Simplity each expression,<br>46°=

What is the perimeter of a polygon with vertices at (−2, 1) , (−2, 7) , (1, 11) , (4, 7) , and (4, 1) ?

Sholpan [36]

Each edge is given by the distance formula, which is the Pythagorean Theorem. When one of the coordinates is the same, we can shortcut that.

A(−2, 1) , B(−2, 7), C(1, 11), D(4, 7), E(4, 1)

$AB=7-1=6$

$BC=\sqrt{(1 - -2)^2 + (11-7)^2}=5$

$CD=\sqrt{(4 - 1 )^2 + (11-7)^2}=5$

$DE=7-1=6$

$EA= 4 - -2 = 6$

$\textrm{perimeter} = 6+5+5+6+6=28$

Answer: 28

7 0

4 years ago

What is the value of x?

Kryger [21]

-1 because -3x+1=2 (4 total spaces) so,
2+1 is 3
you have life numbers and x values separate.
divide positive 3 by negative 3 to get -1.
check your answer by plugging it in
-1*-3 is 3
so - 3+1 world be 4 which is where the 2 is on the number line because it goes into negatives

answer is x= -1

3 0

4 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

So

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

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

$=1-0.9099$

$=0.0901$

3 0

3 years ago

In 2000, the average GPA for Rutgers College students was 3.15. A sample in 2002 showed that the average GPA for Rutgers College

Vladimir79 [104]

Answer:

Null hypothesis: $\mu_{2002}\leq 3.15$

Alternative hypothesis : $\mu_{2002} > 3.15$

C. The mean Rutgers College GPA has increased to more than 3.15

Step-by-step explanation:

Data given and notation

$\bar X_{2000}=3.15$ represent the average score for Rutgers College in 2000

$\bar X_{2002}=3.46$ represent the average score for Rutgers College in 2002

$s_{2000}$ represent the sample standard deviation in 2000

$s_{2002}$ represent the sample standard deviation in 2002

$n$ sample size

State the null and alternative hypotheses. .

What are H0 and Ha for this study?

Null hypothesis: $\mu_{2002}\leq 3.15$

Alternative hypothesis : $\mu_{2002} > 3.15$

For this case we need to take in count that the alternative hypothesis can't have and = sign, and based on the information a good hypothesis here would be if the average GPA increased between 2000 and 2002, so based on this the best option for this case would be:

C. The mean Rutgers College GPA has increased to more than 3.15

4 0

3 years ago

What is the definition of the 3rd batter in a baseball lineup called?

PolarNik [594]

That batteris refered to as a the "heart of the order" and have the function on getting on base and hitting hard.

These batters come before the clean-up batters.

Hope it helped,

BioTeacher101

4 0

3 years ago

Simplity each expression,46°=​

Simplity each expression,46°=