When calculating a loan’s effective rate, if the interest compounds every two months, what value of n do you plug into your equation? a. 2 b. 0.167 c. 6 d. 60

The rule that can be used to find the next term of the sequence 27, 40, 53, 66, 79,... is given by: Option C: a_n = a_(n-1) + 13

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

[tex]a, a + d, a + 2d, ... , a + (n+1)d, ...[/tex]

Its nth term is

[tex]T_n = a + (n-1)d[/tex]

(for all positive integer values of n)

And thus, the common difference is

[tex]T_{n+1} - T_n[/tex]

for all positive integer values of n

Here, the considered sequence is 27, 40, 53, 66, 79,...

We see that:

40-27=13

53-40=13

and so on, the difference between each consequtive pair of terms of this sequence is 13.

Thus, due to having common difference in consequtive terms, this is an arithmetic sequence.

For this series, we've got:

Thus, its nth term is given by:

[tex]T_n = a+(n-1)d= 27 +(n-1)13 = 13n + 14[/tex]

Since the options are using the notation [tex]a_n[/tex] instead of [tex]T_n[/tex], so we will use that too. Thus, nth term and (n-1)th terms are:

[tex]a_n = 13n + 14\\a_{n-1} = 13(n-1) + 14 = 13n + 1\\[/tex]

Thus, we can write nth term in the form of (n-1)th term as:

[tex]a_n = 13n + 14 = 13n + 1 + 13 = a_{n-1} + 13\\\\a_n = a_{n-1} + 13[/tex]

Thus, the rule that can be used to find the next term of the sequence 27, 40, 53, 66, 79,... is given by: Option C: a_n = a_(n-1) + 13

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Answer:

c

Step-by-step explanation:

[tex]\log_x (1)+\log_y (y)\\\\=\log_x x^0 + 1\\\\=0\cdot \log_x x +1\\\\=0+1\\\\=1[/tex]

Step-by-step explanation:

The answer is -2.2y-1.8

The equivalent expression is -2.2y-1.8

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given expression:

1.2y+4.5-3.4y-6.3

To find the equivalent expression:

Simplifying,

= 1.2y - 3.4y + 4.5 - 6.3

= -2.2y-1.8

The above expression is an equivalent expression.

Therefore, -2.2y-1.8 is the equivalent expression.

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By solving a quadratic equation, we will see that the width of the walkway is 3ft.

Remember that for a rectangle of length L and width W, the area is:

A = W*L

Now, we know that for our garden we have:

W = 8ft

L = 12ft

If we add a walkway of width x around the garden, then the new measures are:

W' = 8ft + 2x

L' = 12ft + 2x

So the area is:

A' = ( 8ft + 2x)*( 12ft + 2x)

And we know that it is equal to 192 ft^2, then:

192 ft^2 = ( 8ft + 2x)*( 12ft + 2x)

Now we can solve this for x.

192ft^2 = 96ft^2 + 4x^2 + 20ft*x

0 = 96ft^2 - 192ft^2 + 20ft*x + 4x^2

0 = -96ft^2 + 20ft*x + 4x^2

This is a quadratic equation, and the solutions are given by the Bhaskara's formula:

[tex]x = \frac{-20ft \pm \sqrt{(20ft)^2 - 4*4*(-96ft^2)} }{2*4} \\\\x = \frac{-20ft \pm 44ft}{8}[/tex]

We only take the positive solution, so we get:

x = (-20ft + 44ft)/8 = 3ft

So the width of the walkway is 3ft.

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Answer

x=2 and y=2√2

Step-by-step explanation:

[tex] \sin( \alpha ) = \frac{2 \sqrt{2} }{x } \\ x = \frac{2 \sqrt{2} }{ \sin(45) } \\ x = 4 \\ {x}^{2} = {y}^{2} + 2 \sqrt{2} \\ {4}^{2} = {y}^{2} + (2 \sqrt{2 \: )}^{2} \\ 16 = {y}^{2} + 8 \\ 16 - 8 = {y}^{2} \\ y = \sqrt{8} \\ y = 2 \sqrt{2} [/tex]

The student is wrong because y = 1 represent lienar equation of a horizontal line. Disagree.

Equation of a line in slope-intercept form, is y = mx + b, where m is the slope and b is the y-intercept of the linear graph.

Where m (slope) = 0, the linear equation would be, y = b, which suggest that the line is horizontal, and intersects the y-axis at point b.

Therefore, the student is wrong because y = 1 represent lienar equation of a horizontal line. Disagree.

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Answer:

14 hotdogs

Step-by-step explanation:

Each hotdog is $2.50. Subtract $140 from $175 giving you $25 left to earn. You then take 25 and divide by the unit rate(cost of one hotdog) and you should get 14 more hotdogs need sold to reach $175.

[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}[/tex]

Arrhenius theory of an acid: This theory was discovered by Sir Svante Arrhenius in 1887. According to this theory acids are hydrogen containing compounds, when dissolves in water it gives (H+) ions.

[tex]\large{\underline{\underline{\pmb{\sf{\color {red}{Question:}}}}}}[/tex]

[tex] \sf \red{What \: is \: Arrhenius's \: definition \: of \: an \: acid?}[/tex]

[tex] \implies[/tex] (B) substance that dissociates.in water to produce hydrogen ions (H+).So, option (B) is correct.

[tex] \boxed{ \frak \red{happy \: learning}}[/tex]

The value of the constant k when the value of x and y is 7 and 3 respectively in the equation xy=k is 21.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The value of the constant k when the value of x and y is 7 and 3 respectively in the equation xy=k can be written as,

[tex]xy=k\\\\(7) \times (3 ) =k\\\\k= 21[/tex]

Hence, the value of the constant k when the value of x and y is 7 and 3 respectively in the equation xy=k is 21.

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Answer:

D

Step-by-step explanation:

K=21

Answer:

(x - 4)

Step-by-step explanation:

x² - x - 12

to factor consider the factors of the constant term (- 12) which sum to give the coefficient of the x- term (- 1)

the factors are + 3 and - 4 , since

3 × - 4 = - 12 and + 3 - 4 = - 1 , then

x² - x - 12 = (x + 3)(x - 4) ← in factored form

Answer:

I dont know pls ask you parents...

Step-by-step explanation:

I dont know

Answer:

Step-by-step explanation:

Given, line equation is

We have to find the line equation which is perpendicular to the given line in slope intercept form.

Now, let us find the slope of the given line.ven line is in slope intercept form,  

y = mx + c where m is slope and c is intercept.

So, by comparison, slope of given line is

Now, we know that product of slopes of perpendicular lines = -1

SLope of that perpendicular line And we are also given that, perpendicular line passes x aixs at 36. Which means that intercept of x – axis is 36.

Answer:

(-6,8)

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

147 - 105 = 42

42/105 = .4

.4 × 100 = 40%

Answer:

0.03

Step-by-step explanation:

[tex] \frac{0.21}{7} [/tex]

==>

[tex] \frac{0.21 \times 100}{7 \times 100} [/tex]

===>

[tex] \frac{21}{7} \times \frac{1}{100} [/tex]

==>

[tex]3 \times \frac{1}{100} [/tex]

==>

[tex] \frac{3}{100} [/tex]

==>

[tex]0.03[/tex]

96

In this type of box plot, the two end lines are the absolute maximum and minimum values, each edge of the box is the lower and upper 25%, respectively from left to right, and the line in the box is 50%

So the answer here is the right edge of the box, or 96

Answer:

B

Step-by-step explanation:

31.112 is actually greater than 30.678 because 31 is a greater number than 30. so the statement stated is false.

24.510 is greater than 24.5 because if you add 2 zeros to 24.5, it would be 24.500(adding zeros after decimal point doesnt change the value). 24.500 is less than 24.510. the numbers are not equal.

72.49 is greater than 72.469 because if you add a zero to 72.49, it will be 72.490. 72.490 is greater than 72.469.

Basically only B is true because 81 is greater than 80.

Check the picture below, keeping in mind that opposides sides and interior angles in a parallelogram are congruent.

Answer:

145%

Step-by-step explanation:

140+63 = 203

203/160 = 1.45

1.45x100 = 145%

Answer:

Are you asking for the selling price? If yes the answer should be $50 x (1+25%) = $62.5

Answer:

3^2=9 5^3=125 9^2=81

Step-by-step explanation:

exponent is just multiplying the base by itself however we many times the exponent's (the small number on the top right of the base) value is

base-->5^3<--exponent

3^2=3×3=9

5^3=5×5×5=125

9^2=9×9=81

example

6^4=6×6×6×6=1296

The total points earned depends on the number of correct answers.

Hope this helps!

Answer:

x = 8

Step-by-step explanation:

Theorem

When a secant segment and a tangent segment meet at an exterior point, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

Secant:  a straight line that intersects a circle at two points

Tangent: a straight line that touches a circle at only one point

Given:

⇒ x² = 16 · 4

⇒ x² = 64

⇒ x² = √(64)

⇒ x = ±8

As distance is positive, x = 8

Answer:

Step-by-step explanation:

Vertically opposite angles are congruent.

∠A = ∠C

∠A + ∠C = 254

∠A + ∠A = 254

      2∠A = 254

        ∠A = 254/2

∠A = 127

Linear Pair: In two adjacent angles, if the non common arms are opposite  rays, then they are called linear and they add up to 180

∠A + ∠B = 180  {linear pair}

127 + ∠B = 180

        ∠B = 180- 127

        ∠B = 53°

Answer:

multiply base area by 2 , and add the base perimiter and height

Step-by-step explanation:

hope this helped

Answer:94.5

Step-by-step explanation:First you have to multiply 3.5x4.5 and the multiply that by 2 which gives you 31.5. Then you multiply 9x3.5 and then you also multiply that by 2 which gives you 63 and then you add 31.5 and 63 which would give you 94.5.

Answer:

x ≈ 37.13°

Step-by-step explanation:

using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{13.4}{22.2}[/tex] , then

x = [tex]sin^{-1}[/tex] ( [tex]\frac{13.4}{22.2}[/tex] ) ≈ 37.13° ( to the nearest hundredth )

Answer:

Step-by-step explanation:

Volume of cylinder = base area * height

height of the cylinder = Volume of the cylinder ÷ base area

                                   = 1205.76 ÷ 200.96

                                   = 6 in

Considering that outliers will be disconsidered, the correct statement is:

The coach can use the Interquartile Range to summarize the runners' times.

It is the values of a data-set that are between the 25th percentile and the 75th percentile, that is, the middle 50% of the values. It's advantage in certain situation is that it disconsiders outliers.

In this problem, the best way to summarize the times is disconsidering outliers, hence the Interquartile Range is used, as it indicates how close all runners' times were to each other.

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