Using the binomial distribution, it is found that there is a 0.38 = 38% theoretical probability that all 6 bulbs will last for 4 months.
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 have that:
There are 6 bulbs, hence n = 6.Each bulb has a 0.85 chance of lasting for at least 4 months, hence p = 0.85.The probability that all 6 bulbs will last for 4 months is P(X = 6), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{6,6}.(0.85)^{6}.(0.15)^{0} \approx 0.38[/tex]
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A group of 200 people who exercise regularly reported the following exercise habits :
5 people run
65 people swim or run
30 people swim and run
If a person from this group is selected at random , what is the probability that the person swims ?
Answer:
9/20
Step-by-step explanation:
65 people swim or run
BUT
5 people just run
so
60 people swim or run
+
30 people swim and run
90/200 =
9/20
Find the area of the triangle.
Answer:
20 m²
Step-by-step explanation:
Formula (Area of triangle):
[tex]\text{A (Triangle)} = \dfrac{1}{2} \times \text{Base} \times \text{Height}[/tex]
From the triangle, we can see that the base of the triangle is "7 + 3" m and the height of the triangle is "4" m.
[tex]\implies \text{A (Triangle)} = \dfrac{1}{2} \times (7 + 3) \times (4)[/tex]
Simplify the right-hand-side as needed to evaluate the area.
[tex]\implies \text{A (Triangle)} = \dfrac{1}{2} \times (10) \times (4)[/tex]
[tex]\implies \text{A (Triangle)} = \dfrac{40}{2} = 20 \ \text{m}^{2}[/tex]
Therefore, the area of the provided triangle is 20 m².
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I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
4
Step-by-step explanation:
You have to use Pythagorean Theory which states that a^2+b^2=c^2
It means that:
3^2+b^2=5^2
b^2=25-9
b = root of 16 (25-9=16)
b = 4
I hope that I helped :)
What is the kinetic energy of a 50-kg child running to catch the school bus at 2 m/s
Answer:
100 J
Step-by-step explanation:
The formula for kinetic energy is as follows:
[tex]\boxed{KE= \frac{1}{2} mv²}[/tex]
where
KE= kinetic energy (J)
m= mass (kg)
v= velocity (m/s)
Given: m= 50 kg, v= 2 m/s
Substituting the given information into the formula:
KE
= ½(50)(2²)
= ½(50)(4)
= 100 J
8x+21+16x=25x+19 solve
Answer:
[tex]\Large\boxed{\sf{x=2}}[/tex]Step-by-step explanation:
GIVEN:
In order to solve this, you need to isolate the term x on one side of the equation.
8x+21+16x=25x+19First, combine like terms.
[tex]\Longrightarrow: \sf{8x+16x+21=25x+19}[/tex]
Solve.
8x+16x=24x
[tex]\Longrightarrow: \sf{24x+21=25x+19}[/tex]
You have to subtract by 21 from both sides.
[tex]\Longrightarrow: \sf{24x+21-21=25x+19-21}[/tex]
Solve.
[tex]\Longrightarrow: \sf{24x=25x-2}[/tex]
Subtract by 25x from both sides.
[tex]\Longrightarrow: \sf{24x-25x=25x-2-25x}[/tex]
Solve.
-x=-2
Then, you divide by -1 from both sides.
[tex]\Longrightarrow: \sf{\dfrac{-x}{-1}=\dfrac{-2}{-1}}[/tex]
Solve.
Divide the numbers from left to right.
[tex]\sf{\dfrac{-2}{-1}=2 }[/tex]
SOLUTIONS:
[tex]\Longrightarrow: \boxed{\sf{x=2}}[/tex]
Therefore, the correct answer is x=2.I hope this helps. Let me know if you have any questions.
Answer:
[tex]x = 2[/tex]
Step-by-step explanation:Given equation:
[tex]8x + 21 + 16x = 25x + 19[/tex]Combine like terms on the L.H.S and simplify the expression as needed.
⇒ [tex]8x + 21 + 16x = 25x + 19[/tex]⇒ [tex]x(8 + 16) + 21 = 25x + 19[/tex]⇒ [tex]x(24) + 21 = 25x + 19[/tex]⇒ [tex]24x + 21 = 25x + 19[/tex]Now, rewrite 25x in such a way such that 24x can be repeated on both sides. Clearly, we can rewrite 25x as 24x + x. Then,
⇒ [tex]24x + 21 = \underline{25x} + 19[/tex]⇒ [tex]24x + 21 = \underline{24x + x} + 19[/tex]Since 24x is being repeated on both sides, we can cancel it.
⇒ [tex]\bold{24x} + 21 = \bold{24x} + x + 19[/tex]⇒ [tex]21 = x + 19[/tex]Finally, subtract 19 on both sides to isolate x.
⇒ [tex]21 - 19 = x + 19 - 19[/tex]⇒ [tex]\boxed{2 = x}[/tex]Therefore, the value of x is 2.
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Allen finds the area of the woods to be approximately 9,680
square feet. Why is Allen incorrect?
A
Allen is incorrect because he applied the scale to the
sides and then found the total area of the woods.
B
Allen is incorrect because he found the total area of the
woods and then applied the scale.
Allen is incorrect because he did not apply the scale.
D
Allen is incorrect because he used the formula to find hm
perimeter instead of area.
is it c
(what is the scale)
2) What is the area of the parallelogram?
A. 16 square centimeters
B. 30 square centimeters
C. 60 square centimeters
D. 120 square centimeters
(20 points)
height= 6 cm
base= 10 cm
to find:the area of the parallelogram.
solution:[tex]formula = bh[/tex]
[tex]a = 6 \times 10[/tex]
[tex]a = 60 {cm}^{2} [/tex]
therefore, the area of the parallelogram is 60 square centimeters.
answer= option c.
station at any time?
OA. 100
OB. 80
OC. 40
OD. 20
Step-by-step explanation:
Station at any time A 100
Order the numbers from least to greatest -1 -1/4 -1 1/2 3/4 and 1/8
Answer:
-11/2
-1
-1/4
1/8
3/4
Step-by-step explanation:
-11/2 = -5 1/2
-1 = -1
-1/4 = -1/4
1/8 = 1/8
3/4 = 6/8
Find the circumference of the given circle with a diameter of 40 cm. Use 3.14 as an approximation of pi.
125.66
You can turn the diameter into radius by dividing it by 2, then multiply that by 3.14 and 2!
Hope I could help.
C=2pie(r)
How many lines of symmetry does the picture have?
A. 3
B. 2
C. 1
D. 0
the answers is D cuz there is no line in the picture
Every twentieth customer at a coffee shop gets a $5 gift card. Design a simulation for estimating the probability that a customer would need to visit the coffee shop at least 5 times to win a gift card.
The simulation of the customer visit is an illustration of probability
The probability that a customer would visit the coffee shop at least 5 times to win a gift card is [tex](\frac {11}{12})^{n} - (\frac n{12}) * (\frac {11}{12})^{n - 1} - .......... - ^nC_4 * (\frac 1{12})^4 * (\frac {11}{12})^{n - 4}[/tex]
How to design the simulation?From the question, we understand that every 12th customer gets a $5 gift card.
This means that the probability that a customer gets a gift card is:
p = 1/12
The probability that a customer would visit the coffee shop at least 5 times to win a gift card is calculated using the following complement rule:
P(x ≥ 5) = 1 - P(x <5)
The equation becomes
P(x ≥ 5) = 1 - P(0) - P(1) - P(2) - P(3) - P(4)
Using the binomial formula
[tex]P(x) = ^nC_x * p^x * (1 - p)^{n - x}[/tex]
The equation becomes
[tex]P(x \ge 5) = ^nC_0 * (\frac 1{12})^0 * (1 - \frac 1{12})^{n - 0} - ^nC_1 * (\frac 1{12})^1 * (1 - \frac 1{12})^{n - 1} - .......... - ^nC_4 * (\frac 1{12})^4 * (1 - \frac 1{12})^{n - 4}[/tex]
Simplify
[tex]P(x \ge 5) = (\frac {11}{12})^{n} - (\frac n{12}) * (\frac {11}{12})^{n - 1} - .......... - ^nC_4 * (\frac 1{12})^4 * (\frac {11}{12})^{n - 4}[/tex]
Hence, the estimate that a customer would visit at least 5 times is [tex]P(x \ge 5) = (\frac {11}{12})^{n} - (\frac n{12}) * (\frac {11}{12})^{n - 1} - .......... - ^nC_4 * (\frac 1{12})^4 * (\frac {11}{12})^{n - 4}[/tex]
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Takeru has 4 bird feeders. It takes 4/3 bags of bird seeds to fill each feeder. what is the minimum number of bags Takeru needs to fill all the feeders?
Answer: 6
Step-by-step explanation: You would divide 4 by 3 and divide your answer by 2.
Wilbur has homework assignments in seven subjects. He only has time to do five of them. How many ways are there for him to do five homework assignments?
Answer:
7
Use tables to confirm you answer'
The figure below illustrates the market for steel. If the steel market is competitive, firms can produce steel at a constant marginal cost of $100 per ton. Therefore, the price of steel is $100 per ton, and 100 tons are produced. Assume that if all the steel companies consolidate into a monopoly, the monopoly’s marginal cost will fall to $70 per ton. Use the straight line tool to draw the monopoly’s marginal revenue and marginal cost lines (extend the marginal cost line to 300 tons). Then use the plot point tool to plot the monopoly’s profit-maximizing price and output on the demand curve.
If the market is controlled by a monopoly, total surplus is $____
The monopoly price will be given as 110 dollars per unit. Then the total surplus will be 4800 dollars.
How do determine the monopoly price and the total surplus?The figure below illustrates the market for steel.
If the steel market is competitive, firms can produce steel at a constant marginal cost of $100 per ton.
Therefore, the price of steel is $100 per ton, and 100 tons are produced.
Assume that if all the steel companies consolidate into a monopoly, the monopoly’s marginal cost will fall to $70 per ton.
If the market is controlled by a monopoly, the total surplus will be
The demand curve has to be defined the demand curve will be
P = 150 - 0.5Q
Total revenue, TR = 150Q - 0.5Q^2
MR = 150 - Q
MC = $ 70
The monopolist will maximize profit at MR = MC
150 - Q = 70
=> Q = 80 units
Monopoly price, P = 150 - 0.5 × 80 = $ 110 / unit
Total surplus = (1/2)×(150-110)×80+(110-70)×80
= 1,600 + 3,200
= $ 4,800
The graph is given below.
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How many four- digit numbers can be formed from the digit 1,3,4,5,6&7 where the digit is used at most once?( repetition are not allowed)
a)if the number must be odd
b)if the number must be even
Answer:
A. 24
B. I don't think you can make any since you can't repeat numbers and there is only two even numbers
Also, if you use all six numbers, it's 120 combos
The right triangle has legs a and b and hypotenuse c. If b=12 and c=13, then what does a equal?
Answer:
a = 5
Step-by-step explanation:
a^2 + b^2 = c^2
Substitute
b = 12
c = 13
a^2 + 12^2 = 13^2
a^2 + 144 = 169
a^2 = 25
a = [tex]\sqrt{25} \\[/tex]
a = 5
Mark brainliest please!
Answer:
use Pythagoras theorem
Step-by-step explanation:
[tex]a^{2} + b ^{2} = c ^{2} \\ a ^{2} + 12 ^{2} = 13 ^{2} \\ a = 5[/tex]
kristin exercises 5 hours each week. Make a dot plot of her hours of exercise
and include the hours her friends exercise. Kristin and her friends' total hours
of exercise are shown in the table. How does Kristin's exercise time compare
with her friends
The dot plot is made by representing the frequency of the time spent exercising using dots
Kristin spends more time exercising than her friends
How to make the dot plot?The dataset is given as:
0 6 5 9 5 4 3 5 4 6 4 5 5 4 6
From the dataset, we have the following frequency table:
Time Frequency
0 1
3 1
4 4
5 5
6 3
9 1
See attachment for the dot plot made from the above frequency table
Interpreting the dot plotFrom the dot plot, we can see that Kristin's time of exercise is greater than all of her friend's time of exercise.
Hence, Kristin spends more time exercising than her friends
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cosec2a+cosec4a=cota-cot4a
Answer: Cosec 2 A + Cot 4 A = Cosec 4 A - Cot 2 A
Step-by-step explanation:
Taking LHS :
⇒Cosec 2 A + Cot 4 A
⇒Cosec 2 A + ( Cot 2 A )2
⇒Cosec 2 A + ( Cosec 2 A - 1 )2 ( we know : 1 + Cot 2 θ = Cosec 2 θ )
⇒Cosec 2 A + Cosec 4 A + 1 - 2 Cosec 2 A
⇒ Cosec 4 A + 1 - Cosec 2 A
⇒ Cosec 4 A + 1 - ( 1 + Cot 2 A)
⇒ Cosec 4 A + 1 - 1 - Cot 2 A
⇒ Cosec 4 A - Cot 2 A
or cosec2A+cosec4A=cotA-cot4A
If the vertex angle of an isosceles triangle is 39°, what is the measure of each base angles?
A. 71°
B. 70.5°
C. 81°
D. 80.5°
Other:----------------------------------
Step-by-step explanation:
Total =180°
Top vertex=39°
2base angles=180-39
2base angles=141
base anglez=141/2
base angle=70.5°MARK ME AS BRAINLISTThe product of a number and 7 less than the number is 30. Find the number.
Answer:
-3 or 10
Step-by-step explanation:
[tex]x(x - 7) = 30[/tex]
[tex] {x}^{2} - 7x = 30[/tex]
[tex] {x}^{2} - 7x - 30 = 0[/tex]
[tex](x - 10)(x + 3) = 0[/tex]
x = -3 or 10
Need answer ASAP! Please see screen shot.
Answer:
0.4 or [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
James spun the arrow 30 times which means 30 is the total. In other words, it's your denominator ([tex]\frac{x}{30}[/tex]). It landed on the blue section 12 times which means 12 is the part of the whole. In other words, it's your numerator ([tex]\frac{12}{y}[/tex]). Plug in the entire fraction and you get [tex]\frac{12}{30}[/tex]. Divide 12 by 30 and you get 0.4 or if you divide both the numerator & denominator by 6, you get [tex]\frac{2}{5}[/tex]. Either one works, depending on what your question asks for.
Manufacturers of tires report that tires should be able to last an average of 50,000 miles. A new tire company produces a different type of tread and tests 100 randomly selected tires. This sample of 100 tires lasted an average of 52,000 miles. Assuming the new type of tread does not improve the mileage of the tire, 200 sample means were simulated and displayed on the dotplot.
Using the dotplot and the sample mean mileage, is there convincing evidence that the new type of tread improves the mileage?
Yes, because a mean mileage of 52,000 or more occurred only 7 out of 200 times, the mean mileage is statistically significant. There is convincing evidence the new type of tire tread improves mileage of the tire.
Yes, because a mean mileage of 52,000 or less occurred 193 out of 200 times, the mean mileage is statistically significant. There is convincing evidence the new type of tire tread improves mileage of the tire.
No, because a mean mileage of 52,000 or less occurred 193 out of 200 times, the mean mileage is not statistically significant. There is not convincing evidence the new type of tire tread improves mileage of the tire.
No, because a mean mileage of 52,000 or more occurred 7 out of 200 times, the mean mileage is not statistically significant. There is not convincing evidence the new type of tire tread improves mileage of the tire.
The convincing evidence is Yes, because a mean mileage of 52,000 or more occurred only 7 out of 200 times, the mean mileage is statistically significant.
What is a dot plot?A dot plot is known to have the same characteristics as a bar graph as both are made up of different height of “bar” that consist of dots which is said to be equal to the number of items in any of the stages or categories.
Conclusively, when a person uses a dot plot and the sample mean mileage, one will be able to find a convincing evidence that the new type of tread improves the mileage because out of mean mileage of 52,000 or more, only 7 out of 200 times, took place and this shows that the mean mileage is statistically significant and that the new type of tire tread boast the mileage of the tire.
Therefore, option A is correct.
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Answer:
Theres another question that looks like this one, the awnser to that is
^ ^ ^ ^ ^
No, because a mean mileage of 51,500 or more occurred 14 out of 200 times, the mean mileage is not statistically significant. There is not convincing evidence the new type of tire tread improves mileage of the tire.
Step-by-step explanation:
but the guy above me is correct
Find the greatest common factor of 32 and 36
Marian is 29 and her base premium for auto insurance is $1239.
What does she pay in total premiums?
O$1239.00
O$1379.80
O $1551.60
O $1610.70
Answer: $1239.00
Step-by-step explanation:
I had to recheck on this.
For females that are ages 25-29, they have base auto insurance rate, meaning that the rate is set at 1. So multiply the base premium and base rate, 1239x1, and obviously it's the same 1239.
Hope this helped.
9-12 Use the properties of logarithms to expand the quantity.
11. [tex]\ln \frac{x^{2}}{y^{3} z^{4}}[/tex]
Step-by-step explanation:
lnx² - lny³ - lnz⁴
2lnx - 3lny -4lnz
Tyrone biked 45 miles at an average speed of 18 miles per hour, without stopping. About how long did the ride take him? Use the formula T=d_r division on the d and r
O 2.25 hours
O 3 hours
2.5 hours
O 2.75 hours
Answer:
2.25 long of riding a bicycle
Answer:
2.25
Step-by-step explanation:
3< 2x + 1 < 5 find x as an interval
Answer:
1<x<2
Step-by-step explanation:
1. Subtract 1 from everywhere ⇒ 2<2x<4
2. Divide by 2 everywhere ⇒ 1<x<2
Consider the following graph, which details one bookstore’s sales over the course of one day, divided by genre.
A graph titled Book Sales by Genre has genre on the x-axis and Number sold on the y-axis. Romance, 52; horror, 55; Fantasy, 60; Biograph, 57; Humor, 58; Cookbook, 54.
By percent, how much greater do sales of horror books appear to be than sales of cookbooks? How much greater are they in reality?
The percent by which the sales of horror books is greater than sales of cookbook is 1.85% approx.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Given that:
Genre number sold
Romance 52Horror 55Fantasy 60Biography 57Humor 58Cookbook 54Let we have:
Number of horror books sold = P% greater than number of cookbooks sold
55 = P% greater than 54
55 = 54 + P% of 54
1 = P% of 54
[tex]1 = \dfrac{P}{100} \times 54\\\\P = \dfrac{100}{54} \approx 1.85[/tex]
Thus, the percent by which the sales of horror books is greater than sales of cookbook is 1.85% approx.
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Answer:
Say that you put the set of tiles shown below into a bag and conduct a series of trials in which you draw one tile randomly from the bag, record the color, and replace it. The table below shows the number of times in each set of trials that you drew a blue tile.
Round tiles: 5 purple, 6 orange, 2 yellow, 4 red, 1 white, 10 blue, 5 black, 3 green.
Trial
1
2
3
4
5
# of Draws
54
36
80
22
75
# of Blues
18
11
20
4
32
Between the theoretical probability that you will draw a blue tile and the experimental probability that you will draw a blue tile, which is greater, and how much greater is it? Express all probabilities as percentages to two decimal places, and express differences by number of percentage points (for example, 12% is 2 percentage points greater than 10%).
a.
The theoretical probability is 2.78 percentage points greater than the experimental probability.
b.
The theoretical probability is 1.49 percentage points greater than the experimental probability.
c.
The experimental probability is 4.06 percentage points greater than the theoretical probability.
d.The experimental probability is 2.17 percentage points greater than the theoretical probability. <<<CORRECTStep-by-step explanation:
Edge 2022
What are the coordinates of point J’ after the rotation?
Step-by-step explanation:
(5,4) is the coordinate of the point j after rotation