help please :(( please please please ​

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: 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:

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:

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:

b=48

c=137

enjoy :) ....

Answer:

2n + 18.....

Step-by-step explanation:

yea

Answer:

2(x+3)(x2+1)

Step-by-step explanation:

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:

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

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.

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Answer:

area of rectangle=length ×breadth

area of rectangle=12yd×15yd

area of rectangle=180yd²

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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The simplest ratio is 4:9

Answer:

67 gallons.

Step-by-step explanation:

To determine how many gallons of a 70% antifreeze solution must be mixed with 90 gallons of 15% antifreeze to get a mixture that is 60% antifreeze, the following calculation must be performed:

0.15 x 90 + 0.70 x 10 = 20.5 / 100 = 0.20

0.15 x 90 + 0.70 x 30 = 34.5 / 100 = 0.34

0.15 x 90 + 0.70 x 60 = 55.5 / 100 = 0.55

0.15 x 90 + 0.70 x 67 = 60.4 / 100 = 0.60

Thus, 67 gallons of 70% antifreeze solution will be needed to achieve a 60% mix of that solution.

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:

it's 3 =^_^=

Step-by-step explanation:

Answer:

3 I think :)

Step-by-step explanation:

square root of 9 is 3

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:

∠J=85°

Step-by-step explanation:

Theory to know when answering this question:

1. The sum of the angles in a quadrilateral (shape with four sides) is 360°

2. Similar shapes have the same angles

Point 1 tells us that ∠P+∠Q+∠S+∠R=360

Point 2 tells us that ∠F=∠P, ∠G=∠Q, ∠J=∠S, and ∠H=∠R.

∴∠F+∠Q+∠J+∠R=360

109+122+∠J+44=360

∠J=360-275=85°

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 :)

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

If Y = 5 and the X is = 1 then Y = 125 is X = 25

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:

x = 12

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

The time required to get  a total amount of $ 640.00  from compound interest on a principal of $ 440.00  at an interest rate of 5.6% per year  and compounded 365 times per year  is approximately 7 years.

Step-by-step explanation:

Given

To determine:

Time period t = ?

Using the formula

[tex]A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}[/tex]

solving for t

t = ln(A/P) / n[ln(1 + r/n)]

substituting the values A = 640, P = 440, n = 365 and r = 0.056

t = ln(640/440) / ( 365 × [ln(1 + 0.00015342465753425/365)] )

t = 6.691

t ≈ 7  (nearest year)

Therefore, the time required to get  a total amount of $ 640.00  from compound interest on a principal of $ 440.00  at an interest rate of 5.6% per year  and compounded 365 times per year  is approximately 7 years.

Answer:

36

Step-by-step explanation:

You do 6+6+12+12

*3 times 4= the two twelves

Step-by-step explanation:

a) If the given set of vectors does not span [tex]\mathbb{R}^{3}[/tex] , it means the number of linearly independent vectors are less than 3. So by adding one or more linearly independent vectors with respect to existing vectors, we can convert the set to basis and basis always spans vector space.

eg. [tex]S= \left \{ (1,0,0)^{T},(1,2,0)^{T} \right \}[/tex] this set does not span [tex]\mathbb{R}^{3}[/tex] . Since it has only two vectors and both vectors are linearly independent, so adding one linearly independent vector with respect to the vectors of S viz. (0,0,1)^{T} can span whole [tex]\mathbb{R}^{3} [/tex].

b) It is not possible. Since if a set of vectors is linearly dependent then after adding linearly independent vectors it will also linearly dependent i.e. addition of a linearly independent vector does not effect on the set.

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:

7.5

Step-by-step explanation:

[tex]\frac{6}{8} =\frac{x}{10}\\crossmultiply\\60=8x\\solvefor x\\ x=7.5[/tex]

Similar triangles are those triangles whose corresponding sides are in the same ratio. In the two similar triangles, the value of x is 7.5 units.

Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same. It is denoted by the ‘~’ symbol.

Given that the two of the given triangles are similar triangles. Therefore, the ratio of the sides of the triangle can be written as,

6/x = 8/10

Solving the ratio for x,

x = (6×10)/8

x = 60/8

x = 7.5 units

Hence, in the two similar triangles, the value of x is 7.5 units.

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