The work in an office takes 150 hours to complete every week. Each person in the office works 32hours a week. What is the smallest number of people to complete the work

Answer:

  40%

Step-by-step explanation:

The amount of income allocated to the items listed totals $744, so there is $496 he can spend on other things. As a percentage of income, that is ...

  496/1240 × 100% = 40%

Malaba can spend 40% of his net income on other things.

For a sample size of n=12, the degrees of freedom (df) would be 11, and the critical t value for a two-tailed 95% confidence interval is typically around 2.201, as determined by a t-distribution table or statistical software.

To find the critical t* value corresponding to a 95% confidence level for a sample size of n=12, you must take into account that the degrees of freedom (df) are equal to n - 1, which is 11 in this case. You use a t-distribution, not the z-distribution, because the population standard deviation is unknown. The critical t* value can be found using a t-distribution table or statistical software.

With the degrees of freedom at 11 for a 95% confidence interval (two-sided), the critical t value is typically around 2.201. However, one must look up the exact value using statistical software or a t-distribution table, as the value may vary slightly based on different sources or rounding.

Thus, to answer the student's question: For a two-tailed 95 percent confidence interval and 11 degrees of freedom, the corresponding critical value t* will typically be around 2.201.

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Answer: E. 1200

Step-by-step explanation:

Given : A certain restaurant offers 8 different salads, 5 different main courses, 6 different desserts.

i.e. No. of choices for different salads= 8  -----(1)

No. of choices for different main courses = 5  ----(2)

No. of choices for different desserts = 6

When we choose two different desserts then we use permutation(repeatition not allowed) :

[tex]^6P_2=\dfrac{6!}{(6-2)!}=\dfrac{6\times5\times4!}{4!}=6\times5=30[/tex]----(3)

[∵ No. of ways to choose r things out of n =[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex] ]

If customers choose one salad, one main course and two different desserts for their meal , then By Fundamental principle of counting (Multiply (1) , (2) and (3)), the number of  different meals are possible :-

[tex]8\times5\times30\\\\=1200[/tex]

Hence, the correct answer is E. 1200 .

The selling price will be $232 if he applies a 45% markup.

Step-by-step explanation:

Cost of each stereo = $160

Mark up = 45%

Amount of mark up = [tex]\frac{45}{100}*160[/tex]

Amount of mark up = [tex]\frac{7200}{100} = \$72[/tex]

Selling price = Cost of stereo + mark up

Selling price = 160 + 72 = $232

The selling price will be $232 if he applies a 45% markup.

Keywords: addition, markup

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Answer:

Step-by-step explanation:

We are told the manufacturer expects 0.3% to 0.5% of units to be defected,

So we find 0.3% and 0.5% of the 20,000units

0.3/100 multiplied by 20000 = 60units

0.5/100 multiplied by 20000 = 100units

So we now know from 20000units, between 60units to 100units will be defected

So we find the price of both 60units and 100units knowing that 1unit cost $2,500

60 multiplied by $2,500 equals $150,000

100 multiplied by $2,500 equals $250,000

So the answer is option D, between $150,000 and $250,000

Pilar will pay 30 cents less from the original amount by using reusable bags.

Step-by-step explanation:

Bags used by Pilar = b = 6

Price decrease per bag = 5 cents

Let x be the total amount paid by Pilar.

Decrease will lessen the amount paid by Pilar, therefore, according to statement;

P(x) = x - 5b

As she used 6 bags, therefore, putting b=6

[tex]P(x)=x-5(6)\\P(x)=x-30[/tex]

Pilar will pay 30 cents less from the original amount by using reusable bags.

Keywords: subtraction, function

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Answer: speed of jet A is 704 miles per hour

speed of jet B is 604 miles per hour

Step-by-step explanation:

Let the jets be jet A and jet B

Jet A and Jet B leave an air base at the same time and travel in opposite directions.

Let x = the speed of Jet A

Let y = the speed of jet B

One jet travels 100 miles an hour faster than the other. Let Jet A be the faster Jet. This means that

x = y + 100 - - - - - -1

If the two jets are 3924 miles apart after 3 hours, this means that both Jet A and Jet B travelled a total distance of 3924 miles after 3 hours.

Distance travelled = speed × time

Therefore,

Distance travelled by Jet A in 3 hours will be x × 3 = 3x miles.

Distance travelled by Jet B in 3 hours will be y × 3 = 3y miles.

Therefore, total distance is

3x + 3y = 3924 - - - - - - - -2

Substituting equation 1 into equation 2, it becomes

3(y+100) + 3y = 3924

3y + 300 + 3y = 3924

6y = 3924 - 300 = 3624

y = 3624/6 = 604 miles per hour

x = y + 100 = 604 + 100

x = 704 miles per hour

Answer:

  3.9 mi/h

Step-by-step explanation:

We assume that the given speeds are the speeds of the boats relative to the water. If c is the speed of the current, we have ...

  time = distance/speed

  47/(15 +c) = 40/(20 -c)

  47(20 -c) = 40(15 +c) . . . . . . multiply by (20-c)(15+c)

  940 -600 = 40c +47c . . . . . add 47c-600

  340 = 87c . . . . . . . . . . . . . . . simplify; next divide by 87

  c = 340/87 ≈ 3.9080 . . . . mi/h

The speed of the current is about 3.9 mi/h.

Answer:

Part 1) Option A. The graph of g(x) has the lesser y-intercept

Part 2) Option B. (2,4)

Part 3) Option B. 62.5 miles per hour

Part 4) Option A. The functions will intersect at x=-2 and at x=1

Step-by-step explanation:

Part 1)

Let

x ----->the number of years

g(x) ----> the expected value in dollars of televisions

we know that

The linear equation in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem

In the function g(x)

The slope is

[tex]m=-\$90\ per\ year[/tex] ---> is negative because is a decreasing function

The y-intercept is

[tex]b=\$360[/tex]

substitute

[tex]g(x)=-90x+360[/tex]

Find the x-intercept (value of x when the value of the function is equal to zero)

For g(x)=0

[tex]0=-90x+360[/tex]

[tex]x=4[/tex]

The x-intercept is the point (4,0)

The y-intercept is the point (0,360)

Function f(x)

we have

[tex]f(x)=100(-x+4)[/tex]

[tex]f(x)=-100x+400[/tex]

Find the x-intercept (value of x when the value of the function is equal to zero)

For f(x)=0

[tex]0=-100x+400[/tex]

[tex]x=4[/tex]

The x-intercept is the point (4,0)

The y-intercept is the point (0,400) (value of f(x) when the value of x is zero)

Compare the intercepts both functions

The y-intercept is the same in both functions

The y-intercept is greater in the function f(x)

therefore

The graph of g(x) has the lesser y-intercept

Part 2) we have the equation of the line

[tex]4x-3y=-4[/tex]

Remember that

If a ordered pair is on the given line, then the ordered pair must satisfy the given line

Verify each case

a) (4,4)

Substitute the value of x and the value of y in the equation and compare the result

[tex]4(4)-3(4)=-4[/tex]

[tex]4=-4[/tex] ---> is not true

so

the ordered pair not satisfy the equation

therefore

the ordered pair is not on the line

b) (2,4)

Substitute the value of x and the value of y in the equation and compare the result

[tex]4(2)-3(4)=-4[/tex]

[tex]-4=-4[/tex] ---> is true

so

the ordered pair satisfy the equation

therefore

the ordered pair is on the line

c) (2,-4)

Substitute the value of x and the value of y in the equation and compare the result

[tex]4(2)-3(-4)=-4[/tex]

[tex]20=-4[/tex] ---> is not true

so

the ordered pair not satisfy the equation

therefore

the ordered pair is not on the line

d) (4,-4)

Substitute the value of x and the value of y in the equation and compare the result

[tex]4(4)-3(-4)=-4[/tex]

[tex]28=-4[/tex] ---> is not true

so

the ordered pair not satisfy the equation

therefore

the ordered pair is not on the line

Part 3) we know that

The formula to calculate the average rate of change using the graph is equal to

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

In this problem we have

[tex]f(a)=f(2)=75\ mi[/tex]  

[tex]f(b)=f(4)=200\ mi[/tex]

[tex]a=2\ h[/tex]

[tex]b=4\ h[/tex]

Substitute

[tex]\frac{200-75}{4-2}=125/2=62.5 mi/h[/tex]

Part 4) we know that

The solution of the equation

f(x)=g(x)

are the x-coordinates of the intersection points both graphs

In this problem

If the solutions are x=-2 and x=1

then

The functions will intersect at x=-2 and at x=1

Answer:

A. 25x^2 - 110x + 121

Step-by-step explanation:

(5x - 11)² = (5x)² - 2·5x·11 + (11)² = 25x² - 110x + 121

(a - b)² = a² - 2ab + b²

a. 25x² − 110x + 121

Total assets: $3,450

Total liabilities and equity: $3,450

Explanation:

Cash: $2635

Equipment: $815

Total assets: $3,450

Accounts Payable: $185

Owner's Equity: $3,450 - $185 = $3,265

Total liabilities and equity: $3,450

the guy up there didn't understand.

Brainliest?

Answer:

12 units

Step-by-step explanation:

The quickest way to go about this is;

From the figure, when you count the number of full square boxes inside the rectangle, they add up to 7 full square boxes of 1 unit by 1 unit. And the number of half square boxes inside the rectangle add up to 10 which is equal to 5 full square boxes.

So the total number of full square boxes of 1 unit by 1 unit inside the rectangle add up to 12 full square boxes. The area of each full square box is 1 * 1 =  1 units, therefore the area of the rectangle is equal to 1 * 12 = 12 units.

Answer:

Q = 1.84

Step-by-step explanation:

If we poured  0,5 gallon of mixture A with 0.5 gallon of mixture B we will get a gallon of:

   ( 15 + 50 )/ 2  =  32.5 %

Now by ule of three

        If       with     0, 5 gl    of A     we get    32.5 %

                                ?? x                                   30

x  =  (0.5)*(0.3)/ 0.325

x = 0,462 gl  t get a mixture of 30%

Then for 4 gl

Q = 4 * 0.462

Q = 1.84

Answer:

[tex]\displaystyle 1\frac{119}{250}\:liter[/tex]

[tex]\displaystyle 7,5\:sleps[/tex]

[tex]\displaystyle 37,3\:sleps [/tex]

Step-by-step explanation:

[tex]\displaystyle 1\frac{119}{250} = \frac{1476}{1000}[/tex]

[tex]\displaystyle 1\frac{1}{13} \times 7 = 7\frac{7}{13} ≈ 7,538461538 ≈ 7,5[/tex]

[tex]\displaystyle \frac{41}{1\frac{1}{10}} = 37\frac{3}{11} ≈ 37,3[/tex]

I am joyous to assist you anytime.

Answer:

  10,000 ft

Step-by-step explanation:

We can solve the given relation for h:

  [tex]t=\dfrac{\sqrt{h}}{4}\\\\4t=\sqrt{h}\\\\h=16t^2[/tex]

Putting t=25 into this formula, we get ...

  h = 16(25²) = 10,000

With no air resistance the object will take 25 seconds to fall from 10,000 feet.

Answer:

The probability to draw two red balls = 1/22

The probability to draw one red ball = 9/22

The probability to draw no red ball = 12/22

Step-by-step explanation:

Number of Red balls = 3

Number of White balls = 9

If the player draws two red balls, he receives $4

If the player draws one red ball, he receives $1

If the player draws no red ball, he looses $2

The total number of balls = 3+9

= 12

Let R represent Red balls

Let W represent White balls

The probability that the player earns $4 by picking two red balls is represented as Pr(R1 n R2)

Pr(R1 n R2) = Pr(R1) * Pr(R2)

Pr(R1) = 3/12

= 1/4

Pr(R2) = 2/11(we assume he draws without replacement)

Pr(R1 n R2) = 1/4*2/11

= 2/44

= 1/22

The probability of earning $4 is 1/22

The probability of drawing one red ball is Pr(R1 n W2) or Pr(W1 n R2)

Pr(R1) = 3/12

= 1/4

Pr(W2) = 9/11

Pr(W1) = 9/12

= 3/4

Pr(R2) = 3/11

Pr(R1 n W2) or Pr(W1 n R2) =

(1/4 * 9/11) + (3/4 * 3/11)

= (9/44) + (9/44)

= 18/44

= 9/22

Therefore, the probability of earning $1 is 9/22

The probability that no red ball is chosen is Pr(W1nW2)

Pr(W1) = 9/12

= 3/4

Pr(W2) = 8/12

Pr(W1nW2) = 3/4 * 8/11

= 24/44

= 12/22

therefore. the probability of loosing $2 is 12/22

The probability to draw two red balls is [tex]\(\frac{1}{22}\)[/tex], to draw one red ball is [tex]\(\frac{9}{22}\)[/tex], and to draw zero red balls is [tex]\(\frac{15}{22}\)[/tex].

To find the probability distribution, we need to calculate the probabilities of drawing two red balls, one red ball, and no red balls from the urn containing 3 red balls and 9 white balls. We use combinations to determine these probabilities.

1. Total Possible Combinations:

  The total number of ways to choose 2 balls out of 12 is given by the combination formula:

 [tex]\[ \binom{12}{2} = \frac{12!}{2!(12-2)!} = \frac{12 \times 11}{2 \times 1} = 66 \][/tex]

2. Probability of Drawing Two Red Balls:

  To draw 2 red balls, we select 2 out of the 3 red balls:

  [tex]\[ \binom{3}{2} = \frac{3!}{2!(3-2)!} = \frac{3 \times 2}{2 \times 1} = 3 \][/tex]

  The probability is:

 [tex]\[ P(\text{2 red balls}) = \frac{\binom{3}{2}}{\binom{12}{2}} = \frac{3}{66} = \frac{1}{22} \][/tex]

3. Probability of Drawing One Red Ball:

  To draw 1 red ball and 1 white ball, we select 1 out of the 3 red balls and 1 out of the 9 white balls:

 [tex]\[ \binom{3}{1} = 3 \quad \text{and} \quad \binom{9}{1} = 9 \][/tex]

  The number of ways to draw 1 red and 1 white ball is:

 [tex]\[ \binom{3}{1} \times \binom{9}{1} = 3 \times 9 = 27 \][/tex]

  The probability is:

  [tex]\[ P(\text{1 red ball}) = \frac{\binom{3}{1} \times \binom{9}{1}}{\binom{12}{2}} = \frac{27}{66} = \frac{9}{22} \][/tex]

4. Probability of Drawing Zero Red Balls:

  To draw 0 red balls (i.e., both balls are white), we select 2 out of the 9 white balls:

 [tex]\[ \binom{9}{2} = \frac{9!}{2!(9-2)!} = \frac{9 \times 8}{2 \times 1} = 36 \][/tex]

  The probability is:

 [tex]\[ P(\text{0 red balls}) = \frac{\binom{9}{2}}{\binom{12}{2}} = \frac{36}{66} = \frac{18}{33} = \frac{6}{11} = \frac{15}{22} \][/tex]

5. Probability Distribution for Earnings:

  Now, we summarize the probabilities and corresponding earnings

  - Drawing two red balls: [tex]\(\frac{1}{22}\)[/tex], earning $4

  - Drawing one red ball: [tex]\(\frac{9}{22}\)[/tex], earning $1

  - Drawing zero red balls: [tex]\(\frac{15}{22}\)[/tex], losing $2

Thus, the correct probability distribution for the experiment of playing the game and observing the player's earnings is:

- Probability to draw two red balls: [tex]\(\frac{1}{22}\)[/tex]

- Probability to draw one red ball: [tex]\(\frac{9}{22}\)[/tex]

- Probability to draw zero red balls: [tex]\(\frac{15}{22}\)[/tex]

Answer:

Option a, 0.10

Step-by-step explanation:

Given that of the last 500 customers entering a supermarket, 50 have purchased a wireless phone.

i.e. out of 500 customers 50 customers purchased

Hence probability for any random customer to purchase = [tex]\frac{50}{500} =0.10[/tex]

Thus we find that if the relative frequency approach for assigning probabilities is used, the probability that the next customer will purchase a wireless phone is

Option a)

0.10

This is based on the assumption that the past pattern of purchase determines the probabiltiy

The statements mostly describe properties of an unbiased estimator in statistics, which typically involves large sample sizes, the mean of the sampling distribution being equivalent to the population mean, and the distribution of sample means approaching a normal distribution. One incorrect statement suggests that each individual sample mean will be equivalent to the population mean.

This question pertains to the concept of statistical estimation. The statements reflect the properties of an unbiased estimator in a simple random sample from the population. Let's analyze each choice:

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The sample mean is an unbiased estimator of the population mean when the sample is a simple random sample; the mean of the sampling distribution of the sample mean will equal the population mean.

The student's question relates to the concept of an unbiased estimator in statistics, particularly the sample mean as an unbiased estimator of the population mean. The correct statement that defines an unbiased estimator is:

This means that if you were to take many samples from the population and calculate the mean of each sample, the average of all these sample means would be equal to the population mean. This property is fundamental in inferential statistics for making generalizations about a population from a sample.

Answer:

The final pressure of the gas when its temperature returns to its initial value [tex]1.8234\times 10^6[/tex] Pa.

Step-by-step explanation:

Given : An ideal gas is confined within a closed cylinder at a pressure of [tex]2.026\times 10^5[/tex] Pa by a piston. The piston moves until the volume of the gas is reduced to one-ninth of the initial volume.

To find : What is the final pressure of the gas when its temperature returns to its initial value?

Solution :

Since the temperature is constant .

The relation between P and V is given by,

[tex]P_1\times V_1 = P_2\times V_2[/tex]

[tex]\frac{P_1}{P_2}=\frac{V_2}{V_1}[/tex] ....(1)

The piston moves until the volume of the gas is reduced to one-ninth of the initial volume i.e. [tex]V_2=\frac{V_1}{9}[/tex]

or [tex]\frac{V_2}{V_1}=\frac{1}{9}[/tex]

[tex]P_1=2.026\times 10^5[/tex]

Substitute in equation (1),

[tex]\frac{2.026\times 10^5}{P_2}=\frac{1}{9}[/tex]

[tex]P_2=9\times 2.026\times 10^5[/tex]

[tex]P_2=18.234\times 10^5[/tex]

[tex]P_2=1.8234\times 10^6[/tex]

The final pressure of the gas when its temperature returns to its initial value [tex]1.8234\times 10^6[/tex] Pa.

Answer:

0.2907

Step-by-step explanation:

Given that you are seated next to a stranger on an airplane and you start discussing various topics such as where you were born (what state or country), what your favorite movie of all time is, your spouse's occupation, and so on.

Since each topic is independent we find that probability for success in each topic = constant = 1/50 = 0.02

X no of topics that match is binomial with n = 17 and p = 0.02

Required probability

= Probability to find that you match on at least one of them

=[tex]P(X\geq 1)\\=1-P(X=0)\\=1-(1-0.02)^{17} \\=0.2907[/tex]

It would not be surprising as probability is reasonably large.

Answer:

  9 and 23

Step-by-step explanation:

You can adjust the problem a little bit and make it easier to solve.

Subtracting 5 from the larger number makes it twice the smaller, and their sum be 32-5 = 27. So 27 is 3 times the smaller number, 9, and the larger is 32-9 = 23, which is 5 more than two times 9.

The two numbers are 9 and 23.

_____

You can let x represent "the other number". Then "one number" is 2x+5, and their sum is ...

  (x) +(2x+5) = 32

  3x +5 = 32

  3x = 27 . . . . . subtract 5

  x = 9 . . . . . . . divide by 3

(This working out should look familiar if you followed the above verbal solution.)

"One number" is 27 and "the other number" is 9.

Answer:

Volume = 1346.275 [tex]ft^{3}[/tex]

Step-by-step explanation:

The radius of the pipe is 3.5 ft and height is 35 ft.

The volume of cylinder is found by the formula,

V = (π)([tex]R^{2})(h)[/tex]

(think about the formula as area of individual circles multiplied by the height of cylinder)

taking value of π as 3.14,

Where, the r = radius and h is height of cylinder.

inserting the above values,

[tex]V = (3.14)(3.5^{2})(35)[/tex]

V = 1346.275 [tex]ft^{3}[/tex]

Answer:

The speed of right going rider is 9 mph

The speed of left going rider is 18 mph

Step-by-step explanation:

Given as :

The total distance apart both the riders = 54 miles

Let The speed of right going rider = x mph

and The speed of left going rider = 2 x  mph

The Distance cover by right going rider = D miles

The Distance cover by left going rider = 54 - D  miles

Total time for both = 2 hours

So, Time = [tex]\dfrac{\textrm Distance}{\textrm Speed}[/tex]

Or ,  Distance = speed × Time

For right going rider

       D = x × 2

For left going rider

      54 - D = 2 x × 2

Or, from first equation

     54 - 2 x = 4 x

or, 54 = 4 x + 2 x

or, 6 x = 54

∴   x = [tex]\frac{54}{6}[/tex]

I.e x = 9 mph

So, The speed of right going rider = 9 mph

and The speed of left going rider = 2 × 9 = 18  mph

Hence The speed of right going rider is 9 mph

and The speed of left going rider is 18 mph   answer

Final answer:

Joelle would earn $322.50 for a week in which she works 42 hours.

Explanation:

To calculate Joelle's earnings for a week in which she works 42 hours, we need to determine the regular pay for the first 40 hours and the overtime pay for the additional 2 hours.

Regular pay for 40 hours = $7.50/hour x 40 hours = $300

Overtime pay for 2 hours = 1.5 x $7.50/hour x 2 hours = $22.50

Therefore, Joelle's total earnings for a week of 42 hours would be $300 (regular pay) + $22.50 (overtime pay) = $322.50.

The correct answer is C. $322.50.  Joelle earns $322.50 for a week in which she works 42 hours.

To calculate Joelle's earnings for the week, we need to consider both her regular pay for the first 40 hours and her overtime pay for the additional hours worked beyond 40 hours.

First, let's calculate her regular pay for 40 hours:

Joelle's regular pay rate is $7.50 per hour. Therefore, for 40 hours, her regular pay is calculated as:

Regular pay = Hourly pay rate × Number of regular hours

Regular pay = $7.50/hour ×40 hours

Regular pay = $300.00

Next, we calculate her overtime pay for the 2 hours of overtime work. Joelle earns 1 1/2 times her regular pay rate for overtime hours. So her overtime pay rate is:

Overtime pay rate = 1 1/2 × Regular pay rate

Overtime pay rate = 1.5 × $7.50/hour

Overtime pay rate = $11.25/hour

Now, we calculate her overtime pay for the 2 hours of overtime work:

Overtime pay = Overtime pay rate × Number of overtime hours

Overtime pay = $11.25/hour × 2 hours

Overtime pay = $22.50

Finally, we add her regular pay and overtime pay to find her total earnings for the week:

Total earnings = Regular pay + Overtime pay

Total earnings = $300.00 + $22.50

Total earnings = $322.50

Therefore, Joelle earns $322.50 for a week in which she works 42 hours.

Answer: a) $80 b)$1900

Step-by-step explanation:

a) change in Yolanda total pay y, for each 'English is fun' sold x, i.e ∆y/∆x = dy/dx

y = 1900+80x

differentiating the equation above

dy/dx = 80

Therefore, dy/dx = $80

change in Yolanda total pay y, for each 'English is fun' sold x, is $80

b) if she doesn't sell any copy of ' English is fun ',x=0

Therefore,

y = 1900 + 80x

Substituting x = 0, into the equation above

y = 1900 = $1900

Therefore her total pay is $1900 if she did not sell any ' English is fun'

Answer:

  6%

Step-by-step explanation:

The multiplier on George's money is ...

  $708/$600 = 1.18

This value is ...

  1 + rt = 1.18 . . . . . for t = 3

  3r = 0.18 . . . . . . subtract 1; next divide by 3

  r = 0.06 = 6%

The simple interest rate on George's account is 6%.

Answer:

a) dy/dt = ky(1-y)

b) 3:36pm

Step-by-step explanation:

a) Let the number of people who have heard the rumor = p

Let those who have not heard the rumor= q

Total population = p+q

Fraction of those that heard the rumor = p/p+q = y

Fraction of those who did not hear the rumor = q/p+q = 1-y

The rate at which the rumor spreads = dy/dt

dy/dt varies directly to y(1-y)

dy/dt = ky(1-y) where k is a constant

b) Recall that dy/dt = ky(1-y)

y(t) = y/(y+(1-y) e^-kt)

At 8 am , t= 0

y = p/ p+q

y(0) = 280/3500

y(0) = 0.08

By noon(12pm), t = 4

At this time half of the population has heard the rumor

y(4) = 0.5

Recall that y(t) = y/(y+(1-y) e^-kt)

y(t) = y0/(y0+(1-y0) e^-kt)

y(t) = 0.08/(0.08+(1-0.08) e^-kt)

y(t) = 0.08/(0.08+0 92 e^-kt)

To find k, put y(4) = 0.5 into the equation

y(4) = y/(y+(1-y) e^-4k)

0.5 = 0.08/(0.08+0.92e^-4k)

0.08 + 0.92e^-4k = 0.08/0.5

0.92e^-4k = 0.16 - 0.08

0.92e^-4k = 0.08

e^-4k = 0.08/0.92

e^-4k = 0.087

-4k = ln(0.087)

-4k = -2.422

k = -2.422/ -4

k = 0.611

y(t) = 0.08/(0.08+ 0.92 e^-0.611t)

The time by which 90% of the population would have heard the rumor is

0.9 = 0.08/(0.08+0.92e^-0.611t)

0.08 + 0.92e^-0.611t = 0.08/0.9

0.92e^-0.611t= (0.08/0.9) - 0.08

e^-0.611t = [(0.08/0.9)-0.08] / 0.92

e^-0.611t = 0.00966

-0.611t = ln(0.00966)

-0.611t = -4.640

t = -4.640/ -0.611

t = 7.6hrs

t = 7 hrs + (0.6*60)mins

t= 7 hrs + 36mins

t = 7hrs 36 mins

Therefore 8 am + 7 hrs 36 mins = 3:36pm

The time by which 90% of the rumor spreads = 3:36pm

The differential equation for the spread of a rumor, given the rate is proportional to the product of the fraction of the population who have heard the rumor and the fraction that has not, is dy/dt = k * y * (1 - y). To solve when 90% will have heard it, we find k using initial conditions and integrate to find the time.

To create a differential equation for the spread of the rumor we can say that the rate of spread, which is the derivative of the fraction of the population that has heard the rumor with respect to time (dy/dt), is proportional to the product of the fraction of the population that has heard the rumor (y) and the fraction that has not heard the rumor (1 - y). This gives us the differential equation dy/dt = k * y * (1 - y), where k is the proportionality constant.

To solve the problem for when 90% of the population will hear the rumor, we must first find the value of k using the initial conditions provided. At 8 AM, y(0) = 280/3500 and at noon, which is 4 hours later, y(4) = 0.5. Using this information, we can integrate the differential equation to find k and then use it to determine when 90% (i.e., y(t) = 0.9) of the population will have heard the rumor, applying appropriate integration and exponential growth techniques.

Answer:

4.8 hours

Step-by-step explanation:

Let the time taken to hike uphill be T

Let the time taken taken to hike downhill = 8 -T

The average speed of walking up = 2 mph

Average speed of walking down = 3mph

Distance hiked uphill = Distance hiked downhill

Speed = distance /time

Distance = Speed * Time

2T = 3(8 -T)

2T = 24 - 3T

2T + 3T = 24

5T = 24

T = 24/5

T= 4.8 hours

Time taken to hike uphill = 4.8hours

Answer:

b

Step-by-step explanation:

you first got twerk and this is workable because my wife left me for this reason

Answer:

OPTION C: 60%

Step-by-step explanation:

Chances of raining the next day + Chances that it will not rain = 100%

One of them should definitely be true.

So, if the chance of it raining tomorrow is 40% then there is 60% chance that it will not rain tomorrow.

This can also seen as follows:

Probability of rain tomorrow + Probability of no rain = 1

Given Probability of rain tomorrow = 40% = [tex]$ \frac{40}{100} = \frac{2}{5} $[/tex]

Probability of no rain tomorrow = 1 - Probability of rain tomorrow

⇒ Probability of no rain = 1 - [tex]$ \frac{2}{5} $[/tex]

⇒ Probability of no rain = [tex]$ \frac{3}{5} $[/tex]

Expressing it as percentage: [tex]$ \frac{3}{5} \times 100 $[/tex] = 60%.