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3 years ago

1.

Mathematics

2 answers:

Anna007 [38]3 years ago

5 0

Answer:

1) The correct option is C. (2) The correct option is D. (3) The correct option is B. (4) The correct option is D. (5) The correct option is D.

Step-by-step explanation:

The slope formula is

$m=\frac{y_2-y_1}{x_2-x_1}$

(1)

Two points are (-2,5) and (1,4).

$m=\frac{4-5}{1-(-2)}=\frac{-1}{3}tex]Therefore option C is correct.(2)Use the above mentioned formula for each pair of coordinates.[tex]m=\frac{10-13}{17-12}=\frac{-3}{5}$

$m=\frac{10-15}{13-16}=\frac{-5}{-3}=\frac{5}{3}$

$m=\frac{10-7}{3-0}=\frac{3}{3}=1$

$m=\frac{18-13}{8-11}=\frac{5}{-3}=\frac{-5}{3}$

Therefore option D is correct.

(3)

The pair of points (6, y) and (10, -1). The slope is $\frac{1}{4}$ .

$\frac{1}{4}=\frac{-1-y}{10-6}$

$\frac{1}{4}=\frac{-1-y}{4}$

$1=-1-y$

$y=-2$

Therefore option B is correct.

(4)

For vertical line the x coordinates always remains the same. Therefore when we subtract the same number we get zero in the denominator, therefore the value of slope is undefined for a vertical line.

Therefore option D is correct.

(5)

Two points from the table are (2,110) and (3,165).

$m=\frac{165-110}{3-2}=\frac{55}{1}$

Therefore option D is correct.

Tanya [424]3 years ago

4 0

Answer:

For 1: The correct option is C.

For 2: The correct option is D.

For 3: The correct option is B.

For 4: the correct option is D.

For 5: The correct option is D.

Step-by-step explanation:

For 1:

To calculate the slope of a line formed by two points, we use the formula:

$Slope=\frac{y_2-y_1}{x_2-x_1}$ ....(1)

Points given are (-2,5) and (1,4)

$Slope=\frac[4-5}{1-(-2)}=\frac{-1}{3}$

Hence, the correct option is C.

For 2:

Using equation 1, we calculate the slopes for every options, we get:

Option A: Points are (12,13) and (17,10)

$Slope=\frac{10-13}{17-12}=\frac{-3}{5}$

Option B: Points are (16,15) and (13,10)

$Slope=\frac{10-15}{13-16}=\frac{-5}{-3}=\frac{5}{3}$

Option C: Points are (0,7) and (3,10)

$Slope=\frac{10-7}{3-0}=\frac{3}{3}=1$

Option D: Points are (11,13) and (8,18)

$Slope=\frac{18-13}{8-11}=\frac{5}{-3}=\frac{-5}{3}$

Hence, the correct option is D.

For 3:

We are given two points (6,y) and (10,-1) and the slope of the line is $\frac{1}{4}$

Using equation 1, we get

$\frac{1}{4}=\frac{-1-y}{10-6}$

$\frac{-1-y}{4}=\frac{1}{4}$

$-1-y=1\\y=-2$

Hence, the correct option is B.

For 4:

The slope of any line is $\tan\theta$ , where $\theta$ is the angle made by the line with the positive x-axis in counter-clockwise direction.

So, the vertical line will form 90° with x-axis and hence, $\theta =90^o$

As, $\tan90^o=\infty$

Hence, the correct option is D.

For 5:

The given data is forming a linear relation. So, the slope will be same throughout its entire length.

The points taken for the calculation of slope are (2,110) and (3,165)

$Slope=\frac{165-110}{3-2}=\frac{55}{1}$

Hence, the correct option is D.

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Answer:

a) Let the random variable X= "number of these tracks where SBIRS detects the object." in order to use the binomial probability distribution we need to satisfy some conditions:

1) Independence between the trials (satisfied)

2) A value of n fixed , for this case is 20 (satisfied)

3) Probability of success p =0.2 fixed (Satisfied)

So then we have all the conditions and we can assume that:

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$P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456$

$P(X=16)=(20C16)(0.8)^{16} (1-0.8)^{20-16}=0.218$

$P(X=17)=(20C17)(0.8)^{17} (1-0.8)^{20-17}=0.205$

$P(X=18)=(20C18)(0.8)^{18} (1-0.8)^{20-18}=0.137$

$P(X=19)=(20C19)(0.8)^{19} (1-0.8)^{20-19}=0.058$

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$P(X\geq 15)=0.804208$

e) $E(X) = np = 20*0.8 = 16$

Step-by-step explanation:

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".

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

Let the random variable X= "number of these tracks where SBIRS detects the object." in order to use the binomial probability distribution we need to satisfy some conditions:

1) Independence between the trials (satisfied)

2) A value of n fixed , for this case is 20 (satisfied)

3) Probability of success p =0.2 fixed (Satisfied)

So then we have all the conditions and we can assume that:

$X \sim Bin(n =20, p=0.8)$

Part b

$X \sim Bin(n =20, p=0.8)$

Part c

For this case we just need to replace into the mass function and we got:

$P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456$

Part d

For this case we want this probability: $P(X\geq 15)$

And we can solve this using the complement rule:

$P(X \geq 15) = P(X=15)+ .....+P(X=20)$

$P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456$

$P(X=16)=(20C16)(0.8)^{16} (1-0.8)^{20-16}=0.218$

$P(X=17)=(20C17)(0.8)^{17} (1-0.8)^{20-17}=0.205$

$P(X=18)=(20C18)(0.8)^{18} (1-0.8)^{20-18}=0.137$

$P(X=19)=(20C19)(0.8)^{19} (1-0.8)^{20-19}=0.058$

$P(X=20)=(20C20)(0.8)^{20} (1-0.8)^{20-20}=0.012$

$P(X\geq 15)=0.804208$

Part e

The expected value is given by:

$E(X) = np = 20*0.8 = 16$

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