Determine the solution set of (3x + 1)2

1-i need to mix 25% mineral spirits to the varnish i am using what ratio of spirit to varnish am i using? 2-if i use 240 ml of v

In-s [12.5K]

Answer: (a) The ratio of spirit to varnish is 1 : 3

(b) You will need 80 ml of mineral spirits

(c) Ratio = 3 : 2

Step-by-step explanation: (a) If you have to mix 25% mineral spirit to the varnish as required in the question, then the whole solution would effectively contain 25 percent spirit and 75 percent varnish, giving you a hundred percent solution. To express both quantities in ratio can be done as follows;

Ratio = Spirit : Varnish

Ratio = 25 : 75

Ratio = 1 : 3

(b) Next, if you use 240 ml of varnish, this quantity would constitute 75 percent or ratio 3 out of 4 of your total solution. Therefore 240 ml of varnish can be expressed as follows;

240 : x = 3 : 4

Where x is the total solution and the right hand side (3 : 4) expresses the ratio of varnish in relation to the total solution. Hence,

240/x = 3/4

By cross multiplication you now have,

3x = 240 * 4

x = 960/3

x = 320

If x is the total solution which is 320 ml, and varnish constitutes 240 ml, then spirit equals,

Spirit = Total solution - varnish

Spirit = 320 - 240

Spirit = 80.

Therefore, you would need 80 ml of mineral spirits.

(c) Robson's tapestries all measure 1.5 m by 1 m. This can be expressed in whole numbers by first eliminating the decimal. Multiplying both dimensions by 10 results in,

1.5 (10) x 1 (10)

15 x 10

If both measurements can also be expressed as 15 m by 10 m, then reducing to the least terms would result in 3 by 2. That is,

15/5 by 10/5

3 by 2

Expressed as a ratio, this now becomes

Ratio = 3 : 2

5 0

2 years ago

The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a na

lorasvet [3.4K]

Answer:

a. 95% confidence interval estimate for the population mean amount of paint included in a 1-gallon can is 0.998±0.0055

b. No, because a 1-gallon paint can containing exactly 1-gallon of paint lies within the 95% confidence interval.

c. Yes. The population amount of paint per can is assumed normally distributed, because confidence interval calculations assume normal distribution of the parameter.

d. 90% confidence interval is 0.998±0.0046. The answer in b. didn't change; 1-gallon paint can containing exactly 1-gallon of paint lies within the 90% confidence interval. The manager doesn't have a right to complain to the manufacturer.

Step-by-step explanation:

Confidence Interval can be calculated using M±ME where

M is the sample mean amount of paint per 1-gallon can (0.998 gallon)

ME is the margin of error from the mean

And margin of error (ME) can be calculated using the equation

ME= $\frac{z*s}{\sqrt{N} }$ where

z is the corresponding statistic in the 95% confidence level (1.96)

s is the sample standard deviation (0.02 gallon)

N is the sample size (50)

Then ME= $\frac{1.96*0.02}{\sqrt{50} }$ ≈0.0055

95% confidence interval is 0.998±0.0055

90% confidence interval can be calculated similary, only z statistic is 1.64.

ME= $\frac{1.64*0.02}{\sqrt{50} }$ ≈0.0046

90% confidence interval is 0.998±0.0046

8 0

2 years ago

Sammie bought just enough fencing to border either a rectangular plot or a square plot, as shown. The perimeters of the plots ar

Gekata [30.6K]

Perimeter of square : p = 4a.....
p = 4(x + 2)
p = 4x + 8

perimeter of rectangle : p = 2(L + W)
p = 2(3x + 2 + x - 1)
p = 2(4x + 1)
p = 8x + 2

so if the perimeters are te same, lets set them equal to each other and solve for x

4x + 8 = 8x + 2
8 - 2 = 8x - 4x
6 = 4x
6/4 = x
1.5 = x

the square : p = 4x + 8.....p = 4(1.5) + 8.....p = 14 meters
the rectangle : p = 8x + 2....p = 8(1.5) + 2.....p = 14 meters

so she bought 14 meters of fencing <==

8 0

2 years ago

Patricia can drive 36 kilometers for every 3 liters of gas she puts in her car

Anna35 [415]

Answer:

Patricia will run 132 kilometers with 11 liters of gas.

Step-by-step explanation:

The given table is representing the distance driven by Patricia for every liter of gas she puts in her car.

With 3 liters of gas she drives 36 kilometers.

This means in one liter of gas distance covered by the car = $\frac{36}{3}=12$ kilometers.