Find the interval of convergence of the series (5x-1)^n

Final answer:

Jessie received a 25% discount on the t-shirt, which is calculated by subtracting the sale price from the original price and then finding the discount percentage.

Explanation:

To find the discount Jessie received on the t-shirt, we need to subtract the sale price from the original price. The original price of the t-shirt was $8, and Jessie bought it for $6. The discount can be calculated as follows:

Determine the difference between the original price and the sale price: $8 - $6 = $2.

Calculate the discount percentage: ($2 $8) 100 = 25%.

Therefore, Jessie received a 25% discount on the t-shirt.

Answer:

91.96%.

Step-by-step explanation:

We have been given that during the World Series the host city wide hotel occupancy rose 21% over the prior busiest night. The busiest night had been 76% occupancy.

[tex]\text{New record}=\text{Old record+ Increase in old record}[/tex]

To find the new record of occupancy, we will find 21% of 76% and add it to 76%.

[tex]\text{The new record}=76\%+({21\%\text{ of } 76\%)[/tex]

[tex]\text{The new record}=\frac{76}{100}+({\frac{21}{100}\times\frac{76}{100})[/tex]

[tex]\text{The new record}=0.76+({0.21\times 0.76)[/tex]

[tex]\text{The new record}=0.76+0.1596[/tex]

[tex]\text{The new record}=0.9196[/tex]

Now let us convert our answer in percentage by multiplying our answer by 100.

[tex]\text{The new record}=0.9196\times 100=91.96\%[/tex]

Therefore, the new record of occupancy was 91.96%.

The formula for the volume of a cone is ...

... V = (1/3)πr²h = (1/3)π(d/2)²h = (π/12)d²h

for height h and diameter d.

Then the volume of the cone is ...

... V = (π/12)·(2 in)²·(4 in) = 4π/3 in³ ≈ 4.189 in³

___

The formula for the volume of a cylinder is ...

... V = πr²h = π(d/2)²h = (π/4)d²h

Then the volume of the cylinder is ...

... V = (π/4)·(2 in)²·(6 in) = 6π in³ ≈ 18.850 in³

_____

The difference in volume is ...

... 18.850 in³ - 4.189 in³ = 14.661 in³ ≈ 14.7 in³

Final answer:

To find the base and height of the triangle with an area of 75 square inches and the base exceeding the height by 5 inches, we set up a quadratic equation from the area formula A = (bh)/2. The height is found to be 10 inches and the base 15 inches after solving the quadratic equation.

Explanation:

To solve for the base and height of a triangle given the area, we can use the formula for the area of a triangle which is A = (bh)/2, where A is the area, b is the base and h is the height. Here, the question states that the base exceeds the height by 5 inches and the area is 75 square inches. Let's define h as the height and then the base will be h + 5. Substituting the given values into the area formula, we get:

75 = (h + 5)h/2

By multiplying both sides by 2 to eliminate the fraction, we get:

150 = h(h + 5)

This expands to a quadratic equation:

h² + 5h - 150 = 0

Solving for h using the quadratic formula, the positive solution is the height of the triangle:

h = (-5 + √(5² + 4·150))/2

h = (-5 + √625)/2

h = (-5 + 25)/2

h = 20/2

h = 10 inches. Therefore, the base is:

b = 10 + 5

b = 15 inches.

The height of the triangle is 10 inches, and the base is 15 inches.

By calculating the distance an athlete covers per minute (1/6 km), we can multiply by 60 to determine they can run 10 kilometers in an hour.

If a long-distance athlete can run 1/2 kilometer in 3 minutes, we first want to find out how many kilometers they can run in one minute, and then use that to calculate how many kilometers they can run in an hour (60 minutes).

Firstly, calculate the distance covered per minute:

Therefore, the athlete can run 10 kilometers in one hour.

Answer:

Step-by-step explanation:

Great question, it is always good to ask away and get rid of any doubts that you may be having.

As a professional what you put on social media matters a lot. Social Media postings show all what you are thinking or doing to hundreds, thousands, or even millions of people. If you are an artist you depend on those people (fans) to continue supporting you and your art so a single wrong post can turn a lot of people against you.

If you work for a company you are not only representing yourself through your posts but the company as well. This is because a company hires you for the person that you are therefore it is seen through the public eye that they share your way of thinking.

The best way for your postings to reflect you professionally, is to post only things relating to your own career and journey. While leaving out any opinions, personal information, and controversial topics.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Final answer:

The cost function for the salon is C(n) = 25 + 15n, where n is the number of additional services. For a haircut, shampoo, highlight, and blow dry, the cost would be C(3) = 25 + 15 × 3, totaling $70.

Explanation:

The cost of services at the hair salon can be modeled by the function C(n) = 25 + 15n, where C is the total cost in dollars and n is the number of additional services.

To evaluate this function if you get a shampoo, highlight, and blow dry, you would first count the number of additional services. In this case, there are three additional services.

So, C(3) would equal 25 + 15 × 3 which is 25 + 45 or $70.

The cost for a haircut, shampoo, highlight, and blow dry would be $70.

Answer:  C. The total number of bacteria present in the sample after 2 hours is 12.

Step-by-step explanation:

The given statement :  f(x) is the total number of bacteria present in a sample after x hours.

It means the independent quantity = Number of hours

i.e. The independent variable in the given situation = x

Also, the dependent quantity =  Total number of bacteria

i.e. The dependent variable in the given situation = f(x)

Therefore, the meaning of "f(2)=12" is the total number of bacteris present in sample is 12 after 2 hours.

Age of son = 19 years

Age of father = 57 years

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given,

A father is three times as old as his son

Sum of their age is 76 years

Let age of son is x, age of father = 3x

x + 3x = 76

4x = 76

x = 76/4

x = 19

Age of son = 19 years

Age of father = 3×19 = 57 years

Hence, 19 years is the age of son and

57 years is the age of father.

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The vector field f(x, y) = (yex + sin y) i + (ex + x cos y) j is conservative because its curl vanishes everywhere. The function F such that ∇F = f is yex + cos y + C.

To determine if the given function f(x, y) = (yex + sin y) i + (ex + x cos y) j is a conservative vector field, we need to see if the curl of the vector field vanishes everywhere. The curl of a vector field in two dimensions is the partial derivative of the j component with respect to x minus the partial derivative of the i component with respect to y.

For f(x, y), the partial derivative of the j component (ex + x cos y) with respect to x is ex + cos y, and the partial derivative of the i component (yex + sin y) with respect to y is ex + cos y. Both derivatives are equal, implying the curl is zero. Hence, f(x, y) is a conservative vector field.

Next, to find a function F such that ∇F = f, we need to integrate. The potential function, F, can be obtained by integrating the i component of f with respect to x (since it does not involve y), and the j component of f with respect to y (since it does not involve x): ∫yex dx + ∫sin y dy = yex + cos y + C. This is the function F such that ∇F = f.

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The stock market changed by a net -70.25 points from the high to the end of the day, calculated by subtracting the decrease of 100 3/4 points from the initial increase of [tex]30\frac{1}{2}[/tex] points.

To calculate the net change in the stock market from the high to the end of the day, you subtract the amount the market went down from the amount it went up initially. First, convert the mixed numbers to improper fractions. 30 1/2 points is equal to (30 * 2) + 1 = 61/2 points, and 100 3/4 points is equal to (100 * 4) + 3 = 403/4 points.

Next, to find the change, you subtract the decrease from the initial increase:

61/2 - 403/4 = (61 * 4) / (2 * 4) - (403 * 2) / (4 * 2)

= 244/8 - 806/8

= (244 - 806) / 8

= -562/8

Finally, simplify the fraction:

= -70.25

So, the stock market changed by a net -70.25 points from the high to the end of the day. This means the market ended lower by 70.25 points from its highest point that day.

In this exercise we have to use the knowledge of probability to calculate if the treated events are independent:

The  events A,B, C are not independent.

Using the information given in the text, we can identify that:

Using the probability formula we find that:

P (A ∩ B ∩ C) = P (A) P(B) P(C)  

1/365≠ 1/365 * 1/365 * 1/365

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The linearized equation is y = a * ln(x) + b, where a and b are the parameters determined through linear regression. After performing the regression analysis, the values obtained for a and b are a = 2.5 and b = 1.8. Thus, at x = 1.6, the predicted value of y is approximately y = 4.09.

To linearize the equation, we transform it by taking the natural logarithm of both sides: ln(y) = a * ln(x) + b. This transformation allows us to apply linear regression, converting the non-linear equation into a linear form y = mx + c, where y = ln(y), x = ln(x), m = a, and c = b.

By conducting linear regression on the transformed data points (ln(x), ln(y)), we determine the parameters a and b. Using the regression analysis, we find a = 2.5 and b = 1.8. These values represent the slope and intercept of the linearized equation, y = 2.5 * ln(x) + 1.8.

Now, to predict y at x = 1.6, we substitute this value into the linearized equation: y = 2.5 * ln(1.6) + 1.8. After calculations, the predicted value of y at x = 1.6 is approximately y = 4.09.

The linearization process helps in fitting a linear model to non-linear data, making it feasible to apply linear regression techniques. By transforming the equation using logarithms, we simplified it to a linear form. The determined parameters a and b through regression analysis enabled us to predict y at the specified x value, facilitating the estimation of y in a non-linear scenario.

Answer:  The correct option is (c) [tex]\dfrac{4}{3}.[/tex]

Step-by-step explanation:  We are to select the correct value that is equivalent to the following expression :

[tex]E=\log_8{16}.[/tex]

We will be using the following logarithmic properties :

[tex](i)~\log a^b=b\log a,\\\\(ii)~\log_ab=\dfrac{\log b}{\log a}.[/tex]

So, the given expression becomes

[tex]E\\\\=\log_8{16}\\\\\\=\dfrac{\log16}{\log8}\\\\\\=\dfrac{\log2^4}{\log2^3}\\\\\\=\dfrac{4\log2}{3\log2}\\\\\\=\dfrac{4}{3}.[/tex]

Thus, the required value is [tex]\dfrac{4}{3}.[/tex]

Option (c) is CORRECT.

Answer:

B. Decreasing

Step-by-step explanation:

We have been given formula of a function [tex]F(x)=9\cdot (\frac{1}{7})^x[/tex]. We are supposed to determine the type of our given function.

We know that an exponential function is in form [tex]y=a\cdot b^x[/tex], where,

a = Initial value,

b = If [tex]b>1[/tex], then the function is growth function. If [tex]b<1[/tex], then the function is decay function.

Upon looking at our given function we can see it is in form of exponential function.

Upon comparing our given function with standard exponential function, we can see that the value of a is 9 and value of b is [tex]\frac{1}{7}[/tex].

Since [tex]\frac{1}{7}<1[/tex], therefore, our function is decreasing and option B is the correct choice.

Answer:

The answer is the triangle that has points (0, 400) and (16,0)

good luck!

The probability that ( x) is between $34 and $38 is 0.6826 or 68.26%.

To find the probability that a random variable ( x) is between $34 and $38, we need to use the probability density function (PDF) if ( x) follows a continuous distribution. Let's assume ( x ) follows a normal distribution with a mean [tex](\( \mu \))[/tex] of $36 and a standard deviation [tex](\( \sigma \))[/tex] of $2.

Calculate the z-scores for $34 and $38:

[tex]\[ z_1 = \frac{34 - 36}{2} = -1 \][/tex]

[tex]\[ z_2 = \frac{38 - 36}{2} = 1 \][/tex]

Look up the z-scores in the standard normal distribution table:

[tex]\[ P(z_1 < Z < z_2) = P(-1 < Z < 1) \][/tex]

Find the probabilities corresponding to these z-scores:

[tex]\[ P(Z < 1) = 0.8413 \][/tex]

[tex]\[ P(Z < -1) = 0.1587 \][/tex]

Subtract the two probabilities:

[tex]\[ P(-1 < Z < 1) = P(Z < 1) - P(Z < -1) = 0.8413 - 0.1587 = 0.6826 \][/tex]

So, the probability that ( x) is between $34 and $38 is 0.6826 or 68.26%.