Answer:
[tex] 3x - y = 5 [/tex]
Step-by-step explanation:
The two pint equation of a line:
[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]
We have
[tex] x_1 = 4 [/tex]
[tex] x_2 = 3 [/tex]
[tex] y_1 = 7 [/tex]
[tex] y_2 = 4 [/tex]
[tex] y - 7 = \dfrac{4 - 7}{3 - 4}(x - 4) [/tex]
[tex] y - 7 = \dfrac{-3}{-1}(x - 4) [/tex]
[tex] y - 7 = 3(x - 4) [/tex]
[tex] y - 7 = 3x - 12 [/tex]
[tex] 5 = 3x - y [/tex]
[tex] 3x - y = 5 [/tex]
which graph is the solution to lx| > 10? HELP PICTURE INCLUDED
Answer:
Its the first answer choice.
Step-by-step explanation:
Its open circle because the sign is just greater than. And since x is an absolute value, the negative sign doesnt matter so, it points to the right of 10 and to the left of -10.
Domain and range of T
Answer:
Let's list out the points that belong to T. They are T{(-1, -4), (2, 2), (2, -3)}.
The domain is all of the x values. Therefore the domain is {-1, 2}.
The range is all of the y values. Therefore the range is {-4, -3, 2}.
We don't use ( ) or [ ] because T is a discrete relation.
Solve the equation. y + 3 = –y + 9
A. y = 1
B. y = 3
C. y = 6
D. y = 9
Answer:
y=3
Step-by-step explanation:
y + 3 = –y + 9
Add y to each side
y+y + 3 = –y+y + 9
2y+3 = 9
Subtract 3 from each side
2y+3-3 = 9-3
2y = 6
Divide by 2
2y/2 = 6/3
y =3
Answer:
Hello!
_______________________
Your answer would be (B) y = 3
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
Hope this helped you!
Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. Solve the original equation by solving the new equation
x2y'' + 9xy' - 20y = 0
Answer:
[tex]\boxed{\sf \ \ \ ax^2+bx^{-10} \ \ \ }[/tex]
Step-by-step explanation:
Hello,
let's follow the advise and proceed with the substitution
first estimate y'(x) and y''(x) in function of y'(t), y''(t) and t
[tex]x(t)=e^t\\\dfrac{dx}{dt}=e^t\\y'(t)=\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=e^ty'(x)<=>y'(x)=e^{-t}y'(t)\\y''(x)=\dfrac{d^2y}{dx^2}=\dfrac{d}{dx}(e^{-t}\dfrac{dy}{dt})=-e^{-t}\dfrac{dt}{dx}\dfrac{dy}{dt}+e^{-t}\dfrac{d}{dx}(\dfrac{dy}{dt})\\=-e^{-t}e^{-t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}\dfrac{dt}{dx}=-e^{-2t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}e^{-t}\\=e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt})[/tex]
Now we can substitute in the equation
[tex]x^2y''(x)+9xy'(x)-20y(x)=0\\<=> e^{2t}[ \ e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}) \ ] + 9e^t [ \ e^{-t}\dfrac{dy}{dt} \ ] -20y=0\\<=> \dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}+ 9\dfrac{dy}{dt}-20y=0\\<=> \dfrac{d^2y}{dt^2}+ 8\dfrac{dy}{dt}-20y=0\\[/tex]
so the new equation is
[tex]y''(t)+ 8y'(t)-20y(t)=0[/tex]
the auxiliary equation is
[tex]x^2+8x-20=0\\<=> x^2-2x+10x-20=0\\<=>x(x-2)+10(x-2)=0\\<=>(x+10)(x-2)=0\\<=> x=-10\text{ or }x=2[/tex]
so the solutions of the new equation are
[tex]y(t)=ae^{2t}+be^{-10t}[/tex]
with a and b real
as
[tex]x(t)=e^t\\<=> t(x)=ln(x)[/tex]
[tex]y(x)=ae^{2ln(x)}+be^{-10ln(x)}=ax^2+bx^{-10}[/tex]
hope this helps
do not hesitate if you have any questions
PLEASE AWNSER SOON!!! IM ALMOST OUT OF TIME!!!!!!!Rectangle JKLM is rotated 90° clockwise about the origin. On a coordinate plane, rectangle J K L M has points (negative 4, 1), (negative 1, 1), (negative 1, negative 1), (negative 4, negative 1). What are the coordinates of J’? J’(–1, –4) J’(4, –1) J’(1, 4) J’(4, 1)
Answer:
The answer is C (j' 1,4). It is not B J'(4, 1) because the new coordinate is moving 90 degrees clockwise not 180 degrees.
Step-by-step explanation:
J' will have coordinates (1, 4) after 90° clockwise rotation
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Rectangle JKLM is rotated 90° clockwise about the origin.
On a coordinate plane, rectangle J K L M has points (-4, 1), (-1, 1), (- 1, - 1), (- 4, - 1).
After rotating the rectangle 90° clockwise about the origin, the point J(-4, 1) will be transformed to a new point J' with coordinates (y, -x).
Thus, J' will have coordinates (1, 4).
Therefore, J' will have coordinates (1, 4) after 90° clockwise rotation
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A small regional carrier accepted reservations for a particular flight with 17 seats. 14 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 52% chance.A. Find the probability that overbooking occurs. B. Find the probability that the flight has empty seats.
Answer:B.
Step-by-step explanation: it is better to have empty seats than toforce people to give up their seats.
The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1100 miles. What warranty should the company use if they want 96% of the tires to outlast the warranty? Round the answer to the nearest whole number
Answer:
61,925 miles
Step-by-step explanation:
Given :
The p-value of the tires to outlast the were warranty were given in the the question as = 0.96
Checking the normal distribution table, The probability that corresponds to 0.96
from the Normal distribution table is 1.75.
Mean : 'μ'= 60000 miles
Standard deviation : σ=1100
The formula for z-score is given by
: z= (x-μ)/σ
1.75=(x-60000)/1100
1925=x-60000
x=61925
Therefore, the tread life of tire should be 61,925 miles if they want 96% of the tires to outlast the warranty.
Segu
Find a formula for the nth term in this
arithmetic sequence:
a1 = 7, a2 = 4, a3 = 1, a4 = -2, ...
Answer:
The formula is 10 - 3n
Step-by-step explanation:
For an nth term in an arithmetic sequence
U( n ) = a + ( n - 1)d
Where n is the number of terms
a is the first term
d is the common difference
From the sequence above
a = 7
d = 4 - 7 = - 3
The formula for an nth term is
U(n) = 7 + (n - 1)-3
= 7 - 3n + 3
The final answer is
= 10 - 3n
Hope this helps you.
Please Help ASAP! Consider the function below.
f(x) = 2X - 2.
Which of these graphs represent the inverse of the function F??
Answer:
1st Graph
Step-by-step explanation:
Step 1: Find the inverse
y = 2x - 2
x = 2y - 2
x + 2 = 2y
y = (x + 2)/2
Step 2: Graph the inverse
Simply use a graphing calculator and we should see our answer is the top left graph.
A jar contains 5 brown marbles, 3 yellow marbles, 4 red marbles, 6 blue marbles, and 2 orange marbles. A marble is chosen and replaced. Then another marble is chosen. What is the likelihood that a brown marble AND a red marble were chosen? A: 9/20 B: 1/2 C: 1/20 D: 0
Answer:
1/20
Step-by-step explanation:
5 brown marbles, 3 yellow marbles, 4 red marbles, 6 blue marbles, and 2 orange marbles = 20 marbles
P( brown) = brown / total = 5/20 = 1/4
Replace
5 brown marbles, 3 yellow marbles, 4 red marbles, 6 blue marbles, and 2 orange marbles = 20 marbles
P( red) = red / total = 4/20 = 1/5
P( brown, replace, red) = 1/4 * 1/5 = 1/20
No need of a answer anymore.
Answer:
mean score of class B = 1778/25 = 71.12
Step-by-step explanation:
This was your question : Class A has 12 pupils and class B has 25 pupils. Both classes sit the same maths test. The mean score for class A is 80. The mean score for both classes is 74. What is the mean score (rounded to 2 DP) in the maths test for class B?
mean of class A = Σfx/Σf
mean of class A = 80
Σfx = 80 × 12 = 960
Mean score for both classes = 74
where
b = Σfx of class B
960 + b/37 = 74
cross multiply
960 + b = 2738
b = 2738 - 960
b = 1778
mean score of class B = Σfx/Σf
Σfx = 1778
Σf = 25
Therefore,
1778/25 = 71.12
What is an equation in point-slope form for the line that passes through the points (4,−1) and (−3,4)? y+4=−57(x+3) y+4=57(x+3) y−4=−57(x+3) y−3=−57(x+4) PLEASE HELP MEEEE
Answer:
Step-by-step explanation:
(4+1)/(-3-4)= -5/7
y + 1 = -5/7(x - 4)
or
y - 4= -5/7(x + 3)
Write the limit as a definite integral on the interval [a, b], where ci is any point in the ith subinterval. Limit Interval lim ||Δ|| → 0 n (4ci + 11) i = 1 Δxi [−8, 6]
Answer:
The corresponding definite integral may be written as
[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]
The answer of the above definite integral is
[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98[/tex]
Step-by-step explanation:
The given limit interval is
[tex]\lim_{||\Delta|| \to 0} \sum\limits_{i=1}^n (4c_i + 11) \Delta x_i[/tex]
[tex][a, b] = [-8, 6][/tex]
The corresponding definite integral may be written as
[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]
[tex]\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x[/tex]
Bonus:
The definite integral may be solved as
[tex]\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x \\\\\frac{4x^2}{2} + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\2x^2 + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\ 2(6^2 -(-8)^2 ) + 11(6 - (-8) \\\\2(36 - 64 ) + 11(6 + 8) \\\\2(-28 ) + 11(14) \\\\-56 +154 \\\\98[/tex]
Therefore, the answer to the integral is
[tex]\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98[/tex]
How many ways can a 4-person subcommittee be selected from a committee of 6 people? (B) How many ways can a president comma vice dash president comma secretary comma and treasurer be chosen from a committee of 6 people?
Answer:
A) 360
B) 360
Step-by-step explanation:
Part A)
Given that there are a total of 6 people and 4 person subcommittee is to be selected.
Number of ways to select 1st person = 6
Now, 1 person is selected, total persons left are 5
Number of ways to select 2nd person = 5
Now, 1 person is selected, total persons left are 4
Number of ways to select 3rd person = 4
Now, 1 person is selected, total persons left are 3
Number of ways to select 4th person = 3
So, total number of ways = 6[tex]\times[/tex]5[tex]\times[/tex]4[tex]\times[/tex]3 = 360
Part B)
Given that there are a total of 6 people in the committee
Number of ways to select president = 6
Now, 1 person is selected, total persons left are 5
Number of ways to select vice president = 5
Now, 1 person is selected, total persons left are 4
Number of ways to select secretary = 4
Now, 1 person is selected, total persons left are 3
Number of ways to select treasurer = 3
So, total number of ways = 6[tex]\times[/tex]5[tex]\times[/tex]4[tex]\times[/tex]3 = 360
Express it in slope-Intercept form
Answer:
Y=1/4x-4
Explanation: The y intercept is -4 that is your B. Using the rise over sun method the line rises 1 and goes to the right 4 making the slope 1/4 or .25
Sandy is working with a carpenter to frame a house. They are using 8-foot-long boards, but each board must be cut to be 7 feet inches long. How much is cut off each board? Note: 1 foot = 12 inches A. 1 1/4 inches B. 1 3/4 inches C. 7 inches D. 3/4 inch
Answer:
c
Step-by-step explanation:
plato
The side, s, of a square with area A square feet is given by the formula s = square root A. Find the perimeter of a square with an area of 36 square feet. ______________ ft
Answer:
24 feet.
Step-by-step explanation:
The side of the square = √36 = 6 feet.
The square has 4 equal sides so the perimeter = 4*6 = 24 feet.
In her last semester at SPC, Polly Hedron needs to take Statistics, Composition 2, Ethics, and Physics. Because Polly is registering early, she has 14 choices for her section of Statistics, 12 choices for her section of Composition, 11 choices for her section of Ethics, and 18 choices for her section of Physics. From how many possible schedules can Polly choose? (You may presume that none of these sections interfere with each other)
Answer:
Polly can choose 33264 schedules.
Step-by-step explanation:
None of these sections interfere with each other, so:
For each statistics choice, there are 12 composition choices.
For each composition choice, there are 11 section of Ethics choices.
For each section of Ethics choice, there are 18 Physics choises.
There are 14 statistics choices.
From how many possible schedules can Polly choose?
14*12*11*18 = 33264
Polly can choose 33264 schedules.
The cube of a number is less than five times the square of the number. For what set of numbers is this true?
(–ꝏ, 5)
(5, ꝏ)
(–ꝏ, 0) U (0, 5)
(–ꝏ, 5) U (5, ꝏ)
Answer:
(–ꝏ, 0) U (0, 5)
Step-by-step explanation:
The relation can be written as ...
x³ < 5x²
x³ -5x² < 0
x²(x -5) < 0
This is not true for x = 0. It is true for x < 5, otherwise. Then the solution set is ...
x ∈ {(–ꝏ, 0) U (0, 5)}
Answer:
C
Step-by-step explanation:
got it right on edge
This Question: 1 pt
5
A person earns $15,500 one year and gets a 5% raise in salary. What is the new salary?
The new salary is $
Answer:
The new salary of that person (for the period of a year) would be [tex]\$ 16,\!275[/tex].
Step-by-step explanation:
Start by considering: what is the exact value (in dollars) of that "[tex]5\%[/tex] raise in salary"?
[tex]5\%[/tex] (five percent) is equal to [tex]\displaystyle \frac{5}{100}[/tex].
To find the value of [tex]5\%[/tex] of [tex]\$15,\!500[/tex], simply multiply [tex]\$15,\!500[/tex] by [tex]5\%[/tex]:
[tex]\begin{aligned}&5\% \times \$15,\!500\\ &= \frac{5}{100} \times \$15,\!500 \\ &= 5\times \$155 = \$775 \end{aligned}[/tex].
Add that to the original (one-year) salary of this person to find the new one-year salary:
[tex]\$15,\!500 + \$775 = \$16,\!275[/tex].
Answer:
The new salary is $16,725
Step-by-step explanation:
To find the new salary, multiply 5% and $15,500
5% * $15,500
First, convert 5% to a decimal. Divide 5 by 100 or move the decimal place 2 spaces to the left.
5/100=0.05
5.0 --> 0.5--> 0.05
0.05 * $15,500
Multiply
$775
The raise is equal to $775.
Next, add the raise to the salary.
raise + salary
The raise is $775 and the salary is $15,500
$775 + $15,500
Add
$16,275
The new salary is $16,275
In a test of the effectiveness of garlic for lowering cholesterol, 47 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes (beforeminusafter) in their levels of LDL cholesterol (in mg/dL) have a mean of 2.7 and a standard deviation of 17.8. Construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
The 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199, suggesting that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.
We have,
To construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, we can use the formula:
CI = X ± (Z * (σ/√n))
where:
CI is the confidence interval
X is the sample mean
Z is the critical value corresponding to the desired confidence level (90% confidence level corresponds to Z = 1.645 for a large sample size)
σ is the population standard deviation
n is the sample size
Given that the sample mean X of the net change in LDL cholesterol is 2.7, the standard deviation (σ) is 17.8, and the sample size (n) is 47, we can calculate the confidence interval as follows:
CI = 2.7 ± (1.645 * (17.8/√47))
Calculating the standard error (SE):
SE = σ/√n = 17.8/√47 ≈ 2.587
Substituting the values into the confidence interval formula:
CI = 2.7 ± (1.645 * 2.587)
Calculating the upper and lower bounds of the confidence interval:
Upper bound = 2.7 + (1.645 * 2.587) ≈ 7.199
Lower bound = 2.7 - (1.645 * 2.587) ≈ -1.799
Therefore, the 90% confidence interval estimate for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199.
Interpreting the confidence interval:
Since the confidence interval contains both positive and negative values, it suggests that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.
The interval includes zero, indicating that there is a possibility that the mean net change in LDL cholesterol after the garlic treatment could be zero (no change).
However, it is important to note that further studies or a larger sample size may be needed to draw more definitive conclusions.
Thus,
The 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199, suggesting that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.
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The 90% confidence interval suggests that the true mean net change in LDL cholesterol after the garlic treatment lies between -1.57 and 6.97 mg/dL. Since the interval contains both positive and negative values, it indicates that the garlic treatment may or may not be effective in reducing LDL cholesterol.
What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?To construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, we can use the formula:
CI = mean ± (Z * (standard deviation / √n))
Here, n represents the sample size (47), Z is the critical value corresponding to a 90% confidence level (Z = 1.645 for a 90% confidence level), and the mean is 2.7 with a standard deviation of 17.8.
Plugging in the values:
CI = 2.7 ± (1.645 * (17.8 / √47))
CI = 2.7 ± (1.645 * (17.8 / 6.856))
CI = 2.7 ± (1.645 * (2.596))
CI = 2.7 ± 4.270
CI = 2.7 + 4.270 ; CI = 2.7 - 4.270
CI = 6.97 ; CI = -1.57
Thus, the 90% confidence interval estimate for the mean net change in LDL cholesterol after the garlic treatment is approximately (-1.57, 6.97).
The confidence interval suggests that the effectiveness of garlic in reducing LDL cholesterol is inconclusive. The interval spans both positive and negative values, indicating that the true mean change in LDL cholesterol could be anywhere within this range. Further research or a larger sample size might be needed to draw a more definitive conclusion about the effectiveness of garlic in lowering LDL cholesterol.
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Rationalize the denominator and simplify
Answer:
sqrt(70)/7
Step-by-step explanation:
sqrt(10/7)
sqrt ( a/b) = sqrt(a)/ sqrt(b)
sqrt(10) / sqrt(7)
But we don't leave a sqrt in the denominator, so multiply by sqrt(7) /sqrt(7)
sqrt(10) /sqrt(7) * sqrt(7) / sqrt(7)
sqrt(70)/ sqrt(49)
sqrt(70)/7
**Hello !** I need help to do that algebra homework. I don't really know how that website works, so just tell me how much points you want if your answer is good and i'll give them to your with a lot of pleasure. Here is the homework : Thank you so much for your help ! :)
Answer:
y = √(900 -x²); see below for a graph
Step-by-step explanation:
The high point (30 ft) is the radius of the circle, so the equation is ...
x² +y² = 30²
Subtract the x-term and take the square root to find y.
y² = 30² -x²
y = √(30² -x²) = √(900 -x²)
The graph is shown in the attachment.
_____
Comment on "how that website works"
We don't know what web site you're referring to, but the one I like is Desmos. It only takes a few minutes to learn to graph the equation here.
You don't even need to solve for y to get the desired graph. You can simply specify that y ≥ 0.
Rewrite 19/3 as a mixed number
Answer:
[tex]6\frac{1}{3}[/tex]
Step-by-step explanation:
You can divide 19 by 3 a total of 6 times with a remainder of 1.
which is bigger 1 or
[tex] \frac{19}{9} [/tex]
Answer:
19/9 because it equals to 2.111.. Which is greater than 1
Step-by-step explanation:
By the way if it's right can i get brainliest.
Answer:
1 < 19/9
Step-by-step explanation:
1 vs 19/9
Rewriting 19/9 as 9/9 + 9/9+ 1/9
1 vs 1+1 +1/9
1 vs 2 1/9
1 < 19/9
Consider the matrices. A=⎡⎣⎢4−3−578−2⎤⎦⎥ and B=⎡⎣⎢−27−35−12⎤⎦⎥ What is the result of A−B? Enter your answer by filling in the boxes.
hello
[tex]A-B=\left[\begin{array}{cc}4-(-2)&7-5\\-3-7&8-(-1)\\-5-(-3)&-2-2\end{array}\right] \\\\=\left[\begin{array}{cc}4+2&2\\-10&8+1\\-5+3&-4\end{array}\right] \\\\=\left[\begin{array}{cc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]
hope this helps
Using matrices A and B, the result of A-B is
[tex]A-B=\left[\begin{array}{ccc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]
Given :
Two matrices A and B. We need to subtract both matrix
Lets find out A-B
Given matrices A and B are
[tex]A=\left[\begin{array}{ccc}4&7\\-3&8\\-5&-2\end{array}\right] \\B=\left[\begin{array}{ccc}-2&5\\7&-1\\-3&2\end{array}\right][/tex]
When we subtract A-B we need to subtract the corresponding elements in that matrix
[tex]A-B=\left[\begin{array}{ccc}4&7\\-3&8\\-5&-2\end{array}\right] -\left[\begin{array}{ccc}-2&5\\7&-1\\-3&2\end{array}\right]=\left[\begin{array}{ccc}4-(-2)&7-5\\-3-7&8-(-1)\\-5-(-3)&-2-2\end{array}\right] \\A-B=\left[\begin{array}{ccc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]
The above is the resultant matrix .
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united services and supplies reports net income of $100000 and cost of goods of $353000. If US&S's gross profit rate was 30%, net sales were
Answer:
Net sales is $ 504285.71
Step-by-step explanation:
We have the following:
Let net sales be x.
Net sales - Cost of goods sold = Gross profit
We replace and we are left with:
x - $ 353000 = x * 30%
x - $ 353000 = 0.30 * x
x - 0.30 * x = $ 353000
0.7 * x = $ 353000
x = $ 353000 / 0.7
x = $ 504285.71
Therefore, net sales is $ 504285.71
The management of Acrosonic plans to market the ElectroStat, an electrostatic speaker system. The marketing department has determined that the demand for these speakers is represented by the following function, where p denotes the speaker's unit price (in dollars) and x denotes the quantity demanded. Find the following functions (in dollars), find the value (in dollars) and interpret your results.
p = −0.02x + 610 (0 ≤ x ≤ 20,000)
a. Find the revenue function R.
b. Find the marginal revenue function R'(x).
c. Compute the following value.
R'(5,400) = _______________
Answer:
(a)[tex]R(x)=-0.02x^2+610x[/tex]
(b)[tex]R'(x)=-0.04x+610[/tex]
(c)R'(5400)=$394
Step-by-step explanation:
Given that x is the quantity demanded and the speaker's unit price (in dollars) is p where:
p = −0.02x + 610 (0 ≤ x ≤ 20,000)
(a)Revenue function R.
Revenue = Price X Quantity Demanded
Therefore:
R(x)=xp
[tex]=x(-0.02x + 610)\\R(x)=-0.02x^2+610x[/tex]
(b)Marginal revenue function R'(x)
If [tex]R(x)=-0.02x^2+610x[/tex]
Then, the marginal revenue function
[tex]R'(x)=-0.04x+610[/tex]
(c)We want to compute R'(5,400)
[tex]R'(5400)=-0.04(5400)+610\\R'(5400)=394[/tex]
From the above, we can infer that the revenue that will be generated on the sales of the 5401st item is $394.
All cell phone plans from Mobile USA require an additional $10/month data fee on top of the base plan price.
Lindsay has the $39.99/month base cell phone plan from MobileUSA.
Conjecture: Lindsay pays at least $49.99/month for her cell phone.
Use deductive reasoning to verify the conjecture, or provide a counterexample if the conjecture is false.
A true, law of detachment
В. false, Lindsay does not have a data fee
С. false, Lindsay is not a Mobile USA customer
Dfalse, not all MobileUSA customers have a data fee
Answer:
A
Step-by-step explanation:
Answer:
A True, law of detachment.
Brainliest? Get this correct What is the sum of the rational expressions below?
Answer:
A)
Step-by-step explanation:
Answer:
[tex] \dfrac{5x^2 + 5x + 3}{3x^2 + 3x} [/tex]
Step-by-step explanation:
[tex] \dfrac{2x + 3}{3x} + \dfrac{x}{x + 1} = [/tex]
[tex] = \dfrac{(x + 1)(2x + 3)}{(x + 1)(3x)} + \dfrac{(3x)(x)}{(3x)(x + 1)} [/tex]
[tex] = \dfrac{2x^2 + 3x + 2x + 3}{3x^2 + 3x} + \dfrac{3x^2}{3x^2 + 3x} [/tex]
[tex] = \dfrac{2x^2 + 5x + 3 + 3x^2}{3x^2 + 3x} [/tex]
[tex] = \dfrac{5x^2 + 5x + 3}{3x^2 + 3x} [/tex]