the drawing?
9514 1404 393
Answer:
1 : 400
Step-by-step explanation:
A meter is 100 cm, so 4 m = 400 cm.
1 cm : 4 m = 1 cm : 400 cm = 1 : 400
Answer:
1:400 w7uwuwwuwiwiwyyyuuiyy
Please help! Will award BRAINLIEST if you complete it correctly!
Jen was making cake pops for the bake sale. After 3 hours, she had completed half of the work. She called Maryna for help and together they finished everything in half an hour. How long would it take Maryna to finish the job alone if she replaced Jen after Jen baked for 3 hours?
Answer:
3 hours
Step-by-step explanation:
as jen took 3 hours maryana will take equal amount of time as jen
Well, we already know that it took Jen, 3 hours, by herself to complete half the work. Then, together they both completed it in half an hour. Now, you must summarize your given data.
3 hours = Half of the work for Jen
30 Minutes = Jen and Maryna Together To Finish
If the two girls were working at the same pace, it would take them an hour and a half. However, it only took them 30 minutes to complete that. Now, we realize that Maryna works 3x faster than Jen does.
The question is asking, how long would it take her to FINISH the job.
So that means, we must divide 3 by Jen's time.
3 / 3 = 1
So, that means that it would only take Maryna 1 hour to complete the rest of the job.
Awnser me pkeaeeeeeeeeee
Answer:
46.01
Step-by-step explanation:
i.e sum of all the purchases + 7% of the total purchase.