To solve this problem, let us first assign variables. Let us say that:
X = number of marigold plants
Y = number of sunflower plants
n = number of months
We can see that in the given problem, X is decreasing by a percentage, this means that we have to set-up a geometric equation while for Y the decrease is linear so we set-up an arithmetic equation.
Part A.
For marigold plants X, a geometric sequence has a general form of:
X = Xo * (1 + r)^n
where r = -15% = -0.15 (negative since it is decreasing)
Xo = the initial amount of marigold plants = 150
X = 150 * (1 – 0.15)^n
X = 150 (0.85)^n
For the sunflower plants Y, an arithmetic sequence has a general form of:
Y = Yo + d * n
where d = -8 and Yo = 125
Y = 125 – 8 n
Part B. For n = 3
X = 150 (0.85)^3 = 92.12 = 92
Y = 125 – 8 (3) = 101
Part C. From Part B we see that the two values are very far from each other when n = 3, therefore they must be similar when n < 3. So we try n = 2
X = 150 (0.85)^2 = 108.38 = 108
Y = 125 – 8 (2) = 109
Therefore the two plants have approximately similar amount after 2 months.
A quadratic function and an exponential function are graphed below. Which graph most likely represents the exponential function? graph of function t of x is a curve which joins the ordered pair 0, 1 and 1, 3 and 3, 27. Graph of function p of x is a curve which joins the ordered pair 0, 2 and 1, 3 and 3, 11 and 5, 27 and 6, 38
Final answer:
The function t(x) with ordered pairs (0, 1), (1, 3), and (3, 27) most likely represents the exponential function because it shows rapidly increasing growth rates, which is a defining feature of exponential behavior.
Explanation:
The function that most likely represents the exponential function is the one whose growth rate increases significantly for larger values of x. Examining the ordered pairs, the function t(x), which passes through the points (0, 1), (1, 3), and (3, 27), clearly demonstrates this behavior as the increase between the y-values gets dramatically larger as x increases.
This is a classic characteristic of exponential growth. In contrast, the function p(x) that passes through (0, 2), (1, 3), (3, 11), (5, 27), and (6, 38) shows a more consistent increase in y-values as x increases, indicative of a quadratic function.
The volumes of two similar figures 27mm^3 and 1331mm^3. If the surface area of the smaller figure is 18mm^2, what is the surface area of the larger figure
Branliest and 30 points to who answers first
To make one dose chispa put 2 drops of a herbal remedy into a 30 ml bottle and adds spring water he has now used 54 drops of the 120 that the full bottle contained how many more times can chispa use his herbal remedy
Generally, how would one work out the surface area of a frustum?
see the formula in the picture
R is larger diameter, r is smaller diameter
A number is chosen at random from the integers between 11 and 99, inclusive. what is the probability that the number contains the digit 2?
The hypotenuse of a 45°-45°-90° triangle measures 4 cm. What is the length of one leg of the triangle?
multiply 4 by the cos(45)
4 x cos(45) = 2sqrt(2) approximately 2.828cm
so depending how you are supposed to answer, either 2 sqrt(2) or approximately 2.83 cm
A chi-square test involves a comparison between what is observed and what would be expected by _______.
write the square root of 23 in exponential form
Solve the problem by writing an inequality. A club decides to sell T-shirts for $12 as a fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts. Write and solve an equation to find how many T-shirts the club needs to make and sell in order to profit at least $100. Show your work.
It doesn't matter which of the two points on a line you choose to call (x1, y1) and which you choose to call (x2, y2) to calculate the slope of the line.
A. True
B. False
Answer:
the answer is true
Step-by-step explanation:
it's what I got
17. Evaluate. Show your work.
a. 6!
b. 6P5
c. 12C3
In a binomial experiment the probability of success is 0.06. What is the probability of two successes in seven trials? a. 0.0554
For two successes in seven binomial trials with a success probability of 0.06, use the binomial probability formula. Calculate (7 choose 2) * (0.06^2) * (0.94^5) to get the probability of 0.0554.
Explanation:To calculate the probability of two successes in seven trials with a success probability of 0.06, you can use the binomial probability formula, which is P(X = k) = (n choose k) * p^k * q^(n-k), where 'n' is the number of trials (7), 'k' is the number of successes (2), 'p' is the probability of success (0.06), and 'q' is the probability of failure (q = 1 - p = 0.94).
First, calculate the binomial coefficient using 'n choose k', which is (7 choose 2). Then, raise the probability of success to the power of the number of successes (0.06^2) and the probability of failure to the power of the number of failures (0.94^5). Lastly, multiply these values together to get the probability.
The calculation is as follows:
(7 choose 2) * (0.06^2) * (0.94^5) = 21 * 0.0036 * 0.7339 = 0.0554
I am confused about this question in trigonometry:
use AE and CE to find the angle
AE = 20, CE = 6
so the angle FOR CAE = tan^-1(6/20) = 16.7 degrees
to Find DF
a^2 = b^2 +c^2-2abcos(A)
a^2 = 10^2 + 14^2 -2(14)(10)cos(16.7)
a^2 = 30
sqrt((30)=5.47 rounded to 5.5
EF =
a^2 = b^2 +c^2-2abcos(A)
a^2 = 20^2 + 14^2 -2(14)(20)cos(16.7)
a^2 = 64
sqrt(64)=8
A country population in 1991 was 231 million in 1999 it was 233 million . Estimate the population in 2003 using the exponential growth formula. Round you answer to the nearest million
Answer:
population in 2003 is 234 million.
Step-by-step explanation:
A country's population in 1991 was 231 million
In 1999 it was 233 million.
We have to calculate the population in 2003.
Since population growth is always represented by exponential function.
It is represented by [tex]P(t)=P_{0}e^{kt}[/tex]
Here t is time in years, k is the growth constant, and is initial population.
For year 1991 ⇒
233 = [tex]P_{0}e^{8k}[/tex] = 231 [tex]e^{8k}[/tex]
[tex]\frac{231}{233}= e^{8k}[/tex]
Taking ln on both the sides ⇒
[tex]ln(\frac{233}{231})=lne^{8k}[/tex]
ln 233 - ln 231 = 8k [since ln e = 1 ]
5.451 - 5.4424 = 8k
k = [tex]\frac{0.0086}{8}=0.001075[/tex]
For year 2003 ⇒
[tex]P(t)=P_{0}e^{kt}[/tex]
P (t) = 231 × [tex]e^{(0.001075)(12)}[/tex]
= 231 × [tex]e^{0.0129}[/tex]
= 231 × 1.0129
= 233.9 ≈ 234 million
Therefore, population in 2003 is 234 million.
parallel lines r and s are cut by two transversals, parallel lines t and u
PLEASE HELP!!!! Solve the equation. Check for extraneous solutions. Type your answers in the blanks. Show your work.
x = _____ or _____
Answer:
-3
Step-by-step explanation:
Where does the normal line to the parabola, given below, at the given point, intersect the parabola a second time? illustrate with a sketch. (round the answers to three decimal places.) y = 4 x - 2 x^ 2 p = (2, 0)?
Can someone please help me with math for college readiness
Has 320 yards of fencing to enclose a rectangular area. find the dimensions of the rectangle that maximize the enclosed area. what is the maximum area
The dimensions of the rectangle that maximize the enclosed area are L = 80 yards and W = 80 yards. The maximum area is A = 80 * 80 = 6400 square yards.
To find the dimensions of the rectangle that maximize the enclosed area using 320 yards of fencing, we'll use the concept of optimization. Let's solve it step by step:
Let's assume the length of the rectangle is L and the width is W.
Perimeter constraint:
The perimeter of the rectangle is given as 2L + 2W, which must equal 320 yards:
2L + 2W = 320
Simplify the perimeter equation:
Divide both sides by 2 to get:
L + W = 160
Express one variable in terms of the other:
Solve the equation for L:
L = 160 - W
Area equation:
The area of the rectangle is given by A = L * W.
Substitute the value of L from the previous step into the area equation:
A = (160 - W) * W
A = 160W - W^2
Maximize the area:
To find the maximum area, we need to maximize the function A = 160W - W^2. This is achieved when the derivative is zero.
Take the derivative of A with respect to W:
dA/dW = 160 - 2W
Set dA/dW = 0 and solve for W:
160 - 2W = 0
2W = 160
W = 80
Substitute the value of W back into the perimeter equation to find the corresponding value of L:
L = 160 - W = 160 - 80 = 80
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The optimization problem involves finding the dimensions of a rectangle to maximize its area using a fixed amount of fencing. The dimensions that maximize the area are both 80 yards, making the maximum area 6400 square yards.
Explanation:The subject of this question is Mathematics, specifically a problem about optimization in the field of Calculus. In the given problem, we wish to find a rectangular area that can be enclosed by 320 yards of fencing that maximizes the area.
Let's designate the rectangular area's width and length as x and y respectively. The problem can now be rephrased. With the total length of fencing equal to 320 yards, you can express this as 2x + 2y = 320. Simplifying this equation, we get x + y = 160, or y = 160 - x.
The area of a rectangle is computed as width times length, or in this case, x(160 - x). This is a quadratic function, and its maximum value happens at the vertex of the parabola defined by this function. For a quadratic in standard form like y = ax^2 + bx + c, the x-coordinate of the vertex is at -b/2a. In this case, the maximum area happens when x = 160/2 = 80.
Substituting this value back into the equation for the rectangle's dimensions gives y = 160 - 80 = 80. So, the dimensions that maximize the area for a rectangle with a parameter of 320 yards are both 80 yards. Therefore, the maximum area possible is 80*80 = 6400 square yards.
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Find the 4th term if the sequend in which a1 = 2 and a n+1 = -4a n + 2
***PLEASE HELP**
What is the slope of the line shown below?
Answer:
correct option is B) 2
Step-by-step explanation:
Slope of line is calculated by formula :-
Suppose two points on line are [tex](x_1, y_1) and (x_2 ,y_2)[/tex] then slope 'm' is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].
We can see two points on line of graph are :- (-1, -4) and (2,2)
then slope will be calculated as,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
since [tex]x_1 = -1, x_2 =2, y_1=-4\;and\; y_2=2[/tex]
now, put in formula
[tex]m=\frac{2-(-4)}{2-(-1)}[/tex]
[tex]m=\frac{2+4}{2+1}[/tex]
[tex]m=\frac{6}{3}[/tex]
[tex]m=2[/tex]
Hence, slope is 2 of the provided graph.
Therefore, correct option is B) 2
A survey asked 30 people what their favorite genre of television broadcasting was, and the results were tabulated above. Find the probability that a person chosen at random was female, given that they like comedy. Round the answer to the nearest hundredth.
The probability that a person chosen at random is female, given they like comedy, is approximately 0.53 or 53% .
First, let's find the total number of females who like comedy. In the Venn diagram, there are 8 females who like comedy. There are also 7 males who like comedy. So, there are 15 people who like comedy in total.
Next, we need to determine the total number of females. There are 16 females who like drama, and 4 females who like sports. Adding these together, we get 20 females in total.
Now, we can calculate the conditional probability that a female likes comedy given that she was chosen at random. The formula for conditional probability is P(A|B) = P(AnB) / P(B). In this case, event A is "being female" and event B is "liking comedy."
P(A|B) = (Number of females who like comedy) / (Total number of people who like comedy)
P(A|B) = 8 / 15
To express this as a percentage, multiply by 100:
P(A|B) * 100 ≈ 0.5333
Rounded to the nearest hundredth, the probability is 0.53 or 53%.
The probability that a person chosen at random is female, given they like comedy, is approximately 0.53 or 53% .
First, let's find the total number of females who like comedy. In the Venn diagram, there are 8 females who like comedy. There are also 7 males who like comedy. So, there are 15 people who like comedy in total.
Next, we need to determine the total number of females. There are 16 females who like drama, and 4 females who like sports. Adding these together, we get 20 females in total.
Now, we can calculate the conditional probability that a female likes comedy given that she was chosen at random. The formula for conditional probability is P(A|B) = P(AnB) / P(B). In this case, event A is "being female" and event B is "liking comedy."
P(A|B) = (Number of females who like comedy) / (Total number of people who like comedy)
P(A|B) = 8 / 15
To express this as a percentage, multiply by 100:
P(A|B) * 100 ≈ 0.5333
Rounded to the nearest hundredth, the probability is 0.53 or 53%.
A researcher wishes to find out whether giving a student $1 million in cash will improve or ruin the student's grades in school. A high school class consists of the 8 students numbered in the following list. 0 Juanita 1 Tuan 2 Harry 3 Greta 4 William 5 Hiroshi 6 Betty 7 Jane Help the researcher by using the line from a table of random numbers (shown below) to assign 4 of these students to the treatment group. 39661 55832 02589 52612 25414 19879 60880 30641 55259 35324 Which students go in the treatment group?
Answer:
Greta, Betty, Tuan and Hiroshi
Step-by-step explanation:
Start from the beginning:
3 - Greta
Then, continue with the next numbers:
9 - skip (there is no student numbered with a 9)
6 - Betty
6 - skip (Betty is already chosen)
1 - Tuan
5 - Hiroshi
What is the area for this problem?
C = 2* pi *r = 36 pi
r = 36pi/2pi = 18
We know that A= r^2 * pi
A = 18^2 * pi = 324 pi
the area would be 324PI square units
The area of a certain rectangle is 288 yd2. the perimeter is 68 yd. what are the dimensions of the rectangle?
The dimensions of the rectangle are a length of 16 yds and a width of 18 yds.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
Given that the perimeter is 68 yd
We know that the perimeter of a rectangle is:
P = 2(L + W)
∴ P = 68
68 = 2(L + W)
68/2 = L + W
34 = L + W
34 - L = W ....(i)
The area of a rectangle is:
A = L × W ....(ii)
∴ A = 288
Substitute the value W = 34 - L in equation (ii), and solve for L
288 = L(34 - L)
288 = 34L - L²
L² - 34L + 288 = 0
(L - 16)(L - 18)
L - 16 = 0 and L - 18 = 0
L = 16 and L = 18
Take L = 16 and substitute the value in the equation (i)
So, W = 34 - 16 = 18
Therefore, the rectangle's length is 16 yds and its width is 18 yds.
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Solve △ABC if B=120°, a=10, c=18
Write the total population of india and china.estimate the total population by rounding off each population to nearest 100000
As of Thursday, August 17, 2017, based from the data of the latest United Nations estimates, the current population of China is 1,388,979,446.
China’s population is equivalent to 18.47% of the total world population.
18.47% of
the total world population is composed by China’s population.
China is ranked number 1 in the list of countries by population.
Rounding that number off to the nearest 100,000, it would be 1,388,980,000.
As of Thursday, August 17, 2017, based from the data of the latest United Nations estimates, the current population of India is 1,344,431,890.
17.86% of the total world population is composed by India’s population.
India is ranked number 2 in the list of countries by population.
Rounding that number off to the nearest 100,000, it would be 1,344,400,000.
Can you check my work please!! And don't joke about it! Thanks
1 oz of walnuts were mixed with 4 oz of peanuts which cost $4/oz to make mixed nuts which cost $5/oz. what is the price per oz of walnuts
What is the vertex of the graph of y + 2x + 3 = –(x + 2)2 + 1?