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masha68 [24]
2 years ago
12

These are isosceles equatorial triangle questions

Mathematics
1 answer:
vovikov84 [41]2 years ago
6 0

Answer:

Step-by-step explanation:

1) ABCD rectangle

In Δ ABE

∠BAE +  ∠B + ∠AEB = 180 {angle sum property}

   39 + 90 + ∠AEB = 180

             129 + ∠AEB = 180

                       ∠AEB = 180 - 129

                      ∠AEB = 51

∠AEB + ∠AED + ∠CED = 180      {Straight line angles}

            51 + x + 66 = 180

              117 + x  = 180

                      x = 180 - 117

                    x = 63

2) XYZ  equilateral triangle

In equilateral triangle each angle = 60°

∠XZY = 60

∠XZY + ∠XZW = 180            {linear pair}

 60+ ∠XZW = 180

            ∠XZW = 180 - 60

∠XZW = 120

In ΔXZW,

120 + 35 +x = 180  {angle sum property of triangle}

        155 +x = 180

                 x = 180 - 155

                x = 25

PQR isosceles triangle

PQ = PR

∠PRQ = ∠Q =  69°

∠PRS + ∠PRQ = 180   {linear pair}

 ∠PRS + 69 = 180

        ∠PRS = 180 - 69

        ∠PRS = 111

In ΔPRS

x + 111 + 31 = 180         {Angle sum  property of triangle}

         x + 142 = 180

                x = 180 - 142

              x = 38

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(ii) Angle DOE would equal 42°. We can see this because angles on a straight line add up to 180°, and 90 + 48 = 138, so we can do 180 - 138 = 42°.


I hope this helps!

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Assume that females have pulse rates that are normally distributed with a mean of μ=73.0 beats per minute and a standard deviati
Gennadij [26K]

Answer:

a. the probability that her pulse rate is less than 76 beats per minute is 0.5948

b. If 25 adult females are randomly​ selected,  the probability that they have pulse rates with a mean less than 76 beats per minute is 0.8849

c.   D. Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

Step-by-step explanation:

Given that:

Mean μ =73.0

Standard deviation σ =12.5

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 76 beats per minute.

Let X represent the random variable that is normally distributed with a mean of 73.0 beats per minute and a standard deviation of 12.5 beats per minute.

Then : X \sim N ( μ = 73.0 , σ = 12.5)

The probability that her pulse rate is less than 76 beats per minute can be computed as:

P(X < 76) = P(\dfrac{X-\mu}{\sigma}< \dfrac{X-\mu}{\sigma})

P(X < 76) = P(\dfrac{76-\mu}{\sigma}< \dfrac{76-73}{12.5})

P(X < 76) = P(Z< \dfrac{3}{12.5})

P(X < 76) = P(Z< 0.24)

From the standard normal distribution tables,

P(X < 76) = 0.5948

Therefore , the probability that her pulse rate is less than 76 beats per minute is 0.5948

b.  If 25 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.

now; we have a sample size n = 25

The probability can now be calculated as follows:

P(\overline X < 76) = P(\dfrac{\overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{ \overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}})

P( \overline X < 76) = P(\dfrac{76-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{76-73}{\dfrac{12.5}{\sqrt{25}}})

P( \overline X < 76) = P(Z< \dfrac{3}{\dfrac{12.5}{5}})

P( \overline X < 76) = P(Z< 1.2)

From the standard normal distribution tables,

P(\overline X < 76) = 0.8849

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

In order to determine the probability in part (b);  the  normal distribution is perfect to be used here even when the sample size does not exceed 30.

Therefore option D is correct.

Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

5 0
2 years ago
The following table shows a proportional relationship between mmm and nnn.
Marina CMI [18]

Answer:

70707mmm = 111nnn

Step-by-step explanation:

Using the basic equation of a line:

y = mx + c;. where m is slope and c is intercept on y axis.

Let mmm = y and nnn = x

(i) 333 = 212121m + c

(ii) 555 = 353535m + c

Making c the subject of the formula in both (i) and (ii)

c = 333 - 212121m = 555 - 353535m

353535m -212121m = 555 - 333

141414m = 222

m = 111/70707

Substitute in (i) above

c = 333 -333 = 0

Hence; y = 111/70707x + c

Finally, mmm = 111/70707 nnn

i.e. 70707mmm = 111nnn

Hope this helps.

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