Answer:
The number of computers that must be surveyed is 1681.
Step-by-step explanation:
The formula to find the sample size is given by:-
[tex]n=p(1-p)(\frac{\frac{z_{\alpha } }{2} }{E} )^{2}[/tex]
where p = prior population proportion,
[tex]\frac{z_{\alpha }}{2}[/tex]= Two-tailed z-value for ∝
E= Margin of error.
As per the given, we have
Confidence level :
1 - ∝ = 0.90
⇒∝= 1 - 0.90= 0.10
Two -tailed z-value for ∝= 0.10 : [tex]\frac{z_{\alpha }}{2}[/tex] = 1.64
E= 2%=0.02
We assume that nothing is known about the percentage of computers with new operating systems.
Let us take p=0.5 [we take p= 0.5 if the prior estimate of proportion is unknown.]
The required sample size will be:-
[tex]n= 0.5(1-0.5)(\frac{1.64}{0.02} )^{2}[/tex]
=> [tex]0.25(82)^{2}[/tex]
=> 1681
Hence, the number of the computer must be surveyed = 1681
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Which graph shows y=1/2⌈x⌉?
The correct answer is option B which is the graph that represents the equation y = (1/2)x will be the second option in the figure. At every value of y, the value of x is double.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The graph of the equation y =1/2x is represented in the answer below we can see in the graph that at every value of y the value of x is double for example if we put y = 1 then the value of x will be 2.
y = 1/2 x
at x = 2
y = 1/2 x 2
x = 1
Therefore the correct answer is option B which is the graph that represents the equation y = (1/2)x will be the second option in the figure. At every value of y, the value of x is double.
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I need help ASAP please
Which statement is true about whether Z and B are independent events?
A: Z and B are independent events because P(Z | B) =P(Z).
B: Z and B are independent events because P(Z | B) = P(B).
C: Z and B are not independent events because P(Z | B) ≠ P(Z).
D: Z and B are not independent events because P(Z | B) ≠ P(B).
which expression is equivalent to...
Answer:
B
Step-by-step explanation:
What is the value of x in the equation 1/5x - 2/3y=30 when y= 15
Substituting in y=15,
[tex]\frac{1}{5}x-\frac{2}[3}(15)=30\\\\\frac{1}{5}x-10=30\\\\\frac{1}{5}x=40\\\\x=\boxed{200}[/tex]
A sells an article to B at profit of 20% and B sells it to C at a profit of 25%. If C buys it for Rs.225, what did A pay for it?
Answer:
A pay 120 for itLet the cost price be X
A Sells to B
profit = 20%
= cost price + 20%
= X + 20/100 of X
= 6x/ 5
B sells to C
profit = 25%
= Cost price + + 25%
= cost price + 25%
= 6x/5 + 25/100*6x/5
= 6x/5.+ 3x/10.
= 3x/2
3x/2 = 225.
3x = 450
x = 150.
sp = C. p + profit
S. p - profit = C. p
X - X/5
4x/5
4(150)/5.
120
Need help with this geometric question
Answer: A
Step-by-step explanation:
[tex]V=\frac{1}{3}Bh\\\\V=\frac{1}[3}(6.3)(2.4)(3.6)=\boxed{18.144}[/tex]
It has been estimated that only about 40% of California residents have adequate earthquake supplies suppose you randomly survey 22 California residents we are interested in the number who have adequate earth quake supplies
The answers are as follows:
a) X denotes the number of the california residents that have adequate earthquake insurance
b) x = 1 ,2 ,3 ......
c) P( X=x ) = 0.3(1-0.3) ^ (x-1)
d) P( X=1) + P( X=2) + P( X=3) + P( X=4)
e) 0.49
f)0.42
g)0.33
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
The complete question is
It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose we are interested in the number of California residents we must survey until we find a resident who does not have adequate earthquake supplies. a. In words, define the random variable X. b. List the values that Xmay take on. c. Give the distribution of X.X~ _____(_____,_____) d. WhatistheprobabilitythatwemustsurveyjustoneortworesidentsuntilwefindaCaliforniaresidentwhodoes not have adequate earthquake supplies? e. What is the probability that we must survey at least three California residents until we find a California resident who does not have adequate earthquake supplies? f. HowmanyCaliforniaresidentsdoyouexpecttoneedtosurveyuntilyoufindaCaliforniaresidentwhodoesnot have adequate earthquake supplies? g. How many California residents do you expect to need to survey until you find a California resident who does have adequate earthquake supplies?
given that 30% of California residents have adequate earthquake supplies.
a) variable X denotes the number of the california residents that have adequate earthquake insurance
b) x = 1 ,2 ,3 ......
c) p=0.3
P( X=x ) = 0.3(1-0.3) ^ (x-1)
d) P( X=1) + P( X=2) + P( X=3) + P( X=4)
= 0.3(1-0.3) ^ 0 + 0.3(1-0.3) ^1 + 0.3(1-0.3)^ 2 +...
e) P( X≥ 3) = 1- P(X<3)
= 1- (P(X=1) + (X=2))
= 1- 0.051
= 0.49.
f) E(X)= 1/P
p is the resident who does not have adequate earthquake supplies
p= 1-0.3
p = 0.7
E(X) = 1/0.7
= 0.42
g) E(X) = 1/q
= 1/0.3
= 3.333
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Which expression can be used to convert 80 US to Australian dollars?
Answer:
0.9668 USD
Step-by-step explanation:
1 USD=1.0343 AUD 1AUD=0.9668 USD.
On a unit circle, Ø = 60°. Identify the terminal point and Tan Ø
The terminal points when the value of r is 1 will be 0.5 and 0.86 and the value of tan 60 will be 1.732.
What is angle measurement?An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).
Given;
Ø = 60°
Let's assume the value of r = 1 units
The terminal points are;
x= rcosΘ
x=1 × cos 60°
x=0.5
y=rsinΘ
y=rsin60°
y = 0.86
The terminal points when the value of r is 1 will be 0.5 and 0.86.
The value of the tan for the given value of the angle;
Tan 60° = 1.732
Hence, the terminal points when the value of r is 1 will be 0.5 and 0.86 and the value of tan 60 will be 1.732.
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The amount of a pollutant (measured as parts per million) in a local lake can be modeled by the function of A(t)=14(2.71)^-.016*t, where t is the number of years since a government program was began to help clean up the lake. About how long will it take for the amount of pollutant to reach 7 parts per million?
Solving the exponential function, it is found that it will take 43.5 years for the amount of pollutant to reach 7 parts per million.
What is the exponential function for the amount of the substance?It is given by, after t years:
[tex]A(t) = 14(2.71)^{-0.016t}[/tex]
It will reach an amount of 7 parts per million when A(t) = 7, hence:
[tex]A(t) = 14(2.71)^{-0.016t}[/tex]
[tex]7 = 14(2.71)^{-0.016t}[/tex]
[tex](2.71)^{-0.016t} = 0.5[/tex]
[tex]\log{(2.71)^{-0.016t}} = \log{0.5}[/tex]
[tex]-0.016t\log{(2.71)} = \log{0.5}[/tex]
[tex]t = -\frac{\log{0.5}}{0.016\log{2.71}}[/tex]
t = 43.5.
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P is a polynomial of degree 4 with three zeros: -1 and 2 are zeros of multiplicity one, and 3 is a zero with multiplicity two. If P(0) = 90, what is the lead coefficient of P ?
Answer:
[tex]P(x) = (x+1)(x-2)(x-3)^2 + 108[/tex]
Step-by-step explanation:
let me know if you want an explanation
The interior angle of a regular polvgon is 9 times the size of its exterior angle
Work out how many sides the polygon has
==================================================
Work Shown:
x = exterior angle
9x = interior angle
interior + exterior = 180
9x+x = 180
10x = 180
x = 180/10
x = 18
n = number of sides
n = 360/x
n = 360/18
n = 20
There are 20 sides to the regular polygon.
Side notes:
The formula to determine n only works for regular polygons.A polygon with 20 sides is known as an icosagon.Any pair of adjacent interior and exterior angles are supplementary. They add to 180 degrees.If a=(-1 -3 2 2 5 -1 -4 -5 -4) and b=(3 3 5 2 -5 2 -4 -1 1) find AB?
Answer:
what is the control ofprice floir or price celling then scplain one advantage an one dissvantage
Determin d/dx (x²+1) (7x-3) and d/dt(3t-2/5t+1)
Answer:
2x(7x-3) + (x²+1)(7)
Step-by-step explanation: use product rule
Find the value below using your calculator. Round to the nearest hundredth. e³ Find the value below using your calculator . Round to the nearest hundredth . e³
The value of e³ = 20.079.
What is Euler's number , e ?e is an irrational number , It is a numerical constant used in mathematical constant .
The value of e = 2.718
It is asked in the question to determine the value of e³
Therefore
e³ = ( 2.718)³
e³ = 20.079
Therefore the value of e³ = 20.079.
The image of the calculation is attached with the answer.
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can someone please help me solve this question step by step not just give me the answer I want to learn lol
find f(x)•g(x)
if f(x)=8x+1 and g(x)=-5+9.
Answer: 32x+4
Step-by-step explanation:
[tex]f(x) \cdot g(x)=(8x+1)(-5+9)=4(8x+1)=\boxed{32x+4}[/tex]
Write an equation of the line that passes through a pair of points: On a coordinate plane, a line goes through (4, 1) and (5, 2). a. y = x + 3 c. y = -x + 2 b. y = x - 3 d. y = -x - 2 Please select the best answer from the choices provided A B C D
Answer:
b. y = x - 3
Step-by-step explanation:
The general form of the equation of the line is y = mx + c.
1) Find for m (gradient) using the following formula:
m = y2 - y1 / x2 - x1
Substitute the values into it and solve for m.
m = 2 - 1 / 5 - 4
m = 1 / 1
m = 1
2) Substitute into m of the y = mx + c.
y = 1x + c
3) Choose one the coordinates that the line goes through ((4, 1) or (5, 2)) to find c (y-intercept). I will choose (4, 1). Then, substitute your chosen coordinates into your newfound equation (y = 1x + c)
1 = 1(4) + c
1 = 4 + c
1 - 4 = c
-3 = c
Substitute -3 in place of c.
y = 1x - 3, which can be simplified to y = x - 3. Therefore, the correct choice is b.
A number is equal to the sum of half a second number and 3. The first number is also equal to the sum of one- quarter of the second number and 5. The situation can be represented by using the graph below, where x represents the second number. 16 NO 8 K 3₂ 5 2 4 st 6 8 10 12 14 16 Which equations represent the situation? Hurry
Can someone answer this question for me? Thanks!
Answer:
The costco basmati rice
Step-by-step explanation:
Under the label it is given that the bag is 18.14 kg
When converted to lbs= 18.14*2.2~39.91
39.91lbs>10lbs, so it has more quantity of rice: Costco Basmati
Answer:
The Costco bag is a better deal as each pound is $0.65 cheaper
Step-by-step explanation:
Let make the weight of each bag in a common unit
18.14kg = about 40 pounds (formula: multiply the mass value by 2.205)
Now find how much it cost per pound for each bag,
Costco: 49.99 / 40 = $1.25 per pound
Bulkmarket: 18.99 / 10 = $1.90 per pound
1.25 < 1.90
What is the simplified form of √ 144x36?
Answer:
12x^18
Step-by-step explanation:
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: a = -1[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
For a function f(x) = y,
x represents the value ( x - coordinate ) at which the function has a value y.
[tex]\qquad \tt \rightarrow \: f(x) = a {x}^{2} + 2[/tex]
for point (-1 , 1) to satisfy the equation, we have to calculate the value of a
[tex]\qquad \tt \rightarrow \: f( - 1) = a( - 1) {}^{2} + 2[/tex]
[tex]\qquad \tt \rightarrow \: 1 = a + 2[/tex]
[tex]\qquad \tt \rightarrow \: a = 1 - 2[/tex]
[tex]\qquad \tt \rightarrow \: a = - 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Substitute -1 into x
Substitute 1 into y
f(x)= a (-1) ^2+2=1
a=-1
What is the equation of the line that is parallel to the given line and passes through the point (−3, 2)?
3x − 4y = −17
3x − 4y = −20
4x + 3y = −2
4x + 3y = −6
Answer:
4x + 3y = - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
• Parallel lines have equal slopes
calculate the slope of the line using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (3, - 1) ← 2 points on the line
m = [tex]\frac{-1-3}{3-0}[/tex] = [tex]\frac{-4}{3}[/tex] = - [tex]\frac{4}{3}[/tex] , then
y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation
to find c substitute (- 3, 2 ) into the partial equation
2 = 4 + c ⇒ c = 2 - 4 = - 2
y = - [tex]\frac{4}{3}[/tex] x - 2 ← equation in slope- intercept form
multiply through by 3 to clear the fraction
3y = - 4x - 6 ( add 4x to both sides )
4x + 3y = - 6 ← in standard form
Select the correct answer from each drop-down menu.
Consider the function Ax) = 3x+ 1 and the graph of the function g(x) shown below.
Answer:
write three methods of writing set. Give one example of each methods.
OLLEGE
>
For the given functions, find (fog)(x) and (gof)(x) and the domain of each.
f(x) = 4x + 1, g(x)=√x
(fog)(x) =
(gof)(x) =
The domain of fog is ☐.
(Type your answer in interval notation.)
The domain of g of is.
(Type your answer in interval notation. Use integers or fractions for any numbe
Part 1
[tex](f\circ g)(x)=f(\sqrt{x})=4\sqrt{x}+1[/tex]
We need to make sure the radical is defined, meaning the radicand has to be non-negative. Thus, the domain is [tex]\boxed{[0, \infty)}[/tex]
Part 2
[tex](g \circ f)(x)=g(4x+1)=\sqrt{4x+1}[/tex]
We need to make sure the radical is defined, meaning the radicand has to be non-negative. Thus,
[tex]4x+1 \geq 0\\\\4x \geq -1\\\\x \geq -\frac{1}{4}[/tex]
Thus, the domain in interval notation is [tex]\boxed{\left[-\frac{1}{4}, \infty)}[/tex]
Need help anyone please!!!
I need the answer for number 4 please!!
Answer:
-3 - false
0 - true
1 - true
2 - false
4 - true
Step-by-step explanation:
the "zeros" of a function are its x-intercepts
(because that is when the function = zero [0])
So, we can look at the x-intercepts of the graph to find the zeros:
at 0, 1, and 4 the function = 0, meaning that those are zeros of the function
hope this helps!! have a lovely day :)
What is the value of 6¹?
6° = 1
6 = 6
6 = 36
6 = 216
Answer:
6=6
Step-by-step explanation:
This is because the exponent is multiplying it by one so technically you don't have to do anything but multiply 6*1
Hope this helps
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Fun fact: ANY number powered to the}\\\huge\textbf{1 it automatically that number(just }\\\huge\textbf{regular multiplication).}[/tex]
[tex]\mathsf{6^1}\\\\\\\mathsf{\approx 6\times1}\\\\\\\large\text{So, you're making it 6 ONE TIME}\\\\\mathsf{= \bf 6}\\\\\\\\\\\\\huge\text{Thus, your answer should be: \boxed{\mathsf{Option\ B.\ 6^1 = 6}}}\huge\checkmark[/tex]
[tex]\large\text{Random\ note\ for\ rest\ of\ equations:}\\\\\mathsf{6^0\rightarrow \bf 1}\\\\\mathsf{6^2\rightarrow 6\times 6 \rightarrow \bf 36}\\\\\mathsf{6^3\rightarrow 6\times6\times6\rightarrow 36\times6\rightarrow \bf 216}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
T(h) = - A - B * cos((pi*h)/12) Where T is the temperature in degrees Fahrenheit and h is the number of hours from midnight (0 <= h <= 24) . a. The initial temperature at midnight was - 15 degrees * F and at Noon of New Year's Day it was 5 degrees * F Find A and B. b. Find the average temperature for the first 10 hours. C. Find an expression for the rate that the temperature is changing with respect to h.
The value of A and B is 5 , 10 ;The average temperature for first ten hours is -7.466 degree F ; an expression for the rate that the temperature is changing with respect to h ; dt/dh = +B sin ((pi*h)/12)
What is a Function ?A function is a mathematical statement used to correlate two variables.
The function given is
T(h) = - A - B * cos((pi*h)/12)
T is the temperature in degrees Fahrenheit and
h is the number of hours from midnight (0 <= h <= 24)
a. The initial temperature at midnight was - 15 degrees * F and
at Noon of New Year's Day it was 5 degrees * F
At midnight h = 0
T(h) = -15 degrees F
-15 = -A-B* cos 0
-15 = -A-B
A+B = 15------------------- (1)
At noon , h = 12 , T(h)= 5
- A - B* cos(pi) = 5
-A - B (-1) = 5
B -A = 5 ----------------------- (2)
Solving equation 1 and 2
2B = 20
B = 10
A = 5
The value of A and B is 5 , 10
The average temperature for first ten hours is -7.466 degree F
Find an expression for the rate that the temperature is changing with respect to h
dt/dh = +B sin ((pi*h)/12)
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Find the area of the trapezoid. TOP 11ft, RIGHT4√3ft , BOTTOM 15ft ,LEFT 8ft
Answer:
[tex]52\sqrt{3} ft^{2}[/tex]
Step-by-step explanation:
Please refer to the attached picture.
First we will find the area of rectangle BCDE.
Area of Rectangle = Length x Breadth = DE x CD
= 11 x [tex]4\sqrt{3}[/tex]
[tex]=44\sqrt{3} ft^{2}[/tex]
Next we will find Area of Triangle ABE.
Area of Triangle = 0.5 x Base x Height
[tex]0.5*4*4\sqrt{3} \\=8\sqrt{3} ft^{2}[/tex]
Area of Trapezoid = Area of Rectangle + Area of Triangle
[tex]=44\sqrt{3} +8\sqrt{3} \\=52\sqrt{3} ft^{2}[/tex]
Answer:
A = 52[tex]\sqrt{3}[/tex] ft² ≈ 90.1 ft²
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height and b₁ , b₂ the parallel bases
here h = 4[tex]\sqrt{3}[/tex] , b₁ = 15 , b₂ = 11 , then
A = [tex]\frac{1}{2}[/tex] × 4[tex]\sqrt{3}[/tex] × (15 + 11)
= 2[tex]\sqrt{3}[/tex] × 26
= 52[tex]\sqrt{3}[/tex] ft²
≈ 90.1 ft² ( to the nearest tenth )
Describe the graph of a function g by observing the graph of the base function ƒ.
A. g(x) = 2ƒ(–x) g(x)
B. g(x)= -1/2f(x)
C. g(x)= 1/2f(-x)
D. g(x)= f(-1/2x)
The correct answer is option B which is g(x)= 1/2f(-x).
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
As we can see in the graph that the value of the function g(x) will be calculated by the distance formula:-
[tex]g(x) = \dfrac{ 0 + 2}{2 - 0 }=\frac{2}{2}=1[/tex]
The value of the function f(x) will be:-
[tex]f(x) =\dfrac{2-0}{-4+0}=\dfrac{-1}{2}[/tex]
So g(x) = ( -1/2) f(x)
Therefore the correct answer is option B which is g(x)= 1/2f(-x).
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