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Answer:

76 natural number not including the first

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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.

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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

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:

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:

0.0005m^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 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

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:

D. 3

Step-by-step explanation:

A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.

Simply stated, any polygon with three (3) lengths of sides is a triangle.

In Geometry, a triangle is considered to be the most important shape.

Generally, there are three (3) main types of triangle based on the length of their sides and these include;

I. Equilateral triangle: it has all of its three (3) sides and interior angles equal.

II. Isosceles triangle: it has two (2) of its sides equal in length and two (2) equal angles.

III. Scalene triangle: it has all of its three (3) sides and interior angles different in length and size respectively.

In Geometry, an acute angle can be defined as any angle that has its size less than ninety (90) degrees.

Hence, we can deduce that the greatest number of acute angles that a triangle can contain is three (3) because the sum of all the interior angles of a triangle is 180 degrees.

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:

8.33 hours

Step-by-step explanation:

120-45 = 75

75 ÷ 9 = 8.33

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.

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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:

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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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:

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: I think the answer is A

Step-by-step explanation:

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]        

Answer:

6'2

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) Probability-Above 30 min = 5.72% = .0572

b) Probability-Above 15 min =  99.11% = .9911

c) *Probability-Between  1 - 59.49% = .4051

d) 19.136 minutes  z = -1.28

a) The probability that trip will take at least 1/2 hour will be 0.0606.

b) The percentage of time the lawyer is late for work will be 99.18%.

c) The probability that lawyer misses coffee will be 0.3659.

d) The length of time above which we find the slowest 10​% of trips will be 0.5438.

e) The probability that exactly 2 out of 3 trips will take at least one half

1/2 hour is 0.0103.

What do you mean by normal distribution ?

A probability distribution known as a "normal distribution" shows that data are more likely to occur when they are close to the mean than when they are far from the mean.

Let assume the time taken for a one way trip be x .

x ⇒ N( μ , σ ²)

x  ⇒ N( 24 , 3.8 ²)

a)

The probability that trip will take at least 1/2 hour or 30 minutes will be :

P ( x ≥ 30)

= P [ (x - μ) / σ ≥ (30 - μ) / σ ]

We know that , (x - μ) / σ = z.

= P [ z ≥ (30 - 24) / 3.8)]

= P [ z ≥ 1.578 ]

= 1 - P [  z ≤ 1.578 ]

Now , using the standard normal table :

P ( x ≥ 30)

= 1 - 0.9394

= 0.0606

b)

The percentage of the time the lawyer is late for work will be :

P ( x  ≥ 15)

= P [ z ≥ -2.368 ]

= P [  z ≤ 2.368]

= 0.9918

or

99.18%

c)

The probability that lawyer misses coffee :

P ( 15 < x < 25 ) = P ( x < 25 ) - P ( x < 15)

= P [  z < 0.263] - P ( z < -2.368)

or

= 0.3659

d)

The length of time above which we find the slowest 10​% of trips :

P( x ≥ X ) ≤ 0.10

=  0.5438

e)

Let's assume that y represents the number of trips that takes at least half hour.

y ⇒ B ( n , p)

y ⇒ B ( 3 , 0.0606)

So , the probability that exactly 2 out of 3 trips will take at least one half

1/2 hour is :

P ( Y = 2 )

= 3C2 × (0.0606)² × ( 1 - 0.0606)

= 0.0103

Therefore , the answers are :

a) The probability that trip will take at least 1/2 hour will be 0.0606.

b) The percentage of time the lawyer is late for work will be 99.18%.

c) The probability that lawyer misses coffee will be 0.3659.

d) The length of time above which we find the slowest 10​% of trips will be 0.5438.

e) The probability that exactly 2 out of 3 trips will take at least one half

1/2 hour is 0.0103.

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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:

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:

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:

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:

  9

Step-by-step explanation:

If x is the number of 10-inch stones, then (x-1) is the number of 5-inch stones, and the total width is ...

  10x +5(x-1) = 130

  15x -5 = 130 . . . . . . . eliminate parentheses

  15x = 135 . . . . . . add 5

  x = 9 . . . . . . . divide by 15

Wesley will need 9 10-inch stones for one row.

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

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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

https://brainly.com/question/16863924

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]

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