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marishachu [46]

2 years ago

12

in the figure below line de is parallel to line f g with a transversal AG write and solve a system of liner equation to determin

e the values of x and y

1 answer:

Kay [80]2 years ago

7 0

The complete question in the attached figure

we know that

angle y and angle (5y-18) are supplementary angles
then
y°+(5y-18)°=180°------> 6y=180+18------> y=198/6-----> y=33°
and
angle x and angle y are also supplementary angles
then
x+y=180--------> x=180-y-----> x=180-33-----> x=147°

the answer is
x=147°
y=33°

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Jason wanted to place all 540 marbles in the 3 newly bought boxes. If he wants to

kotegsom [21]

Answer:

The first box will have 90 marbles, the second 180 and the third 270.

Step-by-step explanation:

Division in a ratio of 1:2:3

1 + 2 + 3 = 6

So

The first box will have 1/6 of the marbles.

The second box will have 2/6 = 1/3 of the marbles

The third box will have 3/6 = 1/2 of the marbles.

First box:

One sixth, so:

(1/6)*540 = 540/6 = 90

Second box:

One third, so:

(1/3)*540 = 540/3 = 180

Third box:

One half, so:

(1/2)*540 = 540/2 = 270

The first box will have 90 marbles, the second 180 and the third 270.

7 0

2 years ago

Benjamin bought a 5-pound bag of flour for $7.95. What is the unit price per ounce of flour? (1 pound = 16 ounces)

Advocard [28]

Answer:

7.95 divided by 5 times 16 so 7.95 divided by 80= so about 10 cents

Step-by-step explanation:

7 0

2 years ago

A researcher measures IQ and weight for a group of college students. What kind of correlation is likely to be obtained for these

Sunny_sXe [5.5K]

Answer:

Option b

Step-by-step explanation:

Given that a researcher measures IQ and weight for a group of college students.

In general, we think that the weight has nothing to do with IQ of a person and hence not correlated.

But if we go deep, we find that after a certain weight, the person becomes lazy and inactive with a chance to have reduced IQ

Weight gain causes also health problems including less activity of both brain and body and hence there is a chance for less IQ

So we find that as weight increases iq decreases and when weight decreases, IQ increases.

Thus we can say that there is a negative correlation but not necessarily near to one.

Hence option b is right

8 0

2 years ago

Triangular numbers can be represented with equilateral triangles formed by dots. The first five triangular numbers are 1, 3, 6,

Novosadov [1.4K]

Position in the sequence triangular number relation

1 1 1 = 1*(1+1)/2

2 3 3 = 2(2+1)/2

3 6 6 = 3(3+1)/2

4 10 10 = 4(4+1)/2

5 15 15= 5(5+1)/2

Call n the position in the sequence, then the triangular number is: n(n+1)/2

7 0

2 years ago

Read 3 more answers

A store sells 8 colors of balloons with at least 28 of each color. How many different combinations of 28 balloons can be chosen?

Len [333]

Answer:

(a) $Selection = 6724520$

(b) $At\ most\ 12 = 6553976$

(c) $At\ most\ 8 = 6066720$

(d) $At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638$

Step-by-step explanation:

Given

$Colors = 8$

$Balloons = 28$ --- at least

Solving (a): 28 combinations

From the question, we understand that; a combination of 28 is to be selected. Because the order is not important, we make use of combination.

Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.

So:

$n => 28 + 8-1$ $= 35$

$r = 28$

$Selection = ^{35}^C_{28$

$Selection = \frac{35!}{(35 - 28)!28!}$

$Selection = \frac{35!}{7!28!}$

$Selection = \frac{35*34*33*32*31*30*29*28!}{7!28!}$

$Selection = \frac{35*34*33*32*31*30*29}{7!}$

$Selection = \frac{35*34*33*32*31*30*29}{7*6*5*4*3*2*1}$

$Selection = \frac{33891580800}{5040}$

$Selection = 6724520$

Solving (b): At most 12 red balloons

First, we calculate the ways of selecting at least 13 balloons

Out of the 28 balloons, there are 15 balloons remaining (i.e. 28 - 13)

So:

$n => 15 + 8 -1 = 22$

$r = 15$

Selection of at least 13 =

$At\ least\ 13 = ^{22}C_{15}$

$At\ least\ 13 = \frac{22!}{(22-15)!15!}$

$At\ least\ 13 = \frac{22!}{7!15!}$

$At\ least\ 13 = 170544$

Ways of selecting at most 12 =

$At\ most\ 12 = Total - At\ least\ 13$ --- Complement rule

$At\ most\ 12 = 6724520- 170544$

$At\ most\ 12 = 6553976$

Solving (c): At most 8 blue balloons

First, we calculate the ways of selecting at least 9 balloons

Out of the 28 balloons, there are 19 balloons remaining (i.e. 28 - 9)

So:

$n => 19+ 8 -1 = 26$

$r = 19$

Selection of at least 9 =

$At\ least\ 9 = ^{26}C_{19}$

$At\ least\ 9 = \frac{26!}{(26-19)!19!}$

$At\ least\ 9 = \frac{26!}{7!19!}$

$At\ least\ 9 = 657800$

Ways of selecting at most 8 =

$At\ most\ 8 = Total - At\ least\ 9$ --- Complement rule

$At\ most\ 8 = 6724520- 657800$

$At\ most\ 8 = 6066720$

Solving (d): 12 red and 8 blue balloons

First, we calculate the ways for selecting 13 red balloons and 9 blue balloons

Out of the 28 balloons, there are 6 balloons remaining (i.e. 28 - 13 - 9)

So:

$n =6+6-1 = 11$

$r = 6$

Selection =

$^{11}C_6 = \frac{11!}{(11-6)!6!}$

$^{11}C_6 = \frac{11!}{5!6!}$

$^{11}C_6 = 462$

Using inclusion/exclusion rule of two sets:

$Selection = At\ most\ 12 + At\ most\ 8 - (12\ red\ and\ 8\ blue)$

$Only\ 12\ red\ and\ only\ 8\ blue\ = 170544+ 657800- 462$

$Only\ 12\ red\ and\ only\ 8\ blue\ = 827882$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = Total - Only\ 12\ red\ and\ only\ 8\ blue$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 6724520 - 827882$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638$

3 0

2 years ago