Answer:
Step-by-step explanation:
Let a = the number of apples
And b = the number of bananas. Then,
![\begin{array}{rcll}(1) \, 1.75a + 0.40 b & = & 7.65&\\(2)\, \, \, \, \quad \qquad a + b & = &9&\\(3) \, 0.40a + 0.40b & = &3.60&\text{Multiplied (2) by 0.40}\\1.35a & =&4.05\\(4) \, \, \quad \qquad \qquad a & =& \mathbf{3}&\text{Divided each side by 1.35}\\3 + b & = &9& \text{Substituted(4) into (2)}\\b &=& \mathbf{6}&\text{Subtracted 3 from each side}\\\end{array}\\\text{They bought $\large \boxed{\textbf{3 apples and 6 bananas}}$}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcll%7D%281%29%20%5C%2C%201.75a%20%2B%200.40%20b%20%26%20%3D%20%26%207.65%26%5C%5C%282%29%5C%2C%20%5C%2C%20%5C%2C%20%5C%2C%20%5Cquad%20%5Cqquad%20a%20%2B%20b%20%26%20%3D%20%269%26%5C%5C%283%29%20%5C%2C%200.40a%20%2B%200.40b%20%26%20%3D%20%263.60%26%5Ctext%7BMultiplied%20%282%29%20by%200.40%7D%5C%5C1.35a%20%26%20%20%3D%264.05%5C%5C%284%29%20%5C%2C%20%5C%2C%20%20%5Cquad%20%5Cqquad%20%5Cqquad%20a%20%26%20%3D%26%20%5Cmathbf%7B3%7D%26%5Ctext%7BDivided%20each%20side%20by%201.35%7D%5C%5C3%20%2B%20b%20%26%20%3D%20%269%26%20%5Ctext%7BSubstituted%284%29%20into%20%282%29%7D%5C%5Cb%20%26%3D%26%20%5Cmathbf%7B6%7D%26%5Ctext%7BSubtracted%203%20from%20each%20side%7D%5C%5C%5Cend%7Barray%7D%5C%5C%5Ctext%7BThey%20bought%20%24%5Clarge%20%5Cboxed%7B%5Ctextbf%7B3%20apples%20and%206%20bananas%7D%7D%24%7D)
Check:
![\begin{array}{cccl}3(1.75) + 6(0.40) = 7.65 & \qquad & 3 + 6 = 9\\5.25 + 2.40 = 7.65 & \qquad & 9 = 9\\7.65 = 7.65 & \qquad & \\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bcccl%7D3%281.75%29%20%2B%206%280.40%29%20%3D%207.65%20%26%20%5Cqquad%20%26%203%20%2B%206%20%3D%209%5C%5C5.25%20%2B%202.40%20%3D%207.65%20%26%20%5Cqquad%20%26%209%20%3D%209%5C%5C7.65%20%3D%207.65%20%26%20%5Cqquad%20%26%20%5C%5C%5Cend%7Barray%7D)
OK.
Scientific notation is a way of expressing a number as a number between 1 and to multiplied by a power of 10.
Answer:
<h2>The volume is
![3946.17cm^3](https://tex.z-dn.net/?f=3946.17cm%5E3)
</h2>
Step-by-step explanation:
We need to convert the radius and the height to cm first
1 cm = 0.393701 in
r (cm)= 3.7 in
![h(cm)= \frac{3.7}{0.393701}= 9.398 cm](https://tex.z-dn.net/?f=h%28cm%29%3D%20%5Cfrac%7B3.7%7D%7B0.393701%7D%3D%209.398%20cm)
1 cm = 0.393701 in
h (cm)= 5.6 in
![h(cm)= \frac{5.6}{0.393701}= 14.22 cm](https://tex.z-dn.net/?f=h%28cm%29%3D%20%5Cfrac%7B5.6%7D%7B0.393701%7D%3D%2014.22%20cm)
The formula the volume of cylinder is
![volume= \pi r^2h\\\\volume= 3.142*9.398^2*14.22\\volume=3946.17cm^3](https://tex.z-dn.net/?f=volume%3D%20%5Cpi%20r%5E2h%5C%5C%5C%5Cvolume%3D%203.142%2A9.398%5E2%2A14.22%5C%5Cvolume%3D3946.17cm%5E3)
88.1% is the markup. Hope this helps!
Answer:
a. 22/425
b. 368/425.
c. 7/425.
Step-by-step explanation:
There are a total of 32+12+7 = 51 people in the group.
a. Probability (First one is Asian) = 12/51 = 4/17.
Probability(second one is Asian) = 11/50.
So the probability that both are Asian is 4/17 * 11/50
= 22/425.
b. Prob(First is Australian) = 32/51
Prob( Second is not Australian) = 19/50.
Prob( first is Australian and Second is not) = 32/51 * 19/50.
Prob( First is not Australian and the second is) = 19/51 * 32/50.
Prob ( Both are Australian) = 32/51 * 31/50)
Prob( At least one is Australian = 32/51 * 19/50 + 19/51 * 32/50 + 32/51 * 31/50
= 368/425.
c. Prob ( First choice born in Europe) = 7/51 and probability second was also born in Europe = 6/50
So the answer is 7/51 * 6/50 = 7/425.