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2 months ago

Guest #7880

2 months ago

The probability is 8/18 or 44%.

Since there are 3 sculptors and 5 photographers, and the question is asking for either a sculptor or photographer, you add them together. There are a total of 18 artists, and the probability is the chance of a certain thing happening over the total amount of things that can happen (i.e. a coin landing on heads is 50%).

The answer would be 8/18.

Guest #7881

2 months ago

8/18

3+5=8

18 is the total number of artists.

3+5=8

18 is the total number of artists.

Question

The longer leg of a right triangle is 4 more than twice the shorter leg. The hypotenuse is 4 less than three times the short leg. What is the value of the hypotenuse?

Solution 1

Let the shorter leg = x

shorter leg =x

longer leg = 2x + 4

hypotenuse = 3x - 4

Given that a² + b² = c²

x² + (2x + 4)² = (3x - 4)²

Remove brackets : (a + b)² = a² + 2ab + b²:

x² + 4x² + 16x + 16 = 9x² - 24x + 16

Moved all terms to the left:

x² + 4x² + 16x + 16 - 9x² + 24x - 16 = 0

Combine like terms:

-5x² + 40x = 0

Multiply all terms by -1:

5x² - 40x = 0

Take out 5x as common factor:

5x(x - 8) = 0

Apply zero product property:

5x = 0 or x - 8 = 0

Evaluate:

x = 0 or x = 8

Since length cannot be zero, shorter leg = 8

shorter leg = 8

Hypotenuse = 3(8) - 4 = 20

**Answer: 20 units**

shorter leg =x

longer leg = 2x + 4

hypotenuse = 3x - 4

Given that a² + b² = c²

x² + (2x + 4)² = (3x - 4)²

Remove brackets : (a + b)² = a² + 2ab + b²:

x² + 4x² + 16x + 16 = 9x² - 24x + 16

Moved all terms to the left:

x² + 4x² + 16x + 16 - 9x² + 24x - 16 = 0

Combine like terms:

-5x² + 40x = 0

Multiply all terms by -1:

5x² - 40x = 0

Take out 5x as common factor:

5x(x - 8) = 0

Apply zero product property:

5x = 0 or x - 8 = 0

Evaluate:

x = 0 or x = 8

Since length cannot be zero, shorter leg = 8

shorter leg = 8

Hypotenuse = 3(8) - 4 = 20

Question

If you want to put a 4x8 piece of plywood through a 3 foot square opening in your ceiling by turning it diagonally is the opening big enough? use a 45-45-90 since its a square

Solution 1

Answer: Yes, the 3 foot 3 foot square opening in your ceiling is big enough to insert a 4x8 piece of plywood.

In a 3x3 foot square, we can form two right triangles with same diagonal side or hypotenuse. .

Using the Pythagorean theorem/formula, we can find the length of the hypotenuse or the longest side of the triangle ( c) given the two sides a and b

Substitute values a=3 and b=3 to formula

a^2^+b^2^=C^2^=

3^2^+3^2^=C^2^=

9+9= C^2^

C= square root of 18

C=4.24

A 4x8 piece of plywood can be inserted in a 4.24 opening diagonally.

Question

From 1992 through 2007, the purchasing power of a dollar decreased by about 3.5% per a year. Using 1992, as the base for comparison, what was the purchasing power of a dollar in 2007? Formula: y=C(1−r)t $0.48
$0.57
$0.44
$0,59

Solution 1

1) Given formula: y=C(1−r)^t

I will change t for x just due to editor limitations:

2) In that:

C =$1,

r = 3.5% = 3.5/100 = 0.035

x = t = 2007 - 1992 = 15

3) Compute

Answer: $0.59

Question

What is 150000000 times 10

Solution 1

150,000,000 × 10 =

1,500,000,000

All you have to do is add another zero.

**Answer = 1,500,000,000**

~Hope this helped~

1,500,000,000

All you have to do is add another zero.

~Hope this helped~

Question

A newly hatched channel catfish typically weighs 0.3 grams. During the first 6 weeks of life, its growth is approximately exponential, increasing by about 10% each day. Find the weight at the end of four weeks. (Hint: Be sure to change the number of weeks to days before plugging into the formula!) Formula: A=C(1+r)t 0.53g
4.33g
16.43g
1.14g

Solution 1

1) The formula is given:

2)

3) C is the initial weight and A is the final weight after x (or t) days.

4) The equation leads to:

x = number of days = 7 × number of weeks = 7 × 4 =

4) Compute:

Question

If it takes for men six hours to repair a road how long will it take three men to do the job if they work at the same rate?

Solution 1

It will take three men seven hours and thirty minutes to repair the road. Hope it helps, God bless

Question

A wise man once said, "500 reduced by 3 times my age is 200." What is his age?

Solution 1

The answer is: "** 100** " .

**_________________________________________________________**

**Explanation:**

**_________________________________________________________**

Let "x" represent the numerical value of [the man's age].

500 - 3x = 200 ; Solve for "x" ;

Subtract "500" from each side of the equation:

500 - 3x - 500 = 200 - 500 ;

to get:

- 3x = -300 ;

Now, divide each side of the equation by "-3" ; to isolate "x" on one side of the equation; & to solve for "x" ;

- 3x / -3 = -300 / -3 ;

** x = 100** .

**_______________________________________________________**

The answer is: "** 100** " .

**_______________________________________________________**

Let "x" represent the numerical value of [the man's age].

500 - 3x = 200 ; Solve for "x" ;

Subtract "500" from each side of the equation:

500 - 3x - 500 = 200 - 500 ;

to get:

- 3x = -300 ;

Now, divide each side of the equation by "-3" ; to isolate "x" on one side of the equation; & to solve for "x" ;

- 3x / -3 = -300 / -3 ;

The answer is: "

Question

Madison bought an empty lot for $2000 in later sold it for a 25% profit how much did Madison sell the lot for?

Solution 1

She sold it for $2,500 if you add 2000+25% you'll get 2,500

Question

Rebecca is planting an orange grove that covers 32 acres she uses the same amount of ground space for each tree Rebecca plants 15 trees in a section of the grove that measures 250 feet by 25 feet what is the population density of this section of the grove use 1 acre= 43,560 square feet

Solution 1

Area of the garden that 15 trees are planted will be:

Area=250×25=6250 ft²

but 1 acre= 43560 ft²

thus converting our area to acres we get:

6250/(43560)

=0.1435 acres

thus the population density will be:

(Population)/(area)

=15/0.1435

=104.544 trees/acre

Area=250×25=6250 ft²

but 1 acre= 43560 ft²

thus converting our area to acres we get:

6250/(43560)

=0.1435 acres

thus the population density will be:

(Population)/(area)

=15/0.1435

=104.544 trees/acre

Question

Ellie made a cube-shaped cardboard box with side-length s. The area of cardboard she used is given by the formula A = 6s2￼, where s represents the side length of the cube.

Solution 1

The correct question is

Ellie made a cube-shaped cardboard box with side-length s. The area of cardboard she used is given by the formula A = 6s2￼, where s represents the side length of the cube.

Which equation correctly solves the formula for s?

we know that

A = 6s²---------> clear the variable s

s²=A/6------> applying square root both members

s=√(A/6)--------> s=(1/6)*√(6*A)

**the answer is**

**s=(1/6)*√(6*A)**

Ellie made a cube-shaped cardboard box with side-length s. The area of cardboard she used is given by the formula A = 6s2￼, where s represents the side length of the cube.

Which equation correctly solves the formula for s?

we know that

A = 6s²---------> clear the variable s

s²=A/6------> applying square root both members

s=√(A/6)--------> s=(1/6)*√(6*A)

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