The combination of 6 are total samples (without replacement) of size five can be selected from this population
What is permutation and combination?
Combination and permutation are two alternative strategies to divide up a collection of elements into subsets in mathematics. The components of the subset may be arranged in any order when combined. The subset's components are listed in a permutation in a certain order.ⁿCr = n!/( n-r)! r!
r = 5
total samples
⁶C₅ = 6!/(6-5)!5!
= 6!/1!5!
= 6 * 5!/1*5!
= 6
Hence, there are 6 ways
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For the functions f(x) = 3x - 4 and g(x) = x - 41, find the value of ƒ(4) - 2g(3)
For the functions f(x) = 3x - 4 and g(x) = x - 41,
ƒ(4) - 2g(3) = 6How to solve the expressionInformation given in the question
functions f(x) = 3x - 4
functions g(x) = x - 41
ƒ(4) - 2g(3) = ?
the expression ƒ(4) - 2g(3) is solved by substituting x = 4 in f(x)
f(4) = 3 * 4 - 4
f(4) = 12 - 4
f(4) = 8
and x = 3 in g(x)
2g(3) = 2(3 - 4)
2g(3) = 2 *-1
2g(3) = -2
substituting ƒ(4) - 2g(3)
= 8 - 2
= 6
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Do a first then Do b by the way OMG this is urgent
Answer:
The answer for questions A is 2 over 8
Step-by-step explanation:
The robot can complete 7 tasks is one 2 over 5 hour so you multipy 7 by 2 over 5 because then you get 2 over 8
If m/DAB = 74°, m/CAD = 37°, and BC= 9.2,
what is the value of CD?
Answer:
If RU = 16, UT = 20, and SR = 16, what is the perimeter of △SUT? S U
If SV = 38, SU = 26, and the perimeter of △SUV is 102, what is the value of RU?
If S‾V ≅ U‾V , SR = 4x − 1 and RU = x + 8, what is the value of SU? V
How does the solution to a system of equations compare to the solution of a system of inequalities?.
A collection of equations with the same variables is known as a system of equations. The only difference is that you're working with inequalities rather than equations in a system of inequalities.
What are inequalities?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
A system of equations has one solution for each variable, whereas a system of inequalities has a range of possible values for each variable.
Set up the equations as follows:
ax + by = c
dx +ey = f
Let the inequitable system exist:
ax + by <c
dx +ey > f
The same technique, such as graphing, substitution, and elimination, can be used to solve both systems.
But there's a difference because:
A system of equations can only have one solution for each variable, whereas a system of inequalities can have any number of solutions for each variable.
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Johnson electronics sells electrical and electronic components through catalogs. Catalogs are updated and printed every year. The variable production cost is $5 per catalog. Data indicate that, on average, each printed catalog generates a profit of $35 from sales (i. E. , $40 revenue). What is the optimal service level for the catalogs printing decision?.
Johnson electronics sells electrical and electronic components through catalogs. Catalogs are updated and printed every year. The variable production cost is $5 per catalog. Data indicate that, on average, each printed catalog generates a profit of $35 from sales.
The optimal order quantity will be 11450.
Let’s use the news vendor model here.
The profit means that if we print less we will incur a certain opportunity loss. This is also known as cost of understocking (Cu) = 35
The production cost is $5 and if the product is not sold, we will incur a cost of (Co) = 5. The fixed cost is incurred either way in a year. As a result we need to consider the critical fractile value
C.F. = Cu/(Cu + Co) = 35/(40) = 0.875
The value of z at 0.875 is 1.15. This means that the optimal order/production will be 8000 + 1.15*3000 = 11450
Hence the answer is, the optimal order quantity will be 11450.
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pls help, correct answer awarded with points
The simplified expression for the given functions f and g is 11-x
What is the value of the function?
The value of the function at a point can be found by substituting the point in the function. This value also depend on the nature of the Function.
We are given a function
f(x) =6-x
Now when we say f(2x) it means the x in the function should be replaced with 2x
Hence the function becomes
f(2x) =6-2x
Similarly
g(x) = (x/3)+8
g(3x-9)= (3x-9/3)+8
g(3x-9)= x-3+8
g(3x-9) = x+5
Now we are asked to add the functions, we simply add the new functions and simplify them
f(2x) + g(3x-9)
=6-2x+x+5
=11-x
Which is the required value
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Answer:
a) 11 - x, b) x = - 12.=========================
Givenf(x) = 6 - x, g(x) = x/3 + 8Part a)Simplify f(2x) + g(3x - 9):
f(2x) + g(3x - 9) = 6 - (2x) + (3x - 9)/3 + 8 = 6 - 2x + x - 3 + 8 = 11 - xPart b)Firstly find the inverse of g(x):
x = g⁻¹(x) /3 + 83x = g⁻¹(x) + 24g⁻¹(x) = 3x - 24Now solve the equation:
g⁻¹(x) = 5x3x - 24 = 5x5x - 3x = - 242x = - 24x = - 12Which equation represents a line passing through the point (8, 9)(8, 9) with a slope of 3?.
The equation represent a line passing through the point (8,9) with a slope of 3 is y= 3x-15.
Linear EquationTo make a linear equation, there is several methods depending on what known:
Given 2 pointsIf you know 2 points, for example point A(x1, y1) and B(x2, y2). Then the formula that can be used is:
[tex]\frac{y-y_{1} }{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Given 1 point and slopeIf one point is known, for example point A(x1,y1) and slope m. Then the formula that can be used is:
[tex]y-y_{1}=m(x-x_1)[/tex]
Given 1 point and other related linear equationsIf there are other linear equations that have certain properties (parallel or perpendicular) to the linear equation to be searched for, then we can first find out the slope of the linear equation. If the gradient of another linear equation is m1 and the gradient of the linear equation to look for is m2
If the two lines are parallel
[tex]m_{2}=m_1[/tex]
If the two lines are perpendicular
[tex]m_2=\frac{-1}{m_1}[/tex]
In the problem, it is known 1 point and slope. Then the formula that can be used is:
[tex]y-y_{1}=m(x-x_1)[/tex]
1 known point is (8,9) and the slope of m is 3. Then substitute it into the formula:
[tex]y-9=3(x-8)\\y-9=3x-24\\y=3x-24+9\\y=3x-15[/tex]
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0.7 divided by 33.3
round answer to 2 decimal places
Answer:
0.02
Step-by-step explanation:
How might I rewrite 125% of 440 is B as a simpler equation?
A) 125(440)=B
B) 1.25 (440) = B
C) 1.25A = 440
Answer:B
Step-by-step explanation:
6q+4-q+5 please answer quickly ik this question may seem easy but I’m not that smart hah
Answer:
5q + 9
Step-by-step explanation:
The Concept in that Question is adding Like-Terms
6q + 4 - q + 5 = ( 6q - q ) + ( 4 + 5 ) = 5q + 9
After a model rocket reached its maximum height, it then took 5. 0 seconds to return to the launch site. What is the approximate maximum height reached by the rocket?.
The maximum height reached by the rocket is 122.5 m.
In this question, given parameters:
time (t) = 5.0 seconds
By applying second equation of motion the maximum height of the model rocket would be,
h = v₀t + 1/2 (gt²)
where, v₀ is the initial velocity
g is acceleration due to gravity
(9 = 9.8 m/s²)
Since initial velocity v₀ = 0 we get an equation,
h = 0 + 1/2 (gt²)
h = 1/2 (9.8 x 5²)
h = 122.5 m
Therefore, the maximum height is 122.5 m.
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I need help solving this equation please show me your work! I will give a brainly
Answer:
n = 4/21
Step-by-step explanation:
[tex]\frac{7}{3} =\frac{4}{9n}[/tex]
==> cross multiply (multiply top of first fraction by bottom of second fraction and top of second fraction by bottom of first fraction)
7 x 9n = 4 x 3
==> simplify
63n = 12
==> divide both sides by 63
n = 12/63
==> simplify fraction
n = 4/21
The function f(x)=5000(0. 98)0. 3x represents the number of white blood cells, per cubic millimeter, in a patient x days after beginning treatment for a virus. What is the average rate of change in white blood cells between days 1 and 5?.
The average rate of change in white blood cells between days 1 and 5 is -29.75 mm³/day.
Given that
The function f(x)=5000(0. 98)0. 3x represents the number of white blood cells.
We need to evaluate this, for this
f ( x ) = 5000 * ( 0.98 ) ^(0.3 x)
f ( 1 ) = 5000 * 0.98^(0.3) = 5000 * 0.99396 = 4,969.788
f ( 5 ) = 5000 * 0.98 ^(5*0.3) = 5000 * 0.98^(1.5) = 5000 * 0.97 = 4,850.753
Average rate of change:
( 4,850.753 - 4,969.788 ) / ( 5 - 1 ) = - 29.75
Hence the answer is The average rate of change in white blood cells between days 1 and 5 is -29.75 mm³/day.
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The locations of student desks are mapped using a coordinate plane where the origin represents the center of the classroom. Maria's desk is located at (1 −1), and Monique's desk is located at (−4, 5). If each unit represents 1 foot, what is the distance from Maria's desk to Monique's desk? square root of 7 feet square root of 14 feet square root of 85 feet square root of 61 feet
The distance from Maria's desk to Monique's desk is √61 feet.
According to the question,
We have the following information:
Maria's desk is located at (1 −1), and Monique's desk is located at (−4, 5). And each unit represents 1 foot.
Now, we know that the following formula is used to find distance between two points:
Distance = [tex]\sqrt{(y2-y1)^{2} +(x2-x1)^{2} }[/tex]
In this case, we have x1 = 1, y1 = -1, x2 = -4 and y2 = 5.
D = [tex]\sqrt{(5+1)^{2} +(-4-1)^{2} }[/tex]
(We have converted -1 of y1 directly to 1 because the multiplication of two negative integers give positive results.)
D = [tex]\sqrt{(6)^{2} +(5)^{2} }[/tex]
D = [tex]\sqrt{36+25}[/tex]
D = [tex]\sqrt{61}[/tex] feet
Hence, the correct option is D (the last one).
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Answer:
The solution to this question is (D) - Square root of (61) feet
Step-by-step explanation:
suppose that for a given least-squares regression, the sum of squares for error is 100 and the sum of squares for regression is 105. find the coefficient of determination.
51.21% is the coefficient of determination.
What does coefficient of determination mean?
A statistical model's ability to predict a result is indicated by the coefficient of determination (R2), a value between 0 and 1. The proportion of variation in the dependent variable that the statistical model predicts can be understood as the R2 value.SST = SSE + SSR
Here, SSE = 100 and SSR = 105
SST = 100+105 = 205
Coefficient of determination , R^2 = 105/205 = 51.21%
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Do You KNOW HOW?
Solve each literal equation for the given variable.
5. y = x + 12; x
The given equation is y = x + 12 and in terms of x is x = y - 12
Define Linear equation
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.
The given expression is ,
y = x + 12
Now, we have to solve for 'x'
so, for that just take constant term right side
y - 12 = x
Next, swap the sides like this
x = y - 12
Hence, the equation in terms of x is x = y - 12.
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It cost the class $15 to make cookies for the
bake sale. How many cookies must they sell at
10¢ each to make a profit?
Answer:
more than 150 cookies
Step-by-step explanation:
Let the number of cookies = x.
Since they sell each cookie at 10 cents. each cookie sells for $0.10.
x number of cookies sell for 0.1x.
To turn a profit, the amount of sales must be greater than the cost.
0.1x > 15
x > 15/0.1
x > 150
Answer: They must sell more than 150 cookies
Answer: 151 cookies
150 cookies = $15 so selling 151 cookies gives a 10 cent profit ($15.10)
An experimenter would like to construct a 99% confidence interval with a width at most 0. 5 for the average resistance of a segment of copper cable of a certain length. If the experimenter knows that the standard deviation of such resistances is 1. 55. How big a sample should the experimenter take from the population? what happens if the standard deviation and the width of the confidence interval are both doubled?.
A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.
In the given question,
The confidence level = 99%
Given width = 0.5
Standard deviation of resistance(\sigma)= 1.55
We have to find a big sample that should the experimenter take from the population and what happens if the standard deviation and the width of the confidence interval are both doubled.
The formula to find the a big sample that should the experimenter take from the population is
Margin of error(ME) [tex]=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}[/tex]
So n [tex]=(z_{\alpha /2}\frac{\sigma}{\text{ME}})^2[/tex]
where n=sample size
We firstly find the value of ME and [tex]z_{\alpha /2}[/tex].
Firstly finding the value of ME.
ME=Width/2
ME=0.5/2
ME=0.25
Now finding the value of [tex]z_{\alpha /2}[/tex].
Te given interval is 99%=99/100=0.99
The value of [tex]\alpha[/tex] =1−0.99
The value of [tex]\alpha[/tex] =0.01
Then the value of [tex]\alpha /2[/tex] = 0.01/2 = 0.005
From the standard table of z
[tex]z_{0.005}[/tex] =2.58
Now putting in the value in formula of sample size.
n=[tex](2.58\times\frac{1.55}{0.25})^2[/tex]
Simplifying
n=(3.999/0.25)^2
n=(15.996)^2
n=255.87
n≈256
Hence, the sample that the experimenter take from the population is 256.
Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.
The new values,
Standard deviation of resistance([tex]\sigma[/tex])= 2×1.55
Standard deviation of resistance([tex]\sigma[/tex])= 3.1
width = 2×0.5
width = 1
Now the value of ME.
ME=1/2
ME=0.5
The z value is remain same.
Now putting in the value in formula of sample size.
n=[tex](2.58\times\frac{3.1}{0.5})^2[/tex]
Simplifying
n=(7.998/0.5[tex])^2[/tex]
n=(15.996[tex])^2[/tex]
n=255.87
n≈256
Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.
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I need help with this as soon as possible
Answer: 763*42 = 32,046
32,046/82 = 390.8048
what is the unit rate of 1/8 and 1/4
The unit rate of 1/8 is 0.125 and the unit rate of 1/4 is 0.25.
What is the unit rate?
A unit rate is the price for one unit of something. This is written as a ratio with a denominator of one. For instance, if you ran 70 yards in 10 seconds, you averaged 7 yards per second. Both ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but only the latter is a unit rate.
For 1/8,
Divide the numerator and denominator by '8', to make the denominator 1.
[tex]=\frac{\frac{1}{8}}{\frac{8}{8}} \\\\\=\frac{0.125}{1} \\=0.125[/tex]
for 1/4,
Divide the numerator and denominator by '4', to make the denominator 1.
[tex]=\frac{\frac{1}{4}}{\frac{4}{4}} \\\\\\\=\frac{0.25}{1} \\\\=0.25[/tex]
Hence, the unit rate of 1/8 is 0.125 and the unit rate of 1/4 is 0.25.
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Which expression is equivalent to -5(b-2)?
-7b
-2(b - 5)
-5b + 10
10b-5
A soda manufacturing plant manufactures 12,000 bottles of soda in an 8 hour shift. The soda produced varies directly with the hours worked.
Which equation can be used to determine the number of bottles produced, b, in terms of the number of hours the manufacturing plant is producing bottles, h?
The Equation used to determine the number of bottles produced in terms of the number of hours the plant is producing bottles is b = 1500h
Number of soda produced in 8 hours = 12000
We know
The number of soda produced varies directly with the hours works
Consider the number of bottle produced = b
Number of hours = h
Then the relationship will be b directly proportional to h
b ∝ h
b = k × h
Where k is the constant
Then substitute the values in the equation and find the value of k
12000 = k × 8
k = 12000/8
k = 1500
The equation will be
b = 1500h
Hence, equation used to determine the number of bottles produced in terms of the number of hours the plant is producing bottles is b = 1500h
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On Monday, the drama club starts a bake sale to earn money for supplies. The equation 3 = -3x + 24 represents that there are 3 remaining treats after a number of days since Monday.
How many complete days have passed when the club has 3 remaining treats?
The complete days have passed when the club has 3 remaining treats will be 7.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the equation 3 = -3x + 24 represents that there are 3 remaining treats after a number of days since Monday.
If the club has 3 remaining treats, we have to find complete days that have passed, which is x in the given equation,
3 = -3x + 24
-3x= 3 -24
-3x= -21
x=21/3
x=7
Thus, the complete days that have passed when the club has 3 remaining treats will be 7.
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4
-3-2-10
Graph of f
2. The graph of the function f is shown in the figure above. The value of lim ƒ(1-x²) is
x-0
(A) 1
(B) 2
(C) 3
(E) does not exist
can somebody help please
Answer:
The lim for f(1-x^2) is 1
Step-by-step explanation:
Lim f(1 - x^2) as x -> 0
break them apart
Lim (1) - lim (x)^2
where the lim of 1 = 1
for the lim of x^2, sub the value of x = 0, so now:
Lim (1-0) = 1
The graph of the function f is shown in the figure above. The value of lim ƒ(1-x²) is 1. Therefore, the correct option is option A.
What is mathematical function?
In mathematics, a function is a phrase, regulation, or statute that establishes the connection between an independent variable and a dependent variable.
In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. The German mathematician Peter Dirichlet initially offered the contemporary definition of function in 1837.
Lim f(1 - x²) as x -> 0
Lim (1) - lim (x)²
where the lim of 1 = 1
for the lim of x², substituting the value of x = 0, so now:
Lim (1-0) = 1
Therefore, the correct option is option A.
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4. In the diagram below, ABC is shown with AC extended through point D. If mzBCD = 6x + 2,
m/BAC = 3x + 15, and mLABC = 2x - 1, what is the value of x?
Answer:
x = 12----------------------------------------------
According to the diagram, angle BCD is exterior angle and angles BAC & ABC are remote interior angles of the triangle ABC.
As we know, the exterior angle is the sum of remote interior angles.
Set this as equation and solve for xm∠BCD = m∠BAC + m∠ABC 6x + 2 = 3x + 15 + 2x - 16x + 2 = 5x + 146x - 5x = 14 - 2x = 12Answer:
x = 12
Step-by-step explanation:
Exterior Angle Theorem
The interior angles of a triangle sum to 180°. Angles on a straight line sum to 180°. Therefore, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.
Given angles:
[tex]\textsf{Exterior angle}: \quad m \angle BCD = 6x+2[/tex][tex]\textsf{Non-adjacent interior angle}: \quad m \angle BAC= 3x+15[/tex][tex]\textsf{Non-adjacent interior angle}: \quad m \angle ABC= 2x-1[/tex]Apply the exterior angle theorem and solve for x:
[tex]\implies m \angle BCD=m \angle BAC+m \angle ABC[/tex]
[tex]\implies 6x+2=3x+15+2x-1[/tex]
[tex]\implies 6x+2=3x+2x+15-1[/tex]
[tex]\implies 6x+2=5x+14[/tex]
[tex]\implies 6x+2-5x=5x+14-5x[/tex]
[tex]\implies x+2=14[/tex]
[tex]\implies x+2-2=14-2[/tex]
[tex]\implies x=12[/tex]
Find the missing length indicated.
Answer:
18 unitsStep-by-step explanation:
Let the missing part be x.
According to triangle proportionality theorem we have:
x/54 = 8/24x/54 = 1/3x = 54/3x = 18I’m confused on how to do this
After 9,075 minutes, both divers will be the same distance from the surface, that is, 181.5 feet.
How to find the time when both divers are the same distance from the surface?To find the distance at which both divers are the same distance from the surface we must try the following mathematical operation:
Diver 1 descends at a rate of 20 feet per minute.
Diver 2 ascends at a rate of 60 feet per minute.
Diver 1 starts from sea level 0.
Diver 2 starts from 726 meters deep.
Accordingly, we must use time as a variable. For example, if diver 1 dives 20 feet every minute, after 9 minutes how deep will he be? We solve this like this:
20 * 9 = 180ftAccording to the above, the diver will be at a depth of 180ft. On the other hand, to find the depth of diver 2 we do the following operation.
60 * 9 = 540726 - 540 = 186ftIn this case, we must modify the time to obtain different depths, until we find the one that places the divers at the same depth. The correct time is 9.075
20 * 9.075 = 181.5ft60 * 9,075 = 544.5726 - 544.5 = 181.5ftAccording to the above, after 9,075 minutes, both divers are at a depth of 181.5ft.
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Need help with similarity here
Answer:
see explanation
Step-by-step explanation:
Since the figures are similar then the ratios of corresponding sides are in proportion.
(a)
[tex]\frac{PQ}{AB}[/tex] = [tex]\frac{RS}{CD}[/tex] ( substitute values )
[tex]\frac{PQ}{6}[/tex] = [tex]\frac{12}{8}[/tex] ( cross- multiply )
8 × PQ = 72 ( divide both sides by 8 )
PQ = 9 cm
(b)
[tex]\frac{AD}{PS}[/tex] = [tex]\frac{CD}{RS}[/tex] ( substitute values )
[tex]\frac{AD}{10.5}[/tex] = [tex]\frac{8}{12}[/tex] ( cross- multiply )
12 × AD = 84 ( divide both sides by 12 )
AD = 7 cm
(c)
given 2 similar figures with ratio of sides = a : b , then
ratio of areas = a² : b²
here ratio of sides CD : RS = 8 : 12 = 2 : 3
then ratio of areas = 2² : 3² = 4 : 9
let the area of PQRS be x , then using proportion
[tex]\frac{4}{48}[/tex] = [tex]\frac{9}{x}[/tex] ( cross- multiply )
4x = 432 ( divide both sides by 4 )
x = 108
then area of PQRS = 108 cm²
quick question what is x(3x+2) because its so confusing tried almost every single calculation
Answer:
3x² + 2x
Step-by-step explanation:
x(3x + 2) ← multiply each term in the parenthesis by x
= 3x² + 2x
Answer: 3x^3 + 2x
Step-by-step explanation:
when multiplying 3x and another x, it combines and adds up to making 3x^2. You add coefficients. Thus 2 being the coefficient. And same matter for x times 2, they go together as 2x.
3x + x = 3x^2
x + 2 = 2x
George baked a cake to share with his family. Jenny ate 15 of the cake and Brett ate 13 of the cake. How much of the cake did Jenny and Brett eat in all? Responses 215 of the cake 2 over 15 of the cake 28 of the cake 2 eighths of the cake 815 of the cake 8 over 15 of the cake 85 of the cake 8 fifths of the cake
The fraction of the cake that Jenny and Brett eat in all is C. 8 over 15 of the cake.
What is fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
Jenny ate 1/5
Brett ate 1/3.
The fraction that they eat will be:
= Jenny + Brett
= 1/5 + 1/3
= 3/15 + 5/15
= 8/15
Therefore, the correct option is C.
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