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A juice stand sells smoothies in cone-shaped cups that are 8 in. tall. The regular size has a 4 in. diameter. The jumbo size has

nirvana33 [79]

All cone-shaped cups have the same height in 8 inches. They just differ in their diameters. To solve for the volume of the regular and jumbo sizes, let's use the formula for the volume of cone

V = (1/3)*pi*(r^2)*h

r is just the half of the diameter, h is the height which is equal to 8

Regular size:
V = (1/3)*pi*((4/2)^2)*8
V = 33.5 cube inches

Jumbo size:
V = (1/3)*pi*((8/2)^2)*8
V = 134.0 cube inches

3 0

3 years ago

18÷3(5-4+1) =??<br> 3 or 12 <br> how ?!

sergejj [24]

Answer:

12

Step-by-step explanation:

Parenthesis first:

5-4+1

5-4=1+1=2

18÷3×2

Divide:

18÷3×2

Multiply:

6×2=12

3 0

4 years ago

Read 2 more answers

The function f(x) = 830(1.2)x represents the number of students enrolled at a university x years after it was founded. Each year

Aleks04 [339]

Answer:

1.2 times or 20%

Step-by-step explanation:

Given the function ; f(x) = 830(1.2)^x

This is an exponential function ;

Recall the general form of an exponential function ; f(x) = ab^x ;

Where a = Initial value ; b = growth rate

Hence, b = 1.2

Also, b = 1 + r

1.2 = 1 + r

r = 1.2 - 1

r = 0.2

r = 0.2 * 100% = 20%

4 0

3 years ago

2. Suppose 27 blackberry plants started growing in a yard. Absent constraint, the blackberry plants will spread by 80% a month.

Marta_Voda [28]

Explanation

The question indicates we should use a logistic model to estimate the number of plants after 5 months.

This can be done using the formula below;

$\begin{gathered} P(t)=\frac{K}{1+Ae^{-kt}};A=\frac{K-P_{0_{}}}{P_0}_{} \\ \text{From the question} \\ P_0=\text{ Initial Plants=27} \\ K=\text{Carrying capacity =140} \end{gathered}$

Workings

Step 1: We would need to get the value of A using the carrying capacity and initial plants that started growing in the yard.

This gives;

$\begin{gathered} A=\frac{140-27}{27} \\ A=\frac{113}{27} \end{gathered}$

Step 2: Substitute the value of A into the formula.

$P(t)=\frac{140}{1+\frac{113}{27}e^{-kt}}$

Step 3: Find the value of the constant k

Kindly recall that we are told that the plants increase by 80% after each month. Therefore, after one month we would have;

$\begin{gathered} P(1)=27+(\frac{80}{100}\times27) \\ P(1)=\frac{243}{5} \end{gathered}$

We can then have that after t= 1month

$\begin{gathered} \frac{140}{1+\frac{113}{27}e^{-k\times1}}=\frac{243}{5} \\ Flip\text{ the equation} \\ \frac{1+\frac{113}{27}e^{-k}}{140}=\frac{5}{243} \\ 243(1+\frac{113}{27}e^{-k})=700 \\ 243+1017e^{-k}=700 \\ 1017e^{-k}=700-243 \\ 1017e^{-k}=457 \\ e^{-k}=\frac{457}{1017} \\ -k=\ln (\frac{457}{1017}) \end{gathered}$

Step 4: Substitute -k back into the initial formula.

$\begin{gathered} P(t)=\frac{140}{1+\frac{113}{27}e^{\ln (\frac{457}{1017})t}} \\ =\frac{140}{1+\frac{113}{27}(e^{\ln (\frac{457}{1017})})^t} \\ P(t)=\frac{140}{1+\frac{113}{27}(\frac{457}{1017}^{})^t} \\ \end{gathered}$

The above model is can be used to find the population at any time in the future.

Therefore after 5 months, we can estimate the model to be;

$\begin{gathered} P(5)=\frac{140}{1+\frac{113}{27}(\frac{457}{1017}^{})^5} \\ P(5)=\frac{140}{1.07668} \\ P(5)=130.029\approx130 \end{gathered}$

Answer: The estimated number of plants after 5 months is 130 plants.

8 0

1 year ago

When randomly selecting adults, let M denote the event of randomly selecting a male and let B denote the event of randomly sele

aksik [14]

Answer:

See explanation

Step-by-step explanation:

Given

$M \to$ randomly selecting a male

$B \to$ randomly selecting someone with blue eyes

Solving (a): Interpret P(M|B)

The above implies conditional probability

The interpretation is: the probability of selecting a male provided that a person with blue eyes has been selected

Solving (b): is (a) the same as P(B|M)

No, they are not the same.

The interpretation of P(B|M) is: the probability of selecting a person with blue eyes provided that a male has been selected

3 0

3 years ago