average of 2721 2557 2999 2278 4339

Answer:

18 minutes

Step-by-step explanation:

A = A₀ (½)^(t / T)

where A is the final amount,

A₀ is the initial amount,

t is the time,

and T is the half life.

A = 140 when t = 10.  Solve for the half life:

140 = 700 (½)^(10 / T)

0.2 = ½^(10 / T)

log 0.2 = (10 / T) log 0.5

10 / T = 2.32

T = 4.31

When A = 40, t is:

40 = 700 (½)^(t / 4.31)

0.057 = ½^(t / 4.31)

log 0.057 = (t / 4.31) log 0.5

t / 4.31 = 4.13

t = 17.8

Rounded to the nearest whole number, it takes 18 minutes.

The time taken for bacteria to reach 40 according to the exponential half-life decay formula is 18 minutes.

In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.

The half-life decay formula is given as,

N(t) = N₀ [tex](1/2)^{(t / T)}[/tex]

Where T is half-life while t is the time taken.

N₀ is the initial amount,

As per the given,

N(t) = 140 when t = 10.

140 = 700 [tex](1/2)^{(t / T)}[/tex]

Take log both sides,

log 0.2 = (10 / T) log 0.5

10 / T = 2.32

T = 4.31 minutes

Put N(t) = 40

40 = 700[tex](1/2)^{(t / 4.31)}[/tex]

Take log both sides,

log 0.057 = (t / 4.31) log 0.5

t / 4.31 = 4.13

t = 17.8 ≈ 18 minutes

Hence "The time taken for bacteria to reach 40 according to the exponential half-life decay formula is 18 minutes".

For more about exponential function,

https://brainly.com/question/15352175

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Answer:

The system of equations you want to be solved is not given. I would however give an example with which the method of elimination will be shown, and can be used in solving problems of the nature.

Step-by-step explanation:

Consider the system of equations:

x + y = 7 ................................(1)

2x - y = 8 ..............................(2)

To eliminate x:

First multiply (1) by 2 to have

2x + 2y = 14 ...........................(3)

Next, subtract (2) from (3) to have

3y = 6

y = 6/3 = 2

To eliminate y:

Add (1) and (2) to have

3x = 15

x = 15/3 = 5

Therefore, (x, y) = (5, 2).

Answer:

Thus, Amit ran 3.33 KM

calculation needed:

conversion of time (40 minutes to hour)

multiplying velocity  and time (which we got in hours)

Step-by-step explanation:

Given

to calculate the distance: . v times t

that is multiply v with t

where v is average velocity

t is the  time

__________________________________

Given

v = 5 km/hour

time = 40 minutes

since speed is in Km per hour and also we have to find distance in km

lets convert time which in 40 minutes to hour

we know

60 minutes = 1 hour

1 minute = 1/60 hour

40 minutes = 40/60 hour = 2/3 hour

distance = v times t

distance = 5*2/3 = 10/3 = 3 1/3 km = 3.33 km

Thus, Amit ran 3.33 KM

calculation needed:

conversion of time (40 minutes to hour)

multiplying velocity  and time (which we got in hours)

Answer:

5 • 40/50

Is the correct answer

Answer:

2.7 in²

Step-by-step explanation:

Area of ∆BAC : ∆Area of EDF = BC² : EF² (based on the area of similar triangles theorem)

Thus:

[tex] 6 in^2 : x in^2 = (3 in)^2 : (2 in)^2 [/tex]

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

[tex]\frac{6}{x} = 2.25[/tex]

[tex]\frac{6}{x}*x = 2.25*x[/tex]

[tex]6 = 2.25x[/tex]

[tex]\frac{6}{2.25} = \frac{2.25x}{2.25}[/tex]

[tex]2.67 = x[/tex]

Area of ∆EDF = 2.7 in²

Answer:

254 x 10^5

Step-by-step explanation:

Hope this helps :)

If anything is misunderstood plz comment and I will change to the answer which you give me thank you very much :)

Answer:

2.54 x 10^5

hope this answer helps u ._.

Explanation:

Let the 11 numbers be {a1, a2, ..., a11} such that a1 is the smallest and a11 is the largest. So, a1 < a2 < ... < a11. Furthermore, these numbers are consecutive.

If we add consecutive numbers to get a negative result, then each of the numbers must be negative. So every value in the set {a1, a2, ..., a11} is a negative value which makes it impossible to have a1+a2+...a11 be a positive sum.

Answer:

[tex]D = 42.5\ inch[/tex]

Step-by-step explanation:

Given

[tex]L = Length[/tex] and [tex]W = Width[/tex]

[tex]L:W = 8: 5[/tex]

[tex]Perimeter = 117[/tex]

Required

Determine the Diagonal

First, the dimension of the screen has to be calculated;

Recall that; [tex]L:W = 8: 5[/tex]

Convert to division

[tex]\frac{L}{W} = \frac{8}{5}[/tex]

Multiply both sides by W

[tex]W * \frac{L}{W} = \frac{8}{5} * W[/tex]

[tex]L = \frac{8W}{5}[/tex]

The perimeter of a rectangle:

[tex]Perimeter = 2(L+W)[/tex]

Substitute [tex]L = \frac{8W}{5}[/tex]

[tex]Perimeter = 2(\frac{8W}{5}+W)[/tex]

Take LCM

[tex]Perimeter = 2(\frac{8W + 5W}{5})[/tex]

[tex]Perimeter = 2(\frac{13W}{5})[/tex]

Substitute 117 for Perimeter

[tex]117 = 2(\frac{13W}{5})[/tex]

[tex]117 = \frac{26W}{5}[/tex]

Multiply both sides by [tex]\frac{5}{26}[/tex]

[tex]\frac{5}{26} * 117 = \frac{26W}{5} * \frac{5}{26}[/tex]

[tex]\frac{5 * 117}{26} = W[/tex]

[tex]\frac{585}{26} = W[/tex]

[tex]22.5 = W[/tex]

[tex]W = 22.5[/tex]

Recall that

[tex]L = \frac{8W}{5}[/tex]

[tex]L = \frac{8 * 22.5}{5}[/tex]

[tex]L = \frac{180}{5}[/tex]

[tex]L = 36[/tex]

The diagonal of a rectangle is calculated using Pythagoras theorem as thus;

[tex]D = \sqrt{L^2 + W^2}[/tex]

Substitute values for L and W

[tex]D = \sqrt{36^2 + 22.5^2}[/tex]

[tex]D = \sqrt{1296 + 506.25}[/tex]

[tex]D = \sqrt{1802.25}[/tex]

[tex]D = \sqrt{1802.25}[/tex]

[tex]D = 42.4529150943[/tex]

[tex]D = 42.5\ inch[/tex] (Approximated)

Answer:

I have not answer

plz follow me....

Answer:

I think you should change it to 4x + 3y

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

a) The sample space, n(S) = 6^6 = 46656

Let the number fair dice toss that show 6 = n(A)

Hence, the probability of getting, P(A) = n(A)/n(S)

b) Sample space, n(S) = 6^42

n(A) = 6^9

∴ P(A) = n(A)/n(S) = 6^9/6^42 = 1/(6^33) = 2.09 X 10^(-26)

c) No

Answer:

The velocity is  [tex]v = 886.96 \ m/s[/tex]

Step-by-step explanation:

From the question we are told that

    The period of each revolution is  [tex]T = 1\ day = 24 \ hours[/tex]

    The angle  is [tex]\theta = 30^o[/tex]

     The radius is  [tex]r = 3387.5 \ miles[/tex]

Generally the linear speed is  mathematically represented as

        [tex]v = w * r[/tex]

Where  [tex]w[/tex] is the angular speed which is mathematically represented as

       [tex]w = \frac{2 \pi }{T}[/tex]

substituting values

       [tex]w = \frac{2 *3.142 }{24}[/tex]

        [tex]w = 0.2618 \ rad/s[/tex]

Thus  

         [tex]v = 0.261833 * 3387.5[/tex]

        [tex]v = 886.96 \ m/s[/tex]

Answer:

Hey there!

All of the values: 0, 3, and 4 are in the domain.

This is because h(x) = (x - 3)^2 is a parabola, or a quadratic. By definition, the domain, or the possible x values of a parabola are infinite.

Hope this helps :)

Answer:

Your question indicates the ladder is at an angle of 60° to the wall, meaning the angle between the wall and the ladder is 60° and the angle between the ladder and the ground must be 30°. Not a very efficient way to set up a ladder.

5.7735 meters. The top of the ladder is 2.8868 meters off the ground.

Now, if you meant the ladder is 60° from the ground, that’s a different story.

Then, the ladder is 10 meters long and reaches 8.6603 meters from the ground.

A 30–60–90 right triangle is half of an equalateral triangle. Therefore the hypotenuse is double the length of the short leg, and by the Pythagorean theorum, we can determine that the other leg is the length of the short leg times the square root of 3.

All lengths in this answer are rounded to the nearest tenth of a millimeter.

Step-by-step explanation:

Answer:

No, F* < Fc

Step-by-step explanation:

Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I  error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis .

Answer:

(-∞,-3) and (3,∞)  

Step-by-step explanation:

f(x) = x³ − 27x + 3

1. Find the critical points

(a) Calculate the first derivative of the function.

f'(x) = 3x² -27  

(b) Factor the first derivative

f'(x)= 3(x² - 9) = 3(x + 3) (x - 3)

(c) Find the zeros

3(x + 3) (x - 3) = 0

x + 3 = 0      x - 3 = 0

     x = -3          x = 3

The critical points are at x = -3 and x = 3.

2. Find the local extrema

(a) x = -3

f(x) = x³ − 27x + 3 = (-3)³ - 27(-3) + 3 = -27 +81 + 3 = 57

(b) x = 3

f(x) = x³ − 27x + 3 = 3³ - 27(3) + 3 = 27 - 81 + 3 = -51

The local extrema are at (-3,57) and (3,-51).

3, Identify the local extrema as maxima or minima

Test the first derivative (the slope) over the intervals (-∞, -3), (-3,3), (3,∞)

f'(-4) = 3x² -27 = 3(4)² - 27  = 21

f'(0) = 3(0)² -27 = -27

f'(4) = 3(4)² - 27 = 51

The function is increasing on the intervals (-∞,-3) and (3,∞).

The graph below shows the critical points of your function.

Answer:

The answer is below

Step-by-step explanation:

The box contains 5 red and 4 white balls.

A) The probability that at least 1 ball was​ red = P(both are red) + P(first is red and second is white) + P(first is white second is red)

Given that the first ball was (Upper A )Replaced before the second draw:

P(both are red) = P(red) × P(red) = 5/9 × 5/9 = 25/81

P(first is red and second is white) = P(red) × P(white) = 5/9 × 4/9 = 20/81

P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/9 = 20/81

The probability that at least 1 ball was​ red = 25/81 + 20/81 + 20/81 = 65/81

B) The probability that at least 1 ball was​ red = P(both are red) + P(first is red and second is white) + P(first is white second is red)

Given that the first ball was not Replaced before the second draw:

P(both are red) = P(red) × P(red) = 5/9 × 4/8 = 20/72 (since it was not replaced after the first draw the number of red ball remaining would be 4 and the total ball remaining would be 8)

P(first is red second is white) = P(red) × P(white) = 5/9 × 4/8 = 20/72

P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/8 = 20/72

The probability that at least 1 ball was​ red = 20/72 + 20/72 + 20/72 = 60/72

Answer:

25 : 63 and 63 : 25

Step-by-step explanation:

This is a complete question

The table shows the educational attainment of the population of Country X, ages 25 and over. Use the data in the table, expressed in millions, to solve the problem. of 10 questions ge 1: Ages 25 and Over, in Miltions 4 Years igh College 4 Years High School (Less than College School Only 4years) Cor Moce) Total Male 29 19 25 89 Female 11 28 23 Total 2 57 42 50 [176 Find the odds in favor and the odds against a randomty selected person from Country X.age 25 and over, with the stated amount of education. four years (or more) of college 21:67, 67:21 63:88, 88:63 25:63, 63:25 25:88, 88:25

According to the question, the relevant data provided in the question for the solution is as follows

Four years or more of college

Number of students = 50

Total = 176 students

Number of students does not belong = 126

So odds in favor is

= 50 : 126

= 25 : 63

And automatically out against the favor is 63 : 25

Answer:

36.9°

Step-by-step explanation:

Sin x = 9/15 = 3/5

x = sin^-1 3/5

x= 36.87

x= 36.9° to nearest tenth

Answer:

x = 20°

Step-by-step explanation:

So when I learned it we called it the exterior angle theorem not the angle sum theorem but here goes.

Since exterior angle = 110 Degrees,

--> The Inner 2 angles's sum = 110 Degrees

so, 70 + 2x = 110

=> 2x = 40

x = 20

x = 20°

Hope this helps!

Answer:

1/4

Step-by-step explanation:

If the 4 sections have equal areas, then each section has 1/4 of the original circle's area.

Answer: 0.20

Step-by-step explanation:

The given probability distribution of number of televisions per household in a small town:

x          0       1     2      3

​P(x) ​ 0.05 0.15 0.25 0.55

To find : The probability of randomly selecting a household that has one or two televisions ( in both parts a. and b.).

The computations for this would be :

P( 1 or 2) = P(1)+P(2)

= 0.05+0.15

= 0.20

Hence, the required probability= 0.20

Answer:

Step-by-step explanation:

Answer:

6 years

Step-by-step explanation:

A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:

[tex]y=ab^x[/tex]

Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8

[tex]y=ab^x\\8=ab^0\\a=8[/tex]

Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2

Therefore:

[tex]y=ab^x\\y=8(1.2^x) \\[/tex]

To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x

[tex]20=8(1.2)^x\\20/8=1.2^x\\1.2^x=2.5\\Taking \ natural\ log\ of \ both\ sides:\\ln(1.2^x)=ln2.5\\xln(1.2)=0.9163\\x=0.9163/ln(1.2)\\x=5.026[/tex]

x = 6 years to the nearest year

Answer:

5 years

Step-by-step explanation:444

Answer:

2y= 6-3x when x=0

2y= 6-3(0)

2y= 6-0

2y= 6

y= 6/2

y= 3

#i'm indonesian

#hope it helps.

Answer:

[tex] \boxed{y = 3}[/tex]

Step-by-step explanation:

Given, x = 0

[tex] \mathsf{2y = 6 - 3x}[/tex]

plug the value of x

⇒[tex] \mathsf{2y = 6 - 3 \times 0}[/tex]

Multiply the numbers

⇒[tex] \mathsf{2y = 6 - 0}[/tex]

Calculate the difference

⇒[tex] \mathsf{2y = 6}[/tex]

Divide both sides of the equation by 2

⇒[tex] \mathsf{ \frac{2y}{2} = \frac{6}{2} }[/tex]

Calculate

⇒[tex] \mathsf{y = 3}[/tex]

Hope I helped!

Best regards!

Hey there! I'm happy to help!

To find the volume of a cube, you simply take whatever the side length is and multiply it by itself 3 times, which is also known as cubing the number!

16×16×16=4096

You can also write it as 16³=4096

This is because the length is 16, the width is 16, and the height is 16, so you multiply them all together!

I hope that this helps! Have a wonderful day!

Answer: -3

Step-by-step explanation: 2x = -2 then you subtract 1 from that which is the same as adding negative one so -2 - 1 or -2 + -1 = -3

Answer:

Mean= $21.5067

Median = $15.8

Standard deviation= $19.02

Coefficient of skewness= $0.8991

Step-by-step explanation:

Mean =( $4.0 +$6.0 +$7.4+ $10.6 +$12.5+ $13.6+ $15.4+ $15.8 +$16.8

+$17.4+ $19.1 +$22.3+ $37.1 +$43.2 +$81.4)/15

Mean =$ 322.6/15

Mean= $21.5067

Median= middle number

Median = $15.8

Variance=( ($4.0-.$21.5)²+( $6.0. -.$21.5)²+( $7.4 -.$21.5)²+( $10.6 -.$21.5)²+( $12.5 -.$21.5)²+( $13.6. -.$21.5)²+ ($15.4 -.$21.5)²+( $15.8 -.$21.5)²+ ( $16.8 -.$21.5)²+ ($17.4-.$21.5)² +($19.1 -.$21.5)²+ ($22.3 -.$21.5)²+ ($37.1 -.$21.5)²+ ($43.2-.$21.5)²+( $81.4-.$21.5)²)/15

Variance=$ 5424.79/15

Variance=$ 361.65

Standard deviation= √ variance

Standard deviation= √361.65

Standard deviation= $19.02

Coefficient of skewness

=3( mean-median)/standard deviation

= 3(21.5-15.8)/19.02

= 3(5.7)/19.02

= 17.1/19.02

Coefficient of skewness= 0.8991

Answer:

Step-by-step explanation:

The graph tells you the zeros of the function are x=-3/4 and x=4.

The y-intercept is the constant in the function: 12.

The maximum is 22.5625 at x = 1.625.

Answer:

Z= 0.253

Z∝/2 = ± 1.96

Step-by-step explanation:

Formulate the null and alternative hypotheses as

H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test

Here ∝= 0.005

For alpha by 2 for a two tailed test Z∝/2 = ± 1.96

Standard deviation = s= 15

n= 10

The test statistic used here is

Z = x- x`/ s/√n

Z= 2058- 2046 / 15 / √10

Z= 0.253

Since the calculated value of Z= 0.253 falls in the critical region we reject the null hypothesis.

There is  evidence at the 0.05 level that the doors are too short and unusable.