Step-by-step explanation:
first you group like terms.
-3s-s+8+1-2
-4s+7
Answer:
-4s + 7
Step-by-step explanation:
We need to combine like terms. Like terms are terms whose variables (and exponents) are the same (note that they could be constants as well). Basically, they are "like" each other. In this case, the like terms are -3s and - s and also 1, 8, and -2. -3s - s = -4s and 1 + 8 - 2 = 7 so the answer is -4s + 7.
The cost and revenue are defined, in dollars, as C(x) = 30x + 100 and R(x) = -x2 + 90x.
Required:
a. Find and simplify the profit function, defined by P(x).
b. Use a. to find the marginal profit function.
Answer:
a) The profit function is [tex]P(x) = -x^{2}+60\cdot x -100[/tex], b) The marginal profit function is [tex]P'(x) = -2\cdot x + 60[/tex].
Step-by-step explanation:
a) Let be [tex]C(x) = 30\cdot x + 100[/tex] (cost function) and [tex]R(x) = -x^{2}+90\cdot x[/tex] (revenue function), the profit function is found by subtracting the cost function from the revenue function. That is:
[tex]P(x) = R(x)-C(x)[/tex]
[tex]P(x) = -x^{2}+90\cdot x -(30\cdot x + 100)[/tex]
[tex]P(x) = -x^{2}+90\cdot x -30\cdot x -100[/tex]
[tex]P(x) = -x^{2}+60\cdot x -100[/tex]
b) The marginal profit function is the first derivative of the profit function:
[tex]P'(x) = -2\cdot x + 60[/tex]
n the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.1 inches, and standard deviation of 5.8 inches. A) What is the probability that a randomly chosen child has a height of less than 46.3 inches
Answer:
The probability is 0.0643 to 4 decimal places
Step-by-step explanation:
To calculate this probability, we find the z-score
Mathematically;
z-score = (x-mean)/SD
where in the question;
x = 46.3
mean = 55.1
SD = 5.8
Plugging these values, we have;
z-score = (46.3-55.1)/5.8 = -8.8/5.8 = -1.52
The probability we want to calculate is;
P(z < -1.52)
We can get this answer by using the standard normal distribution table;
Thus from the table, we have;
P(z < -1.52) = 0.064255 which is 0.0643 to 4 decimal places
What is 5x100? .................................................
Answer:
500
Step-by-step explanation:
Answer:
it is 500
Step-by-step explanation:
it is 500 because if you take the 5 and multiply it by the 1 you get one then all you do after you do that is add the zeros at the end.
In a physics class, the teacher proposes that the velocity of a car in miles per hour and the stopping distance in feet are represented by inverse functions. Assuming this is true, which graph includes a pair of functions for a specific velocity function and the corresponding stopping distance that can be verified as inverses?
Answer:
the answer is b
Step-by-step explanation:
2nd graph includes a pair of functions for a specific velocity function and the corresponding stopping distance that can be verified as inverses.
The answer is option B.
Which statement verifies that f(x) and g(x) are inverses of each other?The test to verify if a function f is the inverse of another function g is given by using the composition of the functions such as this, f(g(x))= x. Therefore, to answer your question, f(g(x))=x is saying f is the inverse of g. f(g(x))=x is saying f is the inverse of g but g is not the inverse of f, g(f(x))≠x.
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A similar follow-up study is done on a sample of 25 meat-lovers who never eat vegetables, again randomly selected from the same general population (population mean life expectancy = 75, population standard deviation = 5). This new sample of meat-eaters live to an average age of 77. What is the lower limit and upper limit of the 95% confidence interval for the life expectancy of this sample of meat-lovers?
Answer:
The lower limit is 75.04
The upper limit is 78.96
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 25[/tex]
The sample mean is [tex]\= x = 77[/tex]
The standard deviation is [tex]\sigma = 5[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100 - 95)\%[/tex]
[tex]\alpha = 0.05[/tex]
The critical value for [tex]\frac{\alpha }{2}[/tex] obtained from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96* \frac{5 }{\sqrt{25} }[/tex]
=> [tex]E = 1.96[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
=> [tex]77 - 1.96 < \mu < 77 + 1.96[/tex]
=> [tex]75.04 < \mu < 78.96[/tex]
HELP ASAP ROCKY!!! will get branliest.
your $440 gets 5.8% interest compounded annually for for 8 years what will your $440 be worth in 8 years l?
Answer:
The answer is $690.78
Step-by-step explanation:
What rotation about the origin is equivalent to R−200°?
Answer:
Answer:
160°
Step-by-step explanation:
If you add or subtract a full 360° rotation (or multiple of 360°) you get the same rotation.
Add 360° to -200°:
-200 + 360 = 160
solve 7x-3y=14 for y
Answer:
y = - 14/3 +7x/3
Step-by-step explanation:
The reason for my answer is because let us move the -3y so it is before the equal sign. Let us also move 7x to the other side but make it so 14 would be to the right side of the equal sign. Now, that would mean 7x would be after 14. Our equation is now -3y=14-7x. We need to divide both sides of the equation by -3. There, we just divided -3y by 3 which equals to y. 14 divided by -3 equals to -14/3. -7x divided by -3 would equal to +7x/3. Finally, we get the answer of y = - 14/3 +7x/3.
Answer:
Step-by-step explanation:
● 7x-3y = 14
This a 1st degree equation with two variables.
● 7x-3y = 14
Substract 7x from both sides
● 7x-7x -3y = 14-7x
● -3y = 14-7x
Mulitply both sides by -1
● (-1)×(-3y) = (-1)×(14-7x)
● 3y = -14+7x
● 3y = 7x+14
Divide both sides by 3
● 3y/3 = (7x+14)/3
● y = (7/3)x + 14/3
There are infinite solutions for this equation. Keep replacing x with value and the output will change everytime.
Perimeter is the sum of the sides of a shape. If a triangle has sides of 12, 27, and 38, what is its perimeter?
Answer: 77
Add the three given values to get that result above.
Please help !
The kinetic energy of an object is the energy it has due to its motion. The kinetic energy E, in joules, of an object with a mass of m kilograms moving at v meters per second is modeled by the function -
Answer:
v (E) = √(2E/m)
Step-by-step explanation:
From the question given:
E = ½mv²
E is the kinetic energy
m is the mass of object
v is the velocity.
To find a model v(E) for the velocity of the object, we simply make V the subject of the above equation.
This can be obtained as follow:
E = ½mv²
Cross multiply
mv² = 2E
Divide both side by m
v² = 2E/m
Take the square root of both side
v = √(2E/m)
Therefore, the model v(E) for the velocity of the object is given by:
v (E) = √(2E/m)
Lulu Ruby and Emma went shopping went a total of £261. Each of them had different amount of money. Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money. Each of them spent the same amount of money.how much did money did they begin with? please help me on this
Answer:
Lulu= £81
Ruby=£108
Emma=£ 72
Step-by-step explanation:
Let Lulu's money be x
Let Ruby's money be y
Let Emma's money be z
The total money they went shopping with is = £261
So
x+y+z= 261
Lulu spent 2/3 of her money Ruby spent 1/2 of her money and Emma spent 3/4 of her money.
Money spent by each
Lulu= 2/3x
Ruby=1/2y
Emma= 3/4z
Each of them spent the same amount of money.
2/3x= 1/2y= 3/4z
2/3x= 1/2y
x(2*2)/3 = y
4/3(x) = y
2/3x=3/4z
x(2*4)/(3*3)= z
8/9x= z
x+y+z= 261
x+4/3x+8/9x= 261
9x +12x +8x= 2349
29x= 2349
X= 81
4/3(x) = y
4/3(81) = y
108= y
8/9x= z
8/9(81)= z
72= z
the difference between the number in three fourths is one half
Answer:
3
Step-by-step explanation:
WILL GIVE BRAINIEST, THANKS AND 5 STARS PLS SOLVE Angie walks ⅓ mile to school and ⅓ mile home each day. If she gets a ride each way to school half the time, how many miles does she walk to and from school each school year? (Hint: You can assume there are 180 days in the school year)
Answer:
60 miles
Step-by-step explanation:
all you do is 1/3 + 1/3 and get 2/3. then times that by 180. You get 120. divide that by 2 because half the time she gets a ride and you get 60.
A café offers a lunch special that consists of a sandwich, salad, chips, and a drink. There are 4 sandwich choices, 3 salad choices, 2 chip choices, and 5 drink choices. How many different lunch specials can be ordered?
Answer:
4
Step-by-step explanation:
there are only for sandwiches.
How to calculate the decimal form of a given fraction. Please help ASAP mam/sir.
In a fraction, the fraction bar means divided by. So to find the decimal form equivalent of a fraction like 1/4 you need to solve the math problem 1 dived by 4.
1 ÷ 4= 0.25
James walks two miles from her door to the park, then returns home to her door.
A rancher wishes to build a fence to enclose a rectangular pen having area 24 square yards. Along one side the fence is to be made of heavy duty material costing $6 per yard, while the remaining three sides are to be made of cheaper material costing $3 per yard. Determine the least cost of fencing for the pen.
At the point of the least cost of fencing the cost function has a zero
derivative.
The least cost of fencing for the pen is $72.00Reasons:
Shape of the pen = Rectangular
Area of the pen = 24 yd²
Cost of material on one side of the fence = $6 per yard
Cost of material on the remaining three sides = $3 per yard
Required:
The least cost of fencing the pen
Solution:
The least cost is a minimum value of the cost function
Let L represent the length of the fence and let W represent the width of the fence
We have;
The perimeter of the fence = 2·L + 2·W
The area of the pen, A = L × W = 24
One of the length, L, of the fence costs $6 per yard and the other length L,
of the opposite side costs $3 per yard.
The cost of fencing, C 3 × 2·W + 3 × L + 6 × L = 6·W + 9·L
C = 6·W + 9·L
[tex]\displaystyle W = \mathbf{\frac{24}{L}}[/tex]
Which gives;
[tex]\displaystyle C = 6 \cdot \frac{24}{L} + 9 \cdot L = \frac{144}{L} + 9 \cdot L = \mathbf{\frac{144 + 9 \cdot L^2}{L}}[/tex]
The shape of the above function is concave upwards.
At the minimum value, we have;
[tex]\displaystyle \frac{dC_{min}}{dL} = \frac{d}{dL} \left(\frac{144}{L} + 9 \cdot L\right) = 9 - \frac{144}{L^2} = 0[/tex]
Which gives;
[tex]\displaystyle \frac{144}{L^2} = 9[/tex]
[tex]\displaystyle \frac{144}{9} = L^2[/tex]
By symmetric property, we have;
[tex]\displaystyle L^2 = \frac{144}{9}[/tex]
[tex]\displaystyle L = \sqrt{ \frac{144}{9}} = \frac{12}{3} = 4[/tex]
The length of the fence that gives the least cost, L = 4 yards
[tex]\displaystyle At \ L = 4, \ W = \frac{24}{4} = 6[/tex]
The width of the fence at least cost, W = 6 yards
Cost, C = 6·W + 9·L
Least cost, [tex]C_{min}[/tex] = 6 × 6 + 9 × 4 = 72
The least cost of the fencing, [tex]C_{min}[/tex] = $72.00
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Find the value of x such that l ⊥ m. A) 10.7 B) 16 C) 46 D) 48
Santa's Wonderland is an extravagant holiday light display that is open from early November through January each year. The entry fee is $15 per vehicle for up to and including 5 people, with an additional $1.50 for each person over 5. Express this information as a piecewise function of x, where x represents the number of people in the vehicle.
Answer:
The expression
Y(x)= 15(v)+1.5(x)
Step-by-step explanation:
The entry fee is $15 per vehicle for up to and including 5 people, with an additional $1.50 for each person over 5.
Let the entrance fee be Y
Let the number of vehicle be V
Let X be the number of people more than 5
The expression
Y(x)= 15(v)+1.5(x)
If you’re pro at geometry, could you please help me with this? :)
Answer:
From the given information, the value of n is 1. By using that information, the measure of JL is 29.
Step-by-step explanation:
For this problem, we have to not only find the value of n but, we also have to find the value of JL. We are given information in this problem.
ΔABC ≅ ΔJKL
AC = 10n + 19
JL = 9n + 20
From this information, we can conclude that AC and JL are congruent meaning they are equal in measure. So, let's set up an equation where they set equal to each other.
10n + 19 = 9n + 20
Subtract 9n from 10n.
n + 19 = 20
Subtract 19 from 20.
n = 1
So, the value of n is 1. We can use this to find the value of JL.
JL = 9(1) + 20
JL = 9 + 20
JL = 29
Answer:
JL is equal to 29
Step-by-step explanation:so JL= 29 is the answer
Jack plants a 5 centimeter beanstalk in his back yard. For the next month, Jack notices that each day the beanstalk is 15% taller than it was the previous day. Which formula represents the height of the beanstalk (in centimeters) as a function of the number of days, t, since it was planted
Answer:
[tex]H= 0.15x+ H[/tex]
Step-by-step explanation:
This problem requires that we produce a model that describes the daily height of the beans stalk
let us describe some variables
the daily height is H
let the initial height be h= 5 cm
and the daily increment be 15%= 0.15
and also the number of days be x
We can use the equation of straight line to model the daily height of the beans stalk
i.e
[tex]y= mx+c[/tex]
hence the formula for the height of the beanstalk is
[tex]H= 0.15x+ H[/tex]
What is the solution for this inequality?
5x< 45
O A.
OB.
Oc.
XS-9
Answer:
x < 9
Step-by-step explanation:
Hello!
We solve inequalities the same we would solve equations. What we do to one side we have to do to the other.
5x < 45
Divide both sides by 5
x < 9
The answer is x < 9
Hope this helps!
Answer:
x<9 I hope help you Mark as Brainliest
The inequality 5m-7 > 16 holds true for all numbers than in set {1,2,3,4,5,6,7,8,9,10}
Answer:
Greater than 4
The area of the triangle shown is 40.0 cm2.
?
12.5 cm
* not drawn to scale
What is the height of the triangle?
Answer:
The height of the triangle is 6.4cm
Step-by-step explanation:
- If the triangle has a side that measures 12.5cm, it means that two of its sides are equal in length.
Which is equivalent to the description of an isosceles triangle.
To find the height, use the equation of the area.
Area = (Base * height) / 2
- We know the value of the area and its shorter side that could be the base.
40cm = (12.5 cm * h) / 2
- Clearing the height would give that:
80cm / 12.5cm = h
h = 6.4cm
The height of the triangle is 12.5cm
A triangle is a plane figure with edges that are all straight with three sides and three angles.
The formula for calculating the area of a triangle is;
[tex]\mathbf{Area = \dfrac{1}{2}\times Base \times Height}[/tex]
Given that:
The area = 40 cm²
Since the diagram for the triangle is not given;
Let us assume the base of the triangle = 12.5 cm, provided we are to determine the height.∴
Using the formula form above:
[tex]\mathbf{40.0 cm^2 = \dfrac{1}{2}\times 12.5 cm \times Height}[/tex]
[tex]\mathbf{40.0 cm^2 \times 2 = 1\times 12.5 cm \times Height}[/tex]
[tex]\mathbf{80.0 cm^2 = 12.5 cm \times Height}[/tex]
[tex]\mathbf{Height = \dfrac{80.0 cm^2}{ 12.5 cm} }[/tex]
Height of the triangle = 6.4 cm
Therefore, we can conclude that the height of the triangle = 6.4 cm
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what is (3⁴×5⁴)-³ =?
Answer:
The solution to the given expression is 1/2562890625
Step-by-step explanation:
(3⁴ × 5⁴)⁻²
Simplify the terms inside the parentheses. 3⁴ × 5⁴ is the same as 15⁴ because even though the base numbers are different, the exponents are the same which makes it similar.
(15⁴)⁻²
Now, for this step, we are going to add the exponents because when multiplying, the exponential numbers add together. So 4 × -2 = -8.
15⁻⁸
Since we can not have a negative exponent, we are going to change this into a fraction. We do this by putting this term in a fraction where 1 is the numerator and the term is the denominator.
1 / 15⁻⁸
Now, we simplify the term on the bottom.
1 / 2562890625
So, this is the solution to the problem.
How do we write 0.76 in expanded form
Answer:
0 ones
7 tenths
6 hundredths
I'm sorry if I misunderstood.
Good luck though! :)
Please add Brainliest if you'd like, not that it matters.
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n2+5/2n
Answer:
[tex]n^2 + \frac{5}{2}n + \frac{25}{16}[/tex]
[tex](n + \frac{5}{4})^2[/tex]
Step-by-step explanation:
Given
[tex]n^2 + \frac{5}{2}n[/tex]
Required
(a) Make a perfect square trinomial
(b) Write as binomial square
Solving (a)
Let the missing part of the expression be k;
This gives
[tex]n^2 + \frac{5}{2}n + k[/tex]
To solve for k, we need to square half the coefficient of n;
i.e. Since the coefficient of n is [tex]\frac{5}{2}[/tex], then
[tex]k = (\frac{1}{2} * \frac{5}{2})^2[/tex]
[tex]k = (\frac{5}{4})^2[/tex]
[tex]k = \frac{25}{16}[/tex]
Hence;
[tex]n^2 + \frac{5}{2}n + k[/tex] = [tex]n^2 + \frac{5}{2}n + \frac{25}{16}[/tex]
Solving (b)
[tex]n^2 + \frac{5}{2}n + \frac{25}{16}[/tex]
Expand [tex]\frac{5}{2}n[/tex]
[tex]n^2 + \frac{5}{4}n+ \frac{5}{4}n + \frac{25}{16}[/tex]
Factorize
[tex]n(n + \frac{5}{4})+ \frac{5}{4}(n + \frac{5}{4})[/tex]
[tex](n + \frac{5}{4})(n + \frac{5}{4})[/tex]
[tex](n + \frac{5}{4})^2[/tex]
Hence:
[tex]n^2 + \frac{5}{2}n + \frac{25}{16}[/tex] = [tex](n + \frac{5}{4})^2[/tex]
Ron made a mistake casting a spell, and 25 frogs start to appear each second in the classroom. After 10 seconds, Hermione cast another spell, and 35 frogs start to disappear as 25 frogs appear each second. For how many seconds was there at least one frog in the classroom?
bhai ap apne ap kar lo ye question
what is the real part of 4-5i
a. 5
b. 4
c. -5i
d. -5
PLEASE HELP!
Answer:
4Step-by-step explanation:
A complex number in its rectangular form is expressed as x+iy where x is the real part of the complex number and y is the imaginary because it is attached to the imaginary number i.
Given the complex number 4-5i, comparing the complex number with x+iy
4 = x and iy = -5i
Hence x = 4 and y = -5.
Since x is the real part of the complex number x+iy, hence 4 will be the real part of the complex number 4-5i based on comparison.