y = (x^2/2) + x + 2; [-5, 3]
For each problem, approximate the area under the curve over the given interval using 4 left endpoint rectangles

Due to the fact that the two candidates were chosen at random, we may assume that all options are equally likely, hence each sample point has a chance of 1/6.

(a) The four candidates are marked as [tex]$A_1, A_2, A_3$[/tex], and M. The sample space is as follows because order doesn't matter (we just need two persons and it doesn't matter what order we choose):

[tex]$\mathcal{S}=\left\{A_1 A_2, A_1 A_3, A_1 M, A_2 A_3, A_2 M, A_3 M\right\}$[/tex]

(b) We may assume equally likely possibilities because the two candidates were selected at random, hence each sample point has a probability of 1 / 6

(c) Let  C = {minority hired} Then P(C) =

[tex]P\left(A_1 M\right)+P\left(A_2 M\right)+P\left(A_3 M\right)=3 / 6=1 / 2$[/tex]

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The required sets of all real and satisfying numbers are:

(-∞ ,  -4) ,  (-4, -2), (-2, - 1), (-1, 1), and (1, ∞)

Sets are groups of clearly defined objects or elements in mathematics.

A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.

The empty set, finite set, singleton set, equivalent set, subset, power set, universal set, superset, and infinite set are the various types of sets.

Now, solve for (x^2 + 3x - 1)^2  = 9:

To make this true, either

x^2 + 3x - 1  =  3  or x^2 + 3x - 1  =  -3

x^2 + 3x - 4  = 0, x^2 + 3x + 2  = 0

(x + 4) ( x - 1)  = 0, (x + 1) ( x + 2)  = 0

x = -4, x= 1, x = -1, x = -2

Therefore, we have five potential intervals to test.

(-∞ ,  -4) ,  (-4, -2), (-2, - 1), (-1, 1), and (1, ∞)

Therefore, the required sets of all real and satisfying numbers are:

(-∞ ,  -4) ,  (-4, -2), (-2, - 1), (-1, 1), and (1, ∞)

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The solution of the equation are x = 8 , x = -4 + 4i√3 and x = -4 - 4i√3.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An equation of the form ax³+bx²+cx+d=0 with a nonzero an is referred to as a cubic equation in one variable. The roots of the cubic function defined by this equation's left side are the answers to this equation.

The equation is given as

x³ = 512

⇒ x³ - 512 = 0

⇒x³ - 8³ = 0

⇒(x-8)(x² + 8x + 64) = 0

So, the solutions are

x = 8 and

x² + 8x + 64 = 0 .....(A)

Solving equation A we get,

x = [tex]\frac{-8 + \sqrt{8\x^{2} - 4*1*64} }{2} = \frac{-8 + \sqrt{64 - 256} }{2}[/tex] = -4 ± 4i√3

The solution of the equation are x = 8 , x = -4 + 4i√3 and x = -4 - 4i√3.

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The method of moments estimate and the maximum likelihood estimate are the same.

The method of moments estimate is the sample mean, which can be calculated by adding the numbers together and dividing by 5. In this example, the mean is 52. The maximum likelihood estimate is the mean of the population distribution, which can be estimated by maximizing the likelihood function. This involves taking the partial derivatives with respect to the parameters and solving for the values that make the derivative equal to zero. In this example, the maximum likelihood estimate will also be 52. Thus, the method of moments estimate and the maximum likelihood estimate are the same.

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On solving -11 + 3(b + 5) = 7, we get the value of b = 1.

Solving an equation indicates finding the value of variables in a given expression that can satisfy the given condition in the equation.

To solve an equation we can add or subtract the same integer which cannot change the condition of the equation. Similarly, we can multiply or divide by the same integers on both sides.  

Here we have

Solve  -11 + 3(b + 5) = 7  

The given expression can be solved as follows

=> -11 + 3(b + 5) = 7  

Multiply 3 and (b + 5)

=> - 11 + 3b + 15 = 7

=> 3b + 4 = 7

Subtract 4 from both sides

=> 3b + 4 - 4 = 7 - 4

=> 3b = 3

Divide by 3 into both sides

=> 3b/3 = 3/3

=> b = 1

Therefore,

On solving -11 + 3(b + 5) = 7, we get the value of b = 1.

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The triangle ABC is shown in the figure below. All 3 sides of the triangle are labeled a, b, and c, and the right angle is located at the vertex C.

To verify that the triangle ABC is a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that the sum of the squares of the two shorter sides of the right triangle is equal to the square of the longest side (hypotenuse). Therefore, in the case of triangle ABC, we can calculate a^2 + b^2 = c^2. When we calculate, we can see that the equation is true, meaning that the triangle ABC is indeed a right triangle.

To find the area of triangle ABC, we can use Heron's formula. Heron's formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c), where s is the semiperimeter (the sum of the three sides divided by 2). Therefore, in the case of triangle ABC, the area is equal to the square root of s(s-a)(s-b)(s-c), which is equal to 6.

Therefore, triangle ABC is a right triangle with an area of 6.

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:

The the area of the real patio is = 50 m²

Recall that area deals with the floor space occupied by the rectangular field

The area of the lawn is represented by

Area = L*W

2 cm for length = 5 m.

4 cm for width = 10 m.

Area = width • length. 10•5=50cm²

Having computed the area, we now conclude that the the area of the real patio 50cm²

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The triangles having one angle as 45° have been constructed below.

What is a triangle?

Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point.

We need to draw 2 triangles which contains one angle as 45 degrees.

The first triangle is the triangle with angles 45°, 60° and 75°.

So, the second triangle is a right-angled triangle with angles 90°, 45° and 45°.

The two triangles stated above have been drawn below.

Hence, there are 2 different triangles with one angle as 45°.

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Since there are multiple questions, so the question answered above is as follow:

For the problem, draw 2 triangles that have the listed properties. Try to make them as different as possible.

1. One angle is 45 degrees.

You can use collections of objects such as blocks to model a number. Each type of block can be used to show the value of each digit in the number

The values of adjacent places in base-ten representations of numbers are related as each place is always 10 times the value represented by the place to its imme- diate right

Unit blocks, rods, flats, and cubes are the names of base ten block types. The digit in the ones place is represented by the unit blocks. To demonstrate how many tens are in a number, rods are each worth one ten, i.e., ten rods equal one flat, which is worth one hundred each.

Students use base ten blocks, also referred to as multibase arithmetic blocks or Dienes blocks, as a type of math manipulative to learn the basics of addition, subtraction, number sense, place value, and counting.

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The scale factor applied to the triangle is k = 1/2.

When we have a length L and we apply to it a scale factor K, the new length will be:

L' = k*L

Then the scale factor is:

L'/L = k

And if a scale factor is applied to a polygon, like a triangle, all the sides get affected by the scale factor in the same way.

Then if the original length of the given side is:

L = 5ft

And the new length is:

L' = 2.5ft

The scale factor is:

k = 2.5ft/5ft = 1/2

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Option 1 is the more cost-effective option for preventive maintenance.

Option 1:  Flat fee of $400 per month

Option 2:  Pay a fee of $25 per breakdown

Option 1 is the more cost-effective option since the cost is fixed. This option would provide a guaranteed cost of $400 per month, regardless of the frequency of breakdowns.

On the other hand, Option 2 would cost more in the long run if the frequency of breakdowns is high. The cost would be calculated as follows:

Frequency of Breakdowns x Cost per Breakdown = Total Cost

For example, if the frequency of breakdowns is three times per month, the total cost would be 3 x $25 = $75 per month.

In comparison, the cost of Option 1 would remain at $400 per month, regardless of the frequency of breakdowns. Therefore, Option 1 is the more cost-effective option for preventive maintenance.

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Answer:

x = 3

Step-by-step explanation:

using the perpendicular bisector theorem B

MB is the perpendicular bisector of JK and JB = KB

then Δ MJK is isosceles with legs being congruent , that is

MJ = MK , so

9x - 18 = 3x ( subtract 3x from both sides )

6x - 18 = 0 ( add 18 to both sides )

6x = 18 ( divide both sides by 6 )

x = 3

U1 ≠ U2. The claim is therefore false in general

Let V = R2 over R, U1 the x-axis, U2 the y-axis, and W = V.

Obviously, U1 + W, U2 + W ⊆ V is clear since U1,U2,W ⊆ V .

Let v ∈ V be any vector. Then v ∈ W = V .

Here, instead of vectors, U1, U2, and W are vector spaces. Therefore, we are unable to demonstrate the evidence by using U1, U2, and W as separate vectors.

Here we assume that U1={(x, 0), x ∈ R} and U1={(0, y), y ∈ R} and W=V={(x, y), x,y ∈ R}

So v = 0 + v ∈ U1 + W. Also, v = 0 + v ∈ U2 + W.

Hence, V ⊆ U1 +W, U2 +W.

Thus, U1+W = U2+W = V.

But U1 ≠ U2. The claim is therefore false in general.

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Answer:

Step-by-step explanation:

5800 divided by 100=58x4.6=126 something like that

These events would be considered as: Subjective, Independent, Dependent, Classical

Subjective event: An event that is based on individual opinion or belief. This event would not be represented by a formula or calculation.

Independent event: An event that is not influenced by other events. This event can be represented by a formula such as P(A) = P(A) which calculates the probability of an event occurring on its own.

Dependent event: An event that is influenced by other events. This event can be represented by a formula such as P(A|B) = P(A ∩ B) / P(B) which calculates the probability of an event occurring given that another event has already occurred.

Classical event: An event that is determined by predetermined probabilities or odds. This event can be represented by a formula such as P(A) = n(A) / n(S) which calculates the probability of an event occurring based on the number of favorable outcomes divided by the total number of outcomes.

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a) Both events occur: A ∩ B

b) At least one event occurs: A ∪ B

c) Neither event occurs: A' ∩ B'

d) Exactly one event occurs: (A ∩ B') ∪ (A' ∩ B)

In Event A and B, the intersection A ∩ B tells us the outcome where both events occur. The Union of A and B tells us the outcome where at least one event occurs. The intersection of the complements of A and B (A' ∩ B') tells us the outcome where neither event occurs.

Finally, the union of the intersection of A and the complement of B and the intersection of the complement of A and B ( (A ∩ B') ∪ (A' ∩ B) ) tells us the outcome where exactly one event occurs.

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The basis for the nullspace of A is {(-1, -1, 1)}.

Let A be the given matrix. The nullspace of A is the set of all vectors x such that Ax = 0. To find a basis for the nullspace of A, we need to solve the following system of equations:

Ax = 0

Since A is a 2x3 matrix, we must have 3 variables and 2 equations. We can solve this system of equations by using Gaussian elimination. We start by subtracting the first equation from the second equation and then eliminating the middle variable by subtracting the first equation from the third equation. This gives us the following:

x1 + x3 = 0

x2 + x3 = 0

We solve this system of equations by setting x1 = -x3 and x2 = -x3. This gives us the basis for the nullspace of A as {(-1, -1, 1)}. Thus, the basis for the nullspace of A is {(-1, -1, 1)}.

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Using the intermediate value theorem, the equation x5 - 2x4 - x - 3 = 0 is continuous on the closed interval [2, 3], there is a root of the equation in the interval (2,3).

Given, the equation is x5 - 2x4 - x - 3 = 0

We have to find the root of the equation in the interval (2, 3) using the intermediate value theorem.

Let f(x) = x5 - 2x4 - x - 3

f(2) = (2)5 - 2(2)4 - 2 - 3

f(2) = 32 - 32 - 5

f(2) = -5

f(3) = (3)5 - 2(3)4 - 3 - 3

f(3) = 243 - 162 - 6

f(3) = 75

Intermediate value theorem states that if a continuous function f(x) on the interval [a,b] has values of opposite sign inside an interval, then there must be some value x = c on the interval (a,b) for which f(c) = 0.

f(x) is continuous on the interval [2, 3] because it is a polynomial function, and is continuous at each point in the interval.

Here, f(2) is negative and f(3) is positive.

Therefore, f(x) is continuous on the closed interval [2, 3], there must be some value x = c on the interval [2, 3] for which f(c) = 0.

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A circle is formed by all points on a plane equidistant from a given point

The possible x-coordinates of Q are -134.71 and +134.71

Known parameters are;

The radius of the golf course, r = 30 feet

Point the ball exits the green = The right-most edge

Speed of the ball = 8 ft./sec

Location of the cup = The origin (0, 0)

Location the ball starts = (-40. -50)

Required:

To find the possible x-coordinates of Q, the point where the line L parallel to the path of the ball is tangent to the circle

The coordinates of the rightmost edge of the golf course = (30, 0)

[tex]slope,m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

the slope of the path: [tex]m=\frac{-50-0}{-40-30}[/tex]

m=-50/-70

m=5/7

The equation of a circle is (x - h)² + (y - k)² = r²

The center of the circular green, (h, k) = (0, 0)

The equation of the given circle is (x - 0)² + (y - 0)² = x² + y² = 30²

the slope of the radius at the tangent Point [tex]m_{r} =-\frac{1}{m}[/tex]

The equation of the radius at a tangent point is therefore;

[tex]y=-\frac{7}{5} .x[/tex]

Which gives the equation of the circle as follows;

[tex]x^{2} +(-\frac{7}{5} .x)^2=30^2\\\\\frac{31.x^2}{25} =30^2\\\\x=\frac{\sqrt{30^2*25} }{31} \\\\x=\frac{750}{31}*\sqrt{31}[/tex]

x=±134.70

The possible x-coordinates of point Q are -134.70 and +134.70

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Answer:

Step-by-step explanation:

=42+\frac{8}{9}\left(-\frac{1}{2}\right)

=42+\frac{8}{9}\left(-\frac{1}{2}\right)=42+\frac{8}{9}\left(-\frac{1}{2}\right)

Answer:

Step-by-step explanation:

Answer:

f(x) has a global minimum at x = 4.08628

Step-by-step explanation:

Find and classify the global extrema of the following function:

f(x) = x^4 - 4 x^3 - 9 x^2 + x - 16

Find the critical points of f(x):

Compute the critical points of x^4 - 4 x^3 - 9 x^2 + x - 16

To find all critical points, first compute f'(x):

d/(dx) (x^4 - 4 x^3 - 9 x^2 + x - 16) = 4 x^3 - 12 x^2 - 18 x + 1:

f'(x) = 4 x^3 - 12 x^2 - 18 x + 1

Solving 4 x^3 - 12 x^2 - 18 x + 1 = 0 yields x≈-1.13994 or x≈0.0536696 or x≈4.08628:

x = -1.13994, x = 0.0536696, x = 4.08628

f'(x) exists everywhere:

4 x^3 - 12 x^2 - 18 x + 1 exists everywhere

The critical points of x^4 - 4 x^3 - 9 x^2 + x - 16 occur at x = -1.13994, x = 0.0536696 and x = 4.08628:

x = -1.13994, x = 0.0536696, x = 4.08628

The domain of x^4 - 4 x^3 - 9 x^2 + x - 16 is R:

The endpoints of R are x = -∞ and ∞

Evaluate x^4 - 4 x^3 - 9 x^2 + x - 16 at x = -∞, -1.13994, 0.0536696, 4.08628 and ∞:

The open endpoints of the domain are marked in gray

x | f(x)

-∞ | ∞

-1.13994 | -21.2213

0.0536696 | -15.9729

4.08628 | -156.306

∞ | ∞

The largest value corresponds to a global maximum, and the smallest value corresponds to a global minimum:

The open endpoints of the domain are marked in gray

x | f(x) | extrema type

-∞ | ∞ | global max

-1.13994 | -21.2213 | neither

0.0536696 | -15.9729 | neither

4.08628 | -156.306 | global min

∞ | ∞ | global max

Remove the points x = -∞ and ∞ from the table

These cannot be global extrema, as the value of f(x) here is never achieved:

x | f(x) | extrema type

-1.13994 | -21.2213 | neither

0.0536696 | -15.9729 | neither

4.08628 | -156.306 | global min

f(x) = x^4 - 4 x^3 - 9 x^2 + x - 16 has one global minimum:

Answer: f(x) has a global minimum at x = 4.08628

Answer:

  65,900 mL

Step-by-step explanation:

You want to know the volume in mL of a sink with a volume of 65.9 dm³.

The relation between dm³ and mL is ...

  1 dm³ = 1000 mL . . . . . . . . . . also, 1 L (liter)

Multiplying the above relation by 65.9, we have ...

  65.9 dm³ = 65,900 mL

__

Additional comment

For many problems involving volumes in liters and dimensions in centimeters or meters, it can be convenient to convert the dimensions to decimeters (dm). Since 1 dm³ = 1 L, that can make the desired volume easily calculated.

The dot plot consists of ten dots, each representing the data value of a single person at the talk. The data values are spread out as far as possible, resulting in the largest possible standard deviation.

A dot plot is a graph that is used to represent the distribution of data. It consists of dots, each of which represents a single data value. In this case, the dot plot represents the distribution of possible data values from a talk with ten people. To achieve the largest possible standard deviation, the data points should be spread out as far as possible. Each dot should be placed on the graph in such a way that the difference between any two adjacent data points is maximized. This is done by placing the highest and lowest values at opposite ends of the graph, and then evenly spacing out the remaining data points in between. All of this should result in the largest possible standard deviation of the data set.

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Answer:

Q9:
[tex]\boxed{V = \dfrac{7}{96}\;cubic\;feet}}[/tex]

Q10

[tex]\boxed{V = \dfrac{64}{125}\;cubic\;yards}[/tex]

Step-by-step explanation:

For a rectangular prism, the volume = length x width x height

Given these 3 dimensions simply multiply them to get the volume

Q9

[tex]V = \dfrac{7}{8} \cdot \dfrac{2}{3} \cdot \dfrac{1}{8}\\\\[/tex]

[tex]V = \dfrac{7\cdot 2\cdot 1}{8\cdot 3 \cdot 8}\\\\V = \dfrac{14}{192}\\\\[/tex]

Divide numerator and denominator to reduce to lowest fraction

[tex]V = \dfrac{14 \div 2}{192\div 2}\\\\\boxed{V = \dfrac{7}{96}\;cubic\;feet}}[/tex]

Q10

This is a cube since each side is the same length

For a cube of side a, the volume = a³

So for this particular cube

[tex]V = \left(\dfrac{4}{5}\right)^3\\\\\\\boxed{V = \dfrac{64}{125}\;cubic\;yards}[/tex]

The correct answer is C. Airport S has 100 on-time flights, and Airport T has 200 on-time flights. Since 100 is one-half of 200, Airport S has one-half the number of on-time flights that Airport T has.

Given that,

The number of flights that were either on time or delayed at three separate airports on a given day is depicted in the segmented bar chart below.

Which of the following statements is the bar chart evidence for?

The options are : In comparison to the other two airports, A Airport T has the highest proportion of on-time flights.

In comparison to the other two airports, B Airport R has the lowest percentage of on-time flights.

C The proportion of on-time flights at Airport S is less than half that at Airport T.

D The proportion of on-time flights at Airport R is lower than that at Airport S.

E There are exactly as many flights at Airport T as there are at Airports R and S put together.

As the number of flights that were either on time or delayed at three different airports on one day can be exactly represented by

The correct answer is less than half as many flights arrive on time at Airport S than at Airport T.

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The Complete Question is :

Which of the following statements is the bar chart evidence for the number of flights that were either on time or delayed at three different airports on one day.?

First, we translate b and place the tail at the tip of a, being careful to draw a copy of b that has the same length and direction. then we draw the vector a+b (see the middle figure) starting at the initial point of a and ending at the terminal point of the copy of b.

Alternatively, we could place b so it starts where a start and construct a+b by the parallelogram law as in the bottom figure.

The parallelogram law says that if we place two vectors so they have the same initial point, and then complete the vectors into a parallelogram, then the sum of the vectors is the directed diagonal that initiates at the same point as the vectors.

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Answer: 272 miles

Step-by-step explanation:

The scale factor is [tex]\frac{816}{1.5}=544[/tex] inches per mile.

So, the distance from Chicago to STL is [tex]544(0.5)=272[/tex] miles.

The ratio between home fires to bush fires is 4:3.

We can determine how much of one quantity is in the other by comparing two amounts of the same units and finding the ratio. Ratios can be divided into two groups. One is the part-to-whole ratio, and the other is the part-to-part ratio. The link between two distinct entities or groupings is depicted by the part-to-part ratio.

Given the number of home fires = 8

number of bushfires = 6

ratio of home fires to bush fires = 8:6

the common factor of 8 and 6 is 2

divide both terms by 2

(8/2) : (6/2)

= 4:3

Hence the rations in the lowest terms is 4:3.

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Answer: (-1, 5)

Step-by-step explanation:   I wrote down all the explanations refer to the image please

The equation to find all x in the given matrix that are mapped into the zero vector by the transformation is ax = 0, where a is the matrix. Solving this equation yields the solutions for the x values that map to the zero vector.

In order to find all x in the given matrix that are mapped into the zero vector by the transformation, we have to solve the equation ax = 0. Here, a is the matrix we are given. This equation is a system of linear equations, and can be solved using various methods, such as Gaussian elimination, matrix inversion, or Cramer's rule. Once the equation is solved, we can obtain the solutions for the x values that map to the zero vector. For example, if we are given the matrix A = [[1, 2], [3, 4]], then the equation to solve is 1x + 2y = 0, 3x + 4y = 0. Solving this equation yields the solutions x = 2, y = -1. Therefore, the x values that are mapped into the zero vector by the transformation are (2, -1).

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