The functions f(x) and g(x) are defined below. (in the image attached)




Which expression is equal to f(x) + g(x)?

Answer:

cos(3π/4) = -√2/2

Step-by-step explanation:

According to the unit circle, the exact value of cos(3π/4) is -√2/2.

The exact value of cos 3π/4 is - 1/√2

Here we have to find the exact value of

cos 3π/4

Since we know that,

The values of all trigonometric functions depending on the ratio of sides of a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.

We can write,

cos 3π/4 = cos(π/2 + π/4)

Since we know that,

cos(π/2 + θ) = - sin θ

Therefore,

⇒ cos(π/2 + π/4)   = - sin π/4

                             = - 1/√2

Hence,

⇒ cos 3π/4 = - 1/√2

To learn more about trigonometric ratios visit:

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Step-by-step explanation:

first find the value of 1km

1km= 10/25

1km= 0.4cm

now,

54km= 0.4× 54

= 21.6 cm

The volume = Base × height = 12× 7 = 84 Cm³

Answer:

84

Step-by-step explanation:

Step-by-step explanation:

there are 13 cards per 4 suits, totalling 52 cards in an entire deck

13 represents an entire 1 suit out of 52 cards

13/52 = 0.25

thus your answer is 0.25% or 1/4

Answer:

The Answer to the Ultimate Question of Life, the Universe, and Everything is 42

Step-by-step explanation:

In this equation, the number 42 is called a minuend.

15 is a subtrahend because it is being subtracted from another number.

The number 27 would be called the difference.

Answer:

The answer is:

C. The median for town A, 20°, is less than the median for town B, 30°.

Step-by-step explanation:

Median is the middle (center) value.

Option (C) the median for town A, 20°, is less than the median for town B, 30°.

Box plot is a type of chart often used in explanatory data analysis. A graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.

For the given situation,

The diagram shows the box plot of the daily low temperatures for a sample of days in two different towns.

From the box plot, the median of town A is 20° and the median of town B is 30°.

From the data,

⇒ [tex]20 < 30[/tex]

Hence we can conclude that option (C) the median for town A, 20°, is less than the median for town B, 30°.

Learn more about box plot here

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Answer:

y=60 degrees ; x=120 degrees.

Step-by-step explanation:

All triangles' angles must add up to 180 degrees. An equilateral triangle has 3 equal sides and degrees. If it gives the angle of one all the other angles are the same. For x you see the parallel line below it with the line to the left going through with the same angle as the one below. The angles are the same and if it is labeled in one then it is the same in the other.

Answer:

x = 4.48

Step-by-step explanation:

read the picture

Answer:

b. 96

Step-by-step explanation:

triangle area= b x h / 2

5 x 6 /2= 15

15 x 4 (4 triangles)= 60

square area= b x h

6x6=36

36 + 60 = 96

Answer:

tan90°=p/b

or,1/0=10/x

therefore x=0

Answer:

20

Step-by-step explanation:

Have a nice day :)

Answer:

options 2, 3 and 5

Step-by-step explanation:

first of all, because

n²+3n+2n = 6n simplifies to n²+5n = 6n, which simplifies to

n² = n, which is not true for all n not equal to 0 or 1.

option 6 is not a valid reason, as it made a calculation error.

options 1 and 4 make invalid simplifications.

Answer:

5/12 is already in simplest form

Step-by-step explanation:

12m =  5r + 3y + 4b

red is chosen = 5r / 12 = 5/12

Step-by-step explanation:

the answer is 5/12. It's quite simple

Answer:

hey. pls post the graphs with the question so we may help you. you can add the pictures as an attachment.

Answer:

A 180-pound kangaroo's recommended height is 6 feet.

Step-by-step explanation:

Since 120-pound kangaroo is 5 feet tall and for every inch over this height we add 5 pounds to the total weight, we can make this formula. [tex]120+x=180[/tex]. Using this we can figure out the weight difference between a 120-pound kangaroo and a 180-pound kangaroo. After solving for x we get [tex]x=60[/tex].

Now that we know the 180-pound kangaroo weighs 60 more pounds than a 120-pound kangaroo we can divide that weight difference by 5 to figure out the height difference. [tex]60/5=12[/tex]

After getting the height difference from the weight difference we can conclude that a 180-pound kangaroo's recommended height is 5 feet and 12 inches. Since 12 inches = 1 foot we can easily convert 5' 12" to 6'. This means that a 180-pound kangaroo is 6 feet tall.

Answer:

5,-5

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

ok

Answer:

[tex]r =5[/tex]

Step-by-step explanation:

Given

[tex](h,k) = (-3,2)[/tex] -- center

[tex](x,y) = (1,5)[/tex] --- pass through

Required

The radius (r)

The equation of circle is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

So, we have:

[tex](1 - -3)^2 + (5 - 2)^2 = r^2[/tex]

[tex](4)^2 + (3)^2 = r^2[/tex]

[tex]16+9 = r^2[/tex]

[tex]25 = r^2[/tex]

Take square roots of both sides

[tex]5 = r[/tex]

[tex]r =5[/tex]

Answer:

The mean is 19.

Step-by-step explanation:

To find the mean, you add up all of the numbers then divide by how many numbers there are. So you would do 3+8+10+11+14+17+22+24+25+35+40, then divide it by 9 since there are 9 numbers shown, which gets you to 19.

Answer:

0.7408 = 74.08% probability that there are no surface flaws in an auto's interior.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of successes

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Mean of 0.03 flaws per square foot of plastic panel.

This means that [tex]\mu = 0.03n[/tex], in which n is the number of square feet.

Assume an automobile interior contains 10 square feet of plastic panel.

This means that [tex]n = 10[/tex], so [tex]\mu = 0.03(10) = 0.3[/tex]

What is the probability that there are no surface flaws in an auto's interior?

This is [tex]P(X = 0)[/tex]. So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = x) = \frac{e^{-0.3}*(0.3)^{0}}{(0)!} = 0.7408[/tex]

0.7408 = 74.08% probability that there are no surface flaws in an auto's interior.

Answer:

-25

Step-by-step explanation:

-24×(-25)=600

Hope this helps! :)

Answer: It's -25

edg 2023

Answer:

7 hrs

Step-by-step explanation:

$187 for 11 hrs

$119 for x hrs

write a proportion.

187/11 = 119/x since Reuben is making money at the same rate.

solve for x:

187x = 1309

x=7

7 hours

Answer:

7 hours

Step-by-step explanation:

Reuben works for 11 hours to earn $187

This means, his earnings rate is $187 per 11 hours of work

In 1 hour he would earn = 187/ 11 = $17

Therefore, he earns $17 in 1 hour

To find out how many hours he has to work to make $119, we multiply this by the rate.

He will earn $119 in = $119 x (1 hour/ $17) = 7 hours

Reuben has to work 7 hours to make $119

Answer:-7

Step-by-step explanation: -3^3+ 2

-9+2= -7

Answer:

128π ft³ ; 401.92 ft³

Step-by-step explanation:

The volume of the cylinder Given above :

Volume of cylinder, V = πr²h

r =Radius = 4 ; h = 8 ft

V = π * 4² * 8

V = 16 * 8 * π

V = 128π ft³

Using π = 3.14

V = 128 * 3.14 = 401.92 ft³

Answer:

18133.333... units

Step-by-step explanation:

the shortest circumference for a given area based on rectangles is a square (all sides of equal length).

we cannot split a square completely into 3 equal area squares (only 4).

the best approach is then to split this main square into 3 equal area rectangles (not equal rectangles).

area of square 3200² = 10240000

a third of that area is 3413333.333...

now, splitting the main square into 3 equal "strips" of land creates 3 narrow and long rectangles, which is bad for minimizing the circumference. the best solution is to get as closely as possible to a square shape.

that we get by splitting one side in half and go in as far as the land area allows, which would be

half a side = 1600

3413333.33.../1600 = 2133.33...

so, we get 2 areas of 1600 × 2133.33...

and one area of (3200-2133.33...)×3200 = 1066.66...×3200

the length of fence needed is then

around the main square = 4×3200 = 12800

plus one length of fence between the first 2 parts : 2133.33...

plus one intensive long side between the first 2 parts and the remaining third part : 3200

in total : 18133.33...

to check : the three slices would require the 12800 plus 2 long lines inside between the 3 slices : 2×3200

in total : 19200

and an attempt to simply build one long strip of 3 equal area squares next to each other :

the side length of one such square is

sqrt(341333.33...) = 1847.520861...

as fence we would need 6 times that side length for the top and the bottom of the long strip, 2 times that side length for the sides left and right if the strip, and 2 times inside as additional delimiters between the 3 squares.

in total : (6+2+2) × 1847.520861... = 10×1847.520861...

= 18475.20861...

this is all larger than the original solution.

Answer:

sheet needed=45

Step-by-step explanation:

1 sheet=120 words

x sheet=5400 words

x sheet=5400/120

x sheet =45