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3 years ago

Please help me - Homework

Mathematics

1 answer:

wolverine [178]3 years ago

4 0

Answer:

Step-by-step explanation:

A= 2(5*2) + 2(1*4) + (3*5) + 2(2*3) + (1*3) + (4*3) + (6*3) = 88 cm^2

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Here is a sequence of numbers:

Anettt [7]

Triangular number sequnce

8 0

3 years ago

Simplify (-2x^4y^-3)^4

elixir [45]

Answer:

$( - 2 {x}^{4} {y}^{ - 3} )^{4} = \frac{16 {x}^{16}}{ {y}^{12} }$

Step-by-step explanation:

We want to simplify:

$( - 2 {x}^{4} {y}^{ - 3} )^{4}$

We need to apply the exponential property for products of powers.

Recall that:

$( {a}^{m} \times {a}^{n} )^{p} = {a}^{mp} \times {a}^{np}$

We apply this rule to get:

$( - 2 {x}^{4} {y}^{ - 3} )^{4} = ( { - 2)}^{4} x \times {x}^{16} \times {y}^{ - 12}$

This simplifies to:

$( - 2 {x}^{4} {y}^{ - 3} )^{4} = 16 {x}^{16} \times {y}^{ - 12}$

We rewrite as positive index to get:

$( - 2 {x}^{4} {y}^{ - 3} )^{4} = \frac{16 {x}^{16}}{ {y}^{12} }$

7 0

3 years ago

The lifetime of a certain type of battery is normally distributed with mean value 10 hours and standard deviation 1 hour. There

Oksi-84 [34.3K]

Answer:

$z=1.64$

And if we solve for a we got;

$10 +1.64*1=11.64$

So the value of height that separates the bottom 95% of data from the top 5% is 11.64

Step-by-step explanation:

Previous concepts

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".

Solution to the problem

Let X the random variable that represent certain lifetime of a population, and for this case we know the distribution for X is given by:

$X \sim N(10,1)$

Where $\mu=10$ and $\sigma=1$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.05$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.64$

And if we solve for a we got;

$10 +1.64*1=11.64$

So the value of height that separates the bottom 95% of data from the top 5% is 11.64

4 0

3 years ago

Please help me!!!!with this!!!

kodGreya [7K]

5x+9-3x=11

5x-3x=11-9

2x=2

2:2

x=1

8 0

3 years ago

Which of these sets could represent the side lengths of a right triangle?

Jlenok [28]

Answer:

{6, 8, 10} is a set which represents the side length of a right triangle.

Step-by-step explanation:

In a right triangle:

$(Base)^{2} + (Perpendicular)^{2} = (Hypotenuse)^{2}$

Now, in the given triplets:

(a) {4, 8, 12}

Here, $(4)^{2} + (8)^{2} = 16 + 64 = 80\\\implies H = \sqrt{80} = 8.94$

So, third side of the triangle 8.94 ≠ 12

Hence, {4, 8, 12} is NOT a triplet.

(b) {6, 8, 10}

Here, $(6)^{2} + (8)^{2} = 36 + 64 = 100\\\implies H = \sqrt{100} = 10$

So, third side of the triangle 10

Hence, {6, 8, 10} is a triplet.

Here, $(6)^{2} + (8)^{2} = 36 + 64 = 100\\\implies H = \sqrt{100} = 10$

So, third side of the triangle 10 ≠ 15

Hence, {6, 8, 15} is NOT a triplet.

(d) {5, 7, 13}

Here, $(5)^{2} + (7)^{2} = 25 + 49 = 74\\\implies H = \sqrt{74} = 8.60$

So, third side of the triangle 8.60 ≠ 13

Hence, {5, 7, 13} is NOT a triplet.

4 0

3 years ago