If you list the number of tickets sold over time, the kind of sequence will you see is a geometric sequence.
What is a geometric sequence?
A geometric progression sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Here,
We assume that the variable x represents the number of tickets sold previously (initial year) and it sold 7 times as many tickets each year as it did the year before, a mathematical expression that models this situation is given by geometric sequence:
x, 7x, 49x, 343x, .....
Verification:
7/1 = 49/7 = 343/49 = 7
Hence, this is a geometric sequence.
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A researcher found the average cost of one and two-bedroom apartments for different cities and graphed the data in a scatter plot, with costs of one-bedroom apartments along the x-axis. The variables have a strong linear correlation and the equation for the regression line is yˆ=1.182x+19.096 .
Based on the equation, what should the researcher expect for the average cost of a two-bedroom apartment in a city where the average cost of a one-bedroom apartment is $815?
Answer:
About $982.
Step-by-step explanation:
The average cost is:
[tex]y = 1.182x + 19.096[/tex]
When the cost of a one-bedroom apartment is 815, we have [tex]x = 815[/tex], so we should expect the cost to be:
[tex]y = 1.182(815) + 19.066 = 982.4[/tex]
So:
About $982.
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Answer:
.
<_>
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()_()
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Step-by-step explanation:
Helpp!!! Im stuck on this question!!!
for an inequality graph, if the line is dashed, that means that the border line is not part of the shaded region, so any points on it are not a solution of it, any points inside the shaded region or "true" region are solutions to it, only if the border line is solid then the border is part of the "true" region, Check the picture below.
The diagram shows a triangle.
13.4 cm
1
7.6 cm
Work out the area of the triangle.
Answer:
50.92
Step-by-step explanation:
13.4 x 1 x 7.6=101.84
101.84÷2=50.92
I think that might be it but if I am wrong I am sorry that is just what I learned
Answer:
31.0
Step-by-step explanation:
13.4
+17.6
=====
31.0
Find m and b of y
= mx + b.
1
X
1
3
10.9
5
14.5
7
19.8
10
26.0
15
35.2
y / 6.4
Answer:
m = 2.25
b = 4.15
Step-by-step explanation:
Let us consider the points (1, 6.4) & (3, 10.9)
Slope (m) = (10.9 - 6.4)/(3 - 1) = 4.5/2 = 2.25
Now, by point slope formula of a line, we have:
[tex] y - y_1 = m(x - x_1) [/tex]
[tex] \therefore y - 6.4 = 2.25(x - 1)[/tex]
[tex] \therefore y - 6.4 = 2.25x - 2.25[/tex]
[tex] \therefore y = 2.25x - 2.25+6.4[/tex]
[tex] \therefore y = 2.25x + 4.15[/tex]
Equating it with y = mx + b, we find:
m = 2.25
b = 4.15
5. Jackson purchased a pack of game cards that was on sale for 22% off. The sales tax in his county is 6%. Let y represent the original price of the cards. Write an expression that can be used to determine the final cost of the cards.
The decimal value is exact without any rounding.
==========================================================
Explanation:
If Jackson saves 22%, then he pays the remaining 100% - 22% = 78%, which leads to the decimal value 0.78
An increase of 6% leads to 100%+6% = 106% and that converts to 1.06
Multiply those decimal values: 0.78*1.06 = 0.8268; this trick is useful to chain together multiple discounts and/or tax increases.
Therefore, the final cost expression is 0.8268y where the variable y is the original price before the discount and taxes.
---------
Extra info:
The expression 0.8268y tells us that Jackson is paying 82.68% of the original price. Note how 100% - 82.68% = 17.32%
This means Jackson is getting a real discount of 17.32% after the taxes have been considered.
Solve each equation for both variables help please
Answer:
x=2 y= -1
Step-by-step explanation:
Took me 5 minutes to write steps and unfortunately it disappeared. I am so sorry. But the answer is correct
My new year's resolution using mathematics word essay 200 words
d^2a/db^2 +a = 4b+10sin(b)
The given equation is a second order differential equation
What is a differential equation?In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.
Isaac Newton listed three kinds of differential equations given -
[tex]${\displaystyle {\begin{aligned}{\frac {dy}{dx}}&=f(x)\\[4pt]{\frac {dy}{dx}}&=f(x,y)\\[4pt]x_{1}{\frac {\partial y}{\partial x_{1}}}&+x_{2}{\frac {\partial y}{\partial x_{2}}}=y\end{aligned}}}[/tex]
Given is a differential equation as follows -
d²a/db² + a = 4b + 10sin(b)
The given equation is -
d²a/db² + a = 4b + 10sin(b)
Let y = a and x = b, then we can write -
d²y/dx² + y = 4x + 10sin(x)
A second order differential equation is one that expresses the second derivative of the dependent variable as a function of the variable and its first derivative. It is of the form -
d²y/dx² + P(x) dy/dx + Q(x) y = f(x)
For the equation given -
d²y/dx² + y = 4x + 10sin(x)
On comparing, we get -
P(x) = 0
Q(x) = 1
f(x) = {4x + 10sin(x)}
Therefore, the given equation is a second order differential equation.
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r
Assignment
and
A rectangular patio is 10.2 mlong
6.8 m wide
a calculate the area of the patio
If hes cost # 3500
the cost of thing the patio
c If the cost of labour is at 1300 /m2.
Calculate the amount paid for the
per m2, calculate
patio
Answer:
a) 69.36 square meters
b) 242,760 cost of tiles
c) 332,928 total paid for patio
Step-by-step explanation:
A rectangular patio is 10.2 m long 6.8 m wide
a) calculate the area of the patio
b) If tiles cost # 3500/m^2, calculate the cost of tiling the patio
c) If the cost of labour is 1300 /m2.
Calculate the amount paid for the patio
---------------------------------------------------
Area of the patio is length x width:
10.2 x 6.8 = 69.36 square meters
---------------------------------------------------
Tile cost = area x cost of tiles/square meter :
69.36 x 3500 = 242,760
---------------------------------------------------
Labour cost = area x cost of labour/square meter:
69.36 x 1300 = 90,168
----------------------------------------------
Total paid for the patio = cost of tiles + cost of labour
= 242,760 + 90,168 = 332,928
simplify -1.5 (-3.6 +2)
Answer:
2.4
Step-by-step explanation:
Add -3.6 and 2 inside the bracket. Then multiply the result by -1.5.
[tex]-3.6 + 2 = -1.6\\-1.5(-1.6) = 2.4[/tex]
Note: Two negatives make a positive.
Step-by-step explanation:
(-1 5x-3.6)+(-1.5x2)
=5.4+-3
=5.4-3
=2.4
The temperature today will be 2 times lower than last year's temperature on the same day. What will today's temperature be if it was -8.2° last year?
Answer:
Two times lower than last year's temperature
Let today's Temperature be x
x/2 = -8.2°
x = -8.2°*2
x = -16.4°✓What are the dimensions of this shape in terms of the dimensions of the circle?
The diameter or radius of the circle is the dimension of a circle.
What is a circle?The circular line is drawn equidistant from the center point of a circle, which is a two-dimensional geometry object on a plane.
A geometrical rule states that the dimension of an object with n dimensions is n+1. For instance, a square is made up of line segments that are 1d and a cube is built up of squares that are 2d. The circle is therefore 2d or two-dimensional space since it is made up of 1d diameters.
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Answer:
The length of the parallelogram is half of the circumference of the circle, and its height is equal to the radius of the circle.
Step-by-step explanation:
What is the solution to the linear equation?
+pag+
O p = 1
O p = 2
o p= 8
O p = 10
The solution of the equation will be 1. Then the correct option is A.
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
The equation is given below.
2/5 + p = 4/5p + 3/5
Simplify the equation for p, then we have
2/5 + p = 4/5p + 3/5
p - 4/5p = 3/5 - 2/5
1/5 p = 1/5
p = 1
The solution of the equation will be 1. Then the correct option is A.
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Aftab pays £3.10 per concrete slab. (b) How much will it cost Aftab to buy enough concrete slabs to make the patio?
To determine how much it will cost Aftab to buy enough concrete slabs to make the patio, you will need to know the size of the patio and how many slabs are needed to cover it. Once you have this information, you can multiply the number of slabs by the cost per slab to find the total cost. For example, if the patio is 10 square meters and requires 20 concrete slabs to cover it, the total cost would be 3.10 * 20 = £62.
given the points (5,7)and(2,4)
find the equation passing through
these points
Answer:
y=x+2
Step-by-step explanation:
Im going to start by presuming its a linear equation so the formula is:
y=mx+n so now we just make a simulanious equation:
7=5m+n
4=2m+n
which we subtract to get
3=3m
m=1
then we plug it into the first equation
7=5+n
n=2
so the equation is:
y=x+2
How do you rewrite p(x)=-5x2+120x-315 in vertex form
Answer:
[tex]p(x)=-5(x-12)^2+405[/tex]
Step-by-step explanation:
Hi there!
Vertex form: [tex]f(x)=a(x-h)^2+k[/tex]
[tex]p(x)=-5x^2+120x-315[/tex]
Factor out -5 from the first two terms
[tex]p(x)=-5(x^2-24x)-315[/tex]
Complete the square by adding [tex](\frac{24}{2} )^2[/tex] (the square of half of the x-coefficient)
[tex]p(x)=-5(x^2-24x+(\frac{24}{2} )^2)-315-(-5)(\frac{24}{2} )^2[/tex]
We're subtracting [tex](-5)(\frac{24}{2} )^2[/tex] because we need to keep the equation balanced and we can't just add new values.
Complete the square
[tex]p(x)=-5(x-(\frac{24}{2} ))^2-315-(-5)(\frac{24}{2} )^2[/tex]
Simplify
[tex]p(x)=-5(x-12)^2-315+720\\p(x)=-5(x-12)^2+405[/tex]
Summary:
Complete the squareSimplifyI hope this helps!
PLEASE HELP FASTT
Write the equation of the line that has a slope of -3 and passes through (2, -5)
show work if possible
Answer:
y = -3x + 1
Step-by-step explanation:
Plug in your x (2) and y (-5) values into your slope-intercept formula (y=mx+b).
-5 = -3(2) +b
Solve for b:
-5 = -3(2) + b
-5 = -6 + b
1 = b
Plug in the value of b, and the slope (-3) for the formula:
y = -3x + 1
A case of tomato cans weighs 563 dekagrams. A case of soup cans weighs 458 dekagrams. How much do the two cases weigh together in decigrams? Use the metric table to help answer the question.
Metric Table
kilo-
hecto-
deka-
unit
deci-
centi-
milli-
1,000
100
10
1
0.1
0.01
0.001
1,021 decigrams
10,210 decigrams
102,100 decigrams
1,021,000 decigrams
Answer:
102200
Step-by-step explanation:
564+458= 1022
1 decagram=100 decigram
So multiply the sum by 100
1022*100=102200
What is the area of the triangle? 20 16 12 heh sorry !!!!!!
Answer:
96 units^2
Step-by-step explanation:
The formula for the area of a triangle: b*h/2
b= 12
h= 16
Work:
12*16/2
192/2
96 uints^2
Answer:
[tex] {96} \: cm[/tex]^{2}Step-by-step explanation:
Hope it is helpful...Help I don’t know how to do this
Answer:
[see below]
Step-by-step explanation:
[tex]3*2^t[/tex]
When 't' is 1:
[tex]3*2^1\\\\3*2\\\\\boxed{6}[/tex]
When 't' is 4:
[tex]3*2^4\\\\3*16\\\\\boxed{48}[/tex]
Hope this helps.
Answer:
Step-by-step explanation:
3 time 2 with the power of t
You see the given values, 1 and 4?
All you need to do is replace those values with 1 and 4.
3 x 2 with the power of 1.
2 times the power of one is just 2 because you aren't multiplying it with another 2.
So, 3 times 2 is 6.
3 x 2 with the power of 4
2 x 2 x 2 x 2 = 16
It's not 2 times 4; it's 2 times the power of 4-- which means we multiply the number by itself depending on the given value we're given.
I hope this helps!
Find 45% of 60???????
Answer:
27
Step-by-step explanation:
To find 45% of 60, you can multiply 60 by 0.45
60 x 0.45 = 27
45% of 60 is 27.
Which equation represents exponential growth?
y=(0.25)^x
y= 1/3(0.1)^x
y=(7)^x
y=(2/3)^x
Answer:
y=(7)^x represents the exponential growth
Answer:y=(7)^x exponential growth, and do you use monarch aop? cause i do and i was wondering
Step-by-step explanation:
The sum of the age of a girl and her brother is 34. The girl is 8 years older than her heather, how old is her brother
Answer:
26
Step-by-step explanation:
if she is 8 years older, then is just 34-8 which is 26
Find the value of x
144 (x-36)
Answer:
it answer is 180
Step-by-step explanation:
plz mark me as brainlist
Answer:
[tex]\huge\boxed{\fcolorbox{green}{violet}{Answer}}[/tex]
[tex]144(x - 36) \\ = 144 \times x - 144 \times 36 \\ = 144x - 5184 \\ x = \frac{5184}{144} \\ x = 36[/tex]
Summary
Suppose a quadratic expression in standard form has a value of c = 0. Can this quadratic expression be
factored? How do you know?
Answer:
yesx is a factorStep-by-step explanation:
You want to know if the standard form quadratic equation ax² +bx +c = 0 can be factored when c=0.
C = 0When the constant is zero, the equation becomes ...
ax² +bx = 0
Factoring out x, we have a factored form as ...
x(ax +b) = 0
showing that the equation can always be factored.
A quadratic polynomial which has zeros at -7 and 5. ?
Answer:
x^2 + 2x - 35
Step-by-step explanation:
Sum of zeros
= - 7 + 5
= - 2
Product of zeros
= - 7 x 5
= - 35
x^2 - ( sum of zeros )x + product of zeros
= x^2 - ( - 2 ) x + ( - 35 )
= x^2 + 2x - 35
The Quadratic polynomial is x^2 + 2x - 35.
How many ounces each of a 63% acid solution and a 33% acid solution must be mixed to produce 100 ounces of a 39% acid solution?
Answer:
20 ounces of the 63% solution and 80 ounces of the 33% solution.
Step-by-step explanation:
Let x = number of ounces of 63% solution.
Let y = number of ounces of 33% solution.
The total solution to be made is 100 oz.
x + y = 100
x ounces of 63% solution is 0.63x ounces of acid.
y ounces of 33% solution is 0.33y ounces of acid.
100 ounces of 39% solution is 39 ounces of acid
0.63x + 0.33y = 39
The system of equations is
x + y = 100
0.63x + 0.33y = 39
Multiply the both sides of the first equation by -0.33. Then add it to the second equation.
-0.33x - 0.33y = -33
+ 0.63x + 0.33y = 39
---------------------------------
0.3x = 6
x = 6/0.3
x = 20
x + y = 100
20 + y = 100
y = 80
Answer:
20 ounces of the 63% solution and 80 ounces of the 33% solution.
Radius of 256/3π cm³
-50 POINTS- Already asked 3 times someone help pls. Don’t guess either.
Answer:
To find the coordinates of the point on the x-axis that is reflected over the x-axis from the point P, you can use the formula (x, -y). In this case, the x-coordinate of point P is 4, so the x-coordinate of the reflected point will also be 4. The y-coordinate of point P is 7, so the y-coordinate of the reflected point will be -7. Therefore, the coordinates of the reflected point are (4, -7).