The Empirical Rule is being used to calculate the height distribution for the male students at a school. Based on the mean height of 71 inches and standard deviation of 2.5 inches, the height interval that represents the middle 95% of the male heights at this school is approximately from 66 to 76 inches.
Explanation:In the context of this question, we're using statistics, specifically the Empirical Rule, to find a range that represents the middle 95% of heights for the male students. The Empirical Rule states that, in a normal distribution:
About 68% of values fall within 1 standard deviation of the mean About 95% of values fall within 2 standard deviations of the mean About 99.7% of values fall within 3 standard deviations of the mean
Here, the mean height is 71 inches and the standard deviation is 2.5 inches, so applying the Empirical Rule- two standard deviations from the mean would capture about 95% of the heights:
Lower limit = Mean - 2(Standard Deviation)
= 71 - 2(2.5) = 66 inches
Upper limit = Mean + 2(Standard Deviation)
= 71 + 2(2.5) = 76 inches
So the height interval that represents the middle 95% of heights for the males at this school is 66 to 76 inches.
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Using the empirical rule and a normal distribution with a mean of 71 inches and a standard deviation of 2.5 inches, the middle 95% interval of male heights is between 66 inches and 76 inches.
Explanation:The student from the all-boys school is asking about an application of the empirical rule in statistics, which is useful for understanding data that follows a normal distribution. To find the interval that represents the middle 95% of heights, we apply the empirical rule, which states that 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Since we are interested in the middle 95%, we calculate the interval by subtracting and adding two standard deviations from the mean.
Calculation steps:
Therefore, the middle 95% of the males heights from this school fall between 66 inches and 76 inches.
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A line with a slope of 4 passes through the point (2, 1). What is the equation of this line?
Write your answer using the form y=mx+b.
Please i need help ASAP
Answer:
y = 4x-7
Step-by-step explanation:
We have a slope and a point
m = 4 (2,1)
Using the slope intercept form of the equation
y = mx+b
y = 4x+b
From the point x=2 and y =1
1 = 4(2)+b
1 = 8+b
Subtract 8 from each side
1-8 =8-8+b
-7 = b
We can write the equation by using m=4 and b = -7
y = 4x-7
Answer:
A
Step-by-step explanation:
The circumference of a circle measures 11.27π ft.What is the measure of the diameter of this Circle?
1. Complete the inequality below to describe the
domain of the graph shown.
Domain
2. Complete the inequality below to describe the
range of the graph shown.
Range: <_y <5
Domain is the entire span left to right (on the x-axis) that the graph is on. Since the graph goes from x=-4 and ends at x=4, the domain would be from -4 to 4. The circle at -4 is open, so it does not include the point at -4, just everything leading up to it. So, the domain would be
[tex] - 4 < x \leqslant 4[/tex]
The range is similar, it is the entire span that the graph goes up and down (on the y-axis). The graph starts at the bottom at y=-2, and ends at y=5. The bottom point (4,-2) is closed, so the graph includes that point, and the top point (-4,5) is open and doesn't include the point. Therefore, the range would be
[tex] - 2 \leqslant x < 5[/tex]
Answer:
1) -4 2) -2
Step-by-step explanation:
i got it right
what is the general solution to the differential equation dy/dx= cos(8x)/cos(4y) ?
A. sin =(4y) - sin(8x) = C
B. sin (4y) - 2 sin(8x) = C
C. 2 sin(4y) - sin(8x) = C
D. 2 tan(4y) - sin(8x) = C
Answer:
2sin4y - sin8x = K (C)
Step-by-step explanation:
Given the differential equation
dy/dx= cos(8x)/cos(4y)
This can be solved by using the variable separable method.
Step 1;
Separate the variables
Cos4ydy = cos 8xdx
step 2:
Integrate both sides of the equation
∫cos4y dy = ∫cos8x dx
sin4y/4 = sin8x/8
Step 3:
Add constant of integration to the side containing x variable
sin4y/4 = sin8x/8+ C
Taking sin8x to the other side we have:
sin4y/4-sin8x/8 = C
Multiplying through by 8:
2sin4y - sin8x = 8C
2sin4y - sin8x = K (where K = 8C )
To solve the given differential equation we have apply variable separation method.
The correct option is (c) 2 sin(4y) - sin(8x) = C.
Variable separation:In mathematics, variable separation method used to calculate the partially and ordinary differential function in which we rewrite the equation so that two variable occurs on two side.
Given:
The given differential equation is as follows,
[tex]\dfrac{dy}{dx}=\dfrac{\cos(8x)}{\cos(4y)}[/tex]
How to calculate the Separate the variable?Separate the variable.
[tex]\cos 4y \:dy =\cos 8x\:dx\\[/tex]
Integrate both side of the equation.
[tex]\int \cos4y dy = \int \cos8x dx\dfrac {1}{4}\sin4y = \dfrac {1}{8}\sin8x\\\dfrac {1}{4}\sin4y-\dfrac {1}{8}\sin8x=C\\2\sin4y - \sin8x = 8C[/tex]
Thus, the correct option is (c) 2 sin(4y) - sin(8x) = C.
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Alonzo and Miguel scored a total of 40 points in the basketball game. Miguel scored four more points than twice Alonzo's score. How many points did Miguel score? Write the system of equations and then solve. Question 2 options: Blank # 1 Blank # 2 Blank # 3
Rosario was able to get a great interest rate on her house. She financed $150,000 for 15 years with an interest rate of 2.75%
When she pays off her mortgage, how much will she have spent in all ?
To calculate the total amount spent on a mortgage, multiply the monthly payment by the total number of months. For a $150,000 loan at an interest rate of 2.75% and a 15-year term, the total amount spent is approximately $181,884.60.
Explanation:To calculate the total amount spent on a mortgage, we need to find the monthly payment and multiply it by the total number of months. Using the formula for the monthly payment of a mortgage, we can calculate that the monthly payment for a $150,000 loan with an interest rate of 2.75% and a term of 15 years is approximately $1,010.47. Multiplying this monthly payment by the total number of months (15 years * 12 months per year) gives us the total amount spent, which is approximately $181,884.60.
at high school 40% of the students buy yearbooks. you select 6 students at random. Find P(exactly two buy yearbooks) and P(at least two buy yearbooks). Explain.
Answer:
P(exactly two buy yearbooks) = 0.31104
P(at least two buy yearbooks) = 0.76672
Step-by-step explanation:
We are given that at high school 40% of the students buy yearbooks.
You select 6 students at random.
The above situation can be represented through binomial distribution;
[tex]P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,.......[/tex]
where, n = number trials (samples) taken = 6 students
r = number of success
p = probability of success which in our question is probability that
students buy yearbooks, i.e; p = 0.40
Let X = Number of students who buy yearbooks
So, X ~ Binom(n = 6, p = 0.40)
(a) Now, Probability that exactly two buy yearbooks is given by = P(X = 2)
P(X = 2) = [tex]\binom{6}{2} \times 0.40^{2} \times (1-0.40)^{6-2}[/tex]
= [tex]15\times 0.40^{2} \times 0.60^{4}[/tex]
= 0.31104
(b) Probability that at least two buy yearbooks is given by = P(X [tex]\geq[/tex] 2)
P(X [tex]\geq[/tex] 2) = 1 - P(X = 0) - P(X = 1)
= [tex]1- \binom{6}{0} \times 0.40^{0} \times (1-0.40)^{6-0}-\binom{6}{1} \times 0.40^{1} \times (1-0.40)^{6-1}[/tex]
= [tex]1- (1 \times 1 \times 0.60^{6})-(6 \times 0.40^{1} \times 0.60^{5})[/tex]
= 1 - 0.04666 - 0.18662
= 0.76672
30 POINTS!!! EASY QUESTION!!!!
If it takes Laine 2 hours to wash the windows, Leslie 4 hours to wash the same windows, and Lance 5 hours to wash the windows, how long would it take them all working together?
0.55 hours
1.1 hours
5 hours
2.2 hours
Answer:
5 Hours
Step-by-step explanation:
Assuming their time is cut in half (roughly), you could do 1 + 2 + 2 = 5
It would take 1.1 hours for all working together, option B is correct.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
We use the formula 1 / (time taken by all three to complete the job) = (1 / time taken by Laine) + (1 / time taken by Leslie) + (1 / time taken by Lance)
Plugging in the values given in the question, we get:
1 / (time taken by all three) = (1 / 2) + (1 / 4) + (1 / 5)
To simplify this equation, we first find a common denominator, which is 20.
Then we can rewrite the fractions:
1 / (time taken by all three) = (10 / 20) + (5 / 20) + (4 / 20)
1 / (time taken by all three) = 19 / 20
Multiplying both sides by 20, we get:
time taken by all three = 20 / 19
Hence, it would take 1.1 hours for all working together,
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When graphed, which parabola opens downward?
y = –3x2
y = (x – 3)2
y = one-third x squared
y = x2 – 3
The parabola that opens downward when graphed is y = –3x^2, as the negative coefficient of the x^2 term determines the downward opening direction.
The student has asked which parabola opens downward when graphed. The general form of a parabola is y = ax2 + bx + c. The direction in which the parabola opens is determined by the coefficient a of the x2 term. If a is negative, the parabola opens downward, and if a is positive, the parabola opens upward. Looking at the provided equations, we can identify the equation with a negative a value:
y = –3x2 (The coefficient of the x2 term is -3, so this parabola opens downward.)y = (x – 3)2 (The coefficient here is positive after expanding, so this parabola opens upward.)y = one-third x squared (The coefficient is positive 1/3, so this parabola opens upward.)y = x2 – 3 (The coefficient is positive 1, so this parabola opens upward.)Therefore, the equation of the parabola that opens downward when graphed is y = –3x2
Suppose vanilla beans cost $600 per kilogram. Julie bought 9 grams of vanilla beans. Jacques bought 70 grams of vanilla beans. How much more did Jacques pay for his vanilla beans? A.$5.40 B.$12.00 c.$36.60 D.$42.00
Answer:
The correct option is c,$36.60
Step-by-step explanation:
The key to solving this question lies around measurement conversion,specifically converting grams into its equivalence in kilograms.
1000 grams equal one kilogram
9 grams=9/1000 kg
9 grams=0.009 kg
70 grams=70/1000 kg
70 grams=0.07 kg
Julie pays=$600*0.009=$5.4
Jacques pays=$600*0.07=$42
Jacques pays $36.60 more ($42-$5.4) than Julie paid
Option is wrong because that was what Julie paid
Option D is wrong because that was what Jacques paid
Option B is obviously wrong
a) 15/20
b) 20/25
c) 20/25
d) 20/15
Answer:
a 15/20
Step-by-step explanation:
A=25in
B15in
C20in
Answer:
15/20
Step-by-step explanation:
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Pure acid is to be added to a 10% acid solution to obtain 21 L of a 40% acid solution.
7 gallons of pure acid and 14 gallons of 10% acid
7 liters of pure acid and 14 liters of 10% solution should be added.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
let a = amount of pure acid to be used
then (21-a) = amount of 10% solution required
A typical mixture equation
a + 0.10(21-a) = .40(21)
a+2.1-0.1a=8.4
0.9a+2.1=8.4
Subtract 2.1 on both sides
0.9a=6.3
Divide both sides by 0.9
a=7
7 liters of pure acid
21- 7 = 14 liters of 10% solution
Hence, 7 liters of pure acid and 14 liters of 10% solution should be added.
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A wooden door contains a rectangular window. The width of the window is (x - 2) feet. The area of the window can be represented by x ^ 2 - 3x + 2 .
a. Write a binomial that represents the height of the window.
b. The height of the door is 5 feet more than the height of the window. Write a polynomial that represents the height of the door.
c. The area of the door can be represented by x ^ 2 + 4x . The area is 32 square feet . Find the width and the height of the window.
Answer: height of the door is x+4
Step-by-step explanation:
The arithmetic sequence a_ia
i
a, start subscript, i, end subscript is defined by the formula:
a_1 = 5a
1
=5a, start subscript, 1, end subscript, equals, 5
a_i = a_{i - 1} + 2a
i
=a
i−1
+2a, start subscript, i, end subscript, equals, a, start subscript, i, minus, 1, end subscript, plus, 2
Find the sum of the first 700700700 terms in the sequence.
Answer:
492,800
Step-by-step explanation:
Given ith term of an arithmetic sequence as shown:
ai = a(i-1)+2
and a1 = 5
When i = 2
a2 = a(2-1)+2
a2 = a1+2
a2 = 5+2
a2 = 7
When i = 3
a3 = a(3-1)+2
a3 = a2+2
a3 = 7+2
a3 = 9
It can be seen that a1, a2 and a3 forms an arithmetic progression
5,7,9...
Given first term a1 = 5
Common difference d = 7-5= 9-7 = 2
To calculate the sum of the first 700 of the sequence, we will use the formula for finding the sum of an arithmetic sequence.
Sn = n/2{2a1+(n-1)d}
Given n = 700
S700 = 700/2{2(5)+(700-1)2}
S700 = 350{10+699(2)}
S700 = 350{10+1398}
S700 = 350×1408
S700 = 492,800
Therefore, the sum of the first 700 terms in the sequence is 492,800
Final answer:
To calculate the sum of the first 700 terms of the arithmetic sequence, we apply the arithmetic series sum formula using the number of terms (700), the first term (5), and the common difference (2), resulting in a sum of 492800.
Explanation:
To find the sum of the first 700 terms of an arithmetic series, we use the formula for the sum of an arithmetic series: S = (n/2)(a1 + an), where n is the number of terms, a1 is the first term, and an is the last term. Given that a1 is 5, and the common difference d is 2, we can calculate the nth term (an) using the formula for the nth term of an arithmetic sequence: an = a1 + (d)(n - 1).
We know n = 700, d = 2, and a1 is 5. Thus, an = 5 + 2(700 - 1) = 5 + 2(699) = 5 + 1398 = 1403. The sum can then be calculated as S = (700/2)(5 + 1403) = 350(1408) = 492800.
Therefore, the sum of the first 700 terms of the arithmetic sequence is 492800.
which lengths can be used directly or indirectly to calculate volume of a hexagon right pyramid select three options
Answer:
A: XY and ST
B: VU and TW
D: TX and WX
Step-by-step explanation:
Just took test.
Identify the x-intercepts of the function graphed below.
A. (-3,0) and (-2,0)
B. (-2,0) and (3,0)
C. (0,0) and (-6,0)
D.(-3,0) and (2,0)
Answer:
(-2,0) and (3,0)
Step-by-step explanation:
The parabola passes through both points on the graph.
Answer:
B. (-2,0) (3,0)
Step-by-step explanation:
thats where the line passes through the X axis
what does it take to get brailiest like no one marks it these days
Answer:
you really just have to tell them to and if they are nice they will
Step-by-step explanation:
Answer: A competent person with correct answers
PLZ HELP FASTTT (including brainliest
Solve and graph the inequality 4x – 10 < 18. Which of the following are true about the graph of the solution? Check all that apply. The graph has an open circle at 2. The graph has a closed circle at 2. The graph has an open circle at 7. The graph has a closed circle at 7. The arrow points left. The arrow points right.
Answer:
open circle at 7; arrow points left
Step-by-step explanation:
To Solve:
4x - 10 < 18
+ 10 +10
4x < 28
/4 /4
x < 7 *only flip sign when multiply/divide by negative
< means the arrow will point left and that it will be an open circle
Answer:
Its is C. The graph has an open circle at 7 and E. The arrow points left.
Step-by-step explanation:
Can i get brainliest please?
what is the distance between the points (1,5) and (5,-4)?
Answer:
[tex]\sqrt{97}[/tex]
Step-by-step explanation:
Using the pythagorean theorem, you can find that the distance between the two points is [tex]\sqrt{(5-1)^2+(5-(-4))^2}=\sqrt{4^2+9^2}=\sqrt{97}[/tex]. Hope this helps!
Answer:
it 95 good luck
Step-by-step explanation:
1000^m / 100^n can be written in the form of 10^z express z in terms of m and n
Answer:
z = 3m - 2n
Step-by-step explanation:
[tex] \frac{ {1000}^{m} }{ {100}^{n} } = {10}^{z} \\ \\ \frac{ {10}^{3m} }{ {10}^{2n} } = {10}^{z} \\ \\ {10}^{3m - 2n} = {10}^{z} \\ \\ 3m - 2n = z \\ \\ \huge \red{ \boxed{z = 3m - 2n}}[/tex]
mr.brown wants to withdraw 1,000 from his bank in ten dollar bills. how many ten dollar bills should he receive
Answer:
100 ten dollar bills
Step-by-step explanation:
1000 / 10 = 100
help pleaseeee i don’t know
Answer:
C, at least that's what I think.
15 / x equals 50 / 4
Answer:
Step-by-step explanation:
Solve for x by cross multiplying.
Exact Form:
x=6/5
Decimal Form:
x=1.2
Mixed Number Form:
x=1 1/5
i hope its correct plz tell me if im wrong
A line plot titled Household T V Ownership has Number of televisions on the x-axis. There is x about 0, 2 above 1, 4 above 2, 7 above 3, 0 above 4, 1 above 5, 1 above 6, and 0 above 7.
The line plot shows the number of televisions students have at home.
students have two televisions at home.
How many televisions do most students have at home?
televisions
Answer
4
3
Step-by-step explanation:
i did the test.
Which situation can be represented by the expression -2 + (-1)−2+(−1)minus, 2, plus, left parenthesis, minus, 1, right parenthesis.
Choose 1 answer:
(Choice A)
A
A badger was in a den 222 feet below ground level. The badger dug a tunnel that went down 111 additional foot.
(Choice B)
B
A badger was in a den 222 feet below ground level. The badger climbed up 111 additional foot.
(Choice C)
C
A badger was on a hill 222 feet above ground level. The badger dug a tunnel that went down 111 foot.
Answer:
Its A
Step-by-step explanation:
Answer:
hola ITS A
Step-by-step explanation:
Find the circumference of the circle. Use 3.14 for π. Round to the nearest hundredth, if necessary.
Answer:
15.7
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d where d is the diameter
C = 3.14*5
C= 15.7
Answer:
15.7
Step-by-step explanation:
C=3.14(5 inches) <---Formula
If LM bisects Angle JLK find LJ
Answer:
14 units
Step-by-step explanation:
Given: LM bisects [tex]\angle JLK[/tex]
To find: LJ
Solution:
According to angle bisector theorem,
an angle bisector of a triangle divides the interior angle's opposite side into two segments that are proportional to the other two sides of the triangle.
In [tex]\Delta JKL[/tex], LM bisects [tex]\angle JLK[/tex]
Using angle bisector theorem,
[tex]\frac{LK}{LJ}=\frac{KM}{JM}\\\frac{LK}{LJ}=\frac{KM}{JK-MK}\\\frac{8}{x+3}=\frac{4}{x-4}\\8(x-4)=4(x+3)\\8x-32=4x+12\\8x-4x=12+32\\4x=44\\x=\frac{44}{4}=11[/tex]
So,
[tex]LJ=x+3=11+3=14\,\,units[/tex]
Answer:
14 units
Step-by-step explanation:
To convert 6,986 g to kg, you move move the decimal point _____ places to the _____.
Answer:
Step-by-step explanation:
I’m gay
Z
What is the distance from (-6, 2) to the origin?
PUPUL 2
What is 1,630 divided by 44 as a decimal?
37.045
37.045
37.045
37.0454
Submit
Answer:
37.045
Step-by-step explanation:
Answer:37.045
Step-by-step explanation:
there is a little line over 45