What is the interquartile range of the set of data this box-and-whisker plot represents?

The events A and B are independent events, and the values of P(A) and P(B) are 7/12 and 1/2, respectively

The event A is given as:

A : Sum greater than 6

In the sample space of a roll of two dice, there are 21 outcomes that are greater than 6, out of a total of 36 outcomes

This means that:

P(A) = 21/36

Simplify

P(A) = 7/12

The event B is given as:

B : Sum is divisible by 2

In the sample space of a roll of two dice, there are 18 outcomes that are divisible by 2, out of a total of 36 outcomes

This means that:

P(B) = 18/36

Simplify

P(B) = 1/2

Hence, the probability values of P(A) and P(B) are 7/12 and 1/2, respectively

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Answer:

B

Step-by-step explanation:

1.

- 9 < 2x + 1

- 10 < 2x

X > - 5

2.

2x + 1 < 5

2x < 4

X < 2

Answers:

BD = 6

AC = 7.5

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

Work Shown:

BD/BA = BE/BC

x/9 = 4/6

6x = 9*4

6x = 36

x = 36/6

x = 6

BD = 6

---------

DE/AC = BE/BC

5/y = 4/6

5*6 = y*4

30 = 4y

4y = 30

y = 30/4

y = 7.25

AC = 7.5

Answer:

  p(x) = x⁴ -7x³ +59x² -343x +490

Step-by-step explanation:

Each root is the zero of a binomial factor. That is, for root x = a, the polynomial has a factor (x -a). Complex roots come in conjugate pairs, so if there is a root 7i, there is also a root -7i.

__

The given roots mean the polynomial can be written in factored form as ...

  p(x) = (x -2)(x -5)(x -7i)(x -(-7i))

We can combine multiply these factors together to simplify the polynomial.

  p(x) = (x² -7x +10)(x² +49)

  p(x) = x⁴ -7x³ +59x² -343x +490

_____

Additional comment

Combining the conjugate complex roots uses the special form for the factoring of the difference of squares.

  a² -b² = (a -b)(a +b)

  (x -7i)(x +7i) = x² -(7i)² = x² -49i² = x² +49 . . . . . where i = √(-1)

Answer:

d=6 & p=13

Step-by-step explanation:

1. P+d=19

×9

2. 9p +5.50d=150

×1

9p+9d=171

-

9p +5.50d=150

3.5d=21

d=6

Substituting d=6 in 1.

P+6=19

P=13

Answer:

20/39.

Step-by-step explanation:

There are a total of 13 students.

Prob(Boy is selected) = 8/13

Prob(Girl is then selected) = 5/12

So probability ( Boy selected then a girl)  = 8/13 * 5/12 = 10/39

- and the probability of Girl then a boy selected is also  10/39

So the required probability = 2 * 10/39

= 20/39.

Answer:

(4+5) ÷ 3 + 6 x 5

Step-by-step explanation:

pemdas

From the graph, we concluded that line passes through the points (0, 3) and (1, 4) respectively.

So, slope of the line (m) passing through the points (a, b) and (c, d) is

m = d - b/ c - a

m = 4 - 3 / 1 - 0 = 1/1 = 1

Also, line makes an intercept of 3 units in positive direction of y - axis.

So, c = 3

y = mx + c

y = 1 × x + 3

We know, Equation of line passing through the points (a,b) and (c, d) is given by

y - b = d - b / c - a (x - a)

a = 0

b = 3

c = 1

d = 4

y - 3 = 4 - 3 /1 - 0 ( x - 0 )

y - 3 = 1/1 ( x - 0 )

y - 3 = x

1. Equations of horizontal and vertical lines

Equation of line parallel to x - axis passes through the point (a, b) is y = b.

Equation of line parallel to y - axis passes through the point (a, b) is x = a.

Equation of line passing through the point (a, b) having slope m isy - b = m(x - a)

Equation of line which makes an intercept of c units on y axis and having slope m is y = mx + c.

Equation of line which makes an intercept of a and b units on x - axis and y axis respectively is x/a + y/b = 1.

Equation of line which is at a distance of p units from the origin and perpendicular makes an angle B with the positive X-axis is x cosB + y sinB = p.

Pull out a factor of 1/n from the summand and the result follows.

[tex]\displaystyle \lim_{n\to\infty} \sum_{i=1}^n \frac{i^4}{n^5} = \lim_{n\to\infty} \frac1n \sum_{i=1}^n \left(\frac in\right)^4 = \boxed{\int_0^1 x^4 \, dx}[/tex]

Answer:

The average mass of one coffee bag is 75kg.

Step-by-step explanation:

The lorry on its own weighs 3500kg.

If it weighs 7250kg alongside coffee bags, we can make the assumption that to find the total mass of the coffee bags, we must take the combined total and subtract the lorry's weight from it.

7250kg subtract 3500kg is 3750kg.

There are 50 coffee bags, so this is the mass of all 50.

If we want to find the mass of one coffee bag, we have to divide the mass of 50 coffee bags by 50.

3750kg divided by 50 is 75kg.

The average mass of one coffee bag is 75kg.

Answer:

243 in²

Step-by-step explanation:

Diameter = 18 in

Radius ( r ) = Diameter / 2 = 18 / 2

r = 9 in

π = 3

To find : Area of circle ( A )

Formula : -

A = πr²

A = 3 x 9²

   = 3 x 9 x 9

A = 243 in²

The number  2√5×3√6 is irrational, number √42/√168 is rational as we know π is an irrational number but 22/7 is rational.

It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words the irrational number cannot be expressed in the form of p/q form.

A rational number is a sort of real number that has the form p/q and does not equal zero.

= 2√5×3√6

= 6√30

= √1080 = 32.863353450309965

The number is irrational.

= √42/√168

= 1/2

The number is rational.

= 5(4√5 - 3√5)

= 5√5

= √125 = 11.180339887498949

The above number is irrational.

= √64/32

= 1/4

The above number is rational.

= (5√3—√3)/2√3

= 2

The above number is rational.

Similarly, we can find whether a number is irrational or rational

Thus, the number  2√5×3√6 is irrational, number √42/√168 is rational as we know π is an irrational number but 22/7 is rational.

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Answer:

the answer to this question is 184cm^2 because the formula to find the area for a rectangular prism is A= BH so  we need to multiply 20 which is the base times 9.2 which is the height and when we do those steps of multiplying we get an answer of 184cm^2 so 184 cm^2 is hopefully the correct answer for this problem.

Step-by-step explanation: hopefully that is the correct and have a great day.

Answer:  6 inches equals 0.16666667 yards, or about 0.2 yards.

Step-by-step explanation: 1 yard equals 36 inches. By that reasoning, we can divide 6 by 36, since we are trying to find out how many yards are in 6 inches.

6/36 = 0.16666667

The answer is 0.16666667 yards, or about 0.2 yards.

Answer:

Step-by-step explanation:

Remark

You are trying to convert the base function f(x) = x^2 into the child function g(x) = -(x + 3)^2 + 5

UP

Start with the simplest part of the transformations. + 5

If you have g(x) = f(x)+5 what you have done is move the function up 5 units on your grid.

Up side Down

Next is the - sign.

f(x) = x^2

g(x) = - f(x) = - x^2

This has the affect of turning x^2 upside down. It looks like a cup opening towards the counter or down.

Left right

The last step is left / right. This is the hard one. It moves in the opposite direction that you think it should. x +3 moves the parabola left, not right. If you want it to move right, use (x - 3)

Graph

I have enclosed a graph to show you exactly what is going on. The red  line is f(x)=x^2

The blue line is g(x) = -(x + 3)^2 + 5

the amount of maturity is 254583

Answer:

42 units ^2

Step-by-step explanation:

Break in to a top triangle   a middle rectangle and a bottom triangle

area =   1/2 7 *2      +    4 * 7        1/2 * 2 * 7 = 42 units ^2

Answer:

b

Step-by-step explanation:

[tex] = \frac{68}{5} - \frac{18}{5} \\ [/tex]

[tex] = \frac{50}{5} \\ [/tex]

Change into lowest term

[tex]10...[/tex]

The surface area of the solid is 4 + 6b

The solid consist of the following shapes:

The area of the solid is:

Area = Area of square + 4 * area of triangle

This gives

Area = 2 * 2 + 4 * 0.5 * 3 * b

Evaluate

Area = 4 + 6b

Hence, the surface area of the solid is 4 + 6b

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Answer:

0,5

Step-by-step explanation:

Answer:

b = 5 ± √5 / 5

Step-by-step explanation:

Given :

Subtract 10b from both sides :

Splitting the middle term :

Answer:

270

Step-by-step explanation:

 x = k/y     This is an inverse relationship with k = constant of proportion (or variation)

-9 = k/(-30)

k = -9  *  -30 = 270

Answer:

Constant of variation  = 270.

Step-by-step explanation:

y = k/x

-30 = k / -9

k = -30 * -9

k = 270

Answer:

  (x, y) = (12, 15)

Step-by-step explanation:

The given expression for y suggests that using substitution would be a good choice for the method of solution.

__

  x +(x +3) = 27 . . . . substitute for y using the second equation

  2x = 24 . . . . . . . subtract 3

  x = 12 . . . . . . . divide by 2

  y = 12 +3 = 15 . . . . use the second equation to find y

The solution is (x, y) = (12, 15).

Answer:

There are a total of 144 students in soccer training.

Step-by-step explanation:

12x5=60

60-12=48

48=4/5

4/5=1/3

1/3 = 48

48x3= 144

Answer:

Quadrant IV is always in the bottom right corner.