the following is a probability distribution of a weighted die. 10 9 8 weight 7 6 5 4 3 2 1 1 2 3 4 5 6 die number a. (5 pts) what is the probability of rolling a 1, 2, 3, 4, or 5? b. (5 pts) what is the standard deviation of this distribution? c. (5 pts) what has better odds: getting a heads on flipping a coin or rolling a 2 or 3 with two of these die?

Answer:

A)Only Line A is well placed line of best fit

Step-by-step explanation:

Best fit line :A line through a scatter plot of data points that best expresses the relationship between those points is called best fit line

The least-squares method provides the closest relationship between the dependent and independent variables by minimizing the distance between the residuals and the line of best fit

By considering both the given graphs

We can see that Line A gives the minimum distance between residuals and line of best fit whereas Line B does not give the minimum distance between residuals and line of best fit

So,Option A is true

A)Only Line A is well placed line of best fit

Answer: a) only line A is a well placed line of best fit

Step-by-step explanation:

\(The given function is 2 / 17x^2 − 17 + 17 cos x.\)The Taylor series at The given function is 2 / 17x^2 − 17 + 17 cos x. \(The given function is 2 / 17x^2 − 17 + 17 cos x.\)

\(The exact answer of the Taylor series at x=0 for cos x is ∑ n=0 to ∞ (-1)^n × (2n)! / (x^(2n))\)

Using power series operations and the Taylor series at x=0 for cosx to find the Taylor series at x=0 for the given function, \(we get: 2 / 17x^2 − 17 + 17 cos x= 2/17x^2 - 17 + 17 ∑ n=0 to ∞ (-1)^n × (2n)! / (x^(2n))= 2/17x^2 - 17 + ∑ n=0 to ∞ (-1)^n × (2n)! / (x^(2n-2))= ∑ n=2 to ∞ (-1)^n × (2n)! / (17x^(2n-2))\)

Therefore, the Taylor series at x=0 for the given function is ∑ n=2 to ∞ (-1)^n × (2n)! / (17x^(2n-2)).

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Answer:

Tyler runs 4 miles, and Han runs 5 miles.

Step-by-step explanation:

60 minutes in an hour.

60/12=5 miles for Han

60/15=4 miles for Tyler

Answer:

120

Step-by-step explanation:

10 choose 3

theres really no simple way to do that with work unless you have a fancy calculator.

The given statement "For a sample with a standard deviation of s = 8, a score of x = 42 corresponds to z = -0.25. The mean for the sample is m = 40." is False because the calculated z-score does not match the given value.

To calculate the z-score, we use the formula z = (x - m) / s, where x is the score, m is the mean, and s is the standard deviation. Substituting the given values, we have z = (42 - 40) / 8 = 0.25. However, the given statement states that the z-score is -0.25, which is incorrect. Therefore, the statement is false.

The correct z-score for x = 42 with a mean of m = 40 and standard deviation of s = 8 is 0.25, not -0.25.

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Answer:

Step-by-step explanation:

a) Let the side of the larger box be x, then the side of the smaller box is 0.3x.

Their volumes are:

The difference in volumes:

b) The sides are 20 in and 20*0.3 = 6 in

c) The other two boxes with sides x and 0.75x

Sum of the volumes:

Sides of the boxes are 12 in and 12*0.75 = 9 in

Answer:

3.07meters

Step-by-step explanation:

9-5.93=3.07

Answer: Population

In statistics, a population is the entire group of people you want to determine some fact about (eg: average height). A sample is a subset of the population that should ideally represent the population.

Answer:

16

Step-by-step explanation:

its just 16

Answer:

16

Step-by-step explanation:

I just used my calculator

The number of friends that  will know the secret by the end of the day on sunday are 21 friends.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that :on monday, a student tells a secret to 3 people. on tuesday, each of the 3 friends tells the secret to 3 different people, who in turn each tell the secret to 3 different different people.

on monday- 3 persons

on Tuesday-3×3=9

Since the 3 person will tell the secret to other 3-3 persons each

So, we can relate it to the table of 3

3 x 7=21

Therefore the number of friends will know the secret = 21

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Answer:jkd

Step-by-step explanation:

d

Answer:

7x^2-49x+42

Step-by-step explanation:

X*x=x^2 X*-6=-6x -1x*x=-1x -1*-6=6

7(x^2-6x-1x+6)

The answer

You ate 3/12 of the carton of 12 eggs, which simplifies to 1/4.

Your brother ate 1/12 more than you, which means he ate:

1/4 + 1/12 = 3/12 + 1/12 = 4/12

Simplifying 4/12 gives 1/3.

So, you ate 1/4 of the carton of eggs and your brother ate 1/3 of the carton of eggs. To find out how much of the carton was eaten in total, we need to add these two fractions. However, we can't add them directly because they have different denominators.

To add fractions with different denominators, we need to find a common denominator. In this case, the smallest common multiple of 4 and 3 is 12. We can convert the fractions to have a denominator of 12:

1/4 = 3/12

1/3 = 4/12

Now we can add them:

3/12 + 4/12 = 7/12

Therefore, you and your brother ate 7/12 of the carton of eggs in total.

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Answer:

4.25 gallons of juice

Step-by-step explanation:

4 quarts = 1 gallon

3 quarts = 3/4 gallon

2 1/2 + 1 + 3/4 = 3 2/4 + 3/4 = 3 5/4 = 4 1/4

4 1/4 = 4.25

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Answer:

about 23.09 ft

Step-by-step explanation:

Let h = height of pole and b = distance from base of pole to bottom of wire 2.

Please put your calculator in degree mode.

\( \tan(41) = \frac{h}{34} \)

\(h = 34 \tan(41) \)

\( \tan(38 ) = \frac{b}{34 \tan(41) } \)

\(b = 34 \tan(41) \tan(38) = 23.09\)

Answer:

A

Step-by-step explanation:

These are cross angles

Calculating this expression will give us the amount the farmer needs to save annually over the 8-year period.

Given:

Payment required at the end of each year: P50,000

Number of years until the daughter starts college: 8

Interest rate: 7% (compounded annually)

We can calculate the annual savings using the formula for the present value of an ordinary annuity:

P = \dfrac{PMT \times (1 - (1 + r)^{-n}{r}

Where:

P = Present value (amount to be saved annually)

PMT = Payment amount (P50,000)

r = Interest rate per period (7% or 0.07)

n = Number of periods (8)

Let's substitute the given values into the formula:

\[ P = \dfrac{50,000 \times (1 - (1 + 0.07)^{-8}{0.07} \]

Calculating this expression will give us the amount the farmer needs to save annually over the 8-year period.

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Answer:

She ate 5 apple slices

Step-by-step explanation:

25% of 20 is 5.

That means if she ate 5 slices, she ate 25% of the apple slices.

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Answer:

5

Step-by-step explanation:

25% of 20 is 5

Answer:72.5

Step-by-step explanation:

On delta

Answer: 56

Step-by-step explanation:

Let the number of $5 be x

Let the number of $2 be y.

Based on the information given, we can form an equation as:

x + y = 128 ........ i

5x + 2y = 424 ....... ii

Multiply equation i by 2

Multiply equation ii by 1

2x + 2y = 256 ...... iii

5x + 2y = 424 ....... iv

Subtract iii from iv

3x = 168

x = 168/3

x = 56.

Therefore, there were 56 $5 bills.

The value of the tangent TU for the circle with secant through U which intersect the circle at points V and W is equal to 12

Circle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, secants, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.

For the tangent TU and the secant through U which intersect the circle at points V and W;

TU² = UV × VW {secant tangent segments}

(5x)² = 9 × 16

(5x)² = 144

5x = √144 {take square root of both sides}

5x = 12

x = 12/5

so;

TU = 5(12/5)

TU = 12

Therefore, the value of the tangent TU for the circle with secant through U which intersect the circle at points V and W is equal to 12

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The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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well, let's just divide them anyway and check it out.

hmmm 6.1 ÷ 0.1, well, when dividing decimals, we can first check the decimals on each hmmm 6.1 has one decimal and 0.1 has one decimal, so for the one decimal on 6.1 0.1 gets one "0" and for each decimal on 0.1, 6.1 gets  one "0".

That means we can change the values with no dots to say 610 and 10, so we end up with a division of 610 ÷ 10 = 61.  We can write that as 61.0 hmmm woopsie, the dot moved to the right by one slot.

Given:

The set of data points on the graph.

To find:

The equation of line that connects the set of data points.

Solution:

From the given graph it is clear that the data points are (20,40), (35,50), (50,60), (65,70).

If a line passes through two points \((x_1,y_1)\) and \((x_2,y_2)\), then the equation of line is

\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)

Let as consider the line passes through (20,40) and (50,60), then the equation of line is

\(y-40=\dfrac{60-40}{50-20}(x-20)\)

\(y-40=\dfrac{20}{30}(x-20)\)

\(y-40=\dfrac{2}{3}(x-20)\)

Multiply both sides by 3.

\(3(y-40)=2(x-20)\)

\(3y-120=2x-40\)

Isolate variable terms.

\(-2x+3y=120-40\)

\(-2x+3y=80\)

Therefore, the standard form of the required line is \(-2x+3y=80\).

We can use the radical rules to simplify the product 3(4x2). To start, we simplify 4 to its square root, which equals 2. Next, we employ the power property of radicals, which asserts that (a,m) = (a(m/2)), to simplify the cube root (x2) by using it. In this instance, (x2) = x.

We now get 3 * 2 * x, which simplifies to 6x when the simpler terms are combined.The result is that the product 3(4x2) has the simplest form (6x).We can dissect the constituent parts and use the radical-simulation principles to simplify the product 3(4x2).In the beginning, we may reduce the square root of 4 to 2: 3(2x2).Then, since it contains a square (2) and a cube root (), we can reduce them as follows:

3 * 2 * x^(²/³)Taking the square root before the cube root is shown by the exponent 2/3. We may calculate the exponent by reducing it to: 3 * 2 * x(2/3)The terms are then combined when we multiply the coefficients: 6 * x(2/3)As a result, 6x(2/3) is the product of 3(4x2) in its simplest form.

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The Above expression can be Evaluated to get :

or