For instance: Let f(x) = 2x + 1 and g(x) = x^2. Find (f ∘ g)(3). First, we need to find g(3) which is 3^2 = 9. Then we plug this value into f: f(g(3)) = f(9) = 2(9) + 1 = 19. Therefore, (f ∘ g)(3) = 19.
What is the description of a function composition?Function composition is a mathematical concept that is used to combine two or more functions into a single function. This concept is widely used in real life situations, such as in computer programming, engineering, and physics.
For example, in computer programming, function composition is used to break down complex programs into smaller, more manageable parts. By using function composition, programmers can create complex programs that are easier to read and maintain. Therefore, function composition is a powerful tool that is used in various fields to simplify complex problems and create more accurate models of the world around us.
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5) A submarine is cruising at -40 meters (40 meters below the surface). It
descends 20 meters, then rises 35 meters. What is the submarine's new depth? *
-25 m
-95 m
25 m
15 m
Answer:
-25
Step-by-step explanation:
You begin with -40, then decrease by 20 so your new value is -60, then increase by 35 so your final value is -25m... hope this helps (:
a seven-digit telephone number has two identical missing digits so that it reads 276-9?4?. if the seven-digit number is divisible by 7, how many phone numbers are possible?
The total number of phone numbers that are possible is 11 x 10 = 110.
A seven-digit phone number is to be formed that has two identical missing digits so that it reads 276-9?4?. And, the seven-digit number should be divisible by 7. We need to find how many phone numbers are possible?Let's analyze given the telephone number - 276-9?4?
For any number to be divisible by 7, the difference of the sum of its digits in odd places and the sum of its digits in even places should be either 0 or a multiple of 7.
Let's say the missing digits in the telephone number are 'x' and 'y'. Therefore, we need to find all possible values of 'x' and 'y'.Since the phone number is divisible by 7,
we can find the possible values of 'x' and 'y' by calculating the values of (4y-3x). If (4y-3x) is divisible by 7, then the given phone number is divisible by 7.If x = 1, then y can take any value from 0 to 9 such that (4y-3) is divisible by 7. This gives us two pairs of values:
(x, y) = (1,2) and (1,9).If x = 2, then y can take any value from 0 to 9 such that (4y-6) is divisible by 7. This gives us two pairs of values: (x, y) = (2,0) and (2,7).If x = 3, then y can take any value from 0 to 9 such that (4y-9) is divisible by 7.
This gives us two pairs of values: (x, y) = (3,1) and (3,8).If x = 4, then y can take any value from 0 to 9 such that (4y-12) is divisible by 7. This gives us two pairs of values:
(x, y) = (4,3) and (4,0).If x = 5, then y can take any value from 0 to 9 such that (4y-15) is divisible by 7. This gives us only one pair of values: (x, y) = (5,7).If x = 6, then y can take any value from 0 to 9 such that (4y-18) is divisible by 7.
This gives us two pairs of values: (x, y) = (6,0) and (6,4).So, we have a total of 11 possible values for the pair (x, y). For each pair, we can have 10 possible phone numbers (since y can take any value from 0 to 9).
Hence, there are 110 possible phone numbers that can be formed with two identical missing digits so that it reads 276-9?4?, and the seven-digit number is divisible by 7.
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Rewrite 0.895 as a simplified fraction someone help if u do tysm:)
Please help! Urgent! Will mark Brainliest!
Answer:
\(x = 15\)
Step-by-step explanation:
Since lines f and g are parallel, that means that the top angles will be the same, while the bottom angles will also be the same.
The angles of any quadrilaterals all add up to 360°, so we can create the equation like this:
\(3x + 3x + (6x + 45) + (6x+45) = 360\)
Combine like terms so we can get a simpler equation:
\(6x + 12x + 90 = 360\\18x + 90 = 360\)
Now let's solve for x!
\(18x + 90 - 90 = 360 - 90\\18x = 270\\18x\div18 = 270\div18\\x = 15\)
So \(x = 15\).
Hope this helped!
Answer:
15
Step-by-step explanation:
3x + 6x + 45 = 180
9x = 135
x = 15
HI I really need help with this its in the picture
Explanation:
The blue rectangle has area of 4a^2*6a^2 = 24a^4
The red rectangle has area 4a^2*9a = 36a^3
The green rectangle has area 4a^2*3 = 12a^2
The total area is 24a^4 + 36a^3 + 12a^2
Write an equivalent fraction if needed. Add. Write each sum in simplest
form. 2 1/10 + 5 7/10 =
Answer:
7 4/5
Step-by-step explanation:
2 1/10 + 5 7/10 = 2 + 5 + 1/10 + 7/10 = 7 8/10 = 7 4/5
How many times will the graph of this equation cross the x-
axis?
y= 22^2– 7x - 9
What is the formula for test statistic Z?
The formula for the test statistic Z depends on the specific hypothesis test being conducted. However, the test statistic Z can be computed as:
Z = (x - μ) / (σ / √n)
The formula for the test statistic Z is:
Z = (x - μ) / (σ / √n)
where:
x is the sample mean
μ is the population mean (under the null hypothesis)
σ is the population standard deviation (under the null hypothesis)
n is the sample size
This formula is used for a z-test, which is a statistical test that assumes that the population is normally distributed and uses the standard normal distribution to calculate the p-value.
In some cases, the population standard deviation is unknown, and so the sample standard deviation (s) is used as an estimate. In these cases, the formula for the test statistic Z is:
Z = (x - μ) / (s / √n)
where s is the sample standard deviation.
It's important to note that the formula for the test statistic Z can vary depending on the specific hypothesis test being conducted.
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An elevator starts on the ground floor. It goes up by 7 floor and then down 9 floors. what floor does it land on?
Answer:
-2 floor so underground
Help me very fast!!!!!!! Damon’s car can go an average of 18 miles on each gallon of gas.
Choose the equation that models the situation, where m represents the number of miles and g represents the number of gallons of gas.
Answer:
m= 18g
Step-by-step explanation:
m = 18 × g
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. x = 63 − 7y^2, x = 7y^2 − 63 Find the area of the region.
The area of the region enclosed by the given curves is:
Area = Area1 - Area2 = 504
What is a Polynomial Function?A polynomial function is a fundamental mathematical concept expressed as a sum of powers of an independent variable, multiplied by constants known as coefficients. It is a versatile tool used to model various phenomena such as physical processes, economic trends, and social behavior. a polynomial function is a function of the form:
f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0
where a_n, a_{n-1}, ..., a_1, a_0 are constants, x is the independent variable, and n is a non-negative integer.
To sketch the region enclosed by the curves and determine whether to integrate with respect to x or y, let's first graph the given curves:
Curve 1: x = 63 - 7y²
Curve 2: x = 7y²- 63
We can start by finding the y-intercepts and the points of intersection between the two curves:
For Curve 1:
When x = 0, 63 - 7y^2 = 0
7y² = 63
y² = 9
y = ±3
For Curve 2:
When x = 0, 7y² - 63 = 0
7y² = 63
y² = 9
y = ±3
So the y-intercepts and points of intersection are at y = -3 and y = 3.
Next, let's determine the bounds for y by looking at the range of y-values enclosed by the curves. We can see that the curves are symmetric about the y-axis, and they intersect at y = -3 and y = 3. Therefore, we can integrate with respect to y from y = -3 to y = 3 to calculate the area.
To find the area of the region, we need to integrate the difference between the curves with respect to y:
Area = ∫[from -3 to 3] [(63 - 7y²) - (7y² - 63)] dy
Simplifying the expression:
Area = ∫[from -3 to 3] (126 - 14y²) dy
To find the integral of (126 - 14y²) with respect to y, we can distribute the integral and integrate term by term:
Area = ∫[from -3 to 3] 126 dy - ∫[from -3 to 3] 14y² dy
The first term, ∫[from -3 to 3] 126 dy, represents the area of a rectangle with a constant height of 126 and a width of 6 (from y = -3 to y = 3):
Area1 = 126 * 6
The second term, ∫[from -3 to 3] 14y² dy, represents the area between the curves. We can integrate term by term:
∫[from -3 to 3] 14y² dy = 14 * [(1/3)y³] | [from -3 to 3]
= 14 * [(1/3)(3)³ - (1/3)(-3)³]
= 14 * [(1/3)(27 - (-27))]
= 14 * [(1/3)(54)]
= 14 * 18
= 252
Therefore, the area of the region enclosed by the given curves is:
Area = Area1 - Area2
= 126 * 6 - 252
= 756 - 252
= 504
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Solve each inequality. Check your solution. (x/3) + 5 ≥ 1/6
The inequality given by (x/3) + 5 ≥ 1/6 has the solution x ≥ -29/2 or [-29/2 , +∞).
Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.
To solve an inequality is to find the values of x such that when we substitute that number for x we have a true statement.
Given the inequality (x/3) + 5 ≥ 1/6, subtract 5 from both sides.
(x/3) + 5 - 5 ≥ 1/6 - 5
x/3 ≥ -29/6
Multiply both sides by 3.
3(x/3) ≥ 3(-29/6)
x ≥ -29/2
To check, let x = -29/2
x = -29/2 ≥ -29/2
Substitute this value to the inequality.
(x/3) + 5 ≥ 1/6
(-29/2)/3 + 5 ≥ 1/6
1/6 ≥ 1/6
let x = -14,
x = -14 ≥ -29/2
Substitute this value to the inequality.
(x/3) + 5 ≥ 1/6
-14/3 + 5 ≥ 1/6
1/3 ≥ 1/6
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You and your friend walk to school together every day. You meet at the halfway point between your houses first and then walk to school. Each unit in the coordinate plane corresponds to 50 yards. A) What are the coordinates of the midpoint of the line segment joining the two houses? B) What is the distance that the two of you walk together?
Please show the steps
Answer:
no se
Step-by-step explanation:
The coordinate of the midpoint joining the two houses, since each unit on the coordinate is 50 units is (150, 250) and the distance walked to school is 254.95 yards
From the graph given :
The x - coordinate of the midpoint is 3 units from the origin = (3 × 50) = 150 yards
The y-coordinate of the midpoint is 5 units from the origin = (5 × 50) = 250 yards
Hence, the coordinate of the midpoint is (150, 250)
The distance walked to school :
Distance = √(y2 - y1)² + (x2 - x1)²
Distance = √(400 - 150)² + (300 - 250)²
Distance = √250² + 50²
Distance = 254.95 yards
Therefore, the distance the boys walk to school is 254.95 yards.
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Consider the equation ut = Uxx, 0 < x < 1, t > 0. Suppose u(0,t) = 0, u(1, t) = 0. Suppose u(x,0) = 1 sin(TX) + 6 sin(27x) + 7 sin(31x) + 11 sin(41x) Fill in the constants in the solution: 2t u(x, t) = sin(7x) + e e-(27) e-(36)t sin(31x) + sin(21x) + e-(47)’t sin(47x)
The boundary and initial conditions provided, we can fill in the constants in the solution: u(x,0) = 1 sin(πx) + 6 sin(27πx) + 7 sin(31πx) + 11 sin(41πx)
To match the solution format, let's fill in the constants:
u(x, t) = (1)e^(-π^2t)sin(πx) + (6)e^(-27^2π^2t)sin(27πx) + (7)e^(-31^2π^2t)sin(31πx) + (11)e^(-41^2π^2t)sin(41πx)
Here, the constants are: 1, 6, 7, and 11 for the amplitudes of each sine term
π, 27π, 31π, and 41π for the sine argument multipliers
-π^2, -27^2π^2, -31^2π^2, and -41^2π^2 for the exponents of e in the time-dependent coefficients.
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Which statements are true regarding the prism? Check
all that apply.
The prism has no vertices.
The prism has 9 edges.
The bases of the prism are triangles.
The bases of the prism are rectangles.
The prism has 5 faces.
Answer:
The prism has 9 edges, The bases of the prism are triangles, and the prism has 5 faces.
Would really appreciate a brainliest! Hope this helped! =)
Answer: B, C, E
Step-by-step explanation: dude trust me c'mon
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.The distribution of grades was left-skewed, but the mean, median, and mode were all the same.A.This does not make sense because the mean and median should lie somewhere to the right of the mode if the distribution is left-skewed.B.This makes sense because when outliers have low values, the mean, median, and mode are the same.C.This does not make sense because the mean and median should lie somewhere to the left of the mode if the distribution is left-skewed.D.This makes sense because when outliers have high values, the mean, median, and mode are the same.
The statement "This does not make sense because the mean and median should lie somewhere to the right of the mode if the distribution is left-skewed" is correct. The correct answer is B
In a left-skewed distribution, the mode is the highest point and it is located to the right of the median, which in turn is located to the right of the mean.
This is because the mean is influenced by extreme values on the left tail, which pull it to the left, whereas the median is unaffected by extreme values and is only determined by the middle value(s) in the data set.
Thus, if the mean, median, and mode are all the same in a left-skewed distribution, this indicates that the data set is either symmetric or approximately symmetric.The correct answer is B
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Perform the indicated operation. Be sure the answer is reduced.
2a + 1 5 2a-3
———— + — - ——— =
3a 4 6a^2
What is the measure of angle SAR?
Answer:
53 degrees
Step-by-step explanation:
75 - 22 = 53
Answer:
53
Step-by-step explanation:
75 - 22
ocean sunfishes are well-known for rapidly gaining a lot of weight on a diet based on jellyfish. the relationship between the elapsed time, ttt, in days, since an ocean sunfish is born, and its mass, m {\text{day}}(t)m day (t)m, start subscript, start text, d, a, y, end text, end subscript, left parenthesis, t, right parenthesis, in milligrams, is modeled by the following function: mday(t)
The mass of the sunfish increases by a factor of 9/7 every 1.05 days.
The growth rate of the ocean sunfish is described by the function M(t) = 3.5(1.05)^t, where t represents the elapsed time in days since the sunfish was born and M(t) represents its mass in milligrams.
To determine the rate at which the mass increases by a factor of 9/7, we need to find the value of t when the mass increases to 9/7 times its initial value.
Let's set up the equation:
M(t) = 3.5(1.05)^t
9/7 × M(0) = 3.5(1.05)^t
Dividing both sides by M(0) (the initial mass), we get:
9/7 = (1.05)^t
Taking the logarithm of both sides, we have:
log(9/7) = log((1.05)^t)
Using logarithmic properties, we can bring down the exponent:
log(9/7) = t × log(1.05)
t = log(9/7) / log(1.05)
Evaluating this expression, we find that the mass of the sunfish increases by a factor of 9/7 approximately every 4.347 days (rounded to three decimal places).
Therefore, the mass of the sunfish increases by a factor of 9/7 every approximately 4.347 days.
Complete Question: Ocean sunfishes are well-known for rapidly gaining a lot of weight on a diet based on jellyfish.
The relationship between the elapsed time, t, in days, since an ocean sunfish is born, and its mass, M(t), in milligrams, is modeled by the following function:
M(t)=3.5(1.05)^t
The mass of the sunfish increases by a factor of 9/7 every _______ days.
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Is y=2x+3 proportional
Answer:
no
Step-by-step explanation:
I calculated
No because something proportional can't have a y-intercept, the 3 is the y intercept so your statement is not proportional.
1. According to the podcast, why and how is chicken the reason American trucks dominate the truck market in the United States? Briefly explain. 2. Name two reasons a party (e.g., a politician or an industry association) may want to impose a tariff? 3. Who are they usually trying to protect? Who would be hurt by a tariff on automobiles? Explain. 4. Describe how competition encourages innovation? In your answer to this question, include a discussion on why American trucks "basically stayed the same over the years. 5. Describe ways foreign companies tried to get around American-imposed tariffs on automobiles. 6. Do you think the methods you described in your previous answer are efficient for an economy? Why or why not? 7. Lastly, how can a tariff be used as a bargaining chip? In your opinion, is that a good reason to impose tariffs - why or why not?
1. Chicken became the key product that drove the creation of the Interstate Highway System, which led to the dominance of American trucks in the US truck market.
2. A party may want to impose a tariff to protect domestic industries from foreign competition or to generate revenue for the government.
3. A party is usually trying to protect domestic industries, but a tariff on automobiles would hurt both domestic consumers who would pay higher prices and foreign producers who would face reduced demand.
4. Competition encourages innovation by providing incentives for companies to improve their products and services to stay ahead of their rivals; American trucks stayed the same because they faced little competition due to protectionist policies.
5. Foreign companies tried to get around American-imposed tariffs on automobiles by establishing factories in the US, forming joint ventures with American companies, or exporting through third countries.
6. The methods used to get around tariffs can be efficient in the short term, but they may not be sustainable or desirable in the long term as they can lead to trade imbalances and undermine the competitiveness of domestic industries.
7. Tariffs can be used as a bargaining chip to negotiate better trade deals, but they should be imposed judiciously and only as a last resort to avoid damaging the economy and harming consumers.
1. In the podcast, chicken is cited as the reason why American trucks dominate the truck market in the United States.
This is because in the 1960s, the government imposed regulations on the trucking industry that limited the amount of weight a truck could carry.
To get around these regulations, the industry started using smaller trucks to transport goods, which were often not strong enough to handle the weight.
However, they found that if they put chicken on the back of the trucks, the weight of the cargo would distribute more evenly and the smaller trucks could handle the load.
This led to the development of the modern pickup truck, which is now a staple of the American automobile market.
2. Parties may want to impose tariffs for various reasons, such as to protect domestic industries and jobs from foreign competition, to raise revenue for the government, or to level the playing field in international trade.
Two specific reasons for imposing tariffs could be to protect national security interests or to address unfair trade practices by other countries.
3. Tariffs are usually imposed to protect domestic industries and jobs, and the parties that are being protected are typically the producers of the goods or services in question.
However, tariffs can also harm consumers who may have to pay higher prices for imported goods or may have fewer choices in the marketplace. For example, if a tariff is imposed on automobiles, domestic car manufacturers may benefit, but consumers may have to pay more for cars, and foreign automakers may lose market share.
4. Competition encourages innovation by creating incentives for companies to improve their products or services to gain a competitive advantage.
In the case of American trucks, the lack of competition may have contributed to their lack of innovation over the years. Since they dominated the market, there was little pressure to improve or innovate, and as a result, they have largely stayed the same.
However, the rise of foreign competition in recent years has led American truck manufacturers to invest more in innovation to stay competitive.
5. Foreign companies have tried to get around American-imposed tariffs on automobiles in various ways, such as by moving production to countries not subject to the tariffs, by exporting parts and assembling them in the United States, or by lobbying the government for exemptions or tariff reductions.
6. The methods used by foreign companies to get around tariffs may not be efficient for the economy as a whole because they can lead to higher costs and inefficiencies in the supply chain.
However, they may be necessary for individual companies to remain competitive in the short term.
Ultimately, a more efficient solution would be to address the root causes of the trade imbalances that lead to tariffs in the first place.
7. A tariff can be used as a bargaining chip by threatening to impose tariffs on imports from a country unless they make concessions in trade negotiations.
While this can be an effective strategy in certain situations, it can also lead to a trade war and harm both economies.
In general, tariffs should be used sparingly and as a last resort, and efforts should be made to address underlying trade issues through diplomacy and negotiation.
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A point A is graphed at (0, 5). Complete the coordinates of a shape that can be rotated about the y-axis to create a cone. Provide an explanation for your answer please
Answer:
(0, 5), (0, 1), and (3, 1).
Step-by-step explanation:
If the shape should be rotated about the y-axis to make a cone, then the shape needs to be a right triangle. It will have its length on the y-axis, and the other length either parallel to, or on, the x-axis.
Since we already have a point at (0, 5), we can have another point at (0, 1). That means that the side length is 4. Now, we can make a 3-4-5 right triangle by having another point at (3, 1).
Hope this helps!
The graph of f(x) is shown below of g(x) and f(x) are inverse functions, which graph represents g(x)
Answer:
It's B
Step-by-step explanation:
Given that we have the graph of f(x), we want to see which one is the graph of its inverse. i just had that question and i got a 100 on it
Which of the following Excel's functions is used to calculate the right-tailed probability for a value x on the F(df1,df2) distribution?a. F.DIST.RT(x, n1, n2)b. F.DIST.RT(x, Deg_freedom1, Deg_freedom2, Cumulative)c. F.DIST.RT(x, Deg_freedom1, Deg_freedom2)d. F.DIST.RT(x, n1â1, n2â2)
Option-c is correct that is F.DIST.RT(x, Deg_freedom1, Deg_freedom2) when the right-tailed probability for a value x on the F(df1,df2) distribution.
Given that,
We have to find which option is correct for the right-tailed probability for a value x on the F(df1,df2) distribution.
We know that,
What is F.DIST.RT function?returns the degree of diversity (right-tailed) F probability distribution for two data sets. This function can be used to compare the levels of diversity between two data sets. For instance, you may compare the test results of high school freshmen who are men and women to see if there is a difference in the variability between the sides.
Syntax
F.DIST.RT(x,deg_freedom1,deg_freedom2)
The following arguments are used with the F.DIST.RT function syntax:
The value at which the function should be evaluated.
Degrees of freedom numerator required: Deg freedom1.
Degrees of freedom in the denominator, required by Deg freedom2.
Therefore, Option-c is correct that is F.DIST.RT(x, Deg_freedom1, Deg_freedom2) when the right-tailed probability for a value x on the F(df1,df2) distribution.
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Put the following integers in order from
greatest to least:
-3, 12, 9, -8, 13
Answer:
-8 -3 9 12 13
Vote me
The measure of an angle in standard position is given. Find two positive angles and two negative angles that are coterminal with the given angle. (Write your final answers here, and be sure to show your work in your File Upload to receive full credit) 20°
The two positive angles that are coterminal with 20° are 380° and 740°. The two negative angles that are coterminal with 20° are -340° and -700°.
To find angles that are coterminal with 20°, we can add or subtract multiples of 360°.
Positive angles:
20° + 360° = 380°
20° + 2(360°) = 740°
Negative angles:
20° - 360° = -340°
20° - 2(360°) = -700°
These angles are coterminal with 20° because adding or subtracting a multiple of 360° leaves us in the same position on the unit circle.
Therefore, the two positive angles that are coterminal with 20° are 380° and 740°, and the two negative angles that are coterminal with 20° are -340° and -700°.
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The area of a square is 676 square root. what is the perimeter of the square?
Answer:
the perimeter of the square is 104
Step-by-step explanation:
to find the perimeter of a square we need to use the formula P = 4a
P is perimeter and a is the side of the square
if a is the side and the formula of Area is A = a^2
that means the side of the square is a = 26 because 26 * 26 = 676
now we take 26 and place it in the a spot of the perimeter formula
P = 4 * 26 (P = 104)
can i get brain if this helps and is correct plz and thxs <(^w^)>
Answer:
It's 104
Step-by-step explanation:
\( \sqrt{676 = 26} \)Square perimeter formula : P=4×aP=4×aP=4×26P=104jorge makes fruit snacks for his friends. He uses 1 1/2 apples to make 3 fruit snacks.
How many apples does jorge need to make 1 fruit snack
Answer:
Jorge needs 1/2 apple to make the snack.
Using the GCF, what is the factored form of 24v – 84?
3(8v – 28)
6(4v – 14)
12(2v – 7)
24(v – 60)
Answer: 2(3+x)(5-x)
Step-by-step explanation:
Answer:
2(3+x)(5-x)
Step-by-step explanation:
Ms. Ouzts wants to by a purse for $100. Sales tax in SC is 8.5%. If she has $125 to spend on the purse, will she have enough to purchase it? Why or why not?
Yes, Ms. Ouzts will have enough to purchase the purse as $125 is greater than the total cost of the purse including tax, which is $108.50.
The sales tax in South Carolina is 8.5%, which means that the total cost of the purse including tax will be
= Cost of purse + Sales tax
Substitute the values in the equation
= $100 + (8.5% of $100) = $100 + $8.50 = $108.50
If Ms. Ouzts has $125 to spend on the purse, then she will have enough to purchase it because $125 is greater than $108.50.
In fact, she will have $125 - $108.50 = $16.50 left over after buying the purse.
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