State whether each of the following series converges absolutely, conditionally, or not at all.
253. Σ(1-1943 Στ 1-1

Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

Answer:

4739 CDs

Step-by-step explanation:

Given the function that models the rate at which the disc is sold expressed as;

R(t)=20,000e^−0.12t

t is the number of weeks since the CD was first released

We are to look for the number of CDs that are expected to be sold during the first 12 weeks after the release. To do this, you will simply substitute t = 12 into the modeled function and get R(12) as shown;

R(t)=20,000e^−0.12t

R(12)=20,000e^−0.12(12)

R(12)=20,000e^−1.44

R(12)=20,000(0.2369)

R(12) = 4738.56

Hence the total number of CDs expected to be sold to nearest thousand is 4739 CDs

Answer:

127,000

Step-by-step explanation:

you take the integral from 0 to 12 of R(t)

The steps for each expression here is

a.

Step 1: (x)-2

Step 2: 9-2

Step 3: 7

b.

Step 1: 3(y)+2

Step 2: 3*7+2

Step 3: 23

c.

Step 1: 8+((r)/6)

Step 2: 8+(24/6)

Step 3: 12

What is meant by expression?

An expression is a representation of a mathematical equation, logical statement, or string of characters using symbols, numbers, and operators. It can be evaluated to produce a value or result. In programming, expressions can be used to assign values to variables, perform mathematical operations, or compare values. They are an essential part of most programming languages and play a crucial role in the execution of computer programs.

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The graph of the equation given is mentioned below.

What is plot point in graph ?

Whenever we draw a point on our grid, we'll call it "plotting a point." The grid is really called a "graph" and the points we plot are called "coordinates." These are really locations on a plane -- we're just finding and labeling them.

Equation given,

y = 3/5x - 1    ----eq(i)

y = 2/5x        -----eq(ii)      

Now, for this two equation we infinite points for real numbers.

Now, take some points to plot the graph.

First for the eq(i)

Put x = 0, so y = -1

Put x = 5, so y = 2

Points for eq(i) is (0, -1) and (5, 2)

Now, for eq(ii)

Put x = 0, so y = 0

Put x = 5, so y = 2

Points for eq(ii) is (0, 0) and (5, 2)

Common point is (5, 2)

Now, plot this point on graph.

Hence, for more clarity graph of the equation given is mentioned below.

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Answer: x=32, y=45, z=45

Step-by-step explanation:

Now, x is cut in half on a flat plane which is a supplementary angle (2 angles that add up to 180 degrees) so just subtract 148 from 180 and you get 32.

Since a line cuts y and z equally in half and the line it is connected to is perpendicular (right angle), we can safely say both angles are equal to 45 degrees.

Answer:

30x + 5 < 120

30x < 20 - 5

30x < 15

x < 0.5

4x - 9 > 90

4x > 90+9

4x > 99

x = 24.75

28x + 4 < 140

28x < 140-4

28x < 136

x = 4/6/7

HOPE IT HELPS!!

Answer: the x-intercept would be (2,-2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Dot product. ... In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used and often called "the" inner product (or rarely projection product) of Euclidean space even though it is not the only inner product that can be defined on Euclidean space; see also inner product space.

Step-by-step explanation:

Answer:

- A dot product is the product of the magnitude of the vectors and the cos of the angle between them.

- A cross product is the product of the magnitude of the vectors and the sine of the angle that they subtend on each other.

- An inner product is a generalization of the dot product.

Step-by-step explanation:

Dot product - the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates.

Cross Product - The cross product is a mathematical operation which can be done between two three-dimensional vectors. It is often represented by the symbol. After performing the cross product, a new vector is formed. The cross product of two vectors is always perpendicular to both of the vectors which were "crossed".

Inner product - In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar.

Answer:

Step-by-step explanation:

2

The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;

A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;

Solving the above inequality, we have;

2•x + 3 ≤ -3

2•x ≤ -3 - 3 = -6

2•x ≤ -6

Therefore;

x ≤ -6 ÷ 2 = -3

x ≤ -3

Which gives;

-∞ < x ≤ -3 in interval notation is (-∞, -3]

The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;

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Answer:

1033.92

Step-by-step explanation:

I multiplied 16 and 18 to get the area of the room which was 288. Then I multiplied 288 by how much it would cost for one square foot ( 3.59) and got my answer. Sorry if I'm wrong!

Answer:

$1,033.92 I believe

Step-by-step explanation:

you would multiply 16 and 18 then once you get that answer multiply the answer by 3.59

she got a 110 score

explanation: sorry ignore just had to do 20 characters

Answer:

I think less than 14

Step-by-step explanation:

Answer:

less than 14

Step-by-step explanation:

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator polynomial is not zero. In general, a rational function takes the form:

f(x) = P(x) / Q(x)

Here, P(x) and Q(x) are polynomials, and Q(x) ≠ 0. The numerator polynomial P(x) and the denominator polynomial Q(x) can have various degrees and coefficients.

Rational functions often have certain characteristics, such as vertical asymptotes, horizontal asymptotes, x-intercepts, and y-intercepts. These characteristics can be identified by analyzing the behavior of the function for different values of x.

Let's look at a couple of examples:

Example 1:

Consider the rational function f(x) = (3x^2 - 2x - 8) / (x - 2).

Here, the numerator polynomial is 3x^2 - 2x - 8, and the denominator polynomial is x - 2.

To find the vertical asymptote(s), we need to determine the value(s) of x for which the denominator Q(x) equals zero. In this case, we have x - 2 = 0, which gives x = 2. Therefore, the vertical asymptote is x = 2.

To find the x-intercept(s), we need to solve the equation P(x) = 0. In this case, we solve 3x^2 - 2x - 8 = 0. The solutions are x = -1 and x = 8/3. So, the x-intercepts are x = -1 and x = 8/3.

Example 2:

Consider the rational function g(x) = (2x + 1) / (x^2 + x - 6).

Here, the numerator polynomial is 2x + 1, and the denominator polynomial is x^2 + x - 6.

To find the vertical asymptote(s), we determine the values of x for which the denominator Q(x) equals zero. In this case, we need to solve x^2 + x - 6 = 0. Factoring the quadratic equation gives us (x - 2)(x + 3) = 0. So, the solutions are x = 2 and x = -3. Therefore, the vertical asymptotes are x = 2 and x = -3.

To find the x-intercept(s), we solve the equation P(x) = 0. In this case, we solve 2x + 1 = 0, which gives x = -1/2. So, the x-intercept is x = -1/2.

These are just a few examples illustrating the basic concepts of rational functions. Depending on the specific characteristics of the numerator and denominator polynomials, rational functions can exhibit a variety of behaviors. Analyzing their properties helps us understand their graphs and behavior in different regions of the coordinate plane.

To prove that 3x ≤ y, assume the opposite, that is, 3x > y, rearrange the inequality substitute x < 2y and simplify, contradict the given condition that x < 2y, therefore, concluding that 3x ≤ y.

Start by assuming the opposite, that is, 3x > y.

From the given inequality,\(7xy \leq 3x^2 + 2y^2,\), we can rearrange to get:
\(7xy - 3x^2 \leq 2y^2\)

We can substitute \(x < 2y\) into this inequality:
\(7(2y)x - 3(2y)^2 \leq 2y^2\)

Simplifying, we get:
\(y(14x - 12y) \leq 0\)

Since y is a real number, this means that either y ≤ 0 or 14x - 12y ≤ 0.

If y ≤ 0, then 3x ≤ y is trivially true.

If 14x - 12y ≤ 0, then we can rearrange to get:
3x ≤ (12/14)y
3x ≤ (6/7)y
3x < y (since we assumed 3x > y)

But this contradicts the given condition that x < 2y, so our assumption that 3x > y must be false.

Therefore, we can conclude that 3x ≤ y.

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(a) the slope of the secant line on the interval [-1,1] is 3.

(b) the slope of the secant line on the interval [-1,0] is 5.

(c) the slope of the secant line on the interval [-2,-1] is 9.

(d) The estimated slope of the tangent line of f(x) at x = -1 is 7.

To find the slope of the secant line of the function f(x) = 3x - 2x^2 - 2 on different intervals, we need to calculate the average rate of change of the function over those intervals.

(a) On the interval [-1,1]:

The slope of the secant line on this interval is equal to the average rate of change of the function over the interval [-1,1].

Average rate of change = (f(1) - f(-1)) / (1 - (-1)).

Substituting the values into the function:

f(1) = 3(1) - 2(1)^2 - 2 = 3 - 2 - 2 = -1.

f(-1) = 3(-1) - 2(-1)^2 - 2 = -3 - 2 - 2 = -7.

Average rate of change = (-1 - (-7)) / (1 - (-1)) = 6 / 2 = 3.

Therefore, the slope of the secant line on the interval [-1,1] is 3.

(b) On the interval [-1,0]:

Following the same process, we calculate the average rate of change on this interval.

Average rate of change = (f(0) - f(-1)) / (0 - (-1)).

Substituting the values into the function:

f(0) = 3(0) - 2(0)^2 - 2 = -2.

Average rate of change = (-2 - (-7)) / (0 - (-1)) = 5 / 1 = 5.

Therefore, the slope of the secant line on the interval [-1,0] is 5.

(c) On the interval [-2,-1]:

Again, we calculate the average rate of change on this interval.

Average rate of change = (f(-1) - f(-2)) / (-1 - (-2)).

Substituting the values into the function:

f(-1) = -7.

f(-2) = 3(-2) - 2(-2)^2 - 2 = -6 - 8 - 2 = -16.

Average rate of change = (-7 - (-16)) / (-1 - (-2)) = 9 / 1 = 9.

Therefore, the slope of the secant line on the interval [-2,-1] is 9.

(d) To estimate the slope of the tangent line of f(x) at x = -1, we can use the slopes of the secant lines computed in parts (b) and (c) above. The slope of the tangent line is the limit of the secant line slopes as the interval approaches zero.

Since the slope of the secant line on the interval [-1,0] is 5 and the slope of the secant line on the interval [-2,-1] is 9, we can estimate the slope of the tangent line at x = -1 as the average of these two slopes:

Estimated slope of tangent line at x = -1 = (5 + 9) / 2 = 14 / 2 = 7.

Therefore, the estimated slope of the tangent line of f(x) at x = -1 is 7.

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increase=(30/100)*50

=15

so,

value after increase

=50+15

=65

Answer:

\(5^{-4}\)

Step-by-step explanation:

\(\frac{5^3}{5^7}=5^{3-7}=5^{-4}\)

Answer: The answer is 0.0016 Or 1/625

Step-by-step explanation:

First step you Simplify 5^3  and 5^7 which is going to look like this:

5^3 =  5x5x5  = 25x5 = 125

and

5^7= 5x5x5x5x5x5x5=25x5x5x5x5x5= 125x5x5x5x5= 625x5x5x5=3125x5x5=15625x5= 78125

then divide 125 with 781225

you will get 0.000160005 but you would take out what goes after 16 and it would just have to grab 0.00016 and done

Answer:

the measure of angle P is 61.93°

The value of angle P of the triangle ΔPQR is ∠P = 61.93°

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be ΔPQR

Let the angle ∠P = θ

Triangle ΔPQR  is a right angle triangle

where ∠Q = 90°

Now , the value of the sides are

PQ = 8 cm

QR = 15 cm

PR = 17 cm

Now , from the trigonometric relations

∠QPR = θ

tan θ = opposite side / adjacent side

Opposite side of Triangle PQR is QR

Adjacent side of Triangle PQR is PQ

So , substituting the values in the equation , we get

tan θ = opposite side / adjacent side

tan θ = QR / PQ

tan θ = 15 / 8

tan θ = 1.875

Now , the value of θ is

The value of θ = tan⁻¹ ( 1.875 )

The value of θ = 61.93°

Therefore , the value of θ is 61.93°

Hence , The value of angle P of the triangle ΔPQR is ∠P = 61.93°

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c. a sample

A sample acts as a representative of the population. In statistics, a sample is a subset of individuals or observations taken from a larger group, known as the population.

By studying the characteristics of a sample, statisticians can make inferences or draw conclusions about the population as a whole.

The goal is to ensure that the sample is selected in a way that is representative of the population, so that the findings can be generalized.

By carefully selecting a sample, researchers aim to minimize bias and ensure that the characteristics of the sample closely reflect those of the population. This process is known as sampling. There are various sampling techniques, such as simple random sampling, stratified sampling, and cluster sampling, which help ensure that the sample is representative.

Once a representative sample is obtained, researchers can make statistical inferences about the population based on the characteristics and behaviors observed within the sample. This process is the foundation of inferential statistics.

In summary, a sample acts as a representative of the population by providing valuable information about the larger population, allowing researchers to draw meaningful inferences and make accurate generalizations.

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Answer:

Total number of ways = 20

Step-by-step explanation:

Given:

Total number of panels = 6

Total number of color = 3

Find:

Total number of ways

Computation:

Total number of ways = ⁶C₃

Total number of ways = !6/!(6-3)!3

Total number of ways = !6/(!3)!3

Total number of ways = 20

Answer:20

Step-by-step explanation:

idk

Nikki's speed during the second part of her trip is the same as her speed during the first part of her trip, 54 miles/hour.

Nikki has to travel a total of 351 miles, and she travels the first 216 miles in 4 hours. The second part of her trip is the remainder of the distance she needs to travel, so we can calculate it by subtracting the distance she traveled in the first part from the total distance:

Second part of the trip = 351 miles - 216 miles = 135 miles

It takes Nikki 2.5 hours to travel the second part of her trip. To calculate her speed, we can divide the distance she traveled by the time it took her:

Speed = Distance / Time

Speed for the second part of the trip = 135 miles / 2.5 hours = 54 miles/hour

To compare her speed during the first and second parts of the trip, we can calculate the speed of Nikki during the first part of the trip:

Speed for the first part of the trip = 216 miles / 4 hours = 54 miles/hour

Nikki's speed during the second part of her trip is the same as her speed during the first part of her trip, 54 miles/hour.

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Both the expressions from parts are correct.

In calculus, integration by substitution, also known as μ substitution, inverse chain rule, or change of variables , is a method of evaluating integrals and antiderivatives. This is the counterpart of the chain rule for differentiation and can loosely be thought of as using the chain rule backwards.

In first option we integrate the equation

Consider the integral

∫7x(x²+1) dx

A. First, rewrite the integral by multiplying out the integrand:

∫7 x (x² + 1) dx = ∫(7x^3)+(7x)

Then evaluate the resulting integral term-by-term:

∫7x(x²+1)dx = 7(x^4/4+x^2/2)+C

B. Next, rewrite the integral using the substitution w =(x² + 1):

∫7 x (x² + 1) dx= ∫1/(2sqrt(w-1))

Evaluate this integral (and back-substitute for w) to find the value of the original integral:

∫7x(x²+ 1) dx = 7x^4/4+7x^2/2+7/4+C

C. How are your expressions from parts (A) and (B) different? What is the difference between the two? (Ignore the constant of integration.)

(answer from B)-(answer from A) = 7/4

And in second way we used substitution so both the methods are correct.

Therefore both the Answers are correct .

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The correct answer is (d) The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution.

When the value of a public good cannot be expressed in monetary terms, the Samuelson condition still holds, but some modifications are required. In this case, the per-unit price (p) used in the Samuelson condition needs to be replaced with a relative price, which represents the trade-off between the public good and other goods or services. Additionally, the marginal values (MV) of the public good need to be replaced with the Marginal Rates of Substitution (MRS), which measure the rate at which one person is willing to substitute the public good for another good.

Therefore, to determine the efficient level of the public good, the modified Samuelson condition uses a relative price and the corresponding Marginal Rates of Substitution.

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Answer:

D. 7

Step-by-step explanation:

The question is incomplete. Here is a possible complete question

For the given expression, which whole number (w) will make the expression true? 5/6 < w/6

A. 3

B. 4

C. 5

D. 7

Given the inequality expression:

5/6 < w/6

Cross multiply

5×6 < 6×w

30<6w

Divide both sides by 6

30/6 = 6w/6

5<w

Reciprocate both sides(this will change the sense of the inequality)

1/5>1/w

Cross multiply

w > 5×1

w>5

This shows that the value of w is a value greater than 5 but not 5. According to the option, the only value greater than 5 is 7. Hence the whole number (w) that will make the expression true is 7