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A population of bacteria is growing at an hourly rate of r so that at the end of each hour the population of the sample is multiplied by the growth factor of
z = 1+r. The beginning population is 800 bacteria, an additional 300 are present after 1 hour, and an additional 400 are present after the following
hour.
Write an expression for the population at the end of three hours in terms of the growth factor.

The solution set to the inequality m-7>-2(m+0.5) is all real numbers greater than -0.75.

Real numbers are the set of all rational and irrational numbers, which includes all positive and negative numbers, fractions, decimals, and integers. They are represented on the number line and are composed of an infinite amount of numbers between any two given numbers.

This can be represented graphically on a number line by selecting a ray starting at -0.75 and extending infinitely in the positive direction. The point on the ray at -0.75 represents the boundary between the solution set and the numbers not included in the solution set.

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At the end of 4.5 hours, Nell and Kristin will be at a distance of 9 miles apart.

Here, we are given that Nell and Kristin start from the same point and skate in the same direction.

Speed of Nell = 8 miles per hour

Time for which he skates = 4.5 hours

Thus, the distance travelled by Nell will be-

Distance = Speed × time

= 8 × 4.5

= 36 miles

Similarly, Speed of Kristin = 10 miles per hour

Time for which he skates = 4.5 hours

Thus, the distance travelled by Kristin will be-

= 10 × 4.5

= 45 miles

Thus, the distance between them will be-

45 - 36 = 9 miles.

Thus, at the end of 4.5 hours, Nell and Kristin will be at a distance of 9 miles apart.

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Nell and Kristin, two inline skaters, begin at the same location and move in the same direction. While Kristin skates at 10 miles per hour, Nell skates at 8 miles per hour. 5 miles apart will they be at the conclusion of the 4.5 hours if they maintain their current rate.

Distance =Rate x time ....... d=rt

The difference in the distances traveled will be how far apart they are 12(2.5)-10(2.5)=2(2.5)=5 miles apart

Note that you can find their individual distances and subtract those to get the same answer:

Nell: distance =10(2.5)=25 miles

Kristin: distance =12(2.5)=30$ miles

30-25=5 miles apart

Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.

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The image of the transformation on the graph are (7, -7), (7, -2) and (-1, -14)

The graph represents the given parameter

On the graph, we have the coordinates of the triangle to be

(3, 1), (3, 6) and (-5, -6)

The transformation rule is given as

Translated 4 units to the right, and 8 units down.

Mathematically, the transformation rule is given as

(x, y) = (x + 4, y - 8)

When the above transformation rule is applied to the coordinates of the triangle, we have

(3 + 4, 1 - 8), (3 + 4, 6 - 8) and (-5 + 4, -6 - 8)

Evaluate the sum and the difference

So, we have

(7, -7), (7, -2) and (-1, -14)

Next, we plot the image of the transformation on the graph

See attachment for the image of the transformation of the triangle on the graph

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A number in which value of 3 is ten times greater than the value of 3 is 375,786.

Here,

We have to find a number in which the value of the 3 is ten times greater than the value of the 3 in 135,864.

What is Place value?

Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

Now,

The value of 3 in 135,864 is 30,000.

And, We want to write a number that is ten times greater than 30,000.

Hence, We have to write any other number in which the value of 3 is 300,000.

Since, There are infinitely many numbers that we can write.

Some numbers are:

375,786

2,345,576

9,387,988  ........  and so on.

Therefore, A number in which value of 3 is ten times greater than the value of 3 is 375,786.

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The two numbers that you would subtract to find the interquartile range (IQR) of the set of values are: A. 22 - 18.

The interquartile range (IQR) = Upper quartile (Q3) = lower quartile (Q1).

Given the data set, 17, 21, 19, 23, 16, 22, 19, 20, 24, 18, we have the following:

Upper quartile (Q3): 22 (center of the second half of the data)

Lower quartile (Q1): 18 (the middle/center of the first part of the data)

Interquartile range (IQR) = 22 - 18

Interquartile range (IQR) = 4

Therefore, the two numbers that you would subtract to find the interquartile range (IQR) of the set of values are: A. 22 - 18.

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Answer:

Answer for this question is C because, 1 input has 2 outputs. And that's why C doesn't represent a function.

Using the relation between acceleration, velocity and distance, it is found that:

a) The differential equation for the velocity is: [tex]\frac{dV}{dt} = 0.5[/tex]

b) The formula for the velocity is given by: V(t) = 0.5t + 6.

c) The initial value problem to find the position is: [tex]\frac{dS}{dt} = 0.5t + 6, S(0) = 0[/tex]

d) The formula for the position of the car is S(t) = 0.25t² + 6t.

e) The car is at a velocity of 21 m/s after 30 seconds.

We have that:

For item a, we have that the acceleration is constant of 0.5 m/s², hence the differential equation for the velocity is:

[tex]\frac{dV}{dt} = 0.5[/tex]

For item b, we apply separation of variables, and find the velocity as follows:

[tex]\frac{dV}{dt} = 0.5[/tex]

[tex]\int dV = \int 0.5 dt[/tex]

V(t) = 0.5t + v(0).

v(0) is the initial velocity and is the constant of integration, hence:

The formula for the velocity is given by: V(t) = 0.5t + 6.

For item c, we have that the position is the integral of the velocity, hence:

The initial value problem to find the position is: [tex]\frac{dS}{dt} = 0.5t + 6, S(0) = 0[/tex]

For item d, applying separation of variables, we have that:

[tex]\frac{dS}{dt} = 0.5t + 6[/tex]

[tex]\int dS = \int (0.5t + 6) dt[/tex]

S(t) = 0.25t² + 6t + s(0).

Since s(0) = 0, we have that:

The formula for the position of the car is S(t) = 0.25t² + 6t.

The velocity after 30 seconds is of:

v(30) = 6 + 0.5(30) = 21.

The car is at a velocity of 21 m/s after 30 seconds.

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Answer:

B. Irrational

Step-by-step explanation:

The √14 = 3.74 recurring. This isn't an integer and therefore can't be written as a fraction. Therefore it's an irrational number.

Whereas, if it was √16 which equals 4, the answer would be rational as it is an integer which can be written as a fraction such as 4/1 or 8/2 etc.

By using multiplication, we get that the number of pounds of rice will be 19.8 pounds.

We are given that:

1 kg of rice = 2.2 pounds of rice.

We need to find the number of pounds of rice in 9 kg of rice.

So, we will use the operation of multiplication to covert the units from kg into pounds.

So, we get that:

9 kg of rice = 2.2 × 9 pounds of rice

9 kg of rice = 19.8 pounds of rice.

Therefore, by using multiplication, we get that the number of pounds of rice will be 19.8 pounds.

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Answer:

15-(6+7)

Step-by-step explanation:

Answer:

15 - (6+7)

Step-by-step explanation:

The number sentence is 5 - 7 and temperature at midnight is equal to -2°F .

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.

The temperatures are given at different time of a day. It is given that the final temperature was the temperature that existed at midnight. Firstly temperature rise between 6 AM and 3PM by 11° from - 6 °F at 6 AM and then between 3PM and midnight it fell by 7°.

So , we can show these variations as follows :

At 6AM temperature = - 6 °F

Between 6AM and 3 PM temperature rose by 11° , so temperature at 3 PM will be :

= - 6 + 11

= 5 °F

Between 3PM and midnight the temperature fell by 7° , so the number sentence will be :

= 5 - 7

And the temperature at midnight will be :

= -2°F

Therefore , the number sentence is 5 - 7 and temperature at midnight is equal to -2°F .

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The distance of Neptune from the sun than Mercury will be B. Subtract the distances by getting the same power of 10: (4.5 x 10^10) - (5.8 x 10^7)-(4.5 x 10^10)-(.0058 x 10^10) = 44.99 x 10/10km.

From the information, Mercury is 5.8 x 10^7 km from the sun and Neptune is 4.5 x 10^10 km from the sun.

It should be noted that since we want to find the difference, therefore, we've to subtract.

Therefore, distance of Neptune from the sun than Mercury will be Subtract the distances by getting the same power of 10: (4.5 x 10^10) - (5.8 x 10^7)-(4.5 x 10^10)-(.0058 x 10^10) = 44.99 x 10/10km.

In conclusion, the correct option is B.

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Error: They failed to account for when x-5 is negative.

Solution:

[tex]|x-5|<20 \\ \\ -20<x-5<20 \\ \\ \boxed{-15<x<25}[/tex]

One person took a loan A monthly payment is $530.65. An interest rate is 5.90%. APR is over 29 years. The present value of a loan is 100.69.

Given that,

One person took a loan

A monthly payment is $530.65

An interest rate is 5.90%

APR is over 29 years.

We have to find the present value of a loan

The formula for present value of a loan is

The present value (PV) formula is used in finance to determine the present worth of money received in the future. The compound interest formula serves as the foundation for the present value formula (PV formula). The formula for compound interest is,

PV = [tex]\frac{FV}{(1+\frac{r}{n)} ^{nt}}[/tex]

Where,

PV=present value

FV=future value

r= rate of interest

n=When frequently the amount compounds

t=time

Given FV=$530.65

r= 5.90% =0.059

t=29 years

n=1(Due to the amount's annual compounding).

PV=[tex]\frac{530.65}{(1+\frac{0.059}{1})^{1\times29} }[/tex]

PV=[tex]\frac{530.65}{(1+0.059)^{29}}[/tex]

PV=[tex]\frac{530.65}{(1.059)^{29}}[/tex]

PV=[tex]\frac{530.65}{5.27}[/tex]

PV=100.69

Therefore, The present value of a loan is 100.69.

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Answer:

In those questions you asked, we can use equation to find the answer but the 1st question's x did not get an exact value so you can do no solution. Thank you

Answer:

x = -26

Step-by-step explanation:

[tex](f-g)(x)=\frac{4}{x-3}-\frac{3}{x+5}=\frac{3}{x^2 +2x-15} \\ \\ \frac{4(x+5)-3(x-3)}{x^2 +2x-15} \\ \\ =\frac{4x+20-3x+9}{x^2 +2x-15}=\frac{3}{x^2 +2x-15} \\ \\ \frac{x+29}{x^2 +2x-15}=\frac{3}{x^2+2x-15} \\ \\ x+29=3 \\ \\ x=-26[/tex]

This is in the domain of the equation, and is thus a solution.

Answer:

[tex]A_{new}=(-3,0)\\B_{new}=(0,-1)\\C_{new}=(1,-4)\\D_{new}=(-3,-5)[/tex]

Step-by-step explanation:

Looking at the diagram, you can see and determine the following points, write them down:

A=(-1,4)

B=(2,3)

C=(3,0)

D=(-1,-1)

Translating 2 units left means x changes by (-2)

Translating 4 units down means y changes by (-4)

Old Point + Point Change = New Point

[tex]A_{old}+T=A_{new}\\A_{old}=(-1,4)\\T=Translation=(-2,-4)\\A_{old}+T=(-1,4)+(-2,-4) = A_{new}=(-3,0)[/tex]

[tex]B_{old}=(2,3)\\C_{old}=(3,0)\\D_{old}=(-1,-1)\\T=(-2,-4)\\B_{new}=(2,3)+(-2,-4)=(0,-1)\\C_{new}=(3,0)+(-2,-4)=(1,-4)\\D_{new}=(-1,-1)+(-2,-4)=(-3,-5)[/tex]

Step-by-step explanation:

that's why it is so important to always write also the units a number represent.

and for a fully nice scientific notation you write also at least 1 digit after the decimal point.

(a) 6.0 × 10²⁴ kg

(b) 4.0 × 10² g

now,

1 kg = 1000 g ("kilo" means 1000)

so, in order to be able to compare the 2 numbers, you have to bring both numbers to the same unit. either both to kg or both to g.

6.0 × 10²⁴ kg = 6.0 × 10²⁴ × 1000 g = 6.0 × 10²⁷ g

or

4.0 × 10² g = 4.0 × 10² / 1000 kg = 4.0 × 10^-1 kg

once you have both showing the same unit, you can truly compare them.

Answer:

Step-by-step explanation:

You want the next number in the sequence 31, 27, 23, 19, 15, ... such that it follows the same pattern.

It is often useful to look at the differences between successive terms of a sequence. This can quickly reveal a pattern if the sequence is polynomial or exponential.

Here, the differences are ...

  27 -31 = -4

  23 -27 = -4

  19 -23 = -4

  15 -19 = -4

It appears reasonable to assume that the pattern is that each term is 4 less than the previous one.

The number that is 4 less than 15 is ...

  15 -4 = 11

The next number in the pattern is 11.

Answer: 1/7

Step-by-step explanation:

The total amount of cars that had AC problems is 30+20=50. The total amount of cars is 30+20+200+100=350. 50/350 = 1/7

The system of inequalities that represents the graph are:

y−6≤−11x

y+3x≥−4

−2x+3y>15

Option B

This is further explained below.

Generally, The term "set of simultaneous equations" refers to a finite collection of equations in the subject of mathematics, all of which are looking for the same solution.

A system of equations or an equation system is a name that is sometimes used to refer to this kind of collection of equations.

In conclusion,

y−6≤−11x

y+3x≥−4

−2x+3y>15

represents the graph

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Answer:

Yes, 14 × 216 = 3024

Step-by-step explanation:

The coordinate of B is (1,-3)

In coordinate system mid point is the point which is exactly at the middle

The coordinates of point A are (5,1)

The coordinate of  mid point M are (3,-1)

It is to be noted that mid point divides both sides in the ratio 1:1

We are required to find the coordinates of point B

Let the coordinates of B be (x,y)

For mid points, section  formula further simplifies to

m's x coordinate= (a's x coordinate + b's x coordinate)/2

m's y coordinate = (a's y coordinate + b's y coordinate)/2

therefore,

3 = (5+x)/2

6=5+x

x=6-5 =1

-1 = (1+y)/2

-2 =1+y

y=-3

Hence the coordinates of B are (x,y) which is (1,-3)

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Answer:

send the image of the exercise

Over the course of three weeks, she practiced for 609 minutes to become ready. The constant of proportionality is k=203.

Given that,

Rochelle planned out additional practice because she was getting ready for a big swim meet.

Over the course of three weeks, she practiced for 609 minutes to become ready. Every week she practiced for the same amount of time.

We have to find the constant of proportionality (k) between Rochelle's weekly practice time (w) and the number of minutes she practiced each week (m).

3 week =609 minutes

3w=609m

1w=609m/3

1w=203m

For 1 week she practiced 203 minutes.

Now,

Constant of proportionality is

m=kw

203=k(1)

k=203

Therefore, the constant of proportionality is k=203.

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Answer:

when one of them is done

Step-by-step explanation:

you can't meet together because you don't run fast the

The standard deviation of the portfolio return is 3.14%

What is Sharpe ratio?

Sharpe ratio measures the by extent to which the risk of an investment portfolio is compensated as it indicates the return per unit of risk inherent in the portfolio whereas the standard deviation measures the risk of expected return of the portfolio.

It should be noted that the Sharpe ratio can be determined as the expected return of the portfolio minus the risk-free rate of return divided by the standard deviation of the portfolio.

Sharpe ratio=(expected return-risk-free rate)/standard deviation

Sharpe=2.99

expected return=12.9%

risk-free rate=3.5%

standard deviation=unknown(assume it is x)

2.99=(12.9%-3.5%)/x

2.99*x=9.40%

x=9.40%/2.99

x=3.14%

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Answer:

18/5 which also equals 3 3/5 would be the answer