Consider the matrix. What is the value of |C|?

You roll a six-sided number cube. Which events are mutually exclusive?

maksim [4K]

Events are mutually exclusive only if they cannot both be true.
Only C is alright.

4 is a multiple of two so it can't be right.
Same logic works for B.

And then 2 is prime so then D is out too.

7 0

3 years ago

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A rocking horse has a weight limit of 60pounds. What percentage of the weight limit is 33 pounds? What percentage of the weight

bixtya [17]

Answer:

The percentage is 55% when weight limit is 33 pounds.

The percentage is 190% when weight limit is 114 pounds.

The 95% of the limit weighs 57 pounds.

Step-by-step explanation:

Given:

Weight limit of rocking horse = 60 pounds.

We need to find:

a) What percentage of the weight limit is 33 pounds.

b)What percentage of the weight limit is 114 pounds.

c) What weight is 95% of the limit.

Now Solving for a we get;

Weight limit = 33 pounds

Now percentage of the weight limit can be calculated by dividing given weight limit with total weight limit and then multiplying by 100 we get;

framing in equation form we get;

percentage of the weight limit = $\frac{33}{60}\times100 = 55\%$

Hence The percentage is 55% when weight limit is 33 pounds.

Now Solving for b we get;

Weight limit = 114 pounds

Now percentage of the weight limit can be calculated by dividing given weight limit with total weight limit and then multiplying by 100 we get;

framing in equation form we get;

percentage of the weight limit = $\frac{114}{60}\times100 = 190\%$

Hence The percentage is 190% when weight limit is 114 pounds.

Now Solving for c we get;

Percentage Weight = 95%

Now Amount of weight limit can be calculated by multiplying Percentage weight limit with total weight limit and then Dividing by 100 we get;

framing in equation form we get;

percentage of the weight limit = $\frac{95}{100}\times60 = 57 \pounds$

Hence The 95% of the limit weighs 57 pounds.

4 0

3 years ago

What is the solution to 3(–3x + 9) = −18?

Rus_ich [418]

Answer:

x = 5 (If solved algebraically)

No Solution (If the parentheses are absolute value lines)

Step-by-step explanation:

Result when solving this way: 3|-3x + 9| = -18

1) Divide both sides by 3
|-3x + 9| = -18/3

2) Simplify 18/3 to 6

|-3x + 9| = -6

3) Break down the problem into these 2 equations.

-3x + 9 = -6

- (-3x + 9) = -6

4) Solve the 1st equation: -3x + 9 = -6

- Subtract 1 from both sides.

-3x = -6 - 9

-Simplify -6 - 9 to -15.

-3x = -15

-Divide both sides by -3.

x = -15/-3

- Two negatives make a positive.

x = 15/3

- Simplify 15/3 to 5.

x = 5

6) Solve the 2nd equation: - (-3x+ 9) = -6

1 - Remove parentheses

3x - 9 = -6

2 - Add 9 to both sides

3x = -6 + 9

3 - Simplify -6 + 9 to 3.

3x = 3

- Divide both sides by 3.

x = 1

6) Collect all solutions.

x = 1,5

7) Check solution.

When x = 1, the original equation 3|-3x + 9| = -18 does not hold true.

We will drop x = 1 from the solution set.

8) Check solution.

When x = 5, the original equation 3|-3x + 9| = -18 does not hold true.

We will drop x = 5 from the solution set.

9) Therefore,

No solution exists.

Result when solving algebraically:

Simplifying

3(-3x + 9) = -18

Reorder the terms:

3(9 + -3x) = -18

(9 * 3 + -3x * 3) = -18

(27 + -9x) = -18

Solving

27 + -9x = -18

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-27' to each side of the equation.

27 + -27 + -9x = -18 + -27

Combine like terms: 27 + -27 = 0

0 + -9x = -18 + -27

-9x = -18 + -27

Combine like terms: -18 + -27 = -45

-9x = -45

Divide each side by '-9'.

x = 5

Simplifying

x = 5

5 0

1 year ago

Which equation will create a system of equations with infinitely many solutions?

SashulF [63]

Answer:

A and D

Step-by-step explanation:

for infinitely many solutions, ratio of coefficients should be equal.

since ratio = 1/4 so they will have infinitely many solutions.

6 0

3 years ago

A machine at a factory produces 30 toy cars every 2 minutes. What is the unit rate for producing a toy car using this machine

Lera25 [3.4K]

THE ANSWER IS A 24% YUNIT RATE

7 0

3 years ago

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