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lakkis [162]
3 years ago
12

KM bisects ∠LKJ. If m∠LKM = 4x + 12 and m∠MKJ = 6x - 6, find the value of x. *

Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
6 0

Given that,

KM bisects ∠LKJ.

m∠LKM = 4x + 12 and m∠MKJ = 6x - 6

To find,

The value of x.

Solution,

As KM bisects ∠LKJ. It would mean that,

m∠LKM = m∠MKJ

Putting the above values,

4x+12=6x-6

We can solve the above equations as follows :

4x-6x=-12-6

-2x=-18

x=9

Therefore, the value of x is equal to 9.

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The correct option is;
b. Stem and leaf plot

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A stem-and-leaf plot shows the data shape and the densities of the different classes in a graphical form such that the information in the data such as the data characteristics are self displayed by the data numbers arranged in the stem-and-leaf plot. The stem-and-leaf plot keeps the raw numerical data, in the form they were obtained and by their arrangement, outliers are easily spotted.
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Which ordered pair is the best estimate for the solution of the system of equations
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The ordered pair that is the best estimate for the solution of the system of equations is (7, 1/2)

The given system of equations is:

y=-\frac{1}{2}x + 4.......................(1)\\\\y = \frac{1}{2}x-3..........................(2)

Equate equations (1) and (2)

-\frac{1}{2}x + 4=\frac{1}{2}x -3

Solve for x in the equation above

-\frac{1}{2}x -\frac{1}{2}x =-3-4\\\\-x=-7\\\\x=7

Substitute x = 7 into equation (1)

y=-\frac{1}{2}x + 4\\\\y=-\frac{1}{2}(7) + 4\\\\y=\frac{1}{2}

The ordered pair that is the best estimate for the solution of the system of equations is (7, 1/2)

Learn more on system of equations here: brainly.com/question/13729904

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2 years ago
32​% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and a
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Answer:

a) P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

b) P(X> 2)=1-P(X\leq 2)=1-[0.0211+0.0995+0.211]=0.668

c) P(2 \leq x \leq 5)=0.211+0.264+0.218+0.123=0.816

Step-by-step explanation:

1) Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

2) Solution to the problem

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=10, p=0.32)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Part a

P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

Part b

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

P(X=0)=(10C0)(0.32)^0 (1-0.32)^{10-0}=0.0211  

P(X=1)=(10C1)(0.32)^1 (1-0.32)^{10-1}=0.0995

P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

P(X> 2)=1-P(X\leq 2)=1-[0.0211+0.0995+0.211]=0.668

Part c

P(2 \leq x \leq 5)=P(X=2)+P(X=3)+P(X=4)+P(X=5)

P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

P(X=3)=(10C3)(0.32)^3 (1-0.32)^{10-3}=0.264

P(X=4)=(10C4)(0.32)^4 (1-0.32)^{10-4}=0.218

P(X=5)=(10C5)(0.32)^5 (1-0.32)^{10-5}=0.123

P(2 \leq x \leq 5)=0.211+0.264+0.218+0.123=0.816

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