Rewrite 6/4 as a percent. Make sure to label your answer with %.

Answer:

[tex]a_{n}[/tex] = 3n - 1

Step-by-step explanation:

There is a common difference d between consecutive terms, that is

d = 5 - 2 = 8 - 5 = 11 - 8 = 14 - 11 = 3

This indicates the sequence is arithmetic with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = 3 , thus

[tex]a_{n}[/tex] = 2 + 3(n - 1) = 2 + 3n - 3 = 3n - 1

The expression for the nth term of the series is [tex]a_n = 3n-1[/tex].

Given that,

Sequence; 2, 5, 8, 11, 14.

We have to find, the expression in terms of n for the nth term of the following given sequences?

According to the question,

The nth of the arithmetic sequence is,

[tex]\rm a_n = a+ d(n-1)[/tex]

Where a is the first term of the sequence,

d is the common difference between the terms,

n is the number of terms.

Then,

The given sequence is 2, 5, 8, 11, 14.

Here, the common difference between the terms is 3.

And the first term of the sequence is 2.

Substitute all the values in the formula,

Therefore,

The nth term of the given terms is,

[tex]\rm a_n = a+ d(n-1)\\\\a_n = 2+ 3(n-1)\\\\a_n + 2+3n-1\\\\a_n = 3n-1[/tex]

Hence, The required expression for the nth term of the series is [tex]a_n = 3n-1[/tex].

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Answer:

vertex = (4, 5 )

Step-by-step explanation:

The equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

f(x) = 3(x - 4)² + 5 ← is in vertex form

with vertex = (4, 5 )

Answer:

2(L+W)H

Step-by-step explanation:

Surface area= 2(L+W)H

Answer: 0

I didn't see an 'x' so I was very confused but I simplified and got "0"

Answer:

X = 1

Step-by-step explanation:

2x^2 + x - 1 = 2

2x^2 + x - 3 = 0

2x^2 + 3x -2x - 3 = 0

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

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

x-1=0

x=1

2x+3=0

2x=-3

x=-3/2.

Answer:

4.3 cm

Step-by-step explanation:

By the theorem of intersecting secants outside of a circle.

[tex]3 \times (y + 3) = 2 \times (2 + 6 + 3) \\ 3(y + 3) = 2 \times 11 \\ 3y + 9 = 22 \\ 3y = 22 - 9 \\ 3y = 13 \\ y = \frac{13}{3} \\ y = 4.3 \: cm[/tex]

Answer:the answer is 2 it will take jasmine 3hrs to travel 135 miles

Step-by-step explanation:

Answer: 1; -5

Step-by-step explanation:

For this problem, we are asked to find the slope and y-intercept.

We see that this linear line goes through the y-axis at (0,-5). therefore, our y-intercept is -5.

To find the slope, we would use the formula [tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]. We can use the points (0,-5) and (5,0) since we can clearly see the line goes through these 2 points.

[tex]m=\frac{0-(-5)}{5-0} =\frac{5}{5} =1[/tex]

From our formula, we found that the slope is 1.

For the first box, you would fill in 1, the slope. The second box would be -5, the y-intercept.

Answer:

y = x - 5

Step-by-step explanation:

One can immediately read off the slope, m, from the graph:  m = 5 / 5 = 1.

The y-intercept is (0, -5).

In slope-intercept form the equation of this graph is y = x - 5

Answer:

103.8

Step-by-step explanation:

Length of diagonal of a cube is given by the formula:

[tex]d = side \times \sqrt{3} \\ \\ \therefore \: d = 60 \times \sqrt{3} \\ \\ \therefore \: d = 60 \times 1.73 \\ \\ \therefore \: d = 103.8 \: units[/tex]

The length of the diagonal of the cube is 103.9 units.

What is a cube?

A cube is a three dimensional figure or object which has all the side with equal length.

The length of each side of the cube = a = 60 units.

Therefore, the length of the diagonal of the cube = d = a[tex]\sqrt{3}[/tex] = 60[tex]\sqrt{3}[/tex] units = 103.9 units.

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Answer:

Answer:  The box measurements are as follows: Box A: height = 5 inches, length = 18 inches, width = 10. Box B: height = 8 inches, length = 10 inches, ..

Step-by-step explanation:

is this the answer you were looking for

Answer:

43 2/5

Step-by-step explanation:

change each of the mixed fractions to improper fraction.

-11  2/3 = -31/3

-4 1/5 = -21/5.

Multiply them now:

-31/3 x -21/5 = 651/15

Then turn 651/15 to a mixed fraction because the question was in mixed fractions:

43 6/15 = 43 2/5 (simplified)

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1.50 for beads x 5 necklaces = 7.50

Total.

18.50 -7.50 = 11.00

11.00 / 5 = $2.20 for was pendant

Answer:

( 3x + 1) (2x+5)

Step-by-step explanation:

6 x ^2 + 17 X + 5​

We break the 6 into 3 and 2

(3x    ) (2x   )

We need the middle term to be 17

( 3x + 1) (2x+5)

3*5+2 = 17 so it works

Answer:

x=-4.22222

The 2 is repeating

Step-by-step explanation:

First you subtract 18 from both sides

9x=--38

Then divide both sides by 9

x=-4.22222

The 2 is repeating

AnsWER

X=-2/9

Step-by-step explanation:

9X=-20-18

9X=you will divide both sides by -9

X=-2/9

Answer:

Proper fraction.

Step-by-step explanation:

[tex] \frac{85}{100} \\ \\ simplify to= \frac{17}{20} [/tex]

Answer:

x value is 10 as per as the question its value is 10

Answer:

d. (3, 8)

Step-by-step explanation:

the coordinates of point W " on the final image is (3 8) Solution-means first the point is translated left by 4 units and translated up by 2 units then it is reflected across y axis. (the rules follow right to left approach) The co-ordinate of point W is ( 1 6 ). After 4 units translation to left and 2 units translation to up the co-ordinates

Answer:

{-12,12}

Step-by-step explanation:

-|-x| = -12 multiply both sides by -1

|-x| = 12 apply rule for solving absolute value equations

-x = 12 and -x = -12 solve

x = -12 and x =12

Answer:

301.44 cm ^ 2

Step-by-step explanation:

We have that the total surface area of a cone would be the sum of the base area and the lateral surface area.

the area of the base, being a circle is pi * r ^ 2

the lateral area would come being the multiplication between the inclined height, the radius and the number pi, that is to say pi * r * l

the inclined height is calculated using the Pythagorean theorem, the legs being the radius and the altitude, thus:

l ^ 2 = 6 ^ 2 + 8 ^ 2

l ^ 2 = 100

l = 10

Therefore, we can replace:

A = 3.14 * 6 ^ 2 + 3.14 * 10 * 6

A = 301.44

It means that the total surface area is 301.44 cm ^ 2

Answer:110

Step-by-step explanation:x^2+17x=15x+35

x^2+17x-15x-35=0

x^2+2x-35=0

delta=2^2-4*1*(-35)=4+140=144

x1=(-2+V144)/2=(-2+12)/2=10/2

x=5

so 15*5+35=75+35=110

Answer:

Step-by-step explanation:

In a regular polygon, each side has the same length.

Therefore we have the equation:

[tex]x^2+17x=15x+35[/tex]

We must specify the domain:

[tex]x^2+17x>0\ \wedge\ 15x+35>0\\\\x(x+17)>0\ \wedge\ 15x>-35\\\\(x<-17\ \vee\ x>0)\ \wedge\ x>-\dfrac{7}{3}\Rightarrow x>0[/tex]

[tex]x^2+17x=15x+35\qquad\text{subtract}\ 15x\ \text{from both sides}\\\\x^2+17x-15x=15x-15x+35\\\\x^2+2x=35\qquad\text{add 1 to both sides}\\\\x^2+2x+1=35+1\\\\x^2+2(x)(1)+1^2=36\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+1)^2=36\to x+1=\pm\sqrt{36}\\\\x+1=\pm6\qquad\text{subtract 1 from both sides}\\\\x+1-1=\pm6-1\\\\x=-7\ \vee\ x=5[/tex]

[tex]x<-7\notin\text{domain};\ x=5\in\text{domain}[/tex]

The length of a side:

[tex]x^2+17x=5^2+17(5)=25+85=110\\\\15x+35=15(5)+35=75+35=110[/tex]

Answer:

0.427

Step-by-step explanation:

Standard error for the sampling distribution refers to the standard deviation of the samples taken from a population. The standard error equals the standard deviation divided by the square root of the sample size

The probability of customers who drink tea (p) = 24% = 0.24, the sample size of customers (n) = 300.

Standard error = [tex]\frac{\sigma}{\sqrt{n} }[/tex] where σ is the standard deviation.

[tex]\sigma=\sqrt{np(1-p)}[/tex]

Standard error = [tex]\frac{\sigma}{\sqrt{n} }= \frac{\sqrt{np(1-p)} }{\sqrt{n} } =\sqrt{\frac{np(1-p)}{n} } =\sqrt{p(1-p)}=\sqrt{0.24(1-0.24)} =0.427[/tex]

Answer: a=2

Step-by-step explanation:

-14a=-28

divide both sides by -14

a=2

Answer:

x = 5, y = 9.

Step-by-step explanation:

8^x / 2^y = 64

3^4x * (1/9)^(y -1) = 81

From the first equation

2^3x / 2^y = 2^6

2^(3x-y) = 2^6

So 3x - y = 6  ..........(1)

From the second equation:

3^4x * 9^(-(y-1)) =  3^4

3^4x * 3^2(-(y-1)) = 3^4

3^(4x+ 2(1 - y)) = 3^4

So 4x + 2(1 - y) = 4

4x - 2y = 2

2x - y = 1   .............(2)

Subtract: (1) - (2):

x = 5.

and  2(5) - y = 1

so y = 9.

Solving the simultaneous equations we get x is 5  and y is 9 .

Simultaneous equations in algebra are those that concurrently involve two or more variables, such as x and y. Even though they are solved simultaneously, the equations are known as simultaneous equations. Just these equations alone have innumerable answers.

A system of equations, often known as an equation system, is a collection of finite equations for which common solutions are sought.

The two given equations can be simplified as:

[tex]8^x \div 2^y = 64\\\\or,\frac{2^{3x}}{2^y} =2^6\\\\or, 2^{3x-y}=2^6\\\\or, 3x-y = 6[/tex]

And :

[tex]3^{4x} \times (\frac{1}{9})^{y-1}=81\\\\or, 3^{4x} \times 3^{-2(y-1)}=3^4\\\\or, 3^{4x+2-2y}=3^4\\\\or, 4x-2y = 2\\\\or,2x-y=1[/tex]

Now we can solve the two simultaneous equations :

3x - y = 6 and 2x - y = 1

Subtracting the equations we get:

x = 5

and

y = 9

Solving the simultaneous equations we get the value of x as 5 and the value of y as 9 .

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Answer:

You can't use this rule because the two exponents have different bases. In order to use this rule the two exponents must have the same base.

Answer:

It is because both expressions have different base value. For this question, the bases are 3 and 2 where the product rule cannot be applied. Product rule can only be used when both expressions have the same bases.

The required linear regression equation is [tex]y = 21.6x + 1093.2[/tex].

The projected number of new cases for 2013 is 1352.

Given that,

The number of newly reported crime cases in a county in New York State is shown in  the accompanying table,

Where x represents the number of years since 2001, and y  represents number of new cases.

We have to determine,

The linear regression equation that represents  this set of data.

And Using this  equation, find the projected number of new cases for 2013.

According to the question,

The line of best-fit is given by:

[tex]y = bx+a[/tex]

Assume [tex]y = kx + b[/tex]

And,

[tex]k = \dfrac{change \ in \ y} {change \ in \x }\\\\k = \dfrac{1194-1086}{5-0}\\\\k = \dfrac{108}{5}\\\\k = 21.6[/tex]

Then, pass from the point (3, 1158),

[tex]y = kx + b \\\\1158 = 21.6 \times 3 + b \\\\1158 = 64.8 +b \\\\b = 1158 - 64.8\\\\b = 1093.2[/tex]

Then ,

The projected number of new cases -  the number of years since 2001

[tex]= 2013-2001 \\\\= 12[/tex]

Therefore,

[tex]y = 21.6\times 12 + 1093.2\\\\y = 259.2 + 1093.2 \\\\y = 1352.4\\\\y = 1352 \ approx[/tex]

Hence , The required linear regression equation is [tex]y = 21.6x + 1093.2[/tex].

And The projected number of new cases for 2013 is 1352.

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Answer:

240g of cocoa

Step-by-step explanation:

96/24 = 4 times as many brownies, 4 times as many ingredients needed. To find the amount of cocoa, multiply the original amount by four to get 60g × 4 = 240g.