Answer: The null and the alternative hypotheses are given below:
Under null hypothesis, the test statistic is:
Now we have to find the left tailed critical value at 0.01 significance level using the standard normal table.
The critical value is:
Since the test statistic is -0.26 lies in acceptance region because the critical region is beyond -2.33, therefore, we fail to reject the null hypothesis.
Answer:
there are no graphs
Step-by-step explanation:
but the slope is -2/1
Answer:
3. 12 airplanes and 6 cars
4. 30 swirled marbles and 22 solid marbles
Step-by-step explanation:
In each case, it is easy enough to check the offered answer to see if it matches problem requirements.
3. You are correct.
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4. All answers total 52 marbles, so we need to check to see which has 8 more swirled marbles.
a) 28 more swirled marbles
b) 28 fewer swirled marbles
c) 8 fewer swirled marbles
d) 8 more swirled marbles -- as required by the problem
The correct choice is the last one: 30 swirled marbles; 22 solid marbles.
_____
The first step in solving any problem is to understand what the problem is and what a solution will look like. When the questions are multiple-choice, it is often easier to check the choices than to solve the problem from scratch. Knowing what the solution must look like often lets you eliminate half or more of the answer choices, simplifying the remaining checking.
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Both of these are "sum and difference" problems. You are given the total of two items and the difference between them. The generic solution is that the larger quantity is half the sum of the two given numbers.
<u>For 3</u>, this means the number of airplanes (the larger quantity) is half of 18+6=24, so is 12. The number of cars is 6 less than that: 12-6=6.
<u>For 4</u>, this means the number of swirled marbles (the larger quantity) is half of 52+8=60, so is 30. The number of solid marbles is 8 less than that: 30-8=22.
Step-by-step explanation:
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A) The answer is $38.95
Two walls have dimensions: 14 ft x 8 ft, each with area A1 = 14 · 8 = 112 ft²
Two walls have dimensions: 18 ft x 8 ft each with area A2 = 18 · 8 = 144 ft²
The area that needs to be painted is:
A = 2A1 + 2A2 = 2*112 + 2*144 = 224 + 288 = 512 ft²
Since you need two coats of paint, total area that needs to be painted is
512 × 2 = 1024 ft²
Now, make a proportion:
If 1 gallon covers 250 ft², how many gallons will cover 1024 ft²
1 : 250 = x : 1024
x = 1024/250 = 4.096 gallons ≈ 4,1 gallons
Since 1 gallon costs $9.50, 4.1 gallons will cost $38.95:
$9.50 × 4.1 gallons = $38.95
b) The answer is $1,260.
The dimensions of the floor are: 18 ft × 14 ft
Therefore, the area that needs to be covered with carpet is:
A = 18 · 14 = 252 ft²
Since 1 ft² costs $5, that means that 252 ft² will cost $1,260:
252 ft² × $5 = $1,260
c) The answer is $1,890.
The ceiling will have the same dimensions and the same area as the floor.
The dimensions of the ceiling are: 18 ft × 14 ft
Therefore, the area that needs to be covered is:
A = 18 · 14 = 252 ft²
Since 1 ft² costs $7.50, that means that 252 ft² will cost $1,890:
252 ft² × $7.5 = $1,890
d) The answer is $3,188.95.
We now know that:
- the cost of painting the four walls with two coats of paint is: $38.95
- the cost of carpeting the floor with carpet is: $1,260
- the cost of ceiling with acoustic tile is: $1,890
All we have to do is to sum it up to find the total cost of renovating the walls,floor, and ceiling:
$38.95 + $1,260 + $1,890 = $3,188.95
