Using geometric sequence concepts, it is found that:
a) The rule is: [tex]P_n = 750000(0.5)^{n-1}[/tex].
b) An exponential relationship exists between the two variables.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
A geometric sequence represents an exponential relationship between the variables.
In this problem, considering that the first-place finisher wins half of $1.500.000 in total prize money, and each finisher earns half of the one who finished above, the first term and the common ratio are given by:
[tex]a_1 = 750000, q = 0.5[/tex].
Hence the nth term of the sequence is given by:
[tex]P_n = 750000(0.5)^{n-1}[/tex]
More can be learned about geometric sequence concepts at https://brainly.com/question/11847927
#SPJ1
Does anybody want to help with math?
2a(-5a^8b+a^2-12ab)
Ty :D
Answer: 18a4 - 6a3b - 5a2b4 - 45a2b2 + 36ab2 - 12ab + 3b
———————————————————————————————-
3
Step-by-step explanation:
1. whats -3 x - 5 = 6
2. whats -4 ( y - 2 ) =12
show work
Answer:
x = -11/3 or 3.666y = -1Step-by-step explanation:
Given:
1) -3x -5 = 6
2)- 4 ( y - 2 ) =12
To Find:
Value of x for no. 1Value of y for no. 2Solved:
1)-3x -5 = 6
Transpose -5 from LHS to RHS
=> -3x = 6+5=> -3x = 11Transpose -3 from LHS to RHS
=> x = (11/-3)=> x = -11/3=> x = -3.6662) -4(y-2) = 12
Apply distributive property
=>(−4)(y)+(-4)(-2)=12=>-4y+8 = 12Transpose 8 to RHS
=> -4y = 12-8=> -4y =4Transpose -4 to RHS
=> y = 4/-4=> y = -1Rewrite the radical expression as an exponential expression, and then simplify.
StartRoot 121 EndRoot = one-half (121) = 60.5
StartRoot 121 EndRoot = 121 squared = 14,641
StartRoot 121 EndRoot = 121 Superscript one-half Baseline = 11
StartRoot 121 EndRoot = 121 Superscript one-half Baseline = 60.5
The radical expression written as an exponent, and simplified, is given by:
[tex]\sqrt{121} = (121)^{\frac{1}{2}} = 11[/tex].
How to transform an exponent to a power?It happens according to the following rule:
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
The inverse is also valid, hence, in this problem, the expression written as an exponent and simplified is given by:
[tex]\sqrt{121} = (121)^{\frac{1}{2}} = 11[/tex].
More can be learned about the conversion between radicals and exponents at https://brainly.com/question/27565901
#SPJ1
In circle H with m/GHJ = 82 and GH = 12 units, find the length of arc GJ.
Round to the nearest hundredth.
H
The length of the arc GJ is 17.17 units if the in circle H with m/GHJ = 82 and GH = 12 units.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have angle GHJ = 82 units
Length of GH = 12 units
We know:
s = 2πr(θ/360)
s = (2π)12(82/360)
s = 17.17 units
Thus, the length of the arc GJ is 17.17 units if the in circle H with m/GHJ = 82 and GH = 12 units.
Learn more about circle here:
brainly.com/question/11833983
#SPJ1
I need some help on this question please
Answer:
D
Step-by-step explanation:
everything that should happen at x+4 happens now at x. that is what that means.
so, the graph shifts 4 units to the left.
Envision Geometry 10-1 Circles 22. page 425
The segment area of the circle that's given in the envision geometry is 2.568.
How to calculate the segment area?It should be noted that the segment area is given as:
= (a/360)π × R² - Area of triangle
= (90/360)π × 3² - (1/2 × 3²)
= 9π/4 - 9/2
= 2.568
In conclusion, the segment area of the circle that's given in the envision geometry is 2.568.
Learn more about geometry on:
https://brainly.com/question/24375372
#SPJ1
Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero. Which statement must be true?
The pool must have been empty for the entire interval.
The pool must have been the same depth at the start of the interval as it was at the end of the interval.
The pool must have been deeper at the end of the interval than it was at the start of the interval.
The pool must have been more shallow at the end of the interval than it was at the start of the interval.
The pool must have been the same depth at the start of the interval as it was at the end of the interval, option second is correct.
What is the average rate of change?Finding out how much something changes over time is what the average rate of change is all about.
We have Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero.
As we know that the average rate of change can be calculated using:
= (Last quantity - starting quantity)/Time interval
The average rate of change, on the other hand, does not account for intermediate values, therefore you can't draw any conclusions about them.
In the given problem:
The average rate of change in depth = (Last quantity - starting quantity)/2
0= (Last quantity - starting quantity)
Final depth = Initial depth
Thus, the pool must have been the same depth at the start of the interval as it was at the end of the interval, option second is correct.
Learn more about the average rate of change here:
https://brainly.com/question/2530409
#SPJ1
which postulate or theorem proves that these two triangles are congruent?
a. ASA Congruence Postulate
b. SAS Congruence Postulate
c. AAS Congruence Theorem
d. HL Congruence Theorem
2. f(x)=4x+1 and g(x)=x2−4x−5, find (g◦f)(4).
Answer:
(g · f)(4) = 45
Step-by-step explanation:
f(x)=4x+1
g(x)=x² - 4x- 5
(g · f)(x) = 4(x² - 5) + 1
(g · f)(4) = 4(4² - 5) + 1
Following pemdas
(g · f)(4) = 4(16 - 5) + 1
(g · f)(4) = 4(11) + 1
(g · f)(4) = 44 + 1
(g · f)(4) = 45
You are in business and have a product that sells for $10 that 1,000 people buy each month You want to make a profit and wonder whether you should raise the price in increments of a dollar For each dollar you raise the price , you lose 100 customersHow many dollars can you increase in price to maximize your profit or should you increase in price at all?
Based on the attached photo and explanation below, the price should not be increased at all.
How to know when profit is maximized?Note: See the attached photo for the calculation of Revenues at Different Number of Customers and Prices.
Every other being equal, profit is maximized when revenue is at the maximum,
From the attached photo, it can be seen that revenue is at the maximum or the highest when the price is $10 and the number of customers is 1,000.
Increasing the price in increments of a dollar results in a fall in revenue progressively until it reaches $0.
Therefore, the price should not be increased at all.
Learn more about revenue here: https://brainly.com/question/13383966.
#SPJ2
Use formulas to find the lateral area and surface area of the given prism. Round your answer to
the nearest whole number. The figure is not drawn to scale. The bases are right triangles.
8.94 m
4m
8m
41 m
Answer:
The answer is option B
[tex]859[/tex] [tex]m^2[/tex] [tex],[/tex] [tex]891[/tex] [tex]m^2[/tex]
Step-by-step explanation:
Step 1
Find the lateral area
we know that
The formula to calculate the lateral area is equal to
[tex]LA=Ph[/tex]
where
P is the perimeter of the base of the prism
h is the height of the prism
In this problem we have
[tex]P=4+8+8.94=20.94[/tex] [tex]m[/tex]
[tex]h=41[/tex] [tex]m[/tex]
substitute in the formula
[tex]LA=20.94*41=858.54[/tex] [tex]m^2[/tex]
[tex]LA=859[/tex] [tex]m^2[/tex]
Step 2
Find the surface area
we know that
The formula to calculate the surface area is equal to
[tex]SA=2B+Ph[/tex]
where
B is the area of the base of the prism
P is the perimeter of the base of the prism
h is the height of the prism
In this problem we have
[tex]B=8*4/4=8[/tex] [tex]m^2[/tex]
[tex]P=4+8+8.94=20.94[/tex] [tex]m[/tex]
[tex]h=41[/tex] [tex]m[/tex]
substitute in the formula
[tex]SA=4(8)+20.94*41=890.54[/tex] [tex]m^2[/tex]
[tex]SA=891[/tex] [tex]m^2[/tex]
x: y = 1:5 Which is the correct equation? A y = 5x By= C y=x-4 D y=x+4
I'm leaning towards A but don't want totake the risk with a hour detention on the line if I get it wrong
Find the magnitude of the sum of the vectors <4,5> and <-2,2>. Round your answer to the nearest 100th.
Answer:
[tex]||v||\approx7.28[/tex]
Step-by-step explanation:
Sum of the vectors
[tex]\langle4,5\rangle+\langle-2,2\rangle=\langle4+(-2),5+2\rangle=\langle2,7\rangle[/tex]
Magnitude of the resultant vector
[tex]||v||=\sqrt{x^2+y^2}=\sqrt{2^2+7^2}=\sqrt{4+49}=\sqrt{53}\approx7.28[/tex]
What is the area of triangle ABC?
C
12
60°
60°
A
D
B
Answer:
Area of the triangle is 36√3
Step-by-step explanation: Hope this will help
The hypotenuse of each 30 - 60 - 90 triangle is 12
The base length is 6 + 6 = 12 because the triangle is equilateral and the
altitude of the triangle divides the base into two equal parts and the altitude (DC) is the height of the triangle.
Now you have two 30 - 60 - 90 triangles with the hypotenuse of 12, the short leg = 6 and you need to find the length of DC.
Finding DC .
a² + b² = c²
6² + b² = 12² 0r the long leg = short leg times √3
36 + b² = 144 6√3
b² = 108
b = 6√3
Area of a triangle = 1/2bh
= 1/2(12)(6√3)
= 6(6√3) = 36√3
if you have 48 apples and you gave your friend molly 20 and you gave your brother and mom 18 each how much apples do you have now?
Answer:
10
Step-by-step explanation:
48-20=28
28-18=10
that is how I see it at least
What is the sum of the two
expressions?
(4/5x+13) - (5/8x − 6)
Answer: 7/40x + 19
Step-by-step explanation:
---Distribute the negative sign
4/5x + 13 - 5/8x + 6
---Get common denominators on the fractions
32/40x + 13 - 25/40x + 6
---Combine like terms
(32/40x - 25/40x) + (13 + 6)
7/40x + 19
Answer: 7/40x + 19
Hope this helps!
PLS HELP! What is the linear function rule for this table?
Answer:
f(x) = 4x + 6
Step-by-step explanation:
Using f(x) = 4x + 6
lets find some answers
lets take x as (-2)
f(-2) = 4(-2) + 6
f(-2) = -8 + 6
= -2
Also, take x as (-1)
f(-1) = 4(-1) + 6
f(-1) = -4 + 6
= 2
write 8.31752 to correct 3 decimal places
Answer:
8.318
Step-by-step explanation:
writing a number in three decimal places means writing the number in a way that there will be three digits in the number after the decimal point.
to three decimal places= 8.318
Mai put $4250 in the bank at 4.4% interest compounded annually. How much was in her
account after 7 years?
Answer:
$5745.03
Step-by-step explanation:
A = 4250(1 + 0.044)7 = $5745.03
The required amount in the Mai accounts after 7 years will be $5745.03.
What is compound interest?Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.
Amount = principal[1 + r/n]ⁿᵃ
Here,
Principal = 4250, rate = 4.4%, Time = 7 ,
Amount = 4250[1 + 0.044]⁷
Amount = $5745.03
Thus, the required amount in the Mai accounts after 7 years will be $5745.03.
Learn more about compound interest here: https://brainly.com/question/14295570
#SPJ2
Allison wants to ride her bicycle 60 miles this week. She has already ridden 12 miles. If she rides for 6 more days, what is the average number of miles she would have to ride each day to meet her goal?
Answer:
8 miles a day
Step-by-step explanation:
First you have to subtract the amount of miles she had already gone.
60 - 12 = 48
Next you have to divide by the remaining amount of days (6 days).
48/6 = 8
7. The points (−2,−4) and (5,6) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.
Answer
6.10
Use the distance formula:
[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
where (x1, y1), (x2, y1) are points
[tex]\rightarrow \sf d =\sqrt{(5-(-2))^2 + (6-(-4))^2}[/tex]
[tex]\rightarrow \sf d =\sqrt{(7)^2 + (10)^2}[/tex]
[tex]\rightarrow \sf d =\sqrt{149}[/tex]
This is the length of diameter.
Then radius:
· diameter/2
[tex]\sf \cdot \dfrac{\sqrt{149 } }{2}[/tex]
[tex]\sf \cdot 6.103277808[/tex]
[tex]\sf \cdot 6.10 \ \ (rounded \ to \ nearest \ hundreth)[/tex]
help for 10 points that is all i have
Answer:
22 in. and o.5 ft i think so
Two sets of data are each symmetrical and do not contain outliers. Which measures of center and
variability would be most effective to use when making comparisons between the two data sets?
A.
mean and MAD
B. mean and IQR
C. median and MAD
D. median and IQR
Solution:
As, two set of data are each symmetrical and do not contain outliers.
To find the center , the best way is to find Median of data set.Median of Data set is the mid value of Data that is center of Data.
As, you have to find variability , mean can't measure variability. Mean deviation would have been better option.
So, MAD=Median absolute Deviation , would be better tool to measure variability. Because it is Absolute difference between median and Each value of data set.
So, Option (C) median and MAD, would be best way to compare the two given data set.
Please help me find the answer to this problem.
Answer:
numerator - is 2, 15, 18, 6
denominator - is 12, 14, 33, 8, 64
Step-by-step explanation:
2/10, 4/12, 8/14, 9/33, 1/8, 12/64, 15/55, 18/66, 6/32
Here are two rectangles. the area of the shaded rectangle is 1/4 the area of the large rectangle. work out the value of x
The area of the rectangle is the product of length and width. The value of the variable x is 3.6 cm
What is the area of the rectangle?Let L be the length and W be the width of the rectangle.
Then the area of the rectangle will be
Area of the rectangle = L × W square units
The diagram is given below.
Let A₁ be the area of the small rectangle and A be the area of the large rectangle.
A₁ = 1/4 A
4A₁ = A
4 × 2× (12 - x) = 12 × (x + 2)
8(12 - x ) = 12x + 24
96 - 8x = 12x + 24
72 = 20x
x = 3.6
Then the value of the variable x is 3.6 cm
More about the area of the rectangle link is given below.
https://brainly.com/question/20693059
#SPJ1
please help i dont get it... (average rate of change)
10.
The graph shows the price, in dollars, of a new digital toy for different levels of supply.
(image provided)
What is the average rate of change?
Answer:
-3
Step-by-step explanation:
Formula for average rate of change :
A(x) = f(a) - f(b) / a - bSolving :
A(x) = 115 - 85 / 5 - 15A(x) = 30/-10A(x) = -3HELPPPP WITH MATH HOMEWORK PLS
Answer:
The length of the wing is 480 centimeters
Step-by-step explanation:
2 cm on the drawing is 192 cm on the acutal wing
2 = 192
divide both sides by 2
1 = 96
since the drawing has a length of five cm, multiply both sides by 5
5 = 480
therefore, 5 cm on the drawing is equal to 480 cm on the actual wing
Find the equation of a line that passes through the point (2,4) and has a gradient of 1/3 . leave your answer in the form y = m x + c
Answer:
y = mx + b
y = 1/3x + b
Use (2,4) to find b
4 = 1/3(2) + b
b = 4 - 2/3
b = 12 - 2
3
b = 10/3
The equation will be:
The equation will be: y = 1/3x + 10/3
12 is 48 percent of what number?
Answer:
25
Step-by-step explanation:
12 x 100 = 1200
1200 / 48 = 25
What is the simplified value of the exponential expression 16 Superscript one-fourth?
2
4
Answer:
[tex]2[/tex]
Step-by-step explanation:
[tex] {16}^{ \frac{1}{4} } \: is \: the \: same \: as \\ \\ \sqrt[4]{16} = \sqrt[4]{ {4}^{2} } [/tex]
Note we broke down the 16 into 4 squared*. This is because 4 squared is the same as 16. The four and the two would cancel each other leaving:
[tex] \sqrt[2]{4} \;\\ or \\ \: \sqrt [2]{{2}^{2}} [/tex]
Like before the two and the two would cancel each other out leaving:
[tex]2[/tex]
Answer:
C. 2
Step-by-step explanation:
edge
