14 Which equation describes the nth term of the arithmetic sequence
7, 10, 13, 16, ...?
A a=3n + 4
B a₁ = 7+3n
C a = - 4n+ 3
D a₁ = 3n - 4

Answer:11.4

Step-by-step explanation: Set up a proportion: [tex]\frac{15}{x}[/tex]=[tex]\frac{5}{3.8}[/tex]

To solve a proportion, multiply the numbers diagonal from each other, then divide by the last number. In this problem, we would multiply 15 and 3.8, which equals 57, then we would divide by 5. That is why the answer is 11.4.

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Answer:

Step-by-step explanation:

1. Definition of Least common multiple: The least common multiple of two numbers is the smallest number that is a multiple of both of the numbers

2. Find the LCM 8 and 10=

Multiplies of 8= 8,16,24,32,40....

Multiplies of 10= 10,20, 30,40 ,50....

3. We found it!

40 is the least common multiple!

The amount invested in the account that yields a 5% interest is $18,000.

The amount invested in the account that yields a 5% interest is $12,000.

The system of equations that represent the question is:

a + b = 30,000 equation 1

0.05a + 0.13b = 2460 equation 2

Where:

The elimination method would be used to solve the system of equations.

Multiply equation 1 by 0.05

0.05a + 0.05b = 1500

Subtract equation 3 from equation 2:

0.08b = 960

Divide both sides of the equation by 0.08:

b = 960 / 0.08

b = $12,000

Substitute for b in equation 1:

a + 12,000 = 30,000

a = 30,000 - 12,000

a = 18,000

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A permutation is an arrangement of objects in a specific order

i.e. AB ≠ BA

In Permutation order is important.

Here there are 12 Letters and symbols

Out of which E is repeated.

here we are given that duplicates from the list of 12 are not allowed, and We see that letter E is repeated.

So There are 12 letters in all, out of which we need 7 letters and symbol, where order is important.

So formula for permutation is nPr = [tex]\frac{n!}{(n-r)!}[/tex] where ! is called fractional symbol n! = n*(n-1)*(n-2)

*3*2*1x! = reputation of any word.

So Permutation with reputation of any letter or object is [tex]\frac{nPr}{x!}[/tex]

for example 4! = 4*3*2*1 = 24

So the answer is,

12P7 = [tex]\frac{12!}{2!*(12-7)!} = \frac{12!}{5!*2!} = \frac{12*11*10*9*8*7*6*5!}{5!*2!}[/tex] If we cancel 5! from both numerator and denominator.

12P7 = 12*11*10*9*8*7*3 = 1995840

So the answer is 1995840.

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Equation can be used to find  the number of candles (c) Katie ordered is 54 = 3c + 6. correct option is (C).

given that

3c+6=54                            --------------------------------- (1)

reduce the greatest common factor on both side of the equation, we get:

2+ c= 18                            ----------------------------------(2)

rearranging the equation (2), we get,

c + 2 = 18

⇒ c = 18 - 2

⇒ c= 16

∴ putting the value of c in option 3, we get,

    3 X 16 + 6 = 54

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The question was incomplete. Check below the complete question.

Katie ordered candle that cot $3 each from a webite. She wa charged a flat hipping fee of $6 and no ale tax. If he pent a total of $54, which equation can be ued to find c, the number of candle he ordered?

A. 3c = 54

B. 6c = 54

C. 3c + 6 = 54

D. 3c – 6 = 54

Emmanuel paid $50 for each watch.

Profit describes the financial benefit realized when revenue generated from a business activity exceeds the expenses, costs, and taxes involved in sustaining the activity in question.

Given that, Emmanuel started a business selling watches. He sells each watch for 30% more than he pays for them. Last week, he sold 7 watches for a total of $455.

Let the original price of each watch be x

According to question,

x*130% = 455/7

x = 65*100/130

x = 50

Hence, Emmanuel paid $50 for each watch.

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The different combinations of reggaeton and hip-hop songs that Jae could use for his playlist include:

In this scenario, Jae makes a playlist of 24 songs for a party and he prefers reggaeton and hip-hop music and then builds the playlist from the two music types.

In this case, the combination will be gotten by the addition of two values that can give 24.

The combination can include:

10 reggaeton + 14 hip hop music = 24 songs

18 reggaeton + 6 hip hop music = 24 songs.

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Answer:

2.375 inches

Step-by-step explanation:

Main Steps

1. Identifying important parts of the question

2. Solving the problem

Step 1. - Identifying important parts of the question

In the question, there is some extraneous information.  For instance, the question introduces the terms "diameter" and "loaded in shear" and "with a safety factor of 1.5".  However, given the information in the problem, and the question asked, it isn't necessary to know that it is "loaded in shear" means, or to know what a diameter is (since everything stays with diameters, and doesn't involve another dimension), and the problem gives the result that will satisfy "a safety factor of 1.5".

Sifting through the problem/question, these are the important parts:

- "to the nearest 1/8 inch" (meaning round to the nearest 1/8th of a unit)

- with "units of inches to 3 decimal places"

- The number to round is "2.4183 inches

Step 2. - Solving the Problem

To round to the nearest 1/8 inch, we can divide the number 2.4183 by 1/8.  

[tex]2.4183 \div(1/8)[/tex]

Recall that dividing by a fraction is the same as multiplying by the reciprocal

[tex]2.4183 * 8[/tex]

19.3464

So, there are approximately 19, one-eighth-inches in the measurement.  (Note that 19.3464 is closer to 19 than it is to 20).  To find the final rounded measurement, multiply 19 by 1/8

[tex]19 * (1/8)[/tex]

2.375 inches

So, the diameter of the bolt that should be used (if rounded to the nearest 1/8 inch, to allow for a factor of safety of 1.5) is 2.375 inches

Answer:

6

Step-by-step explanation:

24/6 = 4

36/6 = 6

6 bags, 4 lollipops and 6 pieces of gum in each bag.

Answer:

12 bags

Step-by-step explanation:

You would need to find the GCF of both numbers: 12

24*12 = 2

38*12 = 4

12 bags with 2 lollipops and 4 pieces of gum in each

The linear function that represents the cost of an adult ticket in dollars for a customer who contributes x cans of pet food is of:

y = 9.5 - 0.75x.

The graph is given by the image shown at the end of the answer.

The general format of a linear function is given by the rule shown as follows:

y = mx + b.

The terms of the linear function are listed and explained as follows;

The values of these terms in this function are given as follows:

The costs for the amounts of cans are given as follows:

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Answer:

Step-by-step explanation:

the answer would be 73 since the angle is split in half which means that they are both equal to each other

The Proportion of exam results between 82 and 89.2 points is 0.3330.

What is standard deviation?

A measurement of a data set's deviation from the mean is referred to as "standard deviation" (or ""). A low standard deviation means that the data are grouped around the mean, whereas a large standard deviation says that the data are more spread out..

For instance, the mean of the two integers 2, 7, 14, 22, 30 and 15, 15, 15, 14, 16 is the same. But the second is clearly more diffused.

Given:

Mean is 83.2 points, and

8 points is the standard deviation.

Consequently, the proportion is

P(82 ≤ x ≤ 89.2)

=P( 82- 83.2 / 8 ≤ z ≤ 89.2 - 83.2/8)

=P (0.75) - P(-0.15)

=0.7734 -(0.4404)

= 0.3330

So, the Proportion of exam results between 82 and 89.2 points is 0.3330.

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The solutions of the given equations are:

1. x = 5, -5

2. x = -6, 4

3. x = 3, -3

4. x = 1/2, -3

What is factorization?

Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.

Here, we have

1. x²-7= 18, by applying factorization

x² = 18 + 7

x² = 25

x = 5, -5

2. x² + 2x -24 = 0, by applying factorization

x² + 6x - 4x - 24 = 0

x(x+6)-4(x+6) = 0

(x-4)(x+6) = 0

x = 4,-6

3. 4x² + 2 = 38, by applying factorization

4x² = 36

x² = 9

x = 3, -3

4. 2x² + 5x -3 = 0, by applying factorization

2x² + 6x - x - 3 = 0

2x(x +3) -1(x+3) = 0

(2x-1)(x+3) = 0

x = 1/2, -3

Hence, The solutions of the given equations are:

1. x = 5, -5

2. x = -6, 4

3. x = 3, -3

4. x = 1/2, -3

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The dimensions of the box of height 36in and the side of the square is 18in.

A topological measure of the size of an object's covering properties is its dimension. It is roughly the number of coordinates required to specify a point on the object.

Given that the u.s.post office will accept a box for shipment only if the sum of height and girth(the distance around of bottom) is at most 108 in.

We must first determine the box's dimensions.

Let s be the side of the square base and h be the height of the box

So , h + 4s = 108

H = 108 – 4s -----(1)

Volume = s^2 h

V = s^2(108-4s)

= 108s2 – 4s3

V’ = 216s – 12s2

Let v’ = 0

S[216-12s] = 0

216 – 12s = 0

12s = 216

S = 216/12

S = 18

V” = 216 – 24s for s =18

V” = 216 – 432

= -216(-ve)

Volume is maximum when s =18

So h= 108-72

=36 in

Therefore the dimensions of the box of height 36in and the side of the square is 18in.

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Answer:

  A. 1/2

  D. -1/3

Step-by-step explanation:

You want to know the solutions to 6x² -x -1 = 0.

We can factor the equation as ...

  6x² -3x +2x -1 = 0

  3x(2x -1) +1(2x -1) = 0

  (3x +1)(2x -1) = 0

The solutions will make the factors zero:

  3x +1 = 0   ⇒   x = -1/3

  2x -1 = 0   ⇒   x = 1/2

The solutions are 1/2 and -1/3.

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The angle in radians and the sector area are 2/9 π and 804.248 m² respectively

A sector of a circle is the part of a circle made of the arc along with its two radii

Given:  angle = 40° and distance(r) = 48m

To convert the angle to radians, multiply the angle by π/180:

Angle in radian(α) = 40 x π/180  = 2/9 π radian         (Note: π = 180°)

The formula for sector area = (α×r²)/2

Thus, sector area = (2/9π × 48²)/2 = 804.248 m²

Therefore, the angle in radians is 2/9 π and the sector area is 804.248 m²

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Answer:

C. Both

Step-by-step explanation:

You would substitute the coordinates into the equation to find the answer.

(4,-1)

-1 + 1 = 3 (4-4)

0 = 0

(5,2)

2 + 1 = 3(5-4)

3 = 3

The value of d i s 1 .

ie. d=1

Define linear equation .

An equation between two variables that gives a straight line when plotted on a graph.

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables .

Given:

d - 10 - 2d + 7 = 8 + d - 10 - 3d

On rearranging the given equation ,we get

In other words on taking the like terms to on one side ,so

⇒(d-2d-d+3d)=(8-10+10-7)

⇒d=1

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The number of students studying abroad in 2001 is 150.38 thousand

The number of students studying abroad in 2018 is 467.53 thousand

The given equation is known as an exponential equation. An exponential equation is a non-linear equation.

The given equation is 123.1(1.069)^x

Where:

Number of students studying abroad in 2001 = 123.1(1.069)^3= 150.38 thousand

Number of students studying abroad in 2018 = 123.1(1.069)^20 = 467.53 thousand

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Answer:

Step-by-step explanation:

4x - 3y = 8

5x - 2y = -11

8x - 6y = 16

-15x + 6y = 33

-7x = 49

x = -7

4(-7) - 3y = 8

-28 - 3y = 8

-3y = 36

y = -12

The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

[tex]\pi[/tex](R +3)^2

Area of the pool is:

[tex]\pi R^2[/tex]

Now, Our equation is:;

[tex]\pi[/tex](R +3)^2 - [tex]\pi R^2[/tex] = 198

[tex]\pi[/tex]((R+3)^2 - [tex]R^2[/tex]) = 198

Open the inner bracket :

[tex]\pi[/tex]([tex]R^2+6R+9-R^2[/tex]) = 198

[tex]\pi[/tex](6R +9) = 198

6R+9 = 198/[tex]\pi[/tex]

6R = 198/[tex]\pi[/tex] - 9

R = (198/[tex]\pi[/tex] - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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Answer: 30,000

Step-by-step explanation: 50,000 - 20,000 = 30,000

If Tina's score is in the 50th percentile and the grades were normally distributed, Tina's score on the exam is 78.

A percentile refers to the comparison score between a particular score and the scores of the rest of a group. It represents the percentage of scores that a specific score surpassed. For example, if the score of 75 points on a test is ranked in the 85th percentile, it implies that the score 75 is higher than 85% of the scores. The 50th percentile, which is also the median score implies that 50% of the score is below or above the average score in a normally distributed data. In the given situation, if the grades are normally distributed with a mean of 78, that implies that 50% of the scores are above 78 and 50% of the scores are below 78. The standard deviation in this case is irrelevant. As Tina’s score is at the 50th percentile, her score on the exam would be 78.

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Answer:

a(647)

b(25)

Step-by-step explanation:

The exact value for the following expression {sec π/4 cos 2π/3}/{tan π/6 csc 3π/4} is - [tex]\sqrt{3} /2[/tex]

The expression is given that

{sec π/4 cos 2π/3}/{tan π/6 csc 3π/4}

Here we have to use the trigonometric functions

Find the each values of the term

sec π/4 = 1 / cos π/4

= 1 / (1 / [tex]\sqrt{2}[/tex] )

= [tex]\sqrt{2}[/tex]

Next term is cos 2π/3

cos 2π/3 = -1 / 2

Next term is tan π/6

tan π/6 = [tex]\sqrt{3}[/tex] / 3

Next term is csc 3π/4

csc 3π/4 =  [tex]\sqrt{2}[/tex]

Substitute the values in the expression

{sec π/4 cos 2π/3}/{tan π/6 csc 3π/4}

= (    [tex]\sqrt{2}[/tex] × (-1/2) ) / ( [tex]\sqrt{3}[/tex] / 3 ×  [tex]\sqrt{2}[/tex])

= - [tex]\sqrt{3} /2[/tex]

Hence, the exact value for the following expression {sec π/4 cos 2π/3}/{tan π/6 csc 3π/4} is - [tex]\sqrt{3} /2[/tex]

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The length of RT is 12 units.

What is length?

Distance is measured by length. Length is a quantity having the dimension distance in the International System of Quantities. Most measuring systems use a base unit for length from which all other units are derived. The metre is the basic unit of length in the International System of Units (SI). The greatest extended dimension of a stationary item is typically believed to be its length. This is not always the case, as it may depend on the location of the item. When there is a basis from which vertical measurements may be made, height is employed. When length is the greatest dimension, width or breadth generally relate to a lesser dimension.

given, RS+ST=RT

or, 9 + x - 1 = 3x

or, 8 + x = 3x

or, 3x - x = 8

or, 2x = 8

or, x = 8/2

or, x=4

Then, the length of RT = 3x = 3.4 = 12 units

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Answer:

4 (x+4)

Step-by-step explanation:

4x+16      =     4 * x   +   4*4    =   4 (x+4)