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IrinaK [193]
3 years ago
7

In the diagram, line x|| line y. Find the angle measures below.

Mathematics
1 answer:
Yanka [14]3 years ago
5 0

Answer:

<1 = 95

<2 =85

Step-by-step explanation:

<1 = 95

They are alternate exterior angles and alternate exterior angles are equal when the lines are parallel

<1 + <2 = 180  since they form a straight line

95+ <2 =190

Subtract 95 from each side

95-95+<2 =180-95

<2 =85

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Consider a binomial experiment with 15 trials and probability 0.35 of success on a single trial.
DedPeter [7]

Answer:

a

   P(X =  10 ) =  0.0096

b

   P(X = 10 ) =  0.0085

c

 Option A is correct

Step-by-step explanation:

From the question we are told that

     The sample size is   n =  15

     The  probability of success is  p =  0.35

     The number of success we are considering is  r = 10  

 

Now the probability of failure is mathematically evaluated as

        q =  1- p

substituting value

       q =  1- 0.35

       q = 0.65

Now using  the binomial distribution  to find the probability of exactly 10 successes we have that

    P(X =  r ) =  [\left n } \atop {r}} \right. ] * p^r *  q^{n- r}

substituting values

    P(X =  10 ) =  [\left 15 } \atop {10}} \right. ] * p^{10}*  q^{15- 10}

Where  [\left 15 } \atop {10}} \right. ] mean 15 combination 10  which is evaluated with a calculator to obtain  

       [\left 15 } \atop {10}} \right. ]  = 3003

So

      P(X =  10 ) =  3003 * 0.35 ^{10}*  0.65^{15- 10}

       P(X =  10 ) =  0.0096

Now using  the normal distribution to approximate the probability of exactly 10 successes, we have that

  P(X = r ) =  P( r  <  X <   r )

Applying continuity correction

          P(X = r ) =  P( r -0.5 <  X <   r +0.5)

substituting values

        P(X = 10) =  P( 10-0.5 <  X <   10+0.5)

       P(X = 10 ) =  P( 9.5 <  X <   10.5)

Standardizing  

         P(X = r ) =  P( \frac{9.5 -  \mu }{\sigma }  <  \frac{X - \mu }{\sigma }  <  \frac{10.5 - \mu}{\sigma }  )

The  where  \mu is the mean which is mathematically represented as

        \mu  =  n *  p

substituting values

        \mu  =  15 *  0.35

         \mu  =  5.25

The standard deviation is evaluated as      

     \sigma  =  \sqrt{n  *  p  * q }

substituting values

    \sigma  =  \sqrt{15   *  0.35  * 0.65 }

    \sigma  = 1.8473

Thus  

     P(X = 10 ) =  P( \frac{9.5 -  5.25 }{1.8473 }  <  \frac{X - 5.25 }{1.8473 }  <  \frac{10.5 - 5.25}{1.8473 }  )

     P(X = 10 ) =  P( 2.30 < Z <  2.842  )

     P(X = 10 ) = P(Z <  2.842 ) -  P(Z <  2.30   )

From the normal distribution table we obtain the P(Z < 2.841) as

      P(Z < 2.841) = 0.99775

And  the  P(Z < 2.30)

     P(Z < 2.30) =  0.98928

There value can also be obtained from a probability of z calculator at (Calculator dot net website)

So  

    P(X = 10) =   0.99775 - 0.98928

     P(X = 10 ) =  0.0085

Looking at the calculated values for question a and b  we see that the values are fairly different.

8 0
4 years ago
A box is to be constructed with a rectangular base and a height of h cm. the length, l, of the box is 10 cm, and the width, w, i
vivado [14]
There are several information's already given in the question. based on those information's, the answer can be easily determined.
Height of the box = h cm
Length of the box = 10 cm
Width of the box = 2h
Then
Volume of the box = Length * height * width
                              = 10 * h * 2h cubic cm
                              = 20h^2 cm^3
I hope that the above procedure is clear enough for you to understand and it has actually come to your desired help.
5 0
3 years ago
In ΔEFG, the measure of ∠G=90°, EF = 38 feet, and FG = 30 feet. Find the measure of ∠F to the nearest degree.
Mamont248 [21]

Answer:

∠F = 42° to the nearest degree

Step-by-step explanation:

In this question, we are asked to calculate the value of the angle.

Kindly note that since one of the angles we are dealing with in the triangle is 90°, this means that the triangle is a right-angled triangle

Please check attachment for the diagrammatic representation of the triangle

From the diagram, we can identify that the EF is the hypotenuse and the length FG is the adjacent. Thus , the appropriate trigonometric identity to use is the cosine

mathematically;

Cosine of an angle = length of adjacent/length of hypotenuse

Cos F = \frac{30}{38}\\Cos F =  0.7895\\F = Cos^{-1} 0.7895\\

F = 42.07

∠F = 42° to the nearest degree

4 0
3 years ago
Read 2 more answers
1. A trebuchet is a large spring loaded catapult. The spring is attached 23cm on
Rus_ich [418]

Answer:

I think it sould be 16m

Step-by-step explanation:

8 0
3 years ago
1. x=1/(root3-root2). find rootx-(1/rootx) 2. if x=[root(a+2b)+root(a-2b)]/[root(a+2b)-root(a-2b]. show that bx^2-ax+b=0
timofeeve [1]
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6 0
3 years ago
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