Example 2
A black die and a white die are thrown at the same
time. Display all the possible outcomes. Find the
probability of obtaining:
a) a total of 5
b) a total of 11
c) a 'two' on the black die and a six' on the white die.
It is convenient to display all the possible outcomes
on a grid. This is called a possibility diagram


It’s example 2 please help:)

Answer:

The last option

Step-by-step explanation:

Source: Trust bro

Answer:

d) y sqrt 5

Step-by-step explanation:

radicals are like if they have the same index and radicand, here they are both square roots and have a radicand of five

Answer:

Subtract 3 and one-fifth from both sides of the equation

Step-by-step explanation:

Well to find n you gotta separate it.

3 1/5 + n = 9

-3 1/5

n = 5.8

Thus,

to seperate it you subtract 3 1/5 from both sides.

Answer:

Subtract 3 and one-fifth from both sides of the equation

Step-by-step explanation:

Answer:

Surface area of the roof of the kennel, including the bottom face is 58.96 ft^2

Step-by-step explanation:

The image is attached below

For the triangular sides of the roof, area is

A = [tex]\frac{1}{2}bh[/tex]

where b is the base = 4 ft

h is the vertical height = 2.24 ft

A =  [tex]\frac{1}{2}*4*2.24 =[/tex] 4.48 ft^2

for the two faces we have 2 x 4.48 ft^2 = 8.96 ft^2

For the rectangular sections of the roof, area is

A = [tex]lh[/tex]

where [tex]l[/tex] is the length of the rectangle = 5 ft

h is the height of the rectangle = 3 ft

A = 5 x 3 = 15 ft^2

For the two rectangular faces, we have 2 x 15 ft^2 = 30 ft^2

For the bottom face, area is

A = [tex]lw[/tex]

where [tex]l[/tex] is the length of the house = 5 ft

w is the width of the house = 4 ft

A = 5 x 4 = 20 ft^2

Surface area of the roof of the dog kennel is

8.96 ft^2 + 30 ft^2 + 20 ft^2 = 58.96 ft^2

Answer:

22.5 cm

Triangle area is (L x W) / 2

7.5 x 6 = 45

45 / 2 = 22.5

Step-by-step explanation:

brainlist plzzzz

Answer:

Step-by-step explanation: I hope it helps :)

1.

[tex]Surface\: area=\:2\pi rh+2\pi r^2\\h = 2ft\\diameter = 2ft\\Radius = d/2=2/2=1ft\\\\A=( 2\times 3.141\times1\times2)+(2\times 3.141 \times 1^2)\\A = (12.564)+(6.282)\\A = 18.846\\A = 18.85ft^2[/tex]

2.

[tex]Area \:of\: square = A=a^2\\A = 3^2\\A=9\\Area\:of \:one \:rectangle\: = (l\times b)\\ A = (8\times 3)\\A = 24cm^2\\\\A = 2(Area\: of\: square)+2(Area\: of \:rectangle)\\A = 2(9)+4(24)\\A = 18+96\\A =114cm^2[/tex]

3.

[tex]Area \: of\: base=?\\ r = 7\:in\\h = 12\:in\\A = \pi \times r^2\\A = 3.141 \times 7^2\\A = 153.909\\\\Height \: of \:the \:cylinder = 12\:inches\\Circumference = 2\pi \times r\\C= 2 \times 3.141 \times 7\\ C =43.98\\\\S.A= 2B+Ch\\S.A = 2(153.909)+43.98(12)\\S.A = 307.818+527.76\\S.A =835.578[/tex]

4.

[tex]Perimeter = a+b+c\\P = 10+8+6\\P = 24\\S.A =2B+Ph\\S.A = 2(24)+24(8)\\S.A =48+192\\S.A = 240\:yd^2[/tex]

Answer:

9 squares

Step-by-step explanation:

An equilateral has three equal sides.  You can have two squares on each side: AB, one in which the triangle, ABC, falls within the square and the other where the square does not contain the triangle, ABC.  You can also have two squares on each side - BC, one in which the triangle, ABC, falls within the square and the other where the square does not contain the triangle, ABC.  Again, you can have two squares on each side - CA, one in which the triangle, ABC, falls within the square and the other where the square does not contain the triangle, ABC.  In addition, AB, BC and CA can be a diagonal of squares.  

TL;DR

In conclusion, you have 9 squares in all - 3 as diagonals of squares and 6 as sides of squares. Brainliest appreciated!

No square shares more than two vertices with the equilateral triangle, so we can find the number of squares having two of their vertices at two given points and triple the result. Given 2 points, 3 squares may be drawn having these points as vertices. The figure below shows a red equilateral triangle with the 3 squares that correspond to one of the sides of the triangle. Therefore, 9 squares share two vertices with the equilateral triangle.

Answer:

  (x +1)^2 + (y +2)^2 = 25

Step-by-step explanation:

A diagram of the given triangle shows you it has side lengths of 3 and 4, so the square of the hypotenuse is ...

  (AC)^2 = (AB)^2 +(BC)^2 = 3^2 +4^2

  (AC)^2 = 25

The center of the circle is at A(-1, -2), so the equation is ...

  (x -h)^2 +(y -k)^2 = r^2

for the circle centered at (h, k) with radius r.

We know that the square of the radius (r^2) is 25, so we can write the equation as ...

  (x +1)^2 +(y +2)^2 = 25

Answer:

(x + 1)2 + (y + 2)2 = 25

Step-by-step explanation:

Hope this helps :)

Answer: About 99.74% of births would be expected to occur within 24 days of the mean pregnancy length.

Step-by-step explanation:

Complete question is attached below.

Given: The lengths of pregnancy terms for a particular species of mammal are nearly normally distributed about a mean pregnancy length with a standard deviation of 8 days.

i.e. [tex]\sigma= 8[/tex]

let X denotes the random variable that represents the lengths of pregnancy.

The probability of births would be expected to occur within 24 days of the mean pregnancy​ length:

[tex]P(\mu-24<X<\mu+24)=P(\dfrac{\mu-24-\mu}{8}<\dfrac{X-\mu}{\sigma}<\dfrac{\mu+24-\mu}{8})\\\\=P(\dfrac{-24}{8}<Z<\dfrac{24}{8})\ \ \ [\because Z=\dfrac{X-\mu}{\sigma}]\\\\=P(-3<Z<3)\\\\=P(Z<3)-P(Z<-3)\\\\=P(Z<3)-(1-P(Z<3))\\\\=2P(Z<3)-1[/tex]

[tex]= 2(0.9987)-1\ \ \ [\text{ By z-table}]\\\\=0.9974[/tex]

=99.74%

Hence, about 99.74% of births would be expected to occur within 24 days of the mean pregnancy length.

Answer:

when t is increased , h will increased too

Answer:

Th relationship is linear because  H increases by 30 each time t increases by 1.

Step-by-step explanation:

H is linear if it changes at a constant rate per unit interval. In other words, constant differences in t should correspond to constant differences in H.

Answer:

Step-by-step explanation:

1. We can clear fractions and solve the resulting quadratic. We clear fractions by multiplying the equation by the product of the denominators.

  [tex]\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}=\dfrac{8}{3}\\\\3((2x+1)^2-(2x-1)^2)=8(2x-1)(2x+1)\\\\3(8x) = 8(4x^2 -1)\\\\4x^2 -3x -1 = 0\qquad\text{factor out 8, subtract 3x}\\\\x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(4)(-1)}}{2(4)}=\dfrac{3\pm\sqrt{25}}{8}\\\\x=\dfrac{3\pm5}{8}=\left\{-\dfrac{1}{4},1\right\}[/tex]

__

2. Using the same idea here, we get ...

  [tex]\dfrac{2}{x-2}+\dfrac{3}{x}=\dfrac{9}{x+3}\\\\2(x)(x+3)+3(x-2)(x+3)=9(x-2)(x)\\\\2x^2+6x+3(x^2+x-6)=9x^2-18x\\\\4x^2-27x+18=0\\\\x=\dfrac{-(-27)\pm\sqrt{(-27)^2-4(4)(18)}}{2(4)}=\dfrac{27\pm\sqrt{441}}{8}\\\\x=\dfrac{27\pm21}{8}=\left\{\dfrac{3}{4},6\right\}[/tex]

Answer:

Step-by-step explanation:

P (m) = a (m + 1) + b (m + 1) - c (m + 1)

P (m) = (a + b - c) (m + 1)

There are 2 prime factors

Answer:

1360cm²

Step-by-step explanation:

Since the shape of the cake is in L shape, we can divide the cake in to rectangles..

The amount of space covered by the frosting = The sum of the areas of the sides that we can find in this L shaped cake diagram.

The sides of this cake, are shaped like a rectangle.

Hence, Area of a Rectangle = Length × Width

a) Side 1 = Rectangle on the left

Area of a Rectangle = Length × Breadth

Length = 30cm

Breadth =10cm

Area = 30 × 10 = 300cm²

Since we have another side with this measurement/ dimensions also,

Side 2 = 300cm²

Side 3 = The front face of the cube by the right

Area of a Rectangle = Length × Breadth

Length = 22cm - 10cm = 12cm

Breadth =10cm

Area = 12 × 10 = 120cm²

Likewise, we have the another side with the same dimensions as well

Hence, Side 4 = 120cm²

Side 5

30 × 5 = 150cm²

Side 6

10 × 5 = 50cm²

Side 7

20 × 5 = 100cm²

Side 8

22cm × 5 cm = 110cm²

Side 9

10cm × 5cm = 50cm²

Side 10

12cm × 5cm = 60cm²

The amount of space covered by the frosting = Area of Sides( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)

= (300 + 300 + 120 + 120 + 150 + 50 + 100 + 110 + 50 + 60) cm²

= 1360cm²

Answer:

1360

Step-by-step explanation:

it is correct on khan academy

Answer:

p²q³ + pq and pq(pq² + 1)

Step-by-step explanation:

Given

3p²q² - 3p²q³ +4p²q³ -3p²q² + pq

Required

Collect like terms

We start by rewriting the expression

3p²q² - 3p²q³ +4p²q³ -3p²q² + pq

Collect like terms

3p²q² -3p²q² - 3p²q³ +4p²q³ + pq

Group like terms

(3p²q² -3p²q²) - (3p²q³ - 4p²q³ ) + pq

Perform arithmetic operations on like terms

(0) - (-p²q³) + pq

- (-p²q³) + pq

Open bracket

p²q³ + pq

The answer can be further simplified

Factorize p²q³ + pq

pq(pq² + 1)

Hence, 3p²q² - 3p²q³ +4p²q³ -3p²q² + pq is equivalent to p²q³ + pq and pq(pq² + 1)

Answer: 36

Step-by-step explanation:

From the question, we are informed that six numbers has an average of 42. This means that the total number will be equal to:

= 42 × 6

= 252

When three of this numbers were removed the remaining three numbers had an average of 72. The total of this will be:

= 72 × 3

= 216

The sum of the removed numbers will be the difference between the two numbers above. This will be:

= 252 - 216

= 36

Answer:  x + 2x + x-40 = 180

First angle= 55º

Second angle= 110º

Third angle= 15º

​Step-by-step explanation:  The sum of the angles of a triangle is 180º

Take the values given and  use x as the unknown first angle. then create terms for the other two angles based on that:

The second angle of a triangle is double the first angle  becomes 2x

The third angle is 40 less than the first angle becomes x-40

x + 2x + x-40 = 180  Solve by adding like terms . x + 2x + x = 4x

4x -40 = 180   Add 40 to both sides to "cancel" the -40 on the left

4x + 40 -40 = 180 + 40   becomes  

4x = 220  Divide both sides by 4 to "cancel" the 4 on the left side

4x/4 = 220/4

x = 55   This is the first angle. Substitute 55 for the  "x" in the original terms

2(55) = 110   The second angle

(55) -40 = 15   the third angle

Answer:

Plug in the x and y values into the equation

Step-by-step explanation:

Answer:

The option B, perfectly gives it to the target, because if you think about it, four less, means 4-, but backwards, and three times, means 3x, and if you put that together, that perfectly matches the one you are looking for. Hope that this would help you!

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

58 square units.

Step-by-step explanation:

From the graph attached,

Area of the figure = Area of the rectangle A + Area of two squares B and C

Area of rectangle A = Length × width

                                 = 10 × 5

                                 = 50 square units

Area of the square B = (Side)²

                                   = (2)²

                                   = 4 square units

Similarly area of the square C = 2² = 4 square units

Area of the total figure = 50 + 4 + 4

                                      = 58 square units

Therefore, 58 square units will be the answer.

Answer: sample space

Step-by-step explanation: In determining the probability of a certain event occurring or obtaining a particular outcome from a set of different possible outcomes, such as in the toss of coin(s), rolling of fair die(s), the sample space comes in very handy as it provides a simple breakdown and segmentation of all possible events or outcomes such that in Calculating the probability of occurrence of a certain event, the event(s) is/are located in the sample space and the ratio taken over the total number of events.

Answer:

fourth option

Step-by-step explanation:

Given

3x³ + 3x² - 18x ← factor out 3x from each term

= 3x(x² + x - 6) ← factor the quadratic

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (+ 1)

The factors are + 3 and - 2, since

3 × - 2 = - 6 and 3 - 2 = + 1, thus

x² + x - 6 = (x + 3)(x - 2) and

3x³ + 3x² - 18x = 3x(x + 3)(x - 2) ← in factored form

Answer:

Proved.

Step-by-step explanation:

The functions are:

1.) f(x) = 3x - 27 (* I am giving an answer using this equation. Perhaps you did't copy the question well!)

2.) g(x) = [tex]\frac{1}{3} x[/tex] + 9

If two functions are inverses of each other, then:

f(g(x)) = x and g(f(x)) = x situation must be satisfied.

f(g(x)) = 3([tex]\frac{1}{3}x + 9[/tex]) + 27

We simply it to get;

f(g(x)) = x - 27 + 27 = x (*This is correct)

g(f(x)) = [tex]\frac{1}{3}[/tex](3x - 27) + 9 = x - 9 + 9 = x (* This is also correct!)

Answer:

22

Step-by-step explanation:

Evaluate!

5(5)-3

25-3

22

Answer:

Step-by-step explanation:

The ceiling function is a python programming function that rounds a decimal point number to the nearest whole number.

Given the function expression  f(1.5), the ceiling function will round 1.5 to the nearest whole number which is 2

Answer:

15.7 yd

Step-by-step explanation:

Arc length is given as 2πr(θ/360).

Where,

Radius (r) = 10 yd,

Measure of arc (θ) = 90°

π = 3.142

Arc length = 2*3.142*10(90/360)

Arc length = 62.84(¼)

Arc length = 62.84/4

Arc length = 15.71 yd

The act length is approximately 15.7 (to the nearest tenth)

Answer:

(1,-2)

Step-by-step explanation

y = -3x + 1

y = 2x - 4

-3x + 1 = 2x - 4

-5x + 1 = -4

-5x = -5

x = 1

y= 2(1) - 4

y = 2 - 4

y = -2

(1,-2)

Answer:

1/2

Step-by-step explanation:

Answer:

Exponential

Step-by-step explanation:

The liner function represents that there is a constant change in the original value of the asset

While on the other hand the ex[onential function refers to that function in which there is an increase or decreased in the value of the asset that contains the current value of the asset

Hence, the given situation denotes the exponential function

Answer: 0.00000565

Step-by-step explanation:

Required to win:

6 number match $10,000

5 number match $ 5,000

4 number match $ 1000

3 number match $ 5,00

2 number match $ 50

1 number match $ 10

Therefore, to win $10,000 ;

All 6 numbers must match

Number of right numbers = 6

Total numbers = 25

Since it is without replacement :

Probability = required outcomes / Total possible outcomes

P(First number match) = 6/25

P(second number match) = 5/24

P(third number match) = 4/23

P(fourth number match) = 3/22

P(fifth number match) = 2/21

P(sixth number match) = 1 / 20

Therefore, Probability of winning $10000 :

(6/25) * (5/24) * (4/23) * (3/22) * (2/21) * (1/20) = 720 / 127512000 = 0.0000056465

= 0.00000565

Step-by-step explanation:

You have to retain a certain amount of money

in that account forever. Say you need $50 to

start an account, you have $200 in that account.

You cannot take out more than $150 from that

account.

Answer:

A: If you do not keep at least that much money in the account, you will be assessed fees.

Step-by-step explanation:

Answer:

My conclusion about Quadrilaterals ABCD and EFCD is that both quadrilaterals are similar to each other.

THE REASON IS BECAUSE THE SIDES OF QUADRILATERAL ABCD ARE THE SAME AS THE SIDES OF QUADRILATERAL EFCD.

Step-by-step explanation:

When we are given vertices, (x1, y1) , (x2 ,y2), we use the formula:

√(x2 - x1)² + (y2 - y1)²

For quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4)

Side AB: A(4, 8), B(10, 10)

√(x2 - x1)² + (y2 - y1)²

√(10 - 4)² + (10 - 8)²

= √6² + 2²

= √40

Side BC: B(10, 10), C(10, 4)

√(x2 - x1)² + (y2 - y1)²

= √(10 - 10)² + ( 4 - 10)²

= √ 0² + (-6)²

= √36

= 6

Side CD: C(10, 4), D(4, 4)

√(x2 - x1)² + (y2 - y1)²

= √ (4 - 10)² + ( 4 - 4)²

= √-6² + 0²

= √36

= 6

Side AD: A(4, 8), D(4, 4)

=√(x2 - x1)² + (y2 - y1)²

= √(4 - 4)² + (4 - 8)²

= √0² + (-4²)

= √16

= 4

Therefore, for Quadrilateral ABCD

Side AB = √40

Side BC = 6

Side CD = 6

Side AD = 4

For quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4).

Side EF: E(4, 0), F(10, -2)

√(x2 - x1)² + (y2 - y1)²

= √(10 - 4)² + (-2 - 0)²

= √6² + 2²

= √40

Side FC: F(10, -2), C(10, 4)

√(x2 - x1)² + (y2 - y1)²

= √(10 - 10)² + (4 -(-2))²

= √ 0² + 6²

= √36

= 6

Side CD: C(10, 4), D(4, 4)

√(x2 - x1)² + (y2 - y1)²

= √(10 - 4)² + (4 - 4)²

= √6² + 0²

= √36

= 6

Side ED: E(4, 0), D(4, 4)

√(x2 - x1)² + (y2 - y1)²

= √(4 - 4)² + (4 - 0)²

= √0² + 4²

= √16

= 4

Therefore, for Quadrilateral EFCD

Side EF = √40

Side FC = 6

Side CD = 6

Side ED = 4

My conclusion about Quadrilaterals ABCD and EFCD is that both quadrilaterals are similar to each other.

THE REASON IS BECAUSE THE SIDES OF QUADRILATERAL ABCD ARE THE SAME AS THE SIDES OF QUADRILATERAL EFCD.