Answer:
33
Step-by-step explanation:
3 years ago, the difference in ages was twice Daniel's age. So, Daniel was 20/2 = 10 years old at that time. Ben was 30.
Now, Ben is 33.
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If two numbers have a ratio of 3:1, their difference is (3-1) = 2 times the smaller number.
Answer:
The ratio of sixth-grade students to fifth-grade students on the team was <u>7 : 8</u>.
Step-by-step explanation:
Given:
The girl's basketball team had 8 fifth-grade students and 7 sixth-grade students.
Now, to find the ratio of sixth-grade students to fifth-grade students on the team.
<em>Number of fifth-grade students = 8.</em>
<em>Number of sixth-grade students = 7.</em>
Now, to get the ratio of sixth-grade students to fifth-grade students on the team :
Therefore, the ratio of sixth-grade students to fifth-grade students on the team was 7 : 8.
Find a common denominator to begin. The common denominator is the LCM of both denominators. In this case, the common denominator will be 24.
Now, multiply the numerator by the number you multiplied the denominator. For 2/3, you multiplied 3 by 8, so multiply 2 by 8 to get 16. The fraction is now 16/24. Multiply 4 by 3 since you multiplied 8 by 3 to get 24. You will get 12 and the fraction will become 12/24.
Then, compare. 16/24 is closer to 24/24, or one whole, so 16/24, or 2/3, is greater.
The value of the correlation is -0.0721 and it is a weak negative correlation
<h3>
How to determine the correlation coefficient?</h3>
The points are given as:
(12, 28), (15, 50), (18, 14), (21, 28), (24, 36)
Enter the above points in a graphing calculator.
From the graphing calculator, we have the following summary:
<u>X Values</u>
- Sum X = 90
- Mean = 18
- ∑(X - Mx)^2 = SSx = 90
<u>Y Values</u>
- Sum Y = 156
- Mean = 31.2
- ∑(Y - My)^2 = SSy = 692.8
<u>X and Y Combined</u>
- N = 5
- ∑(X - Mx)(Y - My) = -18
<u>R Calculation</u>
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
This gives
r = -18 / √((90)(692.8)) = -0.0721
So, the correlation coefficient is -0.0721
The above is a negative correlation because it is less than 0 and it is a weak correlation because it is closer to 0 than -1
Hence, the correlation is a weak negative correlation
Read more about correlation coefficient at:
brainly.com/question/27226153
#SPJ1
Step-by-step explanation:
(a) ∫₋ₒₒ°° f(x) dx
We can split this into three integrals:
= ∫₋ₒₒ⁻¹ f(x) dx + ∫₋₁¹ f(x) dx + ∫₁°° f(x) dx
Since the function is even (symmetrical about the y-axis), we can further simplify this as:
= ∫₋₁¹ f(x) dx + 2 ∫₁°° f(x) dx
The first integral is finite, so it converges.
For the second integral, we can use comparison test.
g(x) = e^(-½ x) is greater than f(x) = e^(-½ x²) for all x greater than 1.
We can show that g(x) converges:
∫₁°° e^(-½ x) dx = -2 e^(-½ x) |₁°° = -2 e^(-∞) − -2 e^(-½) = 0 + 2e^(-½).
Therefore, the smaller function f(x) also converges.
(b) The width of the intervals is:
Δx = (3 − -3) / 6 = 1
Evaluating the function at the beginning and end of each interval:
f(-3) = e^(-9/2)
f(-2) = e^(-2)
f(-1) = e^(-1/2)
f(0) = 1
f(1) = e^(-1/2)
f(2) = e^(-2)
f(3) = e^(-9/2)
Apply Simpson's rule:
S = Δx/3 [f(-3) + 4f(-2) + 2f(-1) + 4f(0) + 2f(1) + 4f(2) + f(3)]
S ≈ 2.5103
