[tex]~~~~125x^9+64\\\\=(5x^3)^3+4^3\\\\=(5x^3 +4)[(5x^3)^2 - (5x^3)(4) + 4^2]\\\\=(5x^3 +4)(25x^6-20x^3+16)[/tex]
Which of the following exponential regression equations best fits the data shown below?
X -4 -3 -2 -1 0 1 2 3 4
y 1.07 1.98 2.93 3 9 10 16 25 36
A. y 3.02 3.67*
B. y 6.61 1.55*
C. y 2.27 2.09*
D. y = 8.04.0.98*
The exponential regression equation that fits the data is D. y = 8.04.0.98ˣ.
How to depict the equation?The quickest way is probably to do direct substitution. First, let's try f(0). The values of y predicted by the four equations are, respectively, 3.14, 5.32, 10.84, and 8.46.
From here, it looks like C and D are the closest to the observed data. Let's try f(4) on C and D.
10.84(1.77)⁴ = 10.84 × 9.815 = 106.4
8.46(3.51)⁴ = 8.46 × 151.4 = 1284
Therefore, the exponential regression equation that fits the data is y = 8.04.0.98ˣ.
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A book store is hosting a special night in which families can enjoy a story and craft time. Tickets to the event must be purchased ahead of time and are $1.50 for children and $2.50 for adults. So far, 45 children's tickets have been sold, which is 60% of the total tickets sold. How many tickets have been sold so far? Show your calculations or explain how you got your answer.
Need help pls
A book store is hosting a special night in which families can enjoy a story and craft time. The ticket have been sold so far would be 75.
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.
We have given that 45 children's tickets have been sold, being 60% of the total tickets having been sold.
So, we have to solve for x:
60% × x = 45
60/100 × x = 45
Multiplying both sides by 100 and dividing both sides by 60,
x = 45 × 100/60
x = 75
Thus, the ticket have been sold so far would be 75.
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Which algebraic expression is equivalent to the expression below? 2(x - 5) + 13(x + 7) please help!!
Answer:
C
Step-by-step explanation:
What is the volume of a cylinder of radius 3.5m and height 12m ?
Answer:
462
Step-by-step explanation:
Base=π × r²
=> π × 3.5²
=>38.48
Volume:
Base times height
=>38.48 x 12
=>461.81
Answer:
426m²Step-by-step explanation:
Given ;
radius = 3.5m , hieght = 12mVolume of cylinder = π2²h
22/7 × ( 3.5 )² × 1222/7 × ( 7/2 )² × 12 22/7 × 7/2 × 7/2 × 12462m²Volume of the cylinder is 426m².
how to find the volume of a room
multiply the height x the length x the width to find the volume of a room (or another 3d object)
compare the graph of g(x) = x^2 + 6 with the graph of f(x)=x^2
If the parent graph is transformed to x^2 + 6, this shows that the parent function translated 6 units up the graph to create the graph x^2+6
What are quadratic graphsThese are graph with function of leading degree of 2. The parent function for a quadratic graph is x^2
f(x)= x^2
If the parent graph is transformed to x^2 + 6, this shows that the parent function translated 6 units up the graph to create the graph x^2+6
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Question 3 of 21
The graphs below have the same shape. The equation of the blue graph is
f(x)=Ix. Which of these is the equation of the red graph, g(x)?
y f(x) = |x|
g(x) = ?
A. g(x) = x +5
B. g(x) = x+ 51
C. g(x) = 1x1-5
OD. g(x)=Ix-51
The equation of the red graph, g(x) is g(x) = |x| - 5
How to determine the equation of the red graph, g(x)?The graph that completes the question is added as an attachment
The function f(x) is given s:
f(x) = |x|
From the attached graph, we can see that the function f(x) is shifted 5 units down to get to g(x).
This means that:
g(x) = f(x) - 5
Substitute f(x) = |x|
g(x) = |x| - 5
Hence, the equation of the red graph, g(x) is g(x) = |x| - 5
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You have a spinner with red and blue regions. When you spin, it comes up blue 60 percent of the time. You do an experiment where you spin the spinner 180 times, and it comes up blue 114 times. (a) What proportion of spins came up blue in your sample
Explanation:
Divide the number of times blue came up (114) over the number of spins total (180). Ignore the 60% given to you. That's a theoretical value that doesn't play any part in determining an experimental probability.
114/180 = 0.633 approximately
The '3's go on forever. Round that however your teacher instructs.
In a survey of 100 people, 60 like farming, 65 like civil service. Draw a venn-diagram and find the number of people who like farming as well as civil service.
Answer:
Ur question is wrong..
Step-by-step explanation:
In a survey of 100 people, 60 like farming and 65 like civil service?
60+65=125..?
5/9 divided by 20/27 in its simplist form
Answer: 3/4
Step-by-step explanation: Find the reciprocal of the divisor
Reciprocal of 20/27: 27/20
Now, multiply it with the dividend So, 5/9 ÷ 20/27 = 5/9 × 27/20= 5 × 27/9 × 20 = 135/180
After reducing the fraction, the answer is
3/4
2 ^ x = 3 ^ (x + 1) solve for x
Answer:
-2.71
Step-by-step explanation:
This exponential equation can be solved by rewriting it so there is only one base, then using logarithms.
__
solve for x2^x = 3^(x+1) . . . . . given
2^x = 3·3^x . . . . . . eliminate the constant in the exponent
(2/3)^x = 3 . . . . . . . divide by 3^x
x·log(2/3) = log(3) . . . . take logarithms
x = log(3)/log(2/3) ≈ -2.7095113
The value of x is about -2.71.
__
Alternate solution
Taking logarithms transforms this exponential equation to a linear equation.
x·log(2) = (x +1)·log(3) . . . . take logs
x(log(2) -log(3)) = log(3) . . . . . . subtract x·log(3)
x = log(3)/(log(2) -log(3)) = log(3)/log(2/3) . . . . . same result as above
_____
Additional comment
In the attached, we have used a graphing calculator to find the x-intercept of the function f(x) = 0, where f(x) = 2^x -3^(x+1). This is the solution to the given equation.
The applicable rules of logarithms are ...
log(a^b) = b·log(a)
log(a/b) = log(a) -log(b)
A bag contains 6 white marbles and 4 black
marbles. A marble is drawn from the bag
and then a second marble is drawn without
replacing the first one.
What is the probability of drawing a white
marble on the first draw, followed by a black
marble on the second?
The probability of drawing a white marble on the first draw, followed by a black marble on the second is 4/15
How to determine the probability?The distribution of the marbles is given as:
White = 6
Black = 4
When the white marble is drawn, the probability is:
P(White) = 6/10
Now, there are 9 marbles left.
When the black marble is drawn, the probability is:
P(Black) = 4/9
The required probability is:
P = 6/10 * 4/9
Evaluate
P = 4/15
hence, the probability is 4/15
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If a, a²+ 1 and a+6 are in an AS, find the possible values of a.
it's of optional math. If someone know how to solve this. please help me I have been trying this for like half hour
a, a² + 1 and a + 6 are all in arithmetic progression, in which there is a fixed difference d between consecutive terms. This mean we have
a² + 1 = a + d
a + 6 = a² + 1 + d
Eliminate d and solve for a :
(a² + 1) - (a + 6) = (a + d) - (a² + 1 + d)
a² - a - 5 = -a² + a - 1
2a² - 2a - 4 = 0
a² - a - 2 = 0
(a - 2) (a + 1) = 0
a - 2 = 0 or a + 1 = 0
a = 2 or a = -1
find the smallest number of terms of the AP "-54,-52.5,-51,-49.5" ....that must be taken for the sum of the terms to be positive
The smallest number of terms of the AP that will make the sum of terms positive is 73.
Since we need to know the number for the sum of terms, we find the sum of terms of the AP
Sum of terms of an APThe sum of terms of an AP is given by S = n/2[2a + (n - 1)d] where
n = number of terms, a = first term and d = common differenceSince we have the AP "-54,-52.5,-51,-49.5" ....", the first term, a = -54 and the second term, a₂ = -52.5.
The common difference, d = a₂ - a
= -52.5 - (-54)
= -52.5 + 54
= 1.5
Number of terms for the Sum of terms to be positive
Since we require the sum of terms , S to be positive for a given number of terms, n.
So, S ≥ 0
n/2[2a + (n - 1)d] ≥ 0
So, substituting the values of the variables into the equation, we have
n/2[2(-54) + (n - 1) × 1.5] ≥ 0
n/2[-108 + 1.5n - 1.5] ≥ 0
n/2[1.5n - 109.5] ≥ 0
n[1.5n - 109.5] ≥ 0
So, n ≥ 0 or 1.5n - 109.5 ≥ 0
n ≥ 0 or 1.5n ≥ 109.5
n ≥ 0 or n ≥ 109.5/1.5
n ≥ 0 or n ≥ 73
Since n > 0, the minimum value of n is 73.
So, the smallest number of terms of the AP that will make the sum of terms positive is 73.
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Rewrite \sqrt((1+cos45)/(2)) using a half-angle identity
[tex]\stackrel{\textit{Half-Angle Identities}}{cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}}} \\\\[-0.35em] ~\dotfill\\\\ \sqrt{\cfrac{1+cos(45^o)}{2}}~~ = ~~cos\left( \cfrac{45^o}{2} \right)\implies \sqrt{\cfrac{1+cos(45^o)}{2}}~~ = ~~cos(22.5^o)[/tex]
Find the area of the shade regions. Give your answer as a completely simplify exact value in terms of pie(no approximation). a=
Answer:
41.87 cm²
Step-by-step explanation:
Area of shaded region :
Area (sector of radius 7 cm) - Area (sector of 3 cm)π × θ/360° (r₁² - r₂²)3.14 x 120/360 (49 - 9)3.14 x 1/3 x 40125.6/341.87 cm²Evaluate the following limit:
[tex]\displaystyle \lim_{x \to \infty}{\frac{(x^2 + 1)^2 - 3x^2 + 3}{x^3 - 5}}[/tex]
If we evaluate the function at infinity, we can immediately see that:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle L = \lim_{x \to \infty}{\frac{(x^2 + 1)^2 - 3x^2 + 3}{x^3 - 5}} = \frac{\infty}{\infty}} \end{gathered}$}[/tex]
Therefore, we must perform an algebraic manipulation in order to get rid of the indeterminacy.
We can solve this limit in two ways.
Way 1:By comparison of infinities:
We first expand the binomial squared, so we get
[tex]\large\displaystyle\text{$\begin{gathered}\sf \displaystyle L = \lim_{x \to \infty}{\frac{x^4 - x^2 + 4}{x^3 - 5}} = \infty \end{gathered}$}[/tex]
Note that in the numerator we get x⁴ while in the denominator we get x³ as the highest degree terms. Therefore, the degree of the numerator is greater and the limit will be \infty. Recall that when the degree of the numerator is greater, then the limit is \infty if the terms of greater degree have the same sign.
Way 2Dividing numerator and denominator by the term of highest degree:
[tex]\large\displaystyle\text{$\begin{gathered}\sf L = \lim_{x \to \infty}\frac{x^{4}-x^{2} +4 }{x^{3}-5 } \end{gathered}$}\\[/tex]
[tex]\ \ = \lim_{x \to \infty\frac{\frac{x^{4} }{x^{4} }-\frac{x^{2} }{x^{4}}+\frac{4}{x^{4} } }{\frac{x^{3} }{x^{4}}-\frac{5}{x^{4}} } }[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=\lim_{x \to \infty}\frac{1-\frac{1}{x^{2} } +\frac{4}{x^{4} } }{\frac{1}{x}-\frac{5}{x^{4} } } \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\frac{1}{0}=\infty } \end{gathered}$}[/tex]
Note that, in general, 1/0 is an indeterminate form. However, we are computing a limit when x →∞, and both the numerator and denominator are positive as x grows, so we can conclude that the limit will be ∞.
I start a walk at 2.47pm. The walk takes 85 minutes. What time does the walk finish?
Answer:
4:12pm
Step-by-step explanation:
85 minutes = 1 hour and 25 minutes
2:47pm + 1 hour 25 minutes = 3:72 pm
72 minutes = 1 hour 12 minutes so add another 1 hour to 3 and the balance is 12 minutes so walk ends at 4:12pm
Another way to look at it is as follows:
After 13 minutes, the time is 2:47 + 0:13 = 3pm
Remaining time left is 85-13 = 72 minutes = 1 hour: 12 minutes. Add that to 3pm and you get 4:12pm
Evaluate the expression 2(8-4)2-10/2
Step-by-step explanation:
here is your answer
hope it help u
Answer:
16
Step-by-step explanation:
2(8 - 4) 2
first, you'll subtract 4 from 8 to get 4.
Next 2 X 4 X 2
Multiply 2 and 4 by doing that you'll get 8
lastly 8 X 2
Multiply 8 and 2 to get your answer 16.
Pls mark brainiest pls
What is the approximate distance between points A and B?
A
-4-3-2
06.32
06.95
07.62
08.56
B
432
052 37
-1
-4
12345
Answer: 7.62
Step-by-step explanation:
[tex]AB=\sqrt{(-2-1)^{2}+(-3-4)^{2}}=\sqrt{9+49}=\sqrt{58} \approx 7.62[/tex]
A, B & C lie on a straight line.
D, C & E lie on a different straight line.
Angle y= 107° and angle z = 56°.
Work out x
Answer:
x = 129°
Step-by-step explanation:
∠ ABD and ∠ DBC are a linear pair and sum to 180° , then
y + ∠ DBC = 180°
107° + ∠ DBC = 180° ( subtract 107° from both sides )
∠ DBC = 73°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles , then
x = ∠ DBC + z = 73° + 56° = 129°
Consider these dimensions for a cylindrical aquarium.
A cylinder with height 14 feet and radius 25 feet.
The measures have been substituted in the formula for the volume of a cylinder.
V = π252(14)
Approximately how much water will fill the tank?
Use the calculator to approximate the amount to the nearest hundredth.
cubic feet
The amount of water that will fill the tank is 11100 cu.ft to the nearest hundredth.
What is a Cylindrical figure ?A cylinder is a three dimensional figure with two identical circular faces at each end , and a curved surface.
It does not have an edges or vertices.
It is given in the question that
A cylinder with height 14 feet and radius 25 feet.
The volume of a cylinder.
V = π252(14)
The water than can be filled is equal to the volume of the cylinder
V = 11088 cu.ft
There the amount of water that will fill the tank is 11100 cu.ft to the nearest hundredth.
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Answer: 27,488.94 cubic feet
Step-by-step explanation:
The table below shows the different combinations of honey and oats that can be used in making granola
Answer:
10:4
Step-by-step explanation:
it can be simplified
We can actually deduce here that the honey to oats ratio that doesn't follow the pattern in the table is: 10:4.
What is ratio?Ratio actually refers to the way that two or more numbers are compared in relation to their size to each other. It shows how much of one number is found in another.
From the honey to oats ratio, we can see that the pattern goes thus:
5 - 2 = 3 (this should be the number of cups of oat for the next role of ratio).This is because 10 - 3 = 7
Then 15 - 7 = 8
Therefore, the ratio that doesn't follow the pattern is 10:4.
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Which of the following could be the equation of a line perpendicular to the line 2x−5y=7?
The equation of a line perpendicular to the line 2x − 5y = 7 is y = (-5/2)x + b
What is an equation?An equation is an expression that shows the relationship between two or more variables or numbers.
Two lines are said to be perpendicular if the product of their slopes is equal to -1.
The slope of the line:
2x - 5y = 7
5y = 2x - 7
y = (2/5)x - 7
The slope of the line 2x - 5y = 7 is 2/5. The slope of the line perpendicular is -5/2
Hence:
The equation of a line perpendicular to the line 2x − 5y = 7 is y = (-5/2)x + b
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A population of aardvarks is growing at a rate of 2% per year. This year there are 714 aardvarks. How many aardvarks were there last year
A population of aardvarks is growing at a rate of 2% per year, there are 714 aardvarks this year and 700 aardvarks were there last year.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the amount of aardvarks after x years.
It can be represented by the equation:
y = a(1.02)ˣ
If this year there are 714 aardvarks, the amount in the last year is:
714 = a(1.02¹)
a = 700
A population of aardvarks is growing at a rate of 2% per year, there are 714 aardvarks this year and 700 aardvarks were there last year.
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A line passes through the points (-3,-4) and (6,2)
What is the x intercept of this line?
Answer: x - int : (3,0)
Step-by-step explanation:
point-slope form: y - y1 = m(x - x1)
m = y2-y1/x2-x1
= -4-2/-3-6
=-6/-9
= 2/3
y1 = 2
x1 =6
y - 2 = 2/3(x-6)
x -int: when y = 0, what is x?
0-2 = 2/3(x-6)
-2 = 2/3x - 4
2 = 2/3x
x=3
~Hope this helps!~
What is the value of y in the equation 5x 2y = 20, when x = 0.3? 2.5 2.8 9.25 10.75
Answer:
Y = 9.5
(option C)
Hallar la ecuación de la recta qué pasa por el punto (2,3) y cuya abscisa en el origen es el doble que la ordenada en el origen
Complete the steps to identify all potential rational roots of f(x) = 3x2 – x – 4.
De vergelijking moet je gelijk zetten aan 0. Vervolgens bereken je discriminant.
Beide x zijn de snijpunten met de x-as.
-4 is de snijpunt met de y-as
Iam sorry for this language.
its dutch, you can translate it to english
The measure of Angle DCG is 145° What is AngleDCE?
Answer:
Divide each term in
D
C
G
=
145
°
by
C
G
and simplify.
D
=
145
°
C
G
Step-by-step explanation:
ty