MATHEMATICS COLLEGE

2) Mr. Riley dove off a cliff that was 30 feet above the surface of the water and descended a total of 100 feet. Which of the equations below can be used to determine his elevation at the bottom of his dive?a) 30 + 100
b) 30-100
C) 30 + (-100)
d) Both b and c​

Answers

Answer 1
Answer:

Answer:

B

Step-by-step explanation:

Mr.Riley was 30 feet above the water, which means he is at +30 above sea level. If he descends 100 feet, that means he goes 100 feet lower then that. 30 - 100 is equal to -70. He is 70 feet under water after he dived. You do not need to know the answer, but it helps to visualize the problem you have, therefore, finding the answer

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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 .

The probability that an adult possesses a credit card is .70. A researcher selects two adults at random. By assuming the independence, the probability that the first adult possesses a credit card and the second adult does not possess a credit card is:

Answers

Answer: 0.21

Step-by-step explanation:

We know that if two events A and B are independent , then the probability of A and B is given by :-

\text{P and B}=P(A)* P(B)

Given: The probability that an adult possesses a credit card P(A)= 0 .70

The probability that an adult  does not possess a credit cardP(B)= 1-P(A)=0 .30

By assuming the independence, the probability that the first adult possesses a credit card and the second adult does not possess a credit card is given by :-

0.70*0.30=0.21

Hence, the probability that the first adult possesses a credit card and the second adult does not possess a credit card is 0.21.

F(x)=-x^2-10x find f(-7)

Answers

=Answer:

Step-by-step explanation:

f(-7) = -(-7)^2 - 10(-7) = -49 +70 = 21

Percent * $3.32 = $0.32 + $0.184

Answers

The missing percentage of the given algebraic expression when calculated is; 15.18%

How to work with Percentages?

We want to find;

Percent * $3.32 = $0.32 + $0.184

First of all, let us add the terms on the right side of the equation to get;

Percent* $3.32 = $0.504

Next operation is to divide both sides by 3.32 using division property of equality to get;

Percent = 0.1518 = 15.18%

Read more about Percentages at; brainly.com/question/843074

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A new television is on sale for $680.00, which is 20% off of its original price. What was the original price of the television?

Answers

x= original price
% off= 20%
Sale $= $680

STEP 1:
Find discount amount

Discount Amount= % off * Original $
= 20% * x
change % to decimal (% ÷ 100)
= 0.20 * x
= 0.20x

STEP 2:
Find sale price

Sale Price= Original $ - Discount
= x - 0.20x
= 0.80x

STEP 3:
Sale= $680= 0.80x
Solve for x

$680= 0.80x
divide both sides by 0.80
$680/0.80= x
$850= x

ANSWER: The original price is $850

Hope this helps! :)

A bookstore keeps track of books sold in one day? Approximately how many books sold were hardcover nonfiction?

Answers

Answer:

27%

Step-by-step explanation:

The total books sold were 182 and the amount of books sold that were nonfiction hardcover were 49 as represented in the frequency table.

To find the percentage we must divide the nonfiction hardcover by the total books.

49/182≈0.269 or 0.27

Multiply the decimal by a 100 to change it into a percentage, so our answer is 27%.

Answer:a 27%

Step-by-step explanation:
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