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3 years ago

What is the first step in simplifying the following expression: 2 + 3(4 + 5×2) − 8 + 3^2

Mathematics

1 answer:

ch4aika [34]3 years ago

4 0

Answer:

5 x 2 inside the parenthesis

Step-by-step explanation:

We need an order of operations to ensure we always arrive at the correct answer. It gives us a consistent way to work with numbers. We use the mnemonic device like PEMDAS to remember the correct order.

P-parenthesis

E-exponents

M-multiplication

D-division

A-add

S-subtract.

We apply them left to right doing inner operations before outer operations.

There fore our first step is in the parenthesis and multiplication because it is the inner most operations. 5 x 2 inside the parenthesis.

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50/23 Xander's friends prefer to stay home on Friday nights. What percent of Xander's friends prefer to stay home on Friday nigh

Dmitry_Shevchenko [17]

27 of them decided to stay home :)

3 0

3 years ago

Read 2 more answers

Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 104 eligible vot

crimeas [40]

Answer:

The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.

Step-by-step explanation:

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 distributions 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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this case, assume that 104 eligible voters aged 18-24 are randomly selected.

This means that $n = 104$ .

Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.

This means that $p = 0.22$

Mean and standard deviation:

$\mu = 104*0.22 = 22.88$

$\sigma = \sqrt{104*0.22*0.78} = 4.2245$

Probability that exactly 27 voted

By continuity continuity, 27 consists of values between 26.5 and 27.5, which means that this probability is the p-value of Z when X = 27.5 subtracted by the p-value of Z when X = 26.5.

X = 27.5

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

$Z = \frac{27.5 - 22.88}{4.2245}$

$Z = 1.09$

$Z = 1.09$ has a p-value of 0.8621

X = 26.5

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

$Z = \frac{26.5 - 22.88}{4.2245}$

$Z = 0.86$

$Z = 0.86$ has a p-value of 0.8051

0.8621 - 0.8051 = 0.057

The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.

5 0

3 years ago

Select the equation that represents a line with a slope of 2 and that contains the point (1, -5).

kondor19780726 [428]

To get the equation of a line, you can use the following:

y - y1 = m (x - x1)

Where:

m is the slope (2)
y1 is the y coordinate of a point (1, -5)
x1 is the x coordinate of the same point (1, -5)

Just substitute in the values:

y - y1 = m (x - x1)

y - (-5) = 2(x - 1) <em>( - - 5 = + 5 )</em>

y + 5 = 2(x - 1)

_________________________

Answer:

B. y + 5 = 2(x - 1)

6 0

3 years ago

HELP ASAP!!!!!!!!! Please answer both

maks197457 [2]

Step-by-step explanation:

questions 8, obviously the mid part of the parabola is 3, that is the axis of symmetry.

question 9, only one solution because you only have one parabola.

3 0

3 years ago

Joe’s hat shack has fixed cost of $1,000 per week. She buys hats that are $1,500 for 300 hard and she sells the hats for $12.50

katrin [286]

1000+1500=2500 is how much she owes right now
If each hat is sold for 12.50, all you have to do is 2500/12.50=200
She needs to sell 20 hats to break even.

4 0

3 years ago