The wildflowers at a national park have been decreasing in numbers. There were 300 wildflowers in the first year that the park started tracking them. Since then, there have been one fourth as many new flowers each year. Create the sigma notation showing the infinite growth of the wildflowers and find the sum, if possible.
I chose C, but can someone check for me? Thanks :)
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
Initial wildflowers in the first year = 1200
Every year, the number of wildflower is one fourth of the previous year.
So, it form a geometric series:
1200,300,75............
so, using sigma notation we can express the infinite growth of the wildflowers:
[tex]\sum ^{\infty}_{i=1}1200(\dfrac{1}{4})^{i-1}[/tex]
As we know that sum of infinite terms in case of geometric series is given by
[tex]S_{\infty}=\dfrac{a}{1-r}\\\\S_{\infty}=\dfrac{1200}{1-0.25}\\\\S_{\infty}=\dfrac{1200}{0.75}\\\\S_{\infty}=1600[/tex]
Therefore, there are 1600 wildflowers.
Hence, Third option is correct.
Please help!!! (-x/2)+(1/2x)=(-4/x)
The tangent of an angle is 3.4. what is the measure of the angle to the nearest tenth? 99.8° 73.6° 68.2° 52.9°
A man wishes to construct a pultry house 12 feet long, in which to keep 20 hens. if each hen requires 4 square feet of floor space, how wide should he contruct the poultry house
PLEASE HELP!!!!!
Which function has the following domain and range?
Domain: {−7,−3,0,4,12}
Range: {−5,1,2}
Select one:
a. {(−7,12),(−5,2)}
b. {(−7,−5),(−3,1),(0,2),(−4,5),(3,−1)}
c. {(4,1),(−3,−5),(12,2),(0,−5),(−7,1)}
d. {(−5,4),(2,12),(1,−3),(−5,−7),(1,0)}
Which inequality is correctly represented by this graph
A) 3x-y>3
B) x-3y>=2
C) 3x-y<=3
D)x-3y>2
You should first solve each equation for y.
Eliminate answer choices with wrong slopes or y intercepts.
Then, because it is a dotted line, the answer will only be < or >.
And because the area is shaded to the right, it would mean that x > y.
So the answer is A) 3x - y > 3
Answer:
The correct option is A.
Step-by-step explanation:
If a line passing through two points then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
From the given graph it is clear that the related line passing through the points (0,-3) and (1,0). So, the equation of related line is
[tex]y-(-3)=\frac{0-(-3)}{1-0}(x-0)[/tex]
[tex]y+3=3x[/tex]
The (0,0) is not in the solution set. So check the equation be (0,0).
[tex]0+3=3(0)[/tex]
[tex]3=0[/tex]
This condition is false if the sign of inequality is < or ≤. Since the related line is a solid line, therefore the sign of inequality must be <.
The required inequality is
[tex]y+3<3x[/tex]
[tex]3<3x-y[/tex]
It is also written as
[tex]3x-y>3[/tex]
Therefore the correct option is A.
Trey went to the batting cages to practice hitting. he rented a helmet for $4 and paid $0.75 for each group of 20 pitches. if he spent a total of $7 at the batting cages, how many groups of pitches did he pay for?
Justin wants to use 376 ft of fencing to fence off the greatest possible rectangular area for a garden what dimensions should he use what will be the area of the garden
the greatest rectangular area is actually a square
so 376/4 = 94 feet.
each side will be 94 feet
area of a square is 94^2
= 94 * 94 = 8836 square feet
Find the number of ways to listen to 4 different cds from a selection of 15 cds.
Answer:
The First person who answered it was wrong! Its 32,760 I took the test lol!
Step-by-step explanation:
nPr = n!/(n-r)! <-- The equation used for this.
Alive the equation 2 k+2= k+1
Find the length of the missing side. The triangle is not drawn to scale.
A. 36
B. 6
C. 4
D. 13
The human eye blinks about 6.25x10 to the 6th power times each year. A seal blinks about 1.01x10 to the 3rd power times per year. How many times do a human and a seal blink in one year?
The human eye blinks about [tex]\( 6.25 \times 10^6 \)[/tex] times each year, and a seal blinks about [tex]\( 1.01 \times 10^3 \)[/tex] times per year.
To find out how many times a human and a seal blink in one year, we simply take the given values for each. The question provides us with the number of times a human eye blinks in one year as [tex]\( 6.25 \times 10^6 \)[/tex]times. Similarly, it gives us the number of times a seal blinks in one year as [tex]\( 1.01 \times 10^3 \)[/tex] times.
Therefore, without the need for any additional calculations, we can state that in one year:
- A human blinks [tex]\( 6.25 \times 10^6 \)[/tex] times.
- A seal blinks [tex]\( 1.01 \times 10^3 \)[/tex] times.
These values are already given in the question and represent the total number of blinks for each species in a year. No further calculations are required to answer the question as it is asking for the number of blinks in one year, which is directly provided.
Quadrilateral $abcd$ is a parallelogram. if the measure of angle $a$ is 62 degrees and the measure of angle $adb$ is 75 degrees, what is the measure of angle $adc$, in degrees?
In the given parallelogram ABCD, angle $a$ is 62 degrees and angle $adb$ is 75 degrees. Angle $bd$ is calculated to be 105 degrees making angle $adc$ the supplementary to $bd$, and therefore also 75 degrees.
Explanation:In a parallelogram, opposite angles are equal and consecutive angles are supplementary (adding up to 180 degrees). In your given quadrilateral $abcd$, the measure of angle $a$ is 62 degrees and $a$ and $adb$ are consecutive angles. Therefore, knowing that angle $adb$ is 75 degrees, angle $bd$ should be the supplementary to $adb$, which is 180 - 75 = 105 degrees. Finally, since $adc$ is a straight line and $bd$ and $dc$ are parts of it, therefore angle $dc$ = 180 - angle $bd$ = 180 - 105 = 75 degrees. So, the measure of angle $adc$ is 75 degrees.
Learn more about Angles in a Parallelogram here:https://brainly.com/question/16578666
#SPJ12
What type of equation would best model this data
What is the right answer to this?
A carpenter is building a bookcase. The perimeter of the top is 108 in. If the width is 8 in., what is the length of the shelf?
The function f(x) = –x2 + 60x – 116 models the monthly profit, in dollars, a shop makes for repairing windshields, where x is the number of windshields repaired, and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points) Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
Answer:
I believe Homer "the genius" math to be incorrect for Part A. (-30)^2+60(30)-116= 900+1800-116=2584; not 784 as he got -900 when squaring -30.
Step-by-step explanation:
a factor of the quadratic 6x2-11x-35
What is the slope of y-9=-2(x-8)
The table below represents the displacement of a horse from its barn as a function of time:
Time(hours) x.
0
1
2
3
4
Displacement from barn (feet) y
8
58
108
158
208
part a: what is the y-intercept of the function, and what does this tell you about the horse? part b: calculate the average rate of change of the function represented by the table between x=1 to x=3 hours, and tell what the average rate represents. part c: what would be the domain of the function of the horse continued to walk at this rate until it traveled 508 feet from the barn?
PLEASE HELP!! WILL RATE BRAINLIEST!!
A. The y-intercept (b) of a linear equation is obtained when x = 0. Therefore from the given table,
y - intercept = 8
Since at time zero the displacement is 8 ft, this means that the horse was already outside the barn initially.
B. The average rate of change of the function represents the slope of the linear equation (m). This can be calculated using the formula:
average rate of change = m = (y2 – y1) / (x2 – x1)
m = (158 – 58) / (3 – 1)
m = 50
C. Since we have determine the y-intercept and the slope, we can formulate the linear equation:
y = m x + b
y = 50 x + 8
The domain is the value of x. When y = 508, x is equivalent to
508 = 50 x + 8
x = 10 hrs
What is the simplified form of the quantity of x plus 5, all over the quantity of 9 − the quantity of x plus 4, all over the quantity of x plus 6
fgh is a right triangle
Answer:
there is no picture
Step-by-step explanation:
What is the factored form of 2x2 − 7x − 15? (2x + 3)(x − 5) (2x + 5)(x − 3) (2x − 7)(x + 8) (2x + 8)(x − 7)
Write a compound inequality that represents the situation:
all real numbers at least -6 and at most 3
A) -6 < x ≤ 3
B) -6 ≤ x ≤ 3
C) -6 ≥ x ≥ 3
D) -6 < x < 3
help me please help me
What is [tex] 3\sqrt{18} [/tex] + [tex] 2\sqrt{50} [/tex] simplified?
F.[tex] 19\sqrt{2} [/tex]
G.[tex] 39\sqrt{2} [/tex]
H.[tex] 77\sqrt{2} [/tex]
I. [tex] 90\sqrt{2} [/tex]
IF THERE IS WORK PLEASE SHOW THANKS:)
What is the solution set of the equation x^2 - 7x - 18 = 0
Factoring this trinomial as the product of two binomials,
we have (x - 9)(x + 2) and set that equal to 0.
So we have (x - 9)(x + 2) = 0.
So either x - 9 = 0 or x + 2 = 0.
Solving for x in each equation, we find that our solution is {9, -2}.
Find the function h(x) = f(x) ∘ g(x) if f(x) = x(2 - x) and g(x) = 3x.
h(x) = 0
h(x) = -32x
h(x) = 2(32x)
h(x) = 3x(2 - 3x)
Answer: h(x) = 3x(2 - 3x)
Step-by-step explanation:
Here the given functions are,
[tex]f(x) = x(2-x)[/tex]
[tex]g(x) = 3x[/tex]
[tex]h(x) = f(x) \circ g(x) = (f\circ g)(x) = f[g(x)][/tex]
[tex]= f( 3x )[/tex]
[tex]= (3x)[2-(3x)][/tex]
[tex]= 3x(2-3x)[/tex]
Hence,
[tex]h(x) = 3x(2-3x)[/tex]
⇒ Fourth option is correct.
What is -4x - 5x <18 need help
which equation represents the statement thirteen less then a number is forty two
Answer:
The equation which represents the statement thirteen less then a number is forty two is:
x-13=42
Step-by-step explanation:
Let x be any number
we are given that:
thirteen less then a number is forty two
i.e. x-13=42
Hence, the equation which represents the statement thirteen less then a number is forty two is:
x-13=42