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katen-ka-za [31]
3 years ago
10

Two points sit on a line with the following coordinates p(2,2) and Q(3,7) which is the distance from p to q

Mathematics
1 answer:
Alja [10]3 years ago
8 0

ANSWER

\sqrt{26}

EXPLANATION

Given the coordinates p(2,2) and Q(3,7),

we can use the distance formula to find the distance between P and Q.

The distance formula is given by,

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

We substitute the coordinates to get,

d=\sqrt{(3-2)^2+(7-2)^2}

d=\sqrt{(1)^2+(5)^2}

d=\sqrt{1+25}

d=\sqrt{26}

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3 0
2 years ago
The probability that a lab specimen contains high levels of contamination is 0.10. Five samples are checked, and the samples are
raketka [301]

Answer:

(a) 0.59049 (b) 0.32805 (c) 0.40951

Step-by-step explanation:

Let's define

A_{i}: the lab specimen number i contains high levels of contamination for i = 1, 2, 3, 4, 5, so,

P(A_{i})=0.1 for i = 1, 2, 3, 4, 5

The complement for A_{i} is given by

A_{i}^{$c$}: the lab specimen number i does not contains high levels of contamination for i = 1, 2, 3, 4, 5, so

P(A_{i}^{$c$})=0.9 for i = 1, 2, 3, 4, 5

(a) The probability that none contain high levels of contamination is given by

P(A_{1}^{$c$}∩A_{2}^{$c$}∩A_{3}^{$c$}∩A_{4}^{$c$}∩A_{5}^{$c$})=(0.9)^{5}=0.59049 because we have independent events.

(b) The probability that exactly one contains high levels of contamination is given by

P(A_{1}∩A_{2}^{$c$}∩A_{3}^{$c$}∩A_{4}^{$c$}∩A_{5}^{$c$})+P(A_{1}^{$c$}∩A_{2}∩A_{3}^{$c$}∩A_{4}^{$c$}∩A_{5}^{$c$})+P(A_{1}^{$c$}∩A_{2}^{$c$}∩A_{3}∩A_{4}^{$c$}∩A_{5}^{$c$})+P(A_{1}^{$c$}∩A_{2}^{$c$}∩A_{3}^{$c$}∩A_{4}∩A_{5}^{$c$})+P(A_{1}^{$c$}∩A_{2}^{$c$}∩A_{3}^{$c$}∩A_{4}^{$c$}∩A_{5})=5×(0.1)×(0.9)^{4}=0.32805

because we have independent events.

(c) The probability that at least one contains high levels of contamination is

P(A_{1}∪A_{2}∪A_{3}∪A_{4}∪A_{5})=1-P(A_{1}^{$c$}∩A_{2}^{$c$}∩A_{3}^{$c$}∩A_{4}^{$c$}∩A_{5}^{$c$})=1-0.59049=0.40951

6 0
3 years ago
I need help, I don't know how to do it.
Sindrei [870]

Answer:

Step-by-step explanation:

to solve this problem we can use the Pythagorean theorem

UT and TL are the legs, while LU is the hypotenuse

We have to find LU so we can proceed like this

x^2 + (x+1)^2 = LU^2

x^2 + x^2 + 1 + 2x = LU^2

2x^2 + 2x + 1 = LU^2

LU = +/- \sqrt{2x^2+2x+1

we have to take only the positive value because a length can’t be negative.

2x^2 + 2x + 1 is positive for every value of x, so the final answer is

\sqrt{2x^2+2x+1}

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schepotkina [342]
Consider this option; make a design according to the local requirements.

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3 years ago
Tom deposited $2410 in a bank that pays 12% interest, compounded monthly. Find the amount he will have at the end of 3 years.
OLEGan [10]

Answer:

Base amount: $2,410.00

Interest Rate: 12% (yearly)

Effective Annual Rate: 12.68%

Calculation period: 3 years

$3,448.15

Step-by-step explanation:

The generic formula used in this compound interest calculator is

V = P(1+r/n)^(nt)

V = the future value of the investment

P = the principal investment amount

r = the annual interest rate

n = the number of times that interest is compounded per year

t = the number of years the money is invested for

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