Find the LCM of:

x² - 3x + 2, x² + x + 2​

The probability of rolling the dies and getting greater than 4 will be [tex]\dfrac{2}{6}[/tex].

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Given that the 6-sided die is rolled, the probability of getting a number greater than 4 will be calculated as,

Sample space = {1, 2, 3, 4, 5, 6} = 6

Favourable outcomes = {5,6} = 2

[tex]\rm Probability = \dfrac{Favourable \ events}{Sample\ space}[/tex]

[tex]\rm Probability = \dfrac{2}{6}[/tex]

Therefore, the probability will be [tex]\dfrac{2}{6}[/tex].

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Therefore, it is not possible to determine how much Jim was charged for each shirt, each pair of slacks, and each sports coat with the given information.

To solve this problem, we can use a system of linear equations. Let x be the cost of each shirt, y be the cost of each pair of slacks, and z be the cost of each sports coat. Then we can write the following equations based on the information given in the problem:

3x + 2y = 18.45 (equation 1)

7x + 2y + z = 35.40 (equation 2)

4x + 2z = 23.94 (equation 3)

Now we can use the elimination method to solve for the variables. First, we can subtract equation 1 from equation 2 to eliminate the y variable:

4x + z = 16.95 (equation 4)

Next, we can multiply equation 1 by -2 and add it to equation 3 to eliminate the y variable:

-6x - 4y + 4x + 2z = -36.9 + 23.94

-2x + 2z = -12.96 (equation 5)

Now we can subtract equation 4 from equation 5 to eliminate the x variable:

2z - z = -12.96 - 16.95

z = -29.91

This value for z does not make sense, so there must be a mistake in the calculations or the original problem. Therefore, it is not possible to determine how much Jim was charged for each shirt, each pair of slacks, and each sports coat with the given information.

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Answer:

please give brainliest

Step-by-step explanation:

P(x)=(x+5)(x−4)(x−5)

is the lowest order of all polynomials with given zeroes.

The ratio of investment is 3:4:5, which means the total ratio is 3+4+5 = 12.

Let the common ratio be x, then the amount invested by each entrepreneur is:

3x + 4x + 5x = 12x

According to the problem, 12x = $875,000

So, x = $875,000/12 = $72,916.67

Therefore, the second largest share is 4x = 4*$72,916.67 = $291,666.68

Rounding off to the nearest 100th, the second largest share is $291,666.67.

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Answer: not my answer but an answer from ai, scan through, see if right, its all explained out for you

To evaluate g(f(5)), we first need to find the value of f(5) by substituting x = 5 into the definition of f(x):

f(x) = x^2 - 6x + 14

f(5) = 5^2 - 6(5) + 14

f(5) = 25 - 30 + 14

f(5) = 9

Now that we know that f(5) = 9, we can evaluate g(f(5)) by substituting 9 into the definition of g(x):

g(x) = x + 14

g(f(5)) = g(9)

g(f(5)) = 9 + 14

g(f(5)) = 23

Therefore, the value of g(f(5)) is 23.

Below, you will learn how to solve the problem.

(a) To find the linear relationship y = mx + b between x = year and y = profit, we first need to find the slope (m) and the y-intercept (b).

The slope (m) is the change in y (profit) divided by the change in x (year):
m = (17 - 5)/(6 - 2)

m = 12/4

m = 3

Next, we can use one of the data points (2, 5) and the slope (3) to find the y-intercept (b):
5 = 3(2) + b
b = 5 - 6

b = -1

So the linear relationship between x = year and y = profit is:

y = 3x - 1

(b) To find the company's profit at the end of 3 years, we can plug in x = 3 into the equation:
y = 3(3) - 1

y = 8

So the company's profit at the end of 3 years is $8 million.

(c) To predict the company's profit at the end of 8 years, we can plug in x = 8 into the equation:

y = 3(8) - 1 = 23

So the company's profit at the end of 8 years is predicted to be $23 million.

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Check the picture below.

[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-3\\ k=1\\ a=2\\ b=1 \end{cases}\implies \cfrac{(x- (-3))^2}{ 2^2}+\cfrac{(y-1)^2}{ 1^2}=1\implies \cfrac{(x+3)^2}{ 4}+\cfrac{(y-1)^2}{ 1}=1[/tex]

Answer: To find the equation of the ellipse, we need to use the standard form equation of an ellipse:

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

where (h,k) is the center of the ellipse, a is the distance from the center to the vertices (the major axis), and b is the distance from the center to the co-vertices (the minor axis).

First, let's find the center of the ellipse. The center of the ellipse is the midpoint of the line segment joining the vertices (-5,1) and (-1,1). Using the midpoint formula, we get:

$(h,k) = \left(\frac{-5+(-1)}{2}, 1\right) = (-3,1)$

Now, we need to find the values of a and b. Since the distance between the vertices is 2a, we have:

$2a = |-5-(-1)| = 4$

So, $a = 2$.

Similarly, the distance between the co-vertices is 2b, we have:

$2b = |2-0| = 2$

So, $b = 1$.

Now, we have all the values we need to write the equation of the ellipse:

$\frac{(x+3)^2}{2^2}+\frac{(y-1)^2}{1^2}=1$

Simplifying this equation, we get:

$\frac{(x+3)^2}{4}+(y-1)^2=1$

So, the equation of the ellipse is:

$(x+3)^2/4 + (y-1)^2/1 = 1$

Step-by-step explanation:

Answer: (x - 4, y - 5)

Step-by-step explanation: (x, y) --> (x - 4, y - 5)

Answer:

2/3 of the fruits in the basket are red apples.

Step-by-step explanation:

5 apples of 6 total fruit are in a basket.

4 apples are red.

Take 4 and divide it by 6, you will get 0.67 or 2/3.

2/3 cannot be simplified.

The value of the given algebraic expression is 7. The solution has been obtained by using arithmetic operations.

A mathematical expression called an algebraic expression can have variables or integers in it. It cannot be solved because it lacks an equals sign. A sequence of algebraic expressions are separated by an equals sign and are part of an algebraic equation, which can be solved.

We are given an algebraic expression as (f + g)/j.

The values of f = 6, g = 8, h = 12 and j = 2.

On substituting these in the expression, we get

⇒(6 + 8)/2

⇒14/2

⇒7

Hence, the value of the given algebraic expression is 7.

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Question: Evaluate the algebraic expression (f + g)/j when f = 6, g = 8, h = 12 and j = 2.

Answer:

see below

Step-by-step explanation:

net worth = assets- liabilities

assets = what u have (good stuff)/own eg money

liabilities = what u owe/spending

so work backwards or put numbers in place

672 = assets- 314

672+314 = assets (ans)

Answer:

(2, 1) is the point where the two lines intersect.

To prove it I'll use substitution

The equations are:

y = 2x - 3 and y = -3x + 7

I'll plug in 2x - 3 for y in y = -3x + 7 so...

2x - 3 = -3x + 7

Simplify:

5x = 10

x = 2

Now I'll plug 2 for x in y = 2x - 3

y = 2(2) - 3

y = 4 - 3

y = 1

So the ordered pair/solution is (2, 1)

Hope that explains it!

1. The probability of finding 1 toy in the 24 packages is 0. This is because the company offers a toy in every 5 cereal packages, so if the father buys 24 packages, he is guaranteed to find at least 4 toys (24/5 = 4.8, rounded down to 4). Therefore, the probability of finding only 1 toy is 0.

2. The probability of finding no toy at all is also 0, for the same reason as above. The father is guaranteed to find at least 4 toys in the 24 packages he bought.

3. The mean number of toys in the 24 packages is 4.8, which is the result of 24/5. The standard deviation can be calculated using the formula sqrt(np(1-p)), where n is the number of packages, p is the probability of finding a toy in each package, and 1-p is the probability of not finding a toy. In this case, n=24, p=1/5, and 1-p=4/5. Plugging these values into the formula gives us:

Standard deviation = sqrt(24*(1/5)*(4/5)) = 1.732

So the mean number of toys in the 24 packages is 4.8, and the standard deviation is 1.732.

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Answer:

Part A
Option C

Part B
Option A

Step-by-step explanation:

Part A

The equation for revenue gained for x tickets sold by Alpacas team

is y = 7.5x

This indicates the slope is 7.5 which means for every ticket sold the revenue increases by $7.50

Or in other words, cost of each ticket = $7.50

The revenue - ticket relationship for the Stingrays is given in the form of a graph with a linear equation

The slope of the graph can be found by rise/run where rise

= difference in y values for 2 points on the graph and run

= difference in the corresponding x values

Let's take points (0, 0) and (100, 1500) to find the slope
rise = (1500 - 0)/(10-0) = 1500/10 = 150

run = 10 - 0 = 10

Slope = 150/10 = 15

Equation is y = 15x

So for every ticket sold, the revenue increases by $15

Or in other words, cost of each ticket = $15

Therefore each Stingrays ticket costs 15/7.5 = 2 times each Alpacas ticket

Correct Answer:
Option C

---------------------------------------------------------------------------------------------------------

Part B

For the Geckos swim team we can see that as the number of tickets increases from 6 to 18(difference of 18- 6 = 12), the revenue increases by 180 - 60 = $120

Cost for ticket between 6 and 18 tickets = $120/12 = $10

When tickets sold increases from 18 to 54 (difference of 54 - 18= 36), the revenue increases by $540 - $180 = $360

Therefore the price for each ticket within this range = $360/36 = $10

So the price per ticket is the same regardless of the number of tickets sold

Therefore Gecko's revenue can be modeled as y = 10x

Alpacas charge $7.50 per ticket and Gecko's charge $10 per ticket
So the difference between a Gecko's ticket and an Alpacas ticket

= $10 - $7.50

= $2.50 more than Alpacas

or, alternatively

Alpacas charge $2.50 less than Gecko per ticket

Correct Answer

Option A

In response to the supplied query, we may state that Hence, Brenda's Pythagorean theorem home is around 7.2 kilometers away from the school.

The fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean Theorem, sometimes referred to as the Pythagorean Theorem. This rule states that the areas of squares with the other two sides added together equal the area of the square with the hypotenuse side. According to the Pythagorean Theorem, the square that spans the hypotenuse (the side that is opposite the right angle) of a right triangle equals the sum of the squares that span its sides. It may also be expressed using the standard algebraic notation, a2 + b2 = c2.

Points A, B, and C can be used to create a right triangle in this situation. The hypotenuse of the line segment between points A and C is its length, while the other two sides are the lengths of the segments connecting A and B and B and C.

We'll refer to the separation between positions A and C as "x". Next, we have:

[tex]x2 = 6 + 4, x2 = 36 + 16, x2 = 52, x = \sqrt(52) = 7.2.[/tex]

Hence, Brenda's home is around 7.2 kilometers away from the school.

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The statement (3)/(2)>(4)/(5) is true because cross-multiplication shows that 15>8.

To determine whether a statement is true or false, we can cross-multiply the fractions and compare the products.

In this case, (3)*(5)>(2)*(4), which simplifies to 15>8. Since 15 is greater than 8, the statement is true and does not need to be rewritten.

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By answering the above question, we may infer that Hence, when equation Mr. Haustra's tank is just 1/4 full, he can go around 70 miles.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

There are the following if Mr. Hamstra's automobile contains 14 2/5 gallons of fuel and his tank is only 1/4 full:

There are 3 1/2 gallons of gas in the tank (1/4) x 14 2/5.

If the automobile gets 20 miles per gallon on average, it may go as far as:

3 1/2 gallons x 20 miles per gallon is 70 miles.

Hence, when Mr. Hamstra's tank is just 1/4 full, he can go around 70 miles.

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All four statements are logically equivalent.

The statements (a), (b), (c), and (d) are all logically equivalent because they all describe the same concept: that the matrix A has a solution for every possible vector b.

Let's start with statement (a): For each b∈Rm, the matrix equation Ax=b has a solution. This means that for any vector b in Rm, there exists a vector x in Rn such that Ax=b.

Now, let's look at statement (b): Each b∈Rm is a linear combination of the columns in A. This means that for any vector b in Rm, we can write b as a linear combination of the columns of A, which is equivalent to saying that Ax=b has a solution.

Statement (c) says that the columns of A span Rm. This means that the columns of A can be combined in a linear combination to produce any vector in Rm, which is equivalent to saying that Ax=b has a solution for any vector b in Rm.

Finally, statement (d) says that the reduced echelon form of A has a pivot in every row. This means that the matrix A is of full rank and that there are no free variables in the equation Ax=b. This implies that there is a unique solution for every vector b in Rm, which is equivalent to saying that Ax=b has a solution for any vector b in Rm.

Therefore, all four statements are logically equivalent because they all describe the same concept: that the matrix A has a solution for every possible vector b.

The solution to this question is to understand that all four statements are logically equivalent because they all describe the same concept: that the matrix A has a solution for every possible vector b.

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Answer:

The samples randomly and independently.

True. When comparing the means of two populations, it is important that the two samples be drawn randomly and independently from both populations. This ensures that the samples are representative of the populations and that the results are not biased. By drawing the samples randomly and independently, we can ensure that the comparison of the means is accurate and reflects the true differences between the populations.

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The probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is approximately 0.1736 or 17.36%. The probability that the ballot measure might pass in Region B can be calculated using a confidence interval approach.

The confidence interval for the population proportion of voters who support the ballot measure in Region B:

CI = p ± z × SE

where p is the sample proportion, z is the critical value for the desired confidence level (e.g., z=1.96 for 95% confidence), and SE is the standard error of the sample proportion.

the standard error of the sample proportion:

SE = [tex]sqrt [p ×\frac{(1-p)}{n} ][/tex]  = [tex]sqrt[0.51 ×\frac{(1-0.51)}{400} ][/tex] = 0.025

where p is the sample proportion and n is the sample size.

the confidence interval using a 95% confidence level:

CI = 0.51 ± 1.96  0.025 = (0.46, 0.56)

Therefore, we can be 95% confident that the true population proportion of voters who support the ballot measure in Region B falls within the range of 0.46 to 0.56. Since the lower bound of the confidence interval is above 0.50, there is a possibility that the ballot measure might pass in Region B. However, the exact probability would depend on the actual population proportion and the sample size.

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The answer is 0(zero)

The remainder when dividing 4x4 - 2x2 by x3 - x2 + 1 can be found using polynomial long division.

The calculation is shown below:

Therefore, the remainder when dividing.

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-4

The equation for the vector v given is: \( v=\left[\begin{array}{c} -4 \\ a \\ -5 \\ -9 \end{array}\right] \).

The set \( H \) is defined as the span of the vector \( \left[\begin{array}{c} 4 \\ 4 \\ 4\end{array}\right] \).

To find the value of a, we need to express the vector v in terms of the basis vector for H.

We can solve for a using the following equation: \( v = -4\left[\begin{array}{c} 4 \\ 4 \\ 4 \end{array}\right] + a\left[\begin{array}{c} 4 \\ 4 \\ 4 \end{array}\right] \)

Since the vector v has the same magnitude in each component, we can set the components equal:

\(-4 = a\)

Therefore, the value of a is -4.

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Answer:

Step-by-step explanation:

based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest who

[tex]y=\frac{6}{5} x+1[/tex]

Slope-intercept form is a common way to express a linear function.

Solving For Slope-Intercept

In the question, we are given standard form. In order to find slope-intercept, we need to solve for y. This means we need to use the properties of equality to isolate y from the other values.

First, add 6x to both sides.

Then, divide both sides by 6.

This gives us the final slope-intercept form of the given equation.

Interpreting the Equation

Slope-intercept form is written in the format of y = mx + b. In this equation, m is the slope and b is the y-intercept. Our equation is [tex]y=\frac{6}{5} x+1[/tex]. So, 6/5 is the slope. This means that the rate of change of the graph is 6 units per 5 units. Additionally, the y-intercept is 1. So, the graph crosses the y-axis at y = 1.

If you have a rectangle with a length of 5 and a width of 3, the area would be 5 * 3 = 15.

To factorise a quadratic equation, you need to find two numbers that multiply to give the constant term and add to give the coefficient of the x term.

For example, if you have the equation x^2 + 5x + 6 = 0, the two numbers you need to find are 2 and 3, because 2 * 3 = 6 and 2 + 3 = 5. So the equation can be factorised as (x + 2)(x + 3) = 0.

In terms of finding the area of a rectangle, you need to multiply the length and the width. So if you have a rectangle with a length of 5 and a width of 3, the area would be 5 * 3 = 15.

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The length of AC is 224 meters to 3 significant figures.

a² + b² = c²

where c is the hypotenuse (the side opposite the right angle) and a and b are the two legs (the sides adjacent to the right angle).

In this case, we can treat Stanley's path as a right triangle with legs AB and BC, and hypotenuse AC. Since we are given the lengths of AB and BC, we can plug those into the Pythagorean theorem and solve for AC.

AC² = AB² + BC²

AC² = (200 m)² + (160 m)

AC² = 40,000 m² + 25,600 m²

AC² = 65,600 m²

To find AC, we take the square root of both sides:

AC = [tex]\sqrt{65600}[/tex] m

AC ≈ 256

Finally, we round to 3 significant figures to get length of AC ≈ 224 meters.

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For toss 21 it is 2 dollars, for toss 41 it is 4 dollars, for toss 63 it is 6.

Graphs can take many forms, depending on the type of data being represented and the purpose of the graph. Some common types of graphs include:

Bar graphs: These use bars or columns to represent numerical values or frequencies.

Line graphs: These use lines to show the relationship between two variables over time or other intervals.

Pie charts: These use slices of a circle to represent parts of a whole.

Scatterplots: These show the relationship between two variables by plotting individual data points.

Graphs can be used to identify patterns, trends, and relationships in data, and to make predictions and draw conclusions based on that data. They are commonly used in fields such as statistics, economics, engineering, and science to help visualize and analyze complex data sets.

TOSS              DOLLARS

21                    2

42                   4

63                   6

Plotting the points on the coordinate axes, we have:

 |

7 -

 |

6 -

 |

5 -

 |

4 -         • (21,2)

 |               \

3 -                • (42,4)

 |                       \

2 -                        • (63,6)

 |________________________________

   0   20   40   60   80   100

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The altitudes of a triangle are the angle bisectors of the orthic triangle is true because the orthic triangle is formed by the feet of the altitudes of the original triangle. The circle whose diameter is the side of the triangle passes through the opposite vertices of the orthic triangle is true because circumcircle of a triangle passes through all three vertices.

To prove the first statement, we can use the fact that the altitudes of a triangle are perpendicular to the sides and intersect at the orthocenter. The orthic triangle is formed by the feet of the altitudes of the original triangle.
1. Let ABC be the original triangle and D, E, F be the feet of the altitudes from A, B, and C, respectively.
2. Since AD is an altitude, ∠ADB and ∠ADC are right angles.
3. Similarly, ∠BEC and ∠BFC are right angles.
4. Therefore, ∠BDC and ∠EDF are supplementary angles, meaning they add up to 180 degrees.
5. Since ∠BDC and ∠EDF are supplementary and they share a common side, they are also the angle bisectors of the orthic triangle DEF.
6. The same logic can be applied to the other two altitudes to show that they are also angle bisectors of the orthic triangle.

To prove the second statement, we can use the fact that the circumcircle of a triangle passes through all three vertices.
1. Let ABC be the original triangle and D, E, F be the feet of the altitudes from A, B, and C, respectively.
2. Let O be the circumcenter of the original triangle ABC.
3. Since the circumcircle passes through all three vertices, OD, OE, and OF are all radii of the circle.
4. Since all radii of a circle are equal, OD = OE = OF.
5. Therefore, the circle whose diameter is the side of the triangle passes through the opposite vertices of the orthic triangle, as they are all equidistant from the center of the circle.

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