Answer:
a) 0.0005 = 0.05% probability that an automotive light has two or more defective bulbs.
b) 4000 automotive lights.
Step-by-step explanation:
For each LED, there are only two possible outcomes. Either it is defective, or it is not. Defective bulbs occur independently, which means that we use the binomial probability distribution 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.
An array of 30 LED bulbs is used in an automotive light. The probability that a bulb is defective is 0.001.
This means that, respectively, [tex]n = 30, p = 0.001[/tex].
a. Probability that an automotive light has two or more defective bulbs.
This is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{30,0}.(0.001)^{0}.(0.999)^{30} = 0.9704[/tex]
[tex]P(X = 1) = C_{30,1}.(0.001)^{1}.(0.999)^{29} = 0.0291[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.9704 + 0.0291 = 0.9995[/tex]
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9995 = 0.0005[/tex]
0.0005 = 0.05% probability that an automotive light has two or more defective bulbs.
b. Expected number of automotive lights to check to obtain one with two or more defective bulbs.
0.0005 = 0.05% probability that an automotive light has two or more defective bulbs.
The number of expected trials to obtain n successes with p probability is given by:
[tex]E = \frac{n}{p}[/tex]
In this case, we have that [tex]n = 2, p = 0.0005[/tex]. So
[tex]E = \frac{n}{p} = \frac{2}{0.0005} = 4000[/tex]
4000 automotive lights.
What is the b term of the product of (x – 4) and (2x + 3) ?
Answer:
the "b" term is the term "-5 x" in the final quadratic expression
Step-by-step explanation:
Normally the "b" is the "linear term" in a quadratic equation.
So, perform the product of binomials and combine like terms to identify the final "b" term of the quadratic expression you get:
[tex](x-4)*(2x+3)=2x^2 +3x-8x-12=2x^2-5x-12[/tex]
Therefore the "b" term is the term "-5 x" in the final quadratic expression.
A movie theater charges $12.00 for adults and $4.50 for children under the age of ten. A group of adults and children went to the movies and spent $75.00 on 10 tickets. How many adults and how many children went to the move?
Answer:
4 Adults and 6 Children went to the movies.
Step-by-step explanation:
(Children) $4.50 x 6 = $27.00
(Adults) $12.00 x 4 = $48.00
$48.00 + $27.00 = $75.00
Classify each pair of numbered angles as corresponding, alternate interior, alternate exterior, or none of these.
Drag and drop the choices into the boxes to correctly complete the table.
Check the attachment below, it's self explanatory.
three positive numbers form an arithmetic progression with d=8 If 7 is subtracted from the first number, 3 is subtracted from the second number, and the third numbers is first decreased by 1 and then the result is multiplied by 3, the resulting numbers form a geometric progression find the original three numbers
Answer:
10, 18, 26
Step-by-step explanation:
Which product is less than 5/8
Answer:
7/10 * 5/8 is less than 5/8 because 7/10 * 5/8= 0.4375. And 5/8=0.625
Step-by-step explanation:
Answer:
4/8
I don't really have an explanation-
Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car results in 460 miles o. 20 gallons of gas. How far could you drive on 70 gallons of gas.
Answer:
1,610 miles
Step-by-step explanation:
If you do 460/20 you get the gas mileage. The gas mileage is 23. If you do 23*70 you get 1610 miles out of 70 gallons of gas. (Double-check to make sure I'm correct)
Will mark brainliest!
(please don't just copy your answer from another one. The other one available is wrong, so if you were to copy it, it would be a waste.)
How are rational exponents and radicals related? Summarize how to rewrite a rational power as a radical term using an example of your own.
Answer:
Hi
Step-by-step explanation:
Rational exponent are exponents written in the form of a fraction.
A rational power can be rewritten as a radical in the following way: the bottom of the rational exponent is the root, while the top of the rational exponent is the new exponent on the radical.
Example: X^(1/2)= √X
4.0681 to the nearest thousand
5) Graph the following inequality. (3 points) 6x-2y>8
Answer:
Step-by-step explanation:
Graph x < or = to -4.5 on the number line
HELP ME PLS ASAP PLS PLZ PLS HELP
Answer:
it would be a closed circle and to the right
Step-by-step explanation:
I have a little tip whenever the greater or less than sign is underlined it will always be closed, and when x is greater than -4.5 all the numbers that are greater than -4.5 will be on the right side so that will be your answer.
Please help anyone im begging
Answer:
A- Root 16
B- Root 27
C- Root 32
Step-by-step explanation:
So A is root 16 because root 16 is equal to 4.
B is root 27
And C is root 32
Factor each expression:
27+12
12+36
16+20
2x+8
30+12x
42x+49
an online photo service charges 20 to make a standard photo book with 16 pages. each extra page costs 1.75 write an exspression to determine the total cost of in dollars to make a standyard photo book with p extra pages
Answer:
$20 + (1.75 * p)
Step-by-step explanation:
This is just a guess hope this is correct.
Hope this helps! :)
16 .Write an equation that represents the statement
below.
"Twelve less than a number, x, is 18."
Answer:
x-12=18
Step-by-step explanation:
Answer: if X = 30, then the equation is 30 - 12 = 18
A taxi driver uses the formula 3.00 +1.5m to calculate the cost of a taxi
ride where m is the number of miles driven. What is the fair for a taxi
ride that is 12 miles long? Use the correct units.
Answer:
24$
Step-by-step explanation:
12m/1.5m=8 8*3=24
A company is expanding its building area from 13,500 square feet to 19,440 square feet. What is the percentage increase of the area of the building space?
A.
4.4%
B.
44%
C.
59.4%
D.
56%
It costs $14.50 to rent a canoe and $6 to use the canoe for an hour. You have $32.50. Write an equation that represents the number h of hours you can rent the canoe. An equation is BLANK =32.50.
Answer:
The answer would be, you have 3 hours to use the canoe
Find the missing sides of the triangle.. Please Help
Answer:
there is no possible triangle
Step-by-step explanation:
an obtuse side has to have the largest angle, therefore there is no solution
The University of South Texas is interested in determining if there is a difference in the average weight gain between male students (group 2) and female students (group 1) during their freshman year. They take a random sample of 10 male students and 10 female students. Find the confidence interval with 95% confidence. The 95% confidence interval is (2.4, 20.4). A. We are 95% confident that the population mean weight gain for male University of South Texas students is 2.4 more to 20,4 more than female University of South Texas students. B. We are 95% confident that the population mean weight gain for female University of South Texas students is 2.4 more to 20.4 more than male University of South Texas students. C. We are 95% confident that the sample mean weight gain for female University of South Texas students is 2.4 more to 20.4 more than male University of South Texas students. D. We are 95% confident that the sample mean weight gain for male University of South Texas students is 2.4 less to 20.4 more than female University of South Texas students.
Answer: A. We are 95% confident that the population mean weight gain for male University of South Texas students is 2.4 more to 20,4 more than female University of South Texas students.
Step-by-step explanation:
Given a 95% confidence interval of : (2.4, 20.4)
The lower boundary of the interval = 2.4
The upper boundary of the interval = 20.4
Male = group 2, Female = group 1
P2 - P1 is between lower boundary more and upper boundary more ;
Hence
Population mean weight for male is 2.4 more to 20.4 more than female
A body of mass 2 kg moves in a (counterclockwise) circular path of radius 3 meters, making one revolution every 5 seconds. You may assume the circle is in the xy-plane, and so you may ignore the third component.
A. Compute the centripetal force acting on the body.
B. Compute the magnitude of that force.
Answer:
a) [tex]\vec{F_{c}}=mR\omega^{2}[/tex]
[tex]\vec{F_{c}}=9.53 \: N \vec{r}[/tex]
b) [tex]|\vec{F_{c}}|=9.53 \: N [/tex]
Step-by-step explanation:
a) The centripetal force equation is:
[tex]\vec{F_{c}}=m\vec{a_{c}}[/tex]
[tex]\vec{F_{c}}=mR\omega^{2}[/tex]
Now, we know that the body makes one revolution every 5 seconds, so we can find the angular velocity:
[tex]\omega=\frac{1 rev}{5 s}=0.2\: \frac{rev}{s}=1.26\: \frac{rad}{s}[/tex]
[tex]\vec{F_{c}}=2*3*1.26^{2}=9.53 \: N \vec{r}[/tex]
The centripetal force is a vector in the radius direction.
b) The magnitude of that force will be:
[tex]|\vec{F_{c}}|=9.53 \: N [/tex]
How is your mental health?
Answer:
bad
Step-by-step explanation:
cause of school so yea my mental health
Answer:
It is bad at some points but on certain days it is okay.
Step-by-step explanation:
With school mainly, but I tend to manage. And I know that this isn't a school question but do you think you could give Brainliest.
7n - 5
The polynomial is__
Answer:
polynomial have 7 side...
Solve for v. 9 2 V-2 > 6
Answer:
V>[tex]\frac{2}{23}[/tex]Step-by-step explanation:
An equation of a line through (-1, 1) which is parallel to the line y = 5x + 1 has slope:
and y-intercept at:
Answer:
The slope is 5 and the y-intercept is at (0, 6)
Step-by-step explanation:
Parallel lines have the same slope, so the slope of the equation is 5. The equation is y = 5x + 6, so the y-intercept is 6.
Please help ! 1. Kenken puzzle 3x3
Answer:
Step-by-step explanation:
guys i need help on this problem I'm stuck
Answer:
y=mx+b is slope intercept form
Step-by-step explanation:
letter B :)
Which fraction has a terminating decimal?
- 11/19
- 4/7
- 1/3
- 3/150
==========================================================
Explanation:
With the use of a calculator, we see that,
11/19 = 0.57894736842106...., the decimals eventually repeat; but unfortunately my calculator ran out of room to show the repeating portion4/7 = 0.5714285714285714..., the block "571428" repeats forever1/3 = 0.333333.... the 3s go on forever3/150 = 0.02So 3/150 converts to the terminating decimal 0.02
The word "terminate" means "stop". In the other decimal values, the decimal digits go on forever repeating the patterns mentioned.
----------------------
A non-calculator approach will have us simplify 3/150 into 1/50 after dividing both parts by the GCF 3. Then notice how 50 has the prime factorization of 2*5*5. The fact that the denominator 50 can be factored in terms of only 2's and 5's is enough evidence to conclude that the fraction converts to a terminating decimal.
If the denominator factors into some other primes, other than 2s and 5s, then we don't have a terminating decimal. So that's why 11/19, 4/7 and 1/3 convert to non-terminating decimals.
If this figure is dilated by a scale factor of 3, what would the new coordinates be?
Answer:
J (-3,3), G (0,3), H (4,9), I (3,3)
Step-by-step explanation:
When your dilating a figuring it either gets larger or smaller. Since this is a positive number, and it is not a fraction then the figure is getting larger. Now you multiply each of the original coordinates by 3 to get the dilated coordinates.
(For learning purposes only)
Buffy ate 10 hot dogs every 35 minutes. At that rate, how long, in minutes will it take to eat 6 hot dogs
Answer:
21 minutes
Step-by-step explanation:
35 ÷ 10 = 3.5
3.5 × 4 = 14
35 - 14 = 21
=21
Need help asap! Solve question b.
Answer:
D.
Step-by-step explanation:
This is the only one that sounds correct
Answer:
i cant read it oh i zoomed in B
Step-by-step explanation: