Answer:
girls = 90
boys = 125
adults = 20
Detailed explanation:
Total attendees at the summer camp = 235
Let
girls = x
boys = x + 35
adults = x - 70
Total attendees = girls + boys + adults
235 = x + (x + 35) + (x - 70)
235 = x + x + 35 + x - 70
235 = 3x - 35
Add 35 to each side
235 + 35 = 3x
270 = 3x
Divide both sides by 3
x = 270/3
= 90
x = 90
girls = x = 90
boys = x + 35
= 90 + 35
= 125
adults = x - 70
= 90 - 70
= 20
Total = 90 + 125 + 20
= 235
Answer:
Step-by-step explanation:
If you compare numbers based on the hundreds digit, the digits to the left (thousands and ten-thousands) remain the same, while the hundreds digit differs.
This applies for any five-digit numbers structured like:
(3)(5)(not 7)(any digit)(any digit).
Digits to the right of the decimal point, as well as those in the tens and ones places, don't impact this comparison.
The answer is 10. Between 10 and 35, there are 7 prime numbers: 11, 13, 17, 19, 23, 29, and 31. Multiplying 11 by any of the others yields a product smaller than 350, resulting in 6 products. The product of 13 with anything below 26 will also be less than 350, adding 3 more products. Similarly, the product of 17 with anything below 20 yields 1 additional product. Therefore, the total count of different products under 350 amounts to 10.
The tension does not approach infinity.
<span>Let's analyze free body diagrams (FBDs) for each mass, considering the direction of motion of m₁ as positive.
For m₁: m₁*g - T = m₁*a
For m₂: T - m₂*g = m₂*a
Assuming a massless cord and pulley without friction, the accelerations are the same.
From the second equation: a = (T - m₂*g) / m₂
Substitute into the first:
m₁*g - T = m₁ * [(T - m₂*g) / m₂]
Rearranging:
m₁*g - T = (m₁*T)/m₂ - m₁*g
2*m₁*g = T * (1 + m₁/m₂)
2*m₁*m₂*g = T * (m₂ + m₁)
T = (2*m₁*m₂*g) / (m₂ + m₁)
Taking the limit as m₁ approaches infinity:
T = 2*m₂*g
This aligns with intuition since the greatest acceleration m₁ can have is -g. The cord then accelerates m₂ upward at g while gravity acts downward, leading to a maximum upward acceleration of 2*g for m₁.</span>
Response:
Step-by-step explanation:
Shift the decimal points in both the divisor and the dividend.
Transform the divisor (the number you're dividing by) into a whole number by moving its decimal to the furthest right. Simultaneously, adjust the dividend's decimal (the number being divided) the same number of places to the right.
In the quotient (the result), place a decimal point directly over where the decimal point is now located in the dividend.
Proceed with the division as normal, ensuring proper alignment so the decimal point appears correctly.
Align each digit in the quotient directly over the last digit of the dividend utilized in that step.
