Answers
Number of shaded triangles in the second figure = 3
Number of shaded triangles in the third figure = 9
If we observe these values, we can conclude that a Geometric Series is being formed.First number is multiplied by 3 to get the second number and second number is multiplied by 3 to get the third number. So the summation can be expressed using the Geometric Series.
The summation uses the general term to express the sum over the interval. So first we find the general term of geometric series.
First term of the series = 1
Common ratio = 3
So, the general term of the series will be: [tex]1(3)^{n-1} [/tex]
This general term gives the terms of given geometric series for different values of n. For n = 1, we will have the first term which will is 1. Similarly for n=2, we will have the second term which is 3.
So the summation will start with first term and end on 15th term. Therefore, correct summation for this case is expressed by first option.
Related Questions
NEED HELP ASAP PLEASE
A 72° sector in a circle has an area of 16.4π yd².
What is the area of the circle?
Use 3.14 for pi.
Enter your answer as a decimal in the box.
Answers
Solution :
Give that, a 72° sector in a circle ,
Area of Sector in a circle =
[tex] \pi \times r^{2} \times( \frac{\theta}{360} )\\ \:\: where, r = radius\, of\, the\, circle\ \\ \theta = angle \,in \, degrees [/tex]
Suppose radius of circle is r .
then Volume of sector of circle
[tex] \pi \imes r^{2} \times (\frac{72}{360} )= 16.4\pi\\\\r^{2} = \frac{16.4 \pi}{\pi \times \frac{72}{360} } = \frac{16.4 \times 360}{72} [/tex]
Area of a Circle of radius, r, [tex] A = \pi\times r^{2} [/tex]
Put [tex] r^{2} = \frac{16.4 \times 360}{\times 72} [/tex]
Area of Circle, A = [tex] \pi \times \ \frac{16.4 \times 360}{72} =82 \pi[/tex]
given, [tex] \pi =3.14 [/tex]
[tex] volume =82 \times 3.14 = 257.48 [/tex]
Hence, Area of circle= 257.48
Answer:257.48 yd sq
Step-by-step explanation: took de quiz
The side of a square is 12 feet. What is the area of the square?
a.12 sq. ft.
b.24 sq. ft.
c.48 sq. ft.
d.144 sq. ft.
Answers
Area of the square = 12 x 12
Area of the square = 144 sq ft (Answer D)
---TF---
Which of the following represents the graph of f(x) = 2(x + 3)?
A. https://cdn.flvsgl.com/assessment_images/algebra2_v14_gs-xml/93228_559e8103/08_14_17.gif
B. https://cdn.flvsgl.com/assessment_images/algebra2_v14_gs-xml/93228_559e8103/08_14_18.gif
C. https://cdn.flvsgl.com/assessment_images/algebra2_v14_gs-xml/93228_559e8103/08_14_19.gif
D. https://cdn.flvsgl.com/assessment_images/algebra2_v14_gs-xml/93228_559e8103/08_14_20.gif
Answers
the correct expression is
y=2^(x+3)
using a graph tool
see the attached figure
the answer is the option C
Answer:
c
Step-by-step explanation:
A radius is a0 the diameter
Answers
you write half in the blank
Answer:
Hence, A radius is half the diameter.
Step-by-step explanation:
The question is asked as:
A radius is [tex]a_0[/tex] the diameter.
i.e. what is the value of the constant [tex]a_0[/tex] such that the radius and the diameter are related to each other.
We know that:
The Radius is the length of the line through the center that touches a point on the edge of the circle.
The diameter is the length of the line through the center that touches two points on the edge of the circle.
Hence Radius is half the diameter.
so the value of [tex]a_0=\dfrac{1}{2}[/tex]
( Or we can say Diameter is twice the radius of the circle.
[tex]d=2r\\\\r=\dfrac{1}{2}d[/tex]
where d denotes the diameter of the circle and r denotes the radius of the circle ).
The area of a right triangle is 336 square centimeters. The base of the right triangle is 48 centimeters. What is the length of the hypotenuse of the right triangle? Enter your answer in the box.
Answers
[tex]336 = \frac{1}{2} 48h [/tex]
[tex]336 = 24h [/tex]
[tex] \frac{336}{24} = h [/tex]
[tex] 14 = h [/tex]
Then using Pythagorean theorem
[tex] b^{2} + h^{2} = Hyp^{2} --> 48^{2} + 14^{2} = hyp^{2} [/tex]
[tex] hyp = \sqrt{2304 + 196} = 50 cm [/tex]
Answer:
50
Step-by-step explanation:
First we have to find the height. Since we know the area we can use it to find the height. The area of a triangle is A=bh1/2 or half of the base times the height. So if we plug in what we know and solve, we can find the height. 336=48 x h x 1/2. The height is 14. Now we can solve for the hypotenuse using the Pythagorean Theorem. a^2 + b^2 = c^2 plug in what we know... 14^2 + 48^2 = c^2 simplify to get 196+2304= c^2 and further 2500= c^2 so find the square root of 2500. You will get 50.
2. A cake in the shape of a circus tent is used as a centerpiece at a celebration. The cake consists of a cylinder and a cone. The cylinder has a diameter of 12 inches and a height of 14 inches. The cone has a height of 6 inches. What is the volume of the cake? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.
Answers
Hope this helped!
the answer is 1808.64
Hope i helped <33
Hero's Challenge: Cars At A StopLight
There are five cars in line at a stoplight. Each of these cars is a different color and different type of car. Diego is driving the red car. Ingrid is driving the sedan. The green car is immediately behind the white car. The minivan is third in line. Rachel is driving the first car in line. Anton is just behind the driver in the SUV. Yuna is driving the green car. The driver in the yellow car is just in front of the convertible. Rachel is just in front of the blue car. The sedan is white. One of the cars is a pickup truck. Who is driving the pickup truck?
Answers
Diego=Red
Ingrid=Sedan
White then Green
Rachel then 2 then Minivan
SUV then Anton
Yuna = Green
Yellow then Convertible
Rachel then Blue
Sedan=white
Now begin to combine in order:
1. Rachel
2 Blue
3 Minivan
Since IngridSedanWhite is followed by YunaGreen, these do not fit as 1,2 or 3 so they must be 4 and 5
4 IngridSedanWhite
5 YunaGreen
The only place yellow then convertible will fit is in 1 and 2. So:
1. RachelYellow
2 ConvertibleBlue
3 Minivan
4 IngridSedanWhite
5 YunaGreen
The SUV has to be 1 or 5, but Anton is behind it so the SUV must be #1. So:
1. RachelSUVYellow
2 AntonConvertibleBlue
3 Minivan
4 IngridSedanWhite
5 YunaGreen
The only color missing is Red so Diego must be driving the minivan:
1. RachelSUVYellow
2 AntonConvertibleBlue
3 DiegoMinivanRed
4 IngridSedanWhite
5 YunaGreen
This leaves Yuna to be driving the green pickup truck.
A ship is 2.8 degree off course .If the ship is traveling at 14.0 miles per hour,how far off course will it be after 2 hours?
Answers
Tanya wants to find the height of the tree. She walks away from the base of the tree so the tip of her shadow coincides with the tip of the tree's shadow at point C. BE is two and a half times EC. Tanya is 5 feet, 3 inches tall. How tall is the tree in feet?
Answers
18 feet and 4.5 inches
Explanation
You are going to use the concept of similar triangle.
∆CED≡∆CBA
This is because they share the angle at C and also they both have an angle of 90o.
Let EC = X, then BE = 2.5X. So, BE = (X + 2.5X) = 3.5X
The scale factor EC/BC=x/3.5x=2/7
EC/BC=ED/BA=2/7
BA=7/2×63 in
The height of the tree = 220.5 inches. This is equal 18 feet and 4.5 inches.
HELPPPPPPPP AND EXPLAIN
Answers
29)
what is "c", namely one of those x-values where it touches? look at the graph, it hits at 0.5, 1, 2, 3, pick your poison.
30)
how many? well, you already know.
64,55,46,37,28,19 find the math patter what goes next
Answers
From one number to the next, the number decreases by 9.
10 goes next, since 19 - 9 = 10
Hope This Helps!
What is the approximate volume of a cone with a height of 9 ft and radius of 3 ft?
Use 3.14 to approximate pi, and express your final answer to the nearest tenth.
@phi,
Answers
Kevin and Randy Muise have a jar containing 85 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $ 14.25. How many of each type of coin do they have?
Answers
total number of coins will be:
x+y=85
thus
x=85-y.........i
total amount of money will be:
0.25x+0.05y=14.25....ii
substituting i in ii we get:
0.25(85-y)+0.05y=14.25
21.25-0.25y+0.05y=14.25
7=0.2y
y=7/0.02
y=35
thus
x=85-35=50
the number of quarters was 50 and that of nickels was 35
F + H ARE WRONG
HELP ME JIM!
Answers
===========================================
Reason H is "linear pair postulate" which says that if two angles form a linear pair then they are considered supplementary. This is simply what "supplementary" means. The two angles add to 180 degrees. A "linear pair" is where you have two angles that are adjacent and the angles combine to form a straight angle (180 degrees).
===========================================
Side note: It seems like some of this proof has been cut off. There should be more lines to this proof because the last line is always what you want to prove. In this case, the thing we want to prove is "angle DEC and angle BEC are right angles" so that should be the last statement.
3. Which of the following is a solution to the equation 16= 4x-4?
a.-5
b.-4
c.5
d.16
please help. I'll give a medal + fan I wanna know how
Answers
4x-4=16
taking (-4) to opposite side,
since it has (-) sign , it becomes (+) when we take it to the opposite side
now the equation becomes
4x=16+4
i.e.
4x=20
now, we take 4 to the opposite side
the equation becomes
x=20/4
i.e. x=5
so the answer is
c.5
A cone with a radius of 12 cm and a height of 12 cm has the same volume as a cylinder with a radius of 8 cm. What is the height of the cylinder?
A) 3 cm
B) 6 cm
C) 9 cm
D) 12 cm
Answers
Answer:
The correct option is C. The height of the cylinder is 9 cm.
Step-by-step explanation:
The radius of cone is 12 cm and the height of cone is 12 cm.
The volume of cone is
[tex]V=\frac{1}{3}\pi r^2h[/tex]
[tex]V_1=\frac{1}{3}\pi (12)^2(12)[/tex]
[tex]V_1=576\pi[/tex]
The radius of cylinder is 8 cm. The volume of cylinder is
[tex]V=\pi r^2h[/tex]
[tex]V_2=\pi (8)^2h[/tex]
[tex]V_2=64\pi h[/tex]
It is given that the volume of cone and cylinder is same.
[tex]V_1=V_2[/tex]
[tex]576\pi=64\pi h[/tex]
[tex]\frac{576\pi}{64\pi}=h[/tex]
[tex]9=h[/tex]
Therefore the height of the cylinder is 9 cm and option C is correct.
To find the height of the cylinder that has the same volume as a cone, we can compare their volumes. By setting the volumes equal to each other and simplifying the equation, we find that the height of the cylinder is 9 cm.
Explanation:To find the height of the cylinder, we need to compare the volumes of the cone and the cylinder. The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height. The volume of the cone with radius 12 cm and height 12 cm is (1/3)π(12^2)(12) = 576π cm³. Now, let's calculate the volume of the cylinder using the formula V = πr^2h, with radius 8 cm. We know that the volumes of the cone and the cylinder are equal, so 576π = π(8^2)h. Simplifying this equation, we get 576π = 64πh. Dividing both sides of the equation by 64π, we find h = 9 cm. Therefore, the height of the cylinder is 9 cm.
Learn more about Volume of Shapes here:https://brainly.com/question/36761114
#SPJ3
PLEASE HELP ME ON THIS
Answers
[tex]\sqrt[5]{224x^{11}y^8} = \sqrt[5]{32*7*x^5*x^5*x*y^5*y^3}[/tex]
[tex]\sqrt[5]{224x^{11}y^8} = \sqrt[5]{32}*\sqrt[5]{7}*\sqrt[5]{x^5}*\sqrt[5]{x^5}*\sqrt[5]{x}*\sqrt[5]{y^5}*\sqrt[5]{y^3}[/tex]
[tex]\sqrt[5]{224x^{11}y^8} = 2*\sqrt[5]{7}*x*x*\sqrt[5]{x}*y*\sqrt[5]{y^3}[/tex]
[tex]\sqrt[5]{224x^{11}y^8} = 2x^2y*\sqrt[5]{7xy^3}[/tex]
Thanks.
Liam works at a zoo. He was looking at some data showing the masses of their 5 African elephants. The mean mass of the elephants was 3,800 kilograms and the median mass was 3,600 kilograms. The heaviest elephant, named Omar, was recorded as 6,000 kilograms. Liam then found out that Omar's mass was written down incorrectly, and that Omar actually has a mass of 7,000 kilograms. How will increasing Omar's mass affect the mean and median?
Answers
The increase of Omar's mass from 6000kg to 7000kg will raise the mean mass of the elephants because the mean involves all values. However, it won't affect the median mass because the position of the middle value in the set won't change.
Explanation:The correction of Omar's mass from 6,000 kilograms to 7,000 kilograms will affect both the mean and the median mass of the elephants. However, the effect on each measure of central tendency will be different.
The mean is the average, calculated by adding up all values and then dividing by the number of values. If Omar's weight is increased, the total mass of the elephants will increase, leading to an increase in the mean mass of the elephants.
However, the median, which is the middle value when all values are arranged in ascending order, will not change because it only depends on the arrangement of values, not their actual size. Since Omar's mass is already the largest value, an increase in his mass will not change the position of the middle value.
Learn more about Effects on Mean and Median here:https://brainly.com/question/32770946
how many isosceles triangles appear in this figure?
Answers
There is exactly 1 isosceles triangle in the figure.
M is the midpoint of PQ, N is the midpoint of MQ, and L is the midpoint of MN. If MN =14, find ML.
Answers
Please mark Brainliest! Lemme know if I can help you with anything else!
-Belle
Distance LN = 6
Distance MQ = 6 X 2
=12 (Remember N is the midpoint of MQ)
Distance MQ = Distance PM = 12units
Hope this helps.
Instead of focusing on the absence of mental illness as an indication of mental health, Abraham Maslow and CarlRogers would focus more on____________ (1 point),
Answers
satisfying basic physiological needs
creating pyramidal charts
outcome and behavior
the full realization of an individual's self
Then the answer is the last option.
Abraham Maslow and CarlRogers would focus more on the full realization of an individual's self.
Kim had 160 cards in a box.She gave 4/10 of the cards to maddy.How many cards did Kim have left in the box
Answers
[tex]\text {Cards gave to Maddy = } \dfrac{4}{10} \times 160 = 64 [/tex]
[tex]\text {Cards left = } 160 - 64 = 96 [/tex]
------------------------------------
Answer: Cards left = 96
------------------------------------
Scoring a hole-in-one is the greatest shot a golfer can make. once 7 professional golfers each made holes-in-one on the 8th hole at the same golf course at the same tournament. it has been found that the estimated probability of making a hole-in-one is 12287for male professionals. suppose that a sample of 7 professional male golfers is randomly selected. what is the probability that they all score a hole in one
Answers
Two large numbers of the Fibonacci sequence are f(50)=12,586,269,025 and f(51)= 20,365,011,074 if these two numbers are added what number results
Answers
Answer:
f(52) = 32,951,280,099
Step-by-step explanation:
In Fibonacci sequence, the sum of the two preceding sequence of the sequence is always equivalent to the next sequence.
For example, this is a Fibonacci sequence 1,2,3,5,8... As you can see that the sum of the two preceding sequence gave the next sequence i.e 1+2 = 3, 2+3 = 5, 3+5 = 8 etc and the chain continues like that.
If we are now given two large numbers of. Fibonacci sequence to bef(50)=12,586,269,025 and f(51)= 20,365,011,074
The next sequence f(52) will be the sum of the preceding sequences f(50) and f(51) that is;
f(52) = f(50) + f(51)
f(52) = 12,586,269,025 + 20,365,011,074
f(52) = 32,951,280,099
The resulting numbers if they are added is 32,951,280,099.
How many lines of symmetry does a regular hexagon have? 8 6 4 2
Answers
Answer:
it is 6 so have a merry christmas
Step-by-step explanation:
Take a look at the figure. What are the coordinates of the point labeled B in the graph shown?
A. (3, 2)
B. (–3, 2)
C. (–2, 3)
D. (–2, –3)
Answers
At LaMar’s birthday party, his parents served slices of plain, sausage, or pepperoni pizza. They also served cups of milk, orange juice, apple juice, or lemonade. If each guest at the party chose one slice of pizza and one type of drink, how many different combinations were possible?
Answers
Answer: 12 different combinations were possible.
Step-by-step explanation:
Given: At LaMar’s birthday party, his parents served slices of plain, sausage, or pepperoni pizza.
i.e. The number of types of pizza = 3
They also served cups of milk, orange juice, apple juice, or lemonade.
i.e. The number of types of drinks = 4
Now, if each guest at the party chose one slice of pizza and one type of drink, then the number of different possible combinations are :
[tex]3\times4=12[/tex]
Hence, there were 12 different combinations .
Perform the indicated operation. (2x + y)(3x^2 + y)
Answers
Answer:
[tex](2x+y)(3x^2+y)=6x^3+3x^2y+2xy+y^2)[/tex]
Step-by-step explanation:
The given expression is [tex](2x+y)(3x^2+y)[/tex].
We expand the parenthesis using the distributive property to obtain;
[tex](2x+y)(3x^2+y)=2x(3x^2+y)+y(3x^2+y)[/tex]
We expand further to get;
[tex](2x+y)(3x^2+y)=6x^3+2xy+3x^2y+y^2)[/tex]
This gives us;
[tex](2x+y)(3x^2+y)=6x^3+3x^2y+2xy+y^2)[/tex]
use the formula a=h/n to find the batting average a of a batter who has h hits in n times at bat.Solve the formula for h. if a batter has a batting average of .290 and has at bat 300 times, how many hits does the batter have?,
Answers
The formula given is:
a = [tex] \frac{h}{n} [/tex]
To solve for h, we need to isolate the h on one side of the equation.
This can be done as follows:
a = [tex] \frac{h}{n} [/tex]
Multiply both sides by n:
an = [tex] \frac{h}{n} [/tex] * n
h = a*n
Part 2: getting the value of h:
We are given that:
The average (a) = 0.290
n = 300 times
Substitute with the givens in the equation we got in part (1) to get the value of h as follows:
h = a * n
h = 0.290 * 300
h = 87 hits
Hope this helps :)
FULL ANSWERS WITH EVERY STEP PLEASE (10 pts)
for the functions f(x)=3x-6\sqrt(x)+6, and g(x)=7x-12-(4)/(x) find
1- where (f*g)(x) is differentiable
2- where ((f)/(g))(x) differentiable
Answers
=======
(f(g))x = 3(7x - 12 + 4/x) - 6sqrt(7x - 12 + 4/x ) + 6 Here I have put g(x) into f(x)
Now you want to differentiate this thing. As much as you can remove the brackets.
21x - 36 + 12/x - 6*sqrt(7x - 12 + 4/x) + 6
Now differentiate.
f(g(x))' = 12 - 12/x^2 + 6 (7 - 4/x^2) / sqrt (7x - 12 + 4/x)
How come there is now a plus in front of the 6?
Part Two
=======
I can find no interpretation for the second part other than the obvious. It's been 57 years since I was in a classroom as a student, and any special interpretation to these questions was not discussed.
I take it to mean F(x) / G(x) and then differentiated. If that is not correct, then someone else will have to answer for you. Sorry.
So the question will look like this.
y = [3x - 6(x)^(1/2) + 6] / [7x - 12 - 4/x]
The quotient rule for f(x)/g(x) = [f ' * g - f * g' ] / g^2
So you need to differentiate f to f ' and g to g'
f ' = 2 + 6/2(x ^ (-1/2 ))
g' = 7 + 4/x^2
Now you can put them in for f and g and f ' and g' to get the answer. It's a lot of typing. Be careful how you put this in. Correct any typos before you send it.
The domain in any question is any value for x except x = 0