Answer:
The statement is true.
Step-by-step explanation:
Let us assume that x is the required number.
Now, given that the number minus 3 is at most 12.
Hence, x - 3 ≤ 12
⇒ x ≤ 15 ......... (1)
And also given that 1 more than 2 times the number is at least 25.
Hence, 2x + 1 ≥ 25
⇒ 2x ≥ 24
⇒ x ≥ 12 .......... (2)
Therefore, from equations (1) and (2) we get the number must be greater than or equal to 12 or less than or equal to 15.
So, the statement is true. (Answer)
Answer: year 2194
Explanation:
1) Model the jump of the women:
i) initial jump = 70.0 in
ii) increase rate = 0.48% per year
iii) equation: h = 70.0(1 +0.0048)ⁿ
2) Model the jump of the men:
i) initial jump 86.5 inches.
ii) increase rate, 0.4%.
iii) equation: h = 86.5 (1 + 0.004)ⁿ
3) Equal the two equations (h = h) to find when the jumps will be equal:
i) 70.0(1 +0.0048)ⁿ = 86.5 (1 + 0.004)ⁿ
ii) 70.0(1.0048)ⁿ = 86.5 (1.004)ⁿ
ii) [1.0048ⁿ / 1.004ⁿ] = 86.5/70.0
iii) [1.0048/ 1.0040]ⁿ = 86.5/70.0
iv) n log (1.0048 / 1.0040) = log ( 86.5/70)
v) n = log (86.5/70) / log (1.0048/1.0040) ≈ 266
3) year = 1928 + 266 = 2194
That is in the year 2194
Step-by-step explanation:
Regression analysis is used to infer about the relationship between two or more variables.
The line of best fit is a straight line representing the regression equation on a scatter plot. The may pass through either some point or all points or none of the points.
<u>Method 1:</u>
Using regression analysis the line of best fit is: 
Here <em>α </em>= intercept, <em>β</em> = slope and <em>e</em> = error.
The formula to compute the intercept is:

Here<em> </em>
and
are mean of the <em>y</em> and <em>x</em> values respectively.

The formula to compute the slope is:

And the formula to compute the error is:

<u>Method 2:</u>
The regression line can be determined using the descriptive statistics mean, standard deviation and correlation.
The equation of the line of best fit is:

Here <em>r</em> = correlation coefficient = 
and
are standard deviation of <em>x</em> and <em>y</em> respectively.

The question is telling you that the length of the rectangle is 3 metres more than twice the width.
So let:
<em>w= width</em>
<em>L= length</em>
Because the length is 3 metres more than twice<em> </em>the width: <em>L= </em><em>2</em><em>w+</em><em>3</em>
They also tell you the perimeter is 48 metres.
<em>P= L+L+w+w</em>
So the equation of the perimeter is:
<em>48= (2w+3)+(2w+3)+2w +2w</em>
<em>48= 2(2w+3) + 4w</em>
To find w, expand and simplify.
<em>48= 4w+6+4w</em>
<em>48= 8w + 6</em>
<em>42= 8w</em>
<em>5.25=w</em>
Now that you know the width, plug in the value into the length equation:
<em>L= 2w+3</em>
<em>L=2(5.25)+3</em>
<em>L=10.50+3</em>
<em>L=13.5</em>
If I am wrong let me know! I hope this helps.