What is length of DF?

The fourth term of the given expansion is [tex]-280x^{3}[/tex].

The binomial expansion is used to expand and write the terms which are equals to the natural number exponent of the sum or differences of two terms.

[tex]T_{r+1} =nC_{r} x^{n-r} y^{r}[/tex]

According to the given question

We have,

A binomial expression, [tex](1-2x)^{n}[/tex]

and, the binomial coefficients are taken from the row of Pascal's triangle 1  6  15  20  15  6  1

⇒ n = 7

Therefore,

The fourth term of the expansion of [tex](1-2x)^{n}[/tex] is given by

[tex]T_{3+1} = 7C_{3} 1^{7-3} (-2x)^{3}[/tex]

[tex]T_{4} =\frac{(7)(6)(5)(4)(3!)}{3!(4)(3)(2)} (1)(-2x)^{3}[/tex]

[tex]T{4} = -280x^{3}[/tex]

Hence, the fourth term of the given expansion [tex](1-2x)^{3}[/tex] is [tex]-280x^{3}[/tex].

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Answer:

a = 14

b = 24

c = 24.9

A = 33.2 degrees

B = 70 degrees

C = 76.8 degrees

Step-by-step explanation:

a/sin(A) = b/sin(B) = c/sin(C)

14/sin(A) = 24/sin(70)

sin(A)×24 = sin(70)×14

sin(A) = sin(70)× 14/24 = sin(70) × 7/12 = 0.548154029...

A = asin(0.548154029...) = 33.240464... degrees

the sum of all angles in a triangle is airways 180 degrees.

C = 180 - 70 - 33.240464... = 76.75954... degrees

24/sin(70) = c/sin(76.75954...)

c = 24×sin(76.75954...)/sin(70) = 24.86133969...

Answer:

OK!!.

N=N(½)ⁿ

n= Time/half life

N=Remaining Mass

N°=Initial Mass or Mass before decay.

t= time taken to decay(Its in Months in this case)

t½= Half Life of the Material. This is the time taken to decay to half its initial value.

N°= 2000mg

a).Equation that Models this is

since n=t/t½

N=N°(½)ⁿ =

N=N°(½)^t/t¹'². This should be your answer.

b). We're asked to find the remaining mass of substance in 4years.

t= 4years

Our Half life is in Months... So we gotta convert or time t from year to Months too.

4yrs === 4x12 = 48Months.

N° was given as 2000mg

N=N°(½)^t/t½

N= 2000(½)^48/3

N=2000(½)^16

Using your calc to evaluate (½)^16... Then multiply by 2000

N=0.0305mg will remain after 4years.

Or After 16Half Lives since 1 half life is 3months

c). We're looking for t this time

N=N°(½)^t/t½

Since it asked for 750mg to remain ... 750 is now our N --- Remaining Mass

750 = 2000(½)t/3

To Isolate "t" and make it the subject

750/2000 = (½)^t/3

0.375 = (½)^t/3

Taking ln(natural log) of both sides

Ln(0.375) = Ln(0.5)^t/3

From the rule of logarithm...

You can bring the power (I.e t/3) to the front

You'll have

Ln(0.375) = t/3Ln(0.5)

Dividing both sides by Ln(0.5) to isolate t

Ln(0.375)/Ln(0.5) = t/3

t/3 = 1.415

t= 3x1.415

t=4.25months.

Have a great day.

Hope this helps... I'm open to questions if you have any too.

Answer:

Just plus everything together

X-3+4X+4+2X+1

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

The absolute value (the lines both sides of x) simply mean the number in between is positive. Since 1 is already positive, just add it to 7!

where is the graph????

Step-by-step explanation:

y – 8 = –y minus 8 equals negative StartFraction 2 Over 3 EndFraction left-parenthesis x plus 3 right-parenthesis.(x + 3)

Step-by-step explanation:

9514 1404 393

Answer:

  35

Step-by-step explanation:

The 16 onion bagels are twice as many as plain bagels, so there were 8 plain bagels.

There were 4 more sesame bagels than plain bagels, so there were 12 sesame bagels.

Adam has 8 plain, 12 sesame, and 15 onion bagels left, for a total of 35 bagels left.

Answer:

16 ounces.

Step-by-step explanation:

An 8% solution is 2 times stronger than a 4% solution.

So in the 8% solution we will have 1/2 of the volume as a 4% , so 1/2 * 32

= 16 ounces of water must be evaporated.

The number 16 ounces of water must be evaporated from 32 ounces of a 4% salt solution to make an 8% salt solution.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

To find the amount of water that must be evaporated from 32 ounces of a 4% salt solution to make an 8% salt solution:

0.96(32) - x = 0.92(32 - x)

30.72 - x = 29.44 - 0.92x

x - 0.92x = 30.72 - 29.44

0.08x = 1.28

x = 16

Therefore, 16 ounces must be evaporated.

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Answer:

____ 1 _____ 2 ____ 3

1 __ 1, 1 ____ 1, 2 __ 1, 3

2 __2, 1 ____2, 2 __ 2, 3

Step-by-step explanation:

Given that :

Steps required for procedure One  : Either 1, 2, or 3

Steps required for procedure two  : Either 1 or 2

The first procedure has 3 possible steps

The second procedure has 2 possible steps

. The experimental outcome associated with performing the blood analysis is displayed in the table below :

____ 1 _____ 2 ____ 3

1 __ 1, 1 ____ 1, 2 __ 1, 3

2 __2, 1 ____2, 2 __ 2, 3

i don't think this is complete question there isn't value for x

Answer: 3-7x

Step-by-step explanation: x represents the "a number" portion since it is a variable

Answer: Arithmetic Sequence

Step-by-step explanation: It has a common difference of +3 at a constant rate

Answer:

2.89, rounded to the nearest hundredth

Step-by-step explanation:

Given that GPA is weighted by credits, we must first multiply each grade by its credit amount and sum those up to weigh the credits. Then, we divide by the total amount of credits to get the GPA per credit.

So, we start with math,

3.7 *5 + 1.8 *3 + 2.8 * 5 + 2.8 * 4 = 49.1 as the total GPA weighted per credit.

Then, to find the average per credit, we divide by the total amount of credits, which is 5 + 3 + 5 + 4 = 17.

Our answer is 49.1/17 = 2.89, rounded to the nearest hundredth

Answer:

We reject  H₀, and conclude thet the mean lifetime of the bulbs differ from 51 month

Step-by-step explanation:

Manufacturing process under control must produce items that follow a normal distribution.

Manufacturer information:

μ  =  51 months     mean lifetime

σ  =  7 months       standard deviation

Sample Information:

x  =  51 months

n  =  60

Confidence Interval  =  90 %

Then significance level  α  =  10 %  α  =  0.1    α/2  =  0,05

Since it is a manufacturing process the distribution is a normal distribution, and with   n = 60 we should use a Z test on two tails.

Then from z- table z(c) for  α = 0,05  is  z(c)  = 1.64

Hypothesis  Test:

Null Hypothesis                              H₀            x  =  μ

Alternative Hypothesis                  Hₐ            x ≠  μ

To calculate z statistics  z(s)

z(s)  =   (  x   -  μ )  / σ /√n

z(s)  =   (  53  -  51 ) / 7 /√60

z(s)  =  2 * 7.746 / 7

z(s)  = 2.213

Comparing  z(s)  and  z(c)

z(s)  >  z(c)   then  z(s)  is in the rejection region

We reject  H₀, and conclude thet the mean lifetime of the bulbs differ from 51 month

1.) The answers:

A) BME

B) MER

C) Mm

D) xBy

E) Straight

F) REB

G) MEB and BER

H) xBy

Answer:

1. [tex]2^{3}[/tex] x [tex]3^{6}[/tex]

ii. 18

b. -12

2. nth = a + (n - 1)d

ii. k = 103

3. [tex]x^{o}[/tex] = [tex]27^{o}[/tex]

4. Volume = 25.025 [tex]m^{3}[/tex]

Step-by-step explanation:

1. Prime factors of 5832 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3

                                       = [tex]2^{3}[/tex] x [tex]3^{6}[/tex]

ii. [tex]\sqrt[3]{5832}[/tex] = 18

b. 2[tex]a^{2}[/tex] - 3[tex]b^{2}[/tex] + 3abc

a = 3, b = 2, c = -1

Thus,

2[tex](3)^{2}[/tex] - 3[tex](2)^{2}[/tex] + 3(3 x 2 x -1)

= 18 - 12 - 18

= -12

2. The required formula is;

nth = a + (n - 1)d

where: a is the first term, n is the number of terms in the sequence and d is the common difference.

b. kth term = 304, then

304 = -2 + (k - 1) 3

      = -2 + 3k -3

      = 3k - 5

3k = 304 + 5

3k =  309

k = [tex]\frac{309}{3}[/tex]

  = 103

k = 103

3. Comparing <DAB and < EBC;

<DAB ≅ <EBC = [tex]x^{o}[/tex]

<BEC = [tex]90^{o}[/tex] (right angle property)

<C = [tex]63^{o}[/tex]

Thus,

<B + <C + <E = [tex]180^{o}[/tex] (sum of angles in a triangle)

[tex]x^{o}[/tex] + [tex]63^{o}[/tex] + [tex]90^{o}[/tex] = [tex]180^{o}[/tex]

[tex]x^{o}[/tex] + 153 = [tex]180^{o}[/tex]

[tex]x^{o}[/tex] = 180 - 153

   = 27

[tex]x^{o}[/tex] = [tex]27^{o}[/tex]

4. Volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h

where r is the radius and h is the height of the cylinder.

Diameter = 3.5 m, h = 2.6 m

r = [tex]\frac{3.5}{2}[/tex]

r = [tex]\frac{7}{4}[/tex] m

So that,

Volume = [tex]\frac{22}{7}[/tex] x [tex](\frac{7}{4}) ^{2}[/tex] x 2.6

             = [tex]\frac{22}{7}[/tex] x [tex]\frac{49}{16}[/tex] x [tex]\frac{13}{5}[/tex]

             = 25[tex]\frac{1}{40}[/tex]

Volume = 25.025 [tex]m^{3}[/tex]

Answer:

[tex]3e^{2} + 12e[/tex]

Step-by-step explanation:

[tex]3ee+3e4[/tex]

[tex]3ee+3 * 4e[/tex]

[tex]3e^{2} + 12e\\[/tex]

[tex]3 \: {e}^{2} + 12 \: e[/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]3 \: e \: ( \: e + 4 \: ) \\ \\ = 3 \: e \times \: e + 3 \: e \times 4 \\ \\ = 3 \: {e}^{2} + 12 \: e[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique }}{\orange{♡}}}}}[/tex]

Answer:

[tex]2/3[/tex]

Step-by-step explanation:

The total number of sums (not distinct) is [tex]4\cdot 3=12[/tex], because we're removing without replacement.

Count the sums that fit the stipulation (sum [tex]\leq[/tex] 5):

[tex]1,2,\\2,1\\1,3\\3,1\\1, 4\\4, 1\\2, 3, \\3,2[/tex]

There are 8 sums that work. Therefore, the desired answer is [tex]\frac{8}{12}=\boxed{\frac{2}{3}}[/tex]

Answer:

Line 3 is incorrect; we don't know anything about the lengths of HG, FG, HE, and EF, so this line is not valid based on the given information.

Step-by-step explanation:

In the Noah's poof of the construction, segment EG would divide angle FGH into two equal parts, which makes line 2 to be valid. i.e <EGH ≅ <EGF. And it can also be observed that line 4 is a valid theorem in proving the congruent nature of triangles.

But line 3 is not valid because of the condition of the statement. Furthermore, segments FG, EG, HG, HE and FE may not be congruent. Thus, the condition of the statement in line 3 is incorrect.

Answer in fraction form = -3/2

Answer in decimal form = -1.5

=========================================

Work Shown:

[tex]m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(1)-g(-3)}{1-(-3)}\\\\m = \frac{0-6}{1-(-3)}\\\\m = \frac{0-6}{1+3}\\\\m = \frac{-6}{4}\\\\m = -\frac{3}{2}\\\\m = -1.5\\\\[/tex]

Effectively, we're finding the slope through the points (-3, 6) and (1, 0)

The g(b)-g(a) represents how y changes when going from x = a to x = b.

Answer:

110 basic plans and 200 standard plans were purchased.

Step-by-step explanation:

This question is solved using a system of equations.

I am going to say that:

x is the number of basic plans.

y is the number of standard plans.

310 new subscribers

This means that [tex]x + y = 310[/tex], and so, [tex]y = 310 - x[/tex]

A cable network offers members a Basic plan for ​$7.26 per month. For ​$3.00 more per​ month. Total paid of $2580.60.

This means that:

[tex]7.26x + 10.26y = 2580.6[/tex]

Since [tex]y = 310 - x[/tex]

[tex]7.26x + 10.26(310 - x) = 2580.6[/tex]

[tex]7.26x + 3180.6 - 10.26x = 2850.6[/tex]

[tex]3x = 330[/tex]

[tex]x = \frac{330}{3}[/tex]

[tex]x = 110[/tex]

Then

[tex]y = 310 - x = 310 - 110 = 200[/tex]

110 basic plans and 200 standard plans were purchased.

Answer:

hey. pls complete your question.

Answer:

12.86 cm³ of water is saved

Step-by-step explanation:

✔️Since width of new ice ball must be the same as the length of original cube, therefore, diameter of the ice ball = 3 cm

Radius of ice ball = ½(3) = 1.5 cm

Volume of the new sphere ice ball = ⁴/3πr³

Substitute

Volume of new sphere ice ball = ⁴/3 × π × 1.5³ = 14.14 cm³

✔️To find out how much water would be saved using the new sphere ice ball, let's find the volume of the cube then find the difference of both.

Volume of original ice cube with length 3 cm:

Volume of cube = s³

s = 3 cm

Volume of cube = 3³ = 27 cm³

Volume of water saved = 27 cm³ - 14.14 cm³

= 12.86 cm³

Answer:

500 men

740 total people in community

Step-by-step explanation:

25:12 ratio

When using a ratio both sides should go up the same amount of times to get the number you are trying to reach. Since the women's amount was 240 we need to find the times it took to get from 12 to 240. You take the 240 and divide by 12. We find that the 12 was multiplied 20 times to get to 240. So you turn to the men's side and find the amount using the 25. We use X to signify the amount we are trying to find and the amount of times that 25 goes into X will be 20 to keep the ratio of men to women as specified. When solving for X you multiply both sides of the equation by 25 to find the amount. X will equal 500 (=20*25).

Then 240 women plus 500 men equals to 740 people in the community.

Women

240/12 = 20

Men

X/25=20

X=20*25

X=500

240 women+500 men=740 people

The Fourier series expansion of f(x) is

[tex]\displaystyle\frac{a_0}2+\displaystyle\sum_{n=1}^\infty \left(a_n\cos\left(\frac{2\pi nx}P\right)+b_n\sin\left(\frac{2\pi nx}P\right)\right)[/tex]

where P = 4 is the period of f(x), and the coefficients are

[tex]a_0=\displaystyle\frac2P\int_{-2}^2f(x)\,\mathrm dx=2[/tex]

[tex]a_n=\displaystyle\frac2P\int_{-2}^2f(x)\cos\left(\frac{2\pi nx}P\right)\,\mathrm dx=\frac{2\sin(n\pi)}{n\pi}=0[/tex]

[tex]b_n=\displaystyle\frac2P\int_{-2}^2f(x)\sin\left(\frac{2\pi nx}P\right)\,\mathrm dx=\frac{2(\cos(n\pi)-1)}{n\pi}=\begin{cases}0&\text{for }n=2k\\-\frac4{(2k-1)\pi}&\text{for }n=2k-1\end{cases}[/tex]

(where k is a positive integer)

The series for f(x) reduces to

[tex]\displaystyle f(x)=1-\displaystyle\sum_{k=1}^\infty \frac4{(2k-1)\pi}\sin\left(\frac{\pi(2k-1)x}2\right)[/tex]

(I've attached a plot showing the original function in blue and the Fourier expansion with k = 10 terms)

Answer:

34/3, -2/3

Step-by-step explanation:

See image below:)

Step-by-step explanation:

2x + 3y = 34

3y = 34 - 2x

y = 3x - 2x/3

Answer:

The second answer

Y=X³-4X²+2X

Y=0

The system of equations can be used to find the roots of the given equation is y = 4x², y = x³+2x

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

For example, 3x – 5 = 16 is an equation.

Given is an equation, 4x² = x³+2x, we need to identify the system of equations can be used to find the roots of this,

An equality can be transformed in a system of equations by making each side equal to a new variable. In this case the variable y was made equal to each side.

See that may find the solution of such system by graphing both functions in a same coordinate system, where the intersection of the functions would show the solution of the system.

The attached image. In such graph, the red curve is the function y = x² and the blue function is y = x³ + 2x.

The intersection point is (0,0) meaning that the solution is x = 0, y = 0.

Hence, the system of equations can be used to find the roots of the given equation is y = 4x², y = x³+2x

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Answer: A and C

Step-by-step explanation: To see if it can be the side lengths of a right triangle we have to use the Pythagoras Theorem which is [tex]a^2 +b^2 = c^2\\[/tex]

C is always the largest length. Now we can sub the numbers in

[tex]5^2+\sqrt{6} ^2=\sqrt{31} ^2[/tex]

The squares and the square roots cancel each other out so we end up with

25+6=31

this is true so those are possible sides for a right triangle

Now for b:

[tex]\sqrt{5}^2 + \sqrt{5}^2 =50^2[/tex]

Again the squares and square roots cancel each other out

5+5=2500

This isn't true so it isn't the possible sides for a right triangle

Finally option C:

[tex]9^2+12^2=15^2[/tex]

81+144=225

225=225

This is true so it can be the side lengths that form a right triangle