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3 years ago

Prove (correctly) that if 1 = -1, then 2=1

Mathematics

1 answer:

Nitella [24]3 years ago

6 0

Answer:

This may not be entirely satisfied proof but you should get the idea.

Proof: Start with 1 = -1.

Then we know that if a= b then a + c = b + c and also a / c = b / c.

So we can add 1 to both sides.

We have 1 + 1 = -1 + 1 ⇒ 2 = 0.

Now divide both sides by 2 and we would have 1 = 0.

Now add both sides by 1. This yields 2 = 1.

Therefore if 1 = -1 then 2 = 1.

QED

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Use the vertex formula to find the vertex of the quadratic function f(x)=-x^2+6x-10

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Step-by-step explanation:

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Anna enjoys dinner with her family at a restaurant in Washington, D.C. She leaves a 15% tip on the price of her meal. She also h

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Step-by-step explanation:

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A certain company sends 40% of its overnight mail parcels by means of express mail service A1. Of these parcels, 4% arrive after

Harrizon [31]

Answer:

(a) The probability that a randomly selected parcel arrived late is 0.026.

(b) The probability that a parcel was late was being shipped through the overnight mail service A₁ is 0.615.

(d) The probability that a parcel was late was being shipped through the overnight mail service A₃ is 0.192.

Step-by-step explanation:

Consider the tree diagram below.

(a)

The law of total probability sates that: $P(A)=P(A|B)P(B)+P(A|B')P(B')$

Use the law of total probability to determine the probability of a parcel being late.

$P(L)=P(L|A_{1})P(A_{1})+P(L|A_{2})P(A_{2})+P(L|A_{3})P(A_{3})\\=(0.04\times0.40)+(0.01\times0.50)+(0.05\times0.10)\\=0.026$

Thus, the probability that a randomly selected parcel arrived late is 0.026.

(b)

The conditional probability of an event A provided that another event B has already occurred is:

$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$

Compute the probability that a parcel was late was being shipped through the overnight mail service A₁ as follows:

$P(A_{1}|L)=\frac{P(L|A_{1})P(A_{1})}{P(L)} \\=\frac{0.04\times 0.40}{0.026} \\=0.615$

Thus, the probability that a parcel was late was being shipped through the overnight mail service A₁ is 0.615.

(c)

Compute the probability that a parcel was late was being shipped through the overnight mail service A₂ as follows:

$P(A_{2}|L)=\frac{P(L|A_{2})P(A_{2})}{P(L)} \\=\frac{0.01\times 0.50}{0.026} \\=0.192$

Thus, the probability that a parcel was late was being shipped through the overnight mail service A₂ is 0.192.

(d)

Compute the probability that a parcel was late was being shipped through the overnight mail service A₂ as follows:

$P(A_{3}|L)=\frac{P(L|A_{3})P(A_{3})}{P(L)} \\=\frac{0.05\times 0.10}{0.026} \\=0.192$

Thus, the probability that a parcel was late was being shipped through the overnight mail service A₃ is 0.192.

4 0

3 years ago

Please help!<br> Thanks<br> BRIANLIEST OF 2 PPL ANSWER

vlada-n [284]

Answer:

PS = 7

k = 9

Step-by-step explanation:

RS = PQ Given

3x - 7 = x - 1 Substitute algebraic terms. Subtract x from both sides

3x-x - 7 = x - 1 - x Combine

2x - 7 = - 1 Add 7 to both sides.

2x - 7+7 = -1+7 Combine

2x = 6 Divide by 2

2x/2 = 6/2

x = 3

Length of PS = x - 1 + x + 3x - 7

Length of PS = 5x - 8

Length of PS = 5*3 - 8

Length of PS = 7

=========================

f(x) = k - x^2

x = 2

f(x) = 5 is the given point

5 = k - x^2 Substitute for x^2

5 = k - 2^2 Expand

5 = k - 4 Add 4 to both sides.

5+4=k-4+4 Combine

k = 9

8 0

3 years ago