Answer:
a) the probability that the next ream out- lasts the present one by more than 2 days is 0.0787
b) the number of reams that must be purchased is 19
Step-by-step explanation:
Given the data in the question;
Lets X₁ and X₂ be the two random variables that represents the first and second ream lasts
given that both random variables follow normal distribution with mean 4 and standard deviation 1.
a)
Find the probability that the next ream out- lasts the present one by more than 2 days.
P( X₂ - X₁ > 2 ) = P( [(X₂ - X₁ - E(X₂ - X₁)) / √(V(X₂ - X₁)] > [ (2-E(X₂ - X₁))/√(V(X₂ - X₁) ]
= 1 - P( Z ≤ [2-(μ₂ - μ₁)] / [√( V(X₂) + V(X₁) ) ] )
= 1 - P( Z ≤ [2-(4 - 4)] / [√( 1 + 1 )] )
= 1 - P = ( Z ≤ 2 / √2 )
= 1 - p( Z ≤ 1.4142 )
from excel; p( Z ≤ 1.41 ) = 0.9213
P( X₂ - X₁ > 2 ) = 1 - 0.9213
P( X₂ - X₁ > 2 ) = 0.0787
Therefore, the probability that the next ream out- lasts the present one by more than 2 days is 0.0787
b)
How many reams must be purchased if they are to last at least 60 days with probability at least 80%
total value is 4n
standard deviation is nσ
so
P(nX ≥ 60 ) = 0.80
P( nX-nμ /nσ ≥ 60-nμ/nσ) = 0.80
P( Z ≥ 60-4n/n) = 0.80
1 - P( Z ≥ 60-4n/n) = 0.80
P( Z < z ) = 0.20
now since z = 60-4n/n
from standard normal table
critical value of z corresponding to cumulative area of 0.20 is -0.841
so
z = - 0.841
60-4n/n = -0.841
60 - 4n = -0.841n
60 = -0.841n + 4n
60 = 3.159n
n = 60 / 3.159
n = 18.99 ≈ 19
Therefore, the number of reams that must be purchased is 19
Steven paid $60 for 3 cardio dance workout classes. He’s trying to set up an equation to help him find the cost of each class. What should Steven put in the blank of the following equation? c=$___÷3?
Answer:
c=$60/3. $20 dollars per class.
Step-by-step explanation:
I Need help plz will give brainlyist for the correct answer
A bookmark is shaped like a rectangle with a semicircle attached at both ends. The rectangle is 14 cm long and 4 cm wide. The diameter of each circle is the width of the rectangle. What is the area of the bookmark? Use 3.14 for π.
_____
The area of the bookmark is_____cm2.
Answer:
The area of the bookmark is 68.56 cm².
Step-by-step explanation:
Separate the bookmark into simpler shapes as described in the problem: a rectangle and a circle (two semicircles of the same size).
Find the area of the simpler figures.
Rectangle
A = LW
A = 14 · 4
A = 56
The area of the rectangle is 56 cm2.
Circle
A = πr2
A = 3.14(2)2
A = 3.14(4)
A = 12.56
The area of the circle is 12.56 cm2.
Find the area of the bookmark.
A = 56 + 12.56
A = 68.56
The area of the bookmark is 68.56 cm².
Sarah is solving for X by the process of completing the square for the following problem..
2x^2+16x-12=0
She got to this point below - type the number that goes in the (?) spot
(x+?)^2=22
Answer:4
Step-by-step explanation: Since she did it by completing the square, then you must do the same thing to get the same form so you can see what that number is.
So first subtract the constant which is -12 so we need to add twelve to get the constant on the other side. So we now have 2x^2+16x=12
The constant of the x^2 must be 1 so we need to divide by 2 on every term to get x^2+8x=12
So to make it so to get a perfect factor we need to divide the x factor by 2 so we get 4.
So the answer is 4 cause it is a perfect factor so were going to get 4 on both factors.
Answer:
4
Step-by-step explanation:
x²+2(x)(?)+?²=22
multiply by 2 because the coefficient of the higher degree in the first equation is 2
2x²+2(2(x)(?))+2(?²)-2(22)=0
2x²+4x(?)+2?²-44=0
Comparison
4x(?)=16x
?=4
2?²-44=-12
So, 2?²=-12+44
2?²=32
?²=16
?=4
Maximize −4x + 5y + 70 subject to the constraints:
2x + y ≤ 8
x + 3y ≥ 5
x + y ≤ 6
x ≥ 0,
y ≥ 0
a. Fix any constraints, as needed, and then convert the linear programming problem into a system of linear equations.
b. Give a fully labeled initial tableau, and circle the pivot element.
Answer:
Step-by-step explanation:
[tex]\text{To maximize -4x + 5y + 70 subject to } \\ \\ 2x + y \le 8 --- (1) \\ \\ x + 3y \ge 5 --- (2) \\ \\ x + y \le 6----(3) \\ \\ x \ge 0, y \ge 0[/tex]
[tex]\text{From above equationn (1)} : 2x + y = 8 \\ \\ \text{Divide boths sides by 8} \\ \\ \dfrac{2x}{8} + \dfrac{y}{8} = \dfrac{8}{8}[/tex]
[tex]\dfrac{x}{4} + \dfrac{y}{8} = 1 \\ \\ x = 4; y = 8[/tex]
[tex]\text{From above equationn (2)} : x + 3y = 5 \\ \\ \text{Divide boths sides by 5} \\ \\ \dfrac{x}{5} + \dfrac{3y}{5} = \dfrac{5}{5} \\ \\ x = 5; \ y = 1.66[/tex]
[tex]\text{From above equation (3)} : x + y = 6 \\ \\ \text{Divide boths sides by 5} \\ \\ \dfrac{x}{6} + \dfrac{y}{6} = \dfrac{6}{6} \\ \\ x = 6; \ y = 6[/tex]
[tex]\text{From the image attached below, we can see the representation in the graph}[/tex]
- [tex]\text{Now from equation (1) ad (III)} \\ \\ 2x + y = 8 \\ \\ x+y = 6[/tex]
[tex]x[/tex] [tex]= 2[/tex]
[tex]From : x + y = 6 \\ \\ 2 + y = 6 \\ \\ y = 6-2 \\ \\ y =4[/tex]
[tex]\text{From equation (1) and (II) } \\ \\ \ \ 2x + y = 8 \\ - \\ \ \ x + 3y = 5 \\ \\[/tex]
[tex]-5y = -2 \\ \\ y = \dfrac{2}{5} \ o r\ 0.4 \\ \\ From : 2x+ y = 8 \\ \\ 2x = 8 - \dfrac{2}{5} \\ \\ x = \dfrac{ 8 - \dfrac{2}{5} }{2} \\ \\ x = 3.8[/tex]
What is 0.11 / 22.77
Answer:
is your answer
0.00483091
Step-by-step explanation:
Pineapple Corporation (PC) maintains that their cans have always contained an average of 12 ounces of fruit. The production group believes that the mean weight has changed. They take a sample of 15 cans and find a sample mean of 12.05 ounces and a sample standard deviation of .08 ounces. What conclusion can we make from the appropriate hypothesis test at the .01 level of significance
Answer:
We accept the null hypothesis, that is, that the mean weight of the cans is still of 12 ounces of fruit.
Step-by-step explanation:
Pineapple Corporation (PC) maintains that their cans have always contained an average of 12 ounces of fruit.
This means that the null hypothesis is: [tex]H_0: \mu = 12[/tex]
The production group believes that the mean weight has changed.
This means that the alternate hypothesis is:
[tex]H_a: \mu \neq 12[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
12 is tested at the null hypothesis:
This means that [tex]\mu = 12[/tex]
They take a sample of 15 cans and find a sample mean of 12.05 ounces and a sample standard deviation of .08 ounces.
This means, respectibely, that [tex]n = 15, X = 12.05, \sigma = 0.08[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{12.05 - 12}{\frac{0.08}{\sqrt{15}}}[/tex]
[tex]z = 2.42[/tex]
Pvalue of the test:
We are testing if the mean is different from a value, which means that the pvalue is 2 multiplied by 1 subtracted by the pvalue of z = 2.42.
Looking at the z-table, z = 2.42 has a pvalue of 0.9922
1 - 0.9922 = 0.0078
2*0.0078 = 0.0156
What conclusion can we make from the appropriate hypothesis test at the .01 level of significance?
0.0156 > 0.01. This means that at the 0.01 level, we accept the null hypothesis, that is, that the mean weight of the cans is still of 12 ounces of fruit.
please help me thanks.
Answer:
I hope this helps you
Step-by-step explanation:
1/8 ÷ 3 = 1/8 × 1/3
= 1/24
= 0.0416666667
In a town, 65% of people had high speed internet in their homes. If the population of the town is 80,000, how many
people do not have access to high speed internet in their homes?
Show work
WILL GIVE BRAINLIST PLS HELP Find x. Round your answer to the nearest tenth.
Answer:
i think x= 13.5
Step-by-step explanation:
Write this equation in standard form y=3x+10
Answer:
to standard form
3x-y = -10
NO LINKS (QUESTION BELOW)
Answer:
D
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Could someone please solve?
Answer:
a) y=4
b) x=8
Step-by-step explanation:
we know the a line is on point 4 on the y axis. So it would be y=4
The second one is the same. line b is on the point 8 on the x axis, so x=8
Find the length of side x in simplest radical form with a rational denominator.
Answer:
x = 2√3
Step-by-step explanation:
x² = √6² + √6²
x² = 6 + 6 = 12
x = √12 = 2√3
Diego has run 4/5 of a race distance. He has run 7 2/3
given the qintic equation below, solve it to find the values of x. 2x^5_6x^3_4x^2_2x+4 =0
9514 1404 393
Answer:
x = {-0.5-√1.25, -0.5+√1.25, 2, -0.5+i√0.75, -0.5-i√0.75}
Step-by-step explanation:
I like to use a graphing calculator to find clues as to the roots of higher-degree polynomials. Here, we see that x=2 is the only real rational root. Dividing that out by synthetic division, we see the remaining quartic factor is ...
2x^5 -6x^3 -4x^2 -2x +4 = 0
2(x -2)(x^4 +2x^3 +x^2 -1) = 0
We can recognize that the quartic factor is actually the difference of two squares:
x^4 +2x^3 +x^2 -1 = (x^2 +x)^2 -1 = 0
So it resolves to two quadratic factors.
(x^2 +x +1)(x^2 +x -1) = 0
One will have real roots, as shown by the graph. The other will have complex roots.
x^2 +x + 1/4 = 1 +1/4 . . . . complete the square for the factor with real roots
(x +1/2)^2 = 5/4
x = -1/2 ± √(5/4) . . . . . . irrational real roots
__
x^2 +x = -1 . . . . . . . . . . the quadratic factor with complex roots
(x +1/2)^2 = -1 +1/4 . . . complete the square
x = -1/2 ± i√(3/4) . . . . irrational complex roots
__
In summary, the values of x that satisfy the equation are ...
x = 2
x = -1/2 ± √(5/4)
x = -1/2 ± i√(3/4)
Can someone please help me?
I will try i had this unit last year, basically the diameter is 5 in this problem, which you multiply by pi (in this case I will use 3.14 as the shortened version since its on-going) which gives you 15.7, then you multiply that by 3 in this problem to get 47.1!
Answer:
Step-by-step explanation:
Volume of a cylinder formula = πr^2h
r (radius) = 5/2 = 2.5
h (height) = 3
Answer: 3π(2.5)^2 = 3π(6.25) = 18.75π cubic units
Solve 4c + 10 = 2. A. c = 2 B. c = -3 C. c = 3 D. c = -2
Answer:
d.c=-2
Step-by-step explanation:
Answer: A. c=-2
Step-by-step explanation:
4c + 10 = 2
4c = -8
c = -2
What is the 3rd quartile in the following data set? You may want to draw a box & whisker plot
to find the 3rd quartile. *
(5 Points)
{5, 16, 12, 3, 20, 15, 8)
16
12
15
5
Answer:
16
Step-by-step explanation:
Arrange date in order
3,5,8,12,15,16,20
find median in this case its 12 also khown as 2nd quartile know find the themedian of data that is on the right right of median or 2nd Quartiles That will be the 3rd quartile...
A rectangular poster has an area of 26 square feet. It is 4 1/3 feet wide at it's base. What is the height of the poster?
Answer:
6 square feet
Step-by-step explanation:
Area = L * w
26 = L * 4 1/3
26 = L * 13/3
L = 26 divided by 13/3
L = 26 * 3/13 = 6
answer = 6
please help it due rn
Answer:
B) (1/2, -8)
Step-by-step explanation:
(1, -6) and (0, -10)
Midpoint formula:
((x1+x2)/2, (y1+y2)/2)
Solving for x:
(x1+x2)/2
(1 + 0)/2
1/2
Solving for y:
(y1+y2)/2
(-6-10)/2
(-16)/2
-8
What is the area of the trapezoid shown below?
Answer: where is the trapezoid
Step-by-step explanation:
Pls help. Im so lost.
Answer:
x = 35 degrees
Step-by-step explanation:
supplementary angles = 180 degrees
m<A + m<B = 180
(2x - 5) + 3x = 180
5x - 5 = 180
5x = 175
x = 35
What is the equation of the horizontal asymptote?
A. y = 0
B. x = 0
C. y = x
D. x = 2
Answer:
horizontal asymptote at y = 0
Step-by-step explanation:
According to the definition of asymptotes, it is a line that the function gets closer and closer to as x goes to plus or minus infinity. The definition clearly does not mention anything about the finite value of x.
However, crossing of asymptotes does not happen in the case of vertical asymptotes because for a given x, the function has only one value but the same y can be obtained for different values of x.
It is a common misconception that graphs of functions can’t cross the asymptotes. This is true only for vertical asymptotes. In fact, there are several examples of functions whose graphs cross the horizontal asymptote. For example:
f(x) = (xe)^((-x)^2)
The horizontal asymptote of the above function is y=0 but it still crosses the x axis at x=0.
hope that helps, I really don't know thought. Quite tricky
If 78% of the total is 156 marks, find the total marks in the test
200
206
176
210
Classify each triangle by its angles and its sides.
PLSSS ANSWER!
Answer:
9 . right triangle
Step-by-step explanation:
9. has right angle
Which expression is equivalent to 6x^2+16x-6
The answer is (2x+6)(3x-1)
what is the value of angle x?
Answer:
x=66
Step-by-step explanation:
Hello There!
∠BAC ≅ ∠CDB because in a parallelogram opposite angles are congruent
So all we have to do is solver for ∠BAC
Remember the sum of the triangles angles is 180 so to find ∠BAC
we subtract the given angles (83 and 31) from 180
180-83-31=66
so ∠BAC = 66
like stated before
∠BAC≅∠BDC so if ∠BAC = 66 then x also equals 66
Answer:
x = 66
Step-by-step explanation:
x = 66 degree
Ms. Cathy bought a package of pens. Out of every 10 , pens, 7 are black. If there are 20 pens in the pack, what fraction of the pens in the pack are black? What percent of the pens in the pack are black? What fraction of the Owens in the pack is black?
Answer:
Step-by-step explanation:
7/10 are black therefore 14/20 are black
(X8.6.PS-12
Question Help
A circular flower bed is 20 m in diameter and has a circular sidewalk around it that is 2 m wide.
Find the area of the sidewalk in square meters. Use 3.14 for it.
The area of the sidewalk is m2.
(Round to the nearest whole number as needed.)
Enter your answer in the answer box and then click Check Answer.
Clear All
Check Answer
All parts showing
Answer:
area = 138 m²
Step-by-step explanation:
radius of large circle = 12 m
radius of small circle = 10 m
large circle area = πr² = (3.14)(12²) = 452.16 m²
small circle area = πr² = (3.14)(10²) =314 m²
452.16 - 314 = 138.16 m²