16x²+40xy + 25y²
(4x+5y) (4x+5y)
(4x+5y)²
I hope I helped you^_^
The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific ten-hour period, one defective circuit board was found. (a) Find the probability that it was produced during the first hour of operation during that period. (Round your answer to four decimal places.) (b) Find the probability that it was produced during the last hour of operation during that period. (Round your answer to four decimal places.) (c) Given that no defective circuit boards were produced during the first five hours of operation, find the probability that the defective board was manufactured during the sixth hour. (Round your answer to four decimal places.)
Answer:
a) the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
b) the probability that the defective board was produced during the last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
c) the required probability is 0.2000
Step-by-step explanation:
Given the data in the question;
During a specific ten-hour period, one defective circuit board was found.
Lets X represent the number of defective circuit boards coming out of the machine , following Poisson distribution on a particular 10-hours workday which one defective board was found.
Also let Y represent the event of producing one defective circuit board, Y is uniformly distributed over ( 0, 10 ) intervals.
f(y) = [tex]\left \{ {{\frac{1}{b-a} }\\\ }} \right _0[/tex]; ( a ≤ y ≤ b )[tex]_{elsewhere[/tex]
= [tex]\left \{ {{\frac{1}{10-0} }\\\ }} \right _0[/tex]; ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]
f(y) = [tex]\left \{ {{\frac{1}{10} }\\\ }} \right _0[/tex]; ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]
Now,
a) the probability that it was produced during the first hour of operation during that period;
P( Y < 1 ) = [tex]\int\limits^1_0 {f(y)} \, dy[/tex]
we substitute
= [tex]\int\limits^1_0 {\frac{1}{10} } \, dy[/tex]
= [tex]\frac{1}{10} [y]^1_0[/tex]
= [tex]\frac{1}{10} [ 1 - 0 ][/tex]
= [tex]\frac{1}{10}[/tex] or 0.1000
Therefore, the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
b) The probability that it was produced during the last hour of operation during that period.
P( Y > 9 ) = [tex]\int\limits^{10}_9 {f(y)} \, dy[/tex]
we substitute
= [tex]\int\limits^{10}_9 {\frac{1}{10} } \, dy[/tex]
= [tex]\frac{1}{10} [y]^{10}_9[/tex]
= [tex]\frac{1}{10} [ 10 - 9 ][/tex]
= [tex]\frac{1}{10}[/tex] or 0.1000
Therefore, the probability that the defective board was produced during the last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
c)
no defective circuit boards were produced during the first five hours of operation.
probability that the defective board was manufactured during the sixth hour will be;
P( 5 < Y < 6 | Y > 5 ) = P[ ( 5 < Y < 6 ) ∩ ( Y > 5 ) ] / P( Y > 5 )
= P( 5 < Y < 6 ) / P( Y > 5 )
we substitute
[tex]= (\int\limits^{6}_5 {\frac{1}{10} } \, dy) / (\int\limits^{10}_5 {\frac{1}{10} } \, dy)[/tex]
[tex]= (\frac{1}{10} [y]^{6}_5) / (\frac{1}{10} [y]^{10}_5)[/tex]
= ( 6-5 ) / ( 10 - 5 )
= 0.2000
Therefore, the required probability is 0.2000
pls help me with this. You need to graph the equation or smt
What’s v=(324pie)(3)
write your answer in simplest radical form
Answer:
a = 3√6 in
Step-by-step explanation:
From the question given above, the following data were obtained:
Angle θ = 60°
Adjacent = 3√2 in
Opposite = a =?
The value of 'a' can be obtained by using the tan ratio as illustrated below:
Tan θ = Opposite / Adjacent
Tan 60 = a / 3√2
√3 = a / 3√2
Cross multiply
a = √3 × 3√2
Recall:
c√d × n√m = (c×n) √(d×m)
Thus,
√3 × 3√2 = (1×3)√(3×2)
√3 × 3√2 = 3√6
a = 3√6 in
Write an equation and solve it to answer each question. A pile of 55 coins consisting of nickels and dimes is worth $3.90. Find the number of each. I only need the equation plz. WILL MARK BRAINLIEST.
Answer:
0.05x + 0.1(55 - x) = 3.9
Step-by-step explanation:
There are 55 coins.
Let x = number of nickels.
The number of dimes is 55 - x.
The value of a nickel is $0.05, and the value of a dime is $0.10.
The value of x nickels is 0.05x
The value of 55 - x dimes is 0.1(55 - x)
The total value of the coins is 0.05x + 0.1(55 - x)
The total value of the coins is $3.90
0.05x + 0.1(55 - x) = 3.9
Find the slope of the graphed line
Answer:
4
Step-by-step explanation:
Pick two points on the line
(0,-5) and (1,-1)
We can find the slope using
m = (y2-y1)/(x2-x1)
= ( -1 - -5)/(1 - 0)
(-1+5)/(1-0)
4/1
= 4
Oak street and elm street run parallel to each other. When main street intersects them, it forms exterior 8, measuring 60. What is the measure of 1?
Answer:
0 is the answer measure 1
Farah is x years old. Ibtisam is 3 years younger than Farah. Muna is twice as old as Ibtisam. Write and expression in terms of x, for
(a) Ibtisam's age,
(b) The sum of their three ages, giving your answer in its simplest form.
Answer:
Farah: x
Ibtisam: x-3
Muna: 2(x-3) or 2x-6
Sum of all their ages: 4x-6
Step-by-step explanation:
Farah is x, so we don't need an expression for that.
Ibtisam is 3 years younger than Farah, which means that we need to subtract 3 from Farah, and that would be Ibtisam's age. x-3.
Muna is 2 TIMES Ibtisam's age, so we need to multiply whatever expression taht was used for Ibtisam by 2. Put brackets around the equation with 2 outside: 2(x-3). Solve and you get 4x-6
Now, you have all their ages in expression form, now you need to simplify by adding:
x+x+2x-6
We cannot simplify -6, so we put that aside. Add all the x's and you get 4x, insert the minus 6 at the end:
4x-6
Hope this helps!
--Applepi101
Answer:
a) X -3
b) 4x - 9
Step-by-step explanation:
a) Farah's age is X so Ibtisam will be X - 3 old since he is 3years younger than Farah
b) Farah is X years old
Ibtisam is X - 3 years old
Muna is 2(X -3) since she is 2 times older than Ibtisam.
the sum of Thier ages will be
X + X -3 + 2(x-3)
= 2x - 3 + 2x - 6
= 4x - 9
equation of a line with slope -1 and y intercept 0,-2
Answer:
y = - x - 2
Step-by-step explanation:
y=mx+b
m refers to slope
b refers to y intercept
y = (-1)x + (-2)
y = - x - 2
Answer:
y=-1x-2
Step-by-step explanation:
plug in the slop and y intercept to the equation y=mx+b
Calvin and Jamel each havr cats as pets. Calvin buys cat food in cylindrical can that are 6 centimeters in diameter and 12 centimeters high. Jamel buys cat food in cylindrical can that 12 centimeters in diameter and 6 centimeters high. What is the ratio of the volume of one of Calvin's cans of to the volume of one of Jamel's cans?
Answer:
see below
Step-by-step explanation:
CALVIN
v=[tex]\pi[/tex]× r ² × h
v=3.14 × 3² × 12
v=3.14×9 × 12
v=3.14 × 108
v = 339.12
JAMEL
v=[tex]\pi[/tex] × r ²×h
v=3.14× 6 ² × 6
v=3.14 × 36×6
v=3.14×216
v=678.24
Can you provide a solution or a formula?
144 x 1.25 = 180
Answer: 144
Answer:
144
Step-by-step explanation:
144 × 1.25 = 180
We add the 1 to .25 to represent the original value plus the 25% increase.
Or you could have divided 180 by 1.25 to find original price.
HELP PLEASE! INEEED HELPPP RIGHT NOW The graph of y=x−2−−−−√ is is transformed to become y=x+3−−−−√−2. Which of the following statements best describes the effect this transformation has on the graph of y=x−−√?
Answer:
I think it's D but I don't know how to do this, but I ask my Friend and he gave me this graph I hope it helps.
Option (C) the graph is translated 5 units left and 2 units down is the correct answer.
What is graph of a function?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).
For the given situation,
The function is [tex]y=\sqrt{x-2}[/tex]
This function is transformed to become the function as [tex]y=\sqrt{x+3}-2[/tex]
Now compare this transformation with the function [tex]y=\sqrt{x}[/tex].
These functions are plotted in the graph below.
On comparing this transformation,
The graph is translated 5 units left and 2 units down.
Hence we can conclude that option (C) the graph is translated 5 units left and 2 units down is the correct answer.
Learn more about graph of a function here
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Can someone help me with this?
9514 1404 393
Answer:
CNBD -- using the given statement regarding perpendicularityΔLAW ≅ ΔWKL by ASA -- using the markings on the figureStep-by-step explanation:
The given information tells us there is one congruent side in the two right triangles. That is not sufficient to claim congruence of the triangles.
CNBD
__
The figure shows one congruent angle in addition to one congruent side, so the figures can be shown to be congruent using the ASA theorem.
ΔLAW ≅ ΔWKL
_____
Additional comment
We don't know which answer is expected. You should discuss this question with your teacher, since it appears to be missing the statement that
∠ALW ≅ ∠KWL
a film lasts 45 minutes what fraction of the film is left after 15 minutes and 25 minutes ?
Answer: i) [tex]\frac{1}{3}[/tex]
ii) [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
Total length of film = 45 mins
Fraction of time left after 15 mins = [tex]\frac{15}{45}[/tex]
= [tex]\frac{1}{3}[/tex]
Fraction of time left after 25 mins = [tex]\frac{25}{45}[/tex]
= [tex]\frac{5}{9}[/tex]
Marie's backyard deck cost $68.29 per square meter to build. The deck is 9 meters wide and 9 meters long. How much did it cost to build the deck?
$5531.49
(9×9)×$68.29
For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. A random sample of 5240 permanent dwellings on an entire reservation showed that 1613 were traditional hogans.
(a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.)
(b) Find a 99% confidence interval for p. (Round your answer to three decimal places.) What is the lower limit? What is the upper limit?
Answer:
Step-by-step explanation:
point est. 0.307824427
99% 2.58
Confidence Interval - "P" values
(0.2914 , 0.3243 )
The curve y=2x^3+ax^2+bx-30 has a stationary point when x=3. The curve passes through the point (4,2).
(A) Find the value of a and the value of b.
#secondderivative #stationarypoints
A stationary point at x = 3 means the derivative dy/dx = 0 at that point. Differentiating, we have
dy/dx = 6x ² + 2ax + b
and so when x = 3,
0 = 54 + 6a + b
or
6a + b = -54 … … … [eq1]
The curve passes through the point (4, 2), which is to say y = 2 when x = 4. So we also have
2 = 128 + 16a + 4b - 30
or
16a + 4b = -96
4a + b = -24 … … … [eq2]
Eliminate b by subtracting [eq2] from [eq1] and solve for a, then for b :
(6a + b) - (4a + b) = -54 - (-24)
2a = -30
a = -15 ===> b = 96
Simplify: y^-3
a) 3/y
b) - 1/y^3
c) -3y
d) 1/y^3
Answer:
1/y^3
Step-by-step explanation:
We know that a^-b = 1/a^b
y ^-3 = 1/y^3
bionomial probabilities
Answer:
Binomial probability refers to the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes (commonly called a binomial experiment).
Hope this will help you :)A loaf of bread costs $1.40 and the markup is 30% of the selling price. Find the selling price.
Answer:
The selling price after the markup is $1.82
Step-by-step explanation:
$1.40 * .30 =
Multiply $1.40 times .30 (which is same as 30%)
$1.40 * .30 = $0.42
Add $1.40 and $0.42
= $1.82
Hope this helps.
The point A(−8,−4) is reflected over the origin and its image is point B. What are the coordinates of point b?
9514 1404 393
Answer:
B(8, 4)
Step-by-step explanation:
Reflection across the origin negates both coordinate values.
(x, y) ⇒ (-x, -y) . . . . . reflection across the origin
A(-8, -4) ⇒ B(8, 4)
What information is NOT necessary to find the area of a circle?
a.
pi
c.
diameter
b.
radius
d.
height
Answer:
D. Height
General Formulas and Concepts:
Geometry
Area of a Circle: A = πr²
r is radiusStep-by-step explanation:
In order to find the area of a circle, we must follow the formula. Out of all the options given, height is not incorporated into the formula.
It wouldn't make sense to use height anyways since it would be 3-dimenional and we're talking 2-dimensional.
∴ our answer is D.
Whats the volume of this aquarium?
PLZ HELP!!
Jan needs 1/3 of chocolate chips to make cookies and 3/4 cup to make brownies. How many cups does she need altogether?
Answer:
She needs 1½ cups
Step-by-step explanation:
Number of cups she needs altogether = 1/3 + 3/4 =(4+9)/12 = 13/12 = 1½
The blueprints of a house have a scale factor of 30. If one side of the house measures 4 inches on the blueprint, how long is the actual side length (in feet)?
A. 7.5 feet
B.10 feet
C. 90 feet
D. 120 feet
If the scale factor is 30, then all you have to do is multiply each measurement by the scale factor. In this case, 4 · 30 = 120.
what translation was the similarity moved through ?
Identify the errors made in the finding the inverse of y= x^2 +12x
X= y^2+12x
Y^2= x- 12x
Y^2 = -11x
Y=√11x, for x greater than or equal to 0
9514 1404 393
Answer:
y was not substituted for every x
Step-by-step explanation:
To find the inverse of ...
y = f(x)
you need to solve ...
x = f(y)
Here, f(x) = x^2 +12x, so f(y) = y^2 +12y
This is not the expression we see on the right of ...
x = y^2 +12x
Apparently y was not properly substituted into f(x).
The triangle below is equilateral. Find the length of side
x in simplest radical form with a rational denominator.
===========================================================
Explanation:
Any equilateral triangle has all three angles of 60 degrees each. Splitting the triangle in half like this produces two identical copies of 30-60-90 triangles.
Any 30-60-90 triangle will have its hypotenuse twice as long compared to the short leg. The short leg here is 5 (it's opposite the smallest angle), so that doubles to 2*5 = 10 which is the value of x.
Note: the other side of this right triangle is 5*sqrt(3).
Answer:
x=10
Step-by-step explanation:
∵ Δ IS Equilateral.
∴ sides are equal.
perpendicular from vertex bisects it.
x=2×5=10
been stuck on this for a few days now, help on even one would be greatly appreciated!!!
Answer:
-5-9i
Step-by-step explanation:
-1-8i-4-i
-1-4-8i-i
-5-9i
A publisher reports that 54% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 200 found that 44% of the readers owned a personal computer. Is there sufficient evidence at the 0.10 level to support the executive's claim
The null and alternate hypotheses are
H0 : u = 0.44 vs Ha: u > 0.44
Null hypothesis: 44% of readers own a personal computer.
Alternate Hypothesis : greater than 44% of readers own a personal computer.
This is one tailed test and the critical region for this one tailed test for the significance level 0.1 is Z > ±1.28
The given values are
p1= 0.54 , p2= 0.44 ; q2= 1-p2= 0.56
Using z test
Z = p1-p2/√p2(1-p2)/n
Z= 0.54-0.44/ √0.44*0.56/200
z= =0.1/ 0.03509
z= 2.849
Since the calculated value of Z= 2.849 is greater than Z= 1.28 reject the null hypothesis therefore there is sufficient evidence to support the executive's claim.
Null hypothesis is rejected
There is sufficient evidence to support the executive's claim at 0.10 significance level.
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