The rate of change in sales S is inversely proportional to time t (t > 1), measured in weeks. Find S as a function of t when the sales after 2 and 4 weeks are 162 units and 287 units, respectively.

Answers

Answer 1

Answer:

S = 250/t

Step-by-step explanation:

If the rate of change of sales is inversely proportional to the time t, this is expressed mathematically as ΔS ∝ 1/Δt

ΔS = k/Δt where k is the constant of proportionality

If ΔS = S₂-S₁ and Δt = t₂-t₁

S₂-S₁ = k/ t₂-t₁

If the sales after 2 and 4 weeks are 162 units and 287 units respectively, then when S₁  = 162, t₁ = 2 and when   S₂ = 287, t₂ = 4.

On substituting this values into the given functions, we will have;

287 - 162 = k/4-2

125 = k/2

cross multiplying

k = 125* 2

k = 250

Substituting k = 250 into the function ΔS = k/Δt

ΔS = 250/Δt

S = 250/t

Hence the value of S as function of t when the sales after 2 and 4 weeks are 162 units and 287 units, respectively is expressed as S = 250/t


Related Questions

ASAP Which condition does not prove that two triangles are congruent? A. ASA ≅ ASA B. SAS ≅ SAS C. SSA ≅ SSA D. SSS ≅ SSS

Answers

Answer:

The answer is C. SSA ≅ SSA.

Step-by-step explanation:

To check for similar triangles, SSA congruence would not work because the other side can be any length. Also, there is not an SSA postulate because this theorem by itself cannot prove congruence.

The other three properties do work because they show congruence unlike the other congruent factors.

m= -1/2 and the point (3, -6) which is the point -slope form of the equation

Answers

Answer:

y+6=-1/2(x-3)

Step-by-step explanation:

Point slope form: y-y1=m(x-x1)

Given that:

m=-1/2 and point (3, -6), you just add these numbers into the equation, and this gives:

y+6=-1/2(x-3)

Hope this helped!

Have a nice day!

Find a particular solution of the differential equation
-(5/4)y" + 2y' + y = 3x*e^(3x)
using the Method of Undetermined Coefficients (primes indicate derivatives with respect to x).
Find the following particular solution
yp= ?

Answers

Note that the characteristic solutions to this ODE are [tex]e^{-2x/5}[/tex] and [tex]e^{2x}[/tex], so we can safely assume a particular solution of the form

[tex]y_p=(ax+b)e^{3x}[/tex]

with derivatives

[tex]{y_p}'=ae^{3x}+3(ax+b)e^{3x}=(3ax+a+3b)e^{3x}[/tex]

[tex]{y_p}''=3ae^{3x}+3(3ax+a+3b)e^{3x}=(9ax+6a+9b)e^{3x}[/tex]

Substitute these expressions into the ODE and solve for a and b. Notice that each term on either side contains a factor of [tex]e^{3x}[/tex], which we can cancel.

[tex]-\dfrac54(9ax+6a+9b)+2(3ax+a+3b)+(ax+b)=3x[/tex]

[tex]-\dfrac{17a}4x-\left(\dfrac{11a}2+\dfrac{17b}4\right)=3x[/tex]

[tex]\implies\begin{cases}-\frac{17a}4=3\\\frac{11a}2+\frac{17b}4=0\end{cases}[/tex]

[tex]\implies a=-\dfrac{12}{17}\text{ and }b=\dfrac{264}{289}[/tex]

So the particular solution is

[tex]y_p=\left(-\dfrac{12x}{17}+\dfrac{264}{289}\right)e^{3x}=\boxed{\dfrac{12}{289}(22-17x)e^{3x}}[/tex]

Fresno County, California is the largest agricultural producing county in the country and almonds are an important crop with more than 99,000 acres harvested. Each acre produces about a ton of almonds and sold at a price of $4300 a ton. The Sagardia Brothers grew 600 acres of almonds . How many tons would the brothers sell if they priced the almonds at $4500 a ton?

Answers

Answer:

0 ton

Step-by-step explanation:

The question states that 99,000 acres are harvested. This suggest that there are plenty sellers of almonds.The Sagardia Brothers grew 600 acres of almonds. this is a small percentage of the total output of almonds. This suggests that the market for almonds is perfectly competitive.

In this type of market, if the price of a seller is above equilibrium price, zero units of the commodity would be bought. This is because the goods sold are homogenous and buyers can easily purchase from other buyers that sell at the market price

Can someone help me, please?

Answers

Answer:

16

Step-by-step explanation:

7x+20+2x-5=159

9x+15=159

9x=159-15

9x=144

x=16

Write each expression in a simpler form that is equivalent to the given expression. Let F be a nonzero number. f-4

Answers

Answer:

f-4

Step-by-step explanation:

f-4  cannot be simplified

This is the simplest form

Answer:

[tex]\large \boxed{f-4}[/tex]

Step-by-step explanation:

[tex]f-4[/tex]

[tex]\sf f \ is \ a \ nonzero \ number.[/tex]

[tex]\sf The \ expression \ cannot \ be \ simplified \ further.[/tex]

Draw a Venn diagram and use the given information to fill in the number of elements in each region.

Answers

Answer: Check out the diagram below for the filled in boxes

14 goes in the first box (inside A, but outside B)

7 goes in the overlapping circle regions

5 goes in the third box (inside B, outside A)

3 goes in the box outside of the circles

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

Explanation:

[tex]n(A \cup B) = 26[/tex] means there are 26 items that are in A, B or both.

n(A) = 21 means there are 21 items in A

n(B) = 12 means there are 12 items in B

We don't know the value of [tex]n(A \cap B)[/tex] which is the number of items in both A and B at the same time. This is the intersecting or overlapping regions of the two circles. Let [tex]x = n(A \cap B)[/tex]

It turns out that adding n(A) to n(B), then subtracting off the stuff they have in common, leads to n(A u B) as shown below.

--------

[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)\\\\26 = 21+12 - x\\\\26 = 33 - x\\\\x+26 = 33\\\\x = 33-26\\\\x = 7\\\\n(A \cap B) = 7\\\\[/tex]

So there are 7 items in both regions.

This means there are [tex]n(A) - n(A \cap B) = 21 - 7 = 14[/tex] items that are in set A only. In other words, 14 items are in circle A, but not in circle B.

Notice how the values 14 and 7 add back up to 14+7 = 21, which represents everything in set A.

Similarly, there are [tex]n(B) - n(A \cap B) = 12 - 7 = 5[/tex] items that are in circle B, but not in circle A. The values 5 and 7 in circle B add to 5+7 = 12, matching with n(B) = 12.

The notation n(A') means the number of items that are not in set A. We're given n(A') = 8. We already know that 5 is outside circle A. So if 5+y = 8, then y = 3 must be the missing value for the box that is outside both circles.

Again the diagram is posted below with the filled in values.

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

The filled Venn diagram is given below.

What is a Venn diagram?

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

We have,

n(A) = 21

This is the total of all the items included in Circle A.

n(B) = 12

This is the total of all the items included in Circle A.

n(A') = 8

The items that are not in circle A.

n(A U B ) = 26

The items that are in both circle A and circle B.

Now,

n (A U B) = n(A) + n(B) - n(A ∩ B)

26 = 21 + 12 - n(A ∩ B)

n(A ∩ B) = 33 - 26

n(A ∩ B) = 7

Thus,
The filled Venn diagram is given below.

Learn more about the Venn diagram here:

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The weights of a sample of college textbooks has a bell-shaped distribution with a mean of 8.1 p o u n d s ( l b s ) and a standard deviation of 2.1 l b s . According to the Empirical Rule, what percent of all college textbooks will weigh between 1.8 and 14.4 l b s ?

Answers

Answer:

The interval    ( 1,8 ; 14,4 ) will contains 99,7 % of all values      

Step-by-step explanation:

For Normal Distribution  N ( μ ; σ ) the Empirical Rule establishes that in the intervals:

( μ  ±  σ )   we find  68,3 % of all values

( μ  ±  2σ ) we find  95,4 % of all values

( μ  ±  3σ ) we find  99,7 % of all values

Then we have a normal distribution  N ( 8,1 ; 2,1 )

3*σ  =  3* 2,1 = 6,3

And   8,1 - 6,3  = 1,8             8,1  + 6,3  = 14,4

Then the interval    ( 1,8 ; 14,4 ) will contains 99,7 % of all values      

You have a $5,000 limit on your credit card. What is the largest balance you should carry on this card to maintain an acceptable debt ratio? Recall that your debt ratio should never exceed 50% of your limit

Answers

Answer:

Amount of balance maintain = $2,500

Step-by-step explanation:

Given:

Limit of credit card = $5,000

Debt ratio = 50%

Find:

Amount of balance to maintain

Computation:

Amount of balance to maintain = Limit of credit card × Debt ratio

Amount of balance to maintain = $5,000 × 50%

Amount of balance to maintain = $2,500

In kickboxing, it is found that the force, f, needed to break a board, varies inversely with the length, l, of the board. If it takes 7 pounds of pressure to break a board that is 3 feet long, how long is a board that requires 5 pounds of pressure to break?

Answers

Answer:

4.2

Step-by-step explanation:

f varies inversly with L can be translated matimatically as:

● f = k/L

It takes 7 pounds of pressure to break a 3 feet long board.

Replace f by 7 and L by 3.

● 7 = k/3 => k=7×3=21

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's find tge length of a board that takes 5 pounds of pressure to be broken.

● 5 = k/L

● 5 = 21/L

● L = 21/5 = 4.2

So the board is 4.2 feet long

if it can be assumed that the population is normal, then what is the probability that one man sampled from this population has a weight between 72kg and 88kg

Answers

Answer:

The probability that one man sampled from this population has a weight between 72kg and 88kg is 0.6826.

Step-by-step explanation:

The complete question has the data of mean = 80 kg and standard deviation = 8kg

We have to find the probability between 72 kg and 88 kg

Since it is a normal distribution

(x`- u1 / σ/ √n) < Z >( x`- u2 / σ/ √n)

P (72 <x>88) = P ( 72-80/8/√1) <Z > ( 88-80/8/√1)

= P (-1<Z> 1) = 1- P (Z<1) - P (Z<-1)

= 1- 0.8413- (- 0.8413)= 1- 1.6826= 0.6826

So the probability that one man sampled from this population has a weight between 72kg and 88kg is 0.6826.

When she graduates college, Linda will owe $43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was $1,585. What is the amount of each loan?

Answers

Answer:

federal loans = $29,000

private loans = $14,000

Step-by-step explanation:

x + y = 43000

.045x + .02y = 1585

x = 29,000

y = 14,000

Answer:

Amount of loan from federal : $ 29,000

Amount of loan from private bank : $ 14,000

Step-by-step explanation:

We know that Linda owes $43,000 in student loans. It is also given that the interest rate on the federal loans is 4.5%, while the interest rate on private loans is 2%, the total interest for a year being $1,585.

If Linda were to say own x dollars in federal loans, and y dollars in private loans, we know that she owns a total of $43,000, so -

x + y = 43,000

At the same time the loan interest amount is $1,585, while the interest rate on the federal loans is 4.5%, and the interest rate on private loans is 2%. The loans from each account will add to $1,585 -

0.045x + 0.02y = 1585

Let's solve the following system for x and y, the amount of each loan,

[tex]\begin{bmatrix}x+y=43000\\ 0.045x+0.02y=1585\end{bmatrix}[/tex] ( Substitute x = 43000 - y )

[tex]0.045\left(43000-y\right)+0.02y=1585[/tex] ( Simplify )

[tex]1935-0.025y=1585[/tex],

[tex]1935000-25y=1585000[/tex],

[tex]-25y=-350000[/tex],

[tex]y=14000[/tex],

[tex]x=29000[/tex]

Thus, the amount of loan from federal is $ 29,000 and the amount of loan from private bank is $ 14,000.

WHY CAN'T ANYONE HELP ME PLEASE?A ​40% solution of fertilizer is to be mixed with a ​80% solution of fertilizer in order to get 80 gallons of a ​70% solution. How many gallons of the ​40% solution and ​80% solution should be​ mixed? 40% solution =? gallons, 80% solution =? gallons

Answers

Answer:

40% solution = 20 gallons

80% solution = 60 gallons

Step-by-step explanation:

x = gallons of 40% solution

y = gallons of 80% solution

Total volume is:

x + y = 80

Total amount of fertilizer is:

0.40 x + 0.80 y = 0.70 (80)

Solve by substitution.

0.40 x + 0.80 (80 − x) = 0.70 (80)

0.40 x + 64 − 0.80 x = 56

0.40 x = 8

x = 20

y = 60

Factor 13ab3 + 39a2b5.

Answers

[tex]13ab^3+39a^2b^5\\\\\boxed{\boxed{\boxed{13ab^3(1+3ab^2)}}}\\\\[/tex]

Brazil number one.

Answer:

there's no answer for that equation

Find the probability.
Two dice are rolled. Find the probability that the score on the dice is either 5 or
10.

Answers

Answer:

7/36

Step-by-step explanation:

1 die has 6 faces

When two dice are rolled, the total number of outcomes

= 6 × 6 = 36

The Probability of having(5) =

(1 & 4), (2 & 3) , ( 3 & 2), (4 & 1)

= 4

The probability of having (10) =

(5 & 5), (4 & 6) , ( 6 & 4)

= 3

The probability that the score on the dice is either 5 or 10.

P(5) + P(10)

= 4/36 + 3/36

= 7/36

Answer: 7/36

Step-by-step explanation:

36 outcomes

4 chances of getting 5 (1+4, 2+3, 4+1, 3+2)

3 chances of getting 10 (4+6, 5+5, 6+4)

4+3=7

so 7/36 chance

If Company X has 1600 employees and 80% of those employees have attended the warehouse training course how many employees have yet to attend?

Answers

Answer:

320

Step-by-step explanation:

Total no of employees = 1600

% of employees attended the training = 80%

no. of employee who attended the training = 80/100* 1600 = 1280

No. of employees who are yet to attend the training = Total no of employees - no. of employee who attended the training =  1600-1280 = 320

Thus, 320 employees have yet to attend the training

Determine the equation of the tangent line to the given path at the specified value of t. (sin(7t), cos(7t), 2t9/2); t=1

Answers

Answer:

P(t) = {sin7, cos7, 2} + (7cos7, -7sin7, 9)(t-1)

Step-by-step explanation:

The equation of the tangent line to the given path at the specified value of t is expressed as;

P(t) = f(t0) + f'(t0)(t - t0)

f(t0) = (sin(7t), cos(7t), 2t^9/2)

at t0 = 1;

f(t0) = {sin7(1), cos7(1), 2(1)^9/2}

f(t0) = {sin7, cos7, 2}

f'(t0) = (7cos7t, -7sin7t, 9/2{2t^9/2-1}

f'(t0) = (7cos7t, -7sin7t, 9t^7/2}

If t0 = 1

f'(1) = (7cos7(1), -7sin7(1), 9(1)^7/2)

f'(1) =(7cos7, -7sin7, 9)

Substituting the given function into the tangent equation will give:

P(t) = f(t0) + f'(t0)(t - t0)

P(t)= {sin7, cos7, 2} + (7cos7, -7sin7, 9)(t-1)

The final expression gives the equation of the tangent line to the path.

Chris wanted to know how likely he is to win at his favorite carnival game. He conducted 50 tests and won 15 times. What is the probability that he will win next time he plays? All answers are rounded to the nearest hundredth. a.) 0.15 b.) 0.30 c.) 0.50 d.) 0.35 SUBMIT MY ANSWER g

Answers

Answer:

b.) 0.30

Step-by-step explanation:

15/50 = 0.3

1 = prt is an example of
O
a variable
an expression
a constant
a formula

Answers

Complete Question

I = prt is an example of

• a variable

• an expression

• a constant

• a formula

Answer:

A formula

Step-by-step explanation:

I = prt is an example of a formula called Simple Interest.

Simple Interest can be defined as the formula that is used to calculate the interest that is accumulated on a particular amount of money which was saved in a financial institution or loaned out to a person at a given interest rate for a particular period of time.

The formula for Simple Interest is Expressed as:

I = PRT

Where :

I = Simple Interest

P = Principal = Amount saved, or loaned out

R = Interest rate that is given in percentage form

T = Time that has elapsed in Years.

Answer:

D. A Formula

Step-by-step explanation:

A formula is an equation that uses variables to state a rule.

Hope I was able to help you!

A researcher is interested in finding a 90% confidence interval for the mean number of times per

day that college students text. The study included 147 students who averaged 44.7 texts per

day. The standard deviation was 17.9 texts. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a tv distribution.

b. With 90% confidence the population mean number of texts per day is between

and

texts.

Answers

Answer:

90% confidence the Population mean number of texts per day

(42.2561 ,47.1439)

Step-by-step explanation:

Step(i):-  

Given sample size 'n' = 147

mean of the sample size x⁻ = 44.7

standard deviation of the sample 'S' = 17.9

90% confidence the Population mean number of texts per day

[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,(x^{-} + t_{\alpha } \frac{S}{\sqrt{n} })[/tex]

Step(ii):-

Degrees of freedom

       ν=n-1=147-1=146

t₀.₁₀ =  1.6554

[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,(x^{-} + t_{\alpha } \frac{S}{\sqrt{n} })[/tex]

[tex](44.7 - 1.6554 \frac{17.9}{\sqrt{147} } ,(44.7 + 1.6554 \frac{17.9}{\sqrt{147} })[/tex]

(44.7 - 2.4439 ,44.7 + 2.4439 )

(42.2561 ,47.1439)

Conclusion:-

90% confidence the Population mean number of texts per day

(42.2561 ,47.1439)

Let U = {q,r,s,t,u,v,w,x,y,z}, A={q,s,u,w,y}, B={q,s,y,z}, and C={v,w,x,y,z}. List the elements in the set open parentheses A union B close parentheses to the power of apostrophe intersection C

Answers

[tex]A\cup B=\{q,s,u,w,y,z\}\\(A\cup B)'=\{r,t,v,x\}\\\boxed{(A\cup B)'\cap C=\{v,x\}}[/tex]

:( I Need help! Show work please! Aviva has a total of 52 coins, all of which are either dimes or nickels. The total value of the coins is $4.70. Find the number of each type of coin.

Answers

Answer:

42 Dimes, 10 Nickels.

Step-by-step explanation:

Dimes are worth $0.10, nickels are worth $0.05.

If D = number of dimes, and N = number of nickels, then the following equations are true:

0.10D + 0.05N = 4.70

D + N = 52

Next, let's multiply the first equation by 10 so that we can subtract the second one from it.

D + 0.50N = 47

(-) D + N = 52

Subtracting the second equation from the first one gives:

-0.5N = -5

-0.5N/-0.5 = -5/-0.5

N = 10

Finally, substitute N in the original second equation to find D.

D + 10 = 52

D + 10 - 10 = 52 - 10

D = 42

Suppose 232subjects are treated with a drug that is used to treat pain and 50of them developed nausea. Use a 0.01significance level to test the claim that more than 20​%of users develop nausea. Identify the null and alternative hypotheses for this test.
A. Upper H0?: p equals 0.20
Upper H1?: p not equals 0.20
B. Upper H0?: p equals 0.20
Upper H1?: p greater than 0.20
C. Upper H0?: p greater than 0.20
Upper H1?: p equals 0.20
D. Upper H0?: p equals 0.20
Upper H1?: p less than 0.20
Identify the test statistic for this hypothesis test. Identify the​ P-value for this hypothesis test.
Identify the conclusion for this hypothesis test.
A. Reject Upper H 0. There is sufficient evidence to warrant support of the claim that more than 20?% of users develop nausea.
B. Fail to reject Upper H 0. There is sufficient evidence to warrant support of the claim that more than 20?% of users develop nausea.
C. Reject Upper H 0. There is not sufficient evidence to warrant support of the claim that more than 20?% of users develop nausea.
D. Fail to reject Upper H 0. There is not sufficient evidence to warrant support of the claim that more than 20?% of users develop nausea.

Answers

Answer:

A

   The  correct option is B

B

   [tex]t = 0.6093[/tex]

C

 [tex]p-value = 0.27116[/tex]

D

The  correct option is  D

Step-by-step explanation:

From the question we are told that

    The  sample size is  [tex]n = 232[/tex]

    The  number that developed  nausea  is X =  50

    The population proportion is  p  =  0.20  

 

The  null hypothesis is   [tex]H_o : p = 0.20[/tex]

The  alternative hypothesis is  [tex]H_a : p > 0.20[/tex]

Generally the sample proportion is mathematically represented as

     [tex]\r p = \frac{50}{232}[/tex]

     [tex]\r p = 0.216[/tex]

Generally the test statistics is mathematically represented as

 =>           [tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1- p )}{n} } }[/tex]

=>           [tex]t = \frac{ 0.216 - 0.20 }{ \sqrt{ \frac{ 0.20 (1- 0.20 )}{ 232} } }[/tex]

=>        [tex]t = 0.6093[/tex]

The  p-value obtained from the z-table is

       [tex]p-value = P(Z > 0.6093) = 0.27116[/tex]

  Given that the  [tex]p-value > \alpha[/tex]  then we fail to reject the null hypothesis

20
#1. Which statement is the converse to: If a polygon is a triangle, then it
has 3 sides. *
O A polygon is a triangle, if and only if, it has 3 sides.
If a polygon has 3 sides, then the polygon is a triangle.
If the polygon does not have 3 sides, then it is not a triangle
If a polygon is not a triangle, then it does not have 3 sides

Answers

Answer:

If a polygon has 3 sides, then the polygon is a triangle.

Step-by-step explanation:

Bold = hypothesis

Italic = conclusion

Statement:

If p, then q.

Converse: If q, then p.

To find the converse, switch the hypothesis and conclusion.

Statement:

If a polygon is a triangle, then it  has 3 sides.

Now we switch the hypothesis and the conclusion to write the converse of the statement.

If it  has 3 sides, then a polygon is a triangle.

We fix a little the wording:

If a polygon has 3 sides, then it is a triangle.

Answer: If a polygon has 3 sides, then the polygon is a triangle.

The converse statement will be;

⇒ If a polygon has 3 sides, then the polygon is a triangle.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The statement is,

''If a polygon is a triangle, then it has 3 sides. ''

Now,

Since, The statement is,

''If a polygon is a triangle, then it has 3 sides. ''

We know that;

The converse of statement for p → q will be q → p.

Thus, The converse statement is find as;

⇒ If a polygon has 3 sides, then the polygon is a triangle.

Learn more about the triangle visit:

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The circumference of the circle shown below is 75 inches. Which expression

gives the length in inches of DE?

D

A.

. 75

72

O B.

360

75

O C.

361

. 75

O D.

360

75%

Answers

Answer:

B. 360 .75

Step-by-step explanation:

The circumference of the circle is represented by π * diameter of the circle. The circumference of the circle is its perimeter. The circumference is arc length of the circle.  The perimeter is curve length around the figure of the circle. The circumference of the circle of 75 inches is represented by 75/360.

Answer: 72/360 multiply by 75

Step-by-step explanation:

i just did this question

what is a prime number

Answers

A number that can be divided exactly only by itself and 1.

For Eg:- 7, 10, 13.

Answer:

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic:

In a random sample of 205 people, 149 said that they watched educational television. Find the 95% confidence interval of the true proportion of people who watched educational television. Round intermediate answers to at least five decimal places.

Answers

Answer: Given a sample of 200, we are 90% confident that the true proportion of people who watched educational TV is between 72.1% and 81.9%.

Step-by-step explanation:

[tex]\frac{154}{200} =0.77[/tex]

[tex]1-0.77=0.23[/tex]

[tex]\sqrt{\frac{(0.77)(0.23)}{200} }[/tex]=0.049

0.77±0.049< 0.819, 0.721

Find the sum of the infinite geometric series -27, -9, -3, … The ratio is /3 and u1 is -27

Answers

Answer: C) -81/2

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

Work Shown:

a = -27 = first term

r = 1/3 = common ratio, note how this is between -1 and 1

We start with -27 and multiply by 1/3 each time to get the next term

S = infinite sum

S = a/(1-r), which only works because -1 < r < 1 is true

S = -27/(1-1/3)

S = -27/(2/3)

S = (-27/1) divided by (2/3)

S = (-27/1) times (3/2)

S = (-27*3)/(1*2)

S = -81/2

As you generate and add up the terms of the sequence, the infinite sum slowly starts to approach -81/2 = -40.5; we'll never actually achieve this sum exactly. Think of it as approaching an asymptote.

75% of this
number is 13.5

Answers

Answer:

10.125

Step-by-step explanation:

Hello!

To find this we first have to convert the percentage to a decimal

We do this by moving the decimal point two times left

75.0% = 0.75

Now we multiply this by the number

13.5 * 0.75 = 10.125

The answer is 10.125

Hope this helps!

Let y represent the number.

13.5 = 0.75y
(Divide both sides by 0.75)
y = 18

Therefore the number is 18.

8 sin2 x + cos x - 5 = 0

Answers

[tex]8 {sin}^{2} x + cos \: x - 5 = 0[/tex]

[tex]recall \: that \: {sin}^{2} x + {cos}^{2} x = 1[/tex]

[tex]then \: {sin}^{2} x = 1 - {cos}^{2} x[/tex]

then substitute,

[tex]8( 1 - {cos}^{2} x) + cos \: x - 5 = 0[/tex]

After Further Simplication,

[tex]8 {cos}^{2} x - cos \: x - 3 = 0[/tex]

[tex]let \: y = \cos(x) [/tex]

[tex]8 {y}^{2} - y - 3 = 0[/tex]

use quadratic formulae

[tex]y = 0.375 \: or \: - 0.25[/tex]

therefore

[tex] \cos(x) = 0.375 \: or \: - 0.25[/tex]

[tex] x = 70degrees \: or \: 104.5degrees[/tex]

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