The following inequalities represent a system.

y ≥ 5x + 2
y > −3x − 2

Which of the following graphs represents the system?

Answer:

The reason why -2^2=-4 and (-2)^2=4 is due to the rules of mathematical operations and the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

According to the order of operations, when you have an expression with multiple operations, you must perform the operations in a specific order. Exponents come before multiplication and division, and before addition and subtraction.

So, when evaluating -2^2, you first evaluate the exponent, which is 2. However, the negative sign in front of the 2 is not part of the exponent, but rather an arithmetic operation. Therefore, the expression is equivalent to -(2^2), which is equal to -4.

On the other hand, when evaluating (-2)^2, the parentheses indicate that the negative sign is part of the base, so you must first evaluate the base, which is -2, and then apply the exponent of 2. This gives you (-2)^2 = 4.

Step-by-step explanation:

The minus in (-2)^2 is enclosed in parentheses, so it is also squared:

minus × minus = plus

And talking about this one: -2^2, the minus is not included in the parentheses, that's why we only square the number (2 in this case) and keep the minus in front of it

I hope this will help...

1. The 95% confident that the true population mean is 64.97 and 435.03 hours. 2. The 99% confident is between 0.407 and 0.500. 3. The 95% estimate of the mean is (45,424, 48,576). 4. Sample size is 91.27.

A fundamental idea in statistics known as the central limit theorem (CLT) argues that, under specific circumstances, the sampling distribution of the mean of a random sample from any population tends to resemble a normal distribution as the sample size rises.

1. For 95% confidence interval we have:

CI = x ± z*(σ/√n)

Substituting the values:

CI = 400 ± 1.96*(39/√30) = (364.97, 435.03)

2. For 99% confidence interval we have:

CI = p-cap ± z*(√(p - cap(1- p-cap)/n))

Substituting the values:

CI = 165/360 ± 2.58*(√((165/360)*(195/360)/360)) = (0.407, 0.500)

Hence, we can be 99% confident that the true population proportion of married men, 18 or older, is between 0.407 and 0.500.

3. 95% estimate of the mean:

CI = x ± t*(s/√n)

Substituting the values:

CI = 47,000 ± 2.064*(1,050/√26) = (45,424, 48,576)

4. For sample size:

CI = 47,000 ± 2.064*(1,050/√26) = (45,424, 48,576)

Substitute the values:

n = (1.96*39 / 20)^2 = 91.27

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We can conclude that m∠MNP has a measure of 0 degrees in parallelogram MNPQ.

A parallelogram is a four-sided geometric shape in which opposite sides are parallel and congruent (equal in length) to each other. It is a special case of a quadrilateral, which is any four-sided polygon.

In the given question,

Since opposite angles in a parallelogram are equal, we know that:

m∠MNP = m∠QMN

We also know that the sum of the interior angles of a triangle is 180 degrees. Therefore, we can find the measure of angle MQN as follows:

m∠MQN = 180 - m∠PQM = 180 - 135 = 45 degrees

Now, we can use the fact that the opposite angles in a parallelogram are equal to find the measure of angle QMN:

m∠QMN = m∠PQM = 135 degrees

Finally, we can use the fact that the angles in a triangle add up to 180 degrees to find the measure of angle MNP:

m∠MNP = 180 - m∠MQN - m∠QMN

= 180 - 45 - 135

= 180 - 180

= 0 degrees

Therefore, we can conclude that m∠MNP has a measure of 0 degrees. This means that the sides MN and PQ are parallel and do not intersect, so angle MNP does not exist.

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Answer:

a. To complete the table:

# of times floss per week Frequency Relative Frequency Cumulative Frequency

0 6 0.0857 6

1 7 0.1 13

2 4 0.0571 17

3 11 0.1571 28

4 15 0.2143 43

5 11 0.1571 54

6 6 0.0857 60

7 7 0.1 67

Step-by-step explanation:

b. To find the cumulative relative frequency for flossing 3 times per week, we need to add up the relative frequencies for all values of flossing less than or equal to 3.

Cumulative relative frequency for flossing 3 times per week:

= relative frequency for flossing 0 times per week + relative frequency for flossing 1 time per week + relative frequency for flossing 2 times per week + relative frequency for flossing 3 times per week

= 0.0857 + 0.1 + 0.0571 + 0.1571

= 0.4

Therefore, the cumulative relative frequency for flossing 3 times per week is 40%.

The probability of exactly 3 out of 10 vehicles exceeding the speed limit on US 131 is 0.250.

This problem can be solved using the binomial distribution. We are given that the probability of any given vehicle exceeding the speed limit is p = 0.6, and we are interested in the probability of 3 out of 10 vehicles exceeding the speed limit, i.e., X = 3.

The probability mass function of the binomial distribution is given by:

P(X = k) = (n choose k) ×p^k ×(1-p)^(n-k)

where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose k) is the binomial coefficient, which is equal to n!/(k! (n-k)!).

Substituting the given values, we get:

P(X = 3) = (10 choose 3) × 0.6³ ×0.4⁷

P(X = 3) = 0.250

Therefore, the probability of exactly 3 out of 10 vehicles exceeding the speed limit on US 131 is 0.250, rounded to three decimal places.

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Answer:

4.67

Step-by-step explanation:

Camila's decision to return to work part-time instead of relying solely on her benefits reflects her personal investment in her human capital. By continuing to work, she is not only earning a salary but also investing in herself and her future career prospects.

How to solve the problem?

Camila's decision to return to work part-time after her accident instead of maintaining all her benefits without working shows that she values her human capital and is invested in it. Human capital refers to the skills, knowledge, and abilities that individuals possess, which are gained through education, training, and experience. By choosing to work, Camila is not only earning a salary, but she is also developing and enhancing her skills, knowledge, and abilities, thereby increasing her human capital.

Furthermore, Camila's decision to return to work part-time also shows that she has a strong work ethic and is committed to her career. She understands the importance of staying active in the workforce, even if it means working part-time, to maintain her professional network and stay up-to-date with industry developments. This commitment to her career and her willingness to work despite her physical limitations is a testament to her determination and resilience.

Overall, Camila's decision to return to work part-time instead of relying solely on her benefits reflects her personal investment in her human capital. By continuing to work, she is not only earning a salary but also investing in herself and her future career prospects.

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To determine which graph has the larger range, we need to understand what is meant by the term “range” in the context of graphs. the answer is: O The first graph has the larger range.

In statistics, the range is defined as the difference between the maximum and minimum values in a dataset. It provides a measure of how spread out the data is, and can be used to identify the extent of variability within a dataset.

Looking at the first graph, we can see that the range of race times is from approximately 10 minutes to 25 minutes. Therefore, the range of this dataset is [tex]25 - 10 = 15[/tex] minutes.

Looking at the second graph, we can see that the range of race times is from approximately 8 minutes to 22 minutes. Therefore, the range of this dataset is [tex]22 - 8 = 14[/tex] minutes.

Since the range of the first graph is  [tex]15[/tex] minutes and the range of the second graph is  [tex]14[/tex] minutes, we can conclude that the first graph has the larger range.

Therefore, the answer is: O. The first graph has the larger range.

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A binomial experiment has given number of trails n and the given success probability n=2, p=0.2 then P(0) = 1.

A binomial experiment is an experiment where there have a fixed number of independent trials with only have two outcomes either success or failure.

A binomial experiment has given number of trails n and the given success probability p.

n=2, p=0.2

The probability of obtaining x successes in n independent trials of a binomial experiment, where the probability of success is p, is given by binomial probability distribution   P(x)= ₙ c ₓ p ˣ  (1-p)ˣ

Where x = 0, 1, 2, ---- , n

so, P(0)= ₂C₀ (0.2)⁰ (1-0.2)⁰

             = 1×1×1

             =1

Hence P(0)= 1

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Complete question:

La hipotenusa mide 137 cm.

Podemos utilizar el teorema de Pitágoras para resolver este problema, que establece que en un triángulo rectángulo, el cuadrado de la hipotenusa es igual a la suma de los cuadrados de los catetos.

Sea "a" la medida del otro cateto, entonces:

a² + 77² = (a+49)²

Desarrollando los cuadrados y simplificando, tenemos:

a² + 5929 = a²+ 98a + 2401

Restando a ambos lados a², obtenemos:

5929 = 98a + 2401

Restando 2401 a ambos lados, obtenemos:

3528 = 98a

Dividiendo por 98, obtenemos:

a = 36

Por lo tanto, el otro cateto mide 36 cm, y la hipotenusa se puede calcular utilizando el teorema de Pitágoras:

h² = a² + b²

h2 = 36² + 77²

h² = 12996 + 5929

h² = 18925

Tomando la raíz cuadrada en ambos lados, obtenemos:

h = 137

Por lo tanto, la hipotenusa mide 137 cm.

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Answer:

y = 4 meters

Step-by-step explanation:

to find a volume of a cube you do (y × y) y

so if Y equals 4 then it would look like this:

(4 × 4)4 which = 64

Answer:

Let the height be represented as x

width = 14 + x

Length of diagonal = 34 inches.

Taking one diagonal of the rectangle to form a triangle.

using the Pythagoras theorem.

34² = (14 + x)² + x²

1156 = 196 + 28x + x² + x²

2x² + 28x - 960 = 0

divide through by 2

x² + 14x - 480 = 0

x² + 30x - 16x - 480 = 0

x(x + 30) - 16 (x + 30) = 0

(x - 16) = 0 or (x + 30) = 0

x = 16 or x = - 30

since the length can't be negative

therefore 16 inches is correct

According to the given question we can conclude that statement I and statement II are correct but not statement III.

Interest is the cost incurred when lending and borrowing a specific amount of money from a financial standpoint. It is crucial to note that interest is calculated as a percentage.

given,

Statement I is correct because the inflation rate averaged 1.3%, and Maria's savings account earned interest at a rate of 0.725%, which is lower than the inflation rate. This means that the buying power of her gift decreased by approximately 1.3% - 0.725% = 0.575% or 0.6% (rounded).

Statement II is also correct because Maria's savings account earned interest on the deposit of $2,000 for one year at a rate of 0.725%. The interest earned can be calculated as:

Interest = Principal x Rate x Time

Interest = $2,000 x 0.00725 x 1 year

Interest = $14.50

However, statement III is not correct. Since Maria deposited the entire gift of $2,000 into the savings account and did not make any withdrawals during the year, the balance in the account at the end of 2016 would be the sum of the initial deposit and the interest earned, which is $2,000 + $14.50 = $2,014.50. Therefore, the correct option is:

Statement III is incorrect, however Statements I as well as II are true.

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The graph of y = sec(x) will have vertical asymptotes at these three values of x.

Vertical asymptotes are vertical lines on a graph where a function approaches either positive or negative infinity as the independent variable approaches a certain value.

The secant function, y = sec(x), is defined as the reciprocal of the cosine function:

sec(x) = 1/cos(x)

The cosine function has vertical asymptotes at x = (2n + 1)π/2 for any integer n, since cosine is undefined at these points (division by zero). Therefore, the secant function will have vertical asymptotes at the same points, since dividing 1 by a very small number (close to zero) results in a very large number (tending towards infinity).

So, the values of x in the interval -2π ≤ x ≤ 2π that will cause the secant function to have vertical asymptotes are:

x = (2n + 1)π/2, where n is an integer

For n = -2, we have x = -5π/2, which is outside the interval, so we can ignore it.

For n = -1, we have x = -π/2

For n = 0, we have x = π/2

For n = 1, we have x = 3π/2

For n = 2, we have x = 5π/2, which is also outside the interval.

Therefore, the values of x in the interval -2π ≤ x ≤ 2π that will cause the secant function to have vertical asymptotes are:

x = -π/2, π/2, 3π/2

So, the graph of y = sec(x) will have vertical asymptotes at these three values of x.

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Answer: Technically its π (pie) 4

Step-by-step explanation:

If tan (x)=1 , then sin x = cos x . We know this is true for x=π4 as a base case. p = nπ , where n is an integer. The first positive value x0 for which tanx=1 is, as stated before, π4 . yw.

To solve the integral [tex]\rm\int_0^7 e^x \sin(x) dx\\[/tex], we can use integration by parts. Let u = sin(x) and dv = [tex]\rm e^x[/tex] dx, then we have:

[tex]\begin{align} \rm\int \rm e^x \sin(x) dx &= \rm-e^x \cos(x) + \rm\int e^x \cos(x) dx \\&= \rm -e^x \cos(x) + e^x \sin(x) - \int e^x \sin(x) dx\end{align}[/tex]

Rearranging, we get:

[tex] \begin{align}2 \rm \int e^x \sin(x) dx &= \rm e^x (\sin(x) - \cos(x)) \bigg|^7_0 \\& \rm= e^7 (\sin(7) - \cos(7)) - 1\end{align}[/tex]

Dividing both sides by 2, we get:

[tex] \rm\int_0^7 e^x \sin(x) dx = \frac{e^7 (\sin(7) - \cos(7)) - 1}{2} \\ [/tex]

Therefore, the value of the integral is

[tex] \rm \boxed{ \rm\frac{e^7 (\sin(7) - \cos(7)) - 1}{2}}[/tex]

That sounds like a smart plan! Before investing his savings, Jose should do some research to determine the best investment strategy for his goals.

What is research?

He will need to consider factors such as his risk tolerance, the potential return on investment, and the length of time he has to invest. Once he has identified an investment strategy that aligns with his goals, he should start investing his savings.

Over time, as his investments generate returns, he can use these returns to fund his business venture. It is important for Jose to regularly monitor his investments and adjust his strategy as needed to ensure that he is on track to achieve his goals. With careful planning and a well-executed investment strategy, Jose can achieve his goal of retiring early and starting his own coaching classes.

What is an investment ?

An investment refers to the purchase of an asset with the goal of generating income, capital appreciation, or both. The asset could be anything of value, such as stocks, bonds, real estate, commodities, or mutual funds. Investors typically make an investment with the expectation of earning a return on their investment over a period of time.

The return could be in the form of interest, dividends, or capital gains, depending on the type of investment. Investors may choose to invest in different types of assets based on their investment goals, risk tolerance, and investment horizon. The process of investing involves conducting research, analyzing market trends, and making informed decisions based on the available information.

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Complete question is: Jose is a middle-aged professor who wants to retire early and start his own coaching classes. He decides to invest his savings and use the returns to fund his business venture. Before investing his savings, Jose should do some research to determine the best investment strategy for his goals.

a. f(x) = x³

b. g(x) = -f(x-2)

Answer:

  a) parent: f(x) = x³

  b) g(x) = -f(x -2)

Step-by-step explanation:

You want the parent function and the given function written in terms of the parent function for g(x) = -(x -2)³.

The parent function is the function that remains after scale factors and translations are removed. In general, a transformed function will look like ...

  g(x) = c·f((x-a)/b) +d

which scales the function f(x) horizontally by a factor of b, vertically by a factor of c, and translates the result by (a, d).

Here, we recognize that ...

  g(x) = -(x -2)³

has c = -1, a = 2, b = 1, d = 0

and the parent function is ...

  f(x) = x³

Using the values for a, b, c, d that we recognized above, we have ...

  g(x) = -f(x -2)

__

Additional comment

When scale factors are negative, they reflect the function over the relevant axis. Here, the negative vertical scale factor reflects the function vertically over the x-axis. The translation is 2 units to the right.

Answer:

Step-by-step explanation:

scale factor is -4

D(-1 , -1) and if you divide either the x coordinate or the y coordinate by

4 - you get negative four which is the scale factor.

the length of side AB of triangle ABC is 6 units.

How to find the length?

To find the length of side AB of triangle ABC, we can use the distance formula which is given by:

distance = sqrt((x2 - x1)² + (y2 - y1)²)

Where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment.

Using the distance formula, we can calculate the length of side AB as follows:

AB = sqrt((2 - (-4))²+ (3 - 3)²)

AB = sqrt((6)²+ (0)²)

AB = sqrt(36)

AB = 6

Therefore, the length of side AB of triangle ABC is 6 units.

We can also visualize the triangle on the graph and see that side AB is a horizontal line segment between the points (-4,3) and (2,3), which have the same y-coordinate. This makes the length of AB equal to the horizontal distance between these two points, which is simply 2 - (-4) = 6.

It is important to note that the distance formula can be applied to find the length of any line segment in the coordinate plane, as long as we know the coordinates of its endpoints.

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The probability of choosing all diet drinks is then: P(all diet drinks) = 24 / 70 ≈ 0.343 or about 34.3%. P(first two are diet drinks and second two are regular) = 288 / 70 ≈ 4.114 or about 4.1%

It is expressed as a number between 0 and 1, where 0 represents an impossible event (i.e., it will never happen), and 1 represents a certain event (i.e., it will always happen).

There are a total of 8 cans of soft drinks, and the child chooses 4 cans to arrange in a row. The total number of ways to choose 4 cans out of 8 is:

C(8,4) = 8! / (4! * 4!) = 70

(a) To find the probability that all four cans are diet drinks, we need to count the number of ways to choose 4 cans that are all diet drinks. Since there is one diet drink for each brand, there are 4 choices for the first can, 3 choices for the second can, 2 choices for the third can, and 1 choice for the fourth can. Therefore, the number of ways to choose 4 cans that are all diet drinks is:

4 * 3 * 2 * 1 = 24

The probability of choosing all diet drinks is then:

P(all diet drinks) = 24 / 70 ≈ 0.343 or about 34.3%

(b) To find the probability that the first two cans are diet drinks and the second two cans are regular drinks, we can count the number of ways to choose 2 diet drinks out of 4 and the number of ways to choose 2 regular drinks out of 4, and then multiply these two numbers together. There are:

C(4,2) = 4! / (2! * 2!) = 6

ways to choose 2 diet drinks out of 4, and also 6 ways to choose 2 regular drinks out of 4. Once we have chosen the 2 diet drinks and 2 regular drinks, there are 4! ways to arrange them in a row. Therefore, the total number of arrangements that have the first two cans as diet drinks and the second two cans as regular drinks is:

6 * 6 * 4! = 288

The probability of this arrangement is then:

P(first two are diet drinks and second two are regular) = 288 / 70 ≈ 4.114 or about 4.1%

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Using division, we can find that Marcus will take 2 hours or 120 minutes to read the book.

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. By dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.

Marcus is reading a book with 80 pages.

He reads first 20 pages in 30 mins.

So, to read 1 page time taken

= 30/20

= 3/2

= 1.5 mins

Now to read 80 pages, time taken will be:

80 × 1.5

= 120 mins.

Therefore, Marcus will take 2 hours or 120 minutes to read the book.

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Answer: To find the points where the two skaters might collide, we need to solve the system of equations:

y = -2x + 14 (Equation 1)

y = -2x^2 + 14x (Equation 2)

We can substitute Equation 1 into Equation 2 to eliminate y and get:

-2x + 14 = -2x^2 + 14x

Simplifying, we get:

2x^2 - 16x + 14 = 0

Dividing both sides by 2, we get:

x^2 - 8x + 7 = 0

This quadratic equation factors as:

(x - 1)(x - 7) = 0

So the possible values of x where the skaters might collide are x = 1 and x = 7.

To find the corresponding y-values, we can plug each value of x into either Equation 1 or Equation 2. For x = 1:

y = -2(1) + 14 = 12 (using Equation 1)

y = -2(1)^2 + 14(1) = 12 (using Equation 2)

So the skaters might collide at the point (1, 12).

For x = 7:

y = -2(7) + 14 = 0 (using Equation 1)

y = -2(7)^2 + 14(7) = 0 (using Equation 2)

So the skaters might collide at the point (7, 0).

Therefore, the two skaters might collide at points (1, 12) and (7, 0).

Step-by-step explanation:

Answer:

(-1.29, 8.29) or (9.29,-2.29)

Step-by-step explanation:

Find what y equals in terms of x for both equations.

Set those two equations equal to each other (Because y=y)

Solve for x (you may need to use the quadratic formula for this step)

Plug the value(s) of x into the original equation to find y.

Step-by-step explanation:

if we extend the line VT to reach also the opposite side of the circle, we see that this line cuts the circle in half.

the whole arc angle of a half-circle is 360/2 = 180°.

now we can use the exterior angle rule :

the vertex angle (V) = 1/2 × difference of the angles of the intersected arcs.

the intersected arcs are

shorter = angle at T : the arc from U to the circle intersection with the line VT.

longer : the arc from U to the circle intersection with the extended line VT.

shorter + longer = 180°

longer = 180 - shorter

30 = 1/2 × ((180 - shorter) - shorter) =

= 1/2 × (180 - 2×shorter) = 90 - shorter

-60 = -shorter

shorter = 60°

the angle at T = 60°.

Step-by-step explanation:

Here , the eqn is given as,

Let 1 kg onion cost Rs. y and 1kg potato cost Rs. y then,

3x + 2y= 240....eqn i

The When rate of potato increases by 20 percent,

New rate of unit kg potato becomes,

[tex]x \: + \: 20\% \: of \: x[/tex]

i.e. Rs.6x/5

And when price of onion decreases by 10% ,

New unit price is ,

[tex]y - 10\% \: of \: y[/tex]

i.e. Rs.9y/10

Now the second eqn becomes ,

20x + 21y= 2060

By using elimination method we get x= Rs 40 and y= Rs.60

Finally, we have to find percent change i.e

{(cost of 1kg onion - cost of 1kg potato)/ cost of 1kg potato}x 100%

This gives the ans as 50%

Answer:

45.32

Step-by-step explanation:

Answer:

  147.6 m²

Step-by-step explanation:

You want the surface area of a triangular pyramid with base sides of length 8 m and a slant height of 10 m. (The altitude of the base triangle is approximately 6.9 m.)

The surface area is the sum of the areas of the triangular faces.

  SA = 1/2(8 m)(6.9 m) + 3 × 1/2(8 m)(10 m)

  = 1/2(8 m)(6.9 m + 3×10 m) = (4)(36.9) m² = 147.6 m²

The surface area of the pyramid is 147.6 square meters.