The electric bills of household in a state are normal distribution the average of $85 with a standard deviation of $8. A sample of 25 households are selected random. Find the probability that the mean bill is less than $83.
Answer:
0.106
Step-by-step explanation:
We can plug this into normalcdf using the following values:
Lower bound = -1000
Upper bound = 83
Mean = 85
Standard deviation = pop. standard deviation / √(sample size) = 8/5 = 1.6
The total length of 3 pipes is 24 inches. The middle-sized pipe is 6 inches longer than the smallest. The largest is twice as long as the smallest. How long is the middle-sized pipe?
Answer:
18
Step-by-step explanation:
let the be x
if the middle sized pipe is 6 inches longer than the smallest.
so 24 subtract from 6=18
find the divergence and curl of the vector
F=(3x²y² +2z)i + (3x² + y +yz )j - (3x²z² +2yx + xyz)k
Divergence:
div(F) = ∂(3x²y² + 2z)/∂x + ∂(3x² + y + yz)/∂y - ∂(3x²z² + 2yx + xyz)/∂z
div(F) = 6xy² + 1 + z - 6x²z - xy
Curl:
curl(F) = [∂(3x² + y + yz)/∂z + ∂(3x²z² + 2yx + xyz)/∂y] i
… … … … … - [∂(3x²y² + 2z)/∂z + ∂(3x²z² + 2yx + xyz)/∂x] j
… … … … … + [∂(3x²y² + 2z)/∂y - ∂(3x² + y + yz)/∂x] k
curl(F) = (-xz - 2x - y) i + (6xz² + yz + 2y + 2) j + (6x - 6x²y) k
What is the solution to the trigonometric inequality sin(x)>1+cos(X) over the interval 0<=x<=2pi radians?
Answer:
Last choice
Step-by-step explanation:
First, convert (sinx)^2 to 1-(cosx)^2 via trigonometric identity derived from (sinx)^2 + (cosx)^2 = 1
[tex]\displaystyle \large{\sin^2x + \cos^2x=1 \longrightarrow \sin^2x=1-\cos^2x}[/tex]
Thus, the rewritten inequality is [tex]\displaystyle \large{1-\cos^2x>1+\cos x}[/tex]
Notice how the inequality has a quadratic pattern since we have (cosx)^2 and cosx in the inequality, simply arrange degrees in order.
[tex]\displaystyle \large{1-\cos^2x>1+\cos x}\\\displaystyle \large{0>1+\cos x-1+\cos^2x}\\\displaystyle \large{0>\cos x+\cos^2x}\\\displaystyle \large{\cos^2x+\cos x < 0}[/tex]
Then we factor cosx since the expression has cosx as a common factor.
[tex]\displaystyle \large{\cos x(\cos x+1)<0}[/tex]
Then we have to consider each inequalities which are cosx<0 and cosx+1<0 then merge both intervals once obtaining the solutions.
(1) [tex]\displaystyle \large{\cos x < 0}[/tex]
This inequality means that we have to find the x-value(s) that satisfy(ies) it.
Since cosx becomes negative after π/2 (Refer to unit circle, cosx becomes negative in second quadrant and this quadrant), that means it becomes negative until it reaches or < 3π/2.
Thus, [tex]\displaystyle \large{\frac{\pi}{2}<x<\frac{3\pi}{2}}[/tex] is the solution to cosx > 0.
The another way to solve inequality is to find the intersections by solving the equation then joint the interval together.
[tex]\displaystyle \large{\cos x<0 \longrightarrow \cos x=0}[/tex]
From the unit circle, cosx becomes 0 at x = π/2 and x = 3π/2 between interval [0,2π]
Therefore:
[tex]\displaystyle \large{\cos x = 0 \longrightarrow x = \frac{\pi}{2}, \frac{3\pi}{2}}\\\displaystyle \large{\boxed{\frac{\pi}{2}<x<\frac{3\pi}{2}}}[/tex]
(2) [tex]\displaystyle \large{\cos x+1<0 \longrightarrow \cos x <-1[/tex]
For this inequality, it appears that there have no solutions because cosine function is defined between [-1,1] in range hence there are no x-values in real plane that make cosx even less than -1.
Because only π satisfies cosx = -1 but not cosx < -1, we restrict π and every values.
Hence no solutions which cause a break of interval between π and π/2 < x < 3π/2
If you substitute x = π in, the inequality is false and therefore the answer is:
[tex]\displaystyle \large{\frac{\pi}{2}<x<\pi, \pi<x<\frac{3\pi}{2}}[/tex]
Answer:
D.
Step-by-step explanation:
The first two don't work, so it's between the last two.
This equation doesn't work for 180, so the answer is the last choice.
:)
In a video game, Adrien earns 5 bonus spins on each of the first three levels and 2 bonus spins on each of the next three levels. How many bonus spins does Adrien earn on all six levels?
Answer:
I think the answer is 21.
Step-by-step explanation:
So, there are 5 spins for 3 levels + 2 spins for another 3 levels. This would be 5(3)+2(3)
15+6
21
what is the value of x in x(a+b)=b(c-x)
Answer:
x = [tex]\frac{bc}{a+2b}[/tex]
Step-by-step explanation:
x(a + b) = b(c - x) ← distribute parenthesis on both sides
ax + bx = bc - bx ( add bx to both sides )
ax + 2bx = bc ← factor out x from each term on the left side
x(a + 2b) = bc ← divide both sides by (a + 2b)
x = [tex]\frac{bc}{a+2b}[/tex]
−4 1/2÷(−2 2/3) i need help
Answer:
[tex]1\frac{11}{16}[/tex]
Step-by-step explanation:
Convert mixed numbers into improper fractions.
= [tex]\frac{-\frac{9}{2}}{\left(-2\frac{2}{3}\right)}[/tex]
= [tex]\frac{-\frac{9}{2}}{\left(-\frac{8}{3}\right)}[/tex]
= [tex]\frac{\frac{9}{2}}{\frac{8}{3}}[/tex]
= [tex]\frac{9\cdot \:3}{2\cdot \:8}[/tex]
= [tex]\frac{27}{2\cdot \:8}[/tex]
= [tex]\frac{27}{16}[/tex]
Convert improper fraction into mixed number.
= [tex]1\frac{11}{16}[/tex]
x+3<9 answer pls 2x+5<12
Answer:
first one: x<9 second: x<3.5 or 7/2
Step-by-step explanation:
first: substract 3 from both sides
second: substract 5 and then divide by 2
On the 1st January 2014 Carol invested some money in a bank account.
The account pays 2.5% compound interest per year.
On 1st January 2015 Carol withdrew £1000 from the account.
On 1st January 2016 she had £23517.60 in the account.
Work out how much Carol originally invested in the account.
Answer:
didn't know how to workout iam only 3rd standard
Answer:
Step-by-step explanation:
bubble gum
Solve the exponential equation: 2^3x+1 = 128
Answer:
So x=2.32956156226
Step-by-step explanation:
First subtract 1 on both sides
2^3x=127
Now you can rewrite this as
(2^3)^x
As it still equals the same thing
Now 2^3 is 8
So the equation is now
8^x=127
So we use log formula
log8 127=x
So how many times do we have to multiply 8 by itself to get 127?
The answer is: 2.32956156226
Hope this helps!
Marie bought 1/2 gallon of milk, which she finished after 6 days, If she drank the same amount of milk each day, how many gallons in a day did she drink?
Answer:
Marie drunk 0.083 gallons of milk each day
Find the value of the variable.
Answer:
Step-by-step explanation:
Draw a line from S to T'
T' is where the angle PTQ intersects the circle when SR is extended so that it hits the circumference of the circle.
This line bisects the 50 degree angle (which is given. It also bisects PRS.
y is shown on the diagram.
Your first job is to find y
It's y + 90 + 25 = 180 because all triangles are made up of 180 degrees.
y it turns out is 65 degrees.
Now comes the interesting part. PRT' is supplementary to y. It is labeled as 180 - y
<PRT' + Y = 180
y = 65
<PRT' = 180 - 65 = 115
Since PRT' = 115 and since PR = PT' (They are both radii). x/2 + x/2+ 115 = 180 I'll talk about x/2 down below this.
x + 115 = 180 All triangles = 180
x = 65.
Where did x/2 come? As long as PTQ is situated on the arc that it is on then <PTQ is always going to be x. You will have to piece together the two diagrams to make this work.i
It's a very good application of circles and lines well worth your time to get to know.
Read the below scenario and then answer the questions that follow. The Ancestry Society of North Carolina is compiling records so they can learn about the history of African Americans in North Carolina from 1820 to 1980. They have complied records of all 15,125 gravestones in cemeteries across all 15 counties. They want to choose a sample of 600 records to check their accuracy by visiting the actual gravestones.
a) Using the hat method explain how they could gather a simple random sample of 600 gravestones to visit.
b) Explain why it would be better to take a sample 40 gravestones from all 15 counties.
c) For what population could they make inference about after gathering and examining the sample?
Using the hat method they can randomly choose the tombstones they are going to visit in each county, the best option is to visit 40 tombstones in each county so that it is the same number of tombstones analyzed in each county. This study will benefit the residents of these counties because the information is specific to them.
When conducting research, it is sometimes necessary to take samples to analyze and study and obtain a result. In the situation presented there are a large number of tombstones to study, however it is difficult for researchers to visit each of the tombstones.
Therefore, the best option is to take a sample, that is, to study a small proportional part of the tombstones to obtain an estimated result of the study. The best way to do this is by taking the same number of samples in each county.
Additionally, the information resulting from this study will directly impact the residents of these counties because they are issues related to their past and their evolution through the years, especially the African American population.
Learn more about research in: https://brainly.com/question/1596108
How do you solve radical word problems
Answer:
1) Isolate the radical symbol on one side of the equation
2) Square both sides of the equation to eliminate the radical symbol
3) Solve the equation that comes out after the squaring process
4) Check your answers with the original equation to avoid extraneous values
Step-by-step explanation:
you have to solve for X
Answer:
x = 5/8Step-by-step explanation:
(1/2) / 4 = x / 51 / 8 = x / 5x = 5 / 8Done
It costs 3 tickets to play a game at the fair. If you spent 21 tickets on the game, which equation could you use to solve for the number of games, g?
Answer:
3×g=21
..............
How would the expression x3 -3 sqrt 3 be rewritten using difference of cubes?
O A. (x- 13 )(x2-3x - 3)
O B. (x+ 3)(x + 13 x + 3)
C. (x - 13 )(x2 + 3x + 3)
O D. (x- vb)(x2 + v3 x+3)
Answer:
x^3 - (√3)^3
I'm not so sure since it's not even an option
Step-by-step explanation:
x^3 - 3√3 = x^3 - 3^1 × 3^(1/2)from the laws of indices: 3^1 × 3^(1/2) = 3^(1 + 1/2)= 3^(3/2) which is the same as (√3)^3so it could be written as x^3 - (√3)^3which is greater?
1.4 or 1.41421356237
Answer:
1.41421356237
Step-by-step explanation:
After every decimal place value, or decimal point, there are infinite rows of invisible 0's
In 1.4, there are countless invisible 0's, which would look like this
1.40000000000000000...
Same for 1.41421356237
1.4142135623700000000...
So now, you can compare and see that 1.41421356237 has a 1 in the hundredths place, while 1.4 has a 0 in the hundredths place
Thus, 1.41421356237 is greater than 1.4
if you dont wear a retainer after braces can your teeth still be straight without wearing one cause mine still are and its been 6 months?
PLEASE HELP!! DUE SOON!!! WILL GIVE 5 STARS ALONG WITH A HEART!!!
Answer:
8
Step-by-step explanation:
What is the y-intercept of a line that has a slope of -3 and passes through point (-5, 4)?
О-17
О-11
O-7
O-19
Answer:
0, -11
Step-by-step explanation:
y-4=-3(x-(-5))
y-4=-3x-15
y=-3x-15+4
y=-3x-11 the ordered to the origin is -11
the y-intercept is at the point (0, -11)
Hope this helps
Statsssssssssssssssssssssssssssss
Help help help help hell
Answer:
51°
Step-by-step explanation:
angle2 is equal to 51 degrees
Answer:
∠2 = 51°
Step-by-step explanation:
These are consecutive interior angles that add up to 180°. Same as the other problem, you can solve for the angle like this:
[tex]x+129=180\\x=51[/tex]
Suppose you have 57 coins in a jar consisting entirely of dimes and quarters, worth a total of $10.65. How many dimes are in the jar?
Answer:
24
Step-by-step explanation:
Let d represent the number of dimes. Then (57-d) is the number of quarters, and the total value (in cents) is ...
10d +25(57 -d) = 1065
-15d +1425 = 1065 . . . . . . simplify
-15d = -360 . . . . . . . . . . subtract 1425
d = -360/-15 = 24 . . . divide by the coefficient of d
There are 24 dimes in the jar.
WILL GIVE BRAINLYIEST Rita goes to the mall. If x is the number of items she bought, the expression 18.54x+23 gives the amount she spent in dollars at one store. Then she spent 25 dollars at another store. Find the expression which represents the amount Rita spent at the mall. Then estimate how much Rita spent if she bought 2 items.
I only know the first part (the expression which represents the amount Rita spent at the mall)
18.54x + 48
HELLLP PLSSS QUICK
29 + 9x ≤ 65
solve for x
Answer:
x <= 4
Step-by-step explanation:
29+9x<65
-29. -29
9x<36
divide both sides by 9
x less than or equal to 4
Answer:
x ≤ 4
Step-by-step explanation:
29 + 9x ≤ 65
subtract 29 from both sides
29 - 29 + 9x ≤ 65 - 29
9x ≤ 36
divide both sides by 9
9x / 9 = x and 36 / 9 = 4
we're left with x ≤ 4
Bob paid $54 for shoes if they were on sale for 10% off what was the original price
6(2u) what is the answer
12u
there's no step by step
Write an equation for a line passing through the points (-1, 8) and (0, 5).
Answer:
y=-3x+5
Step-by-step explanation:
y=mx+c
point 1: (-1;8)
point 2: (0;5)
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]m = \frac{5 - 8}{0 - ( - 1)} [/tex]
[tex]m = - \frac{ 3}{1} [/tex]
[tex]m = - 3[/tex]
subs point and gradient to get c
5=-3(0)+c
Therefore c=5
The equation is y=-3x+5
judy gave 1/9 of her candies that she had to janet. with what she had remaining, she gave 1/2 to her brother. Judy now has 12 candies left. how many candies did she have at the beginning?