The equation that models the given situation is; 175x - 100x + 47750 = 50500 - 200x
The number of months it will take the populations to be equal is 10 months
How to model the equation of the word problem?Let us suppose after x months the population of both town's will be equal.
From the given directions, we have;
The population of the first town after x months is given by;
175x - 100x + 47750
The population of the second town after x months is given by;
50500 - 200x
Now, In order to the population of the both town's to be equal, we have;
175x - 100x + 47750 = 50500 - 200x
275x = 50500 - 47750
x = 2750/275
x = 10
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A rectangular flowebed is 6.1 meters long.and 3.6 meters wide. What is the area of the flower bed? Use the area model to solve?
A student bikes 5000 m East to school in 30.0 min (1800 seconds), realizes he forgot his calculator for physics, spends 30.0 min (1800 seconds) going back going home, and then races back to school in 27.0 minutes (1620 seconds).
What is the student’s total distance traveled?
_______ meters
The number of seconds it took the student to travel back and forth is ________
seconds.
Determine the student’s average speed. ________
m/s
The total distance covered is 15000 m. The total time taken is 5220 seconds and the speed is 2.87 m/s.
What is the speed?We know that speed has to do with the ratio of the distance that has been covered to the time taken. The speed is a scalar quantity and as such we do not consider the direction hence we would not consider that going back in the opposite direction. The total distance can be obtained algebraically.
The total distance that the student travelled can be obtained from;
5000 m + 5000 m + 5000 m
= 15000 m
The total time taken in seconds = 1800 seconds + 1800 seconds + 1620 seconds
= 5220 second
Speed = Distance/ Time
= 15000 m/5220 second
= 2.87 m/s
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For a certain company, the cost function for producing x items is C(x)=50x+100 and the revenue function for selling x items is R(x)=−0.5(x−90)2+4,050 . The maximum capacity of the company is 150 items.
Assuming that the company sells all that it produces, what is the profit function?
P(x)=
What is the domain of P(x) ?
The company can choose to produce either 40 or 50 items. What is their profit for each case, and which level of production should they choose?
Profit when producing 40 items =
Profit when producing 50 items =
Can you explain, from our model, why the company makes less profit when producing 10 more units?
The profit function is P(x) = −0.5x² + 40x - 100
The domain is 3 < x < 75Profit when producing 40 items = 700Profit when producing 50 items = 650The company makes less profit when they produce moreHow to determine the profit function?From the question, we have the following equations that can be used in our computation:
Cost function, C(x) = 50x + 100
Revenue function, R(x) = −0.5(x − 90)² + 4050
The profit function is the difference between the revenue and the cost
So, we have
P(x) = R(x) -CP(x)
Substitute the known values in the above equation, so, we have the following representation
P(x) = −0.5(x − 90)² + 4050 - 50x - 100
Evaluate the like terms
P(x) = −0.5(x − 90)² - 50x + 3950
Expand
P(x) = −0.5(x² − 180x + 8100) - 50x + 3950
Expand
P(x) = −0.5x² + 90x - 4050 - 50x + 3950
Evaluate the like terms
P(x) = −0.5x² + 40x - 100
The domain of the functionIn (a), we have
P(x) = −0.5x² + 40x - 100
Using a graphing calculator, the reasonable domain is
3 < x < 75
So, the domain is 3 < x < 75
The profit at each productHere, we have
x = 40 or 50
So, we have
P(40) = -0.5(40)² + 40(40) - 100 = 700
P(50) = -0.5(50)² + 40(50) - 100 = 650
Why the profit makes less profitIn (d), we have
P(40) = 700
P(50) = 650
This means that the profit reduces as they produce more
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Write the number 476 in
each form.
Word:
Expanded:
Answer:four-hundred-seventy-six
400+70+6
Step-by-step explanation:
four-hundred-seventy-six
400+70+6
The polynomial
p(x)=24x3−46x2+29x−6
has three real roots. One of them is x=2/3 Find the others and list them in increasing sequence:
The other roots of the cubic equation p(x) = 24·x³ - 46·x³ + 29·x - 6 are;
x = 1/2
x = 3/4
What is a cubic equation in mathematics?A cubic equation is an equation that has 3 as the highest index.
The specified polynomial in the question is presented as follows;
P(x) = 24·x³ - 46·x² + 29·x - 6
The solution of the equation is; x = (2/3)
Therefore, (x - 2/3) is a factor of the equation and we get;
(24·x³ - 46·x² + 29·x - 6) ÷ (x - 2/3) has a remainder of 0
Dividing the above expression using long division, we get;
24·x² - 30·x + 9
(x - 2/3) [tex]{}[/tex] |(24·x³ - 46·x² + 29·x - 6)
[tex]{}[/tex] 24·x³ - 16·x² + 29·x - 6
[tex]{}[/tex] -30·x²
[tex]{}[/tex] -30·x² + 20·x
[tex]{}[/tex] 9·x - 6
[tex]{}[/tex] 9·x - 6
The other real roots of the specified equation can be found as follows;
The equation for the roots is; P(x) = 24·x³ - 46·x² + 29·x - 6 = 0
From the above long division, therefore;
24·x³ - 46·x² + 29·x - 6 = (24·x² - 30·x + 9) × (x - 2/3) = 0
Which indicates; (24·x² - 30·x + 9) = 0 or (x - 2/3) = 0
The other solution are;
24·x³ - 30·x + 9 = 0
3·(·8·x² - 10·x + 3) = 0
8·x² - 10·x + 3 = 0
Solutions for the above equation in the form; a·x² + b·x + c = 0 can be obtained using the quadratic formula as follows;
The quadratic formula; x = [tex]\dfrac{-b\pm\sqrt{b^2 - 4\cdot a\cdot c} }{2\cdot a}[/tex]
By comparing the equation, 8·x² - 10·x + 3 = 0 to the equation, a·x² + b·x + c = 0, we get;
a = 8, b = -10, and c = 3
Therefore;
x = (10 ± √((-10)² - 4 × 8 × 3))/(2 × 8)
((-10)² - 4 × 8 ×3) = 2
Therefore;
x = (10 ± √((-10)² - 4 × 8 × 3))/(2 × 8) = (10 ± 2)/(16)
x = 3/4, and x = 1/2
Therefore, the other other roots in increasing sequence are;
x = 1/2 and x = 3/4
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Which is the best estimate of 756 ÷ 26?
The division between 756 and 26 can be represented as a fraction or decimal as 378/13 or 29.1 respectively
FractionsFractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
We can say the fraction of a number is a ratio between the numerator and denominator of two numbers.
Fractions are often as a result of dividing two numbers and they probably don't give a whole number.
In this case, the division between 756 and 26 will result in a fraction because both numbers are not completely divisible by one another.
To divide 756 by 26;
756 ÷ 26 =
Divide both sides by 2
756 ÷ 26 = 378 / 13
Both numbers are not divisible by one another from here, but we can represent this as a fraction of one another;
756 ÷ 26 = 29.076923
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This is NOT multiple choice
Solve the equation 15e^4x = 12 for x
Show your work please
A) identify the exact solution
B) approximate the solution to the nearest thousandth.
Step-by-step explanation:
15 e^(4x) =12
divide both sides by 15
e^(4x) = 0.8
if e^y = X
then y = ln x
4x=ln 0.8
4x=-0.22314
dividing both sides by 4
4x/4= -0.22314/4
x = -0.0558
what is 5 to the power of 3?
Answer:
5 to the power of 3 is 125, you get this b/c 5 times 5 is 25 & 25 times 5 is 125.
Use properties of operations to write an expression equivalent to the expression below.
p6+(q+8)
A. p6+8q
B. 8(p6+q)
C. (p6+q)+8
D. 6p+q+8
The expression (p⁶ +q) + 8 is equivalent to the given expression. which is the correct answer would be an option (C).
What is the Commutative Property?The commutative property is associated with mathematical operations such as addition and multiplication. It indicates that switching the order or location of two integers while adding or multiplying them has no effect on the outcome. For example, 4 + 5 gives 9, and 5 + 4 also gives 9.
The expression is given in the question below as
p⁶ + (q + 8)
We have to determine the expression equivalent to the given expression.
As per the given question, we have
⇒ p⁶ + (q + 8)
Using the commutative property of addition, we get
⇒ (p⁶ +q) + 8
Thus, the expression (p⁶ +q) + 8 is equivalent to the given expression.
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X^2-9/2x+
Find the term to make the trinomial into a perfect square
The base of a triangle is twelve more than twice its height. If the area of the triangle is 50 square centimeters, find its base and height.
The height of the triangle is 4.68 cm and base of the triangle is 21.36 cm.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
Given that,
Base of triangle is twelve more than twice its height.
Also, area of triangle = 50 square centimeters.
Let height of the triangle is x cm,
Therefore, the base of triangle will be 2x+12 cm.
The area of triangle = 50
1/2 × (2x+12) × x = 50
x (x+6) = 50
x² + 6x -50 = 0
By solving the equation,
x = -3 + √59 and -3 - √59
Length can not be negative,
Therefore, x = -3 + √59 or x = 4.68114
Height of triangle = 4.68 cm
Base of triangle = 21.36 cm
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Use the graph below to fill in the blank with the correct number:
f(2)=
Answer:
1
Step-by-step explanation:
[tex]f(2)[/tex] is equal to the [tex]y[/tex] coordinate of the point on the graph of the function with [tex]x[/tex] coordinate 2.
8 x 5 = (4 X 5) + (_______ x 5
8 X 5 = 20 +
8 X 5 =
Answer:
4
20
40
Step-by-step explanation:
Since the final line says 8 x 5, I know that the final answer is 40.
That means that the blank on the first line has to be 4
The second line is missing a 20 because 20 + 20 = 40
Which of the following shows an example of the identity property of 0?
Answer:is 1
identity property of 0 the definition is adding 0 to any number results in the number itself. and one 1 is have the same but other 3 is not.
If 9 cows can fit in a field, how many fields are necessary to make sure 65 cows are all in a field?
fields
Answer: 8 fields are needed
Step-by-step explanation:
65 ÷ 9 = 7.222
You can't have a partial field, so you round up to find the number of fields for all 65 cows.
8 fields will fit 65 cows
Answer: 8
Step-by-step explanation:
you divide 65 by 9 but you cant have 7.222 cows so its 8
Suppose you have the Exam 1 and Exam 2 scores of all
students enrolled in U.S. History. The slope of the
regression line for predicting the scores on Exam 2 from
the scores on Exam 1 is 0.51. The standard deviation for
Exam 1 scores is 11.6, and the standard deviation for Exam
2 scores is 7.0. Use only this information to find the
correlation between Exam 1 scores and Exam 2 scores.
The correlation coefficient between Exam 1 scores and Exam 2 scores is given as follows:
0.8452.
How to obtain the correlation coefficient?The equation for this problem is given as follows:
b = r x Sy/Sx.
The variables of the equation are given as follows:
b is the slope.r is the correlation coefficient.Sy is the standard deviation of the output variable.Sx is the standard deviation of the input variable.The input and the output variables in this problem are given as follows:
Input variable: Exam 1 score.Output variable: Exam 2 score.Hence the values of the parameters are given as follows:
b = 0.51, Sx = 11.6, Sy = 7.
Hence the numeric value of the correlation coefficient is obtained as follows:
b = r x Sy/Sx.
r x 7/11.6 = 0.51
0.6034r = 0.51
r = 0.51/0.6034
r = 0.8452.
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Callan is making pizza using flour, tomatoes, and mozzarella cheese. This table gives the cost, per kilogram, of each ingredient, and the amount, in kilograms, that Callan uses: Ingredient Price per kilogram Amount Flour 0.800.800, point, 80 dollars per kilogram xxx kilograms Tomatoes 3.303.303, point, 30 dollars per kilogram yyy kilograms Mozzarella zzz dollars per kilogram 0.50.50, point, 5 kilograms The total amount Callan spends on ingredients is CCC dollars.
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The total amount spent on the ingredients is
80x + 30y + 5z
Where x is the amount of flour, y is the amount of tomatoes and z is the cost of Mozzarella per kg.
What is an expression?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Ingredients Amount Cost per kg
Flour x $80
Tomatoes y $30
Mozzarella 5 $z
The total amount spent on the ingredients can be given by the expression.
= 80x + 30y + 5z
Where x is the amount of flour, y is the amount of tomatoes and z is the cost of Mozzarella per kg.
Thus,
The total amount spent on the ingredients is
80x + 30y + 5z
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Answer:
C=0.8x+3.3y+0.5z
Step-by-step explanation:
khan
you`re welcome :)
Having a really hard time with this question, so if anyone kindly can let me know.
Answer:
Plane PQY
Step-by-step explanation:
A plane is defined by 3 non-linear points. This is because if 3 linear points are given, only a line has been defined; its plane could be at any angle. The only answer choice that has non-linear points is PQY.
Jim made $165 for 11 hours of work. At the same rate, how much would he make for 7 hours of work?
$105
Earnings for 1 hour=165÷11=$15
Earnings for 7 hours=15×7=$105
At a certain high school, the Prom Committee is going to choose new members. There are 10 students from the Junior class and 3 students from the Senior
class who are willing to be new members. In how many ways can 7 new members be chosen if 2 or fewer must be from the Senior class?
The number of ways that 7 new members be chosen if 2 or fewer must be from the Senior class is; 705 ways
How to solve permutation and combination?The formula for probability combination is;
nCr = n!/(r! * (n – r)!)
where;
n is the total number of items.
r is the number of things that may be selected at one time.
The number of ways that 2 students can be selected from the senior class is;
N(2 students from the SR class) = 3C2 * 10C2 = 135 ways
Similarly;
N(1 student from the SR class) = 3C1 * 10C3 = 360
N(0 students from the SR class) = 3C0 * 10C4 = 210
Thus, number of ways that 7 new members be chosen if 2 or fewer must be from the Senior class is;
135 + 360 + 210 = 705 ways
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Answer PLEASE!!!! 30 points
Simplify −4r(−15r + 3r − 10).
−48r2 + 40r
−48r2 − 40r
48r2 + 40
48r2 + 40r
Answer:
[tex]\huge\boxed{\sf 48r\² + 40r}[/tex]
Step-by-step explanation:
Given expression:= -4r(-15r + 3r - 10)
Add -15r and 3r
= -4r(-12r - 10)
Distribute
= (-4r)(-12r) - (-4r)(10)
= 48r² - (-40r)
= 48r² + 40r[tex]\rule[225]{225}{2}[/tex]
Find the average rate of change from x=4 to x=14
The average rate of change is given by -2/5. The correct option is (d).
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
The given graph shows different values of y at x = 4 and x = 14 as follows,
At x = 4, y = 7
And at x = 14, y = 3.
Now, the average rate of change can be determined by taking the ratio of the difference of the values of y to that of x as follows,
(3 - 7)/(14 - 4)
= -4/10
= -2/5
Hence, the average rate of change x = 4 to x = 14 is given as -2/5.
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encuentra el producto: (2) (3) (-4) (-2)
ayuda porfa.
Answer:
48
Step-by-step explanation:
Start with 2 x 3 to get 6
then take 6 and multiply by -4 which is -24 (The negative stays from the four)
Last, take -24 and multiply by negative 2 to get 48. The negatives cancel out
Solve for x.
412≤1.2x
Responses
x≥334
x is greater than or equal to 3 and 3 over 4
x≤334
x is less than or equal to 3 and 3 over 4
x≥525
x is greater than or equal to 5 and 2 over 5
x≤525
The solution for x in the inequality is x ≥ 343
How to determine the solution for x?From the question, we have the following inequality expression that can be used in our computation:
412≤1.2x
Divide both sides of the inequality by 1.2
So, we have
412/1.2 ≤ 1.2x/1.2
Evaluate the quotients
343 ≤ x
Rewrite the expression as
x ≥ 343
Hence, the solution is x ≥ 343
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Last month the price of one pound of carrot was $2 1/5 and joe sold 12 1/12
Answer:[tex]26\frac{7}{12}[/tex]
Step-by-step explanation:
2 1/5 * 12 1/2 = 319/12
319/12 = [tex]26\frac{7}{12}[/tex]
Convert 5 feet into inches.
*Note: you must use these exact conversion factors to
get this question right.
Answer:
60 inches.
Step-by-step explanation:
There are 12 inches in one foot:
12 x 5 = 60
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 5 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer:
60 inches
Step-by-step explanation:
(5 feet) = [tex]\frac{12inches}{1foot}[/tex] The word feet can cancel and you are left with
(5)(12 inches) = 60 inches.
DUE SOON! PLEASE SHOW WORK! JUST DONT KNOW WHERE TO START! BEEN STUCK ON THIS FOREVER ITS DUE SOON!!
Answer:
(0,-7)
Step-by-step explanation:
Plug in the X and Y's from the answer choices to get your answer. If the left of the equation (Y) is less than the right side (-1/2x - 6) it is correct!
Hope this helps!
Having difficulty with this
For the function y = 4x⁵, the value of d⁴y/dx⁴ = 320x.
What is a expression? What is a mathematical equation? What is Equation Modelling? What is differentiation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. We can write -
y = f(x)
y' = dy/dx = (d/dx)[f(x)]
We have the following function -
y = 4x⁵
The given function is -
y = 4x⁵
dy/dx = 20x⁴ {y = xⁿ, then y' = nxⁿ ⁻ ¹}
d²y/dx² = 80x³
d³y/dx³ = 160x²
d⁴y/dx⁴ = 320x
Therefore, for the function y = 4x⁵, the value of d⁴y/dx⁴ = 320x.
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If a boy grows 5 inches, he will be one half as tall as his sister , his sister is 68 inches tall. How tall is the boy?
29.7 divided by 12 i need a anwser
Answer:
2.475
Step-by-step explanation:
Answer:
2.475
Step-by-step explanation:
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