The trees at a national park have been increasing in numbers. There were 1,000 trees in the first year that the park started tracking them. Since then, there has been one fifth as many new trees each year. Create the sigma notation showing the infinite growth of the trees and find the sum, if possible.
1 1000
2 200
3 40
Answers
Term 1: 1000
Term 2: 200
Term 3: 40
From term 1 to term 2, there's a decrease by [tex] \frac{1}{5} [/tex]
From term 2 to term 3, there's a decrease also by [tex] \frac{1}{5} [/tex]
The rule to find the [tex]n^{th} [/tex] term in a sequence is
[tex]n^{th}=a r^{n-1} [/tex], where [tex]a[/tex] is the first term in the sequence and [tex]r[/tex] is the ratio
So, the formula for the sequence in question is
[tex]n_{th} [/tex] term = [tex]1000( \frac{1}{5} ^{n-1} )[/tex]
The sequence is a divergent one. We can always find the value of the next term by dividing the previous term by 5 and if we do that, the value of the next term will get closer to 'zero' but never actually equal to zero.
We can find a partial sum of the sequence using the formula
[tex]S_{∞} = \frac{a}{1-r} [/tex] for -1<r<1
Substituting [tex]a=1000[/tex] and [tex]r= \frac{1}{5} [/tex] we have
[tex] S_{∞} [/tex] = [tex] \frac{1000}{1- \frac{1}{5} } [/tex] = 1250
Hence, the correct option is option number 1
Answer:
A
Step-by-step explanation:
Related Questions
If csc 0=8÷7 which equation represents cot 0
Answers
Answer: [tex]Cot\theta =\frac{\sqrt{15} }{7}[/tex]
Step-by-step explanation:
Since, given [tex]cosec\theta=\frac{8 }{7}[/tex]
And we know that [tex]Cot\theta=\sqrt{cosec^2\theta-1}[/tex]
Therefore, [tex]Cot\theta=\sqrt{cosec^2\theta-1} = \sqrt{(8/7)^2-1}= \sqrt{64/49-1}[/tex]
⇒[tex]Cot\theta=\sqrt{64-49/49}=\sqrt{15/49}=\sqrt{15}/7[/tex]
Thus, [tex]Cot\theta =\frac{\sqrt{15} }{7}[/tex]
Answer:
CotA=√15/7
Step-by-step explanation:
cosecA=8/7=hypotenuse/perpendicular
We have to find cotA
We do this by right angled triangle
We use pythagoras theorem to find the base
Base²+Perpendicular²=hypotenuse²
Base²+7²=8²
Base²=15
Base=√15
cotA=Base/Perpendicular
= √15/7
The three sides of sail A are each half the length of the three sides of sail B. How do the areas of the two sails compare?
Answers
Area of sail A is 1/4 of area of sail B
Answer:
Step-by-step explanation:
It is B
Find the area of the shaded region.
Answers
To find the area of a rectangle, multiply base times height.
5 x 10 = 50
Now we need to subtract the area of the non-shaded part.
2 x 2 = 4
50 - 4 = 46
The answer is 46
Hope this helps! :)
Hope the explanation helped!
Please Help! Math Question!
Variable g is 8 more than variable w. Variable g is also 4 less than w. Which pair of equations best models the relationship between g and w?
A) g = w − 8
g = w + 4
B) w = 8g
w = g − 4
C) g = w + 8
g = w − 4
D) w = 8g
w = g + 4
Answers
g = 8 more than w
g = 8+w
g = w+8
"g is also 4 less than w" means
g = 4 less than w
g = w-4
The two equations are therefore:
g = w+8
g = w-4
which means the answer is choice C
Answer:
The answer is C.
g = w + 8
g = w − 4
Hope This Helps!
How do you explain how to get h(t)=7(t-25)
Answers
To Solve for t.
[tex]h(t)=7(t-25)[/tex]
Distribute the brackets.
[tex]h(t)=7*t-7*25[/tex]
[tex]h(t)=7t-175[/tex]
Subtract 7t from both sides.
[tex](h(t))-7t=(7t-175)-7t[/tex]
[tex](h(t)-7t=-175[/tex]
[tex]h*t-7t=-175[/tex]
Factor out variable, t.
[tex]t(h-7)=-175[/tex]
Divide both sides by h-7.
[tex](t(h-7))/h-7=(-175)/h-7[/tex]
[tex]t=-175/h-7[/tex]
Hope this helps!
-Benjamin
What is the are of the triangle below??
Answers
it is 9 squares high and the base is 6 squares wide
9*6 = 54
54/2 = 27
area = 27 square units
The water level of a river is 170 feet. The river recedes 4 feet each year. Ingrid claims that the equation that represents this scenario is y = 170x – 4. Is her equation correct? Explain
Answers
Sample Answer: No, Ingrid is incorrect. The initial value in the scenario is 170 feet, which represents the y − intercept. Receding 4 feet in the scenario represents the rate of change, which is the slope. In slope-intercept form, y = mx + b, where m represents slope and b represents the y−intercept, so the correct equation is y = −4x + 170.
Answer:
No, Ingrid is incorrect. The initial value in the scenario is 170 feet, which represents the y − intercept. Receding 4 feet in the scenario represents the rate of change, which is the slope. In slope-intercept form, y = mx + b, where m represents slope and b represents the y−intercept, so the correct equation is y = −4x + 170.
Step-by-step explanation:
why is a stem and leaf plot called a stem and leaf plot?
Answers
Stem = the first digit, or digits
Leaf = the last digit
Ex: The stem of 32 would be 3 and the leaf would be 2.
A stem-and-leaf plot gets its name from the way the data is structured. The 'stem' represents the highest place value digits of the numbers in the dataset, and the 'leaf' represents the lower place value digits. These plots keep the actual numerical data intact, providing more detail than other data representations like bar graphs or histograms.
Explanation:The term stem-and-leaf plot, also known as a stemplot, originates from the way data is structured in this type of graphical representation. The 'stem' in a stem-and-leaf plot stands for the highest place value digits of the numbers in the dataset, similar to the stem of a plant that holds up the leaves. The 'leaf' stands for the lower place value digits, similar to the leaves that extend from the stem. For example, in a dataset [23, 24, 33, 35], 2 and 3 would be stems, and the various units (3, 4 for 2 and 3, 5 for 3) would be leaves.
One of the main purposes of a stem-and-leaf plot is that it keeps the actual numerical data intact, as opposed to other graphical representations like bar graphs or histograms which group data into classes, thus providing a more detailed view of the data distribution.
Learn more about stem-and-leaf plot here:https://brainly.com/question/32830750
#SPJ12
What is the solution to the inequality l2n+5l > 1
Answers
l2n+5l > 1
(2n+5) > 1
2n > - 4
n > -2
-(2n+5) > 1
-2n - 5 > 1
-2n > 6
n < -3
answer
n<-3 or n>-2
How to divide fractions
Answers
For example:
3/7÷ 5/8 = 3/7×8/5
Dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division sign to multiplication and flip the second fraction. Let's try an example.
[tex]\frac{1}{2}[/tex] ÷ [tex]\frac{5}{9}[/tex] can be rewritten as [tex]\frac{1}{2}[/tex] × [tex]\frac{9}{5}[/tex].
Now, we are simply multiplying fractions.
Multiply across the numerators and the denominators
[tex]\frac{1}{2}[/tex] × [tex]\frac{9}{5}[/tex] = [tex]\frac{9}{10}[/tex]
Therefore, [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{5}{9}[/tex] = [tex]\frac{9}{10}[/tex]
(03.01)
A newly made car will have a model number, a parts number, and a serial number. A model number is assigned by the manufacturer to identify each type of car. A parts number identifies one part of the smaller parts that make up the car. A serial number is unique to each car produced and identifies it.
Which relation is a function?
(parts number, serial number)
(model number, parts number)
(serial number, model number)
(serial number, part number)
Answers
Answer:
Hi!
The corrects answers are:
•(serial number, model number)
Step-by-step explanation:
First, you have to understand the meaning of a function, that is an a relation but have the condition:
The input must be relationed with only one output.
The question says:
"A serial number is unique to each car produced and identifies it." so this will be you input, and will be related with only one model number.
The graph of f(x) = x3 – 6x2 + 9x is shown. Based on the graph, what are the solutions of the equation x3 – 6x2 + 9x = 0? x = 3 x = –3, 0 x = 0, 3 x = –3, 0, 3
Answers
f(x) = x3 – 6x2 + 9x
the solutions of the equation x3 – 6x2 + 9x = 0 are : 0 , 3
because : f(0) 0 and f(3) = 0
The solutions of the equations [tex]x^3-6x^2+9x=0[/tex] is:
x=0 or x=3
Step-by-step explanation:The solutions of the graph of the equation are the possible values of x at which the graph meets the x-axis at a point.
The function f(x) is given by:
[tex]f(x)=x^3-6x^2+9x[/tex]
The function f(x) could also be written as:
[tex]f(x)=x^3-3x^2-3x^2+9x\\\\i.e.\\\\f(x)=x^2(x-3)-3x(x-3)\\\\i.e.\\\\f(x)=(x^2-3x)(x-3)\\\\i.e.\\\\f(x)=x(x-3)(x-3)[/tex]
i.e. If
[tex]f(x)=0[/tex]
then
[tex]x(x-3)(x-3)=0\\\\i.e.\\\\x=0\ or\ x=3[/tex]
By the help of the graph we may observe that the function meets the x-axis at x=0 or x=3.
A video game sets the points needed to reach the next level based on the function g(x) = 12(2)x − 1, where x is the current level. The hardest setting promises to multiply the points needed in each level according to the function h(x) = 3x. How many points will a player need on the hardest setting of level 6?
A 18 points
B 384 points
C 4020 points
D 6912 points
Answers
The difference of twice a number g and 10 is 24
Answers
How to find csc theta where theta equals -120
Answers
= -sin 60 = -sqrt3/2
csc is 1/sine so ur answer is -2/sqrt3
Answer:
[tex]\frac{-2}{\sqrt{3} }[/tex]
Step-by-step explanation:
Cosec of -120 is to be found out
We can do this in steps
cosec (-120) consider only the - sign.
This implies angle lies in IV quadrant and hence cosec is negative
cosec (-120) =-cosec (120)
Now 120 is written as 180-60
cosec (-120) =- cosec(180-60)
=-cosec 60
(since II quadrant cosec is positive)
= [tex]\frac{-2}{\sqrt{3} }[/tex]
Spencer Ward purchased a new riding mower for $1,989. He made a 15% down payment and financed the remainder. What amount did he finance?
Answers
1,989×0.15=298.35
Amount financed is
1,989−298.35=1,690.65
A rectangular table with sides in the ratio 3:5 has a perimeter equal to 240 inches. what is the area of the table in square inches?
Answers
Total ratio=8
length=5/8*240=150 inches
width=3/8*240=90 inches
The area of the table will be:
A=length*width
=150*90
A=13,500 square inches
Which inequality describes the graph?
Answers
The line is the same in all answers, so you may look at the inequality signs. The shaded area is on top, this means greater than, and the line is not dashed, so it belongs to the solution: greater or equal than
Also, the division between the two is solid so it can be "equal to".
The answer is D
A diagonal of a cube measures 30 inches. The diagonal of a face measures 600 SQUARE ROOTED inches. In inches, what is the length of an edge of the cube? Round the answer to the nearest tenth. HOW MANY? inches
Answers
d^2=x^2+y^2+z^2 but since we are dealing with a cube, x=y=z=s where s is a side lenght...
d^2=3s^2 and we are told that the diagonal is 30 in. so
3s^2=30^2
3s^2=900
s^2=300
s=√300
s=10√3 in. exact
s≈17.3 in. (to the nearest tenth of an inch)
Answer:
The correct answer is 17.3
Step-by-step explanation:
Let me know if it helped you
James, caleb and abigail bought a pizza. james ate 1/6 of the pizza, caleb ate 1/4 of the pizza what fracion did james and caleb eat together
Answers
[tex] \frac{1}{6} + \frac{1}{4} [/tex]
You have to multiply the 6 by 2 to get to 12, so you have to multiply the 1 by 2 to get the equivalent fraction of 2/12. Do the same with the 1/4: you have to multiply 4 by 3 to get to 12, so you have to multiply the 1 by 3 to get to the equivalent fraction of 3/12.
[tex] \frac{2}{12} + \frac{3}{12}= \frac{5}{12} [/tex]
Given the following geometric sequence, find the common ratio: {225, 45, 9, ...}.
5
-5
1/5
-1/5
Answers
so
common ratio in 225 and 49 and 9 is
49/225 or 9/45=1/5
the common ratio is 1/5
Answer:
1/5
Step-by-step explanation:
A student solved a system of equations by elimination. The answer is not correct. Describe the error made in the part of the solution shown.
Answers
The error made in the part of the solution is when equation (2) is multiplied by -4 it is not multiplied both side .
What is elimination method?The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.
According to the question
5x + 4y= 2 ------------------- (1)
3x + 3y = -3 ------------------- (2)
Now,
solving both equation by elimination method
Multiplying equation (1) by 3 and by 2 to equation (-4)
So, y can be eliminated
3(5x + 4y)=2 * 3
15x + 12y = 6 -------------- (3)
-4(3x + 3y) = -3*-4
-12x - 12y = 12 -----------------(4)
Now,
Adding both eq(3) and (4)
3x = 18
x = 6
Putting value of x in eq(1)
5*6 + 4y = 2
30 + 4y = 2
4y = 2 - 30
4y = - 28
y = -6
Hence, the error made in the part of the solution is when equation (2) is multiplied by -4 it is not multiplied both side .
To know more about elimination method here:
brainly.com/question/14619835
#SPJ2
a rectangular room measures 3.8 meters in length and 4.9 meters in width. Jana multiples both numbers together. Which expression would be best for her to use to check the reasonableness of her decimal multiplication?
A) 3x4
B)3x5
C)4x4
D)4x5
Answers
Answer:
d 4 x 5
Step-by-step explanation:
round
if trapezoid jklm is translated according to the rule (x,y) ,(x+8,y-3) what are the coordinates of point L
Answers
-5 + 8 = 3
-2 - 3 = -5
New coordinates of L: (3, -5)
Hope this helps :)
Please give brainliest
With the given translation rule, to find new coordinates of a point L in trapezoid JKLM, apply it to the original coordinates by moving right by 8 units and down by 3 units. If original coordinates of L were (2,5), new coordinates will be (10,2).
Explanation:In geometry, a translation is a type of transformation that slides a figure along a straight line. In this case, the translation rule given is (x, y) -> (x+8, y-3). This means that every point in the trapezoid is being moved 8 units to the right (increase in x-coordinate) and 3 units down (decrease in y-coordinate).
Per your question, to find the new coordinates of point L after the translation, you simply need to apply this rule to the original coordinates of point L. If for example, the original coordinates of point L were (2, 5), its new coordinates after the translation would be calculated as follows: (2+8, 5-3) = (10, 2).
This is how you find the new coordinates of a point after a translation in geometry.
Learn more about Translation in Geometry here:https://brainly.com/question/32226769
#SPJ3
Identify the x-intercept and y-intercept of the line
4x−2y=−12
4x−2y=−12
.
Select one:
a. The x-intercept is (0,-3) and the y-intercept is (6,0).
b. The x-intercept is (-3,0) and the y-intercept is (0,6).
c. The x-intercept is (4,0) and the y-intercept is (0,-2).
d. The x-intercept is (0,6) and the y-intercept is (-3,0).
Answers
-2y = -4x - 12
y = 2x + 6
The y-intercept is b, in the equation y = mx + b.
So that means here the y-intercept is 6.
Now to get the x-intercept, you need to put the y at 0.
0 = 2x + 6
-6 = 2x
-3 = x
X-intercept is -3.
Also remember that the x and y intercepts look like this: (x, y). For the x-intercept, the y has to be at 0. For the y-intercept, the x has to be at 0.
So the answer is B.
The x-intercept is (-3,0) and the y-intercept is (0,6).
The correct option is B,
What are intercepts?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
Given information:
4x - 2y = -12.
To find the x-intercept, we set y to zero and solve for x:
4x - 2y = -12
4x - 2(0) = -12
4x = -12
x = -3
So the x-intercept is (-3, 0).
To find the y-intercept, we set x to zero and solve for y:
4x - 2y = -12
4(0) - 2y = -12
-2y = -12
y = 6
So the y-intercept is (0, 6).
Therefore, the answer is b. The x-intercept is (-3,0) and the y-intercept is (0,6).
To learn more about the intercepts;
https://brainly.com/question/14180189
#SPJ2
A parabola is defined by the equation (x − 5)2 = 12(y + 2). In which direction will the parabola open? upward downward right left
Answers
Answer:
From the given expression of parabola, it is clear that the parabola is upward opening.
Step-by-step explanation:
Concept: In the equations of parabolas, when the expression having x variable has the power of 2, then the parabola opens in the y-axis. The equation of parabola is of the form X² = 4aY.
In this case, if a > 0, then the parabola opens in the upward direction.
Given equation is (x - 5)² = 4×3(y + 2). Here the expression of x has the power 2 and a = 3 > 0. So, the parabola is upward opening.
For more explanation, refer the following link:
https://brainly.com/question/1390640
#SPJ10
Final answer:
The given parabolic equation has a positive coefficient for the (y + 2) term, indicating that it opens upward.
Explanation:
The equation given is in the form of a transformed parabolic equation, which can be identified as [tex](x - h)^2 = 4p(y - k),[/tex]where the vertex of the parabola (h,k) and the value of p determine the direction in which the parabola opens.
In the equation [tex](x - 5)^2 = 12(y + 2),[/tex] the presence of the squared term on x and the fact that the coefficient of the (y + 2) term is positive indicates that the parabola opens upward.
In this case, if a > 0, then the parabola opens in the upward direction.
The coefficient of the squared term is 4p, which in this case is positive, confirming the direction of the parabola as opening upwards.
Davis electronics manufactures a certain type of radio that requires 15 working resistors per radio. If one out of 25 resistors is defective, are 30,150 resistors enough to assemble 1922 radios?
Answers
Therefore,
15/1 ≤ 30150(24/25)/1922
15 ≤ 15.06
The symbol '≤' means less than or equal to. It is the inequality to be used because 15/1 is the minimum limit. As long as the ratio is equal to 15 or more than 15, then 30,150 is enough to make 1,922 radio. Since it is true that 15.06 is greater than 15, then the amount of resistors would be enough.
No, 30,150 resistors are not enough to assemble 1922 radios.
To determine if 30,150 resistors are enough to assemble 1922 radios, we need to calculate the total number of resistors required and then account for the defective resistors.
First, let's calculate the total number of resistors needed for 1922 radios. Since each radio requires 15 resistors, the total number of resistors required is:
[tex]\[ 1922 \text{ radios} \times 15 \text{ resistors/radio} = 28830 \text{ resistors} \][/tex]
Next, we need to account for the defective resistors. Given that one out of every 25 resistors is defective, we can calculate the number of defective resistors in a batch of 28830 resistors. However, to simplify the calculation, we can calculate the number of non-defective resistors we expect to get from every 25 resistors. Since 24 out of 25 are expected to be non-defective, we have:
[tex]\[ \frac{24}{25} \[/tex] { non-defective resistors per 25 resistors}
To find out how many non-defective resistors we would get from 28830 resistors, we multiply the total number of resistors by the ratio of non-defective to total resistors:
[tex]\[ 28830 \times \frac{24}{25} = 28224 \[/tex] { non-defective resistors}
Now, we compare the number of non-defective resistors needed (28830) to the number of non-defective resistors we can expect to have (28224). We find that:
[tex]\[ 28830 - 28224 = 606 \text{ resistors} \][/tex]
This means we are short by 606 non-defective resistors to assemble all 1922 radios. Therefore, 30,150 resistors are not enough.
To confirm this, let's calculate the total number of resistors needed including the defective ones. Since we know that for every 28830 non-defective resistors we need 1/25 more to account for the defective ones, we have:
[tex]\[ 28830 \times \frac{25}{24} = 30156.25 \text{ resistors} \][/tex]
This shows that we actually need more than 30,150 resistors to account for the defective ones and meet the requirement for 1922 radios. Hence, the answer is no, 30,150 resistors are not enough."
There are 40 vehicles in a parking lot.Twenty percent of the vehicles are pickup trucks.How many pickup trucks are in the parking lot?
Answers
20% of 40....turn ur percent to a decimal..." of " means multiply
0.20(40) = 8.....there are 8 pickup trucks <==
8 times the total of x and 3
Answers
Answer: The expression would be [tex]8x+24[/tex]
Step-by-step explanation:
Since we have given that
8 times the total of x and 3
total of x and 3 means sum of x and 3.
Mathematically it is expressed as
[tex]x+3[/tex]
Now, 8 times the above sum.
Mathematically, it is written as
[tex]8(x+3)\\\\=8x+24[/tex]
Hence, the expression would be [tex]8x+24[/tex]
Determine the domain of the function. f(x) is equal to four divided by x squared.
A. x ≥ 0
B. All real numbers except 0
C. All real numbers except 3
D. All real numbers
Answers
Think what values of x give real values of f(x)
negative numbers are Ok andso are positive ones
What about x = 0? What is the value of 4 / (0)^2 ?