A monkey is swinging from a tree. On the first swing, she passes through an arc of 10 m. With each swing, she passes through an arc 9/10 the length of the previous swing.
What is the total distance the monkey has traveled when she completes her 25th swing? Round your final answer to the nearest meter.
The total distance the monkey has traveled when she completes her 25th swing is 92.82 m if the monkey is swinging from a tree.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have:
A monkey is swinging from a tree. On the first swing, she passes through an arc of 10 m. With each swing, she passes through an arc 9/10 the length of the previous swing.
In first swing = 10 m
In second swing = (9/10)10 m = 9 m
In the second swing = (9/10)9 =81/10
10, 9, 81/10,..
This is the geometric sequence with the first term being 10 and the common ratio being 9/10.
a = 10
r = 9/10
The sum of geometric sequence up to 25th terms:
S = a(1 - rⁿ)/(1 - r)
S = 10(1 - (9/10)²⁵)/(1 - 9/10)
S = 92.82 m
Thus, the total distance the monkey has traveled when she completes her 25th swing is 92.82 m if the monkey is swinging from a tree. On the first swing, she passes through an arc of 10 m. With each swing, she passes through an arc 9/10 the length of the previous swing.
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Please answer these two question please please I need helpppppp
Answer:
Step-by-step explanation:
10.
a. y=30x + 50
b. 30(2.5)+50= 125
c. y= 60x+100
d. 60(2.5)+100= 250
Answer:
10)
a) y = 50+30x
b) y=50+30(2.5)
50+75 = 125
c) y = 2(50+30x)
d) y=2(50+30(2.5))
2(50+75)
2(125) = 250
13)
a) P = 2 ( L + W )
10x+2
b) A = W L
5x+1
c) for A its 15x+3 and for B its 54 x 2 + 18 x
PLEASE HELP SOON AND TRY TO EXPLAIN.
Prove that if a, b, c, d are non zero real numbers, not all equal, and if a+1/b=b+1/c=c+1/d=d+1/a then |abcd|=1. Thx!
Answer:
because any number over 0 is 0 and if |abcd|=1 that it is not possible to be 0
Step-by-step explanation:
HELP ASAP! PLSS! 1 over 3b = 4 over 5. Which of the following equals b in this equation?
22 over 5
11 over 8
2 over 5
1 over 4
Rearrange the equation so xxx is the independent variable.
-5x-4y=-8
y=
Answer:
[tex]\displaystyle x = \frac{4y - 8}{-5}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle -5x - 4y = -8[/tex]
Step 2: Solve for x
[Addition Property of Equality] Add 4y on both sides: [tex]\displaystyle -5x = 4y - 8[/tex][Division Property of Equality] Divide -5 on both sides: [tex]\displaystyle x = \frac{4y - 8}{-5}[/tex]Answer:
4y-8/ -5
Step-by-step explanation:
An adult ticket is twice the cost of a child's ticket. Angela paid $ 28 for two adult tickets and three children's tickets. Which of the
following equations could be used to find the price of a child's ticket?
(A) x + 2x = 28
(B) 3x + 2(2x) = 28
(C)3(2x) + 2x = 28
(D) 3x + 2x = 28
The following equations could be used to find the price of a child's ticket, 3x + 2(2x) = 28, the correct option is B.
What is an Equation?An equation is a mathematical statement formed when two expressions are equated using an equal sign.
The equations are useful in determination of unknown parameters.
The equations are of various types, such as Trigonometric equations, quadratic equations.
The system of equations are used to solve complex problems.
Let the cost of child ticket is $x
An adult ticket is twice the cost of a child's ticket.
Let the cost of adult ticket is $2x
The total amount Angela paid is $28 for two adult tickets and three children's tickets.
The equation that will be formed is
4x + 3x = 28
It can also be written as 3x + 2(2x) = 28.
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Write an absolute value equation to satisfy the given solution set shown on a number line.
<————•—————————-•——————->
-1/2 1/2 a
Thanks!
An absolute value equation to satisfy the given solution set shown on a number line is -1/2 ≤ a ≤ 1/2.
What is magnitude and sign?A number has both magnitude(its absolute value) and its sign(positive or negative).
Thus, for -5, the magnitude is 5, and sign is –ve.
Also, positive numbers > 0 > negative numbers.
In the number line we can clearly see that our possible values of a are in the range:
-1/2 ≤ a ≤ 1/2
And we need to find an absolute value equation such that this set is the set of possible solutions.
An example can be:
Ia - 1/2I ≤ 1/2
Notice; using the minor and equal sign, this is because the black dots means that the values a = -1/2 and a = 1/2 are included, if the dots were empty dots, it would be an open set and we should use the < > signs.
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There are 20 children at a library. Six of the children have an average age of 5 years. The remaining children have an average age of 8 years. What is the average age of the children at the library?
Answer:
7.1
Step-by-step explanation:
6 children with an average age of 5 = 6*5 = 30 so the sum of their ages is 30
20 - 6 = 14
14 children have an average age of 8 14*8 =112 so the sum of their ages is 112
Add the two sums
30+112 = 142
Divide by the total number of children
142/20 =7.1
The average age of all the 20 children is 7.1
Answer: 7.1
Step-by-step explanation:
There is a blueprint for a house that is a scale drawing for the entire house. One part of the house has a triangular base. The drawing of the width of the triangle is 4cm and the length is 6cm. If the width of
On a coordinate plane, a curved line with a minimum value of (0.6, 2.5) and a maximum value of (negative 1.2, 18.3), crosses the x-axis at (negative 1.8, 0) and crosses the y-axis at (0, 5).
What is x when f(x)=0?
-1.8
-1.2
0
5
given m=-2 and y intercept (0,-2) find the equation of the line in standard form.
Answer:
the answer is -2x-y=2
Step-by-step explanation:
Ax+By=C
y=mx+b
y=2x-2
-2x-y=2
Answer:
y=−2x−2
Step-by-step explanation:
Fill in the blanks to complete the steps and solve the equation in the image attached.
S is being divided.
What is the opposite of subtracting 5?
Move 5 to the right side.
It is being divided by 6. What is the inverse of dividing by 6.
Multiply each side by 6.
Hope this helps!! :)
Modeling Real Life
Question:
At a town hall meeting, 37/50 of the members are present. Of those who are present, 1/2 vote in favor of a new park. What fraction of the members do not vote in favor of the new park?
Fraction:_______
William has a 26-liter glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with water until it's completely full. If he uses 85 marbles, he will have to add 20.9 liters of of water.
What is the volume of each marble?
How much water is necessary if William uses 200 marbles?
Answer: 0.06/marble | 14 liters
The volume of the marbles is 26-20.9 = 5.1 l and there ar e85 marbles
5.1/85 = .06 l/marble
then 200 marbles would requrie .06 l/marble x 200 marbles = 12 liters
so he would only need 26-12= 14 liters of water to fill the tank !
Answer:
14 marbles
Step-by-step explanation:
Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form or standard form. Express numbers as integers or simplified fractions.
The line passes through the point (-6, -2) and has a slope of 9.
Step-by-step explanation:
Given the following configurations, the followed may be constructed and fabricated into the following:
Point-Slope Form:
Point: (-6, -2).
Slope: 9
Y - y1 = m(x - x1)
Y + 2 = 9(x + 6)
Y + 2 = 18x + 48
Y = 18x + 46 <== Slope-Intercept Form.
-18x + y = 46 <== Standard (General) Form.
Thus, the ameliorated answer, subject to the proposed interrogated is identified as Y = 18x + 46, whom is the Slope-Intercept Form format, as well as -18x + y = 46, whom is, likewise, identified as the Standard (General) Form.
*I hope this helps.
Answer:
Given the following configurations, the followed may be constructed and fabricated into the following:
Point-Slope Form:
Point: (-6, -2).
Slope: 9
Y - y1 = m(x - x1)
Y + 2 = 9(x + 6)
Y + 2 = 18x + 48
Y = 18x + 46 <== Slope-Intercept Form.
-18x + y = 46 <== Standard (General) Form.
Thus, the ameliorated answer, subject to the proposed interrogated is identified as Y = 18x + 46, whom is the Slope-Intercept Form format, as well as -18x + y = 46, whom is, likewise, identified as the Standard (General) Form.
*I hope this helps.
Step-by-step explanation:
Hey! Can anybody help? I’m stuck on this question
Some 10-13 year olds were asked where to buy snacks. If 12% or 24 children, said a convenience store, how many children were asked to buy snacks?
Answer:
200 children
Step-by-step explanation:
so 12% is 24 children
12/24
simplify
1/2
1% is 2 children
multiply 1% by 100 to get 100%, along with 2 for the children
200 children
Si a cero se le resta cualquier número entero el resultado siempre es el
mismo número, pero con signo positivo.
Please comment this in english.
explain how to find the difference between 9^10/9^11 and 9^11/9^10
Answer:
jhv
Step-by-step explanation:
kjbb
Solve the word problem in the picture attached
In triangle JKL, JKL is a right angle, KM and is an altitude. JL=20 and ML=15, find KL
Answer:
KL = 17.32
Step-by-step explanation:
KL² = (M L)(J L)
KL² = (15)(20)
KL²=300
√KL²= √300
KL = 17.32
Rewrite 18y • 4x using the commutative property.
Answer:
(1)18y x 4x(1)
Step-by-step explanation:
A veterinarian asked each of her 18 patrons if they have a dog. She also asked each patron if they have a
cat. The Venn diagram below shows the data she collected.
Complete the following two-way frequency table
Answer:
7(top left) 5(top right)
6(bottom left) 0(bottom right)
Answered by GAUTHMATH
What is the Tenth COMMON FACTOR of 6 and 9? (DO NOT respond with the LCM of 6 and 9)
50 POINTS
My neighborhood is full of one-way streets. To drive from my house to the grocery store, I have to go 1 block south, then 1 block east, then 5 blocks north, then 2 blocks east. Each block is 1/16 of a mile. How much shorter would my trip be if I could fly like a bird (that is, travel in a straight line)?
I FOUND THE distance for non bird which is 9/16. I wanna apply the pythagoreum theorum and draw a straight line to make it a triangle so I can do so but don't know where to place it
Please help with these two problems and give an accurate explanation. Thank you!
The domain is all of the x-values a function can have. The range is all of the y-values a function can have.
#50.
Domain: [-5, 10]
---The function starts at the x-value -5 and stops at the x-value 10.
Range: [-3, 5]
---The smallest y-value is -3 and the largest y-value is 5.
#51.
Domain: [-2, infinity)
---The function starts at the x-value -2 and has an arrow to indicate that it goes on forever.
Range: [0, infinity)
---The smallest y-value is 0 and an arrow indicates that the functions goes up and on forever.
Hope this helps!
Can anyone please help?
Answer:
see below
Step-by-step explanation:
<4 and <7 are same side interior angles since they are on the same side of the transversal p and between parallel lines m and n
<4 and <12 are corresponding angles since they are on the same side of the parallel lines p and t and on the same side of the transversal m
<14 and <7 are alternate interior angles since they are between the parallel lines p and t and are on opposite sides of the transversal n
<4 and <1 are vertical angles since they are formed by the same lines and share a vertex and are opposite each other
Answer:
<4 and <7 are same side interior angles since they are on the same side of the transversal p and between parallel lines m and n
<4 and <12 are corresponding angles since they are on the same side of the parallel lines p and t and on the same side of the transversal m
<14 and <7 are alternate interior angles since they are between the parallel lines p and t and are on opposite sides of the transversal n
<4 and <1 are vertical angles since they are formed by the same lines and share a vertex and are opposite each other
Step-by-step explanation:
Find the slope of the line that passes through the points A(–3, 1) and B(2, –5).
PLZ ANSWER ACCURATELY AND QUICKLY WILL MARK BRAINLIEST
Answer:
- 6/5
Step-by-step explanation:
To find the slope
m = ( y2-y1)/(x2-x1)
= ( -5-1)/(2- -3)
= (-5-1)/(2+3)
- 6/5
Answer:
-6/5 or -1 1/5
Step-by-step explanation:
The formula to find the slope with any 2 points of a line is rise/run, or
(y2-y1)/(x2-x1)
In this case, y2 is -5, y1 is 1, x1 is -3, and x2 is 2.
So, the slope is:
(-5-1)/(2-(-3))
-6/5 which, as a mixed number, is -1 1/5.
You can also graph out the points on a coordinate plane, draw the line between the points, and count the rise/run, but that might take a minute or two, which is not the best if you have a timed test.
The animal shelter needs to split 6 1/2 pounds of dog food equally among the 13 dogs in the facility. How much dog food will each dog receive?
Answer:
1/2 pound for each dog.
Step-by-step explanation:
Don't get confused. There are only 2 numbers which will give 2 different answers: 2 and 1/2. Which one is correct?
You want the units to be pounds per dog or pounds/ number of dogs.
The numerator is 6.5
The denominator is dogs (13)
Food per dog = 6.5 / 13 = 1/2
Greshak Corp. reports the following revenues:
2015 $10,000,000
2016 $11,250,000
2017 $12,500,000
2018 $13,500,000
2019 $12,750,000
2020 $12,900,000
What was Greshak’s compound annual growth rate (CAGR) in revenues over the 6-year period 2015 through 2020?
Answer
around 10%
Step-by-step explanation:
