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3 years ago

Work out the volume of this sphere. Give your answer to 1 decimal place. 4.7 cm

Mathematics

1 answer:

Dmitry [639]3 years ago

7 0

Answer:

434.9 cm³

Step-by-step explanation:

Volume of a sphere: 4/3πr³

Substitute the information to find the volume.

4/3π(4.7)³ = 434.9

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There is a triangle with a perimeter of 63 cm, one side of which is 21 cm. Also, one of the medians is perpendicular to one of t

NemiM [27]

Answer:

21cm; 28cm; 14cm

Step-by-step explanation:

There is no info in the problem/s text which one of the triangle's side is 21 cm. That is why we have to try all possible variants.

Let the triangle is ABC . Let the AK is the angle A bisector and BM is median.

Let O is AK and BM cross point.

Have a look to triangle ABM. AO is the bisector and AOB=AOM=90 degrees (means that AO is as bisector as altitude)

=> triangle ABM is isosceles => AB=AM (1)

1. Let AC=21 So AM=21/2=10.5 cm

So AB=10.5 cm as well. So BC= P-AB-AC=63-21-10.5=31.5 cm

Such triangle doesn' t exist ( is impossible), because the triangle's inequality doesn't fulfill. AB+AC>BC ( We have 21+10.5=31.5 => AB+AC=BC)

2. Let AB=21 So AM=21 and AC=42 .So BC= P-AB-AC=63-21-42=0 cm- such triangle doesn't exist.

3. Finally let BC=21 cm. So AB+AC= 63-21=42 cm

We know (1) that AB=AM so AC=2*AB. So AB+AC=AB+2*AB=3*AB

=>3*AB=42=> AB=14 cm => AC=2*14=28 cm.

Let check if this triangle exists ( if the triangle's inequality fulfills).

BC+AB>AC 21+14>28 - correct=> the triangle with the sides' length 21cm,14 cm, 28cm exists.

This variant is the only possible solution of the given problem.

6 0

3 years ago

In science class, the girl to boy ratio is 3 to 7.

Mariana [72]

Answer:

There are <u>35 boys</u> in the class.

Step-by-step explanation:

Girls to Boys ratio = 3:7

Total number of students in class = 50

Let total number of girls be '3x' and total number of boys be '7x'

Total number of girls + Total number of boys = Total number of students

3x + 7x = 50

10x = 50

x = 50/10

x = 5

$\therefore$

Total number of girls = 3 × 5 = 15

Total number of boys = 7 × 5 = 35

7 0

3 years ago

I don’t know the answer and I’m not good at math at all

ch4aika [34]

Answer: Tia payed .15 more

Step-by-step explanation:

Divide the Money amount by the number of juice boxs and then subtract

3 0

3 years ago

Read 2 more answers

g On any day, the probability of rain is 0.3. The occurrence of rain on any day is independent of the occurrence of rain on any

Ksju [112]

Answer:

0.249579

Step-by-step explanation:

P(rain) = 0.3

P(no rain) = 1 - 0.3 = 0.7

The event of rain falling a second time within the next 5 days is possible in these ways

1. Rain on days 1 and 2

2. Rain on days 1 and 3; none on day 2

3. Rain on days 1 and 4; none on days 2 and 3

4. Rain on days 1 and 5; none on days 2, 3 and 4

5. Rain on days 1 and 6; none on day 2, 3, 4 and 5

$P(\text{second rain within 5 days}) = 0.3^2+0.3^2\times0.7+0.3^2\times0.7^2+0.3^2\times0.7^3+0.3^2\times0.7^4 = 0.3^2(1+0.7+0.7^2+0.7^3+0.7^4)= 0.09\times2.7731=0.249579$

5 0

4 years ago

Which of the following is an arithmetic sequence?

enot [183]

Answer:

The third sequence.

Step-by-step explanation:

In an arithmetic sequence, the difference between two consecutive terms is the same.

For each option, find the difference between consecutive terms:

First option:

$4 - 2 = 2$ .
$8 - 4 = 4$ .
$16 - 8 = 8$ .

The differences are not the same. As a result, this option is not an arithmetic sequence.

Second option:

$4 - 12 = -8$ .
$\displaystyle \frac{4}{3} - 4 = -\frac{8}{3}$ .
$\displaystyle \frac{16}{3} - \frac{4}{3} = \frac{12}{3} = 4$ .

The differences are not the same. As a result, this option is not an arithmetic sequence, either.

Third option:

$\displaystyle -\frac{1}{2} - \frac{1}{2} = -1$ .
$\displaystyle -\frac{3}{2} - \left(-\frac{1}{2}\right) = -\frac{3}{2} + \frac{1}{2} = -1$ .
$\displaystyle -\frac{5}{2} - \left(-\frac{3}{2}\right) = -\frac{5}{2} + \frac{3}{2} = -1$ .

The differences are all $-1$ . As a result, this option is indeed an arithmetic sequence. Its common difference is $(-1)$ .

Fourth option:

$\displaystyle -\frac{1}{2} - \frac{1}{2} = -1$ .
$\displaystyle \frac{1}{2} - \left(-\frac{1}{2}\right) = \frac{1}{2} + \frac{1}{2} = 1$ .
$\displaystyle -\frac{1}{2}\right - \frac{1}{2} = -1$ .

The differences are varying between $1$ and $-1$ . As a result, this option is not an arithmetic sequence.

3 0

3 years ago