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o-na [289]
2 years ago
7

The sum of interior angles in a triangle are 180 degrees. Angle B and C are congruent. Angle B is twenty less than angle A. Writ

e and solve a system of equations using substitution.
Mathematics
1 answer:
Margarita [4]2 years ago
6 0

Answer:

A = 73.33

B = 53.33

C = 53.33

Step-by-step explanation:

Mathematically, adding the 3 angles would equal 180

Thus;

A + B + C = 180 •••••(i)

Since B and C are congruent, that means they are equal ( we are looking at isosceles triangle)

B = C •••••••••(ii)

Lastly;

B = A -20 ••••••••(iii)

Make a substitution in equation 1;

A + A -20 + A -20 = 180

Since B = C ; C also is A-20

3A -40 = 180

3A = 220

A = 220/3 = 73.33

B = C = A -20 = 73.33 -20 = 53.33

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Noah ran around the track two times. How far did he run in feet? Round your answer to the nearest whole number.
AfilCa [17]

Answer:

237 feet

Step-by-step explanation:

take the circumference (5), square it, and multiply it by pi. Then add 40 for the distance of the two sides. Multiply your answer by two to find the distance for twice around

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What is the solution to the system of equations below? 3x-2y=7 and -3x+5y=5
Zolol [24]

Step-by-step explanation:

So you add one over the other

3x-2y=7

-3x+5y=5

=

3y=12

Then you divide 3 from both sides

(3y)/3=12/3

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Then you substitute the y=4 in to the equation of your choice

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3 years ago
The average THC content of marijuana sold on the street is 9.3%. Suppose the THC content is normally distributed with standard d
velikii [3]

Answer:

a) X \sim N(9.3,1)  

b) P(X>9.2)=P(\frac{X-\mu}{\sigma}>\frac{9.2-\mu}{\sigma})=P(Z>\frac{9.2-9.3}{1})=1-P(Z

c) The value of height that separates the bottom 75% of data from the top 25% is 9.9745.  

Step-by-step explanation:

1) 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".  

2) 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(9.3,1)  

Where \mu=9.3 and \sigma=1

3) Part b

We are interested on this probability

P(X>9.2)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

P(X>9.2)=P(\frac{X-\mu}{\sigma}>\frac{9.2-\mu}{\sigma})=P(Z>\frac{9.2-9.3}{1})=1-P(Z

4) Part c

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=0.6745. On this case P(Z<0.6745)=0.75 and P(z>0.6745)=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=0.6745

And if we solve for a we got

a=9.3 +1*0.6745=9.9745

So the value of height that separates the bottom 75% of data from the top 25% is 9.9745.  

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3 years ago
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madreJ [45]

Answer:

Brainliest

Step-by-step explanation:

y=2.78(4)-4.4 = 6.72

5 0
3 years ago
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