True, there exists a function f such that f(x) > 0, f'(x) < 0, and f"(x) > 0 for all x.
An example of such a function is[tex]f(x) = e^(-x)[/tex], where e is the base of the natural logarithm (approximately 2.718).
Let's verify the given conditions:
f(x) > 0:
Since e^(ax) is always positive for any real value of x and any constant a, [tex]e^(-x)[/tex]is also always positive for any real value of x.
f'(x) < 0:
To find the first derivative, apply the chain rule: [tex]f'(x) = -e^(-x). As e^(-x)[/tex] is always positive, the derivative
[tex]f'(x) = -e^(-x)[/tex] is always negative for all x.
f"(x) > 0:
To find the second derivative, apply the chain rule again:
[tex]f"(x) = e^(-x). As e^(-x)[/tex]is always positive, the second derivative[tex]f"(x) = e^(-x)[/tex] is always positive for all x.
Thus, it is true that there exists a function f with the given conditions.
for such more question on function
https://brainly.com/question/11624077
#SPJ11
The function [tex]f(x) = e^(-x)[/tex] meets all the given conditions.
True. There exists a function f such that [tex]f(x) > 0, f'(x) < 0, and f"(x) > 0[/tex] for all x. One example of such a function is [tex]f(x) = e^(-x)[/tex].
True. There exists a function f(x) that satisfies the given conditions: f(x) > 0, f'(x) < 0, and f''(x) > 0 for all x.
Consider the function [tex]f(x) = e^(-x)[/tex]. This function has the following properties:
1. f(x) > 0 for all x because the exponential function is always positive.
2. [tex]f'(x) = -e^(-x)[/tex]which is always negative because e^(-x) is always positive, and the negative sign in front makes the derivative negative.
3. [tex]f''(x) = e^(-x)[/tex]which is always positive.
Thus, the function [tex]f(x) = e^(-x)[/tex]meets all the given conditions.
Learn more about function here:
https://brainly.com/question/31423868
#SPJ11
When the function f(x) is divided by 3x + 1, the quotient is 3x² − 4x − 1
and the remainder is -10. Find the function f(x) and write the result in
standard form.
The function f(x) is f(x) = 9x³ - 7x² - 13x - 11 written in standard form.
What is the polynomial equation?
A polynomial equation is an equation in which the variable is raised to a power, and the coefficients are constants. A polynomial equation can have one or more terms, and the degree of the polynomial is determined by the highest power of the variable in the equation.
When f(x) is divided by 3x + 1, the quotient is 3x² - 4x - 1 and the remainder is -10. We can use polynomial long division to write f(x) in the form:
f(x) = (3x² - 4x - 1)(3x + 1) - 10
Multiplying out the right side gives:
f(x) = 9x³ - 7x² - 13x - 11
Therefore, the function f(x) is f(x) = 9x³ - 7x² - 13x - 11 written in standard form.
To learn more about the polynomial equation visit:
https://brainly.com/question/1496352
#SPJ1
When you went to know the mass of a bowling ball what unit do you choose
Standard unit chose to measure the mass of a bowling ball is equal to kilogram .
The unit typically used to measure the mass of a bowling ball is the pound (lb) or the kilogram (kg).
It depends on the country as different countries have different standard unit for measuring mass.
In the United States, the weight of a bowling ball is often measured in pounds.
While in many other countries, the weight is measured in kilograms.
When measuring the mass of a bowling ball,
It is important to use a calibrated scale that is designed to handle the weight of the ball.
Some scales are specifically designed for weighing bowling balls.
And they may have a higher weight capacity than a typical bathroom scale.
It is also important to ensure that the scale is on a flat, stable surface to ensure an accurate measurement.
learn more about mass here
brainly.com/question/9497577
#SPJ4
if a garden box is 4x by 3x and the area of the box in square feet is equal to four times the perimeter in feet what is the value for x that satisfies these requirements
The answer to this question is x = 6
If you were to use the substitution method to solve the following
system, choose the new equation after the expression equivalent to x
from the second equation is substituted into the first equation.
3x + 2y = -21
x-3y = 4 (6 points)
Answer:
Step-by-step explanation:
Making x the subject in the second equation gives:
x = 4+3y
substituting x = 4 +3y into the first one gives:
3(4 + 3y) + 2y = -21
12 + 9y +2y = -21
11y = -33
y = -3
Can someone help me on these last 3 question it’s 3,5 and 6 I js need help on these
The required area of the given triangle is 63 ft² respectively.
What is a triangle?A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon.
There are three sides and three angles in every triangle, some of which may be the same.
A unique triangle and plane (i.e., a two-dimensional Euclidean space) are determined by any three non-collinear points in Euclidean geometry.
In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.
Area of a triangle:
1/2 * b * h
Now, insert values as follows:
1/2 * b * h
1/2 * 14 * 9
7 * 9
63 ft²
Therefore, the required area of the given triangle is 63 ft² respectively.
Know more about triangles here:
https://brainly.com/question/17335144
#SPJ1
can you give me a simple fast answer
The mapping that is a function will be B). X
How to explain the functionEvery function got a set of input values called " Domain " and a set of respective output values as " Range"
And function worked as Function( Input value ) = Output value
There are basic rules for function :
1. There always exist output value for every single input value.
2. Every input value should have one and only one output value
For W : Rule 2 is violated
Here, Input value 6 result to two output value 2 and 4
Learn more about functions on
https://brainly.com/question/14065888
#SPJ1
PLEASE HELP ME
I’LL GIVE YOU BRAINLIEST
The profit function of the company is given by P(x)=-4x^3 + 32x^2 - 64, where x is the number of toys sold in hundreds, and P(x) is the profit in thousands of dollars.
How to explain the graphThe key features of the graph of the profit function are the following:
The degree of the polynomial function is 3, which means that the graph is a cubic curve.
The coefficient of the leading term is negative (-4), which means that the graph opens downwards.
The coefficient of the quadratic term is positive (32), which means that the graph is concave up.
The y-intercept of the graph is -64, which means that the company will incur a loss of $64,000 if it does not sell any toys.
It should be noted that to find the maximum profit, we need to evaluate the profit function at x = 5.33:
P(5.33) = -4(5.33)^3 + 32(5.33)^2 - 64 = 23.78
Therefore, the maximum profit that the company can make is $23,780.
In summary, the graph of the profit function reveals that the company will incur a loss if it does not sell any toys, but it can make a profit if it sells at least some toys. The profit function has a cubic shape that opens downwards, indicating that the profit decreases as the number of toys sold increases beyond a certain point. The maximum profit occurs at x = 5.33, where the profit is $23,780.
Learn more about graph on;
https://brainly.com/question/19040584
#SPJ1
Suppose an earthquake can be felt up to 76 miles from its epicenter. You are located at a point 65 miles west and 40 miles south of the epicenter. Do you feel the earthquake?
The distance between your location and the epicenter is just slightly larger than the maximum distance that the earthquake can be felt (76 miles), so you would be able to feel the earthquake.
What is triangle?A triangle is a polygon with three sides and three angles. The sum of the angles in a triangle is always 180 degrees. There are different types of triangles such as equilateral, isosceles, scalene, right-angled, obtuse-angled, and acute-angled triangles. Triangles are used in geometry and other fields of mathematics to solve problems related to areas, angles, and side lengths.
Here,
Yes, you feel the earthquake.
To see why, imagine drawing a circle around the epicenter with a radius of 76 miles. This circle represents the maximum distance that the earthquake can be felt. Then, draw a line from the epicenter to your location. This line represents the distance between you and the epicenter.
To determine whether you feel the earthquake, we need to calculate the distance between your location and the epicenter using the Pythagorean theorem:
distance = √(65² + 40²)
distance ≈ 76.06 miles
To know more about triangle,
https://brainly.com/question/28600396
#SPJ1
3. A sporting goods store received an order of 64 baseball caps, of which 16 were green. If 1 (1 point)
of the 64 caps is selected at random, what is the probability it will not be green?
25%
75%
80%
50%
The answer is option (b) 75%.
What is Probability?
Probability is a measure of the likelihood that a particular event will occur. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be determined by dividing the number of ways the event can occur by the total number of possible outcomes.
The probability of selecting a non-green cap is the number of non-green caps divided by the total number of caps:
P(non-green) = 48/64 = 3/4 = 0.75
Therefore, the probability that a randomly selected cap will not be green is 0.75 or 75%.
So the answer is option (b) 75%.
to know more about probability
brainly.com/question/30034780
#SPJ1
What percent of U.S. vice presidents were at least 60 years old when they took office? Explain how you found your answer.
(Please help asap!!)
The percent of U.S. vice presidents were at least 60 years old when they took office is 26.5%
How to determine the percentage?It may interest you that US America has had about 49 vice presidents till date
Out of this 49 vice presidents,
13 of them were more than 60 years at the beginning of their office
This implies that 13/49 * 100 = 26.53%
In conclusion the percentage of US America vice presidents is 26.53%
for clarity, read the article below.
Americans over 60 hold many of the highest offices in the U.S. government. An analysis of the current 117th Congress revealed that it’s the oldest, on average, of any Congress in at least the past 20 years. The average age of U.S.
Presidents are also being elected at older ages than in the past; at 70, President Donald Trump was the oldest to take office, though his record was quickly surpassed by his successor, President Joe Biden, who took office at age 78.
As the average age of elected officials has risen, some have questioned whether we should restrict individuals over a certain age from holding office. In 2019, former President Jimmy Carter expressed concern over the age of the presidential candidates in the 2020 election, stating:
Learn more about list of US of America vice presidents above 60 years on https://brainly.com/question/31235410
#SPJ1
Directions: find the value of the hypotenuse for each of the following right triangles.
1. a = 5, b = 8
2. a = 6, b = 7
3. a = 4, b = 9
4. a = 3, b = 12
5. a = 11, b = 10
6. a = 8, b = 7
7. a = 9, b = 4
8. a = 7, b = 11
9. a = 13, b = 15
10. a = 5, b = 6
By Pythagoras Hypotenuse for 1. 9.43 , 2. 9.22 , 3. 9.85 , 4. 12.37, 5. 14.87 , 6. 10.63
7. 9.85 , 8. 13.04 , 9. 19.85 , 10. 7.81
Theorem of Pythagoras defined?The Pythagorean theorem, commonly referred to as Pythagoras' theorem, is a key relationship in Euclidean geometry between a right triangle's three sides. It declares that the hypotenuse's square, which is the side that is opposite the right angle, is equal to the sum of the squares of the other two sides. In other words, if the hypotenuse is length c and the legs of a right triangle are lengths a and b, then a² + b² = c².
The Pythagorean theorem, which asserts that the square of the hypotenuse is equal to the sum of the squares of the other two sides, can be used to determine the hypotenuse of a right triangle.
This theorem allows us to calculate the hypotenuse value for each of the right triangles presented as follows:
1. a = 5, b = 8
c = √(a² + b²) = √(5² + 8²) = √(25 + 64) =√(89) ≈ 9.43
2. a = 6, b = 7
c = √(a² + b²) = √(6² + 7²) = √(36 + 49) = √(85) ≈ 9.22
3. a = 4, b = 9
c = √(a² + b²) = √(4² + 9²) = √16 + 81) = √(97) ≈ 9.85
4. a = 3, b = 12
c =√(a² + b²) = √(3² + 12²) = √(9 + 144) = √(153) ≈ 12.37
5. a = 11, b = 10
c = sqrt(a^2 + b^2) = sqrt(11^2 + 10^2) = sqrt(121 + 100) = sqrt(221) ≈ 14.87
6. a = 8, b = 7
c = √(a² + b²)= √(8² + 7²) = √(64 + 49) = √(113) ≈ 10.63
7. a = 9, b = 4
c =√(a² + b²)=√(9² + 4²) = √(81 + 16) = √(97) ≈ 9.85
8. a = 7, b = 11
c = √(a² + b²)= √(7² + 11²) = √(49 + 121) ≈√(170) ≈ 13.04
9. a=13,b=15
c=√(a² + b²)=√((13²)+(15²))=√((169)+(225))=√(394))≈19.85
10.a=5,b=6
c=√(a²+b²)=sqrt((5²)+(6²))=s√((25)+(36))=√(61))≈7.81
To know more about Pythagoras visit:
brainly.com/question/10174253
#SPJ1
Based on this data, what is a reasonable estimate of the probability that Patsy sells fewer than 5 feathers next festival?
A reasonable estimate of the probability that Patsy sells fewer than 2 feathers at the next festival is about 0.2485.
How to estimate the probability of given data?
To estimate the probability that Patsy sells fewer than a certain number of feathers at the next festival, we need to use the given data to calculate the mean and standard deviation of the number of feathers she has sold in the past festivals.
The mean, denoted by μ, is calculated by adding up all the number of feathers sold and dividing by the total number of festivals. So,
μ = (3 + 6 + 1 + 4 + 2 + 3 + 7 + 2) / 8 = 3.375
The standard deviation, denoted by σ, is a measure of how spread out the data is. It is calculated by first finding the variance, which is the average of the squared differences between each data point and the mean, and then taking the square root of the variance. So,
Variance = ((3-3.375)² + (6-3.375)²+ (1-3.375)² + (4-3.375)² + (2-3.375)² + (3-3.375)² + (7-3.375)² + (2-3.375)²) / 8 = 4.0898
σ = √(4.0898) = 2.022
Now, to estimate the probability that Patsy sells fewer than a certain number of feathers at the next festival, we need to standardize the value by subtracting the mean and dividing by the standard deviation. So, let X be the number of feathers sold at the next festival, then,
Z = (X - μ) / σ
Let's say we want to estimate the probability that Patsy sells fewer than 2 feathers at the next festival. Then,
Z = (2 - 3.375) / 2.022 = -0.679
We can use a standard normal distribution table or calculator to find the probability that a standard normal random variable is less than -0.679, which is approximately 0.2485.
Therefore, a reasonable estimate of the probability that Patsy sells fewer than 2 feathers at the next festival is about 0.2485.
Learn more about estimate here,
https://brainly.com/question/29436481
#SPJ1
Correct question is "The number of feathers Patsy 3, 6, 1, 4, 2, 3, 7, 2 Peacock sold at each of the festivals this year. Based on this data, what is a reasonable estimate of the probability that Patsy sells fewer than feathers next festival? "
Please help me with these 4 questions
The total surface area of each figure are:
1) 2,557.3 yd²
2) 601.02 m₂
3) 3782.5 mm²
4)750 in²
How to find the total surface area?1) The total surface area of a cylinder is:
2πrh + 2πr².
where:
r is radius
h is height
Thus:
TSA = 2π(11 * 26) + 2π(11)²
TSA = 2π(286) + 2π(121)
TSA = 2π(407)
TSA = 2,557.3 yd²
2) The total surface area is:
2(¹/₂ * 9 * 11.12) + (16 * 15) + (16 * 12) + (9 * 16)
= 25.02 + 240 + 192 + 144
= 601.02 m₂
3) The total surface area of a cylinder is:
2πrh + 2πr².
where:
r is radius
h is height
Thus:
TSA = 2π(14 * 29) + 2π(14)²
TSA = 2π(406) + 2π(196)
TSA = 2π(602)
TSA = 3782.5 mm²
4) The total surface area of the pyramid is:
TSA = (15 * 8) + (21 * 17) + (21 * 15) + (8 * 21)
TSA = 120 + 147 + 315 + 168
TSA = 750 in²
Read more about Total Surface Area at: https://brainly.com/question/27812847
#SPJ1
a road perpendicular to a highway leads to a farmhouse located 1 1 mile away. an automobile traveling on the highway passes through this intersection at a speed of 45mph. 45 mph . how fast is the distance between the automobile and the farmhouse increasing when the automobile is 9 9 miles past the intersection of the highway and the road? the distance between the automobile and the farmhouse is increasing at a rate of miles per hour.
The distance traveling between them is increasing at a rate of miles per hour = 45 m/h.
The distance between the automobile and the farmhouse is increasing by 45 mph, since the automobile is traveling at this speed.
When the automobile is 9 miles past the intersection of the highway and the road, the distance between the automobile and the farmhouse is increasing at a rate of 45 mph, due to the automobile traveling at this speed.
When the automobile is 9 miles past the intersection of the highway and the road, the distance between the automobile and the farmhouse is increasing at a rate.
So,
The rate at which the distance between the automobile and the farmhouse is increasing when the automobile is 9 miles past the intersection is 45 mph.
For similar question on distance traveling:
brainly.com/question/509450
#SPJ11
In order to study the cause and effect relationship between two variables, a researcher must perform what type of study ?
A. correlational
B. descriptive
C. experimental
D. meta-analysis
of study?
Answer: C. experimental study.
Experimental studies are used to establish cause-and-effect relationships between variables by manipulating one variable (independent variable) and observing the effect on another variable (dependent variable) while controlling for other potential factors. Correlational studies examine the relationship between two variables but do not establish causality, descriptive studies describe a phenomenon without manipulating variables, and meta-analysis is a statistical method that combines the results of multiple studies to provide an overall summary.
Step-by-step explanation:
4 out of 7 questions. PLEASE help me.
A tangent line is line GJ.
A secant line is line HF.
A chord is line GF.
What is the chord of a circle?In Mathematics and Geometry, the chord of a circle can be defined as a line segment that typically join any two (2) points on a circle. This ultimately implies that, a chord simply refers to the section of the line that is used for connecting two (2) separate points on a circle such as line GF.
What is a secant line?In Mathematics and Geometry, a secant line can be defined as a type of line that intersects the edge of a circle twice i.e it goes through the interior of the circle twice and intersects its boundary twice such as line HF.
In conclusion, a tangent line is a type of line that lies outside of a circle and intersects the edge of a circle exactly once i.e it touches the outside of the circle only once such as line GJ.
Read more on chord here: https://brainly.com/question/27695913
#SPJ1
how do i write an inequality for this?
The inequality expression representing the area of the shaded region, indicating both the shaded area and the broken line is; y > 0
What is an inequality?An inequality is a mathematical statement consisting two expressions joined with inequality symbols, which includes; '<', '>', '≠', '≤', and '≥'.
The area of the shaded region is the part of the coordinate plane above the x-axis.
The region shaded can therefore be indicated by the area y > 0
The x-axis on the coordinate plane representing the boundary of the shaded region consists of broken line, which indicates that the line is not included in the shaded region.
The inequality representing the area of the shaded region is therefore;
y > 0
Learn more on writing inequalities here: https://brainly.com/question/21575354
#SPJ1
Make sure you click on the answer in the drop box that goes in the blank for each numbered blank.
BLANK #1 PLEASE ANSWER ALL THE BLANKS 100 points
1 - THEOREM, 2 - RIGHT, 3 - SUM, 4 - LEGS, 5 - SQUARE, 6 - A, 7 - B, 8 - C, 9 - HYPOTENUSE, 10 - 90-DEGREES
The full statement reads: The pythagoras theorem tells us how the side lengths of right triangles are related. In any right triangle the sum of the squares of the two legs should equal the square of the hypotenuse. The legs are called A and B and the hypotenuse is C. The hypotenuse is always the longest side of a right triangle and its across from the 90-degrees angle.
Some properties of right angled trianglesLet us assume the triangle is ABC, and the angle C is 90 degrees. let the length the side AB = c, the length of side AC = b, the length of side BC is a.
1. The sum of the two non 90 degree angles is equal to 90 degrees.
2. cos(B) = a/c , sin(B) = b/c
3. cos(A) = b/c, sin(A) = a/c
4 [tex]c^2 = a^2 + b^2[/tex]
5 the diameter of the circumcircle of this triangle is c.
6 tan(A) = a/b
To know more about pythagoras theorem, visit:
https://brainly.com/question/343682
#SPJ1
An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 1850 feet apart. As the airplane
passes over the line joining them, each observer takes a sighting of the angle of elevation to the plane,
as indicated in the figure. If A=25°, and B=25°, how high is the airplane?
Answer: We can use trigonometry to solve this problem. Let's call the height of the airplane H, and let's call the distance from observer X to the airplane D. Then the distance from observer Y to the airplane is L - D.
From the point of view of observer X, we can write:
tan(A) = H / D
tan(25°) = H / D
From the point of view of observer Y, we can write:
tan(B) = H / (L - D)
tan(25°) = H / (L - D)
We now have two equations with two unknowns (H and D). We can solve for one of the unknowns in terms of the other, and then substitute that expression into the other equation to eliminate one of the unknowns.
Let's solve the first equation for D:
D = H / tan(25°)
Substituting this expression for D into the second equation, we get:
tan(25°) = H / (L - H / tan(25°))
Multiplying both sides by (L - H / tan(25°)), we get:
tan(25°) (L - H / tan(25°)) = H
Expanding the left-hand side, we get:
tan(25°) L - H = H tan^2(25°)
Adding H to both sides, we get:
tan(25°) L = H (1 + tan^2(25°))
Dividing both sides by (1 + tan^2(25°)), we get:
H = (tan(25°) L) / (1 + tan^2(25°))
Now we can substitute this expression for H into the equation D = H / tan(25°) to get:
D = ((tan(25°) L) / (1 + tan^2(25°))) / tan(25°)
Simplifying, we get:
D = L / (1 + tan^2(25°))
Now that we know the distance D, we can use the equation tan(A) = H / D to find H:
tan(25°) = H / D
H = D tan(25°)
Substituting D = L / (1 + tan^2(25°)), we get:
H = (L / (1 + tan^2(25°))) tan(25°)
Plugging in the given values L = 1850 feet and A = B = 25°, we get:
H = (1850 / (1 + tan^2(25°))) tan(25°)
H ≈ 697.3 feet
Therefore, the airplane is about 697.3 feet high.
Step-by-step explanation:
Triangle PQR has vertex coordinates at P(4, 0), Q(4, 3), R(5, 1). If the triangle is translated so that Q′(4, −5), determine the translation direction and number of units.
8 units down
8 units up
8 units to the right
8 units to the left
Answer:
To determine the translation direction and number of units, we need to find the vector that connects Q to Q', and then determine the magnitude and direction of that vector.
The vector that connects Q to Q' can be found by subtracting the coordinates of Q from the coordinates of Q':
Q' - Q = (4, -5) - (4, 3) = (0, -8)
This vector indicates a translation 8 units downwards, in the negative y direction. Therefore, the translation direction is downwards and the number of units is 8.
So the correct answer is: 8 units down.
Triangle PQR was translated 8 units down.
Explanation:In mathematics, particularly in the field of geometry, a translation refers to moving each point in a shape or a figure to a different position by sliding it to a certain direction for a fixed number of spaces. Each point is moved the same distance and in the same direction.
In the case of your Triangle PQR, the Q point moves from (4, 3) to the new coordinate Q'(4, -5). The x-coordinate in both points remains at 4. Hence, there's no left or right movement. But the y-coordinate changes from 3 to -5. This indicates a downward movement. The distance between 3 and -5 on the number line is 8 units. Therefore, the triangle was translated 8 units down.
Learn more about Translation in Geometry here:https://brainly.com/question/32226769
#SPJ2
group the data
1-5,6-10,11-15,16-20 to construct a tally chart and work out the frequency of each group
17. Kade has $40 in savings and wants to purchase a video game console that costs $250 plus
8.25% sales tax. Kade wants to wait until he has enough in savings to cover the purchase. If Kade
saves $50 each week, what is the minimum number of weeks Kade should wait before making his
purchase?
A. 3 weeks
B. 4 weeks
C. 5 weeks
D. 7 weeks
The minimum number of weeks Kade should wait before making his purchase is 5 weeks.
Given that, Kade has $40 as his saving, and he wants to buy a video game console that costs $250 plus 8.25% sales tax.
He saves $50 each week to buy the same, we need to find the number weeks in which he can buy the game,
Total cost of the game = 250 + 250 × 8.25%
= 250 + 250 × 0.0825
= 250 + 20.625
= 270.625
Hence, he needs to save = $270.625 - $40 = $230.625
Let the number of weeks be x,
∴ 50x = 230.625
x = 4.61 ≈ 5
Hence, the minimum number of weeks Kade should wait before making his purchase is 5 weeks.
Learn more about percentage, click;
https://brainly.com/question/29306119
#SPJ1
Can someone help me in this?
Answer:
18
Step-by-step explanation:
Since it is an equilateral triangle AB=AC=5
If I sum up all sides u will get 18. How this helps.
Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose six integers are chosen from A. Must there be two integers whose sum is 11
When six integers are chosen from the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, there must be at least one pair of integers that adds up to 11. This can be proven using a proof by contradiction.
To solve this problem, we can use a proof by contradiction. We assume that there are six integers chosen from A such that no two integers add up to 11.
If there is no pair of integers in the six chosen that sum up to 11, then we can consider the pairs of integers (1,10), (2,9), (3,8), (4,7), and (5,6). These are the only possible pairs of integers in A that add up to 11.
However, since there are five pairs and we can choose at most one integer from each pair, we can choose at most five integers in total. This is a contradiction since we were asked to choose six integers from A. Therefore, our assumption that there are no pairs of integers that add up to 11 is false.
Hence, we conclude that there must be at least one pair of integers among the six chosen that adds up to 11.
To know more about integer here
https://brainly.com/question/4196546
#SPJ4
a tank contains 60 kg of salt and 2000l of water. a solution of a concentration 0.015 kg of salt per liter enters a tank at the rate 9l/min. the solution is mixed and drains from the tank at the same rate. (a) what is the concentration of our solution in the tank initially? (b) find the amount of salt in the tank after 3.5 hours. (c) find the concentration of salt in the solution in the tank as time approaches infinity.
(a) The concentration of the solution in the tank will be changing over time.
(b) The amount of salt in the tank after 3.5 hours is 63.292 kg.
(c) When the inflow and outflow rates are equal, the amount of salt in the tank will remain constant.
(a) To find the concentration of the solution in the tank initially, we can use the formula:
concentration = mass of salt / volume of solution
The mass of salt in the tank initially is 60 kg, and the volume of solution is 2000 liters.
Therefore, the initial concentration is:
concentration = 60 kg / 2000 L
concentration = 0.03 kg/L
However, we know that a solution with a concentration of 0.015 kg/L is entering the tank at a rate of 9 L/min.
Therefore, the concentration of the solution in the tank will be changing over time.
(b) To find the amount of salt in the tank after 3.5 hours, we can use the formula:
amount of salt = initial amount of salt + (concentration of incoming solution - concentration of solution in tank) x rate x time
The initial amount of salt is 60 kg, and the concentration of the incoming solution is 0.015 kg/L.
We need to find the concentration of the solution in the tank after 3.5 hours.
The rate of flow is 9 L/min, so the total volume of solution that has entered the tank after 3.5 hours is:
volume of solution = rate x time
volume of solution = 9 L/min x 210 min
volume of solution = 1890 L
The total volume of solution in the tank after 3.5 hours is:
total volume = initial volume + volume of incoming solution - volume of drained solution
total volume = 2000 L + 9 L/min x 210 min - 9 L/min x 210 min
total volume = 2000 L
Therefore, the concentration of salt in the tank after 3.5 hours is:
amount of salt = 60 kg + (0.015 kg/L - concentration of solution in tank) x 9 L/min x 210 min
amount of salt - 60 kg = (0.015 kg/L - concentration of solution in tank) x 1890 L
concentration of solution in tank = 0.015 kg/L - (amount of salt - 60 kg) / 1890 L
Now we can substitute the concentration of the solution in the tank into the formula and solve for the amount of salt:
amount of salt = 60 kg + (0.015 kg/L - (0.015 kg/L - (amount of salt - 60 kg) / 1890 L)) x 9 L/min x 210 min
amount of salt = 63.292 kg
Therefore, the amount of salt in the tank after 3.5 hours is 63.292 kg.
(c) To find the concentration of salt in the solution in the tank as time approaches infinity, we need to find the concentration that the solution will reach when the inflow and outflow rates of solution are equal.
At this point, the amount of salt in the tank will remain constant.
Let's denote the concentration of salt in the solution in the tank as c.
We know that the volume of solution in the tank remains constant at 2000 L, and that the inflow and outflow rates are both 9 L/min. Therefore, the amount of salt that enters the tank per minute is 0.015 kg/L x 9 L/min = 0.135 kg/min, and the amount of salt that leaves the tank per minute is c x 9 L/min.
When the inflow and outflow rates are equal, the amount of salt in the tank will remain constant.
Therefore, we can set the rate of inflow equal to the rate of outflow and solve for c:
0.015 kg/L x 9.
For similar question on concentration.
https://brainly.com/question/30677144
#SPJ11
Plot points between and beyond each x-intercept and vertical asymptote. Find the value of the function at the given value of x.
f(x)= 2/ x^2+3x-10
the points we plotted are (-6, -1/2), (-4, 1/2), (0, -1/5), (3, 1/2), and (6, 1/5).
What is function?
a function is a relationship or expression involving one or more variables. It has a set of input and outputs.
To find the x-intercepts, we set the numerator of the function equal to zero:
[tex]2 / (x^2 + 3x - 10) = 0[/tex]
This is only true if the numerator is equal to zero, so:
2 = 0
This is not possible, so the function has no x-intercepts.
To find the vertical asymptotes, we look for values of x that make the denominator equal to zero:
[tex]x^2 + 3x - 10 = 0[/tex]
We can factor the quadratic as:
(x + 5)(x - 2) = 0
This means that the function has vertical asymptotes at x = -5 and x = 2.
Now, let's plot some points between and beyond each x-intercept and vertical asymptote:
When x = -6, f(x) = 2 / (-6)² + 3(-6) - 10 = -1/2
When x = -4, f(x) = 2 / (-4)² + 3(-4) - 10 = 1/2
When x = 0, f(x) = 2 / (0)² + 3(0) - 10 = -1/5
When x = 3, f(x) = 2 / (3)² + 3(3) - 10 = 1/2
When x = 4, f(x) = 2 / (4)² + 3(4) - 10 = -1/2
When x = 6, f(x) = 2 / (6)² + 3(6) - 10 = 1/5
Therefore, the points we plotted are (-6, -1/2), (-4, 1/2), (0, -1/5), (3, 1/2), and (6, 1/5).
To know more about function visit,
https://brainly.com/question/11624077
#SPJ1
At midnight, the temperature in a city was 5 degrees celsius. The temperature was dropping at a steady rate of 2 degress celsius per hour. Write an inequalty that represents t, the number of hours past midnight, when the temperature was coler than -4 degrees celsius
( 5 - 2t ) < - 4 is an inequalty that represents t, the number of hours past midnight, when the temperature was coler than -4 degrees celsius.
What is linear equation?
An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.
The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.
The midnight temperature is 5 °C and the temperature is decreasing at the rate of 2°C per hour.
If t is the hours past midnight then after t hours the temperature will be ( 5 - 2t ).
Now, if this temperature is colder than - 4° C, then the inequality can be written as ( 5 - 2t ) < - 4.
Learn more about Linear equation
brainly.com/question/11897796
#SPJ1
The inequality that represents t, the number of hours past midnight, when the temperature was cooler than -4 degrees celsius( 5 - 2t ) < - 4
What is inequality?
The term "inequality" is used in mathematics to describe a relationship between two expressions or values that is not equal to one another. Inequality results from a lack of balance. When two quantities are equal, we use the symbol '=', and when they are not equal, we use the symbol. If two values are not equal, the first value can be greater than (>) or less than (), or greater than equal to () or less than equal to ().
The midnight temperature is 5 °C and the temperature is decreasing at the rate of 2°C per hour.
If t is the hours past midnight then after t hours the temperature will be
=> ( 5 - 2t ).
Now, if this temperature is colder than - 4° C, then the inequality can be written as ( 5 - 2t ) < - 4.
To learn more about inequality refer the below link
https://brainly.com/question/25275758
#SPJ1
Male mosquitos have pretty short lifespans. Males of a certain species have lifespans that are strongly skewed to the right with a mean of 8 88 days and a standard deviation of 6 66 days. A biologist collects a random sample of 36 3636 of these male mosquitos and observes them to calculate the sample mean lifespan. What is the probability that the mean lifespan from the sample of 36 3636 mosquitos x ˉ x ˉ x, with, \bar, on top exceeds 10 1010 days? Choose 1 answer: Choose 1 answer: (Choice A) A P ( x ˉ > 10 ) ≈ 0. 02 P( x ˉ >10)≈0. 02P, left parenthesis, x, with, \bar, on top, is greater than, 10, right parenthesis, approximately equals, 0, point, 02 (Choice B) B P ( x ˉ > 10 ) ≈ 0. 14 P( x ˉ >10)≈0. 14P, left parenthesis, x, with, \bar, on top, is greater than, 10, right parenthesis, approximately equals, 0, point, 14 (Choice C) C P ( x ˉ > 10 ) ≈ 0. 25 P( x ˉ >10)≈0. 25P, left parenthesis, x, with, \bar, on top, is greater than, 10, right parenthesis, approximately equals, 0, point, 25 (Choice D) D P ( x ˉ > 10 ) ≈ 0. 37 P( x ˉ >10)≈0. 37P, left parenthesis, x, with, \bar, on top, is greater than, 10, right parenthesis, approximately equals, 0, point, 37 (Choice E) E We cannot calculate this probability because the sampling distribution is not normal
Given a sample of 36 male mosquitos of a species with a mean lifespan of 8.88 days and a standard deviation of 6.66 days, the probability of the sample mean lifespan exceeding 10 days is approximately 0.14. So, the correct choice is option B is P ( x ˉ > 10 ) ≈ 0. 14 P( x ˉ >10)≈0. 14P, left parenthesis, x, with, \bar, on top, is greater than, 10, right parenthesis, approximately equals, 0, point, 14.
The sampling distribution of the mean lifespan is approximately normal due to the Central Limit Theorem.
The standard error of the mean is 6.66 / sqrt(36) = 1.11. The z-score for a sample mean of 10 is (10 - 8.88) / 1.11 = 1.08. Using a standard normal distribution table or calculator, the probability of a z-score greater than 1.08 is approximately 0.14.
Therefore, the answer is Choice B is P(X > 10) ≈ 0.14.
To know more about Probability:
https://brainly.com/question/11234923
#SPJ4
Choose the word that makes this sentence true.
A square is ____ a rectangle.
Answer: the same as or equal to
Step-by-step explanation: The shapes are the same one's just stretched
Answer:
A square is a special kind of a rectangle
Step-by-step explanation:
Every Square is a rectangle but not every rectangle is a square.
CAN I PLEASE GET HELP!
The result of 10 trials expressed in percentage is 70%.
List out the 10 trials in table format.We can utilize the random number table to produce 10 random numbers between 0 and 1 to approximate Nestor's performance in the ten races. If a number is less than or equal to 0.79, it is considered a "medal," and if it is larger than 0.79, it is considered a "no medal." This approach can be repeated ten times to get a sense of the range of possible outcomes.
For ten trials, we get the following results using the random number table shown below:
To estimate the likelihood that Nestor will win at least six of the following ten races, we count how many trials resulted in six or more medals. Seven of the ten trials resulted in six or more medals. As a result, we estimate the likelihood to be 7/10, or 70%.
The likelihood is 70% when expressed as a percentage.
Learn more about trials here:
https://brainly.com/question/12255499
#SPJ1