Answers
SOLUTION
Part 1
The independent variable are the predicting varaible for which other variable are depends on. The are the x- values
Hence
The indepedent varibles is school year
The dependent variable are the responses variables. They are the y-values for which depends on othere values,
Hence
The dependent variable for the data given is
The Tution
Part 2
To find the function, we need to set up the data as given in the table below.
The years has an interval of 1 and each fees difer by 4, the to obtain the x-values we use the mid-point
\(x=\frac{\text{lower}+\text{higher}}{2}\text{ for each }\)Hence
The data plot will be
The linear is given by the form
\(\begin{gathered} y=ax+b \\ \text{Where }^{} \\ a=561.043,\text{ b=-0.0000}010994 \\ \text{Hence } \\ y=561.043x-0.0000010994 \end{gathered}\)THerefore
The linear regression is y = 561. 043x -0.0000010994
Then for exponenetial we have
\(\begin{gathered} y=e^{ax+b} \\ \text{Where } \\ a=0.0286229,b=-47.2727 \\ \text{Hence } \\ y=e^{0.029x-47.27} \end{gathered}\)Hence
The exponential regression is y = e^(0.029x-47.27)
For the power represion we have
\(\begin{gathered} y=ab^x \\ \text{Where } \\ a=2.9495\times10^{-21,}b=1.02904 \\ \text{Hence } \\ y=2.9495\times10^{-21,}(1.02904)^x \end{gathered}\)Hence
The power regression is
y= 2.9495 x 10^-21 (1.02904)ˣ
Part 3
The graoh lot for linear function is given below
The graph for the exponential plot is
The graph for the power regression plot is given below as
Related Questions
Hank made payments of $219 per month at the end of each month for 30 years to purchase a piece of property. He promptly sold it for $195,258. What interest rate, compounded monthly, would he need to earn on an ordinary annuity for a comparable rate of return?
Answers
To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.
To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.
First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.
Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.
Using the formula for the present value of an ordinary annuity, we have:
PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.
Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.
Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.
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Write the point slope form of a line that passes through (1,-5) and is perpendicular to a line with a slope of 1
Answers
Answer:
y + 5 = -1 (x - 1)
Step-by-step explanation:
y = -1
y + 5 = -1 (x - 1)
The town’s highway department marks a new road with reflective markers. The road is on a 6 3/4 miles stretch in length. How many markers would be needed if the markers are spaced every 1/8 of a mile?
Answers
Answer:
54 markers.
Step-by-step explanation:
First take 6 3/4 which also equals .75 and 1/8 which also equals .125. Now divide 6.75 by 0.125 which equals 54.
a diver dove to a location 6 3/5 meters below sea level. He then dove to a second location 8 1/5 meters below sea level. How many meters are there between the two locations?
Answers
Answer:
\(1\frac{3}{5}\) meter is the difference in depths of locations diver dove.
Step-by-step explanation:
In △ △ ABC, CJ = 18. If CG = BG, what is KJ? Triangle A B C is divided by 4 segments. A H is the height. C J extends from C to side A B. B I extends from B to side A C. H I extends from the height on B C to I on A C. C J and B I intersect at point K. A J and B J are congruent. A I and C I are congruent.
Answers
Solving for CI in terms of the given lengths, we get: \(Cl=\frac{\sqrt{BG^{2} -IM^{2} } }{\sqrt{2} }\)
Substituting this expression for CI and the given value for CG into the expression for BI, we get: \(BI=CG-\frac{\sqrt{BG^{2} -IM^{2} } }{\sqrt{2} }\).
What is triangle?A triangle is a three-sided polygon, which is a closed two-dimensional shape with straight sides. In a triangle, the three sides connect three vertices, or corners, and the angles formed by these sides are called the interior angles of the triangle. The sum of the interior angles of a triangle is always 180 degrees. Triangles can be classified by their side lengths and angle measurements. For example, an equilateral triangle has three sides of equal length, and all of its angles are 60 degrees; an isosceles triangle has two sides of equal length, and its base angles are also equal; a scalene triangle has three sides of different lengths, and all of its angles are also different. Triangles are a fundamental shape in mathematics and geometry, and they have numerous applications in fields such as architecture, engineering, physics, and more.
Given by the question.
Based on the given information, we can start by drawing a diagram of triangle ABC and the segments AH, BJ, CI, CJ, and BI as described.
Since CG = BG, we can draw the perpendicular bisector of side AC passing through point G, which will intersect side AB at its midpoint M.
Now, we can see that triangle CGB is isosceles with CG = BG, so the perpendicular bisector of side CB also passes through point G. This means that G is the circumcenter of triangle ABC, and therefore, the distance from G to any vertex of the triangle is equal to the radius of the circumcircle.
Next, we can use the fact that AJ and BJ are congruent to draw the altitude from point J to side AB, which we will call JN. Similarly, we can draw the altitude from point I to side BC, which we will call IM.
Since AJ and BJ are congruent, the altitude JN will also be the perpendicular bisector of side AB, so it will pass through point M. Similarly, the altitude IM will pass through point G, which is the circumcenter of triangle ABC.
Now, we can use the Pythagorean theorem to find the lengths of JN and IM in terms of the given lengths:
\(JN^{2}= AJ^{2} -AN^{2} \\ = ( AH+HN)^{2} - AN^{2} \\=AH^{2} +2AH*HN+HN^{2}-AN^{2} \\\)
\(IM^{2}= CI^{2} -CM^{2} \\=( CG-GM)^{2} -CM^{2} \\CG^{2}-2CG*GM+GM^{2} -CM^{2}\)
Since CG = BG and GM = BM (since M is the midpoint of AB), we can simplify the expression for IM^2 as follows:
\(IM^{2}\) = \(BG^{2}\) - 2BG * BM + \(BM^{2}\) - \(CM^{2}\)
= \(BG^{2}\) - \(BM^{2}\) - \(CM^{2}\)
Now, we can use the fact that BJ and CI intersect at point K to find the length of KJ:
KJ = BJ - BJ * (CK/CI)
= BJ * (1 - CK/CI)
= BJ * (1 - BM/CM)
To find BM/CM, we can use the fact that triangle BCI is isosceles with BI = CI, so the altitude IM is also a median of the triangle. This means that CM = 2/3 * BI. Similarly, we can find BJ in terms of JN using the fact that triangle ABJ is isosceles with AJ = BJ:
BJ = 2 * JN
Substituting these expressions into the equation for KJ, we get:
KJ = 2 * JN * (1 - 2/3 * BI/CM)
Now, we just need to find BI/CM in terms of the given lengths. Using the fact that triangle BCI is isosceles with BI = CI, we can find BI in terms of CG:
BI = CG - CI
Substituting this expression into the equation for \(IM^{2}\)and simplifying, we get:
\(IM^{2}\) =\(BG^{2}\) - CG * CI
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.......... do it now? Can't I do it later?
a) I've to
b) Have I
c) Do I have to
d) Should I
Answers
Answer:
d
Step-by-step explanation:
You are asking a question trying to suggest whether it can be done later
The function f(x)=4^x-6 is transformed to function G through a vertical compression by a factor of 1/2. Complete the equation of function G .  enter the correct answer in the box. Substitute  numerical values into the equation for a and k.
g(x) = a(4)^x-k
Answers
The equation for the transformed function g(x) is: g(x) = 2.323 (4) raise to the power x-0.872/2
How to solve a function?
If the function f(x) is vertically compressed by a factor of 1/2, the equation for the new function g(x) is given by:
g(x) = a(4) raise to the power x-k/2
where "a" and "k" are constants that need to be determined. To find these constants, we can use the fact that the original function f(x) is equal to g(x) when the compression is applied:
f(x) = g(x)/2
Substituting the expression for g(x) into this equation and simplifying, we get:
4raise to the power x - 6 = a(4)raise to the power x-k/2
To solve for "a" and "k", we need to find two equations involving these variables. One way to do this is to evaluate the expression for f(x) at two different values of x, and then set those equal to the corresponding values of g(x)/2. For example, we can choose x = 0 and x = 1:
f(0) = 4 - 6 = -5
f(1) = 4- 6 = -2
Using the equation g(x)/2 = f(x), we can write:
g(0)/2 = -5
g(1)/2 = -2
Substituting the expression for g(x) into these equations, we get:
a(4) raise to the power -k/2 = -10
a(4) raise to the power 1-k/2 = -4
Taking the ratio of these two equations, we can eliminate the variable "a" and solve for "k":
(4)raise to the power -k/2 / (4) raise to the power 1-k/2 = -10 / -4
Simplifying this equation, we get:
4.raise to the power(1-k/2) = 5
Taking the logarithm of both sides (with base 4), we get:
1-k/2 = log4(5)
Solving for "k", we get:
k = 2 - 2 log4(5)
Substituting this value of "k" back into one of the equations we derived earlier, we can solve for "a":
a = -10 / (4) raise to the power -k/2
Substituting the numerical value of "k", we get:
k = 2 - 2 log4(5) ≈ 0.872
a = -10 / (4) raise ti the power -k/2 ≈ 2.323
Therefore, the equation for the transformed function g(x) is:
g(x) = 2.323 (4)raise to the power x-0.872/2
or equivalently:
g(x) = 1.1615 (4) raise to the power -x0.872
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Answer:
g(x) = 1/2 (4)^x - 3
Step-by-step explanation:
A vertical compression by a factor of 1/2
means that the entire function f is multiplied by 1/2:
1/2 f (x) = 1/2 (4^x - 6)
= 1/2 (4)^x - 3
Eloise's math tutor used algebra tiles to model 3n + 4 - n + 5. What is the simplified form of this expression?
Answers
Answer:
2n + 9
Step-by-step explanation:
3n - n + 4 + 5 = 2n + 9
4. Find the following function values.
(3)/ (3)
( (2))
f(f'(-4))
g(x+2)
Answers
Answer:
1. 9
2.2
3.0
4.gx +2g
Step-by-step explanation:
find the third, fourth, and fifth terms of the sequence defined by
a1 = 1, a2 = 3,
and
an = (−1)nan − 1 + an − 2
for
n ≥ 3.
Answers
The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.
The sequence is defined by the following formula:
a1 = 1, a2 = 3,
and
an = (-1)nan - 1 + an - 2 for n ≥ 3.
To find the third term (a3), we substitute n = 3 into the formula:
a3 = (-1)(3)(a3 - 1) + a3 - 2.
Next, we simplify the equation:
a3 = -3(a2) + a1.
Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:
a3 = -3(3) + 1.
Simplifying further:
a3 = -9 + 1.
Therefore, the third term (a3) is equal to -8.
To find the fourth term (a4), we substitute n = 4 into the formula:
a4 = (-1)(4)(a4 - 1) + a4 - 2.
Simplifying the equation:
a4 = -4(a3) + a2.
Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:
a4 = -4(-8) + 3.
Simplifying further:
a4 = 32 + 3.
Therefore, the fourth term (a4) is equal to 35.
To find the fifth term (a5), we substitute n = 5 into the formula:
a5 = (-1)(5)(a5 - 1) + a5 - 2.
Simplifying the equation:
a5 = -5(a4) + a3.
Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:
a5 = -5(35) + (-8).
Simplifying further:
a5 = -175 - 8.
Therefore, the fifth term (a5) is equal to -183.
In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.
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use the given circle. Find the length s to the nearest tenth A. 33.5 cm B. 8.4 cm C. 16.8 cm D. 5.3 cm
Answers
Answer:
16.8
Step-by-step explanation:
s = ∅ × r
= 2π/3 × 8
= 16/3 * π
= 16.75516
= 16.8
Answer:
C.) 16.8 is your answer
Step-by-step explanation:
Its about fractions please help me
Answers
The times the 7 in the Susan's scores is greater than Sarah's score is 100 times
How many times is the 7 in the scores greater than the otherFrom the question, we have the following parameters that can be used in our computation:
Susan = 87, 325
Sarah = 46, 175
The values of the 7's in their scores are
Susan = 7, 000
Sarah = 70
So, we have
Number of times = 7000/70
Evaluate
Number of times = 100
Hence, the number of times is 100
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What name is given to an angle that
measures 150°?
Answers
Answer:
Obtuse
Step-by-step explanation:
Since 150°>90°, it is an obtuse angle
Usingset notation, what is the solution to the following equation? a ^ 2 + 3 = 19
Answers
What is the solution to x2 – 9x < –18? ASAP will give brainliest
x < –6 or x > 3
–6 < x < 3
x < 3 or x > 6
3 < x < 6
Answers
The solution to the inequality equation \(x^{2}\) – 9x < –18 is 3 < X < 6
Inequality equationInequality equation means a mathematical expression in which the sides are not equal to each other
\(x^{2}\) – 9x < –18
Rewrite in standard form
x^2 -9x +18 < 0
Factorise the equation
\(x^{2}\) - 3x -6x +18 < 0
x (x - 3) - 6 (x - 3) < 0
(x - 3) ( x- 6) < 0
(x - 3) < 0
x < 3
( x- 6) < 0
x < 6
3 < X < 6
Therefore, the solution to the inequality is 3 < X < 6
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A student ran a distance of 3 1/2miles each day for 5 days. Then the student ran a distance of 4 1/4 miles each day for the next 5 days. What was the total distance in miles the student ran during these 10 days?
Answers
Answer:
To find the total distance, we need to add up the distance the student ran in the first 5 days and the distance the student ran in the next 5 days.
Distance for the first 5 days = 3 1/2 miles/day × 5 days = 17.5 miles
Distance for the next 5 days = 4 1/4 miles/day × 5 days = 21.25 miles
Total distance = Distance for the first 5 days + Distance for the next 5 days
Total distance = 17.5 miles + 21.25 miles
Total distance = 38.75 miles
Therefore, the student ran a total of 38.75 miles during these 10 days.
5x + 6y = 20 , 8x - 6y = -46
Answers
Answer:
5x + 6y = 20_____(1)
8x - 6y = -46_____(2)
Solving simultaneously:
Eqn(1) + Eqn(2)
5x + 8x + 6y + (-6y) = 20 + (-46)
13x = -26
x = -2
substituting this into Eqn (1):
5(-2) + 6y = 20
-10 + 6y = 20
6y = 30
y = 5
hence:
x = -2,y = 5.
Instead I’d using the values 1,2,3,4,5,6 on dice, suppose a pair of dice have the following 1,2,2,3,3,4 on one die and 1,3,4,5,6.8 on the other.find the probability of rolling a sum of 12
Answers
Answer:1/24
Step-by-step explanation:
Since the first die has 4 distinct numbers, and second has 6 distinct numbers, so total number of combinations possible = 4 × 6 = 24
Now, the number of chances where we get the rolling sum as 12 is only one. (
Therefore, the probability of getting sum 12 is 1/24
Answer:
1/36
Step-by-step explanation:
For the acellus people
For any positive integer n, the value of n! is the product of the first n positive integers. For example, 4! = 4 * 3 * 2 * 1 =24. What is the greatest common divisor of 5! and 7! ?
Answers
The greatest common divisor of 5! and 7! is 840.
To find the greatest common divisor (GCD) of 5! and 7!, we need to calculate the prime factorization of both numbers.
First, let's calculate the prime factorization of 5!:
5! = 5 * 4 * 3 * 2 * 1 = 120.
The prime factorization of 120 is 2^3 * 3 * 5.
Now, let's calculate the prime factorization of 7!:
7! = 7 * 6 * 5! = 7 * 6 * 120 = 5040.
The prime factorization of 5040 is 2^4 * 3^2 * 5 * 7.
To find the GCD of 5! and 7!, we need to find the common factors in their prime factorizations. We take the smallest exponent for each prime factor that appears in both factorizations.
From the prime factorizations above, we can see that the common factors are 2^3, 3, 5, and 7. Multiplying these factors together gives us:
GCD(5!, 7!) = 2^3 * 3 * 5 * 7 = 8 * 3 * 5 * 7 = 840.
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Select two ratios that are equivalent to 7: 10.
Just trying to get my late work done ✅ thxs
Answers
Answer:
21:30
35:50
Step-by-step explanation:
21 divide by 3 =7 30 divide by 3=10
35 divide by 5=7 50 divide by 5=10
PLZ ANSWER IF U KNOW THE ANSWER
Answers
Answer:
Scott
Step-by-step explanation:
you got it right, -20 absolute value is 20
please simplify this equation
Answers
Answer:
The answer is -24√35
Step-by-step explanation:
-6√7 × 4√5
Using the rules of surds multiply the numbers outside the square root and the ones inside
That's
(-6×4)(√ 7 × √5)
= - 24√7×5
= -24√35
Hope this helps you
Answer:
-24√35
Step-by-step explanation:
-6√7 × 4√5
-6 × √7 × 4 √5
-6 × 4 × √7 × √5
-24 × √(7 × 5)
-24√35
can anyone help. me pass
Answers
Finding the inverse of the cube of a bijective function. i About For a function f : R + R, we will define f-cube as f-cube(x) = (f(x))3 . (a) Prove that if f is a bijection, then f-cube is also a bijection. You can use the fact that for any two real numbers x and y, if x = y, then æ1/ well-defined real number. 1/3 = y1/3. Also for any real number x, x1/3 is a (b) For a bijection f, what is the inverse of f-cube? Justify your answer. Feedback?
Answers
if f is a bijection, then f-cube is also a bijection, and the inverse of f-cube is f^-1(y1/3). These results are important for understanding the properties of functions and their inverses.
Finding the inverse of the cube of a bijective function is an important step in understanding the properties of functions. To prove that f-cube is a bijection if f is a bijection, we can use the fact that for any two real numbers x and y, if x = y, then x1/3 = y1/3. This means that if f(x) = f(y), then (f(x))3 = (f(y))3, or f-cube(x) = f-cube(y). Since f is a bijection, this means that x = y, so f-cube is also a bijection.
To find the inverse of f-cube, we can use the fact that for any real number x, x1/3 is a well-defined real number. This means that if we have f-cube(x) = y, we can take the cube root of both sides to get f(x) = y1/3. Since f is a bijection, it has an inverse function f^-1, so we can apply this inverse to both sides to get x = f^-1(y1/3). This means that the inverse of f-cube is f^-1(y1/3).
In conclusion, if f is a bijection, then f-cube is also a bijection, and the inverse of f-cube is f^-1(y1/3). These results are important for understanding the properties of functions and their inverses.
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will mark brainliest if correct!
Answers
Answer:
240
Step-by-step explanation:
The shape is made up of a rectangle and a triangle.
area = LW + bh/2
area = 20 * 10 + 20 * 4/2
area = 200 + 40
area = 240
y = |x - 5| + |x + 5| if x >5
Answers
Answer:
y = 2x
Step-by-step explanation:
You want the simplified form of y = |x -5| +|x +5| if x > 5.
Turning pointsThe graph of the whole function will have turning points where the absolute value expressions are 0:
x -5 = 0 ⇒ x = 5
x +5 = 0 ⇒ x = -5
For values of x > 5, we are concerned with that portion of the graph that is to the right of both of these turning points. Hence, both absolute value expressions are positive and unchanged by the absolute value bars.
y = (x -5) +(x +5) . . . . . . if x > 5
y = 2x . . . . . . . . . . . . . . collect terms
The simplified function is y = 2x.
__
Additional comment
The attached graph shows y=2x and the given function for x > 5. They are identical. (The y=2x graph is shown dotted, so you can see the red graph of the given function.)
the wheel of a bike has a diameter of 27 inches. find the circumference of the wheel.
Answers
The circumference of the wheel of the bike given the diameter is 84.78 inches
What is the circumference of the wheel?As evident from the task content; it is required that the circumference of the bike's wheel be determined.
Given that the Diameter of the wheel = 27 inches
Recall; Radius = diameter / 2
= 27/2
= 13.5 inches
π = 3.14
Since the formula for the Circumference of the wheel which is circular = 2πr
= 2 × 3.14 × 13.5
= 84.78 inches
In conclusion, the circumference of the wheel according to the given description is 84.78 inches.
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What table of values goes with the equation y = |-2x|?
x y
-2 4
-1 2
0 0
1 -2
2 -4
x y
-2 -4
-1 -2
0 0
1 -2
2 -4
x y
-2 -4
-1 -2
0 0
1 2
2 4
x y
-2 4
-1 2
0 0
1 2
2 4
Answers
Answer:
x y
-2 4
-1 2
0 0
1 2
2 4
let me know if i'm wrong
Have a nice day :)
Step-by-step explanation:
The octane rating of gasoline is the percentage of isooctane in the fuel. For example, 89-octane gasoline contains 89% of isooctane. How many liters of 88-octane gasoline should be mixed with 100 liters of 95-octane gasoline to get a mixture which is 93-octane gasoline ?
Answers
Answer:
40 liters of 88-octane gasoline should be mixed
Step-by-step explanation:
Here in this question, we are interested in calculating the number of liters of 88-octane gasoline that should be mixed with 100 liters of 95-octane gasoline to get a mixture of 93-octane gasoline.
Since we do not know the number of liters, we can represent it by x
This means that the total number of liters of the 93-octane gasoline we are looking at producing is (100 + x) liters.
Thus, if we multiply the number of liters of each gasoline type by their isooctane content and add together, we will obtain the product;
Hence;
88(x) + 100(95) = 93(100 + x)
88x + 9500 = 9300 + 93x
93x -88x = 9500-9300
5x = 200
x = 200/50
x = 40 liters
The sum of the speed of two trains is 725.6miles per hour. If the speed of the first train is 6.4 mph faster than that of the second train find the speeds of each
Answers
Step-by-step explanation:
change it in meter and solve it