Answer: False.
Step-by-step explanation:
Initially, the ratio is 2:7
This means that if we have 2 red marbles, we must have 7 yellow ones.
The quotient here is 7/2 = 3.5
Now, if you add 3 marbles of each colour, then we have:
2 + 3 = 5 red marbles
7 + 3 = 10 yellow marbles.
Now the ratio is 5:10
This means that for every 5 red marbles, we have 10 yellow ones.
But now we can divide both numbers by the same positive integer, because they have a common factor equal to 5.
5/5 = 1
10/5 = 2
Then we have:
5:10 = 1:2
So the new ratio is 1:2
Then the ratio changed when we added the new marbles, which means that Maria was wrong.
Answer:
100
16
Step-by-step explanation:Base is 6x6 so 36 and side is 6x8/3 so 16 4 sides so 16x4 =64+36=100 for surface area and volume is 16
Answer:
54°
Step-by-step explanation:
Multiplication is not involved.
The trig relation that is concerned with the opposite and adjacent sides of an angle in a right triangle is the tangent relation:
Tan = Opposite/Adjacent
tan(θ) = 41/30
The value of the angle is found using the inverse tangent function:
θ = arctan(41/30) ≈ 53.807°
The angle of elevation is about 54°.
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<em>Additional comment</em>
The mnemonic SOH CAH TOA is often used as a reminder of the relationship between right triangle sides and trig functions. The other two relations are ...
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
For finding angles, the inverse trig relations are used. These can be called "arcsine," "arccosine," and "arctangent." They are often shown in functional form as (respectively) sin⁻¹, cos⁻¹, and tan⁻¹. On a calculator, they are often "2nd" or "Shift" or "Alt" functions of the sin, cos, and tan keys.
Answer:
- men: 37 minutes
- women: 59 minutes
Step-by-step explanation:
The problem statement is asking you to identify grooming times for men and for women. It is convenient to assign variables to these. I like to use variable names that help me remember what they stand for, so I would choose "m" and "w" as the variables representing grooming times (in minutes) of men and women, respectively.
The problem statement tells you the sum of these times is 96 minutes:
w + m = 96
and it tells you that the difference of these times is 22 minutes:
w - m = 22
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These two relationships give you enough information so that you can solve the equations for the values of w and m, as the problem requests.
We can rearrange the second equation to get an expression for w:
w = 22 + m
and we can use this expression in the first equation:
(22 +m) +m = 96
2m +22 = 96
This is a 2-step linear equation that can be solved in the usual way.
2m = 74 . . . . . . subtract 22 from both sides
m = 37 . . . . . . . divide both sides by 2
From our equation above, we can find w:
w = 22 +m = 22 +37
w = 59
On average women spend 59 minutes grooming each day; men spend 37 minutes.