What is the 40th term of the arithmetic sequence?

21,18,15,12,9....

A: -99
B: -96
C: 6
D: 138

The perimeter of the rectangle is 35.0 meters, and the area is 66.0 square meters, using the formulas for perimeter (2(length + width)) and area (length × width).

To calculate the perimeter and area of a rectangle, we apply the formulas: Perimeter = 2(length + width) and Area = length × width. In this case, the rectangle has a length of 5.50 m and a width of 12.0 m.

Calculating the Perimeter

Perimeter = 2(5.50 m + 12.0 m) = 2(17.5 m) = 35.0 m

Calculating the Area

Area = 5.50 m × 12.0 m = 66.0 m²

The perimeter of this rectangle is 35.0 meters, and the area is 66.0 square meters.

Answer:

1gm/ cm^3

Step-by-step explanation:

Answer:

The complete factored form of given polynomial  [tex]21x^3+35x^2+9x+15[/tex] is [tex](7x^2+3)(3x+5)[/tex]

Step-by-step explanation:

Given polynomial  [tex]21x^3+35x^2+9x+15[/tex]

We have to factorize the given polynomial completely.

Consider the given polynomial  [tex]21x^3+35x^2+9x+15[/tex]

We will solve it by grouping of terms,

Grouping is collecting terms having some factors common

Taking [tex]7x^2[/tex] common from first two term and 3 from last two terms , we have,

[tex]21x^3+35x^2+9x+15[/tex]

[tex]\Rightarrow 7x^2(3x+5)+3(3x+5)[/tex]

Now taking (3x +5) common from both terms , we have,

[tex]\Rightarrow (7x^2+3)(3x+5)[/tex]

Thus, the complete factored form of given polynomial  [tex]21x^3+35x^2+9x+15[/tex] is [tex](7x^2+3)(3x+5)[/tex]

The converse of the statement “If an angle is a right angle, then it measures 90 degrees” is “If an angle measures 90 degrees, then it is a right angle.”

The converse of the statement “If an angle is a right angle, then it measures 90 degrees” is “If an angle measures 90 degrees, then it is a right angle.” The converse of a conditional statement swaps the hypothesis and conclusion of the original statement. In this case, the original statement states that if an angle is a right angle (hypothesis), then it measures 90 degrees (conclusion). The converse states that if an angle measures 90 degrees (hypothesis), then it is a right angle (conclusion).

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Answer:

1 = b

Step-by-step explanation:

6.8 - 4.2b = 5.6b - 3

First you must add 4.2b to both sides.

Then you will get 6.8 = 9.8b - 3.

Next you must add 3 to both sides.

You will then get 9.8 = 9.8b

Finally divide both sides by 9.8.

You will be left with  1 = b

To find the cost of production for 170 units, consider both fixed costs and variable costs (the integral of the marginal cost function). The cost of producing 171 units can be estimated by adding the marginal cost for the additional unit.

The quantity of interest is C(170), the total cost to produce 170 units. To estimate this value, you can calculate the fixed costs plus the integral of the marginal cost from 1 to 170 (the number of items produced).

So, first, calculate the fixed costs which is given as $13000.

Next, estimate the total variable costs, which is the integral of the marginal cost function over the range from 1 to 170 units. Given marginal cost function is C'(q) = 0.006q^2-q+50. Use the power rule to integrate the function, then evaluate it at q=1 and q=170 and subtract.

The value of C'(170) is simply the value of the marginal cost function at q=170.

After finding the value of C(170) and C'(170), the total cost to produce 171 units, C(171), is approximately the total cost to produce 170 units plus the marginal cost to produce the 171st unit.

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The quadratic equation 3x^2+6x+7=0 has two complex solutions which is x=-1±√(48)i/6.

To solve the quadratic equation 3x^2+6x+7=0 using the quadratic formula, we first need to identify the coefficients a, b, and c from its standard form, which is ax^2+bx+c=0. In this case, a=3, b=6, and c=7.

The quadratic formula is given by x=(-b±√(b^2-4ac))/(2a).

Now, we will calculate the discriminant which is b^2-4ac. In this case, it is 6^2 - 4*3*7, which equals 36 - 84, or -48. Since the discriminant is negative, this means that there are no real solutions to the equation, but two complex solutions.

Applying the quadratic formula, we get the solutions:

x=(-6 ± √(-48))/(2*3)

This simplifies to:

x=(-6 ± √(48)i)/6

Therefore, the solutions are x=-1±√(48)i/6. The quadratic formula helped us to find the complex roots of the quadratic equation.

The angle represents by 3.5 rotations in counterclockwise is 1260 degree or [tex]\frac{7}{2}\pi[/tex] radian.

In one complete rotation, the angle made is = 360 degree or [tex]\pi[/tex] radian

So, In 3.5 rotation, angle made is, = [tex]360*3.5=1260[/tex] degree

       Or,                                                   =  [tex]3.5*\pi=\frac{7}{2}\pi[/tex] radian

Therefore, The angle represents by 3.5 rotations in counterclockwise is 1260 degree or  [tex]\frac{7}{2}\pi[/tex] radian.

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Calculating the total difference between what Bob and Tyree will pay over five years for borrowing $10,000 each involves simple interest calculation. Bob, with an 11.5% interest rate, pays $1,750 more than Tyree, who has an 8.0% interest rate. This demonstrates how credit scores affect loan costs.

The question involves calculating the total difference between what two consumers, Bob and Tyree, will pay for borrowing $10,000 each over five years, given their respective interest rates based on their credit scores.

First, to solve this, we'll use the simple interest formula I = PRT, where I is the interest, P is the principal amount (the initial amount borrowed), R is the annual interest rate, and T is the time in years.

The total difference between what Bob and Tyree pay is $5,750 - $4,000 = $1,750. Therefore, Bob will pay $1,750 more than Tyree over the five years due to his lower credit score and higher interest rate.

Observe the figure below.

The given figure shows that the construction of line segment OS. We can observe clearly that OS is bisector of angle POS.

The bisector divides the angle into two equal angles.

So, [tex]\angle POS = \frac{1}{2} \angle POQ[/tex]

Let us observe the given options.

In first option, [tex]60^\circ = \frac{1}{2} \times 120^\circ[/tex]

Therefore, [tex]m \angle POS = 60^\circ, m \angle POQ=120^\circ[/tex]

So, Option A is the correct answer.

Answer:

[tex]\int {t\times \sec^2(2t)} \, dt \\\\ \text{Integrating by parts}\\\\=\frac{t\times \tan 2t}{2}-\int{(\frac{d}{dt}(t) \times \int{{\ sec^{2}(2t)}}) dt}\\\\=\frac{t\times \tan 2t}{2}-\int{\frac{\tan 2t}{2}} dt\\\\=\frac{t\times \tan 2t}{2}-\frac{\log sec 2t}{4}+C[/tex]

Where C is Constant of Proportionality.

Answer:

Songs cost the same at both stores.

Step-by-step explanation:

Answer:

112

Step-by-step explanation:

then d= 44/3.14 

r= 22/3.14

Answer:  The required value of x is -52.

Step-by-step explanation:  We are given to find the value of x from the following equation :

[tex]x+58=6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the value of x, we need to solve the equation (i).

The solution of equation (i) is as follows :

[tex]x+58=6\\\\\Rightarrow x=6-58\\\\\Rightarrow x=-52.[/tex]

Thus, the required value of x is -52.

The total is: $ 1345.5

It is given that:

I would like to purchase 20 products at a cost 65.00 per product.

This means that the cost of 20 products will be:

[tex]20\times 65=\$\ 1300[/tex]

Also, there is a sales tax of 3.5%

This means that a person has to pay a extra 3.5% on the total cost of the items he purchased.

i.e. he need to pay 3/5% on $ 1300

This means that the amount of tax he need to pay is: 3.5% of 1300

                                                                              =  3.5%×1300

                                                                             = 0.035×1300

                                                                            = $ 45.5.

Hence, the total cost is: $ 1300+$ 45.5

This means that the total cost is: $ 1345.5

Answer: if 3 for every 1000 students quit due serious health issues, then you can see the proportion doing the quotient between this numbers. This is:

3/1000 = 0.003

Then if you choose a random student, you have a 0.003 probability of choosing one who can have a health issue.

and a 0.997 probability to choose a student with no health issues.

Now, the company wins  $50 for the healthy students, and lose ($50 - $8000)  = -$7950 for each student that is sick (because they initially pay the 50$ and latter get the $8000).

Then the insurance company should expect to make in average:

0.997*$50 - 0.003*($7950) = $26

So the company should expect to make 26 dollars per student in a year.

Line QR bisects angle PQS. Solve for x and find measure PQS:
m<PQS = 4x - 6, m<PQR = x + 11 ...?

 m<PQR  = (1/2) (m<PQS) = (1/2)( 4x - 6)

    so  x + 11 = 2x - 3 implies x =14

and then m<PQS = 4x - 6 =50°

The total distance Joel walked is 3/4 of a mile.

To find the total distance, we add up the individual distances:

To add these fractions, they must have a common denominator. The least common denominator for 5, 10, and 20 is 20. So we convert the fractions:

Now we add the fractions:

8/20 + 6/20 + 1/20 = 15/20

Finally, we can simplify 15/20 by dividing both the numerator and the denominator by 5:

15/20 = 3/4

Therefore, the total distance Joel walked is 3/4 of a mile.