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2 years ago

20 points if you answer this question

Mathematics

1 answer:

Svetllana [295]2 years ago

7 0

Answer:

∠ KLJ = 70°

Step-by-step explanation:

The segment KL joins the midpoints of 2 sides of the triangle and is therefore parallel to the third side HG , then

∠ KLJ and ∠ HGL are corresponding angles and are congruent , so

∠ KLJ = 70°

You might be interested in

( adding and subtracting unlike fractions in word problems)

PilotLPTM [1.2K]

Answer:

2/3 cup

Step-by-step explanation:

first you need to convert the fractions so that they have the same denominator (1/3 turns into 2/6)

then you just add up the numerators (2+2=4..... 4/6)

you can stop there or you can simplify it (4/6 turns into 2/3)

5 0

3 years ago

Suppose that 40 percent of the drivers stopped at State Police checkpoints in Storrs on Spring Weekend show evidence of driving

lesantik [10]

Answer:

a) 0.778

b) 0.9222

c) 0.6826

d) 0.3174

e) 2 drivers

Step-by-step explanation:

Given:

Sample size, n = 5

P = 40% = 0.4

a) Probability that none of the drivers shows evidence of intoxication.

$P(x=0) = ^nC_x P^x (1-P)^n^-^x$

$P(x=0) = ^5C_0 (0.4)^0 (1-0.4)^5^-^0$

$P(x=0) = ^5C_0 (0.4)^0 (0.60)^5$

$P(x=0) = 0.778$

b) Probability that at least one of the drivers shows evidence of intoxication would be:

P(X ≥ 1) = 1 - P(X < 1)

$= 1 - P(X = 0)$

$= 1 - ^5C_0 (0.4)^0 * (0.6)^5$

$= 1 - 0.0778$

$= 0.9222$

c) The probability that at most two of the drivers show evidence of intoxication.

P(x≤2) = P(X = 0) + P(X = 1) + P(X = 2)

$^5C_0 (0.4)^0 (0.6)^5 + ^5C_1 (0.4)^1 (0.6)^4 + ^5C_2 (0.4)^2 (0.6)^3$

$= 0.6826$

d) Probability that more than two of the drivers show evidence of intoxication.

P(x>2) = 1 - P(X ≤ 2)

$= 1 - [^5C_0 (0.4)^0 (0.6)^5 + ^5C_1 (0.4)^1 (0.6)^4 + ^5C_2 * (0.4)^2 (0.6)^3]$

$= 1 - 0.6826$

$= 0.3174$

e) Expected number of intoxicated drivers.

To find this, use:

Sample size multiplied by sample proportion

n * p

= 5 * 0.40

= 2

Expected number of intoxicated drivers would be 2

7 0

3 years ago

(x + 7)(x + 10) = what is the answer

ch4aika [34]

We can use FOIL to solve.

(x + 7)(x + 10)

(x * x) + (x * 7) + (7 * x) + (7 * 10)

x² + 7x + 7x + 70

x² + 14x + 70

Best of Luck!

8 0

3 years ago

The olympics are held every four years. In 2016, the XXXI olympiad were held in Rio de Janeiro,Brazil. Determine the year of the

Anna007 [38]

Answer:

First Olympic held in year 1896.

Step-by-step explanation:

Number of Olympiad held in Rio = XXXI = 31st

Difference of years in two consecutive Olympiads = 4 years

Number of years spent in 31 Olympiads can be calculated by,

Number of years spent = (n - 1)d

Here n = number of Olympiads held

d = difference between two consecutive Olympiads

Number of years spent till 31st Olympiads = (31 - 1)×4

= 120 years

Therefore, 1st Olympiad held in the year = 2016 - 120

= 1896

6 0

3 years ago

Does the series converge or diverge? If it converges, what is the sum? Show your work. ∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1

Mekhanik [1.2K]

Answer:

Step-by-step explanation:

Given the series,

∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1

I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)

So,

∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞

There are different types of test to show if a series converges or diverges

So, using Ratio test

Lim n → ∞ (a_n+1 / a_n)

Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))

Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))

Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)

Lim n→ ∞ (-1/2)^(n-n+1)

Lim n→ ∞ (-1/2)^1 = -1/2

Since the limit is less than 0, then, the series converge...

Sum to infinity

Using geometric progression formula

S∞ = a / 1 - r

Where

a is first term

r is common ratio

So, first term is

a_1 = -4(-½)^1-1 = -4(-½)^0 = -4 × 1

a_1 = -4

Common ratio r = a_2 / a_1

a_2 = 4(-½)^2-1 = -4(-½)^1 = -4 × -½ = 2

a_2 = 2

Then,

r = a_2 / a_1 = 2 / -4 = -½

S∞ = -4 / 1--½

S∞ = -4 / 1 + ½

S∞ = -4 / 3/2 = -4 × 2 / 3

S∞ = -8 / 3 = -2⅔

The sum to infinity is -2.67 or -2⅔

Check attachment for better understanding

3 0

3 years ago