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3 years ago

The mean of six numbers is 41. If one number is removed, the mean of the five numbers is 46. Find the unknown number.

1 answer:

5 0

Let n be the sum of all 6 numbers:

In the 1st case n/6 = 41 ==> n =246

in the 2nd case n'/5 = 46===> n' =230, the unknown number is n-n' =246-230

= 16

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What is the best approximation of the projection of (5,-1) onto (2,6)?

Hatshy [7]

Answer:

Hence, the scalar projection of $\vec a$ onto $\vec b$ = $\frac{\sqrt{10} }{5}$ , and the vector projection of $\vec a$ onto $\vec b$ = $\frac{1}{5} \hat i+\frac{3}{5} \hat j$ .

Step-by-step explanation:

We have given two points $(5, -1)$ and $(2, 6)$ .

Let, $\vec a=5\hat {i}-\hat {j}$ and $\vec b= 2\hat {i}+6\hat{j}$ .

and we have calculate the projection of $\vec a$ onto $\vec b$ .

Now,

For the calculation of projection, first we need to calculate the dot product of $\vec a$ and $\vec b$ .

$\vec a.\vec b=(5\hat {i}-\hat{j}).(2\hat{i}+6\hat{j})$

$=10-6$

$=4$

then, we have to calculate the magnitude of $\vec b$ .

$\mid {\vec {b}}\mid$ = $\sqrt{2^{2}+6^{2} }$ = $\sqrt{40}$ = $2\sqrt{10}$ .

Now, the scalar projection of $\vec a$ onto $\vec b$ = $\frac{\vec a.\vec b}{\mid b\mid}$

= $\frac{4}{2\sqrt{10} }$ $\frac{2}{\sqrt{10} } \times\frac{\sqrt{10} }{\sqrt{10} } =\frac{2\sqrt{10} }{10} = \frac{\sqrt{10} }{5}$

and the vector projection of $\vec a$ onto $\vec b$ = $\frac{\vec a. \vec b}{\mid\vec b \mid^{2} } . \vec b$

= $\frac{4}{40} . (2\hat i+ 6\hat j)$

= $\frac{1}{5} \hat i+\frac{3}{5} \hat j$

Hence, the scalar projection of $\vec a$ onto $\vec b$ = $\frac{\sqrt{10} }{5}$ , and the vector projection of $\vec a$ onto $\vec b$ = $\frac{1}{5} \hat i+\frac{3}{5} \hat j$ .

6 0

3 years ago

The equation y = 19.43x +609.077 is the equation of the regression line that predicts the number of people attending a county fa

atroni [7]

Answer:

1,114 people

Step-by-step explanation:

The equation $y=19.43x+609.077$ is the equation of the regression line that predicts the number of people attending a county fair, where x is the number of years after 2000.

To find the number of people that are expected to attend the fair in 2026, we determine how many years have passed and substitute into the equation.

From 2000 to 2026,

$2026-2000=26yrs$

have passed.

The expected number who will attend the fair in 2026 is

$y=19.43*26+609.077$

$y=1114.26$

To the nearest whole number 1,114 people will attend in 2026

5 0

3 years ago

Fred ran 4 miles in 30 minutes. Janet ran 6 miles in 40 minutes. Fred and Janet each continue running at their same rate for 1 h

borishaifa [10]

Fred: 4m: 30 minutes=8 miles per hour
janet: 6m: 40minutes= 3 miles every 20 minutes=9 miles per hour
so janet runs 1 mile more per hour

filled in:

Fred ran 4 miles in 30 minutes. Janet ran 6 miles in 40 minutes. Fred and Janet each continue running at their same rate for 1 hour. fred will run 8 miles in 1 hour. Janet will run 9 miles in 1 hour. Janet will run 1 miles farther in 1 hour

7 0

3 years ago

Read 2 more answers

An apple grower finds that if she plants 40 trees per acre, each tree will yield 150 bushels of apples. She also estimates that

kozerog [31]

Answer:

41 trees per acre

Step-by-step explanation:

For each tree per acre

Yield = 150 bushels of Apple

: Each tree tree will have :

150/40 = 3.75 bushels of Apple

Now;

For an additional tree(= 41 trees)

We would normally have for an acre to be

( 150/40) × 41 = 153.75 bushels of apples

But since in this case, there is a decrease of three bushel, we have

For the 41 trees per acre to be

153.75 - 3 = 150.75

Hence,

For each tree, we would have:

150.73 / 41 = 3.677 bushels of Apple

Conclusion:

40 trees yields 150 bushels of Apple per acre

41 yields 150.75 bushels of Apple per acre

6 0

3 years ago

True or False: The following sequence of numbers is an arithmetic sequence.

slava [35]

Answer:

False

Step-by-step explanation:

3 0

2 years ago