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3 years ago

Can someone help me with this problem, please. The problem is attached.

Mathematics

1 answer:

timurjin [86]3 years ago

3 0

y = 3 is the line of reflection

Under a reflection in a line, corresponding points of the original and it's image should be equidistant from the line of reflection

y = 3 is the horizontal line passing through all the points with a y-coordinate of 3

A is 1 unit above and A' is 1 unit below the line

B is 3 units above and B' is 3 units below

C is 1 unit below and C' is 1 unit above

D is 1 unit below and D' is 1 unit above

The vertices of the figure and the image are all equidistant from y = 3

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A box contains 24 transistors,4 of which are defective. If 4 are sold at random,find the following probabilities. i. Exactly 2 a

zavuch27 [327]

SOLUTION

This is a binomial probability. For i, we will apply the Binomial probability formula

i. Exactly 2 are defective

Using the formula, we have

$\begin{gathered} P_x=^nC_x\left(p^x\right?\left(q^{n-x}\right) \\ Where\text{ } \\ P_x=binomial\text{ probability} \\ x=number\text{ of times for a specific outcome with n trials =2} \\ p=\text{ probability of success = }\frac{4}{24}=\frac{1}{6} \\ q=probability\text{ of failure =1-}\frac{1}{6}=\frac{5}{6} \\ ^nC_x=\text{ number of combinations = }^4C_2 \\ n=\text{ number of trials = 4} \end{gathered}$

Note that I made the probability of being defective as the probability of success = p

and probability of none defective as probability of failure = q

Exactly 2 are defective becomes the binomial probability

$\begin{gathered} P_x=^4C_2\times\lparen\frac{1}{6})^2\times\lparen\frac{5}{6})^{4-2} \\ P_x=6\times\frac{1}{36}\times\frac{25}{36} \\ P_x=\frac{25}{216} \\ =0.1157 \end{gathered}$

Hence the answer is 0.1157

(ii) None is defective becomes

$\begin{gathered} \lparen\frac{5}{6})^4=\frac{625}{1296} \\ =0.4823 \end{gathered}$

hence the answer is 0.4823

(iii) All are defective

$\begin{gathered} \lparen\frac{1}{6})^4=\frac{1}{1296} \\ =0.00077 \end{gathered}$

(iv) At least one is defective

This is 1 - probability that none is defective

$\begin{gathered} 1-\lparen\frac{5}{6})^4 \\ =1-\frac{625}{1296} \\ =\frac{671}{1296} \\ =0.5177 \end{gathered}$

Hence the answer is 0.5177

3 0

1 year ago

Solve inequalities.

grigory [225]

Answer:

10. 7n - 1 < -8

Isolate the variable, n. Do the opposite of PEMDAS. Treat the < as equal sign, what you do to one side, you do to the other. First, add 1 to both sides:

7n - 1 (+1) < - 8 (+1)

7n < - 8 + 1

7n < - 7

Isolate the variable, n. Divide 7 from both sides:

(7n)/7 < (-7)/7

n < -7/7

n < -1

n < -1 is your answer.

11. 3 > -7v + 4v

Combine like terms, then isolate the variable, v. First, add -7v and 4v together.

3 > (-7v + 4v)

3 > (4v - 7v)

3 > (-3v)

Isolate the variable, v. Divide -3 from both sides. Note that since you are dividing a negative number, you must flip the sign:

(3)/-3 > (-3v)/-3

3/-3 > v

-1 < v

v > -1 is your answer.

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3 years ago

Which of the following equations is the result after the first step in solving 3x + 6 = 12?

tensa zangetsu [6.8K]

3x=18 because you add the like terms 6 and 12

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3 years ago

Round 5.785 to the nearest hundreth

lawyer [7]

The answer would be 5.79
Hope I helped :)

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1/6 (12t -18)<br> ANSWER ASAP

NISA [10]

The answer for me is 2t -3 I maybe git it wrong but I hope I got it right

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3 years ago

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