Parameterize this surface (call it S) by
[tex]\mathbf s(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+u^2\,\mathbf k[/tex]
with [tex]0\le u\le2[/tex] and [tex]0\le v\le2\pi[/tex].
The normal vector to S is
[tex]\mathbf n=\dfrac{\partial\mathbf s}{\partial u}\times\dfrac{\partial\mathbf s}{\partial v}=-2u^2\cos v\,\mathbf i-2u^2\sin v\,\mathbf j+u\,\mathbf k[/tex]
Compute the curl of F :
[tex]\nabla\times\mathbf F=-2\,\mathbf i+3\,\mathbf j+5\,\mathbf k[/tex]
So the flux of curl(F) is
[tex]\displaystyle\iint_S(\nabla\times\mathbf F)\cdot\mathrm d\mathbf S=\int_0^{2\pi}\int_0^2(\nabla\times\mathbf F)\cdot\mathbf n\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle\int_0^{2\pi}\int_0^2(5u+4u^2\cos v-6u^2\sin v)\,\mathrm du\,\mathrm dv=\boxed{20\pi}[/tex]
Alternatively, you can apply Stokes' theorem, which reduces the surface integral of the curl of F to the line integral of F along the intersection of the paraboloid with the plane z = 4. Parameterize this curve (call it C) by
[tex]\mathbf r(t)=2\cos t\,\mathbf i+2\sin t\,\mathbf j+3\,\mathbf k[/tex]
with [tex]0\le t\le2\pi[/tex]. Then
[tex]\displaystyle\iint_S(\nabla\times\mathbf F)\cdot\mathrm d\mathbf S=\int_0^{2\pi}\mathbf F\cdot\mathrm d\mathbf r[/tex]
[tex]=\displaystyle\int_0^{2\pi}(20\cos^2t-24\sin t)\,\mathrm dt=\boxed{20\pi}[/tex]
g If two events are mutually exclusive, what is the probability that both occur at the same time? a. 1.00 b. 0.00 c. Cannot be determined from the information given. d. 0.50
The correct answer is B. 0.00
Explanation:
In statistics, two events are mutually exclusive if only one event can occur at one time. For example, if you have a deck of cards with Hearts and Spades, every time you choose a card you will have either Hearts or Spades but not both at the same time as there is not any card that combines Hearts and Spades in the same card. This means it is statistically impossible for two mutually exclusive events to occur at the same time, which means the probability is 0.00.
A United Nations report shows the mean family income for Mexican migrants to the United States is $26,500 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 24 Mexican family units reveals a mean to be $30,150 with a sample standard deviation of $10,560. State the null hypothesis and the alternate hypothesis.
Answer:
The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]
The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]
Step-by-step explanation:
The summary of the given statistics is:
Population Mean = 26,500
Sample Mean = 30,150
Standard deviation = 10560
sample size = 24
The objective is to state the null hypothesis and the alternate hypothesis.
An hypothesis is a claim with insufficient information which tends to be challenged into further testing and experimentation in order to determine if such claim is significant or not.
The null hypothesis is a default hypothesis where there is no statistical significance between the two variables in the hypothesis.
The alternative hypothesis is the research hypothesis that the researcher is trying to prove.
The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]
The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]
The test statistic can be computed as follows:
[tex]z = \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{30150 - 26500}{\dfrac{10560}{\sqrt{24}}}[/tex]
[tex]z = \dfrac{3650}{\dfrac{10560}{4.8989}}[/tex]
[tex]z = \dfrac{3650 \times 4.8989 }{{10560}}[/tex]
z = 1.6933
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Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of w
sailors. She receives a delivery of 4 tons of wood each day. The deliveries can con
afterwards the weather is too bad to allow them. Overall, she wants to build enou
least 2100 sailors.
How much wood does Astrid need to accommodate 2100 sailors?
tons
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This question is incomplete.
Complete Question
Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
Answer:
280 tons of wood.
Step-by-step explanation:
From the above question:
To make 1 ship = we require 40 tons of wood.
1 ship = can accommodate 300 sailors.
Step 1
If :
300 sailors = 1 ship
2100 sailors = y ships
Cross Multiply
300 × y ships = 1 ship × 2100 sailors
y ships = 2100 / 300
y ships = 7
Hence, 2100 sailors can occupy 7 ships.
Step 2
We are told in the question that:
Astrid wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
If:
1 ship = 40 tons of wood
Since 7 ships can accommodate 2100 sailors,
7 ships =
7 × 40 tons of wood = 280 tons of wood.
Therefore , Astrid needs 280 tons of wood to accommodate 2100 sailors.
what would be the answer for f(0) = -3x+7?
Answer: 7
Step-by-step explanation:
f(0) means that x is equal to zero and so you substitute all the x's for zeros which means -3 times 0 plus 7 is equal to 7
Answer:
[tex]x=\frac{7}{3}[/tex]
Step-by-step explanation:
Since any number multiplied by zero equals zero, our equation is really:
0 = -3x+7
First, we'd have to subtract the 7 from both sides:
-7 = -3x
Now we need to divide the negative three from both sides to isolate the x.
7/3 = x
So, our answer is x=7/3
Hope this helps!! <3 :)
Suppose that you begin with 10 grams of magic crystals, and your crystals grow at a
continuous rate of 25% every day (that's why they're magic). How many grams of
crystals will you have after one week (7 days)?!
ANSWER IS BRAINLEIST
Answer:
After 7 days the crystals will be 57.57 grams.
Step-by-step explanation:
In this the continuous exponential growth formula will be used.
y = A e ^rt
Where A = original amount = 10 grams
y is the growth after 7 days
e is Euler's number= 2.719
t is the time in hours , weeks, years etc.= 7 days
r is the rate in decimals = 25% = 0.25
Putting the values in the formula:
y = A e ^rt
y = 10 e ^0.25 (7)
Calculating with the calculator
y = 10* 2.719^1.75
y= 57.57 grams.
After 7 days the crystals will be 57.57 grams.
Answer:
57.55g
Step-by-step explanation:
Use the formula f(t) = aert, where a = 10, r = 0.25, and t = 7. This gives f(7) = 10e(0.25)(7) = 10e1.75 ≈ 10(5.755) ≈ 57.55.
Hi Maths lovers, if someone can explain me when l want to get NR doing NSR way ( going upwards) where this 3/5 b + 2/5 a or 2/5 a + 3/5 b comes from? Thanks
Answer:
see explanation
Step-by-step explanation:
SQ = SP + PQ = - b + a
Since SN : NQ = 3 : 2 then SQ = 3 + 2 = 5 parts , thus
SN = [tex]\frac{3}{5}[/tex] SQ = [tex]\frac{3}{5}[/tex] ( - b + a) = - [tex]\frac{3}{5}[/tex]b + [tex]\frac{3}{5}[/tex] a
Thus
NR = NS + SR
= - (- [tex]\frac{3}{5}[/tex] b + [tex]\frac{3}{5}[/tex] a) + a
= [tex]\frac{3}{5}[/tex] b - [tex]\frac{3}{5}[/tex] a + a
= [tex]\frac{2}{5}[/tex] a + [tex]\frac{3}{5}[/tex] b
Answer:
Yeah
Step-by-step explanation:
Very simple
It was said that
SN:NQ=3:2
→2SN = 3NQ
SN=SR-NR
SN=a - NR
NQ = NR - QR
NQ=NR - b
SQ = SN + NQ
Recall that SN=(3NQ)/2
SQ = (3NQ)/2 + NQ
SQ = (5/2)NQ
a - b = (5/2)(NR - b)
After simplification
NR = (2/5)a - (2/5)b +b
Factorize
NR = (2/5)a + (-2/5 + 1)b
NR = (2/5)a + (3/5)b
If an adult male is told that his height is 3 standard deviation above the mean of the normal distribution of heights of adult males, what can he assume?
Answer:
He can be on either the lower end of that 95%, or on the higher end. this guy is not a too short, nor is he extremely tall.
Sry if it's nor right, It was a little confusing.
Hope this helps!（づ￣3￣）づ╭❤～
He can be on either the lower end of that 95%, or on the higher end.
This guy is not too short, nor is he extremely tall.
We have given that
Height =2
Everything on the normal model is within 2 standard deviations away from the mean.
What is the standard deviation?The standard deviation is a measure of the amount of variation or dispersion of a set of values.
So He can be on either the lower end of that 95%, or on the higher end.
This guy is not too short, nor is he extremely tall.
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Based on all student records at Camford University, students spend an average of 5.30 hours per week playing organized sports. The population’s standard deviation is 3.20 hours per week. Based on a sample of 64 students, Healthy Lifestyles Incorporated (HLI) would like to apply the central limit theorem to make various estimates. Compute the standard error of the sample mean. (Round your answer to 2 decimal places.)
Answer:
The standard error of the sample mean is [tex]\sigma_{\= x } = 0.40[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 5.30 \ hours[/tex]
The population standard deviation is [tex]\sigma = 3.20 \ hours[/tex]
The sample size is [tex]n = 64[/tex]
Generally the standard error of the sample mean is mathematically represented as
[tex]\sigma_{\= x } = \frac{\sigma}{\sqrt{n} }[/tex]
substituting values
[tex]\sigma_{\= x } = \frac{3.20}{\sqrt{64} }[/tex]
[tex]\sigma_{\= x } = 0.40[/tex]
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n^2+5/2n
Answer: [tex]\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]
Step-by-step explanation:
[tex]n^2+\dfrac{5}{2}n+\underline{\qquad}\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{2\cdot 2}\bigg)^2\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{4}\bigg)^2\\\\\\=\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]
Given the exponential function f(x) = 16(0.75)", classify the function as exponential growth or decay and determine the percent rate of growth or decay.
Exponential growth, 75% increase
O Exponential decay, 75% decrease
O Exponential growth, 25% increase
Exponential decay, 25% decrease
Answer:
D
Step-by-step explanation:
To determine if a function is exponential decay or growth, simply look at the rate. If the rate is less than one, it is decay. It it's greater than one, it's growth.
The rate in the given function is 0.75 or 75%. 0.75 is less than one so it's exponential decay.
To determine the percent decrease, simply subtract the rate into 1 or 100%. Thus:
[tex]1-0.75=0.25[/tex]
Therefore, it is a 0.25 or 25% decrease.
The answer is D.
Answer: D
Step-by-step explanation:
1-0.75=0.25
Therefore, it decreases Exponential decay,25 percent decrease
as
8
3) The volume of
a wall, 5 times
high as it is board and 8
times as long as it is high, 12.8
(a.metors) Find The Breadth of the
Wall
Answer:
0.4 meters
Step-by-step explanation:
The volume is ...
V = LHB
12.8 m³ = (8(5B))(5B)(B) = 200B³ . . . fill in given values
0.064 m³ = B³ . . . . . simplify
∛0.064 m = B = 0.4 m
The breadth of the wall is 0.4 meters.
Find the solution set of the inequality and what is the number? 16x − 7 ≤ − 71 A. C. ≤ D. ≥ E. =
x ≤ − 4
Step-by-step explanation:
Answer:
x ≤ -4
Step-by-step explanation:
16x − 7 ≤ − 71
Add 7 to both sides.
16x ≤ -64
Divide both sides by 16.
x ≤ -4
List the sides in order from the largest to the smallest. A. XY, YW, WX B. XY, WX, YW C. WX, YW, XY D. WX, XY, YW
Answer:
Option (D)
Step-by-step explanation:
By applying Sine rule in the given triangle WXY,
[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinY}}{\text{XW}}=\frac{\text{SinX}}{\text{WY}}[/tex]
[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}=\frac{\text{Sin39}}{\text{WY}}[/tex]
[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}[/tex]
[tex]\frac{\text{XW}}{\text{XY}}=\frac{\text{Sin82}}{\text{Sin59}}[/tex]
= 1.1489
XW : XY ≈ 1.15 : 1
[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin39}}{\text{WY}}[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{\text{Sin59}}{\text{Sin39}}[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{1.36}{1}[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{\frac{1}{1}}{\frac{1}{1.36} }[/tex]
[tex]\frac{\text{XY}}{\text{WY}}=\frac{1}{0.7342}[/tex]
XY : WY = 1 : 0.7342
XW : XY : WY = 1.15 : 1 : 0.7342
Therefore, WX > XY > WY
Option (D). will be the correct option.
The ball bearing have volumes of 1.6cm cube and 5.4cm cube . Find the ratio of their surface area.
Answer:
4/9
Step-by-step explanation:
The scale factor for the linear dimensions of the ball bearings will be the cube root of the volume scale factor:
k = ∛(1.6/5.4) = 2/3
Then the scale factor for the areas will be the square of this scale factor:
ratio of surface area = (2/3)² = 4/9
_____
The area is the product of two linear dimensions, so its scale factor is the product of the linear dimension scale factors. That is, the scale factor for area is the square of the linear dimension scale factor.
Similarly, volume is the product of three linear dimensions, so its scale factor is the cube of the linear dimension scale factor.
Mark has a collection of 80 coins. There are only nickels and dimes in the collection. The total value of the coins is $5.00. How many dimes does Mark have?
Answer:
number of nickel = 60
number of dimes = 20
Step-by-step explanation:
1 nickel = 5 cents
1 dimes = 10 cents
$1 = 100 cents
we will use these value to solve the questions
_______________________________
Total no of coins = 80
let the number of nickels be x
let the number of dimes be y
thus,
x+y = 80
y = 80-x equation 2
value of x nickels = 5x
value of y dimes = 10y
Total value of x nickels and y dimes = 5x+10y
The total value of the coins is $5.00
total value of the coins in cents = 5*100 = 500
thus
5x+10y = 500
using y = 80-x from equation 2
5x + 10(80 - x) = 500
5x + 800 - 10x = 500
-5x = 500 - 800 = -300
x = -300/-5 = 60
Thus,
number of nickel = 60
number of dimes = 80-60 = 20
Evaluate the double integral ∬Ry2x2+y2dA, where R is the region that lies between the circles x2+y2=16 and x2+y2=121, by changing to polar coordinates.
Answer:
See answer and graph below
Step-by-step explanation:
∬Ry2x2+y2dA
=∫Ry.2x.2+y.2dA
=A(2y+4Ryx)+c
=∫Ry.2x.2+y.2dA
Integral of a constant ∫pdx=px
=(2x+2.2Ryx)A
=A(2y+4Ryx)
=A(2y+4Ryx)+c
The graph of y=A(2y+4Ryx)+c assuming A=1 and c=2
The evaluation of the double integral is [tex]\mathbf{ \dfrac{105}{2}\pi }[/tex]
The double integral [tex]\mathbf{\int \int _R\ \dfrac{y^2}{x^2+y^2} \ dA}[/tex], where R is the region that lies between
the circles [tex]\mathbf{x^2 +y^2 = 16 \ and \ x^2 + y^2 = 121}[/tex].
Let consider x = rcosθ and y = rsinθ because x² + y² = r²;
Now, the double integral can be written in polar coordinates as:
[tex]\mathbf{\implies \int \int _R\ \dfrac{y^2}{x^2+y^2} \ dxdy}[/tex]
[tex]\mathbf{\implies \int \int _R\ \dfrac{r^2 \ sin^2 \theta}{r^2} \ rdrd\theta}[/tex]
[tex]\mathbf{\implies \int \int _R\ \ sin^2 \theta \ r \ drd\theta}[/tex]
Thus, the integral becomes:
[tex]\mathbf{=\int^{2 \pi}_{0} sin^2 \theta d\theta \int ^{11}_{4} rdr }[/tex]
since 2sin² = 1 - cos2θ∴
[tex]\mathbf{=\int^{2 \pi}_{0} \dfrac{1-cos 2 \theta }{2} \ \theta \ d\theta\dfrac{r}{2} \Big|^{11}_{4}dr }[/tex]
[tex]\mathbf{\implies \dfrac{1}{2} \Big[\theta - \dfrac{sin \ 2 \theta}{2}\Big]^{2 \pi}_{0} \ \times\Big[ \dfrac{11^2-4^2}{2}\Big]}[/tex]
[tex]\mathbf{\implies \dfrac{\pi}{2} \times\Big[ 121-16\Big]}[/tex]
[tex]\mathbf{\implies \dfrac{105}{2}\pi }[/tex]
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in need of assistance answers are greatly appreciated thank you for your time and effort
Answer:
x = (h+g)/-f
Step-by-step explanation:
-fx-g = h
Add g to each side
-fx-g+g = h+g
-fx = h+g
Divide each side by -f
-fx/-f = (h+g)/-f
x = (h+g)/-f
Suppose that a password for a computer system must have at least 8, but no more than 12, characters, where each character in the password is a lowercase English letter, an uppercase English letter, a digit, or one of the six special characters ∗, >, <, !, +, and =.
a) How many different passwords are available for this computer system?
b) How many of these passwords contain at least one occurrence of at least one of the six special characters?
c) Using your answer to part (a), determine how long it takes a hacker to try every possible password, assuming that it takes one nanosecond for a hacker to check each possible password.
Part a)
There are 52 letters (26 lowercase and 26 uppercase), 10 digits, and 6 symbols. There are 52+10+6 = 68 different characters to choose from.
If there are 8 characters for this password, then we have 68^8 = 4.5716 * 10^14 different passwords possible.If there are 9 characters, then we have 68^9 = 3.1087 * 10^16 different passwordsIf there are 10 characters, then we have 68^10 = 2.1139 * 10^18 different passwordsIf there are 11 characters, then we have 68^11 = 1.4375 * 10^20 different passwordsIf there are 12 characters, then we have 68^12 = 9.7748 * 10^21 different passwordsAdding up those subtotals gives
68^8+68^9+68^10+68^11+68^12 = 9.9207 * 10^21
different passwords possible.
Answer: Approximately 9.9207 * 10^21======================================================
Part b)
Let's find the number of passwords where we don't have a special symbol
There are 52+10 = 62 different characters to pick from
If there are 8 characters for this password, then we have 62^8 = 2.1834 * 10^14 different passwords possible. If there are 9 characters, then we have 62^9 = 1.3537 * 10^16 different passwords If there are 10 characters, then we have 62^10 = 8.3930 * 10^17 different passwords If there are 11 characters, then we have 62^11 = 5.2037 * 10^19 different passwords If there are 12 characters, then we have 62^12 = 3.2263 * 10^21 different passwordsAdding those subtotals gives
62^8+62^9+62^10+62^11+62^12 = 3.2792 * 10^21
different passwords where we do not have a special character. Subtract this from the answer in part a) above
( 9.9207 * 10^21) - (3.2792 * 10^21) = 6.6415 * 10^21
which represents the number of passwords where we have one or more character that is a special symbol. I'm using the idea that we either have a password with no symbols, or we have a password with at least one symbol. Adding up those two cases leads to the total number of passwords possible.
Answer: Approximately 6.6415 * 10^21======================================================
Part c)
The answer from part a) was roughly 9.9207 * 10^21
It will take about 9.9207 * 10^21 nanoseconds to try every possible password from part a).
Divide 9.9207 * 10^21 over 1*10^9 to convert to seconds
(9.9207 * 10^21 )/(1*10^9) = 9,920,700,000,000
This number is 9.9 trillion roughly.
It will take about 9.9 trillion seconds to try every password, if you try a password per second.
------
To convert to hours, divide by 3600 and you should get
(9,920,700,000,000)/3600 = 2,755,750,000
So it will take about 2,755,750,000 hours to try all the passwords.
------
Divide by 24 to convert to days
(2,755,750,000)/24= 114,822,916.666667
which rounds to 114,822,917
So it will take roughly 114,822,917 days to try all the passwords.
------
Then divide that over 365 to convert to years
314,583.334246576
which rounds to 314,583
It will take roughly 314,583 years to try all the passwords
------------------------------
Answers:9.9 trillion seconds2,755,750,000 hours114,822,917 days314,583 yearsAll values are approximate, and are roughly equivalent to one another.
A) 9,920,671,339,261,325,541,376 different passwords are available for this computer system.
B) 875,353,353,464,234,606,592 of these passwords contain at least one occurrence of at least one of the six special characters.
C) It would take 314,582.42 years for a hacker to try every possible password.
To determine how many different passwords are available for this computer system; how many of these passwords contain at least one occurrence of at least one of the six special characters; and how long it takes a hacker to try every possible password, assuming that it takes one nanosecond for a hacker to check each possible password, the following calculations must be performed:
26 + 26 + 10 + 6 = 68 A) 68 ^ 12 + 68 ^ 11 + 68 ^ 10 + 68 ^ 9 + 68 ^ 8 = X 9,920,671,339,261,325,541,376 = XB)6 x (68^11) + 6 x (68^10) + 6 x (68^9) + 6 x (68^8) + 6 x (68^7) = X875,353,353,464,234,606,592 = XC)1 nanosecond = 1,66667e-11 minutes9,920,671,339,261,325,541,376 nanoseconds = 165344522321.02209473 minutes165344522321.02209473 minutes = 2755742038.6837015152 hours2755742038.6837015152 hours = 114822584.94515423477 days114822584.94515423477 days = 314582.4245072719059 years
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write the equation of a horizontal ellipse with a major axis of 18, and minor axis of 10, and a center at (-4, 5).
See the attached picture
[tex]\bold{\text{Answer:}\quad \dfrac{(x+4)^2}{81}+\dfrac{(y-5)^2}{25}=1}[/tex]
Step-by-step explanation:
A "horizontal" ellipse means that the x-radius is bigger than the y-radius. Thus, x is the major axis and y is the minor axis.
The equation of an ellipse is: [tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex] where
(h, k) is the center of the ellipsea is the radius on the x-axisb is the radius on the y-axisIt is given that the center is at (-4, 5) --> h = -4, k = 5
It is given that the major axis has a length of 18 --> x-radius = 9
It is given that the minor axis has a length of 10 --> y-radius = 5
Input those values into the equation of an ellipse to get:
[tex]\dfrac{(x-(-4))^2}{9^2}+\dfrac{(y-5)^2}{5^2}=1[/tex]
Simplify to get:
[tex]\dfrac{(x+4)^2}{81}+\dfrac{(y-5)^2}{25}=1[/tex]
What is the slope of the line shown below?
A.
B.
C.
-
D.
3
Answer:
D
Step-by-step explanation:
Option D is correct. Slope of the line shown in the graph is 3.
The slope of the line is the ratio of the rise to the run, or rise divided by the run.
It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=(y₂-y₁)/(x₂-x₁)
The line is passing through point (2, 2) and (4, 8).
Lets find the corresponding point values y₂= 8, y₁ = 2, x₂= 4 and x₁ =2.
Plug in the values in slope formula:
Slope = (8-2)/(4-2)
=6/2
=3
Hence, slope of the line shown in the graph is 3. Option D is correct.
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QUESTION TWO [25 MARKS] a) Your task is to interview a representative sample of attendees for the large concert venue where you work. The new season schedule includes 200 live concerts featuring all types of musicians and musical groups. Since neither the number of attendees nor their descriptive characteristics are known in advance you decide on nonprobability sampling. Based on past seating configurations, you can calculate the number of tickets that will be available for each of the 200 concerts. Thus, collectively, you will know the number of possible attendees for each type of music From attendance research conducted at concerts held by the Glacier Symphony during the previous two years, you can obtain gender data on attendees by type of music. How would you conduct a reasonably reliable nonprobability sampling? T5 marks] (b) A recent article in Nairobi Post Weekly Edition indicated that about 80% of the
Answer:
The answer to this question depends, in part, on the kinds of questions that you want to ask them. If the purpose of the survey is to try and figure out what concert patrons are thinking, then you want to try to get a good variety of ideas. In that case, you're no so interested in having a sample of individuals that's exactly representative of the population of concert goers. You only want to get a wide variety of the ideas that are out there. This is called heterogeneity sampling. That is, in this case, we'll be trying to get a sample not of people, but of ideas. In this case, we'd use brainstorming groups, panel sessions, and other group discussion methods to get all the ideas out there.
This approach is not an appropriate one if the purpose of the questions is to determine the preferences of the population of theater goers. That's because it doesn't communicate the popularity or prevalence of ideas in the sample. If this is a problem, and it likely is, it seems more appropriate to use some sort of purposive sampling method like modal interest sampling. This approach requires determining what the typical concert goer is like . If the company determines that the typical (or modal) attender is a young single person in college, then those people are sought out and interviewed. This is the sort of polling that is used in election polls where they interview "typical voters." For different genres of music and concert, a different typical concert goer could be postulated and different surveys and interview styles determined.
Probably most appropriate to this problem, though, is quota sampling. This form of purposive sampling uses demographic and other information to determine how many of different kinds of people to interview. For instance, if it is determined that only 20% of concert goers for a particular concert were women, then only 20% of the nonprobability sample should be made up of women. As long as these quotas are met, the sample can be sufficiently random.
I recommend using a combination of quota sampling and modal instance sampling. It seems to me that the kinds of people who attend concerts are idiosyncratic in some ways. Inasmuch as we can define universal characteristics of concert goers, we should seek to include only those people in the sample, but since we have demographic data as well, we should use these proportions as quotas as we select typical concert goers. For example, suppose we determine that the vast majority of people who attend operas make over $80,000/year, then we should limit our sample to people with that income level, but if we also know that 80% of opera attenders are women, we should work to insure that not more than 20% of our sample is men.
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 445 gram setting. It is believed that the machine is underfilling the bags. A 12 bag sample had a mean of 442 grams with a standard deviation of 20. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. State the null and alternative hypotheses.
Answer:
The null hypothesis is [tex]H_o : \mu = 445[/tex]
The alternative hypothesis [tex]H_a : \mu < 445[/tex] (This is the original claim[ It is believed that the machine is under filling the bags] )
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 445 \ g[/tex]
The sample size is [tex]n = 12[/tex]
The sample mean is [tex]\= x = 442 \ g[/tex]
The standard deviation is [tex]\sigma = 20[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 445[/tex]
The alternative hypothesis [tex]H_a : \mu < 445[/tex] (This is the original claim )
For f(x) = 3х – 5 and g(x) = х2+ 2, find (f+ g)(x).
ОА. ? + 3х – 7
ОВ. 3х2 – 30
Ос. 3х3 – 3
OD. х2 + 3х - з
Answer:
x^2 +3x -3
Step-by-step explanation:
f(x) = 3х – 5
g(x) = х^2+ 2,
(f+g)(x) = 3х – 5 +х^2+ 2
Combine like terms
= x^2 +3x -3
Factor 4x^2-22x+30.
Answer:
4x^2-22x+30
=2(2x^2 - 11x + 15)
=2(2x^2 -6x -5x +15)
= 2 { 2x(x-3) - 5(x-3) }
= 2 (x-3) (2x - 5)
Step-by-step explanation:
Hey, there!!!
The answer is option B
here, we have;
=4x^2-22x+30
=4x^2-(10+12)x+30
= 4x^2-10x-12x+30
now, taking common,
=2x(2x-5) -6(2x-5)
= 2(x-3)(2x-5).
Hope it helps
What do we use mathematical induction for?
proving statements!
it's the very definition of it
Help Please. I will Give Brainliest.
Answer:
1/2
Step-by-step explanation:
● 1/4 + 4(1/2 - 3/4 )^2
To make it easier convert the fractions to decimal numbers.
● 1/4 = 0.25
● 1/2 = 0.5
● 3/4 = 0.75
So the expression will be:
● 0.25 + 4(0.5 - 0.75)^2
Calculte first 0.5-0.75 (0.5-0.75= -0.25)
● 0.25 + 4 × (-0.25)^2
-0.25^2 is the same as 0.25^2
● 0.25 + 4 × (0.25)^2
0.25^2 is 0.0625
● 0.25 + 4×0.0625
Multiplication has the priority (4 ×0.0625) wich is 0.25
● 0.25 + 0.25
● 0.5
0.5 is 1/2
So the answer 1/2
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4}+4(\frac{1}{2}-\frac{3}{4})^2\\\frac{1}{4}+4(\frac{2-3}{4})^2\\\frac{1}{4}+4(\frac{-1}{4})^2\\\frac{1}{4}+4(\frac{1}{16})\\\frac{1}{4}+\frac{1}{4}=\frac{2}{4}=\frac{1}{2}[/tex]
Which of the following is NOT a property of a paralleogram? * The opposite sides are equal. The opposite angles are equal. Each diagonal bisects the parallogram. The diagonals of all parallograms bisect each other at 90 degree angles. I will give brainliest
Answer:
The diagonals of all parallelograms do not bisect each other at 90 degree angles.
Step-by-step explanation:
solve for x: 7^2x+3 =2401 . show substitution of your solution to verify the equation. show steps. show work.
Answer:
X= 1/2
Step-by-step explanation:
7^2x+3 =2401
7^(2x+3 )=2401
7^(2x+3 )= 7^4
Taking away the base because its equal to 7
Then solving the power as an equation
2x+3= 4
2x= 4-3
2x= 1
X=1/2
Now substituting x into the equation to know if we are correct
7^(2x+3 )=2401
Where x= 1/2
7^(2*(1/2) +3)= 7^4
7^(1+3)= 7^4
7^4= 7^4
7^4= 2401
Please Help me solve it!
Answer:
C. $4.12
Step-by-step explanation:
From 9 a.m. to noon, it's 3 hours.
From noon to 4 p.m. it's 4 hours.
Total rental time: 3 hours + 4 hours = 7 hours
Total rental cost: $28.84
rental cost per hour = (rental cost)/(number of hours)
rental cost per hour = $28.84/(7 hours) = $4.12/hour
MY
A circle with radius of 5 cm sits inside a 11 cm x 11 cm rectangle.
Col
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
MY
11 cm
Pro
Pro
Теа
5 cm
11 cm
cm2
2 of 4 OOO
Help
Step-by-step explanation:
Hi, there!!!
According to the question we must find the area of shaded region, but we must find area of circle and rectangle to find area of shaded region,
So, let's simply work with it,
Firstly, finding the area of rectangle,
length = 11cm.
breadth = 11cm.
now, area= length× breadth.
or, a = 11cm× 11cm.
a= 121cm^2
Now, let's work out the area of circle.
radius= 5cm
and pi. = 3.14 {using pi value as 3.14}
now,
area of a circle = pi× r^2
or, a= 3.14×5^2
or, a = 78.5 cm^2.
Therefore, The area of a circle is 78.5cm^2.
Now lastly finding the area of shadedregion,
area of shaded region = area of rectangle - area of circle.
or, area of shaded region = 121cm^2 - 78.5cm^2
Therefore, the area of shaded region is 42.5 cm^2.
Hope it helps...
