Using it's concept, the standard deviation of the data-set is of 2.39.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.The mean of the data-set in this problem is given by:
M = (6.5 + 11.2 + 13 + 6.3 + 7 + 8.8 + 7.4)/7 = 8.6.
Hence the standard deviation is:
[tex]S = \sqrt{\frac{(6.5-8.6)^2+(11.2-8.6)^2+(13-8.6)^2+(6.3-8.6)^2+(7-8.6)^2+(8.8-8.6)^2+(7.4-8.6)^2}{7}} = 2.39[/tex]
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Suppose you are asked to compare two functions, A and B. Function A written in slope-intercepts form, y= -3x + 4. Function B is graphed on the coordinate plane and has a greater rate of change but lower y-intercept than function A. Describe what is true about the graph of function B.
Answer:
Use the slope and one of the points to solve for the y-intercept (b). One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.
Step-by-step explanation:
What are the potential solutions of log4X+log4(x+6)=2?
Ox=-2 and x=-8
Ox=-2 and x = 8
O x=2 and x=-8
Ox=2 and x=8
Answer:
x = 2 ; x = -8
Step-by-step explanation:
Log rule: Log a + log b = log a*b[tex]\sf \ log_4 \ x +log_4 \ (x +6) = 2\\\\ log_4 \ (x)*(x +6) = 2\\\\[/tex]
log₄ ( x² + 6x) = 2
4² = x² + 6x
x² + 6x - 16 = 0
x² - 2x + 8x - 16 = 0
x(x - 2) + 8(x - 2) = 0
(x - 2) (x + 8) = 0
x - 2 = 0 or x + 8 = 0
x = 2 or x = - 8
Graph the following exponential functions and determine the y-intercept, domain, range, and
asymptote of each function.
f(x)=5(2)^x
The graph of the exponential function f(x) = 5(2)ˣ is as shown in the attached file.
How to draw the graph of an exponential Function?We want to draw the graph of the exponential function;
f(x) = 5(2)ˣ
At input of x = 0, we have;
f(x) = 5(2)⁰ = 5
At input of x = 1, we have;
f(x) = 5(2)¹ = 10
At x = -1, we have;
f(x) = 5(2)⁻¹ = 2.5
At x = -2, we have;
f(x) = 5(2)⁻² = 1.25
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The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the
y-varlable, and what is the solution for this system?
x+3y=42
2x-y=1
=======================================================
Explanation:
The 3y in the first equation must add to -3y so the y terms go away. We have -y in the second equation, which is why we triple everything in that equation
2x-y = 1 becomes 6x - 3y = 3 after tripling everything. This is the same as multiplying both sides by 3.
This is the updated equivalent system
[tex]\begin{cases}x+3y = 42\\6x-3y = 3\end{cases}[/tex]
Add the terms straight down
x+6x becomes 7x3y+(-3y) becomes 0y or 0. The y variables are eliminated.The right hand sides 42 and 3 add to 45We have the equation 7x = 45 which solves to x = 45/7.
Unfortunately it doesn't turn into a nice single whole number because 45 isn't a multiple of 7. So I would leave it as a fraction.
Optionally you could note that 45/7 = 6.42857 approximately. But I prefer the fraction form since it's most exact.
--------------
Use this x value to find y. Pick any equation involving x and y. Plug in that x value and solve for y.
x + 3y = 42
45/7 + 3y = 42
3y = 42 - 45/7
3y = 42*(7/7) - 45/7
3y = 294/7 - 45/7
3y = (294 - 45)/7
3y = 249/7
y = (249/7)*(1/3)
y = 83/7
Like with x, we also don't get a nice whole number.
I used WolframAlpha to confirm the solutions. GeoGebra is another tool you could use.
An angle of measure 120 degrees intersects the unit circle at point (-1/2,√3/2) What is the exact value of cos(120)
The exact value of cos120 if the measure 120 degrees intersects the unit circle at point (-1/2,√3/2) is 0.5
Solving trigonometry identityIf an angle of measure 120 degrees intersects the unit circle at point (-1/2,√3/2), the measure of cos(120) can be expressed as;
Cos120 = cos(90 + 30)
Using the cosine rule of addition
cos(90 + 30) = cos90cos30 - sin90sin30
cos(90 + 30) = 0(√3/2) - 1(0.5)
cos(90 + 30) = 0 - 0.5
cos(90 + 30) = 0.5
Hence the exact value of cos120 if the measure 120 degrees intersects the unit circle at point (-1/2,√3/2) is 0.5
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Answer:
It's -0.5
Explanation:
Answered it
Green’s Sport Shop offers its salespeople an annual salary of $10,000 plus a 6% commission on all sales above $20,000. Every employee receives a Christmas bonus of $500. What are Mr. Cahn’s total earnings in a year in which his sales amounted to $160,000?
(A) $18,900
(B) $18,400
(C) $19,600
(D) $20,100
The total earnings for the year is $18,900.
What is the total earnings?The total earnings is a sum of the annual salary, commission and Christmas bonus.
Commission = 6% x (160,000 - 20,000) =
6% x $140,000
0.06 x 140,000 = $8,400
Total earnings = $8,400 + 10,000 + $500 = $18,900
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Q.3. The slope of line is ¾ and the y - intercept is equal to 4 . Write the equation of the line and draw the graph of the line.
help me now!!
The equation of line with the given slope and y-intercept is y = (3/4)x + 4.
What is the equation of the line?Given that;
Slope = 3/4y-intercept b = 4Equation of the line y = ?We use the formula for equation of line to determine the equation.
y = mx + b
Where m is the slope and b is the y-intercept.
We plug in our values
y = mx + b
y = (3/4)x + 4
Therefore, the equation of line with the given slope and y-intercept is y = (3/4)x + 4.
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can someone please help mee (will give brainliest 20 points!!!)
Assume that y varies directly with x. If y = 24 when
x = 6, find y when x = -4.
y=
Check
Step-by-step explanation:
that means nothing else than
y = k×x
24 = k×6
k = 24/6 = 4
y = k×-4 = 4×-4 = -16
iteration-Find the first 3 iterates of the function look at pic pls help!!!!!
The first 3 iterates of the function are D. 3, -3, 9.
How to calculate the value?The function given is:
f(x) = -2x + 3
= -2(0) + 3
= 3
When x = 3
f(x) = -2x + 3
= -2(3) + 3
= -6 + 3
= -3
When x = -3
f(x) = -2x + 3
= -2(-3) + 3
= 9
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The leaning Tower of Pisa was completed in 1372 and makes 86 degree angle with the ground. The tower is 50 meters tall, measured vertically from the ground to the highest point. If you were to climb to the top then accidentally drop your keys, where would you start looking for them? question 5
Answer:
you would look for them 3.5 meters away from the base
Step-by-step explanation:
so u do tan 86 =50/x
and u solve from there
The square root of the quantity 4 x minus 3 end quantity equals 5.
Answer:
The statement is false.
Step-by-step explanation:
Given,
[tex] \sqrt{4 \times - 3} = 5[/tex]
To Prove
Soln:
[tex] \sqrt{4 \times - 3} [/tex]=[tex]2i \sqrt{3} [/tex]
=>[tex]2i \sqrt{3} ≠5[/tex]
Hence, 2i√3 is not equal (≠) to 5.
How many pairwise comparisons must you make for a case with 15 statistically independent scenarios?
There are 105 comparisons made with 15 statistically independent scenarios.
According to the statement
we have given value of n is 15.
Then r = 2. so,
we use the formula NcR then
Substitute the values in it then
15c2
we open it according to ncr formula
In this formula we arrange the terms according to the following
NcR formula = n! /r! * (n-r)!
then the terms will arrange in this way.
So,
ncr = 15! / 2! * 13!
After solving the statement some terms will be cancel with each other and remaining terms are
ncr = 15*14/2
ncr = 210/2
ncr = 105
here the value becomes 105.
So, There are 105 comparisons made with 15 statistically independent scenarios.
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What are the factors of 3x2 23x − 8? (3x − 4)(x 2) (3x − 2)(x 4) (3x − 8)(x 1) (3x − 1)(x 8)
Answer:
(3x − 1)(x 8)
Step-by-step explanation:
Function f is a rational function with a y-intercept at (0,2). if g(x) = 4f(x), which point represents the y-intercept of function g?
Answer:
(0,8)
Step-by-step explanation:
[tex]g(0)=4f(0)=4(2)=8[/tex]
The monthly income of a government servant is Rs 77,280 and he gets the festival expense of one month's salary, what is his taxable income?
I don't think this question is complete but here's ur answer
The diameter of the earth
at the equator is about
8.000 mi.
Based on this figure, how
far is it around the earth?
Answer:
25,132.74 miles
Step-by-step explanation:
Hello!
We are basically asked to find the circumference of the Earth's cross-section.
Circumference: [tex]C = 2\pi r[/tex]
We can replace 2r with the diameter, because the diameter is 2 times the radius.
Multiply the Diameter by pi:
[tex]C = \pi D[/tex][tex]C = 8000\pi[/tex][tex]C = 25,132.7412287183 \approx 25,132.74[/tex]It is around 25,132.74 miles around.
Given g of x equals cube root of the quantity x plus 6, on what interval is the function negative? (–∞, –6) (–∞, 6) (–6, ∞) (6, ∞)
The interval where the function is negative is (–∞, –6)
How to determine the negative interval?The function is given as:
[tex]f(x) = \sqrt[3]{x + 6}[/tex]
Set the radicand to less than 0
x + 6 < 0
Subtract 6 from both sides
x < -6
Rewrite as an interval notation.
(–∞, –6)
Hence, the interval where the function is negative is (–∞, –6)
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Machine A produces 300 bolts less than three times the number machine B produces. If
machine A produces 4,800 bolts, then how many does machine B produce?
Step-by-step explanation:
what is the best definition of luminous
Someone help pls, its urgent! ASAP!!! (Geometry)
“Fill in the blanks”
14) theorem
15) sides
16) separately
17) equilateral
18) supplementary
What are the first five terms in the
recursive sequence defined by the
following?
The first five terms of the sequence are {0, -1.4, -2.8, -4.2, -5.6}
Recursive functionGiven the nth term of a recursive expression shown below
an =an-1 - 1.4
where
an-1 is the preceding term
a1 is the first term
an is the nth term
an-1 is
Given the following
a1 = 0
For the second term a2
a2 = 0 - 1.4
a2 = -1.4
For the third term a3
a3 = -1.4 - 1.4
a3 = -2.8
For the fourth term a4
a4 = -2.8 - 1.4
a4 = -4.2
For the fifth term a2
a5 = -4.2 - 1.4
a5 = -5.6
Hence the first five terms of the sequence are {0, -1.4, -2.8, -4.2, -5.6}
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Can someone help me with this having trouble and show work please!!
Answer:
7a + b
Step-by-step explanation:
5a + 2a + 3b - 2b
= 7a + 3b - 2b
= 7a + b
+
Select the correct answer.
AABC is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in the image AABC. If A=(2, 2), B=(4, 3), and C= (6, 3).
what is the length of B'C'?
OA
OB.
OC
OD.
3 units
4 units
2 units
1 unit
Answer:
(d) 1 unit
Step-by-step explanation:
The length of the dilated line segment is the product of the dilation factor and the length of the original line segment. It can also be computed as the length of the segment between the dilated coordinates.
Original line segmentThe length of the original horizontal line segment BC is the difference of its x-coordinates:
BC = 6 -4 = 2 . . . . units
(We know the segment is horizontal because the y-coordinates of the end points are the same.)
Dilated segmentMultiplying the length of the original segment by the dilation factor, we find the length of B'C':
B'C' = dilation factor × BC
B'C' = 0.5×(2 units)
B'C' = 1 unit
Dilated Coordinates
The dilation factor multiplies each coordinate value:
B' = 0.5B = 0.5(4, 3) = (2, 1.5)
C' = 0.5C = 0.5(6, 3) = (3, 1.5)
The length of B'C' is the difference of x-coordinates: 3 -2 = 1 unit.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
The radius of the circle is 3 units. TRUE
The center of the circle lies on the x-axis. TRUE
The center of the circle lies on the y-axis. FALSE
The standard form of the equation is (x – 1)² + y² = 3. FALSE
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. TRUE
Step-by-step explanation:
x² + y² - 2x - 8 = 0
x² - 2x + y² = 8
Complete the square in x.
x² - 2x + 1 + y² = 9
(x - 1)² + y² = 3²
Center: (1, 0); radius: 3
The radius of the circle is 3 units. TRUE
The center of the circle lies on the x-axis. TRUE
The center of the circle lies on the y-axis. FALSE
The standard form of the equation is (x – 1)² + y² = 3. FALSE
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. TRUE
write the slope-intercept form of the equation of each line
1. 9x -7y = -7
2. 11x -4y = 32
3. 11x -8y =-48
Please help I NEED IT ASAP
Answer:
she rides her bike at a rate of 8mph during the second part of the trip.
Step-by-step explanation:
for the first part of the trip, she rides 18 miles in 2 hours which means that she bikes at a rate of 9 miles per hour.
subtracting 18 from 58 gives us the distance she biked during the second part of her trip (which is 40 miles). subtracting 2 from 7 gives us that she biked for 5 more hours. Putting this together means she biked 40 miles in 5 hours.
Now divide miles by hours [tex]\frac{40mi}{5hrs} =8mph[/tex] to get your average rate of change for the second part of the trip.
What is the coordinate point of the linear function 5x+3y=15
Answer: Y-intercept: (0,5) X-intercept: (3,0)
Step-by-step explanation: Set x and y equal to 0.
help i’ll give brainliest!
Solve for x: -8 < 3x +1 < 13
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{-8 < 3x+1 < 13 }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{-8+-1 < 3x+1+-1 < 13+-1 \ (Add \ -1 \ to \ all \ parts) }} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{-9}{3} < \frac{3x}{3} < \frac{12}{3} \ (Divide \ all \ parts \ by \ 3) }} \end{gathered}$}[/tex]
[tex]\red{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{-3 < x < 4 }} \end{gathered}$} }}[/tex]
Divide. Reduce the answer to lowest terms.
Answer:
[tex]\frac{4}{15}[/tex]
Step-by-step explanation:
Given the following question:
[tex]\frac{1}{5} \div\frac{3}{4}[/tex]
To find the answer we will use KCF (Keep, Change, Flip) apply it to the following question and then complete by multiplying and reducing. If needed of course.
[tex]\frac{1}{5} \div\frac{3}{4}[/tex]
Apply KCF:
[tex]\frac{1}{5} \div\frac{3}{4}=\frac{1}{5} \times\frac{4}{3}[/tex]
[tex]\frac{1}{5} \times\frac{4}{3}[/tex]
Solve:
[tex]1\times4=4[/tex]
[tex]5\times3=15[/tex]
[tex]=\frac{4}{15}[/tex]
Answer is in simplest terms.
Which means your answer is the first option or "4/15."
Hope this helps.