Buses to Dorchester leave a bus station every 12 minutes,
Buses to Bournemouth leave the bus station every 15 minutes
A bus to Dorchester and a bus to Bournemouth both leave the bus station at 10 am,
When will buses to Dorchester and to Bournemouth next leave the bus station at the same
time?

The value of the given integral \(\( \int_{-2}^{3} x(x+2) d x \)\)    is\($$\int_{-2}^{3} x(x+2) d x = \int_{-2}^{3} (x^2+2x) d x = 11 + 25 = \boxed{36}$$\) Thus, the answer is 36.

The integral can be solved using the distributive property and the power rule of integration. We start by expanding the integrand as follows:\($$\int_{-2}^{3} x(x+2) d x = \int_{-2}^{3} (x^2+2x) d x$$\)

Using the power rule of integration, we can integrate the integrand term by term. Applying the power rule of integration to the first term, we get\($$\int_{-2}^{3} x^2 d x = \frac{x^3}{3}\bigg|_{-2}^{3} = \frac{3^3}{3} - \frac{(-2)^3}{3} = 11$$\)

Applying the power rule of integration to the second term, we get\($$\int_{-2}^{3} 2x d x = x^2\bigg|_{-2}^{3} = 3^2 - (-2)^2 = 5^2 = 25$$\)

Therefore, the value of the given integral is\($$\int_{-2}^{3} x(x+2) d x = \int_{-2}^{3} (x^2+2x) d x = 11 + 25 = \boxed{36}$$\)

Thus, the answer is 36.

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Answer:

2. x^2  -3x

    -x      3

3. x^2   7x

   -2x       -14

Step-by-step explanation:

Im pretty sure this is right, but I am so sorry if it's not tho

Answer:

\(\huge\boxed{x=12}\)

Step-by-step explanation:

If B is the midpoint of line AC, we know that lines AB and BC will be equivalent to each other.

Since we know the measures of AB and BC, we can just set these expressions equal to each other and find the value of \(x\).

\(6x - 27 = 3(x+3)\)

Let's simplify this equation until we have \(x\) on one side of it.

\(6x-27=3x+9\\\\6x=3x+36\\\\3x=36\\\\x=12\)

Hope this helped!

According to 10th Amendment it defines the Federal Government only has those powers delegated in the Constitution .

No law establishing a particular religion, forbidding its practice, restricting press or speech freedom, or restricting the right of the people to peacefully assemble and petition the government for redress of grievances may be passed by Congress.

An amendment is a change or improvement that essentially maintains the integrity of the original document. The Bill of Rights is the collective name for the first ten Amendments of the Constitution. It describes Americans' constitutional rights in relation to their government. People are granted civil liberties and rights, such as the freedom of speech, the press, and religion.

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The number of cups of vinegar that Mike used lies between the whole numbers 2 and 4

If Mike used one cup of vinegar for each salad dressing recipe, then he used a total of 3 cups of vinegar (1 cup x 3 recipes = 3 cups).

However, the question states that he used "a cup of vinegar" in each recipe, which could mean that he used slightly less than one cup, exactly one cup, or slightly more than one cup.

Assuming that Mike used at least 3/4 cup of vinegar in each recipe (which is still close to "a cup"), then he used a minimum of 2 and 1/4 cups of vinegar in total (3/4 cup x 3 recipes = 2 and 1/4 cups).

Assuming that Mike used at most 1 and 1/4 cups of vinegar in each recipe (which is still close to "a cup"), then he used a maximum of 3 and 3/4 cups of vinegar in total (1 and 1/4 cups x 3 recipes = 3 and 3/4 cups).

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Answer:

u/187 = 189

Step-by-step explanation:

Needs more characters, but that's all there is to it.

Answer:

Median without the outlier: 9

Median with the outlier: 9

Step-by-step explanation:

The outlier here is 1, because it's smaller than most of the values in the data set.

Median: the middle value of a data set

Median without the outlier: 9

7, 8, 8, 9, 9, 10, 10, 10, 10

Median with the outlier: 9

1, 7, 8, 8, 9, 9, 10, 10, 10, 10

9 + 9 = 18

18/2 = 9

Hope this helps!

Answer:

the without the outlier 9

set with with the outlier 9

Step-by-step explanation:

In linear regression, the variance around the regression line represents the variability of the dependent variable (response variable) that is not explained by the regression model.

It measures the dispersion of the actual data points around the predicted values from the regression line.

The variance around the regression line can vary with different values of the predictor variable. This is because the relationship between the predictor variable and the response variable may not be constant across the entire range of the predictor variable. In other words, the spread or dispersion of the data points around the regression line may change as the predictor variable changes.

By examining the residuals (the differences between the observed values and the predicted values from the regression line) and calculating their variances, you can assess the variability of the data points around the regression line. This variability is an important aspect of understanding the goodness of fit of the regression model and the accuracy of the predictions.

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Answer:

sam and eric are going on a trip and thought to rent a car. they have to pay a fee of 30 dollars and an extra 7 dollar for each hour they take. sam and eric's are planned to spend $205 or less. how many hours can eric and sam rent the car?

Step-by-step explanation:

first assign a value for the variable, I will take H as hours

Answer:

Sorry i dont know

Step-by-step explanation:

Without the individual probability of a passenger showing up, we cannot calculate the exact probability of the number of people who show up exceeding the capacity of the plane

To solve this problem, we need to determine the probability that more than 65 people (the capacity of the plane) will show up from the 70 booked passengers.

Step 1: Identify the relevant information
- Maximum capacity of the plane: 65
- Number of people booked: 70

Step 2: Calculate the probability of each possible outcome
To exceed the capacity, at least 66 passengers must show up. We need to calculate the probability of 66, 67, 68, 69, and 70 passengers showing up. However, we don't have information on the individual probability of a passenger showing up. If we had this information, we could use the binomial probability formula.

Step 3: Express the final answer
Unfortunately, without the individual probability of a passenger showing up, we cannot calculate the exact probability of the number of people who show up exceeding the capacity of the plane. Please provide the probability of a passenger showing up so we can give you an accurate answer.

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Answer:

1/274

Step-by-step explanation:

Solution 1: Use a fraction simplifier calculator :)

Solution 2: divide by 2 first, then test to find 13, and your there.

Answer: There are two answers ( just for explanation ) 1. 0.0036496350364964    2. 274

Step-by-step explanation:

1. If we do 26 divided by 7124 answer is = 0.0036496350364964  ( check the pic-div1, div2, div3 )

2. If we do 7124 divided by 26 answer is = 274 (check pics-div4, div5)

Answer:

Chart:

x           y

-6         11

3           5

15         -3

-12        15

Step-by-step explanation:

The only things you can plug in are the domain {-12, -6, 3, 15}

Plug in the domain into equation to find y.

-6 :

y = -2/3 (-6) +7

y = +47

y=11

(-6,11)

3:

y = -2/3 (3) +7

y = -2 +7

y = 5

(3, 5)

15:

y = -2/3 (15) +7

y =  -10 +7

y = -3

(15 , -3)

-12:

y = -2/3 (-12) +7

y = 8 + 7

y= 15

(-12,15)

Answer:

1) 11

2) 3

3) -3

4) -12

Step-by-step explanation:

eq(1):

\(y = \frac{-2}{3} x + 7\\\\y - 7 = \frac{-2}{3} x\\\\x = (y - 7)\frac{-3}{2} \\\\x = (7-y)\frac{3}{2} ---eq(2)\)

1) x = -6

sub in eq(1)

\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)

2) y = 5

sub in eq(2)

\(x = (7-5)\frac{3}{2} \\\\x = 3\)

3) x = 15

sub in eq(1)

\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)

4)

sub in eq(2)

\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)

The equation, in standard form, of the parabola that models the values in the table is \(y = 6x^2 + 5x - 4\).

The given table of values represents the relationship between x and y in a parabolic function. To determine the equation of the parabola, we look for a quadratic expression of the form y = ax² + bx + c, where a, b, and c are constants.

By examining the table and matching the values, we find that the equation y = 6x²+ 5x - 4 best represents the given data. This equation is in standard form, with the highest power of x being 2. It describes a U-shaped curve, known as a parabola, which is concave upward.

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Answer:

3 or 7 x i

Step-by-step explanation:

3 or 7 i think thats right

Answer:

81.68 mm

Step-by-step explanation:

C = πd = π · 26 ≈ 81.68141 mm

The expression a d - b c evaluates to 7/6. The expression a d - b c evaluates to 1/3.

To evaluate the expression a d - b c, we substitute the given values of the variables a, b, c, and d into the expression and perform the arithmetic operations.

Given:

a = 1/2

b = -1

c = -(2/3)

d = 2

Substituting these values into the expression, we have:

(1/2)(2) - (-1)(-(2/3))

Simplifying each term:

(1/2)(2) = 1

-(-1)(-(2/3)) = -1(-2/3) = 2/3

Substituting the simplified values back into the expression, we have:

1 - 2/3

To subtract fractions, we need a common denominator, which in this case is 3. Rewriting the expression with a common denominator, we have:

3/3 - 2/3

Subtracting the fractions, we get:

1/3

Therefore, the expression a d - b c evaluates to 1/3.

In summary, by substituting the given values of the variables into the expression and performing the necessary arithmetic operations, we find that a d - b c evaluates to 1/3.

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We can use the z-score formula to help us with this.Using the standard normal distribution, we can calculate the z-score for 1321:

The z-score formula is:
z = (X - μ) / σ
Where z is the z-score, X is the value we want to find the percentage for, μ is the mean, and σ is the standard deviation.

Step 1: Calculate the z-score.
z = (1321 - 1496) / 292
z = (-175) / 292
z ≈ -0.60

Step 2: Find the proportion of students with a z-score below -0.60. You can use a z-table or an online calculator for this. For z = -0.60, the proportion is approximately 0.2743.

Step 3: Convert the proportion to a percentage.
0.2743 * 100 = 27.43%

Step 4: Round the percentage using the appropriate rounding rule. In this case, let's round to two decimal places.
27.43% ≈ 27.43%

So, approximately 27.43% of students from this high school earn scores that fail to satisfy the admission requirement of the local college.

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The false statement among the options provided is 2 ≥ 8. This statement claims that 2 is greater than or equal to 8, which is incorrect.

In reality, 2 is less than 8, so the statement is false.

Answer:

O Yes, because 1 kilogram = 1000 grams, and 1 liter = 100 centiliters.

Yes, because 1 gram per liter is the same as 1 kilogram per centiliter.

Step-by-step explanation:

Step-by-step explanation:

c

From the image given, if angle 1 is congruent with angle 7 (which we see is obviously not a possibility unless the figure formed by the intersection of the parallel lines is a perfect square), we need to decide on which option is the correct one:

So, since the fact that the lines being parallel cannot be enough to guarantee that the two angles are equal, we select the last option: none.

Answer:

X = 62°

Step-by-step explanation:

Since opposite or vertical angles are equivalent, you can form the equation that 28 + x = 90 (In case you didn't know, right angles are always 90°). Subtract 28 from both sides to find the value of x and you'll get x = 90 - 28 or x = 62°.

Given:

The expression is:

\(3x^5-7x^4+6x^2-14x\)

To find:

The complete factor form of the given expression.

Solution:

We have,

\(3x^5-7x^4+6x^2-14x\)

Tanking out the GCF, we get

\(=x(3x^4-7x^3+6x-14)\)

\(=x(x^3(3x-7)+2(3x-7))\)

\(=x(x^3+2)(3x-7)\)

Therefore, the complete factor form of the given expression is \(x(x^3+2)(3x-7)\).

Therefore ,the data they employ includes Second Party Data as a result, which is the solution to the given challenge of plotting data.

The most typical method of utilizing a chart to convey data is to graph the correlation of two additional variables. Diagrams created by hand or using a computer are also acceptable. From the origin, go three up, then 2 pieces to the right. On the reference system, it is important to display the digits for positions 2, 3, and 4. Be really explicit with your points. The pinkish squiggle with the letter P represents the value of 2.3. You must first generate a number line for each number in a collection of data to be able to create a chart.

Here,

Given :

Data gathered from hospitals is frequently used by institutions like the US Center of Disease Control (cdc).

In order to determine what data they use,

From the information provided, it is clear that they are using second-party data.

Therefore ,the data they employ includes Second Party Data as a result, which is the solution to the given challenge of charting the data.

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Answer:

N + 3 = -5

n= -8

N-4=9

n=13

4+N=10

n=6

-10+N=3

n=13

N-10=1

n=11

-11+n=-12

n=-1

N+19=20

n=1

15+N=-10

n=-25

N-6=-12

n=-6

N+4=16

n=12

Step-by-step explanation:

Answer:

x = 6

MP = 30

Step-by-step explanation:

5x = 3x + 12

2x = 12

x = 6

MP = 5x = 5 × 6

MP = 30

The given system of differential equations can be analyzed using a Lyapunov function of the form ax^2 + cy^2, where a and c are to be determined. By computing the derivative of this function along the trajectory of the system, we can determine the stability properties of the critical point at the origin.

First, we compute the derivative of the Lyapunov function along the trajectory of the system:

V'(x,y) = 2ax(x^3 + xy^2) + 2cy(xy' - 2x^2y)

Using the second equation of the system, we can substitute y' = x^3 + xy^2 - 2x^2y to obtain:

V'(x,y) = 2ax(x^3 + xy^2) + 2cy(x^3 + xy^2 - 2x^2y - 2x^2y)

Simplifying this expression yields:

V'(x,y) = 2x(x^2 + y^2)(a + c - 4ac)

For the critical point at the origin to be asymptotically stable, we need V'(x,y) to be negative definite in a neighborhood of the origin. This can be achieved by choosing a and c such that a + c - 4ac < 0 and a, c > 0. For example, we can choose a = 1/4 and c = 1/2, which gives a + c - 4ac = -1/4.

Therefore, the critical point at the origin is asymptotically stable. This means that any trajectory that starts sufficiently close to the origin will converge to the origin as t approaches infinity. The Lyapunov function provides a way to analyze the stability of the critical point without solving the system explicitly, which can be useful for more complex systems.

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Answer:

20 degrees and 85 degrees.

Step-by-step explanation:

105 degrees+ 150 degrees is equal to 255 degrees. 360 degrees - 255 degrees is 105 degrees. To get the ratio equivalent to 105 degrees you have to multiply both sides by 5 in order to get 20 degrees, and 85 degrees. I hope this helps! :)

Answer:

Triangle PST ≅ Triangle PQR by ASA

Step-by-step explanation:

We know that because line segments PS and PR are congruent, then ∠PRS and ∠PSR must also be congruent because of the Isosceles Triangle Theorem, which states that if two sides of a triangle are congruent, then angles opposite those sides are congruent.

Therefore, the angles supplementary to ∠PRS and ∠PSR (∠PRQ and ∠PST respectively) must also be congruent to each other since we've already stated that ∠PRS and ∠PSR are congruent due to the Isosceles Triangle Theorem.

So, we can prove triangles PST and PQR congruent by ASA (Angle-Side-Angle).