A rope is swinging in such a way that the length of the arc traced by a knot at its bottom end is decreasing geometrically. If the third arc is 18 it long and theseventh arc is 8 ft. long, what is the length of the arc on the sixth swing? Round your answer to the nearest tenth of a foot.O A 14.7ftOB. 12.0 ft.O C. 10.5 ftO D. 9.8 ft.
Answers
The length of the arc on the sixth swing is
STEP - BY - STEP EXPLANATION
What to find?
The length of the arc on the sixth swing.
Given:
length of third arc = 18 ft
length of 7t
Related Questions
Using the info from the word problem and graph, who can buy a bike first? You or your friend?
Answers
Given:
There is a bicycle that is cost $175
There are two friends:
The first has $45 and save $5 each week
So, we have the following equation, let (x) is the number of weeks
[tex]45+5x=175[/tex]Solve the equation to find (x):
[tex]\begin{gathered} 5x=175-45 \\ 5x=130 \\ x=\frac{130}{5}=26\text{ w}eeks \end{gathered}[/tex]So, the first can buy the bicycle after 26 weeks
The second friend has an amount (y) after (x) weeks according to the shown graph of the line:
As shown the line passes through the points (0, 15) and (3, 39)
The slope of the line represents the saving each week =
[tex]slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{39-15}{3-0}=\frac{24}{3}=8[/tex]The y-intercept represents the initial saving = $15
So, after (x) week we have the following equation:
[tex]15+8x=175[/tex]Now, solve to find (x)
[tex]\begin{gathered} 8x=175-15 \\ 8x=160 \\ x=\frac{160}{8}=20 \end{gathered}[/tex]So, the second can buy the bicycle after 20 weeks
So, the answer will be
The velocity, in ft/sec of a particle is given by v(t) =-14t + 2. Find the position function s(t) of the particle if it has an initial position s(0) = 4 feet.
Answers
Option B is correct
[tex]s(t)=-7t^{2}+2t+4[/tex]Explanations;Given the velocity of the particle expressed as;
[tex]v(t)=-14t+2[/tex]The position of the object is determined by integrating the velocity function as shown:
[tex]\begin{gathered} s(t)=\int v(t)dt \\ s(t)=\int(-14t+2)dt \\ s(t)=-\frac{14t^2}{2}+2t_+C \\ s(t)=-7t^2+2t+C \end{gathered}[/tex]If the particle has an initial position s(0) = 4 feet, then;
[tex]\begin{gathered} s(0)=-7(0)^2+2(0)+C \\ 4=C \end{gathered}[/tex]Substitute the constant into the position function to have:
[tex]s(t)=-7t^2+2t+4[/tex]This gives the required position of the particle
What is 2/3 divided 1/6? Explain or show your reasoning?
Answers
we have that
2/3 divided 1/6 is equal to
[tex]\frac{2}{3}\colon\frac{1}{6}=\frac{2\cdot6}{1.3}=\frac{12}{3}=4[/tex]that means
the number 2/3 is 4 times the number 1/6
see the figure below
4/6 and 2/3 are equivalent fractions
because
4/6=2/3
4*3=2*6
12=12 ----> is ok
If you divided 2/3 into 4 equal parts, each part is equal to 1/6
If you divided 2/3 by 1/6, the result is 4 parts
The following equation is given.x4 + 6x3 + 6x2 + 6x +5=0a. List all possible rational roots.b. Use synthetic division to test the possible rational roots and find an actual root.Actual rational root: c. Use the root from part (b.) and solve the equation.The solution set of x4 + 6x2 + 6x2 + 6x + 5 = 0
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
x^4 + 6x^3 + 6x^2 + 6x +5=0
roots = ?
Step 02:
a. possible rational roots
rational root theorem:
possible rational roots = factors of the constant / factors of the lead
x^4 + 6x^3 + 6x^2 + 6x + 5=0
lead = 1
constant = 5
factors of the coefficient, 1 are ±1
factors of the constant term, 5 are ±1 , ±5
possible rational roots = (±1 , ±5) / ±1
possible rational roots = ±1 , ±5
Step 03:
b. synthetic division
possible rational root:
(x + 1) ===> x = - 1
-1 | 1 6 6 6 5
| -1 -5 -1 - 5
------------------------------
1 5 1 5 0
The remainder is 0
Step 04:
c. solve the equation
x = -1
x^4 + 6x^3 + 6x^2 + 6x + 5 = 0
[tex]\begin{gathered} (-1)^4+6(-1)^3+6(-1)^2+6(-1)+5=0 \\ 1\text{ - 6 + 6 - 6 + 5 = 0} \\ 0\text{ = 0 } \end{gathered}[/tex]That is the full solution.
find the sum of the interior angles of a regular decagon
Answers
decagon = 10 sides
angles = 180(n - 2)
angles = 180(10 - 2)
angles = 180(8)
angles = 1440°
1-(5k+4)>24-2(k+3) What is the answer to this question
Answers
Given,
[tex]1-(5k+4)>24-2(k+3)[/tex]Substracting 24 from both side.,
[tex]-5k-27>-2k-3[/tex]Adding 3 to both side,
[tex]-5k-24>-2k[/tex]Multiplying by (-1),
[tex]5k+24<2k[/tex]Substrating 2k from both side,
[tex]3k+24<0[/tex]Substracting 24 from both side,
[tex]3k<-24\Rightarrow k<-8[/tex]Thus the answer is k<-8.
simplify the equation: -(3d-4)-4(5-2d)
Answers
We have
[tex]-\mleft(3d-4\mright)-4\mleft(5-2d\mright)[/tex]we sum similar terms
[tex]\begin{gathered} -3d+4-20+8d \\ 5d-16 \end{gathered}[/tex]Problem 1) Y=-x+4 Y=3x Problem 2) Y=2x-10 2y=x-8 Problem 3)2y=x+1-2x-y=7
Answers
Problem 1)
The given equations are
y = -x + 4
y = 3x
We would substitute y = 3x into y = -x + 4. It becomes
3x = - x + 4
Adding x to both sides of the equation, we have
3x + x = - x + x + 4
4x = 4
Dividing both sides of the equation by 4, we have
4x/4 = 4/4
x = 1
Substituting x = 1 into y = 3x, we have
y = 3 * 1
y = 3
Wote the following In the intercepis and domain, and perform the wymmetry text on each of the few lor'259' = 400 4xy!=64 Ox+4y= 36 (h) 7x' w-112
Answers
h) the initial equation is:
[tex]7x^2+8y^2=112[/tex]So to find the intercepts we replace x = 0 and y = 0 so:
[tex]\begin{gathered} 8y^2=112 \\ y^2=14 \\ y=\sqrt[]{14}=\pm3.74 \end{gathered}[/tex]So the y interceps are 3.74 and -3.74 now for x
[tex]\begin{gathered} 7x^2=112 \\ x^2=16 \\ x=\pm4 \end{gathered}[/tex]So the domain will be:
[tex]\mleft\lbrack-4,4\mright\rbrack[/tex]In this case is centered in 0 and the domain is symetic so the function is symetric
List all the subsets of the set {e,d}. Write each subset in your list in roster form. If there are more than one subset in your list, separate them with commas.
Answers
Answer:
{}, {e}, {d} and {e, d}
Explanation
Given the set {e, d}
The subsets are the set of elements that can be founds in the set written as s a single set.
Given thet n(S) = 2
Power of the set P(S) = 2^2
Power of the set P(S) = 4
This shws that there will be 4 subsets and this are;
{}, {e}, {d} and {e, d}
Hence the subsets are {}, {e}, {d} and {e, d}
(a) If Q is the point (x, sin(16)),(1) 2(11)15Xfind the slope of the secant line PQ (correct to four decimal places) for the following values of x.
Answers
Given:
The point P is (1, 0).
The point Q is
[tex]Q(x,sin(\frac{16\pi}{x}))[/tex]Required:
We need to find the slope of the scent line PQ when x=2.
Explanation:
i)
Replace x =2 in point Q.
[tex]Q(2,sin(\frac{16\pi}{2}))[/tex][tex]Q(2,sin(8\pi))[/tex]Consider the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]Substitute\text{ }x_1=1,y_1=0,x_2=2,\text{ and }y_2=sin(8\pi)\text{ in the formula.}[/tex][tex]m=\frac{sin(8\pi)-0}{2-1}[/tex][tex]Use\text{ sin\lparen}8\pi)=0.[/tex][tex]m=\frac{0}{1}=0[/tex]The slope when x=2 is 0.0000.
ii)
Replace x =1.5 in point Q.
[tex]Q(1.5,sin(\frac{16\pi}{1.5}))[/tex][tex]Q(1.5,sin(\frac{32\pi}{3}))[/tex]Consider the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]Subst\imaginaryI tute\text{ x}_1=1,y_1=0,x_2=1.5,\text{ and }y_2=s\imaginaryI n(\frac{32\pi}{3})\text{ }\imaginaryI\text{n the formula}[/tex][tex]m=\frac{sin(\frac{32}{3}\pi)-0}{1.5-1}[/tex][tex]m=1.7320508[/tex][tex]m=1.7321[/tex]The slope when x=1.5 is 1.7321.
iii)
Replace x =1.4 in point Q.
[tex]Q(1.4,sin(\frac{16\pi}{1.4}))[/tex][tex]Q(1.4,sin(\frac{80\pi}{7}))[/tex]Consider the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]Subst\imaginaryI tute\text{ x}_1=1,y_1=0,x_2=1.4,\text{ and }y_2=s\imaginaryI n(\frac{80\pi}{7})\text{ }\imaginaryI\text{n the formula}[/tex][tex]m=\frac{sin(\frac{80}{7}\pi)-0}{1.4-1}[/tex][tex]m=-2.43731978045[/tex][tex]m=-2.4373[/tex]The slope when x=1.4 is -2.4373.
iv)
Replace x =1.3 in point Q.
[tex]Q(1.3,sin(\frac{16\pi}{1.3}))[/tex][tex]Q(1.3,sin(\frac{160\pi}{13}))[/tex]Consider the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]Subst\imaginaryI tute\text{ x}_1=1,y_1=0,x_2=1.3,\text{ and }y_2=s\imaginaryI n(\frac{160\pi}{13})\text{ }\imaginaryI\text{n the formula}[/tex][tex]m=\frac{sin(\frac{160}{13}\pi)-0}{1.3-1}[/tex][tex]m=2.74327955298[/tex][tex]m=2.7433[/tex]The slope when x=1.3 is 2.7433.
v)
Replace x =1.2 in point Q.
[tex]Q(1.2,sin(\frac{16\pi}{1.2}))[/tex]Consider the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]Subst\imaginaryI tute\text{ x}_1=1,y_1=0,x_2=1.2,\text{ and }y_2=s\imaginaryI n(\frac{16\pi}{1.2})\text{ }\imaginaryI\text{n the formula}[/tex][tex]m=\frac{sin(\frac{16}{1.2}\pi)-0}{1.2-1}[/tex][tex]m=-4.33012701892[/tex][tex]m=-4.3301[/tex]The slope when x=1.2 is -4.3301.
vi)
Replace x =1.1 in point Q.
[tex]Q(1.1,sin(\frac{16\pi}{1.1}))[/tex]Consider the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]Subst\imaginaryI tute\text{ x}_1=1,y_1=0,x_2=1.1,\text{ and }y_2=s\imaginaryI n(\frac{16\pi}{1.1})\text{ }\imaginaryI\text{n the formula}[/tex][tex]m=\frac{sin(\frac{16}{1.1}\pi)-0}{1.1-1}[/tex][tex]m=9.89821441881[/tex][tex]m=9.8982[/tex]The slope when x=1.1 is 9.8982
vii)
Replace x =0.5 in point Q.
[tex]Q(0.5,sin(\frac{16\pi}{0.5}))[/tex]Consider the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]Subst\imaginaryI tute\text{ x}_1=1,y_1=0,x_2=0.5,\text{ and }y_2=s\imaginaryI n(\frac{16\pi}{0.5})\text{ }\imaginaryI\text{n the formula}[/tex][tex]m=\frac{sin(\frac{16}{0.5}\pi)-0}{0.5-1}[/tex][tex]m=0[/tex][tex]m=0.0000[/tex]The slope when x=0.5 is 0.0000.
viii)
Replace x =0.6 in point Q.
[tex]Q(0.6,sin(\frac{16\pi}{0.6}))[/tex]Consider the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]Subst\imaginaryI tute\text{ x}_1=1,y_1=0,x_2=0.6,\text{ and }y_2=s\imaginaryI n(\frac{16\pi}{0.6})\text{ }\imaginaryI\text{n the formula}[/tex][tex]m=\frac{sin(\frac{16}{0.6}\pi)-0}{0.6-1}[/tex][tex]m=-2.16506350946[/tex][tex]m=-2.1651[/tex]The slope when x=0.6 is -2.1651
Similarly, we get
The slope when x=0.7 is -1.4463
The slope when x=0.8 is 0.000
The slope when x=0.9 is 6.4279
We see that the values are not approaching any particular value.
As x approaches 1, the slope does not appear to be approaching any particular value.
B)
The graph of the given curve is
There are frequency oscillations near point 1.
We need to take x-values further to 1 to get the exact slope.
C)
The given curve is
[tex]f(x)=sin(\frac{16\pi}{x})[/tex][tex]Slope\text{ of the secent line=}\frac{f(a+h)-f(a)}{h}[/tex]Here a=1.
[tex]Slope\text{ of the secent line=}\frac{f(1+h)-f(1)}{h}[/tex][tex]Slope\text{ of the secent line=}\frac{sin(\frac{16\pi}{1+h})-sin(16\pi)}{h}[/tex][tex]Slope\text{ of the secent line=}\frac{sin(\frac{16\pi}{1+h})}{h}[/tex]Take limit h tends to zero.
[tex]Slope\text{ of the secent line=}\frac{sin(\frac{16\pi}{1+h})}{h}=\frac{0}{0}\text{ = not defined}[/tex]Differentiate with respect to h.
[tex]Slope\text{ of the secent line=}\frac{sin(\frac{16\pi}{1+h})}{h}=\frac{0}{0}\text{ = not defined}[/tex]Assume that when adults with smartphones are randomly selected, 61% use them in meetings or classes. If 9 adult smartphone users are randomly selectedfind the probability that exactly 5 of them use their smartphones in meetings or classes.
Answers
To solve this problem, let's use binominal distribution.
To calculate the probability of an event (P), use the formula below.
[tex]P(X=x)=\frac{n!}{x!\cdot(n-x)!}\cdot p^x\cdot(1-p)^{n-x}[/tex]Where
n = number total of events;
x = number of favorable events;
p = probability of a single event.
In this exercise:
n = 9
x = 5
p = 0.61
Then, substituting the values:
[tex]\begin{gathered} P=\frac{9!}{5!\cdot(9-5)!}\cdot\cdot0.61^5\cdot(1-0.61)^{9-5} \\ P=\frac{9!}{5!\cdot(4)!}\cdot\cdot0.61^5\cdot(0.39)^4 \\ P=\frac{9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2}{5\cdot4\cdot3\cdot2\cdot4\cdot3\cdot2}\cdot\cdot0.61^5\cdot(0.39)^4 \\ P=\frac{9\cdot8\cdot7\cdot6}{4\cdot3\cdot2}\cdot\cdot0.61^5\cdot(0.39)^4 \\ \end{gathered}[/tex]Solving the expression:
[tex]\begin{gathered} P=0.2462 \\ P=24.62percent_{} \end{gathered}[/tex]Answer: P = 0.2462.
I need help please I do on t get it
Answers
Instructions: Write a linear equation in one variable to help you answer the question. Stephen earns $17 an hour (ℎ) at his job. This week, he had to buy a new uniform shirt for $25. He had $825 left of his paycheck that week. How many hours did Stephen work this week?
Answers
Given:
Amount he earns per hour = $17
Cost of new shirt = $25
Amount left = $825
Let's find the number of hours Stephen worked this week.
Let's first write a linear equation representing this situation.
Apply the slope-intercept form:
y = mx + b
Thus, we have the equation:
825 = 17h - 25
Now, let's solve for h.
Add 25 to both sides of the equation:
825 + 25 = 17h - 25 + 25
850 = 17h
Divide both sides by 17:
[tex]\begin{gathered} \frac{850}{17}=\frac{17h}{17} \\ \\ 50=h \\ \\ h=50 \end{gathered}[/tex]Therefore, Stephen worked 50 hours this week.
ANSWER:
• Equation:
17h - 25 = 825
• Number of hours worked:
50 hours
Which of the following equations will produce the graph shown below? +10 +9 +7 -6 -5 -4 -3 2 -1 -10-9 -8 -7 -6 -5-4-3-2-1 1 2 3 4 5 6 7 8 9 10 د ننه من -3 -6 -7 +-10 O A *= 8y O 2
Answers
Answer:
The equation that would produce the given graph is;
[tex]x^2=8y[/tex]Explanation:
Given the graph in the attached image;
The graph shows an exponential function of the form;
[tex]y=ax^2[/tex]From the shape of the graph, we can observe that the value of the coefficient a is less than 1;
[tex]\begin{gathered} a=\frac{1}{8} \\ y=\frac{1}{8}x^2 \\ 8y=x^2 \\ x^2=8y \end{gathered}[/tex]Therefore, the equation that would produce the given graph is;
[tex]x^2=8y[/tex]
Two transformations are applied to the triangle to create triangle LMN so that MN and Mn Will both be parallel to the same access and Ln and l n Will both be parallel to the same axis which pair of trance formations will not result in these corresponding sides of the two triangles being parallel for the same axis?
Answers
Given the vertices of LMN:
L(-5, 1), M(-1, 5), N(-1, 1)
Given that two transformations are applied to triangle so that MN and M'N' will be parallel to the same axis. Also, LN and L'N' are parallel to the sma e axis.
Let's find the pair of transformations that will in result in this pair of corresponding sides not being parallel to the same axis.
Now, we are to find the pair of transoformations.
The set of transformations will be:
A rotation 90 degrees clockwise, followed by a translation 3 units down.
Apply the rotation rule for 90 degrees clockwise :
(x, y) ==> (y, -x)
Thus, we have:
L(-5, 1) ==> (1, 5)
M(-1, 5) ==> (5, 1)
N(-1, 1) ==> (1, 1)
After a translation 3 units down apply the rules of translation:
(x, y) ==> (x, y - 3)
Thus, we have:
(1, 5) ==> (1, 5 - 3) ==> (1, 2)
(5, 1) ==> (5, 1 - 3) ==> (5, -2)
(1, 1) ==> (1, 1 - 3) ==> (1, -2)
Therefore, the coordinates are:
L'(1, 2), M'(5, -2), N'(1, -2)
ANSWER:
A rotation 90° clockwise, followed by a translation 3 units down.
which term applies to numbers that cannot be written in this form
Answers
Answer:
Irrational Numbers.
Explanation:
If a number can be written in the form:
[tex]\frac{a}{b},b\neq0[/tex]Such a number is said to be Rational.
Thus, any number that cannot be written in this form is called an Irrational Number.
2) p(x) = x² + 3; Find p(1)
Answers
Explanation
Step 1
to find p(1) just replace the value of x in the equation
[tex]p(x)=x^2+3[/tex]when x=1
[tex]\begin{gathered} p(x)=x^2+3 \\ p(1)=1^2+3 \\ p(1)=1+3 \\ p(1)=4 \end{gathered}[/tex]I hope this helps you
You'll need the other parts for part CPart CHow does the ratio of corresponding side lengths of the two quadrilaterals compare with the ratio of the areas of the quadrilaterals?
Answers
When the lengths increase by 2 times the area increases by 2².
C) We can see that from part A, and part B the ratio for the areas is:
[tex]\begin{gathered} \frac{\:Area\:A^{\prime}B^{\prime}C^{\prime}D}{\:area\:ABCD^{\text{ }}}=\frac{8}{2}=4 \\ \\ \frac{length\:A^{\prime}B^{\prime}}{length\:AB}=\frac{2.83}{1.41}\approx2 \end{gathered}[/tex]2) So we can tell that when we dilate centered at the origin with a scale factor of 2 the area increases by (2)²=4
This is because the area is a square unit.
I didn’t understand this question, please help thank you very much
Answers
Hello there. To solve this question, we'll have to remember some properties about finding the common denominator of a sum of fractions.
Given the fractions:
[tex]\frac{5y^2+2}{y^2+7y+10}+\frac{3}{y+2}[/tex]We start by factoring the expression in the denominator of the first fraction.
Notice it is something of the form x² - Sx + P, where S = -7 and P = 10.
S and P are the sum and the product of the roots of the expression. In this case, we can easily find values that would give us a sum of -7 and a product of 10:
y = -2 and y = -5
Thus, we write it as:
y² + 7y + 10 = (y + 2)(y + 5)
Then we have:
[tex]\frac{5y^2+2}{(y+2)(y+5)_{}}+\frac{3}{y+2}[/tex]Now, to find the common denominator, we calculate the least common multiple of the expressions:
[tex]\mathrm{lcm}((y+2)(y+5),(y+2))=(y+2)(y+5)[/tex]We can calculate it as:
Therefore this is the common denominator of the fractions, in its factored form.
Lyra is designing a model of a solar system with a planet and a comet. The planet has a circular orbit, centered at the origin with a diameter of 120. The comet follows a parabolic path with directrix x = 85 and vertex at (75, 0).Part A: Write the equation of the planet's orbit in standard form. Show your work. (2 points)Part B: Write the equation of the comet's path in standard form. Show your work. (4 points)
Answers
Given:-
The planet has a circular orbit, centered at the origin with a diameter of 120. The comet follows a parabolic path with directrix x = 85 and vertex at (75, 0).
To find:-
Write the equation of the planet's orbit in standard form and also Write the equation of the comet's path in standard form.
The co-ordinates of center of circle is (0,0) since the diameter is 120 then the radius is 60. so we have,
So the standard equatio is,
[tex]\begin{gathered} x^2+y^2=60^2 \\ x^2+y^2=3600 \end{gathered}[/tex]Now we find the equation of comets path in standard form. The diretrix is x = 85 and vertex is at ( 75,0 ).
Now we find the value of a,
[tex]\begin{gathered} \frac{a}{2}=85-75 \\ \frac{a}{2}=10 \\ a=20 \end{gathered}[/tex]So the equation is,
[tex](y-y_1)^2=-4a(x-x_1)[/tex]Substituing the required value ( 75,0). we get,
[tex]\begin{gathered} (y-0)^2=-4\times20(x-75) \\ y^2=-80(x-75) \end{gathered}[/tex]These are the required equations.
can someone please help me??????
Answers
Answer:
ASA
Step-by-step explanation:
How many quarts of pure antifreeze must be added to 9 quarts of 30 % antifreeze solution to obtain a 50% antifreeze solution ?
Answers
Let
x -----> quarts of pure antifreeze
Remember that
30%=0.30
50%=0.50
so
x+9(0.30)=(x+9)(0.50)
solve for x
x+2.70=0.50x+4.50
x-0.50x=4.50-2.70
0.50x=1.8
x=3.6
therefore
The answer is 3.6 quartsWhich of the following lists of data has the smallest standard deviation?
Answers
To determine which data set has the smallest standard deviation you have to determine the standard deviation of each sample and then compare them. The standard deviation is the square root of the variance, which means that you have to calculate the variance of each sample and then their standard deviation.
The formula for the sample variance is:
[tex]S^2=\frac{1}{n-1}\lbrack\Sigma x^2_i-\frac{(\Sigma x_i)^2}{n}\rbrack[/tex]Where
∑xi represents the sum of all observations of the sample
∑xi² represents the sum of the squares of all observations of the sample
n represents the sample size
Sample 1
Variance
n= 10
[tex]\begin{gathered} \Sigma x_i=30+21+19+17+16+32+26+25+19+16 \\ \Sigma x_i=221 \end{gathered}[/tex][tex]\begin{gathered} \Sigma x^2_i=30^2+21^2+19^2+17^2+16^2+32^2+26^2+25^2+19^2+16^2 \\ \Sigma x^2_i=5189 \end{gathered}[/tex][tex]\begin{gathered} S^2_1=\frac{1}{10-1}\lbrack5189-\frac{(221)^2}{10}\rbrack \\ S^2_1=\frac{1}{9}\lbrack5189-4884.1\rbrack \\ S^2_1=\frac{1}{9}\cdot304.9 \\ S^2_1=33.88 \end{gathered}[/tex]Standard deviation
[tex]\begin{gathered} S_1=\sqrt[]{S^2_1} \\ S_1=\sqrt[]{33.88} \\ S_1=5.82 \end{gathered}[/tex]Sample 2
Variance
n=10
[tex]\begin{gathered} \Sigma x_i=5+11+15+7+5+9+8+16+14+11 \\ \Sigma x_i=101 \end{gathered}[/tex][tex]\begin{gathered} \Sigma x^2_i=5^2+11^2+15^2+7^2+5^2+9^2+8^2+16^2+14^2+11^2 \\ \Sigma x^2_i=1163 \end{gathered}[/tex][tex]\begin{gathered} S^2_2=\frac{1}{10-1}\lbrack1163-\frac{(101)^2}{10}\rbrack \\ S^2_2=\frac{1}{9}\lbrack1163-1020.1\rbrack \\ S^2_2=\frac{1}{9}\cdot142.9 \\ S^2_2=15.88 \end{gathered}[/tex]Standard deviation
[tex]\begin{gathered} S_2=\sqrt[]{S^2_2} \\ S_2=\sqrt[]{15.88} \\ S_2=3.98 \end{gathered}[/tex]Sample 3
Variance
n=10
[tex]\begin{gathered} \Sigma x_i=25+24+28+18+32+34+34+22+28+19 \\ \Sigma x_i=264 \end{gathered}[/tex][tex]\begin{gathered} \Sigma x^2_i=25^2+24^2+28^2+18^2+32^2+34^2+34^2+22^2+28^2+19^2 \\ \Sigma x^2_i=7274 \end{gathered}[/tex][tex]\begin{gathered} S^2_3=\frac{1}{10-1}\lbrack7274-\frac{(264)^2}{10}\rbrack \\ S^2_3=\frac{1}{9}\lbrack7274-6969.6\rbrack \\ S^2_3=\frac{1}{9}\cdot304.4 \\ S^2_3=33.82 \end{gathered}[/tex]Standard deviation
[tex]\begin{gathered} S_3=\sqrt[]{S^2_3} \\ S_3=\sqrt[]{33.82} \\ S_3=5.82 \end{gathered}[/tex]Sample 4
Variance
n=10
[tex]\begin{gathered} \Sigma x_i=17+19+17+18+17+16+16+16+17+20 \\ \Sigma x_i=173 \end{gathered}[/tex][tex]\begin{gathered} \Sigma x^2_i=17^2+19^2+17^2+18^2+17^2+16^2+16^2+16^2+17^2+20^2 \\ \Sigma x^2_i=3009 \end{gathered}[/tex][tex]\begin{gathered} S^2_4=\frac{1}{10-1}\lbrack3009-\frac{(173)^2}{10}\rbrack \\ S^2_4=\frac{1}{9}\lbrack3009-2992.9\rbrack \\ S^2_4=\frac{1}{9}\cdot16.1 \\ S^2_4=1.79 \end{gathered}[/tex]Standard deviation
[tex]\begin{gathered} S_4=\sqrt[]{S^2_4} \\ S_4=\sqrt[]{1.79} \\ S_4=1.34 \end{gathered}[/tex]Sample 5
Variance
n=10
[tex]\begin{gathered} \Sigma x_i=9+16+14+22+20+9+19+16+21+8 \\ \Sigma x_i=154 \end{gathered}[/tex][tex]\begin{gathered} \Sigma x^2_i=9^2+16^2+14^2+22^2+20^2+9^2+19^2+16^2+21^2+8^2 \\ \Sigma x^2_i=2620 \end{gathered}[/tex][tex]\begin{gathered} S^2_5=\frac{1}{10-1}\lbrack2620-\frac{(154)^2}{10}\rbrack \\ S^2_5=\frac{1}{9}\lbrack2620-2371.6\rbrack \\ S^2_5=\frac{1}{9}\cdot248.4 \\ S^2_5=27.60 \end{gathered}[/tex]Standard deviation
[tex]\begin{gathered} S_5=\sqrt[]{S^2_5} \\ S_5=\sqrt[]{27.60} \\ S_5=5.25 \end{gathered}[/tex]So, the standard deviation of the five samples are:
[tex]\begin{gathered} S_1=5.82 \\ S_2=3.98 \\ S_3=5.82 \\ S_4=1.34 \\ S_5=5.25 \end{gathered}[/tex]Sample 4 has the smallest standard deviation.
4y = x + bDIB!Statisti1.LENTIONS8-7-66-1-3-2-1214BPokynoudalFunedomD(5)=?Expression2'3-(1-1)Op 102Use words to describe the transformation shown below. Explain how you know. Be as specificas possible. (Think about some of the vocabulary specific to transformations.) *Get real675d - 50.0 mlEnter your answerITG
Answers
In this problem we have a reflection across the x-axis
The rule of the reflection across the x-axis is
(x,y) -----> (x,-y)
In this transfornations, the x coordinate of the pre image and the image are equal, but the y-coordinate of the image change the sign
The table lists the smoking habits of a group of college students[graph below]If a student is chosen at random, find the probability of getting someone who is a regular or heavy smoker.If a student is chosen at random, find the probability of getting someone who is a man or a non-smoker.
Answers
Answer:
Given that,
The table lists the smoking habits of a group of college students (given in the question)
A computer password is required to be 9 characters long. How many passwords are possible if thepassword requires 3 letter(s) followed by 6 digits (numbers 0-9), where no repetition of any letter or digitis allowed? There are _______ possible passwords
Answers
Since the alphabet has 26 letters and the digits are 10, and where no repetition of any letter or digit is allowed, using the multiplication principle we have:
26 25 24 10 9 8 7 6 5 = 2.36 x 10^9 possible passwords, multiplying
--- ---- ---- ---- ---- ---- ---- ---- ---- the values.
What is 8/15 plus 2/5 equal to
Answers
We have to add 8/15 to 2/5.
To add two fractions we have to make them have the same denominator, so we have to convert 2/5 to have a denominator of 15. To do this, we have to multiply 2/5 by 3 and then we can add the fractions:
[tex]\begin{gathered} \frac{8}{15}+\frac{2}{5} \\ \frac{8}{15}+\frac{2}{5}\cdot\frac{3}{3} \\ \frac{8}{15}+\frac{6}{15} \\ \frac{14}{15} \end{gathered}[/tex]Answer: 14/15
Which inequality represents the price(p) he will need to receive for his crop to make a profit?
Answers
The total cost the farmer needs to pay in fertilizer is $8412, and he will also pay $12.10 per acre in order to harvest it.
Since the total size of crops is 160 acres, he will pay 160 times 12.10.
The amount p he needs to receive should be greater than the sum of all these costs, so we can write the following inequality:
[tex]p>12.10(160)+8412[/tex]Therefore the correct option is the fourth one.
determine if the segments (2, 3) (3, -3) and (-1, 4) (-4,-1) are congruent or not congruent. Show all work.
Answers
Answer
The two segments aren't congruent.
Explanation
The two segments given that we are asked to check if they are congruent are
(2, 3), (3, -3)
and
(-1, 4), (-4, -1)
The only way to know if the segments are congruent is from the values of the slopes of the two segments. If the two segments are congruent, the slopes will be equal.
The slope of a line or segment that has two coordinates given is calculated as
Slope = (Change in y)/(Change in x)
For (2, 3), (3, -3),
Change in y = -3 - 3 = -6
Change in x = 3 - 2 = 1
Slope = (-6/1) = -6
For (-1, 4), (-4, -1)
Change in y = -1 - 4 = -5
Change in x = -4 - (-1) = -4 + 1 = -3
Slope = (-5/-3) = (5/3) = 1.667
The two slopes are evidently not equal, hence, the two segments aren't congruent.
Hope this Helps!!!