One yardstick for measuring how steadily—if slowly—athletic performance has improved is the mile run. In 1958, the local record for the running of a certain distance was 3 minutes, 59.3 seconds, or 239.3 seconds. In the half-century since then, the record has decreased by 0.5 seconds per year.
Answers
Answer:
They will hit 180 seconds in 118.6 year
Step-by-step explanation:
Let M be the record for the mile (in seconds)
Let x be the year after 1958
So, x=(year)-19548
We are given that In the half-century since then, the record has decreased by 0.5 seconds per year
So, slope = m = 0.5
Now we will use point slope form
y = mx+c
So, we can express M as,
Now we are supposed to find when they will hit 180 seconds
Substitute M = 180 in equation
180=239.3-0.5x
x=118.6
So, they will hit 180 seconds in 118.6 year
Final answer:
You can model the decreasing record time with the linear equation y=239.3-0.5x, where x is years since 1958 and y is the run time in seconds. By using this model, you can find the record time for any given year.
Explanation:
The subject of this question is Mathematics, specifically linear equations. The question mentions an initial record of 239.3 seconds for a run which decreases by 0.5 seconds every year. We are tasked to find the running time after a certain number of years.
Let's let x represent the number of years since 1958 and y represent the number of seconds to run the race. Based on the information provided:
- The starting time (y-intercept) in 1958 was 239.3 seconds.
- The rate of decrease (slope) is 0.5 seconds per year.
Therefore, the relationship between x and y can be expressed by the linear equation: y=239.3-0.5x
To find a certain year's running time, we substitute the number of years passed since 1958 into x in the equation above and solve for y. For example, to find the running time in 50 years after 1958 (2008), we replace x with 50: y = 239.3 - 0.5(50) = 214.3 seconds.
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Answers
0.06 x 10 = 0.6
Final answer:
The 6 in the tenths place in the number 51.66 is ten times greater in value than the 6 in the hundredths place, due to positional values in decimal numbers.
Explanation:
In the decimal number 51.66, the value of the 6 in the tenths place is indeed ten times the value of the 6 in the hundredths place. This is because each place to the right of the decimal point is ten times smaller than the place to its immediate left. Therefore, although both of these digits are 6, the 6 in the tenths place represents a value of 0.6 (or 6/10), whereas the 6 in the hundredths place represents a value of 0.06 (or 6/100). So, when you divide 0.6 by 0.06, you get 10, showing that the 6 in the tenths place is ten times the value of the 6 in the hundredths place.
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Answers
write an explicit formula for the Nth term aN.
Answers
Answer:
an=−6n+2
Step-by-step explanation:
First, you need to identify the first term and the common difference of the sequence. The first term is the value of the first element, which is -4. The common difference is the amount that is added or subtracted to each term to get the next one, which is -6 in this case. You can find it by subtracting any two consecutive terms, such as -10 - (-4) = -6 or -16 - (-10) = -6.
Next, you need to use the standard explicit formula for an arithmetic sequence, which is:
an=a1+d(n−1)
where an is the Nth term, a1 is the first term, d is the common difference, and n is any term number.
Finally, you need to substitute the values of a1 and d that you found in the first step into the formula. This gives:
an=−4+(−6)(n−1)
This is the explicit formula for the Nth term aN of the given arithmetic sequence. You can simplify it further by expanding and combining like terms:
an=−4−6n+6
an=−6n+2
4/1 322.95 Beginning balance
4/10 19.87 Purchase
4/14 50.00 Payment
4/19 71.21 Purchase
If Hannah’s credit card company calculates finance charges using the daily balance method, what will her April finance charge be?
a. $2.71
b. $3.20
c. $3.30
d. $3.61
Answers
Answer:
c. $3.30 is correct
Answer:
C. 3.30 is 100% correct
Step-by-step explanation:
1, 2, 4, 8, 16, 32
1, 2, 6, 8, 16, 32
1, 2, 16, 32
Answers
Answer:
1 2 3 4 6 8 12 16 32
Step-by-step explanation: