Answer:
Step 1-Write an equation, letting x represent Kareem’s age:
(x + 3) + x + 2 x = 33
Step 2-Solve the equation:
(x + 3) + x + 2 x = 33. 3 + 4 x = 33. 4 x = 30. x = 7 1/2.
Step 3-Sadie is 10 1/2, Kareem is 7 1/2, and Nadra is 3 3/4.
Which corrects the student’s first error?
1. In Step 1, the student should have used One-half x to represent Nadra’s age, and written the equation (x + 3) + x +1/2x = 33.
2. In Step 2, the student should have added 3 on both sides of the equation to find a solution of x = 9.
3. In Step 3, the solution represents Sadie’s age. Therefore, Sadie is 7 1/2, Kareem is 4 1/2, and Nadra is 2 1/4.
4. In Step 3, Nadra’s age is the difference between 33 and Sadie’s and Kareem’s ages, so Nadra is 15.
At the end of the third year the population of beetles will be 11,576beetles
<h3>Exponential equations</h3>
The standard form of an exponential function is given as:
y = ab^t
Given the following parameters
initial population 'a" = 10,000 beetles
Time = 3 years
rate b = 1.05
Substitute into the formula
y = 10,000(1.05)^3
y = 10,000(1.1576)
y = 11,576 beetles
Hence at the end of the third year the population of beetles will be 11,576beetles
Learn more on exponential function here: brainly.com/question/12940982
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Answer:
12.686cm
Step-by-step explanation:
By using pythagoras, we can find CB.
We know that 
Therefore, 
(it has to be positive since it is distance)
now we look at triangle BCD and use SOH CAH TOA.
Answer:
Step-by-step explanation:
The general formula for continuous exponential growth is A=A0•ert, where A0 is the initial amount, t is the elapsed time, and r is the rate of growth or decay. For this problem, r=0.005, so the formula is A=A0•e0.005t.
Since we want to know how long it takes of the amount to be 275% of the original amount, we can state that A=2.75A0. Substituting that into our formula gives us 2.75A0=A0•e0.005t. Dividing by A0 yields 2.75=e0.005t.
At this point we need to take the natural logarithm of both sides:
ln(2.75)=ln(e0005t)
ln(2.75)=0.005t
t=ln(2.75)/0.005, which is approximately equal to 202.3
We round up to 203 years.
