Answer:1) B. 240(0.92)^t < 115; 9 days is the inequality which represents the situation.
2)After t=9 days the amount of the sample be less than 115 milligrams.
Step-by-step explanation:
The amount of sample which Jordan had in starting a =240 milligrams
rate of decreasing it r =8%=0.08
let t be the number of days the amount of sample took to become 115 milligrams then by the exponential decay function
[tex]f(t)=a(1-r)^t[/tex] where f(t) =115
[tex]115=240(1-0.08)^t....(1)\\\Rightarrow\frac{115}{240}=(0.92)^t\\\Rightarrow0.479=(0.92)^t\\\text{taking log on both sides ,we get}\\log(0.479)=log((0.92)^t)\\\Rightarrow\ log(0.479)=t\ log(.092)\\\Rightarrow\ -0.735=t(-0.0833)....\text{after solving log values}\\\Rightarrow\ t=\frac{-0.735}{-0.833}\approx8.82 days[/tex]or 9 days(approx ).
therefore, after t=9 days the amount of the sample be less than 115 milligrams.
So ,the right inequality which represent the situation is
B. 240(0.92)^t < 115; 9 days (from (1))
Answer:
B. 240(0.92)t < 115
9 days.
Step-by-step explanation:
We are told that Jordan works in a science lab where he is studying the behavior of a certain unstable isotope. He has 240 milligrams of the sample, and the amount of the substance remaining in the sample decreases at a rate of 8% each day. After t days, there are less than 115 milligrams of the substance remaining. We are asked to write an inequality to represent this situation.
An exponential function representing decay will be our inequality.Let us write an inequality for this situation.
[tex]240(1-0.8)^{t} <115=240(0.92)^{t} <115[/tex], where 240 is our initial amount of substance, 0.8 is decrease factor.
Now let us solve our inequality to find out number of days.
[tex](0.92)^{t} <\frac{115}{240}[/tex]
Upon taking natural log of both sides of inequality,
[tex]ln(0.92)^{t} <ln\frac{115}{240}[/tex]
[tex]t\ln \left(0.92\right)<ln(\frac{115}{240})[/tex]
[tex]-0.08338160t < -0.73570679[/tex]
[tex]t>8.82[/tex]
Upon rounding up our answer to nearest integer we can see that option B is correct. Therefore, our answer will be option B.
1052×291 i need answer asap
1052
x 291
1052 multiplied 1 x 1052
94680 multiplied 90 x 1052
210400 multiplied 200 x 1052
306,132 added 1 x 1052 and 90 x 1052 and 200 x 1052
Answer: 306,132
Which number is bigger 1/8,,,,,,,,0.065,,,3/100,,,,0.105
1/8 = 0.125
0.065
3/100 = 0.03
0.105
the bigger is 1/8
4. Solve the following inequality: 3y-1 less than 3
3y - 1 < 3
Isolate the y. Treat the less than or equal like an equal sign.
Do the opposite of PEMDAS. First, add 1 to both sides
3y - 1 (+1) < 3 (+1)
3y < 4
Next, divide 3 from both sides
3y/3 < 4/3
y < 4/3
y < 4/3 is your answer
hope this helps
Stephanie collected data about the high temperature in her city for 7 days in a row. The high temperatures for the 7 days were 70 degrees, 78 degrees, 85 degrees, 73 degrees, 65 degrees, and 89 degrees. She made the following graph to show her data.
She says the temperature in her city is pretty consistent. How could she redraw the graph so that the daily temperature doesn’t see quite so consistent?
We are given the high temperature in her city for 7 days in a row.
First day it is 70 degrees.
Second day it is 78 degrees.
Third day it is 85 degrees.
Fourth day it is 73 degrees.
Fifth day it is 65 degrees.
Sixth day it is 78 degrees.
Seventh day it is 89 degrees.
We can make a a histrogram to show that temperature doesn’t see quite so consistent.
what is 4 to the -5th power
Answer: [tex]\frac{1}{4^5}[/tex] because any exponent that is a negative has to be brought down.
hope that helps :)
Answer:
The answer is 1/45
Step-by-step explanation:
8982 divided by 28 esamation
To divide 8982 by 28, perform the division operation and the result is approximately 320.79.
Explanation:To find the answer to 8982 divided by 28, you can perform simple division. Here's how:
First, take the number 8982. This is your dividend. Next, you divide this by 28. This latter number is your divisor. Perform the division operation. If using a calculator, simply enter 8982, press the division key, enter 28, and then press the equals key.
The result of the division is 320.7857142857143. You can round this to 320.79 for easy representation.
Learn more about Division here:https://brainly.com/question/2273245
#SPJ3
what is 0.012 as a fraction
To convert 0.012 to a fraction, you multiply by 1000 to get 12/1000 and then simplify it to 3/250. Therefore, 0.012 as a fraction is 3/250.
To convert the decimal 0.012 into a fraction, follow these simple steps:
Write down 0.012 as 0.012/1.
Multiply both the numerator and the denominator by 1000 to get rid of the decimal point:
0.012 x 1000 / 1 x 1000 = 12 / 1000.
Simplify the fraction by finding the greatest common divisor (GCD) of 12 and 1000, which is 4:
(12 ÷ 4) / (1000 ÷ 4) = 3 / 250.
Thus, 0.012 as a fraction is 3/250.
Solve −4(x + 10) − 6 = −3(x − 2). (1 point)
Hey there!!
Given equation :
... -4 ( x + 10 ) - 6 = -3 ( x - 2 )
Using the distributive property :
... -4x - 40 - 6 = -3x + 6
Combining like terms :
... -4x - 46 = -3x + 6
Adding 46 on both sides :
... -4x = -3x + 52
Adding 3x on both sides :
... -x = 52
... x = -52
Hope helps!
if (3,n) is a solution of Ax+3y=6 and (n,5) is a solution of 5x+y=20,what is the value of A?
We have 3A + 3n = 6 and 5n + 5 = 20;
Then, 5n = 15;
n = 3;
Finally, 3A + 9 = 6;
3A = -3;
A = -1;
Can you guys help me in number 6
Use the word bank to complete the sentences below
A. x intercept
B. y intercept
C. x coordinate
D. y coordinate
E. solution
Hope this helped!!
a. x-intercept
b. y-intercept
c. x coordinate
d. y coordinate
e. Solution
Jasmine parents allow her to use the family computer 90 minutes each day how many minutes is she allowed to use the computer during that moth is 30 days in length
You earn the same amount each week at your part-time job. The total amount you earn in 4 weeks is $460. How much do you earn per week?
Find the equation of the line that is perpendicular to the line y=-1/3x-1 and passes through the point (1,5)
To find the equation of the line perpendicular to y = -1/3x - 1 and passing through the point (1,5), we use the negative reciprocal of the original slope (which is 3) and the point-slope form to finally arrive at the equation y = 3x + 2.
The student is asking for the equation of a line that is perpendicular to a given line and passes through a specific point. The given line has the equation
y = -1/3x - 1. Because perpendicular lines have slopes that are negative reciprocals of each other, the slope of the line we're looking for is 3. Using the point-slope form of the equation of a line, we plug in the slope and the coordinates of the point (1,5) to get
y - 5 = 3(x - 1).
Simplifying this equation gives us the standard form of the line:
y = 3x + 2.
A triangle has the perimeter of 31". The longest side is 1" less than twice the shortest side and the 3rd side is 4" longer than the shortest site. Find the lengths of the sides
Aaron needs 24 inches of copper wire for an experiment. The wire is sold by the centimeter. Given that 1 inch = 2.54 centimeters, how many centimeters of wire does Aaron need? Hint: 1/2.54 = 24/x , remember you have to keep inches on top and centimeters on bottom of both fractions so they are equal. What is the answer to this problem? PLS HURRY
[tex]\frac{1}{2.54} =\frac{24}{x}[/tex]
Multiply both sides by 2.54.
[tex]1=\frac{24}{x} (2.54)[/tex]
[tex]= \frac{60.96}{x}[/tex]
Multiply both sides by x.
x = 60.96
Hence, Aaron needs 60.96 centimeters of wire.
Final answer:
Aaron needs 60.96 centimeters of copper wire for his experiment, calculated by multiplying 24 inches by the conversion factor of 2.54 cm/inch.
Explanation:
Aaron needs to convert 24 inches of copper wire to centimeters. Since 1 inch equals 2.54 centimeters, Aaron can calculate the length of wire needed by multiplying the number of inches by the conversion factor. By performing the multiplication 24 inches × 2.54 cm/inch, the result will give the length of wire needed in centimeters.
To find the answer, complete the multiplication:
24 inches × 2.54 cm/inch = 60.96 centimeters.
Therefore, Aaron needs 60.96 centimeters of copper wire for his experiment.
75=3(-6n-5)
Having troubles with this one too!! XD. I’m going to fail math this year, I swear ;((
Ann’s car used 7 gallons of gas during a trip how far did Ann drive
i think its 48 miles
−\frac{7}{10} ÷\frac{2}{5}
Answer:
Huh?
Step-by-step explanation:
You work 20 hours a week at a store in our $8.50 per hour. At another job you earn $8.00 per hour and can work as many hours as you want. If you want to earn $370 for the week, how many hours will you need to work at the second job?
For the second job you work for $8.00 per hour and you want to make $370 for the week so its just simple division.
$370/$8.00 is 46.25 hours a day which means you will have to work close to 46-47 hours a day to make $370 in a week.
6x4=8xN
How can I solve this
6×4=24 right so than how many 8 can get you to 24, so you do 8,16,24 or 8×3 So it's 8×3=24 (Your welcome ^.^)
6x4=8xN is the same as 24=8N
Divide both sides by 8 and there's your answer
Math word problem. Mike paid $59.00 for a bike. He paid with FOUR bills. What were the bills? Tell me the denomination of each bill and how many were used. Make sure to explain to me how you know this and how it totals $59.00
The bike costs $59.00
We need four of bill denomination which have sum of $59
The answer will be $50 + $5 + $2 + $2
A pizza eating participant can eat 3 slices ok pizza in 2 minutes if he continues at this rate then how many slices of pizza will he eat in 10 minutes
at this rate, he can eat 15 slices of pizza in 10 minutes **wow!!**
we can do this by setting it up as a proportion: 3slices/ 2 minutes= ?/1 minute
we divide 3 by 2 to get how many slices he can eat in one minute, which is 1.5
so, now, we just have to multiply 1.5 times 10 minutes, and we get 15 slices of pizza per 10 minutes
Larry is 10 and his sister is 7 years old. In how many years time will their total age be 25 years?
Number fifteen, ANSWERS TO BLANKS AND AN EXPLANATION. FIRST ANSWER THAT IS CORRECT WILL BE MARKED BRAINLIEST!
To get from 60 to 100 you multiply by .6, so to get from 36 to what the first place would get you multiply by .6 and you get 60. Hopefully it helps!
The diameter of the moon is about 3,476 kilometers the distance from earth to the moon is about 384,400 kilometers about how many moons could be lined up in a row between earth and the moon round the nearest whole number
384,400 /3476 = 110.587 so 111
because .587 is more than half way from 110 to 111
Remark
You have to make up your own formula here. You also should estimate the answser. That's always good practice. It makes you think about Math.
Estimate
If you take 384,000 and estimate it to be 300000 and do the same with the diameter to make it 3000
300,000 / 3000 = 100 about. You should get an answer of 100
Formula
Distance to the moon (D)= number of moons (n) * diameter of 1 moon (di).
Givens
D = 384000
n = ??
di = 3476
Solution
384000 = n * 3476 Divide by 3476
384000 /3476 = n / 3476
n = 110.5 moons which I think you should like round to 110.
You could fit 110 moons in the given distance
what is the answer of this question2(5x-4)≥6+12
answer: x ≥ 13/5
work:
2 (5x − 4) ≥ 6 + 12 | distribute 2 into the parentheses.
10x - 8 ≥ 6 + 12 | add 12 and 6.
10x − 8 ≥ 18 | add -8 and move it over to 18, and solve.
10x ≥ 26 | divide by 10 to 26
x ≥ 13/5 | final answer.
hope this helps! ❤ from peachimin
The sum of twelve times p and d
[tex]Sum =[/tex] [tex]add (+)[/tex]
[tex]Twelve =[/tex] [tex]12[/tex]
[tex]p[/tex] & [tex]d = [/tex] [tex]p[/tex] & [tex]d[/tex] (since they are unknown numbers)
SO, this means that your answer SHOULD look like this: [tex]12p[/tex] [tex]+ d[/tex]
Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
Write the decimal that 1 tenth of 0.9
0.09
one tenth of 0.9 is 0.9 divided by 10, which means moving the decimal point one place to the left
[tex]\frac{0.9}{10}[/tex] = 0.09
about 47% of the 15152 samples researchers found were bacteria. what number of dna samples were not bacteria
To find what number of DNA samples were not bacteria we have to find what was 47% of the 15,152 samples first.
We can do this by multiplying 0.47 x 15,152 = 7,121.44
Now 7,121.44 is 47% of the samples that DOES have bacteria. To find out how many do not we must subtract.
15,152 - 7,121.44 = 8,030.56
So the number of DNA samples that were not bacteria were 8,030.56.
GOOD LUCK! :)
Mark and his friends Byron were watching a superhero movies. During the movie mark ate 5 pieces of candy . Byron ate 7 times as much candy as mark. How much candy did Byron eat.?
Final answer:
To find out how much candy Byron ate, we multiply the number of candies Mark ate, which is 5, by 7. Byron ate a total of 35 pieces of candy.
Explanation:
The question involves solving a basic multiplication problem to determine how much candy Byron ate if Mark ate 5 pieces of candy and Byron ate 7 times as much. According to the given scenario, we can represent this mathematically as:
Mark ate 5 pieces of candy. Byron ate 7 times as much candy as Mark did. To find out the total pieces of candy Byron ate, we multiply the number of candies Mark ate by 7. Therefore, Byron ate 5 pieces × 7 = 35 pieces of candy.
This arithmetic calculation shows us Byron's total candy consumption during the movie.