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likoan [24]
2 years ago
5

I would really appreciate it if someone helped answer these 4 questions. I will rate 5 stars. Thank you (:

Mathematics
1 answer:
ELEN [110]2 years ago
6 0

Answer:

7. 13.6

8. 19.5

9. 6.5

10. 12.6

Step-by-step explanation:

Recall the three main trig functions

Sine = opposite / hypotenuse

Cosine = adjacent / hypotenuse

Tangent = opposite / adjacent

( remember hypotenuse = longest side length , opposite = side length opposite of angle , and adjacent = side length thats not the opposite or hypotenuse )

We will use these to solve each problem

7.

We are given :

  • An angle with a measure of 39 degrees
  • The angles opposite side length
  • The adjacent side as the unknown

When dealing with opposite and adjacent we use tangent

We have tan = opp / adj

==> plug in opp = 11 and adj = x as well as given angle 39

tan(39) = 11/x

==> multiply both sides by x

xtan(39) = 11

divide both sides by tan(39)

x = 11/tan(39)

plugging this into a calculator , we get x = 13.6 ( rounded )

8.

We are given :

  • an angle with a measure of 46 degrees
  • the hypotenuse which has a length of 28
  • and the adjacent as the unknown

When dealing with adjacent and hypotenuse we use cos

We have cos = adj / hyp

==> plug in given angle 46 , adj = x and hyp = 28

cos(46) = x/28

==> multiply both sides by 28

x = 28cos(46)

plugging this into a calculator we get  x = 19.5 ( rounded )

9.

We are given :

  • an angle with a measure of 51 degrees
  • its opposite side length with a length of 8
  • the adjacent side length as the unknown

When dealing with the opposite and adjacent we use tangent

We have tan = opp / adj

==> plug in 51 degrees for angle , opp = 8 and adj = x

tan(51) = 8/x

==> multiply both sides by x

xtan(51) = 8

==> divide both sides by tan(51)

x=8/tan51

plugging this into a calculator we get that x = 6.5 ( rounded )

10.

We are given:

  • an angle with a measure of 24 degrees
  • the hypotenuse which has a length of 31
  • the side length opposite of given angle as the unknown

When dealing with the opposite and hypotenuse we use sine

We have sin = opp / hyp

==> plug in angle as 24 , opp = x and hyp = 31

sin(24) = x / 31

==> multiply both sides by 31

31sin(24) = x

plugging this into a calculator we get that x = 12.6 ( rounded )

And we are done!

Let me know if you have any doubts in the comments ! : )

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Saul decides to use the IQR to measure the spread of the data. Saul calculates the IQR of the data set to be 27.
padilas [110]

Answer:

78

Step-by-step explanation:

The IQR is quartile 3 - quartile 1. First, we need to find the mean of the dataset, which is 50 -- the fifth number. Then, the median of the dataset on the left of the fifth number is the first quartile, and the median of the dataset on the right is the third. We get Q1 to then be halfway between 30 and 50, or 40, and Q3 to be halfway between 56 and n, so Q3 = (56+n)/2. Since we need Q3-Q1=27, or (56+n)/2-40=27, we have (56+n)/2=67 and 56+n=134, so n = 134-56=78

3 0
3 years ago
11. Maria's age is 3 years more than twice George's age. Which expression represents George's age in terms of Maria's?
leonid [27]

Answer:

C

Step-by-step explanation:

Okay, the catch of this question is that they do a very good job of explaining Maria's age in terms of George's age, but they leave George's age in terms of Maria's all up to you.

First start off by doing an expression of what they explicitly give you. Maria's age in terms of George's age.

Let's use variables g, representing George's age and m representing Maria's age

m = 2g + 3

Okay, this is all dandy and all, but they ask us for George's age in terms of Maria's, so we need to isolate for g.

subtract the 3 from both sides, like so:

m - 3 = 2g

then divide 2 from both sides: (remember we're dividing the whole thing)

(m-3)/2 = g

Now we have an expression for George's age in terms of Maria's.

g = (m-3)/2 or g = \frac{m-3}{2}

The answer that gives us this, is C.

6 0
2 years ago
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