Simplify the expression

At 7:00 A.M., Alicia pours a cup of tea whose temperature is 200°F. The tea starts to cool to room temperature (72°F). At 7:02 A

NeTakaya

Answer:

Part A

The most correct option is;

b. y = 128(0.989)x + 72

Part B

Ella can drink the tea after 7:22

Step-by-step explanation:

Here we have the temperature variation with time given in an exponential equation as follows;

Let the temperature at time x (in minutes) = y

Therefore, y = a × mˣ + b

Where:

b = Shift of the curve or the limit value of the decreasing exponential function as x → ∞

When y = 200, x = 0

Therefore. 200 = a × m⁰ + c = a + c

We note that c is the shift of the graph, the value upon which temperature increases = final temperature = 72°F

Hence a = 200 - 72 = 128°F

When y = 197, x = 2 minutes

Therefore, 197 = 128·m² + 72 =

m² = (197 - 72)/128 = 125/128

m = √(125/128) = 0.98821

Hence the exponential equation of cooling is presented in the following equation;

y = 128 × (0.98821)ˣ + 72

Therefore, the most correct option is b. y = 128(0.989)x + 72

Part B

When the temperature is 172°F we have;

172 = 128 × (0.989)ˣ + 72

∴ (0.989)ˣ = (172 - 72)/128 = 100/128 = 25/32

log(0.989)ˣ = log(25/32)

x·log(0.989) = log(25/32)

x = log(25/32)/log(0.989) = 22.32 minutes

Hence Ella can drink the tea after 7:22.

6 0

2 years ago

Rita gets paid $16 per hour for the first 8 hours she works each day. She earns 1 1 2 times her hourly pay rate for time she wor

omeli [17]

<h3>The total money earned by Rita on Monday = $158</h3>

Step-by-step explanation:

The rate by which Rita is paid first 8 hours = $16

The next per hour rate after 8 hours = $1\frac{1}{2} = 1.5$ times the usual rate.

Now, 1.5 times $16 = 1.5 x 1 6 = $24

So, for each hour worked after 8th hour, Rita is paid $24 per hour.

Now, the intervals she has worked are:

(a) from 8:15 to 12: 45 pm

So, the number of hours worked = 45 minutes + 45 minutes + 3 hours

= 4 hours 30 minutes .... (1) (as 60 minutes = 1 hour)

(b) break of 45 minutes after 12: 45 = 12: 45 + 45 minutes

= 12 hour 90 minutes = 1 : 30 P M

So, she started working at 1: 30 and worked till 6: 15

So, the number of hours worked = 30 minutes + 15 minutes +4 hours

= 4 hours 45 minutes .... (2)

So, by adding (1) and (2) the total hours worked by Rita

= 4 hours 30 minutes + 4 hours 45 minutes

= 8 hours 75 minutes = 9 hours 15 minutes

9 hours 15 minutes = ( 8 + 1 .25 ) ( 15 minutes = 0.25 of an hour)

So, the payment is ( 8 x (16) + 1.25 (24) )

= 128 + 30 = 158

Hence, the total money earned by Rita = $158

6 0

3 years ago

Find the equation of OP.

Bumek [7]

Answer:

G

Step-by-step explanation:

3 0

3 years ago

I need help please! asap

mihalych1998 [28]

Answer:

my guess is c

Step-by-step explanation:

bxnxnnsnsndnjdjdjd

8 0

2 years ago

The sum of the two digit number is 12. If the digit are revesed, then the new number is 18 less than the originaol muber that is

FromTheMoon [43]

Answer:

A) X + Y = 12

B) 10Y + x = 10x + Y -18

B) 9Y = 9x -18 multiplying A) by -9

A) -9Y = 9x - 72 adding A and B we get

0 = 18x -90

x = 5

The number is 75

Double-Check

7 + 5 = 12

75 -57 = 18

Step-by-step explanation:

6 0

3 years ago