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2 years ago

Find the first, fourth, and eighth terms of the sequence. A(n) = –3 • 2^n–1

1 answer:

4 0

A(n) = –3 • 2⁽ⁿ⁻¹⁾

for n = 1 , A₁ = -3.(2)⁰ = -3
for n = 2 , A₂ = -3.(2)¹ = -6
for n = 3 , A₃ = -3.(2)² = -12
for n = 4 , A₄ = -3.(2)³ = -24
...........................................
for n = 8 , A₈ = -3.(2)⁷ = -384

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Describe a real life multiplication situation for which an estimate makes sense

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2 years ago

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2 years ago

2x+y=25. 3y=2x-13 solve by elimination

Mila [183]

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2 years ago

Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours of production time

user100 [1]

The question is incomplete, here is the complete question

Recall the production model from Section 1.3:

Max 10x

s.t. 5x ≤ 40

x ≥ 0

Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours for each unit produced. Assume total production capacity remains 40 units. Use y as the number of units of product 2 produced. . Show the mathematical model when both products are considered simultaneously.

Answer:

Max Profit: 10x + 5y

5x + 2y ≤ 40

x ≥ 0, y ≥ 0

Explanation:

x= number of units of product 1 produced

y = number of units of product 2 produced

Since the first product, x, has a unit profit of $10 and Max1 is 10x

Second product, y, has a unit profit of $5, Max2 = 5y

The maximum profit when both products are considered simultaneously is 10x + 5y

Max Profit = 10x + 5y

Time required for each unit of x is 5hours

Therefore, time required for x units is 5x hours

Time required for each unit of y is 2hours

Therefore, time required for y units is 2y hours

Time required for the simultaneous production of both products is 5x + 2y

Since production capacity remains 40 units, 5x+2y ≤40

NB: The values of x and y cannot be negative

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1 year ago

An annexation suit against a county subdivision of 1200 residences is being considered by a neighboring city. If the occupants o

Sunny_sXe [5.5K]

Answer:

Probability that in a random sample of 10 at least 3 favor the annexation suit is 0.9453.

Step-by-step explanation:

We are given that an annexation suit against a county subdivision of 1200 residences is being considered by a neighboring city. The occupants of half the residences object to being annexed.

Also, a random sample of 10 residents is taken.

The above situation can be represented through Binomial distribution;

$P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 10 residents

r = number of success = at least 3

p = probability of success which in our question is probability that

residents favor the annexation suit, which is calculated as below;

p = $\frac{\text{Number of residents favoring the annexation suit }}{\text{Total number of residents considered } }$ = $\frac{600}{1200}$ = 0.50

<em>LET X = Number of residents favoring the annexation suit</em>

So, it means X ~ $Binom(n=10, p=0.50)$

Now, Probability that in a random sample of 10 at least 3 favor the annexation suit is given by = P(X $\geq$ 3)

P(X $\geq$ 3) = 1 - P(X < 3) = 1 - P(X $\leq$ 2)

= 1 - [P(X = 0) + P(X = 1) + P(X = 2)]

= $1- [\binom{10}{0}\times 0.50^{0} \times (1-0.50)^{10-0} + \binom{10}{1}\times 0.50^{1} \times (1-0.50)^{10-1} +\binom{10}{2}\times 0.50^{2} \times (1-0.50)^{10-2}]$

= $1-[ 1 \times 1 \times 0.50^{10}+10 \times 0.50^{1} \times 0.50^{9}+45 \times 0.50^{2} \times 0.50^{8}]$

= $1-[ 0.50^{10}+10 \times 0.50^{10}+45 \times 0.50^{10}]$

= $1-0.50^{10}[ 1+10 +45 ]$ = $1-0.50^{10} \times 56$

= 0.9453

Therefore, Probability that in a random sample of 10 at least 3 favor the annexation suit is 0.9453.

8 0

2 years ago