Find the average of the numbers 6 4/7, 1 5/56, 9 1/7, 3 5/8. Write the solution as a mixed number or a fraction in lowest terms.

Using the Pythagorean Theorem, it is found that the lot has an area of about 35 acres.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

Researching the problem on the internet, the lot has one leg of 800 feet and the hypotenuse is of 3900 feet, hence the other leg is found as follows:

[tex]800^2 + l^2 = 3900^2[/tex]

[tex]l = \sqrt{3900^2 - 800^2}[/tex]

l = 3817 feet.

The area of a right triangle is given by half the multiplication of it's legs. Hence, the area of the lot, in square feet, is given by:

A = 0.5 x 800 x 3817 = 1,526,800 square feet.

Each square feet is equivalent to 0.000029568 acres, hence the area in acres is given by:

Aa = 0.000029568 x 1,526,800 = 35 acres.

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The measure of the acute angle is 60 degrees

Given the following trigonometry equation

tan x=2sinx

This can also be written as;

sinx/cosx=2sinx

Simplify to have:

1/cosx =2

2cosx = 1

cosx = 1/2

x = arccos(1/2)

x = 60 degrees

Hence the measure of the acute angle is 60 degrees

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Answer: So you want to convert 5 cubic meters into cubic centimeters? If you're in a rush and just need the answer, the calculator below is all you need. The answer is 5000000 cubic centimeters.

Step-by-step explanation:

Answer:

12 pounds of tea-1 and 8 pounds of tea-2 should be used.

Step-by-step explanation:

The expression for the distance from the 1st base to the 3rd base in terms of side length will be c=x√2

Given that the softball diamond is square in shape.

Let the side of the square i.e. distance between consecutive bases is x

The distance from the 1st base to the 3rd base creates the hypotenuse of a right triangle, where each side is equal to x i.e. x is the side length of the square formed by the baseball diamond.  

Using the Pythagorean theorem we have:

x² +x²= c²,

where c is the distance from the 1st base to the 3rd base.

Combining similar terms gives us

2x²=c²

Taking the square root of both sides we have

√2x²= √c²

⇒x√2=c

⇒c=x√2

This is the expression for the distance from the 1st base to the 3rd base in terms of side length.

Therefore the expression for the distance from the 1st base to the 3rd base in terms of side length will be c=x√2.

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Answer:

This is my answer↓:

Step-by-step explanation:

The height of the tree from which Sam is standing 100 feet away from the base is 64.94 feet.

The angle of elevation is an angle that is formed between the horizontal line and the line of sight.

To calculate the height of the tree , we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for H

Hence, the height of the tree is 64.94 feet.

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Step-by-step explanation/Answer:

PE(MD)(AS) (a good way to remember how to solve order of operations)

Start:

P: Parenthesis

E: Exponent

M: Multiplication & D: Division

A: Addition & S: Subtraction

:End

*Multiplication and Division are grouped together because they are on the same level, you decide which to do first depending on which comes first in the equation. The same applies for addition and subtraction.

So:

first thing we can look is the parenthesis, but before we can solve the whole thing we must notice the exponent only on the four. Since it is inside the parenthesis we must solve it first.

1. 4^2 = 16

now we will solve the addition inside the parenthesis

2. 16-13 = 3

now lets continue with pemdas, no more parenthesis so we tackle exponents

3. 5^2 = 25

Lets rewrite our equation with the changes we have made

8 × 3 ÷ 3 + 25 + 4 × 3

Now we solve multiplication and division

Equations is worked left to right, like english is read, so we will start on the left side and continue to the right, only solving multiplication and division.

4. 8 x 3 = 24

5. 24 ÷ 3 = 8

6. 4 x 3 = 12

new equation: 8 + 25 + 12

now we can use addition and subtraction (no subtraction luckily!)

7. 8 + 25 = 33

8. 33 + 12 = 45

Step-by-step explanation:

2and5 is 7

1and 5 is 6

4and 6 is 10

2and 6is 8

The best buy is (d) a 9 oz box of rice $1.25

The best buy is the product that has the least unit rate.

The unit rate is calculated as:

Unit = Price/Weight

So, we have:

Box 1:

Unit rate = $0.90/6 oz = $0.150 per oz

Box 2:

Unit rate = $1.93/12 oz = $0.161 per oz

Box 3:

Unit rate = $2.42/16 oz = $0.151 per oz

Box 4:

Unit rate = $1.25/9 oz = $0.139 per oz

The least unit price is $0.139 per oz for box 4

Hence, the best buy is (d) a 9 oz box of rice $1.25

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Answer:

$57.60

Step-by-step explanation:

2/5 = 0.4

0.4*96 is 38.4

96-38.4 = 57.6

The gadget is discounted $38.40 off the original price of $96 and now costs $57.60

Answer:

40.9 %

Step-by-step explanation:

8.8   is   .4 hours above the mean this is  .4/1.77 = .226 standard deviations above the mean

 Using z-score table this corresponds to ~ .5910    (59.10%)

    this percentage is LESS than 8.8 hours

      the percentage ABOVE this is 40.9%

(Not asked, but this is  40.9 (40 ) = ~ 16 of the 40 mechanics sampled)

The formula for the equation of y, the number of units sold as a function of x is y = 0.00625x + 250

From the information given, when the company spends no money on advertising, it sells 250 units and for each additional $4000 spent, an additional 25 units are sold.

The formula for y will be:

y = (25/4000)x + 250

y = 0.00625x + 250

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Step-by-step explanation:

[tex]h(x) = \frac{3}{x}\\h(h(x)) = \frac{3}{\frac{3}{x}}\\\\h(h(x)) = \frac{3}{1} * \frac{x}{3}\\h(h(x)) = \frac{3x}{3}\\h(h(x)) = x\\\\\\f(f(x)) = (x^2-3)^2-3\\f(f(x)) = x^4+2(x^2)(-3)+(-3)^2-3\\f(f(x)) =x^4-6x^2+9-3\\f(f(x)) = x^4-6x^2+6\\[/tex]

The slope of the given line in  the image is -4 , Option A is the answer.

The equation of the straight line is given by

y =mx +c ,

Where m is the slope , C is the intercept

The line is passing through the point

(-1,8)  ,(2,-4)

The slope is given by

m = (y₂-y₁) /(x₂-x₁)

m  = (-4 - 8 )/(2 +1)

m = -12/3

m = -4

Therefore the slope of the given line in  the image is -4 , Option A is the answer.

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Answer: D

Step-by-step explanation:  

6^4 = 6 x 6 x 6 x 6 = 1,296

6^4 = 1,296

Answer:

6000 meters

Step-by-step explanation:

Each kilometer is 1000 meters so 1000 x 6 is 6000

The population in the year 2023 is 120,780.

The growth is linear hence, the equation of the growth is
y=ax+b where b represents the initial population and a is the number of people growing yearly.

So, according to the question statement, we have that

y=280x+b where x is the number of years past and y is the population in the xth year.

According to the given problem population in 2022 will be 120,500.

Suppose that the initial population is taken at 2000.

Hence, 120,500=280×(2022-2000)+b

⇒b=120,500-280×22

⇒b=120,500-6,160

    =114,340

So, the Linear equation becomes

y=280x+114,340

⇒y=280×(2023-2000)+114,340

⇒y=120,780

Hence, the population in the year 2023 is 120,780.

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Step-by-step explanation:

all the details You can find in the attachment.

The remaining area of the page will be 80 square inches.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.

The area of the remaining part will be calculated as;-

Area of the square page will be = 11 x 11 = 121 square inches.

Area of three pictures will be = 15 x 3 = 45 square inches.

So the remaining area will be = 121 - 45 = 80 square inches.

Therefore the remaining area of the page will be 80 square inches.

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The weight of the each pile yesterday would be 6 and 8 pounds.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given;

Yesterday the ratio of seeds in these piles was 3:4.

Let it be 3x and 4x.

If the 2 pounds of seeds is added in the bigger pile, then it become

4x + 2

He also ate 1/4 pound from the smaller pile, then

3x - 1/4

Now the quantities of seeds in those piles is in the ratio of 5:16.

So, 4x + 2 = 5x

3x - 1/4 = 16x

Solve;

So, 4x + 2 = 5x

2 = 5x - 4x

x = 2

The weight of the each pie would be

3x = 6 pound

4x = 8 pound

Hence, The weight of the each pile yesterday would be 6 and 8 pounds.

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If a system of linear equations has exactly one solution then the slopes of both the lines should be different.

Given A system of linear equations has exactly one solution.

Linear equation is a type of equation  when when plotted on the graph gives a straight line. The slope is the ratio of the vertical change to the horizontal change between two distinct points on a line.

let two equations be who have one solution

2x+3y=7

5x+6y=1

solving them

x=7-3y/2

put the value of x in second equation

5(7-3y)/2+6y=1

35-15y/2+6y=1

35-15y+12y=2

-3y=-33

y=11

put the value of y in x=7-3y/2

x=7-3*11/2

x=7-33/2

x=-26/2

x=-13.

There is only one solution which is (-13,11)

Taking equations and convert them into standard form

first

y=7/3-2/3x

second

y=1/6-5/6x

The standard form is y=a+bx where b is slope

from the above equations we can find that the slope of first equation is -2/3 and the slope of second equation is -5/6. In this way we are able to conclude that slopes should be different for one solution.

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Answer:

K=-3/5

Step-by-step explanation:

y= -3x/5 - 11/5

Answer:

60

Step-by-step explanation:

_---&$'_-4$':/-&$$--(:'##4--&&4___&$$_666&4&&&&&

Answer:

= B

Step-by-step explanation:

Answer:

A. 15

Step-by-step explanation:

Hypotenuse = 22

Since the two angles other than the 90° are both

45° , it means that the two legs of the right triangle are of equal length.

So, (x)²+ (x)² = 22²

2x² = 22²

x² = 484/2

x² = 242

x = √242

x = 15.55

x ≈ 15

Answer:

4,051,500

Step-by-step explanation:

You have 7.3 % that are one native one foreign

Multiply that by the number of households

.073 * 55,500,000

4,051,500

Answer:

x = -3

x = -1

x = 2

Step-by-step explanation:

The zeros of a function are the x-values of the points at which the curve crosses the x-axis.

From inspection of the given graph, the curve crosses the x-axis at:

Therefore, these are the zeros of the function.