1. Use the Trapezoidal Rule b
[ ∫ f(x)dx = Tn = Δx/2 [f(x0) + 2f(x1) + 2f(x2) + 2f(x3) a
+ ... + 2f(xn-2) + 2f(xn-1) + f(xn)], Δx = (b-a)/n, xi = a + i Δx] 7
to approximate ∫ In x/x+1 dx with n = 5. 1
Round your answer to three decimal places. 2. Find an equation of the tangent line to the curve defined by x = t^3 – 5t and y = t^2 – 3t – 10 at the point (2,0).

The range of x are;

1. x < -30

2. x > 8

3. x > 15

4. x < -2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

1. -130 > 50x +20

-130-20> 50x

-150 > 50x

-150/50 > x

-30 > x

x < -30

2. -8(x-3) < -40

-8x +24< -40

collect like terms

-8x < -64

x > -64/-8

x > 8

3. 2x - 22 > 8

collect like terms

2x > 30

divide both sides by 2

x > 30/2

x > 15

4. -35 < -5(x+9)

-35 < -5x -45

collect like terms

10 < -5x

-2 > x

x < -2

learn more about inequality from

https://brainly.com/question/24372553

#SPJ1

The probability of choosing a 5 and then a 6 is 1/49

From the question, we have the following parameters that can be used in our computation:

The tiles

Where we have

Total = 7

The probability of choosing a 5 and then a 6 is

P = P(5) * P(6)

So, we have

P = 1/7 * 1/7

Evaluate

P = 1/49

Hence, the probability of choosing a 5 and then a 6 is 1/49

Read more about probability at

https://brainly.com/question/31649379

#SPJ1

Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6

Answer:

-2/5

Step-by-step explanation:

To find the slope, we use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( -5 - -3)/( 5 - 0)

   = ( -5+3)/( 5-0)

   = -2/5

Hi! I can help you with joy! :)

Answer:

\(\huge\boxed{\bold{Slope=\displaystyle-\frac{2}{5} }}\)

Hope it helps!

~Nature~

Hi there!

\(\large\boxed{f(5) = 17}}\)

f(x) = 3x + 2, find f(5):

To find f(5), we simply substitute in 5 for x:

f(5) = 3(5) + 2

f(5) = 15 + 2

f(5) = 17

Answer:

y = 6

Step-by-step explanation:

You solve by using the pythagorean theorem, which is:

\(a^{2} +b^{2} =c^{2}\)

Where a and b are legs of the triangle, and c is the hypotenuse, or y in this case. So let's rearrange this equation for c:

\(c=\sqrt{a^{2} +b^{2} }\)

Now, we can substitute in the known values and solve:

\(c=\sqrt{3.6^{2} +4.8^{2} } = \sqrt{36} = 6\)

Therefore, the value of y is 6

Hope this helps!

Answer:

the unit rate is $.87

Step-by-step explanation:

You divide $1.74 by two to get the pricing for each unit and you get $.87

Equation:

$1.74/2 = $.87

Answer:

6.93

Step-by-step explanation:

√48 = √16 × √3

√48 = 4 × √3

√48 = 4 × 1.7321

√48 = 6.9284

Rounding up to 2 decimal places;

√48 = 6.93.

Note: In Mathematics, to round a number to 2 decimal places simply means to round up to the nearest hundredths.

1 decimal place = tenths.

2 decimal places = hundredths.

3 decimal places = thousandths.

The value of the given expression 3 x 2,746 is 8,238.

We are given the expression:-

3 x 2,746

We have to find the value of the given expression using place value.

According to the data given in the question, we can write,

In 2746,

The place value of 6 is 6

The place value of 4 is 4*10 = 40

The place value of 7 is 7*100 = 700

The place value of 2 is 2*1000 = 2000

Hence, we can write,

3*2746 = 3*2000 + 3*700 + 3*40 + 3*6 = 6000 + 2100 + 120 + 18 = 8,238.

To learn more about place value, here:-

https://brainly.com/question/27734142

#SPJ1

Answer: 8.49 inches

Step-by-step explanation:

16.4-7.91=8.49 inches

This is the equation of a circle is (x - 14)² + (y - 5)² = 1 with center at (14, 5) and radius 1.

Starting with the x terms:

x² - 28x

= x² - 28x + 196 - 196

= (x - 14)² - 196

And now for the y terms:

y² - 10y

= y² - 10y + 25 - 25

= (y - 5)² - 25

Substituting these into the original equation gives:

(x - 14)² - 196 + (y - 5)² - 25 + 220 = 0

Simplifying gives:

(x - 14)² + (y - 5)² = 1

This is the equation of a circle with center at (14, 5) and radius 1.

To graph this, plot the point (14, 5) and draw a circle with radius 1 around it.

Learn more about Equation of Circle here:

https://brainly.com/question/29288238

#SPJ1

Answer:

2. 0.5. 50%

3. 0.45 45%

4. 0.5 50%

5. 0.25 25%

It is observed that the ice in Leah's glass of juice will melt first that the ice in Philip's glass of juice which sits on the table.

___________________________________

It is given that Leah and Philip both have a glass of juice with ice cubes. Leah stirs her juice with her spoon. Philip let's his sit on the table.

Now, we need to answer whose ice cubes will melt first and why;

Firstly, let us assume that the ice is at a temperature of 0°C and the surroundings of the ice are at a temperature of 20°C.

Now, for the ice to melt, it should gain some energy from it's surroundings which can be transferred to the ice from it's surroundings by conduction through metal piece or a plastic piece.

We know that, metal is a best conductor as compared to plastic which means that the above-mentioned energy will be transferred more quickly through the metal as compared to plastic.

Furthermore, in the given condition, Leah stirs her juice with her spoon which we assume is of metal, proving the above-mentioned statements true.

Therefore, it is observed that the ice in Leah's glass of juice will melt first that the ice in Philip's glass of juice which sits on the table.

To know more about this topic, click here:

https://brainly.com/question/28627239

#SPJ9

Answer:

282.5 hours

Step-by-step explanation:

14 books needs 113 hours

35 books needs x hours

x=(35×113)/14 = 3955/14 = 282.5 hours

Answer:

3 1/5

Step-by-step explanation:

k12 quiz 1.13

Comparing the new optimal profits from each option with the previous optimal profit, we can determine which option is more beneficial.

(a) Linear Programming (LP) Model:

Decision Variables:

Let x be the number of tables to produce.

Let y be the number of chairs to produce.

Objective Function:

Maximize profit: Z = 400x + 100y

Constraints:

Pine Constraint: 50x + 25y ≤ 2500

(The total amount of pine used in tables and chairs should be less than or equal to the available 2500 kg of pine each month.)

Labor Constraint: 6x + 6y ≤ 480

(The total labor hours used in producing tables and chairs should be less than or equal to the available 480 hours each month.)

Chairs-to-Tables Ratio Constraint: y ≥ 2x

(The number of chairs produced should be at least twice the number of tables produced.)

Non-negativity Constraint: x ≥ 0, y ≥ 0

(The number of tables and chairs produced cannot be negative.)

(b) Graph of Constraints and Determining Optimal Solution:

Graph of Constraints:

Let's graph the constraints on a coordinate plane. Label the axes as x (number of tables) and y (number of chairs).

Pine Constraint: 50x + 25y ≤ 2500

Rewrite as y ≤ (2500 - 50x) / 25

Plot the line y = (2500 - 50x) / 25 on the graph.

Labor Constraint: 6x + 6y ≤ 480

Rewrite as y ≤ (480 - 6x) / 6

Plot the line y = (480 - 6x) / 6 on the graph.

Chairs-to-Tables Ratio Constraint: y ≥ 2x

Plot the line y = 2x on the graph.

Non-negativity Constraint: x ≥ 0, y ≥ 0

Shade the area in the first quadrant of the graph.

Feasible Region:

The feasible region is the shaded area where all constraints are satisfied.

Determining Optimal Solution:

To maximize profit, we need to evaluate the objective function (Z = 400x + 100y) at each corner point of the feasible region and choose the point that gives the highest value of Z.

by evaluating the objective function at the corner points of the feasible region, we can determine the optimal number of tables and chairs to produce and the corresponding maximum profit.

(c) Decision on Increasing Pine Wood or Hiring an Additional Employee:

To determine whether it is better to increase the amount of pine wood shipped or hire an additional part-time employee, we need to evaluate the impact on profit.

Option 1: Increase Pine Wood to 2700 kg:

We need to calculate the new optimal profit by adjusting the pine constraint to 50x + 25y ≤ 2700 and solving the LP problem again. If the new optimal profit is higher than the previous optimal profit, this option is recommended.

Option 2: Hire an Additional Part-Time Employee (20 hours):We need to adjust the labor constraint to 6x + 6y ≤ 500 and solve the LP problem again. If the new optimal profit is higher than the previous optimal profit, this option is recommended.

By comparing the new optimal profits from each option with the previous optimal profit, we can determine which option is more beneficial.

For more such questions on optimal profits

https://brainly.com/question/29803009

#SPJ8

The solution to the system of equations is (x, y) = (-1, -1) and (x, y) = (-2, -1).

To solve the system of equations, we need to find the values of x and y that satisfy both equations.

Given:
y = -x² - 3x - 2  (Equation 1)
y = x² + 3x + 2   (Equation 2)

To solve the system, we can set the two equations equal to each other:
-x² - 3x - 2 = x² + 3x + 2

Next, we can combine like terms on both sides:
0 = 2x² + 6x + 4

Now, let's simplify the equation further by dividing all terms by 2:
0 = x² + 3x + 2

To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, we can factor it as follows:
0 = (x + 1)(x + 2)

Setting each factor equal to zero, we get two possible values for x:
x + 1 = 0  -->  x = -1
x + 2 = 0  -->  x = -2

Now, substitute these values of x back into either Equation 1 or Equation 2 to find the corresponding values of y. Let's use Equation 1:
y = -(-1)² - 3(-1) - > y = -1

Therefore, the solution to the system of equations is (x, y) = (-1, -1) and (x, y) = (-2, -1).

To know more about factor visit:

https://brainly.com/question/24182713

#SPJ11

Answer:

even I think

Step-by-step explanation:

Answer:

Neither

Step-by-step explanation:

If f (–x) = f (x), then the function is even. if f (–x) = –f (x), (all the signs are flipped) the it is odd.

To apply this to the function here, simply replace the x in \((x-2)^{2}\) with -x.

\((x-2)^{2}\) = \(x^{2}\) - 4x + 4, and \((-x - 2)^{2}\) = \(x^{2}\) +4x + 4.

Since \(x^{2}\)+4x + 4 doesnt equal \(x^{2}\) - 4x + 4 (even) or \(-x^{2}\)+4x -4 (odd), the function is neither even nor odd.

Answer:

5 degrees

Step-by-step explanation:

Triangle all angles=180

180-75=105

Both Sides are equal

105-75=30

30=4y+10

30-10=20

20/4=5

5 is the Answer

HOPE IT HELPS!

Answer:

y = 5

x = 25

Step-by-step explanation:

B and C are both base angles, so they are equal to each other;

[Equation] 75 = 3x

[Divide both sides by 3] x = 25

Then, all angles of a triangle added up together are equal to 180 degrees;

[Equation] 75 + 3x + 4y + 10 = 180

[Plug in x]  75 + 3(25) + 4y + 10 = 180 -> 75 + 75 + 4y + 10 = 180

[Subtract 160 from both sides] 4y = 20

[Divide both sides by 4] y = 5

Have a nice day!

  I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

x = 1/2 or 0.5

Step-by-step explanation:

-2x + 5 = 4

-2x = 4 -5

-2x = -1

-1(-2x = -1)

2x = 1

x = 1/2 or 0.5

The z-score is -0.428

A z-score, also known as a standard score, provides information on how far a data point is from the mean. Technically speaking, however, it's a measurement of how many standard deviations a raw score is from or above the population mean.

You can plot a z-score on a normal distribution curve.

You must be aware of the mean and population standard deviation to use a z-score.

Z-scores allow results to be compared to a "normal" population.

According to the question,

x=500

μ=533

σ=77

z-score=(x-μ)/σ

On substituting the values,

z-score=(500-533)/77

           = -0.428

Learn more about z-scores here:

https://brainly.com/question/25638875

#SPJ4

To solve the linear programming problem using the method of corners, we first graph the feasible region determined by the constraints.

The feasible region is the shaded triangle in the figure below:

scss

Copy code

           (0,42)  

             /  

            /  

   (6,0)  /______ (2,40)  

Next, we evaluate the objective function at each corner point of the feasible region:

csharp

Copy code

Corner point (0,0): P = 0 + 5(0) = 0

Corner point (0,42): P = 0 + 5(42) = 210

Corner point (2,40): P = 2 + 5(40) = 202

Corner point (6,0): P = 6 + 5(0) = 6

Thus, the maximum value of P is 210, which occurs at the corner point (0,42).

Part B:

Again, we first graph the feasible region determined by the constraints:

scss

Copy code

           (0,82)    (1,81)

             /          /  

            /          /  

   (13,0) /______ (8,0)  

The feasible region is the shaded quadrilateral in the figure above.

Next, we evaluate the objective function at each corner point of the feasible region:

csharp

Copy code

Corner point (0,0): P = 3(0) + 2(0) = 0

Corner point (0,82): P = 3(0) + 2(82) = 164

Corner point (1,81): P = 3(1) + 2(81) = 165

Corner point (8,0): P = 3(8) + 2(0) = 24

Corner point (13,0): P = 3(13) + 2(0) = 39

Thus, the maximum value of P is 165, which occurs at the corner point (1,81).

Part C:

We graph the feasible region determined by the constraints:

scss

Copy code

             (0,8)  

               /  

              /    

     (12,0) /______ (6,0)  

             /|  

            / |  

           /  |  

  (0,16) /____|(0,4)  

           2    6  

The feasible region is the shaded polygon in the figure above.

Next, we evaluate the objective function at each corner point of the feasible region:

csharp

Copy code

Corner point (0,4): P = 4(0) + 5(4) = 20

Corner point (0,8): P = 4(0) + 5(8) = 40

Corner point (2,12): P = 4(2) + 5(12) = 68

Corner point (6,0): P = 4(6) + 5(0) = 24

Thus, the maximum value of P is 68, which occurs at the corner point (2,12).

Part D:

We graph the feasible region determined by the constraints:

javascript

Copy code

              /|  

             / |  

            /  |  

           /___|____ (18,0)  

          /   /  

         /   /  

        /___/    

   (0,15)  (10,0)  

The feasible region is the shaded polygon in the figure above.

Next, we evaluate the objective function at each corner point of the feasible region:

arduino

Copy code

Corner point (0,15): C =

For more questions like linear visit the link below:

https://brainly.com/question/30379103

#SPJ11

The train will travel for approximately 50 kilometres in 1 hours.

The train travels 1 kilometre in 1 minute 20 seconds.

At this rate the number of kilometres the train will travel in 1 hour can be calculated as follows;

Therefore, lets convert 1 minutes and 20 second to hours.

20 seconds = 0.333333 minutes

Hence,

60 minutes = 1 hour

1.33333 minutes = ?

cross multiply

time in hours = 1.3333 / 60

time in hours = 0.02222221666

Therefore,

0.02 hours = 1 km

1 hours = ?

number of kilometres the train will travel in 1 hours = 1 / 0.02 = 50 km

learn more on kilometres here: https://brainly.com/question/24662933

#SPJ1

Answer:

(4, 0)

Explanation:

The difference between -5 and -1 is 4 and the difference between-3 and -3 is 0.

Answer:

6767676767678767876567890-=

Step-by-step explanation:

6787656776787678 just trying to rank up

<EOG =90° AS INDICATED IN THE DIAGRAM

<EOF+<FOG=<EOG(THEY MAKE THE ANGLE)

\(27 + 3y = 90 \\ 3y = 90 - 27 \\ 3y = 63 \\ \frac{3y}{3} = \frac{63}{3} \\ y= 21\)

<AOB =180°( STRAIGHT LINE )

<AOE+EOF+<FOG+<GOB=<AOB(THWY MAKE THE ANGLE)

\(x + 27 + 3(21) + 8x + 18 = 180\)

\(x + 27 + 63 + 8x + 18 = 180 \\ x + 8x + 27 + 63 + 18 = 180 \\ 9x - + 108 = 180 \\ 9x = 180 - 108 \\ 9x =72 \\ \frac{9x}{9} = \frac{72}{8} \\ x = 9\)

ATTACHED IS THE SOLUTION

Answer:

113.15 pounds

Step-by-step explanation:

Radha claims 43p per mile * 341 miles = 43p/mile * 341 miles = 14663p = 146.63 pounds from her employer

Next, we can calculate the amount she pays.

55 miles = 1 gallon

1 gallon/55 miles = 1 (note miles are on the bottom so it crosses out)

341 miles * 1 = 341 miles = 341 miles * 1 gallon/55 miles = 6.2 gallons

1 gallon = £5.40

£5.40/1 gallon = 1 (note gallon is on the bottom so it crosses out)

6.2 gallons * 1 = 6.2 gallons * £5.40/1 gallon = £33.48

how much more she claims than she pays = amount she claims - amount she pays = 146.63 - 33.48 = 113.15 pounds

Answer:

Use colon method

Step-by-step explanation:

So it is more easy