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3 years ago

{4z=8} {3x-2z=11} {x-4y+z=11}

Mathematics

1 answer:

tino4ka555 [31]3 years ago

3 0

Step-by-step explanation:

4z = 8

z = 8/4

z = 2

3x - 2z = 11

3x - 2.2 = 11

3x - 4 = 11

3x = 11 + 4

3x = 15

x = 15/3

x = 5

x - 4y + z = 11

5 - 4y + 2 = 11

-4y = 11 - 5 - 2

-4y = 4

y = 4/-4

y = -1

Solution → {x,y,z} = {5,-1,2}

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An Epson inkjet printer ad advertises that the black ink cartridge will provide enough ink for an average of 245 pages. Assume t

Neko [114]

Answer:

35.2% probability that the sample mean will be 246 pages or more

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, we have that:

$\mu = 245 \sigma = 15, n = 33, s = \frac{15}{\sqrt{33}} = 2.61$

What the probability that the sample mean will be 246 pages or more?

This is 1 subtracted by the pvalue of Z when X = 246. So

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

By the Central Limit Theorem

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

$Z = \frac{246 - 245}{2.61}$

$Z = 0.38$

$Z = 0.38$ has a pvalue of 0.6480.

1 - 0.6480 = 0.3520

35.2% probability that the sample mean will be 246 pages or more

4 0

3 years ago

20 PTSS !!!<br> PLEASE HELPP !!

butalik [34]

Because it is extremely hard to find the area of this figure all together, it would be in our best interest to split this figure up into three different pieces: the two horizontal rectangles, and the verticle rectangle. We can find the area of all three and add them up. Be aware that there are two different ways that you can break this figure up, As shown in the attachments. I will be using the first image (the one with the tall horizontal rectangles, NOT the almost-squares).

So, we see that we have enough information to solve for the area of the left-most rectangle. Area = lw. 10 x 4 = 40, so the area is 40. Next, we have to notice, that the horizontal rectangles are also the same, so both of the areas of the two horizontal rectangles are 40.

Now, we can find the middle rectangle. We know that the length of the entire thing is 18, but it is taken up by 8 (4+4) of the horizontal triangles, so 18-8=10, so the length Is 10. We also know that the height of the horizontal rectangles is 10, so 10-3=7. Our dimensions for the rectangle are 10x7 or 70 square units. If we add them all together, 40+40+70=150.

The area is 150 square units

8 0

3 years ago

Please help immediately!!

JulijaS [17]

Answer:

hjd

Step-by-step explanation:

3 0

3 years ago

Help me please ASAP

uranmaximum [27]

Perimeter is 24.

Length is 4 greater than the width.

Let's use 'x' for width

we can write this as x+4 + x+4 + x + x

x+4 being the width+4 and x being the width

There are 4 sides to a rectangle so you are adding 4 values

Two length and two widths

so we can then combine the two lengths to make 2x+8

and then combine the two widths to make 2x

Then put it together. 2x+2x+8= 4x+8

4x+8=24

Subtract 8 from both sides

4x=16

divide both sides by 4

x=4

The width is 4.

6 0

3 years ago

Those 2 questions I need help with . find sec θ and tanθ

Zielflug [23.3K]

STEP - BY - STEP EXPLANATION

What to find?

The the value of secθ.

Given:

(4, 3)

⇒(x, y) = (4, 3)

Step 1

Draw a sketch.

Step 2

Substitute the values into the trig. ratio formula below.

$tan\theta=\frac{opposite}{adjacent}$

From the sketch above, opposite = 3 and adjacent = 4

$tan\theta=\frac{3}{4}$

Step 3

Find the value of the hypotenuse side using Pythagoras theorem.

let h be the hypotenuse side.

$\begin{gathered} h^2=4^2+3^2 \\ \\ =16+9 \\ \\ =25 \\ \\ h=5 \end{gathered}$

Hence, hypotenuse = 5

Step 4

Substitute the values into the formula below:

$\begin{gathered} cos\theta=\frac{adjacent}{hypotenuse} \\ \\ =\frac{4}{5} \end{gathered}$

But,

$sec\theta=\frac{1}{cos\theta}=\frac{1}{\frac{4}{5}}=\frac{5}{4}$

ANSWER

secθ= 5/4

tanθ=3/4

7 0

1 year ago