Line j passes through points (9, 6) and (6, 8). Line k passes through points (7, 9) and (5, 6). Are line j and line k parallel or perpendicular?

Answer:

A

Step-by-step explanation:

8/15

Answer:

A=-3

Step-by-step explanation:

To begin, a parabola of form a(x-h)² +k opens upward when a is positive. Similarly, when a is negative, the parabola opens downward. Therefore, a must be negative here, as our expression for the parabola is a(x-0)²+0 = ax², with (0,0) being (h,k) and the vertex.

To determine whether a should be -3 or -0.6, we can think about the values on the graph that correspond to these values. A narrower graph would have a steeper slope. A narrower graph would have a large change in y with little change in x. Therefore, as ax² = y is our equation, and when a=-3, y changes more rapidly relative to when a = -0.6, A=-3 is our answer

Answer:

\(y = 9\)

Step-by-step explanation:

1) Add 3 to both sides.

\(3y = 2y + 6 + 3\)

2) Simplify 2y + 6 + 3 to 2y + 9.

\(3y = 2y + 9\)

3) Subtract 2y from both sides.

\(3y - 2y = 9\)

4) Simplify 3y - 2y to y.

\(y = 9\)

Therefor, the answer is y = 9.

Answer:

3y-3=2y+6

3y-2y=3+6 (You will group like terms)

therefore,y=9

Answer:

13: 7x 3y

14: 37

15: 60

16: 23

I'm sorry but my vision is too bad, I can't read 17.

:(

Answer:

14.) 2/3

15.) 1/9

16.) 1/4

17.) 1

Step-by-step explanation:

Sorry I couldn't help you with number 18, it's not in the picture.

Hope this helps!

Answer:

740

Step-by-step explanation:

Let the AP be a, a+d, a+2d, a+3d, ...

The  term of AP is given by:

\(t n =a+(n-1)d\)

We are given that the third term is 7.

\(t 3=7\)

⇒  \(a+(3-1)d=7\)

⇒\(a+2d=7 ---(1)\)

Also, the seventh term is 2 more than three times the third term.

\(t7=3t3+2\)

⇒\(a+ (7-1)d=3(a+(3-1)d)+2\)

⇒\(a+6d=3(a+2d)+2\)

⇒\(a+6d=3a+6d+2\)

⇒\(-2a=2\)

⇒\(a=-1\)

We can put it in (1)

\(a+2d=7\)

⇒\((-1)+2d=7\)

⇒\(2d=8\)

⇒d=4

Now, the Sum of n terms of an AP is given by the formula:

\(sn=\frac{n}{2}(2a+(n-1)d)\)

So, Sum of first 20 terms would be:

\(s 20=\frac{20}{2}(2(-1) +(20-1) x 4)\)

⇒\(s20=10(-2+19 x 4)\)

⇒\(s 20=10 x(-2+76)\)

⇒\(s 20= 10 x 74\)

⇒\(s 20=740\)

Thus, The Sum of first 20 terms of the AP is 740.

Answer: 25

Step-by-step explanation: 10+10=20 and 2+3=5. 20+5=2

A sample, such as the average height of people in a sample of 100 residents from that city. Therefore, the correct option is B. Parameters, statistics.

Parameters are numbers that describe populations, while statistics are numbers that describe samples. A parameter is a numerical value that summarizes specific characteristics of a population, and statistics is the discipline of collecting, analyzing, and interpreting data gathered from a sample of the population.

Parameters are used to make inferences about a population based on sample data, and statistics are used to estimate population parameters when it is not possible to measure all individuals in the population. Parameters refer to a fixed characteristic of a population, such as the average height of all people in a city, whereas statistics.

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If the rank of a matrix A is less than the number of columns (n) and the system is consistent, an infinite number of solutions exist because there are more variables than equations. The dependent variables can take on any value.

1. Rank(A): The rank of a matrix A refers to the maximum number of linearly independent rows or columns it possesses.

2. n: In this context, n represents the number of variables in a given system of linear equations.

3. Consistent System: A system of linear equations is consistent if it has at least one solution.

Now, let's put these terms together to explain the statement:

If the rank of a matrix A is less than n (the number of variables), it means that the system of linear equations has fewer linearly independent equations than variables. In such a case, there will be at least one free variable, which can take an infinite number of values.

Since the system is consistent, there is at least one solution, and due to the free variable, each of these infinitely many values will result in a different answer. Consequently, when the rank of a matrix A is less than n and the system is consistent, an infinite number of solutions exist.

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Answer:

\(5 {x}^{2} - 13x - 6 = 0\)

find the factors:

\((x - 3)(5x + 2) = 0 \\ \\ x = 3 \: \: or \: \: x = - \frac{2}{5} \)

Using a trigonometric relation we can see that:

θ =  57.99°

On the image we can see a right triangle where we know the values of the two catheti.

We want to find the top angle in that right triangle, and with the known information, we could use the trigonometric relation:

tan(θ) = (opposite cathetus)/(adjacent cathetus).

Where:

Opposite cathetus = 8

Adjacent cathetus = 5

Replacing that we will get:

tan(θ) = 8/5

Using the inverse tangent function:

θ = Atan(8/5) = 57.99°

That is the measure of the angle.

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When current is inversely proportional to the resistance in a circuit, the current when the resistance is 90 ohms is equals to 0.540 Ampere.

In an electrical circuit, the current is inversely proportional to the resistance.

Resistance = 200 ohms

Current = 1.2 ampere

If resistance is 90 ohms then we have to determine the value of current. According to condition, I = kR ,

where, I --> current

k --> constant of Proportionality

R--> resistance

Now, the proportionality constant, k = I/R

=> k = 1.2/200

=> k = 0.006

So, value of current when resistance R = 90 ohms, for this plug in above equation,

=> I = 0.006 × 90

= 0.540

Hence, required value is 0.540 ampere.

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Answer:

28

Step-by-step explanation:

1/2xbxh=4

To find the total area of the shape, we can subtract the removed area from the larger area. 32-4=28

Let's say you are approved for a credit card with a $1500 limit and a 19.99% annual interest rate. Assume that your credit card was maxed out and that your minimum monthly payment is $50. The answer is (b) 41.92 months.

To calculate the time it takes to pay off a credit card with only the minimum payment, we can use the following formula:

\(\begin{equation}Number\ of\ months = \frac{Total\ balance}{Minimum\ payment} \div \frac{1 - (1 + Interest\ rate)^{-(Number\ of\ months)}}{1}\end{equation}\)

In this case, the total balance is $1500, the minimum payment is $50, and the interest rate is 19.99%. Plugging these values into the formula, we get:

\(\begin{equation}Number\ of\ months = \frac{1500}{50} \div \frac{1 - (1 + 0.1999)^{-(Number\ of\ months)}}{1}\end{equation}\)

Solving for the number of months, we get:

Number of months = 41.92 months

Therefore, it would take 41.92 months to pay off the credit card with only the minimum payment.

If you only make the minimum payment, you will pay a lot of interest over time. In this example, you will pay $1278.98 in interest. If you can afford to pay more than the minimum payment, you will save money on interest and pay off your debt faster.

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Answer:

Statements 3, 4 and 5 are true.

Step-by-step explanation:

x^2 - 8x + 4

Using the quadratic formula:

x = [ -(-8) +/- √((-8)^2 - 4*1*4)] / 2

= (8 +/- √(64 - 16)) / 2

= 4 +/- √48 / 2

= 4 +/- 4√3/2

= 4 +/- 2√3.

So the third statement is true.

Converting to vertex form:

x^2 - 8x + 4

= (x - 4)^2 - 16 + 4

= (x - 4)^2 -12

So the extreme value is at (4, -12)

So the fourth statement is true.

The coefficient of the term in x^2 is 1 (positive) so the graph has a minimum.

The mean number of garage stalls per home in the sample of 200 homes is 1.09.

The mean is a measure of central tendency in statistics that represents the average value of a set of numerical data. It is calculated by summing up all the values and dividing by the total number of values.

According to the given information:

To find the mean number of garage stalls per home in the sample of 200 homes, we need to calculate the expected value or the average value of X, which is the number of garage stalls per home. We are given the probabilities of X taking the values 0, 1, and 2, which are P(X=0) = 0.06, P(X=1) = 0.45, and P(X=2) = 0.32.

The formula for calculating the expected value of X is:

E(X) = Σ [ x × P(X=x) ]

where Σ represents the sum of all values of x, and P(X=x) is the probability of X taking the value x.

Using this formula, we can calculate the expected value of X as follows:

\(E(X) = (0 * 0.06) + (1 * 0.45) + (2 * 0.32)\)

\(= 0 + 0.45 + 0.64\)

= 1.09

Therefore, the mean number of garage stalls per home in the sample of 200 homes is 1.09. Hence, the correct option is (a) 1.09.

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The mean number of garage stalls per home in the sample of 200 homes is 1.09.

What is mean?

The mean is a measure of central tendency in statistics that represents the average value of a set of numerical data. It is calculated by summing up all the values and dividing by the total number of values.

According to the given information:

To find the mean number of garage stalls per home in the sample of 200 homes, we need to calculate the expected value or the average value of X, which is the number of garage stalls per home. We are given the probabilities of X taking the values 0, 1, and 2, which are P(X=0) = 0.06, P(X=1) = 0.45, and P(X=2) = 0.32.

The formula for calculating the expected value of X is:

E(X) = Σ [ x × P(X=x) ]

where Σ represents the sum of all values of x, and P(X=x) is the probability of X taking the value x.

Using this formula, we can calculate the expected value of X as follows:

E(x) = (0.06*0)+(1*0.45)+(2*0.32)

= 1.09

Therefore, the mean number of garage stalls per home in the sample of 200 homes is 1.09. Hence, the correct option is (a) 1.09.

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The equation 3x₁ + 5x₂ = 30 intersects the x₁-axis at point D (10, 0) and the x₂-axis at point C (0, 6). Option B (0, 8) is not an intercept on the x₂-axis. Option C (6, 10) is not an intercept on the x₁-axis. The correct answer is option D (10, 0) as the x₁-axis intercept.

The equation given is 3x₁ + 5x₂ = 30. To find the axis intercept, we need to determine the points at which the line intersects the x₁ and x₂ axes. To find the x₁-axis intercept, we set x₂ = 0 and solve for x₁ 3x₁ + 5(0) = 30 3x₁ = 30
x₁ = 10

So, the x₁-axis intercept is (10, 0) which corresponds to point D in the given options. To find the x₂-axis intercept, we set x₁ = 0 and solve for x₂: 3(0) + 5x₂ = 30 5x₂ = 30 x₂ = 6 Therefore, the x₂-axis intercept is (0, 6) which corresponds to point C in the given options. To summarize, the equation 3x₁ + 5x₂ = 30 intersects the x₁-axis at point D (10, 0) and the x₂-axis at point C (0, 6).

In the given options, option A (10, 6) is not an intercept on either axis. Option B (0, 8) is not an intercept on the x₂-axis. Option C (6, 10) is not an intercept on the x₁-axis. The correct answer is option D (10, 0) as the x₁-axis intercept.

Remember, the x₁-axis intercept is found by setting x₂ = 0, and the x₂-axis intercept is found by setting x₁ = 0 in the equation.The correct answer is option D

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Simplify would be 0.4x + 2.2

To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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To find the sum of the given series, we need to calculate the sum of each term where n starts from 0 and goes to infinity. The general term of the series is (2n)/(n!).

Let's find the sum of the series:

S = Σ(2n)/(n!) from n=0 to infinity

To determine the convergence of the series, we can use the Ratio Test:

Limit as n → infinity of |((2(n+1))/((n+1)!) / ((2n)/(n!))|

= Limit as n → infinity of |(2(n+1))/((n+1)!) * (n!)/(2n)|

= Limit as n → infinity of |(2(n+1))/(n! * (n+1))|

= Limit as n → infinity of |2(n+1)/(n+1)|

= 2

Since the limit is greater than 1, the Ratio Test indicates that the series is divergent. Therefore, the sum of the series does not exist or approaches infinity.

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W and is orthogonal to all vectors in W except itself, we have shown that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W, and hence W=Rn.

To show that W=Rn, we need to show that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W.

Let v be any vector in Rn. Since the n non-zero orthogonal vectors span W, we can write v as a linear combination of them:

v = c1v1 + c2v2 + ... + cnvn

where c1, c2, ..., cn are scalars, and v1, v2, ..., vn are the n non-zero orthogonal vectors that span W.

To show that v is in W, we need to show that v is orthogonal to all vectors in W except itself. Since the n non-zero orthogonal vectors are linearly independent, any linear combination of them that is orthogonal to v must be the zero vector.

Therefore, if w is any vector in W that is not equal to v, we have:

=  = c1 + c2 + ... + cn = 0

since v is orthogonal to all the non-zero orthogonal vectors. This means that v is orthogonal to all vectors in W except itself.

Therefore, since v is in W and is orthogonal to all vectors in W except itself, we have shown that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W, and hence W=Rn.

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Answer:

2 x 2 x 2 x 2 x 3.

Step-by-step explanation:

The number 48 expressed as a product of its prime factors is 2 x 2 x 2 x 2 x 3.

Answer:

2 x 2 x 2 x 2 x 3.

Step-by-step explanation:

^^^

The most likely to generalize to it's population of interest is a stratified random sample of 120

a stratified random sample 120

Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. In stratified random sampling, or stratification, the strata are formed based on members’ shared attributes or characteristics, such as income or educational attainment. Stratified random sampling has numerous applications and benefits, such as studying population demographics and life expectancy.

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Answer:  10 pillows

Step-by-step explanation:  

[(3/5) yard/pillow]

6 yards

(6 yards)/(3/5 yard/pillow) - 10 pillows

Answer:

K = 30°

Step-by-step explanation:

K = 180 - (35+115)

K= 180 - 150

K =30

Answer:

It costs $1.60 for 1lb of potatoes. It costs $11.70 for 7lb of potatoes.

Step-by-step explanation:

price per pound = 12.8 / 8 = $1.60 per pound

1.6 * 7 = cost for 7 pounds

1.6 * 7 = $11.20 for 7 pounds

The correct function that gives the right syntax for the given data analysis is; =RIGHT(B3,5)

Data cleaning is defined as the process of fixing or removing data that are incorrect,  incorrectly formatted, duplicate, corrupted, or even incomplete data that exists within a dataset.

Now, when we combine multiple data sources, what it means is that there could be many opportunities for the data to be duplicated or mislabeled.

Now, from the question, we can see the given data of the spreadsheet with customer names and address and as such, we can easily say that the correct syntax is =RIGHT(B3,5). This is because the RIGHT Function usually returns a set number of characters from the right side of a text string.

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The value of the test statistic is 6.51.

The test statistic for this problem can be calculated using the formula:

z = (p - P) / √(P * (1 - P) / n)

Where p is the sample proportion (0.67 in this case), P is the hypothesized population proportion (we don't know this value, so we assume it to be 0.5 for a two-tailed test), n is the sample size (380), and z is the standard normal distribution value corresponding to the level of significance.

Plugging in the values, we get:

z = (0.67 - 0.5) / √(0.5 * (1 - 0.5) / 380) = 6.51

So the value of the test statistic is 6.51.

The test statistic is a measure of how far the sample proportion deviates from the hypothesized population proportion under the null hypothesis. In this case, we assume that the population proportion is 0.5 (since we have no reason to believe otherwise), and we calculate the probability of observing a sample proportion of 0.67 or greater assuming this null hypothesis is true.

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Differential equations and boundary value problems are mathematical equations that contain derivatives of unknown functions and their variables.

These equations are used to model a wide range of physical, biological, and chemical processes. The seventh edition of Fundamentals of Differential Equations and Boundary Value Problems by R. Kent Nagle, Edward B. Saff, and Arthur David Snider is a comprehensive textbook that covers the fundamentals of these equations.Differential equations and boundary value problems are mathematical equations that contain derivatives of unknown functions and their variables.  It includes topics such as first order equations, higher order linear equations, systems of equations, Laplace transforms, Fourier series, and numerical methods. It also contains a variety of worked examples, exercises, and applications to help students understand the material. Examples include solving initial value problems, boundary value problems, and inverse problems. The book also provides a step-by-step approach to solving problems, including the use of formulas such as the Euler-Cauchy formula, the Picard-Lindelof formula, the Runge-Kutta formula, the Laplace transform, and the Fourier series.

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Complete question:

Find the solution to the differential equation dy/dx + 4y = 0, given the boundary values y(0) = 2 and y(2) = 0.

Rotation refers to the act or process of turning or spinning around a central axis or point. In physics and mathematics, rotation describes the circular or angular motion of an object or a system around a fixed point or axis.

It involves the movement of an object or system in a circular path, where each point on the object follows the same circular trajectory.The axis of rotation is an imaginary line or point around which the object rotates. All points on the object move in circles or arcs around this axis.

The angle of rotation measures the amount of turning or angular displacement of an object or system. It is usually expressed in degrees or radians.

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