What is the equivalent radian measure of 540°? One-third radians StartFraction 3 Over pi EndFraction radians StartFraction pi Over 3 EndFraction radians 3 pi radians.

Answer:

144cm²

Step-by-step explanation:

The surface area of a shape = area of all the sides added together

area of bottom side (square) = 6 x 6 = 36

area of triangles = [tex]\frac{1}{2}[/tex] x 6 x 9 = 27

27 x 4 =108

108 + 36 = 144

Answer:

[tex]A_{total} = 144\ cm^2[/tex]

Step-by-step explanation:

Step 1:  Determine the area of the bottom square

[tex]A = l * w[/tex]

[tex]A = 6\ cm * 6\ cm[/tex]

[tex]A = 36\ cm^2[/tex]

Step 2:  Determine the area of the triangle

[tex]A= \frac{h *b}{2}[/tex]

[tex]A=\frac{9\ cm * (6\ cm/2)}{2}[/tex]

[tex]A=\frac{9\ cm * 3\ cm}{2}[/tex]

[tex]A=13.5\ cm^2[/tex]

Since we have two of these right triangles on each side we come out to having 8 of these triangles total since we have 4 sides.  We multiply 8 by our area from one triangle.

[tex]A=13.5\ cm^2*8[/tex]

[tex]A = 108\ cm^2[/tex]

Step 3:  Determine the surface area

[tex]A_{total} = 36\ cm^2 + 108\ cm^2[/tex]

[tex]A_{total} = 144\ cm^2[/tex]

Answer:  [tex]A_{total} = 144\ cm^2[/tex]

Step-by-step explanation:

a)

100% = 16.25

1% = 100%/100 = 16.25/100 = 0.1625

the discount was $16.25 - $13.00 = $3.25.

how many % is that ?

well, it is a many % as how many times 1% (0.1625) fits into 3.25.

so,

3.25 / 0.1625 = 20

therefore, the coupon was for 20% off.

b)

30% off means he paid 70% of the normal price.

70% = 10.31

1% = 70%/70 = 10.31/70 = 0.147285714...

100% = 1%×100 = 0.147285714... × 100 = 14.72857143...

so, rounded to the nearest cent the normal price for a medium pizza is $14.73

FYI - the direct method would be to divide the discounted price by the %, so, 10.31 / 0.7 ≈ 14.73

but the reason for this shortcut is in the detailed steps explained above.

c)

as we have seen in a) and b), a large pizza after 20% discount is $13, and a medium pizza after 30% discount is $10.31. both is too much for the available $10 (and even less discount).

so, the only chance is a small pizza.

15% discount means to pay 85%.

100% = 11.6

1% = 0.116

85% = 1%×85 = 9.86

he can afford max. a small pizza after 15% discount for $9.86 with his $10.

to calculate in the other direction : with a 15% coupon it means

85% = 10

1% = 10/85 = 0.117647059...

100% = 1%×100 = 11.76470588... ≈ 11.76

with a 15% coupon and $10 he can afford to buy something with a normal prize of max. $11.76

Both the functions are equal to each other. Then the value of x is -1. And they intersect at (-1, 8).

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

Graph the functions [tex]\rm f \rm (x) =-6x +14[/tex] and [tex]\rm g (x)=-2x +6[/tex] are on the same coordinate plane.

For the value of x, both the function are equal to each other.

[tex]\begin{aligned} f(x) &= g(x)\\\\6x + 14 &= -2x + 6\\\\8x &= -8 \\\\x &= -1\end{aligned}[/tex]

The graphs are shown below.

Thus, the value of x is -1.

More about the function link is given below.

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Answer:

X= 2

X= 4

Step-by-step explanation:

I took the test

Answer:

3796.34164m^3

Step-by-step explanation:

you first need to find the radius of the circle that is the top by dividing 18.2 in two. then you need to square it to find the area of that portion of the circle. then multiply it by 3.14 or pi. then after you do all that you should get 82.81m^2. after that you multiply it by the height of the cylinder which is  14.6m. after that you have your answer of 3796.34164m^3. this might be a little bit off so I recommend using pi.

Answer:

1) 27/2 2) 8pi 3) 48 4) 16+2pi

Step-by-step explanation:

1) The length of the triangle is 9 (found by finding the distance between (-5,-3) and (4,-3)) and the height is 3 (found by finding the distance between (1,0) and (1,-3)). The area of a triangle is 1/2 (length times height) which in this case is 27/2.

2) The shape is a semicircle, so the area is 1/2 pi*r^2.

1/2 * pi * r^2=8pi

3) B*H=8*6=48

4) The figure is a semicircle and a square.

The area of the semicircle is 1/2 * pi * r^2=2pi

The area of the square is b*h=4*4=16

The area is 16+2pi.

Explanation:

Parallel lines always have equal slopes, but different y intercepts.

Line K has a slope of 5, which means line L also has this slope too. Refer to the y = mx+b form.

Plug in the coordinates of (-2,-7) as well as the slope mentioned and solve for b.

y = mx+b

-7 = 5(-2) + b

-7 = -10+b

-7+10 = b

3 = b

b = 3

The y = mx+b updates to the final answer of y = 5x+3

2.2 = 2.6 - 0.4 is 1 standard deviation below the mean, and 3 = 2.6 + 0.4 is 1 standard deviation above it. Then by the empirical rule, the percentage of students with GPA between 2.2 and 3 is

Pr [2.2 ≤ X ≤ 3] = Pr [-1 ≤ Z ≤ 1] ≈ 68%

(where Z is normally distributed with mean 0 and s.d. 1)

This is one single number and not two separate numbers.

Delete the comma if your teacher requires it.

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

Explanation:

I'm assuming letters can repeat.

There are 26 letters in the English alphabet.

There are,

Overall, there are A+B+C+D = 456,976+17,576+676+26 = 475,254 strings of length four or less.

Number in square root is a number multiplied by itself. For example, 10*10 would give us a square root of 100.

Step-by-step explanation:

1. Square root of 36 = 6

2. Square root of 100 = 10

3. Square root of 81 = 9

4. Square root of 49 = 7

Answer:

3/25

Step-by-step explanation:

12% = 12/100 = 6/50 = 3/25

Answer:

[tex]x + 4 + 2x + 1 \\ 3x + 5 \\ x = \frac{ - 5}{3} [/tex]

Answer:

43.1

Step-by-step explanation:

We can figure this out by using a bit of simple trigonometry

Using the available values we know we have to figure out x using cos because it includes the adjacent and hypotenuse values.

"Soh Cah Toa"

Cos(x) = Adjacent / Hypotenuse

Cos(x) = 8/11

Cos(x) = 0.73

Using [tex]cos^{-1}[/tex] we can figure out x from the side length

x = [tex]cos^{-1}[/tex](0.73)

x = 43.1 degrees (rounded)

Answer:

Step-by-step explanation:

Let's rewrite all the fraction to ratios
4:6, 10:12, 2:5, 4:7

Now, using the direct proportion, if one increase/decrease, the other increase/decrease by the same amount

4:6 = (4x2) : (6x)2 = 8:12
10:12 =( 10:2) : (12:2) = 5:6
2:5 = (2x3) : (5x3) = 6:15
4:7 = (4x2) : (7x2)= 8:14

The number of deposits that she has to make in order to reach her goal of saving $475 is 21 weeks.

The equation that represents the total amount Amelia can save is:

Total amount saved ≥ initial deposits + (weekly deposits x number of weeks)

$475 ≥ $60 + $20x

In order to determine the value of x, take the following steps:

Combine similar terms

$475 - $60 ≥ $20x

$415 ≥20x

Divide both sides by 20

x ≥ 20.75

x ≥ 21 weeks

To learn more about inequality, please check: https://brainly.com/question/5031619

Answer:

A, B, and D are all true

Step-by-step explanation:

N/A

The two true statements for the expansion are A and C.

In the expansion of (x + y)ⁿ, each one of the terms will have a total exponent equal to n, this means that we will have terms like:

[tex]x^k*y^j[/tex]

Such that k + j = n.

Particularly, we get the terms xⁿ and yⁿ only once, so the first statement is correct, the coefficients of these terms will be 1.

It is also true that the coefficients of:

[tex]x^k*y^j = x^k*y^k[/tex]

Are equal.

Then the two true statements are A and C.

If you want to learn more about expansions:

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Answer:

Step-by-step explanation:

Using the inequality rule, the third side has to be less than 12 + 16 = 28.
So, any answer of 28 or more than 28 does NOT satisfy the length.
It also has to be more than 4 to satisfy the inequality rule.

In short words, 4 < x < 28.

A, B and C all satisfy, because they are in the range of x

D) 32 is >28, so this is the wrong answer and CANNOT be the value of x.

Answer:

32

Step-by-step explanation:

Any number between 16 - 12 = 2 and 16 + 12 = 28 are possible.

Among given choices, only 32 is not in the above region. so 32 CANNOT be the value.

Hi There!

Given:

803 pages in a book

To Find:

How many days will it take for Mike to finish reading the book, if he reads 36 pages a day?

In order to find the number of days, take the total number of pages and divide it by the number of pages read a day:

803÷36≈22

Answer: It will take Mike 22 days to finish reading the book.

Have an awesome day!

[tex]\huge\textbf{TheStarryNights}[/tex]

First blank is 'left'

Second Blank is 'right'

Answer: Large jar : 154/440 = 3.5x10^-3 price

Step-by-step explanation: Large jar : 154/440 = 3.5x10^-3 price per gram 3.7x10%3 > 3.5 x 10^-3 so Large jar is the best value for money

Answer:

(Option B

(Option C

Step-by-step explanation:

Concept:

We will start by explaining each option one after the other

Step 1:

The sum of two odd numbers

Let the first odd number be

[tex]2a+1[/tex]

Let the second odd number be

[tex]2B+1[/tex]

By adding the two numbers, we will have

[tex]2a+1+2B+1=2(a+B)+2[/tex]

Hence,

The sum of two odd numbers is even

Step 2:

The difference of two odd number

Let the first odd number be

[tex]2a+1[/tex]

Let the second odd number be

[tex]2B+1[/tex]

To find their difference, we will have

[tex]2a+1-(2B+1)=2a+1-2B-1[/tex]

[tex]=2a-2B[/tex]

Hence,

The difference between two odd numbers is even

Step 3:

Let the first even number be

[tex]2a[/tex]

Let the second odd number be

[tex]2B+1[/tex]

By adding the two numbers, we will have

[tex]2a+2B+1[/tex]

Hence,

The sum of an odd number and an even number is odd

Step 4:

The difference between an odd number and an even number

Let the first even number be

[tex]2a[/tex]

Let the second odd number be

[tex]2B+1[/tex]

Hence,

The difference will be

[tex]2a-(2B+1)[/tex]

[tex]2a-2B-1[/tex]

Hence,

The difference between an odd number and an even number is odd

Therefore,

The correct answers are OPTION B and OPTION C

-Good Luck with your Assignment!

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Answer:

5

Step-by-step explanation:

The number of apples bought by him is 113.

A grouping of variables, symbols, and/or numbers used to represent a mathematical quantity or relationship is known as an expression in mathematics. Expressions might be straightforward with just one number or variable or complex with many terms, operations, and functions.

Let's assume that Sam bought x number of apples.

He bought them at 60 cents each, which means the total cost of buying these apples was:

Cost price = 60x cents

He sold all but 5 of these apples at R1.00 each, which means the total revenue he earned from selling them was:

Revenue = (x - 5) x R1.00 = R(x - 5)

Sam made a profit of R5.00, which means his revenue was more than his cost price by R5.00. We can write this as:

Revenue - Cost price = R5.00

Substituting the values of revenue and cost price from above, we get:

R(x - 5) - 60x = 500 cents

Rearranging and simplifying this equation, we get:

40x = 500 + 5R

Substituting R = R1.00, we get:

40x = 500 + 5 = 505

Solving for x, we get:

x = 12.625

Since Sam cannot buy a fraction of an apple, we round up x to the nearest integer:

x = 13

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Answer:

B

Step-by-step explanation:

the 2/3x represents how much it will increase while the -1 represents the y-intercept