Answers
The solution to the inequality 2√(x-3) < √(x+3) is x ∈ (3, 7].
What is an inequality?
In mathematics, an inequality is a statement that compares two values or expressions and states that one is greater than, less than, or not equal to the other. An inequality is typically written using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to). Inequalities are used to represent a wide range of mathematical concepts, such as the relationships between two quantities, the constraints on a system, or the conditions for a particular outcome to occur. Solving inequalities involves finding the set of values that satisfy the inequality, which may be a single value, a range of values, or no values at all.
What are the key steps to solve this inequality?
To solve the inequality, we need to isolate the variable x on one side of the inequality and then square both sides to eliminate the square roots. However, we need to be careful when squaring both sides because this may introduce extraneous solutions. To avoid this, we need to check our solutions at the end to make sure they satisfy the original inequality.
Isolate the square root term on one side of the inequality
2√(x-3) < √(x+3)
Square both sides:
4(x-3) < x+3
Simplify and rearrange the inequality to get x on one side
4x - 15 < 0
x < 15/4
Check the solution by plugging it into the original inequality
2√(15/4 - 3) < √(15/4 + 3)
2√(3/4) < √27/4
2(√3/2) < 3/2
√3 < 3/2 (This is true)
Therefore, the solution to the inequality is x ∈ (3, 7].
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Related Questions
Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over x = −3.
N′(5, −2), M′(2, 1), O′(3, 3)
N′(−5, −8), M′(−2, −7), O′(−3, −9)
N′(−1, 2), M′(−4, 1), O′(−3, 3)
N′(−5, −5), M′(−2, −4), O′(−3, −7)
Answers
The vertices of the image triangle N′M′O′: N′(-1, 2), M′(-4, 1), O′(-3, 3).
What are vertices?
Vertices (singular: vertex) are the points where two or more straight lines or edges meet in a geometric shape such as a polygon, polyhedron, or graph. In two-dimensional shapes like polygons, a vertex is a corner where two sides intersect.
We can do this by finding the difference between the x-coordinate of the preimage vertex and -3, doubling this difference, and then subtracting this result from the x-coordinate of the preimage vertex. This will give us the x-coordinate of the image vertex.
For example, to find the x-coordinate of the image of vertex N, we have:
x-coordinate of N = -5
Difference between x-coordinate of N and -3 = -5 - (-3) = -2
Double the difference = -2 x 2 = -4
Subtract this result from the x-coordinate of N = -5 - (-4) = -1
Therefore, the x-coordinate of the image of vertex N is -1.
Using the same method, we can find the x-coordinates of the image vertices:
x-coordinate of N′ = -1
x-coordinate of M′ = -4
x-coordinate of O′ = -3
To find the y-coordinates of the image vertices, we don't need to do any calculations since the reflection is over a vertical line and does not affect the y-coordinates. Therefore, the y-coordinates of the image vertices are the same as the y-coordinates of the preimage vertices:
y-coordinate of N′ = 2
y-coordinate of M′ = 1
y-coordinate of O′ = 3
Putting it all together, we get the vertices of the image triangle N′M′O′:
N′(-1, 2), M′(-4, 1), O′(-3, 3)
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If the lengths of the legs of a right triangle are 5 and 12, what is the length of the hypotenuse?
Answers
Reasoning:
1) a^2 + b^2 = c^2
2) replace the variables:
(5)^2 + (12)^2 = c^2
3) 25 + 144 = c^2
4) 169 = c^2
5) square root of both sides equals the final side length (the hypotenuse) which is 13
assume that the doctor goes home after the last patient is served, or at 5pm if all patients are finished before 5pm. what is the expected time that the doctor will go home? hint: let t be the time exceeding 5pm in minutes. what are the possible values of t ? determine its pmf.
Answers
The doctor goes home at 5 pm if all patients are finished before 5 pm.
The possible values of t are from 0 to 300.
Let t be the time exceeding 5 pm in minutes.
Therefore, we have to find the expected time for the doctor to go home after the last patient has been served, or at 5 pm if all patients are finished before 5 pm.
We will determine its pmf as well.
Expected time that the doctor will go home
The doctor goes home at 5 pm if all patients are finished before 5 pm.
Let the doctor takes x amount of time to see the patients in hours.
Then the total time taken to see n patients will be xn.
If the doctor sees n patients in the first x hours and leaves the remaining patients, then the time will be (n-x) hours.
The total time that the doctor will go home will be given as:
{(n-x)x} + (n-x) if (n-x) > 0
Otherwise, the doctor will go home at 5 pm.
The pmf of t
To find the possible values of t, we need to find the minimum and maximum value of x.
{(n-x)x} + (n-x) if (n-x) > 0 will be greater than 0 when x is less than n/2.
Therefore, the possible values of t are from 0 to 300.
We know that t is defined as the time exceeding 5 pm in minutes.
pmf of t is given as :
P(t = 0) = P(all patients are done before 5 pm) = 1/32
P(t = i) = P(last patient finishes at 5pm + i minutes) = 31/32 × (1/300) for i = 1, 2, 3, ..., 299.
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Write the linear equation in standard form y=19/14x+13
Answers
The linear equation in standard form is 19x - 14y = -182.
What is Linear equation?
A linear equation is a mathematical equation that describes a straight line on a graph. In other words, it is an equation that relates a variable or variables to a constant through a linear function, where the highest power of the variable is one. A general form of a linear equation is:
y = mx + b
To write the linear equation in standard form Ax + By = C, where A, B, and C are integers and A is positive, we need to get rid of the fraction in the equation.
To do this, we can multiply both sides of the equation by the denominator of the fraction, which is 14. This gives:
14y = 19x + 182
Next, we can rearrange this equation by subtracting 19x from both sides:
-19x + 14y = 182
Finally, we can multiply both sides of the equation by -1 to make the coefficient of x positive:
19x - 14y = -182
So, the linear equation in standard form is 19x - 14y = -182.
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63 decreased by twice Craig's age
use variable c to represent Craig's age
Answers
Answer: 7
Step-by-step explanation:
Salma sells beaded necklaces. Each large necklace sells for $5.10 and each small necklace sells for $4.50. How much will she earn from selling 4 large necklaces
and 1 small necklace?
Answers
let ppnq be the statement that a postage of n cents can be formed using only 3-cent stamps and 5-cent stamps. ppnq can be proved by strong induction. what is the correct basis step?
Answers
The correct basis step for proving the statement P(n) using strong induction is to show that P(8) is true
Strong induction is a method of proving that a statement is true for all values of n by demonstrating that it is true for a base case and that if it is true for all values up to n, then it must also be true for n+1. It can be used to prove the statement P(n) that a postage of n cents can be formed using only 3-cent stamps and 5-cent stamps.
To demonstrate that P(8) is true is to do the proper basis step for strong induction. This is so that we may create an 8 cent postage using a 3-cent and a 5-cent stamp.
The following argument can be used to demonstrate that the basic step is P(8) being true:
A postage of 8 cents can be made with one 3-cent stamp and one 5-cent stamp.
Thus, P(8) must be true.
We don't need to check any other values for the base step because P(n) only depends on the values of P(k), where k n.
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11. Find m
H= 5x+8
J= 7x-16
Answers
Answer:
let angle GJK be x
GJK=GHK (Base angle of isosceles triangle)
Step-by-step explanation:
x=5x+8
5x-x=8
4x=8
x=8/4
x=2 ans.
Hence,
5x+8
5*2+8
10+8
18.ans
Please help I’ll give 50 points please I need this done by tonight!
Answers
According to the given information, the sale price is 160% of the purchase price and she would need to buy at least 4 jackets to make at least $250 in total sales.
What is the percentage?
The percentage is a way of expressing a fraction or proportion out of 100. It is commonly used in many different areas such as finance, math, science, and everyday life.
a. To find the percent of the purchase price that the sale price represents, we can use the formula:
percent = (sale price/purchase price) x 100
Plugging in the given values, we get:
percent = (96 / 60) x 100 = 160%
Therefore, the sale price is 160% of the purchase price.
b. If the owner increases the sale price by 160% when buying jackets for $45, then the new sale price for each jacket will be:
new sale price = 1.6 x $45 = $72
To find the number of jackets the owner must buy to make at least $250 in total sales, we can set up an equation:
number of jackets x $72 = $250
Solving for the number of jackets, we get:
number of jackets = $250 / $72 ≈ 3.47
Since the owner can only sell a whole number of jackets, she would need to buy at least 4 jackets to make at least $250 in total sales.
This is because selling 3 jackets would only bring in $216 in total sales, which is less than $250.
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the adaptive-response-rate single exponential smoothing model is best applied to time series data that are multiple choice non stationary. stationary and non seasonal. seasonal. stationary and seasonal. seasonal and nonstationary.
Answers
The adaptive-response-rate single exponential smoothing model is best applied to time series data that are non stationary and seasonal which means option D is the right answer.
The adaptive response rate single exponential smoothing model is used to demonstrate the changes in the forecasting data and the fluctuation in data values with respect to time which are smoothened by a coefficient. The larger the coefficient, the greater the smoothing effect.
This kind of model is ineffective for stationary time series as it takes into account the smoothing of the information. Adaptive smoothing is computationally difficult. Exponential smoothing produces accurate forecasts. The forecast shows projected demand and actual demand.
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you believe that most american men under the age of 25 prefer pizza over tacos. you design an experiment with 50 men to test this hypothesis. what is the sample in your experiment?
Answers
They represent a more focused sample of people the researcher is interested in examining in order to draw conclusions about the larger community of American men under 25.
what is null hypothesis ?The null hypothesis is a claim made in statistical hypothesis testing that presupposes there is no correlation between groups or any meaningful difference between a set of variables. It is commonly denoted by "H0," and the alternative hypothesis is compared with it ("H1"). The null hypothesis is typically assumed to be true, and in order to determine whether it can be rejected or not, it must be statistically tested. The alternative hypothesis is accepted if there is enough data to refute the null hypothesis. In contrast, the null hypothesis is maintained if there is not sufficient evidence to support it.
given
The group of 50 males who are chosen to take part in the study serves as the sample for the experiment.
They represent a more focused sample of people the researcher is interested in examining in order to draw conclusions about the larger community of American men under 25.
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if the average (arithmetic mean) of 24 consecutive odd integers is 48, what is the median of the 24 numbers?
Answers
Answers: 36
Step-by-step explanation:
The number of boys 7 over 10 of the total number of students in a class if there are 16 more boys than girls in a class how many students are there together
Answers
Answer:
Let's use "x" to represent the total number of students in the class.
According to the problem, the number of boys is 7/10 of the total number of students, and the number of girls is 3/10 of the total number of students. We can set up the following equation based on this information:
Number of Boys = 7/10 x
Number of Girls = 3/10 x
The problem also tells us that there are 16 more boys than girls in the class. We can set up another equation based on this information:
Number of Boys = Number of Girls + 16
Now we can use these two equations to solve for the total number of students:
7/10 x = 3/10 x + 16
Subtracting 3/10 x from both sides, we get:
4/10 x = 16
Multiplying both sides by 10/4, we get:
x = 40
Therefore, there are 40 students in the class. To find the number of boys and girls, we can use the equations we set up earlier:
Number of Boys = 7/10 x = 7/10 * 40 = 28
Number of Girls = 3/10 x = 3/10 * 40 = 12
So there are 28 boys and 12 girls in the class.
the speed of light is approximately 6.7106*10^7 per hour, and the speed of sound is approximately 7.54*10^2 miles per hour. How many times faster is the speed of light than the speed of sound?
Answers
Answer: The speed of light is approximately 89,100 times faster than the speed of sound.
Step-by-step explanation: To find out how many times faster the speed of light is than the speed of sound, we need to divide the speed of light by the speed of sound:
Speed of light / Speed of sound = (6.710610^7) / (7.5410^2)
Simplifying this calculation gives us:
Speed of light / Speed of sound = 8.91*10^4
This means that the speed of light is approximately 89,100 times faster than the speed of sound.
Hope this helps, and have a great day!
the diagonal of a rectangle is 450 millimeters, while the longer side is 393 millimeters. find the shorter side of the rectangle and the angles the diagonal makes with each side rounded to the nearest whole number.
Answers
The shorter side of the rectangle is approximately 237.25 millimeters, and the diagonal makes angles of approximately 41 degrees and 49 degrees with the longer and shorter sides, respectively.
Let us denote the shorter side of the rectangle as x. We can use the Pythagorean theorem to relate the length of the diagonal to the two sides of the rectangle:
diagonal^2 = longer side^2 + shorter side^2
Substituting in the given values, we get:
450^2 = 393^2 + x^2
Solving for x, we get:
x = √(450^2 - 393^2) ≈ 237.25 mm
To find the angles that the diagonal makes with each side of the rectangle, we can use trigonometry. Let θ be the angle between the diagonal and the longer side, and let φ be the angle between the diagonal and the shorter side. Then we have:
sin(θ) = shorter side / diagonal
sin(φ) = longer side / diagonal
Substituting in the given values and solving for θ and φ, we get:
θ ≈ 41 degrees
φ ≈ 49 degrees
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Which inequality statement describes the two numbers on a number line? "2 and a number 9 units to the left of 2"
Answers
Answer:
Step-by-step explanation:
The inequality statement that describes the two numbers on a number line "2 and a number 9 units to the left of 2" would be:
x < 2
where x represents the number that is 9 units to the left of 2.
Solve for x.
3x² + 9x - 30 = 0
x = -5, [?]
Answers
Step-by-step explanation:
3x²+9x-30=0
-(9)+\-√(9)²-4(3)(-30)
=_________________
2(3)
=. x=2. or. X=-5
A refrigerator magnet uses 5/8 inch of magnetic tape. How many refrigerator magnets can you make with 9 3/8 inches of magnetic tape? Explain.
Answers
Answer:
To find how many refrigerator magnets can be made with 9 3/8 inches of magnetic tape, we need to divide the total length of magnetic tape by the length of magnetic tape used for each magnet.
First, we need to convert the mixed number 9 3/8 to an improper fraction:
9 3/8 = (9 x 8 + 3)/8 = 75/8
Next, we divide 75/8 by 5/8 to find how many magnets can be made:
(75/8) ÷ (5/8) = (75/8) x (8/5) = 15
Therefore, 15 refrigerator magnets can be made with 9 3/8 inches of magnetic tape.
from her purchased bags, rachel counted 130 red candies out of 520 total candies. using a 95% confidence interval for the population proportion, what are the lower and upper limit of the interval? answer choices are rounded to the thousandths place.
Answers
Hence, the population proportion's 95% confidence interval is (0.210, 0.290), rounded to the thousandths place.
what is proportionality ?A mathematical concept known as proportionality describes the relationship between two quantities that have different sizes but keep the same ratio or proportion. In other words, to preserve the same ratio, if one item changes, the other quantity must also change in proportion. For instance, if an automobile's speed and distance are proportionate, doubling the distance it travels will cause the car to go twice as quickly while retaining the same speed-to-distance ratio. Equations or ratios in mathematics are frequently used to express proportionality.
given
We can use the following formula to determine the lower and upper bounds of the 95% confidence interval for the population proportion:
Lower limit: sqrt((p * q) / n) * p - z
Upper limit: sqrt((p * q) / n) = p + z
With q = 1 - p, z is the z-score corresponding to the level of confidence, and p is the sample proportion.
Here, p = 130/520 = 0.25, q = 1 - p = 0.75, n = 520, and the z-score is 1.96 at a 95% confidence level (from the standard normal distribution).
Lower limit: 0.210 (0.25" * 0.75") - 1.96 * sqrt(0.25" * 0.75")
The maximum is equal to 0.25 + 1.96 * sqrt((0.25 * 0.75) / 520) = 0.290.
Hence, the population proportion's 95% confidence interval is (0.210, 0.290), rounded to the thousandths place.
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please help !!!
math hw
Answers
Answer: they all include a variable, an "x" in parentheses, and they all have the number 2 in it.
Step-by-step explanation:
kai and David share £84 in the ratio 1:3 calculate the amount of money kai gets
Answers
Answer:
£21
Step-by-step explanation:
We know
kai and David share £84 in the ratio 1:3. Meaning for every £4, Kai receive £1 & David received £3.
Calculate the amount of money kai gets?
To get from 4 to 84, we time 21.
We take
1 x 21 = £21
So, Kai gets £21
IF YESTARDAY IS THE DAY BEFORE YESTARDAY OF SATURDAY, WHAT DAY IS DAY AFTER TOMORROW
Answers
The required day if yesterday is the day before yesterday of Saturday is Thursday and day after tomorrow is Sunday.
If yesterday was the day before yesterday of Saturday,
Yesterday was Saturday
Day before yesterday is Friday,
then yesterday was Thursday.
Now,
If yesterday was Thursday, then today is Friday.
Day representing tomorrow is Saturday.
And day after Saturday is definitely Sunday.
This implies,
The day after tomorrow would be Sunday.
Therefore, day after tomorrow is Sunday as per given situation.
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there are three blue marbles and five yellow marbles. two marbles are selected. what is the probability that both are blue
Answers
Answer:
3
8
Step-by-step explanation:
probability= no. of blue marbles
total no. of marbles
= 3
8
a 95% confidence interval for a proportion is 0.75 to 0.83. is the value given a plausible value of p?
Answers
Yes, the value of 0.75 to 0.83 for a 95% confidence interval is plausible.
A confidence interval is a range of values that has a 95% chance of containing the true population parameter, which in this case is the population proportion (p).
A 95% confidence interval has a margin of error of 5%. Thus, a range of 0.75 to 0.83 has a 95% chance of containing the true population proportion p.
The 95% confidence interval is an estimated range of values which is calculated from sample data, with a 95% chance of containing the true population parameter, p. To calculate the confidence interval, the confidence level and the margin of error must be known.
The confidence level is the probability that the confidence interval will contain the true population parameter, and the margin of error is the amount that the sample statistic can differ from the true population parameter.
A 95% confidence level has a margin of error of 5%, meaning that the sample statistic can be up to 5% away from the true population parameter.
In this case, the 95% confidence interval for the population proportion is 0.75 to 0.83. This means that the range of 0.75 to 0.83 has a 95% chance of containing the true population proportion p, and is thus a plausible value for the population proportion.
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Elise ran 2 miles in 15 minutes. Teagan ran 3 kilometers in 15 minutes. Who ran at a faster rate? Explain.
Answers
Answer: Elise ran faster.
Step-by-step explanation:
Elise 2 mi in 15 min
Tengan 3 km in 15 min
We need to covert the miles (mi) or kilometers (km) so that they are both the same. You should know that 1 mi = 1.6 km. After you convert the measurements, you can compare. Since they both are measured in minutes, you don't have to worry about that, but if they aren't you should convert it one or the other, so that they are the same.
2 mi = 3.2 km (Elise)
3 km (Tengan)
Elise is 0.2 faster than Tengan.
Answer:
Elise ran faster
Step-by-step explanation:
Elise ran faster because 3 kilometers is equal to 1.86 miles. 2 miles is equal to 3.22 kilometers.
which value of n makes the equation true
-[tex]\frac{1}{2}n=-8[/tex]
Answers
Answer:
16
Step-by-step explanation:
When we divide the entire equation by 1/-2 to get rid of the coefficient of n we get n = 16.
R. Davis students are going to run in a relay tournament. In the first round 3 students will run a 1/3 mile relay race
Answers
The R. Davis children are preparing for a relay event in which they will compete in a 1/3 mile relay race. The opening round of the competition will include three kids who will compete in the race.
This means that in the relay event, each kid will have to run 1/9th of a mile. Students will need to improve on their speed, endurance, and coordination in order to prepare for the race. They must be able to effortlessly deliver the baton from one runner to another, maintain their speed throughout the race, and push themselves to the maximum. In addition to physical preparation, students must improve their mental focus and motivation. They will do so. need to stay positive and motivated throughout the race, and work as a team to achieve their goals.
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What is the scenario for R. Davis students in the relay tournament? How many students will run in the first round of the tournament, and what is the distance they will cover?
A certain bookshop has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their sellilng prices are Rs. 80, Rs. 60 and Rs. 40 each respectively. Find the total amount the bookshop will receive by selling all the books, using matrix algebra
Answers
The bookshop will receive a total amount of Rs. 23,200 by selling all the books.
WHAT IS SELLING PRICE ?
The selling price is the price at which a product or service is sold to a customer. It is the amount of money that a seller charges to a buyer for a particular product or service. The selling price may include various factors such as the cost of production, overhead costs, profit margin, taxes, and other charges. It is an important concept in business and commerce, as it determines the revenue generated by a company and its profitability.
We can represent the given information using matrices as follows:
Let A be the matrix of the number of books in dozens, where each row represents a subject and each column represents the number of dozens of books:
A =
| 10 8 10 |
|____________|
Let B be the matrix of the selling prices of each book, where each row represents a subject and each column represents the selling price of each book:
B =
| 80 |
| 60 |
| 40 |
To calculate the total amount the bookshop will receive, we need to multiply the matrices A and B using matrix algebra:
C = A * B
C =
| 10 8 10 | | 80 | | 12000 |
| 60 | = | 7200 |
| 40 | | 4000 |
Therefore, the bookshop will receive a total amount of Rs. 23,200 by selling all the books.
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What are m∠1 and m∠2?
Two triangles intersect at a single vertex. The left triangle has an interior angle measuring 80 degrees and another interior angle labeled 1. The interior angle of the vertices that intersect are unlabeled on both triangles, but the upper exterior angle measures 115 degrees. The other two interior angles in the right triangle are labeled 85 degrees and 2.
1. m∠1 = 30°, m∠2 = 35°
2. m∠1 = 35°, m∠2 = 30°
3. m∠1 = 65°, m∠2 = 60°
4. m∠1 = 85°, m∠2 = 80°
Answers
We know that m∠1 and m∠2 are positive angles that add up to 17 degrees, so the only possible pair of values is: m∠1 = 35°, m∠2 = 30° that is option 2.
What is triangle?A triangle is a polygon with three sides and three angles. It is a two-dimensional shape with three straight sides that intersect at three vertices. The sum of the interior angles of a triangle is always 180 degrees. Triangles can be classified based on the lengths of their sides and the measures of their angles. Some common types of triangles include equilateral triangles, isosceles triangles, scalene triangles, acute triangles, obtuse triangles, and right triangles.
Here,
Using vertically opposite angle, x + x + 115° + 115° = 360°
2x + 230° = 360°
2x + 230° = 360°
2x = 360 - 230
2x = 130
x = 130/2
x = 65°
Then, lets solve for angle 1 using angle sum property:
∠1 + 65° + 80° = 180°
∠1 + 145° = 180°
∠1 = 180° - 145°
∠1 = 35°
Again, lets solve for angle 2 using angle sum property:
∠2 + 65° + 85° = 180°
∠2 + 150° = 180°
∠2 = 180° - 150°
∠2 = 30°
Therefore, the answer is:
m∠1 = 35°, m∠2 = 30° (option 2)
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Imagine that an exchange student from China visits your class. While your teacher discusses how the United States has a limited government, the Chinese student raises his hand and asks why the government has limited power. Which point best highlights why the US government has limited power? A. A limited government means citizens pay fewer taxes. B. A limited government helps people avoid breaking the law. C. A limited government protects individual freedoms. D. A limited government prevents businesses from being too powerful.
Answers
Answer:
C. A limited government protects individual freedoms.
Step-by-step explanation:
There are more individual freedoms as opposed to the lifestyle of those who are under a monarchy