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3 years ago

Help and show all work please

Mathematics

1 answer:

Aloiza [94]3 years ago

3 0

Answer:

all my work is in the picture but srsly pls u should make another question with more points... blank tho :( this took a rlly long time, pls?

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If you roll one die and flip one coin, what is the probability of rolling a 2 and flipping a head? Why?

Nezavi [6.7K]

Answer:

Probability of rolling a 2 and flipping a head will be $\frac{1}{12}$

Step-by-step explanation:

If we roll one die then probability to get any one side is $\frac{1}{6}$

Therefore, probability to get 2 by rolling the die will be P(A) = $\frac{1}{6}$

Now we flip a coin then getting head or tale probability is $\frac{1}{2}$

Or probability to get head by flipping the coin P(B) = $\frac{1}{2}$

Probability of happening both the events (rolling a 2 and flipping a head) will be denoted by

P(A∩B) = P(A)×P(B)

= $\frac{1}{6}\times \frac{1}{2}$

= $\frac{1}{12}$

Therefore, probability of rolling a 2 and flipping a head will be $\frac{1}{12}$

3 0

3 years ago

Read 2 more answers

Match the parabolas represented by the equations with their foci.

Elenna [48]

Function 1 $f(x)=- x^{2} +4x+8$

First step: Finding when $f(x)$ is minimum/maximum
The function has a negative value $x^{2}$ hence the $f(x)$ has a maximum value which happens when $x=- \frac{b}{2a}=- \frac{4}{(2)(1)}=2$ . The foci of this parabola lies on $x=2$ .

Second step: Find the value of y-coordinate by substituting $x=2$ into $f(x)$ which give $y=- (2)^{2} +4(2)+8=12$

Third step: Find the distance of the foci from the y-coordinate
$y=- x^{2} +4x+8$ - Multiply all term by -1 to get a positive $x^{2}$
$-y= x^{2} -4x-8$ - then manipulate the constant of y to get a multiply of 4
$4(- \frac{1}{4})y= x^{2} -4x-8$
So the distance of focus is 0.25 to the south of y-coordinates of the maximum, which is $12- \frac{1}{4}=11.75$

Hence the coordinate of the foci is (2, 11.75)

Function 2: $f(x)= 2x^{2}+16x+18$

The function has a positive $x^{2}$ so it has a minimum

First step - $x=- \frac{b}{2a}=- \frac{16}{(2)(2)}=-4$
Second step - $y=2(-4)^{2}+16(-4)+18=-14$
Third step - Manipulating $f(x)$ to leave $x^{2}$ with constant of 1
$y=2 x^{2} +16x+18$ - Divide all terms by 2
$\frac{1}{2}y= x^{2} +8x+9$ - Manipulate the constant of y to get a multiply of 4
$4( \frac{1}{8}y= x^{2} +8x+9$

So the distance of focus from y-coordinate is $\frac{1}{8}$ to the north of $y=-14$
Hence the coordinate of foci is (-4, -14+0.125) = (-4, -13.875)

Function 3: $f(x)=-2 x^{2} +5x+14$

First step: the function's maximum value happens when $x=- \frac{b}{2a}=- \frac{5}{(-2)(2)}= \frac{5}{4}=1.25$
Second step: $y=-2(1.25)^{2}+5(1.25)+14=17.125$
Third step: Manipulating $f(x)$
$y=-2 x^{2} +5x+14$ - Divide all terms by -2
$-2y= x^{2} -2.5x-7$ - Manipulate coefficient of y to get a multiply of 4
$4(- \frac{1}{8})y= x^{2} -2.5x-7$
So the distance of the foci from the y-coordinate is - $\frac{1}{8}$ south to y-coordinate

Hence the coordinate of foci is (1.25, 17)

Function 4: following the steps above, the maximum value is when $x=8.5$ and $y=79.25$ . The distance from y-coordinate is 0.25 to the south of y-coordinate, hence the coordinate of foci is (8.5, 79.25-0.25)=(8.5,79)

Function 5: the minimum value of the function is when $x=-2.75$ and $y=-10.125$ . Manipulating coefficient of y, the distance of foci from y-coordinate is $\frac{1}{8}$ to the north. Hence the coordinate of the foci is (-2.75, -10.125+0.125)=(-2.75, -10)

Function 6: The maximum value happens when $x=1.5$ and $y=9.5$ . The distance of the foci from the y-coordinate is $\frac{1}{8}$ to the south. Hence the coordinate of foci is (1.5, 9.5-0.125)=(1.5, 9.375)

8 0

3 years ago

Please help and explain.

Agata [3.3K]

Piecewise functions have different definitions, depending on when you evaluate them.

Given an input x, your function returns:

2x if the input is negative
1 if the input lies between 0 (included) and 2 (excluded)
the square root of x if the input is greater than 2 (included)

You want to know what f(0) is. In other words, you want to know what happens if we give 0 as input.

The piecewise definition tells us that, if the input is 0, the function outputs 1.

So, you have f(0) = 1.

4 0

3 years ago

I know the answer but what’s the work

mina [271]

Answer:

(0.5r^2pi) + (0.5r^2pi) + (bh)

Step-by-step explanation:

All you need to do is to find the area of each shape, then add all areas together.

4 0

3 years ago

Read 2 more answers

Write 0.24 as a fraction in simplest form

guapka [62]

The answer is 24/100

4 0

3 years ago