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QUESTION 1 ANSWER

The series is

[tex]\sum_{n=1}^{15}{ (2n-1)}[/tex]

So the nth term of this sequence is

[tex]U_n=2n-1[/tex]

We generate some few terms of the sequence as follows:

When [tex]n=1[/tex],

The first term of the sequence becomes,

[tex]U_1=2(1)-1[/tex]

[tex]U_1=1[/tex]

When [tex]n=2[/tex],

[tex]U_2=2(2)-1[/tex]

[tex]U_2=3[/tex]

When [tex]n=3[/tex],

[tex]U_2=2(3)-1[/tex]

[tex]U_2=5[/tex]

The constant difference is [tex]d=2[/tex].

The sum of the series is given by,

[tex]S_n=\frac{n}{2}(2a+(n-1)d)[/tex]

There are 15 terms in the series, therefore [tex]n=15[/tex]

 [tex]S_{15}=\frac{15}{2}(2(1)+(15-1)2)[/tex]

[tex]S_{15}=\frac{15}{2}(2+14(2))[/tex]

[tex]S_{15}=\frac{15}{2}(30)[/tex]

[tex]S_{15}=15\times 15[/tex]

[tex]S_{15}=225[/tex]

ANSWER TO QUESTION 2

The bottom row has [tex]23[/tex] boxes. This means [tex]a=U_1=23[/tex]

a) Since each row has 3 fewer boxes [tex]d=-3[/tex].

The nth row is given by,

[tex]U_n=23+(n-1)\times(-3)[/tex]

[tex]U_n=23+-3n+3[/tex]

[tex]U_n=23-3n[/tex]

The top row is the 6th row, meaning [tex]n=6[/tex].

[tex]U_6=23-3(6)[/tex]

[tex]U_6=23-18[/tex]

[tex]U_6=5[/tex]

b) The number of boxes in the entire display is given by

[tex]S_n=\frac{n}{2} (a+l)[/tex]

Where [tex]a=23[/tex], the first term(row) and [tex]l=5[/tex], the last term(row).

Since there are 6 rows,

[tex]S_6=\frac{6}{2} (23+5)[/tex]

[tex]S_6=3 (28)[/tex]

[tex]S_6=84[/tex]

ANSWER TO QUESTION 3

The number of visitors in the first week is [tex]a=5[/tex].

Since the number of visitors each week is doubled the number of visitors in the subsequent weeks, the sequence is a geometric progression with a common ratio of [tex]r=2[/tex].

The general term of a geometric sequence is

[tex]U_n=ar^{n-1}[/tex]

So in the 8th week, we have

[tex]U_8=5\times 2^{8-1}[/tex]

[tex]U_8=5\times 2^{7}[/tex]

[tex]U_8=5\times 128[/tex]

[tex]U_8=640[/tex]

Hence 640 people visited the website in the 8th week

Answer: [tex]\text{Length of AG=}\frac{2\sqrt{63}}{3}[/tex]

Explanation:  

Please follow the diagram in attachment.  

As we know median from vertex C to hypotenuse is CM  

[tex]\therefore CM=\frac{1}{2}AB[/tex]

We are given length of CG=4  

Median divide by centroid 2:1  

CG:GM=2:1  

Where, CG=4

[tex]\therefore GM=2[/tex] ft

Length of CM=4+2= 6 ft  

[tex]\therefore CM=\frac{1}{2}AB\Rightarrow AB=12[/tex]

In [tex]\triangle ABC, \angle C=90^0[/tex]

Using trigonometry ratio identities  

[tex] AC=AB\sin 30^0\Rightarrow AC=6[/tex] ft

[tex] BC=AB\cos 30^0\Rightarrow BC=6\sqrt{3}[/tex] ft  

[tex] CN=\frac{1}{2}BC\Rightarrow CN=3\sqrt{3}[/tex] ft

In [tex] \triangle CAN, \angle C=90^0[/tex]  

Using pythagoreous theorem  

[tex]AN=\sqrt{6^2+(3\sqrt{3})^2\Rightarrow \sqrt{63}[/tex]

Length of AG=2/3 AN

[tex]\text{Length of AG=}\frac{2\sqrt{63}}{3}[/tex] ft

we are given

[tex](-3+5i)^2[/tex]

we can expand it

[tex](-3+5i)^2=(-3+5i)(-3+5i)[/tex]

now, we can FOIL it

[tex](-3+5i)^2=-3\times -3-3\times 5i+5i\times -3+5i\times 5i[/tex]

now, we can simplify it

[tex](-3+5i)^2=9-15i-15i+25i^2[/tex]

we know that

[tex]i^2=-1[/tex]

so, we can plug it

[tex](-3+5i)^2=9-30i+25(-1)[/tex]

[tex](-3+5i)^2=9-30i-25[/tex]

[tex](-3+5i)^2=-16-30i[/tex]..............Answer

Answer:

[tex]80\leq x\leq 70[/tex]

Step-by-step explanation:

Mr. Venn knows that 60% of his students will score no more than 5 points above or below the class average, 75%, on the test.

Means the greater marks can be up to 80 and lowest marks can be up to 70.

So, the inequality that represents the test scores of 60% of his students is :

[tex]80\leq x\leq 70[/tex]

11.46% is the percent increase

Answer:

4.44 is your answer

Step-by-step explanation:

Isolate the x. Multiply -4 to both sides

(x/-4)(-4) = (-1.11)(-4)

x = (-1.11)(-4)

Multiply

x = 4.44

4.44 is your answer

~

Answer:

The value of x is 4.44.

Step-by-step explanation:

Given : Expression [tex]\frac{x}{-4}=-1.11[/tex]

To find : What is the value of x?

Solution :

Expression [tex]\frac{x}{-4}=-1.11[/tex]

Multiply both side by 4,

[tex]\frac{x}{-4}\times 4=-1.11\times 4[/tex]

[tex]-x=-4.44[/tex]

Cancel negative sign both side,

[tex]x=4.44[/tex]

Therefore, The value of x is 4.44.

5 x 10^2

= 5 x 100

= 500

Alright, so to solve this we have to use P.E.M.D.A.S. There are no parenthesis, so we move on to exponents. 10^2. Well, we know that 10 multiplied by 10 is 100. So the new equation is 5 multiplied by 100. The answer is 500.

D. 27.6 is your answer

c or a !!!!!!!!!!!!!!!!!!!

-24n2+31 if im correct!

Answer:

[tex]-24n^2 + 31[/tex]

Step-by-step explanation:

[tex]7 - 3[(n^3 + 8n) divide (-n) + 9n^2][/tex]

To simplify it we use order of operation PEMDAS

Parenthesis , exponents , multiply, divide, add and subtract

[tex]7 - 3[(n^3+ 8n) divide (-n) + 9n^2][/tex]

LEts start with parenthesis (divide by -n)

[tex]7 - 3[-n^2-8+ 9n^2][/tex]

Now we simplify the parenthesis by combining like terms

[tex]7 - 3[-8+8n^2][/tex]

multiply by -3

[tex]7+24 -24n^2[/tex]

[tex]-24n^2 + 31[/tex]

 -6x - 2y = -18

-6x - 2(0) = -18

   -6x - 0 = -18

        -6x = -18

         -6      -6

           x = 3

hope this helps :)

Answer: 3

Step-by-step explanation:

a = 0.19

0.38/2 = 0.19

For this case we have the following:

So:

[tex]x ^ 2 + x^{\frac{1}{2} }+ x + 6[/tex] is not a polynomial

Answer:

Option B

The expression which is not a polynomial is:

            B)   [tex]x^2+x^{\dfrac{1}{2}}+x+6[/tex]

We know that the general form of a polynomial expression is given by:

[tex]P(x)=a_nx^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+......+a_2x^2+a_1x+a_0[/tex]

i.e. P(x) is a polynomial of degree n  , where n belongs to natural numbers and [tex]a_i's[/tex] belong to the real numbers.

and [tex]a_n\neq 0[/tex]

A)

[tex]\dfrac{3}{x^{-1}}+\dfrac{3}{2}[/tex]

which could also be written by:

[tex]3x+\dfrac{3}{2}[/tex]

Hence, this expression is a polynomial expression.

Option: a is incorrect.

B)

[tex]x^2+x^{\dfrac{1}{2}}+x+6[/tex]

Since in the second term the power of x does not belong to the set of natural numbers.

Hence, option: b is not a polynomial expression.

Hence, the correct answer is option: b

C)

[tex]x^3-9[/tex]

Since, the expression matches the definition of the polynomial expression.

Hence, option: c is incorrect.

D)

[tex]\sqrt{16x^4}[/tex]

This could also be written as:

[tex]=4x^2[/tex]

Hence, it is a polynomial expression.

Hence, option: d is incorrect.

If s, r and t are given right lines in the same plane and with condition

s⊥t  and r⊥t we can conclude that s║r ( s and r are parallel).

Good luck!!!

The conclusion is;

line r and s are parallel lines.

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.

Given:

We have lines r, s and t in the same plane.

And s⊥t and r⊥t.

That means,

The conclusion is line r and s are parallel lines.

Therefore, r and s are parallel lines.

To learn more about the parallel lines;

brainly.com/question/16701300

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To break even, the Waxmans need to make $5000 in profit. This can be achieved by selling 500 square yards of carpet, considering they make $10 profit per square yard.

In order for the Waxmans to break even, they will need to cover their startup costs through the profits they make selling carpet. The profit made per square yard of carpet sold is the selling price ($18) minus the cost per square yard ($8), which equals $10. Therefore, to break even, they would need to sell $5000 worth of profit. This means selling $5000/$10 = 500 square yards of carpet.

Learn more about Break Even Calculation here:

https://brainly.com/question/34658934

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Answer:

200 visitors went to screen 1.

125 visitors went to screen 2.

175 visitors went to screen 3.

Step-by-step explanation:

We will find number of visitors who went to screen 1 by finding 40% of 500 as we are told that 40% of 500 visitors went to screen 1.

[tex]500*\frac{40}{100} =5*40=200[/tex]

Therefore, 200 visitors went to screen 1.

Now we will find number of visitors who went to screen 2. We are told that 25% of 500 visitors went to screen 2.

[tex]500*\frac{25}{100} =5*25=125[/tex]

Therefore, 125 visitors went to screen 2.

Now we will find the number of visitors who went to screen 3 by subtracting combined number of visitors who went to screen 1 and screen 2 from total number of visitors.

[tex]500-(200+125)[/tex]

[tex]500-325=175[/tex]

Therefore, 175 visitors went to screen 3.

The answers are 2 and 4

The graph of the equation is the set of all points that are solutions of the equation and point (10, 3) is on the graph of the equation thus, options (A) and (D) are correct.

A graph is a diametrical representation of any function between the dependent and independent variables.

The graph is easy to understand the behavior of the graph.

For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.

A graph is the locus of all points that are the solution of the function.

Substitute x = 10 into y = (1/2)x - 2

y = (1/2)10 - 2

y = 5 - 2 = 3 thus, (10,3) will be on the graph.

Hence "The graph of the equation is the set of all points that are solutions of the equation and point (10, 3) is on the graph of the equation".

To learn more about graphs,

brainly.com/question/16608196

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After investing $400 in an account with 3% interest compounded annually, the balance after one year will be $412.

The question is asking how much the balance will be after investing $400 in an account that pays 3% interest compounded annually after one year. The formula to calculate compound interest is [tex]A = P(1 +\frac{ r}{n})^{nt[/tex], where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. As the interest is compounded annually, n is 1.

For this question, we substitute P with $400, r with 0.03 (3% as a decimal), n with 1 (since it's compounded annually), and t with 1 (since it's compounded for one year).

Now, our formula looks like this: [tex]A = 400(1 + \frac{0.03}{1})^{1*1[/tex] = 400(1 + 0.03) = 400 * 1.03 = $412.

Therefore, after one year, the balance in the account will be $412.

Answer: Choice A)

x^2 + (x+2)^2 = (x+4)^2

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Consecutive even integers are whole numbers that are as close as possible and they are also even as well. One example of having 3 of them is {2, 4, 6}. Another example is {4,6,8} and another example is {6,8,10}. You start with any even integer you want, then count up by 2 each time to get the next values.

In general, if x is your first even number, then x+2 is the next number up. Eg: x = 10 so x+2 = 10+2 = 12. Then after that, x+4 is the third number (if x = 10, x+4 = 10+4 = 14)

a = x is the side length of the shorter leg

b = x+2 is the side length of the longer leg

c = x+4 is the side length of the hypotenuse

Use the pythagorean theorem to get

a^2 + b^2 = c^2

x^2 + (x+2)^2 = (x+4)^2

Answer : (0,3) U  (3, ∞)

We need to find  the interval(s) over which the function is decreasing

We look at the intervals of x  where the graph is decreasing

Decreasing interval of the graph is the part where the graph goes down

We look at the part where the graph changes direction

In the middle  inverted U shaped graph , the graph changes direction and start decreasing at x=0

the graph is decreasing till x=3

so first decreasing interval is x=0  to 3. we write it as (0,3)

After x=3 the graph starts decreasing and it goes to infinity

So the second decreasing interval is 3  to infinity . We write it as (3, ∞)

Now combine both intervals by a 'U' union

(0,3) U  (3, ∞)

Graph Behavior u3l10

1. (-∞,-1) U (-1,0)
2. (0,3) U (3,∞)
3. x-intercept: none | y-intercept: (0,-4)
4. x=-1, x=3, y=0
5. even
6. (-∞,-4)
7. x-intercepts: (0,0),(3,0) | y-intercepts: (0,0)
8. f(3)=6
9. There is a jump discontinuity at x=-3
10. neither
11. f(x)=x/x^8+8x^4-7 | f(x)=x^3+4x
12. f(x) --> -∞ as x --> ∞ and f(x) --> 0 as x --> -∞
13. 2nd and 3rd graph (2nd graph has left arm facing down and right arm facing up and 3rd graph looks like a W)
14. 1st and 4th graph (1st graph has 2 lines, the one on the left side is point upwards and the line on the right side is pointing downwards, 4th graph is 1 line with the left arm facing up and right arm facing down)
15. reciprocal; y=1/x
16. f(x)=x^3
17. power; y=x^n | root; y=n√x
18. power; y=x^n ; n is even and greater than 0 | absolute value; y=|x|
19. reflection over the x-axis | horizonal compression by a factor of 3
20. reflection over the y-axis | horizontal shift to the left 2 units
21. reflection
22. 1st graph (starts from the left side (-2,0) and points towards the right side a bit more downwards)
23. 1st graph (ill describe it as a right angle with the curve facing left on the negatives side or a point where the curve is on is (-2,0))

happy "studying"!

The answer is 256.25

EXPLANATION

Let [tex]x[/tex] represent the number.

Then, [tex]\frac{16}{100}x=41[/tex]

We cross multiply yo obtain,

[tex]16x=41\times 100[/tex]

We now divide both sides by 16.

[tex]x=\frac{4100}{16}[/tex]

This will give us,

[tex]x=256.25[/tex]

Therefore the number is 256.26

Hello,

The answer is A or y= 3/2x+9

How to solve;

The formula: Y=mx+b

Now solve the problem: 3x-2y=-18

Subtract -3x from both sides.

Now we have -2y=-3x-18

So divide both sides by y to get y by it self.

-2/-2=-3x-18/-2

Simplify and the answer is y=3/2x+9

Thus answer A

Hope that helps have a great day.

Answers: Angle A is 36 degrees, angle C is 54 degrees

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Work Shown:

The angles A and C are complementary, meaning they add to 90 degrees.

(Angle A) + (Angle C) = 90

(2x-4) + (2x+14) = 90

(2x+2x)+(-4+14) = 90

4x+10 = 90

4x+10-10 = 90-10 .... subtract 10 from both sides

4x = 80

4x/4 = 80/4 ..... divide both sides by 4

x = 20

If x = 20, then,

angle A = 2x-4 = 2*20-4 = 40-4 = 36 degrees

angle C = 2x+14 = 2*20+14 = 40+14 = 54 degrees

Note how A+C = 36+54 = 90 which helps confirm our answers.