Consider the experiment of rolling a die, S={1,2,3,4,5,6). Let the random variable X denote the outcome. What is the variance of X? A. 6 B. 7/2 C. 35/42D. None of the above

The percentile rank of 64 in the twelve students exam result is 42%

Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.

Ordering the data we have:

90 64 99 71 72 93 40 85 45 50 55 66

40 > 45 > 50 > 55 > 64 > 66 > 71 > 72 > 85 > 90 > 93 > 99

The 64 result is the 5th term of all the results, so:

percentile rank = (term / total term) * 100%

percentile rank = 5/12 * 100%

percentile rank = 41.66%

41.66% round to the nearest percentile 42%

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The distance in feet from the bottom of the lighthouse to the ferry is 154 feet.

What is the angle of depression?

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

The angle of depression is always measured from the horizontal.

A triangle is formed by the lighthouse, the ground, and the ferry. The angle of depression is not in the triangle, but it is equal to the angle of elevation at the ferry. (Alternate angles on parallel lines)

The angle at the top of the lighthouse, inside the triangle is:

90° − 37° = 53°

The distance to the boat is the side opposite the angle of 63° while the height of the lighthouse is the adjacent side.

opposite / adjacent = tan53°

distance / 116 = tan53°

distance = 116 × tan53°

= 153.932 feet

= 153.9 feet. (approximately)

Hence, the distance in feet from the bottom of the lighthouse to the ferry is 153.9 feet.

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To complete the square for the equation x2 - 16x + 60 = -12, add 64 to each side of the equation. This will give us x2 - 16x + 124 = 52.

Then, factor out the coefficient of x2 (1) and the coefficient of x (16). This will give us (x - 8)2 = 52. Finally, subtract 52 from both sides to get (x - 8)2 = 0. Solving for x yields x = 8.

Equations are mathematical statements that express the equality of two expressions. They involve one or more unknowns that are represented by variables and involve numbers, constants, and operators. An equation states that the expressions on either side of the equal sign have the same value.

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Answer:

C) 2

Step-by-step explanation:

Mode means which number do you have the most of.  You have the most 2's.

Answer:

answer is 28

Step-by-step explanation:

10(2•4/5)

20 + 8

= 28

When you write it this way you distribute it so 10 is outside the parenthesis so you time 10 to bout of the numbers inside of it then add.

Answer:

Step-by-step explanation:

( 9^2 ) = 23

False, Two data points are not sufficient to determine whether a model is linear or quadratic.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

a linear model has two parameters only (y = a*x+b). You may also remember that two data points are generally enough to fit a straight line. If you consider a quadratic model with three parameters (y = a*x²+b*x+c), you'll need at least three data points.

in regression analysis, many researchers say that there should be at least 10 observations per variable. If we are using three independent variables, then a clear rule would be to have a minimum sample size of 30. Some researchers follow a statistical formula to calculate the sample size.

therefore, At least three Data points are required to determine whether a model is linear or quadratic.

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An algorithm to find all nodes less than some value in a binary heap is binary_heap (int, int)

The term called algorithm is defined as  a set of instructions for solving a problem or accomplishing a task.

Here we have know that the binary heap is a full binary tree that means all of its node full with 2 children except last one it may have one child or even empty Also in min heap, all node has value less than its children values in a max heap all node has a value greater than then it can be written as,

void binary_heap(Node *node, int x)

{

   if (node->value >= o(x))

   {

       return 0;

   }

   printf("%d\n", node->value);

   if (node->left != NULL)

       binary_heap(node->left, x);

   if (node->right != NULL)

      binary_heap(node->right, x);

}

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Answer:

yes 2 is only even prime number because it was divide by only 1 and 2

Answer:

yes

Step-by-step explanation:

Yes....every other even number is divisible by two which means they cannot be prime.  Primes are divisible only by 1 and the number itself.

Concentric circles are internally tangent circles which is the true statement.

Geometry is the description of figures in a space with a specific number of dimensions and types. Plane geometry is the most prevalent sort of geometry (dealing with objects like the point, lines, circles, triangles, and polygons)

Concentric circles are circles that have the same center but different radii.

When two concentric circles are drawn, it is possible for them to be internally tangent, meaning that they touch each other at exactly one point and the point of tangency is inside both circles.

In this case, one circle is entirely contained within the other circle.

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The value of ML is 29.2.

Option B is the answer.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Two similar triangles:

So,

NL/RN = ML/QR

70/48 = ML/20

ML = (70 x 20) / 48

ML = 1400/48

ML = 29.2

Thus,

ML = 29.2

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Answer:

Step-by-step explanation:

64% as a fraction in its simplest form is 32/50.

As a decimal, 64% is equal to 0.64.

The answer will be option C (3.90 cm).

To find the diameter, we need to determine the exact length reading on the main scale and then add the Vernier scale reading. We know that 10 divisions of the Vernier scale coincide with 9 divisions of the main scale.

If the zero of the Vernier scale lies slightly to the left of 3.2 cm on the main scale, then we can assume that it lies between the 3rd and 4th division of the main scale. Since the 4th division of the Vernier scale coincides with a main scale division, we can determine that the length reading on the main scale is 3.3 cm.

Next, we need to determine the Vernier scale reading. Since the 4th division of the Vernier scale coincides with a main scale division, the reading on the Vernier scale is 0.1 cm. Adding the main scale reading (3.3 cm) and the Vernier scale reading (0.1 cm), we get a total length reading of 3.4 cm.

Since the cylinder is tightly placed between the jaws of the callipers, we can assume that this length reading is equal to the diameter of the cylinder. Therefore, the diameter of the cylinder is 3.4 cm. The answer is closest to option C (3.90 cm).

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the probability of success (0.25 in this case), and the number of successes (12 in this case). The command will then calculate the cumulative probability of 12 or fewer employees being late for work.

A company has 20 employees, and each employee has a 25% chance of being late for work. What is the probability that 12 or fewer employees will be late for work?

The calculator command Binomialcdf(20, 0.25, 12) would be used to find the solution.

Binomialcdf is a calculator command used to calculate the cumulative probability of a binomial distribution. The command takes three parameters: the number of trials (20 in this case), the probability of success (0.25 in this case), and the number of successes (12 in this case). The command will then calculate the cumulative probability of 12 or fewer employees being late for work.

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Answer:

In Princeton's wig shop, the total number of wigs is the sum of the number of blonde wigs and the number of brunette wigs. Since 1/4 of the wigs are blonde and 2/3 of the wigs are brunette, the fraction of wigs that are either blonde or brunette is 7/12.

Answer:

[tex]\frac{11}{12}[/tex]

Step-by-step explanation:

[tex]\frac{1}{4}[/tex] + [tex]\frac{2}{3}[/tex]  The common denominator is 12  make equivalent fractions with 12 as the denominator

[tex]\frac{1}{4}[/tex] x [tex]\frac{3}{3}[/tex] = [tex]\frac{3}{12}[/tex]

[tex]\frac{2}{3}[/tex] x [tex]\frac{4}{4}[/tex] = [tex]\frac{8}{12}[/tex]

[tex]\frac{3}{12}[/tex] + [tex]\frac{8}{12}[/tex] = [tex]\frac{11}{12}[/tex]

Container 1: The unit rate for Container 1 from Home Depot is $14.98 per gallon. Container 2: The unit rate for Container 2 from Lowes is $115.00 per gallon. The unit rate for each container tells us how much one gallon of paint costs from each store.

The unit rate for the paint from Home Depot is $14.98 per gallon and the unit rate for the paint from Lowes is $115.00 per gallon. This tells us that the paint from Home Depot is cheaper than the paint from Lowes.

Step 1: To calculate the rate for each container, divide the cost of the container by the number of gallons in the container.

Container 1: $14.98 per gallon = $14.98 / 1 gallon

Container 2: $115.00 per gallon = $115.00 / 1 gallon

Step 2: To calculate the unit rate for each container, divide the cost of the container by the number of units in the container.

Container 1: $14.98 per gallon = $14.98 / 1 unit

Container 2: $115.00 per gallon = $115.00 / 1 unit

Step 3: The unit rate for each container tells us how much one gallon of paint costs from each store.

Container 1: The unit rate for Container 1 from Home Depot is $14.98 per gallon.

Container 2: The unit rate for Container 2 from Lowes is $115.00 per gallon.

The theory used in this question is the concept of unit rate, which is used to compare the prices of different products.

Unit rate is defined as the cost per unit of measure (e.g., price per gallon, price per pound, etc.).

In this case, we are using the unit rate of price per gallon to compare the prices of paint from Home Depot and Lowes.

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The three examples of random experiments and their possible outcomes are stated above.

A random experiment is a type of experiment that has multiple possible outcomes

Given is to write three examples of random experiments and their possible outcomes.

{ 1 } -

Experiment : Tossing a coin three times

Possible outcomes : Number of possible outcomes = 8

Sample space : {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}

{ 2 } -

Experiment : Three coins are tossed simultaneously

Possible outcomes : Number of possible outcomes = 8

Sample space : {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}

{ 3 } -

Experiment : Rolling a pair of dice simultaneously

Possible outcomes : 36

Sample space : {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Therefore, the three examples of random experiments and their possible outcomes are stated above.

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{Question in english -

Write three examples of random experiments and their possible outcomes.}

Step-by-step explanation:

Without doing any math, 1,697.5

35.0 and 16,975 is the original

3.5 is 35.0, but they moved the decimal one point to the left

We do the same for the answer

16,975... we move the comma one point to the left and get 1,697.5

Answer:

Step-by-step explanation:

I don't know what you want to find but

CB ^2 = AC^2 + AB^2 -2AC.AB.Cos(BAC) Cosine Rule

CB^2 = 9 +64 - 2.3.8.Cos(40)

CB ~ 6

The probability that George drove given that he is late is approximately 0.355 or 35.5%.

Let's call the event of George being late "L". The problem is asking for P(Drives | L), which is the probability that George drove given that he is late.

We can use Bayes' theorem to find this probability:

P(Drives | L) = P(L | Drives) * P(Drives) / P(L)

P(L | Drives) is the probability that George is late given that he drove, which is given as 55%.

P(Drives) is the prior probability that George drives, which is given as 20%.

P(L) is the overall probability that George is late, which can be found by summing up the individual probabilities of George being late for each mode of transportation and weighting it by the corresponding prior probability of using that mode of transportation:

P(L) = P(L | Walks) * P(Walks) + P(L | Cycles) * P(Cycles) + P(L | Drives) * P(Drives) + P(L | Bus) * P(Bus)

P(L | Walks) is the probability that George is late given that he walks, which is given as 15%.

P(Cycles) is the prior probability that George cycles, which is given as 30%.

P(Bus) is the prior probability that George takes the bus, which is given as 40%.

P(L | Bus) is the probability that George is late given that he takes the bus, which is given as 20%.

Substituting these values into the formula for P(L) and simplifying:

P(L) = 0.15 * 0.10 + 0.10 * 0.30 + 0.55 * 0.20 + 0.20 * 0.40

= 0.155

Finally, substituting the values for P(L | Drives), P(Drives), and P(L) into the formula for P(Drives | L) and simplifying:

P(Drives | L) = 0.55 * 0.20 / 0.155 = 0.55 / 0.155 = 3.548

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The coordinate points on the first quadrant represent the possible dimensions of the rectangle with an area of 32 m².

A function describes a relationship between a dependent and independent variable. Example -

y = f(x) = 5x + 9

Given is that the area of a rectangle is 32 m².

Assume that the length and breadth of the rectangle are {x} m and {y} m respectively. We can write the area of the rectangle as -

xy = 32

We can write -

y = 32/x                                    .... Eq { 1 }

The dimensions cannot be negative. So, the coordinate points on the first quadrant represent the possible dimensions of the rectangle.

Therefore, the coordinate points on the first quadrant represent the possible dimensions of the rectangle with an area of 32 m².

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Answer:

Step-by-step explanation:

10/100*132

Answer:

Step-by-step explanation:

The formula of C.P is Selling Price - Profit

Here the S.P. =132

Profit = 10%

Converting 10% = 10/100*132

                             = 13.2

Putting values into Formula :

132-13.2 = 118.8

so, the answer is 118.8

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Answer/Step-by-step explanation:

All numbers that are divisible by 9 are also divisible by 3.

Since 3 goes into 9, if 9 is a factor, 3 is also a factor.

Example:

81 is divisible by 9.

So, 81 is also divisible by 3.



Another example:

1,273,050 is divisible by 9.

So 1,273,050 is also divisible by 3.

But the other way around is not necessarily true. If 3 goes into a number, 9 may or may not go into the number.

That is, if a number is divisible by 3, you cannot necessarily know that it is divisible by 9.

Example (seems like it works):

18 is divisible by 3. 18 is also divisible by 9.

But it doesn't work every single time so it cannot be a rule.

Example(sometimes it doesn't work):

24 is divisible by 3.

24 is not divisible by 9.

for both categorical and numerical variables the difference between the relative frequency and the percent frequency is option B: The percent frequency equals the relative frequency multiplied by 100.

Relative frequency and percent frequency are two measures of the frequency of an event or category within a data set.

Relative frequency is the ratio of the number of times an event or category occurs divided by the total number of events or categories.

Percent frequency is the relative frequency expressed as a percentage. This means that it is equal to the relative frequency multiplied by 100. In other words, the percent frequency represents the proportion of occurrences of an event or category as a percentage of the total number of events or categories.

So, the difference between relative frequency and percent frequency is that relative frequency is a ratio, while percent frequency is the same ratio expressed as a percentage.

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See full question below

for both categorical and numerical variables what is the difference between the relative frequency and the percent frequency?

-The relative frequency equals the percent frequency multiplied by 100.

-The percent frequency equals the relative frequency multiplied by 100.

-As opposed to the relative frequency, the percent frequency is divided by the number of observations in the data set.

-As opposed to the percent frequency, the relative frequency is divided by the number of observations in the data set.

There is only 1 possible list of positive integers that have a mean, median, mode, and range of 5

As per the data given,

We have, a lit of 5 positive integers.

The sum of the five positive integers must equal five in order for the mean, median, mode, and range to all be five.

This is because the range of a set of equal numbers will always be 0, the mean of a set of equal numbers will always equal the numbers themselves, the median of a set of equal numbers will always equal the mean, the mode of a set of equal numbers will always equal the numbers themselves, and so on.

Therefore, there is only 1 possible list of positive integers that have a mean, median, mode, and range of 5: [5, 5, 5, 5, 5].

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Answer:

12x^2 - 13x + 3 is a quadratic equation in the standard form ax^2 + bx + c, where a = 12, b = -13, and c = 3. This equation can be factored, completed the square or used the quadratic formula to find the solutions of x.

Therefore , the solution of the given problem of linear equation comes out to be she took 3 days , 5 days and 7 days respectively.

The formula y=mx+b serves as the basis for a linear curve of regression. m is the y-intercept, while B is the slope. Despite the fact that y and y are independent elements, the preceding sentence is usually referred to as a "math equation with two variables." Bivariate linear equations have just two variables in them. Application problems involving linear equations have no known solutions.

Here,

Given :

y= total days

where x is the days she took to do the assignments

=> y = 2x + 3

At x = 0.

=> y = 2(0) + 3 = 3

At x = 1

=> y = 2(1) + 3 = 5

At x =2

=> y = 2(2) + 3 = 7

Therefore , the solution of the given problem of linear equation comes out to be she took 3 days , 5 days and 7 days respectively.

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The graph of the system of inequalities x-y≥3 and x+y≤9 is attached.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

x-y is greater than or equal to 3, x+y is equal to or less than 9

x-y≥3

x+y≤9

Combine the intervals

x≥3 and x≤9

Now merge the overlapping intervals

3≤x≤9

Hence, the graph of the system of inequalities x-y≥3 and x+y≤9 is attached.

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