The lower bound of the 90% confidence interval for the population mean is 44.3.
To calculate the lower bound of the 90% confidence interval for the population mean, we will use the formula:
Lower bound = sample mean - (1.645 * (standard deviation / square root of sample size))
Calculate the sample mean:
Sample mean = (42.3 + 59.2 + 45.4 + 55.8 + 49.0 + 39.7 + 56.2 + 54.6 + 45.8 + 60.6 + 55.7 + 46.1 + 58.3 + 44.4) / 14 = 51.09
Calculate the sample standard deviation:
Sample standard deviation = √(((42.3 - 51.09)2 + (59.2 - 51.09)2 + (45.4 - 51.09)2 + (55.8 - 51.09)2 + (49.0 - 51.09)2 + (39.7 - 51.09)2 + (56.2 - 51.09)2 + (54.6 - 51.09)2 + (45.8 - 51.09)2 + (60.6 - 51.09)2 + (55.7 - 51.09)2 + (46.1 - 51.09)2 + (58.3 - 51.09)2 + (44.4 - 51.09)2) / 13) = 8.37
Calculate the lower bound:
Lower bound = 51.09 - (1.645 * (8.37 / √14)) = 44.3
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Solve the matrix
x+y-z=3
2x+3y+z=10
3x-y-7z=1
point charges of 10.4 nc and 43.9 nc are placed 0.500 m apart. what is the electric field halfway between them? indicate direction by a positive or a negative value. keep in mind that a positive vector is one directed to the right and a negative vector is one directed to the left. your answer should be a positive or a negative number with two decimal places, do not include the unit. hint: 1 nc
The point charges placed 0.500 m apart are 10.4 nC and 43.9 nC. Then, the electric field halfway between these charges will be -4824 N/C.
The physical field that surrounds particles with an electrical charge is called an electric field. All other charged particles in the field are affected by it, either being attracted to it or being repelled by it.
The electric field because of a point charge q is written as [tex]E=\frac{kq}{r^2}[/tex]
Positive point charges cause the electric field to point away from the point, whereas negative point charges cause the electric field to point in the direction of the point. Then, the electric field of the midpoint p in the diagram is written as,
[tex]\begin{aligned}E_p&=\mathrm{\frac{k(10.4\;nC)}{(0.25\;m)^2}-\frac{k(43.9\;nC)}{(0.25\;m)^2}}\\&=\mathrm{\frac{k(10.4-43.9)\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{\frac{9\times 10^9\;Nm^2/C^2\times 33.5\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{4824\;N/C}\end{aligned}[/tex]
The required answer is -4824 N/C.
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Apply the distributive property (assume all variables are non zero):
uq ( 1/u+1/q)
Answer:
below
Step-by-step explanation:
uq ( 1/u + 1/q) = uq/u + uq/q = q + u
Leonel has a soccer game on a rectangular field, which is 15 meters wide and 40 meters long. Marcos wants to know what is the perimeter of the court?
[tex]\therefore[/tex] Leonel will play on his soccer field with a perimeter of 110 m.
Step by step explanation:Data to then substitute into the equation:
Let "a" = 15 meters wideLet "b" = 40 meters longBefore starting to solve, I will show you the formula for the perimeter of the rectangle:
[tex]\bold{ \: P= 2(a) + 2(b)}[/tex]
We substitute equation:
[tex]\bf \: P = 2(15) + 2(40)[/tex]
We multiply:
[tex]\bf \: P= 15 * 2 = 30[/tex]
[tex]\bf \: P= 40 * 2 = 80[/tex]
We add both resultants to obtain the perimeter:
[tex]\bf \: P= 80 + 30[/tex]
[tex]\large\boxed{ \bf \:P = 110 \: m}[/tex]
Rpt: Leonel will play on his soccer field with a perimeter of 110 m.
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
Inga could use the equation 2(x² + 6x) = 3 to solve the quadratic equation.
What is the quadratic equation?The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a).
2(x2 + 6x + 9) = 3 + 18: Inga could use the distributive property to expand the right side of the equation and simplify it.
x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot: Inga could use the quadratic formula to find the two possible values of x that solve the equation.
2(x2 + 6x) = 3: Inga could simplify the left side of the equation by multiplying both sides by 2 and isolating x2 + 6x on one side.
Hence, Inga could use 2(x² + 6x) = 3 to solve the quadratic equation.
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write the constant term and numerical co efficient of the remaining terms of the each of the followin
g -2s -5t +6
The constant term is 6 and the numerical coefficient of g, s and t are 1, -2 and -5.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:
Constant: A constant is a fixed numerical value.
Variable: A variable is a symbol that doesn't have a fixed value.
The given expression is g-2s-5t+6.
In the expression there are 4 terms.
Here, 6 is the constant and the numerical coefficient of g is 1, the numerical coefficient of -2s is -2 and the numerical coefficient of -5t is -5.
Therefore, the constant term is 6.
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I don’t know how to figure this question out:(
The population of the nation as per the provisional figures of Census 2011 is 1210.19 million of which 623.7 million (51.54%) are males and 586.46 million (48.46%) are females.
What is canadian population?Canada is larger than the United States, making it the second-largest country in the world. However, despite this vast territory for a relatively small population, more than 90 percent of Canadians live within 150 miles of the US border.
The population of the country as per the provisional figures of Census 2011 is 1210.19 million of which 623.72 million (51.54%) are males and 586.46 million (48.46%) are females. The provisional figures of Census 2011 were released in New Delhi today by Union Home Secretary Shri G.K.Pillai and RGI Shri C. Chandramouli.
Canada contains the world's seventh-largest Indian diaspora. The highest concentrations of Indian Canadians are found in the provinces of Ontario and British Columbia, followed by growing communities in Alberta and Quebec as well, with the majority of them being foreign-born.
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The polynomial
negative 19 x squared plus 181 x plus 14 comma 420
−19x2+181x+14,420 represents the electricity generated (in gigawatts) by geothermal sources during 2002
minus -2007. The polynomial
866 x squared minus 78 x plus 10 comma 190866x2−78x+10,190 represents the electricity generated (in gigawatts) by wind power during 2002-2007. In both polynomials, x represents the number of years after 2002. Find a polynomial for the total electricity generated by both geothermal and wind power during 2002 - 2007
The polynomial representing the total amount of electricity produced by geothermal and wind power between 2002 and 2007 is 847x2 + 103x + 24,610.
How to solve polynomial equation?Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. The original equations' answers are the solutions to the derived equations. Factoring cannot always be used to solve polynomial problems.We must add the two provided polynomials in order to obtain the polynomial for the total electricity produced between 2002 and 2007 from both geothermal and wind energy.The polynomial would be negative -19x2+ 181x + 14,420 + 866x2 - 78x + 10,190 for the total electricity produced by geothermal and wind power between 2002 and 2007.We obtain: 847x2 + 103x + 24,610 by simplifying.Therefore, the polynomial representing the total amount of electricity produced by geothermal and wind power between 2002 and 2007 is 847x2 + 103x + 24,610.To learn more about polynomial refer to:
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a number y multiplied by -4 is no more than -2/3 write this word sentecne as an inequality
The word sentence as an inequality is -4y ≤ -2/3
What is an inequality?An inequality can be defined as a mathematical relation that makes a non-comparison between two expressions, equations or numbers.
It is also important to note that algebraic expressions can be defined as expressions that are composed of terms, coefficients, variables, constants and factors.
The signs in an inequality are;
< represents less than> represents greater than≤ represents greater than or equal to≥ represents less than or equal toFrom the information given, we have that
The variable is y
The fraction is -4
This can be represented as;
y × -4 ≤ -2/3
multiply the values
-4y ≤ -2/3
Hence, the expression is -4y ≤ -2/3
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cramer's rule is a method of calculating the solution to a system of linear equations by finding the of the determinants.
Cramer's rule is a method of calculating the solution to a system of linear equations by finding the "Quotient" of the determinants.
Hence, option (a) is correct choice.
Cramer's rule is one of the most significant strategies for solving a system of equations. The values of the system's variables are to be computed using determinants of matrices in this technique. As a result, Cramer's rule is frequently referred to as the determinant technique.
If unique solutions exist, this approach is utilized to find them. Cramer's rule cannot be used if the determinant of the coefficient matrix is zero.
To use Cramer's Rule to solve a system of three equations in three variables, substitute a variable column with the constant column for each desired solution: x=DxD, y=DyD, z=DzD.
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The missing option be:
(a) Quotient
(b) Divisor
(c) Factor
(d) Multiple
Suppose we are using a Riemann sum with right rectangles to approximate ∫ 05 f(x) dx for some function f(x). Which of the following sums would you expect to give the best approximation? There is not enough information to tell. O a rectangle approximation with Δx=20
O a rectangle approximation with Δx=2
O a rectangle approximation with Δx=0.02
O a rectangle approximation with Δx=0.2
The approximation is: A1 = f(0) * 2, A2 = f(2) * 2, A3 = f(4) * 2, A4 = f(6) * 2.
To calculate the approximate integral using a Riemann sum with right rectangles, we need to calculate the area of each rectangle and then add them all together. The area of each rectangle is given by the formula A = f(x) * Δx, where f(x) is the value of the function at a given x and Δx is the width of the rectangle.
For a rectangle approximation with Δx=20:
Calculate the x-coordinates of the right endpoints of the rectangles:
x1 = 0, x2 = 20, x3 = 40, x4 = 60.Calculate the values of f(x) at each x-coordinate:
f(x1) = f(0), f(x2) = f(20), f(x3) = f(40), f(x4) = f(60).Calculate the area of each rectangle using the formula A = f(x) * Δx, where
Δx = 20: A1 = f(0) * 20, A2 = f(20) * 20, A3 = f(40) * 20, A4 = f(60) * 20.Add up the areas of all the rectangles to get the approximate integral:
∫0 5 f(x) dx ≈ A1 + A2 + A3 + A4.For a rectangle approximation with Δx=2:
Calculate the x-coordinates of the right endpoints of the rectangles:
x1 = 0, x2 = 2, x3 = 4, x4 = 6.Calculate the values of f(x) at each x-coordinate:
f(x1) = f(0), f(x2) = f(2), f(x3) = f(4), f(x4) = f(6).Calculate the area of each rectangle using the formula A = f(x) * Δx, where
Δx = 2: A1 = f(0) * 2, A2 = f(2) * 2, A3 = f(4) * 2, A4 = f(6) * 2.Add up the areas of all the rectangles to get the approximate integral:
∫0 5 f(x) dx ≈ A1 + A2 + A3 + A4, where:
A1 = f(0) * 2, A2 = f(2) * 2, A3 = f(4) * 2, A4 = f(6) * 2.
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Use the vertex (h,k) and a point on the graph (x,y) to find the general form of the equation of the quadratic function.
(h,k)=(−3,3) , (x,y)=(2,10)
Answer:
y = 7/25x² +42/25x +5 13/25
Step-by-step explanation:
You want the general form of the equation for the quadratic function that has (-3, 3) as its vertex and (2, 10) as a point on the graph.
Vertex formThe vertex form equation is ...
y = a(x -h)² +k
where (h, k) is the vertex and 'a' is a vertical scale factor.
For the given vertex, this becomes ...
y = a(x +3)² +3
We want to find 'a' such that the point (x, y) =(2, 10) satisfies the equation:
10 = a(2 +3)² +3
7/25 = a . . . . . . subtract 3, divide by 25
General formThe expanded equation is ...
y = 7/25(x +3)² +3 = 7/25(x² +6x +9) +3
y = 7/25x² +42/25x +5 13/25
General form of the equation of the quadratic function:
y = (7/25)x² + (42/25)x + 138/25
What is quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.
Given
vertex (h,k) = (−3,3)
Point (x,y) = (2,10)
Standard Form Equation for a Parabola:
a(x-h)² = y-k
for vertex (h,k)
(h,k) = (−3,3)
a(x - -3)² = y - 3
a(x + 3)² = y - 3 ______(1)
(x,y)=(2,10)
a(2+3)² = 10 - 3
25a = 7
a = 7/25
Substituting value of a in equation 1
(7/25)(x+3)² = y - 3
(7/25) (x² + 9 + 6x) = y - 3
7x² + 63 + 42x = 25y - 75
7x² + 63 + 75 + 42x = 25y
7x² + 42x + 138 = 25y
⇒ y = (7/25)x² + (42/25)x + 138/25
Hence, y = (7/25)x² + (42/25)x + 138/25 is the general form of the equation of the quadratic function.
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Two cyclists start at the same point and travel in opposite directions. One cyclist travels 6 mih faster than the other. If the two cyclists are 60 miles apart after 2 hours, what is the rate of each cyclist?
Answer:
12 and 18
Step-by-step explanation:
60 miles in 2 hours, so that means together the cyclists are traveling at 30mph,
one is traveling at 6mph more so 30mph-6mph =24
24/2=12
so the slower one is going at 12mph and the other at 18mph
When there is a _____ relationship, as values of variable X (e.g., elevation) increase, values of variable Y (e.g., temperature) decrease.Answers:a. positiveb. negativec. curvilineard. zerozero
When there is a negative relationship, the values of variable X (e.g., elevation) increase, as the values of variable Y (e.g., temperature) decrease. Hence, option B is the correct option.
Correlation is the relationship between variables. The variables in question are the x-variable (Horizontal) and the y- variable (vertical). This is used to find out the similarities in the measurements of and presentation of two variables across a data set.
A negative correlation is used to define the relationship between two variables such that one variable increases when the other variable decreases. We observe a negative correlation in the given problem. So, option B is the correct answer.
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help me please my mom can't even figure it out
Answer:
I think it's [tex]\frac{12}{5}[/tex]
Step-by-step explanation:
[tex]\frac{4}{5} * \frac{3}{1} = \frac{4}{1} *\frac{3}{5}[/tex]
= [tex]\frac{12}{5}[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{4}{5}\times 3}[/tex]
[tex]\mathsf{= \dfrac{4}{5}\times \dfrac{3}{1}}[/tex]
[tex]\mathsf{= \dfrac{4\times3}{5\times1}}[/tex]
[tex]\mathsf{= \dfrac{12}{5}}[/tex]
[tex]\mathsf{= 2\dfrac{2}{5}}[/tex]
[tex]\star\star\star\star\star\star\start\star\star\star\star \star\star\star\star\star\star\start\star\star\star\star \star\star\star\star\star\star\start\star\star\star\star \star\star\star\star\star\star\start\star\star\star\star \star\star\star\star\star\star\start\star\star\star\ \star[/tex]
[tex]\mathsf{4\times\dfrac{3}{5}}[/tex]
[tex]\mathsf{= \dfrac{4}{1}\times\dfrac{3}{5}}[/tex]
[tex]\mathsf{= \dfrac{4\times3}{1\times5}}[/tex]
[tex]\mathsf{= \dfrac{12}{5}}[/tex]
[tex]\mathsf{= 2\dfrac{2}{5}}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{12}{5}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Maria covered 11/2 km in the morning and 27/5 km in the afternoon. How much did she cover in total?
Answer: In total he traveled 10.9 km.
Step by step explanation:
Data :
In the morning it's 11/2In the afternoon it is 5/27We solve this equation by adding the amounts of morning and afternoon:
[tex]\bf \: \cfrac{11}{2} + \cfrac{27}{5} = \cfrac{55 + 54}{10} = \cfrac{109}{10}[/tex]
In total he traveled 109/10 km.
What are they in division 109/10:
[tex] \bf 109 \div 10 = 10.9 \: \: km[/tex]
Rpt: In total he traveled 10.9 km.
3x – 2 < 4
A. x < 2
B. x < -3
C. x < -2
D. x < 6
Answer: A. x < 2
Step-by-step explanation:
We will isolate the variable with inverse operations.
Given:
3x – 2 < 4
Add 2 to both sides of the equation:
3x < 6
Divide both sides of the equation by 3:
x < 2
A. x < 2
ST has a midpoint at M(8, 4). Point S is at (6, 0). Find the coordinates of point T.
Write the coordinates as decimals or integers.
T=(,)
Answer:
(5,5)
What is the midpoint of MN between the points M(2, 6) and N (8, 4)? . Add the x-values together and divide them by 2, and do the same for the y-values. The midpoint of MN is (5,5).
Step-by-step explanation:
In a recent NBA basketball game, the Hornets were trying to earn a playoff spot with a win over LeBron James and the Cavaliers! In the first quarter, the Cavaliers scored 25 points and the Hornets scored 20 points. In the second quarter, the Hornets scored 25 points, and the Cavaliers scored 20. What was the score for each team after the second quarter? Would it have changed if the Hornets scored 25 in the first quarter and 20 in the second? Why or why not?
Answer:
After the second quarter, the Cavaliers' score would be 25 points and the Hornets' score would be 45 points. The score for each team would not have changed if the Hornets scored 25 points in the first quarter and 20 points in the second quarter because the total number of points scored by each team would still be the same. The order in which the points were scored does not affect the final score of the game.
Determine how (if possible) the triangles can be proved similar (SHOW WORK)
Triangle ABC is similar to triangle XYZ.
What are Similar Triangles?
Similar triangles are those triangles that have the same shape but different sizes.
The length of sides and angles are proportional in similar triangles.
So we know that the length of sides is proportional.
If we find the ratio of the corresponding sides of the two triangles, then they must be equal to a common value.
We have only the length of three sides of each triangle.
If those sides are proportional, we must have an angle of each triangle to be equal.
Let's look if the sides are proportional.
8 / 12.8 = 0.625
10 / 16 = 0.625
15 / 24 = 0.625
So, The sides are proportional, then given triangles are similar.
Hence, Triangle ABC is similar to triangle XYZ.
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Cargo is tied with rope on the roof of a 45-foot tall car. The car travels down a road at 40 mi/h and hits a concrete barrier and the rope snaps, allowing the cargo to propel forward. Find the time it
takes for the cargo to hit the groupd and the horizontal distance the cargo travels. Let y represent height in feet, let x represent horizontal distance in feet, and let rrepresent time in seconds.
Equation 1:7-1611²+ 45
Equation 27-0047x²+45
Answer:5.29 seconds to hit ground 30.86 feet in air
Step-by-step explanation:
The first equation, y = 7.16t^2 - 40t + 45, represents the vertical position of the cargo as a function of time.
The second equation, y = -0.047x^2 + 45, represents the height of the cargo as a function of horizontal distance traveled.
To find the time it takes for the cargo to hit the ground, we need to find when y = 0 in the first equation.
Setting y = 0, we have:
0 = 7.16t^2 - 40t + 45
Solving for t, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
where a = 7.16, b = -40, and c = 45.
t = (40 ± √(40^2 - 4 * 7.16 * 45)) / (2 * 7.16)
t = (40 ± √(1600 - 322.2)) / (2 * 7.16)
t = (40 ± √1277.8) / (2 * 7.16)
t = (40 ± 35.62) / 14.32
t = (75.62 / 14.32, 4.38 / 14.32)
Since t must be positive, t = (75.62 / 14.32) = 5.29 s
Now that we have the time it takes for the cargo to hit the ground, we can use that time in the second equation to find the horizontal distance the cargo traveled.
x = √((45 - 0) / -0.047)
x = √(45 / -0.047)
x = √(45 * -21.28) = √(957) = 30.86 ft
So, it takes the cargo 5.29 seconds to hit the ground, and it travels 30.86 feet horizontally.
PLEASE HELP (GEOMETRY)
Multiple choice question:
a. A reflection over the x-axis followed by 180° rotation centered at origin
b. 180° rotation centered at (0, 5)
c. Reflections over the y-axis followed by another reflection
d. A translation followed by a reflection.
The transformations that could have resulted in the two figures are given as follows:
b. 180° rotation centered at (0, 5)
What is the transformation?The vertices A and B of the original figure are given as follows:
A(-2,5) and B(-5,4).
The equivalent vertices on the transformed figure are given as follows:
A(2,5) and B(5,6).
There is not a constant rule that can be established between the vertices, meaning that a rotation centered at a point different of the origin happened, and thus the correct option is given by option b.
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please help asap will mark brainlistist
Step-by-step explanation:
I understand that when the base area is doubled, the lateral height still stays at 4 in.
the surface area of a cone is in general
pi×r(r + L)
r being the radius, L being the slant or lateral height.
the area of a circle is
pi×r²
r being again the radius.
we are given the base area (a circle) of the cone :
49×pi in²
that means r = sqrt(49) = 7 in.
the lateral height is 4 in.
so, the original total surface area is
pi×7(7 + 4) = 3.14×7×11 = 241.78 in²
and we know now that it takes 2.5 minutes to paint these 241.78 in².
next step : the base area is doubled. it is now
2×49×pi in² = 98×pi in²
the new radius is
r = sqrt(98)
and the new total surface area is
3.14×sqrt(98)×(sqrt(98) + 4) = 432.0576564... in²
it will take
432.0576564.../241.78
times of the original time (2.5 minutes) to paint the new cone.
2.5 × 432.0576564.../241.78 = 4.467466875... minutes ≈
≈ 4.5 minutes
so, it will take about 4.5 minutes to paint the new cone.
FYI
that is all theoretical based on the formula for the surface area.
but - BUT ! - these cones are impossible to exist !
starting with the initial cone with the radius of 7 in.
the lateral height = sqrt(r² + h²).
r is the radius, h is the internal straight height.
4 = sqrt(7² + h²)
16 = 7² + h² = 49 + h²
h² = -33
h = sqrt(-33)
which is impossible for real numbers.
the whole thing is even worse when doubling the base area.
just imagine you are looking directly from above on the cone.
the lateral height must appear to be the same as the radius, which means the lateral height has to be > radius to allow a cone to be formed.
but here the lateral height is smaller than the radius. that means our cone is not a cone, this object can only exist as conical frustum (a cone with the top cut off).
so, many greetings to your teacher for giving you an incorrect problem !
Conservation of momentum states that the total momentum of a non-isolated system must remain constant.True or false?
Answer: This is True.
Can someone pls help me figure out this addition problem in base five?
The 1←5 machine answer in exploding dots format for 645 is 175.
What is explosion of dots?
Exploding Dots is a reconceptualization of the representation of numerals (and polynomials), which allows for a novel way of understanding arithmetic, algebra and series.
The addition of 2 + 4 gives = 6
The addition of 1 + 3 gives = 4
The addition of 3 + 2 gives = 5
The exploding dots diagram is shown for the same.
There are 6 twenty fives.
There are 4 fives.
There are 5 ones.
This all adds up to -
(6 × 25) + (4 × 5) + (5 × 1)
150 + 20 + 5
175
Therefore, the answer is obtained as 175.
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24
x+y+z=9
2₂75y +72=5₂
22² +y=z=0
Using Gaussian elimination method
x=-224/229, y=296/229, Gaussian elimination approach is z=118/229.
Explain about the Gaussian elimination method?The row reduction strategy for solving linear equation systems in mathematics is also referred to as the Gaussian elimination method. A series of procedures are carried out on the corresponding coefficients matrix to create it.
Gaussian elimination is the name of this process, which entails the gradual removal of the variables. Sample 1 Make this system work: The variable x is removed from the second equation by multiplying the first equation by 3, then adding the result. This last formula, 5 y = 5, suggests y = 1 right away.
Systems of linear equations are resolved using the Gaussian elimination (also known as row reduction) approach. It bears the name of Carl Friedrich Gauss, a well-known German mathematician who discussed this approach but did not create it.
-5x-7y-4z=-6
6x+2y+3z=-2
-x+2y-7z=0
(Multiply with -5 and add the result to the first equation; multiply with 6 and add the result to the second equation)
-x+2y-7z=0
-17y+31z=-6.....(mult with 14) (mult with 14)
the sum of 14y-39z=-2 (mult with -17)
-x+2y-7z=0
We have z=118/229 since -229z=-118.
14y-39*(118/229)=-2, thus y=296/229 follows.
-x+2*(296/229)-7*(118/229)=0, hence x=-234/229 is the result.
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How many 11/2 ounce doses of medication are there in a 24 ounce bottle?
Answer:
There are only 4, 11/2 ounce of medication in a 24 ounce bottle
Step-by-step explanation:
11/2 = 5.5, 24/5.5=4.4
A rock falls from a tower that is 352 feet high. As it is falling, it given by the formula h=352-16t/2. How many seconds (in tenths) will it take for the rock to hit the ground (h=0)?
Answer:
Below
Step-by-step explanation:
0 = 352-16t/2 <======are you sure of this equation? (it is incorrect)
-352 = -16t/2
704 = 16t
t = 44 s
The correct equation is
0 = 352-16t^2
which results in t = 4.7 seconds
yaster car sharing offers a membership plan with a $42 per month fee that includes 13 hours of driving each month and charges $8 for each additional hour. let be the cost for a month in which a member uses a car for hours. then is the piecewise function 42, for 13, , for 13 for some scalars and . find . round to the nearest whole number.
The value of b for the cost function F(x)
= mx + b, of a membership plan in car sharing offer ( picewise function) is -64.
We have, yaster car sharing offers a membership plan, the fee of complete month = $42 includes 13 hours of driving each month.
Additional charges for each hour = $8
Let F(x) be the cost for a month in which member uses a car for x hours. F(x) is Piecewise function defined as F(x)= 42, for 0≤x≤ 13,
F(x) = mx+b, for x> 13 for some scalars m and b. We have to determine value of b.
When member uses a car for more than 13 hours, x> 13, For 13 hours monthly fee would be $42 and for hours after 13 hours (x- 13) hours the fee would be $8 for each hour. So, the cost would be
= (x - 13)8+ (42)
Simplify the expression,
= 8x - 104 + 42
F(x) = 8x - 64
Now, comparing the above expression of f(x) with F(x) = mx + b, we get m= 8 , b = - 64 . Hence the required value is - 64.
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Complete question:
Yaster Car Sharing offers a membership plan with a $42 per month fee that includes 9 hours of driving each month and charges $8 for each additional hour. Let F(x) be the cost for a month in which a member uses a car for x hours. Then F(x) is the piecewise function
F(x)= 42, for 0≤x≤ 13
F(x)=mx+b, for x> 13 for some scalars m and b. Find b. Round to the nearest whole number.
A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the weight density of water. Assume that a = 4 m, b = 4 m, c = 18 m, and d = 3 m.)
The work W required to pump the water out of the spout is 6, 115, 200 Joule.
What is Work done ?The product of the displacement and the component of the applied force of the object in the displacement direction is the work done by a force. Work is accomplished when we push a block with some force; the body moves more quickly. Work completed is noted as.
Given:
The first step is to compute the work against gravity performed on a thin layer of the liquid of width Δ y.
A thin layer at height y is a rectangular box of volume 18y Δy and to lift it , we must exert a force against gravity equal to
So, Force on layer = g [ density] [ volume]
≈ 9.8 (1000 ) 18y Δy
and, The layer has to be lifted a vertical distance of 7−y , so
Work on layer ≈ 176400 yΔy [ 7−y ]
Then W= [tex]\int\limits^3_0[/tex] 176400 yΔy [ 7−y ]
= 176400 [ 7 (4)² /2 - 4³/3 - 7 (0)² /2 + 0³/3]
= 176400 x (56 - 64/3)
= 6, 115, 200 Joules
Hence, the work done is 6, 115, 200 Joules.
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