find the mean 164,175,178,166,167,145,176,150,174,162,180,156,173,158,182,184,160,172,186,168,195,169,171,187,170

Answer:

It Is Nonlinear

Step-by-step explanation:

Nonlinearity is a term used in statistics to describe a situation where there is not a straight-line or direct relationship between an independent variable and a dependent variable. In a nonlinear relationship, changes in the output do not change in direct proportion to changes in any of the inputs.

Answer:

Make sure you subtract any rests or stops you made from the total trip duration. If the total distance travelled was 500 miles and the time it took you was 5 hours, then your average speed was 500 / 5 = 100 miles per hour (mph).

Step-by-step explanation:

Answer:

d=99

Step-by-step explanation:

The value of the coin in 2019 would be approximately $132.

To calculate the value of the coin in 2019, we need to consider the annual increase rate of 16.9% from 2010 to 2019. We can use the compound interest formula to find the final value.

Starting with the initial value of $40 in 2010, we can calculate the value in 2019 as follows:

Value in 2019 = Initial value * (1 + Rate)^n

where Rate is the annual increase rate and n is the number of years between 2010 and 2019.

Plugging in the values:

Value in 2019 = $40 * (1 + 0.169)^9

Value in 2019 ≈ $40 * 2.996

Value in 2019 ≈ $119.84

Rounding the value to the nearest dollar, we get approximately $120. Therefore, the value of the coin in 2019 would be approximately $120.

However, please note that the exact value may vary depending on the specific compounding method and rounding conventions used.

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The function that correctly defines S(x) is S(x) = 5x - 2(20 - x) + 20

We have the following definitions in the question

If the total questions is 20, then

Incorrect answers = 20 - x

So, the points gained/lost are

Gained = 5 * x = 5x

Lost = -2 * (20 - x) = -2(20 - x)

Bonus = 20

Add the above points to get the function S(x)

S(x) = 5x - 2(20 - x) + 20

Hence, the definition is S(x) = 5x - 2(20 - x) + 20

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Answer:

-1 is the correct answer

Step-by-step explanation:

Move that many points on the number line

The position of B on number line is at - 1.

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

Given that;

Point A is shown on the the number line below.

And, Another point, B , is to be placed on the number line and will be 2 1/2 unit from point A.

Now,

Since, The position of Point A = 1 1/2

And, Another point, B , is to be placed on the number line and will be 2 1/2 unit from point A.

So, The point B = 1 1/2 + (-2 1/2)

                        = 3/2 - 5/2

                        = - 2/2

                        = - 1

Thus, The position of point B = - 1

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The expansion of the function \((3x - 4)^4\) simplifies to \(81x^4 - 432x^3 + 864x^2 - 768x + 256.\)

To expand the function \(f(x) = (3x - 4)^4\), we can use the binomial theorem. According to the binomial theorem, for any real numbers a and b and a positive integer n, the expansion of \((a + b)^n\) can be written as:

\((a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^{(n-1)} b^1 + C(n, 2)a^{(n-2)} b^2 + ... + C(n, n-1)a^1 b^{(n-1)} + C(n, n)a^0 b^n\)

where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).

Applying this formula to our function \(f(x) = (3x - 4)^4\), we have:

\(f(x) = C(4, 0)(3x)^4 (-4)^0 + C(4, 1)(3x)^3 (-4)^1 + C(4, 2)(3x)^2 (-4)^2 + C(4, 3)(3x)^1 (-4)^3 + C(4, 4)(3x)^0 (-4)^4\)

Simplifying each term, we get:

\(f(x) = 81x^4 + (-432x^3) + 864x^2 + (-768x) + 256\)

Therefore, the expanded form of the function \(f(x) = (3x - 4)^4\) is \(81x^4 - 432x^3 + 864x^2 - 768x + 256\).

Note that the coefficient of \(x^3\) is -432, the coefficient of \(x^2\) is 864, the coefficient of x is -768, and the constant term is 256.

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Note the complete question is

Answer:

Millennium Dairy Product

a) Share of the company that SBI Caps should require today to get a required rate of return of 50%.

= 50%

b) If the company had 1,000,000 (100,000 x10) shares outstanding before the private placement, SBI Caps should purchase

1,000,000 shares = 50% of (1,000,000 + 1,000,000) shares

Assuming the founding promoters are not giving up their shares, instead, new equity shares are being issued.

c) The price per share SBI Caps should agree to pay, if her required return was 50% is

Rs.50 per share, which will provide the required additional equity financing of (Rs.50 million) since Rs.50 x 1,000,000 equals Rs.50 million.

d) Pre money and post money valuations:

These are based on the calculated Market Price of Rs.1,000 per share from the Price/Earnings Ratio.

Pre money valuation will be Rs.1,000 x 1,000,000 shares = Rs.1 billion

Post money valuation will be Rs.1,000 x 2,000,000 shares = Rs.2 billion

e) Carried interests of the VC and the promoters

VC's carried interest = share of profits = 50% xRs.50 million = Rs.25 million

Promoters' carried interest = Rs.25 million

Step-by-step explanation:

a) Calculation of share in the company:

SBI Cap's required rate of return is 50%

If she invests Rs.50 million today, her expected return will be equal to Rs.50 million x 50% = Rs.25 million

Since rate of return = Net Income/Initial Investment or (Current value of investment - Initial Investment)/Initial Investment.

This return will be equal to 50% of the total net income of Rs.50 million

b) Price/Earnings P/E ratio = Market price per share/Earnings per share (EPS)

Since P/E ratio of similar companies = 20 times,

The company's P/E = 20 times x EPS

With calculated EPS = Rs.50 million /1,000,000 = Rs.50

Therefore, price per share = 20 x Rs.50 = Rs.1,000

Pre money valuation = Rs.1,000 x 1 million shares = Rs.1 billion

Post money valuation = Rs.1,000 x 2 million shares = Rs.2 billion

c) The carried interest is the share of profits to which the promoters and the Venture Capitalists are entitled.  Their respective shares are 50% of the net income = Rs.25 million each.

d) The pre money and post money valuations:  The pre money valuation is the valuation of the company before the additional equity financing.  The post money valuation is the valuation of the company after the additional equity financing.  There are many ways to value a company.  In this case, we have used the P/E ratio as a basis for the valuation.  However, we did not dilute the earnings per share post money, for simplicity.

Answer:

165 degrees

Step-by-step explanation:

1 is opposite of 6

1 is 15 degree

half circle is 180 degree

you subtract 15 you got 165

1 and 5 they both will be 15 degree and 6 and 2 they both will be 165 degree

Answer:

Step-by-step explanation:

a) The formula for the regression function is:

Maintenance Cost = 54.7757 + 120.689 x Age of Car

b) The slope of the regression equation is 120.689. This means that on average, for every one year increase in the age of a car, the maintenance cost is expected to increase by $120.689.

c) To construct a 95% interval to predict the maintenance cost for a car that is 7 years old, we can use the formula:

Y = a + bX ± tα/2 * SE

where Y is the predicted maintenance cost, a is the intercept, b is the slope, X is the age of the car, tα/2 is the t-value for the 95% confidence level with n-2 degrees of freedom (11 in this case), and SE is the standard error of the estimate.

Plugging in the values, we get:

Y = 54.7757 + 120.689 * 7 ± 2.201 * 11.8442

Y = 923.167 ± 26.010

Therefore, we can be 95% confident that the maintenance cost for a car that is 7 years old will be between $897.16 and $949.17.

d) The null hypothesis is that there is no significant linear relationship between the average maintenance cost and the age of a car in years. The alternative hypothesis is that there is a significant linear relationship between the average maintenance cost and the age of a car in years.

To test the hypothesis, we can perform a t-test on the slope coefficient using the t-statistic and the p-value provided in the output. The t-statistic is 10.1898, which is much greater than the critical t-value at the 0.05 level of significance for a two-tailed test with 11 degrees of freedom (2.201). The p-value is 0.0000, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant linear relationship between the maintenance cost and the age of the car in years.

The amount of money in Marianna's annuity after 6 years will be approximately $300,516.

To calculate the amount of money in Marianna's annuity after 6 years, we can use the formula for compound interest on an annuity:

A = P * ((1 + r/n)^(n*t) - 1) / (r/n)

Where:

A = the final amount in the annuity

P = the regular contribution (each quarter) = $10,000

r = annual interest rate = 8% = 0.08

n = number of compounding periods per year = 4 (since it's compounded quarterly)

t = number of years = 6

Plugging in the values:

A = 10000 * ((1 + 0.08/4)^(4*6) - 1) / (0.08/4)

Calculating this expression:

A ≈ 10000 * ((1.02)^24 - 1) / 0.02

A ≈ 10000 * (1.601032449136241 - 1) / 0.02

A ≈ 10000 * 0.601032449136241 / 0.02

A ≈ 10000 * 30.05162245681205

A ≈ 300,516.22

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Answer:

304200

Step-by-step explanation:

To find the value of P6, use the savings annuity formula

PN=d((1+r/k)N k−1)r/k.

From the question, we know that r=0.08, d=$10,000, k=4 compounding periods per year, and N=6 years. Substitute these values into the formula gives

P6=$10,000 ((1+0.08/4)6⋅4−1)/(0.08/4).

Simplifying further gives P6=$10,000 ((1.02)24−1)/(0.02) and thus P6=$304,218.62.

Rounding as requested, our answer is 304200.

The time spent higher than 26 meters above the ground is 0.42 minutes. Answer: 0.42

A Ferris wheel is 30 meters in diameter and boarded from a platform that is 4 meters above the ground.

The six o'clock position on the Ferris wheel is level with the loading platform.

The wheel completes 1 full revolution in 2 minutes.

We have to find how many minutes of the ride are spent higher than 26 meters above the ground.

So, let's start with some given data,Consider the height of a person at the six o'clock position = 4 meters

So, the height of a person at the highest point = 4 + 15 = 19 meters (since the diameter is 30 meters, the radius will be 15 meters)

Also, the height of a person at the lowest point = 4 - 15 = -11 meters

Therefore, the Ferris wheel completes one cycle from the lowest point to the highest point and back to the lowest point.

So, the total distance travelled will be = 19 + 11 = 30 meters.

Also, we are given that the wheel completes 1 full revolution in 2 minutes.

We need to calculate the time spent higher than 26 meters above the ground.

So, the angle between the 6 o'clock position and 2 o'clock position will be equal to the angle between the 6 o'clock position and the highest point.

This angle can be calculated as follows:

Angle = Distance travelled by the Ferris wheel / Circumference of the Ferris wheel * 360 degrees

Angle = 30 / (pi * 30) * 360 degrees

Angle = 360 degrees / pi

= 114.59 degrees

So, the total angle between the 6 o'clock position and the highest point is 114.59 degrees.

Now, we need to find out how much time is spent at an angle greater than 114.59 degrees.

This can be calculated as follows:

Time = (Angle greater than 114.59 degrees / Total angle of the Ferris wheel) * Total time taken

Time = (180 - 114.59) / 360 * 2 minutes

Time = 0.42 minutes

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The volume of the log will be 30,70,760 m³.

Mathematically, we can write Archimedes principle as -

F{buoyant} = - fluid density {ρ} x acceleration due to gravity {g} x volume {v}

Given is that a 3080 kg log of wood with a diameter of 1 m and 10 m long, it floats in the water.

Since the log floats on water, the density of both the log and water is same.

So, we can write volume as -

Volume = 3080 x 997 Volume = 30,70,760 m³

Therefore, the volume of the log will be 30,70,760 m³.

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{QUESTION IN ENGLISH -urgent A 3,080 kg log of wood with a diameter of 1 m and 10 m long, it floats in the water. What is the volume of the trunk above the surface of the water?}

Given:

• Width of scale drawing = 4 inches

• Length of scale drawing = 8 inches

• Length of actual park = 320 yards

Let's find the perimeter of the actual park.

Let's first find the width of the actual park.

To find the width of the actual park, we have:

The width of the actual park is 160 yards.

Now, to find the perimeter of the actual park, apply the formula do perimeter of a rectangle:

P = 2(L + W)

Where:

P is the perimeter

L is the length = 320 yards

W is the width = 160 yards

Thus, we have:

P = 2(320 + 160)

P = 2(480)

P = 960 yards

Therefore, the perimeter of the actual park is 960 yards.

ANSWER:

960 yards

Given:

There are given the function:

Explanation:

To the factor, the above function, first find the first zero of the above function:

So,

From the function:

Then,

So,

The factor of the given function is shown below:

Now,

Solve the given inequality:

Then,

Final answer:

Hence, the factor and the solution to the given inequality are shown below;

The number line graph of the inequality is shown below:

From the above graph, we can see that the first value of x is less than and equal to -4 and for the second value, the x has lies between -3 and 3.

Triangle ABC and ADE are similar triangles

Similar triangles have the same corresponding angle measures and proportional side lengths.

This means that for two triangles to be similar, the corresponding angles must be equal and the ratio of corresponding sides of similar triangles are equal.

It has been shown that angles in ABC and ADE are equal.

To show that the ratio of corresponding sides are equal

6/12 = 8/16 = 10/20

The ratios all give a value of 1/2

Therefore we can say that the triangles ABC and ADE are similar.

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The quadratic regressiοn equatiοn fοr the given data pοints is y = 5x² - 20x + 7

A secοnd-degree equatiοn οf the fοrm ax² + bx + c = 0 is knοwn as a quadratic equatiοn in mathematics. Here, x is the variable, c is the cοnstant term, and a and b are the cοefficients.

Tο find the quadratic regressiοn equatiοn fοr the given data pοints, we need tο fit a quadratic equatiοn οf the fοrm y = ax² + bx + c tο the data.

We can start by using the three given pοints tο set up a system οf three equatiοns:

\((1,-8): a(1)^2 + b(1) + c = -8\\\\(2,-4): a(2)^2 + b(2) + c = -4\\\\(3,6): a(3)^2 + b(3) + c = 6\)

SimpIifying each equatiοn, we get:

a + b + c = -8 (equatiοn 1)

4a + 2b + c = -4 (equatiοn 2)

9a + 3b + c = 6 (equatiοn 3)

AIternativeIy, we can use technοIοgy such as a caIcuIatοr οr spreadsheet tο sοIve the system.

SοIving the system using technοIοgy, we get:

a = 5

b = -20

c = 7

Therefοre, the quadratic regressiοn equatiοn fοr the given data pοints is:

y = 5x² - 20x + 7

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Answer:

eeeee

Step-by-step explanation:

Answer:

4

4

Step-by-step explanation:

x litres of 15% solution + y litres of 19% solution= 8 gallons of 17% solution

disinfectant content of the final solution= 8*0.17= 1.36 gallons

0.15x+0.19y=1.36

x+y= 8 ⇒ x=8-y

If you know how to set up the format for long division, the answer is 9.5 because 4 goes into 3 zero times, and you don't necessarily need to write down the zero on top since it equals nothing in a whole number. then, 4 goes into 38 nine times. (yes 38 because you didn't do anything with the 3 so you just make it 38) 4 × 9 = 36. it doesn't exactly make 38, so you take away 36 from 38 and you are left with a remainder of 2. then to get no remainder, add a zero to the end of 38. so it would look something like 4/380 so you take down the zero next to the 2 so it makes 20, 4 × 5 = 20 and you are left with a remainder of 0 and the answer: 9.5 ( P.S.: added the decimal because it wasn't exactly equal when doing 4 × 9 so we had to add a zero)

Answer:

The number of pizzas sold during A- lunch is 64

Step-by-step explanation:

Let us solve the question using the ratio method

∵ The ratio of pizza to nachos sold during A-lunch is 4 to 3

∵ There were 48 nachos sold

→ By using the ratio method

→ Pizza  :  Nachos

→  4        :   3

→  x        :  48

→ use the cross multiplication

∵ x × 3 = 4 × 48

∴ 3x = 192

→ Divide both sides by 3

∵ \(\frac{3x}{3}\) = \(\frac{192}{3}\)

∴ x = 64

∴ The number of pizzas sold during A- lunch is 64

Volume of the cylinder is 15197.60(to the nearest hundredth).

In mathematics, Cylinder is  the basic 3d shapes,  which has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center which is called height of the cylinder.

Given that the radius of the cylinder  is 11yd.

and the height of the cylinder is 40yd.

Formula for the volume of cylinder  is π × r² × h where π=3.14, r= radius and h= height.

Putting the values we get,

Volume of the cylinder is = 3.14 × (11)² × 40 cubic yd.

                                          = 15197.6

Hence, Volume of the cylinder is 15197.60(to the nearest hundredth).

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Answer:

The inverse is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x) = (x+3)^5

Finding the inverse,

\(f(x) = (x+3)^5\\or,\\y = (x+3)^5\)

We replace x with y and vice versa

so,

\(x = (y+3)^5\)

Solving for y,

the the 5th root,

\(\sqrt[5]{x} = y + 3\\y = \sqrt[5]{x} - 3\)

hence the inverse function is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x)=(x+3)×5

Y=5X+15

now

interxchanging x and y we get,

x=5y+15

5y=x-15

y=x-15/5

therefor f~1(x)=x-15/5

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Answer:

b

Step-by-step explanation:

The 6th term of the geometric sequence 27/16, -9/8, 3/4..... is - 2/9

The correct answer option is option B

Given: 27/16, -9/8, 3/4.....

nth term = ar^(n-1)

Where,

First term, a = 27/16

Common ratio, r = -9/8 ÷ 27/16

= -9/8 × 16/27

= -2/3

6th term = ar^(n-1)

= 27/16 × -2/3^(6-1)

= 27/16 × -2/3^5

= 27/16 × -32/243

= - 2/9

In conclusion, negative two ninths is the 6th term of the geometric sequence.

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The inequality value that would be able to show/x/ ≤ 5 is option A

In mathematics, inequality refers to a mathematical statement that expresses a relationship between two quantities, indicating that one quantity is greater than, less than, or not equal to the other.

The symbol that we have  is telling us that the value of the x would be less than  or it would be seen to be equal to five.

We can see that /x/ ≤ 5 would exclude the negative values and this can be seen in the option that is marked option A

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Answer:

= 34

Step-by-step explanation:

(32)-5+7

32 - 5 + 7

= 32 + 2

= 34.

Hence, \(n^2 + 1\geq 2^n\) when \(n\) is a positive integer with \(1 \leq n \leq 4\).

Use principle of mathematical induction, put \(n=1,2,3,4\) in the given inequality

For \(n=1\)

\(1^2+1\geq2^1\)

\(2\geq2\), which is true.

So, \(n^2+1\geq2^n\) is true for \(n=1\)

For \(n=2\)

\(2^2+1\geq2^2\)

\(5\geq4\), which is true.

So, \(n^2+1\geq2^n\) is true for \(n=2\)

For \(n=3\)

\(3^2+1\geq2^3\)

\(10\geq8\), which is true.

So, \(n^2+1\geq2^n\) is true for \(n=3\)

For \(n=4\)

\(4^2+1\geq2^4\)

\(17\geq16\), which is true.

So, \(n^2+1\geq2^n\) is true for \(n=4\)

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The truck driver would deliver 105 packages in a 7 hours day

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let y represent the number of packages delivered by the truck driver in x hours. Using the point (1, 15) and (4, 60). Hence, the equation is:

y - 15 = [(60-15)/(4-1)](x - 1)

y = 15x

For a 7 hour day (x = 7):

y = 15(7) = 105

The driver would deliver 105 packages in 7 hours

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