Solve the problem. Make sure your answer is in simplest form and improper fractions are expressed as mixed numbers.

A marble is selected at random from a jar containing 5 red marbles, 2 yellow marbles & 3 green marbles. What is the probabil

lisabon 2012 [21]

Answer:

5/11

explanation

Probability here is the chance of selection out of a total. So, we need to first find the total number of marbles.

total

=

5

+

3

+

2

+

1

=

11

So there are

11

marbles total. The probability that we pick one of the

3

green marbles out of the

11

is simply that ratio:

P

green

=

3

11

Same idea for yellow:

P

yellow

=

2

11

The probability of picking either of these colors is simply the sum of their probabilities.

P

green or yellow

=

P

green

+

P

yellow

=

3

11

+

2

11

=

5

11

6 0

3 years ago

A trapezoid has an area of 42 square miles. One base is 4 miles long. The height measures 6 miles. What is the length of the oth

loris [4]

The length of other base of trapezoid is 10 miles

Step-by-step explanation:

The formula for area of trapezoid is:

$A=\frac{h}{2}(b_1+b_2)$

We know that

A = 42 square miles

b_1 = 4 miles

h = 6 miles

Putting the values

$42=\frac{6}{2}(4+b_2)\\42=3(4+b_2)\\42=12+3b_2\\Subtracting\ 12\ from\ both\ sides\\42-12=12+3b_2-12\\3b_2=30\\Dividing\ both\ sides\ by\ 3\\\frac{3b_2}{3}=\frac{30}{3}\\b_2=10\ miles$

The length of other base of trapezoid is 10 miles

Keywords: Area of trapezoid

Learn more about area at:

#LearnwithBrainly

7 0

4 years ago

E vertices of ∆ABC are A(2, 8), B(16, 2), and C(6, 2). The perimeter of ∆ABC is units, and its area is square units.

UNO [17]

We can use the distance formula to calculate perimeter: $\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2}$ = Distance

From A to B: √232

From B to C: 10

From C to A: √52

10 + √232 + √52 = 10 + 2√58 + 2√13

Perimeter = 10 + 2√58 + 2√13 units

For Area we can use matrices, but since one of the sides is horizontal, we can just calculate with distance formula and area of triangle formula.

The area of a triangle formula is 1/2(h x b)

h=height

b=base

So the height is 6 and the base is 16. (I graphed it.)

16 * 6 = 96 96/2 = 48 Area: 48 square units.

8 0

3 years ago

An object travels along a horizontal straight path at a constant rate the object travels 1/20 of the length of the path in 3/4 s

Eduardwww [97]

Answer:

15 seconds

Step-by-step explanation:

Simply assume that total length to be covered be 'L'.

Now , $\frac{1}{20}$ of total length L is covered in time $\frac{3}{4}seconds$ .

We know distance traveled =speed×time

Let Object's velocity be V

Using this

$\frac{L}{20}=V×time$

$\frac{L}{20}=V*\frac{3}{4}$

Thus, velocity in terms of total length is

$V=\frac{L}{15}$

Now,

To cover total length L time needed is

$time =\frac{distance}{speed}$

$time=\frac{L}{\frac{L}{15} }$

Time taken =15 seconds

3 0

4 years ago

Nina has $245 in 5-dollar bills and 10-dollar bills. She has ten more 5-dollar bills than 10-dollar bills. How many of each type

Oksana_A [137]

Answer:

Number of 5 dollar bills = 23

Number of 10 dollar bills = 13

Step-by-step explanation:

Let number of 5 dollar bills be x

and the number of 10 dollar bills be y

Total $245, means we can write:

5x + 10y = 245

Ten more 5 dollar bills than 10 dollar bills, means:

x - 10 = y

Now we substitute 2nd equation in first and solve for x:

$5x + 10y = 245\\5x + 10(x-10) = 245\\5x+10x-100=245\\15x=345\\x=23$

Also,

y = x - 10

y = 23 - 10 = 13

So there are 23 5-dollar bills and 13 10-dollar bills

6 0

4 years ago