t takes Audrey 35 hour to paint 25 square yards of wood to be used for making shelves. How many square yards can she paint in 1 hour?
There are 20 alligators in the swamp. Each year, the number of alligators increases by 25%. There are 25 crocodiles in the swamp. Each year, 10 new crocodiles join the swamp.
Part A: Write functions to represent the number of alligators and crocodiles in the swamp throughout the years. (4 points)
Part B: How many alligators are in the swamp after 4 years? How many crocodiles are in the swamp after the same number of years? (2 points)
Part C: After approximately how many years is the number of alligators and crocodiles the same? Justify your answer mathematically. (4 points)
Part A: Alligators: [tex]\(A(t) = 20 \times (1 + 0.25)^t\), Crocodiles: \(C(t) = 25 + 10t\).[/tex]
Part B: After 4 years: Alligators: ~38, Crocodiles: 65.
Part C: Alligators and crocodiles equal: Solve [tex]\(20 \times (1 + 0.25)^t = 25 + 10t\).[/tex]
Part A:
Let's define the functions to represent the number of alligators and crocodiles in the swamp over the years.
For alligators:
[tex]\[A(t) = A_0 \times (1 + r)^t\][/tex]
Where:
[tex]- \(A(t)\) is the number of alligators in the swamp after \(t\) years.\\- \(A_0\) is the initial number of alligators (20 in this case).\\- \(r\) is the growth rate per year (25% or 0.25).\\- \(t\) is the number of years.[/tex]
For crocodiles:
[tex]\[C(t) = C_0 + n \times t\][/tex]
Where:
[tex]- \(C(t)\) is the number of crocodiles in the swamp after \(t\) years.\\- \(C_0\) is the initial number of crocodiles (25 in this case).\\- \(n\) is the number of new crocodiles joining each year (10 in this case).\\- \(t\) is the number of years.[/tex]
Part B:
To find the number of alligators after 4 years, we use the formula:
[tex]\[A(4) = 20 \times (1 + 0.25)^4\][/tex]
To find the number of crocodiles after 4 years, we use the formula:
[tex]\[C(4) = 25 + 10 \times 4\][/tex]
Part C:
To find when the number of alligators and crocodiles are the same, we set [tex]\(A(t) = C(t)\) and solve for \(t\).[/tex]
[tex]\[20 \times (1 + 0.25)^t = 25 + 10 \times t\][/tex]
This equation can be solved numerically to find the value of \(t\) when the number of alligators and crocodiles are the same.
$1.80 in dimes and nickels. she has a total of 23 coins. how many of each kind does she have?
Find the length of AC. Use that length to find the length of CD. What is the length of CD? Round to the nearest tenth.
A) 2.3 cm
B) 4.0 cm
C) 10.7 cm
D) 18.6 cm
length of AC = 10 * sin(30) = 5 cm
Length of CD = 5 /tan(25) = 10.7cm
answer is C
Answer
Find out the what is the length of CD , AC .
To prove
By using the trignometric identity
[tex]sin B = \frac{Perpendicular}{Hypotenuse}[/tex]
As in ΔABC
∠ B = 30° , AB= 10 cm
put in the trignometric identity
[tex]sin 30^{\circ} = \frac{AC}{10}[/tex]
As
[tex]sin30^{\circ} =\frac{1}{2}[/tex]
[tex]\frac{1}{2} = \frac{AC}{10}[/tex]
[tex]AC = \frac{10}{2}[/tex]
AC = 5cm
Now in the ΔADC
[tex]tan D^{\circ} = \frac{Perpendicular}{Base}[/tex]
∠ D = 25° , AC = Perpendicular = 5 cm
[tex]tan 25^{\circ} = \frac{5}{CD}[/tex]
tan 25 ° = 0.46630765815 (approx)
[tex]CD = \frac{5}{0.46630765815}[/tex]
CD = 10 .7cm ( approx )
Option (C) is correct .
The county fair charges $1.25 per ticket for the rides. Jermaine bought 25 tickets for the rides and spent a total of $43.75 at the fair. Jermaine spent his money only on ride tickets and fair admission. The price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a) Define your variables.
(b) Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
(c) Explain your answer to Part b.
PLEASE HELP!!
What is the slope of the line represented by the equation 2x+3y= –12 ?
A)–3/2
B)–2/3
C)2/3
D)3/2
Answer:
the correct answer is B.-2/3
Find the equation of the line with slope = -5 and passing through (4,-17). write your equation in the form y = m x + b y=mx+b.
60 POINTS
Which statement is true about this argument?
Premises:
If an angle measure is greater than 90°, then the angle is an obtuse angle.
The measure of ∠C is 102°.
Conclusion:
∠C is an obtuse angle.
Traveling with a speed of 70 mph, a car covered a distance D miles in T hours. Write an equation that relates the distance D this car travels in T hours. Use the equation to find the distance the car travels between 3:30 p.m. and 5:00 p.m.
Answer:
i need the equation I know that the distance is 105 miles
Step-by-step explanation:
helppppp
Sheila purchased ski equipment for $513 using a six-month deferred payment plan. The interest rate after the introductory period is 18.39%. A down payment of $125 is required as well as a minimum monthly payment of $65. What is the balance at the beginning of the seventh month if only the minimum payment is made during the introductory period?
$65 * 6 = $390 total monthly payments made
The downpayment made is $125, so the total balance at the end is:
balance = $513 – ($125 + $390)
balance = - $2
There is an excess of 2 dollars at the end.
Sheila's balance at the beginning of the seventh month will be approximately $393.95 after considering the deferred payment and applying the interest rate.
To determine the balance at the beginning of the seventh month, follow these steps:
Calculate the initial loan amount: Sheila purchased equipment worth $513 minus a down payment of $125, leaving a balance of $388.Introductory period payments: Over six months, Sheila makes the minimum payment of $65 each month. Therefore, total payments during the introductory period are $65 x 6 = $390.Balance at end of introductory period: Since the deferred payment plan means these monthly payments were applied directly to the purchasing price rather than reducing the balance with interest-free monthly payments, the balance remains $388.Interest application: After the introductory period, interest accrues on the balance of $388 at an annual rate of 18.39%. This translates to a monthly interest rate of 18.39% / 12 ≈ 1.5325%.Calculating the new balance: Applying one month of interest on the balance, $388 increases by 1.5325% or $388 x 0.015325 ≈ $5.95. Therefore, the balance at the beginning of the seventh month is $388 + $5.95 ≈ $393.95.So, Sheila’s balance at the beginning of the seventh month is approximately $393.95.
you have a gift card worth 90$ you want to buy several movies that costs 12$ each. Write and solve an inequality that represents the number of movies you can buy and still have at least 30$ on the gift card
What is 4125 divided by 8
Which of the following statements does not describe the structure of an atom?
An atom has a small, dense center called the nucleus.
Inside the nucleus of an atom are protons and electrons.
Protons are positively charged sub-atomic particles.
Electrons are negatively charged sub-atomic particles.
Final answer:
The incorrect statement is that the nucleus of an atom contains protons and electrons; actually, the nucleus contains protons and neutrons, with electrons orbiting around it.
Explanation:
The statement that does not correctly describe the structure of an atom is 'Inside the nucleus of an atom are protons and electrons'. This statement is incorrect because the nucleus of an atom actually contains protons and neutrons, not electrons. Electrons are negatively charged sub-atomic particles that orbit around the nucleus. The nucleus itself is a small, dense center that is positively charged due to the presence of protons, which are positively charged. Neutrons, which have no electric charge, are also found within the nucleus.
Further expanding on atomic structure, the nucleus is very tiny compared to the rest of the atom, which is mostly empty space. The electrons residing in this space are in perpetual motion, creating a cloud-like region around the nucleus. Despite their small mass compared to protons and neutrons, the number of electrons equals the number of protons in a neutral atom, balancing the charge.
Which of the following expressions represents the area of a trapezoid with bases of 3x and 5x and a height of 6x?
10x
24x
24x2
45x2
Chris runs 7 miles in 80 minutes. at the same rate, how many miles would he run in 64 minutes?
If x represents time, the average rate of change of a function f(x) in the first two seconds is____.
Answer:
The average rate of change of a function f(x) in the first two seconds is 25.
Step-by-step explanation:
Given : Graph , X represent the time , function f(x).
To find : the average rate of change of a function f(x) in the first two seconds is____.
Solution : The rate of change of f(x) with respect to x is the slope of the line.
slope : [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
In first two second ( 0, 50 ) , ( 2, 100).
slope : [tex]\frac{100-50}{2-0}[/tex].
slope : [tex]\frac{50}{2 }[/tex].
the average rate of change of a function f(x) in the first two seconds is 25.
Therefore,The average rate of change of a function f(x) in the first two seconds is 25.
The line x+2y=9 intersects the curve xy+18=0 at the points A and B. Find the coordinates of A and B
When Rosina babysits for 5 hours she charges $40 and when she babysits for 6 hours she charges $48. How much does Rosina charge in one hour?
what is the property of this equation? if 2x=8 then x=4
please show me how to solve ... -5x-10=10
Find the slope of the line that passes through the pair of points (1/10,6) and (3/16,11/5)
Two plans for reaching a goal are given below.
Plan A: Save $450 over the next 8 weeks by working 9 hours per week at $7.20 per hour.
Plan B: Save $450 over the next 6 weeks by working 15 hours per week at $6.50 per hour.
Which of the following is a true statement?
a.
Only plan A will work for achieving the goal.
b.
Only plan B will work for achieving the goal.
c.
Both plans will work for achieving the goal.
d.
Neither plan will work for achieving the goal.
Answer:
The correct option is C) Both plans will work for achieving the goal.
Step-by-step explanation:
Consider the provided information.
Plan A: Save $450 over the next 8 weeks by working 9 hours per week at $7.20 per hour.
For next 8 weeks by working 9 hours per week at $7.20 per hour, you will earn:
[tex]8 \times 9 \times 7.20 = 518.40[/tex]
We need to save $450 which is less than $518.40. Thus, plan A will work.
Plan B: Save $450 over the next 6 weeks by working 15 hours per week at $6.50 per hour.
For next 6 weeks by working 15 hours per week at $6.50 per hour, you will earn:
[tex]6 \times 15 \times 6.50 = $585.00[/tex]
We need to save $450 which is less than $585.00. Thus, plan B will work.
Hence, the correct option is C) Both plans will work for achieving the goal.
Max rode his bike 40 miles in hours.
Which complex fraction can be used to calculate Max’s average speed?
Answer:
40 Miles.
5 hrs.
----------
2
Approximately how many times greater is 8.5×108 than 3.4×105 ? A 2.5 B 250 C 2,500 D 25,000
Solution:
we have been asked to find that , how many times one number is to the other given numbers.
To do this we will divide the larger number by the smaller number and the resulting number will be the answer of the question.
Here the larger number is [tex]8.5\times10^8[/tex]
The smaller number is [tex]3.4\times 10^5[/tex]
Now lets divide as follows
[tex]\frac{8.5\times10^8}{3.4\times 10^5} =\frac{8.5}{3.4}\times 10^{8-5}\\ \\\frac{8.5\times10^8}{3.4\times 10^5} =2.5\times10^3=2500[/tex]
Hence the correct option is C.
Janet has a balance of 125 on a credit card on her next statement she wants to reduce her balance to no more than 60 how much does she need to pay off
Janet has to pay off $65 to reduce her balance to no more than $60.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Janet has a balance of 125 on a credit card on her next statement she wants to reduce her balance to no more than 60.
The amount to be paid will be calculated as,
Amount = 125 - 60
Amount = $65
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The ratio of boys to girls in ms. zombo's class is 33 to 22. in mr. stolarski's class it is 55 to 33. if there are 15 students in ms. zombo's class and 32 students in mr. stolarski's class, what is the ratio of boys to girls in the combined classes?
For combined classes of Ms. Zombo's and Mr. Stolarski's, the number of boys and girls are determined based on their respective ratios and total number of students. The combined ratio of boys to girls is 29:18.
Explanation:The question asks for the combined ratio of boys to girls in both Ms. Zombo's and Mr. Stolarski's classes. Firstly, identify the number of boys and girls in each class based on the given ratio and total students. In Ms.Zombo's class, the ratio of boys to girls is 33:22, and there are total 15 students. So, the number of boys is (33/(33+22))*15= 9 boys and 6 girls. Similarly, in Mr.Stolarski's class the ratio is 55:33, there are 32 students, so there are (55/(55+33))*32 =20 boys and 12 girls.
Next step is to combine the classes. The total number of boys from both classes is 9 (from Ms. Zombo's class) + 20 (from Mr.Stolarski's class) = 29 boys. The total number of girls is 6 (from Ms. Zombo's class) + 12 (from Mr.Stolarski's class) =18 girls.
Therefore, the combined ratio of boys to girls from both classes is 29:18.
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A culture of 1.75×1018 bacteria is in petri dish A. A culture of 6.25×1015 bacteria is in petri dish B. How many times greater is the number of bacteria in petri dish A than petri dish B? Enter your answer, in standard notation, in the box.
To determine the extent of how many times greater is the number of bacteria in petri dish A than petri dish B, we simply have to take the ratio of the two.
1.75 x 10^18 / 6.25 x 10^15 = 280
So the bacteria in petri dish A is 280 times larger.
In scientific notation:
2.8 x 10^2
Answer:
280 is the answer, I did the test.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Check all that apply.
Claire and rachel plays volleyball for different teams .claire team practices seven hours every two days and rachels team practices eight hours every three days match player to the team that represents the average number of hours that they practice each day over a seven day period
Having a savings account can contribute to a person’s overall financial well-being. Which one of the following is NOT a benefit of maintaining a savings account?
a.
A savings account provides security in tough financial times
b.
With a savings account, you can invest when the opportunity presents itself
c.
Having a savings account gives individuals the ability to borrow money from members in the community
d.
A savings account allows an individual to fulfill life long dreams
Answer:
Having a savings account can contribute to a person’s overall financial well-being. Which one of the following is NOT a benefit of maintaining a savings account?
a.
A savings account provides security in tough financial times
b.
With a savings account, you can invest when the opportunity presents itself
c.
Having a savings account gives individuals the ability to borrow money from members in the community
d.
A savings account allows an individual to fulfill life long dreams
Step-by-step explanation:
C) Having a savings account gives individuals the ability to borrow money from members in the community