The probability of the hand containing 4 queens when picked at random is 0.0026.
We can solve the given question easily using probability, permutations, and combinations.
We can pick any card other than the queen in the following number of ways = ⁴⁸C₉ (i)
The queen card can be picked in the following number of ways
= ⁴C₄= 1 (ii)
The total number of ways to choose 13 cards is = ⁵²C₁₃ (iii)
Using the values of (i), (ii), and (iii), we get -
Probability = (⁴⁸C₉ * 1) / ⁵²C₁₃
= [tex]\frac{48!/9!(48-9)! *1 }{52!/13!(52-13)! }[/tex]
= 1677106640 * 1 / 635013559600
= 0.00264
If this is rounded to four decimal places, we get = 0.0026.
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How many solutions does this equation have. QUESTION BELOW please help
Answer:
one solution
Step-by-step explanation:
the solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is (1, 2 )
Since there is only 1 point of intersection then there is only one solution.
Josue earns $.50 for each delivery he makes plus an additional $10.00 per day. Write and solve an inequality to represent the number of packages Joshua has to deliver so that he can make more than $20.00 each day?
Answer:
.5x + 10 > 20
Step-by-step explanation:
x represents each delivery he makes:
.5x + 10 > 20
This shows that for the inequality to be true, it must total over $20
Hope this helped!
What is the slope of a line perpendicular to the line whose equation is x - 6y = 24.
Fully simplify your answer.
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]x-6y=24\implies -6y=-x+24\implies y=\cfrac{-x+24}{-6} \\\\\\ y=\cfrac{-x}{-6}+\cfrac{24}{-6}\implies y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{6}} x-4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{6}} ~\hfill \stackrel{reciprocal}{\cfrac{6}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{6}{1}\implies {\Large \begin{array}{llll} -6 \end{array}}}}[/tex]
Answer:
-6
Step-by-step explanation:
i just got this question and it wasn’t 1/6 it was -6
Identify the value of y.
The figure shows a right triangle. One leg has a length of 9 units. The other leg has a length of y units. The hypotenuse has a length of y plus 3 units.
y = 6
y = 12
y = 3
y = 15
Answer:
Y=12
Step-by-step explanation:
ya bae
mr banda is buying chocolate bars and hot chips for his students who scored meets and masters on the semester exam. chocolate bars cost $1.1 you each and hot chips 0.40 each Mr banda spent $87 on buying 130 chocolate bars and hot chips. how many chocolate bars did Mr banda buy?
The number of chocolate bars which Mr Banda bought is equal to 50 chocolate bars.
How to determine the number of chocolate bars?In order to determine the number of chocolate bars and the number of hot chips that Carter bought, we would have to write a system of linear equation and assign variables to the number of chocolate bars and number of candies respectively, and then translate the word problem into algebraic equation as follows:
Let the x indicate the number of chocolate bars.Let the y indicate the number of hot chips.Since chocolate bars cost $1.1 each and hot chips 0.40 each and Mr Banda spent $87 on buying 130 chocolate bars and hot chips, we would have the following system of linear equation:
1.1x + 0.40y = 87 ......equation 1
x + y = 130 ......equation 2
From equation 2, we have:
y = 130 - x ......equation 3
Substituting equation 3 into equation 1, we have:
1.1x + 0.40(130 - x) = 87
1.1x + 52 - 0.4x = 87
0.7x + 52 = 87
0.7x = 87 - 52
0.7x = 35
x = 35/0.7
x = 50 chocolate bars.
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3.
A pitcher has 17. 6 fluid ounces of iced tea in it. Erin pours
12. 06 fluid ounces of tea into a glass to drink. How many fluid ounces
of tea remain in the pitcher? Show how to solve the problem
by adding on
5.56 fluid ounce of tea remain in the pitcher
In mathematics, a variable is an alphabet that represent an unknown number. We let required amount as variable and then try to calculate its value
According to the question,
Total ounces of iced tea a pitcher contains = 17.6 fluid ounces
Amount of tea Erin pours to drink = 12.06 fluid ounces
Let "x" fluid ounce of tea remain in the pitcher
So , total was 17.6
=> x + 12.06 = 17.6
Solving for x
Subtracting by 12.06 both the sides
=> x + 12.06 - 12.06 = 17.6 -12.06
=> x = 5.56 fluid ounce
Hence , 5.56 fluid ounce of tea remain in the pitcher
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cos x = - 0.809, find the values of x. ( - 180≤ x ≥ 180 )
Answer:
cos x = - 0.809, find the values of x. ( - 180≤ x ≥ 180 )
x = - 135° and x = 45°
A truck that can carry no more than 7200 lb is being used to transport refrigerators and upright pianos. Each refrigerator weighs 200 lb and each piano weighs 425 lb. Write and graph an inequality to show how many refrigerators and how many pianos the truck could carry.Will 18 refrigerators and 11 pianos overload the truck? Explain.
Answer: Yes, it will overload the truck.
Step-by-step explanation:
To begin, form an algebraic equation.
200(r) + 425(f)
Second, substitute your numbers for the variables.
200(18) + 425(11) = ?
Third, multiply your numbers of fridges by the weight of each.
3600 + 4675 = 8275 is the total
Finally, determine whether or not if it is greater than the weight limit the truck has.
7200 < 8275
Therefore, the total weight is greater than the weight limit.
how is factoring symbolically and factoring with algebra tiles similar
The two methods are identical because by both using algebra tiles and factoring symbolically, one need to think of the factors.
What is factoring?Factoring simply has to do with the process of writing a number or another mathematical object as a product of different factors, and this is usually smaller or simpler objects that are of the same kind.
Factoring is a common mathematical process that's used for separating the factors, or numbers, which multiply to form another number. Some numbers are affected by multiple factors.
For example, in a situation when you multiply the factors 6 and 4, 8 and 3, 12 and 2, and 24 and 1, you get the number 24.
Algebra tiles are rectangular and square tiles that represent numbers and variables. Using algebra tiles allows us to solve our problems in a more visual manner. It allows us to see exactly what quantities we're dealing with. It's as if we're using building blocks to assist us.
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Jean is x years old and her younger brother Johnathan is y years old. What is the sum of their ages 5 years ago
The sum of their ages 5 years ago is x + y -10.
What is subtraction?The process of subtracting one number from another is known as subtraction.
Given that, Jean is x years old and her younger brother is y years old.
Age of Jean 5 years ago is:
x - 5
The age of Johnathan 5 years ago is:
y - 5
The sum of their ages 5 years ago is:
x - 5 + y - 5
= x + y -10
Hence, the sum of their ages 5 years ago is x + y -10.
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There are 36 children and 6 adult at the prechool. To keep the ame child-to-adult ratio, how many adult are needed for 108 children?
To maintain the same child-to-adult ratio, the number of adult needed for 108 children are 18.
Explain the term ratio of the number?The amounts (numbers) m as well as n are referred to as the ratio's terms in the ratio m: n. Both the first term (i.e., m) and also the second term (i.e., is n) are referred to as antecedent and consequent, respectively.As the stated question-
At the preschool, there's many 36 children and 6 adults.
Thus, this is solved by using unitary method.
36 children -----> 6 adults.
1 children -----> 6/36 adults.
For 108 children, multiply both sides by 108.
108 children -----> 6 x 108/36 adults.
108 children -----> 18 adults.
Thus, to maintain the same child-to-adult ratio, the number of adult needed for 108 children are 18.
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As a project for his business statistics class, a student examined the factors that determined parking meter rates throughout the campus area. Data were collected for the price ($) per hour of parking, blocks to the quadrangle, and whether the parking is on or off campus.
The population regression model hypothesized is Yi = α + β 1 X 1i + β 2 X 2i + ε
where
Y is the meter price per hour
X 1 is the number of blocks to the quad
X 2 is a dummy variable that takes the value 1 if the meter is located on campus and 0 otherwise
The following Excel results are obtained.
Statistics Regression
Multiple R 0.5536
R Square 0.3064
Adjusted R Square 0.2812
Standard Error 0.4492
Observations 58
ANOVA
df SS MS F Significance F
Regression 2 4.9035 2.4518 12.1501 0.0000
Residual 55 11.0984 0.2018
Total 57 16.0019
Coefficients Standard Error t Stat P-value Lower 99% Upper 99%
Intercept 1.6500 0.2028 8.1359 0.0000 1.1089 2.1912
Block -0.2504 0.0529 -4.7355 0.0000 -0.3915 -0.1093
Campus 0.1552 0.1297 1.1966 0.2366 -0.1908 0.5011
Referring to Scenario 13-12, what is the correct interpretation for the estimated coefficient for X 2?
Holding the effect of the distance from the quad constant, the estimated mean costs for parking on campus is $0.16 per hour more than parking off campus.
Holding the effect of the distance from the quad constant, the estimated mean costs for parking on campus is $0.16 per hour more than parking off campus for each additional block away from the quad.
Holding the effect of the distance from the quad constant, the estimated mean costs for parking off campus is $0.16 per hour more than parking on campus for each additional block away from the quad.
Holding the effect of the distance from the quad constant, the estimated mean costs for parking off campus is $0.16 per hour more than parking on campus.
Holding the effect of the distance from the quad constant, the estimated mean costs for parking on campus is $0.16 per hour more than parking off campus.
According to given data determined parking meter rates throughout the campus area.
What is the hypothesis for regression?
For simple linear regression, the chief null hypothesis is H0 : β1 = 0, and the corresponding alternative hypothesis is H1 : β1 = 0. If this null hypothesis is true, then, from E(Y ) = β0 + β1x we can see that the population mean of Y is β0 for every x value, which tells us that x has no effect on Y .
Holding the effect of the distance from the quad constant, the estimated mean costs for parking on campus is $0.16 per hour more than parking off campus.
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Football player one pushes against football player two, causing player two to slow down from moving any farther down the field. Which term best describes the work in this situation?
Negative work was done on player two.
Positive work was done on player two.
No work was done on either player.
Negative work was done on player one.
The work that has been done on player 2 by player 1 is a negative work. Option A.
What is work done?We define the work done as a situation in which the force that is applied moves a distance in the direction of the force. In this case we ought to know that a negative work is said to be done when the object is found to slow down at te application of the force. The meaning of this is that the force acts in such a way as to slow down motion which makes it a negative force.
For the fact that football player one pushes against football player two, causing player two to slow down from moving any farther down the field, a negative work is done.
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Which ratio is equivalent to 3/15
1/3
3/5
1/5
15/3
Answer:
It should be 1/5
Since the fractional versions of the ratios are equal, the ratios are equivalent.
The volume of the circumscribed cylinder is 2154.04π cm^3. Find the radius of the sphere…show all work and steps.
The measure of the radius of the sphere is given as follows:
r = 359 cm.
How to obtain the volume of the cylinder?
The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h
Which is the base area given by πr² multiplied by the height h.
In the context of this problem, the parameters are given as follows:
The radius of the cylinder is the same as the radius of the sphere, which is of r.The height of the cylinder is twice the radius of the sphere, hence it is or 2r.The volume of the circumscribed cylinder is 2154.04π cm^3, hence the equation to solve for r is given as follows:
πr²h = 2154.04π
2πr³ = 2154.04π
2r³ = 2154.04
r = cube root of (2154.04/2)
r = 359.
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Use the Laplace transform to solve the following initial value problem: y + 10y + 25y = 0 y(0) = - 3, y'(0) = 3 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)} find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y (s) = and write the above answer in its partial fraction decomposition, Y(s) = A/s + a + B/(s+a)2 Y (s) = + Now by inverting the transform, find y(t) =
On solving the given question, by the Help of LaPlace Inverse form we got - [tex]y(t) = \frac{-7}{2} + \frac{1}{2}e^{-8t}[/tex]
What is The Laplace transform?In terms of its usefulness in resolving physical issues, the Laplace transform is an important transform that is probably second only to the Fourier transform. The Laplace transform is especially helpful in solving linear ordinary differential equations, such as those that arise in the analysis of electronic circuits.
Take Laplace for DE we get -
[tex]L(y)" + 8L(y)' =0\\s^2Y (s) - sy(0) - y'(0) 8(sY(s) - y(0))=0\\Y(s)(s^2 + 8s) + 3s 4 + 24 =0\\Y(s)(s^2 + 8s) = -3s - 28\\Y(s) = \frac{-3s - 28}{(s^2 + 8s) } \\Right Side = \\\frac{-7}{2s} + \frac{1}{2(s+8)} \\ Now taking inverse LaPlace - \\y(t) = \frac{-7}{2} + \frac{1}{2}e^{-8t}[/tex]
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Can anyone help me with this?
8^5/8^3
Answer:
64
Step-by-step explanation:
do multiplication :)
when she chooses a password, eloise always uses exactly ten different characters: five letters (a, b, c, d, and e) and five numbers (2, 3, 4, 5, and 6). additionally, she always ensures that no pair of letters is consecutive and that no pair of numbers is consecutive. how many different passwords conform to these rules?
These rules of five letters (a, b, c, d, and e) and five numbers allow for 28,800 different passwords. Additionally, she makes sure that no two letters or two numbers are ever placed back-to-back.
What is counting principle?The basic counting concept is a method for keeping track of all the potential outcomes in a scenario. According to this statement, there are n*m methods to carry out both of these acts if there are n ways to execute one activity and m ways to conduct another action after that.
Here,
Eloise has 10 alternatives since the password's initial character can be any letter or number. She has five alternatives, and her second selection must be from the set (letter or number) that has not previously been utilized. She has four choices remaining, and Choice 3 is from the same group as Choice 1. She gets four possibilities since Choice 4 is the second item in the same set as Choice 2. The choices 5 and 6 come from separate sets, each of which has three possibilities; the choices 7 and 8 come from separate sets, each of which has two options; and the choices 9 and 10 come from separate sets, each of which has only one option left.
10 5 4 4 3 3 2 2 1 1
10 ×5 ×4 ×4 ×3 ×3 ×2 ×2 ×1 ×1 = 28,800
28,800 different passwords conform to these rules of five letters (a, b, c, d, and e) and five numbers (2, 3, 4, 5, and 6). additionally, she always ensures that no pair of letters is consecutive and that no pair of numbers is consecutive.
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a cylinder shaped can needs to be constructed to hold 400 cubic centimeters of soup. the material for the sides of the can costs 0.04 cents per square centimeter. the material for the top and bottom of the can needs to be thicker, and costs 0.08 cents per square centimeter. find the dimensions for the can that will minimize production cost. helpful information: h : height of can, r : radius of can volume of a cylinder: v
The dimensions of the can are radius of can = 4cm and
height of can = 78.6cm
What is the volume of cylinder?
A cylinder can be seen as a collection of multiple congruent disks, stacked one above the other. In order to calculate the space occupied by a cylinder, we calculate the space occupied by each disk and then add them up.
Thus, the volume of the cylinder can be given by the product of the area of base and height.
Volume of cylinder = πr²h
According to the given question:
We have V cylinder = V = 400cc
We will first find the areas involved
Let x = radius of base then area of the base = π*x² and this is the area of the top too
For lateral area we need to get h the height of the cylinder as function of x
V = πx²h ⇒ h= v/πx² ⇒ h = 400/πx²
Now the total area of the cylinder is:
A(x) = Area of the base + area of the top + lateral area
A(x) = 2*π*x² + 2πx h ⇒ A(x) = 2*π*x² + 2πx (V/πx² )
A(x) = 2*π*x² + 800/x
Taking derivatives:
A´(x) = 4πx - 800/x²
A´(x) = 0 4πx - 800/x² =0 ⇒ πx - 200/x² = 0
( πx³ - 200 )/ x² = 0
πx³ - 200 = 0
x = 4 cm
and h = 400/πx² ⇒ h = 78.6 cm
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Using the t Distribution Table, find the critical value(s) for the t test for a right-tailed test with n=8 and a =0.01. Enter the answers separated by a comma if needed. Critical value(s) - Using The Distribution Table, find the critical value(s) for the test for a left-tailed test with n=23 and a =0.05. Enter the answers separated by a comma if needed. Critical value(s)
The critical value for right tailed test is 2.998, the critical value for left tailed test is - 1.717.
How to using t distribution table?First, we must know the following data,
df = degree of freedom = n - 1
α = significance level
Next, t test have three type of test which is
Two or Both tailed test, for this test we use negative and positive value.One right tailed test, for this test we use positive value.One left tailed test, for this test we use negative value.Then, to find critical value using the t distribution table search df value in left column of table and search the α in the top row of the table (depending on the type of test, use one tail row for this case). For example, see attached image.
Thus, the right tailed test critical value is 2.998, and the left tailed test critical value is - 1.717.
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A large conical tank is positioned so that its vertex is pointed downward. Water drains out from a hole at the vertex. As the water drains, the height of the water (measured from the vertex to the top surface) is always twice the radius of the waters surface.
a. draw and label a diagram of the situation, defining any variables you use
b. write a function that gives the volume of the water in the cone as a function of radius of the water at the top surface, using no other variables/parameters.
c. using variable t to represent the time aspect of these changes, what rate of change notation can we use for how the volume of water changes with respect to time and how the radius of the water at the top surface changes with respect to time? (notation for the two quantities only, not an equation)
d. Starting from the original quantity relation in (b) determine the equation that relates their rates of change with respect to time, that is "find the related rates equation"
e.suppose that the water drains from the cone at a constant rate of 15 cm^3 per second. how fast is the radius of the top surface of the water changing when the radius measures 75 cm? write your result in a complete sentence
2. use implicit differentiation to determine dy/dx for the following relation: sin(2x^2y^3)-3x^3=1
1. Radius is changing at the rate of 0.00042cm/sec when the radius is 75cm.
2.The implicit differentiation to determine dy/dx of relation sin(2x^2y^3)-3x^3=1 is 9x² - 4xy³ cos(2x² y³) / 6x²y² cos(2x² y³)
1. a) check the image attached
r= radius
h=height
b) Volume of conical tank ,V = (1/3)πr²h
= (1/3)πr²(2r)
V = 2/3πr³
c) Rate of change of volume with respect to time is denoted as dV/dt
Rate of change of radius is denoted as dr/dt
d) V = 2/3πr³
dV/dt = 2/3π (3r²) dr/dt
dV/dt = 2πr² dr/dt
e) Rate of change in volume, dV/dt = 15cm³ / sec , r =75cm
∴ 15 = 2π(75)² . dr/dt
dr/dt = 15 / (2π(75)²)
dr/dt = 15/35342.92
dr/dt = 0.00042 cm/sec
∴Radius is changing at the rate of 0.00042cm/sec when the radius is 75cm.
2. sin(2x² y³) - 3x³ = 1
Differentiating :
cos(2x² y³) [2x² y³dy/dt + 2y³ 2x] - 9x² = 0
6x²y² dy/dx . cos(2x² y³) + 4xy³ cos(2x² y³) - 9x² = 0
dy/dx = 9x² - 4xy³ cos(2x² y³) / 6x²y² cos(2x² y³)
Hence, the implicit differentiation to determine dy/dx of relation sin(2x^2y^3)-3x^3=1 is 9x² - 4xy³ cos(2x² y³) / 6x²y² cos(2x² y³)
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Which best describes the solution for the
system of linear equations graphed below?
A. (3, 0) only
B. (6,0) only
C. no solution
D. infinitely many solutions
Answer:
C no solution.
Step-by-step explanation:
The lines are parallel, they will never intersect.
in a sample of 62 swim instructors, 37 said that the butterfly stroke is the most difficult to teach. find the critical value used to test a claim that a majority of swim instructors think that the butterfly is the most difficult stroke to teach at the 1% significance level.
The critical value used to test the hypothesis that the butterfly is the most challenging stroke to teach at the 1% significance level is 0.84
Given that,
Of the 62 swim teachers who participated in the survey, 37 claimed that teaching the butterfly stroke is the most challenging. Find the criticial value used to test the hypothesis that the butterfly is the most challenging stroke to teach at the 1% level of significance.
This is right tailed test
Z [tex]\alpha[/tex] = Z 0.01 = 0.84 ( Using z table )
Therefore, the critical value used to test the hypothesis that the butterfly is the most challenging stroke to teach at the 1% significance level is 0.84
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19. For an overdue book, the school library
charges a 25¢ penalty, plus 5¢ for every
day the book is overdue. The town library
charges a 5¢ penalty, plus 10¢ for every
day the book is overdue. For what number
of days is the total fee at both libraries
the same?
Answer:
On the 4th day, the sum of penalties and charges will be the same in both the school library and the town library.
Step-by-step explanation:
School library
Penalty-25
Every day charge-5
City library
Penalty-5
Every day charge-10
Let the day when total fee at both libraries will be same be x
Total charge in school library-25+5x
Total charge in city library-5+10x
They both amount to be equal
A coach has $1280 in the budget to spend on team jackets. The team held a fundraiser and earned $1176. Each jacket costs $75. How many jackets can the coach Buy?
Pls Help
Answer: 32 jackets
Step-by-step explanation:
add 1280 to 1176 then divide the sum by 75
suppose you have a collection of 24 candles. there are 6 candles each of 4 different colors, and they are identical in every other way. how many different ways can 6 candles be chosen?
The different ways in which 6 candles be chosen 84 ways.
What is a combination?
The combination is a method of choosing things from a collection where the order of the choices is irrelevant.
Given, When we have 'n' types of elements and choose 'r' elements from them, then we have C(n+r-1, r) combinations.
n=4(4 types of candles), r=6(no of candles to pick)
Choose 6 different candles, then
=C(4+6-1,6)
=C(9,6)
= 9! / (9-6)! (6!)
= 9!/ 6! 3!
=84
The different ways in which 6 candles can be chosen are 84 ways.
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Write the equation of the parabola in vertex form.
vertex (3,1), point (2,-5)
f(x) = ___
Step-by-step explanation:
vertex form :
y = a(x - h)² + k
(h, k) are the coordinates of the vertex.
"a" is the orientation (up-down) and widening factor.
we use the given h, k and x, y (the given point) to calculate "a".
-5 = a(2 - 3)² + 1 = a(-1)² + 1 = a + 1
a = -6
and the full vertex form is then
y = -6(x - 3)² + 1
just a quick addition to the superb reply by "reinhard10158" above
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=3\\ k=1 \end{cases}\implies y=a(x-3)^2 + 1\hspace{5em}\textit{we also know that} \begin{cases} x=2\\ y=-5 \end{cases} \\\\\\ -5=a(2-3)^2 + 1\implies -6=a(-1)^2\implies -6=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} y=-6(x-3)^2 + 1 \end{array}} ~\hfill[/tex]
1. use the equation to answer these questions. (a) what is the solution to the equation? (b) what is the extraneous solution? why? (c) in general, what is an extraneous solution?
a. The solution of the equation x + 2 = √3x + 10 is x = -3 or x =2.
b. Extraneous solution is x= -3.
c. Extraneous solution does not satisfy original equation.
As given in the question,
Given equation :
x + 2 = √3x + 10
a. Squaring both the sides
( x + 2 )² = ( √3x + 10 )²
⇒ x² + 4x + 4 = 3x + 10
⇒ x² + x - 6 =0
⇒ x² + 3x -2x -6 =0
⇒ ( x+ 3) ( x -2) =0
⇒ x= -3 or x = 2
b. Extraneous solution:
x = -3
-3 + 2 = √3(-3)+ 10
⇒ -1 ≠ 1 extraneous solution.
x= 2
2+ 2 =√3(2) +10
⇒4 = 4 not extraneous.
c. Extraneous solution does not satisfy original equation
Therefore, the solution of the equation is x = -3 or x=2and its extraneous solution is x =-3. Extraneous solution does not satisfy original equation.
The complete question is :
Use the equation below to answer these questions.
x + 2 = √3x + 10
a) What is the solution to the equation?
b) What is the extraneous solution? Why?
c) In general, what is an extraneous solution?
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Given the functions below, find f(2)-g(-7).
f(x)=-|3-8x| g(x)=x^2+4x
The value of f(2)-g(-7) is -34
What is function?A function is defined as a relation between a set of inputs having one output each.
Given are two functions, f(x) = -|3-8x| and g(x) = x²+4x
f(2) = -|3-8x2|
= -|3-16|
= -13
g(x) = (-7)²+4(-7)
= 49-28
= 21
f(2)-g(-7) = -13-21 = -34
Hence, The value of f(2)-g(-7) is -34
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Suppose you are doing a two sample test of means, and assume that the population variances are equal. We have the following data:
Sample 1: n1= 16, XX1 = 44, s1= 5
Sample 2: n2= 9, XX2 = 41, s2= 6
Find the test statistic.
t = 1.341
Correct option is " B " the is the test statistics is 1.341 when sample 1: n₁=16, x₁=44, and s₁=5 and sample 2:x₂ = 41, s₂ = 6, n₂ = 9.
Given that,
Assume you are conducting a two-sample test of averages and that the variances in the population are identical. The information below is ours:
Sample 1: n₁=16, x₁=44, and s₁=5.
Sample 2:x₂ = 41, s₂ = 6, n₂ = 9.
We have to find the test statistic.
We know that,
n₁ = 16
x₁ = 44
s₁ = 5
n₂ = 9
x₂ = 41
s₂ = 6
We have
t= (x₂ - x₁)/√(n₁-1)s₁²+(n₂-1)s₂²/n₁+n₂-2(1/n₁+1.n₂)
t = 1.341.
Therefore, Correct option is " B " the is the test statistics is 1.341 when sample 1: n₁=16, x₁=44, and s₁=5 and sample 2:x₂ = 41, s₂ = 6, n₂ = 9.
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