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3 years ago

A collection of quarters and dimes is worth $18.30. There are 111 coins in all.

1 answer:

7 0

We can set up a system of equations.

x + y = 111
0.25x + 0.10y = 18.30

x + y = 111

Subtract 'y' to both sides:

x = -y + 111

Plug in '-y + 111' for 'x' in the 2nd equation:

0.25(-y + 111) + 0.10y = 18.30

Distribute 0.25 into the parenthesis:

-0.25y + 27.75 + 0.10y = 18.30

Combine like terms:

-0.15y + 27.75 = 18.30

Subtract 27.75 to both sides:

-0.15y = -9.45

Divide -0.15 to both sides:

y = 63

Plug this back into any of the two equations to find the 'x' value.

x + y = 111

x + 63 = 111

Subtract 63 to both sides:

x = 48

So there are 48 quarters and 63 dimes.

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For the given equation find the value a, b, and c, determine the direction in which the parabola opens and determine the y-inter

Y_Kistochka [10]

Answer: Table A

Step-by-step explanation:

The coefficient of x^2 is 1, the coefficient of x is -6, and the constant is 0. This means that a = 1, b = -6, and c = 0.

This eliminates tables B and C.

Now, we need to determine if the graph opens up or down to differentiate between A and B. Since the coefficient of x^2 is positive, the graph opens up.

Thus the answer is <u>Table A.</u>

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2 years ago

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Answer:

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3 years ago

The following six independent length measurements were made (in feet) for a line: 736.352, 736.363, 736.375, 736.324, 736.358, a

horrorfan [7]

Answer:

Assuming population data

$\sigma = \sqrt{0.000354}=0.0188$

Assuming sample data

$s = \sqrt{0.000425}=0.0206$

Step-by-step explanation:

For this case we have the following data given:

736.352, 736.363, 736.375, 736.324, 736.358, and 736.383.

The first step in order to calculate the standard deviation is calculate the mean.

Assuming population data

$\mu = \frac{\sum_{i=1}^6 X_i}{6}$

The value for the mean would be:

$\mu = \frac{736.352+736.363+736.375+736.324+736.358+736.383}{6}=736.359$

And the population variance would be given by:

$\sigma^2 = \frac{\sum_{i=1}^6 (x_i-\bar x)}{6}$

And we got $\sigma^2 =0.000354$

And the deviation would be just the square root of the variance:

$\sigma = \sqrt{0.000354}=0.0188$

Assuming sample data

$\bar X = \frac{\sum_{i=1}^6 X_i}{6}$

The value for the mean would be:

$\bar X = \frac{736.352+736.363+736.375+736.324+736.358+736.383}{6}=736.359$

And the population variance would be given by:

$s^2 = \frac{\sum_{i=1}^6 (x_i-\bar x)}{6-1}$

And we got $s^2 =0.000425$

And the deviation would be just the square root of the variance:

$s = \sqrt{0.000425}=0.0206$

6 0

3 years ago

The side lengths 30, 41, and 70 can form a triangle.

True [87]

A = 30
B = 41
C = 70

A < B + C
30 < 41+70 ==> 30 < 111 (TRUE)

B < A + C ==>
41 < 30 + 70 ==> 41 < 100 (TRUE)

C < A+B
70 < 30 + 41 ==> 70 < 71 (TRUE)

Yes, can!

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NemiM [27]

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Step-by-step explanation

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2 years ago