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4 years ago

Work out the value of angle x

Mathematics

2 answers:

BabaBlast [244]4 years ago

5 0

base angles theorem means that the base angles of an isosceles triangle like this one are always the same

62+62+x = 180

124 +x = 180

subtract 124 from both sides

x = 56 degrees

<em>hope this helps!</em>

sergeinik [125]4 years ago

4 0

Answer:

Step-by-step explanation:

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Solve for x7(x 2) (x 5)44O -16

babymother [125]

7(x + 2) = 6(x + 5)

7x + 14 = 6x + 30 |subtract 14 from both sides

7x = 6x + 16 |subtract 6x from both sides

x = 16

3 0

3 years ago

20 points Return to questionItem 4Item 4 20 points Police records in the town of Saratoga show that 13 percent of the drivers st

Sladkaya [172]

Answer:

a) 0.1423

b) 0.2977

c) 0.56

Step-by-step explanation:

For each driver stopped for speeding, there are only two possible outcomes. Either they have invalid licenses, or they do not. The probability of a driver having an invalid license is independent from other drivers. So we use the binomial probability distribution to solve this problem.

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.

In this problem we have that:

13 percent of the drivers stopped for speeding have invalid licenses.

This means that $p = 0.13$

14 drivers are stopped

This means that $n = 14$

(a) None will have an invalid license.

This is $P(X = 0)$

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

$P(X = 0) = C_{14,0}.(0.13)^{0}.(0.87)^{14} = 0.1423$

(b) Exactly one will have an invalid license.

This is $P(X = 1)$

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

$P(X = 1) = C_{14,1}.(0.13)^{1}.(0.87)^{13} = 0.2977$

(c) At least 2 will have invalid licenses.

Either less than 2 have invalid licenses, or at least 2 does. The sum of the probabilities of these events is decimal 1. Mathematically, this is

$P(X < 2) + P(X \geq 2) = 1$

We want $P(X \geq 2)$

$P(X \geq 2) = 1 - P(X < 2)$

In which

$P(X < 2) = P(X = 0) + P(X = 1) = 0.1423 + 0.2977 = 0.44$

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.44 = 0.56$

8 0

3 years ago

The rabbit population in a forest area grows at the rate of 9% monthly. if there are 270 rabbits in july, find how many rabbits

sukhopar [10]

We will do multiplication, 270x0.9 to find out how many rabbits grow in the area each month. Using that number we will multiply it by 12 because the problem is asking us to find the number of rabbits grown in the are in one year. Our final answer would be 292.

5 0

3 years ago

An Open rectangular tank of length 18 cm and breadth 16 cm contains water to a depth of 13 cm. The water is poured into a cylind

san4es73 [151]

Answer:

Step-by-step explanation

Volume of tank = l* b*h

= 18*16*13

=3744 cubic cm

Volume of cylinder = volume of tank

πr²h = 3744

3.14* (17/2)² * h = 3744

h= 3744 *2 *2/*17*17*3.14

h=16.5 cm

4 0

3 years ago

Suppose that 5 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that all 5 are not black?

lions [1.4K]

Here's the way I see it: 5 cards are drawn, one by one, without replacement. Half (or 26) of the original deck are black and half (26) are white.

P(5 are not black) = P(5 are red)

P(5 are not black) = P(first card is red) * P(second card is red) * P(third card is red)*P(fourth card is red)*P(fifth card is red) =

(26/52) * (25/51) * (24/50) * (23/49) * (22/48) = 0.025 (answer)

We start with 52 cards. We draw one, leaving 51 cards, 25 of which are red. And so on.

6 0

3 years ago