Please solve these coin problems:1) James bought 80 postage stamps for which he paid $18.40. Some were 1 cent stamps and some were 33 cent stamps.how many of each kind did he buy?

2) a postal clerk sold 75 stamps for $19.90. Some were 20 cent and some were 34 cent stamps. How many of each kind did he sell?

Answers

Answer 1

Answer: 1)
Solving from system of equations:
x- amount of 1 cent stamps
y- amount of 33 cent stamps
$\left \{ {{1*x+33*y=18,40} \atop {x+y=80}} \right.\nx=80-y\n0,01*(80-y)+0,33y=18,40\n0,8-0,01y+0,33y=18,40\n0,32y=18,40-0,8\n0,32y=17,60 /:0,32\ny=55\nx=80-55=25$
2)
x- amount of 20 cent stamops
y-amount of 34 cent stamps
From system of equations:
$\left \{ {{0,2x+0,34y=19,90} \atop {x+y=75}} \right.\nx=75-y\n0,2(75-y)+0,34y=19,90\n 15-0,2y+0 ,34y=19,90\n-0,2y+0,34y=19,90-15\n0,14y=4,90/:0,14\n y=35\nx=75-35=40$

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A convex pentagon has the following measurements for its interior angles: (x-8), (3x-11), (x+8), (x), and (2x+7). Which of the following could be measurements for interior angles of the pentagon? Select all that apply.A: 60

B: 68

C: 76

D: 108

E: 193

F: 540

Answers

Answer: A, B, C, E

Explanation:

The sum of the interior angles of a polygon can be determined by the formula: (n - 2)180 ; where n represents the number of sides. Since a pentagon has 5 sides, then (5 - 2)180 = 540

x - 8

3x - 11

x + 8

2x + 7

8x - 4 = 540

+4 +4

8x = 544

÷8 ÷8

x = 68

**********************

x - 8 ⇒ 68 - 8 = 60 (A)

3x - 11 ⇒ 3(68) - 11 = 193 (E)

x + 8 ⇒ (68) + 8 = 76 (C)

x ⇒ (68) (B)

2x + 7 ⇒ 2(68) + 7 = 143

The sumof the pentagon's interior angles is: 540°

According to the Question, we have: (x-8)+(3x-1)+(x+8)+x+(2x+7)=540

x-8+3x-11+x+8+x+2x+7=540

x+3x+x+x+2x=540+8+11-8-7

8x=544

x=544/8=68

(x-8)=68-8=60 (choose letter A)

(3x-11)=3*68-11=193 (choose letter E)

(x+8)=68+8=76 (choose letter C)

(x)=68 (choose letter B)

(2x+7)=2*68+7=143 (cannot select any letter)

In short, we choose letter A, B, C and E.

You backpacked for a distance of 15.75 miles today. If you backpacked at an average speed of 1.26 miles per hour, how many hours did you spend backpacking today

Answers

It would be 12.5. you would divide 15.75 by 1.26

Hi there! First, speed=Distance/time, and the time=distance/speed. The time spent for back packing was 15.75/1.26=12.5 hours. Therefore, the answer is 12.5 hours.

A jar contains five blue marbles and three red marbles. Suppose you choose a marble at random, and do not replace it. Then you choose a second marble. Find the probability of the following event.Both of the selected marbles are red.

Answers

Answer:

The probability that both of the selected marbles are red is $(3)/(28)$

Step-by-step explanation:

Given

Number of red marbles = 3

Number of blue marbles = 5

Required

Probability of selecting two red marbles (without replacement).

First, we need to get the total number of marbles

Total = Red Marbles + Blue Marbles

Total = 3 + 5

Total = 8

Probability is calculated by: Number of required outcome divided by number of possible outcome.

Since there are 3 red marbles out of a total of 8 marbles;

The probability that the first marble you selected is red is 3/8

From the question, you didn't return the marble back to the container.

This means that, there are 2 red marbles and a total of 7 marbles left in the container.

So, the probability that the next marble selected is red is 2/7

Let P(R and R) represent the probability of selecting two red marbles.

This is calculated by multiplying the probability of picking the first red marble and the second red marble.

Hence,

P(R and R) = $(3)/(8) * (2)/(7)$

P(R and R) = $(6)/(56)$ --- Reduce to lowest term

P(R and R) = $(3)/(28)$

Hence, the probability that both of the selected marbles are red is $(3)/(28)$

How do I solve 3 1/2r = 28

Answers

The solution is, the value of r is 8.

What is simplification?

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we get,

given that,

the expression is,

3 1/2r = 28

now, we have to solve the expression to get the value of 'r'.

we get,

3 1/2r=28

7/2r=28

r=(28/1)(2/7)

r=4 × 2

r = 8

Hence, The solution is, the value of r is 8.