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Suppose you're given the formula q = 2o + 6p. If you know that p = o – 7, how could you rewrite the formula?

Answers

Answer 1

Answer:

Answer:

q = 8o - 42

Step-by-step explanation:

Given: The given formula is q = 2o + 6p.

p = o – 7

Now we have to plug in p = o - 7 in the given formula, we get

q = 2o + 6(o - 7)

Now we use the distributive property a(b-c) =ab - ac and expand.

q = 2o + 6o -6(7)

q = 2o +6o - 42

Here 2o and 6o are the like terms, we can add them

q = 8o - 42

Answer 2

Answer:

q = 2o + 6p

p = o – 7

⇒ q = 2o + 6(o - 7) = 2o + 6o - 6 × 7 = 8o - 42

⇒ q = 8o - 42

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A bacteria culture is initially 10 grams at t=0 hours and grows at a rate proportional to its size. After an hour the bacteria culture weighs 11 grams. At what time will the bacteria have tripled in size?

Answers

A bacteria culture is initially 10 grams at t=0 hours & grows at a rate proportional to its size , After an hour the bacteria culture weighs 11 grams , The bacteria takes 11.56 hours to have tripled in size.

To find the time of bacteria when increasing the growth to tripled.

Given : when time=0 hours , weight=10 grams.

when time=1 hours , weight=11 grams.

To find: when time= ? hours , weight=30grams.

Here according to question, initial size = 10 grams we have asked for tripled in size i.e. 30 grams.

Now we knows that,

The formula for exponential growth in population or size is

$\rm (P)=P_0e^(rt)$ where,

$\rm P_0=initial\;size\n\nr= rate\;of\;growth\n\nt= time \;period$

Now, we put the value in formula we get,

$\rm P_0=10\;grams \n\nwhen ,\n\;\;t=1\;hour P(t)=11 grams\nThen,\n11=10e^{r(1)\n1.1 =e^r\n\n\rm Taking \;log(natural)\;both\;the\; side \;on \;solving\;we\;get,\nln(1.1)=r\;ln(e)\nr=ln(1.1)\nr=0.953101798043\approx0.095$

Now when the bacteria increase its size to triple

$\rm P(t) = 3 * 10 = 30$

Then, according to the formula we substitute values in the formula,

$\rm 30=10e^(0.095t)\n\n3=e^(0.095t)\n\nAgain \;we \;take\;natural\;log\;on \;both\;the\;sides, we\;get\nln\;3=0.095t\n\nt=(\rm ln\;3)/(0.095)\n\n\n\n\rm t= (1.09861228867)/(0.095) \n\n\ t=approx \; 11.56$

Therefore, The bacteria takes 11.56 hours to have tripled in size.

Learn more about logical questions here : brainly.com/question/15046576

Answer: It will take 11.56 hours .

Step-by-step explanation:

Exponential growth in population or size formula :

$P(t)=P_0e^(rt)$

, where $P_0$ = initial size

r= rate of growth

t= time period

As per given , we have

$P_0=10$ grams

At t= 1 , P(t)= 11 grams

Then,

$11=10e^(r(1))\n\n 1.1= e^r\n\n\text{Taking natural log on both sides , we get} \n\n\ln (1.1)=r\ln (e)\n\n r=\ln (1.1)\n\n r=0.0953101798043\approx0.095$

When, the bacteria have tripled in size , P(t) = 3 x10 = 30

Then,

$30=10e^(0.095t)\n\n 3=e^(0.095t)$

$\text{Taking natural log on both sides , we get}\n\n \ln 3=0.095t\n\n t=(\ln3)/(0.095)\n\n t=(1.09861228867)/(0.095)\approx11.56$

Hence, it will take 11.56 hours .

On two investments totaling $6,000, Kevin lost 3% on one and earned 6% on the other. If his net annual receipts were $288, how much was each investment?

Answers

ANSWER:

$ 800 was invested in the account at 3%

$5200 was invested in the account at 6%

STEP-BY-STEP EXPLANATION:

We can establish the following system of equations thanks to the help of the statement:

Let x represent the amount invested in the investment that lost value

Let y represent the amount invested in the investment that gained

value.

$\begin{gathered} x+y=6000\rightarrow y=6000-x\text{ (1)} \n -0.03x+0.06y=288\text{ (2)} \end{gathered}$

We replace equation (1) in (2) and solve for x:

$\begin{gathered} -0.03x+0.06\cdot(6000-x)=288 \n -0.03x+360-0.06x=288 \n -0.09x=288-360 \n x=(-72)/(-0.09) \n x=800 \n \text{ Now, for y replacing in (1)} \n y=6000-800=5200 \end{gathered}$

Therefore, $ 800 was invested in the account the lost value, and $ 5200 was invested in the account that gained value.

HELP ASAP PLSS! The graph represents the relationship between the amount of money a babysitter makes, m, and the hours the baby sitter works, h. Which function can be used to determine the amount of money the babysitter makes, d, after h hours? d=17h+5 d = 5h + 7 d = 7h +5 d=15h+7

Answers

Answer:

d = 7h +5

Step-by-step explanation

If you go to K-12 then this is the right answer I just took the quiz.

Answer:

d = 7h +5

An algebraic relationship of that quantity is greater than or less then another quantity ?

Answers

Answer:

Inequality

Step-by-step explanation:

DJ Davon is making a playlist for work; he is trying to decide what 12 songs to play and in what order they should be played. If he has his choices narrowed down to 14 blues, 25 country, and 21 disco songs, and he wants to play an equal number of blues, country, and disco songs, how many different playlists are possible? Express your answer in scientific notation rounding to the hundredths place.

Answers

Answer:

1.80 * 10^19

Step-by-step explanation:

If he has narrowed down his choices to 14blues, 25 country and 21 disco songs and he has to make a list of 12 songs with equal representation of each genre of song, the it means there will be 4 songs from each genre of music.

We select this 4 different songs using the combination formula for selection and multiply our results.

This means we have:

12C4 for blues,

25C4 for country

21C4 for disco.

This gives:

=12C4 * 25C4 * 21C4

= 495 * 12650 * 5985

And the order they can be played = 12!.

We then multiply the number of ways to get these songs by the order they can come in.

That is:

=495 * 12650 * 5985 * 12!

= 1.7951 * 10^19

= 1.80 * 10^19 (nearest hundredth).

Final answer:

DJ Davon can make approximately 3.57 x 10^21 different playlists, if he includes an equal number of blues, country, and disco songs. This calculation utilizes combination and permutation formulas.

Explanation:

DJ Davon wants to play an equal number of blues, country, and disco songs, which means he will play 4 songs from each genre. The number of ways to select 4 songs out of each genre is represented by the combination formula C(n,r) = n! / [r!(n-r)!].

So, for each genre, the number of ways to select 4 songs is:
Blues: C(14,4) = 1001
Country: C(25,4) = 12,650
Disco: C(21,4) = 5985.

After the songs are selected, the order of the playlist matters, so we use the permutation formula. Given 12 slots for the songs, the number of ways to order them is P(n) = n!, which for 12 is 479,001,600. The total number of different playlists is product of blues, country and disco song combinations and the permutations, which gives 3.57 x 10^21. This rounded to the hundredths place in scientific notation is 3.57 x 10^21.

Learn more about Combinations and Permutations here:

brainly.com/question/19917646

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Which expression is equivalent to 6(2x+5y)

Answers

6(2x + 7y) = 6(2x) + 6(7y) = 12x + 42y

12x+42y is equivalent to 6(2x+5y)

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