The possible values of [tex]$m$[/tex] are all real numbers greater than [tex]$\frac{2}{x^2}$[/tex]
A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. It is called a quadratic equation because the highest degree of its unknown variable (x) is two. The solutions of a quadratic equation can be found by solving the equation using the quadratic formula, factoring, or graphing. Quadratic equations are used in many areas of mathematics, from basic algebra to differential equations.
Let [tex]$y = 2x^2mx8$[/tex]
The two distinct real roots of the equation imply that y is a quadratic equation with two distinct real roots.
So,[tex]$y = 0 = 2x^2mx8 \implies 2x^2mx - 8 = 0$[/tex]
Using the quadratic formula , [tex]$m = \frac{8}{2x^2x}$[/tex]
The two distinct real roots of the equation imply that the discriminant of the quadratic equation, [tex]$\Delta = b^2-4ac$[/tex] is greater than 0.
So, [tex]$\Delta = (2x^2)^2-4(2)(-8) > 0 \implies 4x^4 + 64 > 0$[/tex]
[tex]$4x^4 > -64 \implies x^4 > -16$[/tex]
So, [tex]$m > \frac{8}{2x^2x} \implies m > \frac{8}{2x^2(-4)} = \frac{2}{x^2}$[/tex]
Hence, the possible values of m are all real numbers greater than [tex]$\frac{2}{x^2}$[/tex]
Learn more about quadratic equation here:
https://brainly.com/question/17177510
#SPJ4
We want to estimate the mean number of pages per book in the fiction section of the large school library at a 99% confidence level. A sample of 35 fiction books is randomly selected and the mean number of pages is calculated to be 291.8 pages per book with a standard deviation of 47.6 pages per book.
To estimate the mean number of pages per book in the fiction section of the large school library, we can use a t-test. A t-test is a statistical method for determining the probability that a given sample of data comes from a population with a certain mean value.
Given that the sample size is 35 and the standard deviation is 47.6 pages per book, we can use the t-distribution table to find the t-value for a 99% confidence level.
The t-value for a 99% confidence level and 34 degrees of freedom (sample size - 1) is 2.021.
With this information, we can construct a confidence interval for the mean number of pages per book in the fiction section of the large school library. The confidence interval is given by:
Sample mean ± t-value * (Standard deviation / √Sample size)
Therefore, the confidence interval for the mean number of pages per book in the fiction section of the large school library is:
291.8 ± 2.021 * (47.6 / √35)
The margin of error is approximately 12.2 pages per book.
So the mean number of pages per book in the fiction section of the large school library is between 279.6 and 304 pages per book with a 99% confidence level.
wo hot air balloons, one purple and one gold, took off at the same time. the purple balloon started from sea level and the gold balloon started from a hill 15 meters above sea level.the gold balloon began climbing at a constant rate of 2 meters per second. the purple balloon began climbing at 2.5 meters per second. after how many seconds were the balloons at the same altitude?
The balloons reached the same altitude after 30 seconds.
What is unitary method?
The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
Let's say you go to the store to buy six apples.
You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.
Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.
We are aware of the quantity of apples and the amount of money in the aforesaid problem.
According to our question-
Purple balloon altitude = 2.5 t+0 m = 2.5 t
Starting at a height of 15 meters above sea level, the gold balloon rose 2 meters every second.
Altitude of the gold balloon: 2 t + 15 m
Hence , The balloons reached the same altitude after 30 seconds.
learn more about unitary method click here:
https://brainly.com/question/24587372
#SPJ4
The change in altitude over time for several hot air balloons is shown. Find the rate of change in feet per minute for each balloon.
The rate of change in feet per minute for each of the balloons, can be found to be :
Midnight Express ⇒ - 20 ft per minute Neon Lights ⇒ 16 ft per minute Star Wonder ⇒ - 25 ft per minute How to find the rate of change in feet per minute?The rate of change in feet per minute is dependent on the change in altitude given and the change in time in minutes.
For Midnight Express balloon, the change in feet per minute would be:
= Change in altitude / Change in time
= - 2, 700 / 135
= - 20 ft per minute
For Neon Lights balloon, the change in feet per minute is:
= 480 / 30
= 16 ft per minute
For Star Wonder, the change in feet per minute is:
= - 1, 500 / 60
= - 25 ft per minute
Find out more on change in altitude at https://brainly.com/question/23030543
#SPJ1
What is a non zero solution?
Answer: Non zero solution : A solution of a set of homogeneous linear equations in which at least one of the variables has a value different from zero.
Step-by-step explanation:
Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Question 10
[tex]\frac{\sin x}{7}=\frac{\sin 85^{\circ}}{8}\\\\\sin x=\frac{7\sin 85^{\circ}}{8}\\\\x \approx 60.7^{\circ}, 119.3^{\circ}[/tex]
However, the second case does not satisfy the angle sum of a triangle, so [tex]x \approx 60.7^{\circ}[/tex].
Question 12
[tex]\frac{\sin x}{19}=\frac{\sin 34^{\circ}}{12}\\\\\sin x=\frac{19\sin 34^{\circ}}{12}\\ \\ x \approx 62.3^{\circ}, 117.7^{\circ}[/tex]
Both of these cases satisfy the angle sum of a triangle.
A survey of 100100100 randomly selected homes from a large city with over 30{,}00030,00030, comma, 000 homes showed that 939393 of the sampled homes had a television. Lana wants to use this data to create a one-sample zzz interval to estimate the proportion of all homes in the city that have a television
The 95% confidence interval for the population proportion is (0.88, 0.98).
What is confidence interval?A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally employed. The confidence interval is the range of values within which you expect your estimate to fall a given proportion of the time if you repeat your experiment or re-sample the population in the same manner.
Here,
We have to calculate a 95% confidence interval for the proportion.
The sample proportion is p=0.93.
The standard error of the proportion is:
σ=√(p(1-p)/n)
=√((0.93*7)/100)
=0.0255
The critical z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
=1.96*0.0255
=0.05
Then, the lower and upper bounds of the confidence interval are:
LL=0.93-0.05
=0.88
UL=0.93+0.05
=0.98
The population proportion's 95% confidence interval is (0.88, 0.98).
To know more about confidence interval,
https://brainly.com/question/16395613
#SPJ4
What are the 8 types of operating system?
The types of operating system are:-
1. Batch Operating System.
2. Real-Time Operating System.
3. Time-Sharing Operating System.
4. Distributed Operating System.
5. Embedded Operating System.
6. Network Operating System.
7. Mobile Operating System.
What is an operating system?
An operating system can be thought of as a hardware and user interface. It is in charge of several different activities, including resource allocation, CPU management, file management, and the execution of all programmes. An operating system's function is to offer a setting in which a user can run programmes conveniently and effectively.
For more information on operating system:-
https://brainly.com/question/22811693
#SPJ4
a satellite can momve in a circular orbit about a massive planet radius R which of the following can represent the gravitational potential energy U of this satellite as a function of the radius r of the orbit
The following can represent the gravitational potential energy U of this satellite as a function of the orbital radius r: A satellite can move in a circular orbit around a large planet with radius R.
Now that we know the alternatives for planet orbits, let's investigate why elliptical orbits are the most common.
1) The Solar system has been around for 4.6 billion years. Any planets with hyperbolic or parabolic orbits would have long since vanished.
2) To have a circular orbit, the eccentricity must be precisely zero. It's difficult.
3) An elliptical orbit's eccentricity can range from 0 to 1. Easy, that.
Here, GM/r = [tex]V_{1} ^{2}[/tex] & GM/4r = [tex]V_{2} ^{2}[/tex]
or, [tex]V_{1} ^{2}[/tex] = 4 * [tex]V_{2} ^{2}[/tex]
or, [tex]V_{1}[/tex]= 4* [tex]V_{2} ^{}[/tex]
Learn more about gravitational Visit : brainly.com/question/27943482
#SPJ4
I NEED ANSWERS ASAP! PLEASE ANSWER
Answer:
y = 2/3x + 4
Step-by-step explanation:
It intersects at (0, 4)
Which graph represents the function f(x) = 8 1/3x?
The second graph represents the function [tex]f(x)=8^{\frac{1}{3} x}[/tex]
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The given function is
[tex]f(x)=8^{\frac{1}{3} x}[/tex]
At x=0, f(0)=1
At x=1, f(1)=2
At x=2, f(2)=4
The graph of f(x) passing through the points (0,1), (1,2), (2,4),(3,8).
According to these coordinates we can say that the graph of f(x) is represented by option 2.
Therefore correct option is 2.
Hence, the second graph represents the function [tex]f(x)=8^{\frac{1}{3} x}[/tex]
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ1
a garden is in the shape of a square with a perimeter of 32 feet. the garden is surrounded by two fences. one fence is around the perimeter of the garden, whereas the second fence is 3 feet from the first fence on the outside. if the material used to build the two fences is $ 1.48 per foot, what was the total cost of the fences? it costs $ to build the fences.
On solving the provided question we can say that by equation of the cost, 96 x 1.46 = $140.16 = total fencing cost
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
one fence is around the perimeter of the garden,
36/4 = 9 by 9 for the inner fence
6 for the outer fence, 15 by 15
60 + 36 = 96 feet total fence
total fencing cost is 96 x 1.46 = $140.16
To know more about equation visit:
https://brainly.com/question/649785
#SPJ4
Given that z is a standard normal random variable, find z for each situation (to 2 decimals).
a. The area between -z and z is 0.2206 .
b. The area to the left of z is 0.9951 .
Answer:
Step-by-step explanation:
a. The area between -z and z is 0.2206, so we want to find the value of z such that P(-z < Z < z) = 0.2206.
The standard normal distribution is symmetric, so P(-z < Z < z) = 0.5 - P(Z < -z) = 0.5 - P(Z < -z) = 0.5 - 0.2206 = 0.2794
We can use a standard normal table to find the z-value such that P(Z < z) = 0.2794 which is z = 0.68.
b. The area to the left of z is 0.9951, so we want to find the value of z such that P(Z < z) = 0.9951.
We can use a standard normal table to find the z-value such that P(Z < z) = 0.9951 which is z = 2.33.
Question 12 (4 points)
A student solved the following equation using the following steps:
4(2 - 3x) = x - 2(2x + 1)
8 - 3x = x - 4x - 2
8 - 3x = -3x - 2
x = 0
Based on the student's work, the equation was solved .
The equation solved correctly would show that it has solution(s).
What is halfway between 8 and 8.3?
Answer:
8.15
Step-by-step explanation:
halfway means the middle value. Therefore the mean.
(8 + 8.3)/2
= 8.15
Can the three sides of length 6cm 5cm and 3cm form a triangle give reason for your answer?
yes
the two shortest lengths are longer than the longest lenght
when added
5+3=8
8>6
Without random selection, we cannot appropriately apply the laws of probability to perform inference. T/F
The statement without random selection, we cannot appropriately apply the laws of probability to perform inference is true.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
We have to check the given statement without random selection, we cannot appropriately apply the laws of probability to perform inference is true or false.
Random selection is needed to eliminate bias and gives each individual the same probability of being selected.
Hence, the statement without random selection, we cannot appropriately apply the laws of probability to perform inference is true.
To know more about probability, click on the link
https://brainly.com/question/24756209
#SPJ4
Factoriser -
D = (2x + 3)² + (x-2)(2x + 3)
Answer:
Step-by-step explanation:
Answer:
D = (2x + 3)² + (x-2)(2x + 3)
Factoring D, we get:
D = (2x + 3)² + (x-2)(2x + 3)
= (2x + 3)(2x + 3 + x-2)
= (2x + 3)(3x - 2)
a sumbmarine dives 300 feet every 2 minutes, and 6/750 feet every 45 minutes. find the constant rate at which the sumbmarine dives. give our answer in feet per minute and in feet per hour.
the constant rate at which the submarine dives is 30 feet per minute and 1,800 feet per hour.
feet per minute: 30 feet per minute
feet per hour: 1,800 feet per hour
We can calculate the rate of descent of the submarine by dividing the total distance it dives each time by the total time it took to dive.
For the first scenario where it dives 300 feet every 2 minutes, the rate of descent is 300/2 = 150 feet per minute.
For the second scenario, it dives 6/750 feet every 45 minutes so the rate of descent is 6/750 * 60/45 = 30 feet per minute.
Therefore, the constant rate at which the submarine dives is 30 feet per minute and 1,800 feet per hour.
Learn more about rate here
https://brainly.com/question/13481529
#SPJ4
What are the top 10 Excel formulas?
The top 10 Excel formulas are SUM, AVERAGE, COUNT, MAX, MIN, IF, VLOOKUP, CONCATENATE, INDEX and MATCH which are used for performing calculations, counting, finding the maximum and minimum values, testing a condition and returning results, combining text, and searching for a specified item.
1. SUM: Adds the values in a specified range of cells.
2. AVERAGE: Calculates the average of all the cells in a specified range.
3. COUNT: Counts the number of cells in a specified range that contain numbers.
4. MAX: Finds the largest value in a specified range of cells.
5. MIN: Finds the smallest value in a specified range of cells.
6. IF: Tests a condition and provides a value based on the results of the test.
7. VLOOKUP: Searches for a value in the first column of a specified range and returns a value from the same row from another column.
8. CONCATENATE: Combines text from two or more cells into one cell.
9. INDEX: Returns a value from a specified range of cells.
10. MATCH: Searches for a specified item in a specified range and returns its relative position.
Learn more about average here
https://brainly.com/question/24057012
#SPJ4
LN=5x+6 and MP=7x-6
5x+6=7x-6
X=6
LN=?
MP=?
The population of a city decreases by 4.9% per year. If this year's population is 393,000, what will next year's population be, to the nearest individual?
Answer:
Step-by-step explanation:
393,000 x 0.049
= 19257
393,000 - 19,257
=373743
what is the answer??
Answer:
At the beginning, the box has 12 ounces of cereal.
Sue eats 1/6 of the box which is 12*(1/6) = 2 ounces.
Glen eats 2/3 of the box which is 12*(2/3) = 8 ounces.
So, the total ounces that they have eaten is 2+8 = 10 ounces.
Therefore, 12-10 = 2 ounces are left in the box.
Lines Cut by a Transversal (1st Correct Answer Will be Given BRAINLIEST)
Consider parallel lines cut by a transversal.
Parallel lines q and s are cut by transversal r. On line q where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 1, angle 2, angle 4, angle 3. On lines where it intersects line r, 4 angles are created—labeled clockwise, from uppercase left: angle 5, angle 6, angle 8, angle 7.
Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.
With the description of the parallel lines and the transversal line, the alternate exterior angles are angle 1 and angle 8 and they are equal
How to show that alternate exterior angle are equalAccording to the description
angle 1 + angle 2 = 180 degrees (angles of a straight line)
angle 4 + angle 2 = 180 degrees (angles of a straight line)
subtracting will result to
angle 1 - angle 4 = 0
angle 1 = angle 4
the vertical angle theorem
because the line is parallel
angle 1 = angle 5 (corresponding angles)
angle 4 = angle 8 (corresponding angles)
Since angle 1 = angle 4 = angle 8 then applying transitive property
angle 1 = angle 8
This completes the prove that alternate exterior angles are equal.
Another pair of alternate exterior angles are angle 2 and angle 7
Learn more about alternate exterior angles at:
https://brainly.com/question/2398628
#SPJ1
Please help with number 8
The number of Canadians who are at least 100 years old in 2001 is 3793.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Percentage of Canadians who live in British Columbia are at least 100 years old = 14%
The number of Canadians who live in British Columbia who are at least 100 years old in the 2001 census = 531
This means,
14% = 531
Now,
The number of Canadians who are at least 100 years old.
14% = 531
Multiply 100/14 on both sides.
100% = 100/14 x 531
100% = 3792.8
100% = 3793
Thus,
The number of Canadians who are at least 100 years old is 3793.
Learn more about percentages here:
https://brainly.com/question/11403063
#SPJ1
Geometry!!! help!
Triangle DAC is isosceles with congruent sides AD and AC. Which additional given information is sufficient for showing that triangle DBC is isosceles?
Select ALL that apply
1.Line AB is an angle bisector of DAC
2.Angle BAD is congruent to angle ABC
3. Angle BDC is congruent to angle BCD
4.Angle ABD is congruent to angle ABC
5.Triangle DAB is congruent to triangle CAB
1. Line AB is an angle bisector of DAC.
4. Angle ABD is congruent to angle ABC
5. Triangle DAB is congruent to triangle CAB
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
Given, Triangle DAC is isosceles with congruent sides AD and AC.
The statements that are sufficient to for proving triangle DBC is isosceles
are, Line AB is an angle bisector of DAC.
Angle ABD is congruent to angle ABC as the opposite sides are equal.
Triangle DAB is congruent to triangle CAB as they share a common side AB and sides AD and AC are equal in length.
learn more about congruency here :
https://brainly.com/question/7888063
#SPJ1
Hey can you help me with this please it’s hard
The events that correspond to each case are given as follows:
a) Exactly one odd number: OEE, EOE, EEO.
b) More odd numbers than even numbers: OOO, OOE, OEO, EOO.
c) Two or more odd numbers: OOO, OOE, OEO, EOO.
Hence the probabilities of each event are given as follows:
a) Exactly one odd number: 3/8.
b) More odd numbers than even numbers: 1/2.
c) Two or more odd numbers: 1/2.
How to calculate the probabilities?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
For this problem, we have three trials, each with two possible outcomes, hence the total number of outcomes is given as follows:
2³ = 8.
The meaning of the letters is given as follows:
O: odd number.E: even number.Hence, for example, the event OEE means that an odd number was taken, then an even number and then another even number.
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
having trouble understanding; A store hands out 600 reward cards. Customers scan their cards in the store to find out what reward they receive. The probability that a customer receives a $25 gift card is 1/15. How many customers receive a $25 gift card?
A circle centered at $A$ with a radius of $1$ and a circle centered at $B$ with a radius of $4$ are externally tangent. A third circle is tangent to the first two and to one of their common external tangents as shown. What is the radius of the third circle
The radius of the third circle is found out to be as , 1cm.
The radius of 1st circle = 1
radius of second circle = 4
Let XYR be external tangent of the circle which is centered at C,.
Then if we will extend the line PQ to R ,
the result will be , XPR being similar to triangle YQR ,
Therefore,
RQ = x
and length of RP = x + 5
Therefore, x / x+ 5 = 1/4
=> 4x = x + 5
=> x = 1
So , the length of QR is found out to be as 1cm.
A tangent to a circle is known as a straight line which touches the circle exactly at one point . A circle can have infinite number of tangents.
To learn more about Circle
brainly.com/question/30182533
#SPJ4
in a certain town in north america. the time of sunrise for any day of the year can be found using the equation where is the time in hours after midnight and is the number of the day in the year. to the nearest minute, when did the sun rise on december 25th, the 359th day of the year?
Given the equation t = -0.0069d + 7.35, where t is the time of sunrise in hours after midnight and d is the number of the day in the year, To find the time of sunrise on December 25th, the 359th day of the year, we need to substitute 359 for d in the equation.
t = -0.0069(359) + 7.35
t = -2.4471 + 7.35
t = 4.9029
This means that the time of sunrise on December 25th is 4.9029 hours after midnight. To convert this to minutes, we can multiply 4.9029 by 60 (since there are 60 minutes in an hour).
4.9029 x 60 = 294.174
So the sun rose on December 25th at 294.174 minutes after midnight, which is equivalent to 4 hours and 54 minutes (294 minutes) after midnight. To the nearest minute, the sun rose on December 25th at 4:54 AM.
A palindromic number is a number which is the same written forwards and
backwards. For example 525 and 1881 are palindromic numbers.
India says that 33 is a palindrome when written as a decimal number and
also as a binary number.
(a) Show India is correct.
Eva says that 99 is also a palindrome when written as decimal number and
as a binary number.
(b) Show Eva is correct.
please help me and for india please show the binary number in binary
So on solving the provided question, we can say that 121 and 1221 are palindrome numbers
What is palindrome numbers.?A number that remains the same even after the digits are switched is known as a palindrome. With regard to the vertical axis, it is mirror symmetric. The word "palindrome" is derived from the word "palindrome," and it describes words whose spelling remains the same when the letters are switched. A palindromic number, also known as a numeric palindrome or numeric palindrome, is a number (such as 16461), in which the value is unaffected by the order of the digits. Therefore, the first palindromes are 0 and 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, which equals 121.
here the numbers are
33, 121, 1221, 23465
121 and 1221 are palindrome numbers
To know more about palindrome numbers visit:
https://brainly.com/question/13556227
#SPJ1
