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2 years ago

14

gavin is making cranberry lemonade. he wants to make a total of 6 cups. he needs to use 3 times as much lemonade as cranberry ju

ice. how much of each type of juice should he use? if l = cups of lemonade, and c= cups of cranberry, write the equations that you used.

1 answer:

Inessa [10]2 years ago

4 0

Answer:

3l= c

Step-by-step explanation:

as use 3 cup of cranberry juice, lemonade will be used 1 cup.

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Ivanna is playing a game in which she spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a num

saul85 [17]

Answer:

The spinner has 6 equal-sized slices, so each slice has a 1/6 probability of showing up.

I guess that we want to find the expected value in one spin:

number 1: wins $1

number 2: wins $3

number 3: wins $5

number 4: wins $7

number 5: losses $8

number 6: loses $8

The expected value can be calculated as:

Ev = ∑xₙpₙ

where xₙ is the event and pₙ is the probability.

We know that the probability for all the events is 1/6, so we have:

Ev = ($1 + $3 + $5 + $7 - $8 - $8)*(1/6) = $0

So the expected value of this game is $0, wich implies that is a fair game.

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2 years ago

In △ABC, m∠A=15 °, a=10 , and b=11 . Find c to the nearest tenth.

pshichka [43]

Answer:

The answer is:

$\bold{c\approx 20.2\ units}$

Step-by-step explanation:

Given:

In △ABC:

m∠A=15°

a=10 and

b=11

To find:

c = ?

Solution:

We can use cosine rule here to find the value of third side c.

Formula for cosine rule:

$cos A = \dfrac{b^{2}+c^{2}-a^{2}}{2bc}$

Where

a is the side opposite to $\angle A$

b is the side opposite to $\angle B$

c is the side opposite to $\angle C$

Putting all the values.

$cos 15^\circ = \dfrac{11^{2}+c^{2}-10^{2}}{2\times 11 \times c}\\\Rightarrow 0.96 = \dfrac{121+c^{2}-100}{22c}\\\Rightarrow 0.96 \times 22c= 121+c^{2}-100\\\Rightarrow 21.25 c= 21+c^{2}\\\Rightarrow c^{2}-21.25c+21=0\\\\\text{solving the quadratic equation:}\\\\c = \dfrac{21.25+\sqrt{21.25^2-4 \times 1 \times 21}}{2}\\c = \dfrac{21.25+\sqrt{367.56}}{2}\\c = \dfrac{21.25+19.17}{2}\\c \approx 20.2\ units$

The answer is:

$\bold{c\approx 20.2\ units}$

4 0

2 years ago

Apply The axes in the coordinate grid at the right represent the walls of a bedroom. One corner of the room is at the origin. Wh

Novosadov [1.4K]

Answer: 11.2 because I know trust me. I did a worksheet with this same question and got 11.2 and it was correct.

5 0

2 years ago

Emily is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Emily will earn $

Hitman42 [59]

Answer:

(6,2)

Step-by-step explanation:

Variable Definitions:

x= the number of commercials

y= the number of movies

Each commercial earns Emily $50, so x commercials would earn her 50x dollars in royalties. Each movie earns Emily $150, so y movies would earn her 150y dollars in royalties. Therefore, the total royalties 50x+150y equals $600:

50x+150y=600

Since Emily's songs were played on 3 times as many commercials as movies, if we multiply 3 by the number of movies, we will get the number of commercials, meaning x equals 3y.

x=3y

Write System of Equations:

50x+150y=600

x=3y

Solve for y in each equation:

1) 50x+150y=600

150y=−50x+600

y=-1/3x+4

2) x=3y

y=1/3x

The x variable represents the number of commercials and the yy variable represents the number of movies. Since the lines intersect at the point (6,2) we can say:

Emily's songs were played on 6 commercials and 2 movies.

4 0

2 years ago

Steve stayed after school for extra activities 55% of the 180 school days this year. How many days did Steve stay after school?

musickatia [10]

Answer:

11/20 or 99/180 days

Step-by-step explanation:

55/100 converted to ?/180

180/100=1.8

so you would do the same on the numerator which is 55*1.8=99

99/180= 33/60=11/20

7 0

2 years ago