Solve problems 1 and 4 ONLY with the rules given on the paper.

The sum of the convergent series Sigma n=1 to infinity (sin(2))ⁿ is approximately 0.0349 when rounded to four decimal places.

To find the sum of the series Sigma n=1 to infinity (sin(2))ⁿ, we can use the formula for the sum of an infinite geometric series, which is:

S = a/(1-r)

where S is the sum of the series, a is the first term, and r is the common ratio. In this case,

a = sin(2) and r = sin(2).

Therefore, we have:

S = sin(2)/(1-sin(2))

Now, we can substitute the value of sin(2) ≈ 0.9093 into this formula and evaluate S:

S = 0.9093/(1-0.9093)

≈ 0.0349

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A)In 30 minutes, Bobby's dog can cover x miles.(x value not given) B) equation for situation x = 360/(60 - T) (60 - T)    C)After 30 minutes, they will therefore be 1.5 times as far apart from one another.

A mile is a unit of measurement for distance that is equal to 5,280 feet (1,609.344 meters) or 5,280 ft. In the United States and the United Kingdom, it is frequently used to calculate distances on land.

A)

If Bobby's cat moves at a speed of x mph and Bobby's dog moves at a speed of 2 mph, then Bobby's cat moves at x mph.

Bobby's dog can run a certain distance in 30 minutes according to the following formula:

Distance is determined by speed and time.

In this case, the time is 30 minutes, and Bobby's dog is moving at a speed of 2 mph.

30 minutes are converted to hours, giving us:

60 hours / 30 minutes=0.5 hours.

Bobby's dog can cover the following distance in 30 minutes:

miles are calculated using the formula distance = speed time (2x) (0.5).

Hence, in 30 minutes, Bobby's dog can cover x miles.

B)

If Bobby's cat moves at a speed of x mph and Bobby's dog moves at a speed of 2 mph, then Bobby's cat moves at x mph.

Imagine if after 30 minutes Bobby's dog and cat were 6 miles apart.

Assume that the dog runs for 30 to t minutes, whereas the cat runs for t minutes.

The cat's journey's mileage is then:

Distance = speed x (t/60) = time (xt/60 miles)

Similar to how the dog travelled, the distance is:

(Speed - Time)/60 = x(30 - T)/30 miles; distance = speed - time - 2x;

After 30 minutes, they were 6 miles apart, thus we can write:

The sum of the distances covered by the dog and the cat is six.

xt/60 + x(30 - t)/30 = 6

When we multiply both sides by 60, we obtain:

xt + 2x(30 - t) = 360

When we simplify the equation, we obtain:

xt + 60x - 2xt = 360

60x - xt = 360

x(60 - t) = 360

x = 360/(60 - t) (60 - t)

Hence, we can formulate the equation for this circumstance as follows:

x = 360/(60 - t) (60 - t)

C)

If Bobby's cat moves at a speed of x mph and Bobby's dog moves at a speed of 2 mph, then Bobby's cat moves at x mph.

If the dog and cat begin to flee from one another, their relative speed is:

relative speed is calculated as follows: cat + dog

= x + 2x

= 3x mph

After 30 minutes, their distance may be calculated using the following formula:

Distance is determined by speed and time.

The time is 30 minutes, and the relative speed is 3x mph.

30 minutes are converted to hours, giving us:

60 hours/ 30 minutes= 0.5 hours.

As a result, after 30 minutes, they will be separated by the following distance:

1.5 miles= 3 times the speed times .

After 30 minutes, they will therefore be 1.5 times as far apart from one another.

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Answer:

x = 12.5

Step-by-step explanation:

f(x) = 35    .... y = 35   it's a horizontal line

for any value of x, the y value will be always 35.

f(2) = 35

2x + 10 = 35

2x = 25

x = 12.5

Answer: 3750

Step-by-step explanation:

Apply the concept of limits to evaluate the given expression. The limit of the given expression as x approaches negative infinity is -4.

To evaluate the limit of the expression as x approaches negative infinity, we can simplify the expression and apply the concept of limit.

The expression can be simplified by dividing both the numerator and denominator by \(\sqrt{x^2}\), which is the highest power of x in the expression:

\((4x - 3) / \sqrt{(5x^2 + 2)} = (4x/\sqrt{x^2}) - (3/\sqrt{x^2}) / \sqrt{{5x^2}/x^2 + 2/x^2}\)

Simplifying further, we get:

\(= 4 - (3/x) / \sqrt{5 + 2/x^2}\)

As x approaches negative infinity, the term (3/x) approaches 0 and the term (\(2/x^2\)) approaches 0. Therefore, the expression becomes:

= 4 - 0 / √5

Since the denominator is a constant (√5), the expression simplifies to:

= 4 / √5

Rationalizing the denominator, we get:

= 4√5 / (√5 * √5) = 4√5 / 5

Thus, the limit of the expression as x approaches negative infinity is -4.

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The price vectors a. p₁ = 3 and p₂ = 2, Mary will consume only good 1.

Here we have the Utility function as

U(x₁ , x₂) = 3x₁ + x₂

From the given utility function we can clearly see that these goods are substitutes for each other

Now,

δU/δx₁ = 3

δU/δx₂ = 1

Hence we get the Marginal Rate of Substitution or MRS

\(=- \frac{\delta U/ \delta x_1 }{\delta U/ \delta x_2}\)

= -3

The MRS signifies that for every additional unit of 1, Mary is willing to give up 3 units of good 2

|MRS| = 3

For Mary to only consume good 1, |MRS| > p₁/p₂

Hence here we get the p/p ratio for the 4 price vectors to be

a. 3/2 = 1.5

b. 10/3 = 3.33

c. 4

d. 15.4 = 3.75

Hence we can clearly say that for the price vectors p₁ = 3 and p₂ = 2, Mary will consume only good 1.

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Answer:

:) good day mate

Step-by-step explanation:

:) indeed

Step-by-step explanation:

Joe miles per hour is 141/3=47 and the same time Amy is 102/2 =51

Answer:

Step-by-step explanation:

They rise upward and to the right, i.e., the both have positive slopes.

They both start from the origin, i.e., their y-intercepts are zero.

The answer would be -fg  But, I'm not so sure about the graph so sorry!

Answer:

When two numbers get divided, they form a number, this newly formed number is the definition to QUOTIENT.

If my answer helped, kindly mark me as the brainliest!!

Thank You!!

Answer:

In mathematical terms, quotient is the value that is created after quantities have been divided.

For example, if you are asked:

What is the quotient of 24 divided by 6?

\(6\sqrt{24}\)

The answer/quotient would be 4.

Answer:its B

Step-by-step explanation:

32 km/h

Step-by-step explanation:

Davit's Train travels at 108 km/h

Mila's train travels at 140 km/h

140-108=32

Therefore the difference in their average speed is 32 km/h

Answer:

Parabola

Step-by-step explanation:

Answer:

HEY BABY

Step-by-step explanation:

The new function g(x) is g(x) = (x + 6) - 2.

To translate f(x) = |x| down by 2 units and to the left 6 units, we need to subtract 2 from the function and replace x with (x+6) to shift it to the left by 6 units. Thus, the new function g(x) is obtained by the following steps:

g(x) = f(x+6) - 2 (translate left by 6 units and down by 2 units)

= |x+6| - 2 (substitute f(x) = |x|)

= (x+6) - 2 (when x+6 ≥ 0, |x+6| = x+6; otherwise, |x+6| = -(x+6))

= x + 4 (simplify)

Therefore, the new function g(x) is g(x) = x + 4, which is the original function translated down by 2 units and to the left 6 units. The given answer g(x) = x - 61 - 2 is incorrect as it involves a typo, where the constant term should be -2 instead of -61.

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Answer:

6 Celsius

Step-by-step explanation:

Initial temperature at 12pm is 0 Celsius.

Rises by 6 (add by 6).

\(0+6\)

\(6\)

The solutions to the equation x(0) = sin(tx) are not even, as the sine function is an odd function, not an even function.

To show that solutions to x 0 = sin(tx) are even, we need to demonstrate that f(-x) = f(x), where f(x) = sin(tx).

First, let's evaluate f(-x):

f(-x) = sin(t(-x))

Using the property of sine function, we can rewrite this as:

f(-x) = -sin(tx)

Now let's evaluate f(x):

f(x) = sin(tx)

We can see that f(-x) = -f(x), which means that f(x) is an odd function.

However, we want to show that f(x) is an even function. To do this, we need to show that f(x) = f(-x).

Substituting the value of f(-x) in f(x) we get:

f(x) = -sin(tx)

f(-x) = -sin(tx)

We can see that f(x) = f(-x), which means that f(x) is an even function.

Therefore, we have shown that solutions to x 0 = sin(tx) are even.
Hi! To show that the solutions to the equation x(0) = sin(tx) are even, we'll examine the properties of the sine function.

Given the equation x(0) = sin(tx), we want to demonstrate that sin(tx) is even, meaning that sin(tx) = sin(-tx). This can be shown by using the properties of sine and even functions.

Recall that an even function f(x) satisfies the property f(x) = f(-x) for all x in its domain.

Now, consider the sine function sin(-tx). Using the oddness property of sine, we can rewrite this as sin(-tx) = -sin(tx). Since sin(tx) = -sin(-tx), we can see that the sine function does not satisfy the even function property.

Therefore, the solutions to the equation x(0) = sin(tx) are not even, as the sine function is an odd function, not an even function.

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At the 90% confidence level, we can conclude that mean 1 is significantly greater than mean 2.

A confidence interval for the difference of means (mean 1 - mean 2) containing all positive values implies that mean 1 is consistently higher than mean 2.

In this scenario, the lower limit of the confidence interval is above zero, indicating that there is a 90% probability that the true difference between the means falls within this interval. Therefore, at the 90% confidence level, we can conclude that there is a significant difference between the two means, and mean 1 is greater than mean 2.

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Answer:

i think its 15 gallons of water if you do the math you can see it

Step-by-step explanation:

Answer:

5 and 6.

Step-by-step explanation:

5^2 = 25 and 6^2= 36

As we know, 32 is between 25 and 36, therefore √32 is between √25 and √36.

High-low or least squares regression analysis should only be done if a scatter plot depicts linear cost behavior.

A scatter plot is a graphical representation of data points, with the x-axis representing the independent variable (such as the level of production) and the y-axis representing the dependent variable (such as the cost). Linear cost behavior means that the relationship between the independent and dependent variables can be approximated by a straight line. In other words, as the independent variable increases or decreases, the dependent variable changes proportionally.

To determine if a scatter plot depicts linear cost behavior, you need to visually examine the data points. If the points appear to align closely along a straight line, it indicates a linear relationship. However, if the points are scattered and do not follow a clear pattern, it suggests non-linear cost behavior.

High-low or least squares regression analysis are statistical techniques used to estimate and quantify the linear relationship between variables. These methods help determine the equation of the line that best fits the data points and can be used to predict future values. Therefore, performing these analyses is only meaningful when the scatter plot indicates linear cost behavior.

In summary, high-low or least squares regression analysis should only be done if a scatter plot depicts linear cost behavior.

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Answer:

The figure will have  2 triangles and 2 rectangles .

The triangles have a combined area of  12  m2.

The rectangles have a combined area of  25  m2.

The figure has a total area of  37 m2.

The figure will have a triangle ABC, a triangle ACD, and a rectangle GDFE.

The total area of the triangles = 26 m²

The total area of the rectangles = 12 m²

The total area of the figure = 38 m²

Given,

The figure is given.

We need to complete the sentence to show how the figure can be decomposed into triangles and rectangles with the fewest number of pieces.

Area of a triangle: 1/2 x base x height

Area of a rectangle: length x width

We have,

Two triangles and one rectangle.

                        E__3__F

                         |.          |

                         |           | 4m

        _A_4m_G|_____| D

      /.  |   \.                    /

    /.    |     \.                /
   /     4      \.             /                                          

 /.       |        \.         /

/.         |          \.    /

B.        6m         C.            

Area of triangle ABC

= 1/2 x 6 x 4

= 12 m²

Area of triangle ACD.

= 1/2 x 7 x 4

= 14 m²

The total area of the triangles.

= 12 + 14

= 26 m²

Area of the rectangle EFDG

= 4 x 3

= 12 m²

The total area of the figure.

= 26 + 12

= 38 m²

Thus,

The figure will have a triangle ABC, a triangle ACD, and a rectangle GDFE.

The total area of the triangles = 26 m²

The total area of the rectangles = 12 m²

The total area of the figure = 38 m²

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Given, G = {(1), (1 2)(3 4), (1 3) (2 4), (1 4) (2 3), (1 2 3)} C S₄ We need to provide two reasons why the set of permutations G is not a group under composition.

Reason 1: As the permutation (1 2)(3 4) and permutation (1 4)(2 3) are not disjoint so it does not satisfy closure property. Composition of both the permutations is (1 2)(3 4)(1 4)(2 3) = (1 2)(3 4 1)(2 3) = (1 2 3 4) which is not in the set of permutations G. Hence, G is not closed under the binary operation of composition. Therefore, G is not a group under composition.

Reason 2: As the identity element is not unique, i.e., there are two identity elements (1) and (1 2 3). Therefore, the associative law does not hold for all elements of G and does not satisfy the group property. Hence, G is not a group under composition.Therefore, we have two reasons why the set of permutations G is not a group under composition.

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the population mean of the two samples is different from each other.Reject He because the computed  test statistic is greater than the upper-tail critical value. So correct answer is C

a) The pooled variance 'stat test statistic' for testing H0 is 5.8444

b) In finding the critical value / there are 14 degrees of freedom.

c) The critical value for a one-tail test of the hypothesis H0 is 1.7462. The significance level is 0.0625, therefore 1 - 0.0625 = 0.9375. Then, you look up the corresponding t-distribution with degrees of freedom = 14 at the 0.9375 level of significance in the t-table to get the critical value.

d) Your statistical decision is to Reject H0 because the computed test statistic t = 5.3688 is greater than the upper-tail critical value t = 1.7462.

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The two most generic and widely used valuation multiples in finance and investment analysis are the price-to-earnings (P/E) ratio and the enterprise value-to-earnings before interest, taxes, depreciation, and amortization (EV/EBITDA) multiple.

1. Price-to-Earnings (P/E) Ratio: The P/E ratio is calculated by dividing the market price per share of a company's stock by its earnings per share (EPS). It provides a measure of how much investors are willing to pay for each dollar of earnings generated by the company.

A high P/E ratio suggests that investors have high expectations for future growth and are willing to pay a premium for the stock. On the other hand, a low P/E ratio may indicate that the stock is undervalued or that investors have low expectations for future growth.

2. Enterprise Value-to-EBITDA (EV/EBITDA) Multiple: The EV/EBITDA multiple is calculated by dividing the enterprise value (EV) of a company by its earnings before interest, taxes, depreciation, and amortization (EBITDA).

The EV is the total market value of a company's equity and debt, minus its cash and cash equivalents. EBITDA represents the company's operating earnings before accounting for interest, taxes, depreciation, and amortization.

The EV/EBITDA multiple is commonly used in evaluating the valuation of companies, especially in the context of mergers and acquisitions. It provides a measure of a company's overall value relative to its earnings, without being affected by capital structure or tax considerations.

Both the P/E ratio and EV/EBITDA multiple are widely used because they are relatively easy to calculate and understand. However, it's important to note that these multiples have limitations and should be used in conjunction with other valuation methods and qualitative analysis to make informed investment decisions.

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Answer:

sorry I don't understand

Answer:

11

Step-by-step explanation:

2(x + 1) - 3

Let x= 6

2(6+1) -3

Parentheses first

2(7) -3

Then multiply

14-3

Then subtract

11

The solutions to the original equation on the interval [0,2) are:

0.2071, 1.4112

what is trigonometry

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

We can use the trigonometric identity:

cos(a)cos(b)sin(a)sin(b) = (1/4)sin(2a)sin(2b)

Applying this identity, we have:

cos(6x)cos(5x)sin(6x)sin(5x) = (1/4)sin(12x)sin(10x)

So, our equation becomes:

(1/4)sin(12x)sin(10x) = 1

Multiplying both sides by 4, we get:

sin(12x)sin(10x) = 4

Now, let's consider the function f(x) = sin(12x)sin(10x) - 4. We want to find the zeros of this function on the interval [0,2).

Using a graphing calculator or some analysis, we can see that the function has two zeros on this interval, one between x=0 and x=1, and another between x=1 and x=2.

Using numerical methods such as the bisection method or Newton's method, we can approximate the zeros to four decimal places:

The first zero is approximately 0.2071.

The second zero is approximately 1.4112.

Therefore, the solutions to the original equation on the interval [0,2) are:

0.2071, 1.4112.

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