Using the Empirical Rule and z-scores, we have that:
a) 95% of individuals who sleep between 4.9 and 9.7 hours per day.
b) Z = 0.58.
c) Z = -1.08.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In item 2, both 4.9 and 9.7 are 2.4 hours from the mean, that is, 2 standard deviations, hence 95% of individuals who sleep between 4.9 and 9.7 hours per day.
What is the z-score formula?The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
For this problem, the mean and the standard deviation are given as follows:
[tex]\mu = 7.3, \sigma = 1.2[/tex]
The z-score for an adult who sleeps 8 hours per night is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (8 - 7.3)/1.2
Z = 0.58.
The z-score for an adult who sleeps 6 hours per night is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (6 - 7.3)/1.2
Z = -1.08.
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HELP WILL MARK BRAINLEST
Select the correct answer.
To solve this system of equations using substitution, what could be substituted in place of y in the first equation?
4-5-29
y-2x = 7
A. 721
B.
40 - 5
. C.
541
D. 2x + 7
Answer:
y=2x+7
Step-by-step explanation:
your making y the subject
put 2x over the other side of the equal sign
then change it from a negative to a positive
The vault below is in the shape of a cube. If each side is
3y^4 feet, find its volume.
V = s^3
9514 1404 393
Answer:
27y^12 cubic feet
Step-by-step explanation:
Put the given side length into the formula and simplify according to the rules of exponents.
V = (3y^4)^3 = 3^3·y^(4·3) = 27y^12
The volume of the vault is 27y^12 cubic feet.
2. What percent of 80 is 8?
Answer
6.40%
Step-by-step explanation:
Find the area under the standard normal curve more than 3.2. Give your answer to 4 decimal places.
We have that the area under the standard normal curve more than 3.2 is
P(Z>3.2)=0.00069
From the question we are told
Find the area under the standard normal curve more than 3.2. Give your answer to 4 decimal places.
Generally
Standard normal curve
P(z>3.2)
With values of Z is at
Z-(0,1)
Making Proper use of the Z table to identify P(Z>3.2)
P(Z>3.2)=0.00068714
P(Z>3.2)=0.00069
Therefore
the area under the standard normal curve more than 3.2 is
P(Z>3.2)=0.00069
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what is -9/14+2/7 as a fraction in simplest form
_________
[tex] \: [/tex]
[tex] - \frac{9}{14} + \frac{2}{7} = ...[/tex]
[tex] = \frac{2}{7} - \frac{9}{14} [/tex]
[tex] = \frac{(28 - 63)}{98} [/tex]
[tex] = \frac{ -35 }{98} [/tex]
[tex] = \boxed{ \bold{ - \frac{35}{98}}} [/tex]
Answer:
5/14
Step-by-step explanation:
-9 is just 9 so that makes 9/14 - 2/7.
Multiply 7 by 2 and that makes 14, do the same with the numerator and that makes 4/14 and 9/14 - 4/14 = 5/14
What is the place value of the 5 in the number 8.965?
Answer:
it is the ones place.
Step-by-step explanation:
it is not a decimal.
Answer:
Thousandths place
Step-by-step explanation:
A view of the first four places before and after the decimal:
Ex:
1,209.8753
1 is the thousands place
2 is the hundreds place
0 is the tens place
9 is the ones place
8 is the tenths place
7 is the hundredths place
5 is the thousandths place
3 is the ten thousandths place
In your example,5 is in the thousandths place
Points A(8,4) and B(-2,4) lie on a line .AB is parallel to which axis
The speed of an object can be found by taking the distance it travels and dividing it by the time it takes to travel that distance. An object travels 100 feet in 2.5 seconds. Let the speed, S, be measured in feet per second. Write an equation to represent the relationship between the three quantities (speed, distance, and time).
Answer:
Speed of object = 40 feet per second
Step-by-step explanation:
A hamburger shop sold a combined total of 304 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold?
Answer: 76 hamburgers
Step-by-step explanation:
first we will write an equation:
x+3x=304
which simplified turns in 4x=304
x=76
now go back to our equation and solve.
3x is cheese burgers= 228 cheeseburgers
x is hamburgers =76 hamburgers
!!!!!!!!!!!!!!!!!!!!!
1) A, equivalent fractions
2) A, 8/14
3) C, 6/5
4) C, 23/12
5) A, 5 4/5
6) A, 1/2
Two rules for creating a pattern are given below.
Rule 1: Multiply x by 5 to get y.
Rule 2: Add 12 to x to get y.
Which ordered pair, (x,y), works for both rules?
Choose 1 answer:
(Choice A)
(5,25)
(Choice B)
(3,15)
(Choice C)
(0,12)
Which phrase best describes f(x), graphed on the coordinate plane below?
I
6
4
AN
-S
B
Х
4
-6
O f(x) is an odd function.
Of(x) is an even function.
Of(x) is both odd and even.
Answer: f(x) is an odd function
Step-by-step explanation: The major characteristic of odd functions is that one end of the graph goes down to negative infinity, the other end goes up to positive infinity.
-4b - 5 > -25
please show work
Answer:
b<5
Step-by-step explanation:
-4b -5 > -25
add 5 to both sides
-4b>-20
divide by -4
flip the greater than sign
b<5
Hello everyone, please help me out, What type of Triangle is this triangle?
Answer:
I believe this is an acute scalene triangle
Step-by-step explanation:
Hope this helps! :)
Please mark my answer as brainliest *
PLEASE HELP!!!!
In a sporting event, the scoring area (shown here) consists of four concentric circles on the ice with radii of 4 inches, 4 feet, 6 feet, and 8 feet. If a team member lands a (43-pound) stone randomly within the scoring area, find the probability that it ends up centered on the given color (a) red (b) white (c) blue . (a) The probability that it ends up centered on red is ___.
Answer: The probability that it ends up centered on red is 7/16
What is the equation in slope-intercept form that has a slope of -1 and a y-intercept of 4?
pls help
Answer:
y= -1x+4
Step-by-step explanation:
y=mx+b
m=slope
b=slope intercept
x=x-intercept
Find intercepts of: 3x-3y+9=0
X-intercept as a ordered pair
Y-intercept as a ordered pairr
Anthony has 8 times as many lego set a as Brianna. Together they have 36
Answer:
4.5
Step-by-step explanation:
because 4 times 8 is 32 and .5 times 8 is 4 so 32 plus 4 is 36
Use the point and the slope to graph cach line. Write the equation of the line.
The line passes through point (-1, 4) and has slope - 2.
Answer:
y=-2x+2
Step-by-step explanation:
We use the formula
y=mx+b, where m is the slope, b is the y intercept, and x&y are the coordinates.
We know that one point is (-1, 4)
and the slope is -2.
We are trying to find b.
In order to do that, we plug in what we know:
so,
4=-2(-1)+b
4=2+b
4-2=b
b=2
So now we go back to the original equation and use b as our value'
y=-2x+2
John is 5 years 6 months. How old is John in months?
Answer:
66 months
Step-by-step explanation:
12 months are in a year.
12 x 5 = 60
plus the 6 months that we have been told.
60+6 = 66
hope this helps!
Find the magnitude of the vector (4, - 4).
Write your answer in simplified radical form.
Answer:
the magnitude of the vector is given by the √(px^2+py^2) so the value is 5.65
The magnitude of the given vector (4, -4) in the simplified form will be 5.65.
What is a Vector?A vector is a quantity with both magnitude and direction in physics. It is often depicted by an arrow with the same direction as the amount and a length proportionate to the size of the quantity.
A vector lacks position, but has magnitude and direction. A vector is therefore unaffected by displacement parallel to itself as far as its length is unaltered.
As per the given data in the question,
4² + (-4)² = 16 + 16
= 32
Magnitude = √32
Magnitude = 5.65
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i need a help please
Answer:
43
Step-by-step explanation:
1+2->12^-4=1243
a) Irfan took 55 minutes to draw 5 cartoons. How many minutes will he
take to make 12 cartoons? (Give your answer in hours and minute).
Answer:
2 hours and 12 minutes
Step-by-step explanation:
55/5=11
12x11=132
132/60=2 and 12 remain
0.234 is bigger or less than 0.76
Answer: 0.234 is less than 0.76
Step-by-step explanation:
0.234 can be rounded out to 0
0.76 can be rounded out to 1
Find the value of x from the adjacent figure
Answer:
straight line = 180°
2x+3x+5x= 180 combine like terms
10x=180
x=18
Whats the answer!? ( BRANLIEST )
Answer:
(C) None of the above
Step-by-step explanation:
[tex]5 + ( - 3)(6x - 5) \\ 5 + ( - 18x + 15) \\ 5 - 18x + 15 \\ 5 + 15 - 18x \\ 20 - 18x \\[/tex]
Use distributive law
5+(-18x+15)5-18x+15-18x+2020-18xNOTA
Find: 11/3 divided by 2/3
The quotient is 5 and ______
Answer:
1/2
Step-by-step explanation:
11/3 divided by 2/3
=5.5
11/3 divided by 2/3 , the quotient is 5 and remainder is 1.
The divisor is the integer that divides a given number. The resultant number is sometimes referred to as the quotient. The residual is the number that the divisor leaves after partially dividing the original integer.
Let, first number is x and second number is y
On dividing given two number
Division=x/y
[tex]x/y=\frac{11/3}{2/3}[/tex]
[tex]x/y=11/2[/tex]
It is given that the quotient for dividing two numbers is 5.
Using,
Dividend = Divisor x Quotient + Remainder
Here,
Dividend =11
Divisor =2
Quotient =5
On, substituting these values to get Remainder
11=2 x 5+ Remainder
Remainder=1
Thus, remainder is 1.
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-8/9 divided by -2/3 x 4 1/4
Answer:
4/3
Step-by-step explanation:
Remove negatives
8/9*3/2
Cancel 2 and 8 = 4/9*3
Cancel 9 and 3 = 4/3
Ans = 4/3
The sum of three numbers is 88. The first number is 8 more than the second. The third number is 3 times the second. What are the numbers?
Answer:
The numbers are 24, 16 and 48
Step-by-step explanation:
For this equation you need to use all the information you have to add in 3 variables, use the information you have to connect them, so you only use one number. You’ll have the second number (x), the first number (x+8) and the third number (3x) now we use all of that to make an equation.
88=x+(x+8)+3x
Now you simplify the equation,
88=5x+8
Now get the x and it’s coefficient alone on one side
80=5x
Now divide both sides so the x is alone
x=16
Since the second number was x you know the second number
the first number is x+8 since x is 16 the first number is 24
The third number is 3 * x so the third number is 48.
So the numbers are 24, 16 and 48
1. Lucy monitors the position of a large fish in the ocean with a measuring tool. The tool records the depth (how deep the level) of the fish. Initially, the fish swims at a depth of 14 feet below sea level. Suddenly the fish rises 8 feet.
(a) What expression represents the position of the fish relative to sea level after it rises 8 feet?
(b) What is the position of the fish after it rises 8 feet relative to sea level? Show your work. Answer in a complete sentence.
Hint: Draw and label a picture to see and show what is happening.
Answer:
A) -14 + 8 = 6
B) The fish is at -6 feet below the sea level after it rises 8 feet because -14 (14 feet below 0) plus the 8 feet it rises is -6 feet or 6 feet below the sea level.
Hope this helps and sorry if its wrong!