Photo attached please help

Given:

The sum of two terms of GP is 6 and that of first four terms is [tex]\dfrac{15}{2}.[/tex]

To find:

The sum of first six terms.​

Solution:

We have,

[tex]S_2=6[/tex]

[tex]S_4=\dfrac{15}{2}[/tex]

Sum of first n terms of a GP is

[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]              ...(i)

Putting n=2, we get

[tex]S_2=\dfrac{a(1-r^2)}{1-r}[/tex]

[tex]6=\dfrac{a(1-r)(1+r)}{1-r}[/tex]

[tex]6=a(1+r)[/tex]                    ...(ii)

Putting n=4, we get

[tex]S_4=\dfrac{a(1-r^4)}{1-r}[/tex]

[tex]\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}[/tex]

[tex]\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}[/tex]

[tex]\dfrac{15}{2}=6(1+r^2)[/tex]            (Using (ii))

Divide both sides by 6.

[tex]\dfrac{15}{12}=(1+r^2)[/tex]

[tex]\dfrac{5}{4}-1=r^2[/tex]

[tex]\dfrac{5-4}{4}=r^2[/tex]

[tex]\dfrac{1}{4}=r^2[/tex]

Taking square root on both sides, we get

[tex]\pm \sqrt{\dfrac{1}{4}}=r[/tex]

[tex]\pm \dfrac{1}{2}=r[/tex]

[tex]\pm 0.5=r[/tex]

Case 1: If r is positive, then using (ii) we get

[tex]6=a(1+0.5)[/tex]  

[tex]6=a(1.5)[/tex]  

[tex]\dfrac{6}{1.5}=a[/tex]  

[tex]4=a[/tex]

The sum of first 6 terms is

[tex]S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}[/tex]

[tex]S_6=\dfrac{4(1-0.015625)}{0.5}[/tex]

[tex]S_6=8(0.984375)[/tex]

[tex]S_6=7.875[/tex]

Case 2: If r is negative, then using (ii) we get

[tex]6=a(1-0.5)[/tex]  

[tex]6=a(0.5)[/tex]  

[tex]\dfrac{6}{0.5}=a[/tex]  

[tex]12=a[/tex]  

The sum of first 6 terms is

[tex]S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}[/tex]

[tex]S_6=\dfrac{12(1-0.015625)}{1.5}[/tex]

[tex]S_6=8(0.984375)[/tex]

[tex]S_6=7.875[/tex]

Therefore, the sum of the first six terms is 7.875.

Answer:

36

Step-by-step explanation:

You do 6+6+12+12

*3 times 4= the two twelves

Answer and explanation:

Probability = number of favorable outcomes/ total number of outcomes

Since all glasses labelled C, D, and P are all same Cola

Probability that C is ranked first = 1/3

Probability that D is ranked last = 1/3

Answer:

it's 3 =^_^=

Step-by-step explanation:

Answer:

3 I think :)

Step-by-step explanation:

square root of 9 is 3

Answer:

The solution to the given inequality

 [tex]h\geq \frac{-1}{21}[/tex]

Step-by-step explanation:

Given inequality

                      [tex]\frac{-1}{3h} \leq 7[/tex]

             ⇒     -1≤ 7× 3h

             ⇒     -1 ≤ 21 h

             ⇒    21 h ≥ -1

            ⇒       [tex]h\geq \frac{-1}{21}[/tex]

Answer:

The probability is 13.33%

Step-by-step explanation:

Probability

The probability of an outcome is defined as the frequency of the number of times the outcome occurs (f) relative to the number of times that it could have occurred (n).

The formula to calculate the probability is:

[tex]\displaystyle P=\frac{f}{n}[/tex]

Marcus rolled a number cube and the results are recorded in a table where it can be noted that the number five rolled f=24 times. The total number of trials is n=30+45+30+28+24+23=180.

The probability that the next roll is a five is:

[tex]\displaystyle P=\frac{24}{180}[/tex]

Simplifying:

[tex]\displaystyle P=\frac{24}{180}[/tex]

[tex]\displaystyle P=\frac{2}{15}[/tex]

Dividing:

[tex]\displaystyle P=0.1333 = 13.33\%[/tex]

The probability is 13.33%

Answer:

37.50÷75=0.5 so first you are dividing bcus u need to find what percentage she has saved.

Answer:

O.5 because u need to divide and give me brainlessly plz

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

i got this from camellarosegarcia. thank you camellarosegarcia!!!

also got it right on Khan    :)

The answer of probability that the garment Iman chooses is pink or a blue shirt is 1/2

Probability means possibility.

It is a branch of mathematics that deals with the occurrence of a random event.

The value is expressed from zero to one.  

The meaning of probability is basically the extent to which something is likely to happen.

Divide the number of events by the number of possible outcomes. This will give us the probability of a single event occurring.

In this case Iman has 2 choices pink or blue

So the probability that the garment Iman chooses is pink or a  blue shirt

is  1/2 .

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Answer:

2(x+3)(x2+1)

Step-by-step explanation:

let

x = the cost of the cabinet

y = the cost of a chair

z = the cost of a table

A cabinet, 4 chairs and 2 tables cost $825

x + 4y + 2z = 825

The cabinet costs 3 times as much as a chair

x = 3y

The table costs $120 more than a chair

z = 120 + y

by solving the system of equations

x + 4y + 2z = 825

x = 3y

z = 120 + y

we find

x = $195

Answer:

15 gallons of paint

Step-by-step explanation:

5 x 3 = 15

equal groups !

Answer:

- AB is similar to YZ because all the sides from triangle ABC got multiplied by 3/4, and 40 times 3/4 = 30.

- AC is similar to YX because 50 times 3/4 = 37.5.

- CB is similar to XZ because 60 times 3/4 = 45.

hope this helps!

Answer:

0 tablespoons and 2 teaspoons

Step-by-step explanation:

method 1:

Do the calculation in teaspoons for accuracy:

1173 tablespoons and 1 teaspoons = 1173*3 + 1 = 3520 teaspoons

Now 3520 / 1760 = 2 teaspoons exactly.

Hence the answer is 2 teaspoons.

method 2:

1173 / 1760 ≈ 0.666 tablespoons ≈ 1.998 teaspoons

1 / 1760 ≈ 0.00057 teaspoons

1.998 + 0.00057 ≈ 2 teaspoons

Method 1 is clearly more accurate

Answer:

1

Step-by-step explanation:

The simplest ratio is 4:9

The triangle that is similar to this triangle from the given rectangle is triangle FED

Similar shapes are shaped with similar sides and angles. From the given diagram, we are to determine with the triangle is similar to the triangle AED.

Learn more on similar shapes here; https://brainly.com/question/2644832

Answer:

area of rectangle=length ×breadth

area of rectangle=12yd×15yd

area of rectangle=180yd²

Answer:

His school is 1.5 miles away :)

Step-by-step explanation:

6/4 = 1.5 miles

1.5 miles means his house is 1.5 miles from his school

Check the answer (1.5 times 3) = 4.5 miles so his job is 4.5 miles away.

4.5 + 1.5 = 6 miles

The distance between Salvador's house and his school is 1.5 miles

Let :

Therefore;

Then ;

Since, house is in between job and school :

The distance from house to school = d ; hence, distance between his house and school is 1.5 miles.

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Answer: 560

Step-by-step explanation:     2.5 percent (calculated percentage %) of what number equals 14? Answer: 560.

The unknown number will be; 560.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent considered thing is of "a" is b%. Then the percent shows per 100 (since cent means 100).

a x b/100 = a x b%

WE need to find the 2.5% of unknown number is 14.

Let the unknown number be x

Then;

2.5% of x = 14.

Simplify;

2.5/100 × x = 14

0.0025 × x = 14

x = 14/0.0025

x = 560

Hence, the  unknown number will be; 560.

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Answer:

b i think because for it to be imaginary, im sure there has to be an i in the equation

Answer:

A) Two Real Solutions

Step-by-step explanation:

Correct on Big Ideas Math :)

Answer:

340.6

Step-by-step explanation:

355 - 7.2 * 2 =

355 - 14.4 =

340.6

Answer:

C

Step-by-step explanation:

[tex]y = 2x + 3 \\ y = 3x + 1 \\ 2x = y - 3 \\ x = 0.5y - 1.5 \\ y = 3(0.5y - 1.5) + 1 \\ y = 1.5y - 4.5 + 1 \\ y - 1.5y = - 3.5 \\ 0.5y = 3.5 \\ y = 7[/tex]

[tex]x = 0.5(7) - 1.5 \\ x = 3.5 - 1.5 \\ x = 2[/tex]

(2, 7)

3,3

Pretty simple.

1 x 3 = 3

The graph of the direct proportion y = kx for k=1 is shown in figure.

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The direct proportion is defined as,

⇒ y = kx

Now, The equation for k = 1 is,

⇒ y = kx

⇒ y = 1x

⇒ y = x

Clearly, It represent the straight line.

Hence, The graph of y = x is shown in figure.

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160 and 162 and 164

Step-by-step explanation:

To find the three even integers, use the equation

x + (x + 2) + (x + 4) = 486

Then solve:

Add the common terms (the xs and numbers)

3x + 6 = 486

Subtract the 6 from both sides

3x = 480

Then divide

x = 160

So 160 + (160 + 2) + (160 + 4) = 486

160 + 162 + 164 = 486

So your three consecutive even integers are

Answer:

-2x + 3

Step-by-step explanation:

Perimeter means to add all the sides of the triangle. Simply combine like terms:

(3x) + (2x - 5) + (-7x + 8)

(3x + 2x - 7x) + (-5 + 8)

(5x - 7x) + (8 - 5)

-2x + 3

-2x + 3 is your answer.

~

Answer:

1.66

Step-by-step explanation:

We need to conduct a chi square test

The statistic used to check this is given by the below

∑(n, 1) = [(O(i) - E(i)] / E(i)

From the question, we're told the observed value is

Freshmen

Sophomore

Junior

Senior.

After that, we then calculate the expected value.

Freshman

0.3 * 300 = $90

Sophomore

0.24 * 300 = $72

Statistics then finally gives us this

X² = (93 - 90²)/90 + (68 - 72)²/72 + (85 - 78)/78 + (64 -60)²/60

X² = 3² / 90 + 4² / 73 + 13² / 78 + 4² / 60

X² = 0.1 + 0.212 + 2.167 + 0.266 x+

X² = 2.745

X = √2.745

X = 1.66

Answer:

HI BYE 45     SO ME I THINK IT I DONT KNOW SO PEACE GOOD LUCK

Answer:

Greatest number of t-shirts that can be ordered is 540.

Step-by-step explanation:

Given that:

Cost of printing one shirt = $8.25

One time fee to make the silkscreen = $38

Budget for the t-shirts = $4500.00

Let,

x be the number of t-shirts

According to given statement;

8.25x + 38 ≤ 4500.00

8.25x ≤ 4500.00 - 38

8.25x ≤ 4462.00

Dividing both sides by 8.25

[tex]\frac{8.25x}{8.25}\leq \frac{4462.00}{8.25}\\x\leq 540.84[/tex]

Hence,

Greatest number of t-shirts that can be ordered is 540.

Answer:

Angle y is also 40 degrees. Angle x and y are vertical angles, thus they have the same angle measure.

Step-by-step explanation:

Answer:

x is equal to 7

the measure of both angles is 23°

Step-by-step explanation:

1. set both equations equal to each other

2. 4x - x is 3x

3. 16 + 5 is 21

4. 3x = 21

5. divide both sides by 3

6. x equals 7

Answer:

x = 12

Step-by-step explanation: