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2 years ago

Add the following fractions. See the image below

Mathematics

1 answer:

LenKa [72]2 years ago

3 0

Answer:

$\dfrac{19}{840}$

Step-by-step explanation:

The given fraction is:

$\dfrac{1}{168}+\dfrac{3}{180}$

We need to solve it.

The LCM of 168 and 180 is 2520.

So,

$\dfrac{1}{168}+\dfrac{3}{180}=\dfrac{15+3\cdot14}{2520}\\\\=\dfrac{19}{840}$

So, the required answer is equal to $\dfrac{19}{840}$ .

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Juan bought 4 pounds of chocolate

Andru [333]

Answer:

Step-by-step explanation:

This is a system of equations. The 2 equations are:

4c + 2p = 16

2c + 3p = 12

Let's get rid of the p's first. Do this by multiplying the first equation by -3 and the second equation by 2 to get a new system that looks like this:

-12x - 6p = -48

4c + 6p = 24

Now add to get

-8c = -24 and

c = 3

That means that chocolate is $3 per pound. Now sub that back in to either one of the original equations to get the price for peanuts:

4(3) + 2p = 16 and

12 + 2p = 16 and

2p = 4 so

p = 2

The price for peanuts is $2 per pound.

6 0

3 years ago

6/42 in simplest form

Ganezh [65]

6/42 in simplest form :

Divide both the nominator and the denominator by the HCF (highest common factor) : 6

6/42 = 6:6/42:6 = 1/7

6 0

2 years ago

Explain the purposes of inductive and deductive reasoning in mathematics. Be sure to define both inductive reasoning and deducti

uysha [10]

When it comes to deductive reasoning, it is used to reach a logical solution. You start out with the general statement, or hypothesis, and examine all the possibilities so you can reach the final conclusion.
Inductive reasoning is completely opposite - you focus on specific observations, and then make broad generalizations.

7 0

3 years ago

When we toss a coin, there are two possible outcomes: a head or a tail. Suppose that we toss a coin 100 times. Estimate the appr

marin [14]

Answer:

96.42% probability that the number of tails is between 40 and 60.

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .