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3 years ago

Determine the domain and range of the given function

Mathematics

1 answer:

bonufazy [111]3 years ago

3 0

Answer:

The domain: all real numbers;

the range: $[-2,\infty)$

Step-by-step explanation:

The domain and the range of the parent function $y=x^2$ are all real numbers and all real numbers that are greater or equal to 0.

Given graph of the function $f(x)$ is translated graph of the parent function 2 units down. Thus, the domain of the function $f(x)$ is the same as the domain of the parent function and the range is $y\ge -2.$

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A distribution of values is normal with a mean of 220 and a standard deviation of 13. From this distribution, you are drawing sa

Paraphin [41]

Answer:

The interval containing the middle-most 48% of sample means is between 218.59 to 221.41.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributied random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 220, \sigma = 13, n = 35, s = \frac{13}{\sqrt{35}} = 2.1974$

Find the interval containing the middle-most 48% of sample means:

50 - 48/2 = 26th percentile to 50 + 48/2 = 74th percentile. So

74th percentile

value of X when Z has a pvalue of 0.74. So X when Z = 0.643.

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$0.643 = \frac{X - 220}{2.1974}$

$X - 220 = 0.643*2.1974$

$X = 221.41$

26th percentile

Value of X when Z has a pvalue of 0.26. So X when Z = -0.643

$Z = \frac{X - \mu}{s}$

$-0.643 = \frac{X - 220}{2.1974}$

$X - 220 = -0.643*2.1974$

$X = 218.59$

The interval containing the middle-most 48% of sample means is between 218.59 to 221.41.

5 0

3 years ago

HELP ME PLSSS OMG OMG PLS THIS IS A BIG LART OF MY GRADE ON A TWST AND I RLLY RLLY NEED IT PLE HELP

Elza [17]

Answer: The answer is B.

6 0

3 years ago

Read 2 more answers

Find the hypotenuse of each isosceles right triangle when the legs are of the given measure. 6 sqrt 2

Gemiola [76]

Isosceles right triangles have two equal sides (a and b) that are not the hypotenuse (c). And when two sides are equal, so are their opposite angles. There are only 180° degrees in any triangles, thus the right angle = 90°, so 90 left for the two equal, means that 2x=90,
x = 45°.

There are several ways to go about solving a triangle like this. The best and easiest is simply to memorize that the hypotenuse is exactly root2 times the other sides. Or, each isosceles side is the hypotenuse (c) ÷ root2
$a = b = c \div \sqrt{2} \\ c = a\sqrt{2} \\ c = 6 \sqrt{2} \times \sqrt{2} = 6 \times 2 = 12$
Another way to do it is the longer proof of Pythagorean Theorem:
${c}^{2} = {a}^{2} + {b}^{2}... \: \: c = \sqrt{({a}^{2} + {b}^{2})} \\$
$c= \sqrt{({6 \sqrt{2}) }^{2} + ({6 \sqrt{2})}^{2}} \\ = \sqrt{(2 \times{(6 \sqrt{2} )}^{2} )} = \sqrt{2(36 \times 2)} \\ c = \sqrt{144} = 12$

7 0

3 years ago

Plants The world's largest flower, the Giant Raffesia is 91 centemeters in diameter. Use a calculator to find the circumference

Kamila [148]

We know that
circumference=pi*D
where
D is the diameter
D=91 cm
so
pi-----> is the value of the calculator------> 3.1415926535897932
circumference=pi*91------> 285.88 cm------> 285.9 cm

the answer is
285.9 cm

5 0

3 years ago

In which figure is DE BC

stepan [7]

Answer:

Given: DB = 7.2 cm, AE = 1.8 cm and EC = 5.4 cm and DE || BC.

[by basic proportionality theorem which states that if a line is drawn parallel to one side of a triangle the other two sides in distinct points, then the other two sides are divided in the same.

7.2

5.4

1.8

AD=

5.4

7.2×1.8

AD=

⟹AD=2.4cm

4 0

3 years ago