Please help me with the question.

Given:

The two statements.

To find:

The probability of an impossible event.

The probability of a certain event.

Solution:

Formula for probability is:

[tex]P=\dfrac{\text{Possible favorable outcomes}}{\text{Total number of outcomes}}[/tex]

For an impossible event, the possible favorable outcomes is 0. So,

[tex]P=\dfrac{0}{\text{Total number of outcomes}}[/tex]

[tex]P=0[/tex]

For a certain event (sure event), the possible favorable outcomes is equal to total number of outcomes. So,

[tex]P=\dfrac{\text{Total number of outcomes}}{\text{Total number of outcomes}}[/tex]

[tex]P=1[/tex]

Therefore, an event that is impossible has probability 0 and an event that is certain has probability 1.

Answer:

The answer is 5.5 because half of 11 is 5.5 and diameter is half of circumference.

Answer:

5.5

Step-by-step explanation:

diameter=11

radius = diameter÷2

r=11÷2

radius=5.5

Answer:

Mia has 180 counters

Step-by-step explanation:

if Suzy has 20 counters and Mia has nine times as many as Suzy, we can multiply 20 by 9 (20×9) and get 180

Answer:

60°

Step-by-step explanation:

360 - ( 80+115+10) = 60°

Answer:

19

HOPE THIS HELPS

- Todo ❤️

Step-by-step explanation:

45/5=9

9+10=19

Answer:

Step-by-step explanation:

y = ax + b

The trick is to solve for a.

y = 505

x = 8

b = 25

505 = a*8 + 25                Subtract 25 from both sides

-25             -25

480 = 8a

a = 60

What this means is that for each one of the 8 months, he added 60 dollars into his account

The equation is y = 60*x + 25

Answer:

x= −3 and y= 4

not sure if this is what your looking for tho

Step-by-step explanation:

Answer:

Both are false.

Step-by-step explanation:

Elena is right in saying that exponents are repeated multiplication, but shes doing it the incorrect way. 2 to the power of 28 is not multiplication of 28s twice, but instead is multiplication of 2 twenty eight times.

Answer:

t + c = 623

t = c + 135

thomas has 379 songs downloaded, and carl has 244

Step-by-step explanation:

togheter they have 623 songs, aka the sum of thomas (t) and carl (c) is 623.

t + c = 623

thomas has 135 more than Carl. so Carl plus 135 is equal to thomas

t = c + 135

now you can solve it:

t + c = 623

(c+135) + c = 623

c + c = 488

2c = 488

c = 244

carl has 244 songs downloaded

t  + 244 = 623

t = 379

thomas has 379 songs downloaded

The system of equations represents t + c = 623 and t = c + 135 and Tomas has 379 while Carl has 244 downloaded.

An equation can be defined in numerous ways. Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.

As per the given,

Together they have 623 songs downloaded.

t + c = 623

Tomas has 135 more songs downloaded than Carl.

t = c + 135

By substitution,

c + 135 + c = 623

2c = 488

c =244

And , t = 244 + 135 = 379

Hence "The equations in the system show that Tomas has 379 while Carl has 244 downloaded and that t + c = 623 and t = c + 135 are represented".

For more about the equation,

brainly.com/question/10413253

#SPJ2

Answer:

Missing term = 6x

Step-by-step explanation:

We got:

=> 4x by multiplying +4 and x (x * 4 = 4x)

=> 12 by multiplying +4 and +3 (4 * 3 = 12)

=> 2x² by multiplying 2x and x (2x * x = 2x²)

Similarly we will get the "missing term" by multiplying 2x and +3

=> Missing term = 6x, (2x * 3 = 6x)

Hope this helps!

Answer:

8 °C

Step-by-step explanation:

Step 1: Given data

Initial temperature value (T1): -10 °C

Final temperature value (T2): -2 °C

Step 2: Calculate the change in temperature from the morning to the afternoon

To calculate the change in the temperature, we have to perform the subtraction T2 - T1.

ΔT = T2 - T1 = (-2 °C) - (-10 °C) = -2 °C + 10 °C = 8 °C

The temperature change is positive, meaning that the temperature increased.

Answer:

4

Step-by-step explanation:

Number of brownies = 1 dozen

1 dozen = 12

Fraction of brownies that had nut = 2 /6

Hence, Number of brownies dad doesn't eat :

Fraction that had nuts * number of brownies

2/6 * 12

1/3 * 12

= 4

Answer:

1) 69 2) 69 3) 60 4) 60 5) 51

Step-by-step explanation:

Triangles have 180 degrees interior and 360 degrees exterior. Knowing this you add all the values within a triangle and subtract it from 180 to find the missing degrees.

For the purple, the green is supplementary which means the other angle will help it equal 180 degrees. the missing green angle is 38. 38+82=120 and 180-120=60. because of vertical angles, angle 2 is 69 and angle 4 is 60. this makes 129 so 180-129=51.

Hope this helps you in some way. if not, sorry i failed you.

Answers

Be sure to use the actual degree symbol instead of typing in "degrees" after each number.

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

Explanation:

To find angle 1, we can use the remote interior angle theorem. The yellow angles you've highlighted (46 and 65) add up to the measure of angle 1, which is an exterior angle. So angle 1 is 46+65 = 111 degrees

The slightly longer method is to make x be the missing angle of the left-most triangle. Solve x+46+65 = 180 to get x = 69 degrees. Then note how angle x and angle 1 are supplementary, meaning x+(angle1) = 180 leads to angle 1 = 111 degrees (because 180-69 = 111)

------------------------

Angle 2 is 69 degrees since angle x = 69, which is a vertical angle to angle 2. Or you could note that angle 1 and angle 2 are supplementary

(angle1)+(angle2) = 180

(111)+(angle2) = 180

angle2 = 180-111

angle 2 = 69 degrees

This method is used to prove the vertical angles theorem is always true.

-------------------------

Angle 3 can be found using the remote interior angle theorem, but we'll be going in reverse this time. Let y be the measure of angle 3

y+82 = 142

y = 142-82

y = 60

angle 3 = 60 degrees

Like with angle 1, there's also a slightly longer method that follows the same idea as before. If you follow this method, you'll need to find the missing piece of the green angle you highlighted (which his 180-142 = 38 degrees), then use the idea that A+B+C = 180 where A,B,C are the three interior angles of any triangle.

---------------------------

Angle 3 and angle 4 are vertical angles, so they are always congruent and angle 4 is also 60 degrees

---------------------------

Let z = measure of angle 5

Focusing on the smaller triangle in the middle, we can say,

(angle2)+(angle4)+(angle5) = 180

(69) + (60) + (z) = 180

z+129 = 180

z = 180-129

z = 51

angle 5 = 51 degrees

Answer:

Step-by-step explanation:

I am going off of the fact that the radius is 10; you didn't specify what the 10 was, exactly, and that's extremely important!

The volume of a sphere is

[tex]V=\frac{4}{3}\pi r^3[/tex] Filling in what we were given from the problem,

[tex]V=\frac{4}{3}\pi(10)^3[/tex] so

V = 1333.33π inches cubed

If the diameter is 10 and the radius is 5:

[tex]V=\frac{4}{3}\pi(5)^3[/tex] and the volume then is

V = 166.67π inches cubed

Answer:

Step-by-step explanation:

option c is correct

product of two numbers can be written as 4x

Answer:

d. (9,-260°)

Step-by-step explanation:

100° = 100-360 = -260°

Answer:

Over time, the function is DECREASING. Cho ran at a faster rate during segment K.

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

cos(68°)×24= 8.99 which can be rounded to 9

Answer:

[tex]\displaystyle \cos(A + B) =\frac{969}{1769}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \cos A=\frac{20}{29}\text{ and } \tan B=\frac{11}{60}[/tex]

Where A and B are positive acute angles.

And we want to find cos(A + B).

Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using this information, find the opposite side with respect to Angle A:

[tex]o=\sqrt{29^2-20^2}=21[/tex]

Tangent is the ratio of the opposite side to the adjacent side. Find the hypotenuse with respect to Angle B:

[tex]h=\sqrt{11^2+60^2}=61[/tex]

In summary:

With respect to Angle A, the adjacent side is 20, opposite is 21, and the hypotenuse is 29.

With respect to Angle B, the adjacent side is 60, the opposite is 11, and the hypotenuse is 61.

We can rewrite our expression as:

[tex]\displaystyle \cos(A+B)=\cos A\cos B-\sin A\sin B[/tex]

Using the above information, substitute in the appropriate values. Note that since A and B are positive acute angles, all trigonometric values will be positive. Hence:

[tex]\displaystyle \cos(A + B)=\left(\frac{20}{29}\right)\left(\frac{60}{61}\right)-\left(\frac{21}{29}\right)\left(\frac{11}{61}\right)[/tex]

Simplify:

[tex]\displaystyle \cos(A + B) =\frac{1200-231}{1769}=\frac{969}{1769}[/tex]

Answer:ik i am late but it is 4.4 for the people that need it now

Step-by-step explanation:

Answer:

D; 15

Step-by-step explanation:

Because the highest point on the graph is at 15 (or 3 am), that would be the highest temperature. (Also, none of the other choices make sense; they are all at relatively low temperatures).

Answer:

y =   35°

z =  90°

Step-by-step explanation:

the angle labeled as 35° and the angle labeled as 'y' are alternate-interior angles and are congruent

therefore, y = 35°

the third angle of the triangle on the left is 180-(90+35) = 55

therefore, this angle is vertical with the angle opposite it which is also 55°

to find 'z', you can add the two known angles of 55 and 35 and subtract the sum from 180 to get 90°

Answer:

Interesting... go on.

Step-by-step explanation:

Answer:

The answer is "[tex](x + 8)^2 = 58[/tex]"

Step-by-step explanation:

Let the equation is:[tex]x^2+16x=-6[/tex]

by adding and subtracting 64 then:

[tex]x^2 + 16x + 64 = -6 + 64\\\\x^2 + 2\times x\times 8 + 64 = -6 + 64\\\\ (x + 8)(x + 8) = 58\\\\ (x + 8)2 = 58[/tex]

Answer:

No, It is not.

Step-by-step explanation:

Step 1: Divide the 2.45 by 4 (We are doing this to find the difference between them so we can find out what to do next.)

[tex]2.45 \div 4\\\\= 0.6125[/tex]

Step 2: Multiply 0.6125 to 6 (Now, that we've found what 1 magazine cost according to the first data, we are multiplying it by 6 because if you multiply that to 4 the answer will be 2.45. So, if we multiply 6, it will show us if they are both proportional, the same.)

[tex]0.6125 \times 6\\\\= 3.675[/tex]

Therefore, these two prices are not proportional.

Answer:

[tex](g + f)(2) = \sqrt 3 - 3[/tex]

[tex](\frac{f}{g})(-1) = 0[/tex]

[tex](g + f)(-1) = \sqrt{15}[/tex]

[tex](g * f)(2) = -3\sqrt 3[/tex]

Step-by-step explanation:

Given

[tex]f(x) =1 - x^2[/tex]

[tex]g(x) = \sqrt{11 - 4x[/tex]

See attachment

Solving (a): (g + f)(2)

This is calculated as:

[tex](g + f)(2) = g(2) + f(2)[/tex]

Calculate g(2) and f(2)

[tex]g(2) \to \sqrt{11 - 4 * 2} = \sqrt{3}[/tex]

[tex]f(2) = 1 - 2^2 = -3[/tex]

So:

[tex](g + f)(2) = g(2) + f(2)[/tex]

[tex](g + f)(2) = \sqrt 3 - 3[/tex]

Solving (b): [tex](\frac{f}{g})(-1)[/tex]

This is calculated as:

[tex](\frac{f}{g})(-1) = \frac{f(-1)}{g(-1)}[/tex]

Calculate f(-1) and g(-1)

[tex]f(-1) = 1 - (-1)^2 = 0[/tex]

So:

[tex](\frac{f}{g})(-1) = \frac{f(-1)}{g(-1)}[/tex]

[tex](\frac{f}{g})(-1) = \frac{0}{g(-1)}[/tex]

[tex](\frac{f}{g})(-1) = 0[/tex]

Solving (c): (g - f)(-1)

This is calculated as:

[tex](g + f)(-1) = g(-1) - f(-1)[/tex]

Calculate g(-1) and f(-1)

[tex]g(-1) = \sqrt{11 - 4 * -1} = \sqrt{15}[/tex]

[tex]f(-1) = 1 - (-1)^2 = 0[/tex]

So:

[tex](g + f)(-1) = g(-1) - f(-1)[/tex]

[tex](g + f)(-1) = \sqrt{15} - 0[/tex]

[tex](g + f)(-1) = \sqrt{15}[/tex]

Solving (d): (g * f)(2)

This is calculated as:

[tex](g * f)(2) = g(2) * f(2)[/tex]

Calculate g(2) and f(2)

[tex]g(2) \to \sqrt{11 - 4 * 2} = \sqrt{3}[/tex]

[tex]f(2) = 1 - 2^2 = -3[/tex]

So:

[tex](g * f)(2) = g(2) * f(2)[/tex]

[tex](g * f)(2) = \sqrt 3 * -3[/tex]

[tex](g * f)(2) = -3\sqrt 3[/tex]