Box with prime numbers = 2, 3, 5, 7
Box with the other numbers = 1, 4,6,8,9, 10
Possible pairs
12 13 15 17 Four pairs
42 43 45 47 Four pairs
62 63 65 67 Four pairs
82 83 85 87 Four pairs
92 9 3 95 97 Four pairs
102 103 105 107 Four pairs
Total numbers of pairs 24 pairs
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 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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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:
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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Problem 2.1
I monitor the amount of battery left on my computer so I can make sure it doesn't die at the wrong time.
My battery loses charge at a constant rate.
This graph shows the percent of charge left on my computer, c, after I have been awake for h hours.
What was the percent charge when I woke up?
---------------------------------------------------------------------------------
Problem 2.2
This graph shows the amount of charge left on my computer, c, after I have been awake for h hours.
Enter an equation that describes the relationship between c and h.
Using the graph, the percent chare when you woke up was: 90%.
The equation that describes the relationship between c and h is: c = -20h + 90.
How to Write the Graph of an Equation?To write the equation of a graph that represents a linear relationship between two variables, x and y, determine the initial value/y-intercept (b) and the value of the constant rate/slope (m), then substitute the values into y = mx + b.
The graph given shows the relationship between charge left on the computer, c, and the number of hours awake, h.
The initial value/y-intercept, b, represents the percent charge when you woke up = 90%.
The constant rate/slope (m) = change in c/change in h = (30 - 10)/(3 - 4)
m = -20/1
m = -20
To write the equation that describes the relationship between c and h, substitute m = 20 and b = 90 into c = mh + b:
c = -20h + 90
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If f(1) = 5, which expression could represent f (x)?
A- 3x(2) + 14x + 8
B- 3x(2) - 14x - 8
C- 3x(2) + 10x -8
D- 3x(2) - 10x -8
If f(1) = 5, then you can find your answer by substituting 1 in for x in all of the options to figure out which one gives you 5 as a result.
A: 3(1)^2 + 14(1) + 8 = 25 ≠ 5 Nope
B: 3(1)^2 - 14(1) - 8 = -19 ≠ 5 Nope
C: 3(1)^2 + 10(1) - 8 = 5 Yup
D: 3(1)^2 - 10(1) - 8 = -15 Nope
Only C fits f(1) = 5.
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
A chemist is using 347 milliliters of a solution of acid and water. If 13.9 of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
48.233 milliliters of acid are there.
Given:
A chemist is using 347 milliliters of a solution of acid and water.
13.9% of the solution is acid.
converting 13.9% to decimal:
13.9% = 13.9/100
13.9% = 0.139
milliliters of acid = total milliliters*0.139
= 347*0.139
= 48.233 milliliters.
Therefore 48.233 milliliters of acid are there.
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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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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
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."
Can you find the slope and type the correct code? Please remember to type in ALL
CAPS with no spaces.
Puzzle #2
1: Find the slope:
X
Y
-1
7002
9339
-9
Your answer
-3
3: Find the slope:
2: Find the slope:
(-1, 5), (2, -7)
4: Find the slope:
X88
88
HI234
Y
1
answer choices
B:
A: ma
C: I
m=
undefined m=6
4
D: - E
m =
3
G:
m=-4
F:
m=3
m=-6
H:
I:
m = 4 m=0
Type the 4-
letter code into
the answer
box. All CAPS,
no spaces.
8000
Answer:
(-1.5).(2.-7)
Step-by-step explanation:
ECHA. Step-by-step explanation: 1.) E. m = 1/2. 2.) C. y2 - y1/x2 - x1 = m. -4 - (-8)/3 - 1 = m. 8 - 4/3 - 1 = m.
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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A direct variation includes the points (6, 18) and (n, -3). Find n.
Since we have a direct variation, we can use the following equation:
[tex]\frac{y}{x}=k[/tex]where k is the constant of variation.
If we use the point (6,18), then, we have:
[tex]\begin{gathered} (x,y)=(6,18) \\ \Rightarrow\frac{18}{6}=k \\ \Rightarrow k=3 \end{gathered}[/tex]now that we have that the constant of variation is k = 3, we can use this information to find n:
[tex]\begin{gathered} (x,y)=(n,-3) \\ k=3 \\ \Rightarrow-\frac{3}{n}=3 \\ \Rightarrow-3=3\cdot n \\ \Rightarrow n=-\frac{3}{3}=-1 \\ n=-1 \end{gathered}[/tex]therefore, n = -1
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)
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
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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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!
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.
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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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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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12x8.05 Help me with the problem
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)
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
I'll send a pic ! I need a rlly fast response !!
The expression given is:
[tex](3^3\cdot3^{-1})^{-2}[/tex]One property of exponents that we know is:
[tex]a^xa^y=a^{x+y}[/tex]We use this property shown above to simplify the expression:
[tex]\begin{gathered} (3^3\cdot3^{-1})^{-2} \\ =(3^{3-1})^{-2} \\ =(3^2)^{-2} \end{gathered}[/tex]Now, we use the power property of exponents, which is:
[tex](a^b)^c=a^{bc}[/tex]to simplify our expression, fully:
[tex]\begin{gathered} (3^2)^{-2} \\ =3^{2\times-2} \\ =3^{-4} \end{gathered}[/tex]Using the property:
[tex]a^{-n}=\frac{1}{a^n}[/tex]we can write the answer as:
[tex]3^{-4}=\frac{1}{3^4}=\frac{1}{81}[/tex]From the choices, given, we can say:
• 2nd choice is correct
,• 3rd choice is correct
[tex]3^{-11}\cdot3^7=3^{-11+7}=3^{-4}[/tex]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:
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.
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]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;
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.
To know more about multiplication:
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