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lubasha [3.4K]
3 years ago
13

What is the length of the hypotenuse of this triangle? Round to the nearest tenth.

Mathematics
2 answers:
suter [353]3 years ago
7 0
Hey there! :)

You have to use the Pythagorean theorem: a² + b² = c²

A = 3
3² = 3 × 3 = 9

B = 8
8² = 8 × 8 = 64

64 + 9 = 73

√73 = 8.5

Your answer is 8.5

Hope this helps :)
Phantasy [73]3 years ago
7 0
Hi!

Your answer is 8.5 because:

You have to use the Pythagorean Theorem: a² + b² = c²

a = 3
3² = 9 

b = 8
8² = 64

64 + 9 = 73

The square root of 73 ( rounded to the nearest tenth) is 8.5

I hope this helps you and have a wonderful day!


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An article suggested that yield strength (ksi) for A36 grade steel is normally distributed with μ = 42 and σ = 5.5.
alexandr1967 [171]

Answer:

a)P( X

We want this probability:

P( X >64)

And using the z score formula given by:

z = \frac{x -\mu}{\sigma}

We got:

P( X >64) =P(Z> \frac{64-42}{5.5}) =P(Z>4)=0.0000316

b) For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.674

And if we solve for a we got

a=42 +0.674*5.5=45.707

So the value of height that separates the bottom 75% of data from the top 25% is 45.707.  

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

X \sim N(42,25.5)  

Where \mu=42 and \sigma=5.5

And we want this probability:

P( X

And using the z score formula given by:

z = \frac{x -\mu}{\sigma}

We got:

P( X

We want this probability:

P( X >64)

And using the z score formula given by:

z = \frac{x -\mu}{\sigma}

We got:

P( X >64) =P(Z> \frac{64-42}{5.5}) =P(Z>4)=0.0000316

Part b

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.674

And if we solve for a we got

a=42 +0.674*5.5=45.707

So the value of height that separates the bottom 75% of data from the top 25% is 45.707.  

8 0
3 years ago
Write an equation of a line going through (5,7) and (4 , -4)
Ostrovityanka [42]

Answer:

The equation of this line would be y = 11x - 48

Step-by-step explanation:

To get this equation, we first have to find the slope. We do that with the slope eqaution.

m(slope) = (y2 - y1)/(x2 - x1)

m = (-4 - 7)/(4 - 5)

m = -11/-1

m = 11

Now we can use this slope and either point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - 7 = 11(x - 5)

y - 7 = 11x - 55

y = 11x - 48

6 0
3 years ago
A grocery store sells coffee beans in bulk. What is the price per pound for the coffee?
ehidna [41]
Six dollars is the only answer that seems correct using the graph. Hope this helped.
6 0
3 years ago
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AVprozaik [17]

Answer:

-\frac{35}{2}

Step-by-step explanation:

-5 ÷ \frac{2}{7} = 17\frac{1}{2}

17\frac{1}{2} = -\frac{35}{2}

8 0
3 years ago
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Find the midpoint of the segment with the given endpoints.<br> (3,- 9) and (4, -8)
frez [133]
  • (3,-9)
  • (4,-8)

\boxed{\sf (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}

\\ \sf\longmapsto \left(\dfrac{3+4}{2},\dfrac{-9+8}{2}\right)

\\ \sf\longmapsto \left(\dfrac{7}{2},\dfrac{-1}{2}\right)

3 0
3 years ago
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