Answer:
a(n) = 1(2.5)^(n - 1)
Step-by-step explanation:
The geometric sequence is 1, 2.5, 6.25, 15.625, and so on; the first term is 1. The common ratio is 2.5; each new term is 2.5 times the previous term.
The explicit formula desired is thus a(n) = 1(2.5)^(n - 1)
Answer:
ITS CCCCCCC (2.5)
In the circle below, O is the center and mĞ= 128° What is the measure of angle HIG?
Answer:
26 degrees.
Step-by-step explanation:
From the figure it is clear that HI is the diameter and [tex]acr(GI)=128^{\circ}[/tex]. So,
[tex]\angle GOI=128^{\circ}[/tex]
[tex]\angle GOI+\angle GOH=180^{\circ}[/tex] (linear pair)
[tex]128^{\circ}+\angle GOH=180^{\circ}[/tex]
[tex]\angle GOH=180^{\circ}-128^{\circ}[/tex]
[tex]\angle GOH=52^{\circ}[/tex]
Using central angle theorem of a circle, we get
[tex]\angle HIG=\dfrac{\angle GOH}{2}[/tex]
[tex]\angle HIG=\dfrac{52^{\circ}}{2}[/tex]
[tex]\angle HIG=26^{\circ}[/tex]
Therefore, the measure of angle HIG is 26 degrees.
What value, written as a decimal, should Lena use as the common ratio?
Answer:
an=1*2.5^(n-1)
=2.5^(n-1)
Step-by-step explanation:
Complete question below:
What value, written as a decimal, should Lena use as the common ratio? Lena is asked to write an explicit formula for the graphed geometric sequence. On a coordinate plane, 3 points are plotted. The points are (1, 1), (2, 2.5), (3, 6.25).
Solution
Point (1, 1), (2, 2.5), (3, 6.25).
a=1
ar=2.5
ar^2=6.25
From ar and ar^2
r=6.25/2.5
=2.5
r=2.5
an=ar^(n-1)
Therefore, the explicit formula is
an=1*2.5^(n-1)
=2.5^(n-1)
help me meeeeeeeeeeee
Answer:
15 pupcakes
Step-by-step explanation:
Purple is 1 out of 4 sections
1/4 times the number of total pupcakes
1/4 * 60
15
Find m∠CBD,,,,,,,,,,
Answer:
angle CBD=125
Step-by-step explanation:
(8x-41)+(9x+17)=180
17x -24 = 180
17x=204
x=12
9(12)+17=125
Answer:
125
Step-by-step explanation:
The two angles from a straight line so they add to 180
ABC + CBD = 180
8x -41+ 9x+17 = 180
Combine like terms
17x -24 = 180
Add 24 to each side
17x -24+24 = 180 +24
17x = 204
Divide by 17
17x/17 = 204/17
x =12
We want angle CBD
CBD = 9x+17
= 9*12+17
=108+17
= 125
help please. Find the length of x.
Answer:
x=10
Step-by-step explanation:
The triangles are similar so we can use ratios to solve
6.5 (6.5+6.5)
------ = -----------------------
5 x
6.5 (13)
------ = -----------------------
5 x
Using cross products
6.5x = 65
Divide by 6.5
6.5x/6.5 = 65/6.5
x = 10
A swim team must be chosen from 12 candidates. What is the greatest number of different 3-person teams that can be chosen?
==========================================
Explanation:
We have 12*11*10 = 1320 permutations possible. This is where order matters. However, order does not matter with swim teams as there are no positions or ranks. All that matters is the group overall (rather than any individual in the group).
Consider the set {A,B,C}. We have 3*2*1 = 6 ways to arrange this set of letters. When considering a permutation, there are 6 permutations but only 1 combination since order doesnt matter and ABC is the same as BAC. Therefore, we divide 1320 over 6 to get the final answer of 1320/6 = 220.
---------
You can use the combination formula with n = 12 and r = 3. Doing so will give the following:
[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{12} C _3 = \frac{12!}{3!*(12-3)!}\\\\_{12} C _3 = \frac{12!}{3!*9!}\\\\_{12} C _3 = \frac{12*11*10*9!}{3!*9!}\\\\_{12} C _3 = \frac{12*11*10}{3!}\\\\_{12} C _3 = \frac{12*11*10}{3*2*1}\\\\_{12} C _3 = \frac{1320}{6}\\\\_{12} C _3 = 220\\\\[/tex]
As you can see, we get the same result and note how 1320/6 is also present as well.
The greatest number of different 3-person teams that can be chosen is 220.
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?We can use combinations for this case,
The Total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in total of
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.[/tex]
So, total number of choices in that case would be:
[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called permutation of k items chosen out of m items (all distinct).
Consider the set {A,B,C}.
3*2*1 = 6 ways to arrange this set of letters.
When considering a permutation, there are 6 permutations but only 1 combination since order doesnt matter and ABC is the same as BAC.
We can use the combination formula with n = 12 and r = 3.
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!} ways.\\\\^{12}C_3= \dfrac{12!}{3! \times (12-3)!} ways.\\\\\\^{12}C_3= \dfrac{12!}{3! \times (9)!} ways.\\\\^{12}C_3= \dfrac{12 \times 11 \times 10 \times 9}{3! \times (9)!} ways.[/tex]
1320/6 = 220
Thus, the greatest number of different 3-person teams that can be chosen is 220.
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Amanda is ordering an ice cream dessert. She must order a size, a flavor of ice cream, and a topping. There are 2 sizes, 1 flavor, and 6 toppings to choose from. How many different ice cream desserts could she order?
Answer: 12
Step-by-step explanation:
Order requirement:
Size ; flavor and topping
Available variety:
Size = 2
Flavor = 1
Toppings = 6
Number of different ice-cream desserts which can be ordered :
Since one of each of size, topping and flavor must be selected :
(Number of available flavors * number of Toppings available * number of sizes available)
1 * 6 different Toppings = 6 varieties
6 varieties * 2 different sizes = 12 varieties
Therefore, there are 12 different variety of ice-cream dessert she can order.
Line
A.
C.
D.
B.
Defined
Postulates
Theorems
Undefined
Terms
Answer: Undefined
Step-by-step explanation:
In geometry there are three undefined terms that we use to define other terms:
Point → In geometry a point has a location but no dimension.Plane → A plane extends is a 2-dimensional surface that extends infinitely on both sides. Line → A line is a one-dimensional undefined figure that extends infinitely in both the directions. It has length but has no width.Hence, the correct option is "Undefined".
In the diagram, AC and PR are vertical lines, while CB is a horizontal line segment. If CR : RB = 2 : 3, what are the coordinates of point Q? A. (-2, -4) B. (-1, -5) C. (-3, -3) D. (0, -6)
Answer:
A. (-2,-4)
Step-by-step explanation:
If CR:RB is 2:3, and C is (-4,-7), then R is (-2,-7)
You can stop here because only A has the x value as -2.
If you want to look at the y value also, -4 is 2/5 of the way between -2 and -7, which has the same 2:3 proportion.
Hello!! I Need HElp ASAP PLEAASSEE
The line of symmetry of the parabola whose equation is y = ax2 - 4x + 3 is x = -2. What is the value of "a"?
-2
- 1/2
-1
Answer:
a = -1
Step-by-step explanation:
The line of symmetry for the parabola given by ...
y = ax² +bx +c
is
x = -b/(2a)
Using the given values, we have ...
-2 = -(-4)/(2a)
Multiplying by -a/2, we get ...
a = (4/2)(-1/2) = -1
The value of "a" is -1.
What is the middle term of the product of (x - 4)(x - 3)?
Answer:
- 7x
Step-by-step explanation:
Given
(x - 4)(x - 3)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x - 3) - 4(x - 3) ← distribute both parenthesis
= x² - 3x - 4x + 12 ← collect like terms
= x² - 7x + 12
with middle term = - 7x
Answer:
Step-by-step explanation:
= x(x-3) - 4(x-3)
= x²-3x - 4x + 12
= x² -7x +12
So -7x is the middle term
I need help doing this can anyone help?
You posted a lot of questions. I'll do the first four problems to get you started.
============================
Problem 1
This sequence is arithmetic because we add the same amount (4) each time to get the next term. The first term is -2. The first five terms are: -2, 2, 6, 10, 14
============================
Problem 2
This sequence is geometric. We multiply each term by 1/4 to get the next term. We start with 8 as the first term. The first five terms are 8, 2, 1/2, 1/8, 1/32.
============================
Problem 3
Similar to problem 1. This time we're adding -19 to each term to get the next one. The starting term is -6. This sequence is arithmetic and the first five terms are -6, -25, -44, -63, -82
============================
Problem 4
Similar to problem 2. This sequence is geometric with common ratio 2/3. First term is 6. The first five terms are 6, 4, 8/3, 16/9, 32/27
The endpoints of a line segment can be represented on a coordinate grid by the points
A(-4, 1) and ((-4, -3). Graph and label each of the endpoints of the line segment on
the coordinate grid below.
Blue paper chains 4 inches long. Red paper chains are 3 inches long. How many are needed to have 10 inches of paper chains?
1 blue paper chain and 2 red paper chains
Answer:
1 blue paper chains and 2 red
Step-by-step explanation:
becuase 4 plus 3 plus 3 is 10
In the given diagram, find the values of x, y, and z.
Oax = 20°, y = 21°, z = 20°
Ob.x = 64°, y = 21°, z = 64°
Oox = 64°, y = 21°, z = 20°
Odx = 115°, y = 115°, z = 64
Answer:
B) x=64, y=21, z=64
Step-by-step explanation:
X=180-116=64
Y cannot equal 115, and one angle is already 95, and that would put it over 180. The only remaining choice for y=21
z=180-95-21=64
Miss White wants to buy 5 value meals at Mel’s Diner.
What is the reasonable total for her purchase?
A. $25
B. $1,000
C. $100
D. $10
Need answer ASAP
Answer: A
Step-by-step explanation:
Divide each total by 5 to get 5, 200, 20, 2.50. $5 per value meal is the most fair price.
Hope it helps <3
If the total is 25$, then each value meal would equal 25/5 = 5$, which is reasonable. so option A is correct.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
A. If the total is 25$, then each value meal would equal 25/5 = 5$, which is reasonable.
B. If the total is $1000, then each meal would equal 1000/5 = $200, which is not reasonable
C. If the total is $100, then each meal would equal 100/5 = $20, which is not a reasonable price for a value meal
D. If the total is $10, then each meal would equal 10/5 = $2 which is not a reasonable price for a value meal.
Hence, If the total is 25$, then each value meal would equal 25/5 = 5$, which is reasonable. so option A is correct.
Learn more about the unitary method;
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Anton bought a picnic cooler. His total bill, with tax, was $7.95.
He paid 6 percent sales tax. How much did he pay for the cooler
alone without the tax?
Answer:
$ 7.50
Step-by-step explanation:
The cost of the picnic cooler would be 100%.
With the 6% sales tax, Anton would pay 106% of the cost if the picnic cooler.
(since 100% +6%= 106%)
106%(picnic cooler)= $7.95
Cost of picnic cooler= 100%(picnic cooler).
Cost of picnic cooler
[tex] = \frac{7.95}{106} \times 100 \\ = 7.50[/tex]
Thus, he paid $7.50 for the cooler alone.
These dot plots show the ages (in years) for a sample of sea turtles and a
sample of koi fish.
Age (in years)
What are the differences between the centers and spreads of these
distributions?
Select two choices: one for the centers and one for the spreads.
a A. Centers: The sea turtles have a lower median age than the koi.
3. B. Centers: The sea turtles have a greater median age than the koi.
c. Spreads: The ages of the sea turtles are more spread out.
D D. Spreads: The ages of the koi are more spread out.
*see attachment below for the dot plots that completes the question.
Answer:
B. Centers: The sea turtles have a greater median age than the koi.
D. Spreads: The ages of the koi are more spread out.
Step-by-step explanation:
The measure of center that can be used for comparison is the median, while the spread can simply be visualised by mere looking at how spread out the dots on the number line are. The spread of both can also be compared using their range. The greater the range, the more spread a data is.
=>Median Differences:
The median age for turtle = the middle value = 55
The median age for koi = 30
Therefore, sea turtles have a greater median age than the koi.
=>Spread Differences:
Range for turtle = the highest age - the least age represented on the dot plot = 65 - 45 = 20
Range for koi = 55 - 10 = 45
Koi has a greater range value than koi. Therefore, the ages of the koi are more spread out.
What is the length of the short leg in the 30-60-90 triangle shown below?
Answer:
it is D. 5
Step-by-step explanation:
The long side (B) will always be (A root 3) meaning, if you just take away the square root of 3, then you get the short side A
Answer:
[tex]\boxed{Shortest\ Leg = 5}[/tex]
Step-by-step explanation:
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Where θ = 60 , opposite = [tex]5\sqrt{3}[/tex] and adjacent = shortest leg
=> Tan 60 = [tex]5\sqrt{3}[/tex] / shortest leg (Tan 60 = √3)
=> Shortest Leg = [tex]\frac{5\sqrt{3} }{\sqrt{3} }[/tex]
=> Shortest Leg = 5
HELP ME ON THIS ONE PLZ NEED ANSWERS
What is the domain and range of each relation?
Drag the answer into the box to match each relation.
{(−7, 2), (−2, 2), (0, 1), (4, 5)}
A mapping diagram. Element x contains negative 4, negative 3, negative 1, and 1. Element Y contains negative 3, negative 1, and 4. Negative four maps to negative 1. Negative three maps to negative 3 and 4. Negative one maps negative 1. One maps to 4.
Answer:
See below.
Step-by-step explanation:
The domain of a relation are simply its x-values, while the range of a relation are its y-values.
1)
We have the relation:
{(-7,2), (-2,2), (0,1), (4,5)}
Again, the domain of this relation are the x-values. Therefore, the domain is:
{-7, -2, 0, 4}
The range of this relation are the y-values. Therefore, the range is:
{2, 1, 5}
Note that even though the 2 repeats, we only count it once because it's the same.
2)
We have the relation:
{(-4,-1), (-3,-3), (-3,4), (-1,-1), (1,4)}
The domain are the x-values. Therefore, the domain is:
{-4, -3, -1, 1}
Again, the -3 repeats so we only count it once.
And the range would be the y-values:
{-3, -1, 4}
It's customary to place them in ascending order.
Answer:
If there are two set A and B. All the elements of set A are called domain and all elements of set B are range.And element of B which are maping with set A elements are codomain
Step-by-step explanation:
domains are -7,-2,0,4
range are 2,1,5
I hope this is helpful for you
FIRST GETS BRAINLLEST What is the perimeter of the track, in meters? Use π = 3.14 and round to the nearest hundredth of a meter.
Answer:
8110
Step-by-step explanation:
80+80+50+50=260
3.14(50)²=7810
7810+260=8110
what is the smallest number by which 2408 should be multiplied to get a perfect cube
Answer:
90601
Step-by-step explanation:
we have to find smallest number by which 2408 should be multiplied to get a perfect cube.
First lets find prime factor of 2408 and power these prime factors have
2408 = 2*1204 = 2*2*602 = 2*2*2*301= 2*2*2*7*43
thus,
2408 = 2^3*7*31
we know that a cube is a number raised to the power three
in 2408
2 has a power of three
but 7 and 31 and there is power of one,
thus we need to make
power of 7 and 31 three by multiplying
7 with 7*7
and 31 with 31*31
thus,
2^3*7*31*7*7*31*31 is the minimum cube value for this number
2^3*7*31*7*7*31*31 = 2^3*7^3*31^3 = 2408 * 7^2*31^2 = 2408*90601
Thus, smallest number which should be multiplied with 2408 to make it a perfect cube is 90601
Mrs. Lobo earns a salary of $50,000 per year plus a 4% commission on her sales. The average price of a share
she sells is $50.
Write an inequality to describe about how many shares Mrs. Lobo must sell to make an annual income of at
least $70,000
Select one:
O a. 50,000 + 2x > 70,000
O b. 50,000 + 2x < 70,000
O c. 50,000 -- 2x > 70,000
d. 50,000 + 2 > 70,000
Answer:
a) 50,000 + 2x > 70,000
Step-by-step explanation:
Mrs. Lobo has an annual salary of $50000 per year plus 4% commission on her sales.
If she makes $y commission from sales, Mrs Lobo total income per year is:
$50000 + $y.
She makes 4% commission on her sales of share with the average price of a share = $50
Average commission from sales = 4% × $50 = 0.04 × 50 = $2
If she sales x shares in a year, her commission would be $2x for the year. Therefore her total income for that year would be:
50000 + 2x
The amount of shares Mrs Lobbo must sell to make an annual income of at
least $70,000 is given by the inequality:
50,000 + 2x > 70,000
What is the slope of the line shown on the graph? A)3 B)1/3 C)−3 D)−1/3
Answer:
1/3
Step-by-step explanation:
The slope of the line is found by
m = (y2-y1)/(x2-x1)
we have two point ( 0,0) and ( 3,1)
= ( 1-0)/( 3-0)
= 1/3
PLEASE HELLLLLLP MEEE
Answer:
None of the above
Step-by-step explanation:
In my opinion, I believe the answer is none of the above because
answer A says it has a peak from 10 to 15 km but the graph goes higher than 15 km
answer B says it has a gap from 25 to 30 km but the graph doesn't go that high.
Hope did helps:)
is the square root of 34 rational or irrational
Answer:
irrational
Step-by-step explanation:
If a square root is not a perfect square, then it is considered an irrational number.
The square root of the number 34 is not a rational number
How to determine the type of the numberFrom the question, we have the following parameters that can be used in our computation:
The square root of the number 34
When evaluated, we have
The square root of the number 34 = √34
So, we have
The square root of the number 34 = 5.83.....
The above number cannot be represented by the quotient of 2 integers
Using the above as a guide, we have the following:
We can conclude that the number is an irrational number
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An eraser is in the shape of a triangular prism. Its dimensions are shown in the diagram. What is surface area of the
eraser?
50 mm
40 mm
40 mm
30 mm
3,600 square millimeters
4.800 square millimeters
5,400 square millimeters
6,000 square millimeters
Answer:
6000 square millimeters
Step-by-step explanation:
Side length of the slanting side can be calculated using the Pythagorean theorem,
L = sqrt(30^2+40^2) = 50
sufrace area of a triangular prism
= surface area of the end sections + the surface area of the three side faces
= 2*(30*40/2) + 40*(30+40+50)
= 1200 + 4800
= 6000 mm^2
Answer:
D) 6,000 square mm
Step-by-step explanation:
To find the surface area of the triangular prism, find the are of each face.
40 × 30 ÷ 2 = 600 × 2 sides = 120040 × 50 = 200040 × 30 = 120040 × 40 = 1600After adding all the sides' together, you get 6,000 square mm.
Can someone help with this.... thanks!
Answer:
3244.5
Step-by-step explanation:
LxW=A
AssAssessment captures blank growth
How to find constant M ? did I do anything wrong here ?
Answer:
M=-1, N=7
Step-by-step explanation:
Something went wrong on the 4th line.
From the third line, it should read
2x^2-x+6Mx-3M+4
=x(2x-1+6M) - 3M+4
Equating with the RHS,
2x-1+6M = 2x-7
6M = -7+1 = -6
M = -1
Therefore
N = -3M+4 = -3(-1)+4 = 7
or
M=-1, N=7