The interval of hours represents the lifespan of the middle 68% of light bulbs, using the empirical rule is, 1210 hours to 1390 hours.
What is empirical rule?According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.
[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%[/tex]
Here, we had where mean of distribution of X is \mu and standard deviation from mean of distribution of X is \sigma
The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1400 hours and a standard deviation of 50 hours. Thus,
[tex]\mu=1300\\\sigma=90[/tex]
Using the empirical rule, the interval of hours represents the lifespan of the middle 68% of light bulbs is,
[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(1300- 90 < X < 1300+ 90) = 68\%\\P(1210 < X < 1390) = 68\%[/tex]
Thus, the interval of hours represents the lifespan of the middle 68% of light bulbs, using the empirical rule is, 1210 hours to 1390 hours.
Learn more about empirical rule here:
https://brainly.com/question/13676793
#SPJ1
How many kilograms in 1 1/2 pounds?
Answer:
67.5 kgs.
Step-by-step explanation:
1 pound = 0.45 kg
1 1/2 pounds = 0.45 + 1/2 * 45
= 67.5 kgs.
Which fraction make comparison 3/4
Answer:
6/8, 12/16, and so on. I wasn't sure how you wanted this question to be answered, but 3/4 is also 0.75
Step-by-step explanation:
Function or not a function pls help giving brainlest
Answer:
function
Step-by-step explanation:
For every value of 'x' ....there is only ONE value of 'y'
so it IS a function
6) Find the approximate perimeter of the following shape. Use 3.14 for pi
Answer:
where is the shape ???????
Use formula A=LW to find the length of a rectangle when the width is 35 ft and the area is 1,750 sq ft
Answer:
the length of the rectangle is 50 ft
Step-by-step explanation:
A-LW
1,750=L(35)
divide both sides by 35
L= 50
OLZ HELP ILL MARK AS BRAINLEST
find the slope
Answer:
-1
Step-by-step explanation:
Here are the chorus datz: {0, 10, 10, 20, 20, 20, 20,30, 30, 40) What is the mean?
Answer:
7 is 20
8 is 40
Step-by-step explanation:
Mean is the total of all the numbers divided by the amount of numbers
7. 20
8. 40
Add them all up divide by the total amount of them
Pls help with this ;w;
Answer:
79-83= 2
84-88 =4
89-93= 5
94-98=2
Step-by-step explanation:
put in order then you can just count them
Elise, Jake, Malik, and Xiao each solved the same inequality.
Random Reply:
Indeed, so they have.
Please help!! What do I do
Answer:
a(5) = 1.080
a(10) = 0.393
a(20) = 0.122
Step-by-step explanation:
Take the derivative of velocity v(t) -> acceleration a(t)
v(t) -> a(t)
Quotient Rule: [tex]\frac{u*dv-du*v}{u^2}[/tex]
[tex]120*\frac{x}{5x+13}[/tex]
Make u= 5x+13 and v=x
[tex]120*\frac{x'*(5x+13)-x*(5x+13)'}{(5x+13)^2}\\\\120*\frac{1*(5x+13)-x*(5)}{(5x+13)^2}\\\\120*\frac{(5x+13)-5x}{(5x+13)^2}\\120*\frac{13}{(5x+13)^2} \\\\a(t)=\frac{1560}{(5x+13)^2}[/tex]
Now Subsitute your a(5) , a(10) , a(20). Also, round to 3 decimal place.
a(5) = 1.08033241 = 1.080
a(10) = 0.3930461073 = 0.393
a(20) = 0.122170826 = 0.122
Answer:
(a) 1.080 ft/s²
(b) 0.393 ft/s²
(c) 0.122 ft/s²
Step-by-step explanation:
Acceleration is the derivative of velocity. You are being asked to differentiate the given function and evalutate the derivative at three different times. The function is a rational function, so the formula for the derivative of a ratio is applicable.
(u/v)' = (vu' -uv')/v²
__
For the given velocity function, the accleration is ...
v(t) = (120t)/(5t +13)
a(t) = v'(t) = ((5t +13)(120) -(120t)(5))/(5t +13)² = 1560/(5t +13)²
(a)At t=5, the acceleration is ...
a(5) = 1560/(5·5 +13)² = 1560/1444 ≈ 1.080 . . . ft/s²
(b)At t=10, the acceleration is ...
a(10) = 1560/(5·10 +13)² = 1560/3969 ≈ 0.393 . . . ft/s²
(c)At t=20, the acceleration is ...
a(20) = 1560/(5·20 +13)² = 1560/12729 ≈ 0.122 . . . ft/s²
_____
Additional comment
Many graphing calculators are capable of finding the numerical value of the derivative of a function.
Help me pls lol
I don’t understand
[tex]J'= (-5,-6)[/tex]
[tex]K'=(-5,-1)[/tex]
[tex]L'=(-10,-2)[/tex]
See graph below.
[tex]Hope[/tex] [tex]this[/tex] [tex]helps![/tex] [tex]Have[/tex] [tex]a[/tex] [tex]good[/tex] [tex]day![/tex] [tex]:)[/tex]
Find the area of the shape based on the provided measurements
Answer:
375 units²
Step-by-step explanation:
A = bh/2
A = (75)(10)/2
A = 750/2
A = 375
please help!
elect the correct answer.
Which statement is true?
A.
The function is an odd function because its graph is symmetric about the y-axis.
B.
The function is an even function because .
C.
The function is an odd function because .
D.
The function is an even function because its graph is symmetric about the origin.
The true statement is The function f(x)= tan(x) is an odd function because f(-x) = -f(x).
What is odd function?When x is substituted with -x, the odd functions are those that return their negative inverse. When f(-x) = -f(x), it follows that f(x) is an odd function (x). The trigonometric sine function, tangent function, cosecant function, etc. are a few examples of odd functions.
If f(x) = f(x), then the function is odd for all x. An odd function's graph will be symmetrical in all directions around the origin. Consider how unusual f(x) = x³ is. In other words, the function on one side of the x-axis is graphically symmetric about the origin or sign inverted with respect to the other side.
As, we know for the
even function: f(-x) = f(x)
odd function: f(-x)= -f(x)
and, using Trigonometry
tan x = sin x / cos x
Then,
f(-x) = sin (-x) / cos (-x)
= -sin (x) / cos (x)
= -tan (x)
= -f(x)
Thus, tan (x) is an odd function.
Hence, the function f(x)= tan(x) is an odd function because f(-x) = -f(x).
Learn more about odd function here:
https://brainly.com/question/20049729
#SPJ1
A radio station has a broadcast area in the shape of a circle with equation x2+ y2=5,625, where the constant represents square miles.
A.
B.
C.
Highlight answers + work shown pls
I'll give brainliest
find x.
please help whoever egts right gets brainliest
Answer:24
Step-by-step explanation:
a^2+b^2=c^2
c^2 has to be 26 because it is the hypotinuce. 10 could take the place of a^2 or b^2, it dose not matter.
a^2+10^2=26^2
a^2+100=676
subtract 100 from both sides
a^2=576
sqrt576
a=24
x=a
x=24
which angle is conterminal with a 645 degree angle
a. an angle measuring 75 degrees
b. an angle measuring 265 degrees
c. an angle measuring 345 degrees
d. an angle measuring 285 degrees
Answer:
D. An angle measuring 285 degrees
Step-by-step explanation:
An angle that is coterminal is congruent to the other angle whether negative or positive or more than 360.
An angle that is 645 degrees can be broken down into 360 + 285.
Since 360 is one revolution the angle would finish with 285 degrees.
Therefore the coterminal angle to 645 is 285.
please help! a point is chosen at random in the square, what percent of the time will the point be in the circle,round to the nearest tenth of a percent?
Answer:
78.5%
Step-by-step explanation:
You take the area of the circle which is pie*r^2
and divide it by the area of the square
Leo drew a line that is perpendicular to the line shown on the grid and passes through point (F, G). Which of the following is the equation of Leo's line?
A) y - F = -2(x - G)y
B) y + F = 2(x + G)
C) y - G = -1/2(x - F)
D) y - G = -1/2(x + F)
The equation of the perpendicular line drawn by Leo is [tex]y-G=\dfrac{-1}{2}(x-F)[/tex]. Option C is the correct answer.
The equation of the line is [tex]y-y_1=m(x-x_1)[/tex] where, [tex]m[/tex] is the slope of the line and [tex](x_1,y_1)[/tex] is the point through which it is passing.
How to determine the equation of a line?
A line is drawn perpendicular to the line shown in the image. The perpendicular line passes through the coordinate point [tex](F,G)[/tex].
The slope of the line from the graph is-
[tex]m=\dfrac{y-intercept}{x-intercept}\\=2[/tex]
Therefore, the slope of the perpendicular line is [tex]\dfrac{-1}{2}[/tex].
Also, it is being given that Leo's line is passing through the coordinate point [tex](F,G)[/tex].
So, the equation of the Leo's line is-
[tex]y-G=\dfrac{-1}{2}(x-F)[/tex]
Thus, the equation of the perpendicular line drawn by Leo is [tex]y-G=\dfrac{-1}{2}(x-F)[/tex].
Learn more about the equation of line here- https://brainly.com/question/20632687
#SPJ2
helpp pppppppppp ppp
Step-by-step explanation:
use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
and therefore also
sin(A)/a = sin(B)/b = sin(C)/c
where the lines and corresponding angles are always opposite of each other.
and remember, the sum of all angles in a triangle is always 180°.
and sin(x) = sin(180-x).
so, we have
sin(32)/43 = sin(B)/53
sin(B) = 53×sin(32)/43 = 0.653156302...
B = 40.77999844...° ≈ 41°
C = 180 - 32 - 40.77999844... = 107.2200016...° ≈ 107°
43/sin(32) = c/sin(107.2200016...)
c = 43×sin(107.2200016...)/sin(32) = 77.507143... ft
≈ 78 ft
B' = 180 - B = 139.2200016...° ≈ 139°
C' = 180 - 32 - 139.2200016... = 8.779998438...° ≈ 9°
43/sin(32) = c'/sin(8.779998438...)
c' = 43×sin(8.779998438...)/sin(32) = 12.38595519... ft
≈ 12 ft
The maximum grain yield for corn is achieved by planting at a density of 37,000 plants per
acre. A farmer wants to maximize the yield for the field represented on the coordinate grid.
Each unit on the coordinate grid represents one foot. How many corn plants, to the nearest
thousand, does the farmer need? (Hint: 1 acre = 43,560 ft?)
у
5001
E
F
F
х
lo
-500
500
G
-500
H
The farmer needs approximately
corn plants.
Since there are 37000 plants per hectare, the total corn plan required is 475,665.75 corn plants
How to determine the area of a trapezium?The trapezium is a 2 -dimensional shape consisting of a triangle and a square.
The formula for calculating the area of a trapezoid is expressed as:
Area = 0.5(a + b)h
Area = 0.5(500 + 900) * 800
Area = 700 * 800
Area = 560000 square feet
Since 1 acre is equivalent to 43560 square feet, hence the total acre required is expressed as:
Required acre = 560000/43560
Required acre = 12.856 acres
Also since there are 37000 plants per hectare, the total corn plan required is 475,665.75 corn plants
Learn more on area of trapezoid here: https://brainly.com/question/1463152
If the following line segment is reflected across the y-axis, what are the coordinates of the new endpoints?
A. (1, 6) and (3, 2)
B. (-1, -6) and (-3, -2)
C. (6, -1) and (2, -3)
D. (-6, 1) and (-2, 3)
Answer:A
Step-by-step explanation: im right im a god at answering these kind of equations.
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
Step-by-step explanation:
Mike paid $492.60 for 4 new tires for his truck. If each tire cost the same, What was the cost for 1 tire?
Can someone help me with it, plase? :(
Answer:
123.15
Step-by-step explanation:
one ounce of gold can be purchased for $1,195.80.one ounce of silver can be purshased for $16.08.what is the difference between the cost of 5 ounces of gold and 5 ounces of silver?
Answer:
Step-by-step explanation:
Remark
This is a proportion question a proportion is 2 equal ratios equated to each othe. If three parts are known the 4 can be found.
Givens
1 oz silver costs 16.08
1 oz Gold costs 1195.80
Silver
16.08/1 = x / 5 Multiply both sides by 5
5*16.08 = 1*x
80.4 =x
Gold
1195.80/1 = x/5
5 * 1195 = 1 * x
5979 = x
Answer
Difference = Cost of Gold - Cost of Silver
Difference = 5979 - 80.4
Answer Difference = 5898.60Ashley makes 9 dollars for each hour of work. Write an equation to represent her total pay p after working h hours
Answer:
twin what does H mean?
Step-by-step explanation: if you mean 8 the answer is 72.
Write in index form 12 × 12 × 12 × 12 × 12 × 12 × 12 × 12
Answer:
[tex]\sf{12^{8} }[/tex]
Step-by-step explanation:
12 × 12 × 12 × 12 × 12 × 12 × 12 × 12 = [tex]\sf{12^{8} }[/tex]
[tex]\sf{12^{8} }[/tex] = 429,981,696
An easy way to think of this is that there are 12 is being multiplied by itselg 8 times (there are 8 12s). Similar to how squared numbers work...
Hope this helps! If you need further explanation, let me know!
- profparis
Answer:
12⁸
Step-by-step explanation:
Index forms are used to show how many times a number or variable has been multiplied by itself.
Here, 12 is being multiplied by itself eight (8) times.
The index form would be:
12⁸
Hope this helps!
Which of the following describes the polynomial function?
8
==
4
-2
2
09
00
8
X
1
-5
do
9
The function has a negative leading coefficient.
O The function has an even degree.
O The function has zero turning points.
The function has one x-intercept.
Answer:
the function has one x intercept is the correct answer of given statement
Which linear inequality represents the solution set graphed?
Answer:
Your Answer is D.
Step-by-step explanation:
There isn't much to explain but look at the graph.
The slope of m = rise/run.
m = 1/2
b = -3/2
y = mx + b
A rental car company charges $72.37 per day to rent a car and $0.06 for every mile
driven. Colton wants to rent a car, knowing that:
• He plans to drive 275 miles.
• He has at most $450 to spend.
Answer:
5.99 days.
Step-by-step explanation:
If you are asking how many days he can rent the car then this is the correct answer.
So first multiply 275 x .06 to get how much money he will spent on the mileage. Which is $16.50. Then subtract that from $450 which is $433.50 and divided by $72.37.
A box contains 3 orange pencils, 9 yellow pencils, and 5 green pencils.
Two pencils are selected, one at a time, with replacement.
Find the probability that the first pencil is green and the second pencil is yellow.
Express your answer as a decimal, rounded to the nearest hundredth.
The probability that the first pencil is green and the second pencil is yellow is 0.16.
What is the probability?Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the first pencil is green and the second pencil is yellow = (number of green pencils / total number of pencils) x (number of yellow pencils / total number of pencils)
5/17 x 9/17 = 0.16
To learn more about probability, please check: https://brainly.com/question/13234031
#SPJ1