All Common multiples between 2 and 9

Answer: -12 x 4

Step-by-step explanation:

12 times 4 is 48

Rule: A negative multiplied by a positive, will always give you a negative.

So, -12 is a negative number and 4 is a positive number.

Negative x Positive = Negative

Positive x Negative = Negative

-12 x 4 = -48

Answer:

2 - \(\sqrt{52}\) and 2 + \(\sqrt{52}\)

Step-by-step explanation:

let the 2 numbers be x and y , then

x + y = 4 ( subtract x from both sides )

y = 4 - x → (1)

xy = - 48 → (2)

substitute y = 4 - x into (2)

x(4 - x) = - 48

4x - x² = - 48 ( multiply through by - 1 )

x² - 4x = 48

solve using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 2) x + (- 2)² = 48 + (- 2)²

(x - 2)² = 48 + 4 = 52 ( take square root of both sides )

x - 2 = ± \(\sqrt{52}\) ( add 2 to both sides )

x = 2 ± \(\sqrt{52}\)

substitute this value into (1)

y = 4 - (2 ± \(\sqrt{52}\) ) = 4 - 2 ± \(\sqrt{52}\) = 2 ± \(\sqrt{52}\)

then the 2 numbers are

2 - \(\sqrt{52}\) and 2 + \(\sqrt{52}\)

The equation of the plane is 2x + y - z = 3t + 1.

To find the equation of the plane that contains the given line and is parallel to the intersection of the given planes, we can follow these steps:

Step 1:

The given line is z = 3t, y = 1 + t, z = 2t.

Taking t = 0, we get the initial point of the line as (0, 1, 0).

Taking t = 1, we get another point on the line as (2, 2, 3).

Hence, the direction vector of the line is given by(2-0, 2-1, 3-0) = (2, 1, 3).

Step 2:The two planes given are y + z = 1 and 22 - y + z = 0.

Their normal vectors are (0, 1, 1) and (-1, 1, 1), respectively.

Taking the cross product of these two vectors, we get a normal vector to the plane that is parallel to the intersection of the given planes:

(0, 1, 1) × (-1, 1, 1) = (-2, -1, 1).

Step 3:The vector equation of the line can be written as:

r = (0, 1, 0) + t(2, 1, 3) = (2t, t+1, 3t).

A point on the line is (0, 1, 0).

Using this point and the normal vector to the plane that we found in Step 2, we can write the scalar equation of the plane as:-2x - y + z = d.

Step 4: Substituting the coordinates of the line into the scalar equation of the plane, we get:-

2(2t) - (t+1) + 3t = d

=> -3t - 1 = d

Hence, the equation of the plane that contains the line z = 3t, y = 1 + t, z = 2t

and is parallel to the intersection of the planes y+z=1 and 22-y+z= 0 is given by:-

2x - y + z = -3t - 1, which can also be written as:

2x + y - z = 3t + 1.

To know more about equation visit:

https://brainly.com/question/29657983

#SPJ11

Confidence interval refers to a statistical measure that helps quantify the amount of uncertainty present in a sample's estimate of a population parameter.

This measure expresses the degree of confidence in the estimated interval that can be calculated from a given set of data. In this scenario, the task is to build a 95% confidence interval for the regression line's slope. The regression analysis output has already been given. According to the output given, the estimated regression model is:y = 25,000 + 9,000 x, where x represents the number of miles the car has been driven and y represents the car's selling price.

The formula to calculate the 95% confidence interval for the slope is:Slope ± t · SE, where Slope is the point estimate for the slope, t represents the critical t-value for a given level of confidence and degrees of freedom, and SE represents the standard error of the estimate. The value of t can be calculated using the degrees of freedom and a t-table. Here, the number of pairs in the sample size is 20, and the model uses two parameters.

Therefore, the degrees of freedom would be 20 - 2 = 18.The critical t-value for a 95% confidence interval and 18 degrees of freedom is 2.101. Using the formula given above, we can calculate the 95% confidence interval for the slope as follows:Slope ± t · SE= 9000 ± (2.101)(700) ≈ 9000 ± 1,467.7 = [7,532.3, 10,467.7]Therefore, the 95% confidence interval for the slope is [7,532.3, 10,467.7]. This means that we are 95% confident that the true value of the slope for this model falls within the interval [7,532.3, 10,467.7].

It implies that the price of the car increases by $7,532.3 to $10,467.7 for each mile driven by the car. In conclusion, a 95% confidence interval has been calculated for the regression line's slope, which indicates that the actual slope of the model lies between the range [7,532.3, 10,467.7].

To know more about Confidence interval visit

https://brainly.com/question/31736191

#SPJ11

The situation described, where Joe overheard 5 girls talking about their love for princess movies and then concluded that all girls love princess movies, is an example of a hasty generalization.

A hasty generalization occurs when a person makes a broad assumption or generalization based on a small or limited sample size. In this case, Joe is assuming that all girls share the same interest in princess movies based on the opinion of only 5 girls.

It is important to recognize that not all girls have the same preferences and interests, and it would be more accurate to gather a larger and more diverse sample before making such a conclusion.Making hasty generalizations can lead to inaccurate or unfair judgments.

To know more about generalization visit:

https://brainly.com/question/30696739

#SPJ11

We need to check if lines ℓ and k are parallel. For two lines to be parallel, they must have the same slope and different y-intercepts.Let's compare the given lines:Line ℓ: y = 34x + 6Slope of line ℓ = 34Line k: y = 34x - 7Slope of line k = 34We see that the slope of lines ℓ and k is the same (34), which means that they could be parallel.

However, we still need to check if they have different y-intercepts. Line ℓ: y = 34x + 6 has a y-intercept of 6.Line k: y = 34x - 7 has a y-intercept of -7.So, lines ℓ and k have different y-intercepts, which means they are not parallel. Therefore, the correct answer is b) No.In slope-intercept form, the equation of a line is y = mx + b, where m is the slope of the line and b is its y-intercept. In this case, both lines have the same slope of 34 (the coefficient of x). The y-intercepts are different (+6 for line l and -7 for line k). Thus, the lines are not parallel.

To know more about slope,

https://brainly.com/question/3605446

#SPJ11

The answer is option a) Yes. Lines ℓ and k are parallel to each other.

The two distinct lines defined by the following two equations in slope-intercept form are:

Line ℓ: y = 34x + 6

Line k: y = 34x - 7

To determine if the lines are parallel, we need to compare their slopes since two non-vertical lines are parallel if and only if their slopes are equal.

Both lines are in slope-intercept form, so we can immediately read off their slopes:

Line ℓ has a slope of 34, and line k has a slope of 34.

Both the lines ℓ and k have the same slope of 34.

Hence, the answer is option a) Yes. Lines ℓ and k are parallel to each other.

To know more about lines, visit:

https://brainly.com/question/2696693

#SPJ11

Answer:

The equation to find how many hours Joshua spent mowing to earn a profit of $60 is:

20t - (2.5t + 10) = 60

where t represents the number of hours Joshua spent mowing.

In this equation, 20t represents the amount of money Joshua earned by charging $20 per hour and spending t hours mowing. The term (2.5t + 10) represents the costs he incurred, which includes the cost of gas, which is $2.50 per hour on average, multiplied by the number of hours he spent mowing, plus $10 he saves from each job to cover the costs of keeping his lawnmower in good working condition.

The equal sign in the middle of the equation indicates that these two expressions have to balance out to Joshua's net profit on the last lawn mowing job, which is $60.00.

Each term in the equation is a quantity measured in dollars. The 20t and (2.5t + 10) terms both represent the amount of money earned and spent, respectively. The final term, 60, represents the net profit that Joshua earned from the job.

Step-by-step explanation:

Answer:

60;40

Step-by-step explanation: 50* 2 = 100

so multiply every thing else by it to  

in simplest form tho itd be 3;2

The y-intercept of the equation 2x - y = -3 is 3 and in ordered pair form is (0,3).

The slope-intercept formula is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation in the question

2x - y = -3

First, we solve form for y and reorder in slope intercept form.

2x - y = -3

Subtract 2x from both sides

2x - 2x- y = -3 - 2x

- y = -3 - 2x

Divide each term by -1

y = 3 + 2x

Reorder in slope intercept form

y = 2x + 3

To find the y-intercept, replace x with zero and solve for y

y = 2(0) + 3

y = 3

Therefore, the y-intercept is 3.

Learn more about equation of line here: brainly.com/question/2564656

#SPJ1

A structural break occurs when we see A. an unexpected shift in time-series data.

It is the change in a time series's data-generating mechanism, it is a phenomenon that occurs when a significant event or structural shift in the economy alters the underlying data-generating mechanism. A structural break can happen for several reasons, including natural catastrophes, changes in economic policy, new inventions, and other reasons that alter the way the data is generated.

In the presence of a structural break, we can't assume that the relationships between variables before and after the break are the same. The primary objective of identifying structural breaks in the time-series is to detect changes in the behavior of the series over time, such as changes in the variance of the series, changes in the mean of the series, and changes in the covariance of the series. So therefore the correct answer is A. an unexpected shift in time-series data, the structural break occurs.

To know more about economic policy visit:

https://brainly.com/question/30104789

#SPJ11

Answer:

x+4=10 3x=18 and x/2=3

Step-by-step explanation:

x=6 substituting the value,

x+4

=6+4

=10

3x

=3×6

=18

x/2

=6/2

=3

Answer:

Step-by-step explanation:

it will be 10

In comparing line segment lengths in geometry, measure the length of the reference line (in this case, line BG) and then measure the lengths of the other line segments. Those of identical length to line BG are the ones you're looking for.

Given that line BG is the reference, we need to examine the other line segments to determine which are the same length. This is a process of comparison in geometry. Given that no image was provided, I can't specify the segments equal to line BG. However, the process involves measuring the length of line BG and then measuring the lengths of the other line segments one by one. The line segments that are the same length as line BG are the ones we're looking for.

https://brainly.com/question/22642203

#SPJ11

add up the numbers.

9.281 + 7.740 = 17.021.

The total length of the ribbons is 17.021 cm long.

Answer:

6

8

,

9

12

,

12

16

Step-by-step explanation:

Answer:

\( = \frac{33}{14} \)

Step-by-step explanation:

\( - 10 \frac{2}{7} + ( - 4 \frac{4}{11} )\)

➡️ \( - \frac{72}{7} \div - ( \frac{48}{11} )\)

➡️ \( \frac{72}{7} \times \frac{11}{48} \)

➡️ \( \frac{3}{7} \times \frac{11}{2} \)

➡️ \( \frac{33}{14} \) ✅

The smallest positive integer n so that,

$$\renewcommand{\arraystretch}{1.5} \begin{pmatrix} -\frac{\sqrt{2}}{2} \frac{1}{n} \\ \frac{\sqrt{2}}{2} \frac{1}{n} \end{pmatrix}$$is a column matrix that contains integers,

we can write it as follows. $$\begin{pmatrix} -\frac{\sqrt{2}}{2} \frac{1}{n} \\ \frac{\sqrt{2}}{2} \frac{1}{n} \end{pmatrix} = \begin{pmatrix} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix} \frac{1}{n}.$$Since n has to be an integer, we have to find the smallest positive integer n for which the right-hand side is a column matrix containing integers. Since the left-hand side has a factor of 1/n, we can see that the smallest value of n must be a divisor of the denominator of the left-hand side. The denominator of the left-hand side is $\sqrt{2}/2$. If we multiply this by 100, we get 70.710678.

Therefore, the smallest positive integer n that satisfies the equation is the smallest divisor of 70.710678. This is 2, and it gives us the column matrix $$\begin{pmatrix} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix}.$$Therefore, the smallest positive integer n is 2.

for such more questions on integers

https://brainly.com/question/929808

#SPJ11

Step-by-step explanation:

\(6 \cos {}^{2} (x) + 4 \sin {}^{2} (x) = 5\)

\(6(1 - sin {}^{2} x) + 4 \sin {}^{2} (x) = 5\)

\(6 - 6 \sin {}^{2} (x) + 4 \sin {}^{2} (x) = 5\)

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

\( - 2 \sin {}^{2} (x) = - 1\)

\( \sin {}^{2} (x) = \frac{1}{2} \)

\( \sin(x) = \frac{1}{ \sqrt{2} } \)

Take the arc Sine of the function

\(arcsin( \frac{1}{ \sqrt{2} } ) = \frac{\pi}{4} \)

Finally, Sine is a periodic function so it has two answers within the interval (0, 2 pi)

Use the identity

\( \sin(x) = \sin(x + \pi) \)

We know that

\( \sin( \frac{\pi}{4} ) = \frac{1}{ \sqrt{2} } \)

so using the identity

\( \sin( \frac{\pi}{4} + \pi ) = \sin( \frac{5\pi}{4} ) \)

So we have two answers.

\(( \frac{\pi}{4} )\)

\(( \frac{5\pi}{4} )\)

Answer:

2nd Box

4th Box

Step-by-step explanation:

The factors of a graph is whenever the graph touches the x-axis.

A standard factor has the format (x-a), where a is the x-value.

From the graph, we can see that the graph touches the x-axis at x=3 and at x=4.

Therefore, this means that our factors are:

\((x-(4))\text{ and } (x-(3))\)

Simplify:

\((x-4)\text{ or } (x-3)\)

Check the second and fourth boxes.

And we're done!

Answer:

the aswer is 154

Step-by-step explanation:

multiple

Answer:

3 and half

Step-by-step explanation:

half of seven is 3.5

Answer: 16x+3x^3−8

Please mark me brainliest :)

a. P(A) = 1/12, P(B) = 1/3, P(C) = 1/6 based on counting outcomes.

b. P(A|B) = 1/12, calculated using the definition of conditional probability.

c. P(B|C) = 1/3, calculated using the definition of conditional probability.

d. P(A|C) = 1/6, calculated using the definition of conditional probability.

e. A and B are not independent, B and C are not independent, A and C are independent based on the observations and calculations.

a. We have:

P(A): The only ways to get a sum of at least 10 are (4,6), (5,5), (6,4). Each of these outcomes has probability 1/36. So, P(A) = 3/36 = 1/12.

P(B): The only ways to get an odd sum are (1,2), (1,4), (1,6), (3,2), (3,4), (3,6), (5,2), (5,4), (5,6), (6,1), (6,3), (6,5). Each of these outcomes has probability 1/36. So, P(B) = 12/36 = 1/3.

P(C): The blue die has a probability of 1/6 of landing on 5, regardless of what the red die shows. So, P(C) = 1/6.

b. We have:

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

To find P(A and B), we need to count the number of outcomes that satisfy both A and B. There are 6 outcomes that satisfy B: (1,2), (1,4), (1,6), (3,2), (3,4), and (5,4). Out of these, only (5,4) satisfies A as well. So, P(A and B) = 1/36.

Therefore, P(A|B) = (1/36) / (1/3) = 1/12.

c. We have:

P(B|C) = P(B and C) / P(C)

To find P(B and C), we need to count the number of outcomes that satisfy both B and C. There are only two such outcomes: (1,4) and (3,2). So, P(B and C) = 2/36 = 1/18.

Therefore, P(B|C) = (1/18) / (1/6) = 1/3.

d. We have:

P(A|C) = P(A and C) / P(C)

To find P(A and C), we need to count the number of outcomes that satisfy both A and C. Since C requires the blue die to show 5, there is only one outcome that satisfies both A and C: (5,5). So, P(A and C) = 1/36.

Therefore, P(A|C) = (1/36) / (1/6) = 1/6.

e. We have:

A and B are not independent, because knowing that the sum is odd affects the probability of the sum being at least 10 (it makes it impossible).

B and C are not independent, because knowing that the blue die shows 5 affects the probability of the sum being odd (it makes it even).

A and C are independent, because knowing that the blue die shows 5 does not affect the probability of the sum being at least 10.

To learn more about probability visit : https://brainly.com/question/13604758

#SPJ11

Answer:

{x=2,y=2

Step-by-step explanation:

Equation 1:

Multiply both sides of the equation by a coefficient

{ 4(2x-y)=2*4

-5x+4y=-2

Apply Multiplicative Distribution Law

{8x-4y=2*4,-5x+4y=-2

8x-4y+(-5x+4y)=8+(-2)

Remove parentheses

8x-4y-5x+4y=8-2

Cancel one variable

8x-5x=8-2

Combine like terms

3x=8-2

Calculate the sum or difference

3x=6

Divide both sides of the equation by the coefficient of the variable

x=6/3

Calculate the product or quotient

x=2

Equation two:

{-5+4y=-2, x=2

-5*2+4y=-2

Calculate the product or quotient

-10+4y =-2

Reduce the greatest common factor (GCF) on both sides of the equation

-5+2y=-1

Rearrange unknown terms to the left side of the equation

2y=-1+5

Calculate the sum or difference

2y=4

Divide both sides of the equation by the coefficient of the variable

y=4/2

y=2

Hope this helps!!

The probability that at least one of the cards drawn is a 3 is 1/5 0r 0.2000.

What is probability?

Probability shows the likelihood of an event happening.  It can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1

Probability P=no. outcomes/total no. of the possible outcomes

From the question;

No. of total no of cards =5

The probability the card drawn is a 3  =1/5

                                                             =0.2000

Therefore the probability that at least one of the cards drawn is a 3 is 1/5 0r 0.2000.                      

Learn more about probability on

https://brainly.com/question/23704607

#SPJ1

Answer:

X= 1.8

Step-by-step explanation:

If I’m not mistaken then this is how to work it out. X^2 + 4x -9 =0. X^2 + 4x would be 5x. 5x - 9 = 0. +9 on both sides. 5x=9. Divide by 5 on each side. X= 1.8

To show that the decision boundary of the CLOSE classifier is a linear hyperplane, we need to show that it can be represented as sign(w · x + b), where w is the weight vector, b is the bias term, and sign is the sign function that outputs +1 or -1 depending on whether its argument is positive or negative.

Let x be a test example, and let d+ = ||x - C+|| be the distance from x to the center of the positive examples, and d- = ||x - C-|| be the distance from x to the center of the negative examples. The CLOSE classifier assigns x to the positive class if d+ < d-, and to the negative class otherwise. Equivalently, it assigns x to the positive class if

||x - C+\(||^2\) - ||x - C-\(||^2\) < 0.

Expanding the squares and simplifying, we get

(x · x - 2C+ · x + C+ · C+) - (x · x - 2C- · x + C- · C-) < 0,

which is equivalent to

2(w · x) + (C+ · C+ - C- · C-) - 2(w · (C+ - C-)) < 0,

where w = C+ - C- is the vector pointing from the center of the negative examples to the center of the positive examples. Rearranging, we get

w · x + b < 0,

where b = (C- · C-) - (C+ · C+) is a constant.

Thus, the decision boundary of the CLOSE classifier is a hyperplane defined by the equation w · x + b = 0, and the classifier assigns a test example x to the positive class if w · x + b > 0, and to the negative class otherwise.

To compute the values of w and b in terms of C+ and C-, we can use the definition of w and b above. We have

w = C+ - C-,

b = (C- · C-) - (C+ · C+).

To compute the dual weights α's, we need to solve the dual optimization problem for the support vector machine (SVM) with a linear kernel:

minimize 1/2 ||w||^2 subject to yi(w · xi + b) >= 1 for all i,

where yi is the class label of the i-th training example, and xi is its feature vector. The dual problem is

maximize Σi αi - 1/2 Σi Σj αi αj yi yj xi · xj subject to Σi αi yi = 0 and αi >= 0 for all i,

where αi is the dual weight corresponding to the i-th training example. The number of support vectors is the number of training examples with nonzero dual weights.

In our case, the training examples are the positive and negative centers C+ and C-, so we have n+ + n- = 2 training examples. The feature vectors are simply the centers themselves, so xi = C+ for i = 1 and xi = C- for i = 2. The class labels are yi = +1 for i = 1 (positive example) and yi = -1 for i = 2 (negative example). Plugging these into the dual problem, we get

maximize α1 - α2 - 1/2 α\(1^2\) d(C+, C+) - 2α1α2 d(C+, C-) - 1/2 α\(2^2\) d(C-, C-) subject to α1 - α2 = 0 and α1,

Learn more about  decision boundary , https://brainly.com/question/29666634

#SPJ4

The expected value for a student to spend on lunch each day is $7.09.

To calculate the expected value for a student to spend on lunch each day based on the survey data,

we need to find the average amount spent by each student.

We can calculate the expected value by summing up the products of the number of students and the amount spent on lunch for each category, and then dividing by the total number of students:

Expected value = \((2 * 10 + 1 * 8 + 2 * 6 + 3 * 5 + 8 * 4 + 11 * 3 + 10 * 2.59 + 13 * 5.11 + 10 * 5.18 + 10 * 9.07) / 50\)

Expected value = \((20 + 8 + 12 + 15 + 32 + 33 + 25.9 + 55.21 + 51.8 + 90.7) / 50\)

Expected value = $354.71 / 50

Expected value ≈ $7.09

Therefore, based on the survey data, the expected value for a student to spend on lunch each day is approximately $7.09.

Learn more about expected value here,

https://brainly.com/question/24305645

#SPJ4