The function f(x) is decreasing on the interval x∈(1/2,∞) and all the real values.
What is meant by a function?A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.
The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.
Given function,
f(x)=[tex]e^{2 x^{2} +5}[/tex]/-6x
f'(x)=-1/6x([tex]e^{2 x^{2} +5}[/tex])(4x)+[tex]e^{2 x^{2} +5}[/tex](1/6x²)
=[tex]e^{2 x^{2} +5}[/tex]/6x((1/x)-4x)
f'(x)=0
((1/x)-4x)=0
1-4x²=0
4x²=1
x=±1/4
Given that, f(x) is decreasing function then,
f'(x)<0
((1/x)-4x)<0
(1-4x²)/x<0
1-4x²<0
1<4x²
1/4<4x²
x²>1/4
x>1/2
x∈(1/2,∞)
Hence, f(x) is decreasing on the interval x∈(1/2,∞)
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At the toaster company, the weekly cost to run the factory is $1400 and the cost of producing each toaster is an additional $4 per toaster. Find a function rule representing the weekly cost in dollars, f(x), of producing x toasters.
Answer:
I believe... f(x)=1400+4x
Find two positive numbers whose difference is 20 and whose product is 429.
Select the correct answer.
Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h.
A.
h(2) = 16
B.
h(-3) = -1
C.
h(8) = 21
D.
h(13) = 18
Option A. The statement that can be said to be true for h is h(2) = 16
How to get the domainIf we look at the domain and range, we can rule out some straight away.
For h - 3 = -1
this is outside of the range of the such that -1 ∉ 1 ≤ hx ≤ 25
When h is 13 = 18
This is also outside of the domain such that 13 ∉ -3 ≤ x ≤ 11
When h is 8 = 21
there is going to be a contradiction with what the question has stated earlier. This is because we are told that h(8) = 19
Therefore on h(2) = 16
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help help help
like factoring it
[tex]\frac{1}{3}b-\frac{1}{3}$[/tex]
The factoring is the representation of a polynomial in multiplication term thus the factoring of (1/3)b - 1/3 will be 1/3(b - 1).
What is an algebraic factor?An algebraic factor is the multiplication of two algebraic terms.
That term could be in form of summation multiplication or in subtraction.
The root of the quadratic equation formed by the algebraic factor is always real.
As per the given polygon,(1/3)b - 1/3
Take 1/3 as common in the whole polygon,
1/3(b - 1).
Since the terms 1/3 and (b - 1) both are in the multiplication of each other.
Hence "The factoring is the representation of a polynomial in multiplication term thus the factoring of (1/3)b - 1/3 will be 1/3(b - 1)".
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HOME Realty claims that it can sell a detached, residential house faster than any other realty company. With the aim of examining HOME's claim, you sample 20 customers who sold a detached, residential house through HOME and record the selling times (in days) of the houses. Your data are summarized below:
Selling Time Frequency
0 10 3
10 20 4
20 30 6
30 40 4
40 50 3
Find the proportion of selling times in the sample that are less than 20 days claims that it can sell a detached, residential house faster than any other realty company.
The proportion of selling times is 0.35
From the question, we have
Selling Time___ Frequency
0 10____________3
10 20__________ 4
20 30__________ 6
30 40__________ 4
40 50__________ 3
Proportion of selling times in sample above that are less than 20 days :
total frequency = (3 + 4 + 6 + 4 + 3) = 20
Selling time which is less Than 20 days :
(0 - 10) = 3
(10 - 20) = 4
Total = (3 + 4) = 7
Proportion = selling time less Than 20 days / total frequency
= 7 / 20
= 0.35
Addition:
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.
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what percent is 25 of 100
Answer:
25 percent.
Step-by-step explanation:
25 divided by 100 is equal to 0.25. You then multiply that by 100 to get percent, which is 25 percent.
Hope it helps.
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
g(x) = square root 49 - x squared
The critical number are 0, 7 , -7.
Given function:
g(x) = [tex]\sqrt{49-x^{2} }[/tex]
first derivative is,
= -x/([tex]\sqrt{49-x^{2} }[/tex] )
-x = 0 or x = 0
[tex]\sqrt{49-x^{2} }[/tex] = 0
49 - [tex]x^{2} =0[/tex]
49 = [tex]x^{2}[/tex]
x = 7 , -7.
Therefore the critical number are 0, 7 , -7.
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Help Please! Will give brainlest!
Answer:
[tex] = \frac{10}{0.2} = \frac{100}{2} = 50 \\ = \frac{10}{0.02} = \frac{1000}{2} = 500 \\ = \frac{10}{0.002} = \frac{10000}{2} = 5000 \\ \\ [/tex]
hopefully that will help u
already answered 1 and 2. i think 3 is "definition of midpoint". is this correct? what are the other two? thank you
Ali had 457 pieces of clothes for her dolls. She had 235 dresses and 125 shirts. How many pairs of shoes and pants did she have?
Answer:
Step-by-step explanation:
457-235= 222
222-125=97
97÷2= 48.5
≈49 pairs of pants and shoes
FIND THE SLOPE OF YHE LINE
HURRYYY
The slope of given line is 43
The slope of the line is the rate of change of y with respect to xSlope of a line gives the steepness of line.
The formula of finding the slope of line with two given points is as follows,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Thewith[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]TheThe[tex]Hdb\pi[/tex]TheThelinem=y2-yy2-y1/xw-xq
x2-x1
x2-x1
x2-x1
It can be seen from the given image thatthat the line moves 3unit in x direct and 4unit in y direction.So the slope will be
be m=43
Hence,the slope of the give line is 43
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9x^7/3x^2=3x^9 true or false
Answer:
False
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
given
[tex]\frac{9x^7}{3x^2}[/tex]
= [tex]\frac{9}{3}[/tex] × [tex]\frac{x^7}{x^2}[/tex]
= 3 × [tex]x^{(7-2)}[/tex]
= 3[tex]x^{5}[/tex]
Jacob wants to prove that AFGH = A/KL using SAS.
He knows that FG = J and F = J. What additional
piece of information does he need?
The piece of information does he need is ∠F ≅ ∠J.
What is triangle?
A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°. It is a polygon having the least number of sides.
Properties of triangle?
A triangle has three sides, three angles, and three vertices.The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.The sum of the length of any two sides of a triangle is greater than the length of the third side.Given,
ΔFGH = ΔJKL
By SAS property of triangle;
[tex]\bar{FH}[/tex] ≅ [tex]\bar{JL}[/tex], FG ≅ JK
third property ,
∠F = ∠J
By SAS property at least two side their ratio must be equal and one angle.
[tex]\frac{FG}{JK} = \frac{FH}{JL}[/tex]
∠F = ∠J
So, option A is correct.
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Question 8 (1 point)
The selling price of a widget is $15 and the fixed cost per month is $4,800. The variable cost per widget is $9. Calculate the
contribution margin rate.
0000
b
C
d
Question 8 of 20 | Page 8 of 20
40%
60%
30%
50%
The contribution margin rate is 40%.
What is contribution margin rate?
A company's contribution margin rate is the total revenue minus variable costs divided by the revenue.
First we need to determine the contribution margin in order to calculate the contribution margin rate. There are two approaches to determine the contribution margin.
Contribution Margin = Net Sales Revenue – Variable CostContribution Margin = Fixed Costs + Net IncomeContribution Margin = $15 - $9 = $6
The contribution margin is $6.
Now we will calculate the contribution margin rate using this formula,
Contribution Margin Rate = Contribution Margin [tex]/[/tex] Sales Revenue
Contribution Margin Rate = $6 / $15
= 0.4 * 100
= 40%.
Hence the contribution margin rate is 40%.
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DC = 13.4 WHAT IS BD
Answer:
the answer is 6
Step-by-step explanation:
I hope I helped, if you have questions let me know. I'll try to answer.
The cost to attend a public university in a recent year is $16,241. The circle graph to
the right shows the percentage of that cost for tuition/fees, room, board, and
computer costs. Determine the cost, in dollars, for each category.
The cost of tuition and fees is $.
(Round to the nearest cent as needed.)
The cost of room is $.
(Round to the nearest cent as needed.)
The cost of board is $.
(Round to the nearest cent as needed.)
The computer costs are $
(Round to the nearest cent as needed.)
Cost to Attend a Public University
Tuition/Fees 36.9%
Room 31.5%
Board 24.9%
Computer costs 6.7%
Answer:
Tuition and Fees = $5,992.93
Room = $5,115.92
Board = $4,044.01
Computer Costs = $1,088.15
Jasenio is shooting target practice with a bow and arrow. His target is a paper rabbit that runs along a track. The track is 50 meters away from Jasenio and he estimates that by the time the arrow reaches it, the paper rabbit will be at a point about 10 meters to the right of what would be directly in front of him. At what true bearing should Jasenio aim his bow and arrow?
a) 3.49°
b) 11.31°
c) 78.46°
d) 78.69°
The true bearing at which Jasenio should aim his bow and arrow is; b) 11.31°
How to apply Trigonometric Ratios?
We have different trigonometric ratios such as;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
We are told the track is 50 meters away from Jasenio and that by the time the arrow reaches it, the paper rabbit will be at a point about 10 meters to the right of what would be directly in front of him.
This means that there will be a right angle triangle formed with the height as 50 m and the base length as 10m. Thus, by trigonometric ratios, we have;
tan θ = 10/50
where θ is the true bearing angle. Thus;
tan θ = 0.2
θ = tan⁻¹0.2
θ = 11.31°
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Considering the following statements, what is X → Z? X → Y: If the sum of the interior angles of a shape is 180°, then it's a triangle. Y → Z: If a shape is a triangle, then it has three sides. Question 4 options: A) X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides. B) X → Z: If a shape has three sides, then it's a triangle. C) X → Z: If a shape has three sides, then the sum of the interior angles of the shape is 180°. D) X → Z: If the sum of the interior angles of a shape isn't 180°, then it doesn't have three sides.
The correct statement that is a combination of both conditional statements is; X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides.
How to interpret conditional statements?
A triangle is defined as a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees.
We are given the conditional statements as;
X → Y: If the sum of the interior angles of a shape is 180°, then it's a triangle.
Y → Z: If a shape is a triangle, then it has three sides.
Now, transitive property states that “if two quantities are equal to a third quantity, then we can say that all the quantities are equal to each other”.
Thus, applying transitive property to our given statements we can say that; X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides.
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Solve for x if log(x - 1) + log(x + 1) = log21
Answer: [tex]x=\pm \sqrt{22}[/tex]
Step-by-step explanation:
[tex]\log(x-1)+\log(x+1)=\log 21\\\\\log((x-1)(x+1))=\log 21\\\\\log(x^2-1)=\log 21\\\\x^2-1=21\\\\x^2=22\\\\x=\pm \sqrt{22}[/tex]
Answer:
sqrt(22) = [tex]\sqrt{22}[/tex]
Step-by-step explanation:
we can use the logarithm rule, "log x + log y = log(xy)" to solve this problem
log(x-1) + log(x+1) = = [tex]log((x-1)(x+1))[/tex] = log(21)
this means that x^2 - 1 equals 21
xx-1 = 21
xx=22
x=sqrt(22)
10. Seven more than the quotient of a number b
and 45 is greater than 5.
How do you solve -110 + 96
Answer: -14
Step-by-step explanation:
−110+96
Add −110 and 96 to get −14.
−14
Answer: -14
Step-by-step explanation:
In this case, it's best you bring out the negative
- (110 - 96)
- (14)
= -14
Question
Estimate the mean of the number of points deducted from each student on an economics test given in the follow
grouped frequency table.
• Round the final answer to one decimal place.
Value Interval
0-3
4-7
8-11
Frequency
12
20
8
According to the following frequency table, the mean of the number points deducted from each student on an economics is 5.1
Frequency table:
Frequency table means the method of organizing raw data in a compact form by displaying a series of scores in ascending or descending order, together with their frequencies—the number of times each score occurs in the respective data set.
Given,
Here we need to determine the mean of the number of points deducted from each student on an economics test given in the follow grouped frequency table.
For the given table of data, the frequency table of the data is attached below.
In order to find the mean of the frequency table we have to use the following values,
The total frequency is 204
And the number of frequency is 40.
So, the mean is
=> 204/40
=> 5.1
Therefore, the mean of the data is 5.1
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At a fast food restaurant, customers are asked if they want to "round up" their bill to the next highest dollar and
donate the additional money to charity. The cashier is instructed to tell the customer that their bill is X dollars and Y
cents. Assume that the values of Y are equally likely to be any value from 0 to 99 cents and that customers are equally
likely to "round up" regardless of the amount of their bill. The density curve below models Y, the donation amount.
(a) What is the shape of the distribution of donations?
Amount of donation (cents)
(b) What proportion of donations are at least 75 cents?
(a) The shape of the distribution of donations is rectangular.
(b) The proportion of donations are at least 75 cents id 0.24
(a)The density curve is rectangular in shape.
This indicates that donations are distributed uniformly.
(b) From the question, we have
The probability of donations at least 75 cents as follows:
[tex]P(X\geq 75) =\int\limits^a_b {\frac{1}{99-0} } \, dx \\[/tex]
Substituting the limits, we get
[tex]P(X\geq 75) =\frac{99-75}{99} \\=\frac{24}{99} \\=0.24[/tex]
Probability:
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
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Find the y intercept and slope of the linear equation
0 = 4.5 - 2y + 4.8x
Explain in detail the difference of a linear, quadratic, and geometric relationships between two variables.
The difference of a linear, quadratic reation.
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation.
Trigonometric ratios describe these operations. The ide and trigonometric functions In the previous chapters, we discovered that the polynomial equation is the equation that results from equating a polynomial function to zero. A linear equation results from equating a function to zero if it is a linear polynomial. We get a quadratic equation if the function is a quadratic polynomial.
When we graph a linear equation, we get a straight line, however with a quadratic equation, we get a parabola.
Unlike the slope of a linear polynomial, the slope of a quadratic polynomial is constant.
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The population of a city can be modeled using the formula P=100,000e^(0.05t), where t is the number of years after 2012 and P is the city's population. Which of the following equations can be used to find the number of years after 2012 that the population will triple to 300,000?
Group of answer choices
t=3/(0.05e)
t=ln3/0.05
t=(ln200,000)/0.05
t=log3/0.05
The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B t = ln(3) / 0.05
Given,
The population of a city can be modeled using the formula P=100,000e^(0.05t)
t is the number of years after 2012
P is the population of the city
We have to find the equation that can be used to find the number of years after 2012 that the population will triple to 300,000.
Here,
Substitute 300000 in for P and solve for t
300000=100000e^0.05t
Divide both sides by 100000:
We get,
3 = e^0.05t
Multiply both sides by the natural log (ln)
Then,
ln(3) = 0.05t
Now, divide 0.05 on both sides to get t by its self
t = ln(3) / 0.05
Therefore,
The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B t = ln(3) / 0.05
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How do I factor 250n2 + 20n8?
Step-by-step explanation:
[tex]250n^2+20n^8[/tex]
common factor is [tex]10n^2[/tex]:
[tex]10n^2(25 +2n^6)[/tex]
rearrange:
[tex]10n^2(2n^6+25)[/tex]
PLEASE HELP ME ASAP!!!
The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 1, 4
3 1, 2, 6
4 1, 3, 7
5 1, 1
6 5
Key: 3|2 means 3.2
What is the mean, and what does it tell you in terms of the problem?
The mean of the data is 3.85 using the stem-and-leaf plot.
It means the average feet that the heavy ball was thrown is 3.85 feet, which is the typical number.
How to calculate the Mean of a Data?To find the mean of a data set that is represented by a stem-and-leaf plot, first, list out all the data values that are represented on the stem-and-leaf plot, add all the values, and divide by the number of values that were represented on the stem-and-leaf plot.
Given the stem-and-leaf plot, using the key, the data points represented are:
2.0, 2.1, 2.4, 3.1, 3.2, 3.6, 4.1, 4.3, 4.7, 5.1, 5.1, 6.5
Mean = [2.0 + 2.1 + 2.4 + 3.1 + 3.2 + 3.6 + 4.1 + 4.3 + 4.7 + 5.1 + 5.1 + 6.5]/12
Mean = 46.2/12
Mean = 3.85 feet
The mean of 3.85 feet means that the average distance that the heavy ball was thrown in feet is 3.85.
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What is the image point of (- 3, - 2) after the transformation r x-axis R 270^ ?
The image point of the point (-3, -2) after the transformation r x-axis R 270° is; (3, -2).
TransformationsIt follows from the task content that the image point of the pair of coordinates given is to be determined.
Given point is; (-3, -2).
Hence, after a reflection over the x-axis; we have; (-3, 2).
Also, after a rotation of 270°, it follows that we have; (x, y) ==> (-x, -y).
Therefore, the image point is; (-(-3), -(2)).
The image point is therefore; (3, -2).
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The cost to rent a frozen yogurt machine is $150 per day plus $25 per hour of use.
Which inequality can be used to determine the maximum number of hours h the
frozen yogurt machine can be used if the rental cost for the day will not exceed $300?
The inequality that can be used to determine the maximum number of hours h the frozen yogurt machine can be used if the rental cost for the day will not exceed $300 is 150+25h ≤300.
According to the question,
We have the following information:
The cost to rent a frozen yogurt machine is $150 per day plus $25 per hour of use.
And h represents the number of hours.
So, we have the following expression to find the total cost:
150+25h
Now, it is given that the total rental cost should not exceed $300.
So, we have the following inequality:
150+25h ≤300
Hence, the correct option is C.
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