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Natali5045456 [20]
3 years ago
12

Using the triangle theorem solve this triangle.​

Mathematics
2 answers:
timofeeve [1]3 years ago
4 0

Answer:

take 30 degree as reference angle

using sin rule

sin 30=p/h

1/2=8/h(do cross multiplication)

h*1=8*2

h=16

therefore hypotenuse (b)=16

now for base(a)

using cos rule

cos 30 =b/h

\sqrt{3}/2=b/16(do cross multiplication)

b*2=16*\sqrt{3}

b=16\sqrt{3}/2

b=8\sqrt{3}

b=13.85

b=13.9

Step-by-step explanation:

Blizzard [7]3 years ago
3 0

Answer:

8 and 8√3

Step-by-step explanation:

Sin90 = b/8

1 x 8 =b

b=8

Tan 30 = 8/a

1/√3 = 8/a

a=8√3

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Harlamova29_29 [7]

I typed right on the problem set.

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3 years ago
) One year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million. Suppose a samp
Nutka1998 [239]

Answer:

Probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.

Step-by-step explanation:

We are given that one year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million.

Suppose a sample of 400 major league players was taken.

<em>Let </em>\bar X<em> = sample average salary</em>

The z-score probability distribution for sample mean is given by;

                 Z = \frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} }  ~ N(0,1)

where, \mu = mean salary = $1.5 million

            \sigma = standard deviation = $0.9 million

             n = sample of players = 400

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the average salary of the 400 players exceeded $1.1 million is given by = P(\bar X > $1.1 million)

    P(\bar X > $1.1 million) = P( \frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} } >  \frac{ 1.1-1.5}{{\frac{0.9}{\sqrt{400} } }} } ) = P(Z > -8.89) = P(Z < 8.89)

<em>Now, in the z table the maximum value of which probability area is given is for critical value of x = 4.40 as 0.99999. So, we can assume that the above probability also has an area of 0.99999 or nearly close to 1.</em>

Therefore, probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.

4 0
3 years ago
Assertion - if the mean of five observations X, X+2, X+4, X+6, X+8 is 11 then,Mean of last 3 observations is 8. Reason - Range=
FinnZ [79.3K]
A is false but R is true (the mean of the last 3 values is not 8 since x=7)
6 0
2 years ago
Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the sq
TiliK225 [7]

Answer:

The perimeter of rectangle is 18\ cm

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

x=y+5 ----> equation A

120=xy+2x^{2}+2y^{2}  ---> equation B (area of the constructed figure)

substitute the equation A in equation B

120=(y+5)y+2(y+5)^{2}+2y^{2}

120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0

using a graphing calculator -----> solve the quadratic equation

The solution is

y=2\ cm

Find the value of x

x=y+5 ----> x=2+5=7\ cm

Find the perimeter of rectangle

P=2(x+y)=2(7+2)=18\ cm

4 0
3 years ago
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That would be $34.000.000 since it’s just subtracting ( less than ) the main number minus the number she didn’t give away.
7 0
3 years ago
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