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3 years ago

PLZ HELP ME OUT WITH 3 AND 4. RUNNING OUT OF TIME. sorry if it's blurry EXTRA POINTS

Mathematics

1 answer:

Elena L [17]3 years ago

6 0

Answer:

question 3 would be C. and question 4 would be A.

Step-by-step explanation:

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A die is rolled. What is the probability that the number is a factor of 6 or more than 2? Does this scenario represent mutually

goblinko [34]

Factors of 6 are : 1,2,3 and 6.

Let us find probability of getting the number that is a factor of 6.

$P(\text{ The number is a factor of 6})=\frac{4}{6} =\frac{2}{3}$

Now let us find probability of getting a number more than 2 (3,4,5,6).

$P(\text{ The number is a greater than 2})=\frac{4}{6} =\frac{2}{3}$

We can see that these two events are mutually inclusive events. We can find probability of mutually inclusive events by formula $P(\text{X or Y})=P(X)+P(Y)-P(\text{X and Y})$ .

$P(\text{ The number is a factor of 6 and greater than 2})=\frac{2}{6} =\frac{1}{3}$

Now we will find probability of getting the number is a factor of 6 or more than 2 using above formula.

$P(\text{ The number is a factor of 6 or greater than 2})=\frac{2}{3} +\frac{2}{3}-\frac{1}{3}$

$P(\text{ The number is a factor of 6 or greater than 2})= \frac{4}{3}-\frac{1}{3}=\frac{3}{3}=1$

Therefore, our probability will be 1 and this scenario represents mutually inclusive events.

6 0

3 years ago

Rewrite the equation C = 2nr to show the expression that can be used to find the value of r.

STatiana [176]

The process is:

C = 2nr

2nr = c

r (2n) = c

$r = \frac{c}{2n}$

That's the answer☝️☝️☝️☝️

or maybe this one

r = 2n + c

sorry, I'm unsure, it has been too long since I studied that...

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3 years ago

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Match the circle equations in general form with their corresponding equations in standard form. Not all will be used.

Xelga [282]

The standard form of the equation of a circumference is given by the following expression:

 $(x-h)^{2}+(y-k)^{2}=r^{2} \\ \\ where \ (h, k) \ is \ the \ center \ of \ the \ circumference \ and \ r \ the \ radius$

On the other hand, the general form is given as follows:

 $x^{2}+y^{2}+Dx+Ey+F=0 \\ \\ where: \\ D=-2h, \ E=-2k, \ F=h^{2}+k^{2}-r^{2}$ 

In this way, we can order the mentioned equations as follows:

Equations in Standard Form:

 $\bold{a)} \ (x-6)^{2}+(y-4)^{2}=56 \\ \bold{b)} \ (x-2)^{2} + (y+6)^{2}=60 \\ \bold{c)} \ (x+2)^{2}+(y+3)^{2}=18 \\ \bold{d)} \ (x+1)^{2}+(y-6)^{2}=46$

Equations in General Form:

$\bold{1)} \ x^{2}+y^{2}-4x+12y-20=0 \\ \bold{2)} \ x^{2}+y^{2}+6x-8y-10=0 \\ \bold{3)} \ 3x^{2}+3y^{2}+12x+18y-15=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 3, \ the \ equation \ becomes: \\ x^{2}+y^{2}+4x+6y-5=0 \\ \\ \bold{4)} \ 5x^{2}+5y^{2}-10x+20y-30=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 5, \ the \ equation \ becomes: \\ x^{2}+y^{2}-2x+4y-6=0 \\ \\ \bold{5)} \ 2x^{2}+2y^{2}-24x-16y-8=0 \\ \\ If \ we \ divide \ this \ equation \ by \ 2, \ the \ equation \ becomes: \\ x^{2}+y^{2}-12x-8y-4=0$

$\bold{6)} \ x^{2}+y^{2}+2x-12y$

So let's match each equation:

$\bold{From \ a)} \\ \\ (h,k)=(6,4),\ r=2\sqrt{14} \\ D=-12, \ E=-8 \\ F=-4$

Then, its general form is:

$x^{2}+y^{2}-12x-8y-4=0$

First. a) matches 5) 

$\bold{From \ b)} \\ \\ (h,k)=(2,-6),\ r=2\sqrt{15} \\ D=-4, \ E=12 \\ F=-20$

Then, its general form is:

$x^{2}+y^{2}-4x+12y-20=0$

Second. b) matches 1) 

$\bold{From \ c)} \\ \\ (h,k)=(-2,-3),\ r=3\sqrt{2} \\ D=4, \ E=6 \\ F=-5$

Then, its general form is:

$x^{2}+y^{2}+4x+6y-5=0$

Third. c) matches 3)

$\bold{From \ d)} \\ \\ (h,k)=(-1,6),\ r=\sqrt{46} \\ D=2, \ E=-12, \ F=-9$

Then, its general form is: $x^{2}+y^{2}+2x-12y-9=0$

Fourth. d) matches 6)

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Which of the following activities are examples of data gathering?

arsen [322]

the correct answer is d

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