C
Step-by-step explanation:
The volume of a cylinder = πr²h
= 33 cubic inches
The volume of a cone = ¹/3 πr²h
If the cylinder and come share the same radius and height then ‘πr²h’ part of the formulas is the same for both;
It means the difference in proportionality is ¹/3 (because even π is the same across board). The volume of the cone is therefore;
¹/3 (33)
= 11
= 11 cubic inches
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Let production be given by P = bLαK1−α where b and α are positive and α < 1. If the cost of a unit of labor is m and the cost of a unit of capital is n, and the company can spend only p dollars as its total budget, then maximizing the production P is subject to the constraint mL + nK = p. Show that the maximum production occurs when L=αp/m and K=(1-α)p/n.
Answer:
The proof is completed below
Step-by-step explanation:
1) Definition of info given
We have the function that we want to maximize given by (1)
[tex]P(L,K)=bL^{\alpha}K^{1-\alpha}[/tex] (1)
And the constraint is given by [tex]mL+nK=p[/tex]
2) Methodology to solve the problem
On this case in order to maximize the function on equation (1) we need to calculate the partial derivates respect to L and K, since we have two variables.
Then we can use the method of Lagrange multipliers and solve a system of equations. Since that is the appropiate method when we want to maximize a function with more than 1 variable.
The final step will be obtain the values K and L that maximizes the function
3) Calculate the partial derivates
Computing the derivates respect to L and K produce this:
[tex]\frac{dP}{dL}=b\alphaL^{\alpha-1}K^{1-\alpha}[/tex]
[tex]\frac{dP}{dK}=b(1-\alpha)L^{\alpha}K^{-\alpha}[/tex]
4) Apply the method of lagrange multipliers
Using this method we have this system of equations:
[tex]\frac{dP}{dL}=\lambda m[/tex]
[tex]\frac{dP}{dK}=\lambda n[/tex]
[tex]mL+nK=p[/tex]
And replacing what we got for the partial derivates we got:
[tex]b\alphaL^{\alpha-1}K^{1-\alpha}=\lambda m[/tex] (2)
[tex]b(1-\alpha)L^{\alpha}K^{-\alpha}=\lambda n[/tex] (3)
[tex]mL+nK=p[/tex] (4)
Now we can cancel the Lagrange multiplier [tex]\lambda[/tex] with equations (2) and (3), dividing these equations:
[tex]\frac{\lambda m}{\lambda n}=\frac{b\alphaL^{\alpha-1}K^{1-\alpha}}{b(1-\alpha)L^{\alpha}K^{-\alpha}}[/tex] (4)
And simplyfing equation (4) we got:
[tex]\frac{m}{n}=\frac{\alpha K}{(1-\alpha)L}[/tex] (5)
4) Solve for L and K
We can cross multiply equation (5) and we got
[tex]\alpha Kn=m(1-\alpha)L[/tex]
And we can set up this last equation equal to 0
[tex]m(1-\alpha)L-\alpha Kn=0[/tex] (6)
Now we can set up the following system of equations:
[tex]mL+nK=p[/tex] (a)
[tex]m(1-\alpha)L-\alpha Kn=0[/tex] (b)
We can mutltiply the equation (a) by [tex]\alpha[/tex] on both sides and add the result to equation (b) and we got:
[tex]Lm=\alpha p[/tex]
And we can solve for L on this case:
[tex]L=\frac{\alpha p}{m}[/tex]
And now in order to obtain K we can replace the result obtained for L into equations (a) or (b), replacing into equation (a)
[tex]m(\frac{\alpha P}{m})+nK=p[/tex]
[tex]\alpha P +nK=P[/tex]
[tex]nK=P(1-\alpha)[/tex]
[tex]K=\frac{P(1-\alpha)}{n}[/tex]
With this we have completed the proof.
A knitter wants to make a rug for a dollhouse. The length of the rug will be 2 inches more than it's width. The total area of the rug (in square inches ) based on the width W of the rug (in inches ) is given by A (w) = w (2+w) If the desired area of the rug is 15 square inches, what is the width of the rug, in inches ?
Answer:
Step-by-step explanation:
A knitter wants to make a rug for a dollhouse. The length of the rug will be 2 inches more than it's width. Let the width of the rug be represented by w. This means that the length of the rug will be w + 2
The total area of the rug (in square inches ) based on the width W of the rug (in inches ) is given by
A(w) = w (2+w)
If the desired area of the rug is 15 square inches,,the width will be determined by substituting 15 for A(w). It becomes
15 = w^2 + 2w
w^2 + 2w - 15 = 0
w^2 + 5w - 3w - 15 = 0
w(w+5) -3(w+5)
w - 3 = 0 or w+ 5 = 0
w = 3 or w = -5
w cannot be negative. So w = 3 inches
A circular track is 1/4 mile long. Elena runs on this track, completing each lap in 1/20 of an hour. What is Elena's speed? Include the unit of measure
Answer:
5 mph
Step-by-step explanation:
The relation between speed, distance, and time is ...
speed = distance/time
Filling in the given values, we find the speed to be ...
speed = (1/4 mi)/(1/20 h) = (1/4)(20/1) mi/h = 5 mi/h
Elena's speed is 5 miles per hour.
What is the value of x to the nearest foot?
Answer:2097
Step-by-step explanation: it is that it the answer plz trust me
ADD me on fortnite @RaZrtNZT
The value of x in the given triangle is equal to 2097 ft by calculating through trigonometric ratios.
What are trigonometric ratios?These are ratios which are expressed as the ratio of sides of a right angled triangle.
How to find a side of right angled triangle?In the given triangle the hypotenuse is 3750 and x is the perpendicular of the triangle.
We have to use sin to calculate because it expresses the ratio of perpendicular and hypotenuse.
sin34°=x/3750
0.5591=x/3750
x= 2096.625
x=2097 approx.
Hence the value of x in the given right angled triangle is 2097 ft.
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Consider the sequence:
5, 7, 11, 19, 35,....
Write an explicit definition that defines the sequence:
a_n = 2n + 3
a_n = 3n + 2
a_n = 3n^2
a_n = 2^n + 3
Answer:
a_n = 2^n + 3
Step-by-step explanation:
The first differences have a geometric progression, so the explicit definition will be an exponential function. (It cannot be modeled by a linear or quadratic function.) The above answer is the only choice that is an exponential function.
__
First differences are ...
(7-5=)2, 4, 8, 16
Answer: [tex]a_n = 2^n + 3\ \ \ \, n=1,2,3,4,5...[/tex]
Step-by-step explanation:
The given sequence = 5, 7, 11, 19, 35,....
[tex]7-5=2\\11-7=4=2^2\\19-11=8=2^3\\35-19=16=2^4[/tex]
Here , it cam be observe that the difference between the terms is not common but can be expressed as power of 2.
We can write the terms of the sequence as
[tex]2^1+3=5\\2^2+3=4+3=7\\2^3+3=8+3=11\\2^4+3=16+3=19\\2^5+3=32+3=35[/tex]
Then , the required explicit definition that defines the sequence will be
[tex]a_n = 2^n + 3\ \ \ \, n=1,2,3,4,5...[/tex]
If the median of a list of numbers is m, the first quartile of the list is the median of the numbers in the list that are less than m. What is the first quartile of the list of numbers 42, 24, 30, 22, 26, 19, 33 and 35 ?A) 33B) 28C) 27D) 24E) 23
Answer:
First quartile list of number median is 23
Step-by-step explanation:
List of numbers = 42,24, 30 , 22 , 26, 19, 33, 35
Arrange them in a sequence:
List of numbers = 19, 22, 24, 26, 30, 33, 35, 42
The median of {19, 22, 24, 26, 30, 33, 35, 42} is= 26+30/2 = 28
Numbers that are less than the median are { 19 , 22 , 24 , 26}
then
median of the list = 22+24/2 = 23
So the first quartile list of number median is 23.
The median of the first quartile list is 23.
The given set of numbers {42, 24, 30, 22, 26, 19, 33, 35} can be arranged in ascending order as follows:
{19, 22, 24, 26, 30, 33, 35, 42}.
The median of this sequence is calculated as (26 + 30) / 2, resulting in 28.
The numbers less than the median are {19, 22, 24, 26}.
Next, the median of this subset is found by taking (22 + 24) / 2, yielding 23. Therefore, the median of the first quartile list is 23.
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Find the x-intercepts of the function graphed below, and the average rate of change over the interval (-1,4).
x-intercepts:____
Average rate of change:____
Answer:
x-intercepts: -2; 1; 5
Average rate of change: 1.8
Step-by-step explanation:
x- intercepts as per graph are:
-2; 1; 5Average rate of change over the interval (-1, 4) is:
Δy/Δx = (y(4) - y(-1))/(4 - (-1)) = (3 - (-6))/5 = 9/5 = 1.8Answer the correctly fast please I need it right now please show work
Answer:
d) 4(s + 4.5) and (s + 4.5) + (s + 4.5) + (s + 4.5) + (s + 4.5)
Step-by-step explanation:
since you know that one side is (s+4.5) and a square has 4 congruent sides the answer would be 4(s + 4.5) and (s + 4.5) + (s + 4.5) + (s + 4.5) + (s + 4.5)
Answer:
The correct answer is D
Step-by-step explanation:
Step one :
The perimeter of a square is the sum of all four sides given a side as
(s+4.5)+(s+4.5)+(s+4.5)+(s+4.5)
Or
Step 2:
(s+4.5)+(s+4.5)+(s+4.5)+(s+4.5)
Opening bracket we have
s+4.5+s+4.5+s+4.5+s+4.5
Summing all "s'" terms
(4s+18)
4(s+4.5)
What is the measurement of RT?
Answer:
65
Step-by-step explanation:
The money multiplier _______. A. decreases if banks increase their desired reserve ratio B. is 1 if the desired reserve ratio equals the currency drain ratio C. increases if the currency drain ratio increases D. increases if banks increase their desired reserve ratio
Answer:
A. decreases if banks increase their desired reserve ratio
Step-by-step explanation:
Since, the money multiplier is the amount of money produced by banks with each dollar of reserves,
In other words,
It estimates, how an initial deposit can lead to a bigger final increase in the total money supply.
For example :
If a commercial bank gains deposits of 1 crore and this leads to a final money supply of 10 crore, the money multiplier would be 10.
That is,
[tex]\text{Money multipliers}=\frac{1}{\text{Reserve ratio}}[/tex]
[tex]\implies \text{Money multipliers}\propto \frac{1}{\text{Reserve ratio}}[/tex]
Therefore, the money multiplier decreases if banks increase their desired reserve ratio
The money multiplier decreases when banks increase their desired reserve ratio, as they lend out less money, reducing the multiplier effect.
The money multiplier is a key concept in understanding how the banking system can increase the money supply within an economy. It is defined as the quantity of money that the banking system is able to generate from each dollar of bank reserves. The question relates the behavior of the money multiplier in response to changes in the reserve ratio and the currency drain ratio.
Answering the student's query, the money multiplier decreases if banks increase their desired reserve ratio because as they keep more reserves relative to deposits, they can lend out less money, effectively reducing the multiplier effect. Conversely, when banks decrease their reserve ratio, they can lend out a larger proportion of their deposits, which leads to an increase in the money multiplier. Therefore, the correct option is A: decreases if banks increase their desired reserve ratio.
Esteban has 236 trading cards that he wants to put in storage boxes.Each box holds 18 trading cards. If he puts 18 trading cards in every box, how many trading cards will be left over
Divide the total cards by 18:
236 / 18 = 13.111
Use the whole number and multiply by 18:
13 x 18 = 234
This means 234 cards would be in storage boxes.
236 - 234 = 2 cards would be left over.
The designer also programs a bird with a path that can be modeled by a quadratic function. The bird starts at the vertex of the path at (0, 20) and passes through the point (10, 8). What is the slope of the line that represents the turtle's path?
Answer:
-1.2
Step-by-step explanation:
Given that the designer also programs a bird with a path that can be modeled by a quadratic function.
The bird starts at the vertex of the path at (0, 20) and passes through the point (10, 8).
If we treat this curve as line joining these two points then we can find the slope by the formula
Slope = change in y coordinate/change in x coordinate
Here the points given are
(0,20) and (10,8)
[tex]Change in y coordinate = 8-20 = -12\\Change in x coordinate = 10-0 = 10\\Slope = -1.2[/tex]
Slope of the line that represents the turtle's path
=-1.2
Answer: 0.8
Step-by-step explanation: i got it right on edg
second part to the question is
h= 0
k= 20
a= -0.12
third part is letter B
Which of the following lists is not in order from smallest to largest?
The Answer choices are ; The correct answer choice is ; 2.33, 1.87, 3.6, 7.1
10.1, 10.5, 11.2, 12.9 - False
------------------------------
2.33, 1.87, 3.6, 7.1 - Correct
---------------------------
0.5, 1.3, 2.6, 3.8 - False
-------------------------------------
4.75, 4.8, 4.92, 5 - False
Answer: 2.33, 1.87, 3.6, 7.1
Step-by-step explanation:
2.33, 1.87, 3.6, 7.1 is not arranged from smallest to the largest. Arranging the number will be 1.87, 2.33, 3.6, 7.1.
Answer:
B. 2.33, 1.87, 3.6, 7.1
Step-by-step explanation:
This option is not in order from smallest to largest.
Hope it helped!
Expand the expression using the Binomial Theorem and Pascal's Triangle: (3x-1)^3
A bowl in the shape of a hemispere is filled with water to a depth h=3 inches. The radius of the bowl is R inches. Express the radius of the bowl R as a function of the angle theta.
The radius of the bowl R as a function of the angle theta is [tex]\mathrm{R}=\frac{3}{1-\sin \theta}[/tex]
Solution:
The figure is attached below
If we consider the centre of hemisphere be A
The radius be AC and AD
According to question,
A bowl in the shape of a hemispere is filled with water to a depth h=3 inches .i.e. BC = h = 3 inches
And radius of the bowl is R inches .i.e. R = AD =AC
Now , using trigonometric identities in triangle ABD we get
[tex]\sin \theta=\frac{\text { Perpendicular }}{\text { Hypotenuse }}=\frac{A B}{A D}[/tex]
[tex]\begin{array}{l}{\sin \theta=\frac{A B}{R}} \\\\ {A B=R \sin \theta}\end{array}[/tex]
Since , AC = AB + BC
R = R Sinθ + 3
R - R Sinθ = 3
R (1 – Sinθ ) = 3
[tex]\mathrm{R}=\frac{3}{1-\sin \theta}[/tex]
Which is the required expression for the radius of the bowl R as a function of the angle theta
99 POINTS!
Find the standard deviation for the binomial distribution.
n=21; p=0.2
A) 1.83
B) 5.95
C) -0.58
D) 5.10
Standard deviation = √(n * p * q)
You are given n and p
q = 1 - p
q = 1 -0.2 = 0.8
Standard deviation = √(21 * 0.2 * 0.8)
=√3.36 = 1.83
The answer is A.
The standard deviation for a given binomial distribution [tex]n[/tex] and [tex]p[/tex] would be the following:
[tex]\sigma=\sqrt{n \times p \times q}[/tex]
The variable [tex]q[/tex] is equivalent to [tex](p-1)[/tex]
[tex]=\sqrt{n\times p\times(p-1)}[/tex]
Substitute the values of [tex]p[/tex] and [tex]n[/tex] into the equation
[tex]=\sqrt{21\times0.2\times(1-0.2)}[/tex]
[tex]=\sqrt{21\times0.2\times0.8}[/tex]
Use a calculator to solve for this square root since it would be too hard and complicated to do by hand
[tex]=1.83303027798...[/tex]
Round this to the nearest hundredths place since all answer choices are rounded like that
[tex]=1.83[/tex]
Thus, the answer is choice A. Let me know if you need any clarifications, thanks!
~ Padoru
The sum of 5 times the width of a rectangle and twice its length is 26 units. The difference of 15 times the width and three times the length is 6 units. Write and solve a system of equations to find the length and width of the rectangle
Answer: length = 8 units
Width = 2 units
Step-by-step explanation:
Let the length of the rectangle be represented by L
Let the width of the rectangle be represented by W
The sum of 5 times the width of a rectangle and twice its length is 26 units. This means that
5W + 2L = 26 - - - - - - - - 1
The difference of 15 times the width and three times the length is 6 units. It means that
15W - 3L = 6 - - - - - - - - 2
The system equations are equation 1 and equation 2.
Multiplying equation 1 by 3 and equation 2 by 2, it becomes
15W + 6L = 78
30W - 6L = 12
Adding both equations,
45W = 90
W = 90/45 = 2
15W - 3L = 6
15×2 - 3L = 6
-3L = 6 - 30 = - 24
L = - 24/ -3 = 8
The length of the rectangle is 8 units, and the width is 2 units. This solution satisfies both equations given.
Let's denote the width of the rectangle as ( w ) units and the length as ( l ) units.
According to the given information, we have two equations:
1. ( 5w + 2l = 26 ) (sum of 5 times the width and twice the length is 26 units)
2. ( 15w - 3l = 6 ) (difference of 15 times the width and three times the length is 6 units)
We can set up a system of equations using these two equations.
To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method.
First, we'll multiply the second equation by 2 to eliminate the ( l ) term:
( 2 x (15w - 3l) = 2 x 6 )
This gives us:
( 30w - 6l = 12 )
Now, we have the system of equations:
1. ( 5w + 2l = 26 )
2. ( 30w - 6l = 12 )
We can now eliminate the ( l ) term by adding these equations together.
( (5w + 2l) + (30w - 6l) = 26 + 12 )
This simplifies to:
( 35w - 4l = 38 )
Now, we have one equation with only ( w ) as a variable.
Now, we can solve for ( w ):
( 35w - 4l = 38 )
( 35w = 38 + 4l )
[tex]\( w = \frac{38 + 4l}{35} \)[/tex]
Now, we can substitute this value of ( w ) into one of the original equations to solve for ( l ).
Let's use the first equation:
( 5w + 2l = 26 )
Substituting[tex]\( w = \frac{38 + 4l}{35} \)[/tex], we get:
[tex]\( 5\left(\frac{38 + 4l}{35}\right) + 2l = 26 \)[/tex]
Now, we can solve this equation for ( l ).
[tex]\( \frac{190 + 20l}{35} + 2l = 26 \)[/tex]
Multiply both sides by 35 to clear the fraction:
( 190 + 20l + 70l = 910 )
Combine like terms:
( 90l + 190 = 910 )
Subtract 190 from both sides:
( 90l = 720 )
Now, divide both sides by 90 to solve for ( l ):
[tex]\( l = \frac{720}{90} \)[/tex]
( l = 8 )
Now that we have the value of ( l ), we can substitute it back into one of the original equations to solve for ( w ). Let's use the first equation:
( 5w + 2(8) = 26 )
( 5w + 16 = 26 )
Subtract 16 from both sides:
5w = 10
Now, divide both sides by 5 to solve for ( w ):
[tex]\( w = \frac{10}{5} \)[/tex]
w = 2
So, the length of the rectangle is 8 units and the width is 2 units.
A researcher predicts that a special training course will be highly effective for females but will have little or no effect for males. This researcher is predicting an interaction between training and gender.True / False.
The researcher's prediction of an interaction between training and gender is true. An interaction occurs when the effect of one variable on an outcome depends on the level of another variable.
Explanation:The researcher's prediction of an interaction between training and gender is True.
An interaction occurs when the effect of one variable on an outcome depends on the level of another variable. In this case, the researcher predicts that the training course will have a different effect on females compared to males.
For example, if the researcher conducts a study where both males and females participate in the training course, and finds that females benefit significantly from the course while males do not, this would support the researcher's prediction of an interaction between training and gender.
Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? requals=negative 0.387
Answer:
Coefficient of determination = 0.149769
Step-by-step explanation:
We are given the following in the question:
Coefficient of correlation, r = -0.387
We have to find the coefficient of determination.
Coefficient of determination =
[tex]r^2 = (-0.387)^2 = 0.149769 = 14.98\%[/tex]
Coefficient of determination:
It tells us about the variation explained in the model.This correlation of determination tells that 14.98% of the variation is explained in the model that is we can say that the independent variable explains 14.98% changes or prediction in the dependent variable.It ranges from 0 to 1 and a correlation of determination of 1 means that the dependent variable is 100% predicted by the independent variable.Correlation of determination of 0 means that the dependent variable cannot be predicted by the independent variable.The distance that a spring will stretch varies directly as the force applied to the spring. A force of 8080 pounds is needed to stretch a spring 88 inches. What force is required to stretch the spring 1919 inches? A nothing-pound force is required to stretch the spring 1919 inches.
Answer:
176 199 pounds
Step-by-step explanation:
To answer this it is first useful to find the proportionality constant.
F= kx
8080 pounds = k.88 in
k = 91.81 pound/inch
So what force is required to stretch the spring to 1919 inches?
F = kx
= 91.81 pound/inch * 1919 inches
= 176 199 pounds
It is worth noting that this force seems rather large and the spring might have long reached its elastic limit
What would be an appropriate measure to describe the diameter of a music record?
A) millimeters
B) yards
C) Inches
D) kilometers
The Answer is C) Inches
Consider the function represented by the equation 6c = 2p – 10. Write the equation in function notation, where c is the independent variable. F(c) = one-thirdp + five-thirds f(c) = 3c + 5 f(p) = one-thirdp + five-thirds f(p) = 3c + 5
Answer:
f(c) = 3c + 5
Step-by-step explanation:
c is independent variable, p is dependent variable, so p = f(c)
6c = 2p -10
3c = p - 5
p = 3c + 5
f(c) = 3c + 5
Answer:
F(c) = 3c +5
Step-by-step explanation:
6c=2p-10
If c is considered to be as the independent variable, then p is the dependent variable
So we will clear and solve for variable p
6c = 2p-10
Dividing both sides by 2. We will have
6c/2 = 2(p-5)/2
3c= p-5
Adding 5 on both sides
3c+5= p
So p =3c+5
By writing the above equation in the functional notation form
F(c) = 3c +5
If a and b are positive numbers, find the maximum value of f(x)=xa(1−x)b, 0≤x≤1 Your answer may depend on a and b.maximum value =________.
To find the maximum value of f(x) = xa(1−x)b, use calculus to find the derivative of f(x), set it equal to 0, and solve for x to find the critical points. Evaluate f(x) at the critical points and the endpoints of the interval to find the maximum value.
Explanation:To find the maximum value of f(x) = xa(1−x)b, we can use calculus. First, find the derivative of f(x) with respect to x: f'(x) = a(1 - x)b - bx(1 - x)b-1. Set the derivative to 0 and solve for x to find the critical points. The maximum value of f(x) occurs at one of these critical points or at the endpoints of the interval [0, 1]. Plug the values of x into f(x) to find the corresponding maximum values.
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To find the maximum value of f(x)=xa(1−x)b, where a and b are positive numbers and 0≤x≤1, we need to find the critical points by finding when the derivative of the function is equal to zero or does not exist. Then, we evaluate the function at the critical points and the endpoints to determine the maximum value.
Explanation:To find the maximum value of the function f(x)=xa(1−x)b, where a and b are positive numbers and 0≤x≤1, we need to determine when the function reaches its maximum. This can be done by finding the critical points, which occur when the derivative of the function is equal to zero or does not exist.
First, let's find the derivative of f(x):
f'(x) = a(1-x)^{b-1}(bx - (b-1)x -1).
To find the critical points, we set f'(x) = 0 and solve for x.
Solving the equation, we find that the critical point occurs when x = \frac{b}{2b-1}.
Next, we evaluate f(x) at the critical point x = \frac{b}{2b-1} and also at the endpoints x = 0 and x = 1. The maximum value of f(x) will be the largest value among these.
Finally, we compare the values to find the maximum value.
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A book contains 400 pages. If their are 80 typing errors randomly distributed throughout the book, use the Poisson distribution to determine the probability that a page contains exactly 2 errors
Using the Poisson distribution to determine the probability that a page contains exactly 2 errors is 0.0163
Solution:Given that, a book contains 400 pages.
There are 80 typing errors randomly distributed throughout the book,
We have to use the Poisson distribution to determine the probability that a page contains exactly 2 errors.
The Poisson distribution formula is given as:
[tex]\text { Probability distribution }=e^{-\lambda} \frac{\lambda^{k}}{k !}[/tex]
Where, [tex]\lambda[/tex] is event rate of distribution. For observing k events.
[tex]\text { Here rate of distribution } \lambda=\frac{\text { go mistakes }}{400 \text { pages }}=\frac{1}{5}[/tex]
And, k = 2 errors.
[tex]\begin{array}{l}{\text { Then, } \mathrm{p}(2)=e^{-\frac{1}{5}} \times \frac{\frac{1}{5}}{2 !}} \\\\ {=2.7^{-\frac{1}{5}} \times \frac{\frac{1}{5^{2}}}{2 \times 1}} \\\\ {=\frac{1}{2.7^{\frac{1}{5}}} \times \frac{\frac{1}{25}}{2}}\end{array}[/tex]
[tex]\begin{array}{l}{=\frac{1}{\sqrt[5]{2.7}} \times \frac{1}{25} \times \frac{1}{2}} \\\\ {=\frac{1}{50 \sqrt[5]{2.7}}} \\\\ {=0.0163}\end{array}[/tex]
Hence, the probability is 0.0163
determine the intervals on which the function is increasing, decreasing, and constant
Answer:
Step-by-step explanation:
In general, wherever a function is tending from the upper left to the lower right, it is decreasing; wherever a function is tending from the lower left to the upper right it is increasing. Constant functions are horizontal lines.
Our function is tending from upper left to lower right on negative infinity to an x-value of -4. Then it runs as a horizontal line from x values of -4 to +4. Then it tends from lower left to upper right from +4 to infinity.
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Answer:
Answer is
=950
Which choice could be the equation of a line perpendicular to the line represented by this equation?y = 5x− 2A.B.y = 5x +2C.D.y = −5x + 5
Answer:
5y = -× + c
Step-by-step explanation:
If two lines are perpendicular, the product of their gradient equals -1.
We should note that the general equation of a line is y = mx + c, where m is the gradient.
For the line y = 5x - 2 , the slope is 5. The line that will be perpendicular to this line will have a slope of -1/5.
A line like 5y = -x + c fits the description
A total of $150000 is invested in two funds paying 6.25% and 6% simple interest. If the total interest for the year is $9212.50, how much is invested at each rate?
Answer:
$85,000 at 6.25%$65,000 at 6.00%Step-by-step explanation:
Let x represent the amount invested at 6.25%. Then the total interest earned is ...
0.0625x + 0.0600(150,000 -x) = 9212.50
0.0025x = 212.50 . . . . . . subtract 9000, collect terms
x = 212.50/0.0025 = 85,000
150,000 - 85,000 = 65,000 . . . . amount invested at the lower rate
$85,000 is invested at 6.25%; $65,000 is invested at 6%.
simplify the rational expression. state any excluded values.
x^2-3x-10/x+2
Answer:
The answer to your question is x - 5 or x = 5
Step-by-step explanation:
[tex]\frac{x^{2} -3x - 10}{x + 2}[/tex]
1.- Factor the numerator
x² - 3x - 10
find 2 numbers that added equal -3 and multiply equal -10.
These numbers are -5 and + 2
(x - 5)(x + 2)
2.- Simplify
[tex]\frac{(x - 5)(x + 2)}{x + 2)}[/tex]
Delete (x +2) in both numerator and denominator
3.- Result x - 5
x = 5
Matt has a 5lb bag of apples to make a pie he needs to use 3/5 of the bad how many pounds of apples we use for the pie explain what a model for this problem might look like
Answer:
Pounds of apple to be used for a pie = 3 lb
Step-by-step explanation:
Given the bag contains apples weighting = 5 lb
To make a pie [tex]\frac{3}{5}[/tex] of the apples in the bag is used.
To find the pounds of apples to be used to make a pie we will have to find the [tex]\frac{3}{5}[/tex]th part of 5 lb of apples.
In order to do that we multiply the fraction to the total weight of apples.
Pounds of apple to be used to make a pie
⇒ [tex]\frac{3}{5}\ of\ total\ pounds\ of\ apple[/tex]
⇒ [tex]\frac{3}{5}\times 5[/tex]
⇒ [tex]3[/tex]
∴ Pounds of apple to be used for a pie = 3 lb