The question, “How many ways can 4 different students be selected in order from a class of 30 students?”, is a(n) _____. permutation mutually exclusive event combination independent event

Split up the interval [0, 2] into n equally spaced subintervals:

[tex]\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right][/tex]

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

[tex]r_i=\dfrac{2i}n[/tex]

where [tex]1\le i\le n[/tex]. Each interval has length [tex]\Delta x_i=\frac{2-0}n=\frac2n[/tex].

At these sampling points, the function takes on values of

[tex]f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}[/tex]

We approximate the integral with the Riemann sum:

[tex]\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3[/tex]

Recall that

[tex]\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4[/tex]

so that the sum reduces to

[tex]\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}[/tex]

Take the limit as n approaches infinity, and the Riemann sum converges to the value of the integral:

[tex]\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}[/tex]

Just to check:

[tex]\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28[/tex]

Answer:

14/15

Step-by-step explanation:

-4/5 × -7/6

Multiply numerator with numerator and denominator with denominator.

(-4×-7)/(5×6)

28/30

Simplify.

14/15

Answer:

[tex] \frac{14}{15} [/tex]

solution,

[tex] \frac{ - 4}{5} \times \frac{ - 7}{6} \\ = \frac{ - 4 \times ( - 7)}{5 \times 6} \\ = \frac{28}{30} [/tex]

divide 28 and 30 by 2 ,you will get:

[tex] \frac{14}{15} [/tex]

hope this helps..

Good luck on your assignment..

Answer:

I believe it is 12

I'm not 100% sure but if its right let me know

Sry if its not :/

Answer:

5/42

Step-by-step explanation:

11/6 - 12/7

Make denominators equal.

77/42 - 72/42

Subtract the fractions.

5/42

Answer:

Given that,

Slope of line A=2/5

We know that , slope of perpendicular line is product of slopes.

i.e. M1 • M2=-1

[tex] m1 = \frac{2}{5} \: \: [/tex]

m2=?

Now,

[tex] \frac{2}{5} \times m2 = - 1 \\ or \: m2 = - 1 \times \frac{5}{2} \\ \: m2 = - \frac{ 5}{2} [/tex]

Therefore, Slope of line B is -5/2.

Hope this helps..

Good luck on your assignment..

Answer:

x = √3

y = 1

Step-by-step explanation:

The side x, the hypotenuse 2 and the 60 degree angle are related as follows:

                                 x

sin 60 degrees = ----------

                                  2

and so side x is equal to  2 sin 60 degrees, or 2( (√3)/2), or √3.

By the Pythagorean Theorem, x^2 + y^2 = 2^2, or

                                                     3   + y^2 = 4, and so

                                                              y^2 = 1

so side y has length 1

x = √3

y = 1

The question is a True or False question

Answer:

True

Step-by-step explanation:

Given

5 ≤ x ≤ 8

Required

Is [5,8] the interval of the given range?

The interval given shows that the range of x begins at 5 and ends 8.

Start by splitting the interval to different inequalities.

1. 5 ≤ x

This implies that 5 is less than or EQUAL TO x;

The keyword needed here is EQUAL TO;

The fact that the inequality gives room for EQUALITY (=) means that the interval begins exactly at 5

2. x ≤ 8

This implies that x is less than or EQUAL TO 8;

Similarly, the keyword needed here is EQUAL TO;

The fact that this inequality gives room for EQUALITY (=) means that the interval ends exactly at 8

So, this implies that the range of values of 5 ≤ x ≤ 8 is 5, 6, 7, 8

And can be represented with [5,8]

So, the statement is true.

Answer:

8/5x + 5 = -19

8/5x = -24 (Subtract 5)

x = -15 (Multiply by 5/8)

Answer:

No

Step-by-step explanation:

Answer:

x = ±6

y = 10

Step-by-step explanation:

Solve for the top part.

x² + -4 = 32

x² = 32 + 4

x² = 36

x = √36

x = ±6

Solve for bottom part.

y + y - 4 = y + 6

2y - 4 = y + 6

2y - y = 6 + 4

1y = 10

By solving the upper part and the lower part of the matrix equation, the value of x and y are:

[tex]\mathbf{x = \pm6}\\\\\mathbf{y = 10}[/tex]

The given matrix equation can be solved by taking the upperpart to create an equation to solve for x, and also taking the lower part to create an equation to solve for y.

[tex]x^2 + (-4) = 32[/tex] (upper part)

[tex]y + y - 4 = y + 6[/tex] (lower part)

Solve each of the equation in the matrix.

Solve the upper part for x:

[tex]x^2 + (-4) = 32\\\\x^2 - 4 = 32[/tex]

[tex]x^2 - 4 + 4 = 32 + 4\\\\x^2 = 36[/tex]

[tex]x = \sqrt{36} \\\\\mathbf{x = \pm6}[/tex]

Solve the lower part for y:

[tex]y + y - 4 = y + 6\\\\[/tex]

[tex]y + y - 4 = y + 6\\\\2y - 4 = y + 6\\\\2y - y = 4 + 6\\\\\mathbf{y = 10}[/tex]

Thus, by solving the upper part and the lower part of the matrix equation, the value of x and y are:

[tex]\mathbf{x = \pm6}\\\\\mathbf{y = 10}[/tex]

Learn more here:

https://brainly.com/question/13694076

Answer:

64

Step-by-step explanation:

4/7

16x7= 112

4x16=64

Hey there! :)

Answer:

-8/27.

Step-by-step explanation:

Begin by converting 2 1/4 to an improper fraction:

2 1/4 -->   [tex]\frac{9}{4}[/tex]

Divide fractions by multiplying by reciprocal:

[tex]\frac{-2}{3}* \frac{4}{9} = \frac{-2*4}{3*9} = \frac{-8}{27}[/tex]

Therefore, -2/3 divided by 3 1/4 = -8/27.

Answer:

- 8/27

Step-by-step explanation:

-2/3 ÷ 2 1/4= - 2/3 ÷ 9/4 = -2/3 × 4/9 = - 2×4/3×9= - 8/27

Answer: 125

Step-by-step explanation:

For any number to be divisible by 5 it must end in either 0 or 5, thus for a 4 digit odd number it should end with 5 eg.1005,1015,1055 etc.

The exact number of 4 digit odd nos divisible by 5 can be calculated by using Principle of counting:

Therefore, no of possible numbers are: 5x5x5x1=125 numbers

Answer:

p=(0,2) q=(0.5,0)

Step-by-step explanation:

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

            ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                           PEACE!

Answer:

1.  perim is 43.2

2. where are the blanks? dont see any

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

In order to find the the value of x, first we need to calculate the length of the perpendicular dropped from the right angle to the hypotenuse of the given triangle.

Therefore, by geometric mean property, we have:

[tex]l(perpendicular) \\ = \sqrt{9 \times (25 - 9)} \\ = \sqrt{9 \times 16} \\ = \sqrt{144} \\ l(perpendicular) = 12 \: units \\ \\ Now \: by \: Pythagoras \: Theorem:\\ {x}^{2} = {9}^{2} + {12}^{2} \\ {x}^{2} = 81 + 144 \\ {x}^{2} = 225 \\ x = \sqrt{225} \\ x = 15[/tex]

Answer:

x = 4y+28

Step-by-step explanation:

x/4 -7 = y

Solve for x

Add 7 to each side

x/4  -7+7 = y+7

x/4 = (y+7)

Multiply each side by 4

x/4*4 = 4(y+7)

x = 4y+28

Answer: X = 4y + 28

Step-by-step explanation: Our first step will be to solve for x.

To do this, we first add 7 to both sides.

This gives us x/4 = y + 7.

Now we want to multiply each side of the equation by 4.

So we get x/4(4) = 4(y + 7).

On the right, distribute the 4 through the parenthses!

Simplifying from here, we get x = 4y + 28.

So this is our final answer.

Answer:

1152 minutes

Step-by-step explanation:

$104.64-24.00 = $ 80.64

80.64 ÷ 0.07 = 1152

Step-by-step explanation:

Refer to the two diagrams, attached

Start with the first set (soccer balls)

Hexagons (six-sides)

5 orange, 5 light green, 5 dark green, 5 light orange

total of 20 hexagons

Pentagons (5 sided black figures)

1+5+5+1 = 12 pentagons.

For the next set:

Triangles (3 sides)

5 orange+5 dark green+5 light green+5 light orange

= 20 triangles

Squares (4 sides)

5 between orange triangles+5 between light orange triangles

+ 5 between orange and green triangles

+ 5 between light orange and light green triangles

+ 10 between green and light green triangles

= 40 squares

Pentagons (5 sides)

1 at north pole + 5 between orange and green triangles

+ 5 between light green and light orange triangles + 1 at south pole

= 12 pentagons.

Summary:

Soccerball: 20 triangles + 12 pentagons + 20 hexagons

GoalScorerBall: 20 triangles + 40 squares + 12 pentagons

Answer: 1.5cm

Step-by-step explanation:

12-9=3 because it is midpoint 3/2=1.5

Answer:

A. x^11 and B. 8x.

Step-by-step explanation:

A monomial is a polynomial with just one term. That would be Options A and B.

Options C and E are trinomials.

Options D and F are binomials.

Hope this helps!

Answer:

A and B

Step-by-step explanation:

Answer:

[tex]S=6600\pi \text{ mm}^2[/tex]

[tex]S\approx 20724 \text{ mm}^2[/tex]

Step-by-step explanation:

A can of fruit is geometrically a cylinder.

We are talking about the surface area of a cylinder:

[tex]S=2\pi rh+2\pi r^2[/tex]

[tex]\pi \approx 3.14[/tex]

[tex]r: \text{radius}[/tex]

[tex]h: \text{height}[/tex]

Factoring, we have:

[tex]S=2\pi r (h+r)[/tex]

Calculating the surface area of the can of fruit:

[tex]S=2\pi (30) (80+30)[/tex]

[tex]S=2\pi (30) (110)[/tex]

[tex]S=6600\pi[/tex]

[tex]S\approx 20724 \text{ mm}^2[/tex]

Answer:

The required graph is shown below.

Step-by-step explanation:

The given equation is

[tex]4x-3y=12[/tex]

To draw the graph we need at least two points which satisfy the given equation.

At x=0,

[tex]4(0)-3y=12[/tex]

[tex]-3y=12[/tex]

[tex]y=\dfrac{12}{-3}[/tex]

[tex]y=-4[/tex]

At y=0,

[tex]4x-3(0)=12[/tex]

[tex]4x=12[/tex]

[tex]x=3[/tex]

So, (0,-4) and (3,0) are two solutions of the given equation. Plot these two points on the coordinate plane and connect them by a straight line.

The required graph is shown below.

Answer:

B)

Focus = (6,6), directrix is y = 4

Step-by-step explanation:

A parabola is the locus of a point that is equidistant from a fixed line (known as directrix) and a fixed point (known as focus).

The equation of a parabola in vertex form is given as:

[tex]y=a(x-h)^2+k[/tex]

It can be further simplified to:

[tex](x-h)^2=4p(y-k)[/tex]

The directrix of this parabola is given at line y = k - p and the focus is at (h, k + p)

Given that:

[tex]y = \frac{1}{4}(x-6)^2+ 5 \\(y-5)=\frac{1}{4}(x-6)^2\\(x-6)^2=4(y-5)[/tex]

Comparing (x-6)² = 4(y-5) with (x-h)² = 4p(y-k), It can be gotten that h = 6, p =1 and k = 5

The directrix of this parabola is given at line y = k - p = 5 - 1 = 4 and the focus is at (h, k + p) =  (6, 5+1) = (6, 6)

Focus = (6,6), directrix is y = 4

Answer:

21.5

Step-by-step explanation:

Arrange numbers from smallest to largest:

56, 65, 69, 77, 79, 82, 88, 89, 90

The interquartile range is the range in the middle of the data set, we can find it by knowing the upper and lower quartiles.

56, 65, 69, 77, 79, 82, 88, 89, 90

(65+69)/2 = 67

(88+89)/2 = 88.5

The interquartile range:

88.5 - 67

= 21.5

Answer:

B.) False

Step-by-step explanation:

A regular tessellation is a pattern made by repeating a regular polygon. But in this image, it is a demiregular tessellations. Demiregular tessellations are a set of tessellations made from 2 or more regular polygon faces.

Hope this helps you out! : )

The given illustration is not example of a regular tessellation due to overlapping of polygons which is option(B) false.

A regular tessellation is defined as consist of a repeating pattern of one or more regular polygon. There are a few qualifications for a pattern to be a tessellation. These include:

Regular polygon cannot overlap.

Regular polygon cannot have space between them.

The patterns are created by rotating, translating, or reflecting the shapes.

Hence, the given illustration is not example of a regular tessellation due to overlapping of polygons.

Learn more about regular tessellation here:

https://brainly.com/question/12926513

#SPJ5

Answer:

The cost of one large drink is $1.50.

(13.5-10) + 4 = (7.5 ÷ 5) = $1.50

Step-by-step explanation:

The first step is to minus the $10.00 from the $13.50, which gives us $3.50.

13.5 - 10

We've done this because the pizza is irrelevant to what we're trying to figure out, so we subtract the price of the food, which as we already know is $10, to isolate the price of the 5 drinks to make it easier to find the price of just one.

Once we've done that, we're going to add on the $4.00 they got discounted to the $3.50 in order to find the original price of the drinks without using the gift certificate.

(13.5 - 10) + 4

This gives us $7.50, or the price of 5 large drinks. But we're only looking for the price of one. So we're going to divide the 7.50 by the total number of drinks ordered.

(13.5-10) + 4 = (7.5 ÷ 5)

This gives us 1.5, or $1.50.

(13.5-10) + 4 = (7.5 ÷ 5) = $1.50

Answer: B

Step-by-step explanation:

(4/3) x 3.14 x 3.7^3

Plug into a calculator

212.067

Brainliest would be appericiated!

This question is not correctly written

Correct Question

A sector whose central angle measures 120° has an area of 12 square inches. What is the radius of the circle?

Answer:

Radius of the circle = 3.3851375013 inches

Approximately to one decimal place, radius of the circle = 3.4 inches

Step-by-step explanation:

The formula for the area of a sector is given as:

Area of a sector = θ × π/360 × r²

θ = Central angle in degrees = 120°

Area of a sector = 12 in²

12 = (120° × π)/360 × r²

r² = 12 ÷(120° × π)/360

r² = 12 ÷ 1.0471975512

r² = 11.459178217

r = √11.459178217

r = 3.3851375013 inches

Approximately to one decimal place, radius of the circle = 3.4 inches

Answer:

17.5

Step-by-step explanation:

A = [tex]\frac{pq}{2}[/tex]

p = 7

q = 5

7 x 5 = 35

35 ÷ 2 = 17.5

Answer:

The correct answer is 70 square units I took the test and got it right! Good luck! God bless you!

Step-by-step explanation: