Eric takes a train to his parent’s house 320 miles away. If the trip takes 4 hours, what is the unit rate of the train?

Answer:

Twelve less three times a number is at least nine.

Twelve minus the product of three and a number is no smaller than nine.

Step-by-step explanation:

complete question is:

Twelve less than three times a number is greater than or equal to nine.

Twelve less than three times a number is at least nine.

Twelve less three times a number is at least nine.

Twelve minus the product of three and a number is no more than nine.

Twelve minus the product of three and a number is no smaller than nine.

ANSWER:

Twelve less three times a number is at least nine.

The phrase "twelve less three..." means that the "three times a number" is being subtracted from twelve. So, it has to be at least nine.

Twelve minus the product of three and a number is no smaller than nine.

Even the least number you suppose is 1 we'll get 9

e.g: 12-3(1)=9. Therefore, this statement also represent the inequality

Check attachment for the remaining part of the questions.

Answer:

The correct options are:

C. Twelve less three times a number is at least nine.

F. Twelve minus the product of three and a number is no smaller that nine.

Step-by-step explanation:

Given 12 - 3x ≥ 9,

we want to check which phrase from the options can be used to represent the inequality.

12 - 3x: This means the product of 3 and a number is subtracted from 12.

≥: This is the "Greater or equal to" symbol. It is used to show that the quantity on the left hand side of the symbol is at least, the exact quantity on the right. It means the quantity on the right hand side can be equal, or greater, but can never be smaller the quantity on the left hand side.

So, the statement means

When 3 is multiplied my a number, and then the result is subtracted from 12, what we have is at least 9.

The only statements that corresponds to this from the options are:

1. Twelve less three times a number is at least nine.

2. Twelve minus the product of three and a number is no smaller that nine.

Answer:

675 samples

752 samples

Step-by-step explanation:

Given that :

α = 90%

E = 0.03

Previous estimate (p) = 0.34

Estimated sample proportion (n)

n = p *q * (Zcritical /E)

Zcritical = α/2 = (1 - 0.9) /2 = 0.1 / 2 = 0.05

Z0.05 = 1.645 ( Z probability calculator)

q = 1 - p = 1 - 0.34 = 0.66

n = 0.34 * 0.66 * (1.645/0.03)^2

n = 674.70

n = 675

B.) without prior estimate given ;

p and q should have equal probability

Hence ;

p = 0.5 ; q = 0.5

n = 0.5 * 0.5 * (1.645/0.03)^2

n = 751.67361

n = 752

Final answer:

To determine the sample size for the research, a mathematical calculation is required, considering the level of confidence, the desired margin of error, and, if available, a previous estimate. For a 90% confidence level, two calculations are made based on an assumed proportion—first using the existing estimate of 0.34, and second with no prior estimate (commonly taken as 0.5).

Explanation:

The researcher is trying to determine the sample size required for a study on high-speed Internet access. The sample size can be calculated based on the level of confidence desired and the desired margin of error. In this case, (a) she is using a previous estimate of 0.34 and (b) she does not use any prior estimates.

For the calculation, we can use the formula for sample size in hypothesis testing for a population proportion:

n = (Z^2 * p * (1-p)) / E^2

Where:

• n = required sample size
• Z = z-score corresponding to our desired level of confidence
• p = assumed proportion (in part (a) this is 0.34)
• E = desired margin of error

For a 90% confidence level, the corresponding z-score is approximately 1.645. Now we can plug in the numbers.

(a) If she uses a previous estimate of 0.34, the calculation would be:

n = (1.645^2 * 0.34 * 0.66) / (0.03)^2

You will need to round up to the nearest whole number as you cannot have a part of a participant.

(b) If no previous estimate is used, it is common practice to use 0.5 as this will provide the maximum variance and, therefore, the largest sample size. The calculation would be:

n = (1.645^2 * 0.5 * 0.5) / (0.03)^2

Again, round up to the next whole number. Insert the results for these calculations to your answer.

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Answer:

Step-by-step explanation:

Given the supply of land is perfectly inelastic, the drop in prices must have resulted from decreased demand for land. The demand for land would fall if there were less of a return on the land (i.e., rent), so we can safely assume that land rent fell in Japan between 1990 and 2001. The shifts from D3 to D2 to D1 demonstrate graphically what happened in Japan.

Answer:

7.56 quarts of antifreeze in the resulting mixture, and 37.8% of the resulting mixture is antifreeze.

Step-by-step explanation:

8 * .45= 3.6 quarts antifreeze

12 * .33= 3.96 quarts antifreeze

3.6 + 3.96= 7.56 quarts of antifreeze in the resulting mixture

7.56 quarts/ 20 quarts (12 + 8) * 100= 37.8%

Final answer:

In the combined solution, there are 7.56 quarts of anti-freeze, which equals 37.8% of the total solution.

Explanation:

To solve this problem, we first need to calculate how many quarts of anti-freeze are in each solution, then add them together.

First, we have 8 quarts of a solution that is 45% anti-freeze. To find how many quarts of the solution is anti-freeze, we multiply the total amount by the percentage: 8 quarts * 0.45 = 3.6 quarts anti-freeze.

Next, we have 12 quarts of a solution that is 33% anti-freeze. Doing the same calculation as before, 12 quarts * 0.33 = 3.96 quarts anti-freeze.

Now, to find the total quarts of anti-freeze in the combined solution, we simply add the two amounts together: 3.6 quarts + 3.96 quarts = 7.56 quarts.

The total amount of solution is 8 quarts (from the first solution) + 12 quarts (from the second) = 20 quarts.

To find the percent of anti-freeze in the final solution, we divide the total amount of anti-freeze by the total amount of solution: (7.56 quarts / 20 quarts) * 100 = 37.8%. Therefore, the resulting mixture is 37.8% anti-freeze.

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Answer:

Step-by-step explanation:

The square has 4 sides with length 4

The right triangle has the right side equal to 4yd + 4yd(from the square) = 8yd

Using the Pythagorean Theorem, we find that the left side of the triangle has length = 10yd

The area of the whole thing is the area of the square + the area of the triangle

The formula for the area of a square with sides l is

The area of the triangle is trickier, but you can imagine tracing a line in the left side and the upper side to form a rectangle, and the area of that is A = , the area of the triangle will be half the area of the rectangle so it'll be

The total area will be;

Area of the square + Area of the triangle =

Answer:

The correct options are 1, 2 and 4.

Step-by-step explanation:

In a triangle, the side which does not make an angle is called opposite side of that angle.

From the given graph it is clear that

Opposite side of ∠L is NM.

Option 1 is correct.

Opposite side of ∠M is NL.

Opposite side of ∠N is ML.

Option 2 is correct.

The side next to an angle is called adjacent side.

Adjacent sides of ∠L is LM and LN.

Adjacent sides of ∠M is LM and MN.

Adjacent sides of ∠N is LN and MN.

In a right angled triangle, the opposite sides of a right angle is called hypotenuse.

Angle M is a right angled, so the side NM is hypotenuse. Option 4 is correct.

Therefore the correct options are 1, 2 and 4.