. If a = i + 1-2k, b = 21 -1 + 4k, and c = 21 - 13, determine 2 a + b - ) - (a + 25 ) + 3(a - b + c) 4] ]

The data structures are true:  Option (1,3)

Data structures are ways of organizing and storing data in a computer so that it can be accessed and manipulated efficiently. There are several types of data structures, including arrays, linked lists, stacks, queues, trees, and graphs. Each structure has its own unique features and advantages, making it suitable for different scenarios.

For example, arrays are used for storing and accessing data in a linear fashion, while trees and graphs are used for representing hierarchical relationships between data. Data structures are a fundamental concept in computer science and are used in many applications, including databases, compilers, and operating systems. Understanding and implementing data structures is essential for efficient programming and software development

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Full Question: Which of the following statements about the data structures are true? Select ALL CORRECT answers.

Answer:

Divide

Step-by-step explanation:

When you see something say "how many times larger than __ is __" You will Divide

(e.g. how many times larger is 6 than 3? divide 6 by 3 and you'll find out that 6 is 2 times as large as 3)

Hope this helps!

Times= multiplication

How many times larger means how many times that numner can get multiplied by the smaller number.

Hope it helped! :)

Answer:

a = 400+70+6

b= 90 +5

c=900+9

e= 300+20

1=70+2

g=100+1

The system of inequalities to represent the maximum amount of flooring needed and the maximum amount of money Samuel wants to spend is x + y <= 2000 and 4.50x + 8.25y <= 10000.

Let x be the number of square feet of carpet and y be the number of square feet of hardwood.

The most amount of flooring area he can cover is 2000 square feet. So the first inequality represents the maximum amount of flooring area that Samuel can cover:

x + y <= 2000

The carpet is $4. 50 per square foot and the hardwood is $8. 25 per square foot and Samuel has a budget of $10,000. So the second inequality represents the maximum amount of money that Samuel wants to spend:

4.50x + 8.25y <= 10000

So the system of inequalities is:

x + y <= 2000

4.50x + 8.25y <= 10000

This system represents the possible combinations of carpet and hardwood that Samuel can use while staying within his budget and the maximum amount of flooring area he can cover.

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(a) P(X=8) = 0.80^8 = 0.16777216(b) P(X ≤ 6) can be calculated using the formula for binomial distribution as:

P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)P(X = k) = nCk * pk * (1-p)n-k

Where n = 8, p = 0.8, and k = 0, 1, 2, 3, 4, 5, 6. We get: P(X ≤ 6) = 0.00016777216 + 0.0033554432 + 0.0268435456 + 0.1093358848 + 0.2550916792 + 0.34979648384 + 0.268435456P(X ≤ 6) = 0.01304031024(c) P(X ≥ 6) can be calculated as: P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8)P(X = k) = nCk * pk * (1-p)n-k

Where n = 8, p = 0.8, and k = 6, 7, 8We get: P(X ≥ 6) = 0.34979648384 + 0.3670016 + 0.16777216P(X ≥ 6) = 0.88457024384

Therefore, the probability values are: P(X = 8) = 0.16777216P(X ≤ 6) = 0.01304031024P(X ≥ 6) = 0.88457024384

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For the first graph

A = (-5, 2)

B = (5, -4)

To calculate the slope we will use the following formula

The answer would be m = -3/5

For the second graph

A = (-1, -1)

B = (3, 0)

To calculate the slope we will use the following formula

The answer would be m = 1/4

For the third graph

In the third graph, we have a vertical slope at point x = 2

In this case the slope would be equal to infinity and the equation of the line would be equal to x = 2

As there were 75 more nurses than doctors and the no. of nurses exceeded 10 times the no. of doctors by 140, there were 305 nurses in total.

Let 'x' be the no. of doctors and 'n' be the no. of nurses.

The first equation would be,

x + 75 = n, as the no. of nurses are 75 more than the no. of doctors

The second equation would be,

8n = 10x + 140, as 8 times the no. of nurses exceeded 10 times the no. of doctors by 140

Substituting equation 1 in 2 we get,

8( x + 75) = x + 140

8x + 600 = 10x + 140

600 - 140 = 10x - 8x

460 = 2x

x = 460/2

x = 230

Hence, the no. of doctors is 230 and the no. of nurses is 230+75 as 'n = x + 75'

Therefore, the no. of nurses is 305

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The unit rate of commercials per hour is 12 commercials per hour

From the question, we have the following parameters that can be used in our computation:

Time = 1 1/2 hour

Commercials = 18

The unit rate of commercials per hour is calculated as

Unit rate = Commercials/Time

Substitute the known values in the above equation, so, we have the following representation

Unit rate = 18/(1 1/2)

Evaluate

Unit rate = 12

Hence, the unit rate is 12

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Answer: 12

Step-by-step explanation: The unit rate of commercials per hour is 12 commercials per hour

How to determine the unit rate of commercials per hour?

From the question, we have the following parameters that can be used in our computation:

Time = 1 1/2 hour

Commercials = 18

The unit rate of commercials per hour is calculated as

Unit rate = Commercials/Time

Substitute the known values in the above equation, so, we have the following representation

Unit rate = 18/(1 1/2)

Evaluate

Unit rate = 12

Hence, the unit rate is 12

Step-by-step explanation:

(4x+7)/(2x-1)=(f/g)(x)

it means f(x)=4x+7

while g(x) =2x-1

f(g(x))=f(2x-1)

=4(2x-1)+7

=8x-4+7

ans =8x+3

Answer:

Step-by-step explanation:

Formula

V pi * r^2 * h

Givens

r = 3 m

h = 6 m

pi = 3.14 when used.

Solution

V = pi r^2 * h

V = pi * 3^2 * 6

V = 9 * 6 * pi

V = 54 * pi  Volume in terms of pi

V = 54*3.14 Volume using a value for pi

V = 169.56 to the hundred's place.

Answer:

x=12

Step-by-step explanation:

\(x^{2}\)=\(15^{2}\)-\(9^{2}\)

\(x^{2}\)=225-81

\(x^{2}\)=144 /sqrt

x=12

Therefore, the area of the quarter circle of radius 8 cm is 16π square centimeters (or approximately 50.2655 square centimeters if we use a decimal approximation for π).

A circle is a two-dimensional shape that is defined as the set of all points that are a fixed distance (called the radius) from a central point (called the center) in a plane. It is one of the most basic geometric shapes and is often used in a variety of mathematical and scientific contexts. One important thing to note about circles is that they are symmetrical: any line passing through the center of a circle divides the circle into two halves that are mirror images of each other. Circles are commonly used in a variety of contexts, including geometry, trigonometry, physics, engineering, and many other fields. They are also used in everyday life, such as in the design of wheels and other circular objects, the calculation of the areas of circular fields or gardens, and the measurement of circular objects like plates and bowls.

Here,

The formula for the area of a quarter circle is given by:

A = (1/4)πr²

where A is the area of the quarter circle, r is the radius of the circle, and π is the mathematical constant pi (approximately 3.14159).

In this case, the radius of the quarter circle is 8 cm, so we can substitute this value into the formula and simplify as follows:

A = (1/4)π(8 cm)²

A = (1/4)π(64 cm²)

A = 16π cm²

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The probability that Marshall wins a prize on his second spin =  0.1875

Consider an event X = the number of spins until Marshall wins a prize.

Given that a prize wheel with 4 segments of equal size, one of which is labeled winner.

So, the sample space n = 4

For given event x, the possible outcomes = 1

Using the formula of probability,

p = x/n

p = 1/4

p = 0.25

So, the probability of success p = 0.25

q = 1 - p

q = 1 - 0.25

q = 0.75

To find the probability that Marshall wins a prize on his 2nd spin.

Using formula, \(P(X = k) = (1 - p)^{k-1}p\)

For  k = 2,

\(P(X = 2) = (1 - 0.25)^{2-1}\times 0.25\)

P(X = 2) = 0.75 × 0.25

P(X = 2) = 0.1875

Thus, the required probability is  0.1875

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Null hypothesis: Gender and flight destination preference are independent.

Alternative hypothesis: Gender and flight destination preference are not independent.

The null and alternative hypotheses for this chi-square test can be stated as follows:

Null hypothesis (H0): Gender and flight destination are independent variables. There is no association between gender and preferred flight destination

Alternative hypothesis (H1): Gender and flight destination are dependent variables. There is an association between gender and preferred flight destination.

To calculate the chi-square statistic, we need to first construct the observed and expected contingency table. The degrees of freedom for a chi-square test in this case can be calculated as (number of rows - 1) * (number of columns - 1), which in this case is (2 - 1) * (4 - 1) = 3.

Using the chi-square table or a statistical software, we can find the critical chi-square value at a 2% significance level with 3 degrees of freedom.

The decision rule at the 2% significance level is: If the calculated chi-square statistic is greater than the critical chi-square value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

After calculating the chi-square statistic and comparing it with the critical chi-square value, we can make a decision. If the calculated chi-square statistic is greater than the critical chi-square value, we reject the null hypothesis, indicating that there is a significant association between gender and preferred flight destination. If the calculated chi-square statistic is less than or equal to the critical chi-square value, we fail to reject the null hypothesis, suggesting that there is no significant association between gender and preferred flight destination

A graph can be created to illustrate the decision, with the calculated chi-square statistic compared to the critical chi-square value at the 2% significance level. The key numerical values, such as the observed and expected frequencies, can be included in the graph.

Based on the decision made, there are two types of errors that can occur:

Type I error: Rejecting the null hypothesis when it is actually true, indicating a false positive result.

Type II error: Failing to reject the null hypothesis when it is actually false, indicating a false negative result.

The conclusion of the test should be interpreted in the context of the specific hypothesis and the significance level chosen.

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The total savings at the end of the third year will be approximately \(\$417,060.15\).

To calculate the total amount saved at the end of the third year, we need to determine the savings accumulated during each period and then sum them.

In the first 15 years, with a monthly savings of \(\$300\)and an annual interest rate of \(3.5\%\), we can use the future value of an ordinary annuity formula:

\(\[A = P \times \left(\frac{(1 + r)^n - 1}{r}\right)\]\)

where:

- \(A\)is the accumulated savings

- \(P\) is the monthly savings amount

- \(r\) is the monthly interest rate (\(3.5\% / 12\))

- \(n\) is the total number of months (15 years x 12 months/year)

Calculating the first 15-year savings:

\(\[A_1 = 300 \times \left(\frac{(1 + \frac{0.035}{12})^{15 \times 12} - 1}{\frac{0.035}{12}}\right)\]\)

In the next 15 years, with a monthly savings of \(\$650\) and an annual interest rate of \(6.5\%\), we can use the same formula:

Calculating the next 15-year savings:

\(\[A_2 = 650 \times \left(\frac{(1 + \frac{0.065}{12})^{15 \times 12} - 1}{\frac{0.065}{12}}\right)\]\)

Finally, to find the total savings at the end of the third year, we sum the accumulated savings from the first and second periods:

\(\[A_{\text{total}} = A_1 + A_2\]\)

To calculate the total savings at the end of the third year, we first need to find the accumulated savings for the two periods.

Calculating the accumulated savings for the first 15 years:

\(\(A_1 = 300 \times \left(\frac{{(1 + \frac{{0.035}}{{12}})^{{15 \times 12}} - 1}}{{\frac{{0.035}}{{12}}}}\right) \approx 68,081.80\)\)

Calculating the accumulated savings for the next 15 years:

\(\(A_2 = 650 \times \left(\frac{{(1 + \frac{{0.065}}{{12}})^{{15 \times 12}} - 1}}{{\frac{{0.065}}{{12}}}}\right) \approx 348,978.35\)\)

Now, we can find the total savings at the end of the third year:

\(\(A_{\text{{total}}} = A_1 + A_2 \approx 68,081.80 + 348,978.35 = 417,060.15\)\)

Therefore, the total savings at the end of the third year will be approximately \(\$417,060.15\).

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If you Saving $300/month for 15 years at 3.5%, then $650/month for another 15 years at 6.5%, will yield approximately $21,628.59 after three years.

To calculate the total amount you will have at the end of the third year, we can follow these steps:

1. Calculate the future value of the first saving period:

Using the formula for compound interest:

\(\[ \text{Future Value} = P \times \frac{{(1 + r)^t - 1}}{r} \]\)

Where:

\(\( P \)\) = Monthly savings amount

\(\( r \)\) = Annual interest rate (as a decimal)

\(\( t \)\) = Time period in years

For the first saving period:

\(\( P = \$300.00 \)\)

\(\( r = 0.035 \)\) (3.5% annual interest rate)

\(\( t = 15 \)\) (years)

Future Value of the first saving period:

\(\[ \text{Future Value} = \$300.00 \times \frac{{(1 + 0.035)^{15} - 1}}{0.035} \]\)

2. Calculate the future value of the second saving period:

For the second saving period:

\(\( P = \$650.00 \)\)

\(\( r = 0.065 \)\) (6.5% annual interest rate)

\(\( t = 15 - 3 = 12 \)\) (remaining years after the first saving period)

Future Value of the second saving period:

\(\[ \text{Future Value} = \$650.00 \times \frac{{(1 + 0.065)^{12} - 1}}{0.065} \]\)

3. Calculate the total future value at the end of the third year:

Total Future Value = Future Value of the first saving period + Future Value of the second saving period

The calculations for the total amount you will have at the end of the third year are as follows:

Future Value of the first saving period:

\(\[ \text{Future Value of the first saving period}\) = \(\$300.00 \times \frac{{(1 + 0.035)^{15} - 1}}{{0.035}} \approx \$7,648.63\)

Future Value of the second saving period:

\(\[ \text{Future Value of the second saving period}\) = \(\$650.00 \times \frac{{(1 + 0.065)^{12} - 1}}{{0.065}} \approx \$13,979.96\)

Total Future Value at the end of the third year:

\(\[ \text{Total Future Value}\) = \(\text{Future Value of the first saving period} + \text{Future Value of the second saving period}\)

\(\[ \approx \$7,648.63 + \$13,979.96 \approx \$21,628.59 \]\)

Therefore, If you Saving $300/month for 15 years at 3.5%, then $650/month for another 15 years at 6.5%, will yield approximately $21,628.59 after three years.

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At x=0 only, the function f with first derivative f'(x) = x(x-5)²(x+1) has a relative minimum.

Hence the correct option is (A) 0 only.

The first derivative of the function is,

f'(x) = x(x-5)²(x+1)

Differentiating the function with respect to x we get, The second derivative of the function is,

f''(x) = x(x-5)².(1) + x(x+1).2(x-5) + (x-5)²(x+1).1 = (x-5)² (x+x+1) + 2x(x+1)(x-5) = (x-5)²(2x+1) + 2x(x+1)(x-5)

Now, f'(x) = 0 gives,

x(x-5)²(x+1) = 0

We know that if product of more than one terms is zero then either of them is zero.

Either, x=0

Or, (x-5)² = 0

x-5 = 0

x = 5

Or, x+1 = 0

x = -1

So the extremum points of the function are, x = -1, 0, 5.

At x=-1, f''(-1) = (-6)²(-2+1) + 2(-1)(-1+1)(-6) = -36

At x=0, f''(0) = (-5)²*1 + 0 = 25

At x=5, f''(5) = 0 + 0 = 0

Since the value of second derivative is positive at only x = 0.

Thus, at x = 0 only the function has a relative minimum.

Hence the correct option is (A).

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Answer:

3. Yes because it is the same thing. (short answer just elaborate more)

4. No, a trapezoid cannot be a parallelogram. Trapezoid has only one pair of parallel sides while in a parallelogram there are two pairs of parallel sides.

5. see last sentence in 4

6. group 1: the diamond and the square tilted, and the square.

   group 2: the second one, the cup like shape, the cup shape but taller(the last one)

7. hard to see

8. hard to see

Step-by-step explanation:

Hey there! I'm happy to help!

The domain is any possible number you can input into the function to get a real output. The domain of h just means the domain of this entire function, which is called h.

Let's look at the answer options.

OPTION A

All real values of x such that x≠0.

The only way to make it so that we do not have a real output is if we get a negative square root. You cannot multiply any number by itself to get a negative number unless you use imaginary numbers, but using imaginary numbers makes our output not real.

Anyways, plugging in 0 would give us √-10, which is not a real number. That part is correct, but this option says ALL REAL NUMBERS except for 0. The problem is is that we can take any number less than ten and plug it in and we would get a negative square root, a fake number. So, this option is incorrect.

OPTION B

All real values of x such that x≥10.

Let's say we use 10 for our x and plug it in. This gives us √0, which is 0, a real output. Anything bigger than this 10 will give us a real output as well, so this option is correct.

We don't even need to check the other options because we have already found the correct answer. C,D, and E are all incorrect though because they include values less ten, which would give us a negative square root, a fake number.

I hope that this helps! Have a wonderful day!

To find the solution of the compound inequality x − 2 > 4 or 5x ≥ 35, we need to solve each inequality separately and then combine their solutions using the OR operator.

Solving x − 2 > 4, we add 2 to both sides to get x > 6.
Solving 5x ≥ 35, we divide both sides by 5 to get x ≥ 7.

The solution of the compound inequality x − 2 > 4 or 5x ≥ 35 is the set of all values of x that satisfy at least one of the inequalities, which is x > 6 or x ≥ 7.

To graph this solution, we draw a number line and mark the points 6 and 7 with open circles (because they are not included in the solution). Then we shade the region to the right of 6 and/or to the right of 7, as shown below:

<---o---o=========>
6   7

The open circles indicate that 6 and 7 are not included in the solution, because x can be any value greater than 6 or any value greater than or equal to 7, but not both at the same time.

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the problem is x > 6 or x ≥ 7. To explain this solution, we need to solve each inequality separately and then combine the results.

First, we solve x − 2 > 4 by adding 2 to both sides to get x > 6.

Next, we solve 5x ≥ 35 by dividing both sides by 5 to get x ≥ 7.

To combine the results, we take the union of the two solutions, which gives us x > 6 or x ≥ 7. This means that any value of x that is greater than 6 or equal to 7 will satisfy the original compound inequality.

The graph that represents this solution is a number line with an open circle at 6 and a closed circle at 7, shading everything to the right of 6 and including 7.

the solution to the compound inequality x − 2 > 4 or 5x ≥ 35 is x > 6 or x ≥ 7, and the graph that represents it is a number line with an open circle at 6 and a closed circle at 7, shading everything to the right of 6 and including 7.

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The student population of Denver is expected to be approximately 6,460 students in 14 years.

The exponential growth model for the future student population (y) of Denver can be written as: y = 2700(1 + 0.07)^14

Simplifying the expression, we get:

y = 2700(1.07)^14

Using a calculator, we can evaluate this expression to get:

y ≈ 6459.98

Therefore, the student population of Denver is expected to be approximately 6,460 students in 14 years.

Exponential growth models are commonly used to predict the growth or decline of populations over time. In this case, the population of Denver is expected to grow at a rate of 7% per year.

The exponential growth model accounts for the compounding effect of this growth over 14 years, resulting in a significant increase in the student population.

It is important to note that this model assumes that the growth ratio remains constant over time, which may not always be the case.

Additionally, factors such as migration, birth and death rates, and economic conditions can all impact population growth and should be considered when making predictions about future population trends.

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Answer:

heyyyyyyyyyyyyyyyyyyy

(i) As we have proved that [10][0] in R and that [a+bi] = [a+3b], where a, b Z.

(ii) As we have proved that the unique ring homomorphism 6: Z→ Ris surjective

(iii) As we have proved that 1+3i is not a unit and that 1+3i does not divide 2 and 5 in Z[].

(iv) We can then show that Ker(ψ) = 10Z in R, which is the ideal generated by 10 in R.

(i) The first part of the problem asks us to show that i-3 € (1+36) and that [i] = [3] in R. To do this, we need to understand what R represents. R is the ring obtained by taking the quotient of the ring of Gaussian integers Z[i] by the ideal generated by 1+3i. In other words, we consider all the possible integers in Z[i], but we identify any two integers that differ by a multiple of 1+3i. So, [i] represents the equivalence class of all the integers in Z[i] that are equivalent to i modulo 1+3i.

Finally, we can use the fact that [a+bi] = [a+3b] in R for any integers a and b. To see this, note that [a+bi] = [(a-3b) + (b+3a)i], which is equivalent to [a+3b] modulo 1+3i. Therefore, we have [a+bi] = [a+3b] in R.

(ii) The second part of the problem asks us to show that the unique ring homomorphism Φ: Z → R is surjective. In other words, every element of R is the image of some integer in Z under Φ.

Now, let [a+bi] be an arbitrary element of R. We need to show that there exists an integer n such that Φ(n) = [a+bi]. To do this, note that [a+bi] = [(a-3b) + (b+3a)i], which is equivalent to (a-3b) modulo 1+3i. Therefore, we can choose n = a-3b, and we have Φ(n) = [n] = [a+bi]. This shows that Φ is surjective.

(iii) The third part of the problem asks us to show that 1+3i is not a unit in R and that 1+3i does not divide 2 and 5 in Z[i]. We then need to use these facts to conclude that Ker(Φ) = 102, which is the kernel of the homomorphism Φ.

To show that 1+3i is not a unit in R, we need to show that there is no element in R that, when multiplied by 1+3i, gives the multiplicative identity in R. Suppose, for the sake of contradiction, that there exists such an element [a+bi] in R. This means that (1+3i)(a+bi) is equivalent to 1 modulo 1+3i, which implies that 3a+b is a multiple of 1+3i. But this is not possible, since 1+3i is not a divisor of any integer of the form 3a+b in Z[i]. Therefore, 1+3i is not a unit in R.

(iv) The final part of the problem asks us to show that RZ/10Z, which is the quotient of R by the ideal generated by 10 in Z[i], is isomorphic to the ring Z/10Z. To do this, we can define a ring homomorphism ψ: R → Z/10Z by ψ([a+bi]) = a mod 10, which maps each equivalence class in R to its residue modulo 10 in Z/10Z.

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The inequality to represent the number of students who can attend the field trip on the bus will be C. s≤48 s is less than or equal to 48.

From the information, Mrs. Milleman's math class is planning to going on a field trip. The school bus which is taking them can hold at most 48 people.

Therefore, the inequality to represent the number of students who can attend the field trip on the bus will be C. s≤48 s is less than or equal to 48.

In conclusion, the correct option is C.

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Answer:

x = 27

Step-by-step explanation:

\( \frac{1}{3}x - 3 + 4 = 10\)

\( \frac{1}{3}x + 1 = 10 \)

multiply both sides by (3)

\(3 \times \frac{1}{3}x + 3 \times 1 = 3 \times 10\)

x + 3 =30

x = 30–3

x = 27

i hope i helped

The cash price of one radio after a 14% discount is $4644.

The price of a radio is $5400. After giving a 14% discount for each radio, what will be the cash price?

Solution: The given price of the radio is $5400. The discount given on each radio is 14%.

Let's calculate the discount: Discount% = 14% Discount = (Discount%/100%) × Selling Price Discount = (14/100) × $5400 Discount = $756 Therefore, the discount on one radio is $756.

The cash price of one radio after a 14% discount is: Cash Price = Selling Price - Discount Cash Price = $5400 - $756Cash Price = $4644 Therefore, the cash price of one radio after a 14% discount is $4644.

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Answer: Polynomials are algebraic expressions that consist of variables and coefficients.

Step-by-step explanation:

Answer:

an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

Answer:

lld,=dsf=[ghn.pppppppppppppppppppppppppppppppppppppppppp

Step-by-step explanation:

Answer:

It's an acute triangle

Step-by-step explanation:

The integral for finding the area of the region is:

A = ∫[lower bound]^[upper bound] [rightmost bound] dy

A = ∫[1/6]^∞ [6] dy

To sketch the region enclosed by the curves and determine whether to integrate with respect to x or y, let's analyze the given equations:

y = 1/x

y = 1/x^2

x = 6

To begin, let's plot these curves on a coordinate plane:

First, we can observe that both equations involve hyperbolas. The equation y = 1/x represents a hyperbola that passes through the points (1,1), (2,0.5), (-1,-1), etc. The equation y = 1/x^2 represents a hyperbola that passes through the points (1,1), (2,0.25), (-1,1), etc.

Next, the equation x = 6 represents a vertical line passing through the point (6,0) on the x-axis.

Now, to determine the enclosed region, we need to find the limits of integration.

Since the curves intersect at certain points, we need to find these points of intersection. Equating the two equations for y and solving, we get:

1/x = 1/x^2

Multiplying both sides by x^2 yields:

x = 1

Hence, the curves intersect at x = 1.

Therefore, the region enclosed by the curves is bounded by the following:

The curve y = 1/x,

The curve y = 1/x^2,

The vertical line x = 6, and

The x-axis.

To determine whether to integrate with respect to x or y, we need to consider the orientation of the curves. In this case, the curves are defined in terms of y = f(x). Thus, it is more convenient to integrate with respect to y.

To find the area of the region, we need to set up the integral bounds. Since the region is bounded by the curves y = 1/x and y = 1/x^2, we need to find the limits of y.

The lower bound is determined by the curve y = 1/x^2, and the upper bound is determined by the curve y = 1/x. The vertical line x = 6 acts as the rightmost boundary.

Therefore, the integral for finding the area of the region is:

A = ∫[lower bound]^[upper bound] [rightmost bound] dy

A = ∫[1/6]^∞ [6] dy

Now, we can proceed with evaluating this integral to find the area of the enclosed region.

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Answer:

The last option

Step-by-step explanation:

When you have a fraction as a power, the denominator goes to the root, so in this case, it becomes root 4. The base, 5, goes to the outside, and the numerator 1, goes beside the x.

Hope this helps!