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3 years ago

Five toppings for a pizza are available at Polina's Pizza. How many combinations of two different toppings are possible?

1 answer:

8 0

Evaluate

C This gives you the # of combinations possible from 5 choices taken
5 2 2 at a time. The answer is 10. I used my calculator to find this.

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What is the value of y in this system of equations: 3x + y = 9 y = –4x + 10 ?

Ahat [919]

3x + y = 9 (I)
y = –4x + 10 (II)
------------------------
 $\left \{ {{3x + y = 9 } \atop {y = -4x + 10 }} \right.$

Pass the incognito "4x" to the first term, changing the signal when changing sides.
-------------------------
simplify by (-1)
 $\left \{ {{3x + y = 9.(-1)} \atop {4x + y = 10 }} \right.$ 

-------------------------
 $\left \{ {{- 3x - \diagup\!\!\!\!y =-9} \atop {4x + \diagup\!\!\!\!y = 10}} \right. 
$

-------------------------
 $\left \{ {{- 3x = - 9} \atop {4x = 10}} \right.$ 

-----------
 $\boxed{x = 1}$ 

Substitute in equation (I) to find the value of "Y".

3x + y = 9 (I)
3*(1) + y = 9
3 + y = 9
y = 9 - 3
$\boxed{y = 6}$

Answer:
$\boxed{\boxed{ \left \ {{x=1} \atop {y=6}} \right. }}$

6 0

3 years ago

The table and the graph each show a different relationship between the same two variables, x and y:

Oksanka [162]

1. y₁ = 70x
2. y₂ = 55x

Solve y₁ - y₂ for x = 11.

8 0

3 years ago

SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8 and a standard deviation of 4.8.

Y_Kistochka [10]

Answer:

The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.

Step-by-step explanation:

Mean SAT scores = 1026

Standard Deviation = 209

Mean ACT score = 20.8

Standard Deviation = 4.8

We are given SAT and ACT scores of a student and we have to compare them. We cannot compare them directly so we have to Normalize them i.e. convert them into such a form that we can compare the numbers in a meaningful manner. The best way out is to convert both the values into their equivalent z-scores and then do the comparison. Comparison of equivalent z-scores will tell us which score is higher and which is lower.

The formula to calculate the z-score is:

$z=\frac{x-\mu}{\sigma}$

Here, μ is the mean and σ is the standard deviation. x is the value we want to convert to z score.

z-score for junior scoring 860 in SAT exam will be:

$z=\frac{860-1026}{209}=-7.59$

z-score for junior scoring 16 in ACT exam will be:

$z=\frac{16-20.8}{4.8}=-1$

The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.

4 0

3 years ago

Explain how to verify that 3(2x + 5) = 9 + 3x and x = –2 are equivalent equations.

aniked [119]

3 times (2x + 5) is 6x + 15.

6x + 15 = 9 + 3x.

Group by like terms. 6 = -3x

Divide to get x by itself. 6/-3 = -2

Thus -2 = x

6 0

3 years ago

What is the value of tan A? I'm confused

Oliga [24]

Tan(A) = Opp/Adj = CB / AC = 12/9 = 4/3

hope it helps

6 0

3 years ago

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