18.
Given that sin x =
8
and sin y = , where x and y are acute, find the value of cos (x + y).
17
A.
B.
130
221
140
221
140
204
220
22
C.
D.

Answer:

Step-by-step explanation:

1.1 L

Given:

A rectangular container that has:

   a length of 30 cm,

   a width of 20 cm, and

   a height of 24 cm

It is filled with water to a depth of 15 cm.

When an additional 6.5 L of water are poured into the container, some water overflows.

Question:

How many liters of water overflow the container?

The Process:

Step-1: calculate the volume of rectangular container

The volume of rectangular container is 14,400 cm³, then converted to 14,4 L.

Step-2: calculate the volume of water filled in the container to a depth of 15 cm

The volume of water filled is 9,000³ cm, then converted to 9 L.

Step-3: calculate the volume of water overflow when an additional 6.5 L of water is poured into a container.

The volume of water overflow equals the initial water volume is added to the additional water volume then subtracted by the container volume.

The volume of water overflow =

Thus, the volume of water overflow of the container is 1.1 L.

Answer:

40+20 = 72-12 is the simplified version.

Step-by-step explanation:

Your equations

4(10+5) = 6(12-2)

Multiply 4 by 10 and 5 for the "4(10+5)"
Multiply 6 by 12 and -2 for the "6(12-2)"

40+20 = 72-12 is the simplified version.

If you want to solve/verify:

40+20 = 72-12

60 = 60

The nanswer is correct.

Answer:

40 + 20 = 72 - 12

Step-by-step explanation:

The number outside the parenthesis will be multiplied to both numbers inside the parenthesis, making the equation

(4 * 10) + (4 * 5) = (6 * 12) + (6 * (-2))

simplifying the equation...

40 + 20 = 72 - 12

Answer:

*View the attached graph*

Step-by-step explanation:

Hope it helps!

It would take her 10 hours. If it is double the time for one person to complete the task versus two, you can guess that the other person takes the same amount of time

Answer:

Step-by-step explanation:

simple interest=prt

p=principle amount

r=rate

t=time

here p=$2500

r=5 %=0.05

t=2 years

simple interest=2500×2×0.05=$250

The simple interest on the loan of $2500 for 2 years at 5% is $250

The formula for calculating simple interest is expressed as;

I = PRT/100

Such that the parameters of the formula are;

Now, substitute the values, we get;

Simple interest = 2500 × 5 × 2/100

Multiply the values

Simple interest =25, 000/100

Simple interest =$250

Learn about simple interest at: https://brainly.com/question/25793394

#SPJ2

Step-by-step explanation:

in a square 2 sides with a diagonal creates a right-angled triangle, with the diagonal being the Hypotenuse (the side opposite of the 90° angle).

the diagonal is 3+3 = 6 units long.

let's call the square side length "s".

then we have via Pythagoras

6² = s² + s² = 2s²

36 = 2s²

18 = s²

s = 4.242640687 ≈ 4.2 units

Answer:

973.68 times

Step-by-step explanation:

Since you would expect to win 1 in 38, the amount of times you will win in 1000 times is 1000 / 38 which is 26.32. therefore you would expect to lose 1000 - 26.32 times which is 973.68

Answer:

245² ft high or something else

Answer:

7[tex]\geq[/tex][tex]\frac{h}{14}[/tex]

Step-by-step explanation:

Mark brainliest

Answer:

Those ratios are not equivalent

Step-by-step explanation:

3:4 is not the same as 4:3 because 3:4 means 3 out of 4 but 4:3 means 4 out of 3 which means it is more than one while 3:4 is less than one

Answer:

theta= 1.085

Step-by-step explanation:

Answer:

74

Step-by-step explanation: 74 is not divisible by 6 or 9not nor 7 and it's less than 81 and greater than 64

Answer:

60 ft²

Step-by-step explanation:

A = 1/2 × b × h

A = 1/2 × 12ft × 10ft

A = 1/2 × 120 ft

A = 60ft²

Answer:

  CE ≈ 8.24 units

Step-by-step explanation:

The circumference of a circle is given by the formula ...

  C = 2πr

Your circle has a radius CD of 4 units, so its circumference is ...

  C = 2π(4 units) = 8π units

__

The arc of interest is 118°. The whole circle is 360°, so the length of the arc is 118/360 times the circumference of the circle:

  CE = (118/360)(8π units) ≈ 8.24 units

4 * x = 12.44

4/4 * x = 12.44 / 4

x = 3.11

Answer:

x = 3.11

Step-by-step explanation:

To find the value of 'x', divide both sides of the equation by 4

12.44 = 4x

[tex]\dfrac{12.44}{4}=\dfrac{4x}{4}\\\\\\3.11=x[/tex]

Answer:

8.2

Step-by-step explanation:

Hope this helps....

Answer:

The answer is 8 1 / 2

Step-by-step explanation:

See the Image

Option 1 is easier to understand

Answer:

13

Step-by-step explanation:

the sum to n terms of a geometric sequence is

[tex]S_{n}[/tex] = [tex]\frac{a(r^{n}-1) }{r-1}[/tex]

where a is the first term and r the common ratio

here a = 6 , r = [tex]\frac{12}{6}[/tex] = 2 and [tex]S_{n}[/tex] = 49146 , then

[tex]\frac{6(2^{n}-1) }{2-1}[/tex] = 49146

6([tex]2^{n}[/tex] - 1) = 49146 ( divide both sides by 6 )

[tex]2^{n}[/tex] - 1 = 8191 ( add 1 to both sides )

[tex]2^{n}[/tex] = 8192 ( take log of both sides )

log [tex]2^{n}[/tex] = log 8192 , that is

n log 2 = log 8192 ( divide both sides by log 2 )

n = [tex]\frac{log8192}{log2}[/tex] = 13

[tex]\red{ \underline { \boxed{ \sf{Common \: Ratio,r = \frac{any\:observed\:term}{previous\:term}}}}}[/tex]

[tex]\longrightarrow[/tex][tex]\sf Common \: Ratio,r = \frac{12}{6} [/tex]

[tex]\quad \boxed{\sf {Common \:Ratio,r = 2 }}[/tex]

Now,

[tex]\green{ \underline { \boxed{ \sf{Sum\: of \: G.P. \: to\: n\:term,S_n = \frac{a(r^n-1)}{r-1}}}}}[/tex]

where

Putting Values -

[tex]\begin{gathered}\\\implies\quad \sf 49146 = \frac{6(2^n-1)}{2-1} \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf \frac{\cancel{49146}}{\cancel{6}} = \frac{2^n-1}{1} \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf 8191= \frac{2^n-1}{1} \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf 2^n-1 =8191 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf 2^n =8191+1 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf 2^n =8192 \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\implies\quad \sf 2^n =2^{13}\quad(8192= 2^{13}) \\\end{gathered} [/tex]

Comparing powers on both sides-

[tex]\begin{gathered}\\\implies\quad \boxed{\sf{ n = 13}}\\\end{gathered} [/tex]

[tex]\longrightarrow[/tex]Therefore, to get a sum of 49146 , 13 terms of this G.P. should be taken.

Answer:

A leprechaun (Irish: leipreachán/luchorpán) is a diminutive supernatural being in Irish folklore, classed by some as a type of solitary fairy. They are usually depicted as little bearded men, wearing a coat and hat, who partake in mischief. In later times, they have been depicted as shoe-makers who have a hidden pot of gold at the end of the rainbow.

Answer:

Step-by-step explanation:

Answer:

120

Step-by-step explanation: 4x10x2 +2x5x4 =80+40=120 cubic inches

Answer:

Step-by-step explanation:

This value is approximate since pi = 3.14 is approximate.

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

Work Shown:

r = radius = diameter/2 = 20/2 = 10 inches

L = slant height = 40 inches

SA = surface area of the cone

[tex]\text{SA} = \pi*r^2 + \pi*r*L\\\\\text{SA} = \pi*10^2 + \pi*10*40\\\\\text{SA} = \pi*100 + \pi*400\\\\\text{SA} = 100\pi + 400\pi\\\\\text{SA} = (100+400)\pi\\\\\text{SA} = 500\pi \text{ ... exact surface area in terms of pi}\\\\\text{SA} \approx 500*3.14\\\\\text{SA} \approx 1570\\\\[/tex]

The surface area of the cone is approximately 1570 square inches.

We can abbreviate "square inches" into [tex]\text{in}^2[/tex]

If you want to get a more accurate surface area value, then use more decimal digits of pi.

Answer:

(8, -2)

Step-by-step explanation:

While reflection over x-axis, the x-coordinate remains the same  and the y-coordinate changes to it's opposite.

So,

Rx-axis =>  = (8, -2)

Answer:

Probability that the number cube will land with the number 5 facing up

=5/6

Hope this helps, just used my mind

Step-by-step explanation:

Please mark me brainliest if correct

Step-by-step explanation:

please mark me as brainlest

Step-by-step explanation:

Simple Interest is calculated using the following formula: SI = P × R × T/100, where P = Principal , T is time and r is interest rate.

So , by the values given

Principal :-rs 4000

Time :-2

rate of interest :- 10%

[tex] \frac{p \times r \times t}{100} [/tex]

[tex] \frac{4000 \times 10 \times 2}{100} [/tex]

[tex] = 800 \: rs[/tex]

Answer:

D

Step-by-step explanation:

Remark

The first thing you must do is notice that <D = <BEA. Mark it that way on your diagram.

The Second thing you need to notice is that <BEA and <A are equal because <A and <D are marked as equal.

So both the large triangle and the small one are isosceles. because 2 of the 3 angles are equal.

Now are you ready for this? That means that BA = 10 because BA is opposite one of the 2 equal angles in the small triangle. So now you are ready to set up a proportion.

Proportion

AB / AC = AE/AD

Givens

AB = 10

AC = 18

AE = 8

AD = x + 8

Solution

Substitute the Givens into the Proportion.

10/18 = 8/(x + 8)                      Cross multiply

10(x + 8) = 8 * 18                     Simplify both sides

10x + 80 = 144                        Subtract 80 from both sides

10x + 80 - 80 = 144 - 80

10x = 64                                   Divide by 10

10x/10 = 64/10

Answer: x = 6.4

Answer:

Step-by-step explanation:

The given function is quadratic.

The maximum of the quadratic function is its vertex.

The x-coordinate is determined by x = - b/(2a)

Apply the x-value and find the value of f:

Answer:

18.25

Step-by-step explanation:

we are given a quadratic function

[tex] f(x) = - 16 {x}^{2} + 20x + 12[/tex]

where:

To find the maximum value of f(x) in other words, the maximum height, in feet, reached by the arrow.

Differentiate both sides:

[tex] f'(x) = \dfrac{d}{dx}( - 16 {x}^{2} + 20x + 12)[/tex]

with sum differentiation rule, we acquire:

[tex] \displaystyle f'(x) = \frac{d}{dx}( - 16 {x}^{2} )+ \frac{d}{dx} 20x + \frac{d}{dx} 12[/tex]

recall that,

utilizing the rules we acquire:

[tex] \displaystyle f'(x) = - 32 {x}^{} + 20 [/tex]

now equate f'(x) to 0:

[tex] \displaystyle - 32 {x}^{} + 20 = 0[/tex]

solving the equation for x yields:

[tex]x _{max}= \dfrac{5}{8} [/tex]

plug in the maximum value of x into the quadratic function:

[tex]f(x )_{max}= - 16 {( \frac{5}{8} )}^{2} + 20( \frac{5}{8} ) + 12[/tex]

simplify:

[tex]f(x )_{max} = 18.25[/tex]

hence,

The maximum height reached by the arrow is 18.25 feet

Answer:

the means to and reroof is 10

the distributions are somewhat similar

Step-by-step explanation:

Answer:

78°

Step-by-step explanation:

Angles on a straight line = 180°

AD is the straight line

Angle BFA = 48

Angle CFD = 54

54 + 48 = 102

180 - 102 = 78

Therefore, Angle BFC = 78°

Answer:

C, D, E,

Step-by-step explanation:

All of these will round to 187.55