Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.0 , x<0f(x) = ((x^2)/4) , 0 <= x <= 21 , 2<= xUse the cdf to obtain the following. (If necessary, round your answer to four decimal places.)(a) P(X %u2264 1)(b) P(0.5 %u2264 X %u2264 1)(c) P(X > 1.5)(d) The median checkout duration [solve 0.5 = F(mew)](e) Use F'(x) to obtain the density function f(x)(f) Calculate E(X)(g) Calculate V(X) and %u03C3x(h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].

Answer:

62%

Step-by-step explanation:

Percentage markdown = \(\frac{inital price - new price}{initial price}\) × 100

\(\frac{325 - 123.50}{325}\) x 100

\(\frac{201.50}{325}\) x 100 = 62%

Divide number of pens given by percentage:

2/0.25 = 8

She has 8 pens total.

Answer:

49.629629...

Step-by-step explanation:

1211 = 1 + 3 + 2*3^2 + 1* 3^3

=  4 + 18 + 27

= 49.

0.122

= 1 *3^-1 + 2*3^-2+2*3^-3

= 0.629629....

30.3 m/s is the correct answer.

Answer:

both

Step-by-step explanation:

given sss, you will need to use Law of Cosines.

However, one you get one of the angles, the easiest way to solve for the second angle is to just use law of sines.

The value of x can be found by using the formula for the area of a trapezoid. The value of \($x$\) is \($4$\) inches.

Area is a two-dimensional measurement that is used to measure the size of a shape or surface. It is measured in square units, such as square centimeters, square meters, square kilometers, and so on. The formula for the area of a trapezoid is: \((a+b)/2 *h\), where a and b are the lengths of the parallel sides, and h is the height. Mrs. Katz needs to calculate the value of x by plugging in the lengths of the parallel sides and the height into the formula.

We know that the opposite sides of a trapezoid are parallel, so we have \(AB \parallel DC.\)

Using the given information, we can set up an equation in terms of \($x$\) and solve for it. We know that the height of the trapezoid is \($8$\) inches, and we know that the bases are \($x$\) inches and \($16$\) inches.

Using the formula for the area of a trapezoid, we have:

\(\text{Area} = \frac{1}{2}(AB+DC)(\text{height})\)

Plugging in the values we know, we get:

\(\text{Area} = \frac{1}{2}(x+16)(8)\)

We are also given that the area of the trapezoid is \($100$\) square inches, so we can set up an equation:

\(100 = \frac{1}{2}(x+16)(8)\)

Simplifying and solving for \($x$\), we get:

\(100 &= \frac{1}{2}(x+16)(8)\20 &= (x+16)\x &= 4\)

Therefore, the value of \($x$\) is \($4$\) inches.

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The surface area of the prism in this problem is given as follows:

S = 636 m².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

The figure for this problem is composed as follows:

Hence the surface area for this problem is given as follows:

S = 2 x (14 x 6 + 14 x 7 + 6 x 7 + 4 x 6 + 4 x 7 + 6 x 7)

S = 636 m².

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There are 11/18 miles does the car travel in 1 minute.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A car travels 2 3/4 miles in 4 1/2 minutes.

Now,

Since, A car travels 2 3/4 miles in 4 1/2 minutes.

Hence, The distance cover by car in 1 minute = 2 3/4 ÷ 4 1/2

                                                                       = 11/4 ÷ 9/2

                                                                       = 11/4 × 2/9

                                                                       = 11/18 miles

Thus, The car travel 11/18 miles in 1 minute.

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Answer:

x = 124

y = 56

z = 124

Step-by-step explanation:

Vertical angles are congruent (equal) , so Y and angle of 56° are equal

angles x and angle of 56° are equivalent to 180° , so

180 - 56 = 124° -> x = 124°

angle x and z are vertical angles (such as that of y and angle of 56°) so they are equivalent! Making Z = 124°

Answer :-

x = 124°

y° = 56°

z° = 124°

Step-by-step explanation :-

x and 56° are linear angles.

Sum of linear pair of angles is always 180°

x + 56 = 180

x = 180 - 56

x = 124° _____(i)

Opposite angles are always equal :-

y° = 56°

From eqn (i) we have , x = 124°

x = z°

z° = 124°

When two lines intersect, we have following results.

It is true that when you design an algorithm, it should be general enough to provide a solution to many problem instances, not just one or a few of them.

In mathematics, an algorithm is a process, a description of a series of steps that may be used to solve a problem; however, they are now far more prevalent than that.

Although many areas of research (and daily life) employ algorithms, long division's step-by-step process is probably the most prevalent example.

Thus, It is true that when you design an algorithm, it should be general enough to provide a solution to many problem instances, not just one or a few of them.

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The probability for getting the different numbers when two dice are thrown is: 5/6.

The sample space formed by rolling two dice are: 6*6 = 36.

Total number of pairs having same number = (1,1), (2,2),(3,3),(4,4),(5,5),(6,6) = 6 samples.

Thus,

Number of outcomes having different numbers:

36 - 6 = 30

Probability (different numbers) = total number of different number / total outcomes.

Probability (different numbers) = 30 / 36

Probability (different numbers) = 5/6

Thus, the probability for getting the different numbers when two dice are thrown is: 5/6.

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Answer:

He will burn 224 calories.

Step-by-step explanation:

Multiply 8 by 28 to get your answers because he runs 8 times more in 24 minutes.

:))

To access the first element of an array of integers called "numbers," you can use the expression:
numbers[0]`
This expression uses the array name "numbers" and the index "0" to access the first element.

To access the last element of "numbers," assuming it contains 10 elements, use the expression:

`numbers[9]`

Here, we use the index "9" since arrays are zero-indexed, meaning the last element in a 10-element array has an index of 9.
To access the first element of the array called numbers, we would use the expression "numbers[0]."

To access the last element of the array, assuming it contains 10 elements, we would use the expression "numbers [9]" since arrays are zero-indexed in most programming languages.

To access the last element of the array regardless of its length, we can use the expression "numbers [numbers.length-1]," which subtracts 1 from the length of the array to access the last element.
To access the last element, regardless of its length, use the expression:

'numbers [numbers. length - 1]'

This expression uses the "length" property of the array to find the total number of elements and subtracts 1 to get the correct index for the last element.

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Answer:

num 1 is answer...

The mean of the new set of scores can be calculated by summing up all the scores and dividing it by the total number of scores. In this case, the scores obtained are 49, 53, 27, 20, 27, 36, 49, 27, 61, and 28.

To find the mean, we add up all these scores: 49 + 53 + 27 + 20 + 27 + 36 + 49 + 27 + 61 + 28 = 377.

Since there are 10 scores in total, we divide the sum by 10: 377/10 = 37.7.

Therefore, the mean of the new set of scores is 37.7.

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The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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Parallel lines are two straight lines that never cross. For this to happen, the lines have to have the same slope.

In this case, the equation given is in what's called "slope-intersect" form. The general form of the slope intercept formula is y=mx + b where m is the slope of the line and b is the point on the Y-axis where the line crosses.

The equation given is y=5x+3 and since the 5 is in the place of m from the general equation, 5 is the slope. Since parallel lines have the same slope, 5 is the answer.

Slope-Intercept Form:

When we're given a linear equation we can immediately see if it's in the slope-intercept form if it follows the format  y=mx+b. As long as y does not have a coefficient the slope and y-intercept are the values of m and b.

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Answer:

x<7

Step-by-step explanation:

65-8x>9

-8x>9-65

-8x>-56

x<7

Answer:

x<7

Step-by-step explanation:

65-8x>9

-8x>9-65

-8x>-56

x<7

Step-by-step explanation:

g(x) = - x² + 10x - 3

To get the g(9) substitute X in the equation for 9

g(9) = - 9² + 10(9) -3

g(9) = 81 + 90 - 3

g(9) = 171 - 3

g(9) = 168

Similarly to get g(-1)

g(-1) = - (-1)² + 10(-1) - 3

g(-1) = - 1 - 10 - 3

g(-1) = - 14

The mean of the price-earning ratios is 7.32 (rounded to two decimal places).

To find the mean of the price-earning ratios, we need to calculate the average.

First, let's list the price-earning ratios and their corresponding frequencies:

-0.5 to -4.5 (frequency: 27)

4.5 to -9.5 (frequency: 33)

9.5 to -14.5 (frequency: 23)

14.5 to -19.5 (frequency: 13)

19.5 to -24.5 (frequency: 1)

24.5 to -29.5 (frequency: 1)

29.5 to -34.5 (frequency: 2)

To find the mean, we multiply each price-earning ratio by its frequency, then sum up the products, and finally divide by the total frequency.

Mean = ((-0.5 * 27) + (4.5 * 33) + (9.5 * 23) + (14.5 * 13) + (19.5 * 1) + (24.5 * 1) + (29.5 * 2)) / (27 + 33 + 23 + 13 + 1 + 1 + 2)

Calculating this expression gives us the mean of the price-earning ratios.

Mean = 7.32

Therefore, the mean of the price-earning ratios is 7.32 (rounded to two decimal places).

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a) The probability that in the next eight tries, the number of free throws he will make exactly 8 is equals to the 0.27249.

b) The probability that in the next eight tries, the number of free throws he will make exactly 5 is equals to the 0.08386.

We have a professional basketball player makes 80% of the free throws he tries.

let X be the number of free throws he will make in the next 8 tries. He makes 80% of the free thwors he tries. So, for binomial distribution, X~Bin(8,0.80)

so the probability mass function of X is P[X =x] = ⁸Cₓ 0.85ˣ (1-0.85)⁽⁸⁻ˣ⁾, x = 0,1, 2,..8

P[ X = x] = 0 otherwise.

a) So, the probability that he makes exactly 8 throws isP,(X=8)

= ⁸C₈(0.85)⁸ (1- 0.85)⁰

=0.27249

b) the probability that he makes exactly 5 throws is, P[X=5]

=⁸C₅0.855(1-0.85)⁽⁸⁻³⁾=56×0.855×0.153

=0.08386

Hence required probability is 0.083.

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Answer:

9/10 or 0.9

Step-by-step explanation:

Slope of a line passing through two points (x1, y1) and (x2, y2) is given by
Slope m = rise/run

where
rise = y2 - y1
run = x2 - x1

Given points (- 6, - 5) and (4, 4),

rise = 4 - (-5) = 4 + 5 = 9

run = 4 - ( - 6) = 4 + 6 = 10

Slope = rise/run = 9/10 or 0.9

Answer:

52

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

The statement "if the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other" is true. The dot product of two vectors is zero if and only if the vectors are perpendicular.

The dot product of two vectors is defined as the product of their magnitudes and the cosine of the angle between them. When the dot product is zero, it means that the cosine of the angle between the vectors is zero, which occurs when the vectors are perpendicular.

In other words, the dot product being zero indicates that the vectors are at a 90-degree angle to each other, supporting the statement that they are perpendicular.

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The value of the sides are;

FG = 4. 06

EF = 6. 59

<E = 38 degrees

From the information given, we have;

Using the tangent identity;

tan 52 = 5.2/FG

cross multiply the values, we have;

FG = 4. 06

Then,

using the sine identity, we have;

sin 52 = 5.2/EF

cross multiply the values, we get;

EF = 6. 59

To determine the angle E, we have;

sin E = 4.06/6. 59

Divide the values

sin E = 0. 6160

E = 38 degrees

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Answer: equation is (y5+g(x)

Step-by-step explanation: Percent change = 56 - 32 |32| × 100% = 24 32 × 100 = 75% (increase). Where: 32 is the old value and 56 is the new value. In this case we have a positive

Answer: 0.2 square meters.

Step-by-step explanation:

We are given the equation:

3600b² = hw

We need to find the value of b, given that h = 168 cm and w = 60 kg.

First, we need to convert the height from centimeters to meters:

h = 168 cm = 1.68 m

Substituting the given values:

3600b² = (1.68)(60)

3600b² = 100.8

b² = 100.8/3600

b² = 0.028

Taking the square root of both sides:

b = √0.028

b ≈ 0.167

Rounding to the nearest tenth:

b ≈ 0.2

Therefore, the body surface area of a person who is 168 centimeters tall and weighs 60 kilograms is about 0.2 square meters.

The term that describes a group of statements that executes as a single unit is a "block". A block of code is a program that is grouped together and treated as a single unit. So, the correct option is D.

In computer programming, a block is a group of statements or declarations that are enclosed within a set of curly braces ({ }). The block serves as a single unit that is executed together. Blocks are used to organize code and to apply control structures, such as loops and conditional statements, to multiple statements.

A block can contain any number of statements, which can include variable declarations, function calls, loops, conditional statements, and other constructs. The statements within a block are executed in sequence, one after another, unless a control statement is encountered that alters the normal sequence of execution.

For example, a while loop in Java consists of a block of code that is executed repeatedly while a certain condition is true:

while (condition) {

   // block of code to be executed while condition is true

}

In this example, the block of code inside the curly braces will be executed repeatedly while the condition specified in the while statement is true. The block can contain any number of statements, and these statements will be executed each time the loop iterates.

Another common use of blocks is to define functions or methods. A function or method is a block of code that can be called from other parts of the program, and can take inputs (arguments) and return outputs. For example, in Python, a function can be defined as follows:

def function(argument1, argument2):

   # block of code to be executed in the function

   return result

In this example, the block of code enclosed within the function definition is executed when the function is called. The function can take inputs (argument1 and argument2), which can be used within the function, and it can return a result using the return statement.

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