In an ecology experiment, a number of mosquitoes are placed in a container with water and vegetation. The population of mosquitoes, P, increases and can be modelled by the function:
P9T)=24*4^0.385t, t is greater than or equal to 0
Where t is the time, in days, since the mosquitoes were placed in the container.
(a) find the number of mosquitoes in the container after 5 days
The maximum capacity of the container is 5000 mosquitoes
(b) Find the number of days until the container reaches its maximum capacity.
Answers
Using the given exponential function, it is found that:
a) The number of mosquitoes in the container after 5 days is of: 346.
b) The number of days until the container reaches the maximum capacity is of: 10 days.
What is the exponential function?The exponential function that models this problem is presented as follows:
P(t) = 24(4)^(0.385t).
Hence, after five days, the number of mosquitoes is of:
P(5) = 24(4)^(0.385 x 5) = 346 mosquitoes.
The number of days that it takes for the container to reach it's maximum capacity of 5000 is obtained solving the exponential function with logarithms as follows:
\(5000 = 24(4)^{0.385t}\)
\((4)^{0.385t} = \frac{5000}{24}\)
\((4)^{0.385t} = 208.3\)
\(\log{(4)^{0.385t}} = \log{208.3}\)
Applying the power property of logarithms, we have that:
\(0.385t\log{4} = \log{208.3}\)
\(t = \frac{\log{208.3}}{0.385\log{4}}\)
t = 10 days.
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Related Questions
A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 999 and a standard deviation of 199. Scores on the ACT test are normally distributed with a mean of 21.6 and a standard deviation of 5.2. It is assumed that the two tests measure the same aptitude, but use different scales.A. If a student gets an SAT score that is the 62-percentile, find the actual SAT score. SAT score = Round answer to a whole number. What would be the equivalent ACT score for this student? ACT score = Round answer to 1 decimal place. B. If a student gets an SAT score of 1563, find the equivalent ACT score. ACT score = Round answer to 1 decimal place.
Answers
Answer:
A.
SAT score = 1060
ACT score = 23.2
B.
ACT score = 36.3
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
SAT:
\(\mu = 999, \sigma = 199\)
If a student gets an SAT score that is the 62-percentile, find the actual SAT score.
This is X when Z has a pvalue of 0.62. So X when Z = 0.305.
\(Z = \frac{X - \mu}{\sigma}\)
\(0.305 = \frac{X - 999}{199}\)
\(X - 999 = 0.305*199\)
\(X = 1059.7\)
Rounding to the nearest whole number.
SAT score = 1060
ACT:
\(\mu = 21.6, \sigma = 5.2\)
The equivalent score is X when Z = 0.305.
\(Z = \frac{X - \mu}{\sigma}\)
\(0.305 = \frac{X - 21.6}{5.2}\)
\(X - 21.6 = 0.305*5.2\)
\(X = 23.19\)
So
ACT score = 23.2
B. If a student gets an SAT score of 1563, find the equivalent ACT score
Z-score for the SAT score.
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{1563 - 999}{199}\)
\(Z = 2.83\)
Equivalent ACT:
\(Z = \frac{X - \mu}{\sigma}\)
\(2.83 = \frac{X - 21.6}{5.2}\)
\(X - 21.6 = 2.83*5.2\)
\(X = 36.3\)
ACT score = 36.3
For items 6-7. use a compass and any straightedge to construct a perpendicular bisector of the segment below (1 point for correct arc markings and 1 point for the
perpendicular bisector)
guys i need your help
Answers
Perpendicular bisector involves dividing a line segment into two equal parts
How to bisect the lineThe image in the question cannot be used; so, I will create a new image (see attachment)
Assume the endpoints of the line segment are points C and D
Place the compass at point C, and draw an arc over the line segment CDRepeat the above step from point DMark the intersection of the arcs drawn in the above stepsTrace the intersection of the arc to line segment CDSee attachment for the figure that illustrates perpendicular bisector
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Please answer number 6 I will give brainliest thank you!
Answers
Answer:
I think it's 65...........
Andrew writes the name of a month on a piece of paper and turns it over. Siobhan then guesses what month Andrew wrote down. To find the probability that Siobhan guesses the correct month, Andrew needs to know the total number of possible outcomes
Answers
There are 12 possible outcomes (12 months). This means the chance Siobhan guesses the month Andrew wrote down is 1/12 or 8.333%
As the CAPS document outlines, the Content Specification and Content Clarification for Patterns, Functions, and Algebra shows sequenced mathematics content topics and a content area spread. In the Intermediate Phase, select one topic and report on the topic sequence and content area spread. Your report should demonstrate mathematics concepts and procedures’ hierarchical and logical progression.
Answers
Answer:
Step-by-step explanation:
In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."
The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:
Introduction to Variables and Expressions:
Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.
Solving One-Step Equations:
Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.
Solving Two-Step Equations:
Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.
Writing and Graphing Linear Equations:
Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.
Systems of Linear Equations:
Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.
Word Problems and Applications:
Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.
The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.
By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.
Write a two-step equation with a solution of 6. Write the equation using both words and symbols.
Answers
Answer:
x+6=y
Step-by-step explanation:
6(x1.5)+30<48 I need help with this Help
Answers
The solution to given linear inequality, 6(x1.5) + 30 < 48, is x < 2
Solving linear inequalitiesFrom the question, we are to solve the given linear inequality
The given linear inequality is
6(x1.5) + 30 < 48
First, we will write this inequality properly.
The inequality can be properly written as
6(1.5x) + 30 < 48
Now, we will solve the linear inequality
6(1.5x) + 30 < 48
Subtract 30 from both sides of the equation
6(1.5x) + 30 - 30 < 48 - 30
6(1.5x) < 18
Divide both sides of the inequality by 6
6(1.5x)/6 < 18/6
(1.5x) < 3
1.5x < 3
Divide both sides of the inequality by 1.5
1.5x/1.5 < 3/1.5
x < 2
Hence, the solution is x < 2
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The graph compares the weights in pounds of 100 dogs and cats that are brought in
to a veterinarian's office. Using the medians, how much more does a typical dog weigh than a typical cat?
Answers
Answer:20
Step-by-step explanation:this is wrong
Answer:
40
Step-by-step explanation:
subtract median of dogs and median of cats
what is the measure of
Answers
2x + 8 > -4. 2.find the solution set of x and express the solutions set in number form
Answers
The solution set of this inequality is {x| x > -6.1}
How to find the solution set?Here we have the inequality:
2x + 8 > -4.2
To find the solution set, we need to isolate the variable x in one of the sides of the inequality. Doing that we will get:
2x + 8 > -4.2
2x > -4.2 - 8
2x > -12.2
x > -12.2/2
x > -6.1
So the set of all numbers larger than -6.1, this in number form is:
{x| x > -6.1}
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2x - 8 = 6
help please
Answers
Answer:
7
Step-by-step explanation:
Move the -8 to the other side and use the rule change side change sign:
2x=6+8
2x=14
Move the 2 and convert the multiplication(as its 2×x ) into division:
x= 14÷2
x=7
Answer:
2x -8 =6
add 8 to -8 and 6.
the 8s cancel each other out and 6 +8 =14.
next you are going to divide 2x diveded by 2 and 14 by 2. the twos cancel out so its just x and then 14/2 is 7.
the answer is 7. hope this helps dude.
Find the unknown coordinate so the line through the
points has the given slope
Answers
Answer:
#1 (0,-4)
#2 (5,0)
#3 (3,1)
Step-by-step explanation:
#1. (-3, 2) (0, y) slope = -2
slope = rise/run therefore slope = -2/1 or down 2 and over 1
so from -3 to 0 you are going over 3 units (or 3 times) Therefore to find y at x=0, you have to move three steps, or 3 times -2 = -6 so 2-6 = -4
so y intercept (b) = -4 0r (0,-4)
#2 (-7,-4) (x,0) slope (m) = 1/3 -7+12=5 x=5
#3 (4,-3) (x, 1) slope (m) = -4 (4/-1) Moving one unit in slope means
-3=4=1 for Y and 4-1=3 for X therefore the point is (3, 1)
i do not understand how this works... b(n)=4−6(n−1)
Answers
Which equation represents a circle with the endpoints of its diameter at (4, –11) and (12, –9)?
Answers
Answer:
Out of all possible choices you've shown, I'd say the best answer would be D
Step-by-step explanation:
could someone please help answer this.
Answers
Answer:
+ 12 yards
Step-by-step explanation:
8-3 = 5
5 + 12 - 5 = 12
A popular brand has introduced a new design of jeans. All major stores have stocked the jeans because the brand usually sells very well. But the cost of these jeans is much higher than those of other brands, so people don't buy them. How will the price of the jeans be affected? Give reasons to your answer
Answers
If the jeans aren't bought at all, or as much as the other brands, then the store owners would have no choice but to lower prices. It's either that option or they would return the merchandise (if possible) or simply throw away the jeans. Setting the right price is more or less trial and error. There are mathematical ways to make an educated guess, but to be fair, there are a lot of factors in play that make trial and error more effective.
For example, if the jeans start at $100 and no one buys them for a week, then the owner may reduce the cost to $75 and see if the 25% discount is effective or not. If people buy, then the price may stay there. If not, then the price may come down even further. The process is continued indefinitely. On the flip side, if demand skyrockets, then prices would likely go up.
the price of the jeans is likely to be affected by the low demand resulting from the high cost.
Based on the given information, it can be inferred that the price of the jeans is not aligned with the market demand due to its high cost relative to other brands. In this scenario, several outcomes are possible:
1. Decrease in Price: If the jeans are not selling well due to their high cost, the brand might experience a decrease in demand. To stimulate sales, the brand may need to lower the price of the jeans to make them more affordable and competitive. This price adjustment aims to attract customers who were previously deterred by the high cost.
2. No Change in Price: The brand may choose to maintain the current price despite the low demand. This decision can stem from factors such as maintaining the brand image or relying on a niche market that is willing to pay a premium for the product. However, in such a situation, the brand may need to focus on marketing and branding efforts to emphasize the unique qualities or benefits of the jeans to justify their higher price.
3. Increase in Price: It is less likely that the brand would increase the price of the jeans if they are not selling well due to their high cost. Increasing the price further would likely deter even more customers and exacerbate the issue. However, if the brand has a particularly strong brand image or a highly loyal customer base that is willing to pay a premium, a price increase may be feasible in rare cases.
In summary, the price of the jeans is likely to be affected by the low demand resulting from the high cost. The brand may choose to decrease the price to boost sales or maintain the current price while focusing on marketing efforts to highlight the unique value proposition of the jeans. An increase in price is less probable given the low demand.
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Clipper Company sells two types of nail clippers. One focuses on the economy oriented customer and the other aims to satisfy the high-end clientele. The economy clipper costs $4 and has a sales price of $9. The high-end model costs $8 and sells for $13. Fixed costs associated with this product line amount to $66,120. Economy clippers constitute 70 percent of the market with the remaining 30 percent being high-end clippers. Based on this information what is the total break-even point (the total number of economy line plus the number of high-end clippers)? Note: Round your final answer to nearest whole number.
Answers
The total break-even point for both products is 16,530 units.
What does break-even point mean?A breakeven point is used in a variety of business and finance situations. It is the level of production at which total production revenue equals total production costs in accounting terms.
Given data
Selling price of economy clipper = $9
Cost of economy clipper = $4
Selling price of high-end model= $13
Cost of high-end model = $4
To calculate the break-even point, we need to determine the total fixed costs and the total variable costs for each product.
Variable costs for the economy clipper:
= $9 (sales price) - $4 (cost)
= $5
Variable costs for the high-end clipper:
= $13 (sales price) - $8 (cost)
= $5
Total variable costs for both products:
= (70% * $5) + (30% * $5)
= $5
The break-even point can be calculated using the formula:
Total fixed costs / (Price - Variable costs)
= $66,120 / ($9 - $5)
= $66,120 / $4
= 16,530 units.
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it's simple but; pls help asap
Answers
Answer:
Hey mate.......
Step-by-step explanation:
This is ur answer......
Two added to eight multiplied by four......Hope it helps!
Brainliest pls!
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Hunter measured the middle school and made a scale drawing. The scale he used was 1 inch : 10 feet. The gym is 7 inches wide in the drawing. How wide is the actual gym?
Answers
Answer:
70 ft
Step-by-step explanation:
You want the actual width of a gym that is represented as 7 inches on a drawing with a scale of 1 in : 10 ft.
Scale factorEach inch represents 10 feet, so 7 inches will represent ...
7 × 10 ft = 70 ft
The gym is 70 ft wide.
__
Additional comment
You can also write and solve an equation that shows the measures are proportional:
actual width / drawing width = (10 ft) / (1 in) = (gym width) / (7 in)
Multiplying both sides of this proportion by 7 in, we have ...
gym width = (7 in) × (10 ft)/(1 in) = 7 × 10 ft = 70 ft
You flip two coins. What is the probability
that you flip at least one head?
Answers
Answer:
\(\boxed{Probability=\frac{1}{2} }\)
Step-by-step explanation:
The probability of flipping at least 1 head from flipping 2 coins is:
=> Total sides of the coins = 4
=> Sides which are head = 2
=> Probability = 2/4 = 1/2
3x - 1 = 5x + 10
I need help with the steps of the problem.
Answers
Answer:
x = -5.5 or -5 1/2
Step-by-step explanation:
3x = 5x + 11-2x = 112x = -11x = -11/2x = -5.5Krista designs quilts using the pattern shown. The table of values describes the shaded area of the pattern in square units, y, as a function of the length of a side,X units. Which equation describes this relationship?
Answers
The equation which describes the relationship between the side length and shaded area of the quilt is y=0.5x²
Modeling relationship between two variablesSide length, x = 1,3,4,5,8
Shaded Area, y = 0.5, 4.5, 8, 12.5, 32
The relationship can be modeled as a quadratic function. Using a graphing calculator for the quadratic function written in the form y = ax² + bx + c
a = 0.5 ; b = 0 ; c = 0
Therefore, the quadratic function can be written as y = 0.5x²
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20 x 321-15 x 141
What is the value of the expression?
Answers
Answer:
4305
Step-by-step explanation:
Please help me solve this, it’s the last question.
Answers
The value of the double integration is 7776 after solving and integration. the answer is 7776.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
It is given that:
Double integration (x + y) dA
y = x²
y² = 216x
y = √216 √x
∫∫(√216 √x + x²)
After solving:
\(\rm \int _0^{36}\int _0^6\:\left(\sqrt{216}\:\sqrt{x}\:+\:\:x²\right)dxdy\)
=7776
Thus, the value of the double integration is 7776 after solving and integration. the answer is 7776.
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Can someone help me please !
Answers
Answer:
y= 0.5 x +2
Step-by-step explanation:
the line crosses the Y line at 2 so you add +2 to the end. Then you see how far up the line goes every vertical line.
Answer:
y= 0.5 x +2
Step-by-step explanation:
Identify the domain of the function pictured below.
Answers
A boat is heading towards a lighthouse, whose beacon-light is 111 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 6^{\circ}
∘
, before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 13^{\circ}
∘
. Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary.
Answers
The required the distance from point A to point B is approximately 855.31 feet.
Explain about angle of elevation.The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.
According to question:Let's call the distance from point A to the lighthouse "x" and the height of the lighthouse "h" (h = 111 feet). We can use the tangent function to relate the angle of elevation to the distance and height:
tan(5°) = h/x
Solving for x, we get:
x = h/tan(5°) ≈ 1268 feet
Now let's call the distance from point B to the lighthouse "y". We can use the same tangent function to relate the angle of elevation from point B:
tan(15°) = h/y
Solving for y, we get:
y = h/tan(15°) ≈ 412.69 feet
The distance between points A and B is just the difference between x and y:
1268 - 412.69 ≈ 855.31 feet
So the distance from point A to point B is approximately 855.31 feet.
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Complete question:
A boat is heading towards a lighthouse, whose beacon-light is 111 feet above the water. From point A, the boat's crew measures the angle of elevation to the beacon, 5º, before they draw closer. They measure the angle of elevation a second time from point B at some later time to be 15°. Find the distance from point A to point B. Round your answer to the nearest tenth of a foot if necessary.
Find the volume of the right triangular prism.
A) 120 cubic centimeters
B) 90 cubic centimeters
C) 60 cubic centimeters
D) 150 cubic centimeters
Answers
In two or more complete sentences, explain how to use ordered pairs of points in and to determine if and are inverses of each other.
Answers
For any point (x, y), that DOESN'T appear in one function, the point (y, x) must NOT appear in the other function.
So if you find any point that DOESN'T meet the above rules, you can prove that the functions are NOT inverses of each other.
But if you want to prove that they ARE inverses of each other, you have to check ALL points in the functions, and there are infinity of them, so that's not practical. Instead, you can write f(x) like this:
y = 3x - 5
Now solve for x:
y + 5 = 3x
x = (y + 5) / 3
Now swap x and y:
y = (x + 5) / 3
This is the same as g(x). Therefore the functions are inverses of each other. oh
Use partial quotients to solve 5,140 ÷ 9 = ___.
Answers
The correct answer is 571 quotient and 1 is remainder.We can solve easily by partial quotients.
What are partial quotients division?Partial quotients division is a deviation from the standard method. The divisor is multiplied with a number and the multiple obtained is deducted from the dividend. This multiple of the divisor is as close as possible to the dividend, that is less than or equal to the dividend.
Why do we use partial quotient division?Partial quotient division provides natural differentiation because we can have students solve at a level they are comfortable with and then we can challenge them to find a more efficient way. And this means using fewer steps and solve easily.
Now we solve
first 9 multiply with 500 so we get 4500. 5140-4500=640
then 9 multiply with 70 so we get 630. 640-630=10
then 9 multiply with 1 so we get 9. 10-9=1
Hence 500+70+1=571
And our remainder is 1.
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