Answer:
Suppose a problem of the form:
A person can choose:
1 out of 2 pants (red or blue)
1 out of 2 shirts (red or blue)
1 out of 2 pairs of shoes (red or blue)
1 out of 2 socks (red or blue)
1 out of 2 hats (red or blue)
Ok,
We have 5 selections with 2 options each, so the number of combinations is:
2^5
Now let's add another restriction, the person can not wear all red clothes, the person must have at least one blue one.
So we removed the combination where the person selects all red clothes, which means that we removed one combination.
So now, the total number of possible combinations is the number that we got before minus one:
2^5 - 1
Notice that subtracting the one is necessary, we first use the math that we know to find the total number of combinations and then we look at the restrictions to remove the restricted combination.
Then the complete problem is:
A person can choose:
1 out of 2 pants (red or blue)
1 out of 2 shirts (red or blue)
1 out of 2 pairs of shoes (red or blue)
1 out of 2 socks (red or blue)
1 out of 2 hats (red or blue)
And the person can not wear all red clothes, the person must have at least one blue one.
How many different combinations there are?
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
Alice wants to estimate the percentage of people who plan
on voting yes for the upcoming school levy. She surveys
380 individuals and finds that 260 plan on voting yes.
Identify the values needed to calculate a confidence interval
at the 90% confidence level. Then find the confidence interval.
zo10 z0.05 zo.025 zo01 z0.005
1.282 1.645 1.960 2.326 2.576
Use the table of common z-scores above.
Answer:
"[tex]0.6450 < p < 0.723[/tex]" is the right solution.
Step-by-step explanation:
Given:
n = 380
x = 260
Point estimate,
[tex]\hat p = \frac{x}{n}[/tex]
[tex]=\frac{260}{380}[/tex]
[tex]=0.6842[/tex]
Critical value,
[tex]Zc = 1.645[/tex]
Standard error will be:
[tex]S.E = \sqrt{\frac{0.6842(1-0.6842)}{380} }[/tex]
[tex]=0.0238[/tex]
Margin of error will be:
[tex]E = Zc\times S.E[/tex]
[tex]=1.645\times 0.0238[/tex]
[tex]=0.0392[/tex]
hence,
Confidence level will be:
= [tex]\hat p \pm E[/tex]
= [tex]0.6842 \pm 0.0392[/tex]
= [tex]0.6450 < p < 0.723[/tex]
Tính tích phân sau bằng cách dùng tọa độ cực I=∫∫ [tex]\frac{1}{\sqrt{x^{2} +y^{2} } }[/tex]dxdy R là miền nằm trọg góc phần tư thứ nhất thỏa mãn 4[tex]\leq x^{2} +y^{2} \leq 9[/tex]
It sounds like R is the region (in polar coordinates)
R = {(r, θ) : 2 ≤ r ≤ 3 and 0 ≤ θ ≤ π/2}
Then the integral is
[tex]\displaystyle \iint_R\frac{\mathrm dx\,\mathrm dy}{\sqrt{x^2+y^2}} = \int_0^{\pi/2}\int_2^3 \frac{r\,\mathrm dr\,\mathrm d\theta}{\sqrt{r^2}} \\\\ = \int_0^{\pi/2}\int_2^3 \mathrm dr\,\mathrm d\theta \\\\ = \frac\pi2\int_2^3 \mathrm dr \\\\ = \frac\pi2r\bigg|_2^3 = \frac\pi2 (3-2) = \boxed{\frac\pi2}[/tex]
Abigail buys two cartons of strawberries. One carton has 191919 berries and the other carton has 262626 berries. She wants to divide the berries into bags so there are exactly 666 berries in each bag.
How many bags will have 666 berries?
Answer:
682
Step-by-step explanation:
191,919 + 262,626
454545 ÷ 666 = 682.5
Thus meaning 682 bags will have 666 berries and one bag will have 333 berries.
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
Zoe earns 22.50 per hour plus 3% commission on sales. last week she worked 34 hours and made sales totalling 15280. Calculate her pay for the week.
Answer: $1,223.40.
Step-by-step explanation:
Since she earns $22.5 per hour, for 34 hours, she would earn:
$22.5 × 34 = $765
She earn 3% of her sales, therefore find 3% of $15,280:
$15280(3%) = $15280(0.03) = $458.4
Add them together:
$765 + $458.4 = $1223.4
9514 1404 393
Answer:
$1,223.40
Step-by-step explanation:
Zoe's total pay is the sum of the products of hours and hourly rate, and sales and commission rate.
Pay = (34 h)($22.50/h) +($15,280)(.03) = $765.00 +458.40
Pay = $1,223.40
Zoe's pay for the week is $1,223.40.
(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:
https://brainly.com/question/15417573
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
https://brainly.com/question/16863924
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
When f(x) =-3 what is x?
Answer:
D or -1
Step-by-step explanation:
It says that f(x) is equal to -3.
f(x) is the same as y-values, and x is the same as the x-values on a coordinate grid because x is the independent variable, meaning y is the dependent variable, where f(x) depends on the value of x to find y.
So if y is -3, it can be found on the graph on the 4th line, so x = -1 when y = -3
51.Tandin Dorji was married to five women. First woman had three
daughters and five sons and the youngest wife had two sons. Two
of the remaining wives had one son each. If the ratio of children of
5th wife was 1:3 with the children of other wives. How many
children does Tandin have
Answer:
Tandin has 16 children.
Step-by-step explanation:
Total of children:
3+5 = 8(first woman)
2(youngest wife)
1 + 1 = 2(two of the remaining wives)
So
8 + 2 + 2 = 12
If the ratio of children of 5th wife was 1:3 with the children of other wives.
Thus the 5th wife has 12/3 = 4 children.
How many children does Tandin have?
12 + 4 = 16
Tandin has 16 children.
Louise has a hard time keeping her workspace clean at her job. She tries, but it just ends up getting messy again. Which of the following is a likely outcome of her consistent messiness? a) She will have fewer safety issues. b) She will feel more productive. c) Customers will think she is very busy. d) She will have a hard time focusing.
Aaron Lloyd what is a?
Answer:
Rugby lawyer
Step-by-step explanation:
Aaron is a partner in the firm’s dispute resolution division. He advises clients on a range of litigious and risk related matters, with particular expertise in the areas of corporate misconduct, white collar criminal and regulatory affairs, sports law and employment law. Aaron leads our sports law practice, and is a member of the firm’s health and safety, public law, and organisational integrity teams.
Well regarded by clients for his ability to analyse and strategise complex situations, Aaron is internationally recognised for his ability to implement pragmatic and commercial strategies to minimise risk and create opportunity. This ability has resulted in clients avoiding significant litigation and commercial consequences.
Aaron is an experienced advocate, having argued cases in the District Court, High Court, Employment Court, the Court of Appeal and Supreme Court of New Zealand, along with numerous tribunals.
He is recognised by international legal directories including by Chambers & Partners (Asia Pacific), Who’s Who Legal, Expert Guides, Best Lawyers and Doyles.
Before joining MinterEllisonRuddWatts Aaron practiced as a barrister with Paul Davison QC, and has lectured at the University of Auckland.
Given a sphere with radius r, the formula 4 r2 gives
O A. the volume
O B. the surface area
O c. the radius
O D. the cross-sectional area
Answer: surface area
Step-by-step explanation:
Add 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
Big sleds must hold 3 children and small sleds must hold 2 children. If 17 children want to go sledding at the same time, how many of each type of sled is needed?
Answer:
5 big sleds and 1 small sled
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
Cho hình hộp chữ nhật ABCD A B C D
Answer:
A B C D
A×B×C×D
3×3×3×6
162
Help me solve the question in picture
9514 1404 393
Answer:
√5 +√6
Step-by-step explanation:
We know that the square of a binomial is ...
(a +b)^2 = a^2 +2ab +b^2
Then the square root of it is ...
a + b = √(a^2 +b^2 +2ab)
Using a=√x and b=√y, this is ...
√x +√y = √(x + y + 2√(xy))
__
For the given expression, we need to find x and y such that ...
xy = 30 and x+y = 11
Using x=5, y=6, we meet those requirements.
[tex]\displaystyle \sqrt{11+2\sqrt{30}}=\sqrt{5+6+2\sqrt{5\cdot6}}=\boxed{\sqrt{5}+\sqrt{6}}[/tex]
Answer:
√5+√6 ≈ 4.68555772
Step-by-step explanation:
I hope it's correct
Can you please help me
Answer: 1/6
Step-by-step explanation:
Given:
4/9 and 11/18
Solve:
STEP ONE: Make the denominators equal by determining the LCM
LCM = Least Common Multiple
First Five multiples of 9 = 9, 18, 27, 36, 45
First FIve multiples of 18 = 18, 36, 54, 72, 90
As we can see from the list above, both 18 and 36 overlap, however, 18 is less than 36. Therefore, 18 is the LCM.
STEP TWO: Compare the size and determine the greater one.
4/9 = (4 × 2) / (9 × 2) = 8/18
11/18 = 11/18
Since 11 > 8, therefore, 11/18 is greater than 8/18
STEP THREE: Find the difference between the two fractions.
11/18 - 4/9
=11/18 - 8/18
=(11 - 8) / 18
= 3 / 18
= 1/6
Hope this helps!! :)
Please let me know if you have any questions
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
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 the lengths the missing side
Answer:
Short leg = x
Longer leg = 12
Hypotenuse = y
Short leg = 4√3
longer leg = 12
Hypotenuse = 8√3
Answered by GAUTHMATH
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]
A canoeist paddled down a river a distance of 2 miles in 45 minutes. Paddling up-stream on his return, it took him 90 minutes. Find the rate of the canoe in still water.
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]
Manatees can swim in water up to 20 feet deep. Write an expression that represents the depth d, that a manatee can swim
Answer:
0 ≤ d ≤ 20
Step-by-step explanation:
You mention that Manatees can swim in water up to 20 feet deep. So, this means that the largest depth that he can swim is 20 feet, not more than this. Also, keep in mind that the depth can't be negative, so ----> 0 ≤ d ≤ 20 feet
We want to write an expression (an inequality actually) that defines the depth at which a manatee can swim. The inequality is: 0ft ≤ d ≤ 20ft.
We know that the manatees can swim in water up to 20 feet deep. This represents the maximum deep at which manatees can swim, the minimum is trivial, it would be 0ft (when the manatees are on the surface of the water).
Then we can write the inequality:
0ft ≤ d ≤ 20ft.
This gives the range of possible values of d, depth at which the manatee can swim.
If you want to learn more, you can read:
https://brainly.com/question/17675534
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]
Describe what is the most difficult part of solving equations, for you personally.
What do you personaly feel like is most dificult.
For me its rembering minus signs
Which is a perfect square?
6’1
6’2
6’3
6’5
Answer:
6'2
Step-by-step explanation:
If(a²-1) x²+(a-1)x+a²-4a+3=0 is an identity in x, then find the value of a
Answer:
Step-by-step explanation:
[tex](a^2-1)x^2+(a-1)x+a^2-4a+3=0\\\\Calculate\ and\ identify\ the\ polynomials\\\\\Longleftrightarrow\ a^2x^2-x^2+ax-x+a^2-4a+3=0\\\\\Longleftrightarrow\ a^2x^2+ax+a^2-4a+3=x^2+x+0\\\\\Longleftrightarrow\ \left\{\begin{array}{ccc}a^2&=&1\\a&=&1\\a^2-4a+3&=&0\\\end{array} \right.\\\\\Longleftrightarrow\ \left\{\begin{array}{ccc}(a-1)(a+1)&=&0\\a-1&=&0\\(a-1)(a-3)&=&0\\\end{array} \right.\\\\\\We\ must\ exclude\ a=-1\ and\ a=3\ (not\ solution)\\\Longrightarrow\ a=1\\[/tex]
