A certain bacteria population obeys the population growth law. It is observed that the doubling time for the population is 3 hours. The length of time it will take for the population to increase to 7-times its original population is

Answer:

Step-by-step explanation:

Set up an equation:

7x + 10x + 13x = 100000 and solve for x:

30x = 100000 so

x = 3333.33

Anna gets 7(3333.33) = 23333.31

Louise gets 10(3333.33) = 33333.33

Lacey gets 13(3333.33) = 43333.29

Answer:

Sammy: 20 Cheng: 30

Step-by-step explanation:

We can say that Sammy can do the job in \(x\) hours. So Cheng would take \(x + 10\) hours. So we can say the the velocity or speed of both of them combined is \(\frac{1}{x} + \frac{1}{x + 10} = 12\). Multiplying , we get \(1 = 12(\frac{1}{x} + \frac{1}{x + 10})\). Simplifying, we get (x-20)(x+6)=0 and this means Sammy takes 20 hours and Cheng takes 20+10=30 hours to do the job.

Sammy can pave a driveway in 15 hours while it takes Cheng 25 hours to do the same work alone. We find these numbers by setting up and solving equations based on their combined work rate.

Let's denote the time it takes for Sammy to pave a driveway as x hours. Because Cheng takes 10 hours longer to do the same job, we'll represent Cheng's paving time as x + 10 hours. The question gives us that together, Sammy and Cheng can pave a driveway in 12 hours.

The work rate for any worker is defined as 'one job' divided by the 'time to complete that job', which gives us 1/x jobs/hour for Sammy and 1/x + 10 jobs/hour for Cheng. The combined rate is 1/12 jobs/hour. Therefore, set the equation for Samy and Cheng's combined work rate: 1/x + 1/x + 10 = 1/12.

Solving this equation will give you:

x = 15 hours for Sammy and x + 10 hours = 25 hours for Cheng.

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Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Answer:

Option B. 7.5 is the correct answer

Step-by-step explanation:

Let us define standard deviation first.

Standard deviation is the square root of variance. Standard Deviation tells us that how far are the values in a data set from the mean.

Now, if a constant is subtracted from all values of a dataset, the standard deviation remains the same. Only the origin or mean of the data changes by subtracting a constant from whole data set.

Given that the standard deviation of dataset is 7.5

Subtracting 2 from each value of dataset will not change the standard deviation as 2 is a constant.

Hence,

Option B. 7.5 is the correct answer

Answer:

7.5 it stays the same

Step-by-step explanation:

a. The teacher can expect the batteries to last at least 92.09 days  on minimum average.

b. The teacher will need to spend at most $49.92 on batteries for calculators over the year.

What is minimum average day?

a. The margin of error of ‡9% means that we can be 95% confident that the true average number of days the batteries will last is within 9% of the sample average. To find the minimum average number of days a teacher can expect to have the batteries last in her classroom, we subtract the margin of error from the sample average:

Minimum average = 101 - (0.09)(101) = 92.09 days (rounded to two decimal places)

Therefore, the teacher can expect the batteries to last at least 92.09 days on average.

What is spend ?

b. The total number of batteries required for the 24 TI-84 calculators is:

24 calculators x 4 batteries per calculator = 96 batteries

The total cost of the batteries will be:

96 batteries x $0.52 per battery = $49.92 (rounded to two decimal places)

Therefore, the teacher will need to spend at most $49.92 on batteries for calculators over the year, assuming all batteries need to be replaced.

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Answer:

Step-by-step explanation:

5.6

The value of x in the solution set is x = 4

The system of inequalities is given as

3x + 4 < 9

-x + 6 ≥ -3

The first step is to solve for x in both inequalities in the system of inequalities

So, we have

3x + 4 < 9

3x < 5

Divide by 3

x < 5/3

Also, we  have

-x + 6 ≥ -3

-x ≥ -9

Divide by -1

x ≤ 9

So, we have

x < 5/3 and x ≤ 9

x ≤ 9 is a superset of x < 5/3

So, we have

x ≤ 9

This means that the values of x do not exceed 9

An example of this value (from the options) is 4

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Replace y(x) with 4:

4 = 4x

Divide both sides by 4:

x = 1

Answer:

x=2

Step-by-step explanation:

10 - (x + 3) = 5

To solve for x, we can start by simplifying the left side of the equation:

10 - (x + 3) = 5

10 - x - 3 = 5

7 - x = 5

Next, we can isolate x on one side of the equation by subtracting 7 from both sides:

7 - x = 5

7 - x - 7 = 5 - 7

-x = -2

Finally, we can solve for x by dividing both sides of the equation by -1:

-x = -2

x = 2

Therefore, the solution to the equation is x = 2.

Answer:

16

Step-by-step explanation:

Plug things in then use PEMDAS:

m * (7+9) * n

= 0.5 * (7+9) * 2

= 0.5 * 16 * 2

= 16

Step-by-step explanation:

=m(7+9)n

putting value of m&n

=0.5(7+9)2

=8×2

=16 ans

hope u need this.

Answer:

hi

Step-by-step explanation:

Answer:498000

Step-by-step explanation:

Answer:

I would need the number that is being increased by 30% to get the answer.

Step-by-step explanation:

Sorry

The exponential function when the coin is worth $25 is v(t) = 25(1.07)^t and when it's worth $40, it is v(t) = 40(1.05)^t

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828. An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form

f(x) = ax

Where a>0 and a is not equal to 1.

x is any real number.

If the variable is negative, the function is undefined for -1 < x < 1.

Here,

“x” is a variable

“a” is a constant, which is the base of the function.

An exponential curve grows, or decay depends on the exponential function. Any quantity that grows or decays by a fixed per cent at regular intervals should possess either exponential growth or exponential decay.

Using the details given;

v(t) = p(1 + r)^t

In the first case, the value of the coin is $25

v(t) = 25(1 + 0.07)^t

v(t) = 25(1.07)^t

When p = 40

v(t) = 40(1 + 0.05)^t

v(t) = 40(1.05)^t

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Answer:

3/8 = 9/24

7/6 = 28/24

Step-by-step explanation:

Answer:

The 95% confidence interval is  \( 3.462 <  \mu <  4.138 \)

Step-by-step explanation:

From the question we are told that

   The sample size is  n  =  50  

    The sample mean is  \(\=  x =  3.80\)

     The standard deviation is  \(\sigma  =  1.19\)

Given that the confidence level is  95%  then the level of confidence is mathematically represented as

     \(\alpha =  (100 - 95)\%\)

=>    \(\alpha =  0.05 \)

Generally from the t distribution table the critical value  of  \(\frac{\alpha }{2}\) at a degree of freedom of  \(df =  50 -1 = 49\) is  

   \(t_{\frac{\alpha }{2} ,49 } =  2.0096\)

Generally the margin of error is mathematically represented as  

      \(E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }\)

=>   \(E =2.0096 *  \frac{1.19}{\sqrt{ 50} }\)

=>   \(E = 0.3381 \)

Generally 95% confidence interval is mathematically represented as  

      \(\= x -E <  \mu <  \=x  +E\)

      \( 3.80 -0.3381 <  \mu <  3.80 +0.3381\)

=>    \( 3.462<  \mu <  4.138 \)

Hello,

answer f: conjugate

if all coefficients are real and a+ib a zero, its conjgate a-ib is also a zero.

Answer:

1999

Step-by-step explanation:

Multiply 3 with x - 2 on LHS and 3 with 2 - x on RHS

Now take -3x to LHS and change its symbol to +. And take 6 to RHS and change it to negative.

-3x and 3x will cancel out and also 6 and -6 will also get cancelled out.

Answer:

x = 0

Hope you could understand.

If you have any query, feel free to ask.

Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

To determine the average speed at which Sphenathi and the other matriculants must travel to reach Uptington by 09:45, we need to calculate the time available for the journey and the distance between the two locations.

The time available is from 07:25 to 09:45, which is a total of 2 hours and 20 minutes. We need to convert this time to hours by dividing by 60:

2 hours + 20 minutes / 60 = 2.33 hours

Now, let's calculate the distance between Bloemfontein and Uptington. Suppose the distance is 'd' kilometers.

We can use the formula for average speed: average speed = distance / time

In this case, the average speed should be such that the distance divided by the time is equal to the average speed.

d / 2.33 = average speed

Now, let's assume that Sphenathi and the other matriculants must travel a distance of 250 kilometers to reach Uptington. We'll substitute this value into the equation:

250 / 2.33 = average speed

To find the average speed to the nearest km/h, we'll calculate the result:

average speed ≈ 107.3 km/h

Therefore, Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

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Therefore , coordinate problem solution is A) 3140 pulses per minute , B) 2915 beats per minute , C) heartbeat of 2915 beats per minute (D) or 2915.5 beats per minute .

When locating points or other mathematical objects precisely on a region, such as Euclidean space, a coordinate system is a technique that uses one or more numbers or coordinates. Locating a point or item on a the double plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y vectors are used to define a point's location on a 2D plane. a collection of numbers that indicate specific locations.

Here,

The slope method can be used to calculate the patient's heart rhythm after 42 minutes that use the secant line connecting the points with the specified values of t:

Heartbeat change / time change is the trend.

The heart rate can then be estimated using this slope value along with the number for heartbeats at t = 42 minutes.

A)Using coordinates 36, 2510, and 42, 2915 as examples:

Cardiac rate at 42 minutes = 2510 + (42 - 36) * 75 = 3140 Slope = (2915 - 2510) / (42 - 36) = 75

b) Using coordinates (38, 2647) and (42, 2915), respectively:

Cardiac rate at 42 minutes = 2647 + (42 - 38) * 67 = 2915 Slope = (2915 - 2647) / (42 - 38) = 67

c) Applying the values (40, 2784) and (42, 2915):

Heart rate at 42 minutes = 2784 + (42 - 40) * 65.5 = 2915.5 Slope = (2915 - 2784) / (42 - 40) = 65.5

Using coordinates (42, 2915), and (44, 3048), respectively:

Cardiac rate at 42 minutes = 2915 + (42 - 42) * 66.5 = 2915 Slope: (3048 - 2915) / (44 - 42) = 66.5

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Hello!

The distance, d, is less than 200 miles.

B. d > 200

Answer:

V'= ( 5,2 )

U'= ( 8,2 )

T'= ( 7,12 )

S'= ( 3,12 )

Answers:

Check out the diagram below

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

Explanation:

When reflecting over horizontal lines like this, the x coordinate stays the same as the original point. Only the y coordinate changes.

To find what the y coordinate changes to, we need to measure the vertical distance from the point to the line. Point S has a y coordinate of y = -5 and the vertical distance to the line of reflection (y = 1) is |-5-1| = |-6| = 6 units. So we move 6 units up to go from point S to the line of reflection. We must move another 6 units to get to the location for S' where its reflected point would end up, which has y coordinate y = 7.

The same applies for the other points as well. Point T also goes up 6 units to get to y = 1, then it moves another 6 units to get to y = 7

Points V and U only move up 1 unit to get to the green dotted line of reflection. So they'll move only one additional unit to have their reflected points have y coordinates of y = 2.

The diagram hopefully visually summarizes everything discussed so far. The mirroring line cuts the distance from S to S' in half, same for T to T', and so on.

Answer:

x = 34 feet  

Step-by-step explanation:

(4/14) = (x/119).

14x = 4(119)

14x = 476

Answer:

6x-3

Step-by-step explanation:

The required number, which is 3 less than 6 time of number n is 6n-3.

An algebraic expression is consists of variables, numbers with various mathematical operations,

Let the number is n,

According to given conditions,

To determine the number, which is 6 times of the number and 3 less,

Use expression form,

The required number can be written as,

3n-6

The required number is 3n-6.

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With four decimal places added, we have P(2.04 Z 3.04) 0.0189.

To round a decimal value to two decimal places, use the hundredths place, which is the second place to the right of the decimal point.

Subtracting the area to the left of 1.25 from the area to the left of 2.15 will give us the standard normal area between 1.25 and 2.15.

The area to the left of 1.25 is 0.8944, and the area to the left of 2.15 is 0.9842, according to a conventional normal distribution table or calculator.

So, the standard normal area between 1.25 and 2.15 is:

P(1.25 < Z < 2.15) = 0.9842 - 0.8944 = 0.0898

Rounding to four decimal places, we get:

P(1.25 < Z < 2.15) ≈ 0.0898

We follow the same procedure as before to determine the standard normal region between 2.04 and 3.04:

P(2.04 < Z < 3.04) = P(Z < 3.04) - P(Z < 2.04)\

The area to the left of 2.04 is 0.9798, and the area to the left of 3.04 is 0.9987, according to a conventional normal distribution table or calculator.

So, the standard normal area between 2.04 and 3.04 is:

P(2.04 < Z < 3.04) = 0.9987 - 0.9798 = 0.0189

Rounding to four decimal places, we get:

P(2.04 < Z < 3.04) ≈ 0.0189

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Answer:

Width is 15, length is 35.We can check our answer by multiplying the length by 2 and the width by two in order for the perimeter to be equal to 200.15 times 2 is 30 and 35 times two equals 70.70+30=100 so our solution satisfies our problem.

Step-by-step explanation:

Let the width be x.Then the length should be x+20.The farmer can’t use more than 100 ft of fencing and by mentioning enclosing a rectangle area for a pigpen, we can tell that 100 is the perimeter.So 2(x+20) + 2(x)=100.2x+ 40 + 2x=100.4x+40=100.4x=60.X is 15 which is the width so then the length is 35.

Answer:

Step-by-step explanation:

3x+30=150

its 120 then divide by 3 which is 40

Part A: what tool can help Jada find possible dimensions for the base of the block? Explain.

     I am not sure what a "tool" is by their wording, but we can use the formula for volume to solve for the base.

-> B is the base, length times width, and H is the height

V = B * H

350 in³ = B * 5 in

70 in² = B

  Answer: The base will be 70 in²

Part B: Give one pair of possible whole-number dimensions for the base.

     Since we know the base will be 70 in², we can find a possible pair of whole-number dimensions for the base.

B = L * W

70 in² = L * W

     Now we just need to find pairs of whole numbers that multiply to 70:

70 / 2 = 35

  Answer: A possible pair of whole-number dimensions for the base is 2 and 35.

Answer: A and C

Step-by-step explanation: