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2 years ago

Expand the brackets

Mathematics

1 answer:

Aneli [31]2 years ago

7 0

$1)\ 3(2x + 5) = 6x + 15\\\\2)\ 7(p + 3q) = 7p + 21q\\\\3)\ 3m(n - 2m) = 3mn - 6m^2\\\\$

Solution:

Given that,

We have to expand the brackets

Use distributive property,

a(b + c) = ab + bc

Multiply the number in front of parenthesis with each term inside the parenthesis and then add them together

$3(2x + 5) = 3 \times 2x + 3 \times 5\\\\3(2x + 5) = 6x+15$

-------------------------------------------------

$7(p + 3q) = 7 \times p + 7 \times 3q\\\\7(p + 3q) =7p + 21q$

----------------------------------------------------

$3m(n-2m) = 3m \times n - 3m \times 2m\\\\3m(n-2m) = 3mn - 6m^2$

Thus the given expressions are expanded using distributive property

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Help please ASAP please I’ll mark you as brainlister

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Answer:

a = 4

Step-by-step explanation:

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3 years ago

Suppose the weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams. The weights

user100 [1]

Answer:

a) 0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b) The weight that 80% of the apples exceed is of 78.28g.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams.

This means that $\mu = 85, \sigma = 8$

a. Find the probability a randomly chosen apple exceeds 100 g in weight.

This is 1 subtracted by the p-value of Z when X = 100. So

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

$Z = \frac{100 - 85}{8}$

$Z = 1.875$

$Z = 1.875$ has a p-value of 0.9697

1 - 0.9696 = 0.0304

0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b. What weight do 80% of the apples exceed?

This is the 100 - 80 = 20th percentile, which is X when Z has a p-value of 0.2, so X when Z = -0.84.

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

$-0.84 = \frac{X- 85}{8}$

$X - 85 = -0.84*8$

$X = 78.28$

The weight that 80% of the apples exceed is of 78.28g.

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2 years ago

The price of a liter of milk increased 10% compared with last year . If the new price is $1.21 per liter , what was last years p

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Answer:

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Step-by-step explanation:

First take if 110% is equals to $1.21 what about 100%

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3 years ago

Can someone please give me the answers to this? ... please ...

Hoochie [10]

Step-by-step explanation:

come on ! based on all the other questions that have been answered AND explained you should be able to find these answers yourself now. what is still unclear ?

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Pythagoras : c² = a² + b²

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c = sqrt(a² + b²)

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a = x1 - x2

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this is simply because, when you look at the coordinate grid, these 3 items make a right-angled triangle.

don't worry about any negative values for a and b, as the square eliminates the negative sign.

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we could use Pythagoras again for this, but the end result is so simple, we can skip this.

at the end the coordinates of the midpoint of 2 points (x1, y1) and (x2, y2) are

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find the other endpoint (x2, y2), when you have one endpoint (x1, y1) and the midpoint (xm, ym) :

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and in the same way

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and you can read a graph, right ?

if not it is high time to learn that very simple and basic skill :

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the y coordinate of a point is how many units above (positive) or below (negative) from the center point it is.

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so, what else do you need ?

I am very busy explaining things. I should not spend my little time doing the basic calculations for you (that I could train a monkey to do).

so, please, oil your brain machinery by following the instructions and formulas using the actual numbers and see how the results build out of this.

if you run into further problems, please ask me for additional explanations.

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Answer:

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