The null hypothesis and the alternate hypothesis are: H0: The frequencies are equal. H1: The frequencies are not equal. Category f0 A 10 B 30 C 30 D 10 State the decision rule, using the 0.05 significance level. (Round your answer to 3 decimal places.) Compute the value of chi-square. (Round your answer to 2 decimal place.) What is your decision regarding H0

Answer:

0.0005m^3

Step-by-step explanation:

V=1/3hπr²

h=6m

d=12m

r=12÷2=6m

V=1/3×6×(3.14)×36

V=1/2034.72

V=0.0005m^3

Answer:

The standard deviation of your weight over a day is of 1.1547 pounds.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b, and the standard deviation is:

[tex]S = \sqrt{\frac{(b-a)^2}{12}}[/tex]

Assume that the changes in water weight is uniformly distributed between minus two and plus two pounds in a day.

This means that [tex]a = -2, b = 2[/tex]

What is the standard deviation of your weight over a day?

[tex]S = \sqrt{\frac{(2 - (-2))^2}{12}} = \sqrt{\frac{4^2}{12}} = \sqrt{\frac{16}{12}} = 1.1547[/tex]

The standard deviation of your weight over a day is of 1.1547 pounds.

Answer:

8.33 hours

Step-by-step explanation:

120-45 = 75

75 ÷ 9 = 8.33

Answer:

Devaughn = 31, Sydney = 25

Step-by-step explanation:

(56-6)÷2= 25

So they would both be 25 if they were the same age but Devaughn is 6 years older so 25+6=31

ATQ

[tex]\\ \sf\longmapsto x+x+6=56[/tex]

[tex]\\ \sf\longmapsto 2x+6=56[/tex]

[tex]\\ \sf\longmapsto 2x=56-6[/tex]

[tex]\\ \sf\longmapsto 2x=50[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{50}{2}[/tex]

[tex]\\ \sf\longmapsto x=25[/tex]

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]

Answer:

Hello,

Answer : 1400 and 1575

Step-by-step explanation:

Let's say a and b the ywo numbers

[tex]HCF(a,b)=a\vee b=175=5^2*7\\LCM(a,b)=a\wedge b=12600\\\\a*b=(a\vee b)*(a\wedge b)=(2^3*3^2*5^2*7)*(5^2*7)=2^3*3^2*(5^2*7^2)^2\\\\Both\ numbers\ are\ greater\ than\ their HCF\\a=175*k_1\\b=175*k_2\\\\k_1=2^3\ and\ k_2=3^2\\\\a=175*2^3=1400\\b=175*3^2=1575\\\\[/tex]

9514 1404 393

Answer:

  5.423 miles

Step-by-step explanation:

Let x represent the distance to run. Then the remaining distance to the point that is closest to the island is (6-x) miles. The straight-line distance (d) to the point x from the island is given by the Pythagorean theorem:

  d² = 1² +(6 -x)² = x² -12x +37

  d = √(x² -12x +37)

The total travel time is the sum of times running and swimming. Each time is found from ...

  time = distance/speed

  total time = x/4 + d/2 = x/4 +(1/2)√(x² -12x +37)

__

The total time will be minimized when its derivative with respect to x is zero.

  t' = 1/4 +(1/4)(2x -12)/√(x² -12x +37) = 0

Multiplying by 4 and combining fractions, we can see the numerator will be ...

  √(x² -12x +37) +2x -12 = 0

Subtracting the radical term and squaring both sides, we get ...

  4x² -48x +144 = x² -12x +37

  3x² -36x +107 = 0

The quadratic formula tells us the smaller of the two roots is ...

  x = (36 -√(36² -4(3)(107)))/(2(3)) = (36 -√12)/6 ≈ 5.423 . . . mi

You should run 5.423 miles west to minimize the time needed to reach the island.

__

A graphing calculator solves this nicely. The attached graph shows the time is a minimum when you run 5.423 miles.

Answer:

$11.25

Step-by-step explanation:

Total money given to the taxi driver=36+25% of 36=45

Each person will pay (45/4)=11.25

Answer:

–81

Step-by-step explanation:

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]

Answer: I think the answer is A

Step-by-step explanation:

Answer:

(2,-1)

Step-by-step explanation:

Solved using math.

Answer:

The solution is (2, -1) to show this by graphing do y = -1 by making a straight horizontal line at (0,-1) . And then for the other equation make a line where it starts at (0,4) and passes point (2,-1). Just plot those two points and connect them and you'll have made the line.

Step-by-step explanation:

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

The 95% confidence interval of the population mean, in years, is (4.3, 5.3). 4 years is not part of the confidence interval, which means that it contradicts the fact that 39% of students get their college degree in four years.

-----------------------------

To solve this question, we need to find the confidence interval for the amount of time it takes the students to get the degree.

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

-----------------------------

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 80 - 1 = 79

-----------------------------

95% confidence interval

Standard level of confidence, we have to find a value of T, which is found looking at the t table, with 79 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.9905.

-----------------------------

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.9905\frac{2.2}{\sqrt{80}} = 0.5[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

-----------------------------

The lower end of the interval is the sample mean subtracted by M. So it is 4.8 - 0.3 = 4.3 years.

The upper end of the interval is the sample mean added to M. So it is 4.8 + 0.3 = 5.3 years.

-----------------------------

The 95% confidence interval of the population mean, in years, is (4.3, 5.3). 4 years is not part of the confidence interval, which means that it contradicts the fact that 39% of students get their college degree in four years.

A similar question is given at https://brainly.com/question/24278748

Answer:

Step-by-step explanation:

Let's solve your inequality step-by-step.

y - 6 > 2y - 4

y - 2y > -4 + 6

-y > 2

now divide by -1 and inequality sign changes

-y/-1 < 2/-1

y < -2

Answer:

Cluster Sampling

Step-by-step explanation:

Cluster Sampling involves the random sampling of observation or subjects, which are subsets of a population. Cluster analysis involves the initial division of population subjects into a number of groups called clusters . From the divided groups or clusters , a number of groups is then selected and it's elements sampled randomly. In the scenario above, the divison of the population into towns where each town is a cluster. Then, the selected clusters (12) which are randomly chosen are analysed.

Answer:

I don't knowledge bro sorry

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

Answer:

6'2

Step-by-step explanation:

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

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.

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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Answer:

option A

Step-by-step explanation:

wx and zy making 90 angle with each other therefore they are perpendicular.

wx and ab making 0 angle with each other therefore they are parallel

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

Answer:

????

Step-by-step explanation:

as in y = 4.95 + 3.99 or points? if so just draw a horizontal line at 8.94

Answer:

8. -2a+14

9. w=3/2

Step-by-step explanation:

8.

The distributive property states that we can multiply each component in the parenthesis separately by the number on the outside, and then add that up to get our final answer.

For -2(a-7), this means that we can multiply -2 by a and then -2 by -7 (as 2 is the number on the outside, and a and -7 are the components in the parenthesis), add them up, and get our answer. This can be expressed as

-2 * a + (-2) * (-7) = final answer

= -2 * a + 14

We know that -2 * -7 = 14 because 2 * 7 = 14, and the two negatives in multiplication cancel each other out

9.

Using the subtraction property of equality, we can isolate the variable (w) and its coefficient (-2/3) by subtracting 5, resulting in

(-2/3)w = 4-5 = -1

Next, we can use the multiplication property of equality to isolate the w. To isolate the w, we can multiply its coefficient by its reciprocal. The reciprocal is the fraction flipped over. For (-2/3), its reciprocal is (-3/2), flipping the 2 and 3. We can multiply both sides by (-3/2) to get

w = (-3/2)

To check this, we can plug (-3/2) for w in our original equation, so

(-2/3) * (-3/2) + 5 = 4

-1 + 5 = 4

4 = 4

This works!

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]

Answer:

0.05547

Step-by-step explanation:

Given :

_____Peter __ Alan __ Sui__total

Before 1838 __ 418 ___1475 _3731

After _ 1420 __ 329 ___1140_2889

Total _3258 __ 747 __ 2615 _6620

The expected frequency = (Row total * column total) / N

N = grand total = 6620

Using calculator :

Expected values are :

1836.19 __ 421.006 __ 1473.8

1421.81 ___325.994__ 1141.2

χ² = Σ(Observed - Expected)² / Expected

χ² = (0.00177817 + 0.0214571 + 0.000974852 + 0.00229642 + 0.0277108 + 0.00125897)

χ² = 0.05547

Answer:

Step-by-step explanation:

210=2x3x5x7

280=2x2x2x5x7

360=2x2x2x3x3x5

Answer:

210= 2×3×5×7

280=2×2×2×5×7

360=2×2×2×3×3×5

common factors=2×2×2×3×5×7=840

uncommon factors=3

L.C.M=Common factors× uncommon factors

L.C.M=840×3

L.C.M=2520

Step-by-step explanation:

i hope it will be helpful

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