No such c exist from 1 and hence mean value theorem fails, an example is given below.
Consider f(x)=[x] on [-1,1]
Then, f is not differentiable on x=0
Note that,
f'(x)=1 for x>0 and f'(x)=-1 for x<0
The Mean Value Theorem states that if a feature f is non-stop at the closed interval [a,b] and differentiable at the open interval (a,b), then there exists a factor c withinside the interval (a,b) such that f'(c) is same to the feature's common price of extrade over [a,b].
According to near value theorem we need,
a c (-1,1).
f'(c)= f(1)-f(-1)/1-(-1)
=|1|-|-1|/2
=1-1/2=0
i.e., f'(c)=0
While, no such c exist from 1 and hence mean value theorem fails.
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is y=-2x - 4 proportional?
Answer:
It does not represent a proportional relationship
Step-by-step explanation:
Answer:
It does not represent a proportional relationship
Step-by-step explanation For a line, the constant of proportionality is a fancy way to say the slope. It makes more sense without the intercept: y=2xclearly, the constant of proportionality is 2.
The lifetime X of a certain brand of sixty-watt light bulb is exponentially distributed with population mean 1000 hours, that is, 5.23 1 e/1000 1000 f(x) x > 0. If 30 light bulbs having this lifetime distribution are placed on test, find the probability that 10 or fewer of these light bulbs survive to time 1200 by (a) writing a mathematical expression, (b) giving an R statement that will compute the probability.
The function given by f(x) = 1/1000×e^(-x/1000) is the expression that represents the function that 10 or fewer of the bulbs survive to time 1200.
Given, the lifetime X of a certain brand of sixty-watt light bulb is exponentially distributed with population mean 1000 hours.
That is, 5.231(e/1000)f(x) x > 0. I
f 30 light bulbs having this lifetime distribution are placed on test.
we have to find the probability that 10 or fewer of these light bulbs survive to time 1200.
as, we have to find the expression for the function f(x) so that 10 or fewer of the given light bulbs survive to time 1200.
f(x) = 1/1000×e^(-x/1000)
So, the function given by f(x) = 1/1000×e^(-x/1000) is the expression that represents the function that 10 or fewer of the bulbs survive to time 1200.
Hence, the function given by f(x) = 1/1000×e^(-x/1000) is the expression that represents the function that 10 or fewer of the bulbs survive to time 1200.
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The water tank at the institution is
full. A water truck begin to full the tank with
water at a rate of 8 litres per minute. After 15 minutes the tank was 5/2 full. Calculate
the number of litres of water that the tank can hold
The number of litres of water the tank can hold is 48 litres
What is Volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
Volume can be measured in cubic units, litres and gallons.
If the rate of pump is 8minutes per minute, therefore in 15 minutes, 15×8 = 120 litres is in the tank.
120 litres is 5/2 full
the volume of the tank will be 120×2/5
= 240/5
= 48litres
Therefore the volume of the tank is 48litres
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A rectangle has length that is 4 inches greater than twice its width. The perimeter of the rectangle is 26 inches. What is the area?
Consider the point of intersection where the vertical line X=2 meets the line y=7x+9
The point of intersection (x,y) is = (2,23)
Replace every x with 2 and simplify
y = 7x+9
y = 7*2 + 9
y = 14 + 9
y = 23 is the y coordinate
The vertical line x = 2 meets the diagonal line y = 7x+9 at the location (x,y) = (2,23)
What are Coordinates ?
The position of a point or points on a graph or grid is shown by its coordinates. The origin is defined as the point (0, 0). The coordinates are two units to the right in the x-direction and four units up in the y-direction according to the point (2, 4).
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use the reflection method to find a green's function that solves the problem on a semicircular region-AG(x, xo)= მ (x-xo) G(x, xo)=0 მ/მy G(x, xo) = 0in Ω = {x=(x, y): x^2+y^2 <1, y>0}, on T1 = {x=(x, y): x^2+y^2=1, y>0}, on T2 = {x=(x, 0): -1< x <1},
The Green's function that solves the problem on a semicircular region is given by G(x, xo) = მ (x-xo)(cos(θ)sin(θ)).
What is Green's function?
Green's function is an important mathematical tool used to solve differential equations. It is defined as a solution to a homogeneous linear differential equation with a source, or delta, function as its input. Green's functions are also known as impulse response functions and can be used to describe the response of a system to an arbitrary input. Green's functions provide a way to solve differential equations without having to solve the entire equation all at once. They are particularly useful for solving equations with boundary conditions that are difficult to solve without the use of Green's functions. Green's functions can also be used to solve integral equations and provide a powerful tool for solving many physical problems.
The reflection method for finding a Green's function for a problem on a semicircular region can be used as follows. First, we solve the problem on the half-plane by finding a Green's function G(x, xo) that satisfies the boundary conditions given. Then, we reflect the solution across the boundary of the semicircle, namely T1 and T2, to obtain the Green's function on the entire semicircle.
The Green's function on the half-plane is given by G(x, xo) = მ (x-xo). Using this solution, we can reflect it across the boundary of the semicircle. For T1, the reflected solution is given by G(x, xo) = მ (x-xo)cos(θ), where θ is the angle between the normal vector to T1 and the vector from xo to x. For T2, the reflected solution is given by G(x, xo) = მ (x-xo)sin(θ), where θ is the angle between the normal vector to T2 and the vector from xo to x.
Therefore, the Green's function that solves the problem on a semicircular region is given by G(x, xo) = მ (x-xo)(cos(θ)sin(θ)).
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find -7x3x(-2)x(-5)x(-1) how do i simplify this?
Answer:
42
Step-by-step explanation:
To simplify the expression -7x3x(-2)x(-5)x(-1), we need to apply the rules of exponentiation and multiplication.
First, we note that the terms -7, -2, -5, and -1 are all negative numbers, which means that they will be multiplied together to give a positive result.
Next, we apply the rule that says that any term raised to the power of 0 is equal to 1. Since -1 raised to the 0 power is 1, this means that the expression -7x3x(-2)x(-5)x(-1) is equivalent to -7x3x(-2)x(-5)x1.
Next, we apply the rule that says that any term raised to the power of 1 is equal to itself. Since 3 raised to the 1 power is 3, and 5 raised to the 1 power is 5, this means that the expression -7x3x(-2)x(-5)x1 is equivalent to -7x3x(-2)x5x1.
Finally, we apply the rule that says that the product of any number and its multiplicative inverse (or reciprocal) is equal to 1. Since the reciprocal of 5 is 1/5, this means that the expression -7x3x(-2)x5x1 is equivalent to -7x3x(-2)x(1/5)x1.
We can now use the rules of multiplication to simplify the expression further. Since any number multiplied by 1 is equal to itself, this means that the expression -7x3x(-2)x(1/5)x1 is equivalent to -7x3x(-2)x(1/5).
Next, we use the rule that says that the product of two negative numbers is a positive number. This means that the expression -7x3x(-2)x(1/5) is equivalent to 7x3x2x(1/5).
Finally, we can apply the rules of exponentiation and multiplication to evaluate the expression. Since any number raised to the power of 1 is equal to itself, this means that the expression 7x3x2x(1/5) is equivalent to 7x3x2. We can then multiply these terms together to get the final result:
7x3x2 = 42
Therefore, the simplified expression is equal to 42.
Given inputs A, B, C, D, E, design a CMOS circuit to implement the logic function: Y(not) = A(B+C) + D + E
Given inputs A, B, C, D, E, design a CMOS circuit to implement the logic function: Y(not) = A(B+C) + D + E has 5-c-mos, 5-pmos total 10 mos transistors
this can be realize by takeing three c-mos in parallel which gives ABC ,two c-mos are series which is in serires with
another c-mos whic gives D(A+B), now connect ABC and D(A+B) in series
the out put will be (ABC + D(A+B) )'
so we require total 6-mos and 6-pmos total 12mos transistors
F = AC + BD
pull down
this can be realize by takeing two c-mos in series which gives AB ,two cmos are in series
which whic gives BD, now connect AC and BD in parallel
pull up
this can be realize by takeing two c-mos in parallel which gives Ac ,two c-mos are in parallel
which whic gives BD, now connect AC and BD in series
the output is (AC+BD)'
to avoid the complement we have to connect the output to c-mos inverter then we get AC+BD
so we require 5-nmos, 5-pmos total 10 mos transistors
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let r be the distance from a uniformly randomly chosen point in the unit disk and the origin (0,0). find the probability density function fr(r) and cumu- lative distribution function fr(r) of r. (hint: do not attempt to use your answer from part (a)).
The probability density function fr(r) of the distance from a uniformly randomly chosen point in the unit disk to the origin is r, and the cumulative distribution function Fr(r) is (r² / 2).
To find the probability density function (PDF) and cumulative distribution function (CDF) of the distance from a uniformly randomly chosen point in the unit disk to the origin, we can first find the area of the unit disk and the area of the annulus centered at the origin and bounded by two circles with radii r and r + dr. The PDF is then the ratio of the area of the annulus to the total area of the unit disk, and the CDF is the ratio of the area of the annulus to the total area of the unit disk up to radius r.
The area of the unit disk is simply the area of a circle with radius 1, which is pi. The area of the annulus centered at the origin and bounded by two circles with radii r and r + dr is equal to the difference between the areas of the two circles, which is pi(r + dr)² - pi(r²). Therefore, the PDF of r is:
fr(r) = [pi(r + dr)² - pi(r²)] / pi = r + dr²
The CDF of r is the sum of the PDFs up to radius r, which is:
Fr(r) = ∫fr(t)dt from 0 to r = ∫(t + dt²)dt from 0 to r = (r² / 2) + (r × dt) + (dt³ / 3)
We can take the limit as dt approaches 0 to get the final expression for the CDF:
Fr(r) = (r² / 2)
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Question 1 A corporation has the following account balances: Common Stock, $1 par value, $80000; Paid-in Capital in Excess of Par Value, $2700000. Based on this information, the a. legal capital is $2780000 b. average price per share issued is $3.48 c. number of shares outstanding is 2780000. d. number of shares issued is 80000
The correct option is D , as the number of shares issued is 80000.
What is stock ?
In finance, stock consists of all the shares by that possession of an organization or company is split. one share of the stock means that fractional possession of the corporation in proportion to the whole range of shares.
Main body:
as per the information given in the question , Common Stock, $1 par value, $80000 which means the number of shares issued is 80000.
hence ,correct option is D as the number of shares issued is 80000.
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yolanda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $70 and costs and costs and additional $0.30 per mile driven. The second plane has no initial fee but costs $0.80 per mile driven. How many miles would Yolanda need to drive for the two plans to cost the same?
The two plans will cost the same when Yolanda has driven 233 miles distance. That is, $70 + (0.30 x 233) = $233 = 0.80 x 233.
To find out how many miles Yolanda needs to drive for the two plans to cost the same, we need to set up an equation. The equation should calculate the total cost of each plan. For the first plan, the total cost is the initial fee plus the cost of the miles driven. For the second plan, the total cost is just the cost of the miles driven. We can then set the two equations equal to each other and solve for the number of miles distance driven. The final result is that Yolanda needs to drive 233 miles for the two plans to cost the same.
Plan 1: C = F + (D × CPM)
Plan 2: C = (D × CPM)
Plan 1 = Plan 2
F + (D × CPM) = (D × CPM)
F = 0
D × CPM = D × CPM
D = 233
Therefore, Yolanda needs to drive 233 miles for the two plans to cost the same.
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Let X denote the random variable that gives the sum of the faces that fall uppermost when two fair dice are rolled. Find P(X = 4). (Round your answer to two decimal places.)
The likelihood or the probability is 121, or 8.33%.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.
We must make a table for easier comprehension in order to determine the P(x=4);
Refer to the attachment for table:
There are three different ways that P(x=4) can occur based on the table. Out of 36 possible results (6 x 6 = 36), they are (1,3), (2,2), and (3,1). As a result, the chance of the event is 363; it is then reduced to 121, or 8.33%.
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Nellie is shopping for a new bicycle. She is most interested in color and type of tires.
What is the probability that a randomly selected bike is green given that the bike has bike tires?
Simplify any fractions.
The probability that a randomly selected bike is green given that the bike has road bike tires is 0.66
Given :
Nellie is shopping for a new bicycle. She is most interested in color and type of tires.
Probability :
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event .
From the table given :
Total number of 6 road bikes = 4
Total road bikes = 2 + 4 = 6
Probability = 4 / 6
= 2 / 3
= 0.66
Hence the probability that a randomly selected bike is green given that the bike has road bike tires is 0.66 .
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Your goal here is to find the least squares line y(x) = mx + b for the following data: (-2, 1), (2, 1), (-1,-1), (0, -2), (2,-2), and (-2, 1) Feel free to use a calculator! The normal equation for determining the approximating parameters ħ and în are: Then the least squares line is: y(x) = = number + number
The least squares line , y = mx + b form from given data is y = ( -32/100 )x + ( -39/100).
We have an equation of line is
y(x) = mx + b --(1)
given data, (-2, 1), (2, 1),(-1,-1), (0,-2), (2,-2) and (-2, 1)
plugging each point on above equation we get, 1 = -2m + b ; 1 = 2m + b ; -1 = -m + b ; -2 = 0m + b ;
-2 = 2m +b ; 1 = -2m + b
The above equations can be written in matrix form as,
[ -2 1 ; 2 1 ; -1 1 ; 0 1 ; 2 1 ; -2 1] [ m ; b]
= [ 1 ; 1 ; -1 ; -2 ; -2 ; 1]
AX = B
X = (Aᵀ A)⁻¹ AᵀB where Aᵀ is transpose of matrix A and (Aᵀ A)⁻¹ is inverse of (Aᵀ A).
AᵀA = [ -2 2 -1 0 2 -2 ; 1 1 1 1 1] [ -2 1 ; 2 1 ; -1 1 ; 0 1 ; 2 1 ; -2 1] = [ 17 -1 ; -1 6 ]
so, X = [ 17 -1 ; -1 6 ] ^-1 [ -2 2 -1 0 2 -2 ; 1 1 1 1 1][ 1 ; 1 ; -1 ; -2 ; -2 ; 1]
let [ 17 -1 ; -1 6 ] = P
[ 17 -1 ; -1 6 ]⁻¹ = adj.P/det P
det P = 17×6 - 1 = 101
P⁻¹ = 1/101 [ 6 1 ; 1 17 ]
Now, X = 1/101 [ 6 1 ; 1 17 ] [ -2 2 -1 0 2 -2 ; 1 1 1 1 1][ 1 ; 1 ; -1 ; -2 ; -2 ; 1]
=> X = 1/101[ 6 1 ; 1 17 ] [ -5 ; -2 ]
=> X = 1/101 [ -32 ; -39] = [ -32/100 ; -39/100 ]
=> [ m ; b ] = [ -32/100 ; -39/100 ]
=> m = -32/100 , b = -39/100
then, y = mx + b
=> y = ( -32/100 )x + ( -39/100)
Hence, the required equation is
y = ( -32/100 )x + ( -39/100).
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The ticket sales at a movie theater were $3,402. Adult tickets are $11, and senior tickets are $8. The number of senior tickets sold was 27 less than twice the number of adult tickets. Determine the number of adult tickets and senior tickets sold.
Answer:
Adults: 134
Senior: 241
Step-by-step explanation:
Known
Number of adult tickets sold: x
Revenue from adult tickets: $11x
Number of senior tickets sold: y
Revenue from senior tickets: $8y
From the problem, we found the equation [tex]y = 2x - 27[/tex] and 3,402 = 11x + 8y
Combining the two equation:
[tex]3,402 = 11x + 8(2x-27)\\3,402 = 11x + 16x - 216\\3,402 + 216 = 27x\\27x = 3,618[/tex]
Divided both side by 27
[tex]x = 134[/tex]
Since
[tex]y = 2x - 27[/tex]
Inserting the value of x,
[tex]y = 2(134) -27\\y = 268 - 27\\y = 241[/tex]
So, there are 134 adult tickets sold and 241 senior tickets sold.
PLEASE HELP
find the sum of ( 2.25 x 10^19) and ( 6.7 x 10^17) Write the answer using proper scientific notation.
A) 231.7 X 10^15
B) 2.317 X10^19
C) 231.7 X 10^17
D) 2.317 X 10^15
Answer:
Step-by-step explanation:
The sum of (2.25 x 10^19) and (6.7 x 10^17) is (2.317 x 10^19).
To find the sum of these two numbers, we first need to line up the decimal points and add the numbers as we would with any other addition problem:
2.25 x 10^19
+ 6.7 x 10^17
Then, we can carry the 1 and add the numbers:
2.25 x 10^19
6.7 x 10^17
2.317 x 10^19
The sum of these two numbers is 2.317 x 10^19, which is equal to choice B.
3. Find the composition (fog)(-2) for the functions f(x) = 2x+1 and g(x)=x²-3
Answer:
3
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=2x+1\\g(x)=x^2-3\end{cases}[/tex]
Function composition is an operation that takes two functions and produces a third function.
The given composite function f o g(-2) means to substitute the function g(-2) in place of the x in function f(x):
[tex]\begin{aligned}(f \circ g)(-2)&=f[g(-2)]\\&=2[g(-2)]+1\\&=2(2^2-3)+1\\&=2(4-3)+1\\&=2(1)+1\\&=2+1\\&=3\end{aligned}[/tex]
Let X be a random variable representing the number of rolls of a fair die until we see the first 6. Next, choose with replacement a sample of size X from an urn with 5 red and 4 green balls. Let Y be the number of green balls in the sample. Find Var(Y).
As per the binomial distribution, the value of var(Y) is 0.00008
What is meant by binomial distribution?
In math, the Binomial distribution counts the number of successes in n trials, where sampling is done with replacement or the probability of success is constant from trial to trial
Here we have given that, X be a random variable representing the number of rolls of a fair die until we see the first 6. Next, choose with replacement a sample of size X from an urn with 5 red and 4 green balls. Let Y be the number of green balls in the sample.
And we need to find the value of var(Y).
Here we know that the value of n = 6 and the value of x is 4 and the probability is 0.05.
Then as per the binomial distribution formula, it can be calculated as,
By using a calculator, you can enter trials=6, p=0.05, and X=4 into a binomial probability distribution function (PDF). If doing this by hand, apply the binomial probability formula:
=> [6!/4!(6-4)!] x 0.05⁴ x (1- 0.05)⁶⁻⁴
=> 0.00008
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of 649 adults selected randomly from one town, 54 of them smoke. construct a 92.5 percent n interval for the true percentage of all adults in the town that smoke.
The 92.5% of confidence interval for the percentage of adults is
(-1.176 , 1.342).
as per given in the question,
The total number of adults (n) is 649
The number of smokers (x) = 54
the probability of getting a smoker is P =x/n
=> P = 54/649
=> 0.083
not getting a smoker is
1 - P = 1-0.083
=> 0.916
At 92.5% confidence level the Z critical value is ,
[tex]\alpha[/tex] = 1 - 92.5%
=> 1 - 0.925
=> 0.075
[tex]\alpha[/tex] / 2 = 0.075/ 2
=> 0.0375
now,
for the two tail test
Z[tex]\alpha[/tex]/2
= Z(0.0375)
= 1.7805
Margin of error
E = [tex]Z\alpha / 2 * \sqrt{( p * (1 - p) / n)}[/tex]
= 1.780 [tex]\times (\sqrt{((0.083 \times 0.916 ) / 649)}[/tex]
= 1.2596
A 92.5 % confidence interval for population proportion p is ,
P- E < P < P + E
0.083- 1.259 < P < 0.083 + 1.259
-1.176 < p < 1.342
(-1.176 , 1.342) is the interval
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you are given a rectangular matrix m. your goal is to write a program that, if an element of m is equal to 0, sets that element's entire row and column to 0.
The program for a given rectangular matrix m, if an element of m is equal to 0, sets that element's entire row and column to 0
def zeroify_matrix(m):
rows = len(m)
cols = len(m[0])
rows_to_zeroify = []
cols_to_zeroify = []
for i in range(rows):
for j in range(cols):
if m[i][j] == 0:
rows_to_zeroify.append(i)
cols_to_zeroify.append(j)
for i in range(rows):
for j in range(cols):
if i in rows_to_zeroify or j in cols_to_zeroify:
m[i][j] = 0
return m
It is coded in python for the given problem of recreating a rectangular matrix, for a single element to be 0, the whole row nad column will contain zero elements.
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I need help with this question
The equation has one repeated irrational number solution. thus Option A is correct.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
The given equation is the quadratic equation by
[tex]-4x^2+ 24x-36=0[/tex]
We need to determine the number and type of solutions.
Noted that If the discriminant equals zero, the equation has one repeated rational number solution.
Since we know that If the discriminant is positive, then the equation has two real solutions.
And If the discriminant is negative, then the equation has two imaginary solutions.
To Calculate the discriminant of the equation [tex]-4x^2+ 24x-36=0[/tex] by substituting a= -4, b= 24 and c= -36 into the discriminant formula:
Since the discriminant equals zero, it follows that the equation has one repeated irrational number solution x = 3
The equation has one repeated irrational number solution.
Option A is correct.
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help me find the slope
Answer: Rise over Run
Step-by-step explanation: Take the change in the x coordinates, and divide by the change in y coordinates.
For example, to find slope when given 2 coordinates:
(2,5) (5, 10)
The change in the x coordinates is 3, because from 2-->5 it moves 3 places to the right. (run)
The change in the y coordinates is 5, because from 5-->10 it moves 5 places upwards. (rise)
Use rise/run.
Rise= 5 (change in y coordinate)
Run = 3 (change in x coordinate)
5/3 is the slope.
On questions like #6, the slope is -3. That is because the equation for slope is y=mx+b.
m is the coefficient of the x, so -3 is the slope.
Likewise, the slope of #2 is 7. The slope of #10 is 3/4.
Gerolamo Cardano in his book, The Gambling Scholar, written in the early
1500s, considers the following carnival game. There are six dice. Each of the
dice has ve blank sides. The sixth side has a number between 1 and 6|a
dierent number on each die. The six dice are rolled and the player wins a
prize depending on the total of the numbers which turn up.
(a) Find, as Cardano did, the expected total without nding its distribution.
(b) Large prizes were given for large totals with a modest fee to play the
game. Explain why this could be done.
Therefore , [tex](\frac{1}{6})^{2}[/tex] is the probability of getting 5 of same number on all the dice.
what is probability?The probability of winning is actually closer to 1/3 (25/72). Carnival game operators want you to think that a game is fair like I did, so that you will play. If you knew that the probability of winning a game was only about 1/3, most likely you would not waste your money.
Mathematical descriptions of the likelihood that an event will occur or that a claim will be true are called probabilities.
Here,
[tex](\frac{1}{6})^{2}[/tex] is the probability of getting 5 of same number on all the dice.
Therefore , [tex](\frac{1}{6})^{2}[/tex] is the probability of getting 5 of same number on all the dice.
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a small island is 3 miles from the nearest point p on the straight shoreline of a large lake. if a woman on the island can row a boat 3 miles per hour and can walk 4 miles per hour, where should the boat be landed in order to arrive at a town 7 miles down the shore from p in the least time? let x be the distance (in miles) between point p and where the boat lands on the lakeshore.
The point where the boat should be landed is the point 3.4 miles from point P towards the town.
The point where the boat should be landed can be found by expressing
the distance traveled on the boat and walking as a function of time.
Given that x represents the distance from point P to the boat landing point.
Therefore, distance of rowing the boat = √((12 - x)² + 3²)
The total time, t, is, therefore;
[tex]t=\frac{12-x}{4} +\frac{\sqrt{x^2+3^2} }{3}-----------(1)[/tex]
differentiate the above equation we get:
[tex]\frac{dt}{dx} =\frac{d}{dx} (\frac{12-x}{4} +\frac{\sqrt{x^2+3^2} }{3} )\\\\\\=\frac{12.(-3+4*\frac{2x}{2*\sqrt{x^2+9} } )}{144} \\\\\\=\frac{12(-3+4*\frac{2x}{2*\sqrt{x^2+9} }) }{144}\\\\=-\frac{1}{4} +\frac{x}{3*\sqrt{x^2+9} } \\\\\frac{x}{3*\sqrt{x^2+9} }=\frac{1}{4} \\\\cross multiplying both terms we get:\\\\4x=3*\sqrt{x^2+9}[/tex]
squaring on both sides we get:
16x^2=9(X^2+9)
16x^2=9x^2+81
7x^2=81
[tex]x=\frac{9*\sqrt{x} }{7}[/tex]
Approximately,x=3.4 miles.
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It takes Christina 2 minutes to read one page of her 250 page book. Which of the following represents the appropriate domain and range for a function relating the total time she has spent reading the book, x, and the number of pages she has read, y?
Answer:
Domain: 0<=x<=500
Range: 0<=y<=250
Step-by-step explanation:
I'm not sure if this is what you asked for. She spend 2 minutes reading 1 page, there are 250 pages, therefore: 250*2=500
the range is simply the total pages
Hope this help!
24. The average price of a new car is a function of the year it was purchased. In 1994.
the average price of a new car was $16.930. In 2002, the average price was
$19.126. Find the rate of change of the average price of a new car. Include units
in your answer.
please help me i’m struggling
The rate of change of the average price of the new car is $274.50 per year.
What is the rate of change?The rate of change of the average price of the new car is a function of the change in average price over the years and the change in the number of years.
Rate of change = change in the average price / change in the number of years
Rate of change = (price in 2002 - price in 1994) / difference in the number of years
Rate of change = (19,126 - 16,930) / (2002 - 1994)
Rate of change = 2196 / 8
Rate of change = $274.50
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PLEASE HELP WILL MARK BARINLIEST
Answer:
<CYZ = 60 degrees
Step-by-step explanation:
CY = CZ ==> both segments are radiuses of the circle since they both have
a CenterPoint at Point C and a point touching the edge of the
circle
CY = YZ ==> Since CY=CZ and YZ=CZ, CY also equal YZ. In addition, this
means that CY, YZ, and CZ are all radiuses of the circle
Hence, CY = YZ = CZ.
Since all sides of the triangle are equal, that means that all angles of the triangle are equal as well:
<CYZ + <CZY + <YCZ = 180 ==> 180 is the total degrees in a triangle
<CYZ + <CYZ + <CYZ = 180 ==> all angles have the same measure
3 * <CYZ = 180 ==> solve for <CYZ
(3 * <CYZ)/3 = 180/3 ==> divide by 3 on both sides to isolate <CYZ
<CYZ = 60 degrees
Answer: [tex]\angle CYZ=60^{\circ}[/tex]
Step-by-step explanation:
[tex]\overline{CZ}=\overline{CY}[/tex] (radii of a circle)
[tex]\implies \overline{YZ}=\overline{CZ}=\overline{CY}[/tex]
[tex]\therefore \angle CYZ=60^{\circ}[/tex] (equilateral triangle)
16.13- cerebral tumors and cell phone use. in a case-controlled study on cerebral tumors and cell phone use, tumors occurred more frequently on the same side of the head where cellular telephones had been used in 26 of 41 cases. test the hypothesis that there is an equal distribution of contralaterial and ipsilateral tumors in the population. use a two-sided alternative.
Null Hypothesis: H0: There is an equal distribution of contralateral and ipsilateral tumors in the population.Ha: There is not an equal distribution of contralateral and ipsilateral tumors in the population.
1) Calculate the observed value:
The observed value is 26 out of 41 cases.
2) Calculate the expected value:
The expected value is 20.5 out of 41 cases.
3) Calculate the test statistic:
The test statistic is (26-20.5)/sqrt(20.5) = 2.44
4) State the critical value:
The critical value for a two-sided test with a significance level of 0.05 is 1.96.
5) The test statistic (2.44) is greater than the critical value (1.96), so we reject the null hypothesis and conclude that there is not an equal distribution of contralateral and ipsilateral tumors in the population.
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If the simple interest on $2,000 for 7 years is $1,120, then what is the interest rate?
The rate is %.
Answer:
Rate= I*100/P*T
R= 1120 * 100/2000*7
R= 112000/14000
R= 8%
Can anyone pls help me find the answer to this problem. I will give brainliest
Answer:
[tex]\log_{10}\sqrt{a} -\dfrac{3}{4}=\dfrac{1}{2}\log_{10}a-\dfrac{3}{4}[/tex]
Step-by-step explanation:
Given:
[tex]x=\dfrac{\sqrt{10a\sqrt{0.1}}}{10}[/tex]
Therefore:
[tex]\implies \log_{10}x=\log_{10}\left(\dfrac{\sqrt{10a\sqrt{0.1}}}{10} \right)[/tex]
[tex]\textsf{Apply the log quotient law}: \quad \log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay[/tex]
[tex]\implies \log_{10}\sqrt{10a\sqrt{0.1}}-\log_{10}10[/tex]
[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]
[tex]\implies \log_{10}\sqrt{10a\sqrt{0.1}}-1[/tex]
[tex]\textsf{Apply radical rule: $\sqrt{ab}=\sqrt{a}\sqrt{b}$, \quad assuming $a \geq 0,\;b\geq 0$}[/tex]
[tex]\implies \log_{10}\left(\sqrt{10}\sqrt{a}\sqrt{\sqrt{0.1}}}\right)-1[/tex]
[tex]\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\implies \log_{10}\sqrt{10} + \log_{10}\sqrt{a} + \log_{10}\sqrt{\sqrt{0.1}}}\right)-1[/tex]
Rewrite the radicals:
[tex]\implies \log_{10} \left(10\right)^{\frac{1}{2}} + \log_{10}\sqrt{a} + \log_{10}\left(0.1\right)^{\frac{1}{4}\right)-1[/tex]
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies \dfrac{1}{2}\log_{10} 10 + \log_{10}\sqrt{a} + \dfrac{1}{4}\log_{10}0.1-1[/tex]
[tex]\textsf{Apply log laws}: \quad \log_aa=1 \quad \textsf{and} \quad \log_a\dfrac{1}{a}=-1[/tex]
[tex]\implies \dfrac{1}{2}(1) + \log_{10}\sqrt{a} + \dfrac{1}{4}(-1)-1[/tex]
[tex]\implies \dfrac{1}{2}+ \log_{10}\sqrt{a} -\dfrac{1}{4}-1[/tex]
[tex]\implies \log_{10}\sqrt{a} -\dfrac{3}{4}[/tex]
If you want to simplify further:
[tex]\implies \log_{10}\left(a\right)^{\frac{1}{2}} -\dfrac{3}{4}[/tex]
[tex]\implies \dfrac{1}{2}\log_{10}a-\dfrac{3}{4}[/tex]
Answer:
56
Step-by-step explanation: 10a+10 0.1 -=