Show that (1 + 2V3)2 = 13 +4V3

To compute a student's Grade Point Average (GPA) for a term, the student's grades for each course are weighted by the number of

postnew [5]

Answer:

The student's GPA for that term is 3.07

Step-by-step explanation:

So this is a problem where we need to compute a weighted arithmetic mean.

To compute the weighted arithmetic mean of a set, we need to multiply each value of the set by their respective weight, add them, and then divide by the sum of the weights.

I will write the set in a {V,W} way, where V is the value(the grade) and W is the weight of V.

So your set G will be

G = {{3.8, 5}, {1.8,3}, {3.1,5}, {3.1,5}}.

Multiplying each value by it's respective weigth and then adding, we have:

3.8*5 + 1.8*3 + 3.1*5 + 3.1*5 = 19 + 5.4 + 15.5 + 15.5 = 55.4

The sum of the weigths is 5 + 3 + 5 + 5 = 18

So the student's GPA for that term, rounded to two decimal places, is: 55.4/18 = 3.07

4 0

2 years ago

21. In the figure given below, AC is parallel to DE. Find the valuesof xy and z and hence find the 2DBE.

algol13

Answer:

X= 50°

Y= 70°

Z= 30°

BDE= 30°

2BDE= 60°

Step-by-step explanation:

(2x -70 )+z+(2x+20)=180...(sum of angle on a straight line)

2x -70 = BDE... alternate angles

Y + (2x-70)+(50+x-20) = 180...(sum of angles in a triangle)

X-20 = z ... alternate and opposite angles

(2x -70 )+z+(2x-+20)=180

2x-70 + x-20 +2x +20= 180

5x -70= 180

5x = 250

X= 50°

X-20 = z

50-20= z

30° = z

2x -70 = BDE

2(50) -70 = BDE

100-70 = BDE

30°= BDE

Y + (2x-70)+(50+x-20)

Y + 100-70 +50 +50 -20 = 180

Y + 200-90=180

Y= 70°

2BDE = 2*30

2BDE= 60°

8 0

2 years ago

Amy wants to sell at most 25 cookies and at least 10 sprites

Inga [223]

Answer:

$x\leq 25\\y\geq 10\\.50x + y\geq 30$

Step-by-step explanation:

It is given that,

Amy wants to sell at most 25 cookies ,

Let number of cookies be ' $x$ ' , then $x$ should be less than or equal to 25

Which is represented by $x\leq 25$ ,

Further,

Let number of sprites be ' $y$ ', then ' $y$ ' should be greater than or equal to 10

Which is represented by $y\geq 10$

Also,

Given,

she profits $.50 on every cookie

and $1.00 on every sprite.

So total profit on selling cookies would be

= Profit on each cookie times the number of cookies

= $.50\times x$

= $.5x$

Similarly, total profit on selling sprites would be

=profit on each sprite times the number of sprites

= $1.00\times y$

= $y$

Now, combining these two should be greater than or equal to $30

representing this through an equation,

$.50x+y\geq 30$

Thus the sysytem of equations is given as:

$x\leq 25\\y\geq 10\\.50x + y\geq 30$

6 0

3 years ago

A dog breeder would like to know how many Dalmatian puppies are typically born in a litter. He conducts some research and select

podryga [215]

Answer:

c. 6.2 ± 2.626(0.21)

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 101 - 1 = 100

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 100 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.99}{2} = 0.995$ . So we have T = 2.626