if a boy grows 5 inches, he will be one-half as tall as his sister. His sister is 68 inches tall. How tall is the boy?
2 answers:
Answer:
The height of boy is 29 inches.
Step-by-step explanation:
Given : If a boy grows 5 inches, he will be one-half as tall as his sister. His sister is 68 inches tall.
To find : How tall is the boy?
Solution :
Let x be the boy's height and y be his sister's height.
We have given, His sister is 68 inches tall i.e. y=68 inches
Now, If a boy grows 5 inches i.e. x+5
then he will be one-half as tall as his sister i.e.
or
We know, y=68 substitute in above equation
Therefore, The height of boy is 29 inches.
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Answer:
Is plausible that the successive throws are independent
Step-by-step explanation:
1) Table with info given
The observed values are given by the following table
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First shot Made Second shot missed Total
__________________________________________________
Made 152 33 185
Missed 37 8 45
__________________________________________________
Total 189 41 230
2) Calculations and test
We are interested on check independence and for this we need to conduct a chi square test, the next step would be find the expected value:
Null hypothesis: Independence between two successive free throws
Alternative hypothesis: No Independence between two successive free throws
_____________________________________________________
First shot Made Second shot missed
_____________________________________________________
Made 189(185)/230=152.0217 41(185)/230=32.9783
Missed 189(45)/230=36.9783 41(45)/230=8.0217
_____________________________________________________
On this case all the expected values are higher than 5 and the sample size 230 is enough to apply the chi squared test.
3) Calculate the chi square statistic
The statistic for this case is given by:
Where O represent the observed values and E the expected values. Replacing the values that we got we have this
Now with the calculated value we can find the degrees of freedom
on this case r means the number of rows and c the number of columns.
Now we can calculate the p value
On this case the pvalue is a very large value and that indicates that we can fail to reject the null hypothesis of independence. So is plausible that the successive throws are independent.
Answer:
Step-by-step explanation:
Let represent the number of monitors sold.
Given:
is the number of years since 1990.
So, for the year 1990, .
For the year 2000, 10 years passed. So, .
Now, monitors sold in 1990 are 150. So, at
Monitors sold in 2000 are 900. So, at
Thus, the two points are and
.
The slope of a line with points and
is given as:
Slope,
For the points and
, the slope is given as:
Slope,
Now, the y-intercept is the point where . So, the point
has
value as 0.
So, the y-intercept is 150.
Equation of a line in slope-intercept form is given as:
Where, is the slope and
is the y intercept.
Here, and
.
Therefore, the equation that represents the above data is given as:
Given:
The value is .
To find:
The value as a base 2 logarithm.
Solution:
We know that,
where, a is any positive value.
We have,
Using the above property of logarithm, we get
For a=2,
Therefore, the given value as a base 2 logarithm can be written as .