Answer:
The Mean and Standard deviation for the given data would be as follows:
μ =79.7
б =7.81
Step-by-step explanation:
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Standard deviation is the square root of the arithmetic mean of the squares of deviations of the items from their mean values.
Frequency Distribution
Given that,
Temperature Lower Limit Upper Limit Days([tex]f_{i}[/tex])
50-59 50 59 2
60-69 60 69 313
70-79 70 79 1419
80-89 80 89 1503
90-99 90 99 319
100-109 100 109 9
Average([tex]x_{i\\}[/tex])
[tex]\frac{50+59}{2} = 54.5\\ \\\frac{60+69}{2} = 64.5\\ \\\frac{70+79}{2} = 74.5\\\\\frac{80+89}{2} = 84.5\\ \\\frac{90+99}{2} = 94.5\\ \\\frac{100+109}{2} = 104.5[/tex]
As we know,
Mean (μ) =∑ [tex](x_{i}f_{i})[/tex]/∑[tex]f_{i}[/tex]
= { (54.5 * 2) + (64.5 * 313) +(74.5 * 1419)+(84.5*1503)+(94.5*319) + (104.5*9)/ (2+313+1419+1503+319)
∵ μ = 79.7
As we know,
Standard Deviation:-
[tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}[/tex]
by putting the values, we get
∵ б = 7.81
Hence, μ = 79.7 and б=7.81 are the correct answers.
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Which of the following is the standard equation of the ellipse with vertices at (1, 0) and (11, 0) and an eccentricity of three fifths question mark
quantity x minus 6 end quantity squared over 100 plus y squared over 64 equals 1
quantity x plus 6 end quantity squared over 64 plus y squared over 100 equals 1
quantity x plus 6 end quantity squared over 16 plus y squared over 25 equals 1
quantity x minus 6 end quantity squared over 25 plus y squared over 16 equals 1
The equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.
What is an ellipse?An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.
We have:
The vertices of the ellipse = (1, 0) and (11, 0)
Eccentricity of ellipse = 3/5
We have equations:
[tex]\rm \dfrac{\left(x-6\right)^{2}}{100}+\dfrac{y^{2}}{64}=1[/tex]
[tex]\rm \dfrac{\left(x+6\right)^{2}}{64}+\dfrac{y^{2}}{100}=1[/tex]
[tex]\rm \dfrac{\left(x+6\right)^{2}}{16}+\dfrac{y^{2}}{25}=1[/tex]
[tex]\rm \dfrac{\left(x-6\right)^{2}}{25}+\dfrac{y^{2}}{16}=1[/tex]
From the fourth equation:
The vertices of the ellipse:
(1, 0) and (11, 0)
The eccentricity:
c² = a² - b²
c² = 25-16
c = 3
e = c/a = 3/5
Thus, the equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.
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If m∠1 = 72º, then find the value of m∠2. vertical angles
If the angle 1 and angle 2 are vertical angles, hence they must be equal to each other, therefore m∠1 = m∠2 = 72º
What are vertical angles?Angles angle are angles that are equal to equal to each other in a line geometry.
Given the following parameters
m∠1 = 72º,
If the angle 1 and angle 2 are vertical angles, hence they must be equal to each other, therefore m∠1 = m∠2 = 72º
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Which graph represents the function
there are 2 more graphs but it won't add it
Answer:
[tex]f(x) = 9x^2+9x - 18/3x + 6\\= 9(x^2 + x - 2)/3(x+2)\\= 3(x^2+x-2)/x+2\\= 3(x+2)(x-1)/x+2\\= 3x - 3[/tex]
so y = 3x - 3
since 3x + 6 is on the bottom,
[tex]3x + 6\neq 0\\3x\neq -6\\x\neq -2[/tex]
so this means it should be the graph of y = 3x - 3, but with a hole at (-2, -9)
ments
nts
ns
Mai says, "I know how to find the area of a sector or the length of an arc for central angles like 180
degrees or 90 degrees. But I don't know how to do it for central angles that make up more complicated
fractions of the circle."
1. In the diagram, the sector's central angle measures 8 degrees and the circle's radius is r units. Use
the diagram to tell Mai how to find the area of a sector and the length of an arc for any angle and
radius measure.
2. This image shows a circle with radius and central angle measurements. Find the area of the shaded
sector, and the length of the arc defined by the sector.
160%
5 in
The sector area and the arc length are 34.92 square inches and 13.97 inches, respectively
How to find a sector area, and arc length?For a sector that has a central angle of θ, and a radius of r;
The sector area, and the arc length are:
[tex]A = \frac{\theta}{360} * \pi r^2[/tex] --- sector area
[tex]L = \frac{\theta}{360} * 2\pi r[/tex] ---- arc length
How to find the given sector area, and arc length?Here, the given parameters are:
Central angle, θ = 160
Radius, r = 5 inches
The sector area is
[tex]A = \frac{\theta}{360} * \pi r^2[/tex]
So, we have:
[tex]A = \frac{160}{360} * \frac{22}{7} * 5^2[/tex]
Evaluate
A = 34.92
The arc length is:
[tex]L = \frac{\theta}{360} * 2\pi r[/tex]
So, we have:
[tex]L = \frac{160}{360} * 2 * \frac{22}{7} * 5[/tex]
L = 13.97
Hence, the sector area and the arc length are 34.92 square inches and 13.97 inches, respectively
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Help !! I’ll mark brainliest !!
Answer:
9
Step-by-step explanation:
The opposite sides of a parallelogram are congruent.
Answer:
9
Step-by-step explanation:
Parallel sides are always equal. :)
Help please!!! I will give 20 points to the correct answer !!!
Answer:
-3 and -7
Step-by-step explanation:
Factors of 21: 1, 3, 7, 21
3 and 7 add up to 10, but what about -10? Well, -3 * -7 is also 21, and -3 + -7 gives you -10.
Brainliest, please :)
Solve x2 + 4x + 12 = 0 by completing the square.
x = –2 + 2i, x = –2 –2i
x = –2 + i, x = –2 – i
x = –2 + 2i, x = –2 – 2i
x = 0, –4
Answer:
See below
Step-by-step explanation:
x2 + 4x + 12 = 0 Complete the square ( take 1/2 of the 'x' coefficient, then square it and add it to both sides of the equation
x^2 + 4x + 2^2 + 12 = 2^2 Subtract 12 from both sides
x^2 + 4x + 4 = -8
(x+2)^2 = - 8 sqrt both sides
(x+2) =± sqrt (-8) simplify just a bit
x+2 = ±(2i sqrt2) subtract 2 from both sides
x = -2 ± 2i sqrt 2 <===== I do not see that answer listed
If x/3 = 5/6 , then x =
Answer:
x = 5/2
Step-by-step explanation:
Given that,
[tex] \cfrac{x}{3} = \cfrac{5}{6} [/tex]
x = ?Solution:
Multiplying using criss-cross method;
[tex]x \times 6 = 5 \times 3[/tex][tex]6x = 15[/tex]Divide both sides by 6;
[tex] \cfrac{6x}6 = \cfrac{ \cancel{15} {}^{5} }{ \cancel6 {}^{2} } [/tex][tex]x = \cfrac{5}{2} [/tex]Done!
Hence x = 5/2.
Answer:
x = 2.5
Step-by-step explanation:
x = 3*(5/6)
Select the correct answer from each drop-down menu.
Are these lines perpendicular, parallel, or neither based off their slopes?
6x - 2y = -2
y = 3x + 12
The __ of the slope is __ so the lines are __ .
From the slope, it is possible to classify the lines as parallel.
Linear FunctionA line can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:
a= the slope
b=constant term that represents the y-intercept.
The lines are classified as parallel when they have the same slope. You will have perpendicular lines when one line is the negative reciprocal of the second line. If the lines intersect, none of the previous conditions presented are met.
The given equations are:
6x-2y=-2 (1)
y=3x+12 (2)
First, you should write the equation 1 in the standard form.
-2y=-6x-2
-y=-3x-1
y=3x+1
Therefore, the slope for equation 1 is m=3.
After that, you should indicate the slope for equation 2. Thus, m also is 3.
As, both equations present the same slope (m=3). The lines are parallel.
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Answer: The Product(?) of their slopes is 3, so the lines are parallel
Step-by-step explanation:
summary of what the other person said
rewrite each pair of fractions to have the same denominator 1/3 and 1/4
Answer:
1/3 and 1/4
multiplying 1/3 by 1/4 and 1/4 by 1/3 we get
1/3 * 1/4
1 *1 /3*4
1/12
1/4 * 1/3
1*1 / 4*3
1/12
now, both have same denominator.
3. When using set builder notation, what does it mean to 'Define a set'?
Answer:
A set is a well-defined collection of distinct mathematical objects.
The total cost of a tie and a pair of pants was $87.18. If the price of the tie was $2.12 less than the pair of pants, what was the price of the tie? Express your answer as a simplified fraction or a decimal rounded to two places.
Integration by Parts Evaluate e-2x cos(2x) dx.
Let
[tex]I = \displaystyle \int e^{-2x} \cos(2x) \, dx[/]tex
Integrate by parts:
[tex]\displaystyle \int u \, dv = uv - \int v \, du[/tex]
with
[tex]u = e^{-2x} \implies du = -2 e^{-2x} \, dx \\\\ dv = \cos(2x) \, dx \implies v = \dfrac12 \sin(2x)[/tex]
Then
[tex]\displaystyle I = \frac12 e^{-2x} \sin(2x) + \int e^{-2x} \sin(2x) \, dx + C[/tex]
Integrate by parts again, this time with
[tex]u = e^{-2x} \implies du = -2 e^{-2x} \, dx \\\\ dv = \sin(2x) \, dx \implies v = -\dfrac12 \cos(2x)[/tex]
so that
[tex]\displaystyle I = \frac12 e^{-2x} \sin(2x) - \frac12 e^{-2x} \cos(2x) - \int e^{-2x} \cos(2x) \, dx + C\\\\ \implies I = \frac{\sin(2x)-\cos(2x)}{2e^{2x}} - I + C \\\\ \implies 2I = \frac{\sin(2x) - \cos(2x)}{2e^{2x}} + C \\\\ \implies I = \boxed{\frac{\sin(2x) - \cos(2x)}{4e^{2x}} + C}[/tex]
URGENT: Click on the graph to choose the correct answer to the equation. x > 2
The graph of x >2 is attached below
Clearly, the graph of x> 2 could be area beyond 2 on positive X axis
What is graph?
The graph is a demonstration of curves which gives the relationship between x and y axis.
The question seems to be incomplete, because options are missing.
so the option can be of several graphs.
Thus, The correct Graph of x >2 has been attached below.
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A car travels at 80 km an hour. How far will it travel in 2 1/2 hours?
Which products result in a difference of squares? Select three options. a (x minus y)(y minus x) b (6 minus y)(6 minus y) c (3 + x z)(negative 3 + x z) d (y squared minus x y)(y squared + x y) e (64 y squared + x squared)(negative x squared + 64 y squared)
Answer:
By comparing all the expressions with the formula (a - b)(a + b) = (a² - b²), we find that c, d and e options are correct.
Step-by-step explanation:
Concept: The condition is that, the product should result in a difference of squares. In mathematics, we have such a formula which is (a - b)(a + b) = (a² - b²). So, we need to compare all the options with this relation.
(x - y)(y - x) = -(x² - 2xy + y²)
(6 - y)(6 - y) = 36 - 12y + y²
(3 + xz)(-3 + xz) = (xz + 3)(xz - 3) = x²z² - 9 . This expression is correct
(y² - xy)(y² + xy) = [tex]y^{4} - x^{2} y^{2}[/tex]. This expression is correct
(64y² + x²)(-x² + 64y²) = (64y² + x²)(64y² - x²) = [tex]4096y^{4} -x^{4}[/tex]. This expression is correct.
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Which of the following linear equations represents the data chart?
X Y
1 6
2 5
3 4
4 3
y=x+5
y=x+3
y = -x + 7
None of these choices are correct.
Answer: y = -x + 7
Step-by-step explanation:
The slope is [tex]\frac{5-6}{2-1}=-1[/tex], so we know the equation is of the form [tex]y=-x+b[/tex].
Substituting in the coordinates (1,6) to find b,
[tex]6=-1+b\\\\b=7[/tex]
Thus, the equation is y = -x + 7
What is the main difference between confirmatory and exploratory factor analysis? (CFA vs EFA)
O a. In CFA, SPSS is required to build the model
O b. In CFA, the researcher does not define the model
O c. In CFA, the researcher defines the model
O d. In CFA, factor rotation is required
Oe In CFA, there is no model
Answer:
in exploratory factor analysis all the measures variables are related to every legend variable but in confirmatory factor analyse CFA research 10 specifically the number of factors required in the data in which measures variable is related with talent variable
Find the equation of the line using the given information.
(x, y) = (−3, 0)
and
(x, y) = (−3, 7)
are points on the line
If y varies directly as the square of x and Y--54 when x-9, then -- when x-6.
True or false
Answer:
24.012
Step-by-step explanation:
y=kx^2
54=81k
k=54/81
k=0.667
y=kx^2
y=0.667×36
y=24.012
its false ik this because im one of the boyzz
Translate and solve using proportions what percent of 120 is15
Answer:
12.5%
Step-by-step explanation:
To find what percent of 120 15 is, we must find what 15/120 is.
15/120 = 0.125. To convert to a percent, we move the decimal two places to the right. So, the answer is 12.5%.
Brainliest, please :)
Answer:
12.5%
Step-by-step explanation:
If the center of a circle is at (5,-7)
and its radius is 6, complete its
equation:
The equation is:
(x-5)^2+(y-(-7))^2=36
I hope it helps!
Answer: [tex]\boldsymbol{(x - 5)^2 + (y + 7)^2 = 36}[/tex]
=========================================
Work Shown:
[tex](h,k) = (5,-7) = \text{center}\\\\r = 6 = \text{radius}\\\\(x - h)^2 + (y - k)^2 = r^2\\\\(x - 5)^2 + (y - (-7))^2 = 6^2\\\\\boldsymbol{(x - 5)^2 + (y + 7)^2 = 36}\\\\[/tex]
Find the area of the following triangle. Round your answers to the nearest hundredth. b = 0.923 km, c = 0.387 km, A = 43.333°
O 0.26 km²
O 0.358 km²
O 0.06 km²
O 0.12km ²
Using approximations to 1 significant figure, estimate the value of:
[tex]\frac{0.482 * 61.2x^{2} }{\sqrt{98.01}}[/tex]
* = times by :D
Will pick Brainliest if right!
Answer:
3x²
Step-by-step explanation:
0.482 to 1sf is 0.5
61.2x² to one sf is 60x²
√98.01 to 1sf is √100
√100 = 10
0.5 x 60x² = 30x²
30x² / 10 = 3x²
In 2005, an area vocational school had an enrollment of 325 men and 123 women. In 2006, there were 149 women. What was the percent increase of women students? Your final answer should be rounded to the nearest whole percent.
The percent increase of women students is 21.13%.
Given that, an area vocational school had an enrollment of 325 men and 123 women.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
In 2006, there were 149 women.
Percentage increase = (New value - original value)/Original value × 100
= (149-123)/123 × 100
= 26/123 × 100
= 21.13%
Therefore, the percent increase of women students is 21.13%.
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What is the ratio of the weight of two castings that weigh 32 lbs. and 38 lbs
Answer:
16 : 19
Step-by-step explanation:
Given weights of the two castings : 32 lbs and 38 lbs respectively.
Now,
Ratio of the weights of the two castings ;
= 32 : 38
= 16 : 19
32:38
16:19
Answer:
this is my answer
work hours
frequency
0 - <10
45
10 - <20
33
20 - <30
20
30 - <40
7
40 - <50
8
Use your calculator to find the mean and standard deviation
The mean and the standard deviation are 16.15 and 12.03, respectively
How to determine the mean and the standard deviation?The table of values is given as:
Work hours Frequency
0 - <10 45
10 - <20 33
20 - <30 20
30 - <40 7
40 - <50 8
Start by rewriting the table using the midpoint of each class
x f
5 45
15 33
25 20
35 7
45 8
The mean is then calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
This gives
[tex]\bar x = \frac{5 * 45 + 15 * 33 + 25 * 20 35 * 7 + 45 * 8}{45 + 33 + 20 + 7 + 8}[/tex]
Evaluate the sum and the products
[tex]\bar x = \frac{1825}{113}[/tex]
Divide
[tex]\bar x = 16.15[/tex]
The standard deviation is:
[tex]\sigma =\sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]
This gives
[tex]\sigma= \sqrt{\frac{45 * (5 - 16.15)^2 + 33 * (15 - 16.15)^2 + 20 * (25 - 16.15)^2 + 7 * (35 - 16.15)^2 + 8 * (45 - 16.15)^2 }{45 + 33 + 20 + 7 + 8}}[/tex]
Evaluate the sum and the products
[tex]\sigma= \sqrt{\frac{16350.4425}{113}}[/tex]
Divide
[tex]\sigma= \sqrt{144.694181416}[/tex]
Take the square root
[tex]\sigma= 12.03[/tex]
Hence, the mean and the standard deviation are 16.15 and 12.03, respectively
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A
Choose the correct statement about best-fit lines.
a.
A best-fit line is close to most of the data points.
b. A best-fit line describes the exact coordinates of each point in the data set.
C.
A best-fit line always has a positive slope.
d. A best-fit line must go through at least two of the data points.
Please select the best answer from the choices provided
Α
B
C
D
Answer:
Your answer would be A.
Step-by-step explanation:
okay so, with a best fit line, it needs to match up with your points. unless your points go up evenly. its not going to connect to all your points.
2015-{2015÷5(x-5)÷5}=2014
Answer:
x=80.8
Step-by-step explanation:
follow BODMAS
2015-(2015÷5(x-5)÷5)=2014
2015-(2015÷5x-25÷5)=2014
2015-(405/x-5)=2014
2015-(405-5x)=2014
2015-405+5x=2014
1610+5x=2014
5x=2014-1610
(5x=404)1/5
x=80.8
find the lenght of (a) using the pytoagorean theorem.
Longest line is 8
shortest line is 6
Answer:
5.29
Step-by-step explanation:
8
[tex] \sqrt{8 { = }^{2} { - 6 {?}^{2} }^{2} } [/tex]
Answer: Missing side length (b) = 5.3 units
Step-by-step explanation:
Hii, I'd love to help you out! (:
We are provided with two sides, which are:
Longest side = 8Shortest side = 6Luckily, there's a formula to find the third side!
The Pythagorean TheoremThe Pythagorean Theorem ([tex]\pmb{a^2+b^2=c^2}[/tex]) is the formula that we will use to find the missing side. In this formula "a" and "b" denote the "legs" of the triangle (the two shorter sides) and "c" denotes the hypotenuse (the longest side which is opposite the right angle (the 90 degree angle)
NB: a and b are interchangeable, because a+b is the exact same thing as b+a; c is always the hypotenuse.
Now it's time for us to stick in the values.
[tex]\bigstar\underbrace{\boxed{\sf a=6;\;c=8}}[/tex]
This is what we obtain upon sticking in the values:
[tex]\tt 6^2+b^2=8^2[/tex]
Now we can solve for b.
[tex]\tt 36+b^2=64}\\b^2=64-36\\b^2=28\\b\approx5.3[/tex]
Thus, the value of "b" is 5.3. (Rounded to the nearest tenth, or one decimal place - one digit after the decimal point)
_____________
Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
_____________
[tex]\underbrace[/tex]