Problem 1
Select all of the ordered pairs (x, y) that are solutions to
the linear equation 2x + 3y = 6.
(Select all that apply.)
(0,2)
(0,6)
(2,3)
(3,-2)
(3,0)
(6, -2)

The period of y=csc x is  2π. This means that the graph of y=csc x repeats itself every 2π units along the x-axis.

The domain of y=csc x is all real numbers except for the values where sin x equals zero. This is because the csc function is undefined when the sine function equals zero.

The range of y=csc x is the set of all real numbers greater than or equal to 1, and less than or equal to -1.

This is because the csc function outputs values that are reciprocals of the sine function, which can take on any value between -1 and 1, excluding 0.

The period of y=csc x is 2π. This means that the graph of y=csc x repeats itself every 2π units along the x-axis.

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Answer:

18

Step-by-step explanation:

n/2 + 15 = 24

subtract 15 from both sides

n/2 = 9

Multiply both sides by 2

n=18

Answer:

21

Step-by-step explanation:

3 (7) - 2(4) + 8

21 - 8 + 8

13 + 8

21

Answer:

21

Step-by-step explanation:

3k - 2c + 8

k = 7 and c = 4

Substitute the values of k and c in the algebraic expression

3(7) - 2(4) + 8 = 21 - 8 + 8 = 21

The least number of seats the manger could order to 270 seats

The information that the the seats are sold only in groups of 10 will help to know that the order will be in a multiple of 10.

The manager wants to order 267 seats and this is not a multiple of 10 the nearest multiple of 10 is 270.

This is because, 260 will be short of want the manager want however ordering for 270 will be in excess with three seats.

Hence the manager will order 270 and heave 3 extra seats

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Although a bigger random sample can aid in increasing the precision and decreasing the variability of a national opinion poll, it cannot ensure a decrease in bias, which is dependent on the efficacy of the sampling technique and the sample's representativeness.

A nationwide opinion poll's results are often less variable as the random sample size is increased since the bigger sample size more accurately represents the people being sampled.

It does not necessarily lessen bias, which is the term for systemic mistakes in the sampling process or polling methodology that may endure even with a larger sample size.

The accuracy of the poll's results can be improved by reducing random mistakes like sampling and measurement errors with a bigger sample size.

The standard error of the mean, a measurement of the variability of the sample mean from sample to sample, is often less the bigger the sample size.

A national opinion poll's measure of interest, the population mean, can be more accurately estimated with a smaller standard error.

If the sample is not completely random or representative of the population being investigated, bias may still exist in a bigger sample.

For instance, the findings may be biassed if the pollsters oversample a certain demographic group or geographic area.

Non-response bias can also happen if a certain group of people is less likely than others to reply to the survey.

As a result, while a bigger random sample can aid in increasing the precision and decreasing the variability of a national opinion poll, it cannot ensure a decrease in bias, which is dependent on the efficacy of the sampling technique and the sample's representativeness.

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Answer:

This means that f(x)→∞ as x→−∞ and f(x)→∞ as x→∞.

Step-by-step explanation:

Since the leading term of the polynomial (the term in a polynomial which contains the highest power of the variable) is x4, then the degree is 4, i.e. even, and the leading coefficient is 1, i.e. positive.

This means that f(x)→∞ as x→−∞ and f(x)→∞ as x→∞.

Answer:

90+15x+8x-2=180

Step-by-step explanation:

answer is 4

have a great day love!

Answer:

The answer is 4

90+15x+8x-2=180

The probability that a randomly selected adult does not own shares of stock is 66.84%.

To calculate the probability that a randomly selected adult does not own shares of stock, we need to subtract the probability that the person is a shareholder from the probability that the person has some college education. We can use the formula:

P(A') = 1 - P(A)

where P(A) is the probability that the person is a shareholder, and P(A') is the probability that the person is not a shareholder.

P(A) = 52%

P(A') = 100% - P(A') = 100% - 52% = 48%

Next, we need to calculate the probability that the person has some college education.

We can use the formula:

P(B) = 47%

Now we can use the formula for conditional probability to calculate the probability that the person has some college education given that they are not a shareholder:

P(B|A') = P(A' and B) / P(A')

To calculate P(A' and B), we can use the formula:

P(A' and B) = P(B) - P(A and B)

P(A and B) = P(A) x P(B|A) = 52% x P(B|A)

To calculate P(B|A), we can use Bayes' theorem:

P(B|A) = P(A|B) x P(B) / P(A)P(A|B) = P(A and B) / P(B) = (52% x P(B|A)) / P(B)

Now we can substitute this expression into the formula for P(A' and B):

P(A' and B) = P(B) - P(A) x P(A|B) x P(B) / P(A) = 47% - (52% x P(B|A)) x 47% / P(B)

Now we can substitute these expressions into the formula for P(B|A') and simplify:

P(B|A') = (47% - (52% x P(B|A)) x 47% / P(B)) / 48%

We are given that 16% of all shareholders have some college education, so we can substitute this value for P(B|A):

P(B|A') = (47% - (52% x 16%)) x 47% / P(B) / 48% = 33.16%

Finally, we can substitute this value into the formula for P(A'):

P(A') = 100% - P(A') = 100% - 33.16% = 66.84%

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a) The formula for P(t) is: \(P(t) = 25000 × e^(0.063t)\)

b) The population increases by approximately 6.488% each year (rounded to 0.001%).

(a) The formula for P(t), the population in year t, can be found using the continuous growth formula:

\(P(t) = P(0) × e^(rt)\)

where P(0) is the initial population, r is the continuous growth rate (in decimal form), and e is Euler's number

(approximately 2.71828).

In this case, P(0) = 25000 and r = 0.063 (since the population grows at a continuous rate of 6.3% per year).

So, the formula for P(t) is:

\(P(t) = 25000 × e^(0.063t)\)

(b) The population increases by a continuous rate of 6.3% per year.

To find the annual percent increase, we can use the formula:

annual percent increase = \(100 × (e^(r) - 1)\)

where r is the continuous growth rate (in decimal form).

In this case, r = 0.063, so:

annual percent increase = \(100 × (e^(0.063) - 1)\)

Using a calculator, we get:

annual percent increase ≈ 6.488%

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The toothpicks lennon should use in each row is 185.

Algebra is the study of abstract symbols, and logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction also. This approach is used to answer the given problem correctly and completely.

We are given that;

Total number of toothpicks= 3330

Number of rows= 18

Now,

To find the number of toothpicks in each row

=3330/18

=1665/9

=185

Therefore, by algebra the answer will be 185.

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Answer:

42.94$ is the answer.....

The rate of change of the width with respect to time when the length is 6 ft is -7 ft/s.

When the area of a rectangle remains constant, changes in its dimensions affect the rates of change of its length and width. Let's denote the width of the rectangle as w and the length as l. We know that the area (A) is given by the formula A = l * w. Since the area is fixed at 42 ft², we have the equation 42 = 6w, which implies w = 7 ft. Now, we can differentiate both sides of the equation with respect to time (t) to find the rates of change. dA/dt = (dl/dt) * w + l * (dw/dt). Given that dl/dt = 2 ft/s, l = 6 ft, and w = 7 ft, we can solve for dw/dt. Substituting the known values into the equation, we have 0 = 2 * 7 + 6 * (dw/dt), which simplifies to dw/dt = -7 ft/s. Therefore, the rate of change of the width with respect to time when the length is 6 ft is -7 ft/s.

Calculus and its applications in various real-life scenarios, such as determining rates of change and optimizing quantities, in order to solve problems involving dynamic systems and relationships between variables. Understanding calculus can enable you to analyze and predict how variables interact and change over time, making it a powerful tool in fields like physics, engineering, economics, and more. By delving deeper into the concepts and techniques of calculus, you can enhance your problem-solving skills and gain a better understanding of the world around you.

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Answer:

w = -6

Step-by-step explanation:

\(9w=-54~(Given)\\\\\frac{9w}{9}=\frac{-54}{9}~(Divide~9~on~both~sides)\\\\w=-6~(Simplify)\)

The way that the correlation will be affected if the units are changed from minutes to seconds is that the correlation will still be the same.

Correlation simply means a statistical measure which expresses the extent to which two variables are linearly related.

From the information, it was stated that twenty-five trials are completed and the correlation coefficient between typing speed and time is determined to be -0.622.

In this case, even when the units for time are changed from minutes to seconds, the correlation won't change. This is because the change in units has no effect on the correlation.

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Answer:

The correlation would stay the same because the change in units for time would have no effect on it.

Step-by-step explanation:

Kevin spinner that has 10 equal sections and 2 sections of each color-red, blue, green, yellow, and purple. Kevin spins the spinner 180 times. Kevin should land on red or purple about 72 times in 180 spins.

To solve this problem, we can use the concept of probability. The probability of landing on red or purple is the total number of red and purple sections divided by the total number of sections on the spinner.

Since there are 10 equal sections, each section has a probability of 1/10 of being landed on. Since there are 2 sections of each color, the total number of red and purple sections is 2 + 2 = 4.

Therefore, the probability of landing on red or purple is 4/10 or 2/5.

To find out how many times Kevin should land on red or purple in 180 spins, we can multiply the probability by the total number of spins:

2/5 x 180 = 72

It's important to note that this is an estimate based on probability, so Kevin may not actually land on red or purple exactly 72 times. However, as the number of spins approaches infinity, the number of times Kevin lands on red or purple should approach the expected value of 72.

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Answer:

3. 10x

4. 72x

5. 50x

6. 60x

7. 15x

8. 72y

10. 48x

Step-by-step explanation:

1, 2, and 9 couldn't be factored any further, so they stay the same.

According to the question The coefficient of variation for the given data set is 40%.

The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation (SD) by the mean (μ) and expressing the result as a percentage.

The formula for the coefficient of variation is:

\(\[ CV = \left(\frac{SD}{\mu}\right) \times 100 \]\)

In this case, the standard deviation is 4 units and the mean is 10 units. Plugging these values into the formula, we get:

\(\[ CV = \left(\frac{4}{10}\right) \times 100 \]\)

\(\[ CV = 0.4 \times 100 \]\)

\(\[ CV = 40 \]\)

Therefore, the coefficient of variation for the given data set is 40%.

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I think your answer is 10 minutes and 30 seconds. . .

What I did was I took 6 and 7 and multiplied them together, then i divided 42 by 4, and got 10.5. which would give you 10 minutes and 30 seconds.

6*7=42/4=10.5 (aka 10min 30sec)

Answer:

40

Step-by-step explanation:

SF of KP to KN = 4

If LM = 32, then we would have to divide 32 by 4 in order to get the missing length of KL.

32 ÷ 4 = 8

Length of KL = 8

Length of LM = 32

Length of KM = 32 + 8 = 40

Answer:

\(10r^2+3r-18\) sq. units

Step-by-step explanation:

The area of a rectangle is its length multiplied by its width, so in this case:

\(A=(5r-6)(2r+3)\)

We can solve this using the distributive property to expand the right side, and then combine like terms to simplify:

\((5r-6)(2r+3)=\\=2r(5r-6)+3(5r-6)\\=10r^2-12r+15r-18\\=10r^2+3r-18\)

If two-thirds cups of black beans provide 25% of the potassium needed daily and you must obtain the remaining 2,040 milligrams from other sources, your total daily potassium consumption would be 8,160 milligrams.

Let's break down the problem step by step. If two-thirds (2/3) cups of black beans provide 25% of the potassium needed daily, we can calculate the amount of potassium provided by those black beans.

Let's assume that the total daily potassium requirement is represented by "x" milligrams. Since two-thirds cups of black beans provide 25% of this requirement, we can set up the following equation:

(2/3)x = 0.25x

To find the value of "x", we can solve this equation:

2/3 = 0.25

Cross-multiplying, we get:

0.25x = (2/3)x

Multiplying both sides by 3 to eliminate the denominator:

0.75x = 2x

Subtracting 0.75x from both sides:

0.75x - 0.75x = 2x - 0.75x

This simplifies to:

0.25x = 0

Since the left side of the equation equals zero, we can't determine the value of x based solely on the information given. However, we know that you must obtain the remaining 2,040 milligrams of potassium from other sources. Therefore, your total daily potassium consumption would be the sum of the potassium provided by the black beans (25% of the total) and the additional 2,040 milligrams.

Total daily potassium consumption = (25/100)x + 2,040

Without knowing the specific value of x, we cannot calculate the exact milligram amount. However, this equation represents the relationship between the potassium obtained from the black beans and the additional potassium needed from other sources to reach a total of x milligrams.

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Answer:

2

Step-by-step explanation:

To obtain the slope of the perpendicular line, we first have to identify the slope of the given line.

\(\textcolor{steelblue}{\text{How to identify slope?}}\)

Given line: y= -½x +5

Slope of given line= -½

After finding the slope of the given line, we can now proceed to find the slope of the perpendicular line.

The product of the slope of two perpendicular lines is -1.

Let the slope of the perpendicular line be m.

m(-½)= -1

m= -1 ÷(-½)

\(\text{m} = - 1 \times ( - \frac{2}{1} )\)

m= 2

Thus, the slope of the perpendicular line is \(\textcolor{red}{2}\).

Other notes:

\(\textcolor{steelblue}{\text{What is coefficient?}}\)

The limit of the function f(x) = ln(x - 8)/(x^2 + x) as x approaches 8 is DNE (does not exist).

To determine the limit of the given function as x approaches 8, we can evaluate the left-hand limit and the right-hand limit separately.

Let's first consider the left-hand limit as x approaches 8. We substitute values slightly less than 8 into the function to observe the trend.

As x approaches 8 from the left side, the expression (x - 8) becomes negative, and ln(x - 8) is undefined for negative values. Simultaneously, the denominator (x^2 + x) remains positive. Therefore, as x approaches 8 from the left, the function approaches negative infinity.

Next, we consider the right-hand limit as x approaches 8.

By substituting values slightly greater than 8 into the function, we find that the expression (x - 8) is positive.

However, as x approaches 8 from the right side, the denominator (x^2 + x) becomes infinitesimally close to zero, which causes the function to tend toward positive or negative infinity. Thus, the right-hand limit does not exist.

Since the left-hand limit and right-hand limit are not equal, the overall limit of the function as x approaches 8 does not exist.

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Answer:

5/13

Step-by-step explanation:

Cos = opp/hyp

5 is opposite of angle R and 13 is the hypotenuse.

Step-by-step explanation:

Today, we are going to be talking about the three-way principle of mathematics. Basically, there are three ways to solve a problem in math: verbally, graphically, or by example. In this lesson, we will discuss each of these principles by solving sample problems using each type.

there are 126 ways to make a package consisting of only bananas and 71 ways to make a package with at least 4 apples.

(i) To find the number of ways to make a package of 5 fruits consisting only of bananas, we can use combinations. Since we have 9 bananas and we need to select 5 of them, the number of ways is given by the combination formula: C(9, 5) = 9! / (5! * (9-5)!) = 126.

(ii) To find the number of ways to make a package with at least 4 apples, we need to consider two cases:

Case 1: Selecting exactly 4 apples and 1 banana.

The number of ways to select 4 apples from 8 is given by C(8, 4) = 8! / (4! * (8-4)!) = 70.

Since we have only 1 banana left, we have 1 way to select it. So the total number of ways in this case is 70 * 1 = 70.

Case 2: Selecting all 5 apples.

Since we have 8 apples, we can select all 5 of them in 1 way.

Therefore, the total number of ways to make a package with at least 4 apples is 70 + 1 = 71.

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Answer:

Step-by-step explanation:

Let the height be x

1. It is the opposite side

2. The ratio of the opposite side to the adjacent side is called the tangent

3. As per definition of the tangent we got:

In order to map P to P' using two reflections, assuming that the intersecting lines form an acute or right angle.

According to the Reflection in intersecting line theorem, " A reflection in line k followed by a reflection in line m is equivalent to a rotation about point P if line k and m cross at a point P. The rotational angle in this instance is 2x° where x° is the measurement of the acute or right angle formed by lines k and m.

As (x,y)⇒(y, -x) means 270 degrees counterclockwise or 90-degree clockwise rotation.

Therefore, acute angle=90°/2

Acute angle = 45°

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Answer:

1/12

Step-by-step explanation:

P(4) = number of 4's/ total

There is one 4 on dice and there are 6 different numbers

P(4) = 1/6

P(tail) = number of tails/ total

There are 2 sides on a coin and only one is a tail

P(tail) = 1/2

P(4 and a tail) = P(4)*(Ptail)  since they are independent events

                       = 1/6*1/2

                        = 1/12