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Llana [10]
3 years ago
9

While doing back to school shopping on tax-free weekend, Mrs. Michaels bought 2 packs of mechanical pencils and 3 binders for a

total cost of $21.00. Mr. Lawrence bought 5 of the same packs of mechanical pencils and 2 of the same binders for a total of $25.00. How much does each pack of pencils cost? *
Mathematics
1 answer:
IRISSAK [1]3 years ago
4 0

Answer:

$3.00  

Step-by-step explanation:

Let p = the cost of a pack of pencils

and b = the cost of a binder

Then we have two simultaneous equations.

(1)  2p + 3b  = 21.00

(2) 5p + 2b = 25.00

1. Multiply each equation by numbers to give one of the variables the same coefficient.

Multiply (1) by 2 and (2) by 3.This gives

(3)  4p + 6b = 42.00

(4) 15p + 6b = 75.00

2. Subtract (3) from (4)

This gives

(5) 11p = 33.00

3. Solve equation (5) for p

Divide each side by 11

p = 3.00

Each pack of pencils costs $3.00.

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Howard is standing 109 yards from the bottom of a water reservoir. He estimates that the angle of elevation to the top of the wa
pav-90 [236]

Answer:

70.1 yards

Step-by-step explanation:

See the attached diagram.

Let AC is the reservoir with A as the bottom and C is the top.

Now, B is the position of Howard which is 109 yards from A i.e. AB = 109 yards.

Again, the angle elevation from B to C is 50 degrees.

So, ∠ ABC = 50°  

Now, \cos 50 = \frac{AB}{BC} = \frac{109}{x}

⇒ x = 109 cos 50 = 70.1 yards.

Therefore, the distance between the top of the reservoir and Howard i.e. BC is equal to 70.1 yards. (Answer)

8 0
2 years ago
Which equation and solution represents each situation? Solutions may be rounded to the nearest tenth. What number is 74% of 58?
Zolol [24]

Given:

A number is 74% of 58.

To find:

The number.

Solution:

Let the unknown number be n.

The number n is 74% of 58.

n=\dfrac{74}{100}{58}

n=0.74\times 58

n=42.92

The required equation is n=0.74\times 58 and the solution (unknown number) is n=42.92.

Therefore, the correct option is B.

8 0
3 years ago
In a doctor's waiting room, there are 14 seats in a row. Eight people are waiting to be seated. Three of the 8 are in one family
lianna [129]
There are 14 chairs and  8 people to be seated. But among the 8. three will be seated together:

So 5 people and (3) could be considered as 6 entities:

Since the order matters, we have to use permutation:

¹⁴P₆ = (14!)/(14-6)! = 2,162,160, But the family composed of 3 people can permute among them in 3! ways or 6 ways. So the total number of permutation will be ¹⁴P₆  x 3! 

2,162,160 x 6 = 12,972,960 ways.

Another way to solve this problem is as follow:

5 + (3) people are considered (for the time being) as 6 entities:

The 1st has a choice among 14 ways
The 2nd has a choice among 13 ways
The 3rd has a choice among 12 ways
The 4th has a choice among 11 ways
The 5th has a choice among 10 ways
The 6th has a choice among 9ways

So far there are 14x13x12x11x10x9 = 2,162,160 ways
But the 3 (that formed one group) could seat among themselves in 3!
or 6 ways:

Total number of permutation = 2,162,160 x 6 = 12,972,960

4 0
3 years ago
Can someone please help
USPshnik [31]

Answer:

-40

Step-by-step explanation:

Since x is 10 you need to multiply 10*-4 which equals -40.

8 0
3 years ago
Which statement is always true?
ryzh [129]
The correct answer is C. <span>Similar polygons are never congruent.</span>
3 0
3 years ago
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