The weight of a blue whale

The chi-square distribution provides a good approximation to the sampling distribution of the chi-square statistic if the expected frequency in each cell is at least 5.

The chi-square statistic is a measure of how different an observed frequency is from the expected frequency. It is calculated by taking the difference between the observed and expected frequency in each cell, squaring it, and then summing the results. This measure can then be compared to a chi-square distribution with degrees of freedom equal to the number of cells minus one. If the calculated statistic is larger than the expected value from the chi-square distribution, then it can be concluded that the observed frequency differs significantly from the expected frequency.
In order to use the chi-square approximation, it is important that the expected frequency in each cell is at least 5. This is because the chi-square approximation only works well when there are large expected frequencies. When expected frequencies are smaller than 5, the chi-square statistic is not an accurate measure of the difference between the observed and expected frequencies.

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Answer:

360 meters

Step-by-step explanation:

15 x 24 = 360

24 is how many seconds

The cheetah runs 15 meter PER second

Answer:

The answer is 1800.

Step-by-step explanation:

3/540 = 10/x

3x = 540 × 10

x = 5400/3

x = 1800

Answer: Accounting profit=$90,000 and Economic profit loss= $28,500

Step-by-step explanation:

Accounting profit = Total revenue - Explicit costs Accounting profit = ($65 × 4,000) - ($50,000 + $120,000) Accounting profit = $260,000 - $170,000 Accounting profit = $90,000

Economic profit = Total revenue - (Explicit costs + Implicit costs) Economic profit = ($65 × 4,000) - ($50,000 + $120,000 + Forgone interest on savings + Forgone wages) Economic profit = ($65 × 4,000) - [$50,000 + $120,000 + (0.06 x $25,000) + $60,000] Economic profit (loss) = $28,500

To find the means, variances, covariance, and correlation coefficient of random variables X and Y with a joint PMF:

- Calculate the means: E[X] and E[Y].

- Compute the variances: Var(X) and Var(Y).

- Find the covariance: Cov(X, Y).

- Determine the correlation coefficient: ρ(X, Y).

Based on the covariance, we can determine if X and Y are independent or dependent.

Let the random variables X and Y have a joint probability mass function (PMF). We need to find the means (expected values), variances, covariance, and correlation coefficient of X and Y, and determine whether they are independent or dependent.

The mean of a random variable X is denoted by E[X] or μX, and it is calculated as the sum of all possible values of X weighted by their respective probabilities. Similarly, the variance of X, denoted by Var(X) or σ²X, measures the spread or dispersion of the values of X around its mean.

The covariance between two random variables X and Y, denoted by Cov(X, Y), measures the degree to which they vary together. It is calculated as the sum of the products of the differences of the values of X and its mean, and the differences of the values of Y and its mean, weighted by their joint probabilities.

The correlation coefficient between X and Y, denoted by ρ(X, Y), quantifies the strength and direction of the linear relationship between them. It is calculated by dividing the covariance of X and Y by the product of their standard deviations.

To determine the means and variances, we can use the following formulas:

E[X] = ∑x∑y x * P(X = x, Y = y)

E[Y] = ∑x∑y y * P(X = x, Y = y)

Var(X) = E[X²] - (E[X])²

Var(Y) = E[Y²] - (E[Y])²

To calculate the covariance, we use the formula:

Cov(X, Y) = E[XY] - E[X]E[Y]

Once we have the means and variances, we can calculate the correlation coefficient using the formula:

ρ(X, Y) = Cov(X, Y) / (√Var(X) * √Var(Y))

Based on the calculations of means, variances, covariance, and correlation coefficient, we can determine whether X and Y are independent or dependent. If the covariance is zero (Cov(X, Y) = 0), then X and Y are independent. Otherwise, they are dependent.

In summary, to find the means, variances, covariance, and correlation coefficient of X and Y, we use the formulas mentioned above. Based on the calculated values, we can determine whether X and Y are independent or dependent.

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Answer:

We are given that triangle PQR is an isosceles triangle in which PQ = PR .

Since the base angles of an isosceles triangle are equal,

angle PQR = angle PRQ  

Also, And we are given that

angle MRQ = angle NQR

In ΔQNR and  ΔRMQ

∠NQR=∠MRQ (given)

QR = QR   (common)

-triangles QNR is congruent to triangles RMQ - ASA - angle side angle

Answer:

20

Step-by-step explanation:

Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.

And 18+3... 21, that is smaller than 21.

If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.

The given expression is:

It is required to simplify the product using the distributive property.

Apply the distributive property to the product:

Apply the distributive property again to simplify the expression on the right:

The answer is x²+2x-8.

Answer:

She will donate P-50/3 each time

Step-by-step explanation:

Now assuming total donation needed to be in the silver category Is P

We can assume also the three additional and equal donations be Q

So

Then 50 + 3Q = P

So we still don't know P

We can get Q by saying

3Q= P - 50

Q = (P - 50) /3

The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point

To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we have:

∂f/∂x = 24x^2 + 6y = 0.

Taking the partial derivative with respect to y, we have:

∂f/∂y = 2y + 6x = 0.

Solving these two equations simultaneously, we get:

24x^2 + 6y = 0,

2y + 6x = 0.

From the second equation, we can solve for y in terms of x:

Y = -3x.

Substituting this into the first equation:

24x^2 + 6(-3x) = 0,

24x^2 – 18x = 0,

6x(4x – 3) = 0.

Therefore, we have two possibilities for x:

1. x = 0,

2. 4x – 3 = 0, which gives x = ¾.

Substituting these values back into y = -3x, we get the corresponding y-values:

1. x = 0 ⇒ y = 0,

2. x = ¾ ⇒ y = -9/4.

Hence, the critical points of the function are (0, 0) and (3/4, -9/4).

To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.

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Answer:

A

Step-by-step explanation:

because if you put in the radius of 3.7 you get 43.01 and if you round that up you get 43 which is A

Answer:

7.3 ft

Step-by-step explanation:

The information given represents a right angle triangle with the following:

reference angle = 52°

Adjacent side length = 5.7 ft.

Opposite side length = height of the statue = h

Applying the trigonometric ratio formula, we would have:

\( tan(52) = \frac{h}{5.7} \)

Multiply both sides by 5.7

\( tan(52) \times 5.7 = \frac{h}{5.7} \times 5.7 \)

\( tan(52) \times 5.7 = h \)

\( h = 7.3 ft \) (nearest tenth)

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Answer:

110 - 2x

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180

x + 50 + 5x - 40 + 110 - 2x = 180, that is

4x + 120 = 180 ( subtract 120 from both sides )

4x = 60 ( divide both sides by 4 )

x = 15

Thus

x + 50 = 15 + 50 = 65°

5x - 40 = 5(15) - 40 = 75 - 40 = 35°

110 - 2x = 110 - 2(15) = 110 - 30 = 80°

The largest angle is (110 - 2x)° = 80°

a. Own Price Elasticity of Demand = (-30) / (0) = undefined. Since the own price elasticity of demand is undefined, we cannot determine if the demand is elastic, inelastic, or unitary elastic based on this information.

b. Cross-Price Elasticity of Demand = (12/7) / 0 = undefined. Since the cross-price elasticity of demand is undefined, we cannot determine if goods X and Y are substitutes or complements based on this information.

c. Income Elasticity of Demand = (-2860.71) / (0) = undefined. Since the income elasticity of demand is undefined, we cannot determine if good X is a normal or inferior good based on this information.

d. We cannot calculate the own advertising elasticity of demand with the provided data.

a. To determine the own price elasticity of demand, we need to use the formula:

Own Price Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)

Given the demand equation OX​d​ = 7−15PX​+2Py​+0.5M+A, we can calculate the derivative of demand with respect to price:

d(OX​d​) / d(PX​) = -15

Now, let's plug in the values:

% Change in Quantity Demanded = (d(OX​d​) / d(PX​)) * (PX​ / OX​d​) = (-15) * (15 / 7) = -30

% Change in Price = (ΔPX​ / PX​) = (15 - 15) / 15 = 0

b. To determine the cross-price elasticity of demand between goods X and Y, we use the formula:

Cross-Price Elasticity of Demand = (% Change in Quantity Demanded of Good X) / (% Change in Price of Good Y)

Using the same demand equation, we calculate the derivative of demand with respect to the price of good Y:

d(OX​d​) / d(Py​) = 2

Now, let's plug in the values:

% Change in Quantity Demanded of Good X = (d(OX​d​) / d(Py​)) * (Py​ / OX​d​) = (2) * (6 / 7) = 12/7

% Change in Price of Good Y = (ΔPy​ / Py​) = (6 - 6) / 6 = 0

c. To determine the income elasticity of demand, we use the formula:

Income Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Income)

Using the same demand equation, we calculate the derivative of demand with respect to income:

d(OX​d​) / d(M) = 0.5

Now, let's plug in the values:

% Change in Quantity Demanded = (d(OX​d​) / d(M)) * (M / OX​d​) = (0.5) * (-40000 / 7) = -2860.71

% Change in Income = (ΔM / M) = (-40000 - (-40000)) / (-40000) = 0

d. The own advertising elasticity of demand measures the responsiveness of quantity demanded to changes in advertising expenditure. Unfortunately, the given demand equation does not provide any information about advertising expenditure or its impact on quantity demanded.

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Amelia got 42 more marks in the music test than in the history test.

To find out how many more marks Amelia got in the music test than the history test, we need to calculate the actual marks obtained in each test.

For the music test:

Percentage correct = 67.5%

Total marks = 80

Marks obtained in music test = (67.5/100) x 80 = 0.675 x 80 = 54

For the history test:

Percentage correct = 18.75%

Total marks = 64

Marks obtained in history test = (18.75/100) * 64 = 0.1875 * 64 = 12

To calculate the difference in marks, subtract the marks obtained in the history test from the marks obtained in the music test:

Difference = Marks in music test - Marks in history test

= 54 - 12

= 42

Therefore, Amelia got 42 more marks in the music test than in the history test.

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Answer:

yes

Step-by-step explanation:

The two unit vectors that are orthogonal to both i −k and i − 3j + 2k are:i - j / √2- i + j / √2

Given i - k and i - 3j + 2k.

Find two unit vectors that are orthogonal to both i −k and i − 3j 2k.

The two unit vectors orthogonal to both i - k and i - 3j + 2k are as follows:

First we find the cross product between i - k and i - 3j + 2k.

(i - k) × (i - 3j + 2k) = i × i - i × 3j + i × 2k - k × i + k × 3j - k × 2k= 0 + 2j - 3j - 0 + 0 + i = i - j

The cross product is (i - j).

Let v be any vector orthogonal to (i - j).

Let v = ai + bj + ck where (a, b, c) is a non-zero vector such that ai + bj + ck is orthogonal to (i - j).

We know that the dot product of two orthogonal vectors is zero. i.e (ai + bj + ck) • (i - j) = 0

(ai + bj + ck) • (i - j) = ai + bj + ck - aj - bj= (a - c)i - (a + b)j + ck

So we need to have (a - c) = (a + b) = 0 since (a, b, c) is non-zero implies ai + bj + ck is non-zero.

Therefore a = c and a = - b and a ≠ 0.

So a = - b and c = a.

Thus v = ai - aj + ak or v = -ai + aj + ak, both of which are unit vectors.

The two unit vectors that are orthogonal to both i −k and i − 3j + 2k are:i - j / √2- i + j / √2

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Answer: D. f(x)-2

Step-by-step explanation:

Changes insides the parenthesis translate left and right. If it is [+] a number, then it is moving to the left. If it is [-] a number, then it is moving to the right.

Changes outside the parenthesis translate up and down. If it is [+] a number, then it is moving upward. If it is [-] a number, then it is moving downward.

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

Given

Translate f(x) 2 units downward

Solve

According to the rules, it should be -2 units outside of the parenthesis

Therefore, it should be f(x)-2

Hope this helps!! :)

Please let me know if you have any questions

Answer:

D. f(x) – 2

Step-by-step explanation:

In Python, the range() function is a built-in function that returns a sequence of numbers, starting from 0 , and increments by 1  and ends at a specified number.

A function is a section of code that only executes when called. You can supply parameters—data—to a function. As a result, a function may return data.

Guido van Rossum created Python, an interpreted, object-oriented, high-level programming language with dynamic semantics. It was first made available in 1991. The name "Python" is a tribute to the British comedy group Monty Python and is meant to be both simple and entertaining. Because it manages much of the complexity for the user, Python has a reputation for being a beginner-friendly language, displacing Java as the most popular beginning language and allowing beginners to concentrate on completely understanding programming ideas rather than minute details.

In Python, the range() function is a built-in function that returns a sequence of numbers, starting from 0 by default, and increments by 1 (also by default), and ends at a specified number.

The syntax for the range() function is as follows:

range(stop)

range(start, stop[, step])

for eg:

# Generate a sequence of numbers from 0 to 9

for i in range(10):

   print(i)

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The perimeter of the pentagon is 76 units. The solution is obtained using tangent to circle.

What is tangent to a circle?

A line that touches a circle only once is said to be tangent to it. A point to circle can only have one tangent.

In the figure, the circle is circumscribed by the pentagon.

We are given QZ = 10, YX = 9, WX = 9, UW = 17, and US = 10

VW = WX = 9   (tangent of circle)

So, VU = UW - VW

VU = 17-9= 8

Since, VU and UT are tangents of circle, therefore

UT = 8

US = UT + TS

⇒10 = 8 + TS

⇒TS = 2

Now, TS and SR being tangents, therefore

TS = SR = 2

Also, RQ and QZ are tangents, therefore

RQ = QZ = 10

Similarly, ZY and YX are tangents, therefore

ZY = YX= 9

Thus, Perimeter = SQ + QY + YW + WU + US

⇒Perimeter = SR+ RQ+ QZ+ ZY+ YX+ XW+ UW+ US

⇒Perimeter = 2+ 10+ 10+ 9+ 9+ 9+ 17+ 10

⇒Perimeter = 76 units

Hence, the perimeter of the pentagon is 76 units.

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Answer:

The occurrence of one event (e.g., A) precludes the occurrence of the other event (e.g., B), and vice versa.

Step-by-step explanation:

The pair of events A and B, "Your new skateboard design is a success" and "Your new skateboard design is a failure," are mutually exclusive.

This is because the two events cannot occur simultaneously; the design cannot be both a success and a failure at the same time.

Therefore, the occurrence of one event (e.g., A) precludes the occurrence of the other event (e.g., B), and vice versa.

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Answer:

slope: 1

Step-by-step explanation:

(1, 2) and (3, 4)

To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(4 - 2) / (3 - 1)

Simplify the parentheses.

= (2) / (2)

Simplify the fraction.

2/2

= 1

This is your slope.

Hope this helps!

Answer:

The angle between the two sides of the right triangle is aproximately 31.003º.

Step-by-step explanation:

From image attached on question we infer that we need to find the angle between sides of lengths 6 (adjacent leg) and 7 (hypotenuse) in the right triangle. The angle can be found by means of this trigonometric ratio:

\(\cos \alpha = \frac{6}{7}\)

\(\alpha = \cos^{-1} \frac{6}{7}\)

\(\alpha \approx 31.003^{\circ}\)

The angle between the two sides of the right triangle is aproximately 31.003º.

Taking the given data into consideration we reach the conclusion that
a) the probability that a randomly selected runner will take between 2.35 and 2.85 hours to complete the half-marathon is 0.1974, or about 19.74%.
This means that if we randomly select a runner, there is a 19.74% chance that their completion time will be between 2.35 and 2.85 hours.
b) randomly select 5 customers from the restaurant, there is a 63.68% chance that the proportion of customers who wait longer than 25 minutes for their order will be greater than 0.1276.

a) To solve this problem, we can use the binomial probability formula:
\(P(X \leq 2) = \sum n=0,1,2 (nC_x) * p^n * (1-p)^{(n-x)}\)
where:
X =  count  of incorrect bills in the sample
n = sample size, which is 12 in this case
p = evaluated probability of an incorrect bill, which is 1/10 or 0.1
\(nC_x\) =  count of combinations of n things taken x at a time
Applying this formula, we can calculate the probability of no more than two incorrect bills in the sample:
\(P(X \leq 2) = (0C_0 * 0.1^0 * 0.9^{12} ) + (1C_1 * 0.1^1 * 0.9^{11} ) + (2C_2 * 0.1^2 * 0.9^{10} )\)
\(P(X \leq 2) = (1 * 1 * 0.2824) + (12 * 0.1 * 0.2824) + (66 * 0.01 * 0.3487)\)
\(P(X \leq 2) = 0.2824 + 0.3389 + 0.0229\)
\(P(X \leq 2) = 0.6442\)
Hence , the probability that no more than two of the bills will be incorrect is 0.6442, or about 64.42%. This means that if we randomly select a sample of 12 bills, there is a 64.42% chance that no more than two of them will be incorrect.
The time taken to complete a half-marathon is normally distributed, with an average time (m) of 3.15 hours and a standard deviation (\(\sigma\)) of 0.95 hours.
To solve this problem, we need to standardize the range of times using the z-score formula:
\(z = (x - m) / \sigma\)
where:
x = time taken to complete the half-marathon
m =  average time, which is 3.15 hours
\(\sigma\) =  standard deviation, which is 0.95 hours
For the lower bound of 2.80 hours:
\(z = (2.80 - 3.15) / 0.95\)
\(z = -0.3684\)
For the upper bound of 3.25 hours:
\(z = (3.25 - 3.15) / 0.95\)
\(z = 0.1053\)
Applying a standard normal distribution table , we can find the area under the curve between these two z-scores:
\(P(-0.3684 \leq z \leq 0.1053) = 0.3557\)
Then, the probability that a randomly selected runner will take between 2.80 and 3.25 hours to complete the half-marathon is 0.3557, or about 35.57%. This means that if we randomly select a runner, there is a 35.57% chance that their completion time will be between 2.80 and 3.25 hours.
To evaluate this problem, we need to standardize the range of times using the z-score formula:
\(z_1 = (2.35 - 3.15) / 0.95\)
\(z_1 = -0.8421\)
\(z_2 = (2.85 - 3.15) / 0.95\)
\(z_2 = -0.3158\)
Applying a standard normal distribution table , we can find the area under the curve between these two z-scores:
\(P(-0.8421 \leq z \leq -0.3158) = 0.1974\)

Now for the second question
b) In the given problem, we are told that 12% of customers at a particular restaurant wait longer than 25 minutes for their order, and we assume normal distribution. We randomly select 5 customers.
The standard error for a sample proportion is given by the formula:
\(SE = \sqrt(p * (1 - p) / n)\)
where:
p is the sample proportion, which is 0.12 in this case
n is the sample size, which is 5 in this case
Substituting the values, we get:
\(SE = \sqrt(0.12 * (1 - 0.12) / 5)\)
SE = 0.219
Therefore, the standard error for this sample is 0.219.
To evaluate this problem, we need to standardize the sample proportion using the z-score formula:
\(z = (p - P) / SE\)
where:
p = sample proportion, which is 0.12 in this case
P = population proportion, which is 0.1276 in this case
SE = standard error, which we calculated to be 0.219
Staging the values, we get:
\(z = (0.12 - 0.1276) / 0.219\)
\(z = -0.346\)
Applying a standard normal distribution table or calculator, we can find the area under the curve to the right of this z-score:
\(P(z > -0.346) = 0.6368\)
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The number 48,000,000,000 can be written in scientific notation as:

4.8 × 1010 or 48 × 109

Scientific notation is a way of expressing numbers in a concise form. It is typically used when dealing with very large or very small numbers. In scientific notation, a number is written as the product of two factors: a number between 1 and 10, and a power of 10.

For example, to express the number 48,000,000,000 in scientific notation we must first determine the two factors.

First factor: This is the number between 1 and 10. To determine this factor, we must count the number of places to the right of the decimal point (in this case, 0 places) and then move the decimal point that many places to the left.

48,000,000,000 → 4.8

Second factor: This is the power of 10. To determine this factor, we must count the number of places we moved the decimal point and then express this number as a power of 10.

In this example, we moved the decimal point 10 places to the left. Therefore, our power of 10 is 10.

Therefore, the number 48,000,000,000 can be written in scientific notation as:

4.8 × 1010 or 48 × 109

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Answer: A, A

Explanation:

48,000,000,000 g = 4.8 × 1010 g

0.000000655 mL = 6.55 × 10-7 mL

The the function to estimate the average age of employee of a company is A(s)=0.285s + 59  , then the average age of employee in 2003 is 65.27 and in 2009 is 66.98

To estimate the average age of an employee in 2003, we need to find the value of A(s) when s = 22  ;

because the number of years between 2003 and 1981 is = 22 years ;

So , A(22) = 0.285×22 + 59 = 65.27  ;

The average age of an employee in 2003 is approximately 65.27.

To estimate the average age of an employee in 2009,

we need to find the value of A(s) when s = 28

because the number of years between 2009 and 1981 is = 28 years ;

So , A(28) = 0.285×28 + 59 = 66.98  ;

The Average age of employee in 2009 is approximately 71.48.

The given question is incomplete , the complete question is

The function​ A(s) given by ​A(s)=0.285s + 59  can be used to estimate the average age of employee of a company in the year 1981 to 2009. Let​ A(s) be the average age of an​ employee, and "s" be the number of year since​ 1981; that​ is, s=0 for 1981 and s=9 for 1990. What is the average age of the employee in 2003 and in​ 2009 ?

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