Do the terms of an arithmetic sequence correspond to the domain or to the range of the related function? Explain

Answer:

hi :)

Step-by-step explanation:

Answer:

[tex]\dfrac{2+n}{7}[/tex]

Step-by-step explanation:

      [tex]\dfrac{2x + nx - 2y - ny}{7x - 7y}=\dfrac{2x - 2y + nx - ny}{7x - 7y}[/tex]

                                     [tex]=\dfrac{2(x - y) + n(x - y)}{7(x - y)}\\\\\\=\dfrac{(x -y)(2 +n)}{7(x - y)}\\\\\\=\dfrac{2 +n}{7}[/tex]

Answer:

[tex]\dfrac{9}{6}=\dfrac{8}{v}[/tex]

 Similar polygons are two polygons with same shape and different size.

In similar polygons  

To find the value f 'x'

          [tex]\dfrac{ED}{E'D'} = \dfrac{CD}{C'D'}\\\\\dfrac{9}{6}=\dfrac{8}{v}[/tex]

The necessary equation in the case at hand will be 40x + 50 = P, where P represents the total number of pages read and x represents the number of hours read.

A mathematical equation compares two numbers or values to a meaningful word, for instance, 6 x 4 = 12 x 2.

An equation is employed when more than one factor needs to be considered in order to fully understand or describe a situation.

So, to answer the question:

Chole has read the first fifty pages of the book.

Every hour, he reads forty pages.

For more than x hours, he reads.

The equation will then be as follows:

40x + 50 = P

P is the total number of pages read, while x denotes the number of hours spent reading.

Therefore, the necessary equation in the case at hand will be 40x + 50 = P, where P represents the total number of pages read and x represents the number of hours read.

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Answer:

2yfhyfjcxdddzònbɓchgghhhhhbbv xfbv xxg

Answer: To convert miles per gallon to kilometers per liter, we can use the conversion factor 1 mile = 1.60934 kilometers and 1 gallon = 3.78541 liters.

54 miles per gallon is equivalent to:

54 * 1.60934 km/mile / (1 gallon * 3.78541 liters/gallon) = 21.63 km/liter.

Rounding to the nearest hundredth, the equivalent rate is 21.63 km/liter.

Step-by-step explanation:

The original price of the board game for which Neal pays $1.54, which includes a sales tax on the original price of 5.5% (5.5 percent) is about $1.46

A percentage is a proportion or rate of an item within a set of items per one hundred (100) units of the set of items.

Percentages indicates the proportion of an item to be selected or received, such that percentage of each item within a set of items can be easily calculated.

The amount Neal pays for the board game = $1.54

The sales tax rate for the purchase = 5.5%

The sales tax is the percentage amount of an original price, each buyer pays when purchasing an item, and which is collected for the government agency by the seller of the item.

The original price of the board game can be found as follows;

Let x represent the original price of the board game, we get;

Therefore, we get;

x + 5.5% of x = 1.54

(1 + 0.055) × x = 1.54

1.055 × x = 1.54

x = 1.54/1.055 ≈ 1.46

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Kweku would save $180 in a year buying electricity for the Desla electric compared to buying gas for the Deswagon, To make up for the higher sale price, it will take him more than 66 years.

Subtraction is a mathematical operation. Which is used to remove terms or objects in the expression.

Given:

Deselectric costs $11900 more than the Deswagon.

Unit cost:

Deselectric: $0.11 per mile.

Deswagon: $0.12 per mile.

Kweku drives about 18,000 miles a year.

That means

The cost for each car;

Deselectric: 18000 x 0.11 = $1980

Deswagon: 18000 x 0.12 = $2160

The more cost is,

= $2160 - $1980

= $180 of savings in a year.

Now, the make-up for the higher sale price,

= 11900/180

= 66.11 in years.

Hence, it will take him more than 66 years.

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The value of a1 in a geometric series for which Sn=21825, an=125, r=15 will be 5/9.

The formula for the nth term in a geometric series is given by:

an = a1 * r^(n-1)

Where a1 is the first term, r is the common ratio, and n is the number of terms.

We are given Sn, an and r, and we can use the formula for the sum of a geometric series to solve for n:

Sn = a1 * (1 - r^n) / (1 - r)

Substituting the given values, we get:

21825 = a1 * (1 - 15^n) / (-14)

Multiplying both sides by -14, we get:

-304350 = a1 * (1 - 15^n)

Since we are given that an = 125, we can substitute this into the formula for an and solve for n:

125 = a1 * 15^(n-1)

Substituting a1 = -304350 / (1 - 15^n) from the equation above, we get:

125 = -304350 / (1 - 15^n) * 15^(n-1)

Dividing both sides by 15^(n-1), we get:

125 * 15^(1-n) = -304350 / (1 - 15^n)

Multiplying both sides by (1 - 15^n), we get:

125 * 15^(1-n) * (1 - 15^n) = -304350

Expanding the right-hand side, we get:

125 * (15 - 15^n) = -304350

Dividing both sides by 125, we get:

15 - 15^n = -2434.8

Adding 15^n to both sides, we get:

15^n = 15 - (-2434.8) = 2449.8

Taking the natural logarithm of both sides, we get:

n * log(15) = log(2449.8)

Dividing both sides by log(15), we get:

n = log(2449.8) / log(15)

Since n is the number of terms, it must be a positive integer. The closest positive integer to this value is 3, so n = 3.

Finally, we can use the formula for an to find a1:

an = a1 * r^(n-1)

Substituting the given values and n = 3, we get:

125 = a1 * 15^(3-1)

Dividing both sides by 15^(3-1), we get:

125 / 15^2 = a1

Calculating, we get:

a1 = 125 / 15^2

= 125 / 225

= 5/9.

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Answer:

2.1. 92 = 2 x 2 x 23, 146 = 2 x 73

2.2. LCM = 1148, HCF = 2

2.7. Percentage increase = 6.11%

2.4.1. It will take her 18 minutes to walk to school.

2.4.2. This is an indirect proportion as the time taken is inversely proportional to the speed.

2.5. He will get £157.63 if he pays the agent commission.

2.8. The car must drive at 120 km/h to travel the same distance in 2 hours 35 minutes.

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Here the relation between number of weeks and Cost can be formulated as 42 = 15+ 8x. By simplifying the equation we get x= 3.375. So you need to save for 4 weeks to get enough money to buy the hamster.

Here you are saving money to buy a hamster. We have to formulate an equation to find out the number of weeks you should save to obtain the money.

The cost of the hamster =  $42

Amount you have with you = $15

Amount you can save a week = $8.

Let the number of weeks is x

Then, the equation is

 42 = 15 + 8x

  8x = 42 -15

  8x = 27

    x = 27/8 = 3.375

Since it is the number of weeks, we could take only whole numbers. Here x is greater than 3. So the number of weeks to save the money to reach the target would be 4.

So by saving $8 for 4 weeks, you could buy the hamster.

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Answer: $88

Step-by-step explanation:

$99/9= $11 per hour

If Brian works 8 hours:

8x11= 88

The percent of change is -1/15 which represent a decrease. percentage of change is 6.7%

Percentage change is  the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

From the question,

The old amount is 2/5

The new amount is 1/3

We substract the new amount from the old amount

1/3 - 2/5

= -1/15

The percent of change is -1/15 which represent a decrease

To calculate the percentage change

1/15 x 100

= 6.7%

hence, the percentage of change is 6.7%

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A collection of clearly defined objects is referred to as a set, and the universal set is the set that includes the components of all other sets, including the null set. The letter U is used to represent the universal set.

There are n sets and a finite Universal set U.

Defining the Union A∪B : If either of the two strings has a 1 on the ith bit, then the union of the two strings will also have a 1 on the ith bit, but if both strings have a 0 on the ith bit, then the union of the two strings will also have a 0 on the ith bit.

Defining the Intersection A∩B : If there is a 1 on the ith bit of both strings, then the intersection of the two strings will also have a 1 on the ith bit, but if there is a 0 on either string's ith bit, then the intersection of the two strings will also have a 0 on the ith bit.

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The relative frequency for the event tails is given as follows:

53.64%.

The expected relative frequency should be closed to the theoretical probability of 0.5.

The relative frequency is given by the division of the number of desired outcomes by the number of total outcomes.

The relative frequency for all the throws is obtained as follows:

132/(114 + 132) = 132/146 = 53.64%.

Considering a fair coin, it is equally as likely to come up heads or tails, hence increasing the number of trials, the relative frequency of each outcomes is expect to be closer to 50%.

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Answer:

I don't

Step-by-step explanation:

In other words, altering the sampling distribution in this way increases the likelihood of making a type 1 error.

The arithmetic mean, arithmetic average, or simply the mean or average, is the sum of a collection of numbers divided by the number of numbers in the collection in mathematics and statistics. The collection is frequently a collection of results from an experiment, observational research, or survey.

Here,

The sampling distribution is a distribution of the values of a statistic (such as the mean or median) calculated from a set of sample data. It gives us information about how the statistic is likely to vary from sample to sample, and it is used in hypothesis testing to calculate the probability of observing certain results if the null hypothesis is true.

Filtering out all values below the mean has the effect of changing the shape, location, and spread of the sampling distribution. For example, if the original sampling distribution is normally distributed with a mean of 0 and a standard deviation of 1, filtering out all values below the mean would result in a new sampling distribution with a mean greater than 0 and a standard deviation smaller than 1.

When the sampling distribution is altered, for example by filtering out all values below the mean, it can have an effect on type 1 errors. Type 1 errors occur when we reject the null hypothesis when it is actually true.

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Answer:

∠A = 49°

Step-by-step explanation:

Vertically opposite angles are congruent.

          ∠A = ∠B

   8x - 23 = 6x - 5

Add 23 to both sides,

          8x = 6x - 5 + 23

          8x = 6x + 18

Subtract 6x from both sides,

      8x - 6x = 18

            2x = 18

Divide both sides by 2,

              x = 18 ÷ 2

             x = 9

∠A = 8x - 23

     = 8*9 - 23

     = 72 - 23

     = 49°

Answer:

Step-by-step explanation:

50%. 24 is half of 48. So, 50% of 48 if 24.

Answer:

Step-by-step explanation:

Given the formula for the volume of a torus (v = πh(R + r)), you can isolate R by dividing both sides of the equation by πh(R + r), as follows:

v / (πh(R + r)) = R

πh(R + r) * R = v

R^2 = v / (πh(R + r))

R = √(v / (πh(R + r)))

So, R is the square root of the volume divided by πh(R + r).

The volume of the dough will be 4200 cubic inches in about 7.9 hours later.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A bread dough doubles in size every hour and is represented by the function y = 35(2ˣ⁻¹).

Now, The volume of the dough would be 4200 cubic inches when,

4200 =  35(2ˣ⁻¹).

2ˣ⁻¹ = 4200/35.

2ˣ⁻¹ = 120.

2ˣ/2 = 120.

2ˣ = 240.

[tex]log_22^x = log_2240[/tex].

[tex]x = 7.9[/tex].

So, About 7.9 hours later.

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The measure of {x} in the figure is 14.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Given is a parallelogram as shown in the image.

Opposite sides of a parallelogram are equal. So, we can write -

9x - 77 = 3x + 7

9x - 3x = 7 + 77

6x = 84

x = 14

Therefore, the measure of {x} in the figure is 14.

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{Question in english -

Help please, I need to find the values, well, I'll settle for one...}

Thr solution to the inequality - 3a < -5 is -6 < -5. This can be written as negative 6 less than negative 5

- 3a < -5

if a = 2

- 3a < -5

substitute into the inequality

= -3(2) < -5

= -6 < -5

Hence, the solution to the given inequality when a = 2 is negative 6 less than negative 5

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The quadratic equation that is satisfied here is given as x^2 + 5x - 176 = 0

Let's call the two integers x and y, where x is the smaller integer (N). Then, we have:

xy = 176

and

y = x + 5

We can substitute the second equation into the first equation to get:

x(x + 5) = 176

Expanding the left side, we get:

x^2 + 5x - 176 = 0

This is a quadratic equation that N satisfies.

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Answer:

So the derivative of the function F(x) = x^2 - 1/x + 1 is F'(x) = 2x - (x - 1)/x^2.

Step-by-step explanation:

The derivative of the function F(x) = x^2 - 1/x + 1 can be found by using the limit definition of the derivative. The derivative is the rate of change of the function at a given point and it is calculated as:

F'(x) = Lim h=0 (x + h)^2 - 1/(x + h) + 1 - (x^2 - 1/x + 1)/h

Expanding the expression inside the limit and simplifying, we get:

F'(x) = Lim h=0 2xh + h^2 - (1 - hx)/(x + h)^2

Using L'Hopital's Rule, we get:

F'(x) = Lim h=0 2x + 2h - (x - 1)/(x + h)^2

As h approaches 0, the limit becomes:

F'(x) = 2x + 2(0) - (x - 1)/x^2 = 2x - (x - 1)/x^2

So the derivative of the function F(x) = x^2 - 1/x + 1 is F'(x) = 2x - (x - 1)/x^2.

Answer:

  y = -3cos(πx/4) +3

Step-by-step explanation:

You want a possible trig function that describes the values in the given table.

Looking at the table, we find the minimum y-value is 0, and it corresponds to x=0 and x=8. This means the period (P) of the function is 8.

The maximum y-value is 6. This means the midline (M) of the function is 3, the average of the minimum and maximum: (0 +6)/2 = 3.

The amplitude (A) of the function is the difference between the maximum value and the midline value: 6 -3 = 3.

The sine and cosine functions both oscillate back and forth between a value of -1 and a value of +1. The cosine function has its maximum at x=0, but the function needed here will have a minimum at x=0. We can use the cosine function, but it needs to be reflected over the x-axis (or midline).

In general the trig function we're looking for will have the form ...

  y = Acos(2πx/P) +M

As discussed above, the value of A will need to be negative to reflect the function over its midline. For A=-3, M=3, P=8, the function is ...

  y = -3cos(2πx/8) +3

  y = -3cos(πx/4) +3

__

Additional comment

In the case where the extreme values (cosine) or the midline values (sine) are not at x=0, there is a "phase shift" involved. That is, the trig function will need to be translated horizontally to match values in the table. That translation is accomplished by adding or subtracting a value from x. Translation of the cosine function is not needed in this case.

The length of the fencing will be 92 feet. And the total cost of the fencing will be $92.

Let W be the rectangle's width and L its length.

The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be

Perimeter of the rectangle = 2(L + W) units

Judith's vegetable patch is 21 feet wide and 25 feet long. Judith wants to build a fence around the vegetable patch. The length of fencing is given as,

P = 2(21 + 25)

P = 2 x 46

P = 92 feet

The fencing material costs $1.00 per foot. Then the total cost of the fencing is given as,

Total cost = $1 x 92

Total cost = $92

The length of the fencing will be 92 feet. And the total cost of the fencing will be $92.

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$51.21

Total surface area of cylindrical tank:

height = h = 2.1m

diameter = 0.7m

radius= diameter +2

r = 0.7 +2=0.35 m

[tex](2\pi r{}^{2} ) + (\pi dh)[/tex]

[tex](2 \times 3.14 \times {0.35}^{2} ) + (3.14 \times 0.7 \times 2.1) [/tex]

[tex]2 \times 3.14 \times 0.35 {}^{2} = 0.77 [/tex]

[tex]3.14 \times 0.7 \times 2.1 = 4.62[/tex]

[tex]0.77 + 4.62 = 5.39m {}^{2} [/tex]

To find the cost of painting the surface area of tank, multiply the cost of painting per square meter by the total surface area of tank.

[tex]5.39 \times 9.50[/tex]

= $51.21

The value of the variable x is  125 degrees

It is important to note that alternate angles are equal.

Also, angles at a point is 360 degrees

From the information given in the diagram, we have that;

70 degrees and and the angle tangent to C are equal, so we have;

70 degrees + x degrees + x degrees + 40 degrees = 360 degrees

Let's represent mathematically;

70 + x + x + 40 = 360

collect the like terms

70 + 2x + 40 + 360

2x = 360 - 110

Subtract the values

2x = 250

make 'x' the subject of formula

x = 250/2

divide the values

x = 125 degrees

Hence, the value is 125 degrees

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Answer:

36 Degrees

Step-by-step explanation:

First the entire angle of BAC is 71 degrees, so all you have to do is subtract the known angle (2) by the entire angle. 71-35= 36. So that means the measure of angle 1 is 36 degrees.