Answer:
a. A point estimate of the BMI for adults in the United States can be calculated from the sample mean, which has a value M=44.57.
b. The sample standard deviation is s=79.9507.
c. The 95% confidence interval for the BMI of adults in the United States is (26.18, 62.96).
Step-by-step explanation:
We start by calculating the sample mean and standard deviation of the BMI data:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{75}(16.2+31.1+24.8+. . .+22.9)\\\\\\M=\dfrac{3343}{75}\\\\\\M=44.57\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{74}((16.2-44.57)^2+(31.1-44.57)^2+(24.8-44.57)^2+. . . +(22.9-44.57)^2)}\\\\\\s=\sqrt{\dfrac{473016.8667}{74}}\\\\\\s=\sqrt{6392.1198}=79.9507\\\\\\[/tex]
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=44.57.
The sample size is N=75.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{79.9507}{\sqrt{75}}=\dfrac{79.9507}{8.66}=9.232[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=75-1=74[/tex]
The t-value for a 95% confidence interval and 74 degrees of freedom is t=1.993.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=1.993 \cdot 9.232=18.39[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 44.57-18.39=26.18\\\\UL=M+t \cdot s_M = 44.57+18.39=62.96[/tex]
The 95% confidence interval for the BMI of adults in the United States is (26.18, 62.96).
A group of 4 friends went to lunch and spent a total of $40, which included the $34 food bill and the tip. They decided to split the bill and tip evenly among themselves.
One of the friends used the equation One-fourth (t + 34) = StartFraction 40 over 4 EndFraction to represent the situation, where t represents the total amount of the tip. Which describes the amount each friend paid for the food and for the tip?
Answer:
The individually paid $1.5 for the tip and $8.5 for the food
Step-by-step explanation:
Total money spent = $40
Food bill = $34
if the situation is represented by the equation [tex]\frac{1}{4}(t+34) = \frac{40}{4}[/tex] where t is the amount of the tip, the amount for the tip can be calculated as shown;
[tex]\frac{1}{4}(t+34) = \frac{40}{4}\\ t+34 = 40\\t = 40-34\\t = 6[/tex]
Amount of the tip = $6
If they decided to split the bill and tip evenly among themselves, amount paid by each friend for the food and the tip can be gotten using the equation representing the situation where t = $6 as shown;
[tex]= \frac{1}{4}(t+34) \\= \frac{1}{4}(6+34)\\= \frac{1}{4}(6)+\frac{1}{4}(34)\\= 1.5+8.5\\[/tex]
From the result above, it can be seen that each friend paid $1.5 for their tip and $8.5 for their food
Answer:
A) Each friend paid $8.50 for the food and $1.50 for the tip.
Select the correct answer. If g = 8, what is the value of the expression g/2+3 ? A. 8/5 B.11/2 C. 7 D. 19
Answer:
7Option C is the correct option
Step-by-step explanation:
g = 8 ( given )
Now,
[tex] \frac{g}{2} + 3[/tex]
Plugging the value of g
[tex] \frac{8}{2} + 3[/tex]
[tex] \frac{8 + 3 \times 2}{2} [/tex]
[tex] \frac{8 + 6}{2} [/tex]
[tex] \frac{14}{2} [/tex]
[tex]7[/tex]
Hope this helps...
Good luck on your assignment...
A student earned grades of B, B, A, C, and D. Those courses had these corresponding numbers of credit hours: 4, 5, 1, 5, 4. The grading system assigns quality points to letter grades as follows: Aequals=4, Bequals=3, Cequals=2, Dequals=1, and Fequals=0. Compute the grade point average (GPA) and round the result to two decimal places.
Answer:
1.69Step-by-step explanation:
Let the five courses with their corresponding credit hours be represented as shown;
FST 201 = 4
FST 203 = 5
FST 112 = 1
FST 219 = 5
FST 223 = 4
If a student earned grades of B, B, A, C, and D respectively in those courses with the following grading system A =4, B =3, C =2, D =1, and F =0, before we can get the student GPA, we need to know the total credit point for the five courses.
Credit point for each course = Number of credit hour * point for each grade
FST 201 = 4 * 4 = 16points (A)
FST 203 = 5 * 4 = 20points (A)
FST 112 = 1 * 4 = 4points (A)
FST 219 = 5 * 4 = 20points (A)
FST 223 = 4 * 4 = 16points (A)
Total credit point = 16+20+4+20+16 = 76points
Total credit point gotten by the student is calculated as thus;
FST 201 = 4 * 3 = 12points (B)
FST 203 = 5 * 3 = 15points (B)
FST 112 = 1 * 4 = 4points (A)
FST 219 = 5 * 2 = 10points (C)
FST 223 = 4 * 1 = 4points (D)
Total credit point gotten by the student = 45points.
student's Grade Point Average (GPA) = Total credit point/Total credit point gotten by the student = 76/45 = 1.69 (to 2dp)
For the data set represented by this box plot, what is the value of the maximum? maximum:
Answer:
140
Step-by-step explanation:
The maximum is the furthest the line that goes out the furthest, the minimum would be about 83-84
Answer:
the other person is correct!
Step-by-step explanation:
Each of 100 students in the Allen School can only take 1 CSE class each, between the four classes CSE 311, CSE 312, CSE 331, and CSE 332. Each student (independently of others) takes CSE 311 with probability 0.3, CSE 312 with probability 0.4, CSE 331 with probability 0.1, and CSE 332 with probability 0.2. What is the probability that exactly 31 sign up for CSE 311, 39 sign up for CSE 312, 7 sign up for CSE 331, and 23 sign up for CSE 332
Answer:
[tex]P(a=31,b=39,c=7,d=23) = 0.000668[/tex]
Step-by-step explanation:
Sample space, n = 100
Let the number of students signed up for CSE 311 = a
Let the number of students signed up for CSE 312 = b
Let the number of students signed up for CSE 331 = c
Let the number of students signed up for CSE 332 = d
Probability of taking CSE 311, [tex]P_a[/tex] = 0.3
Probability of taking CSE 312, [tex]P_b[/tex] = 0.4
Probability of taking CSE 331, [tex]P_c[/tex] = 0.1
Probability of taking CSE 332, [tex]P_d[/tex] = 0.2
[tex]P(a,b,c,d) = \frac{n!}{a! b! c! d!} p_a^{a} p_b^{b} p_c^{c} p_d^{d} \\P(a=31,b=39,c=7,d=23) = \frac{100!}{31! 39! 7! 23!} * 0.3^{31} * 0.4^{39} * 0.1^{7} 0.2^{23}\\P(a=31,b=39,c=7,d=23) = \frac{4.58*10^{111}}{2.13*10^{56}* 5040 }* (1.57*10^{-55})\\P(a=31,b=39,c=7,d=23) = 0.000668[/tex]
Need Help!!!! What is 1495486+73940426 Thanks!
Answer:
75435912
Step-by-step explanation:
1495486+73940426
= 75435912
Answer:
75,435,912
Step-by-step explanation:
=> 1495486 + 73940426
Using Calculator
=> 75,435,912
simplify the expression into form a+bi, where rational numbers
(4-i)(-3+7i) - 7i(8+2i)
Answer:
-12+28i+3i-7i-65i+28
14 -41i
How many gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze? Use the six step method.
Answer:
x = 270 gallons
270 gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze
Step-by-step explanation:
Let x represent the number of gallons of the 50% antifreeze solution.
The volume of the 10% antifreeze is = 90 gallons
The volume of the mixture that is 40% antifreeze = 90+x
The amount of antifreeze in the two solutions must be equal to the amount of anti freeze in the mixture;
50% of x + 10% of 90 = 40% of (90+x)
0.50(x) + 0.10(90) = 0.40(90+x)
0.50x + 9 = 36 + 0.40x
Collecting the like terms;
0.50x - 0.40x = 36-9
0.10x = 27
x = 27/0.10
x = 270 gallons
270 gallons of a 50% antifreeze solution must be mixed with 90 gallons of 10% antifreeze to get a mixture that is 40% antifreeze
Randomthing2143 help me please! Range of: 1, 2, 3, 1, 5, 2, 1, 8, 9, 7?
Answer:
8solution,
Highest score=9
lowest score=1
now,
range= highest score-lowest score
=9-1
=8
Hope this helps...
Answer:
8
Step-by-step explanation:
The range of the sequence is the largest number - the smallest number.
The largest number is 9.
The smallest number is 1.
9 - 1
= 8
The range of the sequence is 8.
T or F? Is 3y=5x If x is 3 and y is 5?
Answer:
True
Step-by-step explanation:
3y=5x
Put x as 3 and y as 5.
3(5) = 5(3)
15 = 15
Hence, true.
Answer:
trueX=3
y=15
[tex]3y = 5x \\ 3 \times 5 = 5 \times 3 \\ 15 = 15[/tex]
Proved.
Hope it helps..
which of the following descriptions represent the transformation shown in the image? Part 3c
Answer: c) rotation of 180° & shift right 1 unit and down 2 units
Step-by-step explanation:
Rotation of 180° changes the signs of x and y
(x, y) → (-x, -y)
Shift right one unit adds 1 to x, Shift two down subtracts 2 from y
(-x, -y) → (-x + 1, -y - 2)
(x, y) (-x + 1, -y - 2)
(-1, -2) → (2, 0)
(-4, -1) → (5, -1)
(-4, -3) → (5, 1)
Select all that apply. A direct variation equation is graphed. The point (6, 4) is on the graph. Which of the following points are also on the graph of the equation? (3, 2) (-9, -6) (-12, 8) (-6, -3)
Answer:
(3,2)
(-9,-6)
Step-by-step explanation:
Given that the graph is a direct variation.
The equation of variation is:
[tex]x=ky[/tex]
Since point (6, 4) is on the graph
[tex]6=4k\\\\k=\dfrac64[/tex]
Therefore, the equation connecting x and y is:
[tex]x=\dfrac64y[/tex]
[tex]\text{When y=2},x=\dfrac64 \times 2 =3\\\\\text{When y =}-6,x=\dfrac64 \times -6 =-9\\\\\text{When y =}8,x=\dfrac64 \times 8 =12\\\\\text{When y =}-3,x=\dfrac64 \times -3 =-4.5[/tex]
Therefore, the points that are also on the graph are:
(3,2) and (-9,-6)
Answer:
(-9, -6) and (3, 2)
Step-by-step explanation:
Simplify e^ln4
A. 1/4
B. 4
C. 1n4
D. E^4
Answer:
The answer is option B.
4Step-by-step explanation:
Using the expression
[tex] {e}^{ ln(x) } = x[/tex]
[tex] {e}^{ ln(4) } = 4[/tex]
Hope this helps you
Which parent function is f(x) = x^2?
O A. An exponential parent function
OB. The linear parent function
C. The absolute value parent function
D. The quadratic parent function
Answer:
D. Quadratic parent function.
Step-by-step explanation:
The organization that Jones works for is running for a father son dinner for those employees is invited to attend along with his youngest son. If Jones is known to have two children, what is the condition probability that they are both boys given that he is invited to the dinner?
Answer:
25%
Step-by-step explanation:
The probability of having a boy is 50%
To calculate the probability of him having 2 boys, multiply the probabilities together
0.5(0.5) = 0.25
Find value of z and simplify completely.
Answer:
3√10Given:
A right triangle in which an altitude is drawn from the right angle vertex
To find: value of X
We have leg rule in similarity in right triangle as:
[tex] \frac{leg}{part} = \frac{hypotenuse}{leg} \\ [/tex]
Plugging the given values,
[tex] \frac{z}{3} = \frac{3 + 27}{z} \\ z \times z = 3(3 + 27) \: \: (cross \: multiplication) \\ {z}^{2} = 9 + 81 \\ {z}^{2} = 90 \\ z = \sqrt{90} \\ z = 3 \sqrt{10} [/tex]
Hope this helps...
Good luck on your assignment..
Kajol has $75. This is 3/8 of the amount she earned. How much did she earn?
Answer:
$200
I hope this helps!
Answer:
200rupees
Step-by-step explanation:
according to the question ,kajol has 75 rupees
amount earned=3/8* amount earned
=75/3*8
=200 rupees
4) →BRAINLIEST & 10+ POINTS! ← A wheel with diameter 44 cm completes four revolutions in 0.5 seconds. Find the linear speed of the edge of the wheel in cm per second. ⇒Round to the nearest whole number. Linear speed = ____ cm/s
Answer:
352 cm/s
Step-by-step explanation:
circ = 44pi
speed = distance * time
distance = circ * 4 = 176pi
speed = 176pi/0.5
Answer:
≈ 1106 cm/s
Step-by-step explanation:
linear speed = angular speed x radius of the rotation
v = ωr
v = linear speed (m/s)
ω = angular speed (radians/s)
r = radius of the rotation (m)
------------
Given:
d= 44 cm ⇒ r= 44/2 cm= 22 cmω= 4 rev/0.5 s= 8 rev/s= 8*2π/s= 16π/s (converted rev to radians)Linear speed is:
v= 22*16π cm/s ≈ 1106 cm/s (rounded to full number)
Find the value of x
Answer:
8
Step-by-step explanation:
the value of x is 8 because the sides are the same
5x is equal to 8X raise to power - 1/3
Answer:
No solutions.
Step-by-step explanation:
5x = 8x^-1/3
Divide 8 into both sides.
5/8x = x^-1/3
Divide both sides by x.
5/8 = x^-4/3
Multiply both sides by the exponent -3/4.
5/8^-3/4 = x
1.422624 = x
Plug in 1.422624 for x to check.
It does not work. There are no real solutions.
In the figure, a//b, and both lines are intersected by transversal t. Complete the statements to prove that m<1=m<5.
Answer:
Transitive Property of EqualityAlternate Interior Angles TheoremStep-by-step explanation:
a) You're trying to justify that two sums equal to 180° are equal to each other. The Transitive Property of Equality is that justification.
__
b) You're trying to justify that angles 3 and 6 are congruent. These are between the parallel lines, so are "interior" angles. They are on opposite sides of the transversal, so are "alternate" angles. They do not share a vertex, so cannot be vertical angles. The applicable theorem is the Alternate Interior Angles Theorem.
Answer:
Step-by-step explanation:
What are the characteristics of a socialist economy? What are the pros and cons of this type of economy?
Answer:
The pro is Political Control, the cons, however, are many.
Step-by-step explanation:
However, A Socialist Economy cons outweigh its pros. The only thing that is a PRO is you dictating it, preventing people from success. Wanna know the cons? The Cons are more Regulations, to which chokes more businesses of their money, they function, & motive. To which it has a chain reaction of: The Businesses not employing people, more people are out of work, which means more people ain't buying stuff to support the businesses, which means the businesses are out of business, they shut down.
The Economy ain't something that you can stop, or go, & it ain't statistics. An Economy is just.. people, that's it. It's just people, they are the ones that work, run businesses & factories, they are the ones that buy N' sell. They create, craft, invent, innovate, etc.
Here's a quote that I have: "The more you choke it from breathing in, the less it breathes out". That's my stance on regulation & Socialism, to which Socialism is just Voluntary Communism, & A Permanent Ideological belief that Big government Involvement is the way to go.
To which, it's not!
PLEASE HELPP! f(x)= -3x + 3
Which of the graphs represent the inverse of the function F??
Answer:
Answer is Y
Step-by-step explanation:
What is the measure of angle ABC? Please answer quickly!
Answer:
ABC = 88
Step-by-step explanation:
Angle Formed by Two Chords = 1/2( sum of Intercepted Arcs)
ABD = 1/2 ( 131+ 53)
ABD = 1/2 (184)
=92
ABC = 180 -ABD
ABC = 88
A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are at least 30 batteries of each type.
Required:
a. How many ways can a total inventory of 30 batteries be distributed among the eight different types.
b. How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory must include at least four A76 batteries?
c. How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory includes at most three A7b batteries?
Answer:
a. 10295472 ways
b. 4272048 ways
c. 6023424 ways
Step-by-step explanation:
Given that:
Camera shop stocks ----- 8 different types of batteries
one of which is ---- A76
Assume that there are ------ at least 30 batteries of each type.
a.
How many ways can a total inventory of 30 batteries be distributed among the eight different types.
The number of ways a total inventory of 30 batteries be distributed is :
[tex]= \left \{ {{30+8-1} \atop {30}} \right. \}[/tex]
[tex]= \left \{ {{37} \atop {30}} \right. \}[/tex]
[tex]=\dfrac{37!}{30! *7!}[/tex]
[tex]= \dfrac{37*36*35*34*33*32*31*30!}{30!*7*6*5*4*3*2*1}[/tex]
[tex]= \dfrac{37*36*35*34*33*32*31}{7*6*5*4*3*2*1}[/tex]
= 10295472 ways
b.
How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory must include at least four A76 batteries?
If we must include 4 A76 batteries; then the number of ways a total inventory of 30 batteries can be distributed among eight different types of batteries will be:
30 - 4 = 26 batteries
Now;
[tex]= \left \{ {{26+8-1} \atop {26}} \right. \}[/tex]
[tex]= \left \{ {{33} \atop {26}} \right. \}[/tex]
[tex]=\dfrac{33!}{26! \ \ 7!}[/tex]
[tex]=\dfrac{33*32*31*30*29*28*27*26!}{26! \ * \ 7*6*5*4*3*2*1}[/tex]
[tex]=\dfrac{33*32*31*30*29*28*27}{ \ 7*6*5*4*3*2*1}[/tex]
= 4272048 ways
c. If we must include at most three A7b batteries. the number of ways that a total inventory of 30 batteries can be distributed among eight different types of inventory is:
[tex]= \sum \limits ^3 _{x=0} \left \{ {{(30-x)+7-1} \atop {30-x}} \right. \} \\ \\ \\ = \sum \limits ^3 _{x=0} \left \{ {{(30-0)+7-1} \atop {30-0}} \right. \} = (^{36}_{30})+(^{35}_{29})+ (^{34}_{28})+ (^{33}_{27})[/tex]
[tex]= \dfrac{36!}{30! * 6!} + \dfrac{35!}{29! * 6!} + \dfrac{34!}{28! * 6!} + \dfrac{33!}{27! * 6!}[/tex]
= 1947792 + 1623160 + 1344904 + 1107568
= 6023424 ways
Write 6 17/20 as a decimal
Answer:
6.85
Step-by-step explanation:
6 17/20
Convert to improper fraction.
137/20
Divide.
= 6.85
Answer:
6.85
Step-by-step explanation:
17/20 = 85/100
17 x 5 = 85
20 x 5 = 100
so,
6 + 85/100 = 6.85
There are members on the board of directors for a certain non-profit institution. a. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible? b. If they must form an ethics subcommittee of four members, how many different subcommittees are possible?
Answer: a. 1320
b.495
Step-by-step explanation:
Complete question is provided in the attachment.
Total members on the board = 12
a. Persons to chose : chairperson, first vice chairperson, second vice chairperson, and secretary
i.e. Total 3 posts in an order.
Number of ways to choose 3 persons from 12 in an order = [tex]^{12}P_3[/tex] [By permutation]
[tex]=\dfrac{12!}{(12-3)!}\\\\=\dfrac{12!}{7!}\\\\=12\times11\times10\\\\=1320[/tex]
hence, 1320 different slates of candidates are possible .
b. number of ways to choose 4 members out of 12 ( order not matters)=[tex]^{12}C_{4}[/tex] [By combinations]
[tex]=\dfrac{12!}{4!8!}\\\\=\dfrac{12\times11\times10\times9}{24}\\\\=495[/tex]
Hence, the number of different subcommittees are possible =495
will give brainliest help plz i can't get back on the password won't go to my email and my little brother changed the password I am scared I lost everything PLZ HELP ME
How much time will it take Jenny to bike 15 miles if she bikes at a speed of 6 mph?
Answer:
this lesson, we will investigate the relationship between the distance traveled, the rate or speed or travel, and the time that it takes to travel that distance at that rate. We will also look at a few other related products.
Distance = (Rate)(Time)
The equation that relates distance, rate, and time is
d = rt
Where d is the distance traveled, r is the rate, and t is the time. On the CAHSEE exam, you will be given two of these and will be asked to use the above equation to find
took Markus half an hour to drive home from work. He averaged 34 miles per hour. How far does Markus live from his work?SolutionWe are given that it takes 1/2 an hour for the trip. This is a time: t = 1/2We are given that he averages 34 miles per hour. This is a rate: r = 34We are asked how few he has traveled. This is a distance. We use the d=rt equation: d = rt = (34)(1/2) = 17Answer:
2.5 hours
Step-by-step explanation:
First, try rewriting Jenny's speed in it's fraction form: 6 mi/hr
Next, use the units to set up an equation that relates Jenny's speed to the distance they want to travel. Let's call the unknown time t:
6mi/hr=15mi/t
1/t=6/15 (mi/hr•1/mi)
t=15/6 (hrs/mi•mi)= 15/6 (hrs•mi/mi)= 15/6 hrs
t=2.5hrs
So it'd take Jenny 2.5hrs at 6mph to go 15 miles. The key here is to keep track of the units. You can treat them like fractions and reduce them away as if they were numbers or variables.
Tom takes a cancer test and the test is advertised as being 99% accurate: if you have cancer you will test positive 99% of the time, and if you don't have cancer, you will test negative 99% of the time. If 1% of all people have cancer and Tom tests positive, what is the prob that Tom has the disease
Answer:
99% chance tommy has it
Step-by-step explanation:
cuz do da math