For the data set below, calculate the standard deviation to the nearest hundredth decimal place. 27 38 47 42 33 56 37 57 38 52
Answers
Final answer:
The standard deviation of the given data set is 10.03, and the value that is one standard deviation below the mean is 32.67. Calculations involve finding the mean, computing squared deviations, calculating the sum of squared deviations, finding the variance, and taking the square root of the variance.
Explanation:
The mean is calculated as: (27 + 38 + 47 + 42 + 33 + 56 + 37 + 57 + 38 + 52) ÷ 10 = 427 ÷ 10 = 42.7.
Now we calculate each deviation from the mean, square it, and sum them:
(27 - 42.7)² = 246.49
(38 - 42.7)² = 22.09
(47 - 42.7)² = 18.49
(42 - 42.7)² = 0.49
(33 - 42.7)² = 94.09
(56 - 42.7)² = 176.89
(37 - 42.7)² = 32.49
(57 - 42.7)² = 204.49
(38 - 42.7)² = 22.09
(52 - 42.7)² = 86.49
A sum of squared deviations = 904.61.
The variance is 904.61 ÷ (10-1) = 100.51.
The standard deviation is the square root of the variance,
which is √100.51 equal to approximately 10.03.
To find the value that is one standard deviation below the mean, we subtract one standard deviation from the mean: 42.7 - 10.03 = 32.67.
Therefore, the standard deviation to the nearest hundredth is 10.03, and the value that is one standard deviation below the mean is approximately 32.67.
Related Questions
What is the value of x in the following equation 1/5x=5^8
A)-8 B) 8 C)40 D)-40
Answers
What is the value of x in the following equation (1/5)^x=5^8
Applying logarithms both members
log(1/5)^x=log(5^8)
x*log(1/5)=8*log(5)
x=8*log(5)/log(1/5)
we know that
log (1/5)----> log (1)-log (5)----> 0-log (5)-----> -log (5)
so
x=8*log(5)/-log (5)------> x=-8
the answer is
-8
For the particular problem raised in the introduction, assume that the total bill is $44. to answer the question "how should the bill be split?" we will create a linear equation. the unknown is how much money a single person (besides anika) must pay, so call that x. although four people (you plus three friends) went to dinner, only three are paying the unknown amount x for a total of 3x. since anika is paying $2, the total amount paid is 3x+2 dollars, which must equal the amount of the bill, $44. thus, the equation to find x is 3x+2=44. the steps for solving a linear equation are as follows: move all of the constants to the right side. move all of the variable terms (terms containing x) to the left side. divide both sides by the coefficient of the variable to isolate the variable. you will go through these steps one at a time to solve the equation and determine how much each person should pay.
Answers
3x+2(-2)=44-2
3x=42
3x/3=42/3
x=14
So each person would have to pay $14, except Anika
Construct a 90% confidence interval for the population mean, µ. assume the population has a normal distribution. a sample of 15 randomly selected math majors has a grade point average of 2.86 with a standard deviation of 0.78. round to the nearest hundredth
Answers
The 90% confidence interval for the population mean [tex]\( \mu \)[/tex] is approximately (2.50, 3.21) .
To construct a 90% confidence interval for the population mean [tex]\( \mu \)[/tex], we can use the formula:
[tex]\[ \text{Confidence Interval} = \bar{x} \pm \left( \text{Critical Value} \times \frac{s}{\sqrt{n}} \right) \][/tex]
where:
- [tex]\( \bar{x} \)[/tex] is the sample mean,
- s is the sample standard deviation,
- n is the sample size, and
- the critical value corresponds to the desired confidence level and degrees of freedom.
Given:
- Sample mean [tex]\( \bar{x} = 2.86 \),[/tex]
- Sample standard deviation s=0.78
- Sample size n=15
- Confidence level = 90%.
First, we need to find the critical value corresponding to a 90% confidence level and 14 degrees of freedom (since ( n - 1 = 15 - 1 = 14 )). We can find this value using a t-distribution table or a statistical calculator. For a 90% confidence level and 14 degrees of freedom, the critical value is approximately 1.7613.
Now, let's calculate the confidence interval:
[tex]\[ \text{Confidence Interval} = 2.86 \pm \left( 1.7613 \times \frac{0.78}{\sqrt{15}} \right) \]\[ \text{Confidence Interval} = 2.86 \pm \left( 1.7613 \times \frac{0.78}{\sqrt{15}} \right) \]\[ \text{Confidence Interval} = 2.86 \pm \left( 1.7613 \times \frac{0.78}{3.87298} \right) \]\[ \text{Confidence Interval} = 2.86 \pm \left( 1.7613 \times 0.20172 \right) \]\[ \text{Confidence Interval} = 2.86 \pm 0.35587 \][/tex]
Lower Limit:
[tex]\[ 2.86 - 0.35587 \approx 2.5041 \][/tex]
Upper Limit:
[tex]\[ 2.86 + 0.35587 \approx 3.2141 \][/tex]
PLZ HELP ASAP FEATURES OF A CIRCLE FROM ITS EXPANDED EQUATION
Answers
[tex] x^{2} +y^{2} +14x-10y+65=0 \\ \\ x^{2} +2(x)(7)+ y^{2}-2(y)(5)=-65 \\ \\ x^{2} +2(x)(7)+ (7)^{2}+ [y^{2}-2(y)(5)+ (5)^{2}]=-65+(7)^{2}+(5)^{2} \\ \\ (x+7)^{2}+(y-5)^{2}=9 [/tex]
The above equation is in standard form.
The center of the circle is (-7, 5) and its radius is 3.
Please Help!
Khalid has a game board as shown below, which is a square with 20-cm sides. The area of the largest circle is 320 square centimeters.
What is the probability of scoring 1, 3, or 5 points with one randomly thrown dart?
A. 1/2
B. 5/8
C. 3/4
D. 4/5
Answers
Answer:
Option D. 4/5
Step-by-step explanation:
we know that
The probability of scoring 1, 3, or 5 points with one randomly thrown dart is equal to divide the area of the largest circle by the area of the square game board
step 1
Find the area of the square game board
[tex]A=b^{2}[/tex]
we have
[tex]b=20\ cm[/tex]
substitute
[tex]A=20^{2}[/tex]
[tex]A=400\ cm^{2}[/tex]
step 2
Find the probability
[tex]P=320/400[/tex]
[tex]P=0.8=8/10=4/5[/tex]
0.88 cm equals how many mm
Answers
0.88*10=8.8
Your answer would be 8.8mm
Is 7+8x=y proportional, if so what is the constant proportionality?
Is y=-2/5x proportional, if so what is the constant proportionality?
Answers
b) Yes. The constant is the coefficient of x, -2/5.
One method of slowing the growth of an insect population without using pesticides is to introduce into the population a number of sterile males that mate with fertile females but produce no offspring. let p represent the number of female insects in a population and s the number of sterile males introduced each generation. let r be the per capita rate of production of females by females, provided their chosen mate is not sterile. then the female population is related to time t by t = p + s p[(r − 1)p − s] dp. suppose an insect population with 10,000 females grows at a rate of r = 1.2 and 400 sterile males are added. evaluate the integral to give an equation relating the female population to time. (note that the resulting equation can't be solved explicitly for p. remember to use absolute values where appropriate.)
Answers
To be clear, the given relation between
time and female population is an integral:
[tex]t = \int { \frac{P+S}{P[(r - 1)P - S]} } \,
dP [/tex]
[tex]t = \int { \frac{P+400}{P[(1.2 - 1)P - 400]} } \, dP [/tex]
= [tex] \int { \frac{P+400}{P(0.2P - 400)} } \, dP [/tex]
In order to evaluate this integral, we need to write this rational function in a simpler way:
[tex]\frac{P+400}{P(0.2P - 400)} = \frac{A}{P} + \frac{B}{(0.2P - 400)} [/tex]
where we need to evaluate A and B. In order to do so, let's calculate the LCD:
[tex]\frac{P+400}{P(0.2P - 400)} = \frac{A(0.2P - 400)}{P(0.2P - 400)} + \frac{BP}{P(0.2P - 400)} [/tex]
the denominators cancel out and we get:
P + 400 = 0.2AP - 400A + BP
= P(0.2A + B) - 400A
The two sides must be equal to each other, bringing the system:
[tex] \left \{ {{0.2A + B = 1} \atop {-400A = 400}} \right. [/tex]
Which can be easily solved:
[tex] \left \{ {{B=1.2} \atop {A=-1}} \right. [/tex]
Therefore, our integral can be written as:
[tex]t = \int { \frac{P+400}{P(0.2P - 400)} } \, dP = \int {( \frac{-1}{P} + \frac{1.2}{0.2P-400} )} \, dP [/tex]
= [tex]- \int { \frac{1}{P} \, dP + 1.2\int { \frac{1}{0.2P-400} } \, dP[/tex]
= [tex]- \int { \frac{1}{P} \, dP + 6\int { \frac{0.2}{0.2P-400} } \, dP[/tex]
= - ln |P| + 6 ln |0.2P - 400| + C
Now, let’s evaluate C by considering that at t = 0 P = 10000:
0 = - ln |10000| + 6 ln |0.2(10000) - 400| + C
C = ln |10000| - 6 ln |1600|
C = ln (10⁴) - 6 ln (2⁶·5²)
C = 4 ln (10) - 36 ln (2) - 12 ln (5)
Therefore, the equation relating female population with time requested is:
t = - ln |P| + 6 ln |0.2P - 400| + 4 ln (10) - 36 ln (2) - 12 ln (5)
Use parametric equations of the ellipse, ???? 2 16 + ???? 2 9 = 1, to find the area that it encloses in the first quadrant.
Answers
1. Clyde has the chance to buy a piece of old Pennsylvania Dutch pottery that he thinks he can resell for $500. If Clyde needs a 125% markup on cost, what price should he pay?
2. Orchard Supply sells lawn fertilizer at a price of $12.50 per bag. If the markup is 25% of cost, find the cost.
Answers
2.25*cost = 500
cost = 500/2.25 = 222.22
Clyde should pay $222.22 or less for the pottery.
2. cost +0.25*cost = $12.50
1.25*cost = $12.50
cost = $12.50/1.25 = $10.00
The cost to Orchard Supply of a bag of fertilizer is $10.00.
What is the first step in solving ln(x − 1) = ln6 − lnx for x?
Answers
Answer:
[tex]ln(x - 1) = ln(\frac{6}{x})[/tex]
Step-by-step explanation:
[tex]ln(x - 1) = ln6 - lnx[/tex]
To solve for x we need to simplify the ln
To simplify logarithmic function we use log property
[tex]ln(a) - ln(b) = ln(\frac{a}{b})[/tex]
we apply the same property on the right hand side of the given equation
[tex]ln(x - 1) = ln6 - lnx[/tex]
[tex]ln(6) - ln(x) = ln(\frac{6}{x})[/tex]
[tex]ln(x - 1) = ln(\frac{6}{x})[/tex]
This is the first step in solving the given equation
Twelve people are entered in a race. If there are no ties, in how many ways can the first three places come out?
Answers
[tex] 12\cdot11\cdot10=1320 [/tex]
The number of ways the first three places in a race with twelve competitors can be filled is 1320, calculated by the permutations formula which multiplies the choice for each of the three places -- 12 for first, 11 for second, and 10 for third.
The student's question asks for the number of different ways the first three places in a race can be filled when there are twelve competitors. This is a problem of permutations where we do not consider the remaining positions after the third place. To solve this, we calculate the number of permutations for the first three places, which is a sequence of choices. We have 12 choices for the first place, 11 choices for the second place after the first place has been filled, and 10 choices for the third place after the first two places have been filled.
The total number of permutations can be calculated as:
First place: 12 possibilitiesSecond place: 11 possibilities (since one person is already in the first place)Third place: 10 possibilities (as two contestants are in the first and second place)By the counting principle, we multiply these choices together to find the total number of permutations for the first three places, which is 12 x 11 x 10.
Therefore, the total number of ways the first three places can be awarded is 12 x 11 x 10 = 1320 different permutations.
the square in this figure has a side length of 14 inches. the radius of the quarter circle is 7 inches. what is the estimate area
Answers
The area of the shaded region is 42.14 square inches.
How the area of the shaded region is determined:
We are given a square with side lengths of 14 inches, and each corner of the square has a quarter circle with a radius of 7 inches. We need to find the area of the shaded region, which is the area of the square minus the area of the quarter circles.
To calculate the area of the figure, we need to consider both the square and the quarter circles.
1. Calculate the area of the square:
The square has a side length of 14 inches.
Area of the square = [tex]side^2[/tex] = [tex]14^2[/tex] = 196 square inches
2. Calculate the area of the quarter circles:
The quarter circle has a radius of 7 inches.
The area of a full circle is given by:
Area of the circle = [tex]\pi r^2[/tex]
Area of the quarter circle = 4/4 x [tex]\pi r^2[/tex]
= 1 x 3.14 x [tex]7^2[/tex]
= 153.86 square inches
Therefore, the area of the shaded region = Area of the square - Area of the quarter circles:
= 196 - 153.86
= 42.14 square inches
Complete Question:
The square in the figure has a side length of 14 inches. The radius of the each quarter circle is 7 inches. What is the area of the shaded region?
Solve the equation: Sin2x - Sinx = 0
Answers
(search the net for proof if you wish)
So the original equation becomes
2sinxcosx-sinx=0
The two terms both have sinx that can be taken out to get:
sinx(2cosx-1)=0
This is true if sinx=0 or 2cosx-1=0 , rewritten: cosx=1/2
sinx=0 than x=2kπ
cosx=1/2 than x=π/3+2kπ
where k is an integer
Runners in a long distance race start out going 5 kilometers south and then head west for the remainder of the race. The finish line is 13 kilometers from the starting line. How far did the runners travel?
Answers
5 km +12 km = 17 km
_____
By the Pythagorean theorem, ...
(straight-line distance)² = (distance south)² +(distance west)²
In km, this is
13² = 5² +(distance west)²
169 -25 = (distance west)²
√144 = 12 = distance west
a dress was reduced from $100 to $85. express the discount as a % of the original price
Answers
$15/$100 = 15/100 = 15%
_____
It can be helpful to think of "%" as another way to write "/100".
hey can you please help me posted picture of question
Answers
The solutions are 3 and -3
Explanation:
To get the solution, we will need to isolate the x on one side of the equation as follows:
10x² - 56 = 88 - 6x²
10x² - 56 + 56 = 88 - 6x² + 56
10x² = 144 - 6x²
10x² + 6x² = 144 - 6x² + 6x²
16x² = 144
x² = 144/16
x² = 9
x = ±√9
either x = +√9 = 3
or x = -√9 = -3
Hope this helps :)
What are some uses for the distance formula? Finding the perimeter of polygons. Finding the area of rectangles. Finding the equation of a circle. Finding the midpoint of segments. Finding how much gas you will need on a trip.
Answers
-Finding the perimeter of polygons
-finding the area of rectangles
The Distance Formula is used widely in mathematics to calculate the distance between two points, which includes finding the perimeter of polygons, the equation of a circle and the midpoint of segments.
Explanation:The Distance Formula is a valuable tool in mathematics that has a wide range of practical uses and applications. It is primarily used to calculate the distance between two specific points on a coordinate plane. Some uses include the following:
Finding the perimeter of polygons: Distance Formula can be used to calculate the length of each side of the polygon, and then by summing these lengths, we get the perimeter. Finding the equation of a circle: By using Distance Formula, we can establish the radius of the circle - the distance from the center of the circle to any point on the circle. Finding the midpoint of segments: Distance Formula helps to identify the exact middle point between two defined points.
However, usage of the Distance Formula to determine the amount of gas needed for a trip would be incorrect as it requires additional factors like the fuel efficiency of your vehicle and the nature of your trip.
Learn more about Distance Formula here:https://brainly.com/question/11231122
#SPJ6
Solve the equation <(a-5)-5=3
Answers
a - 5 - 5 = 3
Calculate the difference between -5 and 5.
a - 10 = 3
Now move the constant to the right side of the equation and change its sign.
a = 3 + 10
Add the numbers on the right side together to get your final answer.
a = 13
Let me know if you have any further questions.
:)
Design amanda wants to make this design of circles inside an equilateral triangle.
a. what is the radius of the large circle to the nearest hundredth of an inch?
b. what are the radii of the smaller circles to the nearest hundredth of an inc
Answers
the answer in the attached figure
Answer:
Using theorem
AE=8.66
Thus radius of large circle is one third of equilateral triangle altitude.
Radius of larger circle=2.9 inch
And radius of inner circle will be 0.96 inch
A rectangular page is to contain 95 square inches of print. the margins on each side are 1 inch. find the dimensions of the page such that the least amount of paper is used.
Answers
Let the dimensions for the Print Region be M,N
Additional Margin is summed up to get :
New Dimensions of the Page = (M + 2)(N)
[ 2 inches - 1 inch on either side ]
Hence, the Area = [ MN + 2N ] = [ 95 + 2N ]
Note that 'N' has to be a factor of 95
=> Least Possible Area is achieved when N = 5
=> Dimensions of the Page = { 21 inches x 5 inches ]
A student conducted a poll of 100 internet users and found the average time spent online per day was 2 hours. The student described 2 hours as a parameter. The student is incorrect because the value is a numerical measurement describing a characteristic of _____.
a ratio
a sample
a population
quantitative data
Answers
In statistics A sample is a part of a population .A sample statistic is any quantity we derive from a sample taken from a population . A sample refers to a set of observations drawn from a population.
We are given A student conducted a poll of 100 internet users and found the average time spent online per day was 2 hours .Here 2 hours is an observation derived from the set of observations made .So 2 hours is a characterstic of a sample.
The second option a Sample is the right answer.
Joey got a 25% raise on his salary. if his original salary was 1,200, how much was it after the raise was implemented?
Answers
Help with this one please
Answers
A=G^2/H; H=G^2/A
The explanation is shown below:
1. To solve the exercise shown in the figure attached, you must apply the proccedure shown below:
2. You have the following equation to calculate G:
G=√AH
3. Now, to find the formula to calculate A, you must clear the A, as below:
G^2=(√AH)^2
G^2=AH
A=G^2/H
4. Then, you must apply the same proccedure to find the formula for calculate H, as following:
G^2=(√AH)^2
G^2=AH
H=G^2/A
Rewriting;
G=sqrt(AH)
//square both sides//
G^2=[sqrt(AH)]^2
G^2=AH
A=G^2/H
G=sqrt(AH)
//square both sides//
G^2=[sqrt(AH)]^2
G^2=AH
H=G^2/A
Thus, the answer is the first option which has A=G^2/H and H=G^2/A
The Root-Mean Square-Arithmetic Mean-Geometric Mean-Harmonic Mean Inequality (RMS-AM-GM-HM), is an inequality of the root-mean square, arithmetic mean, geometric mean, and harmonic mean of a set of positive real numbers that says:
with equality if and only if . This inequality can be expanded to the power mean inequality.
As a consequence we can have the following inequality: If are positive reals, then with equality if and only if ; which follows directly by cross multiplication from the AM-HM inequality.This is extremely useful in problem solving.
The "Let's Roll" game uses a number cube with the numbers 2,4,6,8,10, and 12. There are prizes for rolling any number less than 6. How likely is it to roll a number less than 6?
Answers
The probability of rolling a number less than 6 in the 'Let's Roll' game is 1/3.
Explanation:To find the probability of rolling a number less than 6 in the 'Let's Roll' game, we need to count the number of favorable outcomes (numbers less than 6) and divide it by the total number of possible outcomes (numbers on the number cube). In this case, the favorable outcomes are 2, 4, and the total number of outcomes is 6.
Therefore, the probability of rolling a number less than 6 is 2/6 or 1/3.
Therefore the probability of getting a number less than 6 will be 33.3%
Probability is defined as the ratio of the
number of favorable outcomes to the total
number of outcomes in other words the
probability is the number that shows the
happening of the event.
Sample space we have = [ 2,4,6,8,10,12 ] = 6
Desirable outcome will be = [2,4] = 2
Probability = 2 / 6
Probability = 1/3
Probability = 0.33 = 33%
Therefore the probability of getting a number less than 6 will be 33.3%
Find the 15th term of the arithmetic sequence.
a+1, 2a+1, 3a+1
a. a+15
b. 15a+15
c. 15a + 1
d. 14a+14
Answers
The coefficient of "a" in the given sequence is the term number (1, 2, 3, ...) and the constant remains constant at 1. Thus the 15th term can be expected to be ...
c. 15a + 1
c. 15a + 1
The scatter plot shows the relationship between the number of car accidents in a month and the number of drivers attending a program on distracted driving. The equation represents the linear model for this data. y=−0.0067x+17 What does the number -0.0067 in the equation mean in this context? There were 0.67 accidents per month. The number of accidents was reduced by 0.67 per month for every additional 100 drivers in the program. The number of accidents was reduced by 0.67 per month for every additional driver in the program. The number of accidents increased by 0.67 per month for every additional 100 drivers in the program. The number of accidents was reduced by 0.67 per month every month.
Answers
Answer:
the answer is A
Dustin is stuck at the top of a ferris wheel. his mother is standing 38 feet from the base of the wheel watching him. if the angle of elevation from dustin's mom to Dustin is 73 degrees, how far off the ground is nick?
A. 118.2 ft
B. 120.9 ft
C. 124.3 ft
D. 126.5 ft
E. 128.1 ft
Answers
tan θ=opposite/adjacent
θ=73°
opposite=h ft
adjacent=38 ft
plugging our values we get:
tan 73=h/38
thus
h=38 tan 73
h=124.29~124.3 ft
Answer: C. 124.3 ft
The correct option is A. [tex]118.2\ ft[/tex]. Dustin is approximately [tex]118.2\ ft[/tex] off the ground.
To find how far Dustin is off the ground, we can use trigonometry, specifically the tangent function.
Let [tex]\( h \)[/tex] denote the height of Dustin above the ground.
Given:
Angle of elevation [tex]\( \theta = 73^\circ \)[/tex]
Distance from Dustin's mother to the base of the ferris wheel [tex]\( d = 38 \)[/tex]feet
We can set up the tangent function:
[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{d} \][/tex]
Substitute the given values:
[tex]\[ \tan(73^\circ) = \frac{h}{38} \][/tex]
Now, solve for [tex]\( h \)[/tex]
[tex]\[ h = 38 \times \tan(73^\circ) \][/tex]
Use a calculator to find [tex]\( \tan(73^\circ) \)[/tex]
[tex]\[ \tan(73^\circ) = 3.0985 \][/tex]
Therefore,
[tex]\[ h = 38 \times 3.0985 \][/tex]
[tex]\[ h = 117.839 \][/tex]
Rounding to the nearest tenth, Dustin is approximately [tex]\( 117.8 \) feet[/tex] off the ground.
Two planes are flying in opposite directions, away from each other, one with the speed of 800 km per hour and the other with the speed of 840 km per hour. How much farther from each other are the planes getting every hour?
Answers
Given the parent function of y=|x|, state the type of transformation that occured to get the function below. y=1/4|x|
Answers
the transformation that occurred to the parent function[tex]\( y = |x| \)[/tex] to get the function[tex]\( y = \frac{1}{4}|x| \)[/tex] is a vertical compression by a factor of 4.
The parent function ( y = |x| ) represents the absolute value function, which takes the absolute value of \( x \) and outputs its positive value.
The function [tex]\( y = \frac{1}{4}|x| \)[/tex] is a transformation of the absolute value function. Specifically, it involves the following transformations:
1. **Vertical Compression:**
The coefficient[tex]\( \frac{1}{4} \)[/tex] before[tex]\( |x| \)[/tex] compresses the graph vertically. It shrinks the height of the graph by a factor of 4 compared to the parent function [tex]\( y = |x| \).[/tex]
So, the transformation that occurred to the parent function[tex]\( y = |x| \)[/tex] to get the function[tex]\( y = \frac{1}{4}|x| \)[/tex] is a vertical compression by a factor of 4.