Consider the series ∑n=0∞2e−n.

a. The general formula for the sum of the first n terms is S_n=__?__. Your answer should be in terms of n.

b. The sum of a series is defined as the limit of the sequence of partial sums, which means ∑n=0∞2e−n=limn→∞=(__?__)=(__?__).

c. Select all true statements (there may be more than one correct answer):
A. The series is a telescoping series (i.e., it is like a collapsible telescope).
B. The series converges.
C. The series is a geometric series.
D. The series is a p-series.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by

[tex]\text{Z}=\dfrac{\text{X}-\mu}{\sigma}[/tex]

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X.

In this problem, we have that:

A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm, so [tex]\mu=49.9,\sigma=3.74[/tex].

What is the length in cm of the longest 15% of Atlantic cod in this area?

We have to find the value of X for the value of Z that has a p-value of 0.85.

Looking at the z-score table, we have that Z = 1.04 has a p-value of 0.8508. So, we have to find the value of X when .

So

[tex]\text{Z}=\dfrac{\text{X}-\mu}{\sigma}[/tex]

[tex]1.04=\dfrac{\text{X}-49.9}{3.74}[/tex]

[tex]\text{X}-49.9=3.8896[/tex]

[tex]\text{X}=53.7896[/tex]

The length of the longest 15% of Atlantic cod in this area is 53.79 cm, rounded to 2 decimal places.

Answer:

554.76 miles per hour

Step-by-step explanation:

[tex]\frac{248 meters}{1 second}[/tex] x [tex]\frac{3600 seconds}{1 hour}[/tex] x [tex]\frac{1 mile}{1609.34 meters}[/tex]

= 554.76 miles per hour

[tex]\sf 554.76(mi/h).[/tex]

[tex]\sf \dfrac{248(m)}{s}[/tex]

a) First, convert the meters to kilometers.

[tex]\sf 248(m)*\dfrac{1(km)}{1000(m)} =0.248(km)[/tex]

Here, the meters cancel, since one is on the numerator and the other one is expressed as a denominator, and we simpyl multiply the value by the fraction, resulting in a number that would be a value for kilometers.

b) Convert from kilometers to miles.

[tex]\sf 0.248(km)*\dfrac{1(mi)}{1.60934(km)} =0.1541(mi)[/tex]

[tex]\sf 1(seconds)*\dfrac{1(hour)}{3600(seconds)} =\frac{1}{3600}(h)[/tex]

[tex]\sf \dfrac{0.1541(mi)}{\dfrac{1}{3600} (h)} =554.76(mi/h)[/tex]

The range of function for the given domain are {25, 8, -7, 11}

Given that, a function f(x) = 2x²-7, we need to find the range of the function, for the given domain, x = {-4, -2, 0, 3},

So,

Domain = All the input values.

Range = All the output values.

So, to find the range we will put the value of x which is the domain and the value obtained of f(x) will be the range,

f(x) = 2x²-7

For, x = -4,

f(-4) = 16×2 - 7 = 25

f(-4) = 25

f(-2) = 4 × 2 - 7 = 8

f(-2) = 8

f(0) = -7

f(3) = 9 × 2 - 7

f(3) = 11

Hence the range of function for the given domain are {25, 8, -7, 11}

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Step-by-step explanation:

The given equation is:

4x - 3y = 21

To solve for y, we can rearrange the equation as follows:

4x - 21 = 3y

Dividing both sides by 3, we get:

y = (4x - 21) / 3

Therefore, the solution to the equation is:

y = (4x - 21) / 3

She can make 20 6-ounce servings to make fruit punch

How to determine this

Cassie uses 1 quart cranberry juice,

1/2 gallon ginger ale,

1 1/2 pint orange juice.

1 quart of cranberry juice when converted to ounce

1 quart = 32 ounces

1/2 gallon of ginger ale when converted to ounce

1 gallon = 128 ounces

1/2 gallon = 128/2

1/2 gallon = 64 ounces

1 1/2 pint orange juice to make fruit punch

1 pint = 16 ounces

1 1/2 pint = 16 + 16/2 ounces

= 16 + 8

= 24 ounces

How many 6-ounces servings can she make

32 + 64 + 24

= 120 ounces

6-ounces that can be made

= 120 ounces/6 ounces

= 20 servings

Therefore, 20 6-ounce servings can be make for fruit punch

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a.

i. 10% of $110,000 = $11,000 down payment

ii. Loan (mortgage) = $110,000 - $11,000 = $99,000

iii. Monthly payment = P * r * (1 + r)n / ((1 + r)n - 1), where P represents the principal amount, r represents the monthly interest rate, and n represents the number of monthly installments.

First, we must determine the quantity of monthly payments. Because it is a 30-year loan, the monthly installments are 30 * 12 = 360.

The monthly interest rate of 9% divided by 12 equals 0.0075.

When we plug in the values, we get:

$793.07 monthly payment

iv. Loan total interest paid = (monthly payment * number of instalments) - principal amount = ($793.07 * 360) - $99,000 = $184,465.20

b

i. Reduction in loan balance = $99,000 - $88,536 = $10,464

ii. To date, the total amount paid to the loan firm is (monthly payment * a number of payments) = ($793.07 * 120) = $95,168.40.

We multiplied by 120 (rather than 10*12) because we're computing total payments made so far, not the total payments made over the life of the loan.

iii. Total interest paid thus far = total money given to the loan business minus principal amount = $95,168.40 - $99,000 = -$3,831.60

The negative figure shows that the interest paid thus far has been less than the principal amount. This is because, in the early phases of the loan, the majority of the monthly payment goes towards interest, with only a little portion going toward principal reduction.

iv. Home equity  = value of the home - remaining debt

= $150,000 - $88,536

= $61,464

c.

i. New monthly payment = P * r * (1 + r)n / ((1 + r)n - 1), where P represents the remaining loan value, r represents the new monthly interest rate (6% / 12 = 0.005), and n represents the number of monthly payments remaining (360 - 120 = 240).

When we plug in the values, we get:

$63.63 is the new monthly payment.

Total interest paid on the new loan during the life of the loan = (new monthly payment * number of payments) - remaining loan balance = ($63.63 * 240) - $88,536 = $32,028.40

d.

Monthly savings = old monthly payment minus new monthly payment = $793.07 - $63.63= $729.44

Total interest paid on the new loan during the life of the loan = (new monthly payment * number of payments) - remaining loan balance = ($63.63 * 360) - $88,536 = $37,847.80

Because the new loan is being paid off over a longer period of time, the total interest paid during the life of the new loan is more than the remaining interest on the previous loan.

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Answer:

He took 3 3/4 hours to clean both rooms.

Step-by-step explanation:

1/2 = 2/4

3 1/4 + 2/4 = 3 3/4

Therefore, he took 3 3/4 hours.

Answer:

The correct answer is D. 5.4% after rounding my answer off to the nearest tenth of a percent.

Answer:

1. f(x)= -2x^2-12x-19

2. f(x)= 2x^2+12x+17

3. f(x)= -2x^2+12x-17

4. f(x)= 2x^2-12x+17

Step-by-step explanation:

Hope this helps!

Answer: f(x)=-2x^2+12x-17 is the 3rd picture (vertex at (3,1))

f(x)=2x^2-12x+17 is the 4th picture (vertex at (3,-1))

f(x)=2x^2+12x+17 is the 2nd picture (vertex at (-3,-1))

f(x)=2x^2+12x-17 does not correlate to a picture.

f(x)=-2x^2-12x-19 is the 1st picture (vertex at (-3,-1))

Answer:

Any number multiplied by 10 equals to the number and a 0 at the end

Therefore 3×10=3

Answer:

10.8

Step-by-step explanation:

14+10+8+10+12

_______________

5

= 54/5

= 10.8

So the person would save approximately 244 yards by walking diagonally across the field instead of walking the length and width of the field separately.

what is  approximately  ?

"Approximately" is a word that is used to indicate that a value, quantity, or measurement is close to the actual or precise value, but not exactly the same. It means that the stated value is an estimate or approximation, and may be slightly different from the true value.

In the given question,

Using the Pythagorean theorem, we can find the length of the diagonal of the soccer field:

diagonal² = length² + width²

diagonal² = 110² + 80²

diagonal² = 12,100 + 6,400

diagonal² = 18,500

diagonal = √18,500

diagonal ≈ 136 yards

So the person walking diagonally across the field would cover a distance of approximately 136 yards.

To compare this with the distance they would cover if they walked the length and width of the field separately, we can use the formula for the perimeter of a rectangle:

perimeter = 2(length + width)

perimeter = 2(110 + 80)

perimeter = 2(190)

perimeter = 380 yards

Therefore, if the person walked the length and width of the field separately, they would cover a total distance of 380 yards.

The difference between these two distances is:

380 - 136 = 244 yards

So the person would save approximately 244 yards by walking diagonally across the field instead of walking the length and width of the field separately.

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So the person would save approximately 244 yards by walking diagonally across the field instead of walking the length and width of the field separately.

what is  approximately  ?

"Approximately" is a word that is used to indicate that a value, quantity, or measurement is close to the actual or precise value, but not exactly the same. It means that the stated value is an estimate or approximation, and may be slightly different from the true value.

In the given question,

Using the Pythagorean theorem, we can find the length of the diagonal of the soccer field:

diagonal² = length² + width²

diagonal² = 110² + 80²

diagonal² = 12,100 + 6,400

diagonal² = 18,500

diagonal = √18,500

diagonal ≈ 136 yards

So the person walking diagonally across the field would cover a distance of approximately 136 yards.

To compare this with the distance they would cover if they walked the length and width of the field separately, we can use the formula for the perimeter of a rectangle:

perimeter = 2(length + width)

perimeter = 2(110 + 80)

perimeter = 2(190)

perimeter = 380 yards

Therefore, if the person walked the length and width of the field separately, they would cover a total distance of 380 yards.

The difference between these two distances is:

380 - 136 = 244 yards

So the person would save approximately 244 yards by walking diagonally across the field instead of walking the length and width of the field separately.

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The quadrant or axis for each of the given ordered pairs is:

a. (-x, y) - second quadrant

b. (-x, 0) - X-axis

c. (x, -y) - fourth quadrant

d. (0, y) - Y-axis

a. (-x, y):

As the x-coordinate is negative (-x), and the y-coordinate is positive (y), the ordered pair (-x, y) will lie in the second quadrant.

b. (-x, 0):

The x-coordinate being negative (-x), and the y-coordinate 0 renders that the ordered pair (-x, 0) lies on the x-axis. This horizontal axis records an unchanging value for y: zero.

c. (x, -y):

The x-coordinate here is a positive value (x), and the y coordinate a negative one (-y); it implies that the ordered pair (x, -y) lies within the fourth quadrant.  

d. (0, y):

In this case, the x-coordinate is 0 and the y-coordinate is positive (y); therefore, the ordered pair (0, y) has its place on the y-axis. The y-axis is the vertical line on which x retains a permanent numerical value of zero.

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Answer:

y = 4

Step-by-step explanation:

[tex]y = -3*-2 - 2\\y = 4[/tex]

The quadratic regression equation is y = -140.61x² + 2,954.23x - 7,512.85 and the ball's initial height is 14 feet.

Given the set of data

Using a graphing tool, we have

A quadratic regression equation is represented as

y = Ax² + Bx + C

So, we have

y = -140.61x² + 2,954.23x - 7,512.85

When the selling price is 7.75, we have

y = -140.61(7.75)² + 2,954.23(7.75) + -7,512.85

Evaluate

y = 6937

The ball's initial height is the height when t = 0, which means we need to evaluate the function h(0).

h(0) = -16(0)^2 + 14

h(0) = 0 + 14

h(0) = 14

Therefore, the ball's initial height is 14 feet.

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We can deduce that option A is likely to be true based on the given graph of rolling dice median data.

The median is the value in the middle of a data set, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median.

The graph illustrates that the median value of the rolls is closer to the center of the possible outcomes (numbers 3, 4, and 5) than the extremes (numbers 1 and 6).

This implies that when rolling a dice several times, the median is less likely to fall between the numbers 1 and 6.

However, because rolling the dice is a random process, there is always a degree of uncertainty in predicting the outcomes.

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The statement  that is true about standard deviation is

Option D is the correct answer.

We have,

Standard deviation is a measure of how spread out the data is in a set.

A smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation indicates that the data points are more spread out from the mean.

Since the standard deviation of set A is 6 and the standard deviation of set B is 9, we can conclude that the data in set A varies less than the data in set B.

So,

The data in set A varies less than the data in set B.

Thus,

The statement  that is true about standard deviation is

The data in set A varies less than the data in set B.

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The statement  that is true about standard deviation is

Option D is the correct answer.

We have,

Standard deviation is a measure of how spread out the data is in a set.

A smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation indicates that the data points are more spread out from the mean.

Since the standard deviation of set A is 6 and the standard deviation of set B is 9, we can conclude that the data in set A varies less than the data in set B.

So,

The data in set A varies less than the data in set B.

Thus,

The statement  that is true about standard deviation is

The data in set A varies less than the data in set B.

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The limits on the vertical asymptotes of the function are given as follows:

lim x→6- f(x) = ∞

lim x→6+ f(x) = - ∞

lim x→2- f(x) = ∞

lim x→2+ f(x) = - ∞

lim x→6- f(x) = - ∞

lim x→6+ f(x) = ∞

The values of x that are outside of the domain—in a fraction, the zeroes in the denominator—are the vertical asymptotes.

When a graph reaches its vertical asymptotes, it just approaches the point rather than crossing it.

The limits on the vertical asymptotes of the function are given as follows:

lim x→6- f(x) = ∞

lim x→6+ f(x) = - ∞

lim x→2- f(x) = ∞

lim x→2+ f(x) = - ∞

lim x→6- f(x) = - ∞

lim x→6+ f(x) = ∞

The vertical asymptotes are then provided as x = -6, x = -2, and x = 2.

Each asymptote has limits to the left (shown by the minus sign) and the right (shown by the plus sign).

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Answer:

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Step-by-step explanation:

We can use the trigonometric identity:

cos 2a = 1 - 2 sin^2 a

to rewrite 1 + 2cos a as:

1 + 2cos a = 1 + 2(1 - sin^2 a/2)

= 1 + 2 - 2(sin^2 a/2)

= 3 - 2(sin^2 a/2)

Now, using another trigonometric identity:

sin a = 2 sin(a/2) cos(a/2)

we can rewrite sin^2 a/2 as:

sin^2 a/2 = (1 - cos a)/2

Substituting this into the expression for 1 + 2cos a, we get:

1 + 2cos a = 3 - 2((1 - cos a)/2)

= 3 - (1 - cos a)

= 2 + cos a

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

The area and circumference of a circle with diameter of 3 m is 7.0165 m² and 9.42 m² respectively

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The diameter (d) of the circle is 3 meter. Hence:

Area = π * diameter²/4 = π * 3²/4 = 7.0165 m²

Circumference = π * diameter = π * 4 = 9.42 m²

The area and circumference are 7.0165 m² and 9.42 m²

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Answer:

Step-by-step explanation:

After 5 years at a simple interest rate of 10%, Patrick would have earned $500 in interest ($1000 x 10% x 5 years). So at the end of the 5 years, he would have $1500 in the account.

If this entire amount is deposited into a new account that earns 10% compounded quarterly, we need to determine the quarterly interest rate first.

The quarterly interest rate is (1 + 0.10/4)^4 - 1 = 0.025 (rounded to three decimal places).

After 10 years (or 40 quarters) at a quarterly interest rate of 0.025, the compounded amount is:

$1500 x (1 + 0.025)^40 = $4045.56

Therefore, Patrick would have $4045.56 in the account after 10 years when rounding to the nearest cent.

Hope that Helps :)

The creation of an isosceles triangle quilt can only be achieved through a number of discreet steps:

Initially, select the bespoke size of both individual triangles and the full-scale length and breadth of the snug.

Subsequently, draft a lattice on either a sheet of paper or digital drafting software, with each square serving as a single triangular unit.

Commencing your task from the bottom row, resonate along the equidistant bases while drawing with precision to ensure an immaculate line-up.

Then, for the succeeding section, diverge by slightly altering the position of the point of each triangle in accordance with the intermediary gap that exists between two triangles below it.

Continue repeating this pattern while constructing rows, enveloping further ground until fully complete coverage has been ensured.

Last but not least, rigorously maintain accuracy by exploiting straight edges strategically laid beside precise measuring instruments.

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Answer:

Step-by-step explanation:

Use a simple Equation

Price = Number x Price

So Price = 536.

Since it was 67% off we multiple the price of the original by .67.

So

536 = .67x

Solve for x = 536/.67 = 800

The original Price is $800.

check by multiplying by the sale %.

Answer:

if you park for 12 hours in both parking lots A and B, it will cost the same amount, which is $64.50.

Step-by-step explanation:

Let's assume that the cost of parking for x hours in both lots is the same, then we can set up the following equations:

For 5 hours of parking:

36.50 = 38.00

This is not true, so we know that the cost for parking in both lots will not be the same for 5 hours.

For 7 hours of parking:

49.50 = 50.00

This is also not true, so we know that the cost for parking in both lots will not be the same for 7 hours either.

Let's try setting up the equation for x hours of parking:

Fee for parking in Lot A = Fee for parking in Lot B

36.50 + (x-5)*7 = 38.00 + (x-5)*7

Simplifying the equation, we get:

36.50 + 7x - 35 = 38.00 + 7x - 35

Solving for x, we get:

x = 12

Therefore, if you park for 12 hours in both parking lots A and B, it will cost the same amount, which is $64.50.

After multiplying (−3x+4) with (2x−1) we get a quadratic equation which is equal to −6x² + 11x − 4.

To multiply the expressions (−3x+4)(2x−1), we use the distributive property of multiplication:

(−3x+4)(2x−1) = −3x(2x) + 4(2x) − 3x(−1) + 4(−1)

Simplifying the above expression, we get:

= −6x² + 8x + 3x − 4

= −6x² + 11x − 4

Therefore, the product of (−3x+4)(2x−1) is −6x² + 11x − 4.

We can also use the FOIL method to multiply the two expressions:

(−3x+4)(2x−1) = −3x(2x) −3x(−1) + 4(2x) + 4(−1)

= −6x² + 3x + 8x − 4

= −6x² + 11x − 4

Either method can be used to get the same result.

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When the simultaneous equation is solved, we have that;  x = 2 and y = 3

Simultaneous equations are a set of two or more equations that are solved together to find the values of the variables that satisfy all of the equations at the same time.

We have the equations;

9x - 7y = -3 --- (1)

-3x + 5y = 9 ---- (2)

Multiply (1) by 1 and (2) by (3)

9x - 7y = -3  ---- (3)

-9x + 15y = 27 ----- (4)

Add (3) and (4)

8y = 24

y = 3

Substitute y = 3 into (1)

9x - 7(3) = -3

9x - 21 = -3

9x = -3 + 21

9x = 18

x = 2

Thus the solution is x = 2 and y = 3

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Answer :

Answer : 1.796

The explanation is in the pictures.

If the "Lawyer's-Joke" is rates as the funniest, then the rating which is the top 10% of participant rating for this joke is 20 marks.

A "Normal-Distribution" is defined as a probability distribution that is symmetric, bell-shaped, and characterized by its mean and standard deviation.

First, we standardize the rating of 14.48 using the formula:

⇒ z = (x - μ) / σ;

where x is = rating of 14.48, μ is = mean rating, and σ is = standard deviation,

⇒ z = (14.48 - 14.48) / 4.38,

⇒ z = 0,

Next, we take the "z-score" that corresponds to the top 10% of the standard normal distribution.  We know that the "z-score" is approximately 1.28,

Substituting the value in formula,

We get,

⇒ z = (x - μ) / σ   ⇒ 1.28 = (x - 14.48)/4.38,

⇒ x - 14.48 = 1.28 × 4.38,

⇒ x = 20.97 ≈ 20 marks.

Therefore, the rating that marks the cutoff for the top 10% of participant ratings for this joke is approximately 20 on the scale of 1 to 21.

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