Find the area of the
shaded region.
8m
12m

The events of rainfall and having a full moon on a given date are illustrations of probability

The probability that there will be rainfall and a full moon on that date is 0.0049

From the question, we have the following parameters

P(A) = 1/7 --- the probability that it rains

P(B) = 1/29 --- the probability of having a full moon

So, the probability that is rains and there is a full moon on a given day is:

[tex]p = \frac 17 * \frac 1{29}[/tex]

Simplify

[tex]p = 0.0049[/tex]

Hence, the probability that there will be rainfall and a full moon on that date is 0.0049

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12)

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{4}}}\implies \cfrac{-2}{-8}\implies \cfrac{1}{4}[/tex]

now, I used y₂ - y₁  and x₂ - x₁, is pretty much the same slope the other way.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{\cfrac{1}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-5=\cfrac{1}{4}x-1\implies y=\cfrac{1}{4}x+4[/tex]

13)

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{0}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-2)}}}\implies \cfrac{-2}{-4+2}\implies \cfrac{-2}{-2}\implies 1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_2=m(x-x_2) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{1}(x-\stackrel{x_1}{(-4)}) \\\\\\ y=1(x+4)\implies y=x+4[/tex]

notice, for the point-slope form, we can use either x₁ , y₁  or x₂ , y₂ , doesn't quite matter, so long we use the corresponding coordinates.

Answer:

384sqrt3

Step-by-step explanation:

The formula for the area of a hexagon is A = 3sqrt3 times s^2 /2

Plug in s = 16 to get A = 3sqrt3 times 16^2 (256) / 2

3sqrt3 times 256 is 768sqrt3

You divide that by 2 to get 384sqrt3

Answer:

M = 20

Step-by-step explanation:

given M is directly proportional to r³ then the equation relating them is

M = kr³ ← k is the constant of proportion

to find k use the condition when r = 4, M = 160 , then

160 = k × 4³ = 64k ( divide both sides by 64 )

[tex]\frac{160}{64}[/tex] = k , then

k = 2.5

M = 2.5r³ ← equation of proportion

when r = 2 , then

M = 2.5 × 2³ = 2.5 × 8 = 20

77a)

[tex]y=0.5x-2\implies y=\cfrac{x}{2}-2\implies \stackrel{x-intercept}{0=\cfrac{x}{2}-2} \\\\\\ 2=\cfrac{x}{2}\implies 4=x\qquad \qquad \boxed{(4~~,~~0)} \\\\\\ \stackrel{y-intercept}{y=0.5(0)-2}\implies y=-2\qquad \qquad \boxed{(0~~,~~-2)}[/tex]

77b)

[tex]y=-0.4x+2\implies y=-\cfrac{4x}{10}+2\implies y=\cfrac{2x}{5}+2 \implies \stackrel{x-intercept}{0=\cfrac{2x}{5}+2} \\\\\\ -2=\cfrac{2x}{5}\implies -10=2x\implies \cfrac{-10}{2}=x\implies -5=x~\hfill \boxed{(-5~~,~~0)} \\\\\\ \stackrel{y-intercept}{y=-0.4(0)+2}\implies y=2\qquad \qquad \boxed{(0~~,~~2)}[/tex]

Answer:

about 42 the not rounded is 41.6

Answer:

60

Step-by-step explanation:

Multiply to find that the answer is: 41.6

To estimate, simply round the numbers before multiplying. That would be thirty percent of 200. The answer is 60. This is close to 41.6 and is a reasonable estimate.

Answer:

  y = √(5x+34)

Step-by-step explanation:

The regression formula that matches a square root function to these points can be worked out by a suitable calculator. The attachments shows the points are matched exactly by the function ...

  y = √(5x+34)

__

If you would like to work this by hand, you can put the (x, y) point values into the proposed equation and see what the coefficients need to be:

  y = √(ax +b)

  7 = √(3a +b)   ⇒   49 = 3a +b

  8 = √(6a +b)   ⇒   64 = 6a +b

Subtracting the first equation from the second, gives ...

  (64) -(49) = (6a +b) -(3a +b)

  15 = 3a   ⇒   a = 5

  49 = 3(5) +b   ⇒   b = 34

Answer:

It would be 8 cups of flour.

Answer:

8 cups

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

Angle x and the angle equaling 100 are vertical angles.

the 45 degree angle is just there to confuse you

Solution:

Note that:

Let's substitute x as 2 to find out y.

Let's substitute x as 4 to find out y.

Final answer:

Option B is correct.

Answer:

T=-9

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sides of a triangle measure 6, 8 and 10 cm. What is the area of the triangle?

from the data it is a right triangle, 10 cm is the hypotenuse

so

1/2 (6 * 8) =

1/2 * 48 =

24 units²

Answer:

6 pounds = 96 ounces

4 pounds = 64 ounces

Answer:

116.663333333 repeating

Step-by-step explanation:

do 349.99 divided by 3

Answer:

24, 12, 6, 3, 1.5, 0.75,0.375, 0.1875, 0.09375

The BOLD number is your answer, and the other ones are the sequence. oof, that was a lot of calculating!

Thanks!

Answer:

0.046875

Step-by-step explanation:

Each number is being divided in half each time.

24 / 2 = 12

12 / 2 = 6

6 / 2 = 3

3 / 2 = 1.5

1/5 / 2 = 0.75

0.75 / 2 = 0.375

0.375 / 2 = 0.1875

0.1875 / 2 = 0.09375

0.09375 / 2 = 0.046875 <--- This is the ninth term of the sequence.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{40\% of 59}}{\left( \cfrac{40}{100} \right)59}\implies 23.6~\hfill \underset{sale~price}{\stackrel{59~~ - ~~23.6}{35.4}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{8\% of 35.4}}{\left( \cfrac{8}{100} \right)35.4}\implies 2.832~\hspace{10em}\underset{\textit{sale price plus tax}}{\stackrel{35.4~~ + ~~2.832}{\approx 38.23}}[/tex]

Answer: 86 + 7.5 = 93.5

Step-by-step explanation:

Answer:

9/4 seconds

Step-by-step explanation:

Plug 13 into the equation

13=94-16t^2

subtract 94

-81=-16t^2

divide by -1

81=16t^2

take the square root of both sides

9=4t

divide by 4

t=9/4

Answer:

13.33

Step-by-step explanation:

Write the equation for an inverse variation

⇒ y = k/x

Where x is degrees and y is minutes

Substitute 20 and 20 for x and y

⇒ 20 = k/20

Multiply both sides by 20 to solve k

⇒ 20 × 20 = 20 × k/20

⇒ k = 400

After solving for k, write an equation for the inverse variation

⇒ y = 400/x

Substitute 30 for x

⇒ y = 400/30

⇒ y = 40/3

⇒ y = 13.3333333333

⇒ y = 13.33

[RevyBreeze]

Solution:

We know that:

[tex]\bullet \ \ \tex\text{Area of triangle:} = \frac{1}{2} \times \tex\text{Base} \times \tex\text{Height}[/tex]

Let the base of the triangle be 11 yd. If we extend the base, it will allow us to find the height of the triangle, which is 8 yd.

Using the formula:

[tex]\bullet \ \ \tex\text{Area of triangle:} = \frac{1}{2} \times 11 \times 8[/tex]

Now, let's simplify.

[tex]\bullet \ \ \tex\text{Area of triangle:} = \frac{1}{2} \times 11 \times 8[/tex]

[tex]\bullet \ \ \tex\text{Area of triangle:} = 11 \times 4[/tex]

[tex]\boxed{\bold{\tex\text{Area of triangle:} = 44 \ \tex\text{yd}^{2}}}[/tex]

Given :

⠀

To Find :

⠀

Solution :

Perimeter of the plank :

[tex]\: {\qquad \dashrightarrow \sf 2 \times (Length + Breadth) }[/tex]

[tex]\: {\qquad \dashrightarrow \sf{{ 2 \times (300 + 30) \: cm }}}[/tex]

[tex]\: {\qquad \dashrightarrow \sf{{ 2 \times (330) \: cm }}}[/tex]

[tex]\: {\qquad \dashrightarrow \sf{{ 600 \: cm }}}[/tex]

⠀

Area of the plank :

[tex]\: {\qquad \dashrightarrow \sf (Length \times Breadth) }[/tex]

[tex]\: {\qquad \dashrightarrow \sf (330 \times 30) \: {cm}^{2} }[/tex]

[tex]\: {\qquad \dashrightarrow \sf 9 000 \: {cm}^{2} }[/tex]

⠀

Step-by-step explanation:

Given :-

To find :-

Solution :-

Perimeter of rectangular plank = 2(L+W)

putting the values,

perimeter = 2(300+30)cm

⇝660 cm

Area of rectangular plank = L × W

putting the known values ,

Area = 300 × 30 cm²

⇝ 9000cm²

Answer:

a. x = [tex]\frac{1}{12}[/tex]

b. [tex]\frac{1}{4}[/tex] = 1x

c. 3x = [tex]\frac{3}{3}[/tex]

d. x = [tex]\frac{1}{20}[/tex]

e. x = [tex]\frac{10}{3}[/tex]

Answer:

Step-by-step explanation:

Initial function is

Changed function is

This is best explained when graphed. See below to confirm the correct option

f(x+8)

So

x² is changed to (x+8)²

Change in x

It will shift 8 units left

Option B

Answer:

Given that measure 2 is 79 degrees, we know it'll be supplementary to angle 1 meaning that that both angle measures 1 and 2 will equal 180 degrees:

79 + x = 180

-79        -79

x = 101, ∠1 = 101°

Angles 2 and 4 are vertical, so they are congruent meaning they measure the same degrees:

if ∠2 = 79, then ∠4 is also equal to 79°

Now that we found the measure of angle 1, we can determine the measure of angle 3 since they are vertical as well, (vertical angles are congruent, meaning they measure the same degrees):

if ∠1 = 101, then ∠3 is also equal to 101°

Answer:

Vertical Asymptote at: x = - 1.5

Slanted Asymptote at: y = -x  9/2

Step-by-step explanation:

See image (I HAVE NO IDEA IF YOUR SUPPOSED TO GIVE THE SLANTED ASYMPTOTE. THE PROBLEM ONLY SAYS VERTICAL AND HORIZONTAL ONLY, SO I GUESS ONLY DRAW THE GREEN LINE, NOT THE PURPLE ONE!)

So only draw the x = - 1.5 line that is green!

Answer

A.) As the number of years increased, the population increased.

If the angles are equal, then, x = 9.

Simplification of expressions means rewriting the same algebraic expression with no like terms and in a compact manner.

Given are two angles, 3x -8° and 2x + 1°, simplifying by equating them,

3x -8° = 2x + 1°

x = 9

Hence, If the angles are equal, then, x = 9.

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Answer:

I'm not 100% sure but i think its a  

Step-by-step explanation:

Both have 2 heads and 2 tails so that's 4 and it's a fair game and b is wrong and you will eliminate c.

The game is fair because there is an equal chance of winning an losing the game.

Probability is simply how likely something is to happen.

[tex]P(E )=\frac{Number\ of \ favorable\ outcomes }{Total\ number \ of outcomes}[/tex]

Where,

P(E) is the probability of an event.

A fair game is the game in which there is an equal chance of wining or losing.

According to the given question.

Two coins are tossed.

[tex]\implies sample\ space= \{ HH, HT, TH, TT\}[/tex]

[tex]\implies total\ number \ of outcomes = 4[/tex]

Therefore,

The probability that you win is given by

[tex]P(E_{1} )=\frac{Number\ of \ favorable\ outcomes }{Total\ number \ of outcomes}[/tex]

[tex]\implies P(E_{1} )= \frac{1}{4}[/tex]                            (getting HH is a favorable outcome)

[tex]\implies probability\ of\ losing\ the\ game = 1-\frac{1}{4} =\frac{3}{4}[/tex]

And, the probability that your friend wins the game is given by

[tex]P(E_{2}) = \frac{Total\ number\ of\ favorable\ outcomes\ }{Total\ number\ of\ outcomes}[/tex]

[tex]\implies P(E_{2} )=\frac{1}{4}[/tex]                    (getting TT is the favorable outcome)

[tex]\implies probability\ of\ losing\ the\ game = 1-\frac{1}{4} =\frac{3}{4}[/tex]

Hence, the game is fair because there is an equal chance of winning an losing the game.

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Answer:

The discount is $18.20 which changes the price of the jeans to $27.30.

Answer:

4 containers orange juice

4 containers pinapple

2 containers cranberry

Step-by-step explanation:

1000 milliliters are in a liter

4 liters orange juice, 4*500 = 2,000

4 liters pinapple, 4*500 = 2,000

2 liters cranberry, 2*500 = 1,000

Total 5 liters