Answer:
The volume of foam needed to fill the box is approximately 2926.1 cubic inches.
Step-by-step explanation:
To calculate the amount of foaming that is needed to fill the rest of the box we first need to calculate the volume of the box and the volume of the ball. Since the box is cubic it's volume is given by the formula below, while the formula for the basketball, a sphere, is also shown.
Vcube = a³
Vsphere = (4*pi*r³)/3
Where a is the side of the box and r is the radius of the box. The radius is half of the diameter. Applying the data from the problem to the expressions, we have:
Vcube = 15³ = 3375 cubic inches
Vsphere = (4*pi*(9.5/2)³)/3 = 448.921
The volume of foam there is needed to complete the box is the subtraction between the two volumes above:
Vfoam = Vcube - Vsphere = 3375 - 448.921 = 2926.079 cubic inches
The volume of foam needed to fill the box is approximately 2926.1 cubic inches.
In a large population, 61% of the people are vaccinated, meaning there are 39% who are not. The problem asks for the probability that out of the 4 randomly selected people, at least one of them has been vaccinated. Therefore, we need to add all the possibilities that there could be one, two, three or four randomly selected persons who were vaccinated.
For only one person, we use P(1), same reasoning should hold for other subscripts.
P(1) = (61/100)(39/100)(39/100)(39/100) = 0.03618459
P(2) = (61/100)(61/100)(39/100)(39/100) = 0.05659641
P(3) = (61/100)(61/100)(61/100)(39/100) = 0.08852259
P(4) = (61/100)(61/100)(61/100)(61/100) = 0.13845841
Adding these probabilities, we have 0.319761. Therefore the probability of at least one person has been vaccinated out of 4 persons randomly selected is 0.32 or 32%, rounded off to the nearest hundredths.
This is an isosceles right triangle (AB = BC & ∠ B=90° - Given)
Then the angles at the base are equal and ∠ CAB = ∠ ACB = 45°
Theorem: Segment DE, joining the midpoints of 2 sides is:
1st) parallel to the 3rd side and
2nd) equal to half the measurement of the 3rd side
So if the 3rd side (hypotenuse) = 9 units, DE = 9/2 = 4.5 units
d. Adjustments
Studen loan interests and IRA contributions are deductions found under the heading of ADJUSTMENTS TO INCOME to compute for the Adjusted Gross Income or AGI.
Standard deductions are those based on the filing status of the individual and not his total itemized deductions. Regardless of the actual expenses incurred by an individual, he can claim a standar deduction if he is single, head of household, married filing separately, married filing jointly, qualifying widow(er). at the time he files for his federal tax return.
taxable income is the income left from all the necessary deductions.
For example: Gretchen's income => $56,750
less: Adjustments to income
student loan interest $1,200
IRA Contribution 3,000 - 4,200
===========
Taxable income $52,550
Answer:
Step-by-step explanation:
y = 5x + 20
Start at (0, 20).
Then plot a point at (1, 25).
The line should be going through points (2, 30), (3, 35), (4, 40), (5, 45), etc.
For every time the x number goes up, the y number goes up 5 times for the 5%.
