Complete Question
According to a random sample taken at 12 A.M., body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.13degrees°F and a standard deviation of 0.62degrees°F. Using Chebyshev's theorem, what do we know about the percentage of healthy adults with body temperatures that are within 3 standard deviations of the mean?
What are the minimum and maximum possible body temperatures that are within 3 standard deviations of the mean?
Answer:
a) what do we know about the percentage of healthy adults with body temperatures that are within 3 standard deviations of the mean?
This means that at least 88.89% of healthy adults with body temperatures that are within 3 standard deviations of the mean.
b).What are the minimum and maximum possible body temperatures that are within 3 standard deviations of the mean?
The minimum body temperature within 3 standard deviations of the mean = 96.27°F
The maximum body temperature within 3 standard deviations of the mean = 99.99°F
Step-by-step explanation:
We solve this question using Chebyshev's theorem.
Chebyshev's theorem states that:
1) At least 3/4 of the data lies within two standard deviations of the mean. This means, the interval endpoints :
Mean ± 2Standard deviation
2) At least 8/9 of the data lies within three standard deviations of the mean. This means, the interval endpoints :
Mean ± 3Standard deviation
From the above question,
Mean = 98.13°F
Standard deviation = 0.62°F
The question specified 3 Standard deviation from the mean. Hence,
a) At least 8/9 of the data lies within three standard deviations of the mean. This means, the interval endpoints :
Mean ± 3Standard deviation
Converting this to percentage
8/9 × 100 = 88.89%
Therefore, this means that at least 88.89% of healthy adults with body temperatures that are within 3 standard deviations of the mean.
b) For question B,to find the minimum, maximum value
At least 8/9 of the data lies within three standard deviations of the mean. This means, the interval endpoints :
Mean ± 3Standard deviation
Mean = 98.13°F
Standard deviation = 0.62°F
98.13 - 3 × 0.62
= 96.27°F
98.13 + 3 × 0.62
= 99.99°F
Therefore, the minimum body temperature within 3 standard deviations of the mean = 96.27°F
The maximum body temperature within 3 standard deviations of the mean = 99.99°F
James has saved $560 in two years. He saved 3 times
as much during the first year as during the second
year. How much did he save each year?
Answer:
Year 1:42 Year 2:14
Step-by-step explanation:
Divide $560 x 4=14 then multiply by three to get the amount for year one and the and what's leftover($14) is year 2.
The ratio for 8:11 answers
Answer:
4:5
Step-by-step explanation:
To simplify the ratio 8:10, you find the greatest common divisor of 8 and 10, and then we divide 8 and 10 by the greatest common divisor.
The greatest common divisor that you can use to simplify 8:10 is 2.
Which of the following would be equivalent to 3^2 ⋅ 3^5?
3^10/3^3
3^10/3^7
3^1 x 3^7
3^0
it is 3^1 x 3^7
youre welcome
Answer:
C) 3^1 x 3^7
Step-by-step explanation:
Solve 24x + 2y = 48 for x.
Answer:
x = 2 - 1/12y
Step-by-step explanation:
Step 1: Write equation
24x + 2y = 48
Step 2: Solve for x
Subtract 2y on both sides: 24x = 48 - 2y
Divide both sides by 24: x = 2 - 1/12y
Hello! :)
First thing you do is add -2y to both sides
24x + 2y + -2y = 48 + -2y
24x = -2y + 48
Now divide both sides by 24
24x/24 = -2y + 48/24
x = -1/12y + 2
Hope this helps
THEDIPER
8.EE.5
Identify the unit rate of the proportional relationships:
1)
2)
In mort Answer
Insert Answer
3)
4)
Insert Answer
Insert Answer
Answer:
1.) [tex]slope=2[/tex]
2.) [tex]slope=-3[/tex]
3.) [tex]slope=\frac{1}{4}[/tex]
4.) [tex]slope=-\frac{4}{5}[/tex]
Step-by-step explanation:
The unit rate is also known as slope. Slope is the change in the y values over the change in the x values:
[tex](x_{1},y_{1})\\\\(x_{2},y_{2})\\\\\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=slope[/tex]
However, with certain graphs, the slope can be found in a simpler manner.
You start at one point and move across the y-axis, then move along the x-axis until you reach another point on the same line. Make sure you move on the y-axis first, then the x-axis. Record the slope as spaces moved in each [tex]\frac{y}{x}[/tex] When you move up, the number will be positive [tex](\frac{+y}{x})[/tex]. If you move down, the number will be negative [tex](\frac{-y}{x})[/tex].If you move to the right, the number will be positive [tex](\frac{y}{+x})[/tex]. If you move to the left, the number will be negative [tex](\frac{y}{-x})[/tex].Solve this problem in two different ways, Show your work.
46x37
Answer:
1702
Step-by-step explanation:
46×37 is 1702. Have a great rest of the day!
if f(x)= 2x - 6, find the value
Answer:
3
Step-by-step explanation:
6=2x
6/2=3
x=3
r= m/2 (c + K) for k
Answer:
[tex]\bold{K=\frac{2r}m-c=\frac{2r-cm}m}[/tex]
Step-by-step explanation:
[tex]\bold{r= \frac m2 (c + K)}\\^{\div\frac m2}\qquad^{\div\frac m2}\\ \bold{r\cdot\frac2m=c+K}\\{}\ ^{-c}\qquad^{-c}\\\bold{\frac{2r}m-c=K}[/tex]
Or if you mean r= m/[2(c + K)]
[tex]\bold{\quad r\ =\ \frac m{ 2(c + K)}}\\^{\cdot(c+K)}\quad^{\cdot(c+K)}\\ \bold{r(c+K)=\frac m2}\\{}\qquad ^{\div r}\qquad^{\div r}\\\bold{c+K=\frac m2\cdot\frac1r}\\{}\quad^{-c}\qquad^{-c}\\\bold{K=\frac m{2r}-c}[/tex]
Rewrite Ohm's law, V = lR to solve for the current, l, and then use the formula to find the current when the voltage is 0.6 volts and the resistance is 12 ohms.
Answer:
0.05 amps.
Step-by-step explanation:
I remember this one from high school.
V=IR (V=Voltage, I=Current, and R= Resistor) *Substitue values.
I=V/R
0.6/12
Divide [tex]\frac{6}{120}[/tex] = 0.05 Ampere
What is the slope of the line through (-1,8) and (3,-4)?
Choose 1 answer:
A)-1/3
B)-3
C)1/3
D)3
Answer:
The answer is option BStep-by-step explanation:
The slope of a line given two points can be found by using the formula
[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\[/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-1,8) and (3,-4)
The slope is
[tex]m = \frac{ - 4 - 8}{3 - - 1} = \frac{ - 12}{4} = - 3 \\ [/tex]
We have the final answer as
- 3Hope this helps you
Which image shows a translation?
А
B
с
Answer:
I'm pretty sure it's A :)
Two stores offer differently priced sales for the same paper towels, according to the table below. Which store offers the better deal, based on a lower unit price per roll?
Store 1
Store 2
Paper towel rolls
12
10
Price
$3.60
$3.50
Store _____ has the better deal.
What is the value of j? 40° 30
Answer:
70 degrees
Step-by-step explanation:
To find the value of J, both of the smaller angles need to be added together
40 + 30 = 70
What is the answer to 6+(-6)
What is the slope-intercept form of the equation of the line that contains the points(-3, -3)and(4, 5)?
Answer:
y = 8/7x+3/7
Step-by-step explanation:
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= ( 5 - -3)/( 4 - -3)
= ( 5+3)/ ( 4+3)
=8/7
The slope intercept form of the equation is y = mx+b
y = 8/7x+b
Substitute a point into the equation
5 = 8/7 *4 +b
5 = 32/7 +b
35/7 = 32/7 +b
Subtract 32/7 from each side
35/7 - 32/7 =b
3/7 =b
y = 8/7x+3/7
Answer:
y = 8/7x+3/7
Step-by-step explanation:
in need help to answer this question
Answer:
1 6/7
Step-by-step explanation:
1 & 6/7
What is the image of the point (2,3) after a rotation of 180° counterclockwise
Answer:
(2,3) becomes A'(-2,-3)
Step-by-step explanation:
Using the 180 cc rotation rule (x,y) --> (-x,-y). Points 2 and 3 become negative resulting in (-2,-3)
Hong removed 8 fish from his pond each day for 64 days. What was the total change in the number of fish in the pond?
Answer:
Step-by-step explanation:
512 fish were removed from the pond
Identify the type of function
f(x) =2x+1
Answer:
slope intercept form
Step-by-step explanation:
15 donuts in 3 boxes = how many donuts per box
Answer:
5
Step-by-step explanation:
divide
What is the COMMON DIFFERENCE for the following ARITHMETIC sequence.
-2, - 11, -20...
Answer: The common difference is -9
Step-by-step explanation:
-11 -(-2) = -9
-20 -(-11) = -9
Same difference.
Here are some points. Three points labeled, A, B, and C, plotted on a coordinate grid with the origin labeled “O.” The x axis has the numbers negative 10 through 8 indicated. The y axis has the numbers negative 4 through 6 indicated. Point A is located at negative 6 comma 5. Point B is located at 3 comma 2. Point C is located at 0 comma negative 1. What are the coordinates of A, B, and C after a translation to the right by 4 units and up 1 unit? Plot these points on the grid, and label them A′, B′ and C
The coordinates of A, B, and C after a translation to the right by 4 units and up 1 unit will be A'(-2, 6), B'(7, 3), and C'(4, 0).
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself, and it maintains some spatial correlation between figures.
Here are some points. Three points labeled, A, B, and C, plotted on a coordinate grid with the origin labeled “O”.
Point A is located at (-6, 5).
Point B is located at (3, 2).
Point C is located at (0, -1).
Then the coordinates of A, B, and C after a translation to the right by 4 units and up 1 unit will be given as
Point A: (-6 + 4, 5 + 1) ⇒ (-2, 6)
Point B: (3 + 4, 2 + 1) ⇒ (7, 3)
Point C: (0 + 4, -1 + 1) ⇒ (4, 0)
More about the transformation of a point link is given below.
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Gus plans to install a handrail around a rectangular skating rink. One of the rink's sides is 40 meters long and one of the rink's width is 20 meters wide. How many meters of handrail does Gus need to cover the perimeter of the rectangular skating rink?
Answer:
120 m
Step-by-step explanation:
just mutiply 20 by 2 and 40 by 2. You will get 40 and 80.
so, 20+80=120m
Will someone plz help with these??
18 and 19
Answer:
19 )
do cross multiply
and answer will come
Step-by-step explanation:
w+ý=z/y
Answer:
18)
y=5/2x-23/2
19)
Both equasions equal
x=z/w+y
Step-by-step explanation:
Consider the points R and S in the figure. How many different lines pass through both R and S? Explain.
Answer:
1
Step-by-step explanation:
Two distinct points define exactly one line.
___
We haven't seen the figure. If R and S are the same point, an infinite number of lines will pass through R and S.
(PLEASE HELP ME DX PLEASE) Nate would like to purchase a new laptop for school from Best Buy. The store is offering a $100 mail in rebate on all Lenovo Laptops. Nate is planning to spend anywhere between $300 - $500. Sales tax is 8% of the total cost after the rebate has been given.
(a) Write the compound inequality to represent this scenario.
(b) What price range of laptops can Nate look at so that he meets his budget. Show your work. Be sure to
explain what your answer means.
Answer:
Part A)
[tex]300\leq 1.08(x-100)\leq 500[/tex]
Part B)
[tex]377.78\leq x\leq 562.96[/tex]
Nate wants the original price of the laptop to be between approximately $378 or $563.
Step-by-step explanation:
Part A)
Let's let x be the price of the new laptop.
Since the store is offering a $100 rebate (discount), this means that the total cost of the laptop before tax is:
[tex]x-100[/tex]
So, the total price of the laptop after the 8% tax is:
[tex]1.08(x-100)[/tex]
Since Nate is planning to spend between $300 and $500, this means that we can write the following compound inequality:
[tex]300\leq 1.08(x-100)\leq 500[/tex]
Part B)
To find the range of the price of laptops, let's find the solution to our inequality.
To do so, let's solve them individually. So, let's first find our minimum price:
[tex]300\leq1.08(x-100)[/tex]
Divide both sides by 1.08:
[tex]277.78\leq x-100[/tex]
Add 100 to both sides:
[tex]377.78\leq x[/tex]
So, Nate wants the laptop to be at least approximately $378.00.
Now, let's find our maximum price:
[tex]1.08(x-100)\leq 500[/tex]
Divide both sides by 1.08:
[tex]x-100\leq462.96[/tex]
Add 100 to both sides:
[tex]x\leq 562.96[/tex]
So, Nate wants the maximum price of the laptop to be about $563.00.
So, our compound inequality is:
[tex]377.78\leq x\leq 562.96[/tex]
This means that Nate wants the original price of the laptop to be between approximately $378 or $563.
And we're done!
Answer:
This would be the compound inequality formula for the given situation. This is because Nate is planning on spending somewhere between 300 and 500 dollars. Therefore the price (represented by the variable p) needs to be greater than or equal to 300 but at the same time less than or equal to 500. But this is after the rebate and sales tax have been calculated into the laptop's price. Which in this scenario, the rebate needs to be applied first and then the sales tax is applied after as 1.08 in order to apply the 8% onto the price itself.
1 and 2 are supplements, 3 and 4 supplements and 1 =4. prove 2=3
Step-by-step explanation:
Supplementary angles are angles that have the sum of their angles to be 180°. Hence if <1 and <2 are supplements, then <1+<2 = 180°.... 1
Similarly if <3 and <4 are supplements, then <3+<4 = 180° ....... 2
Equating the left hand side of both equations since they are both equal to 180°, we will have;
<1+<2 = <3+<4 ....... 3
From the question we are told that <1 = <4, substituting this condition into equation 3;
From 3; <1+<2 = <3+<4
<4+<2 = <3+<4 (since <1 = <4)
subtract <4 from both sides
<4+<2 -<4= <3+<4 -<4
<2 = <3 (Proved!)
Answer: I’m not sure if this is what you need but-
Step-by-step explanation:
Julie paid $28 for an item after a 20% discount. What was the original price?
Answer:
33.60
Step-by-step explanation:
Multiply 28 by 20%
28*20%=5.6
Add 5.6 and 28 together
28+5.6=33.60
Sorry if it is wrong Im still really tired
A skier is trying to decide wether or not to buy a season ski pass. A daily pass costs $61. A season ski pass costs $450. The skier would have to rent skis with either pass for $20 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily pass?
Answer:
8 days
Step-by-step explanation:
61x=450
divide each side by 61
then x=7.3 but because of the context you have to round up to 8
also the 20 is just there and can be included in solving but they cancel out so i left it out
I need help!
Triangle ABC with vertices A(0,7), B(7,3),and C(1,4): (x, y) - (x - 3, y-4)
A’
B’
C’
Answer:
This is the correct answer
Step-by-step explanation:
The explanation is on the photo.
I HOPE IT HELPS
The required vertices are [tex]A'(-3,3), B'(4,-1), C'(-2,0)[/tex].
Important information:
The vertices of a triangle A(0,7), B(7,3),and C(1,4).Rule of translation is [tex](x,y)\to (x-3,y-4)[/tex].We need to find the vertices of triangle A'B'C'.
Translation:Using the given rule, we get
[tex]A(0,7)\to A'(0-3,7-4)[/tex]
[tex]A(0,7)\to A'(-3,3)[/tex]
[tex]B(7,3)\to B'(7-3,3-4)[/tex]
[tex]B(7,3)\to B'(4,-1)[/tex]
[tex]C(1,4)\to C'(1-3,4-4)[/tex]
[tex]C(1,4)\to C'(-2,0)[/tex]
Thus, the required vertices are [tex]A'(-3,3), B'(4,-1), C'(-2,0)[/tex].
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