The volume, V, in hundreds of shares, of a company's stock, after being listed on the stock
exchange for t weeks, can be modelled by the relation V = 250t -5t² . Use the discriminant to
determine if the volume will ever reach
a) 275 000 shares in a week; V = 2750
b) 400 000 shares in a week
Answers
(a)the volume will reach 275000 shares in a week at two different times.
(b)the volume will reach 400,000 shares in a week at two different times.
(a) 275,000 shares in a week (V=2750), solve the equation:
what are discriminant?the part of the quadratic formula underneath the square root symbol.
\(250t - 5t^2 = 2750\\5t^2 - 250t + 2750 = 0\)
by quadratic formula,
t = [250 ± (\(\sqrt{250^2 - 4(5)(2750))}\)]/(2(5))
t = [250 ± \(\sqrt{187500}\)]/10
t = [250 ± \(50\sqrt{3}\)]/10
\(t = 25 ± 5\sqrt{3}\)
Since both solutions are real, the volume will reach 275000 shares in a week at two different times.
(b) 400,000 shares in a week, solve the equation:
\(250t - 5t^2 = 4000\\5t^2 - 250t + 4000 = 0\)
by discriminant formula, we have:
\(b^2 - 4ac = (-250)^2 - 4(5)(4000) = 2500\)
the discriminant is positive but not equal to zero, the quadratic equation has two real roots. Therefore, the volume will reach 400,000 shares in a week at two different times.
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Related Questions
the sum of four number is 20500.three of the numbers are 2341.578 and 10690.What is the fourth number?
Answers
Answer:
5216.844
Step-by-step explanation:
Let x be the fourth number.
We know that the sum of the four numbers is 20500:
2341.578 + 10690 + x + 2341.578 = 20500
Simplifying and solving for x:
x = 20500 - 2341.578 - 10690 - 2341.578
x = 5216.844
Select the statement that is not true.
A. The translation of a line is a pair
of parallel lines.
B. The rotation of a pair of parallel lines is a pair of parallel lines.
C. The reflection of a line is a line.
D. The rotation of a line is a line.
Answers
Answer: B. The rotation of a pair of parallel lines is a pair of parallel lines.
Explanation: A translation of a line is a displacement of the line, or a transformation which moves all points of the line, without changing its shape or orientation. This means that a pair of parallel lines will remain parallel after a translation.
A rotation of a line is a transformation in which all points of the line are rotated around a pivot point, and the line will change its orientation.
A reflection of a line is a transformation in which all points of the line are reflected across a single axis. This means that a line will remain a line after a reflection.
Therefore, the statement that is not true is B. The rotation of a pair of parallel lines is a pair of parallel lines.
Can someone help me find the answer?
Answers
Answer: B. This function has no intercept. I think B is the correct answer.
What would you dream about tonight?
Answers
Answer:
I don't have dreams.
Step-by-step explanation:
I left those in my childhood
Flying with the wind, a plane flew 1,200 mi in 4 h. Against the wind, the plane required 6 h to fly the same distance. Find the rate of the plane in calm air and the rate of the wind.
Answers
Answer:
Rate of plane = 250 mph
Rate of wind = 50 mph
Step-by-step explanation:
Let the speed of the plane in calm air be x mph& speed of the wind be y mphSpeed of plane with wind = (x + y) mphSpeed of plane against wind = (x - y) mphFormula relating speed, time and distance is given as: speed*time = distanceAccording to the first condition: (x+y)*4 = 1200-> x + y = 300 (1)According to the second condition: (x-y)*6= 1200-> x - y = 200 (2)Adding equations (1) & (2), we find:2x = 500-> x = 250 (Dividing 500 by 2)-> y = 50 (Plugging x = 250 in eq 1)Rate of plane = 250 mphRate of wind = 50 mphPls, HELP!!
Law of Cosines
Solve for c. Round your final answer to the nearest tenth
Answers
The length of c in the triangle is 4.2 units.
How to find the side of a triangle?The side of a triangle can be found using cosine law as follows:
Hence,
c² = a² + b² - 2ab cos C
where
a, b and c are the side lengthC is angle opposite to side cTherefore,
c² = 7² + 8² - 2(7)(8) cos 32°
c² = 49 + 64 - 112 cos 32°
c² = 113 - 112(0.84804809615)
c² = 113 - 94.9813867695
c² = 18.019
square root both sides of the equation
c = √18.019
c = 4.24487926801
c = 4.2 units
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Quotient of a number x and 45?
Answers
is equal to x45
If the following data were transformed and points with the coordinates
(x, log(y)) were plotted, what points would be plotted? Round log(y) to three
decimal places.
X
1
2
3
y
12
83
580
Answers
If the data were transformed and points with the coordinates
(x, log(y)) were plotted then the points (1, 1.079), (2, 1.919), (3, 2.763) were plotted.
To plot the points with the coordinates (x, log(y)), we need to take the logarithm of the y-values.
Let's calculate the logarithms for the given data:
x y log(y)
1 12 log(12) = 1.079
2 83 log(83) = 1.919
3 580 log(580) = 2.763
Therefore, the points that would be plotted are (1, 1.079), (2, 1.919), (3, 2.763)
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7. Jonathan rolled a 5,1, and 3 on a number cube. He made the greatest number possible. He estimated his number to the nearest 100. What is his number?
Answers
Answer:
500
Step-by-step explanation:
Greatest possible number with digits 5,1,3 is 531.
round to hundred =500
The length of a rectangle is 6 meters shorter than 4 times its width. The area of the rectangle is 238 square meters. How long and wide is the rectangle?
Answers
The width and length of the rectangle given its area is 8.5 meters and 28 meters respectively.
Area of rectangleLength of the rectangle = (4w - 6) metersWidth of the rectangle = wArea of rectangle = 238 square metersArea of a rectangle = Length × width
Substitute the parameters238 = (4w - 6) × w
238 = 4w² - 6w
Change to quadratic equation4w² - 6w - 238 = 0
Using quadratic formulaa = 4
b = -6
c = -238
w = -b ± √b² - 4ac / 2a
= -(-6) ± √(-6)² - 4(4)(-238) / 2(4)
= 6 ± √36 - (-3808) / 8
= 6 ± √36 + 3808 / 8
= 6 ± √3844 / 8
= 6 ± 62 / 8
= 68/8 or -56/8
w = 8.5 or -7
The value of w can not be negativeSo,
w = 8.5 meters
Recall,
Length of the rectangle = (4w - 6) meters
= 4(8.5) - 6
= 34 - 6
= 28 meters
Therefore, the width and length of the rectangle given its area is 8.5 meters and 28 meters respectively.
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A bucket can hold 26 litres of water when it is 8/9 full. How many litres can it hold when it is full?
Answers
Answer:
\(29.25\text{ liters}\)Explanation:
Here, we want to know the amount of water the bucket can hold when full
Let us have the volume as x liters
Mathematically:
\(\begin{gathered} \frac{8}{9}\times x\text{ = 26} \\ \\ 8x\text{ = 9 }\times\text{ 26} \\ x=\text{ }\frac{9\times26}{8} \\ \\ x\text{ = 29.25 liters} \end{gathered}\)Identify the correct graph of the system of equations.
3x + y = 12
x + 4y = 4
Answers
Let's solve the system of equations:
1. 3x + y = 12
2. x + 4y = 4
We can solve this system of equations using various methods such as substitution or elimination. Let's use the elimination method here:
Multiply equation 1 by 4 and equation 2 by 1 to eliminate the y term:
1. 12x + 4y = 48
2. x + 4y = 4
Now, subtract equation 2 from equation 1:
12x + 4y - (x + 4y) = 48 - 4
Simplifying:
11x = 44
Divide both sides by 11:
x = 4
Substitute the value of x into equation 2 to solve for y:
4 + 4y = 4
4y = 4 - 4
4y = 0
y = 0
Therefore, the solution to the system of equations is x = 4 and y = 0.
The correct graph of this system of equations would be two lines intersecting at the point (4, 0) on the coordinate plane.
In the data set below, what is the interquartile range?
26 42 52 61 75 85 93 96
Answers
Answer:
the iqr is 42
Step-by-step explanation:
Can anyone help? Will give Brainly and 45 pts <3
Answers
9514 1404 393
Answer:
2.1 tons
Step-by-step explanation:
Use the given values in the formula and do the arithmetic. The area will be the product of the contact patch dimensions:
A = (7 in)(5 in) = 35 in²
So, the weight is ...
W = (35 in²)(30 #/in²)(4)/(2000 #/ton) = (4200 #)/(2000 #/ton)
W = 2.1 tons
The car weighs about 2.1 tons.
Solving this involves substitution of values into the given formula and applying basic arithmetic.
Weight of Car is 2.1 tons
We are told that the dimensions of the rectangle are 7in and 5in.
Formula for area of a rectangle is;
A = Length x breadth
Thus;
A = 7 × 5
A = 35 in²
We are also given;
Air pressure; P = 30 psi
A car has 4 tires and so;
Number of tire; N = 4
We are told that formula for weight of the car in ton is;
W = APN/2000
Plugging in the relevant values;
W = (35 × 30 × 4)/2000
W = 2.1 tons
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Jasmine wants to use her savings of $1,128 to buy video games and movies. The total price of the movies she bought was $72. The video games cost $43 each. Choose the inequality that would be used to solve for the maximum number of video games Jasmine can buy with her savings. 43 + 72x ≤ 1,128 43 + 72x ≥ 1,128 43x + 72 ≥ 1,128 43x + 72 ≤ 1,128
Answers
Answer:
The answer is 24. First 1128 - 72 equals 1056 then divide by 43 which equals 24.55 but u cant buy 24.55 VD so its just 24
Step-by-step explanation:
I need some help with this problem
Answers
Answer:(-(3x^(3)-x-1))/((x^(2)+1)^(2))
Can a volume of box is 288 and it's measurements are 12x8x3
Answers
yes that is the answer
12 times 8 is 96
96 times 3 is 288
50 PONTS
Complete the following statements:
< A corresponds to <
< B corresponds to <
< C corresponds to <
Side CA corresponds to side?
Side BC corresponds to side?
Side AB corresponds to side?
Answers
Answer:
Step-by-step explanation:
1. j
2. k
3. L
4. Lj
5. kL
6. jk
When would we need to calculate circumference of a circle? Area of a circle?
Answers
There is 1/3 of a pan of cornbread left. Four children are going to share it equally. What fraction of the whole pan of cornbread will each child get?
Answers
The fraction of the whole pan of cornbread each child will get is 1/12.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, 1/3 of a pan of cornbread shared among 4 children.
Here, cornbread share of each child = Total quantity of bread/Number of children
= 1/3 ÷ 4
= 1/3 × 1/4
= 1/12
Therefore, the fraction of the whole pan of cornbread each child will get is 1/12.
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Question
Find the equation of the line shown.
-4-3
9 10
3
2
O-
27
-5
1 2 3 4
Answers
The equation of the line for the given points is y= (1/2)x - 3.
An equation of a line can be written in slope-intercept form, which is:
y = mx + b
where:
y and x are the coordinates of any point on the line.
m is the slope of the line (the rate at which y changes with respect to x).
b is the y-intercept of the line (the y-coordinate of the point where the line intersects the y-axis).
The slope of the line is calculated as,
m = ( y₂ -y₁) / (x₂ - x₁)
m = ( -2+1) / (2-4)
m = 1/2
The y-intercept is calculated as,
y = mx + c
-1 = (1/2)x 4 + c
c = -3
The equation of the line will be,
y = mx + c
y = (1/2)x - 3
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factor
3 What are the factors in the expression 4(5 + x)?
2
Answers
Answer:
4 , 5 + x , 5 + x
Step-by-step explanation:
The given equation is ,
\( 4(5+x)^2 \)
It will be factorised into ,
\( 4\times (5+x)\times (5+x) \)
Therefore , the factors are ,
4 5 + x5 + xRodrick is visiting the local museum exhibit and has a maximum of $30 dollars to spend. The entry ticket cost $7. He can spend g dollars. Write an inequality that can find g and the amount of money Rodrick can spend at the gift shop.
Answers
Entry ticket = $7
Gift shop money = $g
Maximum to spend = $30
Inequality => 7+g ≤ 30
Hope it helps!
A student was asked to give the exact solution to the equation
22x+4-9(2) = 0
The student's attempt is shown below:
22x+49(2)=0
22x+24-9(2) = 0
Let 2* = y
y²-9y+8=0
(y-8)(y-1)=0
y = 8 or y=1
So x = 3 or x = 0
(a) Identify the two errors made by the student.
(b) Find the exact solution to the equation.
Answers
(a) The errors made by the student are:
Incorrectly expanding 49(2) as 24 instead of 98.
Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of
\(y^{2} - 9y + 8.\)
(b) The exact solution to the equation is x = 7/11.
(a) The student made two errors in their solution:
Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.
Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)
(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:
Starting with the original equation: \(22x + 4 - 9(2) = 0\)
Simplifying: 22x + 4 - 18 = 0
Combining like terms: 22x - 14 = 0
Adding 14 to both sides: 22x = 14
Dividing both sides by 22: x = 14/22
Simplifying the fraction: x = 7/11
Therefore, the exact solution to the equation is x = 7/11.
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Lauren's mother gave Lauren $15.00 to buy some things at the store. Lauren has spent $12.79 and still needs to stop at the fruit stand to buy some grapes that are on sale for $0.89 per pound. Lauren uses the following inequality to determine how many pounds of grapes to buy. 0.89g + 12.79 < 15.00 Which could be the number of pounds of grapes that Lauren can purchase? Select all that apply,
2.45
2.5
2.49
2.4
2.39
Answers
The number of pounds of grapes that can be purchased are 2.45, 2.4, 2.39.
The total amount Lauren's mother can spend has to be less than $15. This is why the inequality sign used is the less than sign - <.
Given this equation: 0.89g + 12.79 < 15.00 , in order to determine the pounds of grapes that can be used, take the following steps:
Combine similar terms
0.89g < 15 - 12.79
Add similar terms
0.89g < 2.21
Divide both sides of the equation by 0.89
g < 2.48g
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The weights X of an animal are distributed according to the
probability distribution shown.
What is the probability that the animal's weight will be less than
151 pounds?
O 0.25
O 0.50
O 0.60
O 0.75
Answers
The probability that the animal's weight will be less than 151 pounds is 0.50.
The correct option is B.
What is the probability that the animal's weight will be less than 151 pounds?Since the given probability distribution ranges from 148 to 152, and we need to find the probability that the animal's weight will be less than 151 pounds, we can add the probabilities corresponding to the weights less than 151.
From the distribution, we see that the probability of the animal's weight being less than 151 pounds is 0.2 + 0.3 = 0.5.
Therefore, the answer is O 0.50.
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bought for 15$ sold for 49.50, what is markup percentage?
Answers
Answer:
17.65%
Step-by-step explanation:
https://www.calculatorsoup.com/calculators/financial/markup-calculator.php?cost=49.50&margin=15&action=solve
help
Graph g(x)=4cosx .
Use 3.14 for π .
Answers
5 because the value of pi is 3.14 and therfore the graph must be a rational and a multiple of 3
A value of a variable for which a rational expression is __________ is an excluded valueA. undefinedB. definedC. true D. falseE. simplified
Answers
A rational expression is a quotient of two polynomials.
The value of the variable that makes the denominator equal to 0 makes the rational expression undefined.
Since division by 0 is not allowed [undefined].
So, we exclude the value that makes the rational expression undefined.
Thus, the answer would be:
A value of a variable for which a rational expression is undefined is an excluded value.
Correct Answer
A????????????????????????????
Answers
Answer:
up
Step-by-step explanation:
y = 5ˣ + 4 means every y-value is 4 spaces higher than in y = 5ˣ. So the entire graph moves 4 spaces up.
Hope this helps!