Answer:
C
Step-by-step explanation:
total number of wheels=4*21=84
Answer:
Here we have:
IxI < 7
This also can be written as:
-7 < x < 7
and:
IyI < 2.
As above, we can write this as:
-2 < y < 2.
Then the graph of this region will be a rectangular area, where the perimeter is a dashed line (because here we use the strictly smaller or strictly larger symbols)
Such that the vertical component goes from -2 to 2, and the horizontal component goes from -7 to 7.
The area would be the area inside that rectangle, where i did not shade it so it is easier to read.
To sketch and shade the region defined by the inequalities |x| < 7 and |y| < 2, identify the boundaries and sketch the rectangle, shading the region within it.
To sketch and shade the region defined by the inequalities |x| < 7 and |y| < 2, we first identify the boundaries of the region. The inequalities |x| < 7 and |y| < 2 represent lines parallel to the x-axis and y-axis, respectively. The region is bounded by these lines and lies within the rectangle with vertices (-7, -2), (-7, 2), (7, -2), and (7, 2). We sketch the rectangle and shade the region within it.
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The ratio of the number of cups of apple juice to the number of cups of lemon-lime soda is 6:1
It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
Given that x axis denotes Lemon lime soda in cups and y axis denotes Apple juice in cups
(x) Lemon -Lime Soda ; 0, 1, 2, 3, 4, 5
(y) Apple Juice : 0, 6, 12, 18, 24, 30
Therefore, the ratio can be written as;
the number of cups of apple juice : the number of cups of lemon-lime soda
6 : 1
Then, ratio is 6:1
Hence, the ratio of the number of cups of apple juice to the number of cups of lemon-lime soda is 6:1
Learn more about the ratio here:
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Answer:
y=3x-2
Step-by-step explanation:
You can verify it's not D because the y-intercept is at -2.
You can verify it's not A because that would mean the x-intercept is 2 despite it appearing to be closer to one.
You can verify it's not B because that would mean the x-intercept is 1.5
Answer:
1.) We cannot say for certain which candidate will win. But A has a statistical edge.
2.) We can say certainly that candidate A will win the election; albeit with a not so big margin.
3.) Candidate A will win this election based on the results of the final poll's before the election.
4.) We cannot say for certain which candidate will win. But A has a statistical edge.
The reasons are explained below.
Step-by-step explanation:
Confidence interval expresses a range of values in the distribution where the true proportion or mean can be found with some level of confidence.
Confidence Interval = (Sample Mean or Proportion) ± (Margin of error)
1. Candidate A: 54% & Candidate B:46% with Margin of error: + 5%
The confidence interval for candidate A
(54%) ± (5%) = (49%, 59%)
The confidence interval for candidate B
(46%) ± (5%) = (41%, 51%)
Since values greater than 50% occur in both intervals, we cannot say for certain that either of the two candidates will outrightly win the election. It just slightly favours candidate A who has A bigger range of confidence interval over 50% for the true sample proportion to exist in.
2. Candidate A: 52% & Candidate B:48% with Margin of error: + 1%
The confidence interval for candidate A
(52%) ± (1%) = (51%, 53%)
The confidence interval for candidate B
(48%) ± (1%) = (47%, 49%)
Here, it is outrightly evident that candidate A will win the elections based on the result of the final polls. The overall range of the confidence interval that contains the true sample proportion of voters that support candidate A is totally contained in a region that is above 50%. So, candidate A wins this one, easily; albeit with a close margin though.
3. Candidate A: 53% & Candidate B:47% with Margin of error: + 2%
The confidence interval for candidate A
(53%) ± (2%) = (51%, 55%)
The confidence interval for candidate B
(47%) ± (2%) = (45%, 49%)
Here too, it is outrightly evident that candidate A will win the elections based on the result of the final polls. The overall range of the confidence interval that contains the true sample proportion of voters that support candidate A is totally contained in a region that is above 50%. Hence, statistics predicts that candidate A wins this one.
4. Candidate A: 58% & Candidate B:42% with Margin of error: + 10%
The confidence interval for candidate A
(58%) ± (10%) = (48%, 68%)
The confidence interval for candidate B
(42%) ± (10%) = (32%, 52%)
Since values greater than 50% occur in both intervals, we cannot say for certain that either of the two candidates will outrightly win the election. It just slightly favours candidate A who has A bigger range of confidence interval over 50% for the true sample proportion to exist in.
Hope this Helps!!!
Answer:
a) $1056.33 b) 23 years
Step-by-step explanation:
a) 10000(1+1.85/100)^3=10565.33 (2d.p.)
b) let x be the no. of years
15000 = 10000(1+1.85/100)^x
1.5 = 1.0185^x
ln both sides
ln 1.5 = x ln 1.0185
x = ln 1.5/ln 1.0185
=22.11
=23 years (rounded up)
To calculate the future value of an investment using continuous compounding, you use the formula A = P*e^(rt). For a $10,000 investment at 1.85% annual interest, its value after 3 years is calculated by substituting the given values into the formula. To find out how many years it will take for the investment to reach $15,000, rearrange the formula to solve for t: t = ln(A/P)/r, and substitute the values.
The subject of your question is related to the mathematical concept known as continuouscompound interest, which Stanley Bank is applying to its money market account. In this concept, the formula is A = P×e^(rt), where A is the final amount that will be accumulated after t years, P is the principal amount or the initial investment, r is the interest rate in decimals (1.85% would be 0.0185), and e is Euler's number (~2.72).
a) To calculate the value of an investment of $10,000 after 3 years with an annual interest rate of 1.85%, you would use the formula: A = $10,000 × e^(0.0185 ×3). This will give you the total value of the investment after 3 years.
b) To calculate the number of years it will take for your investment to amount to $15,000 with the same interest rate, you would need to re-arrange the formula to solve for t: t = ln(A/P) / r. So, it would be calculated as: t = ln($15,000/$10,000) / 0.0185. This would give you the number of years it will take for your initial investment to reach $15,000.
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