What is 60 devided by 2v

1. A student took 60 minutes to answer a combination of 20 multiple-choice and extended-response questions. She took 2 minutes t

Darina [25.2K]

Answer:

1) m=15 and r =5

2) 4 and 2 ml

3) x= 0.5 and y = -1

Step-by-step explanation:

given that m multiple choice questions and r extended response questions.

Also given that a) m+r = total no of questions =20 ... i and

2m+6r = total time taken = 60 ... ii

b) Divide second equation by 2, m+3r = 30 ... iii

m+r = 20 ... i

Subtract to get 2r =10 or r =5

m = 20-5 = 15

Verify: m+r = 15+5 =20

and 2m+6r = 30+30 = 60 minutes.

Hence verified

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2) Let a litres of 20% solution and b litres of 50% solution be mixed

a) Then total volume = 6 ml = a+b ... i

Resulting solution = 30% of 6 ml = 1.8 = 0.2a+0.5b ... ii

b) Solve i and ii

b = 6-a: substitute in ii.

0.2a + 3-0.5a = 1.8

Or a = 4 ml and b = 2ml

Verify: Total volume = a+b =6ml and

concentration = 0.2(4)+0.5(2) = 1.8 = 30% of 6 ml.

Thus verified

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3) 2x-3y=4 ...i

2x-5y =6... ii

Because x term has the same coefficient in both the equations, elimination is easier.

i-ii gives 2y =-2 or y =-1

Substitute in i, 2x+3 =4 or x = 0.5

So answer is x = 0.5 and y =1

6 0

2 years ago

Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x=12

lidiya [134]

Answer:

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable.

Given that y varies directly with x, if we introduce a constant of proportionality, k, the expression becomes

y = kx

If y = 8 when x = 3, then

8 = 3k

k = 3/8

Therefore, the direct variation equation that relates x and y is

y = 3x/8

When x = 12, then

y = 3 × 12/8

y = 4.5

3 0

3 years ago

Which ones are true?

Aleks [24]

Answer:

The first, third and last one are true

7 0

2 years ago

Solve the following equation for n 18n^2-50=0

Firdavs [7]

$18n^2-50=0\ \ \ |+50\\\\18n^2=50\ \ \ |:18\\\\n^2=\dfrac{50}{18}\\\\n^2=\dfrac{50:2}{18:2}\\\\n^2=\dfrac{25}{9}\to n=\pm\sqrt{\dfrac{25}{9}}\\\\n=\pm\dfrac{\sqrt{25}}{\sqrt{9}}\\\\\boxed{n=-\dfrac{5}{3}\ \vee\ n=\dfrac{5}{3}}$

$Used:\\\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}$

3 0

3 years ago

The following quote is from a paper on the weight of the bottle as a possible extrinsic cue with which to estimate the price (an

yuradex [85]

Answer:

1. a. Weak

2. r^2=0.0169

The variation in the price of the wine explained by the variation in the weight of the bottle is 1.69%.

Step-by-step explanation:

The correlation between the weight of the wine bottles and the price of the wine is r=0.13.

The values for r goes from r=-1, where a perfect negative correlation to r=1 for a perfect positive correlation. The value r=0 indicates no correlation at all.

Then, a value of r close to 0 indicates very weak correlation between the two variables.

The value for r^2 in this case is:

$r^2=0.13^2=0.0169$

The value of r2 can be interpreted as the proportion of the variation in the dependant variable explained by the independent vairable. In this case, the variation in the price of the wine explained by the variation in the weight of the bottle is 1.69%, which is very close to 0.

8 0

2 years ago