When ordering a sundae, you may choose three toppings from their list of 10 available. Assuming that your chosen toppings must be different, how many different sundaes with three toppings can you order?

Answers

Answer 1

Answer:

Answer:

there are 120 different sundaes with three toppings you can order.

Step-by-step explanation:

If the chosen toppings must be different, then that means it's a Combination where the order doesn't matter (as long as they're all different).

Equation: 10C3

Forming Equation: 10!/(10-3)!*3!=10*9*8*7!/7!*3!=10*9*8/6=720/6=120

Therefore, there are 120 different sundaes with three toppings you can order.

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What is the y-intercept of the line?

y= -2x - 8

y-intercept =

Answers

Like I said on the other question. Slope will ALWAYS be the number beside x and y-intercept will always be after that.

Slope-intercept form = y = mx + b

Slope goes where m is and y-intercept goes where b is.

Hope this helps!

Answer:

-8

Step-by-step explanation:

The ratio of Monarch butterflies to Queen butterflies at a butterfly farm was 9:7. If there are no additional butterflies at the farm, what is the ratio of Queen butterflies to the total number of butterflies at the farm?

Answers

7:16 is the correct answer because you add up all the butter flies and then put them into a ratio is that better.

Answer:

7:16 is the answer your welcome! :)

Step-by-step explanation:

If x + y = 9, z + y = 12, and z + x = 11, what is the average (arithmetic mean) of x, y and z?

Answers

$x+y=9 \n z + y = 12 \n z + x = 11 \n x+y+ z + y+ z + x=9+12+11 \n 2x+2y+ 2z=32 \n x+y+ z=16$

Discontunuity of f(x) = x^2 plus 2x over x plus 2

Answers

Answer:

When we have a function like:

$f(x) = (g(x))/(h(x))$

This function will have a discontinuity only if it diverges, and a divergence can happen when the denominator is equal to zero and the numerator is different than zero.

In this case, we have the equation:

$f(x) = (x^2 + 2*x)/(x + 2)$

Here the denominator is:

h(x) = x + 2

This is equal to zero when:

x + 2 = 0

x = -2

Now we need to see what happens with the numerator when x = -2

g(-2) = (-2)^2 + 2*(-2) = 0

Is equal to zero.

Then we need to see the limit when x -> -2, and use the L'Hopital theorem.

$\lim_(x \to \ - 2) (x^2 + 2*x)/(x + 2)$

Because we have zero over zero at that point, we need to look at the quotients of the derivatives of both numerator and denominator.

$\lim_(x \to \ - 2) (2*x+ 2)/( 2) = (2*-2 + 2)/(2) = -1$

Then the function does not diverge, then the function has no discontinuity.

We also could look at the graph of f(x) to see it:

Our function is a linear function, and this is because the numerator is x times the denominator, then the function is:

f(x) = x.

Mr. and Mrs. Romero are expecting triplets. Suppose the chance of each child being a boy is 50% and of being a girl is 50%. Find the probability of each event. P(at least one boy anf one girl)

P(two boys and one girl)

P(at least two girls)

I don't care if you cab only answer one, I would very much appreciate it if you still answered that one instead of nothing.

Answers

Answer:

1) $\text{P(at least one boy and one girl)}=(3)/(4)$

2) $\text{P(at least one boy and one girl)}=(3)/(8)$

3) $\text{P(at least two girls)}=(1)/(2)$

Step-by-step explanation:

Given : Mr. and Mrs. Romero are expecting triplets. Suppose the chance of each child being a boy is 50% and of being a girl is 50%.

To Find : The probability of each event.

1) P(at least one boy and one girl)

2) P(two boys and one girl)

3) P(at least two girls)

Solution :

Let's represent a boy with B and a girl with G

Mr. and Mrs. Romero are expecting triplets.

The possibility of having triplet is

BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG

Total outcome = 8

$\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}$

1) P(at least one boy and one girl)

Favorable outcome = BBG, BGB, BGG, GBB, GBG, GGB=6

$\text{P(at least one boy and one girl)}=(6)/(8)$

$\text{P(at least one boy and one girl)}=(3)/(4)$

2) P(at least one boy and one girl)

Favorable outcome = BBG, BGB, GBB=3

$\text{P(at least one boy and one girl)}=(3)/(8)$

3) P(at least two girls)

Favorable outcome = BGG, GBG, GGB, GGG=4

$\text{P(at least two girls)}=(4)/(8)$

$\text{P(at least two girls)}=(1)/(2)$

Let's represent a boy with B and a girl with G

For example BBB is three boys and BGB is two boys and one girl.

These are all the possibilities

1) BBB

2) BBG

3) BGB

4) BGG

5) GBB

6) GBG

7) GGB

8) GGG

There is in total 8 different possibilities.

Now let's analyze the conditions

p (at least one boy and one girl)

That excludes only BBB and GGG so they are 6 possibilities out of 8

p = 6/8 = 3/4

p (two boys and one girl).

Those are 3 out of 8

p = 3/8

p (at least two girls)

Those are 3 (two girls) + 1(three girls) = 4

P = 4/8 = 1/2

Please, let me know if this was satisfactory for you.

Given the center of the circle (-3,4) and a point on the circle (-6,2), (10,4) is on the circle.True or False?

Answers

With the center and the point (-6,2) you can deduce the equation of the circle

(x-xo)^2 + (y-yo)^2 = r^2

(x+3)^2 + (y-4)^ = r^2

r^2 is otained from the center and the point (-6,2)

r^2 = (-6 -(-3))^2 + (2-4)^2 = (-6+3)^2 + (-2)^2 = (-3)^2 + 4 = 9 + 4 = 13.

Then the equation of the circle is

(x+3)^2 + (y-4)^ = 13

Now we subsitute the point (10,4) into that equation and see whether it belongs to it:

(10+3)^2 + (4-4)^2 = 13^2

13^2 ≠ 13, so the point does not belong to the equation.

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kirby often forgets to switch the inequity sign when dividing a negative. when solving 3x-10≥x, should kirby collect the variables on the left or the right? why?

Which statement about the solution to the following system of equations is true?3x - 2y = 4-6x + 4y = -8A) There is no solution because the equation represents the same lineB) There is no solution because the equations have the same slopeC) There are infinitely many solutions because the lines have the same slope and different y-intercepts.D) There are infinitely many solutions because the equations represent the same line

The sides of a triangle measures 6 inches, 8 inches, and 10 inches. The triangle has one 90° angle. What type of triangle is it?