Answer:
Reject H0
Step-by-step explanation:
Z = -2.474873734
survey (positive) 26
n (total) 200
p 0.2
p /point est. 0.13
POPULATION(min) 4000
np >= 5 ? YES 40
n(1-p) >= 5 ? YES 160
Sample is valid
Confidence Level - "P" values
99% 2.58
Confidence Interval - "P" values
(0.0686 , 0.1914 )
Reference=0.2 Reject H0
The daily production of electronic motors at a certain factory averaged 120 with a variance of 100. The fraction of days that will have production levels between 100 and 140 assuming doubt about the normality of the data is
In a residual plot against x that does NOT suggest we should challenge the assumptions of our regression model, we would expect to see a _____. a. parabolic band of points b. band of points having a slope consistent with that of the regression equation c. horizontal band of points centered near 0 d. widening band of points
Answer:
In a residual plot against x that does NOT suggest we should challenge the assumptions of our regression model, we would expect to see a _____.
c. horizontal band of points centered near 0
Step-by-step explanation:
This residual graph or plot shows the residual values (or the difference between the observed y-value (from scatter plot) and the predicted y-value (from regression equation line) on the vertical axis and displays the independent variable on the horizontal axis. A linear regression model becomes appropriate for a dataset when the points are randomly dispersed around the horizontal axis near 0; otherwise, a nonlinear model becomes more appropriate.
find the value of the trigonometric ratio. make sure to simplify the fraction if needed
Answer:
Cos C = a/h
= 21/35
Step-by-step explanation:
since cos is equal to adjacent angle over hypotenuse angle, so from the question we conclude Cos C = 21/35
(b) An economy has an agricultural industry and a textile industry. Each unit of agricultural output requires 0.4 unit of agricultural input and 0.1 unit of textiles input. Each unit of textiles output requires 0.1 unit of agricultural input and 0.2 unit of textiles input.
(i) Write the technology matrix for this economy. [2 marks]
(ii) If surpluses of 5 units of agricultural products and 195 units of textiles are desired, find the gross production of each industry
Leontief input output model (technology matrix) is an economic model that shows the quantitative relationship and sectorial interdependency in a national economy
The responses with regards to the question are;
(i) The technology matrix for the economy is presented as follows;
[tex]\mathbf{ A} =\left[\begin{array}{ccc}Agric&&Textile\\0.4&&0.1\\&&\\0.1&&0.2\end{array}\right] \begin{array}{ccc}\mathbf{Per \ Unit}\\Agriculture\\\\Textile\end{array}\right][/tex]
(ii) The required gross production of each industry to meet the desired surplus are;
50 units of agriculture and 250 units of textile
The reason the above values are correct is as follows:
(i) The given parameters are;
The industries in the economy = Agricultural industry and textile industry
Units of agricultural input required per unit of agricultural output = 0.4
Units of textile input required per unit of agricultural output = 0.1
Units of agricultural input required per unit of textile output = 0.1
Units of textile input required per unit of textile output = 0.2
Let X represent agriculture, and let Y represent textile, we have;
[tex]Agric \ for \ agric = \dfrac{0.4 \ units \ of \ agriculture}{1\ unit \ of \ agric \ produced} \times X \ Agric \ produced= 0.4 \cdot X[/tex]
[tex]Agric \ for \ textile = \dfrac{0.1 \ units \ of \ agriculture}{1\ unit \ of \ textile \ produced} \times Y \ textile \ produced= 0.1 \cdot Y[/tex]
We also have;
Textile for agriculture = 0.1·X
Textile for textile = 0.2·Y
Therefore;
X = 0.4·X + 0.1·Y
Y = 0.1·X + 0.2·Y
Therefore;
The technology matrix for the economy is presented as follows;
[tex]\mathbf{Technology \ matrix, A} =\left[\begin{array}{ccc}Agric&&Textile\\0.4&&0.1\\&&\\0.1&&0.2\end{array}\right] \begin{array}{ccc}\mathbf{Per \ Unit}\\Agriculture\\\\Textile\end{array}\right][/tex]
(ii) Let P represent the production vector, and let d represent the demand vector, we have;
[tex]P = \left[\begin{array}{c}X \\Y\end{array}\right][/tex], [tex]d = \left[\begin{array}{c}5 \\195\end{array}\right][/tex]
P = A·P + d
∴ P - A·P = d
Therefore;
[tex]P = \mathbf{ \dfrac{d}{(I - A)}}[/tex]
Where I = The 2 by 2 identity matrix
We get;
[tex]I - A =\left[\begin{array}{ccc}1&&0\\&&\\0&&1\end{array}\right] - \left[\begin{array}{ccc}0.4&&0.1\\&&\\0.1&&0.2\end{array}\right] = \mathbf{\left[\begin{array}{ccc}0.6&&-0.1\\&&\\-0.1&&0.8\end{array}\right]}[/tex]
With the use of a graphing calculator, we have;
[tex]P =\left[\begin{array}{c}X \\Y\end{array}\right] = \dfrac{\left[\begin{array}{c}5 \\195\end{array}\right]}{\left[\begin{array}{ccc}0.6&&-0.1\\&&\\-0.1&&0.8\end{array}\right]} = \left[\begin{array}{ccc}50\\\\\ 250\end{array}\right][/tex]
The required gross product of agriculture, X = 50 units
The required gross product of textile, Y = 250 units
Learn more about the Leontief input output model here:
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We have that he technology matrix for this economy and the the gross production of each industry are
a) [tex]X= \begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}[/tex]
b) [tex]\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}50\\250\end{vmatrix}[/tex]
From the Question we have told that
Each unit of agricultural output requires 0.4 unit of agricultural input
Each unit of agricultural output requires 0.1 unit of textiles input.
Each unit of textiles output requires 0.1 unit of agricultural input
Each unit of textiles output requires 0.2 unit of textiles input.
Generally the technology matrix for this economy is given below
With
X =Agricultural industry Gross output
Y= Textile industry Gross Output
Therefore
[tex]X= \begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}[/tex]
b)
From the Question we are told that
Surpluses of 5 units of agricultural products and 195 units of textiles are desired.
Therefore, we have Desired surplus matrix of
[tex]D= \begin{vmatrix}5\\195\end{vmatrix}[/tex]
Generally the Technology equation is mathematically given as
[tex](I-X)\phi=D[/tex]
Where
X =Agricultural industry Gross output
I=A Unit matrix
\phi=Matrix of gross production
Therefore
[tex]\begin{vmatrix}1 & 0\\0 & 1\end{vmatrix}-(\begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}))\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}5\\195\end{vmatrix}[/tex]
[tex]\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}50\\250\end{vmatrix}[/tex]
In conclusion
The technology matrix for this economy and the the gross production of each industry are
[tex]X= \begin{vmatrix}0.4 & 0.1 \\0.1 & 0.2\end{vmatrix}[/tex]
[tex]\begin{vmatrix}A\\T\end{vmatrix}=\begin{vmatrix}50\\250\end{vmatrix}[/tex] Respectively
In conclusion
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A manufacturer claims that its drug test will detect steroid use (that is, show positive for an athlete who uses steroids) 95% of the time. Further, 15% of all steroid-free individuals also test positive. 10% of the rugby team members use steroids. Your friend on the rugby team has just tested positive. The correct probability tree looks like
Answer:
The probability tree is;
0.95 [tex](+)[/tex]
[tex](S)[/tex]
0.1 0.05 [tex](-)[/tex]
[ P ]
0.9 0.15 [tex](+)[/tex]
[tex](S_{no})[/tex]
0.85 [tex](-)[/tex]
Step-by-step explanation:
Given the data in the question;
10% of the rugby team members use steroids
so Probability of using steroid; P( use steroid ) = 10% = 0.10
Probability of not using steroid; P( no steroid use ) = 1 - 0.10 = 0.90
Since the test show positive for an athlete who uses steroids, 95% of the time.
Probability of using steroids and testing positive = 95% = 0.95
Probability of using steroids and testing Negative = 1 - 0.95 = 0.05
Also from the test, 15% of all steroid-free individuals also test positive.
so
Probability of not using steroids and testing positive = 15% = 0.15
Probability of not using steroids and testing negative = 1 - 0.15 = 0.85
To set up the probability tree, Let;
[tex](S)[/tex] represent steroid use
[tex](S_{no})[/tex] represent no steroid use
[tex](+)[/tex] represent test positive
[tex](-)[/tex] represent test negative
so we have;
0.95 [tex](+)[/tex]
[tex](S)[/tex]
0.1 0.05 [tex](-)[/tex]
[ P ]
0.9 0.15 [tex](+)[/tex]
[tex](S_{no})[/tex]
0.85 [tex](-)[/tex]
What is the slope-intercept equation of the line below?
10 minutes left
Answer:
y=-3x+4
Step-by-step explanation:
The y intercept is 4 because the line crosses the y axis at the 4 tic mark
The slope will be -3 because the y decreases by 3 every time the x incerases by 1
y=mx+b
y=-3x+4
A research center poll showed that 76% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?
Answer:
6/25
Step-by-step explanation:
P(have belief) =76/100 = 19/25
P (does not have belief) = 1-19/25 = 6/25
Which is a perfect square?
6’1
6’2
6’3
6’5
Answer:
6'2
Step-by-step explanation:
Fill in the blanks.
(3b^3)^2 = _b^_
We can seperate (3b³) into two different parts, the constant and the variable.
The constant (3) and the variable (b) can both be squared and multiplied to get the correct answer, so:
3² = 9
(b³)² = [tex]b^{6}[/tex]
So, [tex](3b^{3})^{2} = 9b^{6}[/tex]
Find the final amount of money in an account if $7, 200 is deposited at 2.5 % interest compounded
quarterly (every 3 months) and the money is left for 9 years.
The final amount is $
Round answer to 2 decimal places
The final amount is $7,615.27
A = P(1 + r/n)^t
Where,
A = Final amount
P = principal = $7, 200
r = interest rate = 2.5% = 0.025
n = number of periods = 4
t = time = 9 years
A = P(1 + r/n)^t
= 7,200(1 + 0.025/4)^9
= 7,200(1 + 0.00625)^9
= 7,200(1.00625)^9
= 7,200(1.0576769512798)
= 7,615.2740492152
Approximately,
A = $7,615.27
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Let h(x)=20e^kx where k ɛ R (Picture attached. Thank you so much!)
Answer:
A)
[tex]k=0[/tex]
B)
[tex]\displaystyle \begin{aligned} 2k + 1& = 2\ln 20 + 1 \\ &\approx 2.3863\end{aligned}[/tex]
C)
[tex]\displaystyle \begin{aligned} k - 3&= \ln \frac{1}{2} - 3 \\ &\approx-3.6931 \end{aligned}[/tex]
Step-by-step explanation:
We are given the function:
[tex]\displaystyle h(x) = 20e^{kx} \text{ where } k \in \mathbb{R}[/tex]
A)
Given that h(1) = 20, we want to find k.
h(1) = 20 means that h(x) = 20 when x = 1. Substitute:
[tex]\displaystyle (20) = 20e^{k(1)}[/tex]
Simplify:
[tex]1= e^k[/tex]
Anything raised to zero (except for zero) is one. Therefore:
[tex]k=0[/tex]
B)
Given that h(1) = 40, we want to find 2k + 1.
Likewise, this means that h(x) = 40 when x = 1. Substitute:
[tex]\displaystyle (40) = 20e^{k(1)}[/tex]
Simplify:
[tex]\displaystyle 2 = e^{k}[/tex]
We can take the natural log of both sides:
[tex]\displaystyle \ln 2 = \underbrace{k\ln e}_{\ln a^b = b\ln a}[/tex]
By definition, ln(e) = 1. Hence:
[tex]\displaystyle k = \ln 2[/tex]
Therefore:
[tex]2k+1 = 2\ln 2+ 1 \approx 2.3863[/tex]
C)
Given that h(1) = 10, we want to find k - 3.
Again, this meas that h(x) = 10 when x = 1. Substitute:
[tex]\displaystyle (10) = 20e^{k(1)}[/tex]
Simplfy:
[tex]\displaystyle \frac{1}{2} = e^k[/tex]
Take the natural log of both sides:
[tex]\displaystyle \ln \frac{1}{2} = k\ln e[/tex]
Therefore:
[tex]\displaystyle k = \ln \frac{1}{2}[/tex]
Therefore:
[tex]\displaystyle k - 3 = \ln\frac{1}{2} - 3\approx-3.6931[/tex]
Given: 3x+11=y, solve for x if y = 29
answer is 6
Step-by-step explanation:
3x+11=y
y=29
3x+11=29
3x=29-11
3x=18
x=18÷3
x=6
Answer:6
Step-by-step explanation:
3x+11=29
3x=29-11
3x=18
X=18/3
X=6
I need help with this question!
Help please. For the hign school basketball game, it costs $8 for every 4 tickets. Complete the table below showing the cost and the number of tickets.
Answer:
$2 for 1 ticket, 7 tickets for $14, $18 for 9 tickets, 10 tickets for $20
Step-by-step explanation:
Since we know that it $8 for 4 tickets, we can simplify the ratio down to 2:1, meaning that each ticket is $2.
You're welcome and good luck with your classes young one
PLEASE HELP ASAP
Solve the inequality [tex]\sqrt[3]{x+4} \ \textgreater \ \sqrt[2]{-x}[/tex]
A) x < 2
B) x > 2
C) x > –2
D) x < –2
The 4th of an AP is 15 and the 9th term is 35. find the 15th term
Consecutive terms in this sequence are separated by a constant c, so if the 4th term is 15, then the next terms would be
5th: 15 + c
6th: (15 + c) + c = 15 + 2c
7th: (15 + 2c) + c = 15 + 3c
and so on. More generally, since any given number in the sequence depends on the number that came before it, we can write the n-th term in terms of the 4th term,
n-th: 15 + (n - 4) c
Then the 9th term in the sequence is
15 + (9 - 4) c = 35
and solving for c gives
15 + 5c = 35 ==> 5c = 20 ==> c = 4
Then the 15th term would be
15 + (15 - 4)×4 = 15 + 11×4 = 15 + 44 = 59
Hey community I thank you guys fir your help
Answer:
A, B, and E.
Step-by-step explanation:
A. 5^x * 5^x
= 5^x+x
=5^(2)(x)
=25^x
B. 5^2x
=5^(2)(x)
=25^x
C. 5*5^2x
=5^1+2x
D. 5*5^x
=5^1+x
E. (5*5)^x
=5^x*5^x
=5^(2)(x)
=25^x
F. 5^2*5^x
=5^2+x
5765865876+5737555586=
Answer:
5765865876+5737555586=11503421462
How many natrual numbers in between 68 and 145
Answer:
76 natural number not including the first
Hope this helps <3 Comment if you want more thanks and be sure to give brainliest (4 left) <3
There are 78 natural numbers between 68 and 145.
What are the Natural numbers?The Natural numbers are defined as it used for counting and are a component of the number system, which includes all positive integers from 1 to infinity. It does not include zero (0).
The set of natural numbers includes only the positive integers, i.e., 1, 2, 3, 4, 5, 6, ……….∞.
Sum of natural numbers are n(n+1)/2
Sn = n(n+1)/2
Hence, this is the formula to calculate sum of 'n' natural numbers.
Given that numbers are 68 and 145
We will start counting from 68 to 144
Number of natural numbers between 68 and 145 = (144 - 67)+1
Number of natural numbers between 68 and 145= 77 +1
Number of natural numbers between 68 and 145 = 78
Hence, there are 78 natural numbers between 68 and 145.
Learn more about Natural numbers here:
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11. The unit digit in the expression (31 + 132 + 143 + 414 + 515 +156 + 61) i (A) 4 (B) 3 (C) 2 . (D) 1
Answer:
Step-by-step explanation:
[tex]we \ add \ \ only \ \ units \ we \ do \ not \ need \ the \ rest \\\\ \bf (3\underline 1 + 13\underline2 + 14\underline3 + 41\underline4 + 51\underline5 +15\underline6 + 6\underline1)= \\\\ 1+2+3+4+5+6+1=2\underline 2 \\\\ Answer: C) \ 2[/tex]
HELP ASAP PLEASE I WILL MARK BRAINLEST
Show all work to identify the asymptotes and zero of the function f of x equals 6 x over quantity x squared minus 36.
Answer:
vertical asymptotes
x=6, x=-6
horizontal asymptotes
y=0
zeros (0,0)
Step-by-step explanation:
f(x) = 6x / ( x^2 - 36)
First factor
f(x) = 6x / ( x-6)(x+6)
Since nothing cancels
The vertical asymptotes are when the denominator goes to zero
x-6 = 0 x+6=0
x=6 x= -6
Since the numerator has a smaller power than the denominator (1 < 2), there is an asymptote at y = 0
To find the zeros, we find where the numerator = 0
6x=0
x=0
[tex]\\ \rm\Rrightarrow y=\dfrac{6x}{x^2-36}[/tex]
The h orizontal asymptote
As x has less degree than x²
y=0 is a asymptoteVertical asymptote
x²-36=0x²=36x=±6Add the first 12 terms of this sequence:
15, 45, 135, 405, 1215, ...
Answer:
Step-by-step explanation:
a₁ = 15
a₂/a₁ = 45/15 = 3
a₃/a₂ = 135/45 = 3
...
It is a geometric sequence with a common ratio r=3.
Sum of first 12 terms = a₁·(1-r¹²)/(1-r)
= 15·(1-3¹²)/(1-3)
= 15·(-531,441)/(-2)
= 3,985,800
There are 768 beds in a hospital.
Each floor has 64 beds.
How many floors are there?
Answer:
12 floors
Step-by-step explanation:
768 ÷ 64 = 12.
Answer:
12
Step-by-step explanation:
768 divided by 64 =12
if x+y=2 and x=4 then x+2y
Anna earned $9 an hour babysitting. She wants
to buy a 16 GB iPod that is $120. Anna has
saved $45 so far. How many more hours of
babysitting does she need to do to earn the rest
to purchase the iPod
Answer:
8.33 hours
Step-by-step explanation:
120-45 = 75
75 ÷ 9 = 8.33
create a graph of 4.95 + 3.99
Answer:
????
Step-by-step explanation:
as in y = 4.95 + 3.99 or points? if so just draw a horizontal line at 8.94
Train X traveled 216.6 kilometers in 38 minutes. How many miles per hour was it traveling?
Answer:
210 miles in 1 hour
Step-by-step explanation:
steps are in picture
Mike wants to buy a scooter worth R10000 but cannot afford so he opts for the hire purchase agreement which requires a 13% deposit and a 24 equal monthly installments at a rate of 15% per annum compounded monthly
A.How much will his deposit be?
B.calculate how much does he still need to pay after the deposit
C.calculate the monthly installment
Answer: I think the answer is A
Step-by-step explanation:
Find x.
60°
45°
6
—————
Answer:
Step-by-step explanation:
13 is subtracted from the product of 4 and a certain number. The result is equal to the sum of 5 and the original number. Find the number.
Answer:
The number is 6.
Step-by-step explanation:
[tex]4x-13=x+5\\3x-13=5\\3x=18\\x=6[/tex]