Is the function [tex]f(x)=\sqrt{x}[/tex] differentiable at x=0 and continuous over R?
Answer: No
Explanation:
Apply the derivative
[tex]f(x) = \sqrt{x}\\\\f(x) = x^{1/2}\\\\f'(x) = (1/2)x^{-1/2}\\\\f'(x) = \frac{1}{2x^{1/2}}\\\\f'(x) = \frac{1}{2\sqrt{x}}\\\\[/tex]
Though we run into a problem since f ' (0) is undefined, due to the zero in the denominator.
Therefore, f(x) is not differentiable at x = 0.
The function is continuous, but only on the interval [tex]x \ge 0[/tex] and not over the entire set of real numbers R.
b. calculate the probability that 30% or more of the sample will be living in poverty. assume the sample is collected in such a way that the conditions for using the clt are met.
0.0 65 is the probability that 30% or more of the sample will be living in poverty.
What is an probability in statistics?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.P(P ≥ 0.34 ) = P ( [tex]\frac{p' - p}{\sqrt{p( 1- p )/n} }[/tex] ≥ [tex]{\frac{0.34 - 0.30}{\sqrt{\frac{0.30 ( 1- 0.30)}{300} } } }[/tex]
= P ( 2 ≥ 1.5119)
= 0.0653
= 0.0 65
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The area A of a rectangle with dimensions 4x and 5 is described with the inequality 100 ≤ A ≤ 1,000.
Select the compound inequality for the area written in terms of x.
OA. 100 ≤ 10+ 8x ≤ 1,000
OB. 100 ≤ 18x ≤ 1,000
O C. 100 ≤ 9x ≤ 1,000
OD 100 ≤ 20x ≤ 1,000
The compound inequality for the area written in terms of x is 100 ≤ 20x ≤ 1,000.
We know that, the area of rectangle is given by:
Area = Length × Breadth
Now, we will substitute the values of length as 4x and breadth as 5 in the formula:
= 4x × 5
= 20x
Now. we will substitute this value in the inequality 100 ≤ A ≤ 1,000 to get the compound inequality:
100 ≤ 20 x ≤ 1,000.
Therefore, the compound inequality for the area written in terms of x is 100 ≤ 20x ≤ 1,000.
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Write the formula for the volume of a square prism, V= 1/3 s^2h, in terms of h. Then find the height h of a square prism with volume V=60cm^3 and side length s=6 cm.
The formula in terms of h is h = 3V/s^2 and the value of h is 5
How to write the formula in terms of h?The equation is given as
V = 1/3s^2h
Divide both sides of the equation by 1/3s^2
So, we have
h = 3V/s^2
The given parameters are
V = 60 and s = 6
So, we have:
h = 3 * 60/6^2
Evaluate
h = 5
Hence, the formula in terms of h is h = 3V/s^2 and the value of h is 5
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What is the polynomial regression?
In order to transform linear regression into polynomial regression, certain polynomial terms are added to it due to the non-linear relationship between the dependent and independent variables.
Let's say we have independent data X and dependent data Y. In the preprocessing stage, we turn the input variables into polynomial terms to some extent before feeding the data to a mode.
As a specific example of multiple linear regression, polynomial regression is a type of linear regression that estimates the connection as an nth degree polynomial. The performance can also be negatively impacted by the existence of one or two outliers since Polynomial Regression is sensitive to outliers.
The connection between the dependent and independent variables is best approximated by polynomial. It may be used for a wide range of functions. In general, polynomial suits a large range of curvature.
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4) Sara took a ferry to a nearby island that lasted for 5 days. Although she forgot to check the date when she departed, during the trip she heard someone say the date was August 14". When she arrived on the island, a native told Sara it was August 16th. What date did Sara start her trip?
(2a^-5)(-5a^9)
simplify the expression. show your work and justify each step.
Step-by-step explanation:
[tex] = (2 {a}^{ - 5} ) \times ( - 5 {a}^{9} )[/tex]
[tex] = (2 \times ( - 5)) {a}^{ - 5 + 9} [/tex]
[tex] = - 10 {a}^{4} [/tex]
X-6
=
Solve:
4(x-8) = 28
Answer: 34
Step-by-step explanation:
If there are 52 weeks in a year, how many more hours does a squirrel sleep in a year than a rabbit?
The squirrel sleeps 2548 hours more than the rabbit.
Difference of the numbers
Difference of the numbers means the result of subtracting one number from another.
Given,
If there are 52 weeks in a year,
Then we need to find how many more hours does a squirrel sleep in a year than a rabbit.
First, we have to find the sleeping pattern of squirrel and rabbit.
A squirrel spends up to 60% of its day asleep, which means that an average squirrel sleeps for almost 15 hours each day.
Similarly, the rabbits are sleep six to eight hours each day.
So for one day,
Rabbit = 8 hours per day
Squirrel = 15 hours per day.
Then the sleeping hours for one week is
Rabbit = 8 x 7 = 56 hours
Squirrel = 15 x 7 = 105 hours
So, for 52 weeks, they spend
Rabbit = 56 x 52 = 2912
Squirrel = 105 x 52 = 5460
So, the difference is
=> 5460 - 2912
=> 2548
Therefore, the squirrel sleeps 2548 hours more than the rabbit.
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solve y= 4x + rz + 6 for x
Step-by-step explanation:
y=4x+rx+6
y-6=4x+rxy−6=4x+rx Subtract \ 6 \ from \ both \ sidesSubtract 6 from both sides
y-6=x(4+r)y−6=x(4+r) Factor \ out \ the \ common \ term \ xFactor out the common term x
\dfrac{y-6}{4+r} =x
4+r
y−6
=x Divide \ both \ sides \ by \ 4+rDivide both sides by 4+r
What is 10 times as much as 30
Solve the recurrence relation: t(n) = 3t(n-1) 1, with initial condition of t(0) = 1
A linear recurrence relation is a function or sequence in which each term is a linear combination of the terms that came before it.
The recurrence relation exists [tex]$T(n)=\Theta\left(3^n\right)$[/tex].
What is meant by "recurrence relation"?Recurrence relations are used to simplify complex problems by reducing them to an iterative process based on simpler versions of the problem.
Using the substitution method, we find out that
[tex]T(n) &=n+3 T(n-1) \\[/tex]
[tex]&=n+3(n-1)+3^2 T(n-2) \\[/tex]
[tex]&=n+3(n-1)+3^2(n-2)+3^3 T(n-3) \\[/tex]
[tex]&=\cdots \\[/tex]
[tex]&=n+3(n-1)+3^2(n-2)+\cdots+3^{n-1}(n-(n-1))+3^n T(0) \\[/tex]
simplifying the above equation, we get
[tex]$&=\frac{3^{n+1}-2 n-3}{4}+3^n T(0) \\[/tex]
[tex]&=\Theta\left(3^n\right)[/tex]
Even without doing the full calculation it is not hard to check that [tex]$T(n) \geq 3^{n-1}+3^n T(0)$[/tex], and so [tex]$T(n)=\Omega\left(3^n\right)$[/tex].
A cheap way to obtain the corresponding upper bound is by considering
[tex]$S(n)=T(n) / 3^n$[/tex], which satisfies the recurrence relation
[tex]$S(n)=S(n-1)+n / 3^n$[/tex].
Repeated substitution then gives
[tex]$\frac{T(n)}{3^n}=\sum_{m=1}^n \frac{m}{3^m}+T(0)[/tex]
Since the infinite series [tex]$\sum_{m=1}^{\infty} \frac{m}{3^m}$[/tex] converges, this implies that [tex]$\frac{T(n)}{3^n}=\Theta(1)$[/tex] and so [tex]$T(n)=\Theta\left(3^n\right)$[/tex]
Therefore, the recurrence relation exists [tex]$T(n)=\Theta\left(3^n\right)$[/tex].
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titanium has a density of 4.5g/cm find the volume of a 90g sample
PLEASE HELP ME
Answer:
20cm^3
Step-by-step explanation:
Divide 90 by 4.5.
90/4.5 = 20
We can multiply the density ratio by this quotient in order to find the volume of a sample 20x the size of the ratio's sample.
(4.5 x 20)/(1cm^3 x 20)
90g/20cm^3
In this step, let's identify the clues provided in the questions. We have:
Mass of sample: 90 gramsDensity of sample: 4.5 g/cm³To find: The volume of titaniumSince we know the mass and density of titanium, we can apply the density formula to determine the volume of titanium.
Footnote: I have included the formula in case if you need to know it.
[tex]\boxed{\text{Density} = \frac{\text{Mass (Grams)}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]
Step-2) Substituting the given clues into the Density formulaTo work out the volume of the titanium, we need to substitute the given clues from the question, into the formula. We have:
[tex]\text{Density} = \dfrac{\text{Mass (Grams)}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]
When we substitute the mass and the density of titanium, we have:
[tex]4.5 \ \text{g/cm}^{3}} = \dfrac{\text{90 grams}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]
Step-3) Simplify and solve for volumeFinally, let's simplify the equation.
[tex]4.5 \ \text{g/cm}^{3}} = \dfrac{\text{90 grams}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]
[tex]1 \ \text{g/cm}^{3}} = \dfrac{\text{20 grams}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]
[tex]\text{Volume (cm}^{3}) = \dfrac{\text{20 grams}}{\text{1 g/cm} ^{3} }[/tex]
[tex]\text{Volume (cm}^{3}) = \dfrac{\text{20 grams}}{\text{1 g/cm} ^{3} } = \dfrac{20 \ \text{grams} \ \times 1 \ \text{cm}^{3} }{1 \ \text{grams}} = \boxed{20 \ \text{cm}^{3}}[/tex]
Therefore, the volume of titanium is 20 cm³.
Your friend
participates in a 3.1-mile race. She
walks for 1.4 miles of the race and runs
the rest. About how many miles does
your friend run
1.7 miles, just do the total amount of what can be considered distance, then minus what she walked, resulting in the answer to be the amount of time ran.
(3x5x7) (1/3 + 1/5 -1/7)
Answer:
41
Step-by-step explanation:
(3*5*7)((1)/(3) +( 1)/(5) -(1)/(7))
When you simplify this, the answer is 41.
Answer: 41
Step-by-step explanation:
Find the volume of the solid generated by revolving the region r bounded by y=e^-2x, y=0, x=0, x=ln9
The volume of the solid generated by revolving the region R bounded by
y = [tex]e^{-2x}[/tex], y = 0, x = 0, x = ln 9 around x-axis = 0.25 cubic units
Given the region R bounded by y = [tex]e^{-2x}[/tex], y = 0, x = 0, x = ln 9.
We will find the volume of the solid obtained by revolving this region around the x-axis through disc integration method.
The disc integration method is used to find the volume of a solid obtained by revolving a region around an axis parallel to x-axis.
Then, volume, V = [tex]\int\limits^0_{ln9} {y^2} \, dx[/tex]
= [tex]\int\limits^0_{ln9} {(e^{-2x})^2} \, dx[/tex]
= [tex]\int\limits^0_{ln9} {e^{-4x}} \, dx[/tex]
= [tex]\frac{e^{-4x}}{-4} |_{x=0\ to \ x=ln9}[/tex]
= [tex]\frac{e^{-4 ln9}}{-4} +\frac{1}{4}[/tex]
= [tex]\frac{9^{-4}+1}{4}[/tex] ≈ 0.25 cubic units
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An 8ft length of 4 inch wide crown molding costs $14. how much will it cost to buy 40ft of crown molding?
It would cost $70 to buy 40 ft of crown molding.
What is cost explain?
Cost is the amount of money spent by a business to produce or create goods or services. It excludes the profit margin markup. Cost is the sum of money spent on making a good or product, as seen from the seller's perspective.8 ft length costs $14
To find the cost of 1 ft length,
Divide through by 8
8ft/8 length costs $14/8
1ft costs $1.75
Now, to find the cost of 40 ft length
1ft costs $1.75
1 ft x 40 would cost $1.75
40 ft would cost $70
Therefore, it would cost $70 to buy 40 ft of crown molding.
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Please help me with the photo below thanks
Answer:
A) -12-4-5
B) X^2-X
Step-by-step explanation:
..
..
Can someone solve it please?
is the point with coordintaes (-2,-9) on the line whose equation is y=4x - 1?
Answer:
Yes
Step-by-step explanation:
If you have a graphing calculator or something similar, that could really help because all you would have to do is plug in the equation and look up the table and it would show that coordinate in there.
Please help me with my math
Three consecutive even integers such that the sum of the smallest integer and twice the middle integer is 20 more than the largest integer. What is the largest integer?
14 is the largest integer.
Let x, x+2 & x+4 be the 3 integers.
x + 2 (x+2)= (x+4)+20
x + 2x + 4 = x + 4 + 20
3x + 4 = x + 24
3x - x = 24 - 4
2x = 20
x = 20/2
x=10 for the smallest integer.
10 + 2 = 12 for the middle integer.
10 + 4 = 14 for the largest integer.
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Melissa bought some books. She spent a total of $58 after a discount of $8 off of her total purchase. Each book cost $6. How many books did she buy?
|2x+2| =< 0
If the solution set is”null” also known as the empty set or no solution. Explain why
=========================================================
Explanation:
The output of an absolute value is never negative.
The result of |2x+2| can never be negative, so we will have no solutions for the portion |2x+2| < 0
There will be one solution for |2x+2| = 0 as shown in the steps below
|2x+2| = 0
2x+2 = 0
2x = -2
x = -2/2
x = -1
------------------
Check:
|2x+2| ≤ 0
|2(-1)+2| ≤ 0
|-2+2| ≤ 0
|0| ≤ 0
0 ≤ 0
We get a true statement at the end to fully confirm the single solution of x = -1
Calculate the 95onfidence interval for the true population mean based on a sample with =225, =8.5, and =45. function
The true population mean is (222.52, 227.48) with a 95% confidence interval.
What is the critical factor?The critical factor for a 90% confidence interval for the true population mean is given by;
Critical factor = (x-μ)/(s/√n)
where, x = sample mean repair cost
s = standard deviation of a sample
n = sample of stereos
μ = critical value
⇒ P(-1.96< (x-μ)/(s/√n) < 1.96) = 0.95
⇒ P(-1.96×(s/√n) < (x-μ) < 1.96×(s/√n)) = 0.95
⇒ P(x - 1.96×(s/√n) < μ < x + 1.96×(s/√n)) = 0.95
95% confidence interval for
⇒ μ = (x - 1.96×(s/√n) , x + 1.96×(s/√n))
Here, x = 225, s = 8.5, and n = 45
⇒ μ = (225- 1.96×(10.81/√13) , 225+ 1.96×(10.81/√13))
⇒ μ = (222.52, 227.48)
Hence, the true population mean is (222.52, 227.48) with a 95% confidence interval.
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The question seems to be incomplete the correct question would be
Calculate the 95% confidence interval for the true population mean based on a sample with x=225, s=8.5, and n=45.
Dan and David are marking exam papers. Each set takes Dan 35 minutes and David 1 hour. Express the times Dan and David take as a ratio.
Give your answer in its simplest form
Answer:
35:1
Step-by-step explanation:
Answer:
7 : 12
Step-by-step explanation:
the times must be of the same measure.
1 hour = 60 minutes , then
Dan : David = 35 : 60 = 7 : 12 ← in simplest form
Your hourly wage is $10.05 per hr when you work during the day and $12.01 per hr when you work the night shift .what is your gross pay for one week if you worked 24 hrs at night and 16 hrs during the day.
The gross income over the whole week upon working during the day and at night is; $449.04.
What is the gross pay for one week if you worked 24 hrs at night and 16 hrs during the day?Since, the pay rates during the day and night according to the task content are; $10.05 per hour and $12.01 per hr respectively.
It then means that the total gross total income can be calculated as follows;
(10.05 × 16) + (12.01 × 24)
= 160.8 + 288.24
= $449.04.
Therefore, the gross income over the whole week upon working during the day and at night is; $449.04.
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Suppose when you study 4 hours for an exan, your mark is 80 percent. and if you study for an extra hour, your mark is 85 percernt. the marginal benefir from studying one more hour is:_________
The marginal benefit from studying one extra hour is 5 percent.
What is marginal benefit?The maximum sum of money a consumer will spend on an additional commodity or service is known as the marginal benefit. As spending rises, customer contentment tends to decline.Now,
Given:
Marks scored on studying 4 hours = 80 percentMarks scored on studying 1 hour extra = 85 percentTo find: Marginal benefit on studying one hour extra.
Finding:
Now, marks scored on studying 4 hours is 80 percent and 5 hours is 85 percent.
Thus, the extra percentage that is scored is because of the 1 hour of extra studying.
The extra percentage = marginal benefit of studying extra = 85 - 80 = 5 percent.
Hence, the marginal benefit from studying one extra hour is 5 percent.
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The kitchen wall is a rectangle measuring 7m by 2m.
Each tile is 50cm by 50cm. How many tiles is needed?
Critique Reasoning RT bisects ZQRS. Bailey is
solving for m/QRS when m/QRS = (5x - 5)° and
m/QRT = (2x)°. His work is shown. Describe and
correct Bailey's error in solving for x.
Any 1 of the following transformations will work. There are others that are also possible.
translation up 4 units, followed by rotation CCW by 90°.
rotation CCW by 90°, followed by translation left 4 units.
rotation CCW 90° about the center (-2, -2).
Step-by-step explanation:
The order of vertices ABC is clockwise, as is the order of vertices A'B'C'. Thus, if reflection is involved, there are two (or some other even number of) reflections.
The orientation of line CA is to the east. The orientation of line C'A' is to the north, so the figure has been rotated 90° CCW. In general, such rotation can be accomplished by a single transformation about a suitably chosen center. Here, we're told there is a sequence of transformations involved, so a single rotation is probably not of interest.
If we rotate the figure 90° CCW, we find it ends up 4 units east of the final position. So, one possible transformation is 90° CCW + translation left 4 units.
If we rotate the final figure 90° CW, we find it ends up 4 units north of the starting position. So, another possible transformation is translation up 4 units + rotation 90° CCW.
Of course, rotation 90° CCW in either case is the same as rotation 270° CW.
_____
Answer:
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation i2 = −1; every complex number can be expressed in the form a + bi, where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes. For the complex number a + bi, a is called the real part and b is called the imaginary part. The set of complex numbers is denoted by either of the symbols {\displaystyle \mathbb {C} }\mathbb {C} or C. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world.[1][a]
Step-by-step explanation: