Given the prime factorisation of the each of

Connie collected 50 seashells during her 5-day vacation. Each day she collected 3 more than the previous day. How many seashells

vfiekz [6]

Answer:

The number of seashells collected on day 1 to day 5 is 4, 7, 10, 13 and 16 respectively

Step-by-step explanation:

This is a question that deals with consecutive numbers.

Let x represent the number of seashells collected on her first day.

Given that she collected 3 more each day, then

On day 2, she collected x + 3

On day 3, she collected x + 6

On day 4, she collected x + 9

On day 5, she collected x + 12

Adding up the above will give the number of sea shells collected on day 1;

i.e.

x + x + 3 + x + 6 + x + 9 + x + 12 = 50

Collect like terms

x + x + x + x + x + 3 + 6 + 9 + 12 = 50

5x + 30 = 50

5x = 50 - 30

5x = 20

Multiply ⅕ to both sides

⅕ * 5x = ⅕ * 20

x = 4.

This mean that she found 4 seashells on day 1;

Recall that day 2 = x + 3

So, day 2 = 4 + 3 = 7 seashells

day 3 = x + 6

day 3 = 4 + 6 = 10 seashells

day 4 = x + 9

day 4 = 4 + 9 = 13 seashells

day 5 = x + 12

day 5 = 4 + 13 = 16 seashells

Hence, the number of seashells collected on day 1 to day 5 is 4, 7, 10, 13 and 16 respectively

6 0

2 years ago

Ivan wants to fill with foam the empty space left in a cube-shaped box after he places a basketball in the box. How many cubic i

Ann [662]

Answer:

280 cubic inches

Step-by-step explanation:

Cubic inches of foam required = volume of the box - volume of the basketball

The box has a shape of a cube, so that;

volume of the box = $l^{3}$

where l is the length of the sides of the box.

volume of the box = $9^{3}$

= 729 cubic inches

volume of the box = 729 cubic inches

The basketball has the shape of a sphere, so that;

volume of the basketball = $\frac{4}{3}$ $\pi$ $r^{3}$

= $\frac{4}{3}$ x 3.14 x $(4.75)^{3}$

= 448.693

volume of the basketball = 448.693 cubic inches

Thus,

cubic inches of foam required = 729 - 448.693

= 280.307

The cubic inches of foam to be used is 280 cubic inches.

6 0

2 years ago

Jack's gross weekly pay is $498. He has $52 withheld from each paycheck for federal income

maks197457 [2]

Answer:

A. 56.78 B. 389.22

Step-by-step explanation:

A.Social security: 498x.062=30.88

medicare: 498x.0145=7.22

state tax: 498x.025=12.45

local tax: 498x.0125=6.23

total of above = 56.78

B. Total taxes above (56.78) + federal withheld (52) = total taxes 108.78

total pay 498 - total taxes 108.78 = 389.22

5 0

2 years ago

A cone has a volume of 24 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?

Soloha48 [4]

Answer:

72 cubic inches

Step-by-step explanation:

Volume of cone = $\frac{1}{3}\pi r^{2} h$ --1

Volume of cylinder = $\pi r^{2} h$ --2

We are given that a cylinder should fit exactly inside the cone

On comparing 1 and 2 we can see:

$\text{Volume of cone}= \frac{1}{3} \text{Volume of cylinder}$

Since we are given the volume of cone is 24 cubic inches .

So, $24= \frac{1}{3} \text{Volume of cylinder}$

$24 \times 3= \text{Volume of cylinder}$

$72= \text{Volume of cylinder}$

Hence the volume of cylinder is 72 cubic inches

Option D is correct.

3 0

3 years ago

Read 2 more answers

How much money is saved on an $80 coat that has been reduced 30%. If you could show me how this is done I would be super gratefu

pentagon [3]

You would get 24$ off of it

6 0

3 years ago