Option C and Option D has infinite number of solutions
C. 3x + 2(x - 2) + 6 = 2(2x + 3) + x - 4D. 4(x + 2) + x + 1 = 2x - 3 + 3(x + 4) What is defined as the solution of the equation?Given that we must find equations with an infinite number of solutionsWe have infinite solutions if we end up using the same term on the both sides of a equal sign, including such 4 = 4 or 4x = 4x.There are no solutions if we end up with distinct numbers along both side of the equal sign as in 4 = 5.Option A: -2(x - 2) + 3x = x - 4
Simplify the equation;
-2x + 4 + 3x = x - 4
x + 4 = x - 4
LHS ≠ RHS
Thus, equation does not have infinite solutions.
Option B: 2x + 4(x - 1) = 3(2x + 1) - 2(x - 1)
Simplify the equation;
2x + 4x - 4 = 6x + 3 - 2x + 2
6x - 4 = 4x + 5
6x - 4x = 5 + 4
2x = 9
Obtained equation has only one solution.
Thus, equation does not have infinite solutions.
Option C: 3x + 2(x - 2) + 6 = 2(2x + 3) + x - 4
Simplify the equation;
3x + 2x - 4 + 6 = 4x + 6 + x - 4
5x + 2 = 5x + 2
LHS =RHS
Thus, this equation has infinite solutions.
Option D: 4(x + 2) + x + 1 = 2x - 3 + 3(x + 4)
Simplify the equation;
4x + 8 + x + 1 = 2x - 3 + 3x + 12
5x + 9 = 5x + 9
LHS =RHS
Thus, this equation has infinite solutions.
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The correct question is-
Which equations have an infinite number of solutions?
Select all that apply.
A -2(x - 2) + 3x = x - 4
B 2x + 4(x - 1) = 3(2x + 1) - 2(x - 1)
C 3x + 2(x - 2) + 6 = 2(2x + 3) + x - 4
D 4(x + 2) + x + 1 = 2x - 3 + 3(x + 4)
The perimeter of a triangle is 170 feet and the sides are in the ratio of 25:14:12. Find the area of the triangle.A. 496.08 ft²B. 153.45 ft²C. 494.35 ft²D. 107.24 ft²
The perimeter of a triangle is 170 feet
The sides are in the ratio of 25:14:12
The total ratio 25+14+12=51
Let's calculate each side
[tex]\begin{gathered} \text{First side} \\ \frac{25}{51}\times170=\frac{250}{3}=83.33 \\ \\ \text{second side} \\ \frac{14}{51}\times170=\frac{140}{3}=46.67 \\ \\ \text{Third side} \\ \frac{12}{51}\times170\text{ =40} \end{gathered}[/tex]The three sides are given, so we use the Hero formula to calculate the area of the triangle.
[tex]\begin{gathered} \text{Area =}\sqrt[]{s(s-a)(s-b)(s-c)} \\ \\ S=\frac{a+b+c}{2} \end{gathered}[/tex]a = 83.33ft, b=46.67ft and c=40ft
[tex]\begin{gathered} S=\frac{83.33+46.67+40}{2} \\ \\ S=\frac{170}{2} \\ S=85 \\ \end{gathered}[/tex][tex]\begin{gathered} \text{Area =}\sqrt[]{85(85-83.33)(85-46.67)(85-40)} \\ \\ \text{Area =}\sqrt[]{85(1.67)(38.33)(45)} \\ \\ \text{Area =}\sqrt[]{85(1.67)(38.33)(45)} \\ \\ \text{Area =}\sqrt[]{244842.4575} \\ \text{Area = 494.35 square ft} \end{gathered}[/tex]The correct option is C
An “A” is considered 4.0, a “B” is 3.0, a “C” is 2.0, a “D” is 1.0, and an “F” is 0. A student received the following grades.CourseCreditsGradeSpeech3.0DChemistry4.0FEnglish3.0CNew Student Seminar1.0AFind the student's GPA, rounded to the nearest hundredth.
Answer:
1.18
Explanation:
The GPA is calcuated as follows
[tex]GPA=\frac{grade\text{ points}}{total\text{ credits}}[/tex]where a grade point = score assicated with the grade * number of credit hours for the course.
Now in our case, the grade points earned are
[tex]3(1.0)+4(0)+3(2.0)+1(4)=13[/tex]And the total number of credit hour are
[tex]3+4+3+1=11[/tex]Therefore, the GPA (rounded to the nearest hundredth) is
[tex]GPA=\frac{13}{11}=1.18[/tex][tex]\boxed{GPA=1.18.}[/tex]which is our answer!
12x8.05 Help me with the problem
Write the Coordinates of the verticals after a rotation 90 counter clockwise around the origin
R=
S=
Q=
T=
The preimage's coordinates are R(-3, 6), S(-1, -2), and Q(-7, 1).
How can you spot changes in something?This point can be another point on the graph, though it is often the origin (0,0) of the graph or a point on the picture. Determine whether any of the points on the original figure are oriented differently in the altered version and whether the figure appears to be turned.The pre image R S, and Q locations must be discovered.A point is transformed when it is moved from its original location to a new one. Reflection, rotation, translation, and dilation are examples of different transformations.The new point is at R' if a point R(x, y) is rotated 90 degrees clockwise about the origin (y, -x)Thus, we must follow the rule (-y,x) ——>(x,y).
Applying the law,
R'(6, 3) -----> R(3, -6)
S'(–2, 1) -----> S(1, 2)
Q'(1,7) -----> Q (7, -1)
The preimage's coordinates are R(-3, 6), S(-1, -2), and Q(-7, 1).
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Find an expression which represents the sum of (-6x + 6) and (-3x – 7) insimplest terms.
Given an expression of (-6x +6) and (-3x - 7)
[tex]\text{The sum of the expression (-6x +6) and (-3x -7)}[/tex][tex]\begin{gathered} -6x\text{ + 6 + -3x -7 } \\ \text{collecting like terms} \\ -6x\text{ -3x + 6 - 7 } \\ -9x\text{ - 1} \end{gathered}[/tex]Hence the solution to the above expression is
[tex]-9x\text{ - 1}[/tex]In a running competition, a bronze, silver and gold medal must be given to the top three girls and top three boys. If 8 boys and 6 girls are competing, how many different ways could the six medals possibly be given out?
As given by the question
There are given that the total number of boys is 8 and total numbers of girls is 6.
Now,
Since there are two competitions, one for boys and one for girls and we want all the possible results we will calculate the possible combination for the boys and multiply them by the possible combination for the girls.
Then,
For the boys:
[tex]\begin{gathered} \text{Boys}=\frac{8!}{(8-3!)} \\ \text{Boys}=\frac{8!}{(8-3)!} \\ \text{Boys}=\frac{8!}{(5)!} \\ \text{Boys}=\frac{8\times7\times6\times5!}{(5)!} \end{gathered}[/tex]Then,
[tex]\begin{gathered} \text{Boys}=\frac{8\times7\times6\times5!}{(5)!} \\ \text{Boys}=8\times7\times6 \\ \text{Boys}=336 \end{gathered}[/tex]Now,
For the girl:
[tex]\begin{gathered} Girl\text{s}=\frac{6!}{(6-3)!} \\ Girls\text{s}=\frac{6!}{(3)!} \\ Girls\text{s}=\frac{6\times5\times4\times3!}{(3)!} \end{gathered}[/tex]Then,
[tex]\begin{gathered} Girls\text{s}=\frac{6\times5\times4\times3!}{(3)!} \\ Girls=6\times5\times4 \\ Girls=120 \end{gathered}[/tex]Now,
A total number of possible results:
[tex]\begin{gathered} \text{result}=120\times336 \\ \text{result}=40320 \end{gathered}[/tex]Hence, the ways are 40320.
Is 4/21 and 16/84 proportional
Answer:
yes
Step-by-step explanation:
[tex]\frac{16}{84}[/tex] ( divide numerator and denominator by 4 )
= [tex]\frac{4}{21}[/tex]
they represent the same proportion
Complete the sequence of transformations that produces △X'Y'Z' from △XYZ.
A clockwise rotation
° about the origin followed by a translation
units to the right and 6 units down produces ΔX'Y'Z' from ΔXYZ.
A clockwise rotation 90° about the origin followed by a translation
2 units to the right and 6 units down produces Δ X'Y'Z' from Δ XYZ
There are four types of transformations: reflection, rotation, translation, and dilation.
What are transformations?Translation, rotation, reflection, and dilation are the four primary categories of transformation.
* Let's update the translation and rotation.
-If point (x, y) rotates 90 degrees counterclockwise with respect to the origin, then Its picture is (-y , x)- If point (x, y) rotated 180 degrees counterclockwise with respect to the origin Its picture is (-x , -y)- If point (x, y) rotates 270 degrees counterclockwise with respect to the origin Its picture is (y , -x)- If point (x, y) rotates 90 degrees clockwise with respect to the origin Its picture is (y , -x)- If point (x, y) rotates 180 degrees clockwise with respect to the origin Its picture is (-x , -y)If the point (x, y) rotated.
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Answer:clockwise rotation 90
translation is 2 units
Step-by-step explanation:
How do you graph y=4x at x=-4? What does it look like on a graph
We want to plot the graph of the equation;
[tex]y=4x[/tex]we can do this by assuming to different values of x and deriving the corresponding values of y at those points.
for x= -4;
[tex]\begin{gathered} y=4(-4) \\ y=-16 \end{gathered}[/tex]Also taking a second point.
at x = 0;
[tex]\begin{gathered} y=4(0) \\ y=0 \end{gathered}[/tex]Since the equation is a linear equation, the graph will be a straight line graph;
the graph will be a straight lin passing through the two points derived.
[tex](-4,-16)\text{ and (0,0)}[/tex]the graph of the given equation can be shown below;
Find the missing the side of the triangle.A. √30 ydB. √17 ydC. 2√5 ydD. 0 yd
For the given triangle, hypotenuse side is x and length of legs of right triangle is,
[tex]\sqrt[]{10}\text{ yards}[/tex]Determine the value of x by using pythagoras theorem in right angle triangle.
[tex]\begin{gathered} x=\sqrt[]{(\sqrt[]{10})^2+\sqrt[]{10})^2} \\ =\sqrt[]{10+10} \\ =\sqrt[]{20} \\ =\sqrt[]{2\cdot2\cdot5} \\ =2\sqrt[]{5} \end{gathered}[/tex]Answer: Option C (2√5 yd)
Please help me with this I do not understand. I did the steps but am really looking for the answer if you could help.
ANSWER :
The zeros are 1/2 and -5
EXPLANATION :
From the problem, we have the function :
[tex]f(x)=2x^2+9x-5[/tex]The zeros of the function are the values of x when f(x) = 0
[tex]2x^2+9x-5=0[/tex]Using quadratic formula with a = 2, b = 9 and c = -5
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ x=\frac{-9\pm\sqrt{9^2-4(2)(-5)}}{2(2)} \\ \\ x=\frac{-9\pm\sqrt{81+40}}{4} \\ \\ x=\frac{-9\pm\sqrt{121}}{4} \\ \\ x=\frac{-9\pm11}{4} \\ \\ x=\frac{-9+11}{4}=\frac{1}{2} \\ \\ x=\frac{-9-11}{4}=-5 \end{gathered}[/tex]Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
Although it is impossible to send mail to 1.2 homes in a minute, Mark's solution is valid since 1.2 corresponds to the unit rate of homes per minute.
What is the mark's method?When reset() is performed, the stream is marked as the checkpoint from which the stream read will begin in Java by using the mark() function of the Reader class.
Option 1: Mark's approach is incorrect since there is no way to distribute mail to 1.2 homes in a minute. Only a certain amount of homes can get deliveries from the carrier.
This is untrue because the rate of 1.2 just indicates that the carrier may complete one house in a minute while still having time to begin delivering to the second residence. While the rate is not required, the total number of houses must be a whole number.
Option 2: Mark's approach is incorrect since mail cannot be delivered for 7.5 minutes. Mail delivery by the carrier is limited to a set number of minutes.
Furthermore erroneous is this choice.
Option 3: Mark's approach is accurate because, not with standing the impossibility of delivering mail to 1.2 homes in a minute, 1.2 corresponds to the average number of homes every minute.
This choice is the best one. The mail is delivered by the carrier at a rate of 1.2.
Option 4: Mark's approach is accurate because he can deliver mail for 7.5 minutes, which corresponds to the unit rate of 7.5 minutes per dwelling.
Furthermore erroneous is this choice. Although it is feasible to transport mail for 7.5 minutes, this is the overall time required, not the unit rate.
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Complete question is" A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wants to determine how many houses the carrier can deliver mail to in 7.5 minutes at this rate. He thinks that to find the answer, he should do the following. 1. First divide 36 houses by 30 minutes to find a unit rate of 1.2 houses per minute. 2. Then multiply 1.2 houses per minute by 7.5 minutes to get 9 houses. Which statement is correct? Mark’s method is wrong, because it is impossible to deliver mail to 1.2 houses in a minute. The carrier can only deliver to a whole number of houses. Mark’s method is wrong, because it is impossible to deliver mail for 7.5 minutes. The carrier can only deliver mail for a whole number of minutes. Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute. Mark’s method is correct, because it is possible to deliver mail for 7.5 minutes; 7.5 represents the unit rate of 7.5 minutes per house."
Write an equation in point slope form for the line that passes through (-3,5) with a slope of -3
An equation in point slope form for the line that passes through (-3,5) with a slope of -3 is y + 3x + 4 = 0
The standard equation of a line in point slope form is
y = mx + c
where m represents the slope of the line and c stands for y intercept
We need to find an equation in point slope form for the line that passes through (-3,5) with a slope of -3
y - y₁ = m(x - x₁)
y - 5 = -3(x - (-3))
y - 5 = -3 (x + 3)
y - 5 = -3x - 9
y + 3x + 4 = 0
Therefore, an equation in point slope form for the line that passes through (-3,5) with a slope of -3 is y + 3x + 4 = 0
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Determine the inverse of the function f (x) = 2(x − 3)2 + 4.
The inverse of the function is [tex]f^-1 = \frac{1}{4}x + 2[/tex] .
What is inverse of the function ?
A function that "undoes" another function is known as an inverse in mathematics. To put it another way, if f(x) produces y, then y will produce x when y is fed into f's inverse function. A function f is said to be invertible if it has an inverse, and the inverse is represented by the symbol [tex]f^-1[/tex]
Here the given function is,
=> f(x) = 2(x-3)2+4
=> f(x) = 4(x-3)+4
=> f(x) = 4x-12+4
=> f(x) = 4x -8
Now take y= f(x) then,
=> y = f(x)=4x-8
=> y = 4x-8
Now interchange x and y then,
=> x = 4y-8
Now solve for y then,
=> x+8 = 4y
=> y= [tex]\frac{1}{4} x+ 2[/tex]
Then [tex]f^-1[/tex] = [tex]\frac{1}{4}x+ 2[/tex]
Therefore inverse of the function is [tex]f^-1 = \frac{1}{4}x + 2[/tex] .
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I really need help with this
The mean for the girls as a percentage of the mean for the boys is 160 percent .
What is mean in mathematic?
In mathematics, the mean is the product of the sum of the added values of all the data in a set and the number of data in the set.
We know that, the formula for the calculation of mean is:
Mean = sum of terms / number of terms
Number of terms is given as 40. Whereas the sum obtained as follows:
Boys with average spent 10 is 18: 10(18) = 180
Boys with average spent 30 is 9: 30(9) = 270
Boys with average spent 50 is 7: 50(7) = 350
Boys with average spent 70 is 6: 70(6) = 420
So, the total sum of terms equals to: 180 + 270 + 350 + 420 = 1220
Therefore the mean is:
Mean = 1220/40
Mean = 30.5
Now, calculating the mean for the girls as a percentage of the mean for the boys:
Mean for the girls given is : 48.80
So,
Percentage = (amount*100)/total amount
Percentage = (48.80(100))/30.5
Percentage = 160 %
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PLEASE HELP AS SOON AS POSSIBLE
For the given figure, a parallel to b and l parallel to m
x° = 95°
y° = 95°
z = 85°
From figure,
a || b and l || m
∠RUT = ∠aRU (Alternate interior angle)
∠RUT = 85°
Again,
∠RUT + ∠UTS = 180° (Co-interior angle)
85° + x° = 180°
x° = 180° - 85°
x° = 95°
again from figure,
x° = y° (Vertical opposite angle)
y° = 95°
also,
∠UTS + z° = 180° (Linear Pair)
x° + z° = 180°
z° = 180° - x°
= 180° - 95°
z° = 85°
So from above calculation,
x° = 95°
y° = 95°
z = 85°
Hence option B is correct
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One pound is equal to 0.454 kilogram. If Jim has a mass of 50 kilograms, write an equation to represent how many pounds, p, he weighs.
Answer: p=110.1321 pounds
Step-by-step explanation:
50 divided by 0.454 is equal to 110.1321
Suppose Maya multiplied 9368x68754323 cubes. Then she divided the awnser by 9 and turned the Answer Into a fraction and multiplied that by 38…And then split that awnser into 6 equal groups. How many cubes would she put in each group?
The no of cubes she would put in each group if she multiplied 9368x68754323 cubes. Then she divided the answer by 9 and turned the Answer Into a fraction and multiplied that by 38, And then split that answer into 6 equal groups is 453248868900.
What is multiplication?
Along with addition, subtraction, and division, multiplication is one of the four basic mathematical operations. Multiply in mathematics refers to the continual addition of sets of identical sizes.
The symbols cross (×), asterisk (*) and dot (·) are used to denote multiplication. You most frequently utilize the cross when writing in your notebooks. In computer languages and algebra, the asterisk and dot are both utilized (higher mathematics).
Given:
The no of cubes, n = 9368 × 68754323,
Divide the no of cubes by 9,
n / 9 = 9368 × 68754323 / 9
Now multiplied by 38 and split into 6, we get,
= (9368 × 68754323 × 38) / (9 ×6)
= 453248868900
Therefore, The no of cubes she would put in each group is 453248868900.
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Hank has picked 1.3 pounds of berries and picks about 0.75 pounds per min. Tom has picked 2.5 pounds of berries and picks about 0.5 pounds per minute. In how many minutes where are picked at least as many pounds of berries as Tom?
Hank: 1.3 pounds at a rate of 0.75 pounds per minute
Tom: 2.5 pounds at a rate of 0.5 pounds per minute
rate is given by
r = p / t
where p is the number of pounds picked during a fixed time
The number of berries picked by Hank during a certain time is given by the following equation
[tex]H=1.3+0.75t[/tex]For Tom, the equation is the following:
[tex]T=2.5+0.5\cdot t[/tex]Now, we need to find a time t when T and H are the same
[tex]\begin{gathered} H=T \\ 1.3+0.75t=2.5+0.5t \end{gathered}[/tex]We now just need to solve for t
Let's find t step by step
[tex]\begin{gathered} 1.3\cdot\: 100+0.75t\cdot\: 100=2.5\cdot\: 100+0.5t\cdot\: 100 \\ 130+75t=250+50t \\ 130+75t-130=250+50t-130 \\ 75t=50t+120 \\ 75t-50t=50t+120-50t \\ 25t=120 \\ \frac{25t}{25}=\frac{120}{25} \\ t=\frac{24}{5} \end{gathered}[/tex]Which is the same as t=4.8
g(x) = x2
g
(
x
)
=
x
2
, what is the product of f(x) and g(x)
The product of the functions f(x) = [tex]x^{2}[/tex] and g(x) = x - 8 is f(x).g(x) = [tex]x^{3} -8x^{2}[/tex]
The given functions are :
f(x) = [tex]x^{2}[/tex] --- (1)
g(x) = (x - 8) --- (2)
The product of the functions is obtained by multiplying equations (1) and (2)
f(x). g(x) = [tex]x^{2}[/tex] × (x - 8)
f(x).g(x) = [tex]x^{3} - 8x^{2}[/tex]
Let us take another example:
Let f(x) = [tex]x^{3} -2x^{2} +x-4[/tex] and g(x) = [tex]\frac{1}{2} x[/tex]
The product of the above two functions will be :
f(x).g(x) = [tex](x^{3} -2x^{2} +x-4) * (\frac{1}{2}x )[/tex]
= [tex](x^{3})(\frac{1}{2}x)-(2x^{2})(\frac{1}{2}x) + (x)(\frac{1}{2}x)-(4)(\frac{1}{2}x)[/tex]
= [tex]\frac{x^2}{2} -x+\frac{1}{2}-\frac{2}{x}[/tex]
= [tex]\frac{x^2}{2}-x-\frac{2}{x} +\frac{1}{2}[/tex]
Hence the answer is The product of the functions f(x) = [tex]x^{2}[/tex] and g(x) = x - 8 is f(x).g(x) = [tex]x^{3} -8x^{2}[/tex]
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Please help!!! Factorise this expression
Answer:
Step-by-step explanation:
Let's solve the equation:
3m² + 22m + 7 = 0
Discriminant:
D = b² - 4·a·c = 22² - 4·3·7 = 400
√ D = √ 400 = 20
m₁,₂ = ( - b ± √ D) / (2·a)
m₁ = ( - 22 + 20) / (2·3) = - 2/6 = - 1 / 3
m₂ = ( - 22 - 20) / (2·3) = - 42/6 = - 7
3m² + 22m + 7 = 3·(m - (-1/3))·((m - (-7)) =
= (3m + 1)·(m + 7)
3m² + 22m + 7 = (3m + 1)·(m + 7)
Which of the following expressions is equivalent to the one shown below?312NowΟ Α.OB. 382O c. 3828OD. 8.• (-/-)
Given:
[tex](\frac{3}{2})^8[/tex]Then:
[tex](\frac{3}{2})^8=\frac{3^8}{2^8}^[/tex]ANSWER
C
On this problem, the answer has been worked out, but you must fill in the blanks in the solution.A study of carbon monoxide deaths showed that a random sample of 6 recent years had a standard deviation of 4.1 deaths per year. Find the 99% confidence interval of the variance and the standard deviation. Round answers to the nearest tenth (one digit after the decimal point).Solution: We are finding confidence intervals for the variance and standard deviation, so we use the formulas
You have to calculate the confidence interval for the population variance and population standard deviation of carbon monoxide deaths.
To calculate the confidence interval for the population variance you have to use the following formula, which is derived from the Chi-Square distribution:
[tex]\lbrack\frac{(n-1)S^2}{\chi^2_{n-1;1-\frac{\alpha}{2}}};\frac{(n-1)S^2}{\chi^2_{n-1;\frac{\alpha}{2}}}\rbrack[/tex]For a sample of n=6 years, the sample standard deviation is S=4.1 deaths per year
To calculate the interval, the first step is to determine the values under the Chi-Square distribution with n-1 degrees of freedom and a confidence level of 0.99
The degrees of freedom for this particular distribution is:
[tex]n-1=6-1=5[/tex]The confidence level is 0.99, calculate the value of α:
[tex]\begin{gathered} 1-\alpha=0.99 \\ \alpha=1-0.99 \\ \alpha=0.01 \end{gathered}[/tex]For the chi-Square value of the left bound, the value of probability is
[tex]1-\alpha/2=1-0.01/2=1-0.005=0.995[/tex]The Chi-Square value for the left bound of the interval corresponds to a distribution with 5 degrees of freedom and 0.995 of accumulated probability
[tex]\chi^2_{5;0.995}=16.8[/tex]So the value of the distribution for the left bound is χ²left= 16.8
For the right bound of the interval, the accumulated probability under the distribution is α/2
[tex]\frac{\alpha}{2}=\frac{0.01}{2}=0.005[/tex]The Chi-Square value for the right bound of the interval is for distribution with 5 degrees of freedom and 0.005 accumulated probability:
[tex]\chi^2_{5;0.005}=0.412[/tex]The value of the distribution for the right bound is χ²right= 0.412
The sample variance is equal to the square of the sample standard deviation so that:
[tex]\begin{gathered} S^2=4.1^2 \\ S^2=16.81 \end{gathered}[/tex]Now you can calculate the confidence interval as follows:
Left bound of the interval
[tex]\frac{(n-1)S^2}{\chi^2_{5;0.995}}=\frac{(6-1)16.81}{16.8}=5.00[/tex]Right bound of the interval
[tex]\frac{(n-1)S^2}{\chi^2_{5;0.005}}=\frac{(6-1)16.81}{0.412}=204.00[/tex]The calculation of the interval can be written as follows:
[tex]\frac{(6-1)4.1^2}{16.8}\leq\sigma^2\leq\frac{(6-1)4.1^2}{0.412}[/tex]So, using a 99% confidence level, the interval for the population variance of the carbon monoxide deaths is [5.00;204.00] deaths per year²
Finally, apply the square root to both bounds of the interval to determine the confidence interval for the population standard deviation:
[tex]\begin{gathered} \sqrt[]{\frac{(6-1)4.1^2}{16.8}}\leq\sigma\leq\sqrt[]{\frac{(6-1)4.1^2}{0.412}} \\ \sqrt[]{\frac{5\cdot16.81}{16.8}}\leq\sigma\leq\sqrt[]{\frac{5\cdot16.81}{0.412}} \\ 2.236\leq\sigma\leq14.283 \\ \end{gathered}[/tex]Rounding to the nearest tenth the interval can be expressed as follows
[tex]2.2\leq\sigma\leq14.3[/tex]Using the same confidence level the confidence interval for the population standard deviation is [2.2;14.3] deaths per year.
State the quadratic formula and multiply by the equation of Albert Einstein's theory of special relativity. Write 3-4 complete sentences to explain how you got your answer, and why this can benefit future civilizations.
Answer:
The Sacheverell Theorem of Mathematics is the answer to your question. I got this answer by using the Vasagle formula and distributing throughout the parenthesis. This can benefit future civilizations because it's an undiscovered new species in the winoculous alternate universe.
Step-by-step explanation:
I am from the year 2420 so I know. Do not doubt me.
Write the equation of the sine curve.
The equation of a sine function given in accordance with the given specifications is y = 3sin[(2/3)x + π/8) - 2.
What are trigonometric functions?The trigonometric functions (also called circular functions, angle functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Given is the following specifications for a sine wave -
Amplitude: 3
Period: 3π
Phase Shift: π/8
Vertical Shift: -2
The general equation for sine wave is -
y = A sin(ωx + Ф) + k
Now, we know -
ω = 2π/T
ω = 2π/3π
ω = 2/3
And -
A = 3
Ф = π/8
k = - 2
y = 3sin[(2/3)x + π/8) - 2
Therefore, the equation of a sine function given in accordance with the given specifications is y = 3sin[(2/3)x + π/8) - 2.
To solve more questions on trigonometry, visit the link below-
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Brandon saved 2 gigabytes of music on his mp3 player. Of the music,1/4 is hip hop. What fraction of a gigabyte did Brandon use for his hip hop music??EQUATION: 2 x 1/4 = 2 ÷ _______, or / ? Draw a picture to show the answer
Answer:
2 x 1/4 = 2 ÷ 4, or 1/2
Explanation:
To multiply a number by a fraction, we can use the following equation:
[tex]a\times\frac{b}{c}=\frac{a\times b}{c}[/tex]Then, to know what fraction of gigabyte Brandon uses for his hip hop music, we need to multiply 2 gigabytes by 1/4 to get:
[tex]2\times\frac{1}{4}=\frac{2\times1}{4}=\frac{2}{4}=\frac{1}{2}[/tex]Where 2/4 is equal to 2 ÷ 4 and it is equivalent to 1/2
Therefore, the answer is:
2 x 1/4 = 2 ÷ 4, or 1/2
It means that Brandon uses 1/2 gigabytes for hip hop music
Additionally, we can represent the situation as:
write an equation of the line that passes through the given and is perpendicular to the given line (2,-5);2y=3x+10
An equation of the line that passes through the given and is perpendicular to the given line (2,-5); 2y=3x+10 is 3y = -2x - 11
Let (x1, y1) = (2, -5)
We can write the equation of line 2y=3x+10 as,
y = (3/2)x + 5
The slope of the line 2y=3x+10 is,
m1 = 3/2
Let m2 be the slope of the required line.
We know that the product of the slope of the perpendicular lines is -1
m1 * m2 = -1
(3/2) * m2 = -1
m2 = -2/3
Using slope point form of line,
(y - y1) = m2(x - x1)
y - (-5) = (-2/3) * (x - 2)
y + 5 = -2/3x + 4/3
y = -2/3x + 4/3 - 5
y = -2/3x -11/3
3y = -2x - 11
Therefore, an equation of the line that passes through the given and is perpendicular to the given line (2,-5); 2y=3x+10 is 3y = -2x - 11
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In the diagram below, the cone has a radius of 9 centimeters and a slant height of 15 centimeters.
image 134fcf7d1dc04fbbb16d3bc2b8f9a75f
What is the volume of the cone?
Responses
324π cm3
324 π cm 3
405π cm3
405 π cm 3
972π cm3
972 π cm 3
1,215π cm3
Answer:
405π cm3
Step-by-step explanation:
help me with this please
1. Create a graph of the function G(t) and explain the meaning of the y-intercept in terms of the number of smartphones being shipping to stores.
2. Explain a way you could calculate exactly when smartphone manufacturers were shipping 500 million smartphones to stores around the world.
The y-intercept indicates that 174 million smartphones were shipped to stores in 2009. This implies that after two years, in 2011, smartphone manufacturers shipped 500 million smartphones to stores worldwide.
Since 2009 the number of smartphones shipped from manufacturers to stores around the world has increased exponentially.
The growth from 2009 through 2015 can be modeled using the function G(t) = 174·[tex]1.67^t[/tex] where t is the number of years since 2009 and G(t) is measured in millions of smartphones.
The required graph of the exponential function G(t) has been attached below
Now, finding the y-intercept
G(t) = 174·[tex]1.67^t[/tex] ...(i)
Substitute the value of t = 0 in the above function,
G(t) = 174·1.67⁰
G(t) = 174(1)
G(t) = 174
The meaning of the y-intercept is that 174 million smartphones are being shipped to stores in years 2009.
Substitute the value of G(t) =500 in the exponential function(i),
500 = 174·[tex]1.67^t[/tex]
500/174 = [tex]1.67^t[/tex]
2.8735 = [tex]1.67^t[/tex]
[tex]\ln \left(2.8735\right)=t\ln \left(1.67\right)[/tex]
[tex]t=\dfrac{\ln \left(2.8735\right)}{\ln \left(1.67\right)}[/tex]
t = 2.05827 ≈ 2
This means after 2 years i.e. in 2011, smartphone manufacturers were shipping 500 million smartphones to stores around the world.
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if the bug can come crawl at a rate of 0.107 VUUNITS/seconds, how long would it take the bug to travel from corner A to corner B
Given :
The dimensions of the Box
Length = 23.5 , Width = 24 , Height = 31.5
Task 1 :
The distance from A to B =
[tex]\sqrt[]{23.5^2+24^2+31.5^2}=\sqrt[]{2120.5}=46.05[/tex]The bug fly at a rate of 0.519 Vunits/sec
So, the time of flying = distance/speed = 46.05/0.519 = 88.73 seconds
Task 2 :
The distance from A to B = 46.05 VUNITS
The bug crawl at a rate of 0.107 VUNITS/sec
So, the time of crawling = 46.05/0.107 = 430.36 seconds