All categories

3 years ago

A ladder is leaning against

Mathematics

1 answer:

Svetradugi [14.3K]3 years ago

5 0

Answer:

25 ft

Step-by-step explanation:

This is a right triangle, so we can use the Pythagorean theorem

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

15^2 + 20 ^2 = x^2

225+400= x^2

625 = x^2

Take the square root of each side

sqrt(625) = sqrt(x^2)

25 = x

You might be interested in

Find the volume of the composite figure

Mice21 [21]

Answer:

540m^3

Step-by-step explanation:

find volume of top + volume of bottom

bottom: l*w*h = 16*5*4 =300 m^3

top = area of side times width = area of triangle times width

area of triangle is 1/2*b*h = (6*16)/2 = 48 m^2

multiply by width = 48*5=240m^3

add top and bottom = 300+240=540m^3

3 0

3 years ago

Is 1/3, 2/3, 4/3, 8/3, 16/3 arithmetic sequence

11111nata11111 [884]

The given sequence is not arithmetic sequence

Solution:

Given sequence is:

$\frac{1}{3} , \frac{2}{3} , \frac{4}{3} , \frac{8}{3} , \frac{16}{3}$

We have to find if the above sequence is arithmetic sequence or not

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant

Here in the given sequence

$\text{ first term } = a_1 = \frac{1}{3}\\\\\text{ second term } = a_2 = \frac{2}{3}\\\\\text{ third term } = a_3 = \frac{4}{3}\\\\\text{ fourth term } = a_4 = \frac{8}{3}\\\\\text{ fifth term } = a_5 = \frac{16}{3}$

Let us find the difference between terms

$a_2 - a_1 = \frac{2}{3} - \frac{1}{3} = \frac{1}{3}$

$a_3 - a_2 = \frac{4}{3} - \frac{2}{3} = \frac{2}{3}$

$a_4 - a_3 = \frac{8}{3} - \frac{4}{3} = \frac{4}{3}$

$a_5 - a_4 = \frac{16}{3} - \frac{8}{3} = \frac{8}{3}$

Thus the difference between terms is not constant

So the given sequence is not arithmetic sequence

5 0

3 years ago

A state administered standardized reading exam is given to eighth grade students. The scores on this exam for all students state

Lorico [155]

Answer:

$a=502 +1.28*81=605.68$

So the value of height that separates the bottom 90% of data from the top 10% is 605.68.

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 the heights of a population, and for this case we know the distribution for X is given by:

$X \sim N(502,81)$

Where $\mu=502$ and $\sigma=81$

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

$P(X>a)=0.1$ (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 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

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

$P(X$