Apply the composite rectangle rule to compute the following integral. No need to perform the computation but guarantee that the absolute error is less than 0.2. The integral from 0 to 10 of [x*cos(x)] dx.

Step-by-step explanation:

 For a RIGHT triangle , remember  S-O-H-C-A-H-T-O-A ?

    Cos (Φ) = Adjacent leg / Hypotenuse

  so   cos D =    sqrt (78) / DF =  sqrt (78) / 28

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Principal (P) = $620

Annual percentage rate (r) = 2.5% ; compounded quarterly = 2.5% / 4 = 0.025 / 4 = 0.0063

Period = t

Expression for value of account(A) :

A = P(1 + r)^t*4

A = 620(1 + 0.0063)^4t

Hence, the annual growth percentage can be found thus :

( 1 + r)^4 - 1 ; since compounding occoyrs 4 times a year

[(1 + 0.0063)^4] - 1

1.0063^4 - 1

= 1.0254391417632961 - 1

= 0.0254

By studying the characteristics of a polygon, it can be concluded that there are 9 sides in the polygon.

A polygon is a plane figure represented by a finite number of connected straight lines (the sides), thus forming a closed polygonal chain (or polygonal circuit).

Regarding the angles, the characteristics of polygons are:

Now we take a look at the given problem. If we denote x as the exterior angle, then the interior angle is equal to 3.5x.

An exterior and interior angle are supplementary angles, so:

x + 3.5x = 180°

     4.5x = 180°

          x = 180°/4.5°

             = 40°

The sum of the exterior angles is 360°, so the number of the sides (n) can be calculated as follows:

n * 40° = 360°

        n = 360° / 40°

           = 9

Thus, the polygon has 9 sides.

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The value of g(-5) is 7.5, g(-2) is 4, and g(5) is 7.5 if the value of function g(x) = 1/2x²-5 if x≠-2 and g(x) = 4 if x = -2.

A function is a rule that associates each element in a set (called the domain) with a unique element in another set (called the range). A function takes an input from the domain and produces an output in the range.

To find the value of g(-5), substitute the value in given function

g(-5) = 1/2×(-5)² - 5

= 1/2×25 - 5

= 12.5 - 5 = 7.5

The value of g(-2) is 4 as it is defined in the question only.

To find the value of g(5), substitute the value in given function

g(5) = 1/2×(5)² - 5

= 1/2×25 - 5

= 12.5 - 5 = 7.5

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Answer:

-5

Step-by-step explanation:

Answer:

a= -5    b= 1    c= -5    d= -12

3 and 4 for the missing polynomial factored form spaces

Angles 6 and 8 are adjacent, they are Linear pair οf angles.

Linear pair οf angles are fοrmed when twο lines intersect each οther at a single pοint. The angles are said tο be linear if they are adjacent tο each οther after the intersectiοn οf the twο lines. The sum οf angles οf a linear pair is always equal tο 180°. Such angles are alsο knοwn as supplementary angles.

Angles 1 and 4 are not adjacent, they are vertically opposite.

Angles 5 and 8 are not adjacent, they are vertically opposite.

Angles 6 and 8 are adjacent, they are Linear pair οf angles

Angles 1 and 5 are corresponding exterior angle, so the are not linear pair.

Thus, Angles 6 and 8 are adjacent, they are Linear pair οf angles

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One of three different floors each day during a 4-day work week in 12 different ways, can be assigned to the nursing student.

To find the number of ways a nursing student can be assigned to one of three different floors each day during a 4-day work week, we need to use the multiplication principle of counting.

First, we need to determine the number of options the nursing student has for each day. Since she can be assigned to one of three different floors, she has 3 options each day.

To find the total number of ways she can be assigned over the 4-day work week, we multiply the number of options she has for each day by the number of days in the week:

3 options per day x 4 days = 12 total ways

Therefore, the nursing student can be assigned to one of three different floors each day during a 4-day work week in 12 different ways.

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Particle moves with its position given by x= cos(2t) and y= sin (t), where positions are given in feet from the origin and time t is in seconds. The speed of the particle at any time t is v = \(\sqrt\)(4sin²(2t) + cos²(t)).

For the speed of the particle, we can calculate the magnitude of its velocity vector.

The velocity vector can be obtained by differentiating the position vector with respect to time.

We have the position of the particle as x = cos(2t) and y = sin(t), we can differentiate these equations to find the corresponding velocity components:

vx = dx/dt = -2sin(2t)

vy = dy/dt = cos(t)

The magnitude of the velocity vector (v) is given by the square root of the sum of the squares of its components:

\(\sqrt\)(vx² + vy²) = \(\sqrt\)((-2sin(2t))² + (cos(t))²)

Simplifying this expression:

v = \(\sqrt\)(4sin²(2t) + cos²(t))

This is the speed of the particle at any given time t.

Note that the speed is not constant but varies with time due to the periodic nature of the sine and cosine functions.

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Answer: -2

your welcome :)

Answer:

1/6

Step-by-step explanation:

the form you're using is slope-intercept. That is

y=mx+b

where y= y coordinate

m=slope

x= x coordinate

and b= y intercept

so, m in that equation is 1/6, so the slope is 1/6

Hope this helps!

On closely observing and solving the Probability it can be stated that  the batter will hit around 3 balls out of the next nine balls

What is Probability?

The ratio of the number of outcomes in an exhaustive collection of equally probable options that create a particular event to the entire number of conceivable outcomes.

Solution:

Average of Batter is 0.303 which means that the batter hits 303 shots of 1000 balls

So, in the next nine balls he will hit 9 * 303/1000 = 2.7 balls

Which means the batter will hit around 3 balls

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Answer:

$24750

Step-by-step explanation:

Given data

Principal= $45000

Time=5 years

Rate= 11%

Let us apply the simple interest expression

SI= PRT/100

substitute

SI= 45000*11*5/100

SI= 2475000/100

SI= $24750

Hence, Craig would have paid $24750

Answer:

98 or 105

Step-by-step explanation:

The compound inequality to describe the elevation of Ted's house is 135 > x > 128.

A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now it is given that,

Sakura's house is at an elevation between 113 m and 120 m above sea level.

Let x be the elevation of Sakura's house.

So, 120 > x > 113

Now Ted lives about 15 m below her

Ted's  house elevation = x - 15

So, The compound inequality to describe the elevation of Ted's house,

120 > x - 15 > 113

Adding 15 to the inequality we get,

120 + 15 > x - 15 + 15 > 113 + 15

Solving we get,

135 > x > 128

which is the required compound inequality.

Thus, the compound inequality to describe the elevation of Ted's house is 135 > x > 128.

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Answer:

2 Tetrahedrons combined create an Octahedron.

Step-by-step explanation:

Despite the lack of information.

The Plato Polyhedrons are Tetahedron, Cube (Hexaedron), Dodecahedron, Octahedron and Icosahedron. They are regular ones, made up by regular plane figures.

An Octahedron can be built by combining two pyramids. Each Tetrahedron is made up by 4 equilateral triangle.

The positive value of x that satisfies the equation x = 3.7cos(x) can be found using numerical methods such as the Newton-Raphson method. The approximate value of x to six decimal places is x ≈ 2.258819.

To solve the equation x = 3.7cos(x), we can rewrite it as a root-finding problem by subtracting the cosine term from both sides: x - 3.7cos(x) = 0. The objective is to find the value of x for which this equation equals zero.

Using the Newton-Raphson method, we start with an initial guess for x and iterate using the formula xᵢ₊₁ = xᵢ - f(xᵢ)/f'(xᵢ), where f(x) = x - 3.7cos(x) and f'(x) is the derivative of f(x) with respect to x.

By performing successive iterations, we converge to the value of x where f(x) approaches zero. In this case, starting with an initial guess of x₀ = 2.25, the approximate value of x to six decimal places is x ≈ 2.258819.

It's important to note that trigonometric functions are typically evaluated in radian mode, so the value of x in the equation x = 3.7cos(x) is also expected to be in radians.

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Angie can jog at a speed of x miles per hour, and Payton can jog at a speed of (x - 2) miles per hour.

Let's assume that Angie's jogging speed is x miles per hour. Since Angie can jog x miles per hour faster than Payton, Payton's jogging speed would be (x - 2) miles per hour.

When two people start at the same point and jog in opposite directions, the distance between them increases at a combined rate of their individual speeds. So, after t hours, the distance between Angie and Payton would be given by the equation:

Distance = Angie's speed * t + Payton's speed * t

Given that the distance between them after t hours is 9 miles, we can substitute the values into the equation:

9 = x * t + (x - 2) * t

Simplifying the equation:

9 = xt + xt - 2t

Combining like terms:

9 = 2xt - 2t

2xt - 2t = 9

Factoring out the common term of 2t:

2t(x - 1) = 9

Dividing both sides by 2(x - 1):

\(t = \frac{9}{(2(x - 1))}\)

Therefore, the speed at which Angie can jog is x miles per hour, and the speed at which Payton can jog is (x - 2) miles per hour.

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Answer:

By conducting 30 trials instead of 15, they would improve the accuracy of their simulation, therefore, Elena is correct

Step-by-step explanation:

The parameters given are;

Jada and Elena are trying to estimate the probability that 1 in 4 students selected has asthma where the asthma prevalence rate = 8%

The experiment uses 25 slips to represent 25 students and they labelled 2 of the strips as asthma to indicate the expected number of asthma in 25 students which is 2/25 = 0.08. That is the number of asthma in 25 students is 8% of 25 = 0.08 × 25 = 2

From the 25 slips, they randomly select groups of 4 which represent the team of four students to see if any of the 4 slips is one of the two slips labelled as asthma slips

Therefore, to improve the accuracy of the estimate of the probability they should increase the number of trials from 15 to 30, hence Elena is correct.

Answer:

Y=136

Step-by-step explanation:

Answer:

h(-8)=-8

Step-by-step explanation:

Since we are finding h(-8), we plug -8 into the equation:

h(-8)=((-8)²+3(-8))/(4(-8)+27)

h(-8)=(64-24)/(-32+27)

h(-8)=40/-5

h(-8)=-8

Therefore, h(-8)=-8, which means your answer is correct!

The translated vertices, substitute the values into the area formula:
  Area = \(1/2 * |0(y2 - y3) + (x2 - x1)(y3 - y1) + (x3 - x1)(y1 - y2)|\)

To find the area of triangle R, we can use the formula:

Area =\(1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|\)

Here's how you can apply the hint and solve the problem step-by-step:

1. Translate triangle R to the origin by subtracting one of the vertices. Let's say we subtract vertex 1 (x1, y1) from the other vertices:
  - Vertex 2 becomes (x2 - x1, y2 - y1)
  - Vertex 3 becomes (x3 - x1, y3 - y1)

2. Now we have a new triangle with vertices (0, 0), (x2 - x1, y2 - y1), and \((x3 - x1, y3 - y1).\)
3. Using

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The problem involves proving that the area of a triangle with arbitrary vertices can be calculated using a determinant of a matrix. After placing the vertices coordinates into a 3x3 matrix, we find that the area is half the absolute value of the determinant of this matrix.

The question is asking to prove that the area of a triangle with vertices at (.x1; y1/), (.x2; y2/), and (.x3; y3/) can be calculated using the determinant of a matrix. The first step in the proof is to arrange the coordinates of the vertices into a 3x3 matrix.

The determinant of this matrix will give 2 times the area of the triangle formed by these vertices. The next step is to calculate the determinant of this matrix. This can be done by expanding along a row or a column and making use of the property det(A) = -det(A^transpose).

Doing the calculations, we get that the area of the triangle is half the absolute value of the determinant of the matrix, which confirms the statement.

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Answer:

x=3

Step-by-step explanation:

To solve for x, get x alone on one side of the equation.

First, add 3 to both sides.

3 = 1/3x^2

Multiply each side by 3

x^2 = 9

Take the square root of both sides

x = + or - 3

You want the positive solution, so x = 3

Complete question :

Miranda is braiding her hair then she will attach beads to the braids she wants 1/3 of the beads to be red if the greatest number of beads that will fit on the braid is 12 what other fraction could represent the part of the beads that are red?

Answer:

2 / 6

Step-by-step explanation:

Fraction of red beads on braid = 1/3

greatest number of braids = 12

Fraction of red beads = (1 /3) * 12 = 4 red beads

Thus implies that :

When greatest number of braids = 12

fraction of red beads) = (Number of red beads / greatest number of beads)

Fraction = 4 / 12

Divide by 2 = 2/6 (don't reduce to lowest term).

h(x) = -7/6x - 25/6.

Given h(-1)=-2 and h(-7)=-9

For linear function h(x), we can use slope-intercept form which is y = mx + b, where m is the slope and b is the y-intercept.

To find m, we can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

h(-1) = -2 is a point on the line, so we can write it as (-1, -2).

h(-7) = -9 is another point on the line, so we can write it as (-7, -9).

Now we can find m using these points: m = (-9 - (-2)) / (-7 - (-1)) = (-9 + 2) / (-7 + 1) = -7/6

Now we can find b using one of the points and m. Let's use (-1, -2):

y = mx + b-2 = (-7/6)(-1) + b-2 = 7/6 + b

b = -25/6

Therefore, the linear function h(x) is:h(x) = -7/6x - 25/6

We can check our answer by plugging in the two given points:

h(-1) = (-7/6)(-1) - 25/6 = -2h(-7) = (-7/6)(-7) - 25/6 = -9

The answer is h(x) = -7/6x - 25/6.

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Answer:

x=5

Step-by-step explanation:

Here we are given with a graph.

we have been asked to find the value of x for which

As we know that , to find the value of x for the given value of f(x), we need to look onto the vertical axis, and mark a dot on the given value now draw a line perpendicular to vertical axis so that it cut the given straight line, and where they intersect draw another line perpendicular to the horizontal axis and you will get the value where it crosses the horizontal axis.

Hence we get x=5, then f(x)=7.

Answer:

37.95

Step-by-step explanation:

3.3x2.5x4.6=37.95

Answer: -24

Step-by-step explanation:

This means solve for y when x=0

Plug in 0 for x

y= -2(3)(-2)²

 = -24

The profit of the owner is $2204, if her payment is twice the sum of the

other employees' weekly wages.

A wage is the payment made to employees for the time they put in working for their employer. Always based on a specific period of time, wages are paid. On an hourly basis, typically. This is the origin of the phrase hourly worker. Salary and commissions are some additional types of payment.

Pay for lower level employees is determined by the number of hours worked. To record the number of hours worked each week, these employees typically use a time sheet or time card. To keep track of hourly employee hours, the majority of modern employers use computerised systems.

To enter their hours worked, employees must log in and out of the system. These workers are then paid either weekly or biweekly, depending on the state.

Given that the owner pays herself twice the sum of the other employees' weekly wages.

Sum wage of the employees =  $157.50 + $189.00 + $220.50+ $252.00+ $283.50

= $1102.5

She pays herself twice the sum

2 × $1102

= $2204

Thus, the profit of the owner is $2204.

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The material remained for the blanket after trimming off by Keith is 2.5 yards.

Simple subtraction and multiplication can provide the result. Beginning will be by the multiplication. Firstly finding the exact amount of material trimmed = 3×1/6

Performing multiplication and division on Right Hand Side of the equation

Trimmed material = 1/2 or 0.5

Now, we need to subtract the trimmed material from overall amount of material

Remaining material = 3 - 0.5

Performing subtraction on Right Hand Side of the equation

Remaining material = 2.5 yards

Hence, 2.5 yards of material remained.

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The independent variable of interest in an ANOVA procedure is called a factor. Hence (d).

The independent variable of interest in an ANOVA procedure is referred to as the factor. The factor represents the different categories or levels being compared to assess their impact on a dependent variable. It is the variable that is manipulated or controlled by the researcher to determine its effect on the outcome. In the context of ANOVA, the factor is typically a categorical variable that divides the data into distinct groups or treatments. These groups are compared to evaluate if there are statistically significant differences in the means of the dependent variable across the different levels of the factor. Therefore, the correct answer is factor(d).

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