Please help me I have no clue how to do this
Answer:
Try the answer B.
Step-by-step explanation:
. A study was conducted to analyze the effects on deer population in a particular area. Let f be an exponential function that gives the population of deer t years after the study began.
If f(t) = a · bt and the population is increasing, select all statements that must be true.
a. b>1
B. b < 1
C. The average rate of change from year 0 to year 5 is less than the average rate of change from year 10 to year 15.
D. The average rate of change from year 0 to year 5 is greater than the average rate of change from year 10 to year 15.
e. a > 0
The statements that are true are (a) b > 1, (c) The average rate of change from year 0 to year 5 is less than the average rate of change from year 10 to year 15. and (e) a > 0
What are Exponential Functions?Exponential functions are those functions where the independent variable, x is in the exponent.
Given exponential function is,
f(t) = \(a . b^t\)
The exponential function can be written as,
f(t) = \(a(1+r)^t\), where r is the rate of increase or decrease.
So, b = 1+ r
It is given that the population is increasing, so rate is positive.
So b = 1 + r, is greater than 1.
Average rate of change of a function is the ratio change in function values to the change in t values.
Change in t is same as we are measuring over 5 years.
Since the function is increasing at a constant rate, the function values will also be outgoing a large increase as the time increases.
So the average rate of change from year 0 to year 5 is less than the average rate of change from year 10 to year 15.
a is the initial population of the deer when t = 0. This must be greater than 0.
Hence the options a, c and e are correct statements.
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Samantha won a trip to Europe in a contest she had entered. Rather than take the trip, she opted to take the cash value of the prize and put it in
savings account she uses as a college fund. She plans to keep this money in the college fund and let it earn interest for 8 years. At the end of
8 years, she'll use the total balance to help pay for tuition at law school
Answer:
Domain : 0 ≤ x ≤ 8
Range : 5450 ≤ f(x) ≤ 6588.65
Step-by-step explanation:
Expression representing the money Samantha collected after x years is,
f(x) = \(5450(1.024)^{x}\)
Time 'x' duration for the investment starts from t = 0 and ends at 8 years, so the domain of the given function will be,
Range : 0 ≤ x ≤ 8
Money collected in the fund from 0 to 8 years is,
f(0) = \(5450(1.024)^{0}\)
= $5450
f(8) = \(5450(1.024)^{8}\)
= $6588.6
Therefore, range of the graphed function will be,
Range : 5450 ≤ f(x) ≤ 6588.65
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 19 feet. Container B has a diameter of 16 feet and a height of 12 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.
After the pumping is complete, what is the volume of water in Container B, to the nearest tenth of a cubic foot?
sara chose a date from the calendar. what is the probability that the date she chose is a prime number, given that the date is after the 7th of the month?
The probability that the date sara chose is a prime number is 0.2.
Given that, sara chose a date from the calendar.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Here, total number of outcomes = 30
Number of favourable outcomes = 6
Now, probability = 6/30
= 1/5
= 0.2
Therefore, the probability that the date sara chose is a prime number is 0.2.
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Determine the equation of the parabola graphed below. A parabola is plotted, concave up, with vertex located at coordinates four and two.
The equation of the given parabola is: y = (x - 4)² + 2
The equation of the given parabola graphed below, which is concave up and has a vertex located at coordinates (4, 2), can be determined using the standard form of the equation of a parabola. The equation of the given parabola with a vertex at (4, 2) can be found using the standard form of the equation of a parabola.
The standard form of the equation of a parabola is y = a(x - h)² + k, where (h, k) is the vertex and a is the constant determined by the focus and directrix of the parabola
Since the given parabola is concave up and has a vertex located at (4, 2), we know that the equation of the parabola must be of the form: y = a(x - 4)² + 2The value of a is determined by the distance between the vertex and focus of the parabola. Since the parabola is concave up, the focus is located above the vertex and the directrix is located below the vertex, both equidistant from the vertex.
The distance from the vertex to the focus is equal to a, and the distance from the vertex to the directrix is also equal to a. Since the vertex is located at (4, 2), the focus is located at (4, 2 + a), and the directrix is located at y = 2 - a. The distance between the vertex and focus is given by the formula:
d = |y-coordinate of focus - y-coordinate of vertex|
d = |(2 + a) - 2| = |a|
Similarly, the distance between the vertex and directrix is given by:
d = |y-coordinate of directrix - y-coordinate of vertex|
d = |2 - a - 2| = |-a|
Since the distances are equal, we can equate them:
|a| = |-a|
a = ± a
However, we know that a must be positive since the parabola is concave up. Therefore, a = |a|, and we can write:
a = 2 + a - 2
a = a²
a² - a = 0
a(a - 1) = 0
Thus, a = 0 or a = 1. Since a cannot be equal to 0, we have a = 1. Therefore, the equation of the given parabola is:
y = (x - 4)² + 2
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3
87. 8
98
-
8[?].
the question didn’t have enough letters for me to post so i’m using this to post it
\(i \: need \: help \: \\ \\ (a \: + \: b) {}^{2} = {?} \)
Answer:
I hope this helps you :)...
Answer:
(
\( {a}^{2} + 2ab + {b}^{2} \)
Step-by-step explanation:
(a+b)²
=(a+b)(a+b)
=a(a+b)+b(a+b)
=a²+2ab+b²
What is 2+2x -6=2720=1819
The solution to the equation √(2 + 2x) - 6 = 2 when evaluated is x = 31
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
√(2 + 2x) - 6 = 2
So, we have
√(2 + 2x) = 8
Take the square of both sides
so, we have the following representation
2 + 2x = 64
Evalyate the like terms
2x = 62
Divide by 2
This means that
x = 31
Hence, the solution is x = 31
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Complete question
What is √(2 + 2x) - 6 = 2
A quadrilateral is plotted on a coordinate plane. Each of the vertices of the quadrilateral undergoes the same transformation.Which transformation does not preserve the lengths of the sides of the quadrilateral?
Explanations :
(a) (x;y) →(x-3 ; -y+2 ) ; this preserves the lengths of the side, with a reflection across the x -axis .
(b) (x;y) →(2x +1 ; y-5 ); this does not preserve the length of sides, because the 2 multiply by x will change the length by factor of 2 .
(c) (x;y) → (-x+6 ;-y -8 ), preserves the lengths of sides, with reflection of y = -x .
(d) (x;y) →(-x -5 ; y+10 ) preserves the lenghts of the sides , with a reflection in the y -axis .
Help me on the bottom three please
Answer:
\(x=5,8,-8\) respectively
Step-by-step explanation:
For Q.5, the two angles are supplementary, meaning they sum up to 180 so\((12x+19)+(22x-9)=180\\ 12x+22x+19-9=180\\ 34x+10-(10)=180-(10)\\ 34x=170\\ x=5\) For Q.6, the two angles are alternate exterior angles, meaning they are equal so\(10x-20=7x+4\\10x-(7x)-20+(20)=7x-(7x)+4+(20)\\3x=24\\x=8\) For Q.7, two angles are consecutive interior angles, meaning they sum up to 180 so\((-4x+5)+(-13x+39)=180\\-4x-13x+5+39=180\\-17x+44-(44)=180-(44)\\-17x=136\\x=-8\)Find the average of 40.6, 10, 0.7, and 120.02
Answer:
42.83
Step-by-step explanation:
add all the numbers and divide by how many their are
In the rhombus below, AC = 14 cm and BC = 25 cm. Find the area
In order to calculate the area of the rhombus, first let's draw the diagonal BD.
This diagonal and the diagonal AC will intersect at point M, which is the midpoint of each diagonal.
Since M is midpoint of AC, we have AM = MC = 7 cm.
Now, let's calculate the length of BM, using the Pythagorean theorem in the right triangle BMC:
\(\begin{gathered} BC^2=BM^2+MC^2\\ \\ 25^2=BM^2+7^2\\ \\ BM^2=625-49\\ \\ BM^2=576\\ \\ BM=24 \end{gathered}\)Calculating the area of this triangle, we have:
\(\begin{gathered} A=\frac{MC\cdot BM}{2}\\ \\ A=\frac{7\cdot24}{2}\\ \\ A=84\text{ cm^^b2} \end{gathered}\)The triangles BMC, BMA, DMC and DMA are all congruent, so the area of the rhombus is:
\(A_{rhombus}=4\cdot84=336\text{ cm^^b2}\)Out of 1,200 students that attend Norman Rockwell Middle School, how many would most likely sign up for after school tutoring, if 48 out of 80 students randomly surveyed said they would like to have extra help after school?
Answer:
720
Step-by-step explanation:
Out of 80 students the no. of students who sign up=48
So, out of 1200 students 48×1200÷80=720 students sign up.
what are the terms a0, a1, a2, and a3 of the sequence {an}, where an equals a) 2n 1? b) (n 1)n 1? c) n/2? d) n/2 n/2?
When a\(_{n}\) = \(2^{n}\)+ n, a₀ = 1, a₁ = 3, a₂ = 6, and a₃ = 11
When a\(_{n}\) = n^(n+1)!, a₀ = 0, a₁ = 2, a₂ = 2⁶, and a₃ = 3²⁴
When a\(_{n}\) = [n/2], a₀ = 0, a₁ = 1/2, a₂ = 1, and a₃ = 3/2
When a\(_{n}\) = [n/2] + [n/2], a₀ = 0, a₁ = 1, a₂ = 2, and a₃ = 3/2
Number sequence
A number sequence is a progression or a list of numbers that are directed by a pattern or rule.
Here,
a₀, a₁, a₂, and a₃ are terms of a sequence
from option a, a\(_{n}\) = \(2^{n}\)+ n
⇒ a₀ = 2⁰+ 0 = 1+0 = 1
⇒ a₁ = 2¹+ 1 = 2+1 = 3
⇒ a₂, = 2²+ 2 = 4+2 = 6
⇒ a₃ = 2³+ 3 = 8 +3 = 11
from option b, a\(_{n}\) = n^(n+1)!
⇒ a₀ = 0^(0+1)! = 0
⇒ a₁ = 1^(1+1)! = 2² = 2
⇒ a₂, = 2^(2+1)! = 2^(3)! = 2⁶ [ ∵ 3! = 6 ]
⇒ a₃ = 3^(3+1)! = 3^(4)! = 3²⁴ [ ∵ 4! = 24 ]
from option c, a\(_{n}\) = [n/2]
⇒ a₀ = [0/2] = 0
⇒ a₁ = [1/2] = 1/2
⇒ a₂, = [2/2] = 1
⇒ a₃ = [3/2] = 3/2
from option d, a\(_{n}\) = [n/2] + [n/2]
⇒ a₀ = [0/2] + [0/2] = 0
⇒ a₁ = [1/2] + [1/2] = 1/2 + 1/2 = 1
⇒ a₂, = [2/2] + [2/2] = 1 + 1 = 2
⇒ a₃ = [3/2] + [3/2] = 6/4 = 3/2
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The Complete Question is -
What are the terms a₀, a₁, a₂, and a₃ of the sequence {a\(_{n}\)}, where a\(_{n}\) is where a\(_{n}\) equals
a. \(2^{n}\) + n b. n^(n+1)!
c. [n/2] d. [n/2] + [n/2]
What’s the answer to this
Answer:
\(x = 2 \\y = 3\)
Step-by-step explanation:
g2 + 23 when g = 6??? help
In a sale a clothes shop reduces its prices by 25% a shirt usually costs $34 how much it’s after the sale?
Answer:
$25.5
Step-by-step explanation:
A data-entry clerk spends $86 per week for food. This is 20% of his weekly income. What is the weekly income? Show work please :
Answer:
$430
Step-by-step explanation:
Let the weekly income be x
Money spent on food= $86
% of weekly income spent on food = 20
20% of weekly income in terms = 20/100 * x = x/5
This, income is equal to $86 as given
thus,
x/5 = 86
x = 86*5 = 430
Thus, weekly income is $430.
how are unit rates and equivalent ratios realted?
Answer:
A unit rate is a special kind of ratio, where the second number, or the denominator, is equal to one. With a unit rate, you are comparing a quantity to one. Some common unit rates are miles per gallon, price per pound, and pay rate per hour. ... Next, divide the price by the pounds so you can find the unit rate.
Step-by-step explanation:
Answer:
A unit rate is a special kind of ratio, where the second number, or the denominator, is equal to one. With a unit rate, you are comparing a quantity to one. Some common unit rates are miles per gallon, price per pound, and pay rate per hour. ... Next, divide the price by the pounds so you can find the unit rate.
Step-by-step explanation:
Does convex optimization have unique solution?
Convex optimization problems can have a unique solution, but not always.
A convex optimization problem is a type of optimization problem where the objective function and the constraints are convex. In this type of problem, if there is a solution, it is guaranteed to be the global minimum or maximum.
However, not all convex optimization problems have a solution. The existence of a solution depends on the specific problem, and it requires that the feasible set of solutions is non-empty and that the objective function is bounded. If these conditions are not satisfied, the problem may not have a solution.
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What is the measure of
Answer:
it is 70 degrees because if you count by tens as it does count by tens you would need to count from point b to c.
hope this helped.:)
Help pleaseI don’t understand
Answer:
Angle 3 is 65
Angle 8 is 115
Step-by-step explanation:
A field measurement of 1751.71 ft was made with a steel chain, which was later standardized at a true length of 100.014 ft. What is the true distance measured?
The true distance measured is 1751.71 ft. To find the true distance measured, we can use the concept of proportional relationships.
Let's denote the measured distance as D1 and the true length as D2.
According to the given information, the measured distance with the steel chain is 1751.71 ft, and the true length of the chain is 100.014 ft.
We can set up a proportion to relate the measured distance to the true length:
D1 / D2 = Measured length / True length
Plugging in the given values:
D1 / D2 = 1751.71 ft / 100.014 ft
To find the true distance measured (D2), we can rearrange the equation and solve for D2:
D2 = (D1 * True length) / Measured length
Substituting the given values:
D2 = (1751.71 ft * 100.014 ft) / 100.014 ft
Calculating:
D2 = 1751.71 ft
Therefore, the true distance measured is 1751.71 ft.
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What are the solutions of x2+4x=9?
Question 3 options:
−2±13−−√
−2±413−−√
−4±213−−√
−4±13−−√
Answer:
−2±13−−√
Step-by-step explanation: one answer for sure
Answer:
−2±13−−√
Step-by-step explanation:
Error Analysis: Mr. Hasson is buying a new bike for the summer time. The bike originally costs $150 but he sees it's on sale for 30% off. Mr. Hasson thinks that this means the price is $149.70 because 30% means 0.30 and 150 - 0.30 = $149.70.
What is the error that Mr. Hasson made?
What is the correct way to calculate the sale price?
Answer:
$45
Step-by-step explanation:
30% ÷100 =0.3. 0.3×150= 45
what is a rectangles area formula
Thea are a of rectangle is base times the height of the rectangle
What is the following product?
3v2(5v6-7v3)
Answer:
\(3v^2\left(5v^6-7v^3\right)=15v^8-21v^5\)
Step-by-step explanation:
Given the expression
\(3v^2\left(5v^6-7v^3\right)\)
Apply the distributive law
\(a\left(b-c\right)=ab-ac\)
\(a=3v^2,\:b=5v^6,\:c=7v^3\)
\(=3v^2\cdot \:5v^6-3v^2\cdot \:7v^3\)
\(=3\cdot \:5v^6v^2-3\cdot \:7v^3v^2\)
\(=15v^8-21v^5\)
Thus, we conclude that
\(3v^2\left(5v^6-7v^3\right)=15v^8-21v^5\)
Tipping force practice.. I don’t understand
(7) The weight of the box is 5 pounds.
(8) The weight of the box is 20 pounds.
(9) The tripping force is applied at a height of 24 inches.
What is the height of the applied tripping force?To solve this problem, we can use the principle of moments, which states that the sum of the moments of the forces acting on an object must be zero for the object to be in equilibrium.
The moment of the weight about the base of the block is:
W x (1/2) x 10 inches = 5W
The moment of the tripping force about the base of the block is:
5 pounds x (h - 10 inches)
5 x (15 - 10) = 25
Since the block is in equilibrium, these two moments must be equal. So we can set them equal to each other and solve for h:
5W= 25
W = 25/5
W = 5 pounds
For the second question,
where;
the base = 20 inches, tripping force = 20 pounds andheight of applied tripping force = 30 inches.The moment of the weight about the base of the block is:
W x (1/2) x 20 inches = 10W
The moment of the tripping force about the base of the block is:
20 pounds x (h - 10 inches) = 20 (30 - 20) = 20 x 10 = 200
10W = 200
W = 20 pounds
For the third question;
where;
the base = 12 inchestripping force = 12.5 poundsweight of box = 25 poundsThe height of the tripping force is calculated as;
The moment of the weight about the base of the block is:
25 pounds x (1/2) x 12 inches = 150 inch-pounds
The moment of the tripping force about the base of the block is:
12.5 pounds x (h - 12 inches)
150 inch-pounds = 12.5 pounds x (h - 12 inches)
12 inches = h - 12 inches
h = 24 inches
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if x – 9 is a factor of x2 – 5x – 36, what is the other factor?
If x - 9 is a factor of x^2 - 5x - 36 equation, then the other factor is x + 4.
We can factor x - 9 out of x^2 - 5x - 36 as follows: \(x^{2}\) - 5x - 36 = (x-9)(x+4).
We know that x - 9 is a factor of x^2 - 5x - 36. Therefore, the remaining factor must be x + 4.
We can also verify this by substituting x = 9 into the equation x^2 - 5x - 36 = (x - 9)(x + 4). We get:
9^2 - 5(9) - 36 = 81 - 45 - 36 = 0
Since the left side of the equation is equal to 0, we know that x = 9 is a solution to the equation. Therefore, x - 9 must be a factor of the equation.
Since we know that x - 9 is a factor of x^2 - 5x - 36, the other factor must be x + 4.
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QUESTION:
If x – 9 is a factor of x2 – 5x – 36, what is the other factor?
x – 4
x + 4
x – 6
x + 6