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3 years ago

For an angle θ with the point (−5, −12) on its terminating side, what is the value of cosine?

Mathematics

1 answer:

viva [34]3 years ago

8 0

Answer:

option C. $-\frac{5}{13}$

Step-by-step explanation:

we have that

The point (-5,-12) belong to the III quadrant

The value of the cosine is negative

Applying the Pythagoras Theorem

Find the value of the hypotenuse

$h^{2}=5^{2}+12^{2}\\ h^{2} =25+144\\ h^{2}=169\\h=13\ units$

The value of cosine of angle θ is the ratio between the side adjacent to angle θ and the hypotenuse

$cos(\theta)=-\frac{5}{13}$

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Jason is making a fruit salad. He mixes in 3 1/4 cups of orange melon and 2 2/3 cups of green melon. How many cups of melon does

Strike441 [17]

Answer:

5 11/12 cups of melon

Step-by-step explanation:

The cups of melon he puts in the fruit salad is:

Number of cups of orange melon + Number of cups of green melon

= 3 1/4 cups + 2 2/3 cups

3 + 2 + (1/4 + 2/3)

The Least common denominator is 12

5 + (3 × 1 +4 × 2/12)

5 + (3 +8/12)

5 11/12 cups

Therefore, Jason put in 5 11/12 cups of melon in the fruit salad.

7 0

3 years ago

A school will offer pizza on Friday's if at least 30% of the students will buy it. A sample of 50 students asked if they would b

Whitepunk [10]

Answer:

0.0614

Step-by-step explanation:

Solution:-

- The school offers pizza on friday when at-least 30% students are willing to buy.

- The minimum required proportion of students, p = 30%

- A sample of n = 50 students were taken and out of the sample x = 10 people responded willing to buy pizza.

- We will denote a random variable X: the number of students willing to buy Pizza on fridays.

- For the sample of n = 50, for Pizza to be offered on friday the expected number of student who should opt for buying must be at-least:

Expected ( Mean - u ) = n*p = 50*0.3 = 15 people.

- The standard deviation for the normal distribution can be determined as follows:

standard deviation ( s ) = √n*p*(1-p)

= √50*0.3*(0.7)

= √10.5 = 3.2404

- We will assume that the random variable X follows normal distribution:

X ~ Norm ( 15 , 3.2404^2 )

- To determine the probability of sample of size n = 50 with proportion or lower. The number of people willing to buy pizza on friday as per survey are x = 10.

- Evaluate the standard normal ( Z-score ):

P ( X < x ) = P ( Z < ( x - u ) / s )

P ( X < 10 ) = P ( Z < ( 10 - 15 ) / 3.2404 )

P ( X < 10 ) = P ( Z < -1.54301 )

- Use the standard normal tables to determine the value of P ( Z < -1.54301 ):

P ( X < 10 ) = P ( Z < -1.54301 ) = 0.0614

Answer: The probability of getting a sample with the proportion or lower given a population with a proportion of .30 is 0.0614.

5 0

3 years ago

Kim, Laura and Molly share £385

trapecia [35]

Set x equal to the amount of money Kim gets, and y for Molly's money.

x = 2/5y, since the ratio is 2:5.
y = 105 + x, since Molly has 105 more pounds than Kim.

Substitute x into this equation, so that y = 105 + 2/5y. Subtract 2/5y from both sides to get 3/5y = 105. Divide each side by 0.6 (equivalent to 3/5) and you get y = 175, which is how much Molly has. Kim gets 2/5 of Molly's share (or 105 fewer pounds), so she has 70.

70 + 175 (Kim and Molly's shares) is equal to 245. Therefore, Laura receives the remaining 140 pounds.

140/385 = a/100
Cross multiply so that 385a is 14000. Divide by 385 to get 36.4 (rounded).

Thus, Laura receives about 36.4% of the total money. Hope this helps (:

5 0

3 years ago

Y=3x-1 y=-2x+4 what is the sum of x and y in the solution to the system

prohojiy [21]

Answer:

y=1,2 y=2

Step-by-step explanation:

3 0

2 years ago

My sister can walk from school to home in 35 minutes. I can walk from school to home in 20 minutes. But today I stayed for some

Verizon [17]

Answer: