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3 years ago

The points A,B,C and D lie in a straight line.

Mathematics

1 answer:

sattari [20]3 years ago

5 0

If we had AB: BC: CD, we could easily have solved that problem. In order to combine these ratios, we need to have the same number for BC. We can create this number by finding LCM (Least Common Multiple) for 5 and 3, which is 15. Then, we can write ratios of AB:BC = 6:15 and BC:CD=15:20. Now, we can easily combine these ratios. AB:BC:CD = 6:15:20. Then, 6k+15k+20k = 82 and k=2 cm. And BC = 30 cm

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Which is the x coordinate of the point on the graph ?

dimaraw [331]

Answer:

-5

Step-by-step explanation:

Cuz it lines up to -5 on x-axis

4 0

2 years ago

Read 2 more answers

Please help me due tmm second question

AURORKA [14]

Not sure if the math is correct but I think that it is $199.5

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3 years ago

g An urn contains 150 white balls and 50 black balls. Four balls are drawn at random one at a time. Determine the probability th

xxTIMURxx [149]

Answer:

With replacement, 0.2109 = 21.09% probability that there are 2 black balls and 2 white balls in the sample.

Without replacement, 0.2116 = 21.16% probability that there are 2 black balls and 2 white balls in the sample.

Step-by-step explanation:

For sampling with replacement, we use the binomial distribution. Without replacement, we use the hypergeometric distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Sampling with replacement:

I consider a success choosing a black ball, so $p = \frac{50}{150+50} = \frac{50}{200} = 0.25$

We want 2 black balls and 2 white, 2 + 2 = 4, so $n = 4$ , and we want P(X = 2).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{4,2}.(0.25)^{2}.(0.75)^{2} = 0.2109$

With replacement, 0.2109 = 21.09% probability that there are 2 black balls and 2 white balls in the sample.

Sampling without replacement:

150 + 50 = 200 total balls, so $N = 200$

Sample of 4, so $n = 4$

50 are black, so $k = 50$

We want P(X = 2).

$P(X = 2) = h(2,200,4,50) = \frac{C_{50,2}*C_{150,2}}{C_{200,4}} = 0.2116$

Without replacement, 0.2116 = 21.16% probability that there are 2 black balls and 2 white balls in the sample.

3 0

2 years ago

What is the length of the side labeled x?

Scorpion4ik [409]

Answer:

AB = 42.15 units

Step-by-step explanation:

In triangle ABD,

By applying Cosine rule in this triangle,

cos(30)°= $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

$\frac{\sqrt{3} }{2}$ = $\frac{AD}{AB}$

$\frac{\sqrt{3}}{2}=\frac{AD}{47}$

AD = $\frac{47\sqrt{3}}{2}$

By applying tangent rule in ΔACD,

tan(44)° = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

tan(44)° = $\frac{AD}{x}$

0.9657 = $\frac{\frac{47\sqrt{3}}{2}}{x}$

0.9657 = $\frac{47\sqrt{3}}{2x}$

x = $\frac{47\sqrt{3}}{2(0.9657)}$

x = 42.15

≈ 42.2 units

4 0

2 years ago

PLEASE HELP ASAP!

jarptica [38.1K]

$281 = 5%

The total amount would be $5,620

8 0

3 years ago