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3 years ago

Verify 10 × [ 6 + (- 2) ] = 10 × 6 + 10 × (- 2)

Mathematics

1 answer:

Nana76 [90]3 years ago

8 0

Answer:

Step-by-step explanation:

10 × [ 6 + (- 2) ] = 10 × 6 + 10 × (- 2)

10 × 4 = 10 × 6 + 10 × (- 2)

40 = 60 + -20

40+60+-20= 80

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A practice law exam has 100 questions, each with 5 possible choices. A student took the exam and received 13 out of 100.If the s

Cloud [144]

Answer:

$z=\frac{13-20}{4}=-1.75$

Assuming:

H0: $\mu \geq 20$

H1: $\mu$

$p_v = P(Z$

Step-by-step explanation:

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest (number of correct answers in the test), on this case we now that:

$X \sim Binom(n=100, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We need to check the conditions in order to use the normal approximation.

$np=100*0.2=20 \geq 10$

$n(1-p)=20*(1-0.2)=16 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=100*0.2=20$

$\sigma=\sqrt{np(1-p)}=\sqrt{100*0.2(1-0.2)}=4$

So we can approximate the random variable X like this:

$X\sim N(\mu =20, \sigma=4)$

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean". The letter $\phi(b)$ is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: $\phi(b)=P(z$

The z score is given by this formula:

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

If we replace we got:

$z=\frac{13-20}{4}=-1.75$

Let's assume that we conduct the following test:

H0: $\mu \geq 20$

H1: $\mu$

We want to check is the score for the student is significantly less than the expected value using random guessing.

So on this case since we have the statistic we can calculate the p value on this way:

$p_v = P(Z$

5 0

3 years ago

Is 5/10 equivalent to 1/6

Citrus2011 [14]

Answer:

No, its not equivalent

1/2 is equivalent though

Please mark as brainliest

8 0

2 years ago

Read 2 more answers

Solve for the value of x.x^2 + 4x + 4 = 0

Georgia [21]

Answer:

-2

Step-by-step explanation:

Lets factor

(x+2)(x+2)=0

x=-2

5 0

3 years ago

A light flashes every 1 minute 15 seconds. another flashes every 1 minute 40 seconds. suppose they flash together at certain tim

ASHA 777 [7]

Answer:

5 minutes

Step-by-step explanation:

To get the response to this question, it would be required to convert both times to seconds alone.

For the first, the time It takes to flash is 1 minute 15 seconds which is same as 75 seconds

For the second, it takes 1 minute 40 seconds which is same as 100 seconds.

Now to get the time they would flash together, we need to know their lowest common multiples. The values involved are 75 and 100. Thus, the lowest common multiple of both is 300.

This is equivalent to 300 seconds which is 5 minutes time

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4 years ago

Read 2 more answers

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. What is the volume of t

Temka [501]

Answer:

$V=416\ mm^3$