Explanation:
The margin of error will most likely be reduced by increasing the sample size while randomly selecting participants from
the initial population of interest.
Explanation:
The ratio of boy to girls is 4:7. Therefore, there are 4 boys out of 11 students. To find the answer, first divide the total
number of students by 11, then multiply the result by 4.
44 ÷ 11 = 4 ⇒ 4 × 4 = 16
There are 16 boys and 28(44–16) girls. So, 12 more boys should be enrolled to make the ratio 1:1
Explanation:
The total charge that Jackson will pay is the room rate, the 8% tax on the room rate, and a fixed fee. If Jackson stayed x nights,
then the total charge is (99.95 x + 0.08 x 99.95 x ) + 5, which can be rewritten
as 1.08 (99.95 x ) + 5
Explanation:
The capacity of a yellow box is 20% bigger than the capacity of a green box and it can hold 30 books. Therefore, we want to
find a number that 20% bigger than that number is 30. Let 𝑥 be that number. Then:
1.20× 𝑥 = 30
Divide both sides of the equation by 1.2. Then:
𝑥=301.20=25
Explanation:
One method to find the correct answer is to create an inequality. The income from sales of n items is 12n. For the company to
profit, 12n must be greater than the cost of producing n items; therefore, the inequality 12n greater than 7 n plus 350 can be
used to model the context. Solving this inequality yields n > 70.
Explanation:
The smallest number is −15. To find the largest possible value of one of the other five integers, we need to choose the smallest
possible integers for four of them. Let 𝑥 be the largest number. Then:
−70=(−15)+(−14)+(−13)+(−12)+(−11)+𝑥→−70=−65+𝑥→𝑥=−70+65=−5
Explanation:
The student must reason that because the mean of the males is lower than that of the females, the combined mean cannot
be greater than or equal to that of the females, while also reasoning that because the mean of the females is greater than that
of the males, the combined mean cannot be less than or equal to the mean of the males. Therefore the combined mean must
be between the two separate means.
Explanation:
Since 𝑓(𝑥) is linear function with a negative slop, then when 𝑥=−2,𝑓(𝑥) is maximum and when 𝑥=3,𝑓(𝑥) is minimum.
Then the ratio of the minimum value to the maximum value of the function is:
𝑓(3)/𝑓(−2) = −3(3)+1/−3(−2)+1 = −8/7
Explanation:
A relationship in the data can only be generalized to the population that the sample was drawn from.
Explanation:
Since James car is traveling at an average speed of 50 miles per hour and the car's gas
mileage is 21 miles per gallon, the number of gallons of gas used each hour can be found by
50 miles/1 hour x 1 gallon/2 miles. + 50/21. The car uses50/21 gallons of gas per hour, so it uses
50/21 t gallons of gas in t hours. The car’s gas tank has 17 gallons of gas at the beginning of the trip.
Therefore, the function that models the number of gallons of gas remaining in the tank t hours
after the trip begins is f(t) = 17 — 50t/21.
Explanation:
To determine the linear model, one can first determine the rate at which the pressure due to
the atmosphere and surrounding water is increasing as the depth of the diver increases.
Calculating this gives 20.9 - 18.7/14 - 9 = 2.2/5, or 0.44. Then one needs to determine the
pressure due to the atmosphere or, in other words, the pressure when the diver is at a depth
of 0.Solving the equation 18.7 = 0.44(9) + b gives b = 14.74.Therefore, the model that can be
used to relate the pressure and the depth is p = 0.44d + 14.74.
Explanation:
If x is the number of cars that crossed the bridge in two hours and y is the number of trucks that crossed the
bridge in two hours, then x + y represents the total number of cars and trucks that crossed the bridge in two
hours, and 6.5 x + 10 y represents the total amount collected in two hours. x + y space equals space 187, and
6.5 x s+ 10 y = 1, 338.
Explanation:
The tracking station can receive 118,800 megabits each day
( 3 megabits/1 second x 60 seconds/1 minute x 60 minutes/1 hour x 11 hours),
which is about 116 gigabits each day ( 118.800/1,024).
If each image is 11.2 gigabits, then the number of images that can be received each day
is 115/11.2 = 10.4.
Since the question asks for the maximum number of typical images, rounding the answer
down to 10 is appropriate because the tracking station will not receive a completed 11th
image in one day.
Explanation:
There are two ways to solve this problem: either convert meters to centimeters and then use the conversion factor
to convert centimeters to inches, or else use the table to convert meters to yards, and then convert to inches.
In the first instance, recall that there are 100 centimeters in a meter (centi means “hundredth”).
Therefore 19 m = 1900 cm = (1900/2.34) = 748 inches.
In the second instance, recall that there are 36 inches in a yard, therefore:
19 m = 19x1.094 = 20.786 yd = 20.786x36 = 748 inches.
Proportions are commonly used for conversions. After converting meters to centimeters set up proportions to solve
for an unknown variable, x.
900 cm/x in = 2.54 cm/1 in Cross multiply.
900 = 2.54 Divide each side by 2.54 to solve for x.
x = 748
Explanation:
Since 16 chairs are empty, and this represents 2/5 of the total enrollment, then the full class must consist of
Class = 5/2 x 16 = 40 students
Use proportions
2/5 = 16/x Cross multiply.
2x = 80 Divide each side by 2 to solve for x.
x = 40 students
Explanation:
Begin by determining the total cost of the onions and carrots, since these prices are given. This will equal
(2 x $3.69) + (3 x $4.29) = $20.25. Next, this sum is subtracted from the total cost of the vegetables to
determine the cost of the mushrooms: $24.15 - $20.25 = $3.90. Finally, the cost of the mushrooms is divided
by the quantity (lbs) to determine the cost per pound:
Cost per lb = $3.90/1.5 = $2.60
Explanation:
Begin as you would a regular equation:
4x − 12 < 4 Add 12 to each side.
4x < 16 Divide by 4.
x < 4
Note: The inequality does not change because the division was by positive 4.
Since x must be less than 4, and not equal to it (< not ≤ ), the answer 4 is incorrect: the solution does not include 4.
Only the answer 3 satisfies the condition that it must be < 4.
Explanation:
First, compute the value enclosed by the parentheses, 3b + 5 = 3 x 7 + 5 = 26. Next, compute >br>
4a = -24. Note that a is negative, so this product is also negative. The product, 4a(3b + 5), will therefore be
negative, as well, and equals -624. Finally, add the value of 2b, or 2 x 7 =14, to -624, to get the final
answer: 624 + 14 = -610.
Substitute the given values for the variables into the expression:
4x - 6(3 x 7 + 5) + 2 x 7
Using the order of operations, compute the expression in the parentheses first. Remember that you must first
multiply 3 by 7, and then add 5, in order to follow order of operations.
= 4x -6(21 + 5) + 2 x 7 Next add the values in the parentheses.
= 4x - 6(26) + 2 x 7 Simplify by multiplying the numbers outside of the parentheses.
= -24(26) + 14 Multiply -24 by 26.
= -624 + 14 Add.
= -610
Explanation:
A proportion such as this can be solved by taking the cross product of the numerators and denominators from either side.
12/x = 30/6 Take the cross product by cross multiplication.
30x = 6 x 12 Multiply 6 by 12.
30x = 72 Divide each side by 30.
x = 2.4
Explanation:
There are 32 Hawaiian pizzas and the cost for producing each is $4.25, so the total cost of producing 32 Hawaiian
pizzas is $4.25(32). There are 18 pepperoni pizzas and p more will be added, so the total number of pepperoni pizzas
is (18 + p). If each of these pepperoni pizzas costs $3.75 to produce, the total cost of producing pepperoni pizzas is
$3.75(18 + p). The total cost of producing all pizzas is equal to the sum of producing the Hawaiian pizzas and the
pepperoni pizzas. So the equation $4.25(32) + $3.75(32 + p) = 316 is the correct answer.
Explanation:
The correct answer is b=n×2n
Explanation:
The given expression represents the total profit earned, in dollars, of two types of toys, A and B. Because y represents
the number of toy B sold, 8.25y = (9.50 – 2.45)y represents the profit earned by selling toy B. Therefore, it follows that
the coefficient, 8.25, must represent the profit of selling toy B.
Explanation:
Since line m and line n intersect forming a right angle, they are perpendicular lines. The slopes of two perpendicular lines
are negative reciprocals to each other. So to find the equation of line n, we need first to find the slope of line m.
Step 1: Solve for the slope of line m.
6x+3y=9→3y=-6x+9
Divide both sides of the equation by 3:
→ y=-2x+3
Therefore, the slope of line m is -2. This implies that the slope of line n is –(–12)=12.
Step 2: Identify which of the choices has a slope of 12.
Option C: 2x-y=8 →y=2x-8 →slope is 2. Hence, option A is incorrect.
Option A: 2x-4y=8 →4y=2x-8 →y=12x-2→slope is 12. Hence, option B can be the equation of line n.
Explanation:
The interest formula is I = Prt, where P = borrowed amount, r = rate, t = term (time).
For five years, Sam has to pay $51,600. It means that the total interest for five years is $51,600 – $43,000 = $8,600.
So the yearly interest is $8,600 5 = $1,720.
Using the formula above, we have
$1,720=$43,000r1
Thus, the interest rate is
r=$1,720$43,000=0.04=4%.
When $50,000 is loaned, the yearly interest would be
I=$50,0000.041=$2,000.
Explanation:
The largest possible area can be found by getting a square shape of land with the side length of 900 meters 4 = 225 meters.
Option C satisfies the condition of using the 900 meters perimeter (fencing wire) and the area that will be generated is
225 x 225 = 50,625 square meters.
