a. show that the properties of a probability distribution for a discrete random variable are satisfied.

The amount of interest due on the account is $8.36.

The interest on a loan or deposit can be calculated using simple interest. In order to calculate it, multiply the principal amount by the interest rate and then by the number of time periods (usually in years).

We must first determine the number of days for which the interest will accrue in order to calculate the amount of interest owed on the account. Since the charge was made on the 28th day after the payment was made on the 9th day, the interest will accrue for 19 days instead of the 28 since the payment was made.

We then use the formula for simple interest: Interest = Principal x Rate x Time

In this instance, the Principal is the initial balance of $660, the Rate is the annual percentage rate (APR), which needs to be converted to decimal form by dividing by 100, and the Time is the total number of days over which interest will accrue (19 days).

The Interest = $660 × 0.26 × (19/365) = $8.36

Thus, the total amount of interest due on the account is $8.36.

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Answer:

Step-by-step explanation:

Given the system of equation

3x1 − 2x2 + x3 = −10 ............. 1

2x1 + 6x2 − 4x3 = −10 ............ 2

−8x1 − 2x2 + 5x3 = −26  ............... 3

Reduce the system of equations:

multiply equation 1 by 3 and add to 2

Eqn 1 * 3 gives;

9x1 − 6x2 + 3x3 = −30

Add to equation 2:

9x1+2x1 +(3x3-4x3) = -30-10

11x1 - x3 = -40 ........... 4

multiply eqn 3 by 3 and add to eqn 2

eqn 3 * 3 gives

−24x1 − 6x2 + 15x3 = − 78

Add to eqn 2:

-24x1+2x1)+15x3-4x3 = -78-10

-22x1 + 11x3 = -88 ......... 5

solve 4 and 5:

11x1 - x3 = -40 ........... 4 * 2

-22x1 + 11x3 = -88 ......... 5 * 1

.....................................................

22x1 - 2x3 = -80

-22x1 + 11x3 = -88

Add together:

-2x3 + 11x3 = -80-88

9x3 = -168

x3 = -168/9

x3 = 18.7

subtitute x3 = 18.7 into 4

11x1 - 18.7 = -40

11x1 = -40+18.7

11x1 = -21.3

x1 = -21.3/11

x1 = -1.93

Substitute x1 and x3 into 1

3(-1.93)− 2x2 + 18.7 = −10

- 5.79-2x2 = -28.7

-2x2 = -18.7 +5.79

-2x2 = -22.91

x2 = 11.455

Hey there mate :)

Analysis :

\(401 = 515 - 114 = u - 6\)

And

\(173 = 515 - 3.114 = u - 36\)

\( = \frac{p(u - 36 < u < u + 36) - p(u - 6 < u < u + 6)}{2} \)

\( = \frac{99.73percent - 68.21percent}{2} \)

\( = \frac{31.46percent}{2} \)

\( = {15.73percent}\)

Then, calculating,

\(u - 26 = 515 - 2 \times 114 = 287\)

And

\(u + 26 = 515 + 2 \times 114 = 743\)

Then,

\(The \: Range = (287,743)\)

Final Answers :-

15.73 %

(287,743)

~Benjemin360

Using sampling concepts, the population and the sample are given as follows:

d. population: 6,000 batches of 100 cards sample: every 100th batch.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So I ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and then:

Hence, in the situation described the population is the 6,000 batches of 100 cards, while the sample is every 100th batch, hence option d is correct.

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The perimeter of the shape is 10 inches.

It's important to note that the perimeter of a shape or calculated by adding all the sides together.

In this case, this is a rectangle and the perimeter will be:

Perimeter = 2(length + width)

Length = 4 inches

Width = 1 inch

Perimeter = 2(length + width)

Perimeter = 2(4 + 1)

Perimeter = 10 inches.

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Answer:

  zero

Step-by-step explanation:

You want to know the remainder of the polynomial function for the divisor to be a factor?

A divisor is a factor of the dividend in any division problem if and only if the remainder is zero (0).

The divisor will be a factor of a polynomial function if division of the function by that divisor has a remainder of zero.

Answer:

Step-by-step explanation:

step 1

100%/the total number = percent for one probability

100/5 = 20%

2 and 4 is even.

total even number * percent for one probability = total percent for even number

20% * 2 = 40%

therefore total even number is 40%

The probability is:

Step-by-step explanation:

Remember the formula for probability:

\(\boxed{\!\!\boxed{\bold{Probability=\frac{Favourable~outcome}{total~outcomes}\quad}}\!\!}\)

In this case, the favourable outcome (an even number) is 2, because there are only 2 even numbers in the set.

As for the total outcomes, there are 5 of them, because we have 5 numbers total.

So the probability of choosing an even number is 2/5.

Thus, the value of x and y for the given right angled triangle are found as:   x = 8 and y = 2√3.

The Pythagorean Theorem, a well-known geometric principle that states that the square just on hypotenuse (the side across from the right angle) of a right triangle equals the sum of the squares on its legs, is also known as the

a² + b² = c².

For the larger triangle, applying Pythagorean theorem:

4² + (4√3)² = x²

x² = 16 + 16*3

x² = 16 + 48

x² = 64

x = 8

Then, x - 6 = 8 - 6 = 2

Now applying Pythagorean theorem for smaller triangle:

y² + (x - 6)² = 4²

y² =  4² - 2²

y² =  16 - 4

y² =  12

y² =  √12

y = 2√3

Thus, the value of x and y for the given right angled triangle are found as:   x = 8 and y = 2√3.

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Answer: 8

Step-by-step explanation:

12*2/3=8

Answer:

Step-by-step explanation:

The following is the information provided

number of students is 5

The number of math major = 3

The number of statistic major = 2

Label math students as A, B, C

And statistic students as D, E

The total number of ways to select two students from 5 students is 10

The sample space is S = {AB,AC,BC,AD,AE,BD,BE,CD,CE,DE}

Yes , in the sample space the events are equally alike

What is the probability that both selected students are statistics majors

The selected students of statistic major are DE

the probability that both selected students are statistics majors is \(\frac{1}{10}\)

= 1/10

What is the probability that both students are math majors

The selected students of statistic major are AC,AB,BC

the probability that both selected students are math majors is \(\frac{3}{10}\)

= 3/10

What is the probability that at least one of the students selected is a statistics major

Number of ways to select at least one of the students selected is a statistic major is {AD,AE,BD,BE,CD,CE,DE}

the probability that at least one of the students selected is a statistics major is \(\frac{7}{10}\)

7/10

What is the probability that the selected students have different majors

Number of ways to select students with different major is  {AD,AE,BD,BE,CD,CE,}

the probability that the selected students have different majors is \(\frac{6}{10}\)

6/10

Answer:

I hope this helps!

========================================================

Explanation:

We're given the height in relation to base BC, so we need to find the length of this base. This is the same as finding the distance from B to C.

Turn to the distance formula

\(d = \text{Distance from B to C}\\\\d = \sqrt{(x_1-x_2)^2+(y_1-y^2)^2}\\\\d = \sqrt{(-2-(-3))^2+(-1-(-2))^2}\\\\d = \sqrt{(-2+3)^2+(-1+2)^2}\\\\d = \sqrt{(1)^2+(1)^2}\\\\d = \sqrt{1+1}\\\\d = \sqrt{2}\\\\\)

Coincidentally, the base and height are the same. This won't always be the case.

Now we can find the area of the triangle

\(A = \text{Area of triangle}\\\\A = \frac{1}{2}*\text{Base}*\text{Height}\\\\A = \frac{1}{2}*\sqrt{2}*\sqrt{2}\\\\A = \frac{1}{2}*\sqrt{2*2}\\\\A = \frac{1}{2}*\sqrt{4}\\\\A = \frac{1}{2}*2\\\\A = 1\\\\\)

The area of the triangle is 1 square unit.

See diagram below.

(-3, 3) and (4, -1) are the points that can be used to form a right triangle to derive the distance formula to find the length of the line segment

Given the line on the xy-plane, we are to determine the points on the line that can be used to determine the distance between the two points.

The required points on the line will be the two endpoints on the line. The end points are (-3, 3) and (4, -1). The distance between this points is expressed as:

D = √(-1-3)²+(4+3)²
D = √14 + 49
D = √63

Hence the points that can be used to form a right triangle to derive the distance formula are (-3, 3) and (4, -1)

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Answer: It’s -1,-3

Step-by-step explanation:

got 100 on the test

Answer:

The point-slope equation for a line is:

\(y-\left(-1\right)=\frac{1}{5}\left(x-5\right)\)

Step-by-step explanation:

Given

We know that the point-slope form is

\(y-y_1=m\left(x-x_1\right)\)

where m is the slope of the line

substituting the values m = 1/5 and the point (5, -1)

\(y-y_1=m\left(x-x_1\right)\)

\(y-\left(-1\right)=\frac{1}{5}\left(x-5\right)\)

Thus, the point-slope equation for a line is:

\(y-\left(-1\right)=\frac{1}{5}\left(x-5\right)\)

To find the slope of the curve, first differentiate the equation of the curve and substitute the value of x in the result

The slope of the curve is the change in y coordinates with respect to the change in x coordinates of the line

To find the slope of the curve at a given point

First differentiate the given equation of the curve with respect to x

That is dy / dx.

The derivative of the equation of the curve  is the slope of the curve.

In next step substitute the value of x in the slope of the curve

The result will be the slope of the curve at a given point

Therefore, these are the steps to find the slope of the curve

I have answered the question in general, as the given question is incomplete

The complete question is:

How to find the slope of a curve at a given point?

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Answer:

3/8 or 3:8

Step-by-step explanation:

pink : not pink

6 : 16

Think of it as a fraction. Simplify it in the same way.

6/16 simplifies to 3/8

So the pink:notpink ratio is 3/8 or 3:8

Answer:

3.1

Step-by-step explanation:

23.5-6.8x

x=3

first put 3 in for x

23.5-6.8(3)

now solve the expression

23.5-20.4

3.1

Answer:

$78 i think

Step-by-step explanation:

20%=20/100

20/100x65=13

13+65=78

$78

Answer:

See below.

Step-by-step explanation:

So we have:

\(5\times(2\times1)=(5\times 2)\times1\)

The only difference between them if the placement of the parentheses. However, their value remains the same.

This is an example of the associative property of multiplication.

The identity property of addition states that the sum of any number and zero will be the original number.

In other words, of any number n:

\(n+0=n\)

Note the word "sum." This means addition.

I hope this helps!

\(\huge \bf༆ Answer ༄\)

Let's solve ~

\(\qquad \looparrowright \sf - 2 \sqrt{192 {k}^{4} } \)

\(\qquad \looparrowright \sf - 2 \sqrt{2 {}^{6} \times 3{k}^{4} } \)

\(\qquad \looparrowright \sf - 2 \times 2 {}^{3} \times {k}^{2} \times \sqrt{3} \)

\(\qquad \looparrowright \sf - 16 {k}^{2} \sqrt{3} \)

Hence, the correct choice is D

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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Answer:

268.08 cubic inches

Step-by-step explanation:

I'm sorry if this isn't helpful

Ken will receive a total dividend payment of $75 for that quarter.

We have to given that,

Ken owns 500 shares of LaceNBrace, which makes hockey equipment.

And, He receives a notice stating the company will be paying $0.15 dividend per share.

Now, For the total dividend payment Ken receives for that quarter, we can multiply the dividend per share by the total number of shares he owns:

= $0.15 per share x 500 shares

= $75

Therefore, Ken will receive a total dividend payment of $75 for that quarter.

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Answer:

i think it's x=-1 and x=7

Answer:

2 (w + 4) (w^2 - 4w + 16)

Step-by-step explanation:

Use the formulas you already know for sum of cubes, and plug in the numbers you have in the equation

Hopefully this helps - let me know if you have any questions!

Work Shown:

21/35 = (7*3)/(7*5) = 3/5

Part 5

we have the points

(0,4) and (4,8)

Find the slope

m=(8-4)/(4-0)

m=4/4

m=1

Find the equation in slope intercept form

y=mx+b

we have

m=1

b=4

so

Part 6

we have the points

(0,8) and (2,4)

m=(4-8)/(2-0)

m=-4/2

m=-2

y=mx+b

we have

m=-2

b=8

so

The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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Answer:

The answer would be 201.06

Step-by-step explanation:1. You need to have the radius and not the diameter so you would divide 16 by 2 to get 8.
2. You would plug 8 into the formula A=π\(r^{2}\), meaning it would be A=π\(8^{2}\)
3. 8 Squared is equal to 64 so the formula would now be A=π64
4. 64 x π = 201.06 giving you your final answer.
I hope that helps!

Answer:

200.96 mi²

Step-by-step explanation:

Before, finding the area of the circle, first, let us find the radius.

Given that,

diameter ( d ) ⇒ 16 mi

Let us use the below formula to find the radius of the circle.

d = 2r

16 = 2r

Divide both sides by 2.

8 mi = r

And let us find the area of the circle using the below formula.

A = π r²

A = π × 8 × 8

A = 3.14 × 64

A = 200.96 mi²