Helppppp MARKED BRAINLYEST

Explain how using basic facts can help you find 10x20x30x40 mentally.

sladkih [1.3K]

You know that anything times a one is that number, so multiply 2,3, and 4, and then multiply that by one. once you get the answer, put the zeros behind each multiplied number behind your answer, and there you go.

2×3×4= 24×1=24
there are 4 zeros
240,000

4 0

3 years ago

Find the equation for the parabola that has its vertex at the origin and has directrix at x=1/48

Oksana_A [137]

Answer:

The equation for a parabola with vertex at the origin and a directrix at x = 1/48 is $x= \frac{1}{12}\cdot y^{2}$ .

Step-by-step explanation:

As directrix is a vertical line, the parabola must "horizontal" and increasing in the -x direction. Then, the standard equation for such geometric construction centered at (h, k) is:

$x - h = 4\cdot p \cdot (y-k)^{2}$

Where:

$h$ , $k$ - Horizontal and vertical components of the location of vertex with respect to origin, dimensionless.

$p$ - Least distance of directrix with respect to vertex, dimensionless.

Since vertex is located at the origin and horizontal coordinate of the directrix, least distance of directrix is positive. That is:

$p = x_{D} - x_{V}$

$p = \frac{1}{48}-0$

$p = \frac{1}{48}$

Now, the equation for a parabola with vertex at the origin and a directrix at x = 1/48 is $x= \frac{1}{12}\cdot y^{2}$ .

6 0

3 years ago

In a standard television set, the screen height is 0.75 times the screen width. If a television set measures 34 inches along the

S_A_V [24]

We can solve this by using the Pythagorean theorem which is below:

$a^2 + b^2 = c^2$

Or we can say
 $w^2 + h^2 = d^2$
w = widht
h = height
d = diagonal measure

With that said, we know the height is .75 times the width so .75w. We also know d = 34, which is our diagonal measure.
w = don't know yet but need to find
h = .75w
d = 34
Now lets plugin the information we know into our equation

 $w^2 + h^2 = d^2$
$w^2 + (.75w)^2 = 34^2$
Now lets to the math
$w^2 + (.75w)^2 = 34^2$
$w^2 + (.75w)^2 = 1156$
$w^2 + .5625w^2 = 1156$
Combine like terms
$w^2 + .5625w^2 = 1156$
$1.5625w^2 = 1156$
Divide both sides of the equal sign by 1.5625
$\frac{1.5625w^2}{1.5625} = \frac{1156}{1.5625}$
$w^2 = 739.84$
Now take the square root on both sides of the equal sign
$\sqrt{w^2} = \sqrt{739.84}$
$w = 27.2$

So the width is 27.2
We can check this by putting 27.2 back into our original equation
$w^2 + (.75w)^2 = 34^2$
$27.2^2 + (.75\times 27.2)^2 = 34^2$

3 0

3 years ago

A square fits exactly inside a circle with each of its vertices being on the circumference of the circle

Karo-lina-s [1.5K]

Draw or sketch out any problems like this, otherwise they appear abstract.

A circle’s area can be calculated by (pi d^2)/4 We have an area of 56 cm (^2?), so

pi d^2 = 56 x 4 (or 224) d^2 = 224/pi, d = √(224/pi)

A circle circumscribed around a square has a diameter equivalent to the length of the square’s diagonal, so the square’s diagonal is √(224/pi) (same as the circle diameter…)

A square’s side can be calculated, knowing its diagonal length, by use of Pythagoras’ theorem… The diagonal √(224/pi) is squared, divided by two, since the square’s sides are all equal, and the resulting number’s square root is calculated.

Squaring √(224/pi), we get 224/pi, and dividing by two, we get 112/pi, which is 35.6507 (cm^2), and the square root is 5.9708 cm, the side of the square.

I cannot emphasize enough that a drawing or sketch is an invaluable tool for these tasks, it saves having to retain a “picture” in your head. Note that a calculator was not required up until the last moment, dividing 112 by pi, and finding the square root of that answer. Picking up the calculator too early obliges you to transcribe numbers from the calculator to paper, and that can lead to issues. Try to enjoy maths, see it as a challenge not a chore. (and use correct units!)
2.3K views
Related Questions (More Answers Below)

4 0

3 years ago

Will mark brainiest!! Only answer questions a and b

k0ka [10]

Answer:

f1 ( x ) valid pdf . f2 ( x ) is invalid pdf

k = 1 / 18 , i ) 0.6133 , ii ) 0.84792

Step-by-step explanation:

Solution:-

A) The two pdfs ( f1 ( x ) and f2 ( x ) ) are given as follows:

- To check the legitimacy of a continuous probability density function the area under the curve over the domain must be equal to 1. In other words the following:

- We will perform integration of each given pdf as follows:

Answer: f1 ( x ) is a valid pdf; however, f2 ( x ) is not a valid pdf.

B)

- A random variable ( X ) denotes the resistance of a randomly chosen resistor, and the pdf is given as follows:

if 8 ≤ x ≤ 10

0 otherwise.

- To determine the value of ( k ) we will impose the condition of validity of a probability function as follows:

- Evaluate the integral as follows:

... Answer

- To determine the CDF of the given probability distribution we will integrate the pdf from the initial point ( 8 ) to a respective value ( x ) as follows:

To determine the probability p ( 8.6 ≤ x ≤ 9.8 ) we will utilize the cdf as follows:

p ( 8.6 ≤ x ≤ 9.8 ) = F ( 9.8 ) - F ( 8.6 )

p ( 8.6 ≤ x ≤ 9.8 ) =

ii) To determine the conditional probability we will utilize the basic formula as follows:

p ( x ≤ 9.8 | x ≥ 8.6 ) = p ( 8.6 ≤ x ≤ 9.8 ) / p ( x ≥ 8.6 )

p ( x ≤ 9.8 | x ≥ 8.6 ) = 0.61333 / [ 1 - p ( x ≤ 8.6 ) ]

p ( x ≤ 9.8 | x ≥ 8.6 ) = 0.61333 / [ 1 - 0.27666 ]

p ( x ≤ 9.8 | x ≥ 8.6 ) = 0.61333 / [ 0.72333 ]

p ( x ≤ 9.8 | x ≥ 8.6 ) = 0.84792 ... answer

Hope it helps! ;)

4 0

3 years ago