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3 years ago

Write h(x) = 3x2 – 12x in vertex form.

Mathematics

1 answer:

igomit [66]3 years ago

7 0

Answer:

y=3(x-2)^2-12

please let me know if its right.

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1.) A tower casts a shadow that is 60 feet long when the angle

Fynjy0 [20]

Answer:

128.67 ft

Step-by-step explanation:

Let the height of the tower be x feet.

$\tan \: 65 \degree = \frac{x}{60} \\ \\ 2.1445069205 = \frac{x}{60} \\ \\ x = 2.1445069205 \times 60 \\ \\ x = 128.670415 \\ \\ x = 128.67 \: ft$

8 0

2 years ago

6.371 in lowest terms

kozerog [31]

Well you would have to round this 5 and above goes up. Since 1 is lower than 5 that would leave you at 6.37. 7 rounds up so that would change to 6.4. Lastly 4 would round down, So that would leave you with 6. Now 6 is the simplest form but if your looking for rounded to the nearest tenth the answer would be 6.4. If your looking for rounded to the nearest 100th place 6.37. But over all simplest form is 6.

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

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