Answer:
Step-by-step explanation:
59°
A quality control inspector has drawn a sample of 18 light bulbs from a recent production lot. If the number of defective bulbs is 1 or more, the lot fails inspection. Suppose 30% of the bulbs in the lot are defective.
Required:
What is the probability that the lot will pass inspection?
Answer:
0.0016 = 0.16% probability that the lot will pass inspection.
Step-by-step explanation:
For each bulb, there are only two possible outcomes. Either it is defective, or it is not. The probability of a bulb being defective is independent of any other bulb, 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.
Sample of 18 light bulbs
This means that [tex]n = 18[/tex]
30% of the bulbs in the lot are defective.
This means that [tex]p = 0.3[/tex]
What is the probability that the lot will pass inspection?
It will pass inspection if there are no defective bulbs, that is, we have to find P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{18,0}.(0.3)^{0}.(0.7)^{18} = 0.0016[/tex]
0.0016 = 0.16% probability that the lot will pass inspection.
Determine the area of the given parallelogram with length 11 and altitude five
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Answer:
55 square units
Step-by-step explanation:
The area of a parallelogram is the product of base length and height:
A = bh
A = (11)(5) = 55 . . . area of the given parallelogram in square units
Rewrite the function f(x)=16^x in four different ways, using a different base in each case.
Answer:
X=1
f(x)=16^1
=16
X=2
f(x)=16^2
256
X=3
f(x)=16^3
=4096
X=4
f(x)=16^4
=65536
Here are four different ways to rewrite the function f(x) = 16^x, using a different base for each case:
Using base 2:
f(x) = (2^4)^x = 2^(4x)
Using base 3:
f(x) = (3^2)^x = 3^(2x)
Using base 10:
f(x) = (10^(log10(16)))^x = 10^(log10(16) * x)
Using base e (natural logarithm):
f(x) = (e^(ln(16)))^x = e^(ln(16) * x)
How to explain the functionIn these rewritten forms, the exponentiation of the base is expressed as a simpler expression.
This involves the new base, which helps to illustrate the relationship between the original function and the different bases used.
Learn more about functions
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Solve equation by using the quadratic formula
Answer:
x = -2
Step-by-step explanation:
x^2 + 4x + 4 = 0
quadratic formula:
-b +or- sqrt(b^2-4ac)/2a
-4 +/- sqrt ((-4)^2-4*1*4)/2*1
-4+/- sqrt(16-16) / 2
-4 +/- 0 / 2
-4/2
-2
Write an equivalent expression to 1/2 (2n+6).
Answer:
n+3
Step-by-step explanation:
1/2 × 2(n+3)=n +3
I hope this helps
a yogurt shop offers 7 different flavors of frozen yogurt and 11 different toppings. How many choices are possible for a single serving of frozen yogurt with one topping
answer: 77
Step-by-step explanation:
7×11=77
sorry if I'm wrong
Answer:
fijatebie nl aperguntaa
Step-by-step explanation:
Helpekksdjfkfodldkdkdodidididisj Help
Answer:
The answers to your questions are given below.
Step-by-step explanation:
1. m∠1 and m∠2 are complementary. This statement was given from the question.
2. m∠1 + m∠2 = 90°. Complementary angles add up to give 90°.
3. m∠2 = 74°. This was given in the question.
4. m∠1 + 74 = 90°. Since m∠1 and m∠2 are complementary. Their sum will add up to give 90°
5. m∠1 = 16°
We can prove m∠1 = 16° as shown below:
m∠1 + m∠2 = 90° (complementary angles)
m∠2 = 74°
m∠1 + 74 = 90°
Collect like terms
m∠1 = 90 – 74
m∠1 = 16°
The population of a strain of bacteria doubles in a culture. At noon there were 80 bacteria present and by 4:00 PM there were 20 480 bacteria. Determine algebraically the doubling period. Hint: You DO NOT need to use systematic trials.
Answer:
t = 1/2 hour
Step-by-step explanation:
20480 = 80[tex]x^{t }[/tex]
20480 = 80[tex]x^{4 }[/tex]
20480/80 = [tex]x^{4 }[/tex]
256 = [tex]x^{4 }[/tex]
x = 4
doubling period
2 = [tex]4^{t}[/tex]
t = 1/2 hour
d) A product contains three lasers, and the product fails if any of the lasers fails. Assume the lasers fail independently. What should the mean life equal for 99% of the products to exceed 10000 hours before failure
Solution :
Let the probability laser works = p
The probability that the system works = [tex]$P(\text{all three component works}) = p^3 $[/tex]
= 0.99
Therefore, p = 0.9967
Now for the above probability critical z = -2.72
Hence, the mean life is equal to = [tex]10,000 + 2.72 \times 600[/tex]
= [tex]10,000+1632[/tex]
[tex]=11,632[/tex]
Rewrite the fraction in the sentence below as a percentage. From 125 yards away, a marksman hit 11/20 of the targets last year.
Answer:
Step-by-step explanation:
11/20 = 55/100 = 55%
Question 4 please provide explanation for question
Answer:
A
Step-by-step explanation:
We need to find a equation that is where the domain is all real numbers and the range is all real numbers greater than -3
A square root function cannot equal to all real numbers because we cant take the square root of a negative number. so B and C are already wrong.A cubic function range is all real numbers. so y can be greater than -3 but it would also include. values lesser than -3. so D is Wrong.A is right, the domain of a absolute value function is all real numbers. The range of a absolute value is all numbers greater than or equal to zero but if we subtract 3, it changes into all real numbers greater than or equal to -3
A function of the form f(x)=ab^x is modified so that the b value remains the same but the a value is increased by 2. How do the domain and range of a new function compare to the domain and range of the original function?
Answer:
The domain and range remain the same.
Step-by-step explanation:
Hi there!
First, we must determine what increasing a by 2 really does to the exponential function.
In f(x)=ab^x, a represents the initial value (y-intercept) of the function while b represents the common ratio for each consecutive value of f(x).
Increasing a by 2 means moving the y-intercept of the function up by 2. If the original function contained the point (0,x), the new function would contain the point (0,x+2).
The domain remains the same; it is still the set of all real x-values. This is true for any exponential function, regardless of any transformations.
The range remains the same as well; for the original function, it would have been [tex]y\neq 0[/tex]. Because increasing a by 2 does not move the entire function up or down, the range remains the same.
I hope this helps!
Think of a two-digit number. What is the probability that it has different digits?
Answer:
9/10
Step-by-step explanation:
The first two digit number is 10 and the last is 99. That's a total of 99-10+1 numbers in all. That simplifies to 90. (Just like if we wanted to see how many numbers was 3,4,5, we would do 5-3+1=3 to get the total number.
Anyways, let's consider first how many 2 digjt numbers whose digits are equal. You have 11 22,33,44 55,66,77,88,99 which is 9 numbers total.
So the amount of 2 digits number whose digits differ is 90-9=81.
The probability that a 2 digit number have different digits is 81/90.
This can reduce. Divide top and bottom by 9 giving 9/10.
Please help due tomorrow
Answer: x= 2.5, y = 10
Step-by-step explanation:
I'm going to assume that these photocopies are proportional in relations to each other.
If they're proportional, you can set up two proportions:
[tex]1) \frac{x}{5} =\frac{3}{6} \\\\2) \frac{5}{y} =\frac{3}{6}[/tex]
And cross-multiply:
[tex]1) 6x = 5*3 \\\\2) 3y = 5*6[/tex]
Then solved for x and y:
[tex]1) 6x = 15\\x=\frac{15}{6} =\frac{5}{2} =2.5 \\\\2) 3y = 30\\y=\frac{30}{3} =10[/tex]
Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.)
f(x) = 7/1+x a=2
If f(x) = 7/(1 + x), then
f (2) = 7/3
f '(x) = -7/(x + 1)² ==> f ' (2) = -7/9
f ''(x) = 14/(x + 1)³ ==> f '' (2) = 14/27
f '''(x) = -42/(x + 1)⁴ ==> f ''' (2) = -14/27
Then the Taylor series of f(x) about a = 2 is
7/3 + 1/1! (-7/9) (x - 2) + 1/2! (14/27) (x - 2)² + 1/3! (-14/27) (x - 2)³
= 7/3 - 7/9 (x - 2) + 7/27 (x - 2)² - 7/81 (x - 2)³
Which of the following scatterplots do not show a clear relationship and would not have a trend line?
Answer:
the second one
Step-by-step explanation:
it is not going in any general direction
Answer:
B
Step-by-step explanation:
The figures to the right are similar. Compare the first figure to the second. Give the ratio of the perimeters and the ratio of the areas
(integer or a simplified fraction)
Thank you!
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Answer:
perimeter: 3 : 4area: 9 : 16Step-by-step explanation:
The perimeter ratio smaller : larger is the same as the side length ratio.
18 : 24 = 3 : 4 . . . smaller : larger perimeter ratio
The area ratio is the square of this.
3^2 : 4^2 = 9 : 16 . . . smaller : larger area ratio
Your calculator is showing a result of 248.592.
What is this to the nearest whole number?
There is a close relationship between the air pressure inside a hurricane and its maximum sustained wind speed: y=−1.22x+1250 where x is the air pressure in millibars (kPa) and y is the wind speed in knots (nautical miles per hour).
What does the slope of the line represent?
A. the change in wind speed for every 1 kPa increase in air pressure
B. the wind speed of a hurricane with an air pressure of 1000 kPa
C. the wind speed of a hurricane with an air pressure of 0 kPa
D. the change in wind speed for every hour
Answer:
A. the change in wind speed for every 1 kPa increase in air pressure
Step-by-step explanation:
The equation of a straight line is given by:
y = mx + b;
where y, x are variables, m is the slope (rate of change) of the line and b is the y intercept (value of y when x = 0)
Given the line y=−1.22x+1250 where x is the air pressure in millibars (kPa) and y is the wind speed in knots.
The slope of the line is -1.22. The slope means that there is a decrease in wind speed by 1.22 miles per hour for every increase of 1 kPa in air pressure.
Find the length of BC
A. 6.81
B. 7.64
C. 13.37
D. 29.44
Answer:
13.37 = BC
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = opp / hyp
cos 27 = BC / 15
15 cos 27 = BC
13.36509 = BC
Rounding to the nearest hundredth
13.37 = BC
Simplify the trigonometric expression cos(2x)+1 using Double-Angle identities
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Answer:
C. 2cos²(x)
Step-by-step explanation:
The relevant identities are ...
cos(2x) = cos²(x) -sin²(x)
cos²(x) = 1 -sin²(x)
__
Then the expression can be simplified to ...
cos(2x) +1 = (cos²(x) -sin²(x)) +1 = cos²(x) +(1 -sin²(x)) = cos²(x) +cos²(x)
= 2cos²(x)
what is x divided by one
Answer:
[tex] x \div 1[/tex]
[tex] = x[/tex]
Answer:
[tex]x\div 1=x[/tex]
Step-by-step explanation:
When x is divided by one it is called reciprocal.
reciprocal is the inverse of a number or a value.
examples: The reciprocal of 3 is 1/3, and the reciprocal of 5 is 1/3.
OAmalOHopeO
if (a + b) = 73 and a b =65 find value of a²+ b²
Step-by-step explanation:
Here,
by formula a^2+b^2=(a+b)^2-2ab
so,
or,(a+b)^2-2ab
or,(73)^2-2×65
or,5329-126
=5203 is the answer
How many of 320 million Americans would you predict wear contact lens
Answer:
I think 40 - 60 Million Americans would wear contact lenses.
obtain the value of X for which (X+1),(X-5),(X-2) is a geometric progression.hence find the sum of the first 12 terms of the progression.
If x + 1, x - 5, and x - 2 are in a geometric progression, then there is some constant r for which
x - 5 = r (x + 1)
==> r = (x - 5) / (x + 1)
and
x - 2 = r (x - 5)
==> r = (x - 2) / (x - 5)
Then
(x - 5) / (x + 1) = (x - 2) / (x - 5)
Solve for x :
(x - 5)² = (x - 2) (x + 1)
x ² - 10x + 25 = x ² - x - 2
-9x = -27
x = 3
It follows that the ratio between terms is
r = (3 - 5) / (3 + 1) = -2/4 = -1/2
Now, assuming x + 1 = 4 is the first term of the G.P., the n-th term a(n) is given by
a(n) = 4 (-1/2)ⁿ⁻¹
The sum of the first 12 terms - denoted here by S - is then
S = 4 (-1/2)⁰ + 4 (-1/2)¹ + 4 (-1/2)² + … + 4 (-1/2)¹¹
Solve for S :
S = 4 [(-1/2)⁰ + (-1/2)¹ + (-1/2)² + … + (-1/2)¹¹]
(-1/2) S = 4 [(-1/2)¹ + (-1/2)² + (-1/2)³ + … + (-1/2)¹²]
==> S - (-1/2) S = 4 [(-1/2)⁰ - (-1/2)¹²]
==> 3/2 S = 4 (1 - 1/4096)
==> S = 8/3 (1 - 1/4096)
==> S = 1365/512
round 3/5 to 3 decimal points
Answer:
3/5=0.600
Step-by-step explanation:
I hope this answer helps
The answer is 0.6.
Upto 3 decimal places it is 0.600.
An item is regularly priced at$15.It is now priced at a discount of55%off the regular price
Answer:
$6.75
Step-by-step explanation:
The regular price is $15 dollars. The discount is 55% off the $15.
15 * 0.55 = 8.25
15 - 8.25 = 6.75
Hope this helps.
Answer:
discount =8.25
New price 6.75
Step-by-step explanation:
15 is the regular price
The discount is 55%
15*.55
8.25
The new price is the regular price minus the discount
15-8.25
6.75
Which inequality is shown in the graph?
I need help plz
Answer:
I am pretty sure it is B.
Step-by-step explanation:
This is a line with a positive slope, therefore we can discard c and d.
the sign < will mean that the shaded in area will be on your right side.
What is the slope of the line that contains these points? xxx 454545 494949 535353 575757 yyy 101010 555 000 -5−5minus, 5 slope:
Answer:
-5/4
Step-by-step explanation:
Given :
x : 45, 49, 53, 57
y : 10, 5, 0, - 5
The slope of the line :
Slope = Rise / Run
y2 = - 5, y1 = 10
x2 = 57, x1 = 45
Rise = y2 - y1 = - 5 - 10 = - 15
Run = x2 - x1 = 57 - 45 = 12
The slope = Rise / Run = - 15 / 12 = - 5/4
Answer:
-1
Step-by-step explanation:
i brought the answer correct
Rationalize the denominator and simplify
Answer:
x² - √3x / x² - 3
Step-by-step explanation:
To Do :-
To rationalize the denominator .Solution :-
We need to rationalize ,
x/ x + √3Multiply numerator and denominator by x-√3 :-
x( x - √3 ) / ( x +√3)( x -√3) x² - √3x / (x)² - (√3)² x² - √3x / x² - 3