Frogs have been breeding like flies at the Enormous State University (ESU) campus! Each year, the pledge class of the Epsilon Delta fraternity is instructed to tag all the frogs residing on the ESU campus. Two years ago (t = 0) they managed to tag all 42,000 of them (with little Epsilon Delta Fraternity tags). This year's pledge class discovered that all the tags had all fallen off, and they wound up tagging a total of 54,600 frogs.
Function: 42000 (1.3^t/2)
Assuming exponential population growth, and that all this year's tags have fallen off, how many tags should Epsilon Delta order for next year?
Final answer:
Using the provided exponential growth function for frog population, 42000 (1.3^t/2), with t=3 for next year, the fraternity should order approximately 59621 tags.
Explanation:
To calculate the number of tags the Epsilon Delta fraternity should order for next year, we need to use the exponential population growth function provided: 42000 (1.3^{t/2}), where t is the number of years since the initial tagging. Since two years ago was t = 0, this year is t = 2. Next year will be t = 3.
Plugging t = 3 into the function, we get:
Tags needed = 42000 (1.3^{3/2})
This is an arithmetic problem involving an exponential function representing the population growth of frogs.
To solve the equation, first calculate 1.3^{3/2}, which is approximately 1.41907. Then multiply this by 42000 to get the number of tags needed for next year.
Tags needed ≈ 42000 * 1.41907
Tags needed ≈ 59621
So the fraternity should order approximately 59621 tags for next year.
the equation y equals 0.25 x describes a proportional relationship between X and Y what is the constant of proportionality
What is ↓ when n = 8?
(n-5)•6
------------
n÷4
Shanti has just joined a DVD rental club. She pays a monthly membership fee of $4.95, and each DVD rental is $1.95. If Shanti's budget for DVD rentals in a month is $42, how many DVDs can Shanti rent in her first month if she doesn't want to go over her budget? ________ DVDs
After deducting the monthly membership fee of $4.95 from Shanti's budget, $37.05 remains for DVD rentals. At $1.95 per DVD rental, Shanti can rent 19 DVDs while staying within her budget.
To calculate how many DVDs Shanti can rent without going over her monthly budget of $42, we first need to deduct her monthly membership fee from her total budget. This leaves us with the amount she can spend on renting DVDs.
The monthly membership fee is $4.95. After subtracting this fee from her total budget, we have:
$42 - $4.95 = $37.05 available for DVD rentals.
Each DVD rental costs $1.95. To find out how many DVDs Shanti can rent, we divide the amount available for rentals by the cost per DVD rental:
$37.05 / $1.95 = 19 DVDs (rounded down since you cannot rent a fraction of a DVD)
Therefore, Shanti can rent 19 DVDs in her first month and stay within her budget of $42.
For the function f(x) = (x − 2)2 + 4, identify the vertex, domain, and range.
a. The vertex is (–2, 4), the domain is all real numbers, and the range is y ≥ 4.
b. The vertex is (–2, 4), the domain is all real numbers, and the range is y ≤ 4.
c. The vertex is (2, 4), the domain is all real numbers, and the range is y ≤ 4.
d.The vertex is (2, 4), the domain is all real numbers, and the range is y ≥ 4.
Answer:
The vertex is (2, 4), the domain is all real numbers, and the range is y ≥ 4.
Step-by-step explanation:
The equation of the parabola is [tex]f(x)=(x-2)^2+4[/tex]
The vertex form of the parabola is given by
[tex]f(x)=a(x-h)^2+k[/tex], here (h,k) is the vertex.
Comparing given equation with the vertex form of the parabola, we get
h = 2, k = 4
Hence, the vertex of the parabola is (h,k) = (2,4)
Now, domain is the set of x values for which the function is defined. The given function is defined for all real values of x.
Hence, domain is all real numbers.
Range is the set of y values for which the function is defined.
Since, here a = 1>0 hence it is a upward parabola and the vertex is the minimum point of this parabola.
Since, vertex is (2,4) hence, y values never less than 4.
Hence, range is y ≥ 4.
D is the correct options.
Select the term that best describes the statement.
All lines are straight or a triangle has four sides.
What is an equation that shows that two ratios are equivalent?
An equation that shows two ratios are equivalent is a proportion. Proportions can be applied in various fields like economics to show equivalent satisfaction based on price paid for goods, or in unit conversion to represent equivalent quantities in different units.
Explanation:An equation showing that two ratios are equivalent is a proportion. A proportion is a mathematical statement that two ratios are equal. For example, 2/4 = 1/2 is a proportion because the two ratios are equivalent. Other forms of this equation could be obtained by rearranging terms, showing the direct and indirect proportions.
In a more practical context, ratios are used to compare the relationship between different quantities. For example, we could state the ratio of the prices of two goods should be equal to the ratio of the marginal utilities. When we divide the price of good 1 by the price of good 2, this should equal the marginal utility of good 1 divided by the marginal utility of good 2. This indicates that the utility or satisfaction obtained is equivalent based on the price paid.
Also, proportions can be used as a unit conversion factor where the ratio of two equivalent quantities expressed with different measurement units can lead to a conversion factor. For example, the lengths of 2.54 cm and 1 in. are equivalent, thus providing a ratio that could be used for conversion.
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Find the simplified form of the expression. Give your answer in scientific notation. (9 x 10 5)(6 x 10 -7) A. 5.4 x 10 -34 B. 1.5 x 10 -1 C. 5.4 x 10 -1 D. 1.5 x 10 -34
A horseshoe weigs 8.2 ounces. The nails make up 0.2 of that weight. What is the weight of the horseshoe without the nails?
Graph the function y = 2x3 – x2 – 4x + 5. To the nearest tenth, over which interval is the function decreasing?
(1, ∞)
(–∞, –0.7)
(–0.7, 1)
(–1, 0.7)
Answer:
On (-2/3, 1) the given function is decreasing
Step-by-step explanation:
Do you know calculus? If so:
Differentiate y = 2x^3 – x^2 – 4x + 5 and set the derivative = to 0:
dy/dx = 6x^2 - 2x - 4 = 0, or 3x^2 - x - 2 = 0.
This factors as follows: (x - 1)(3x + 2) = 0.
The roots of this equation are {1, -2/3}.
Plot these two roots on a number line and then set up intervals as follows:
(-infinity, -2/3), (-2/3, 1), (1, infinity)
Choose a test number from each interval: { -1, 0, 2 }
By evaluating the derivative 6x^2 - 2x - 4 at each of these three test numbers, we get:
dy/dx = 6x^2 - 2x - 4 is positive on (-infinity, -2/3), and so we conclude that the given function is increasing on that interval.
dy/dx = 6x^2 - 2x - 4 is negative on (-2/3, 1), and so we conclude that the given function is decreasing on that interval. To the nearest tenth:
(-0.7, 1)
To find where the function y = 2x^3 - x^2 - 4x + 5 is decreasing, calculate the derivative, set it less than zero, solve for x, and use a sign chart to determine the intervals where the function is decreasing. The correct interval is (1, ∞).
Explanation:To determine where the function y = 2x3 − x2 − 4x + 5 is decreasing, we need to analyze its derivative. The first derivative of the function represents the slope of the tangent line to the curve at any given point, and when this slope is negative, the function is decreasing. Let's find the first derivative, f'(x) which is 6x2 − 2x − 4. To find where f'(x) is negative, we look for the x-values that make the derivative less than zero. This inequality can be solved by looking for the critical points where the derivative equals zero or is undefined, and then testing intervals around these points to see when the derivative is negative.
By factoring or using the quadratic formula, we find the critical points of f'(x) and then use a sign chart or test values to determine where the derivative is negative. For example, if we find that the derivative switches from positive to negative at x = 1, we can conclude that the function is decreasing for x values greater than 1. Therefore, the correct answer would be that the function is decreasing over the interval (1, ∞).
Choose the correct simplification of the expression (3x2y3z4)(2x5y2z3).
6x7y5z7
6x10y6z12
5 x7y5z7
5x10y6z12 ...?
yep, your answer is A.
How many 2.00-L bottles could be filled from a 24-can case of cola if in the United States a typical can holds 355 mL?
The number of bottles which could be filled are:
Approx 4 bottles ( since we got 4.260 )
Step-by-step explanation:One can case of cola holds- 355 mL
This means that:
24 can case of cola will hold= 24×355 mL
= 8520 mL
Also, 1 L=1000 mL
This means that:
1 mL= 0.001 L
Hence,
8520 mL= 8.520 L
Total amount of cola is: 8.520 L
Now, the number of bottles of 2 L which could be filled from this liquid is:
8.520/2=4.260 bottles.
Vector a~ points south. vector b~ points west. what is the direction of their cross product a~ × b~ ?
Final answer:
The cross product a~ × b~, where a~ points south and b~ points west, is directed downwards. This direction is determined using the right-hand rule and is perpendicular to the original plane formed by a~ and b~.
Explanation:
If vector a~ points south and vector b~ points west, their cross product a~ × b~ can be determined using the right-hand rule. By pointing the fingers of your right hand towards the direction of a~ (south) and then rotating your wrist to point your fingers towards b~ (west), your thumb will point downwards. Therefore, the direction of a~ × b~ is downwards, which is into the ground if you are standing in the Northern Hemisphere.
The cross product of two vectors is always perpendicular to the plane that contains the original vectors. So in this case, since a~ and b~ are orthogonal and lie in the horizontal plane, their cross product a~ × b~ will be orthogonal to this horizontal plane. As the vectors move from a~ to b~ in an anticlockwise direction, the resultant vector points downward, opposite to the upward direction that would be indicated by b~ × a~.
The shorter tree is 10.5 ft. tall, and casts a shadow that is 11.25 feet long.if the taller tree casts a 17.5 ft. shadow,how tall is the tree?
By using proportions based on the concept of similar triangles, the height of the taller tree is calculated to be approximately 16.3 feet tall.
Explanation:The question asks us to compare the heights and shadows of two trees to determine the height of the taller tree given the height and shadow length of the shorter tree and the shadow length of the taller tree. Since both trees will cast shadows in the same proportions if they're under the same conditions of light, we can use similar triangles to find the height of the taller tree.
The shorter tree is 10.5 ft tall and casts a shadow that is 11.25 feet long. If the taller tree casts a 17.5 ft shadow, we can set up a proportion as follows:
Height of the shorter tree / Shadow of the shorter tree = Height of the taller tree / Shadow of the taller tree
10.5 ft / 11.25 ft = Height of the taller tree / 17.5 ft
From the proportion, we can solve for the height of the taller tree:
Height of the taller tree = (10.5 ft / 11.25 ft) × 17.5 ft
Height of the taller tree = 16.333... ft
So, the taller tree is approximately 16.3 feet tall.
The measure of angle 5 is 80 degrees. The measure of angle 2 is one-eighth the measure of angle 5. What is the measure of angle 4
An object is dropped from a height of 1700 ft above the ground. The function h=-16t^2+1700 gives the object’s height h in feet during free fall at t seconds.
a. When will the object be at 1000ft above the ground?
b. When will the object be 940ft above the ground?
c. What are a reasonable domain and range for the function h?
To calculate when the object would be at a particular height, we use the given equation, input the known height, and solve for the time (t), using the quadratic formula. The time when the object is at 1000ft is approximately 6.6 seconds and at 940ft it's approximately 6.9 seconds. The domain of the function is 0 <= t <= 10.3 and the range is 0 <= h <= 1700.
Explanation:This question involves the application of the quadratic equation, in the context of Physics. You would use the given function h=-16t^2+1700 to solve for t when h is set to the desired height.
For height 1000 ft, you would solve the equation -16t^2 + 1700 = 1000. After simplifying, you get -16t^2 = -700, then t^2 = 43.75, which leads to t = square root of 43.75. Thus t = approximately 6.6 seconds.For height 940 ft, you use the same methodology yielding t = approximately 6.9 seconds.The domain for this function would be all real values of t such that 0 <= t <= 10.3, because the object starts falling at t=0 and hits the ground (height = 0) at about 10.3 seconds. The range would be all real values of h such that 0 <= h <= 1700, because the object's height is initially 1700 ft and reduces to 0 as it hits the ground.Learn more about Quadratic Functions here:
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The object will be at 1000ft and 940ft above the ground approximately 6.65 seconds and 6.87 seconds after being dropped, respectively.
The domain of the function representing this situation is t ≥ 0, and the range is 0 ≤ h ≤ 1700.
Explanation:To find out when the object will be at certain heights, we can set h equal to those heights and solve for t.
a. When will the object be at 1000ft above the ground?
1000 = -16t^2 + 1700
16t^2 = 1700 - 1000
16t^2 = 700
t^2 = 700/16
t = √(700/16)
t ≈ 6.65 seconds
b. When will the object be 940ft above the ground?
940 = -16t^2 + 1700
16t^2 = 1700 - 940
16t^2 = 760
t^2 = 760/16
t = √(760/16)
t ≈ 6.87 seconds
c. What are a reasonable domain and range for the function h?
The domain of the function, which stands for time, would be t ≥ 0 as we do not consider negative time.
The range of the function, corresponding to the height, would be 0 ≤ h ≤ 1700 as we know the object's maximum height is 1700 ft and it can't go below ground level (0 ft).
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simplify the ratio 12:2 ...?
what fraction is equivalent to the expression 4/8 + 2/8
5x^2-3y^2-20x+6y+2=0 what is the value of a
Henry has 2/3 of a bag of popcorn he eats half of the popcorn during the movie what fraction of a bag of popcorn does henry eat during the movie
There are 23 coins in a bank. All the coins are dimes and quarters. The total value of the coins is $3.80. How many dimes are there? How many quarters?
Write the system of equations that would be used to solve this problem.
Let q = quarter
Let d = dime
Here is your system:
q + d = 23
0.25q + 0.10d = 3.80
Take it from here.
PLEASE HELP Indicate the method you would use to prove the two 's . If no method applies, enter "none". SSS
SAS
ASA
None
Answer: 1) ASA
2) none
3) ASA
Step-by-step explanation:
In the first picture we have two angles and one included side of one triangle is congruent to corresponding two angles and one included side of another triangle, therefore by ASA postulate of congruence both triangles are congruent.
In the second picture , the two have two equal angles, the third angle of both triangles by using angle sum property =[tex]180^{\circ}-70^{\circ}-30^{\circ}=80^{\circ}[/tex],
Now, two corresponding angles and one included side (10 units) of both triangles are congruent therefore by ASA postulate of congruence both triangles are congruent.
In the third picture, we have two triangle with one same vertex, then their vertical angles must be congruent.
Thus, in third picture, two angles and one included side of one triangle is congruent to corresponding two angles and one included side of another triangle, therefore by ASA postulate of congruence both triangles are congruent.
Sam earned $450 during winter vacation. He needs to save $180 for a camping trip over spring break. He can spend the remainder of the money on music. Write an inequality to show how much he can spend on music.
true or false. sin(a-b) = -sin(b-a).
explain. ...?
Represent the ratio 6 : 18 in two other ways ...?
According to charles law, the pressure P in pascals of a fixed volume of gas is linearly related to the temperature T in degrees celcius. In an experiment, it was found that when T =40, P=90 and when T=80, P=100.
a. What is the slope of the line containing these 2 points?
b. explain the meaning of slope in this context.
ms. galan spent 55% of her savings on a television that cost $550. how much money did she have in her savings before she bought the television
Answer:$1000
Step-by-step explanation:my frend found this
Please help! After five years of earning interest at an annual rate of 4%, an investment has earned $1,200 in interest. Determine the amount of the initial investment. Show all work for full credit.
What is the y-intercept of the line y=3x-7?
write 0.08 as a decimal and fraction
0.08 is already a decimal.
To make 0.08 into a fraction, look at the image attached.