Question options :
a. They should be between 64 and 76 inches tall.
b. They should be close to the height that is 95% of the mean. That is, 66.5 inches, plus or minus 2 standard deviations.
c. They should be at or below the 95th percentile, which is 74.92 inches.
d. None of the above.
Answer: a. They should be between 64 and 76 inches tall.
Step-by-step explanation:
Given the following :
Assume men's height follow a normal curve ; and :
Mean height = 70 inches
Standard deviation= 3 inches
According to the empirical rule ;
Assuming a normal distribution with x being random variables ;
About 68% of x-values lie between -1 to 1 standard deviation of the mean. With about 95% of the x values lying between - 2 and +2 standard deviation of mean. With 99.7% falling between - 3 to 3 standard deviations from the mean.
Using the empirical rule :
95% will fall between + or - 2 standard deviation of the mean.
Lower limit = - 2(3) = - 6
Upper limit = 2(3) = 6
(-6+mean) and (+6+ mean)
(-6 + 70) and (6+70)
64 and 76
The range of height of adult males in U.S. using the 95% empirical rule is 64 to 76 inches
According to the given data
The mean height for adult males in the U.S. is about 70 inches
The standard deviation of heights is about 3 inches.
Considering the data to be normally distributed
According to the empirical rule for normal distribution we can write that
95.45% of the data lies with in the range of
[tex]\rm \mu - 2\sigma \; to \; \mu +2\sigma\\\\where \\\mu = Mean\\\sigma = Standard \; deviation[/tex]
We have to to determine that using the Empirical Rule 95% of adult males should fall into what height range
According to the given data
[tex]\rm \mu = 70\\\rm \sigma = 3 \\[/tex]
[tex]\rm Lower \; limit \; of \; the\; range \; of\; variation\; of \; height\; range = 70 - 2(3) = 64[/tex]
[tex]\rm Upper \; limit \; of \; the\; range \; of\; variation\; of \; height\; range = 70 +2(3) = 76[/tex]
So we can conclude that the range of height of adult males in U.S. using the 95% empirical rule is 64 to 76 inches
For more information please refer to the link given below
https://brainly.com/question/25394084
Ms. delilio borrowed 1,200 from a bank for 3 months at 12% annual interest. How much interest did she pay?
Answer: $36
Step-by-step explanation:
When taking a loan from a bank, we have to pay interest. The Simple Interest Formula is:
Simple Interest (I) = Principal (P) × Interest Rate (r) × Time (t)
Principal (P) is the borrowed amount.
Interest Rate (r) is the percent of the principal to be paid.
Time (t) is the length of time that money is borrowed.
If Ms. Delilio borrowed $1,200 at an interest rate of 12% per year, for 3 months:
First, we have to convert 3 months into years
3 months = 3/12 =0.25 years
Then, find the interest by using the formula
Simple Interest (I) = Principal (P) × Interest Rate (r) × Time (t)
In this example
P = $1200
I = 12%
t = 0.25 years
Then:
I = 1200 × 0.12 × 0.25
I = 36
Answer: $36
Step-by-step explanation:
3/12x1200x0.12=36
SIMPLE INTEREST FORMULA
TIME(ALWAYS IN YEARS)FOR EXAMPLE 4 MONTH WOULD BE 4/12 SINCE THERE ARE 12 MONTH IN 1 YEAR
DIVIDE BY 100 FOR INTEREST SHOWN
AND MULTIPLY TO SOLVE
Three students used factoring to solve a quadratic equation? The equation was solve correctly by ______.The solutions of the equation are__________.
Answer:Keith
x=5,x=12
Step-by-step explanation:
Answer:
the answers are keith and -5,-12
Step-by-step explanation:
I just took the test and got a 5/5 the other person is incorrect.
solve systems by substitution method x + y = 12 3x - y = 20
Step-by-step explanation:
x+y=12
3×+y=20
×=12-y
3 (12-y)+y=20
36-3y+y=20
36-4y=20
-4y=20-36
-4y= -16
y =16÷4
y=4
×+y=12
×+4=12
×=12-4
×=8
therefoer;y=4,x=8
A doctor prescribes a 100-mg antibiotic tablet to be taken every eight hours. Just before each tablet is taken, 20% of the drug remains in the body. (a) How much of the drug is in the body just after the sec- ond tablet is taken
Answer:
120 mg
Step-by-step explanation:
20% of 100 is 20 so that would be 20mg plus the 100mg they just took
100+20=120mg
i hope this helps you!
HELP
Kevin has $25 in his checking
account. If Kevin has $2.20
less than 4 times the amount
that Molly has in her
account, what is the
amount of money in
Molly's account?
Answer:
$6.8
Step-by-step explanation:
Let x be the amount of money in Molly's amount
according to question,
4x-25=2.20
4x=2.20+25
4x=27.20
x=27.20/4
x=6.8
So,the amount of money in Molly's amont is $6.8
Answer: $6.80
Step-by-step explanation:
We will represent the amount of money that Molly has with a m. So it tells us the relationship between Kevin's amount and Molly's amount. It is says Kevin has 2.20 less that 4 times Molly's amount so we could represent it by the equation.
25 = 4m -2.20 solve for m.
+2.20 +2.20
27.20 = 4m
m= 6.8
4(6.8) = 27.20 - 25 = 2.20
I need help with this please answer
Answer:
B. [tex]1\frac{1}{7}[/tex]
Step-by-step explanation:
[tex]-9\frac{2}{7}[/tex]=[tex]-\frac{65}{7}[/tex]
[tex]-10\frac{3}{7}[/tex]=[tex]-\frac{73}{7}[/tex]
[tex]-\frac{65}{7}[/tex]-([tex]-\frac{73}{7}[/tex])=8/7
8/7=[tex]1\frac{1}{7}[/tex]
Hope this helped!!!
Simplify $\dfrac{1}{\sqrt2+1}+\dfrac{1}{\sqrt2-1}.$[tex]Simplify $\dfrac{1}{\sqrt2+1}+\dfrac{1}{\sqrt2-1}.$[/tex]
Answer:
Step-by-step explanation:
common denominator
[tex](\sqrt(2)+1)(\sqrt(2)-1) = (\sqrt{2})^2-1^{2}=2-1 = 1[/tex]
Add with common denominator
[tex]\dfrac{1}{\sqrt2+1}+\dfrac{1}{\sqrt2-1}.[/tex]
[tex]= \frac{{\sqrt2-1}}{1} + \frac{\sqrt2+1}{1}[/tex]
[tex]=2* (\sqrt2)[/tex]
If you wrote the numbers from 1-8, and it equals to three, how do you make the statement true if you can't change the 3 but you could connect two or more numbers to make the statement true if you also can only do subtraction?
Answer:
Just add 6 to the right side of 3 which will make as 36
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36
Hope it helps u...pls mark as brainliest
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
One fifth of the square of a number
Answer:
The statement, one fifth of the square of a number is written as
[tex] \frac{1}{5} {x}^{2} [/tex]
Hope this helps you
Help me please with kim!
Answer: Kim - Resp after 24 months = $4,416.00
Kim - Technology Fund after 24 months = $1,120.06
Kim's Technology Fund has enough money to buy a laptop.
Kim's Savings (Resp) will last less than 6 months
Step-by-step explanation for Kim:
January - June 2019
$14.50 + 30($0.25) = $22.00/hr
$22/hr x 15 hr x 4 wks x 6 months = $7920 Gross Income
Resp (15%): $7920(0.15) = $1188CPP(5%): $7920(0.05) = $396EI(2%): $7920(0.02) = $158.40Taxable Income is $7920 - $1188 = $6732 (Annual Income $13,464)
Income Tax (0% for 0-9,000 Annual): $4500(0) = $0Income Tax (8% for 9-25,000 Annual): ($6732-$4500)(0.08) = $178.56→ $7,920 -($1188 + $396 + $158.40 + $0 + $158.40) = $5,999.04 Net Income
Tech Fund (5%): $5999.04(0.05) = $299.95
Food Expense (30%): $5999.04(0.3) = $1,799.71
Clothing Expense (30%): $5999.04(0.3) = $1,799.71
Entertainment Expense (25%): $5999.04(0.25) = $1,499.76
Miscellaneous Expense (10%): $5999.04(0.1) = $599.90
Other Expenses: $5,699.08
July - December 2019 (excluding August)
$22/hr x 20 hr x 4 wks x 5 months + $200 = $6800 Gross Income
Resp (15%): $6800(0.15) = $1020CPP(5%): $6800(0.05) = $340EI(2%): $6800(0.02) = $136Taxable Income is $6800 - $1020 = $5780 (Annual Income $12,512)
Income Tax (0% for 0-9,000 Annual): $4500(0) = $0Income Tax (8% for 9-25,000 Annual): ($5780-$4500)(0.08) = $102.40→ $6,800 - ($1020 + $340 + $136 + $0 + $102.40) = $5,201.60 Net Income
Tech Fund (5%): $5201.60(0.05) = $260.08
Food Expense (30%): $5201.60(0.3) = $1,560.48
Clothing Expense (30%): $5201.60(0.3) = $1,560.48
Entertainment Expense (25%): $5201.60(0.25) = $1,300.40
Miscellaneous Expense (10%): $5201.60(0.1) = $520.16
Other Expenses: $4,941.52
January - June 2020
same as January - June 2019
July - December 2020 (excluding August)
same as July - December 2019
[tex]\boxed{\begin{array}{l|r|r|r|r||r}\underline{KIM}&\underline{Jan-Jun'19}&\underline{Jul-Dec'19}&\underline{Jan-Jun'20}&\underline{Jul-Dec'20}&\underline{Totals\quad }\\Gross&\$7920.00&\$6800.00&\$7920.00&\$6800.00&\$29440.00\\Resp&\$1188.00&\$1020.00&\$1188.00&\$1020.00&\$4416.00\\Net&\$5999.04&\$5201.60&\$5999.04&\$5201.60&\$22401.28\\Other&\$5699.08&\$4941.52&\$5699.08&\$4941.52&\$21281.20\\Tech&\$299.95&\$260.08&\$299.95&\$260.08&\$1120.06\end{array}}[/tex]
which is the equation of a line that passes through the point (3,2) and is parallel to the line in the graph?
Answer:
A. 3x - 2y = 5
Step-by-step explanation:
Given line in the graph has the following properties:
using point (2,3)
m = slope = (y2-y1)/(x2-x1) = (5-2)/(2-0) = 3/2
New line passes through y0(3,2), so use the point-slope form
(y-y0) = m (x-x0)
substitute in value y0(3,2)
y - 2 = (3/2) (x - 3)
multiply by 2 on each side
2y - 4 = 3x - 9
simplify and rearrange
3x - 2y = -4 + 9 =5
3x - 2y = 5
Which equation represents a line that has a slope of −2/3 and a y-intercept of 4?
Answer:
y = -2/3x + 4
Step-by-step explanation:
In an equation that represents a line, the number with which no variable is multiplied is the y-intercept.
The number with which "x" is multiplied is the slope.
So in this case, the slope is -2/3; so the equation should be like -2/3x.
The y-intercept is 4, so it is the number with which no variable is multiplied.
So the equation is:
=> y = -2/3x + 4
A circle has a radius of 8cm use the value 3.1 for π to calculate the area of a sector of the circle if the angle at the center is 150°
Answer:
[tex]8\frac23\ cm^2[/tex]
Step-by-step explanation:
sector of the circle if the angle at the center is 150° means [tex]\frac{150^o}{360^o}[/tex] of full circle of given radius
area of a circle of given radius R is: πR²
so area of given sector:
[tex]A=\dfrac{150^o}{360^o}\cdot \pi\cdot8^2=\dfrac5{12}\cdot3.1\cdot64=82,(6)=8\frac23\ cm^2[/tex]
The area of a sector of the circle if the angle at the center is 150° is 82.67 square centimeter.
What is a circle?
A circle is a locus of a point whose distance always remains constant from a given specific point. The general equation is -
x² + y² = r² (for circle centered at origin)
Given is a circle has a radius of 8 cm.
The area of the sector subtending the angle 150° at center is -
A = (150/360) x 3.1 x 8 x 8
A = 82.67 square centimeter.
Therefore, the area of a sector of the circle if the angle at the center is 150° is 82.67 square centimeter.
To solve more questions on circles, visit the link below-
https://brainly.com/question/17006280
#SPJ5
Simplify: 42x^7-(-11x^7)
Answer: 53x^7
Step-by-step explanation:
Subtracting a negative is like adding.
WILL GIVE BRAINLIEST
Answer:
D
Step-by-step explanation:
You know that you have to find y, so eliminate choice B. She reads 30 per day, which is c, so you will have 30x. She also read 15 pages separately, so the 15 will be added on separately. With this, you get y = 30x + 15.
Answer:
D.
Step-by-step explanation:
Since she already read 15 pages in the bookstore, those 15 pages are constant since she cannot unread those pages. Those pages are the y-intercept of the equation.
Gwen is reading 30 pages per day, so her slope will be 30.
D. y = 30x + 15 will be her equation.
Hope this helps!
What are the coordinates of the image of L for a dilation with center (0, 0) and scale factor 4?
Answer:
A. (-8, 20)
Step-by-step explanation:
The formula for dilations is
[tex]\left(x_{1}\cdot t_{1},\ y_{1}\cdot t_{1}\right)[/tex] Where t is the scale factor
The first step is to plug in the numbers appropriately
[tex](-2*4,5*4)[/tex]
Then, multiply -2 by 4 and 5 by 4 to get
[tex](-8, 20)[/tex]
So your answer is (-8, 20)
Hope this helps
Have a great day! :)
What is the standard form of the equation for this circle?
A (x-1)2-(y + 10)² + 4 = 0
B. (x - 1)2 - +10)2 = 2
c. (x + 1)2 + (y- 1072 = 4
D. (x-1)2-(y + 10)² =
Answer:
(x + 1)² + (y - 10)² = 4
Step-by-step explanation:
Standard form of the equation of a circle is given by,
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and 'r' is the radius.
In the given question coordinates of the center A are (-1, 10) and radius of the circle is 2 units.
By substituting these values in the formula,
(x + 1)² + (y - 10)² = 2²
(x + 1)² + (y - 10)² = 4
Therefore, standard form of the equation of the given circle is (x + 1)² + (y - 10)² = 4
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
Option C
Step-by-step explanation:
=> [tex]729x^6+y^6[/tex]
=> [tex](9x^2)^3+(y^2)^3[/tex]
Using Formula [tex]a^3+b^3 = (a+b)(a^2-ab+b^2)[/tex]
=> [tex](9x^2+y^2)[(9x^2)^2-(9x^2)(y^2)+(y^2)^2][/tex]
=> [tex](9x^2+y^2)(81x^4-9x^2y^2+y^4)[/tex]
So, these are the two factors of the expression!
Melinda drives 60 2/5km in 1 hour. How many kilometers dose he drive in 5 hours ?
Answer:
60 2/5 x 5 = 60 x 5 + 2/5 x 5
60 x 5 = 300
2/5 x 5 = 2
300 + 2 = 302 so 302 is the answer
302 km for 5 hours
Step-by-step explanation:
Step-by-step explanation:
Km in 1 hour = 60 2/5 = 60.4km
Km in 5 hours = 60.4 x 5 = 302km
For the example shown, Jesse said “The total monthly cost of using the ceiling light and the dishwasher was $0.74.” Is Jesse correct? Explain.
Answer:
what do u mean
Answer: FLOOR GANG OOOH
Step-by-step explanation:
The speed at which a ball bits the ground is proportional to the
height to which the ball rebounds. If the ball hits the ground at
a speed of 20 miles per hour and rebounds to a height of 10 feet,
then how fast must it be traveling (in miles per hour) to rebound
to a height of 15 feet?
Answer:
30 mph
Step-by-step explanation:
let s represent speed and h represent rebound.
Given that s is proportional to h then the equation relating them is
s = kh ← k is the constant of proportion
To find k use the condition s = 20, h = 10, then
20 = 10k ( divide both sides by 10 )
2 = k
s = 2h ← equation of proportionality
When h = 15 , then
s = 2 × 15 = 30 mph
can someone help me please
Answer:
-3x
Step-by-step explanation:
-3 is the coefficient and x is the variable.
To decrease a number by 40%, what do we multiply by???
Answer:
Step-by-step explanation:
to decrease a number by 40% i would do
100% = number you got
50% divide by 2
10%= dived 100% number by 10 then take the 10% away from the 50% to get 40%
then take the 40% away from the 100%
hope this helps :)
Given: Circle k(O), diameter US , m RU=50°, m UT=30° Find: m∠RUS, m∠STU
Answer:
[tex]\boxed{m<RUS = 65 \ degrees}\\\boxed{m<STU = 90 \ degrees}[/tex]
Step-by-step explanation:
Finding m∠RUS:Given that RU = 50°, So Central Angle ROU = 50° too because the measure of arc is equal to its central angle
Now, Let's assume a triangle ROU. It is an isosceles triangle since RO = RU (Radii of the same circle)
So,
∠ORU ≅ ∠OUR (Angles opposite to equal sides are equal)
So, we can write them as 2(∠RUO)
So,
2(∠RUO)+50 = 180 (Interior angles of a triangle add up to 180)
2(∠RUO) = 180-50
2(∠RUO) = 130
Dividing both sides by 2
∠RUO = 130/2
∠RUO = 65 degrees
m∠RUS = 65 degrees (Both are the same)
Finding m∠STU now:In a semi circle (Given that SU is a diameter) , there must be a 90 degrees angle sin it opposite to the diameter.
So,
m∠STU = 90 degrees
From the diagram of circle k(O), m∠RUS = 65° and m∠STU = 90°
CircleGiven that:
m RU = m∠ROU = 50°, m UT = m∠UOT =30°m∠ORU = m∠OUR (isosceles triangle)
m∠ORU + m∠OUR + m∠ROU = 180° (angle in triangle)
50 + 2 * m∠OUR = 180
m∠OUR = 65°
m∠OUR = m∠RUS = 65°
m∠STU = 90° (angle subtended at circumference by semicircle).
From the diagram of circle k(O), m∠RUS = 65° and m∠STU = 90°
Find out more on circle theorems at: https://brainly.com/question/17023621
Please give me the correct answer
Answer:
e=9.14
Step-by-step explanation:
e²=a²+b²-2abcosФ
e²=36+25-2(30)cos112
e=√36+25-2(30)cos112
e=9.14
In a newspaper, it was reported that yearly robberies in Springfield were down 10% to 90 in 2014 from 2013. How many robberies were there in Springfield in 2013?
Answer:
100.
Step-by-step explanation:
Let the number of robberies be x ( in 2013).
Then x - 0.10x = 90
0.90x = 90
x = 90 / 0.90
= 100.
£1 = 1.18 euros How many pounds will lisa have to exchange to get 300.90 euros. (please answer!)
Answer:
255 pounds.
Step-by-step explanation:
We can set up a proportion.
1 pound / 1.18 euros = x pounds / 300.9 euros
1.18 * x = 1 * 300.9
1.18x = 300.9
x = 255
255 pounds.
Hope this helps!
Answer:
300.90 € = £ 255
Step-by-step explanation:
£ 1 = 1.18 €
So,
1 € = £ 1/1.18
=> 1 € = £ 0.847
Multiplying both sides by 300.90 for getting the exchange rate of 300.90 euros
=> 300.90 € = £ 0.847 * 300.90
=> 300.90 € = £ 255
I will give brainliest pls i need help
Which phrase describes the algebraic expression 3 x minus 4?
the sum of three times a number and four
four less than three times a number
the quotient of three times a number less four
the difference between four and three
Answer:
The option B, perfectly gives it to the target, because if you think about it, four less, means 4-, but backwards, and three times, means 3x, and if you put that together, that perfectly matches the one you are looking for. Hope that this would help you!
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
What is the range of the function?
Identify the x-intercepts of the function graphed below.
Answer:
-2 and 3 along the horizontal line
Step-by-step explanation:
There are two axes, plural for axis; the two main lines. The one that runs vertically is the y axis and the one that runs horizontally is the x axis. Now when you see the parabola which is the curve, it meets at three points. The points are -2 , 6, and 3. the ones we are focusing on are the -2 and 3 since they are the numbers/points on the x axis