Answer:
The smaller number is 11
Step-by-step explanation:
The question is
One number is 3 less than a second number. Twice the second number is 16 less than 4 times the first. Find the smaller of two numbers
Let
x and y the numbers
x=y-3 ----> equation A
2y=4x-16 ----> equation B
Substitute equation A in equation B and solve for y
2y=4(y-3)-16
2y=4y-12-16
4y-2y=12+16
2y=28
y=14
x=14-3=11
Answer:
The average mass of the inner planets is = 2.9531925 x 1024 kg.
The answer is 168. 12% is also 0.12. 150(0.12) is 18. 150+18=168
Let <em>a</em> be the first term in the sequence. If <em>r</em> is the ratio between consecutive terms, then the second term is <em>ar</em>, the third term is <em>ar </em>^2, the fourth is <em>ar</em> ^3, and so on, up to the <em>n</em>-th term <em>ar</em> ^(<em>n</em> - 1).
So the third, fourth, and fifth terms are such that
<em>ar</em> ^2 = 18
<em>ar</em> ^3 = 27
<em>ar</em> ^4 = 81/2
Solve for <em>a</em> and <em>r</em> :
(<em>ar</em> ^3) / (<em>ar</em> ^2) = 27/18 => <em>r</em> = 3/2
<em>ar</em> ^2 = <em>a</em> (3/2)^2 = 9/4 <em>a</em> = 18 => <em>a</em> = 8
Then the <em>n</em>-th term in the sequence is
<em>ar</em> ^(<em>n</em> - 1) = 9 (3/2)^(<em>n</em> - 1)
You can rewrite this by first rewriting 9 = 3^2, then
9 (3/2)^(<em>n</em> - 1) = 3^2 * 3^(<em>n</em> - 1) / 2^(<em>n</em> - 1) = 3^(<em>n</em> + 1)/2^(<em>n</em> - 1)
Answer:
Null hypothesis: There is no relationship between direction of the ball and if it resulted in a hit or an out.
Step-by-step explanation:
In this case, the experiment conducted is to determine whether there is any relationship between the direction of the ball and if it resulted in a hit or an out.
A random sample of 300 balls hit into play in college baseball games is taken. For each ball hit into play, it is recorded whether the ball was hit to the left, center, or right of the field, and whether the ball resulted in a hit or an out.
The regression analysis would be used to determine whether there is any relationship between direction of the ball and if it resulted in a hit or an out.
The hypothesis for the regression analysis is defined as follows:
<em>H</em>₀: There is no relationship between direction of the ball and if it resulted in a hit or an out.
<em>H</em>ₐ: There is a significant relationship between direction of the ball and if it resulted in a hit or an out.
