Answer:
The value is [tex]P(\= X \ge 515 ) = 0.8944[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 500[/tex]
The standard deviation is [tex]\sigma = 60[/tex]
The sample size is n = 25
Generally the standard error of mean is mathematically represented as
[tex]\sigma _{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma _{\= x } = \frac{60}{\sqrt{25} }[/tex]
=> [tex]\sigma _{\= x } = 12[/tex]
Generally the probability that a random sample of size 25 selected from the population will have a sample mean greater than or equal to 515 is mathematically represented as
[tex]P(\= X \ge 515 ) = 1 - P(\= X < 515)[/tex]
Here [tex]P(\= X < 515) = P(\frac{\= x - \mu }{\sigma_{\= x }} < \frac{515 - 500}{12} )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P(\= X < 515) = P(Z < 1.25 )[/tex]
From the z table the probability of (Z < 1.25 )
[tex]P(Z < 1.25 ) = 0.10565[/tex]
So
[tex]P(\= X < 515) = 0.10565[/tex]
So
[tex]P(\= X \ge 515 ) = 1 - 0.10565[/tex]
=> [tex]P(\= X \ge 515 ) = 0.8944[/tex]
What are proper units for measuring leanth in the u. S system of units
Answer:
Yard, foot, inch
Answer:
metres
Step-by-step explanation:
length is distance from one point to another an according to the standard units which are the same all along the world the length should be measured in metres
A farmer uses x lb of fertilizer per acre at a cost of 1.4 per pound, leading to a revenue of R = 700 – 400e -x/100 dollars per acre.
(a) How many pounds of fertilizer should be applied per acre to maximize profit? Write you answer in decimal form rounding to three decimal places
Number
pounds per acre.
(b) What is the maximum profit on a 200 acre farm?
$ Number
Answer:
The cost can be written as:
C(x) = $1.4*x
The revenue can be written as:
R(x) = $700 - $400*e^(-x/100)
And as you know, the profit is written as the difference between the revenue and the cost:
P(x) = R(x) - C(x)
P(x) = $700 - $400*e^(-x/100) - $1.4*x
Now we want to maximize this, then we must look at the zeros in the derivate of P(x)
dP/dx = P'(x) = (-1/100)*$400*e^(-x/100) - $1.4
The maximum will be when P'(x) = 0.
we can solve:
0 = (-1/100)*$400*e^(-x/100) - $1.4
$1.4 = (-1/100)*$400*e^(-x/100)
(-100)*$1.4 = $400*e^(-x/100)
$140 = $400*e^(-x/100)
($140/$400) = e^(-x/100)
0.35 = e^(-x/100)
Now we can apply the Ln() in both sides and get:
ln(0.35) = ln(e^(-x/100) ) = -x/100
-ln(0.35)*100 = x = 104.98
You should apply 104.90 pounds of fertilizer.
b) The profit per acre, is:
P(x) = $700 - $400*e^(-x/100) - $1.4*x
Then if you have 200 acres, the profit will be:
200*P(x) = 200*($700 - $400*e^(-x/100) - $1.4*x)
and the maximum profit is whit x = 104.98 pounds, then:
200*P(104.98) = 200*($700 - $400*e^(-104.98/100) - $1.4*104.98) = $82,604.98
Which equation describes a relationship such that x= 0 must be excluded from the domain?
Answer:
a number divided by x so 2/x 3/x 4/x 5/x
Step-by-step explanation:
Evaluate the double integral. 4y2 dA, D is the triangular region with vertices (0, 1), (1, 2), (4, 1)
Answer:
44/3
Step-by-step explanation:
Let A be the line joining the vertices (0, 1) and (1,2) while B be the equation of the line joining (1, 2) and (4, 1).
The equation of a line joining points [tex](x_1,y_1) \ and\ (x_2,y_2)\ is:\\\\[/tex]
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
The equation of line A joining (0, 1) and (1,2) is:
[tex]y-1=\frac{2-1}{1-0} (x-0)\\\\y-1=x\\\\x=y-1[/tex]
The equation of line D joining (1, 2) and (4,1) is:
[tex]y-2=\frac{1-2}{4-1} (x-1)\\\\y-2=-\frac{1}{3} (x-1)\\\\3y-6=-x+1\\\\x=-3y+7[/tex]
Therefore the change in y is: 1 ≤ y ≤ 2, while change in x is: y-1 ≤ x ≤ -3y + 7. Hence the double integral is:
[tex]\int\limits^2_1\int\limits^{-3y+7}_{y-1} {4y^2} \, dx dy\\\\=4\int\limits^2_1\int\limits^{-3y+7}_{y-1} {y^2} \, dx dy\\\\=4\int\limits^2_1y^2dy[x]^{-3y+7}_{y-1} \\\\=4\int\limits^2_1y^2dy(-3y+7-(y-1))\\\\=4\int\limits^2_1y^2dy(-4y+8)\\\\=4\int\limits^2_1(-4y^3+8y^2)dy\\\\=4[-y^4+\frac{8}{3}y^3 ]^2_1\\\\=4(\frac{11}{3} )\\\\=\frac{44}{3 }[/tex]
To answer this question, we need, first get the equations for the lines that enclosed the surface, and integrate according to the limits obtained from these equations give.
The solution is:
A = 44/3 square units
Let´s call points:
P ( 0 , 1 ) Q ( 1 , 2 ) and R ( 4 , 1 )
The equation for the line between, P and R is:
y = 1
The equation for the line between, P and Q is:
Slope-intercept equation is y = m×x + b
The slope m₁ = ( 2 - 1 ) / ( 1 - 0 ) m₁ = 1
and the line passes over the point x = 0 y = 1 ; then
1 = 0 +b b = 1
y = x + 1 ⇒ x = y - 1
The equation for the line between Q and R is:
m₂ = ( 1 - 2 ) / ( 4 - 1) m₂ = - 1/3
y = ( -1/3)× x + b
when x = 1 y = 2
2 = ( - 1/3)×(1) + b
2 + 1/3 = b
b = 7/3
y = - (x/3) + 7/3 ⇒ x = 7 - 3×y
The double integral becomes:
A = 4×∫∫ y² dx dy ⇒ A = 4 ×∫₁² y²dy ∫dx | (y - 1 ) y ( 7 - 3y)
A = 4×∫₁² y²dy × x | ( y - 1 ) y ( 7 - 3y)
A = 4 ×∫₁² y²dy × [ 7 - 3×y - ( y - 1 )]
A = 4 ×∫₁² y²dy × (8 - 4×y ) ⇒ A = 4 ×∫₁² (8×y² - 4×y³ ) dy
A = 4 × [ (8/3)×y³ - y⁴ | ₁²
A = 4 × [ 64/3 - 16 - (8/3) + 1 ]
A = 4 × ( 56/3 - 15 )
A = 4 × ( 56 - 45 /3)
A = 4 × 11/3
A = 44/3 square units
Related Link :brainly.com/question/9825328
Giving F (x) =-3x +4,find f (-6).
Answer:
22
Step-by-step explanation:
we plug -6 to x which would get us -3(-6) + 4
-3(-6) = 18 + 4 = 22
PLZ mark brainliest :DD
Answer:
22
Step-by-step explanation:
1. -3 times -6 would be +18.
2. 18+4=22
√2y-5+8=4 solve for y.
What is the root? If there is no root, choose none
Answer:
y = 1/2
Step-by-step explanation:
I hope this helps you with the question
On Tuesday, a local hamburger shop sold a combined total of 596 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Tuesday?
Answer:
they sold about 199 hamburgers
Step-by-step explanation:
Help help help help help plaseeee
Answer:
-8
Step-by-step explanation:
I don't have a big brain
Find the quotient.
77/-11 =
Trying to find the equivalent ratio with lower terms
A. 30:36=20: ?
B. 21:35=? :20
What is the perimeter of a polygon with vertices at
(-3, 1), (5, 1), (-3, 4), (5, 4)? Show your work.
Answer:
Answer:8x3=24
Step-by-step explanation:
8 across the x axis and
3 across the y axis
8x3=24
Rewrite using a single positive exponent.
9^-3/9^6
(^ stands for exponents)
(explanations please if you don’t mind
Answer:
Its 9^-9
Step-by-step explanation
Because 9^-3 is on top, you have to take it to the bottom - this makes it positive. Now you have 1/(9^3*9^6). This give you 1/9^9 - or in other words 9^-9
You spend $25 to buy supplies for making gloves, and plan on
selling them for $5 each pair. Find the minimum number of
gloves you have to sell in order to make a profit.
Answer:
You need to sell 6 gloves
Step-by-step explanation:
If you sell 5 gloves you will get 25$ because 5x5 is 25. So you need to sell 6 gloves in order to make a profit.
Based on the density graph below, what is the probability of a value in the sample space being anywhere from 40 to 60? A. 75% B. 50% C. 25% D. 100%
Answer:
A. ap3x quiz!
Step-by-step explanation:
Adam poured 1 liter 460 milliliters of water into a beaker. Over three days, some of the water evaporated. On the fourth day, 979 milliliters of water remained in the beaker. How much water evaporated?
Answer:
481
Step-by-step explanation:
What is an equation for a line perpendicular to y=1/3x+3 that contains (6,16)
Answer: J (y=3x-2)
Step-by-step explanation: In perpendicular equations, opposite reciprocals are required. This means that a slope of 3 is perpendicular to -1/3, thusly J is corret
McKenzie told her friend, “If you increase my age by 8, multiply that quantity by 1/2 , and then subtract 6, you get 5.” Write an equation that matches McKenzie’s description using x as the variable.
a) x+8x1/2-6=5
b)1/2x+8-6=5
c)1/2(x+8-6)=5
d)1/2(x+8)-6=5
Answer:
D
Step-by-step explanation:
This follows PEMDAS
This first thing to do is add 8, so this must be P aka parentheses.
A and B are eliminated
Next is to M aka mutiply by 1/2
This eliminates C because if -6 was in the parentheses this would mean it is the next step as () takes priority. And this is not the case
I hope Im correct!
Simplify the following expression.
11x^2+9–2x–8x^2 - 6x
Answer:
3x^2-8x+9
Step-by-step explanation:
11x2+9−2x−8x2−6x
Subtract 8x2 from 11x2.
3x2+9−2x−6x
Subtract 6x from −2x.
3x2+9−8x
Move 9.
3x^2−8x+9
Hope this helps! :) Plz mark as brainliest
11x2+9−2x−8x2−6x
Subtract 8x2 from 11x2.
3x2+9−2x−6x
Subtract 6x from −2x.
3x2+9−8x
Move 9.
3x^2−8x+9
Thank you :)
The car you just bought keeps breaking down. The parts you need to buy cost $408.97. Your mechanic also charges $53 per hour for labor. Which of these equations best shows the cost to fix your car?
Answer:
repair charge = 53 * hours of labor + 408.97
Step-by-step explanation:
I got this right on TTM/ Imagine Math :)
help! this is due today! 1st gets brainiliest!
What is ethical monotheism and how does it relate to Judaism?
EXPLAIN
Answer:
Ethical monotheism is a form of exclusive monotheism in which God is the source for one standard of morality, who guides humanity through ethical principles.
Step-by-step explanation:
of the company's
A company receives 1.5% commission on the sale price of each house sold. For each house he sells, James earns
commission. James sells a house for $205,000. How much money will James earn?
Answer:
$1,025
Step-by-step explanation:
(205000)(.015)/3 = 1025
James will receive or earn $1,025
A 5 ounce container of Greek yogurt contains 135 calories find the unit rate of calories per ounce
Answer:
27 calories per ounce
Step-by-step explanation:
just divide 135 by 5
QRS is right triangle. Select the correct similarity statement. STR~TQR STR~RST STR~SQR STR~RTQ
Answer:
∆STR~∆RTQ is correct I am pretty sure
Answer:
Option four
Str ~ rtq
Step-by-step explanation:
What is the length of the diagonal of the rectangle?
Answer:
the diagonal of the rectangle is 5
Step-by-step explanation:
[tex]c=\sqrt{a^{2} +b^{2} }[/tex]
[tex]c=\sqrt{3^{2} +4^{2} }[/tex]
[tex]c=\sqrt{9+16}[/tex]
[tex]c=\sqrt{25}[/tex]
[tex]c=5[/tex]
A survey of 1012 teens found that 25% of students aged 14 to 18 plan to borrow no
money to pay for college. What's the margin of error for a 95% confidence interval for
the proportion of all students aged 14 to 18 who plan to borrow no money to pay for
college?
Answer c
Step-by-step explanation: i took the test and got them all right
Select all the correct answers. Which lines in the graph have a slope greater than 1 but less than 2?
line 1
line 2
line 3
line 4
line 5
Answer:
line 3 and 4 I believe
Step-by-step explanation:
Look at the bootom numbers. Look at the one and follow it up, the only lines that are not over two and are still above one are lines 3 and 4.
Answer:
Lines 3 and 4
Step-by-step explanation:
A slope is rise over run. So you have to determine how many you rise (go up) and run (go over). This is represented in a fraction form (such as 1/2 is up 1 and over 2). A slope greater than one would be 1/1 (go up more than one and over more than 1), and less than two (go up less than 2 and over less than 1).
Line 1 goes up 3 and over 1 (3/1 = a slope of 3)
Line 2 goes up 2 and over 1 (2/1= a slope of 2)
Line 3 goes up 3 and over 2 (3/2 = a slope of 1.5 )
Line 4 goes up slightly more than 1 and slight over 1
Line 5 goes up 1 and over 1 (1/1 = a slope of 1)
6.3 x 77 show your work please
Answer:
485.1
Step-by-step explanation:
6 . 3
x 7 7
+ 4 4 . 1
+ 4 4 1 . 0
4 8 5 . 1
basically break up 77 to 70 + 7
multiply 6.3 with both parts of the 77 (70 + 7):
70 x 6.3 = 441
7 x 6.3 = 44.1
then add those two sums together to get 485.1
please help meeeee 100 points!!!!!!!!!!!!!!
Answer:
when you will give us 100 points we will be giving your answers okay dear
Please help me!
what is $1500; 4%; 4 years?
a) $240
b) $120
c) $150
The student in an eighth-grade class had a dance. They spent $500 for a local band. The equation below can be used to find the total profit, y, if the student sold x tickets to the dance.
Y=4x-500
What does the 4 represent in the equation?
A. The price per ticket
B. The cost of the band
C. The number of tickets sold.
D. The profit made from selling x tickets.
Answer:
A
Step-by-step explanation:
Price per ticket
