From the constraint, we have
[tex]x+y+z=9 \implies z = 9-x-y[/tex]
so that [tex]s[/tex] depends only on [tex]x,y[/tex].
[tex]s = g(x,y) = xy + y(9-x-y) + x(9-x-y) = 9y - y^2 + 9x - x^2 - xy[/tex]
Find the critical points of [tex]g[/tex].
[tex]\dfrac{\partial g}{\partial x} = 9 - 2x - y = 0 \implies 2x + y = 9[/tex]
[tex]\dfrac{\partial g}{\partial y} = 9 - 2y - x = 0[/tex]
Using the given constraint again, we have the condition
[tex]x+y+z = 2x+y \implies x=z[/tex]
so that
[tex]x = 9 - x - y \implies y = 9 - 2x[/tex]
and [tex]s[/tex] depends only on [tex]x[/tex].
[tex]s = h(x) = 9(9-2x) - (9-2x)^2 + 9x - x^2 - x(9-2x) = 18x - 3x^2[/tex]
Find the critical points of [tex]h[/tex].
[tex]\dfrac{dh}{dx} = 18 - 6x = 0 \implies x=3[/tex]
It follows that [tex]y = 9-2\cdot3 = 3[/tex] and [tex]z=3[/tex], so the only critical point of [tex]s[/tex] is at (3, 3, 3).
Differentiate [tex]h[/tex] again and check the sign of the second derivative at the critical point.
[tex]\dfrac{d^2h}{dx^2} = -6 < 0[/tex]
for all [tex]x[/tex], which indicates a maximum.
We find that
[tex]\max\left\{xy+yz+xz \mid x+y+z=9\right\} = \boxed{27} \text{ at } (x,y,z) = (3,3,3)[/tex]
The second derivative at the critical point exists
[tex]$\frac{d^{2} h}{d x^{2}}=-6 < 0[/tex] for all x, which suggests a maximum.
How to find the maximum value?Given, the constraint, we have
x + y + z = 9
⇒ z = 9 - x - y
Let s depend only on x, y.
s = g(x, y)
= xy + y(9 - x - y) + x(9 - x - y)
= 9y - y² + 9x - x² - xy
To estimate the critical points of g.
[tex]$&\frac{\partial g}{\partial x}[/tex] = 9 - 2x - y = 0
[tex]$&\frac{\partial g}{\partial y}[/tex] = 9 - 2y - x = 0
Utilizing the given constraint again,
x + y + z = 2x + y
⇒ x = z
x = 9 - x - y
⇒ y = 9 - 2x, and s depends only on x.
s = h(x) = 9(9 - 2x) - (9 - 2x)² + 9x - x² - x(9 - 2x) = 18x - 3x²
To estimate the critical points of h.
[tex]$\frac{d h}{d x}=18-6 x=0[/tex]
⇒ x = 3
It pursues that y = 9 - 2 [tex]*[/tex] 3 = 3 and z = 3, so the only critical point of s exists at (3, 3, 3).
Differentiate h again and review the sign of the second derivative at the critical point.
[tex]$\frac{d^{2} h}{d x^{2}}=-6 < 0[/tex]
for all x, which suggests a maximum.
To learn more about constraint refer to:
https://brainly.com/question/24279865
#SPJ9
A local anime fan club surveyed 81 of its members regarding their viewing habits last weekend, and the following information was obtained: 40 members watched an episode of Naruto, 54 watched an episode of Death Note, 40 watched an episode of Inuyasha, 32 watched both Naruto and Inuyasha, 12 watched Naruto and Inuyasha but not Death Note, 25 watched both Death Note and Inuyasha, and 23 watched only Death Note. a. How many of the club members watched exactly one of the shows? b. How many of the club members watched all three shows? c. How many of the club members watched none of the three shows?
The solutions for the Questions are
a) Given that, the minimum requirement is 58 out of 75.
a=0.7733
b) For 16 out of a total of 75
b=0.2133
c) For 11 out of a total of 75
c =0.1466
How many of the club members watched all three shows? c. How many of the club members watched none of the three shows?Generally, we need to determine the total number of students who exhibit each behavior by seeing the habits and assets contained inside a Venn diagram.
Therefore, let's assume that:
- In Set A, I watched one of the Naruto episodes.
Set B: Observed a new segment of the anime series Death Note.
Hence, 23 of them have seen an episode of Death as well as an episode of Naruto, which means that
(A intercept B) equals 23.
In addition to this, it is a given that 42 has seen one episode of Death Note.
This indicates that B is equal to 42.
This pertains to us:
[tex]B = (B-A)+(A \cap B)[/tex]
In this case, members of B through A are individuals who have only viewed Death Note. So
42=(B−A)+23
(B-A) = 11
Finally, It is a known fact that 39 of the members have seen at least one episode of Naruto.
Therefore, the value of A is 39.
A=(A−B)+(A intercept B)
39=(A−B)+23
(A−B)= 16
(A union B)= 42+ 39- 23
(A union B)=58
In conclusion, the total number of pupils is:
58 with at least one and 17 with none, for a total of 75
a) Given that, the minimum requirement is 58 out of 75.
a=58*100/75
a=0.7733
b) For 16 out of a total of 75
b= 16/75*100
b=0.2133
c) For 11 out of a total of 75
c= 11/75*100
c =0.1466
Read more about probability
https://brainly.com/question/795909
#SPJ1
Which statement is true?
A) All trapezoids are similar.
B) All rectangles are squares.
C) All squares are parallelograms.
D) All equilateral triangles are congruent.
Nationally, patients who go to the emergency room wait an average of 7 hours to be admitted into the hospital. Do patients at rural hospitals have a lower waiting time? The 13 randomly selected patients who went to the emergency room at rural hospitals waited an average of 6.3 hours to be admitted into the hospital. The standard deviation for these 13 patients was 1.3 hours. What can be concluded at the the
α
= 0.01 level of significance level of significance?
For this study, we should use
Select an answer
The null and alternative hypotheses would be:
H
0
:
?
Select an answer
H
1
:
?
Select an answer
The test statistic
?
=
(please show your answer to 3 decimal places.)
The p-value =
(Please show your answer to 4 decimal places.)
The p-value is
?
α
Based on this, we should
Select an answer
the null hypothesis.
Thus, the final conclusion is that ...
The data suggest the population mean is not significantly lower than 7 at
α
= 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 7 hours.
The data suggest the populaton mean is significantly lower than 7 at
α
= 0.01, so there is statistically significant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is lower than 7 hours.
The data suggest that the population mean awaiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is not significantly lower than 7 hours at
α
= 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is lower than 7 hours.
A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.
How to calculate value of the test statistic?The test statistics can be calculated by using this formula:
[tex]t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]
Where:
x is the sample mean.u is the mean.is the standard deviation.n is the number of hours.For this study, we should use t-test and the null and alternative hypotheses would be given by:
H₀: μ = 7
H₁: μ < 7
[tex]t=\frac{6.3\;-\;7}{\frac{1.3}{\sqrt{13} } }\\\\t=\frac{-0.7}{\frac{1.3}{3.6056 } }[/tex]
t = -0.7/0.3606
t = -1.941.
For the p-value, we have:
P-value = P(t < -1.9412)
P-value = 0.0381.
Therefore, the p-value (0.0381) is greater than α = 0.01. Based on this, we should fail to reject the null hypothesis.
Thus, the final conclusion is that the data suggest the population mean is not significantly lower than 7 at α = 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 7 hours.
Read more on null hypothesis here: https://brainly.com/question/14913351
#SPJ1
Find the surface area of the composite figur
2 cm
5 cm
4 cm
3 cm
5 cm
SA =
4 cm
3 cm
5 cm
[?] cm²
By definition of surface area and the area formulae for squares and rectangles, the surface area of the composite figure is equal to 166 square centimeters.
What is the surface area of a composite figure formed by two right prisms?
According to the image, we have a composite figure formed by two right prisms. The surface area of this figure is the sum of the areas of its faces, represented by squares and rectangles:
A = 2 · (4 cm) · (5 cm) + 2 · (2 cm) · (4 cm) + (2 cm) · (5 cm) + (3 cm) · (5 cm) + (5 cm)² + 4 · (3 cm) · (5 cm)
A = 166 cm²
By definition of surface area and the area formulae for squares and rectangles, the surface area of the composite figure is equal to 166 square centimeters.
To learn more on surface areas: https://brainly.com/question/2835293
#SPJ1
there were 3 ponies. rodrick rode each pony 6 times. how many pony rides did sarah take?
Answer: 0
Step-by-step explanation: I am going by the words , there WERE 3 ponies. So Sarah couldn’t take any rides.
What is an equation of the line that passes through the points (-6,0) and (8,7) ?
Answer:
y = 1/2 x + 3
Step-by-step explanation:
Find slope, m = (y1-y2)/(x1-x2) = (7-0) / (8- - 6) = 7/14 = 1/2
( does not matter which one you assign as point 1 or point 2)
Point (-6,0) slope form ( you can use either point)
(y-0) = 1/2 (x- -6)
y = 1/2 x +3
Calculus help please, will give brainiest
The most convenient way to capture [tex]D[/tex] is with the parameterization
[tex]D = \left\{(x,y) \mid -1 \le y \le 3 \text{ and } -\dfrac{y+1}2 \le x \le y+1\right\}[/tex]
so we only need one iterated integral.
[tex]\displaystyle \iint_D e^{x-y} \, dA = \int_{-1}^3 \int_{-(y+1)/2}^{y+1} e^{x-y} \, dx \, dy[/tex]
Compute the integral with respect to [tex]x[/tex].
[tex]\displaystyle \int_{-(y+1)/2}^{y+1} e^{x-y} \, dx = e^{x-y} \bigg|_{x=-(y+1)/2}^{x=y+1} = e^{(y+1)-y} - e^{-(y+1)/2-y} = e - e^{-(3y+1)/2}[/tex]
Compute the remaining integral.
[tex]\displaystyle \int_{-1}^3 \left(e - e^{-(3y+1)/2}\right) \, dy = \left(ey + \frac23 e^{-(3y+1)/2}\right)\bigg|_{y=-1}^{y=3} \\\\ ~~~~~~~~ = \left(3e + \frac23 e^{-(9+1)/2}\right) - \left(-e + \frac23 e^{-(-3+1)/2}\right) \\\\ ~~~~~~~~ = \boxed{\frac{10e}3 + \frac2{3e^5}}[/tex]
If we had chosen the opposite order of variables, we would have used
[tex]D = \left\{(x,y) \mid -2 \le x \le 4 \text{ and } \max\left(-2x-1,x-1\right)\le y\le3\right\}[/tex]
where
[tex]\max(-2x-1, x-1) = \begin{cases} -2x-1 & \text{when } x<0 \\ x-1 & \text{when } x\ge0\end{cases}[/tex]
so we would have needed two iterated integrals,
[tex]\displaystyle \iint_D e^{x-y} \, dA = \int_{-2}^0 \int_{-2x-1}^3 e^{x-y} \, dy \, dx + \int_0^4 \int_{x-1}^3 e^{x-y} \, dy \, dx[/tex]
see attachment for question
The percentage when Potiphar woke up late is 14.4%.
How to calculate the percentage?From the information, it was stated that Potiphar takes a horse and buggy to work everyday. In order to come on time, he must wake up promptly at 6.30am and then hop on the buggy and that anytime he wakes up late or the horse was in traffic, he will be late.
It was further illustrated based on the information given in the question that he was late 24.4% of the time and the horse was in traffic for 10% of the time.
Therefore, the percentage when he woke up late will be gotten by simply subtracting the percentages that we have above. This will be illustrated below:
= 24.4% - 10%
= 14.4%
Therefore, the percentage when Potiphar woke up late is 14.4%.
Learn more about percentages on:
brainly.com/question/19247356
#SPJ1
need heeeelp please
Step-by-step explanation:
For a rational function, we cannot values in the domain that will make the denominator 0.
So set the denominator =0
[tex] {x}^{2} - 1 = 0[/tex]
[tex] {x}^{2} = 1[/tex]
[tex]x = 1[/tex]
or
[tex]x = - 1[/tex]
So the answer is (-1,1)
ASAP HELP ME WITH THIS QUESTIONN
Answer:
inductive reasoning
Step-by-step explanation:
Find the length of the a of a right triangle b=21.5 inches and the hypotenuse c =31.9.use the calculator to estimate the square root to one decimal place
The length of the leg a is approximately?
Answer:
Step-by-step explanation:
a² + b² = c²
a² + (21.5)² = (31.9)²
a² + 462.25 = 1017.61
a² = 555.36
a = 23.6
1. In the process of solving the radical equation, x − 5 =radical 3x −11 , you will need to solve which of the following quadratic equations?
a) x2 −7x+16=0
b) x2 −3x−14=0
c) x2 +13x−36=0
d) x2 −13x + 36 = 0 e)
none of these
In the process of solving the expression x − 5 =radical 3x −11 , you will need to solve the quadratic equation x² - 13x + 36 =0
Solving radical equationsRadical equations are expression that are under the square root. For instance √x is a radical expression.
Given the equation expressed as:
x − 5 = √3x −11
Square both sides to have;
(x-5)² = (√3x −11 )²
This can be further expressed as:
(x-5)² =3x −11
Expand
x² -10x + 25 = 3x - 11
Equate to zero
x² -10x + 25 - 3x +11 = 0
x² -10x - 3x +36 = 0
x² - 13x + 36 =0
Hence in the process of solving the expression x − 5 =radical 3x −11 , you will need to solve the quadratic equation x² - 13x + 36 =0
Learn more on radical expressions here: https://brainly.com/question/6755932
#SPJ1
on a recent trip, the smiths drove at an average speed of 55 miles per hour. if the trip took 5 1/2 hours, how many miles did they drive?
Answer:
302.5
Step-by-step explanation:
5 1/2 = 5.5
55 miles per hour * 5.5 hours
55*5.5
302.5
At the beginning of 2000 Randall's house was worth 234 thousand dollars and Damien's house was worth 110 thousand dollars. At the beginning of 2003, Randall's house was worth 176 thousand dollars and Damien's house was worth 154 thousand dollars. Assume that the values of both houses vary at an exponential rate.
Write a function [tex]f[/tex] ,that determines the value of Randall's house (in thousands of dollars) in terms of the number of years [tex]t[/tex] since the beginning of 2000.
Write a function [tex]g[/tex] that determines the value of Damien's house (in thousands of dollars) in terms of the number of years [tex]t[/tex] since the beginning of 2000.
How many years after the beginning of 2000 will Randall's and Damien's house have the same value?
Using linear functions, we have that:
Randall's value is: f(t) = -19t + 234.Damien's value is: g(t) = 14.67t + 110They will have the same value in 3.68 years since the start of 2000.A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.We consider the initial values as the y-intercepts. Randall's house decayed 58 thousand dollars in 3 years, hence the slope is:
m = -58/3 = -19.
Hence the function for the value, in thousands of dollars, is:
f(t) = -19t + 234.
Damien's initial value was of 110, and it increased 44 thousand in 3 years, hence the slope is:
m = 44/3 = 14.67
Hence the function for the value of Damien's house, in thousands of dollars, in t years after 2003, is:
g(t) = 14.67t + 110
They will have the same value when:
f(t) = g(t)
-19t + 234 = 14.67t + 110
33.67t = 124
t = 124/33.67
t = 3.68
They will have the same value in 3.68 years since the start of 2000.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Consider the following figure:
Answer:
x=90
y=148
Step-by-step explanation:
Since we know a line is 180 degrees, and we know that angle Q is 90, x must be a 90-degree angle as well.
With our given information we can add up the two given angles in the triangle which are 90 and 58
90+58=148
To find what R is, we must subtract 148 from 180 because all the angles in a triangle sum up to 180.
180-148=32
Now that we know that R is 32, because we know that a line is 180 degrees, we can subtract 32 from 180 to get our final answer for y as 148.
180-32=148
Desperately need help and an explanation so I can do it on my own later.
Step-by-step explanation:
since the sumation of f(x) of a probability is 1
thw probability to win is o.5 and to lose is o.5 so expected value is xf(x
your expected value will b 0.5 multiply by 5 thats is 2.5 thats your expected gain
If Jamaal has 13 nickels and dimes in his pocket, and they have a combined value of 110 cents, how many
of each coin does he have?
dimes
nickels
0/4 pts 3 19 0
Find the x - and y -intercepts of the graph of the function f(x)=−4|x−3|+12 .
The x and y-intercept(s) of the graph of the function f(x)=−4|x−3|+12 are: ( 0, 0 ), ( 6, 0 ) and ( 0, 0 ) respectively.
What are the x and y -intercepts of the graph of the function f(x)=−4|x−3|+12 ?Given the function;
f(x) = −4| x-3 | + 12
First, we find the x-intercepts by simply substituting 0 for y and solve for x.
f(x) = −4| x-3 | + 12
y = −4| x-3 | + 12
0 = −4| x-3 | + 12
−4| x-3 | + 12 = 0
−4| x-3 | = -12
Divide both sides by -4
| x-3 | = 3
We remove the absolute value sign
x - 3 = ±3
x = 3±3
x = 3-3, 3+3
x = 0, 3
Hence, x-intercepts are: ( 0, 0 ), ( 6, 0 )
Next, we find the y-intercept by substituting 0 for x and solve for y.
f(x) = −4| x-3 | + 12
y = −4| 0-3 | + 12
y = −4| -3 | + 12
We remove the absolute value sign
y = −4(3) + 12
y = −12 + 12
y = 0
Hence, y-intercept is: ( 0, 0 ).
The x and y-intercept(s) of the graph of the function f(x)=−4|x−3|+12 are: ( 0, 0 ), ( 6, 0 ) and ( 0, 0 ) respectively.
Learn more about graph functions here: https://brainly.com/question/28105390
#SPJ1
what is the range of the function f (x) = lxl +5?
The range of the function f(x)= IxI+5 is x+5 for x>=0 and -x+5 for x<0.
Given that the function is f(x)=IxI+5.
We are required to find the range of the function.
Function is relationship between two or more variables expressed in equal to form. In a function each value of x must have a corresponding value of y. The value of x is known as domain of the function and the value of y is known as codomain of the function. Range of a function is a limit of values in which the values of function lies.
Function is f(x)= IxI+5
We know that IxI=x for x>=0 and -x<0.
We have to just put the value of IxI in f(x) to get the range of function.
f(x)=x+5 for x>=0 and -x+5 for x<0.
Hence the range of the function f(x)= IxI+5 is x+5 for x>=0 and -x+5 for x<0.
Learn more about range at https://brainly.com/question/26098895
#SPJ1
need heeeelp please
Answer:
4[tex]v^{7}[/tex]x³(7[tex]y^{6}[/tex] - 3v²[tex]x^{6}[/tex])
Step-by-step explanation:
28[tex]v^{7}[/tex]x³[tex]y^{6}[/tex] - 12[tex]v^{9}[/tex][tex]x^{9}[/tex] ← factor out 4[tex]v^{7}[/tex]x³ from each term
= 4[tex]v^{7}[/tex]x³(7[tex]y^{6}[/tex] - 3v²[tex]x^{6}[/tex])
Which expression has a value of -24 when a = -2 and b = 3?
A. a√16 + b - 10
B. a(√16 + b) -10
C. a√16 + (b - 10)
D. (a√16) + b - 10
The option B is correct, The second expression gives the correct value -24.
According to the statement
we have given that the some expression and a = -2 and b = 3 and we have to which expression gives a output of answer -24 after put the values in the expressions.
So, For this purpose
First expression:
[tex]a\sqrt{16} + b - 10[/tex]
Put a = -2 and b = 3
then
[tex]= -2\sqrt{16} + 3 - 10\\= -8 -7\\= 15[/tex]
Second expression:
[tex]a(\sqrt{16} + b) -10[/tex]
Put a = -2 and b = 3
then
[tex]a(\sqrt{16} + b) -10\\-2(4 +3) -10\\-14-10\\-24[/tex]
Now,
Third expression:
[tex]a\sqrt{16} + (b - 10)[/tex]
Put a = -2 and b = 3
then
[tex]a\sqrt{16} + (b - 10)-2*4 + (-7)\\-8-7\\-15[/tex]
Now,
Fourth expression and first expression are same,
So,
Fourth expression:
[tex]a\sqrt{16} + b - 10[/tex]
Put a = -2 and b = 3
then
[tex]= -2\sqrt{16} + 3 - 10\\= -8 -7\\= 15[/tex]
The second expression gives the correct value -24.
So, The option B is correct, The second expression gives the correct value -24.
Learn more about Expressions here
https://brainly.com/question/4344214
#SPJ1
The area of a rectangular cocktail table is x^2-18x+32 If the width is x-16 what is its length?
Answer: (x-2)
Step-by-step explanation:
This problem is a middle-term factorization, or factoring by splitting the middle term.
We have the equation
x^2 - 18x + 32
This equation represents the area, and area = length x width for all rectangles. We also know the width, x-16, which makes it easier for us. The length must also be in the same format.
x^2 - 18x + 32
= x^2 - 16x - 2x + 32
= x(x-16) - 2(x - 16)
= (x-16) (x-2) -------> we get this through taking (x-16) common
We could also pretend that the length is x - y, where y is the number we need to finish the equation.
x^2 - 18x + 32
= (x-16) (x-y)
= x^2 -16x - xy + 16y
-16 minus 2 is -18, which is our middle term.
Therefore, y = 2. This is also verified because is 16y = 32, the constant term, then through transposing we get y = 2.
Our answer is that the length is (x-2).
a tree 20 feet tall with a circumference of 3 ft has a vine wound around 7 times how long is the vine?
The length of the vine wounded to the tree is 21 feet.
How to solve circumference?Circumference is the perimeter of a circular object. Therefore,
circumference = 2πr
where
r = radiusThe circumference of the tree is 3 feet. A vine was wound around 7 times .
The length of the vine can be calculated as follows:
Therefore,
circumference = 3 ft
length of the vine = 7 × 3
length of the vine = 21 feet
learn more on circumference here: https://brainly.com/question/15219938
#SPJ1
When a force of 60 N acts on a certain object, the acceleration of the object is 6/ms2. if the acceleration of the object becomes 7/ms2, what is the force?
When the acceleration is 7 m/s², it means that the force will be 70 N.
How to find the force on an object?From newton's first law of motion, we know that;
F = ma
where;
m is mass
a is acceleration
We are given;
F = 60 N
a = 6 m/s²
Thus;
m = F/a = 60/6
m = 10 kg
When acceleration is 7 m/s², we have;
F = 10 * 7
m = 70 N
Read more about force at; https://brainly.com/question/20005124
#SPJ1
HELP PLS BRAINLIEST IF POSSIBLE
For the given set A, A is a set of x, where x depends on n. x= 11, where the values of n in ascending order are 1,2,3,4.
Simply put, a set in mathematics is a grouping of different items.
An element of the set is any component of the set. When writing a set, curly brackets are utilized.
The components of a set can be represented using a variety of notations. Typically, sets are represented using a set builder form or a roster form.
According to the question,
A = {11,22,33,44}
The elements of set A are all multiples of 11. These can be expressed as 11*n, here, n has the values of 1,2,3 and 4.
Learn more about sets here:
https://brainly.com/question/2166579
#SPJ1
FIND THE INDICATED PROBABILITY FOR THE FOLLOWING:
A) IF P(A OR B) = 0.6, P(B) = 0.3, AND P(A AND B) = 0.1, FIND P(A).
The value of the probability P(A) is 0.40
How to determine the probability?The given parameters about the probability are
P(A or B) = 0.6
P(B) = 0.3
P(A and B) = 0.1
To calculate the probability P(A), we use the following formula
P(A and B) = P(A) + P(B) - P(A or B)
Substitute the known values in the above equation
0.1 = 0.3 + P(A) - 0.6
Collect the like terms
P(A)= 0.1 - 0.3 + 0.6
Evaluate the expression
P(A)= 0.4
Hence, the value of the probability P(A) is 0.40
Read more about probability at
https://brainly.com/question/25870256
#SPJ1
Jason wants to receive monthly payments of $3,250 for 15 years. How much does he have to invest now in an annuity that has an annual interest rate of 3.6% to achieve his goal? Round your answer to the nearest hundred.
Answer: $451,500
The amount she should invest today in the annuity is $455,450.40.
How much should be invested today?The first step is to determine the future value of the monthly annuity.
Future value = monthly payment x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 3.6/12 = 0.3%n = number of periods : 15 x 12 = 180Future value : 3250 x [(1.003^180) - 1] / 0.003 = 774,171.92
The second step is to determine the present value of this future annuity:
774, 171.92 / (1.036^15) = $455,450.40
To learn more about annuities, please check: https://brainly.com/question/24108530
#SPJ1
Solve for the value of w.
(4W-8)°
(3w+6)°
Step-by-step explanation:
4W-8=3W+6
4W-3W=6+8
W=14°
lets find the value of W in this straight line
4W-8°=180°(angle on a straight line)
collect like terms
4W=180°+8°
4W=188°
divide both sides by the coefficient of W which is 4
W=47°
if i am correct pls rate it
A customers monthly bill is $50 including taxes. You mom ’ll offer a 30% discount applicable towards the $50 on a monthly basis. The discount started being applied to his account on June 16. Therefore for the month of June the customer will receive a discount on a prorated basis on the monthly bill. The customers billing cycle begins on the first the month. What is the total billed amount for the month of June?
Using proportions, the billed amount for the month of June is:
D. $42.50
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The discount will be applied only for the second half of the month, from June 16 to June 30, hence instead of a discount of 30%, it will count as a discount of 15%, meaning that 85% of the bill will be paid, hence the amount paid will be of:
A = 0.85 x $50 = $42.50.
Hence option D is correct.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
1-cos(12x)=____.
A. 2cos^2(12x)
B. 2cos^2(6x)
C. 2sin^2(12x)
D. 2sin ^2(6x)
By applying trigonometric expressions and algebra properties, the trigonometric equation 1 - cos 12x is equivalent to the trigonometric equation 2 · sin² 6x. (Correct choice: D)
How to simplify a trigonometric equation
Herein we have a trigonometric equation which has to be simplified. Simplification procedure consists in applying trigonometric expressions and algebra properties to transform the function from the form f(cos 12x) to the form f(cos 6x). Now we present the solution in detail:
1 - cos 12x Given1 - cos² 6x + sin² 6x cos 2x = cos² x - sin² x / (- 1) · a = - a1 - 1 + sin² 6x + sin² 6x cos² x + sin² x = 1 / (- 1) · a = - a2 · sin² 6x Definitions of subtraction and addition / Existence of additive inverse / Modulative property / ResultBy applying trigonometric expressions and algebra properties, the trigonometric equation 1 - cos 12x is equivalent to the trigonometric equation 2 · sin² 6x. (Correct choice: D)
To learn more on trigonometric equations: https://brainly.com/question/23599274
#SPJ1
