13.92 x 2.7≈ What’s the answer?

The marketing manager of a soft drink company wants to design a can with a height that is four times the radius of the can. a) e

natka813 [3]

Volume of a cylindrical can = pi r^2 h
We are given that h = 4r , so substituting for h in the above formula:-
Volume = pi * r^2 * 4r = 4pir^3 <---- the answer to Part a.

h = 4r so r = h/4
Substituting for r:-
Volume = pi * (h/4)^2 * h = pi h^3/16 <------- Answer to part b.

6 0

4 years ago

Read 2 more answers

I have these factoring questions I need help with.

snow_lady [41]

$f(x)=4x^2+4x-3$

1. Determine y-intercept.

The y-intercept is (0,-3). Substitute x = 0 in the equation as we get f(x) = -3 as the y-intercept.

2. Determine the zeros.

Factor the polynomials first. $(2x-1)(2x+3)$ This is the factored form. The zeros are the roots of equation. Therefore, the zeros are 1/2 and -3/2

3. Determine the Axis of Symmetry

We can solve this by using the formula of $x=-\frac{b}{2a}$ However, I'll be solving the Axis of Symmetry with Calculus instead.

$f'(x)=2(4x^{2-1})+1(4x^{1-1})-0\\f'(x)=8x+4$

Then let f'(x) = 0 to find the Axis of Symmetry.

$8x+4=0\\8x=-4\\x=-\frac{4}{8}\\x=-\frac{1}{2}$

Therefore, the Axis of Symmetry is -1/2

4. Determine the vertex.

Substitute the value of Axis of Symmetry in f(x).

$f(x)=4(-\frac{1}{2})^2+4(-\frac{1}{2})-3\\f(x)=4(\frac{1}{4})-2-3\\f(x)=1-2-3\\f(x)=-4$

Therefore the vertex is at (-1/2, -4)

5. Does the vertex representing max-pont or min-point?

The vertex represents the minimum point. The graph is upward, meaning the minimum point is the point that gives the LOWEST Y-VALUE.

7. Graph f(x)

Unfortunately I won't be able to graph. But I can tell you to graph a parabola that has the most curve at the vertex and intercepts y-axis at (0,-3).

--------------------------- End of Part 1 --------------------------------

2. Write the general form of Quadratic Function in standard form.

$y=ax^2+bx+c$

The graph can be easily determined about the y-intercept and being an upward or downward parabola along with how narrow or wide the parabola is.

For example, c value is the y-intercept as defined. When a > 0, the parabola is upward and when a < 0, the parabola is downward. The more value of | a | is, the more narrow it will be and the less value of | a | it is, the wider it will be.

3. Write in Factored Form

$y=(x+a)(x+b)\\y=(x-a)(x-b)\\y=(x+a)(x-b)\\y=(x-a)(x+b)$

These are factored forms with different types of operators.

The equation can be easily determined about the roots of equation. For example, if the function is in f(x) = (x+2)(x-1) Then the roots would be x = -2 and 1 as the graph will intercept x-axis at (-2,0) and (1,0)

4. Write in Vertex Form.

$y=a(x-h)^2+k$

The equation can be easily determined for the vertex, axis of symmetry and the same narrow/wide/upward/downward parabola again.

The vertex is at (h,k) and the axis of symmetry is at x = h.

For example, $y=(x-2)^2+3$

The vertex would be at (2,3) and the axis of symmetry is x = 2.

3 0

3 years ago

Could -free, automatic faucets actually be housing more bacteris than the old fashioned, manual kind The concern is that decreas

Volgvan

Answer:

Not enough evidence to reject Null hypothesis

Step-by-step explanation:

Solution:-

- A comparative study for bacterial growth in manual and electronic faucets is made.

- It is observed that there is a higher growth in electronic faucets due to slower flow rates, i.e electronic faucets are not thoroughly flushed; hence, giving more resident time for the scaled bacteria to grow.

- It is known that 15% of cultures from older faucets were tested positive for the Legionella bacteria.

- A study at John Hopkins was conducted on a sample n = 20 electronic faucets with the probability of bacteria growing in a faucet is 0.15.

- We will conduct a hypothesis for at-least half proportion of electronic faucets have cultured bacteria.

- State the hypothesis for the proportion of electronic faucets culturing Legionella bacteria:

Null Hypothesis: P = 0.15

Alternate hypothesis: P > 0.15

- To determine the test statistics for the study conducted at John hopkins. We had a sample size of n = 20, and the probability for a bacteria to grow in a faucet is 0.15.

- Denote random variable, X: The number of electronic faucets culturing Legionella bacteria.

- Since, the probability for a bacteria to grow in a faucet is independent for each new faucet. We will assume the RV " X " to follow binomial distribution with probability of success 0.15:

X ~ Bin ( 20 , 0.15 )

- We are to determine that at-least half of the sample is subjected to the said bacteria. This is the probability of P ( X ≥ 10 ).

- The pmf for a binomially distributed random variable X is given below:

$P ( X = r ) = n_C__r * ( p(success) )^r * ( p (fail) )^(^n^-^r^)$

Where,

p ( success ) = 0.15

p ( fail ) = 1 - p ( success ) = 1 - 0.15 = 0.85

- Use the pmf to determine the required test statistics:

$P ( X \geq 10 ) = 1 - P ( X \leq 9 )\\\\P ( X \geq 10 ) = 1 - [ (0.85)^2^0 + 20*(0.15)*(0.85)^1^9 + 20_C_2 (0.15)^2*(0.85)^1^8 +\\\\ 20_C_3 (0.15)^3*(0.85)^1^7 + 20_C_4 (0.15)^4*(0.85)^1^6 + 20_C_5 (0.15)^5*(0.85)^1^5+\\\\ 20_C_6 (0.15)^6*(0.85)^1^4 + 20_C_7 (0.15)^7*(0.85)^1^3 + 20_C_8 (0.15)^8*(0.85)^1^2 + \\\\ 20_C_9 (0.15)^9*(0.85)^1^1\\\\\\P ( X \geq 10 ) = 1 - [ 0.03875 + 0.13679 + 0.22933 + 0.24282 + 0.18212 + 0.10284 + \\\\ 0.04537 + 0.01601 + 0.00459 + 0.00108 ]\\\\$

$P ( X \geq 10 ) = 1 - [ 0.997 ] = 0.003$

- The probability that 10 or more electronic faucets is found to have Legionella bacteria growing is 0.003

- The test proportion of 10 and more electronic faucets have culturing bacteria is p = 0.003.

- Assuming normality of the population, the Z-statistics would be:

$Z-test = \frac{ (p - P) \sqrt{n} }{\sqrt{P*(1 - P )} } \\\\Z-test = \frac{ (0.003 - 0.15) \sqrt{20} }{\sqrt{0.15*(0.85)} } \\\\Z-test = -1.84109$

- If we were to test the claim to 90% level of confidence:

significance level (α) = 1 - CI = 1 - 0.9 = 0.1

- The rejection region Z-critical is defined by a right-tail:

$Z-critical \geq Z_\alpha \geq Z_0_._2\\\\Z-critical \geq 1.28$

- Compare the test statistics with the rejection criteria defined by the Z-critical:

Z-test < Z-critical

-1.84 < 1.28

Conclusion:

There is not enough evidence that the probability of Legionella bacteria growing in electronic faucets is greater than 15%.

3 0

4 years ago

What is the total surface area of a cube with an edge of 8 centimeters

andre [41]

Answer:

64c²

Step-by-step explanation:

to find this answer you had to two edges together in order to get the surface area.

8×8=64

3 0

3 years ago

There are 8 students who have 3/4 of a cake they want to share. How much cake will each student get if they split it evevly

Troyanec [42]

They would get 3/32 of the cake if they split it evenly

5 0

4 years ago