In this type of exercises, the probability of x successes on n reapeted trials in an experiment is given by the next formula:
[tex]P=\text{nCx}\cdot p^x\cdot(1-p)^{n-x}[/tex]Here the nCx indicates the number of different combinations of x objects selected from a set of n objects. With the given data we can solve it easily:
p = 0.4
n = 5
x = 3
[tex]\begin{gathered} P=5\text{C3}\cdot0.4^3\cdot(1-0.4)^{5-3} \\ P=10\cdot0.064\cdot0.36 \\ P=0.2304 \end{gathered}[/tex]Emma has money into savings accounts. One rate is 8% and the other is 12%. If she has $450 more in the 12% account and the total interest is $220, how much is invested in each savings account?
A account 8% B account 12%
A+$450 = B (1)
Ax8% +Bx12%= $220
Ax0.08 + Bx0.12 = 220
Now we replace (1) on B:
Ax0.08 + (A+450)x0.12 = 220
Ax0.08 + Ax0.12 + 54 = 220
Ax0.2 = 166
A= 830.
Now we replace the value of A on equation (1):
830 + 450 = B
B = 1280
the store bought a bike from the factory for$ 99 and sold I to Andre for $117 what percentage was the markup?
EXPLANATION
Let's see the facts:
Bike Price: $99
Sold Price: $117
The percentage is given by the following relationship:
[tex]\text{Percentage: }\frac{\text{Selling price per unit}-Cost\text{ price per unit}}{Cost\text{ price per unit}}\cdot100[/tex]Replacing terms:
[tex]\text{Percentage =}\frac{117-99}{99}\cdot100[/tex][tex]\text{Percentage = 18.18\%}[/tex]Answer: The markup was 18.18%
i need help with math
A. ∠4 is congruent to ∠5; True.
B. Two lines are parallel; True.
C. The measure of ∠6 = 90.5°; False.
D. ∠2 and ∠3; True.
What are the properties of angles of parallel lines?On a common plane, two parallel lines do not intersect.As a result, the characteristics of parallel lines with respect to transversals are given below.Angles that correspond are equal.Vertical angles are equal to vertically opposite angles.Interior angles that alternate are equal.The exterior angles that alternate are equal.For the give question;
Two line are cut by the transversal.
∠1 = 90.5° and ∠7 = 89.5°
Thus the result for the given statement are-
A. ∠4 is congruent to ∠5 because they are alternate interior angles; True.
B. Two lines are parallel; True.
C. The measure of ∠6 = 90.5°; False.
∠6 = ∠7 = 89.5°.(correct)
D. ∠2 and ∠3 are supplementary because they are same-side exterior Angeles; True.
Thus, the result for the given statement are found.
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Please help. I am not sure how to go about this.
Solution:
(a) Given the functions:
[tex]\begin{gathered} f(x)=x-4 \\ \\ g(x)=x+4 \end{gathered}[/tex]Then:
[tex]\begin{gathered} f(g(x))=f(x+4) \\ \\ f(x+4)=x+4-4 \\ \\ f(g(x))=x \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} g(f(x))=g(x-4) \\ \\ g(x-4)=x-4+4 \\ \\ g(f(x))=x \end{gathered}[/tex]Two functions f and g are inverses of each other if and only if f(g(x))=x for every value of x in the domain of g and g(f(x))=x for every value of x in the domain of f.
ANSWER: f and g are inverse of each other.
(b) Given:
[tex]\begin{gathered} f(x)=-\frac{1}{3x},x0 \\ \\ g(x)=\frac{1}{3x},x0 \end{gathered}[/tex]Then:
[tex]\begin{gathered} f(g(x))=f(\frac{1}{3x}) \\ \\ f(\frac{1}{3x})=-\frac{1}{3(\frac{1}{3x})} \\ \\ f(g(x))=-x \end{gathered}[/tex]Also,
[tex]\begin{gathered} g(f(x))=g(-\frac{1}{3x}) \\ \\ g(-\frac{1}{3x})=\frac{1}{3(-\frac{1}{3x})} \\ \\ g(f(x))=-x \end{gathered}[/tex]ANSWER: f and g are not inverses of each other.
Help me with/ #2 plsUsing the graphs what are the solutions to the following systems
Explanation:
The graph shows a ine crossing the parabola. The solution of the systems is the point where both system of equations intersect.
The line crosses the parabola at two point:
At x = 2, y = 2
This point is applicable to both. Since both have same values at this point, (2, 2) is one of the solution
At x = -2, y = -6
Both graphs have this point . This shows point (-2, -6) is also a solution
Hence, the solutions of the systems are (2, 2) and (-2, -6)
Sarah is saving money to go on a trip. She needs at least $1975 in order to go. Sarah is mowing lawns and walking dogs to raise money. She charges $25 each time he mows a lawn and $15 each time she walks a dog. I have to Define the variables for the problem and Write an inequality to model this problem
We're told from the question that Sarah needs atleast $1975, that means that she can either have exactly $1975 or more but not less;
Let x represent the number times she mows a lawn;
Let y represent the number of times she walks a dog;
The inequality can be modelled thus;
[tex]25x+15y\ge1975[/tex]Please help me!!!!!!!
Answer:
B. (19/24)
Step-by-step explanation:
1 1 5
------ + ------ + -------
4 8 12
1(6) 1(3) 5(2)
------ + ------ + -------
4(6) 8(3) 12(2)
6 3 10 19
------ + ------ + ------- = -------
24 24 24 24
I hope this helps!
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Question
Each equation represents a proportional relationship. Choose the equations for which the constant of proportionality is 14.
Responses
A y = 0.25xy = 0.25x
B 4y = x4y = x
C y = 4xy = 4x
D 32y = 8x32y = 8x
E 14y = 2x
Answer:
its B
Step-by-step explanation: just took the test
Pl3ase help me with Geometry. right angles and perpendicular angles
(Question 3)
Because of the definition of a perpendicular bisector, we know that angle B is a right angle (90°) an that
[tex]\bar{DB}=\bar{BE}[/tex]Note that AB is a segment that is shared by both triangles in the image. By using SAS (Side-Angle-Side), we can find that both the triangles are congruent (they are equal). Therefore,
[tex]\begin{gathered} 3x-9=x+21\rightarrow3x-x=21+9\rightarrow2x=30 \\ \rightarrow x=\frac{30}{2} \\ \rightarrow x=15 \end{gathered}[/tex]We know that
[tex]AE=x+21[/tex]We'll just have to plug in the value of x we calculated to find the lenght of AE
[tex]AE=15+21\rightarrow AE=36[/tex]Therefore, AE = 36
(Question 4)
Because of the definition of a perpendicular bisector, we know that XY splits TS right by the middle. So if TS = 10, RS would be worth half of that
Therefore, RS = 5
In the rectangle below, FH = 4x – 2, EG= 5x-12, and m ZIGF = 53º.Find El and m ZIFE.EFBEI =Хm LIFE =HG
Answer:
The length EI is;
[tex]EI=19[/tex]The measure of angle IFE is;
[tex]m\angle IFE=37^{\circ}[/tex]Explanation:
Given the rectangle in the attached image.
Given;
[tex]\begin{gathered} FH=4x-2 \\ EG=5x-12 \\ m\angle IGF=53^{\circ} \end{gathered}[/tex]Recall that the length of the diagonals of a rectangle are equal so;
[tex]\begin{gathered} FH=EG \\ 4x-2=5x-12 \end{gathered}[/tex]solving for x, we have;
[tex]\begin{gathered} 4x-2=5x-12 \\ 12-2=5x-4x \\ x=10 \end{gathered}[/tex]Since we have the value of x, let us substitute to get the length of diagonal EG;
[tex]\begin{gathered} EG=5x-12 \\ EG=5(10)-12=50-12 \\ EG=38\text{ units} \end{gathered}[/tex]Also, note that the diagonals of a rectangle bisect each other, so the length of EI would be;
[tex]\begin{gathered} EI=\frac{EG}{2}=\frac{38}{2} \\ EI=19 \end{gathered}[/tex]Therefore, the length EI is;
[tex]EI=19[/tex]To get the measure of angle IFE;
[tex]m\angle IGF=m\angle IFG=53^{\circ}[/tex]Reason: base angles of an isosceles triangle are equal.
So;
[tex]m\angle IFE+m\angle IFG=90^{\circ}[/tex]Reason: Complementary angles.
Substituting the value of angle IFG;
[tex]\begin{gathered} m\angle IFE+53^{\circ}=90^{\circ} \\ m\angle IFE=90^{\circ}-53^{\circ} \\ m\angle IFE=37^{\circ} \end{gathered}[/tex]Therefore, the measure of angle IFE is;
[tex]m\angle IFE=37^{\circ}[/tex]Give Line SV parallels Line TU and Triangle SVX =~ Triangle UTXProve: VUTS is a parallelogramWrite a Paragraph Proof.
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the proof are as follows:
Since
[tex]\begin{gathered} \bar{SV}\text{ is parallel to} \\ \bar{TU} \end{gathered}[/tex]and
[tex]\text{Triangle SVX }\cong\text{ Triangle UTX}[/tex]Then,
[tex]VX\cong\text{ XT ( by }CPCTC\text{ ) }[/tex]CPCTC means corresponding parts of congruent triangles are congruent
and
[tex]UX\text{ }\cong XS\text{ ( by CPCTC)}[/tex]Thus,
VUTS is a parallelogram since diagonals of a parallelogram bisect each other
Find the difference: 8.02 - 0.003A) 7.990B) 8.017C) 8.019D) None of these choices are correct.
Given:
[tex]8.02-0.003[/tex][tex]8.02-0.003=8.017[/tex]Option B is the final answer.
Given the polynomial P(x)= x^3 + 10x^2 + 25xa. List all of the potential rational roots b. Find and list all the actual roots of P(x), and the multiplicity of each root
a)
In order to find the list of all potential rational roots, let's find the factors of the division between the constant term and the leading term.
Since the constant term is zero, so the only potential rational root in the list is 0.
b)
Since the constant term is zero, so 0 is a root of the polynomial. Then, let's factor it to find the remaining roots:
[tex]\begin{gathered} x^3+10x^2+25x=0 \\ x(x^2+10x+25)=0 \\ x^2+10x+25=0 \end{gathered}[/tex]Solving this quadratic equation using the quadratic formula, we have:
[tex]\begin{gathered} ax^2+bx+c=0 \\ x^2+10x+25=0 \\ a=1,b=10,c=25 \\ \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_1=\frac{-10+\sqrt[]{100-100}}{2}=\frac{-10+0}{2}=-5 \\ x_2=\frac{-10-0}{2}=-5 \end{gathered}[/tex]Therefore the actual roots of P(x) are:
0 (multiplicity 1) and -5 (multiplicity 2).
The area of a rectangle is given by a=6x^2y+4y^2x and the width of the rectangle is w=2xy. what is the length, l, of the rectangle if l=a/w
Step 1
Given; The area of a rectangle is given by a=6x^2y+4y^2x and the width of the rectangle is w=2xy. what is the length, l, of the rectangle if l=a/w?
Step 2
[tex]\begin{gathered} l=\frac{a}{w} \\ l=\frac{6x^2y+4y^2x}{2xy} \end{gathered}[/tex][tex]\begin{gathered} factorize \\ l=\frac{2xy\left(3x+2y\right)}{2xy} \end{gathered}[/tex]Thus;
[tex]l=3x+2y[/tex]Answer;
[tex]l=3x+2y[/tex]Convert the following expressions to simplify fraction or integer. If it is not a real number, enter none
We are given the expression:
[tex]8^{\frac{2}{3}}[/tex]To get the answer, we will have to apply exponents rules
The rule is:
[tex]a^{\frac{b}{c}}=\sqrt[c]{a}^b[/tex]Thus
we will have
[tex]8^{\frac{2}{3}}=\sqrt[3]{8^2}=\sqrt[3]{64}=4[/tex]Therefore,
The answer is 4
evaluate the expression given sin u = 5/13 and cos v = -3/5 where angle u is in quadrant 2and angle v is in quadrant 2sin ( u - v )
We are given the following information
sin u = 5/13
cos v = -3/5
Where the angle u and v are in the 2nd quadrant.
[tex]\begin{gathered} \cos\theta=\frac{adjacent}{hypotenuse} \\ \sin\theta=\frac{opposite}{hypotenuse} \end{gathered}[/tex]Let us find cos u
Apply the Pythagorean theorem to find the 3rd side.
[tex]\begin{gathered} a^2+b^2=c^2 \\ a^2=c^2-b^2 \\ a^2=13^2-5^2 \\ a^2=169-25 \\ a^2=144 \\ a=\sqrt{144} \\ a=12 \end{gathered}[/tex]Cos u = 12/13
Now, let us find sin v
Apply the Pythagorean theorem to find the 3rd side.
[tex]\begin{gathered} a^2+b^2=c^2 \\ b^2=c^2-a^2 \\ b^2=5^2-(-3)^2 \\ b^2=25-9 \\ b^2=16 \\ b=\sqrt{16} \\ b=4 \end{gathered}[/tex]Sin v = 4/5
Recall the formula for sin (A - B)
[tex]\sin(A-B)=\sin A\cos B-\cos A\sin B[/tex]Let us apply the above formula to the given expression
[tex]\begin{gathered} \sin(u-v)=\sin u\cdot\cos v+\cos u\cdot\sin v \\ \sin(u-v)=\frac{5}{13}\cdot-\frac{3}{5}+\frac{12}{13}\cdot\frac{4}{5} \\ \sin(u-v)=\frac{33}{65} \end{gathered}[/tex]Therefore, sin (u - v) = 33/65
Shelly is rolling a six-sided number cube and recording her results in a chart.Number ofRollsNumber ofTimesLanded on 1Number ofTimesLanded on 2Number ofTimesLanded on 3Number ofTimesLanded on 4Number ofTimesLanded on sNumber ofTimesLanded on 6100141714192019200304237332731300SO54495252600971031051119599AWhich is BEST supported by the data in the chart?А when viewing the data for rolling a one, as the number of rolls Increases, the experimental probability becomes closer to equal to the theoretical probability.when viewing the data for rolling a two, as the number of rolls increases, the experimental probability becomes closer to equal to the theoretical probability.When viewing the data for rolling a four, as the number of rolls increases, the experimental probability becomes closer to equal to the theoretical probability.When viewing the data for rolling a sbc, as the number of rolls increases, the experimental probability becomes closer to equal to the theoretical probability.BСD
We will have the following:
The expression that best describes the information is:
*When viewing the data for tolling a one, as the number of rolls increases, the experimental probability becomes closer to equal to the theoretical probability.
i need to find the independent variable and dependent and make a equation and find the output when input=10
The given situation is about the value of quarters and the number of quarters. If we think this through, we would deduct that the value of quarters depends on the number of quarters there are, for example, if there are 4 quarters, then the value is 1 dollar, and so on.
Hence,
The independent variable is the number of quarters.
The dependent variable is the value of the quarters.
The equation would be v = 0.25n.
If the input is 10, it means n = 10.
[tex]v=0.25n=0.25\cdot10=2.5[/tex]The output would be 2.5.
Use the Distributive Property to simplify the following expression.8(x+4)
Given the expression:
8(x + 4)
Let's simplify using distributive property.
Use distributive property to distribute 8 into x + 4:
8(x) + 8(4)
Evaluate:
8x + 32
ANSWER:
8x + 32
The selling price of a refrigerator is $548.90. If the markup is 10% of the dealer's cost, what is the dealer's cost of the refrigerator?
Answer
Dealer's cost = $499
Explanation
The markup percent is given as
[tex]\text{Markup percent = }\frac{(Selling\text{ Price) - (Cost)}}{Cost}\times100\text{ percent}[/tex]Markup percent = 10%
Selling Price = 548.90 dollars
Cost = ?
[tex]\begin{gathered} \text{Markup percent = }\frac{(Selling\text{ Price) - (Cost)}}{Cost}\times100\text{ percent} \\ \text{10 = }\frac{548.90\text{-(Cost)}}{Cost}\times100\text{ percent} \\ 0.1=\frac{548.90-\text{Cost}}{\text{Cost}} \\ \text{Cross multiply} \\ 0.1(\text{Cost) }=548.90-\text{Cost} \end{gathered}[/tex]0.1 (Cost) + Cost = 548.90
1.1 (Cost) = 548.90
Divide both sides by 1.1
Cost = (548.90/1.1)
Cost = 499 dollars
Hope this Helps!!!
I need help with this problem.It say solve the following inequalities and graph it on the Number Line.
Given the inequality:
[tex]13>-4x-7[/tex]• You can solve it as follows:
1. Apply the Addition Property of Inequality by adding 7 to both sides of the inequality:
[tex]13+(7)>-4x-7+(7)[/tex][tex]20>-4x[/tex]2. Apply the Division Property of Inequality by dividing both sides of the inequality by -4 (since you are dividing both sides by a negative number, the direction of the inequality symbol changes):
[tex]\begin{gathered} \frac{20}{-4}<\frac{x}{-4} \\ \\ -53. You can rewrite the solution in this form:[tex]x>-5[/tex]• In order to graph the solution on the Number Line, you can follow these steps:
1. Since the symbol is:
[tex]>[/tex]You need to draw an open circle over the number -5.
2. Draw a line from the circle to the right.
Then, you get:
Hence, the answer is:
• Solution:
[tex]x>-5[/tex]• Number Line:
Is there enough information to prove the quadrilateral is a parallelogram if so what property proves it
To solve this problem we remember the following statement: a quadrilateral that has opposite sides that are congruent and parallel can be a parallelogram, rhombus, rectangle or square.
From the figure, we see a quadrilateral with congruent opposite sides. Relating this information to the statement above, we see that this quadrilateral can be a parallelogram, rhombus, rectangle or square. So we conclude that there is not enough information to conclude that the quadrilateral is a parallelogram.
Answer
d. Not enough information
Solve the system of linear equations using the substitution method. 4x+4y=12x=-2y+8
Hello there. To solve this question, we'll need to isolate a variable, substitute its expression into the other equation and find both values.
4x + 4y = 12
x = -2y + 8
Plug x = -2y + 8 in the first equation. Before doing so, divide both sides of the first equation by a factor of 4
x + y = 3
-2y + 8 + y = 3
Subtract 8 on both sides of the equation and add the values
-2y + y = 3 - 8
-y = -5
Multiply both sides of the equation by a factor of (-1)
y = 5
Plug this value into the expression for x
x = -2 * 5 + 8
Multiply the values
x = -10 + 8
Add the values
x = -2
These are the values we're looking for.
The solution for this system of equation is given by:
S = {(x, y) in R² | (x, y) = (-2, 5)}
Answer:
x = -2
y = 5
Step-by-step explanation:
Solving system of linear equations by substitution method:4x + 4y = 12
Divide the entire equation by 4,
x + y = 3 -------------(I)
x = -2y + 8 ------------(II)
Substitute x = -2y + 8 in equation (I)
-2y + 8 + y = 3
-2y + y + 8 = 3
Combine like terms,
-y + 8 = 3
Subtract 8 from both sides,
-y = 3 - 8
-y = - 5
Multiply the entire equation by (-1)
[tex]\sf \boxed{\bf y = 5}[/tex]
Substitute y= 5 in equation (II),
x = -2*5 + 8
= - 10 + 8
[tex]\sf \boxed{\bf x = -2}[/tex]
I need help. I have no idea how to respond this question
An angle with its vertex on a circle and chord-shaped sides is said to be inscribed. The arc that is inside the inscribed angle and whose endpoints are on the angle is known as the intercepted arc.
A triangle's internal angles are always divisible by 180 degrees.
The central angle of one radian (s = r) subtends an arc length of one radius. One radian has the same value for all circles because they are all alike. The central angle of a circle is measured by its arc, which is 360 degrees, and its radian measure, which is 2π.
Circles:
A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also known as the location of points that are evenly spaced apart from the center. The radius of a circle is measured from the center to the edge. The line that splits a circle into two identical halves is its diameter, which is also twice as wide as its radius.
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For the piecewise function, find the values g(-2), g(2), and g(8).g(x)=X+7, for xs28- x, for x>2.9(-2)=0
g(x) = x + 7 when x =< 2
g(x) = 8 - x when x > 2
g(-2) Evaluate the first function
g(-2) = -2 + 7
g(-2) = 5
g(2) Evaluate the first function
g(2) = 2 + 7
g(2) = 9
g(8) Evaluate the second function
g(8) = 8 - 8
g(8) = 0
From the entrance, most people will go straight to the roller coaster or straight to the tower. The distance from the entrance to the roller coaster is 461m, and the distance from the entrance to the tower is 707 m. If the paths to these two attractions are separated by a 41o angle, how far apart are the roller coaster and the tower?
The given situation can be illustrated as follow:
In order to determine the distance x between the roller coaster and the tower. Use the law of cosines, as follow:
[tex]x^2=(461)^2+(707)^2-2(461)(707)\cos 41[/tex]By simplifying the previous expression, you obtain:
[tex]\begin{gathered} x^2=220409.5413 \\ x=\sqrt[]{220409.5413} \\ x\approx469.5 \end{gathered}[/tex]Hence, the distance between the tower and the roller coaester is approximately 469.5m
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Frankie and Gus swam for 10 minutes. When the time was up, Frankie had completed 10 7/10 laps and Gus 10 4/5 had completed laps. Frankie wrote the inequality 10 7/10 > 10 4/5 to show who swam the longest distance. Was he correct? Explain your answer by describing where the numbers would be positioned on a number line.
Answer:
Frankie is incorrect.
Step-by-step explanation:
Change 4/5 to 8/10.
You are comparing 10 7/10 to 10 8/10.
10 4/5 (which is also 10 8/10) can be written as 10.8
10 7/10 can be written as 10.7
10.8 > 10.7, so 10 4/5 > 10 7/10 is correct,
and 10 7/10 > 10 4/5 is incorrect.
Frankie is incorrect.
On a number line, show 10 and 11.
Make 10 equal spaces between 10 and 11. Each space is 1/10.
10 7/10 is one space to the left of 10 4/5, so 10 7/10 is less than 10 4/5.
Can you please give me a step by step explanation/solution. Thanks
The Perimeter of a Rectangle
Given a rectangle of width w and length l, the perimeter is calculated as the sum of the side lengths, that is:
P = w + w + l + l
Or, equivalently
P = 2w + 2l
Hermann was calculating the perimeter of a rectangle and built the expression:
P = x + x + 4x + 4x feet
Note this expression is similar to the first one. This means that the width of the rectangle is x and the length is 4x.
a) We'll draw a rectangle with such dimensions:
b) Assuming the base is the length and the height is the width, the relationship between the base and the height is
4x / x = 4
This means the base is four times the height
c) We are given the perimeter as P = 60 feet.
We need to solve the equation
x + x + 4x + 4x = 60
Simplifying:
10x = 60
Dividing by 10:
x = 60/10
x = 6 feet
The base is 4x = 24 feet.
The base of Herman's rectangle is 24 feet
The height of Herman's rectangle is 6 feet
Evaluate. Assume u > O when In u appears. (In x)96 1 dex X O 96(In x)95+C (In x97 97x +C O (In x)97 +C O (In x)97 97 +
EXPLANATION
[tex]\int \frac{(\ln x)^{96}}{x}dx[/tex]Applying subtitution: u=ln(x)
By integral substitution definition
[tex]\int f(g(x))\cdot g^{^{\prime}}(x)dx=\text{ }\int f(u)du,\text{ u=g(x)}[/tex]Substitute: u=ln(x)
[tex]\frac{du}{dx}=\frac{1}{x}[/tex][tex]\frac{d}{dx}=(\ln (x))[/tex]Apply the common derivative:
[tex]\frac{d}{dx}(\ln (x))=\frac{1}{x}[/tex][tex]\Rightarrow du=\frac{1}{x}dx[/tex][tex]\Rightarrow dx=xdu[/tex][tex]=\int \frac{u^{96}}{x}\text{xdu}[/tex]Simplify:
[tex]\frac{u^{96}}{x}x[/tex]Multiply fractions:
[tex]a\cdot\frac{b}{c}=\frac{a\cdot b}{c}[/tex][tex]=\frac{u^{96}x}{x}[/tex]Cancel the common factor: x
[tex]=u^{96}[/tex][tex]=\int u^{96}du[/tex]Apply the Power Rule:
[tex]\int x^adx=\frac{x^{(a+1)}}{a+1},\text{ a }\ne\text{ -1}[/tex][tex]=\frac{u^{96+1}}{96+1}[/tex]Substitute back u=ln(x)
[tex]=\frac{\ln ^{96+1}(x)}{96+1}[/tex]Simplify:
[tex]\frac{\ln ^{96+1}(x)}{96+1}[/tex]Add the numbers: 96+1=97
[tex]=\frac{\ln ^{97}(x)}{97}[/tex][tex]=\frac{1}{97}\ln ^{97}(x)[/tex]Add a constant to the solution:
[tex]=\frac{1}{97}\ln ^{97}(x)\text{ + C}[/tex]The answer is D:
[tex]\frac{(\ln x)^{97}}{97}+C[/tex]A rental car company charges 23.95 per day to rent a car and $0.08 for every mile driven. Nathan wants to rent a car, knowing that:He plans to drive 400 miles.He has at most $440 to spend.Which inequality can be used to determine x, the maximum number of days Nathan can afford to rent for while staying within his budget?
Answer
Explanation
The total charge on the car = (Charge based on number of days) + (Charge based on the number of miles)
Charge based on number of days = (23.95) (x) = (23.95x) dollars
Charge based on the number of miles = (0.08) (400) = 32 dollars
(The total charge on the car) ≤ 440
23.95x + 32 ≤ 440
23.95x + 32 - 32 ≤ 440 - 32
23.95x ≤ 408
Divide both sides by 23.95
(23.95x/23.95) ≤ (408/23.95)
x ≤ 17.04
Hope this Helps!!!