Answer:
D
Step-by-step explanation:
x²-4x-12≤0
x²-6x+2x-12≤0
x(x-6)+2(x-6)≤0
(x-6)(x+2)≤0
x=6,-2
∴ value of x lies between -2 & 6
Find f. f ″(x) = x^−2, x > 0, f(1) = 0, f(6) = 0
If you do in fact mean [tex]f(1)=f(6)=0[/tex] (as opposed to one of these being the derivative of [tex]f[/tex] at some point), then integrating twice gives
[tex]f''(x) = -\dfrac1{x^2}[/tex]
[tex]f'(x) = \displaystyle -\int \frac{dx}{x^2} = \frac1x + C_1[/tex]
[tex]f(x) = \displaystyle \int \left(\frac1x + C_1\right) \, dx = \ln|x| + C_1x + C_2[/tex]
From the initial conditions, we find
[tex]f(1) = \ln|1| + C_1 + C_2 = 0 \implies C_1 + C_2 = 0[/tex]
[tex]f(6) = \ln|6| + 6C_1 + C_2 = 0 \implies 6C_1 + C_2 = -\ln(6)[/tex]
Eliminating [tex]C_2[/tex], we get
[tex](C_1 + C_2) - (6C_1 + C_2) = 0 - (-\ln(6))[/tex]
[tex]-5C_1 = \ln(6)[/tex]
[tex]C_1 = -\dfrac{\ln(6)}5 = -\ln\left(\sqrt[5]{6}\right) \implies C_2 = \ln\left(\sqrt[5]{6}\right)[/tex]
Then
[tex]\boxed{f(x) = \ln|x| - \ln\left(\sqrt[5]{6}\right)\,x + \ln\left(\sqrt[5]{6}\right)}[/tex]
2(−6c+3)+4c2, left parenthesis, minus, 6, c, plus, 3, right parenthesis, plus, 4, c
Answer:
[tex]-8c+6[/tex]
Step-by-step explanation:
[tex]2(-6c+3)+4c=-12c+6+4c=\boxed{-8c+6}[/tex]
Answer:
-8c + 6 and 3(-4c+2) + 4c
Step-by-step explanation:
khan
ASAP help me with this question
Answer:
SAS and SSA
Kindly award branliest
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Congruency refers to the criteria of making two identical shapes that can hide each other properly when overlapped.
The criterias that guarantee congruence are :
SSSSASASAAAS[tex] \qquad \large \sf {Conclusion} : [/tex]
Correct options are : b, c, d, eFind the measures of angles x and y
How many pairs of parallel faces does this shape have?
Answer: one
Step-by-step explanation:
parallel faces are the ones that are opposite to each other.
Answer:
one
Step-by-step explanation:
there is only one pair of parallel faces.
(Subtracting rational coefficients-Mixed numbers)
Simplify by combining like terms:
1/3k - 8 3/4k
[?] ?
_k
?
Answer:
-8 5/12
Step-by-step explanation:
A line with slope
-1/3
passes through the point (-4, 4).
Find the coordinates of another point on the line.
Answer:
(0, 8/3) = y-intercept
Step-by-step explanation:
I chose to find the y-intercept since it is easy to find with the given information.
The equation for a line is y = mx + b
To find the y-intercept, we must plug in the info we have and solve for b:
4 = -1/3 (-4) + b
4 = -4/3 + b
8/3 = b
To find a point on the line, you also could have added -1 to 4 and 3 to -4 since slope means rise/run or change in y/change in x:
(y - 1) / (x + 3) = (4 - 1) / (-4 + 3) = (3, -1) (flip since it's the y and x coordinate) = (-1, 3)
Solve for x
(please write work)
Answer:
x = -9
Step-by-step explanation:
12 + 2x + 24 = 27 + x
(12 + 24) + 2x = 27 + x
36 + 2x = 27 + x
subtract 27 from both sides
36-27 + 2x = 27-27 + x
9 + 2x = x
subtract x from both sides
9 + x = 0
subtract 9 from both sides
x = -9
(the steps could've been faster but that shows the most work)
check:
12 + 2(-9) + 24 = 27 + (-9)
36 - 18 = 18
18 = 18
True!
so -9 is correct
Answer:
Step-by-step explanation:
To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.
a population of bobcats increase by 5% per year if the population is currently 40 in how many years will the population reach 80 round your answer to the nearest tenth. The population will reach 80 in about _____years
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & 80\\ P=\textit{initial amount}\dotfill &40\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 80=40(1 + 0.05)^{t}\implies \cfrac{80}{40}=1.05^t\implies 2=1.05^t\implies \log(2)=\log(1.05^t) \\\\\\ \log(2)=t\log(1.05)\implies \cfrac{\log(2)}{\log(1.05)}=t\implies 14.2\approx t[/tex]
Numbers from 1 to 50.
Find the probability of choosing
numbers with last digit 6.
0.1 or 10%
Step-by-step explanation:The numbers between 1 and 50 that end in 6 are as follows:
6, 16, 26, 36, 46
There are therefore 5 numbers between 1 and 50 that end in 6.
This means there are 5 out of 50, or 5/50.
5/50 is 0.1 as a decimal, or 10% in percentage form.
A circle has a circumference of 50.24 units.
What is the radius of the circle?
Use 3.14 for π and enter your answer as a decimal.
units
Answer: 8 units
Step-by-step explanation:
Write an inequality for the following statement, 1 is greater than x
The inequality suitable if 1 is greater than x is x<1.
Given that 1 is greater than x.
We are required to form an inequality which shows that 1 is greater than x.
Inequality is like an equation showing relationship between two or more variables.It is mostly not found in equal to form.
It shows the range of quantities.
When 1 is greater than x means the greater than sign will be used for 1 not x and the inequality will be as under:
x<1
We have not used equal to sign because 1 is greater than x not equal to x.
Hence the inequality suitable if 1 is greater than x is x<1.
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Difference of Squares gives which complex factors for the expression +3?
A. (x+3i)(x-3i)
B. (x-i-√3)(x-i√3)
C. (x+3i)^2(x-3i)²
D. (x+i√3)(x-i√3)
The difference of squares is:
(x+i√3)(x-i√3)
So the correct option is the last one, D.
Which expression gives x^2 + 3?For a complex number:
[tex]Z = a + b*i[/tex]
We define the complex conjugate of Z as:
[tex]Z' = a - b*i[/tex]
Such that the product between the complex number and its complex conjugate gives:
[tex]Z*Z' = a^2 + b^2[/tex]
Now, of you look at option D, you can see we have the product of a number and its conjugate, then we can write the product and use the above rule to get:
[tex](x + i\sqrt{3} )*(x - i\sqrt{3} ) = x^2 + (\sqrt{3} )^2 = x^2 + 3[/tex]
Which is what we wanted to get, so that is the correct option.
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Suppose a stock qualifies as having moderate risk if the standard deviation of its monthly rate of return is less
than 10%. A stock rating agency randomly selects 36 months and decides the rate of return for a specific fund.
The standard deviation of the rate of return is computed to be 4.95%. Is there sufficient evidence to conclude
that the fund has moderate risk at the α=0.05 level of significance? A standard probability plot shows that the
monthly rates of return are typically distributed.
Test the claim using a hypothesis test.
What are the null and alternative hypotheses for the hypothesis test?
What is the conclusion based on the hypothesis test?
The conclusion of the Hypothesis Conclusion is; that there is sufficient evidence to support the claim that the fund has moderate risk.
How to test hypothesis claim?
We are given;
Sample size; n = 36
Population standard deviation; σ₀ = 10
Sample standard deviation; s = 4.95
Significance level; α = 0.05
Claim: Standard deviation less than 10
The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis needs to contain an equality and the value mentioned in the claim. If the claim is the null hypothesis, then the alternative hypothesis states the opposite of each other. Thus;
Null Hypothesis; H₀: σ = 10
Alternative Hypothesis; H₁: σ < 10
Compute the value of the test statistic:
χ2 = [(n - 1)/(σ²)] * s²
χ2 = [(36 - 1)/(10²)] * 4.95²
χ2 = 8.576
The critical value of the left-tailed test is given in the row with df = n - 1 = 36 - 1 = 35 and in the column with 1 − α = 0.95 of the chi-square distribution table online, we have;
χ2_{1 - α} = 21.77
The rejection region then contains all values smaller than 21.77
If the test statistic is in the rejection region, then reject the null hypothesis:
8.576 < 13.848
Thus, we will reject H₀ and conclude that there is sufficient evidence to support the claim that the fund has moderate risk.
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which table of ordered pairs represents a proportional relationship?
Answer:
B
Step-by-step explanation:
Every (x,y) pair is equal to each other, thus making them proportional :)
Underwood Company is preparing its annual profit plan. As part of its analysis of the profitability of individual products, the controller estimates the amount of manufacturing overhead that should be assigned to each of the two product lines from the information given below. Wall Mirrors Specialty Windows Total units produced 30 30 Total number of material moves 7 18 Direct labor hours per unit 145 145 Budgeted material-handling costs are $30,000. The material-handling cost per wall mirror under activity-based costing is:
The material-handling cost per wall mirror under activity-based costing is $280
What is activity-based costing?
Activity-based costing involves absorbing overheads based on cost drivers which directly impact the incurrence of the overhead, in this case, material moves determine the amount of material-handling costs to be incurred, hence, material-handing overheads would be absorbed into the two products based on material moves, which is the appropriate cost driver.
There 25 materials move in both divisions (i.e. 7+18=25)
Material-handling cost per material move=Budgeted material-handling costs /total material moves
Budgeted material-handling costs =$30,000
Material-handling cost per material move=$30,000/25
Material-handling cost per material move=$1,200
Total material-handing costs for wall mirror=number of material moves for wall mirror*Material-handling cost per material move
Total material-handing costs for wall mirror=7*$120
Total material-handing costs for wall mirror=$8,400
material-handling cost per wall mirror=Total material-handing costs for wall mirror/number of wall mirrors
material-handling cost per wall mirror=$8,400/30
material-handling cost per wall mirror=$280
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Find a formula for the nth term in this arithmetic sequence first term -2 common difference an=
Which rule describes the relationship between the x- and y- coordinates on the following graph? Choose 1 answer:
(Choice A)
A
y
=
2
x
y=2xy, equals, 2, x
(Choice B)
B
y
=
x
+
2
y=x+2
Answer:
A
Step-by-step explanation:
given the points
(0, 0 ) , (2, 4 ) , (4, 8 )
note that the y- coordinate is twice the value of the x- coordinate , so
y = 2x
Hey guys I need some help with #11 so if anyone could help that would be great THANK YOU!!
Find the exact value of x.
X =
11
X
00
8
Given the following function, find f(-5), f(0), and f(3).
f(x) = x^2+5
Answer:
f(-5) = 30
f(0) = 5
f(3) = 14
Step-by-step explanation:
=> f(x) = x²+5
for , f(-5) = (-5)² +5
=> 25 +5
=> 30
for , f(0) = (0)² +5
=> 5
for , f(3) = (3)² + 5
=> 9 + 5
=> 14
Donna has a $300 loan through the bank she is charged a simple rate The total interest she paid on the loan was $63 As a percentage what was the annual interest rate on her loan
Answer:
21%
Step-by-step explanation:
($63*100%) / $300 = 21%
27. Identify the domain of the set (6,2), (-1,-5), (4,4), (9, 2) and tell if the relation is a function.
O {-1, 4, 6, 9); not a function
O {-5, 2, 4}; a function
O {-1,4,6,9}; a function
O {-5, 2, 4); not a function
Answer:
the third one
Step-by-step explanation:
it is function that contain four domain
Choose the number (X) that should come next in this series (1, 2, 6, 15, X, 56, 92)
Answer:
31
Step-by-step explanation:
The numbers in the sequence increase by (n+1)^2. So the sequence is (1, 1+1^2 (which is 2), 2+2^2 , 6+3^2, 15+4^2, 31+5^2, 56+6^2) and the fifth term of that sequence is 15+4^2, which is 31
The unknown number(x) in the series is 31.
The given series 1, 2, 6, 15, x, 56, 92.
We need to find the value of x.
What is a series?In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, and mathematical analysis.
The numbers in the series increase by (n+1)².
So the sequence is 1, 1+1² (which is 2), 2+2², 6+3², 15+4², 31+5², 56+6² and the fifth term of that sequence is x=15+4²=31.
Therefore, the unknown number(x) in the series is 31.
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Which of these tables represent a function
Answer: W
Step-by-step explanation: I remember learning this in school> you can tell it’s a function because no numbers repeat themselves etc .
Suppose follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of so that the following is true.
Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
Answer:
c = 2.25
Step-by-step explanation:
The normal distribution function is symmetrical, so the area not in the central zone is split evenly between the lower and upper tails.
SolutionWe can find -c from ...
P(x < -c) = (1 - 0.9756)/2 . . . . . the area in the lower tail
The calculator tells us -c = -2.25.
c = 2.25
DIRE NEED OF HELP, pleaseee help
(not a lot of points sorry)
Answer:
C. Subtract 4 from both sides.
Step-by-step explanation:
You need the equation in the form x² + ax + b = 0 to then either try factoring or use the quadratic formula.
In order to achieve that, you need to first:
Subtract 4 from both sides.
A rectangular box is designed to have a square base and an open top. The volume is to be 500in.3 What is the minimum surface area that such a box can have?
The minimum surface area that such a box can have is 380 square
How to determine the minimum surface area such a box can have?Represent the base length with x and the bwith h.
So, the volume is
V = x^2h
This gives
x^2h = 500
Make h the subject
h = 500/x^2
The surface area is
S = 2(x^2 + 2xh)
Expand
S = 2x^2 + 4xh
Substitute h = 500/x^2
S = 2x^2 + 4x * 500/x^2
Evaluate
S = 2x^2 + 2000/x
Differentiate
S' = 4x - 2000/x^2
Set the equation to 0
4x - 2000/x^2 = 0
Multiply through by x^2
4x^3 - 2000 = 0
This gives
4x^3= 2000
Divide by 4
x^3 = 500
Take the cube root
x = 7.94
Substitute x = 7.94 in S = 2x^2 + 2000/x
S = 2 * 7.94^2 + 2000/7.94
Evaluate
S = 380
Hence, the minimum surface area that such a box can have is 380 square
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On a map, 3 inches represents 50 miles. Which proportion can be used to find the actual distance represented by 5 inches on the map?
StartFraction 3 over 50 EndFraction = StartFraction x over 5 EndFraction
StartFraction 3 over 50 EndFraction = StartFraction 5 over x EndFraction
StartFraction 3 over x EndFraction = StartFraction 50 over 5 EndFraction
StartFraction x over 3 EndFraction = StartFraction 50 over 5 EndFraction
The correct proportion that can be used to find the actual distance represented by 5 inches on the map is start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.
Given that 3 inches on a map represents 50 miles.
We are told to find the proportion which can be used to represent 5 inches.
Multiplication is basically finding the product of two numbers but it can be used to convert the units also.
If 3 inches represents 50 miles then,
1 mile=50/3
Multiply both sides by 5.
5 miles=5*50/3
If we see the options then we will get that the most appropriate and correct option which represents 5 inches is that start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.
Hence the correct proportion that can be used to find the actual distance represented by 5 inches on the map is start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.
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Answer:
B
Step-by-step explanation:
3/50 = 5/x
Ten students from a school appear in one or more subjects for an inter school quiz competition as shown in the table given below. General Knowledge Math Science Acel Barek Carlin Acton Bay Acton Anael Max Anael Max Kai Kai Carl Anael Dario Dario Carlin Barek Let G represents the set of students appearing for General Knowledge, M represents the set of students appearing for Math, and S represents the set of students appearing for Science. Find G n M and G u S .
The computation shows that:
G n M = Anael and Max
G u S = Acel, Action, Anael, Max, Carl, Dario, Catlin, Kai, and Barek.
How to illustrate the information?From the information, ten students from a school appear in one or more subjects for an inter school quiz competition as shown in the table.
The subjects include general Knowledge Math Science.
Therefore, G represents the set of students appearing for General Knowledge, M represents the set of students appearing for Math, and S represents the set of students appearing for Science. The intersection is illustrated above.
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