Must assume positive values
f is above this line outside [a, b]
So, f(x)f′′(x)<0 cannot hold for all x.
Given,
In the question:
Let f be a twice-differentiable function on R such that f′′ is continuous. Prove that f(x)f′′(x)<0 cannot hold for all x.
Now, According to the question:
Assume that :
f"(0) > 0
Then, f(0) < 0 and as neither factor can change sign.
f"(x) > 0 > f(x) for all x ∈ R and f is strictly convex.
Pick a < b with f(a) ≠ f(b).
Then the line through (a f(b)) and (b f(b)) intersect the x - axis.
By convexity, f is above this line outside [a, b],
Hence, Must assume positive values
f is above this line outside [a, b],
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the width of a rectangular patio is increased by 10 % 10%. its length is increased by 20 % 20%. by what percentage has its area increased?
Answer: 32%
Step-by-step explanation:
Let's set the original dimensions of the rectangular patio as:
width = wlength = lThat'll set the original area(a) of the patio as a = w · l.
The new dimensions of the patio can be calculated as:
width = w + 0.1w = 1.1wlength = l + 0.2l = 1.2lThe new area can then be calculated as 1.1w · 1.2l = 1.32 · w · l = 1.32a
Using the two areas, the percent increase can be calculated as:
[tex]\frac{1.32a-a}{a}*100 =\frac{1.32-1}{1}*100 =0.32*100=32[/tex]
Is 15 a multiple or factor of 5?.
Answer:
Multiple
Step-by-step explanation:
A multiple of 5 is anything that it can multiply into. For example: 5, 10, 15, 20, 25 and so on.
A factor is a number that divides into your number and leaves no remainder. An example of this is 2 is a factor of 4. 15 is not a factor of 5 because it cannot divide evenly. The only factors of 5 are 1 and 5.
how does the mitochondria aids the process of protein synthesis?
Mitochondria use proteins to break down sugars and produce cellular energy in the form of ATP.
I will give brainlest
Answer:
[tex]\huge\boxed{\sf r = 1/4}[/tex]
Step-by-step explanation:
Given that,y = rx -------------------(1)
From the table,
x = 8 when y = 2
Put in the above equation.
2 = r(8)
Divide 8 to both sides
2/8 = r
r = 2/8
r = 1/4
[tex]\rule[225]{225}{2}[/tex]
Aubrey practice the piano 1890 minute in 5 week. At what rate did he practice, in minute per day?
Aubrey has practiced piano at the rate of 54 minutes per day.
What is a unit conversion in mathematics?
Unit conversion is a multi-step process that includes multiplying or dividing by a numerical factor, determining the appropriate number of significant digits, and rounding.
Aubrey practices the piano for 1890 minutes in 5 weeks.
In one week there are 7 days.
So the total number of days will be = 5 * 7
= 35 days.
So Aubrey has practiced piano at the rate of = 1890/35 minutes per day
= 54 minutes per day.
Hence, Aubrey has practiced piano at the rate of 54 minutes per day.
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the histograms show the results of three simulations of a sampling distribution of a sample mean. for each simulation, 1,500 samples of size n were selected from the same population and the sample mean was recorded. the value of n was different for each of the three simulations.
The histograms show the results of three simulations of a sampling distribution of a sample mean. Arranging from the least value of n to the naximum value, the order is A, C, B.
A histogram is a bar graph-like representation of data that groups a range of classes into columns along the horizontal x-axis. The vertical y-axis represents the number count or percentage of occurrences in the data for each column. Columns can be used to visualized as patterns of data distributions.
Lesser the value of n larger the variablity.
Arranging from the least value of n to the naximum value, the order is A, C, B
Therefore, The histograms show the results of three simulations of a sampling distribution of a sample mean. Arranging from the least value of n to the naximum value, the order is A, C, B.
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When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle it means that we are going to use what postulate?.
When two of a triangle's angles and one of its included sides are congruent with the equivalent portion of another triangle, the two triangles are said to be in AAS or ASA congruency.
What is meant by the term SAS congruency?The Angle-Side-Angle Postulate (ASA) states that two triangles are congruent if their two included sides and two included angles are congruent.And we show that triangles ABC and DEF are congruent by applying the Angle-Side-Angle Postulate, as seen in the image to the right.AAS Congruency:
In contrast, two triangles are congruent if their respective non-included sides are congruent with two angles from one triangle and two angles from another, according to the Angle-Angle-Side Postulate (AAS).The triangles ABC and QPR are also shown to be congruent using the Angle-Angle-Side Postulate, as seen in the illustration to the right.Therefore, when two of a triangle's angles and one of its included sides are congruent with the equivalent portion of another triangle, the two triangles are said to be in ASA or AAS congruency.
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Which equation represents the line that passes through (- 6 7 and (- 3 6 )?.
Answer:
y = -1/3 x + 5
Step-by-step explanation:
To write the equation, you need the slope and the y-intercept to write the equation in the slope intercept form. You did not state what form, so this is the form that I will use.
y = mx + b M is the slope and b is the y intercept.
The slope is the change in y over the change in x. For the two points we can find the change in y by using the numbers 6 and 7. We can find the change in x by using the numbers - and -6,
[tex]\frac{6-7}{-3 - -3}[/tex] = [tex]\frac{-1}{-3+6}[/tex] = [tex]\frac{-1}{3}[/tex] This is the slope.
To find the y intercept (b) we will use one point and the slope. It does not matter which point that you use. I am going to use the point (-3,6).
slope (m) = [tex]\frac{-1}{3}[/tex]
x = -3
y = 6 Plug these into the equation and solve for b.
y = mx + b
6 = ([tex]\frac{-1}{3}[/tex]) (-3) + b
6 = 1 + b Subtract 1 from both sides.
5 = b
y = [tex]\frac{-1}{3}[/tex]x + 5
use cross products to determine whether the ratios and form a proportion. do they form a proportion?
No , they do not form a proportion because 77 and 60 are not equal
Hence , not form proportion
Set up a proportion as 4/7 = 11/15
Cross multiply:
7×11
4×15
You should get 77 and 60 for the products. Since the products don't equal each other, they are not proportional.
complete question is
use cross products to determine whether the ratios 4/7 and 11/15 form a proportion. Do they form a proportion? Explain your steps and your conclusion
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What is the solution to the system of equations y =- 5x 3?.
The solution of equation is y = -15, x = 1 .The equation used to obtain the value of y and x is y = -15x.
What is Equations ?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. It will be regarded as a phrase.
The given equation is: y= -5x3
or y= -15x
or y\x=-15
Divide with 1 both side
y/x = -15/1
Then y = -15 , x = 1
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Answer: (5,28)
Step-by-step explanation:
Solve x2−x−3=0 by completing the square.
If the solutions are real rational numbers, list from least to greatest separated by a comma.
If the solutions are not real numbers, write your answer in the form a ± bi.
If the solutions are irrational, write your answer in simplified radical form, using ± to express both solutions.
let's start by grouping the terms with the variable first, so that'd be
(x² - x) -3 = 0
(x² - x + []²) = 3
now, the middle term in a perfect square trinomial is simply the product of "2" and the root of the terms on the left and right sides, so whatever that product is, we know it must yield "x" because that's our middle term above skipping its sign, so hmmm let's check around
[tex]\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] ~\dotfill\\\\ (x^2 - x +\square^2)=3 \\\\\\ 2\sqrt{\square^2}\sqrt{x^2}~~ = ~~x\implies 2\square x=x\implies \square=\cfrac{x}{2x}\implies \square=\cfrac{1}{2}[/tex]
so that's our missing value, now ( 1/2 )² is 1/4, however, let's recall that, all we're doing is borrowing from our very good friend Mr. Zero, 0, so if we add 1/4 we also have to subtract 1/4
[tex]\left(x^2-x+\cfrac{1}{4}-\cfrac{1}{4} \right)=3\implies \left(x^2-x+\cfrac{1}{4} \right)-\cfrac{1}{4}=3 \\\\\\ \left(x^2-x+\left( \cfrac{1}{2} \right)^2 \right)=3+\cfrac{1}{4}\implies \left(x-\cfrac{1}{2} \right)^2=\cfrac{13}{4}\implies x-\cfrac{1}{2}=\pm\sqrt{\cfrac{13}{4}} \\\\\\ x-\cfrac{1}{2}=\pm\cfrac{\sqrt{13}}{2}\implies x=\pm\cfrac{\sqrt{13}}{2}+\cfrac{1}{2}\implies \boxed{x=\pm\cfrac{\sqrt{13}+1}{2}}[/tex]
Provide an appropriate response.
Find the area of the shaded region. The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
Answer:
A) 0.7938---------------------------
Givenμ = 100, σ = 15Find the area between x = 85 and x = 125.
Find z-scores for each endz = (x - μ)/σz₁ = (85 - 100)/15 = - 15/15 = - 1z₂ = (125 - 100)/15 = 25/15 ≈ 1.67Find the corresponding probabilities from z-score tablez₁ = 0.1587z₂ = 0.9525Find the differencez₂ - z₁ = 0.9525 - 0.1587 = 0.7938The matching choice is A
Answer:
0.7938
Step-by-step explanation:
The given graph is a normal distribution curve.
If a continuous random variable X is normally distributed with mean μ and variance σ²:
[tex]\boxed{X \sim \textsf{N}(\mu,\sigma^2)}[/tex]
Given:
mean μ = 100standard deviation σ = 15[tex]\text{If \; $X \sim \textsf{N}(100,15^2)$,\;\;find\;\;P$(85\leq X\leq 125)$\;\;to\;3\;s.f.}[/tex]
Therefore, we need to find the area to the left of x = 125 and subtract the area to the left of x = 85.
Method 1
Using a calculator:
[tex]\begin{aligned}\implies \text{P}(85\leq X\leq 125)&= \text{P}(X\leq 125)-\text{P}(X < 85)\\&=0.9522096477-0.1586552539 \\&=0.7935543938\\&\approx0.7938\end{aligned}[/tex]
Method 2
Converting to the z-distribution.
[tex]\boxed{\text{If\;\;$X \sim$N$(\mu,\sigma^2)$\;\;then\;\;$\dfrac{X-\mu}{\sigma}=Z$, \quad where $Z \sim$N$(0,1)$}}[/tex]
[tex]x=85 \implies Z_1=\dfrac{85-100}{15}=-1[/tex]
[tex]x=125 \implies Z_2=\dfrac{125-100}{15}=1.67[/tex]
Using the z-tables to find the corresponding probabilities (see attachments).
[tex]\begin{aligned}\implies \text{P}(-1\leq Z\leq 1.67)&= \text{P}(Z\leq 1.67)-\text{P}(Z < -1)\\&=0.9525-0.1587\\&=0.7938\end{aligned}[/tex]
What is the angle of each side of a circle?.
The central angle states the property of the center of the circle, So It is called the central angle.
What is a Central Angle?
The central angle is the angle that a circle's arc occupies in its center. The arms of the central angle are formed by the radius vectors. In other words, it's an angle whose vertex is the center of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's center subtends is known as the central angle.
An arc's angle at the circle's center is twice as large as its angle at any other point along the circle's circumference. the angle subtended by the arc in the opposite segment of the circle is twice as large as the angle at the center of the circle.
Hence,
The central angle states the property of the center of the circle, So It is called the central angle.
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The cost, c(x), for a taxi ride is given by c(x) = 3x + 2. 00, where x is the number of minutes. What does the slope mean for this situation?.
The slope of the given function of taxi fare mean the rate of change of the cost of the taxi ride is $3.00 per minute..
What is slope in general equation of line?
In the situation y = mx + c the worth of m is known as the slant, (or angle), of the line. It very well may be positive, negative or zero. Lines with a positive inclination slant upwards, from left to right. Lines with a negative inclination slant downwards from left to right. Lines with a zero inclination are level.
According to question:C(x) = 3x + 2
On comparing with the general equation of line. we get
slope = 3
slope = cost/time
Which says the rate of change of the cost of the taxi ride is $3.00 per minute.
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Consider the formula Distance = speed*time or D = st. Suppose you work 20 miles from your home.
How long would it take to get to work if you were able to travel at a speed of 30mph?
What about 40mph? 50mph?
What do you notice about the relationship between your speed and how long it takes to get to work? Show all work
The time taken to get to work from home with a speed of 30mph will be 40 minutes, 40mph in 30 minutes, and 50mph in 24 minutes.
What is velocity?Velocity is the rate of distance covered per time. Velocity could be average or instantaneous.
Average velocity can be given as;
Average velocity = total distance / total time taken
Units of velocity are given by ⇒ meter/second
As per the given,
Time = distance/speed
Distance = 20 miles
With a speed of 30 mph
Time = 20/30 = 2/3 hour or 40 minutes
With a speed of 40 mph
Time = 20/40 = 1/2 hour or 30 minutes
With a speed of 50 mph
Time = 20/50 = 2/5 hour or 24 minutes
Hence "The time taken to get to work from home with a speed of 30mph will be 40 minutes, 40mph in 30 minutes, and 50mph in 24 minutes".
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note that y in problem 1 is called the sample mean of observations x. in all applications, based on some assumptions, we use sample mean in order to calculate the statistical mean of observations. the difference between the statistical mean of y and the sample mean represents the error of calculating the mean of y using sample mean. now, consider that:
In order for the two-sample z statistic to be valid we need that the following assumptions hold samples must be random
data has to be continuous
each sample and population must be independent from each other
each population must be normally distributed
the population standard deviations must be known or the sample sizes must be ≥ 30
samples must be random
data has to be continuous
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16 deliveries in 4 hours is a unit rate of ______ deliveries per hour.
Answer: 4 deliveries per hour
Step-by-step explanation:
16 divided by 4 = 4 deliveries
Type the correct answer in the box. Use numerals instead of words. A regular pentagonal prism has a volume of 2,850 cubic millimeters. What is the height of the prism? a regular pentagonal prism with height labeled h. The pentagonal base has side edge labeled 12 millimeters. Apothem from center to a base edge is labeled 5 millimeters. The height of the prism is millimeters.
The required height of given regular pentagonal prism is 19 millimeters.
What is the volume of regular pentagonal prism ?We work out the volume of a pentagonal crystal utilizing the recipe is V = 5/2abh where this equation is additionally perceived as V = [1/2 × 5 × base length × apothem] × level of the crystal. The qualities are placed in the recipe and compose the response so got in cubic units.
According to question:We have,
volume of regular pentagonal prism = 2850 cubic millimeters.The pentagonal base has side edge labeled 12 millimeters.Apothem from center to a base edge is labeled 5 millimetersThen
V = 5/2abh
2850 =( 5×12×h)×5/2
h = 19 millimeters
Thus, required height of the pentagonal prism is 19 millimeters.
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Answer:
19 millimeters
Step-by-step explanation:
i took the test and got right hope this helps :)
Peter mixes 413 cups of orange juice, 213 cups of ginger ale, and 612 cups of strawberry lemonade to make some punch. What is the total number of cups of punch that peter makes?.
The total number of cups of punch that peter makes is 13 1/6.
Define the term mixed fraction?The mixed number is a representation of both a whole number and a legal fraction. In most cases, it denotes a number that falls between any 2 whole numbers.The sum of the values 4 1/3, 2 1/3, and 6 1/2 is required. To make adding easier, let's first turn them into improper fractions:
= 13/ 3 + 7/3 + 13/2
We can now simplify it because two of a fractions use the same denominator, resulting in the following:
= 30/3 + 13/2
Next, we must determine which of the two fractions has the lowest common denominator.
We may modify our denominator to 6 because that is the smallest number so both 2 and 3 can fit in:
= 23/3 x (2/2) + 13/2 x (3/3)
= 40/6 + 39/6
= 79/6
We should change this back into such a mixed number for our response:
= 79/6
= 13 1/6
Thus, the total number of cups of punch that Peter makes is 13 1/6.
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The correct question is-
Peter mixes 4 1/3 cups of orange juice, 2 1/3 cups of ginger ale, and 6 1/2 cups of strawberry lemonade to make some punch. What is the total number of cups of punch that Peter makes?
What are the 4 steps to solving inequalities?.
For solving the inequalities, there are more than four steps.
The step to solve given inequalities, the first step is to add the same number to both sides, the second step is to Subtract the same number from both sides and the third step is to Multiply both sides by the same positive number, and the fourth step is to Divide both sides by the same positive number, and the fifth step is to Multiply both sides by the same negative number and reverse the sign and the last step is to Divide both sides by the same negative number and reverse the sign. Out of which steps 2,3,4 and 5 are the most important steps.
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For a continuous random variable x, the probability density function f(x) represents.
The probability density function f(x) represents the probability at a given value of x.
In a distribution, the notation f(x) is the equivalent to the probability of event x, that is:
[tex]f(x) = P(X = x)[/tex]
The area under the curve is given by the cumulative distribution, which is given by:
[tex]P(X\leq x) = \int\limits^x_0f(x)dx[/tex]
Thus it is not f(x).
And f(x) can also be the height of the relative frequency function, but not of the function itself.
Hence the answer is the probability density function f(x) represents the probability at a given value of x.
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A lamina occupies the region inside the circle x2 + y2 = 18y but outside the circle x2 + y2 = 81. Find the center of mass if the density at any point is inversely proportional to its distance from the origin.
If the density at any place is inversely proportional to its distance from the origin, locate the center of mass as (0,4.5).
Given that,
The area inside the circle where x² + y² = 18y and outside the circle where x² + y² = 81 is occupied by a lamina.
We have to find if the density at any place is inversely proportional to its distance from the origin, locate the center of mass.
We know that,
Take the equation
x² + y² = 18y
x² + y² - 18y=0
Adding and subtracting 9².
x² + y² - 18y+ 9²-9²=0
x² + y² - 18y+ 9²=9²
x² + (y-9)²=9²
Which is a circle of radius 9 and center (0,9), And now the second equation
Now,
x²+y²=81
Which is a circle with radius 9 and center (0,0).
We can plot the curves in the picture we can see.
The density will be evenly distributed around the lines x=0 and y=4.5, which are the lines of symmetry, in a more complicated scenario where we would need to utilize integration to identify the Center of Mass.
Therefore, if the density at any place is inversely proportional to its distance from the origin, locate the center of mass as (0,4.5).
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2(x - 2) = -2
solve for x.
Answer:
x = 1
Step-by-step explanation:
2(x - 2)= -2
2x - 4 = -2
2x = 2
x = 1
Answer:
x = 1
Step-by-step explanation:
2(x - 2) = -2
Solve for x
Divide each side by 2
2/2(x - 2) = -2/2
x-2 = -1
Add 2 to each side
x - 2+2 = -1+2
x = 1
A new car is purchased for 23700 dollars. The value of the car depreciates at 15% per year. If you wanted to know the value of the car after 10 years which function would give you that information?.
The value of the car after 10 years is 4668.9 dollars
What is depreciation?Depreciation is the reduction in the value of an asset or commodity over time and such valued reductions are reflected in the balance sheet at the year ended.
According to the given information:
Prize of the new car purchased P = 23700 dollars
the rate at which the value of a car depreciates R = 15% per year
Now, the value of the car after 10 years could be determined by the formula
Amount = P[tex](1-r)^{t}[/tex]
P = 23700 dollars R = 15% per year t = 10 years
Substituting all the values in the above formula:
Amount = [tex]23700(1-0.15)^{10}[/tex]
= [tex]23700(0.85)^{10}[/tex]
= 23700×0.197
= 4668.9 dollars
The value of the car after 10 years is 4668.9 dollars
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What is the ratio of the number of days in the week that do not begin with the letter "T" to the number of days in the week that do begin with the letter "T"? (1 point)
a
7 over 2
b
2:5
c
2 to 7
d
5 over 2
Answer:
i believe it is b)
the no. of days beginning with T (2)
the no. of days not starting with T (5)
The school cook ordered p packages of hot dog buns for the year-end picnic. Each package contains 8 buns. Write an expression that shows how many hot dog buns were ordered.
The school cook ordered p packages of hot dog buns for the year-end picnic. Each package contains 8 buns. Write an expression that shows how many hot dog buns were ordered.
order = 8p
find area and perimeter of the shape below ***SHOW ALL WORK***
Answer:
Here it is :)
Step-by-step explanation:
if this is incorrect, correct me and explain why so you won’t make this mistake I made when you do this on you own!
A you top your car at a traffic light, a pebble become wedged between the tire tread. When you tart off, the ditance of the pebble from the pavement in relation to the ditance you have traveled can be modeled with a inuoidal function. Aume that the diameter of the wheel i 24 inche. Which equation BEST model thi ituation?
A y = 12co(112x) 12y = 12co( 1 12 x) 12
B y = -12co(112x) 24y = -12co( 1 12 x) 24
C y = -12co(112x) 12y = -12co( 1 12 x) 12
D y = -12co(112x) - 12
The equation that best suits the sinusoidal function model in this situation is the option:
(C) y = -12cos(1/12x)+ 12.
What is the sinusoidal funtion?
A sine-based function is one that smoothly oscillates between high and low values on a periodic basis. This type of function is known as a sinusoidal function. The cosine function, which is merely a horizontal shift of the sine function, can also be used as the foundation for sinusoidal functions.
A sine wave, also known as a sinusoidal wave or simply a sinusoid, is a mathematical curve that can be described in terms of the sine trigonometric function, whose graph it is. It is a particular kind of smooth periodic function and continuous wave.
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What kind of line is used when the inequality symbol is ≥ or ≤?.
The kind of line is used when the inequality symbol is ≥ or ≤ is solid line
If the original inequality is ≤ or ≥, the boundary line is drawn as a solid line, since the points on the line will make the original inequality true.
The kind of line is used when the inequality symbol is ≥ or ≤ is solid line
But in case of < or > symbol, the line used is dotted line.
A solution of an inequality is a number which when substituted for the variable makes the inequality a true statement.
Therefore, The kind of line is used when the inequality symbol is ≥ or ≤ is solid line
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using the gcf you found in part b, rewrite 56+96 as two factors. one factor is the gcf and the other is the sum of two numbers that do not have a common factor. show your work. (4 points)
If the one factor is the gcf and the other is the sum of two numbers that do not have a common factor, then the expression will be 8(7 + 12)
The expression is given by
56 + 96
First we have to find the GCF of the numbers
Prime factorization
56 = 2×2×2×7
96 = 2×2×2×2×2×3
The GCF(56, 96) = 8
Write the expression using the GCF
56 + 96 = 8(7) + 8(12)
Here we have to apply the distributive property
AB + AC = A(B + C)
Then,
8(7) + 8(12) = 8 (7 + 12)
Hence, if the one factor is the gcf and the other is the sum of two numbers that do not have a common factor, then the expression will be 8(7 + 12)
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