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3 years ago

Lucy makes green paint by mixing yellow and blue paint in the ratio 5:2. Blue paint costs

Mathematics

1 answer:

ahrayia [7]3 years ago

8 0

Answer:

No, she won’t make a profit

Step-by-step explanation:

Here, we are interested in determining if Lucy made a profit or a loss.

The cost of blue paint is 30 pounds for 5 liters. This means that a liter of blue paint is 30/5 = 6 pounds per liter

The cost of yellow paint is 28 pounds per 7 liters, the cost per liter is 28/7 = 4 pounds per liter

Now, in her mixing, she mixes 5 parts of yellow paint and 2 parts of blue paint.

This means that she mixed them the ratio as follows per liter;

For yellow, we have; 5/(5+2) = 5/7

For blue we have 2/(5+2) = 2/7

Now since a liter of yellow paint cost 4 pounds

5/7 of a liter will cost 5/7 * 4 = 20/7 pounds

For the blue paint, a liter cost 6 pounds, 2/7 of a liter will cost 2/7 * 6 = 12/7

The total cost in pounds in this;

20/7 + 12/7 = 32/7 = £4.57 pounds to 2 decimal place

Now she sells her green paint product at £4.5 per liter. Since this is less than the cost price of production which is £4.57, she is running at a loss

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The ratio of a number and 4 into a algebraic phrase

riadik2000 [5.3K]

Answer:

x : 4

Step-by-step explanation:

The ratio of a number and 4 into algebraic phrase ;

Let the number = x

Expressing the number and 4 as a ratio in algebraic phrase will be written as :

Number : 4

x : 4

4 0

3 years ago

Write the equation of the line passing through the points (-4,5) and (4,1). Show all of your work.

777dan777 [17]

First, find the slope using the equation, y2 - y1 / x2 - x1

1-5 / 4 - - 4 = -4/8 = -1/2

plug this into slope intercept form

y = -1/2x + b

Next use one of the points to find b using point-slope form. I will use (4,1)

y - y1 = m ( x - x1)

y - 1 = -1/2 (x - 4)

y -1 = -1/2x + 2

+1 +1

y = -1/2x + 3 is your equation

5 0

2 years ago

Assume a standard deviation of LaTeX: \sigma = 0.75σ = 0.75. You plan to take a random sample of 110 households, what is the pro

olchik [2.2K]

Answer:

P(2.50 < Xbar < 2.66) = 0.046

Step-by-step explanation:

We are given that Population Mean, $\mu$ = 2.58 and Standard deviation, $\sigma$ = 0.75

Also, a random sample (n) of 110 households is taken.

Let Xbar = sample mean household size

The z score probability distribution for sample mean is give by;

Z = $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

So, probability that the sample mean household size is between 2.50 and 2.66 people = P(2.50 < Xbar < 2.66)

P(2.50 < Xbar < 2.66) = P(Xbar < 2.66) - P(Xbar $\leq$ 2.50)

P(Xbar < 2.66) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{2.66-2.78}{\frac{0.75}{\sqrt{110} } }$ ) = P(Z < -1.68) = 1 - P(Z $\leq$ 1.68)

= 1 - 0.95352 = 0.04648

P(Xbar $\leq$ 2.50) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{2.50-2.78}{\frac{0.75}{\sqrt{110} } }$ ) = P(Z $\leq$ -3.92) = 1 - P(Z < 3.92)

= 1 - 0.99996 = 0.00004

Therefore, P(2.50 < Xbar < 2.66) = 0.04648 - 0.00004 = 0.046

3 0

2 years ago

What s the midpoint of the line segment with endpoints (3.5,2.2) and (1.5,-4.8)

Natali5045456 [20]

Answer:

First, you must find the midpoint of the segment, the formula for which is

(

)

. This gives

(

−

)

as the midpoint. This is the point at which the segment will be bisected.

Next, since we are finding a perpendicular bisector, we must determine what slope is perpendicular to that of the existing segment. To determine the segment's slope, we use the slope formula

−

, which gives us a slope of

Perpendicular lines have opposite and reciprocal slopes. The opposite reciprocal of

−

We now know that the perpendicular travels through the point

(

−

)

and has a slope of

−

Solve for the unknown

−

(

−

)

⇒

Therefore, the equation of the perpendicular bisector is

−