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BartSMP [9]
2 years ago
9

For the polynomial function ƒ(x) = x4 − 12x3 + 46x2 − 60x + 25, find all local and global extrema.

Mathematics
1 answer:
rodikova [14]2 years ago
4 0
\bf f(x)=x^4-12x^3+46x^2-60x+25\\\\
-------------------------------\\\\
\cfrac{df}{dx}=4x^3-36x^2+92x-60\implies 0=4x^3-36x^2+92x-60
\\\\\\
0=x^3-9x^2+23x-15\impliedby \textit{doing some synthetic division with 5}
\\\\\\
0=(x^2-4x+3)(x-5)\implies 0=(x-3)(x-1)(x-5)\\\\
-------------------------------\\\\
\begin{cases}
f(1)=0\leftarrow minimum&1,0\\
f(3)=16\leftarrow maximum&3,16\\
f(5)=0\leftarrow minimum&5,0
\end{cases}\impliedby \textit{3 extrema, locals and globals}
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This is the 4th question
gavmur [86]

Answer:

a) There are 9 outcomes.

b) **i have attached the tree diagram**

c) 1/9

d) 1/9

Step-by-step explanation:

Both events (choosing a shirt and choosing pants) are not mutually exclusive (disjoint). Meaning that both events can occur at the same time.

a) For a sequence of two events in which the first event can occur <em>m</em> ways and the second event can occur <em>n</em> ways, the events together can occur a total of <em>m</em> • <em>n</em> ways. So for this problem, you would do 3 • 3 which equals 9.

b) **tree diagram is attached**

c) Because there are two different events occurring (choosing a shirt and choosing pants) you need to multiply using the Multiplication Rule for Independent Events : P(A and B) = P(A) * P(B)

The probability of event A occurring (choosing a red shirt) is 1/3 and the probability of event B occurring (choosing brown pants) is also 1/3.

1/3 * 1/3 = 1/9

d) You would do the same thing here as part c.

The probability of event A occurring (choosing a blue shirt) is 1/3 and the probability of event B occurring (choosing blue pants) is again 1/3.

1/3 * 1/3 = 1/9

I hope this was helpful!! :)

4 0
2 years ago
a metal bar weighs 80 ounces. 90% of the bar is silver. how many ounces of silver are in the bar? (round to the nearest thousand
UkoKoshka [18]

Answer:72 ounces

Step-by-step explanation:

The correct answer is 72 ounces. In order to reach this answer you need to multiply 80 times .9, which equals 72.

7 0
3 years ago
Which has the bigger surface area? Jamal's, which is 3 by 3 by 4 ft, or Andy's, which is 4 by 2 by 5 ft and why?
oksano4ka [1.4K]

Jamal-3 x 3 = 9 x 4 = 36


Andy-  4 x 2 = 8 x 5 = 45


Andy's surface area is bigger.

6 0
3 years ago
You’ve been asked to order cake for your school dance. Here’s a formula for the scenario: z=xa/y
olga nikolaevna [1]

Answer:

The number of cake for order is 15 cakes .

Step-by-step explanation:

Given as :

Total number of people to attend the dance = x = 60

The number of slices each person will eat = A = 2 slices

The number of slices per cake = y = 8 slices

Let The number of cake for order = z

<u>Now, According to question</u>

Total slices of cake required for 60 people when each people eat 2 slices = total number of people × number of slices each person will eat

i.e Total slices of cake required for 60 people when each people eat 2 slices = x × A

Or, Total slices of cake required for 60 people when each people eat 2 slices = 60 × 2 slices

Or,Total slices of cake required for 60 people when each people eat 2 slices = 120 slices

<u>Again</u>

∵ number of slices per cake = 8

∴ The number of cake for order = \dfrac{\textrm Total slices of cake required for 60 people when each people eat 2 slices}{\textrm number of slices per cake }

Or, z = \frac{x\times A}{y}

i.e z = \frac{120}{8}

∴   z = 15 cakes

So,The number of cake for order = z = 15 cakes

Hence,The number of cake for order is 15 cakes . Answer

7 0
2 years ago
Find the quotient of 394/6
uysha [10]

Answer:

65

Step-by-step explanation:

394/6

When 394 divided by 6 then

we get 65 quotient and 4 remainder

4 0
2 years ago
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