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astra-53 [7]
3 years ago
8

Which of the following is the quadratic parent function?

Mathematics
1 answer:
kipiarov [429]3 years ago
8 0

Answer:

F(x)=x^2

Step-by-step explanation:


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The average Act score follows a normal distribution, with a mean of 21.1 and a standard deviation of 5.1. What is the probabilit
ohaa [14]

Answer:

0.43% probability that the mean IQ score of 50 randomly selected people will be more than 23

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 distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

\mu = 21.1, \sigma = 5.1, n = 50, s = \frac{5.1}{\sqrt{50}} = 0.7212

What is the probability that the mean IQ score of 50 randomly selected people will be more than 23

This is 1 subtracted by the pvalue of Z when X = 23. So

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

By the Central Limit Theorem

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

Z = \frac{23 - 21.1}{0.7212}

Z = 2.63

Z = 2.63 has a pvalue of 0.9957

1 - 0.9957 = 0.0043

0.43% probability that the mean IQ score of 50 randomly selected people will be more than 23

5 0
3 years ago
If a car reaches speeds of 0-100 mph in 0.8 seconds, how many mph will it reach in 1 second?
zvonat [6]

Answer:

125 mph

Step-by-step explanation:

This can be calculated as a simple rule of 3.

In rule of 3 problems, you need to first identify the measures and whether they are direct or inverse to each other.

If they are direct to each other, if one value increases the other will increase too. For example, lets suppose that the Buffalo Bills have won 3 of 4 games. When there are 8 games, then will have won 6, keeping this proportion. Here, the measures are the number of games and the number of Buffalo Bills wins.

Now if they are inverse to each other, if one value increases the other will decrease. For example, if you travel at 60 mph, you will need 6 hours to arrive at your destination. At 80 mph, you will need less time. So, a the average speed increases, the time you need will decrease.

In this case the speeds is proportional to the time. So, if the time increases, the speed will increase too. It can be calculated by the following rule of 3.

   Speed               Time

 100 mph - 0.8 seconds

 x mph      -  1 second

x = 100/0.8 = 125 mph.

4 0
3 years ago
a rectangles perimeter and area have the same numerical value. the width of the rectangle is 9 units . what is the length of the
attashe74 [19]

Answer:

Step-by-step explanation:

let the length of rectangle=l units

width=9

p=2(l+9)

area=9l

9l=2(l+9)

9l=2l+18

7l=18

l=18/7 units

5 0
2 years ago
The shorter leg of a 30°-60°-90° triangle is 4. How long is the hypotenuse?
Lera25 [3.4K]

For a triangle 30-60-90,

If shorter leg is x, then hypotenuse is 2x.

So, if shorter leg is 4,

then hypotenuse is 2*4 = 8.

Answer is 8.

8 0
3 years ago
En un curso hay 11 mujeres y 13 hombres. Si se eligen dos alumnos para representarlos en el campeonato de debate, ¿cuál es la pr
Tresset [83]

Answer:

106.34%  

Step-by-step explanation:

hay 24 personas en total (11 mujeres+13 hombres)

la probabilidad para que uno de los alumnos es un hombre es 13/24 (porque hay 13 hombres en la clase)

Entonces, si uno hombre está elegido, quedan 12 hombres, así que, la probabilidad si es un hombre es 12/23 (porque una persona ya está elegido y quedan 23 personas)

la probabilidad es 13/24+12/23=587/552=106.34%  (Redondeado a la décima más cercana)

(lo siento mi español no es perfecto)

8 0
2 years ago
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