Help please <br> 3 |X-4| +1 = 19

The slope of a line is 1, and the y-intercept is -1. what is the equation of the line written in slope-intercept form?

elena-s [515]

The m in the equation is the slope and the y-intercept is the b.
y=1x-1
y=mx+b

4 0

3 years ago

You toss a pair of dice. (a determine the number of possible pairs of outcomes. you toss a pair of dice. (a determine the number

Eduardwww [97]

(a) $^{6}C_1 * ^{6}C_1 = 36$ different possibilities
(b) $P(even die 1): \frac{1}{2}$
$P(even die 2): \frac{1}{2}$

So, there is a 1 in 4 chance that both dice will show an even.

3 0

2 years ago

Triangle JKL has vertices J(2,5), K(1,1), and L(5,2). Triangle QNP has vertices Q(-4,4), N(-3,0), and P(-7,1). Is (triangle)JKL

Tems11 [23]

Answer:

Yes they are

Step-by-step explanation:

In the triangle JKL, the sides can be calculated as following:

J(2;5); K(1;1)

=> JK = $\sqrt{(1-2)^{2} + (1-5)^{2} } = \sqrt{(-1)^{2}+(-4)^{2} } = \sqrt{1+16}=\sqrt{17}$

J(2;5); L(5;2)

=> JL = $\sqrt{(5-2)^{2} + (2-5)^{2} } = \sqrt{3^{2}+(-3)^{2} } = \sqrt{9+9}=\sqrt{18} = 3\sqrt{2}$

K(1;1); L(5;2)

=> KL = $\sqrt{(5-1)^{2} + (2-1)^{2} } = \sqrt{4^{2}+1^{2} } = \sqrt{1+16}=\sqrt{17}$

In the triangle QNP, the sides can be calculate as following:

Q(-4;4); N(-3;0)

=> QN = $\sqrt{[-3-(-4)]^{2} + (0-4)^{2} } = \sqrt{1^{2}+(-4)^{2} } = \sqrt{1+16}=\sqrt{17}$

Q (-4;4); P(-7;1)

=> QP = $\sqrt{[-7-(-4)]^{2} + (1-4)^{2} } = \sqrt{(-3)^{2}+(-3)^{2} } = \sqrt{9+9}=\sqrt{18} = 3\sqrt{2}$

N(-3;0); P(-7;1)

=> NP = $\sqrt{[-7-(-3)]^{2} + (1-0)^{2} } = \sqrt{(-4)^{2}+1^{2} } = \sqrt{16+1}=\sqrt{17}$

It can be seen that QPN and JKL have: JK = QN; JL = QP; KL = NP

=> They are congruent triangles

7 0

3 years ago

Read 2 more answers

12 1/2 as a fraction in the simplest form

djverab [1.8K]

12 = 12/1 = 24/2, 24/2+1/2=25/2 so 25/2, and it's in simplest form because 2 can't go into 25

8 0

3 years ago

A new security system needs to be evaluated in the airport. The probability of a person being a security hazard is 4%. At the ch

ivolga24 [154]

Answer:

(a) 0.9412

(b) 0.9996 ≈ 1

Step-by-step explanation:

Denote the events a follows:

$P$ = a person passes the security system

$H$ = a person is a security hazard

Given:

$P (H) = 0.04,\ P(P^{c}|H^{c})=0.02\ and\ P(P|H)=0.01$

Then,

$P(H^{c})=1-P(H)=1-0.04=0.96\\P(P|H^{c})=1-P(P|H)=1-0.02=0.98\\$

(a)

Compute the probability that a person passes the security system using the total probability rule as follows:

The total probability rule states that: $P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})$

The value of P (P) is:

$P(P)=P(P|H)P(H)+P(P|H^{c})P(H^{c})\\=(0.01\times0.04)+(0.98\times0.96)\\=0.9412$

Thus, the probability that a person passes the security system is 0.9412.

(b)

Compute the probability that a person who passes through the system is without any security problems as follows:

$P(H^{c}|P)=\frac{P(P|H^{c})P(H^{c})}{P(P)} \\=\frac{0.98\times0.96}{0.9412} \\=0.9996\\\approx1$

Thus, the probability that a person who passes through the system is without any security problems is approximately 1.

7 0

2 years ago

Help please 3 |X-4| +1 = 19