MATHEMATICS COLLEGE

The girls' swim team is hosting a fund raiser. They would like to raise at least $500 . They are selling candles for $5 and flower arrangements for $6. The girls estimate that at most they will sell 200 items. Write a system of inequalities that models what is going on in this problem. Graph it and find a solution.

Answers

Answer 1

Answer:

Answer:

x: # of candles

y: # of flower arrangements

Inequality 1: x + y ≤ 200

Inequality 2: 5x + 6y ≥ $500

Step-by-step explanation:

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A water tank leaked 14 gallons of water over eight hours at a constant rate what was the change in the amount of water in gallons in a tank each hour

Answers

Answer:

7/4 gallons per hour

Step-by-step explanation:

We have to divide the amount of water lost by the lapse of time. So we get

14/8= 7/4

Answer: the answer would be 1.75 gallons/hour

Step-by-step explanation: if you take the 14 gallons divided by the eight hours, you get 1.75

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 .

This is a two-part question: A 12-pack of bottled mineral water sells for $3.85. For the following,state whether to use multiplication or division for the specified amount:
a) The cost of one bottle of water:
b) The cost of four 12-packs of water:

Answers

Answer:

The cost of one water bottle of water would be division, The cost of four 12-packs of water is multiplication.

Step-by-step explanation:

PLZZZ HELP FAST What is the product of Three-fourths and Negative StartFraction 6 over 7 EndFraction? Negative StartFraction 7 over 8 EndFraction Negative StartFraction 9 over 14 EndFraction StartFraction 9 over 14 EndFraction StartFraction 7 over 8 EndFraction

Answers

Answer:

-9/14 so the answer is B

Step-by-step explanation:

Hope this helps

X2 + 16x – 2 = 111) Rewrite the equation by completing the square.
Your equation should look like (x + c)2 = d or (x - c)2 = d.
I
+
utan
pls help

Answers

The equation with completing the squares is (x + 8)² = 77.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

x² + 16x - 2 = 11

We can make completesquares.

x² + 16x - 2 - 11 = 0

x² + 16x - 13 = 0

x² + 2 x 8 x (x) -8² + 8² - 13 = 0

(x² + 16x + 8²) - 64 - 13 = 0

(x + 8)² - 77 = 0

(x + 8)² = 77

Thus,

The equation is (x + 8)² = 77.

Learn more about equations here:

brainly.com/question/17194269

#SPJ2

Answer:

(x+8)^2=77 and x=negative 8±√77

Step-by-step explanation:

After watching a video, I got it right on Khan

Can solve this...(-2e3)4?

Answers

I'm not really sure what you are asking but Exact Form:−8e3-8⁢e3Decimal Form:−160.68429538…

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