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4 years ago

10

A bag contains white marbles and red marbles, 126 in total. The number of white marbles is 6 more than 5 times the number of red

marbles. How many white marbles are there?

1 answer:

mixer [17]4 years ago

4 0

106 should be the answer.

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A number increased by 4 is the same as the number plus 10

slava [35]

X + 4 = x + 10

2x + 4 = 10

2x = 6

x = 3

6 0

3 years ago

The perimeter of the rectangle is 76 units. Find the length of side pq

larisa [96]

Answer: $PQ=16\ units$

Step-by-step explanation:

The missing figure is attached.

The perimeter of a rectangle is:

$P=2l+2w$

Where "l" is the lenght and "w" is the width.

You can identify in the figure that:

$w=SR=PQ=2z+2\\\\l=QR=PS=3z+1$

Then, knowing the perimeter of the rectangle, you can make the subsitution into the formula:

$76=2(3z+1)+2(2z+2)$

Now you must simplify and solve for "z"

$76=6z+2+4z+4\\\\76-6=10z\\\\70=10z\\\\\frac{70}{10}=z\\\\z=7$

Finally, substituting the value of "z" into $PQ=2z+2$ , you get:

$PQ=2(7)+2=16\ units$

6 0

3 years ago

For a craft, each student will need five rubber bands. There are eight students. What rubber bands come in bags of 9. How many b

gizmo_the_mogwai [7]

Answer:

In total 5 packets of rubber bands are needed.

Out of which 5 rubber bands are left.

Step-by-step explanation:

The number of rubber bands needed by 1 student = 5

The total number of students = 8

So, the total rubber bands needed by all students

= Total students x Number of rubber bands needed by 1 student

= 8 x 5 = 40 bands

Now 1 packet of rubber bands = 9 bands

⇒ 2 packets = 2 x ( 9 bands) = 18 bands

⇒ 3 packets = 3 x ( 9 bands) = 27 bands

Similarly, 4 packets = 36 bands , 5 packets = 45 bands

Now, if we buy 4 packet of bands, there are 36 rubber bands which are LESS THAN THE TOTAL STUDENTS.

So, we buy 5 packets.

We have in total 45 bands, but the total students = 40

So, the number of left rubber bands = Total bands - Total students

= 45 - 40 = 5

Hence, in total 5 packets of rubber bands are needed, and out of which 5 rubber bands are left.

5 0

3 years ago

In order to estimate the mean amount of time computer users spend on the internet each month, how many computer users must be s

Sladkaya [172]

Answer:

The minimum sample size required is 5,499 computer users.

The major obstacle is that it is a big sample size if it is a small organization wanting to perform it.

Step-by-step explanation:

We need to calculate a sample size in order to have 95% confidence interval with 12 minutes of witdth.

So, we have that the difference between the upper limit and the lower limit is 12:

$UL-LL=12$

$(\mu+z*\sigma/\sqrt{n})-(\mu-z*\sigma/\sqrt{n})=12\\\\2z\sigma/\sqrt{n}=12\\\\\sqrt{n}=(1/6)*z\sigma\\\\n=(1/36)z^2\sigma^2$

For a 95% CI, the value of z is 1.96. The standard deviation is 227.

$n=z^2\sigma^2/36=(1.96)^2*(227)^2/36=3.8416*51,529/36=5498.72\\\\n=5499$

The minimum sample size required is 5,499 computer users.

6 0

3 years ago

What is the volume of corn held in this cone-shaped grain silo? Use 3.14 for π and round to the nearest cubic foot. Enter your a

MrRa [10]

Answer:

3014 cubit foot

Step-by-step explanation:

Find the diagram attached

Volume of the cone = 1/3πr²h

r is the base radius of the cone

h is the height

Given

r = 6ft

Get the height using the pythagoras theorem

h² = 10² - 6²

h² = 100 - 36

h² = 64

h = √64

h = 8ft

Get the volume

Volume = 1/3πr²h

Volume = 1/3 * 3.14 * 6^2*8

Volume = 3.14 * 12 * 8

Volume =3,014.4

Volume = 3014 cubit foot to the nearest foot

4 0

3 years ago