What is the 101st term in the sequence 997, 989, 981, ...?

197

189

1805

1797

Answer:

E. Converges by limit comparison test.

Step-by-step explanation:

Here is something that might help you on this

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This question involves the application of different series convergence tests in calculus. The first correct reasons why the given series converged were identified using the comparison to a convergent p-series, integral test, and the alternating series test.

This question relates to the convergence of series in calculus. In order to determine why a given series converges, we need to apply various convergence tests. Here are the first correct reasons why the provided series converge:

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Answer:

a. 5218 hot dogs

b. 18 runs per year

c. 1 day per run

Step-by-step explanation:

(a) Let n represent the number of hotdogs in an optimal run. The number of runs needed in a year is ...

r = (260 hotdogs/day)·(365 days/year)/(n hotdogs/run) = 94900/n runs/year

The number of hotdogs in storage decreases from n at the end of a run to 0 just before a run. The decrease is linear, so the average number in storage is n/2.

We can go to the trouble to write the equation for total cost, then differentiate it to find the value of n at the minimum, or we can just jump to the solution. That solution is ...

holding cost = setup cost

(n/2)·0.46 = (94900/n)·66

n^2 = 94900·66·2/0.46 = 27,232,173.9

n ≈ 5218.446

The optimal number of hotdogs in a run is 5218.

___

(b) The number of runs needed per year is (from part (a)) ...

r = 94900/5218 ≈ 18.187

The number of runs per year is 18.

___

(c) The run lenght is 5218 hotdogs, and the run produces them at the rate of 5500 hotdogs/day, so the run length in days is ...

(5218 hotdogs)/(5500 hotdogs/day) = 0.9487 days

The run length is 1 day.

Answer: 4/8

Step-by-step explanation:

Equation: 1/8+x=5/18

                 -1/8     -1/8

                      x=4/8

Double Check: 4/8+1/8=5/8

Answer:

The asnwers for your two question problem are

1. $625

2. 90 building blocks

Step-by-step explanation:

First problem

The fabric Josef is using comes in 100 square-inch pieces that cost $6.25 each. What will his fabric cost?

* The fabric has 100 pieces

* Each piece costs $6.25

Total amount for the fabric  = $6.25*100 = $625

Second problem

A student made a toy chest for his baby sister's square building blocks. Six layers of blocks can fit in the box, and each layer has 15 blocks. How many building blocks can the toy chest hold?

* 6  layers of blocks fit in the box

* Each layer has 15 blocks

Total amount of blocks = 6*15 blocks  = 90 blocks

y = 120 + 75x

y is total charge

75x where 75 is monthly charge and x is number of months

120 is installation charges.

Dish television charges modeled by the equation represents,

Linear equation is the equation in which the highest power of the unknown variable is one. Linear equation are used to model the real life problem in the mathematical expressions.

The linear equation with dependent variable y and independent variable x can be written as,

[tex]y=mx+c[/tex]

Here,  [tex]m[/tex] is the slope of the equation and [tex]c[/tex] is the y intercept.

Given information-

The total cost is modeled by the equation

[tex]y=120+75x[/tex]

In the above equation the, variable y is dependent variable and the variable x is independent variable. The constant term 120 is fixed.

Hence,

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Answer:

The function has no undefined points nor domain constraints, therefore the Domain is (-∞ < x < ∞). Since your answers don't match the real results, the interval notation is (-∞,∞)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h. k) are the coordinates of the centre and r is the radius

here (h, k) = (- 1, 10) and r = 2, thus

(x - (- 1))² + (y - 10)² = 2², that is

(x + 1)² + (y - 10)² = 4 → C

Trigonometry

[tex]Sin\frac{Opposite}{Hypotenuse} Cos\frac{Adjacent}{Hypotenuse} Tan\frac{Adjacent}{Opposite}[/tex]

[tex]S\frac{O}{H} C\frac{A}{H} T\frac{A}{O}[/tex]

You know the hypotenuse and you want to find the opposite therefore you use, sine.

[tex]Opposite = Sin(70) *{20}[/tex]

Opposite = 18.79385242

Answer:

The answer is ellipse of equation 4x² + 5y² - 40x + 60y + 260 = 0 ⇒ answer (b)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

* 4x² + 5y² = 20

∵ A = 4 , B = 0 , C = 5

∴ B² - 4 AC = (0)² - 4(4)(5) = -80

∴ B² - 4AC < 0

∴ The graph is ellipse or circle

* If A and C are nonzero, have the same sign, and are not

 equal to each other, then the graph is an ellipse.

* If A and C are equal and nonzero and have the same

 sign, then the graph is a circle.

∵ A and C have same signs with different values

∴ It is an ellipse

* Now lets study T(5 , -6), that means the graph will translate

 5 units to the right and 6 units down

∴ x will be (x - 5) and y will be (y - -6) = (y + 6)

* Lets substitute the x by ( x - 5) and y by (y + 6) in the equation

∴ 4(x - 5)² + 5(y + 6)² = 20

* Use the foil method

∴ 4(x² - 10x + 25) + 5(y² + 12y + 36) = 20

* Open the brackets

∴ 4x² - 40x + 100 + 5y² + 60y + 180 = 20

* Collect the like terms

∴ 4x² + 5y² - 40x + 60y + 280 = 20

∴ 4x² + 5y² - 40x + 60y + 280 - 20 = 0

∴ 4x² + 5y² - 40x + 60y + 260 = 0

* The answer is ellipse of equation 4x² + 5y² - 40x + 60y + 260 = 0

Answer:

BBBBBB

Step-by-step explanation:

BBBBB

Answer:

[tex]\frac{4\sqrt{3} }{3}[/tex]

Step-by-step explanation:

4sqrt3/3

Answer: it is a

Step-by-step explanation:

It is a because if you add them all together you will see that be is less so you can cross does out so you are left with a or c. C is not the correct ans because none of the kids had a forearm less than 9. And all seven of the kids had a forearm more than 10 inches.

Answer:

Step-by-step explanation:

If N is midpoint between Q and R, then use the formula of a midpoint:

[tex]\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]

We have the points Q(0, 2b) and R(2c, 0). Substitute:

[tex]x=\dfrac{0+2c}{2}=\dfrac{2c}{2}=c\\\\y=\dfrac{2b+0}{2}=\dfrac{2b}{2}=b[/tex]

The answer is 2.58

See attached picture of graph with the solution:

The approximate zeros of the function f(x)=-2x^3+5x^2+1, to the nearest tenth, are x ≈ 0.2, x ≈ -2.58, and x ≈ 1.7.

To find the zeros of the function f(x)=−2x3+5x2+1, one uses a graphing calculator or similar piece of technology. After entering this function and graphing it, you locate the points where the curve intersects the x-axis. These points are the function's zeros or roots, as the function equals zero at these x-values.

For the function given, the zeros are approximately x ≈ 0.2, x ≈ -2.58, and x ≈ 1.7 when rounded to the nearest tenth. These values represent the x-coordinates of the points where the graph of the function intersects the x-axis.

Please note that because we're rounding to the nearest tenth, the actual zero could slightly differ.

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Answer:

(1,0)

Step-by-step explanation:

The given logarithmic function is

[tex]y=\log_ax[/tex]

When [tex]x=1[/tex], the logarithmic function becomes;

[tex]y=\log_a1[/tex]

[tex]\Rightarrow y=\log_aa^0[/tex]

[tex]\Rightarrow y=0(\log_aa)[/tex]

[tex]\Rightarrow y=0(1)[/tex]

[tex]\Rightarrow y=0[/tex]

Therefore the graph always passes through;

[tex](1,0)[/tex]

Answer:

option D

(1,0)

Step-by-step explanation:

Given in the question an expression

y = [tex]log_{a}x[/tex]

This function's graph will always pass through x-axis where y will always be 0

 y = [tex]log_{a}x[/tex]

 0 =  [tex]log_{a}x[/tex]

This situation is only possible when x = 1

0 = [tex]log_{a}1[/tex]

Secondly, x can never be zero

As,

[tex]y = log_{a}0[/tex] is undefined

so this eliminate option (A) and (C)

Negative 6 and negative 9 would :)

Polynomials are mathematical expressions involving variables raised with non-negative integers, coefficients and constants. The value of the solution that will make the polynomial equal to zero is -6 and -9.

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

The values of x that would make a polynomial equal to zero if the factors of the polynomial are (x+6) and (x+9) are -6 and -9.

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Answer:

Not enough info.

Step-by-step explanation:

Not enough information, how big is the fence perimeter wise? What is the shape of the fence? If the fence is square and 2,000 feet long, of course there's room. If its a square fence that's 2 feet long, there is no room at all.

Answer: A. The data is skewed left and shows that on half of the days, Darren received 11 or 12 e-mails from the customer.

Step-by-step explanation: Most of the Data is on the right so it is skewed left, and most of the emails are on 11 and 12 so that is why A is correct.

The little rectangle in the top right means the angle is a right angle which equals 90 degrees.

This also means all the other angles are also 90 degrees.

Solve for x:

2x+8 = 90

Subtract 8 from both sides:

2x = 82

Divide both sides by 2:

x = 82/2

x = 41

Answer:

x = 41

Step-by-step explanation:

Since they are vertical angles, 90 = 2x + 8.

Then isolate the variable by subtracting 8 from both sides.

So 2x = 82.

Then divide each side by 2 to get x = 41.

Answer:

(32/15, -2/5)

Step-by-step explanation:

(1) ³/₂x   -    2y =  4

(2)   x  +    ⅓y =  2

(3)  3x   -     4y =  8              Multiplied (1) by 2

(4)  3x  +       y =  6              Multiplied (2) by 3

                  5y = -2              Subtracted (3) from (4)

(5)                 y = -⅖             Divided each side by 5

       x + ⅓(-⅖) =  2              Substituted (5) into (2)

       x  -  ²/₁₅    =  2

       x              =  2 + ²/₁₅     Added ²/₁₅ to each side

      x              = 32/15

The system of equations has only one solution: (32/15, -2/5).

Answer:

Step-by-step explanation:

#1.

228 ÷ 6 = 38 in

#2.

186 ÷ 3 = 62 ft

#3.

360 ÷ 8 = 45 yd

#4.

119 ÷ 7 = 17 ft

I hope I helped you.

Answer:

Perimeter is the total outside dimension.

To find the length of one side, divide the total perimeter by the number of sides.

1. 228 / 6 = 38 inches.

2. 186 / 3 = 62 feet.

3. 360 / 8 = 45 yards

4. 119 / 7 = 17 feet.

Answer:

Confidence interval:  11.5 < µ < 30.9

Read below to see conclusion:

Step-by-step explanation:

n = 13, x = 79.4, s = 21.2, Z = 1.645 (z score for a confidence interval with 90% confidence)

Use the formula to find the error:  E = Z(s/√n)

We have: E = 1.645(21.2/√13) = 9.7

Now construct the confidence interval:

x - E < µ < x + E

21.2 - 9.7 < µ < 21.2 + 9.7

11.5 < µ < 30.9

Yes, the drug appears to be effective because the estimated wake time for a population using this drug will be between 11.5 and 30.9 minutes.   The upper end of this interval is much lower than 102, so it appears as though the drug is effective.

Answer:

Step-by-step explanation:

see attached

The quadratic function has zeros at x = -2, x = 0 (with multiplicity 2), x = 2, and x = 6. The zeros include simple roots and a double root, determined by the graph's behavior at the x-intercepts.

To determine the type of zeros for a quadratic function based on its graph, we need to consider the behavior of the parabola at the x-intercepts (zeros). The given points where the graph intersects the x-axis are (-2, 0), (0, 0), (2, 0), and (6, 0).

1. **Multiplicity of Zeros:**

  - For the point (0, 0), the zero has multiplicity 2 since the graph touches the x-axis but doesn't cross it.

  - For the points (-2, 0), (2, 0), and (6, 0), the zeros have multiplicity 1 since the graph crosses the x-axis at these points.

2. **Type of Zeros:**

  - For the zero at x = 0 (multiplicity 2), it is a double root or a repeated zero.

  - For the zeros at x = -2, x = 2, and x = 6 (multiplicity 1), they are simple roots.

3. **Discriminant:**

  - The discriminant of a quadratic equation \(ax^2 + bx + c = 0\) is given by \(b^2 - 4ac\).

  - If the discriminant is positive, the quadratic equation has two distinct real roots (simple roots).

  - If the discriminant is zero, the quadratic equation has one real root with multiplicity 2 (double root).

  - If the discriminant is negative, the quadratic equation has two complex conjugate roots.

In this case, the fact that the parabola touches the x-axis at (0, 0) without crossing it indicates a double root at x = 0. The other zeros at (-2, 0), (2, 0), and (6, 0) are simple roots.

Therefore, the type of zeros for the given quadratic function is a mix of simple roots and a double root.

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Answer:150

Step-by-step explanation:75 on 100 multiply by 400 u will get 300.then 50 on 100 multiply 300 .your answer is 150.check???

Answer:

150.

Step-by-step explanation:

The answer is 150 to this question

Answer:

The approximate height of the paint can is 8.2 in

Step-by-step explanation:

we know that

The volume of the cylinder ( can of paint) is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]V=231\ in^{3}[/tex]

[tex]r=3\ in[/tex]

[tex]\pi=3.14[/tex]

Substitute the values and solve for h

231=(3.14)(3)^{2} h

h=231/(3.14*9)=8.2 in

Answer is :    

      8

For IM..

Answer:

x + y = z

y=5

z=10

x = z - y =10-5 =5

Step-by-step explanation:

Answer:

1. B (obtuse)

2. Obtuse

3. 20.92

Step-by-step explanation:

1.

We need to use the converse of the pythagorean theorem to solve this problem. Given that c is the longest side of a triangle, and a and b are the other two sides. The triangle is right triangle if  [tex]c^2=a^2 +b^2[/tex]

The triangle is acute triangle if  [tex]c^2 < a^2 + b^2[/tex]

The triangle is obtuse triangle if  [tex]c^2 > a^2 + b^2[/tex]

the longest side of this triangle is 47, so we check:

[tex]47^2=2209[/tex], and

[tex]34^2 + 20 ^2 =1556[/tex]

Hence, c^2 is GREATER than a^2 + b^2, so the triangle is obtuse.

2. Using the points we showed above, we can again summarize:

This triangle's c (longest side) is 5. Let's check:

5^2 = 25, and

[tex](1.2)^2 + (4.6) ^2=22.6[/tex]

Hence, c^2 is GREATER than a^2 +b^2, so the triangle is obtuse.

3.

The side opposite of the 90 degree angle is the "hypotenuse", that is x. The side opposite the 35 degree angle is "opposite" side.

The trigonometric ratio that related "opposite" side to "hypotenuse" side is SINE. So we can write:

[tex]Sin(35)=\frac{Opposite}{Hypotenuse}\\Sin(35)=\frac{12}{x}[/tex]

Now, cross multiplying and solving:

[tex]Sin(35)=\frac{12}{x}\\x*Sin(35)=12\\x=\frac{12}{Sin(35)}\\x=20.92[/tex]

The first triangle is obtuse since the square of the longest side is greater than the sum of the squares of the other sides. The second triangle is acute since the square of the longest side is less than the sum of the squares of the other sides. Both answers provided are correct.

To determine the type of triangle (acute, obtuse, or right) based on the side lengths, you can apply the Pythagorean theorem. For the triangle with side lengths of 34 in., 20 in., and 47 in., you compare the square of the largest side (472) with the sum of the squares of the other two sides (342 + 202). If the square of the largest side is greater, the triangle is obtuse. Calculating gives us 2209 (472) and 1556 (342) + 400 (202), equaling 1956, thus 2209 > 1956 and the triangle is indeed obtuse. Your answer is correct.

For the second triangle with side lengths of 1.2, 4.6, and 5, we again apply the Pythagorean theorem. If the square of the largest side (52) is equal to the sum of the squares of the other two sides (1.22 + 4.62), the triangle is right. If it’s less, the triangle is acute.

Calculating gives us 25 (52) and 1.44 (1.22) + 21.16 (4.62), equaling 22.60, thus 25 > 22.60 and the triangle is acute. Your answer is correct.

Answer:

C = 16π ft

Step-by-step explanation:

If we know the area

A = pi r^2

64 pi = pi r^2

Divide each side by pi

64 = r^2

Take the square root of each side

8 = r

The radius is 8

Now we can find the circumference

C = 2 *pi*r

C = 2*pi*8

C = 16pi

Answer:

[tex]\large\boxed{C=16\pi\ ft^2}[/tex]

Step-by-step explanation:

The formula of an area of a circle:

[tex]A_O=\pi r^2[/tex]

r - radius

We have

[tex]A_O=64\pi\ ft^2[/tex]

Substitute:

[tex]\pi r^2=64\pi[/tex]               divide both sides by π

[tex]r^2=64\to r=\sqrt{64}\\\\r=8\ ft[/tex]

The formula of a circumference:

[tex]C=2\pi r[/tex]

Substitute:

[tex]C=2\pi(8)=16\pi\ ft[/tex]

Answer:

-60 people

Step-by-step explanation:

The change in population was -300 people.

The change in population was -300 people/5 yr or -60 people/yr.