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3 years ago

In triangle ABC, mZA = (5x – 10), mZB = (12x)", and the exterior

Mathematics

1 answer:

Inessa [10]3 years ago

7 0

Answer:

measure of exterior angle at C = 160°

Step-by-step explanation:

An exterior angle of a triangle equals the sum of the two remote interior angles

A and B are the remote interior angles. So,

m∠A + m∠B = measure of exterior angle at C

5x - 10 + 12x = 16x

17x - 10 = 16x

x = 10

measure of exterior angle at C = 16x = 16(10) = 160°

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How many integers between 10000 and 99999, inclusive, are divisible by 3 or<br> 5 or 7?

Yuki888 [10]

Answer: Hence, there are approximately 48884 integers are divisible by 3 or 5 or 7.

Step-by-step explanation:

Since we have given that

Integers between 10000 and 99999 = 99999-10000+1=90000

n( divisible by 3) = $\dfrac{90000}{3}=30000$

n( divisible by 5) = $\dfrac{90000}{5}=18000$

n( divisible by 7) = $\dfrac{90000}{7}=12857.14$

n( divisible by 3 and 5) = n(3∩5)= $\dfrac{90000}{15}=6000$

n( divisible by 5 and 7) = n(5∩7) = $\dfrac{90000}{35}=2571.42$

n( divisible by 3 and 7) = n(3∩7) = $\dfrac{90000}{21}=4285.71$

n( divisible by 3,5 and 7) = n(3∩5∩7) = $\dfrac{90000}{105}=857.14$

As we know the formula,

n(3∪5∪7)=n(3)+n(5)+n(7)-n(3∩5)-n(5∩7)-n(3∩7)+n(3∩5∩7)

$=30000+18000+12857.14-6000-2571.42-4258.71+857.14\\\\=48884.15$

Hence, there are approximately 48884 integers are divisible by 3 or 5 or 7.

5 0

3 years ago

Genetic Defects Data indicate that a particular genetic defect occurs in of every children. The records of a medical clinic show

Dovator [93]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The probability that there exist 60 or more defected children is $P(x \ge 60)=0.0901$

Looking at the value for this probability we see that it is not so small to the point that the observation of this kind would be a rare occurrence

Step-by-step explanation:

From the question we are told that

in every 1000 children a particular genetic defect occurs to 1

The number of sample selected is $n= 50,000$

The probability of observing the defect is mathematically evaluated as

$p = \frac{1}{1000}$

$= 0.001$

The probability of not observing the defect is mathematically evaluated as

$q = 1-p$

$= 1-0.001$

$= 0.999$

The mean of this probability is mathematically represented as

$\mu = np$

Substituting values

$\mu = 50000*0.001$

$= 50$

The standard deviation of this probability is mathematically represented as

$\sigma = \sqrt{npq}$

Substituting values

$= \sqrt{50000 * 0.001 * 0.999}$

$= \sqrt{49.95}$

$= 7.07$

the probability of detecting $x \ge60$ defects can be represented in as normal distribution like

$P(x \ge 60)$

in standardizing the normal distribution the normal area used to approximate $P(x \ge 60)$ is the right of 59.5 instead of 60 because x= 60 is part of the observation

The z -score is obtained mathematically as

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

$= \frac{59.5 - 50 }{7.07}$

$=1.34$

The area to the left of z = 1.35 on the standardized normal distribution curve is 0.9099 obtained from the z-table shown z value to the left of the standardized normal curve

Note: We are looking for the area to the right i.e 60 or more

The total area under the curve is 1

$P(x \ge 60) \approx P(z > 1.34)$

$= 1-P(z \le 1.34)$

$=1-0.9099$

$=0.0901$

3 0

3 years ago

Can you please show me how to calculate the volume for each prism?

larisa [96]

Answer:

1st: volume = long x wide x high = 7 x [sqrt(25^2-7^2)] x 4 = 7 x 24 x 4 = 672

2nd: volume = area of base(circle) x high = pi x 9^2 x 8 = ~ 2035.8

3rd = volume = area of base(triangle) x high = [sqrt(3)/4] x 14^2 x 20 = ~1697.4

8 0

3 years ago

How do you get the same base for the power

rewona [7]

You use division

over 2 or 4 or 3 or 5 or 7 and so on
in this case 2 is good

64 = 2 * 2 * 2 * 2 * 2 * 2 ( use division) = 2^6

16 = 2 * 2 * 2 * 2 = 2^4

number reminder
64 0
32 0
16 0
8 0
4 0
2 0
1 1

so 64 = 2^6 (number of zeros) no reminder

3 0

3 years ago

Owen receives $10 and puts it into his savings account. He adds $0.50 to the account each day for a number of days, d, after tha

makkiz [27]

Answer:

it is the sum of the initial amount and the additional amount after d days

Step-by-step explanation:

yw!!.

7 0

3 years ago