Answer:
The value is [tex]P(X > 3.30) = 0.12405[/tex]
Step-by-step explanation:
From the question we are told that
The mean GPA is [tex]\mu = 3.25[/tex]
The standard deviation is [tex]\sigma = 0.75[/tex]
The sample size is n = 300
Generally the standard error of mean is mathematically represented as
[tex]\sigma_{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma_{\= x} = \frac{0.75}{\sqrt{300} }[/tex]
=> [tex]\sigma_{\= x} = 0.0433[/tex]
Generally the probability that a random sample of 300 students will have a mean GPA greater than 3.30 is mathematically represented as
[tex]P(X > 3.30) = P(\frac{X - \mu}{\sigma_{\= x}} > \frac{3.30 -3.25}{ 0.0433} )[/tex]
[tex]\frac{\= X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ \= X )[/tex]
[tex]P(X > 3.30) = P(Z> 1.155 )[/tex]
From the z table the probability of (Z > 1.155 ) is
[tex]P(Z> 1.155 ) = 0.12405[/tex]
[tex]P(X > 3.30) = 0.12405[/tex]
1. Let S(x) represents a faculty member's yearly salary x years after beginning a position at a university. a. Use function notation to represent $2300 more than a faculty member's salary after 6 years on the job. b. Use function notation to represent the salary of a faculty member after 3 years more than n years on the job. c. Use function notation to represent a salary that is 2 times as large as the salary of a faculty member after 5 years on the job. d. How many times as large is the salary of a faculty member who has been on the job for 14 years as compared to someone who has been on the job for 3.1 years?
Answer:
a)S(6)+2300
b)S(n+3)
c)2(S(5))
d)S(14)-S(3.1) more than salary of member who has been on the job for 14 years as compared to someone who has been on the job for 3.1 years
Step-by-step explanation:
Let S(x) represents a faculty member's yearly salary x years after beginning a position at a university.
a)Use function notation to represent $2300 more than a faculty member's salary after 6 years on the job
$2300 more than a faculty member's salary after 6 years on the job : S(6)+2300
b)Use function notation to represent the salary of a faculty member after 3 years more than n years on the job.
The salary of a faculty member after 3 years more than n years on the job : S(n+3)
c)Use function notation to represent a salary that is 2 times as large as the salary of a faculty member after 5 years on the job.
A salary that is 2 times as large as the salary of a faculty member after 5 years on the job :
2(S(5))
d)How many times as large is the salary of a faculty member who has been on the job for 14 years as compared to someone who has been on the job for 3.1 years?
S(14)=S(3.1)
S(14)-S(3.1) more than salary of member who has been on the job for 14 years as compared to someone who has been on the job for 3.1 years
The function notations for the given question are:
a. [tex]\rm S(x)=S(6)[/tex]
b. [tex]\rm S(x) = S(n+3)[/tex]
c. [tex]\rm S(x) = 2[S(5)][/tex]
d. [tex]\rm S(x) = S(14) - S(3.1)[/tex]
What is Function Notations?Function notations can be defined as a method of writing functions that are precise and easy to understand. Function notations is a way to convert lengthy texts into functions. The most commonly used functional notation is f(x).
For the given question, let S(x) be the salary of a faculty member after x years.
a.The functional notation to represent a faculty member's salary after 6 years is:
[tex]\rm S(x)=S(6)[/tex] , where 6 is the number of years and S is the salary per year.
b. The functional notation to represent salary of a faculty member after 3 years more than n years on the job is:
[tex]\rm S(x) = S(n+3)[/tex] , where n+3 represents number of years into the job.
c. The functional notation to represent a salary that is 2 times as large as the salary of a faculty member after 5 years on the job is:
[tex]\rm S(x) = 2[S(5)][/tex] , where S(5) is the salary after 5 years into the job.
d. The difference between salary of a faculty member after 14 years and salary of another faculty member after 3.1 years can be represented as:
[tex]\rm S(x) = S(14) - S(3.1)[/tex], where S(14) is the salary after 14 years and S(3.1) is the salary after 3.1 years into the job.
Therefore the functional notations for the given question are:
a. [tex]\rm S(x)=S(6)[/tex]
b. [tex]\rm S(x) = S(n+3)[/tex]
c. [tex]\rm S(x) = 2[S(5)][/tex]
d. [tex]\rm S(x) = S(14) - S(3.1)[/tex]
Learn more about function notations here:
https://brainly.com/question/5025688
How to get the range from a table of values
Answer:
the range is all the y values or output values.
Step-by-step explanation:
example
x y
1 2
2 4
3 6
4 8
range=(2,4,6,8)
g A person who is 6 feet tall is walking away from a lamp post at the rate of 40 feet per minute. When the person is 10 feet from the lamp post, his shadow is 20 feet long. Find the rate at which the length of the shadow is increasing when he is 30 feet from the lamp post.
Answer:
80 ft/min
Step-by-step explanation:
Let h represent the height of the person shadow, x represent the distance between the person and the lamppost, y represent the length of the man shadow.
Therefore:
[tex]\frac{h}{x+y} =\frac{6}{y} \\\\substituting\ x=10,y=20:\\\\\frac{h}{10+20} =\frac{6}{20}\\\\\frac{h}{30} =\frac{6}{20}\\\\h=30*6/20\\\\h=9\ feet\\\\Therefore:\\\frac{h}{x+y} =\frac{6}{y}\\\\\frac{9}{x+y} =\frac{6}{y}\\\\9y=6x+6y\\\\9y-6y=6x\\\\3y=6x\\\\y=2x\\\\The\ person\ is\ walking\ from\ the\ lamppost\ at\ 40ft/min(\frac{dx}{dt}=40\ ft/min) \\\\y=2x\\\\Differentiating\ with\ respect\ to\ t:\\\\\frac{dy}{dt} =\frac{d}{dt}(2x)\\\\\frac{dy}{dt} =2\frac{dx}{dt}\\\\[/tex]
[tex]\frac{dy}{dt} =2(40\ ft/min)\\\\\frac{dy}{dt}=80\ ft/min[/tex]
The rate at which the length of the shadow is increasing when he is 30 feet away from the lamp post is 80 [tex]\frac{ft}{min}[/tex].
The height of the person shadow is to be = h
Given ,
The distance between the person and the man = x = 10
The length of the man shadow is = y = 20
By the similar triangle property corresponding sides of similar triangles are in the same ratio.
[tex]\frac{h}{x+y} = \frac{6}{y}[/tex]
[tex]\frac{h}{10+20} = \frac{6}{20}[/tex]
20h = 60 + 120
20h = 180
h = [tex]\frac{180}{20}[/tex]
h = 9feet
Therefore,
[tex]\frac{h}{x+y} = \frac{6}{y} \\\frac{9}{x+y} = \frac{6}{y} \\[/tex]
9y= 6x + 6y
9y-6y = 6x
6x = 3y
y = [tex]\frac{6}{3}x[/tex]
y = 2x
Differentiating both the sides with respect t,
[tex]\frac{dy}{dt} = 2\frac{dx}{dt}[/tex]
we know that ;
[tex]\frac{dx}{dt} = 40 \frac{ft}{sec}[/tex]
Therefore, by substitute the value
[tex]\frac{dy}{dt} = 2 . 40\frac{ft}{min}[/tex]
[tex]\frac{dy}{dt}[/tex] = 80[tex]\frac{ft}{min}[/tex].
The rate at which the length of the shadow is increasing is 80[tex]\frac{ft}{min}[/tex] .
For more details about the Rate change problem click the link given below.
https://brainly.com/question/20414862
The mean mass of 11 players in football team is 65.2kg .The mean mass of the team plus a substitute is 65.4kg what is the mass of the substitute
Mrs. Oliver has a stick that is 5 feet 8 inches. How many inches long is the stick?
Answer: sorry read it wrong
Answer:
68 inches
Step-by-step explanation:
We know that a foot is 12 inches, so multiply 12 and 5 to get 60, and then add the 8 other inches.
I hope this helps, and if it does, may I have brainliest?
10n + 10(7n + 10) = -10(11 - n)
Answer:
n = -3
Step-by-step explanation:
P E M D A S
10 x 7n = 70n
10 x 10 = 100
10n + 70n + 100 = -10(11 - n )
80n + 100 = -10(11 - n )
80n + 100 = 10n - 110
80n + 100 - 100 = 10n - 110 - 100
80n = 10n - 210
80n - 10n - 10n - 210 - 10n
70n = -210
70n ÷ 70 = -210 ÷ 70
n = -3
The commercial division of a real estate firm is conducting a regression analysis of the relationship between , annual gross rents (in thousands of dollars), and , selling price (in thousands of dollars) for apartment buildings. Data were collected on several properties recently sold and the following computer output was obtained. ANOVA df SS MS F Significance F Regression 1 41587.1 Residual 7 Total 8 51984.8 Coefficients Standard Error t Stat P-value Intercept 20.000 3.2213 6.21 Annual Gross Rents 7.270 1.3627 5.29 a. How many apartment buildings were in the sample
Answer:
The number of apartment buildings in the sample was 9.
Step-by-step explanation:
The ANOVA table is as follows:
ANOVA
df SS MS F Significance F
Regression 1 41587.1 __ ___ ____
Residual 7 ___ __ ___ ____
Total 8 51984.8 __ ___ ____
The degrees of freedom of Total is, n - 1.
Compute the sample size as follows:
DF of total = n - 1
8 = n - 1
n = 9
Thus, the number of apartment buildings in the sample was 9.
A country's postal service will accept a package if its length plus its girth (the distance all the way around) does not exceed 96 inches. Find the dimensions and volume of the largest package with a square base that can be mailed. length in base in × in volume in3
Answer:
Following are the solution to the given point:
Step-by-step explanation:
Let the box length l and the square base side be x, then
[tex]\to l+4x= 96 \\\\\to l=96-4x[/tex]
Calculating the volume of the box is:
[tex]\to V (x) = x^2 \\\\ \to l = x^2(96-4x)[/tex]
To find the critical value in this way, distinguish V with x and equal to zero
[tex]\to V'(x)=0 \\\\\to 4 \frac{d}{dx}(24x^2 - x^3)=0\\\\\to 4 (48x- 3x^2)=0\\\\\to 12x(16-x) = 0\\\\\to x= 12... [x \neq 0][/tex] (because the box will not exists)
Find the second derivative for maximum / minimum control as:
[tex]\to V''(x)= 12 \frac{d}{dx} (16x-x^2) \\\\\to 12 (16 -2x) < 0 \ for \ x = 16 \to \ Maxima \\\\\therefore[/tex]
[tex]Length = 32 \\\\Base = 16 in \times 16 in \\\\Volume= 8,192 \ in^3[/tex]
What is y-6 = 2(x + 5) in standard form?
A. -2x + y= 16
B. 2x-y=-16
C. y= 2x + 16
D. y-6 = 2x + 10
Answer:
Your answer is A
Step-by-step explanation:
I need the value of x
Answer:
9.9
Step-by-step explanation:
Optional (extra) info to understand length of other leg:
This triangle is an iscoceles, how can I (or we) tell?? Well, the angles of a triangle always add up to 180° and we know the angles of 2 corners, 90° and 45° so we can do this to find the last angle where "c" is the unknown corner:
180 - (90 + 45) = c
180 - 135 = c
45 = c
so "c" is also equal to 45° so we can decisively conclude that this figure is an iscoceles triangle.
How to find x:
Use the pythagorean theorem
c = √a² + b²
Then calculate using that equation
c = √7² + 7²
c = 9.9
In this case "c" is for the length of hypotenus but the image asks for x so
x = c
and
c = 9.9
so
x = 9.9
Hope this helps!
Have a nice evening!
If you find my answer helpful
Pls consider marking my answer as Brainliest! It would mean a lot!
Answer:
it x = 9.9
Step-by-step explanation:
A nut mix contains three kinds of
nuts. There are 5 ounces of almonds. The weight of the
cashews is triple the weight of the almonds and the weight
of the peanuts is 10 ounces more than the weight of the
almonds. What is the weight of the mix? Write the equation and the answer.
Answer:
35 oz
Step-by-step explanation:
cashew is 5×3 = 15
almonds 5
peanuts 5+10= 15
15+15+5 = 35 oz
Answer:
thing is im in middle school
dunno if i can do college stuff
sometimes i can do highschool
grab some snacks tho oh yeah here are your utensils️
Step-by-step explanation:
What should be done to both sides of the equation in order to solve -5m = -40?
Divide by -5.
Divide by -40.
Multiply by -5.
Multiply by -40
Answer:
Divide by -5.
what is 12% of $5000 for 3yrs
Answer:
$7,025
Step-by-step explanation:
solve for x/5 - g = a for x
The point-slope form of its equation is
y + 6 = 2(x-0)
y-0 = 2(x + 3)
y + 6 = -2(x-0)
y-0=-2(x-3)
Answer:y+0=-2(x-0)
Step-by-step explanation:
Tabetha spends $1.79 on a 20 oz bottle of Mountain Dew. How much did she pay per ounce?
Answer:9 cents per ounce (0.0895)
Step-by-step explanation: I UNDERSTAND HOW FRUSTRATING IT IS TO PUT AN ANSWER AND NO ONE ANSWERS IT, I DO, SO ALL I ASK IS FOR YOU TO GIVE ME BRAINLIEST. THANK YOU.
if x -12x + 36= 0 what is the value of x
-2(7-15)
What is the value of
O 2
Please I need help
The answer to this is 16
I need help PLEASE!!!!
Step-by-step explanation:
Hope I am not wrong! I did my best I could!
Sorry for the mistakes and my bad writing!
if you answer this question right you will get 100 points what s the answer to Godel's Theorem
i will find the close answer to this problem please put the answers in the comments
don't think that you can try to 100 by putting in the wrong answer i will moderate the points is set up to 10 i will tell you who wins then i will give you the 100 -pandamathhelper
Answer:
Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system capable of modelling basic arithmetic. ... The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.
Answer:
Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system capable of modelling basic arithmetic. ... The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency.
Step-by-step explanation:
y = x +13 solve for y if x = 5
Step-by-step explanation:
y = x+13
If x = 5
Then,
y = 5 + 13
y = 18
Hence,
The value of y is 18.
Answer:
y=18
Step-by-step explanation:
y=(5)+13
5+13=18
y=18
Solve the equation.
3x + 2(4x - 6) = 8x + 1
What is the value for x?
w
Answer:
=
1
3
3
Step-by-step explanation:
Triangle xyz is reflected across the y axis and then dilated which describes the dilation used to create triangle x’y’z?
Answer:
D2/3
Step-by-step explanation:
Answer: D2
Step-by-step explanation:
9 A cuboid has a square base.
The sides of the square are of length (1 + V2) cm.
The height of the cuboid is (5 – V2) cm.
Find the volume of the cuboid.
Express your answer in the form a + bv2, where a and bare integers.
Answer:
please is it a cube or a cuboid please check this out.
what is 83591257 divided by 67
Answer:
1247630.70149
Step-by-step explanation:
calculator
Answer:
1,247,630.7
Step-by-step explanation:
What is the slope of a line that passes throup the points (0,3) and (5,96)?
Answer:
1
48
Step-by-step explanation:
96-0=96
5-3=2
96÷2=1
48
Answer:
It is 93/5
Step-by-step explanation:
describe and solve the error 3x - 5 + 2x² + 9x = 3x + 2x² + 9x - 5
Answer:
3x - 5 + 2x² + 9x = 3x + 2x² + 9x - 5 = TRUE = 2 x^2 + 12 x - 5
Step-by-step explanation:
left: Simplify the following:
2 x^2 + 9 x + 3 x - 5
Grouping like terms, 2 x^2 + 9 x + 3 x - 5 = 2 x^2 + (3 x + 9 x) - 5:
2 x^2 + (3 x + 9 x) - 5
3 x + 9 x = 12 x:
Answer: 2 x^2 + 12 x - 5
_______________________
Simplify the following:
2 x^2 + 9 x + 3 x - 5
Grouping like terms, 2 x^2 + 9 x + 3 x - 5 = 2 x^2 + (3 x + 9 x) - 5:
2 x^2 + (3 x + 9 x) - 5
3 x + 9 x = 12 x:
Answer: 2 x^2 + 12 x - 5
please help put the solution only if you can. thank you!
========================================================
Explanation:
Highlight XY in the sequence XYZ. We've highlighted the first two letters.
This means that we'll need to highlight the first two letters of MNL to get MN.
XY pairs with its corresponding part MN.
Due to the congruent triangles, we know that XY = MN.
The diagram shows MN = 8. Due to substitution or the transitive property (they're similar ideas) we know that XY = 8 as well.
As you can see, the order of the letters is important so we can properly align the letters.
HELP PLEASE IM GOING TO FAIL MATH :(
Answer:
r=11, Hope I helped!
Step-by-step explanation:
I'm to lazy :P
Answer:
r=11
Step-by-step explanation:
Notice on the table how whatever the x value you is it is multiplied by 11, thus giving us our answer to r and answer to the equation y = rx.
Simplify
V-50.
O 5/2
ООО
O 5iv 2
0
-5V2
Answer:
It’s 11, remember pemdas when answering a question like this.
Step-by-step explanation: