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4 years ago

will the product of a fraction less then one and a whole number be less than or greater than the whole number. why?

1 answer:

8 0

The product of a fraction less than one and a whole number will be less than the whole number.

This is because a fraction less than one when multiplied to a whole number will only get a part of a whole number that is equivalent to the portion of the fraction of a whole number.

For example:
fraction less than 1 is 1/2
whole number is 2

2 * 1/2 = 1
one is the product of a fraction less than 1 multiplied to a whole number. it is less than the whole number.

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In a certain small town, 3 professional burglars are currently out of prison: Alex, Becky, and Carl. Alex has in the past commit

NeX [460]

Answer:

Answer explained below

Step-by-step explanation:

Alex has in the past committed 55% of the burglaries committed by the three, Becky 31%, and Carl the rest, hence

probability, P(Carl doing a burglary) = 1 - P(Alex or Becky doing a burglary)

= 1 - (0.55 + 0.31)

= 0.14

a) P(next burglary in town is the burglary of a residence) = P(Alex did a burglary of a residence) + P(Becky did a burglary of a residence) + P(Carl did a burglary of residence

= 0.55*1/3 + 0.31*0.5 + 0.14*1

= 0.4783

b)From Bayes' Theorem: P(A | B) = P(A & B) / P(B)

Hence,

P(Becky | a resident reports a home burglary) = P(Becky did a burglary of a residence) / P(burglary of a residence)

= (0.31 * 0.5)/0.4783

= 0.3240

3 0

3 years ago

Evaluating integral by net area

N76 [4]

The graph of $f(x)=2$ is a horizontal line. So the area under $f(x)$ on [0, 8] is equal to the area of a rectangle with length 8 and height 2, or 16.

The graph of $g(x)=\sqrt{64-x^2}$ is the upper half of a circle with radius $\sqrt{64}=8$ . It's symmetric about $x=0$ , so on the interval [0, 8], we're considering a quarter of the circle. The area of such a sector is $\frac{\pi 8^2}4=16\pi$ .

Then use the fact that the definite integral is distributive over sums, meaning

$\displaystyle\int_0^8f(x)+g(x)\,\mathrm dx=\int_0^8f(x)\,\mathrm dx+\int_0^8g(x)\,\mathrm dx=16+16\pi$

8 0

4 years ago

Cavalieri’s principle states that if two solids of equal height have equal cross-sectional areas at every level parallel to the

kozerog [31]

<h2>Answer:</h2>

one cone within the cylinder.

<h2>Step-by-step explanation:</h2>

First of all we have to start with half of a sphere (also known as a hemisphere), whose radius is r, and calculate its volume. Then we can double our answer at the end to find the volume of the complete sphere. But first to apply the Cavalieri's Principle, we start with a cone with the same radius r and suppose the height is also r, so the volume of this cone is:

$V_{cone}=\frac{1}{3}\pi r^{3}$

Next, let's look at a cylinder and suppose this cylinder also has a radius r and height r, so the volume of this cylinder is:

$V_{cylinder}=\pi r^{3}$

Next, we place the the cone inside the cylinder and the volume that's inside the cylinder, but outside the cone is:

$V_{cylinder}-V_{cone}=\pi r^{3}-\frac{1}{3}\pi r^{3}=\frac{2}{3}\pi r^{3}$

And this is the volume of a hemisphere. Finally, if we double this value we get the volume of a complete sphere, which is:

$V_{sphere}=\frac{4}{3}\pi r^{3}$

7 1

3 years ago

Read 3 more answers

in slope intercept form write the equation of a line that is parallel to 3x - 5y = 7 and passes through (0, -6)

lisov135 [29]

Answer:

The gradient is 3/7 make y the subject. Then put the coordinates in the equation.

Step-by-step explanation:

7 0

3 years ago

Expand the following: 1/3(6/5x-3)

Strike441 [17]

x in (-oo:+oo)

(1/3)*((6/5)*x-3) = 0

1/3*(6/5*x-3) = 0
( 1/3 )

1/3 = 0

x belongs to the empty set

( 6/5*x-3 )

6/5*x-3 = 0 // + 3

6/5*x = 3 // : 6/5

x = 3/6/5

x = 5/2

x = 5/2

7 0

3 years ago

Read 2 more answers