Lake Profondo has a depth of 84 feet. Lake Segundo is 5/6 as deep. What is the elevation at the bottom of Lake Segundo? (Remember, the elevation is below sea level. Account for this in your answer.)(1 point)
Lake Segundo is 5/6 * 84 feet = <<5/6*84=70>>70 feet deep.
Since the elevation is below sea level, the elevation at the bottom of Lake Segundo is -70 feet. Answer: \boxed{-70}.
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Divide −72 by −4 . Then divide the quotient by −9 . What is the final quotient? (1 point)
When you divide −72 by −4, the quotient is 18.
Then, when you divide the quotient 18 by −9, the final quotient is -2.
Answer: \boxed{-2}.
What is the quotient of 100÷(−10)÷5 ?(1 point)
Responses
−50
negative 50
−2
negative 2
−200
negative 200
2
To find the quotient of 100 ÷ (-10) ÷ 5, we first divide 100 by -10, which gives us -10. Then, we divide -10 by 5, which gives us -2.
Therefore, the quotient is \boxed{\text{-2}}.
What is the quotient of 842.4 ÷ −0.6 ?(1 point)
Responses
−140.4
negative 140.4
1,404
1,404
−1,404
negative 1,404
−14.04
To find the quotient of 842.4 ÷ -0.6, we simply perform the division.
The quotient is -1,404.
Therefore, the correct response is \boxed{\text{-1,404}}.
What is 4.65 converted to a fraction? The answer should be given in simplest form.(1 point)
To convert 4.65 to a fraction, we can observe that it is already in decimal form with two decimal places.
The number 4.65 can be represented as 465/100.
To simplify this fraction, we divide both the numerator and denominator by their greatest common divisor, which is 5.
Dividing 465 by 5 gives us 93, and dividing 100 by 5 gives us 20.
Therefore, 4.65 can be simplified to the fraction 93/20.
The final answer, in simplest form, is: \boxed{\frac{93}{20}}.
wrong
I apologize for the incorrect response earlier. Let's correct it.
To convert 4.65 to a fraction, we can multiply both the numerator and denominator by 100 to remove the decimal:
4.65 * 100 = 465
So, 4.65 can be expressed as the fraction 465/100.
To simplify this fraction, we can divide both numerator and denominator by their greatest common divisor, which is 5:
465 ÷ 5 = 93
100 ÷ 5 = 20
Therefore, the simplified fraction form of 4.65 is:
\boxed{\frac{93}{20}}.
as a mixed fracion
To convert the fraction 93/20 to a mixed fraction, we divide the numerator (93) by the denominator (20):
93 ÷ 20 = 4 remainder 13
The whole number part is 4, and the remainder 13 is the numerator of the fractional part. So, the mixed fraction form of 93/20 is:
4 \frac{13}{20}
Therefore, the answer in simplest form as a mixed fraction is:
\boxed{4 \frac{13}{20}}.
Use long division to convert 2716 to a decimal.(1 point)
Responses
2.2857
2.2857
2.4375
2.4375
0.4375
0.4375
2.716
To convert 2716 to a decimal using long division, we divide 2716 by 1 repeatedly, moving the decimal point to the right until we reach the desired number of decimal places.
Here is the long division:
2716.0000...
___________________
1 | 2716 (divide 1 into 2,716)
- 1
------
17 (bring down the next digit 7)
- 17 (divide 1 into 17, the remainder is 0, indicating that the division is complete)
Therefore, 2716 as a decimal is \boxed{2716.0000...}.
Use long division to convert 2 7/16 to a decimal.(1 point)
Responses
2.2857
2.2857
2.4375
2.4375
0.4375
0.4375
2.716
To convert 2 7/16 to a decimal using long division, we perform the following steps:
First, we convert the mixed number 2 7/16 to an improper fraction:
2 7/16 = (2 * 16 + 7)/16 = 39/16
Now, we perform long division to divide 39 by 16:
2. R2
16 | 39
32
----
7
We get a quotient of 2 and a remainder of 7.
Since the remainder is non-zero, we can express the decimal expansion as the quotient plus the remainder divided by the divisor:
2 7/16 = 2 + 7/16 = 2.4375
Therefore, the correct response is \boxed{2.4375}.
Use long division to convert 6 7/15 to a decimal.(1 point)
Responses
≈6.47
approximately equals 6.47
≈6.14285
approximately equals 6.14285
6.715
6.715
≈0.46
approximately equals 0.46
To convert 6 7/15 to a decimal using long division, we perform the following steps:
First, we convert the mixed number 6 7/15 to an improper fraction:
6 7/15 = (6 * 15 + 7)/15 = 97/15
Now, we perform long division to divide 97 by 15:
6. R7
15 | 97
90
---
7
We get a quotient of 6 and a remainder of 7.
Since the remainder is non-zero, we can express the decimal expansion as the quotient plus the remainder divided by the divisor:
6 7/15 = 6 + 7/15
To convert the fraction 7/15 to a decimal, we divide 7 by 15:
6. R7
15 | 97
90
---
7
-7
---
0.466...
The decimal expansion of 7/15 is approximately 0.46667 (rounded to 5 decimal places).
Therefore, the correct response is \boxed{≈6.46667}.
Use long division to convert 6 7/15 to a decimal.(1 point)
Responses
≈6.47
≈6.14285
6.715
≈0.46
To convert 6 7/15 to a decimal using long division, we perform the following steps:
First, we convert the mixed number 6 7/15 to an improper fraction:
6 7/15 = (6 * 15 + 7)/15 = 97/15
Now, we perform long division to divide 97 by 15:
6.47
15 | 97
90
---
7
-5
We get a quotient of 6 and a remainder of 7.
To obtain the decimal form, we add a decimal point after the quotient and continue the division:
6.47
15 | 97
90
---
7
-5
---
20
-15
---
50
-45
---
5
Continuing this pattern, we see that the decimal expansion terminates after one decimal place.
Therefore, the correct response is \boxed{\approx 6.47}.
A pilot is flying an airplane. Due to strong winds, the pilot decides to fly 4,000 feet lower to avoid excessive turbulence. It takes the pilot 3.5 minutes to make this adjustment. Interpret the quotient to describe the rate of change in the plane’s altitude. Give your answer to the nearest hundredth, and remember the plane is descending.(1 point)
The quotient that best represents the rate of change in the plane’s altitude is
feet/minute
To find the rate of change in the plane's altitude, we divide the change in altitude (4,000 feet) by the time it takes to make the adjustment (3.5 minutes).
Rate of change in altitude = Change in altitude / Time
Rate of change in altitude = 4000 feet / 3.5 minutes
Simplifying the division gives us the rate of change in feet per minute:
Rate of change in altitude ≈ 1142.86 feet/minute
Therefore, the correct response is \boxed{1142.86 \text{ feet/minute}}.