use the 68-95-99.7 rule to find the proportion of runners whose body weight is between 48.7 and 67.9 kg.
Answers
Based on the complete question, the Normal Distribution Graph will resemble the one in the figure attached.
Also, note that using the 68-95-99.7 rule, the proportion of runners between 48.7 and 67.9 kg is 0.8385.
What is the 68-95-99.7 rule?
The 68-95-99.7 rule, also known as the empirical rule, is a statistician's shorthand for remembering the percentage of values in a normal distribution that fits within an interval estimate: 68%, 95%, and 99.7% of the variables lie within one, two, and three standard deviations of the mean, correspondingly.
To compute the proportion of runners whose body weight is between 48.7 and 67.9 kg with the help of the 68-95-99.7 rule:
We know given that:
The mean = 63.1 and
the standard deviation (SD) = 4.8.
Where the weight is 67.9kg, we know that the distance between this and the mean is 4.8, that is;
67.9 - mean
= 67.9 - 63.1
= 4.8 [1*SD]
In the same way,
48.7 corresponds to 48.7-63.1 = -14.4 [ -3*SD]
Hence, based on the rule,
the probability of the weight occurring between -1*SD and 1*SD = 68%; and the probability of the weight occurring between -3*SD and 3*SD = 99.7%.Therefore, the probability of the weight occurring between -3*SD and 1*SD = (99.7+68)/2= 83.85%
= 0.8385.
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Full Question:
A study of elite distance runners found a mean body weight of 63.1 Kilograms (kg), with a standard deviation of 4.8kg.
Assuming the distribution of weights is approximately normal, make a sketch of the weight distribution (like the one below) with a horizontal axis marked in kilograms.Use the 68-95-99.7 rule to find the proportion of runners whose body weight is between 48.7 and 67.9 kg
Related Questions
PLease help it’s due tomorrow morning
Explain the step that is used to solve the equation
11 = x - 5
Answers
Answer:
x=16
Step-by-step explanation:
11=x-5
first you need to get x alone on one side so you add 5 on both sides
11=x-5
+5. +5
11 + 5 is 16, so
16=x
Read the question below:
Answers
The rule for the function g(x) is g(x) = x - 5 when f(x) = 5 and vertical down to 5 units.
Functions:
Function refers the relationship from a set X to a set Y assigns to each element of X exactly one element of Y
Given,
Let g(x) indicated the transformation of f(x)
Here we need to write the rule for g(x) when f(x) = x, and vertical translation down 5 units.
Here we have the function f(x) = x.
Considering the normal graph, we know that, the graph has four parts.
And each part refers difference sign. That is,
Horizontal left indicates the positive where as the horizontal right refers the negative for x axis.
Similarly, vertical up refers the positive and the vertical down represents the negative.
Here we have the vertical down translation of 5 units which refers the negative 5.
So, the rule of g(x) = x - 5.
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A water treatment plant needs to maintain the ph of the water in the reservoir at a certain level. To monitor this, they take 2 oz. Of water at 37 locations every hour, measure the ph at each of those locations, and find their average. If the ph level of the reservoir is ok, the results at each location will have varying results, with an average ph of 8. 5 and a standard deviation of 0. 22. If the ph level of the reservoir is ok, what is the probability that the sample average is less than 8. 42?.
Answers
The probability that the sample is less than 8.42 is 0.0029 or 0.29%.
Using the normal distribution and the central limit theorem,
The mean is μ = 8.5
The standard deviation is σ = 0.22 .
A sample of 37 is taken, hence n = 37, s = 0.22/√37 i.e. s = 0.0362
The probability that the sample average is LESS than 8.40 is the p-value of Z when X = 8.4, hence:
Z = X - μ/σ
Z = 8.4 - 8.5/0.0362
Z = 2.76
Z = -2.76 has a p-value 0.0029
0.0029 = 0.29% probability that the sample average is LESS than 8.40.
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How are the solutions to the inequality -2x≥10 different from the solutions to −2x>10? Explain your reasoning.
Answers
Answer:
The difference is that the first equation, -2x≥10 -2x can be greater than or equal to 10 but the second equestion is only greater than ten.
Step-by-step explanation:
Find the derivative, if it exists, of the function at the specified point.() = ^2 − 4 + 3 at = 1
Answers
Find the derivate of the expression using the general procedure to find the derivative of a polynomial function. To do it, multiply the term times the exponent of the variable and raise the variable to the original exponent minus 1:
[tex]\begin{gathered} f(x)=x^2-4x+3 \\ f^{\prime}(x)=2x^{2-1}-4x^{1-1}-0\cdot3 \\ f^{\prime}(x)=2x-4 \end{gathered}[/tex]Now that we have the expression for the derivative of the function, evaluate it at the value of x that is in the question statement, which is 1:
[tex]f^{\prime}(1)=2(1)-4=2-4=-2[/tex]The derivative of the function is -2 at x=1.
In the New York State Numbers Lottery, you pay $1 and pick a number from 000 to 999. If your number comes up, you win $750, which is a profit of $749. If you lose, you lose $1. Your probability of winning is 000.1.
Answers
The measures of the angles of a triangle
are shown in the figure below. Solve for x.
47°
103⁰
(3x-12)°
Answers
Using the sum of angles, we know that the value of 'x' is 14°.
What is the triangle?In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all three angles of a triangle is equal to 180°.The triangle is contained in a single plane.What is the sum of the angles of a triangle?
Some of the angles of a triangle are the property of triangle states that the sum of interior angles of a triangle is 180°.
Given angles are 47, 103, 3x-12:
47+103+3x-12 = 180150 -12 +3x = 180138 +3x = 1803x = 180 - 1383x = 42x = 42/3x = 14°Therefore, using the sum of angles, we know that the value of 'x' is 14°.
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Standard to slope intercept form
Answers
Answer:
[tex]y=-\frac{1}{3} x - 6[/tex]
Step-by-step explanation:
3x+9y=-54
9y=-3x-54
y=-1/3x-6
:] good luck
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{x}{3} - 6[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The given equation is :
[tex]\qquad\displaystyle \tt \rightarrow \: 3x + 9y = - 54[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 9y = - 54 - 3x[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{ - 54}{9} - \frac{3x}{9} [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{x}{3} - 6[/tex]
And this the equation of same line in its slope intercept form, where slope (m) = -1/3 and y - intercept = -6
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Which comparison symbol makes each inequality statement true?
Enter <, >, or = to make each statement true.
Enter your answers in the boxes.
−6.809
−6.812
|−6.809|
|−6.812|
Answers
Comparison symbol makes each inequality statement true is −6.809< −6.812.
The given numbers are −6.809 and −6.812.
What is a inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Comparing decimals involves starting with the digits having the highest place value, just like when comparing other whole numbers. We begin the comparison by putting the provided decimal numbers in a place value table. We move on to the digits in the next place to the right if the digits on the biggest place value match. Up till the digits that are different are reached, we continue comparing digits.
−6.809< −6.812
|−6.809|>|−6.812|
Therefore, comparison symbol makes each inequality statement true is −6.809< −6.812.
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May you guys/girls please help me I have to submit this befoer mid night and I do not fail because my parents will get me , so may y'all please help me out!?
Answers
Answer:
Answer down below!
Step-by-step explanation:
The best way to find the slope of the line is first find a point that rests on the line on an exact point. This exact point is (-1,0)
Then, once you find that point, continue to use rise/run to find the slope.
In this case, it goes up one, and over one
So, your slope would be 1/1 or just 1.
(NOTE: IF YOU CONTINUE TO KEEP GOING ONE UP AND ONE OVER, IT WILL STILL GIVE YOU THE SAME SLOPE, BUT YOU WILL HAVE TO DO MORE WORK!!)
1 In a recipe, for every cup sugar, 3 cup flour is needed. How many cups of sugar 4 are needed for 1 cup of flour? Write your answers in the blanks. 13334 || = 1/ 3 IL *
I need first 2 blanks then 2 more blanks flilled in.
Answers
In the given recipe, 1/3 cup of sugar is needed for 1 cup of flour.
What do you mean by recipe?
A recipe is a set of instructions for preparing a dish or dessert, such as your mother's chocolate chip cookie recipe, which has won numerous awards.
The phrase "recipe" is most frequently used while discussing cookery. It covers both the steps to prepare it as well as a list of the ingredients you'll need. Recipes can be found in cookbooks, newspapers, periodicals, websites, publications, and even passed down via families. A recipe isn't just for cooking; it may also be a formula: the formula for success is a combination of diligence, timing, and a little luck.
As given in the question, In the recipe
For every cup of sugar, 3 cups of flour is needed. we can write it as:
1 cup of sugar = 3 cups of flour
we need to find how many cups of sugar needed for 1 cup of flour.
So, dividing the above equation with 3.
1/3 cups of sugar = 1 cups of flour.
Therefore, In the given recipe, 1/3 cups of sugar is required for 1 cup of flour.
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Help please:):)
Create a table of data for two different linear functions. The table should use that same values of x for both functions. Based on your table, will the graph of these two functions intersect? Explain your answer
Answers
Graph of two linear functions y=2x+7 and y=-x+4 will intersect at (1,5)
What do you means by linear function?
A linear function produces a straight line in the algebraic coordinate plane. It often takes the form of a polynomial function with a maximum degree of 1 or 0.
Calculus and linear algebra are also used to express the linear functions.
The primary distinction can be found in the function notation.
An ordered pair stated in function notation must be understood.
Below is a data table for two distinct linear functions with the identical x values for both functions.
x | y=2x+7 y=-x+4 -3 | 2(-3)+7=-6+7=1| -(-3)+4=3+4=7 -2 | 2(-2)+7=-4+7=3|-(-2)+4=2+4=6 -1 | 2(-1)+7=-2+7=5|-(-1)+4=1+4=5 0 | 2(0)+7=0+7=7 |-(0)+4=0+4=4 1 | 2(1)+7=2+7+9 |-(1)+4=-1+4=3 2 | 2(2)+7=4+7=11|-(2)+4=-2+4=2 3 | 2(3)+7=6+7=13|-(3)+4=-3+4=1
The table demonstrates that the function y = 2x + 7 and the function y = -x + 4 both have values of 5 for x = -1.
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select all segments parallel to fc
CB
AB
EB
DE
FD
FE
DA
Answers
Line segments DA and BE are parallel to FC.
We need to find all the segments parallel to FC.
What are parallel lines?Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.
From the given figure, FC parallel to DA and FC parallel to BE.
Therefore, line segments DA and BE are parallel to FC.
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Please help me. I tried every answer possible. Due today. I’ll give brainliest too
Answers
I WILL GIVE BRAINLIEST!! In 1988, each person in the United States threw out, on average, 1.92 pounds of paper and plastic every day. By weight, the amount of paper thrown away was 5 times greater than the amount of plastic. How many pounds of paper was this?
PLEASE SHOW WORK
Answers
Answer:
1.92x5=9.6 pounds everyday.
Step-by-step explanation:
Write an equation of the line in point-slope form passing through the point and parallel to the given line.3-X + 52(1,-1) y = 2
Answers
Answer:
Explanation:
The slope of the given line is 3/2
A line parallel to this has the same line but different y-intercept.
IIn point-slope form, it is:
[tex]y-y_1=m(x-x_1)_{}[/tex]Where
[tex]\begin{gathered} x_1=1 \\ y_1=-1 \\ m=\frac{3}{2} \end{gathered}[/tex]Using these, we have:
[tex]\begin{gathered} y-(-1)=\frac{3}{2}(x-1) \\ \\ y+1=\frac{3}{2}(x-1) \end{gathered}[/tex]An art teacher found that in a bin of markers, of the caps had been left off the markers. of these markers, of them were dried up. use the model to find what fraction of the markers had the lids left off and were dried up.
Answers
Answer:
there is no model linked
Step-by-step explanation:
Jim and Maureen are training for a marathon. Jim runs 6 kilometers at a time while Maureen prefers to run in blocks of 3 kilometers. At the end of the month, they realize that they have run the same total number of kilometers. What is the smallest number of kilometers that each must run?
Answers
The smallest number of kilometers that each must run is 6 kilometers.
What will be the least common multiple?From the information, Jim runs 6 kilometers at a time while Maureen prefers to run in blocks of 3 kilometers and at the end of the month, they realize that they have run the same total number of kilometers.
It should be noted that the question simony had to do with finding the least common multiple. This will be:
Multiple of 3 = 3, 6, 9, 12
Multiple of 6 = 6, 12
The least common multiple is 6.
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If m<0 and n > 0, then the product of m and n
Is always even
Is always odd
Is always positive
Is always negative
Cannot be zero, but can be any other real
number
Answers
Explanation:
m < 0 tells us m is negative
n > 0 means n is positive
Therefore the product of m and n is always negative due to the rule
negative * positive = negative
Examples:
-2*5 = -10
7*(-3) = -21
three friends ate at a restaurant. they ordered nachos for $19.95 and jalapeno poppers. each friend paid $9.73, not including sales tax or tip, which was one third of the total. determine the cost of the jalapeno poppers. $6.65 $9.24 $18.48 $29.19
Answers
The cost of the jalapeno poppers was $9.24 if each friend paid $9.73.
The cost of the jalapeno poppers can be determined by using multiplication followed by subtraction.
First, we determine the total amount paid by the three friends;
If each friend paid $9.73, then;
Total amount = 9.73 × 3
Total amount = $29.19
Now to find the cost of jalapeno poppers, we subtract the cost of nachos from the total amount paid by the three friends;
cost of jalapeno poppers = total amount - cost of nachos
cost of jalapeno poppers = 29.19 - 19.95
cost of jalapeno poppers = $9.24
Therefore, the cost of jalapeno poppers is calculated to be $9.24.
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PLEASE HELP
Lanny goes to the bank and puts $4000 in a savings account. He earns a simple interest of 2.5%. If he leaves the money in the account for five years, what is the total amount in the account after the five years?
Answers
The total amount in the account after interest will be about $4525.63 .
In the fields of finance and economics, interest is the additional sum that is paid by a borrower or deposit-taking financial institution to a lender or depositor at a certain rate (the amount borrowed).
The borrower may be obliged to pay fees to the lender or another entity, but interest is different.Interest also differs from a dividend, which is money given to shareholders (owners) by a company from its profit or reserve but not at a set rate or proportionally;It is a share of the reward or interest received by risk-taking businesspeople when income is generated that exceeds all expenses.Interest when the principal is $4000 , time is 5 years and rate is 2.5%.
We know that from compound interest:
Amount = principal (1 + rate)ⁿ
Therefore
Amount = 4000 (1 +0.025)⁵
Amount = $4525.6328...
Amount ≈ $4525.63
Therefore adding interest the sum would be worth $657.51
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candy and tim share a paper route. it takes candy 50 min to deliver all the papers, and it takes tim 100 min. how long does it take the two when they work together?
Answers
It takes a time of 33 mi 33 sec for the two when they work together
Let x be the overall quantity of papers that must be delivered.
Candy can deliver x/50 papers in a minute.
Tim can deliver x/100 papers in a minute.
Tim and Candy took their time gathering all the papers together =x/ (x/50 +x/100)
= x/ (3x/ 100)
=100/ 3 minutes
=33 minutes 33 seconds
When Tim and Candy collaborate, it takes them 33 minutes and 33 seconds to distribute all the papers.
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Answer:
Step-by-step explanation:
It takes a time of 33 min 33 sec.
Let x be the overall quantity of papers that must be delivered.
Candy can deliver x/50 papers in a minute. Tim can deliver x/100 papers in a minute. Tim and Candy took their time gathering all the papers together =x/ (x/50+x/100) = x/(3x/ 100) =100/ 3 minutes =33 minutes 33 seconds
That is When Tim and Candy collaborate, it takes them 33 minutes and 33 seconds to distribute all the papers.
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please help meee
xddd
Answers
Answer:
I'm thinking it's 22, but I could be wrong.
Step-by-step explanation:
[(4•(-2)+(-3)]•(4-2-(-3)
Answers
Step-by-step explanation:
hope it helps you
thank you
in 201520152015 the populations of city x and city y were equal. from 201020102010 to 201520152015, the population of city x increased by 20\ , percent and the population of city y decreased by 10\, percent. if the population of city x was 120{,}000120,000120, comma, 000 in 201020102010, what was the population of city y in 201020102010?
Answers
Answer:
Step-by-step explanation:
Answer:
The exact Population of the city Y in 2010 was 160,000.
Step-by-step explanation:
Given that,
1. In the year 2015, the populations of City X and City Y were equal.
2. City X population is increased by 20% and City Y population is decreased by 10% from 2010 to 2015.
3. Also, the population of City X was 120,000 in 2010
With the given data, calculation goes like this,
The population of City X in 2010 is 120000
Population Increased by 20% till 2015,
= 120000×120/100
= 144000
As Population of city Xand Y are same,
Population of city Y in 2015 would be 144000.
Population of Y in 2010 was decreased by 10%,
= 144000×100/90
=160000
Therefore, the Population of city Y in 2010 was 160,000.
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-3(y + 4) + 4 (2y - 2) simplify
Answers
Answer:
7y-20
Step-by-step explanation:
-3y-12+8y-8
7y-20
Answer:
5y - 20
Step-by-step explanation:
Simplify the expression.Remove the parenthesis by multiplying each term of (y+ 4) by (-3) and multiplying each term of (2y - 2) by 4
-3(y + 4) + 4(2y - 2) = (-3)*y + (-3)*4 + 4*2y - 2*4
= -3y - 12 + 8y - 8
= -3y + 8y -12 - 8
Combine like terms (-3y & 8y) and constants (-12 & -8).
= 5y - 20
SAT QUESTION HELLP ME
Answers
Answer:
22.5
Step-by-step explanation:
we can use the ratios to turn x+y+z=180 to x+4x+3x= 180
then solve for 180
x = 22.5
Answer: D.) 22.5°
Have a nice day!
Write an equation that represents the line.
Use exact numbers.
Answers
Answer: y=3/4x-4.5
Step-by-step explanation: Looking at the two points on the line, it goes up 3 times and right 4 times, making it 3/4x. To find the y-intercept, you look where the line intersects the y-axis, and it intersects at y=-4.5.
(1) PQRS is a rhombus. Prove that APQT = APST by using all four conditions of congruency.
Answers
Four conditions of congruency are: SSS, ASA, SAS, RHS
Using SSS congruency,
Side: PS = PQ (by the rule, all sides of rhombus are equal)
Side: ST = TQ (by the rule, diagonals bisect each other)
Side: PT = PT (common)
Therefore, Area(PQT) = Area(PST) by SSS congruency
Using ASA congruency,
Angle: ∠TPS = ∠TPQ (diagonals bisect the angles)
Side: PS = PQ (by the rule, all sides of rhombus are equal)
Angle: ∠PST = ∠PQT (opposite angles are equal, and diagonals bisect the angles)
Therefore, Area(PQT) = Area(PST) by ASA congruency
Using SAS congruency,
Side: ST = TQ (by the rule, diagonals bisect each other)
Angle: ∠PTS = ∠PTQ (by the rule, diagonals bisect each other at 90°)
Side: PT = PT (common)
Therefore, Area(PQT) = Area(PST) by SAS congruency.
Using RHS congruency,
Right angle: ∠PTS = ∠PTQ (diagonals bisect each other at 90°)
Hypotenuse: PS = PQ (all sides of rhombus are equal)
Corresponding Side: ST = TQ (by the rule, diagonals bisect each other)
Therefore, Area(PQT) = Area(PST) by RHS congruency
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what is the value of 1/2/1/4
Answers
Answer:
2
Step-by-step explanation:
all steps are in the picture