I NEED HELP STAT PLZ PLZ PLZ Betty has between $40$ and $50$ pennies that she wants to arrange in a rectangular array. She notices she can arrange the pennies in three different ways without any gaps or spaces. However, if Betty adds two more pennies to her collection, she can only arrange the pennies in one way without any gaps or spaces: a straight line. How many pennies does Betty have?
2 months ago
Solution 1
2 months ago
If she adds two pennies, she can only arrange the pennies in a straight line.
A straight line is one penny wide. If she adds two pennies she ends up with a prime number of pennies.
Since she has between 40 and 50 pennies, she can have 41, 42, 43, 44, 45, 46, 47 ,48, or 49 pennies.
41 + 2 = 43 prime
42 + 2 = 44 not prime
43 + 2 = 45 not prime
44 + 2 = 46 not prime
45 + 2 = 47 prime
46 + 2 = 48 not prime
47 + 2 = 49 not prime
48 + 2 = 50 not prime
49 + 2 = 51 not prime
Only 43 and 47 are prime.
That means she has 41 or 45 pennies.
41 is prime, so it cannot be arranged in any other way than a straight line 1 by 41.
Let's look at 45.
45 = 3 * 3 * 5
45 = 9 * 5 = 3 * 15 = 45 * 1
She has 45 pennies.
A straight line is one penny wide. If she adds two pennies she ends up with a prime number of pennies.
Since she has between 40 and 50 pennies, she can have 41, 42, 43, 44, 45, 46, 47 ,48, or 49 pennies.
41 + 2 = 43 prime
42 + 2 = 44 not prime
43 + 2 = 45 not prime
44 + 2 = 46 not prime
45 + 2 = 47 prime
46 + 2 = 48 not prime
47 + 2 = 49 not prime
48 + 2 = 50 not prime
49 + 2 = 51 not prime
Only 43 and 47 are prime.
That means she has 41 or 45 pennies.
41 is prime, so it cannot be arranged in any other way than a straight line 1 by 41.
Let's look at 45.
45 = 3 * 3 * 5
45 = 9 * 5 = 3 * 15 = 45 * 1
She has 45 pennies.
Solution 2
2 months ago
Answer:
.
Step-by-step explanation:
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ralph is a electrician he charges an initial fee of 24$ , plus 24 per hour. If ralph earned 144$ on the job , how long did the job take.
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Question
ANNA AND ALICE SHARE A RECTANGLE BEDROOM THAT IS 18 FEET LONG AND 14 FEET WIDE. THEY SPLIT THE ROOM INTO TWO HALVES BY PLACING A PIECE OF TAPE FROM THE NORTHWEST CORNWR OF THE ROOM TO THE SOUTHEAST CORNWR OF THE ROOM. WHT IS THE AREA OF EACH GIRLS HALF OF THE ROOM
Solution 1
First, you have to find the area of the WHOLE bedroom.
Equation: 18 × 14 = 252.
The total area of the bedroom is 252^2 feet.
Finally, divide.
252 ÷ 2 = 126.
The area of each of the sections is 126.
Please mark me as brainliest. I really need it.
Equation: 18 × 14 = 252.
The total area of the bedroom is 252^2 feet.
Finally, divide.
252 ÷ 2 = 126.
The area of each of the sections is 126.
Please mark me as brainliest. I really need it.
Question
the original value of an investment is $1,800. if the value has increased by 7% each year, write an exponential to model the situation. then, find the value of the investment after 15 years
Solution 1
For this case we have an equation of the form:
y = A (b) ^ t
Where,
A: initial amount
b: growth rate
t: time
Substituting values we have:
y = 1800 * (1.07) ^ t
For 15 years we have:
y = 1800 * (1.07) ^ 15
y = 4966.256773 $
Answer:
An exponential to model of the situation is:
y = 1800 * (1.07) ^ t
the value of the investment after 15 years is:
y = 4966.256773 $
y = A (b) ^ t
Where,
A: initial amount
b: growth rate
t: time
Substituting values we have:
y = 1800 * (1.07) ^ t
For 15 years we have:
y = 1800 * (1.07) ^ 15
y = 4966.256773 $
Answer:
An exponential to model of the situation is:
y = 1800 * (1.07) ^ t
the value of the investment after 15 years is:
y = 4966.256773 $
Question
Solve the equation <(a-5)-5=3
Solution 1
The first step for solving the equation (a - 5) - 5 = 3 is to remove the parenthesis.
a - 5 - 5 = 3
Calculate the difference between -5 and 5.
a - 10 = 3
Now move the constant to the right side of the equation and change its sign.
a = 3 + 10
Add the numbers on the right side together to get your final answer.
a = 13
Let me know if you have any further questions.
:)
a - 5 - 5 = 3
Calculate the difference between -5 and 5.
a - 10 = 3
Now move the constant to the right side of the equation and change its sign.
a = 3 + 10
Add the numbers on the right side together to get your final answer.
a = 13
Let me know if you have any further questions.
:)
Question
Centennial park is evaluating the capacity of the park and have determined that 15 people can comfortably stand in a section that is 5ft by 8ft , the park has dimensions that are 400yds by 200 yds estimate the number of people who can fit in the park
Solution 1
We have been given that 15 people can comfortably stand in a section that is 5ft by 8ft .
Hence, the area of this section is given by
Hence, we can say that 15 people can comfortably stand in an area 40 square feet.
Now, we know that 1 yard is equal to 3 feet.
Hence, the area of the section 400yds by 200 yds is equal to
Now, in 40ft^2, 15 people can stand comfortably.
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Question
Which expression is not equivalent to the following expression? 15 - 3 + 15 - 3 - 3 + 15
A. 3(15 - 3)
B. 3(15)
C. 3(15 + 3)
D. 3(12)
Solution 1
In the above problem: it appears that the original expression is equal to 36.
A. 3(15-3) = 3(12)=36
B. 3(15) = 45
C. 3(15+3) = 3(18)=54
D. 3(12) = 36
So it looks like choices A and D are equivalent to the original expression.
A. 3(15-3) = 3(12)=36
B. 3(15) = 45
C. 3(15+3) = 3(18)=54
D. 3(12) = 36
So it looks like choices A and D are equivalent to the original expression.
Solution 2
Answer: D
Step-by-step explanation:
Question
Anna and Alice share a rectangle bedroom that is 18 feet long and 14 feet wide. they split the room into two halves by placing a piece of tape from the northwest corner of the room to the southeast corner of the room. what is the area of each girls half of the room?
Solution 1
The area of the whole room = 14 × 18 = 252
Since they divide it by half, divide the are by 2.
252 ÷ 2 = 126
Answer = 126 ft²
Hope this helped☺☺
Since they divide it by half, divide the are by 2.
252 ÷ 2 = 126
Answer = 126 ft²
Hope this helped☺☺
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126 is the area of one hafe of the room
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Solution 1
Answer:
10pi
Step-by-step explanation:
The answer is 10pi
Solution 2
The penguin swam 10 meters
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