Help with the linear equations

Sequence: 2 + 1 + 1/2 + 1/4 + 1/8 + ...

Explanation:

Here Given Sum to Infinity

[tex]\sf S \infty \ =a_1 \ x \ \dfrac{1}{1-r}[/tex]

Identify following

Solve:

[tex]\rightarrow \sf S \infty \ =2 \ x \ \dfrac{1}{1-\frac{1}{2} }[/tex]

[tex]\rightarrow \sf S \infty \ =4[/tex]

The sum of this infinity series is 4

Of the 400 students, 120 students like to drink coffee, 80 students like to drink tea, 160 students like both and 40 students do not like any of these drinks.

Cofee: 70% of 400 = 280 students

Tea: 60% of 400 = 240 students

None: 10% of 400= 40 students

This means that 360 students like coffee, tea or both.

280 + 240 (students who drink either coffe or tea)= 520 - 360 (real number of students who like coffee or tea) = 160 (students who like both coffee and tea.

Moreover, it can be inferred 80 students like tea and 120 studetns like coffee.

Outside the sets 40 students who do not like any of the drinks.

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Using it's concept, it is found that the desired probability is given as follows:

P(the recipient is male) = 0.4242 = 42.42%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there was a total of 224 + 387 + 547 + 776 + 245 + 322 = 2501 recipients, out of which 224 + 547 + 245 = 1016 are males, hence the probability is given by:

P(the recipient is male) = 1016/2501 = 0.4242 = 42.42%.

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Answer:

Step-by-step explanation:

[tex]sin^2({ \theta})+cos^2({ \theta})=1\\cos({ \theta})=-/+\sqrt{1-sin^2({ \theta})} \\cos({ \theta})=-\sqrt{1-sin^2({ \theta})} \\ --- > sin({ \theta})=\frac{1}{3} (known)\\cos({ \theta})=-\sqrt{1-sin^2({ \theta})} =-\sqrt{1-(-\frac{1}{3})} =-\sqrt{\frac{9-1}{9}} =-\frac{2x^{2} }{3}[/tex]

Hello ~

My name is Sxnnysoul, and I will be answering your question today! :D

We can make an explanation of a quick way, or the long way.

⇢ [tex]\sf{\sqrt{34}[/tex]

⇢ [tex]\sf{Refine \: to \: a \: decimal \: form:}[/tex]

⇢ [tex]\sf{= \: 5.83095}[/tex]

Which this one I am talking about of the Square root of an fraction or a prime factorization.

⇢ [tex]\sf{Find \: the \: prime \: factors \: of \: 34.}[/tex]

⇢ [tex]\sf{The \: prime \: factors \: of \: 34 \: are \: 2 \: and \: 17.}[/tex]

⇢ [tex]\sf{34 \: = \: 2 \: ^. \: 17}[/tex]

Hope It Helps! ~

~ Learn With Sxnnysoul ~

[tex]\underline{Answer :}[/tex]

ꜱ x ɴ ɴ ʏ ꜱ ᴏ ᴜ ʟ

Answer:

y = 2x + 3

Step-by-step explanation:

Hi there!

We are given the points (-1, 1) and (3,9) which belong to a line

We want to write the equation of the line in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, let's find the slope of the line

The slope (m) can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

Let's label the values of the points before we start, to avoid confusion and mistakes

[tex]x_1 = -1\\y_1=1\\x_2=3\\y_2=9[/tex]

Now substitute into the formula (note: the formula has SUBTRACTION, and we have NEGATIVE numbers, so we'll end up subtracting a negative)

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{9-1}{3--1}[/tex]

Simplify

m=[tex]\frac{9-1}{3+1}[/tex]

m=[tex]\frac{8}{4}[/tex]

Divide

m = 2

The slope of the line is 2

We can substitute this as m in y=mx+b.

y = 2x + b

Now we need to find b

As the equation passes through the point (-1, 1) and (3, 9), we can use either point to help solve for b.

Taking (3, 9) for example:

substitute 3 as x and 9 as y.

9 = 2(3) + b

Multiply

9 = 6 + b

Subtract 6 from both sides

3 = b

Substitute 3 as b in the equation

y = 2x + 3

Hope this helps!

Topic: finding the equation of the line

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Answer:

[tex]x(3x-7)=3x^2-7x[/tex]

Step-by-step explanation:

[tex]\Large \begin{array}{| c | c | c |}\cline{1-3} \textsf{x} & 3x & -7\\\cline{1-3} x & 3x^2 & -7x\\\cline{1-3}\end{array}[/tex]

[tex]\textsf{Therefore,}\quad x(3x-7)=3x^2-7x[/tex]

The complete statement is 67000 pounds is equivalent to 33.5 tons

The unit is given as:

Weight = 67000 pounds

As a general rule;

1 pound = 0.0005 tons

Multiply both sides by 67000

67000 * 1 pound = 67000 *  0.0005 tons

Evaluate

67000 pounds = 33.5 tons

Hence, 67000 pounds is equivalent to 33.5 tons

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Answer:

B

is the write I think ......!

Answer:

x = 18

Step-by-step explanation:

[tex]\sf x - 3x+9= - 27[/tex]

Let's first combine like terms.

[tex] \sf - 2x+9= - 27[/tex]

Subtract 9 from both sides.

[tex]\sf - 2x= - 27 - 9[/tex]

[tex] \sf - 2x= - 36[/tex]

Divide both sides by −2.

[tex]\sf x=18[/tex]

[tex]y = \sqrt[3]{x - 8} [/tex]

When translating the function in the positive x direction, we have to subtract the value from x

Answer:30.28 cm^2

Step-by-step explanation: area of the rectangle = 6x4 = 24

area of semicircle -> (πr^2)/2

radius of semcircle = 4/2 = 2

area of this question semicricle = (π2^2)/2

= 6.28 (3 s.f.)

total area = 24+6.28 =30.28 cm^2

remember put units ^^

Answer:

68 cups

Step-by-step explanation:

You must divide then multiply the reciprocal

Answer:

$2.5/card

Explanation:

Unit price is the price for buying one item.

Here given:

Unit price :-

Answer:

  1/3

Step-by-step explanation:

The average rate of change of a function f(x) on an interval [a, b] is given by the formula ...

  rate of change = (f(b) -f(a))/(b -a)

__

For the given function and interval, this is ...

  (log₂(4·8) -log₂(4·2))/(8 -2) = (5 -3)/(6) = 1/3

The average rate of change is 1/3.

_____

In the attached graph, the line between the points at the ends of the interval can be seen to have a rise of 1 for a run of 3. Its slope is 1/3.

0.8%

first we divide 4÷500×100

the we get 0.8%

Answer:

This is so easy it's 0.8%

Step-by-step explanation:

I barely pay attention in class but this is easy work

hope it helps anyways!

p.s i am in k12 sooo ^_^

Answer:

Jeff is 15 years younger than Joe who is 10

Step-by-step explanation:

Answer: h₁ = ~2790.9943 meters tall

Step-by-step explanation:

[tex]h_1 = h_2 + h_3[/tex]

h₂

h₃

h₁

Answer:for area you times them and for perimiter you add

Step-by-step explanation:

hope you understand

Answer:

83

Step-by-step explanation:

Answer:

2(-2)-5(-2)+12

-4-(-10)+12

6+12

18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

2(-2)-5(-2)+12

-4+10+12

=18

Hope this helps! ;-)

Answer:

Step-by-step explanation:

In the question, it is given that a right cone has a diameter of 12 units and volume of 168π units³ and we have to find the height of the cone.

[tex] \: [/tex]

To Find the height of the cone, we must know this formula :

[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { \dfrac{1}{3} \: \pi r^2h ={ Volume_{(cone) }}}}}}}}} \\ \\[/tex]

Where,

Now, we will substitute the values in the formula :

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \pi \times (6)^2 \times h = 168 \pi}}}}}}} \\ \\[/tex]

Cancelling π from both sides we get :

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \times \cancel\pi \times 36 \times h = 168 \cancel\pi}}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{1}{3} \ \times 36 \times h = 168 }}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { \dfrac{36}{3} \times h = 168 }}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { 12 \times h = 168 }}}}}}} \\ \\[/tex]

[tex]\\ {\longrightarrow{ \qquad{{ {\pmb{\sf { h = \frac{168}{12} }}}}}}} \\ \\[/tex]

[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { h ={14 }}}}}}}} \\ \\[/tex]

Therefore,

When you distribute, you independently multiply each term inside the parentheses by the term outside the parentheses.

So

6 x 7 = 42

and

6 x -4n = -24n

So the final answer is: 42 - 24n

*You cannot combine this answer any further since you are subtracting an unknown variable (n) from a number.

Answer:

81728

Step-by-step explanation:

1 libra tiene 16onz, entonces 16 onz* 1277 dolares =20432*4=81728  

Answer:

HI = 35

GK = 45

JK = 25

Provided:

Given proportional sides:

Find the scale factor:

Find missing sides:

1) HI = ZV × 5/6 = 42 × 5/6 = 35

2) GK = XY × 5/6 = 54 × 5/6 = 45

3) JK = WX × 5/6 = 30 × 5/6 = 25

Answer:

HI = 35

GK = 45

JK = 25

Step-by-step explanation:

If VWXYZ ~ IJKGH

Then:

YZ and GH is the only pair of corresponding sides for which we have been given the lengths:

YZ = 36  and GH = 30

Therefore,

VWXYZ : IJKGH = 36 : 30 = 6 : 5

Find HI

  ZV : HI = 6 : 5

⇒ 42 : HI = 6 : 5

⇒ 42/HI = 6/5

⇒ 42 · 5 = 6 HI

⇒ HI = 210/6

⇒ HI = 35

Find GK

   YX : GK = 6 : 5

⇒ 54 : GK = 6 : 5

⇒ 54/GK = 6/5

⇒ 54 · 5 = 6 GK

⇒ GK = 270/6

⇒ GK = 45

Find JK

   WX : JK = 6 : 5

⇒ 30 : JK = 6 : 5

⇒ 30 /JK = 6/5

⇒ 30 · 5 = 6 JK

⇒ JK = 150/6

⇒ JK = 25

Answer:

$50.40

Step-by-step explanation:

20% of 63 is 12.5 so subtract that from the price of 63 for the answer of 50.4

The interval for the function to be negative will be (-∞<x<-7).

A function in mathematics set up a relatioship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

Here we have a function:-

g(x) = ∛(x+6)

If we put the value of x lesser than 6 in the function we will always get a negative value so the interval will be:-

(-∞<x<-7).

Therefore interval for the function to be negative will be (-∞<x<-7).

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Answer:

(–∞, –6)

Step-by-step explanation:

I got it right on exam.

Answer:

36

Step-by-step explanation:

The angles of the triangle are equal.

Hence, the sides of the triangle must also be equal.

It is an equilateral triangle.

Equating JK and KL :

Finding KL :

All angles are equal means all sides are equal

KL