Using the binomial distribution, it is found that there is a 0.0058 = 0.58% probability that the sample contains exactly two defective parts.
What is the binomial distribution formula?The formula is:
[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, we want P(X = 2) with p = 0.025, n = 5, hence:
[tex]P(X = 2) = C_{5,2}.(0.025)^{2}.(0.975)^{3} = 0.0058[/tex]
There is a 0.0058 = 0.58% probability that the sample contains exactly two defective parts.
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X + 2x + 8 = X = 10 + 6
Answer:
x = 8/3
Decimal form: 2.66666666667
Step-by-step explanation:
Given:
[tex]x+2x+8=10+6[/tex]
Solution:
[tex]\mathrm{Add\:similar\:terms:}\:x+2x=3[/tex]
[tex]3x+8=10+6[/tex]
[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]
[tex]3x+8-8=16-8[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]3x=8[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}3[/tex]
[tex]\frac{3x}{3}=\frac{8}{3}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x=\frac{8}{3}[/tex]
[tex]x=2.66666666667[/tex]
~lenvy~
Answer/Step-by-step explanation:
Base on the given we are..
Solving for x:
Solve:
X + 2x + 8 = X = 10 + 6 {x+2x= 3x}
3x + 8 = 10 + 6 {10+6=16}
3x + 8-8=16-8 {16-8=8}
3x = 8 {divide both sides by same term}
3x/3 = 8/3
Therefore,
x = 8/3
Decimal form = 2.66666666667
[RevyBreeze]
Which of the following number sentences is an example of the associative property? Select all that apply.
[tex](1\frac{2}{5}*3\frac{1}{2} )*4=1\frac{2}{5} (3\frac{1}{2} *4)[/tex]
[tex]2.5*(1.8+6.3)=(2.5*1.8)+(2.5*6.3)[/tex]
10(4.6 × 3) = (10 × 4.6) × 3
6.3 × 1 = 6.3
Associative property:-
a+(b+c)=(a+b)+cLets check one by one
#1
Here the rule is
(ab)c=a(bc)Hence Yes associative property
#2
Here the rule is
a(b+c)=ab+acHence no it's distributive property
#3
a(bc)=(ab)cYes
#4
ab=baNo
Associative property meaning rearranging the parentheses in an expression which will not change the result.
✔A)
[tex]\rightarrow \sf (1\dfrac{2}{5} \ x \ 3\dfrac{1}{2} ) \ x \ 4 = 1\dfrac{2}{5} (3\dfrac{1}{2} \ x \ 4 )[/tex]
[tex]\rightarrow \sf \dfrac{98}{5} = \dfrac{98}{5}[/tex]
This uses associate property as it is rearranged in a different way and result same.
B)
[tex]\rightarrow \sf 2.5 \ x \ (1.8 +6.3) = (2.5 \ x \ 1.8)+(2.5 \ x \ 6.3 )[/tex]
This property is called distributive property. a(b + c) = a(b) + a(c)
✔C)
[tex]\sf \rightarrow 10(4.6 \ x \ 3) = (10 \ x \ 4.6) \ x \ 3[/tex]
[tex]\sf \rightarrow 138 = 138[/tex]
associate property as the following is rearranged inside the parentheses
D)
[tex]\rightarrow \sf 6.3 \ x \ 1 = 6.3[/tex]
This does not fall under any method or else multiplicative identity property.
120 feet is to 150 feet as 8 feet is to ten feet write the proportion HELP PLEASE!!! AND PLEASE SHOW HOW TO DO IT
Answer:
Step-by-step explanation:
120/150 = 0.8
8/10 = 0.8
8x15=120
10x15=150
Algebra: Right answer pls
Which statement about the graph of y = 4 (1.25)× is true?
The coordinates of the x-intercept are (4, 0)
The coordinates of the y- internet are (0, 4) (ʀɤɢʜʈ Åɴswɛɾ)
The equation of the asymptote is x = 4
The graph includes the point (0, 1.25)
Answer: B
Step-by-step explanation:
What will be the angle A?
Answer: 30 degrees
Step-by-step explanation:
what is 5b^-2/b^-3? I need to know
Answer:
5b
Step-by-step explanation:
Hope this helps <3
NO LINKS!!!
Part 3: Figure A is a dilated image of Figure B. Find the scale factor. #5 and 6
Answer:
Step-by-step explanation:
Scale:- 1box=1units
So
Take one side of each
B=6unitsA=10unitsScale factor(A to B)
[tex]\\ \rm\rightarrowtail \dfrac{6}{10}=\dfrac{3}{5}[/tex]
Scale factor (B to A) is 5/3#6
B=12A=6Scale factor (A to B)
[tex]\\ \rm\rightarrowtail \dfrac{12}{6}=2[/tex]
Scale factor (B to A)
[tex]\\ \rm\rightarrowtail \dfrac{6}{12}=0.5[/tex]
Determine the value of x if the mode is 18
Frankie is saving up to have spending money for her family vacation. If Frankie's current monthly net pay is $490.00 and her monthly expenses are $396.90 what percent of her net pay is left for savings?
19%
23%
67%
81%
Each of two computers can process bills at 160/min a newer model can process bills at 200/min after the first two computers have worked 1.5 min they are joined by the third computer how long will it take fromthe time the first two computers are turned on to process 1780
7*8/10 product lies between what numbers
Answer:
5 and 6.
Step-by-step explanation:
7*8 is 56. 56 divided by 10 is 5 6/10
what is the relationship between the sine and cosine of the complementary angles in this diagram? drag and drop the answers into the boxes to correctly complete the statements.
Both sin(41) and cos(x) can be represented by the ratio ____. the angles measuring 41 and x are complementary angles. this means x+41=____. therefore x=____. since sin(41) = cos(x), this also shows that sin(41)=cos(_____).
Answer:
Step-by-step explanation:
Both sin(41) and cos(x) can be represented by the ratio b/c
What is complementary angles?If the sum of two angles is equal to 90 degrees, then such angles are called complementary angles. The total of the two angles' measurements determines their complement and supplement. The pair of angles is said to be complimentary if the product of the two angles equals the measurement of a right angle. Example:
40° is the complement of 50°.
50° is the complement of 40°.
sin (41) = b/c
cos (x) = b/c
∴both sin(41) and cos(x) can be represented by the ratio b/c
x + 41 = 90 (∵ complementary angles)
x = 90-41 = 49
∵ sin 41 = cos x
∴ sin 41 = cos (90-41)
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What is 1 + 1 x 3 Whoever answers it to
Answer:
It equals 4
Step-by-step explanation:
1 + 1 x 3=4
Answer:
I think it equals 4
Step-by-step explanation:
1 + 1 x 3=4
Find the value of x. Round your answer to the nearest tenth.
Answer:
Value of x is 34.9 (nearest tenth)[tex]~[/tex]
Step-by-step explanation:
In given right angled traingle:
AC (Hypotenuse) = 20∠ACB = 35° AB (Perpendicular) = x[tex]~[/tex]
In ∆ABC,
[tex]\: \: \: \: \dashrightarrow \: \: \: \sf \dfrac {AC}{AB} = \sin35° \\[/tex]
[tex]\: \: \: \: \dashrightarrow \: \: \: \sf \dfrac {20}{x} = 0.5736 \\[/tex]
[tex]\: \: \: \: \dashrightarrow \: \: \: \sf x = \dfrac {20}{0.5736} \\[/tex]
[tex]\: \: \: \:{ \pmb{ \pink{ \sf{ \dashrightarrow \: \: \: { x = 34.867 }}}}}[/tex]
Hence,
Value of x is 34.9 (nearest tenth)find the total area of cardboard used in making a matchbox, complete with the sliding portion, 4cm long, 2.5cm wide, and 1.2cm deep (ignore the thickness of the cardboard)
Answer: 55.2 cm^2
Step-by-step explanation:
2(4x2.5 + 2.5x1.2 + 1.2x4) = 35.6 cm^2
(2x1.2x4 + 4x2.5) = 19.6 cm^2
(35.6 + 19.6) = 55.2 cm^2
Solve for x. -14 - x = 14
Answer:
x= -28
Step-by-step explanation:
1. First you have to add 14 to both sides to get the x by itself. That's always the first thing you have to do. Get x by itself.
2. After that, you should have -x= 28. You can't leave it like that because it is still not simplified. It's basically saying 28 is the opposite of x. What's the opposite of positive? Negative.
3. Therefore, your final answer should be -28
Answer:
x = -28
Step-by-step explanation:
Hey! First, lets establish our equation :)
-14 -x = 14
Now, we are going to get our x alone on a single side, to do this, we are going to add 14 to both sides to be able to cut out -14 on the left side!
-14 -x = 14
+14 +14
-x = 28
The last thing we have to do is divide both sides by -1 to get x by itself without it being negative!
-x = 28
÷-1 ÷-1
x = -28
So, x, is equal to -28 (negative 28!) :)
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
The circumference of the base of a cone is 24 inches. The slant height of the cone is 20 inches.
What is the surface area of the cone? Express the answer in terms of .
240 square inches
384 square inches
480 square inches
624 square inches
The surface area of a cone with circumference base of 24π inches and slant height of 20 inches is 384π inches² in terms of π.
Surface area of a conesurface area = πr(r + l)
where
r = radiusl = slant heightTherefore,
l = 20 inches
24π = 2πr
r = 12
Therefore,
surface area = π(12)(12 + 20)
surface area = 12π(12 + 20)
surface area = 12π × 32
surface area = 384π inches²
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Answer:
B) 384 π square inches
Step-by-step explanation:
E2020
Huntington Medical Center purchased a used low-field MRI scanner 2 years ago for $445,000. Its operating cost is $350,000 per year and it can be sold for $150,000 anytime in the next 3 years. The Center’s director is considering replacing the presently owned MRI scanner with a state-of-the-art 3 Tesla machine that will cost $2 million.The operating cost of the new machine will be $280,000 per year, but it will generate extra revenue that is expected to amount to $550,000 per year. The new unit can probably be sold for $875,000 3 years from now. You have been asked to determine how much the presently owned scanner would have to be worth on the open market for the AW values of the two machines to be the same over a 3-year planning period. The Center’s MARR is 10% per year.
The worth of the old scanner machine in the open market will be $86601.60.
How to calculate the worth on open market?To calculate the worth of the scanner on the open market, it's important to compare the values of the machines.
The calculation of the worth of the scanner goes thus:
Let the worth be represented by x.
x(A/P,10%, 3) - 350000 + 150000(A/F, 10%, 3) = 2000000(A/P, 10%, 3) + 270000 + 875000(A/F, 10%, 3)
= 0.4021x - 350000 + 45315 = -804200 + 270000 + 264337.50
0.4021x = 34822.50
Divide by 0.4021
x = 34822.60/0.4021
x = 86601.60
Therefore, the worth is $86601.60.
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An arrow is shot vertically upward at a rate of 190 feet per second from ground level. Use the projectile formula
h
=
−
16
t
2
+
v
0
t
+
h
0
h
=
-
16
t
2
+
v
0
t
+
h
0
to determine when the height of the arrow will be 471 feet.
The height of the arrow will be 471 feet at 8.35s and 3.53s
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
h represent the height of the arrow after t seconds.
h(t) = -16t² + v₀t + h₀
v₀ is the initial velocity = 190 ft/s, h₀ is the initial height = 0m, hence:
h(t) = -16t² + 190t
At 471 feet:
471 = -16t² + 190t
0 = -16t² + 190t - 471
t = 8.35 or 3.53
The height of the arrow will be 471 feet at 8.35s and 3.53s
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Please help, has t toy cars. Zachary has 3 times as many toy cars as Oliver. Write an expression
that shows how many toy cars Zachary has.
Answer:
z=3t
Step-by-step explanation:
multiply it by 3
If two chords are the same distance from the center of a circle, then they are ______.
Answer:
1 is the answer to have the distance same
You are debating about whether to buy a new computer for $800.00 or a refurbished computer with the same equipment for $640.00. If you are paid $10.00/hour and your deductions are FICA (7.65%), federal tax withholding (12%), and state tax withholding (8%), how many hours do you have to work to pay for the new computer?
111 hours
98 hours
87 hours
Total deduction
7.65+12+819.65+827.65%Now
Earnings after deduction
10-10(0.2765)10-2.7657.335$Total hours:-
640/7.33587.2587hoursYou will have to work 110.5 hours to buy the new computer.
What is tax?A tax is some specific financial amount or some other charged taxpayer by the government in order to fund government spending.
Given is that you have to buy a new computer for $800.00 or a refurbished computer with the same equipment for $640.00. If you are paid $10.00/hour and your deductions are -
FICA (7.65%),
Federal tax withholding (12%)
State tax withholding (8%).
Total money earned after all the deductions -
A{n} = 10 - {7.65% of 10 + 12% of 10 + 8% of 10}
A{n} = 10 - {7.65/100 x 10 + 12/100 x 10 + 8/100 x 10}
A{n} = 10 - {7.65/10 + 12/10 + 8/10}
A{n} = 10 - 2.765
An = 7.235
Cost of new computer = $800.
For 1 hour. you earned $7.235.
Then, you will earn $1 in (1/7.235) hours
So, you will earn $800 in (1/7.235 x 800) = 110.5
Therefore, you will have to work 110.5 hours to buy the new computer.
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the length of a rectagle is twice its width. if the perimeter of the rectangle is 36in, find its length and width
Answer:
Perimeter=36in
Length of one side=12
Length of the other side=12
Width of one side=6
Width of the other side=6
Step-by-step explanation:
6*2=12, so if the length is 12 half would be six. All of them added up is 36
Answer:
Length = 12inWidth = 6inStep-by-step explanation:
[tex]perimeter \: of \: a \: rectangle = 2(2x) + 2(x) \\ 36in = 4x + 2x = 6x \\ \frac{36in}{6} = \frac{6x}{6} \\ x = 6in \\ 2x = 2 \times 6in = 12in[/tex]
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Help help help math math help
Answer:
x = - 4
Step-by-step explanation:
i hope its helped. thank you !
-3/5m + 8 = 20
what is the answer of m
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: - \frac{ 3}{5} m + 8 = 20[/tex]
[tex]\qquad \sf \dashrightarrow \: - \frac{ 3}{5} m = 20 - 8[/tex]
[tex]\qquad \sf \dashrightarrow \: - \frac{ 3}{5} m =12[/tex]
[tex]\qquad \sf \dashrightarrow \: - \frac{ }{} m =12 \times \frac{5}{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: - m = 4 \times 5[/tex]
[tex]\qquad \sf \dashrightarrow \:m = - 20[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
A flashlight is projecting a triangle onto a wall
Answer:
24
Step-by-step explanation:
The the triangles are similar, the lengths of corresponding sides are in proportion.
15/20 = 18/n
3/4 = 18/n
1/4 = 6/n
n = 4 × 6
n = 24
Answer:
n = 24
Step-by-step explanation:
In similar triangles, corresponding sides are in same ratio.
[tex]\dfrac{n}{18}=\dfrac{20}{15}\\\\\\n=\dfrac{20}{15}*18\\\\\\n = 4*6\\\\n = 24[/tex]
Need help Please! Quick
Answer:
please see photo for details
i) Find the first 4 terms in the expansion of
[tex](2 + x ^{2})^{6}[/tex]
in ascending powers of x.
ii) Find the term independent of x in the expansion of
[tex](2 + x ^{2})^{6}(1 - \frac{3}{x {}^{2} } ) {}^{2} [/tex]
Answer:
(i) [tex]64+192 x^2+240 x^4+160x^6[/tex]
(ii) 1072
Step-by-step explanation:
Part (i)
Using Binomial series formula:
[tex](2+x^2)^6=2^6+6C1 \cdot 2^{6-1}\cdot x^2+6C2 \cdot 2^{6-2}\cdot(x^2)^2+6C3 \cdot 2^{6-3}\cdot(x^2)^3[/tex]
[tex]=64+6 \cdot 32\cdot x^2+15 \cdot 16\cdot x^4+20 \cdot 8 \cdot x^6[/tex]
[tex]=64+192 x^2+240 x^4+160x^6[/tex]
Part (ii)
[tex](1-\frac{3}{x^2})^2=(1-\frac{3}{x^2})(1-\frac{3}{x^2})[/tex]
[tex]=1-\dfrac{6}{x^2}+\dfrac{9}{x^4}[/tex]
[tex](2+x^2)^6(1-\frac{3}{x^2})^2=(64+192 x^2+240 x^4+160x^6)\left(1-\dfrac{6}{x^2}+\dfrac{9}{x^4} \right)[/tex]
[tex]=64-\dfrac{384}{x^2}+\dfrac{576}{x^4}+192x^2-1152+\dfrac{1728}{x^2}+240x^4-1440x^2+2160+...[/tex]
There is no need to keep expanding since the remaining will include the variable.
Therefore, the term independent of x = 64 - 1152 + 2160 = 1072
Find the measure of the indicated arc
Step-by-step explanation:
we need the length of the arc ?
the length of the arc fully around the circle (360°) is the circumference of the circle : 2×pi×r
and the arc length for 123° is then
2×pi×r×123/360
but we would need r to calculate that. you did not provide that.
the only other thing that comes to mind is : the arc angle is indeed the angle at the center of the circle and is 123°.
i don't know how else to help you, as i cannot think of anything else you might need there.
Convert 5 3/4 to a decimal. Round to the nearest tenth.
Answer:
5.75
Step-by-step explanation:
Make denominator to 100 by multiplying by 25
4*25=100
3*25=75
75/100=.75