Answer:
B
Step-by-step explanation: pORBABLITY
Using the Central Limit Theorem, it is found that:
a) 174.
b) 26.
c) Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the central limit theorem is applied, and the sampling distribution can be approximated by a normal distribution.
d) 0.87
e) 0.0238
f) 0.2005 = 20.05% probability that the proportion of people in the sample with a high school diploma is less than 85%.
-------------------------------------
The Central Limit Theorem establishes that for a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex] , if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex]
In this problem:
Sample of 200, thus [tex]n = 200[/tex].87% have a diploma, thus [tex]p = 0.87[/tex].Item a:
This is
[tex]np = 200(0.87) = 174[/tex]
Item b:
This is:
[tex]n(1-p) = 200(0.13) = 26[/tex]
Item c:
Since both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the central limit theorem is applied, and the sampling distribution can be approximated by a normal distribution.
Item d:
The mean is:
[tex]\mu = p = 0.87[/tex]
Item e:
The standard deviation is:
[tex]s = \sqrt{\frac{0.87(0.13)}{200}} = 0.0238[/tex]
Item f:
Using z-scores, the probability is the p-value of Z when X = 0.85.
We have that:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.85 - 0.87}{0.0238}[/tex]
[tex]Z = -0.84[/tex]
[tex]Z = -0.84[/tex] has a p-value of 0.2005.
0.2005 = 20.05% probability that the proportion of people in the sample with a high school diploma is less than 85%.
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Identify the sample chosen for the study. The number of hours a group of 12 children in Mrs. Smith's kindergarten class sleep in a day. Answer2 Points The 12 children selected in Mrs. Smith's kindergarten class. All children in Mrs. Smith's kindergarten class. The number of hours children sleep.
Answer:
The 12 children selected in Mrs. Smith's kindergarten class.
Step-by-step explanation:
In this case, the population studied are all children in Mrs Smith's kindergarten class, the sample chosen for the study are the 12 children selected in Mrs. Smith's kindergarten class, and the analyzed variable is the number of hours children sleep.
Therefore, since the question asks for the sample, the answer is The 12 children selected in Mrs. Smith's kindergarten class.
The volume v of any cube with a side length s can be deermind using the formula v=s^3 what is the volume in the cubic cenitermeters of a cube with a side length of 2.3 cenimeters
Answer:
12.167[tex]cm^3[/tex]
Step-by-step explanation:
The volume of any solid shape is the quantity or capacity it can contain. For example, if you have a closed tin of milf that is filled to the brim, the volume of the tin is the quantity of milk that is in the tin.
Given any cube with side length s, the Volume V=[tex]s^3[/tex]
If the cube has a side length of 2.3 centimeters
Volume=[tex]s^3[/tex]= s X s X s = 2.3 X 2.3 X 2.3=12.167[tex]cm^3[/tex]
Volume of the Cube = 12.167[tex]cm^3[/tex]
Answer: 12.167 cubic centimeters
Step-by-step explanation:
Use the polygon tool to draw a rectangle with a length of 4 units and a height of 2 units one of the sides of the rectangle falls on like ef and the rectangle had a vertex of e each segment on the grid represents 1 unit
Answer:
Step-by-step explanation:
Please find the attached photo for your reference how to draw the rectangle.
1. From on point E and draw a segment 2 units long because the height is 2 units and be vertical.
2. Draw horizontally a line 4 units long (the length) to the right
3. Draw a line upwards 2 units long, at that point it must be at the same height than point E.
4. Draw a 4-units line to the left, and you will be back on point E, the rectangle done.
Answer:
Over here
Step-by-step explanation:
What is the value of X in the following parallelogram?
Answer: x = 35
Step-by-step explanation:
In a parallelogram, the opposite sides and the opposite angles are equal and parallel.
Also, the consecutive angles in a parallelogram are supplementary. This means that the sum of the consecutive angles is 180 degrees.
Angle (2x - 10) and angle (2x + 50) are consecutive angles. Therefore,
2x - 10 + 2x + 50 = 180
2x + 2x - 10 + 50 = 180
4x + 40 = 180
4x = 180 - 40 = 140
x = 140/4
x = 35
At Sara's birthday party, 15 guests are sharing 3/5 of a gallon of Liquid Soap Bubbles. What fraction of the liquid is available for each guest to use for blowing bubbles?
Answer:
Each guest uses [tex]\frac{1}{25}[/tex] of a gallon of liquid soap bubble at Sara's party.
Step-by-step explanation:
We are given the following in the question:
Number of guests at Sara's party = 15
Amount of liquid soap bubble used by 15 guest =
[tex]\dfrac{3}{5}\text{ of a gallon}[/tex]
Fraction of liquid soap bubble available for each guest =
[tex]=\dfrac{\text{Liquid soap bubble used by 15 guest}}{\text{Number of guest}}\\\\=\dfrac{\frac{3}{5}}{15}\\\\=\dfrac{1}{25}[/tex]
Thus, each guest uses [tex]\frac{1}{25}[/tex] of a gallon of liquid soap bubble at Sara's party.
Answer:
1/25 of the gallon each person will get
Step-by-step explanation:
DONT SKIP PLZ HELP IM DESPERATE
Answer:
C
Step-by-step explanation:
The slope = rise over run
If you count the blocks, you'll see it goes down 5 for every 6 to the right it goes.
Harold catches fish throughout the day at unpredictable intervals. Which reinforcement schedule is this?a. variable interval b. variable ratio c. fixed interval d. fixed ratio
Answer:
The correct answer to the question is
a. variable interval
Step-by-step explanation:
In a variable interval, the time at which reinforcement or reward is gained occurs at an unpredictable time. That is the animal gets a reinforcement on the grounds of an unpredictable time period.
An example of a variable interval is the catching of fish whereby the fisher catches fishes at an unpredictable time throughout the day.
The result of a variable interval is a controlled but stable response rate. In the case in the question, constant monitoring of the fishing device is important
The reinforcement schedule described is a variable interval schedule where the reinforcement occurs at unpredictable intervals of time.
Explanation:The reinforcement schedule described in the question is a variable interval schedule.
Variable interval refers to a schedule in which the reinforcement (in this case, catching fish) occurs at unpredictable intervals of time. Harold catches fish throughout the day, but the intervals between catching fish are inconsistent and unpredictable.
Examples of variable interval schedules include waiting for a bus that arrives at different times or checking your phone for new messages throughout the day.
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Play some pains 1/4 of the area of his living room walls,w, on Monday. On Tuesday, he paints twice as much as he painted on Monday. Write an expression to find the remaining unpainted area
Answer:
X = 1 - (1/4) - 2 * (1/4)
Step-by-step explanation:
The equation to be raised must take into account what is painted on Monday and Tuesday. First consider the wall as a unit, that is to say painting the entire wall (100%) is equivalent to 1. Therefore the equation would be the following:
Let X be the unpainted part:
X = 1 - (1/4) - 2 * (1/4)
X = 1 - (1/4) - (1/2)
Now, if we solve this, we have that 0.25, therefore 25% or 1/4 is left to be painted on the wall.
Assume the supply curve shifts to the right by a given amount at each price. The price in the market will decline the most if demand is more price-_____ and supply is more price-_____. elastic; elastic inelastic; elastic elastic; inelastic inelastic; inelastic
Answer: c. price inelastic and supply is more price-inelastic.
Step-by-step explanation:
Inelastic price describes the consumers static habit of purchasing irrespective of the rise or fall in price.
Supply inelastic : This is a sitiuation when percentage change in supply is less than a percentage change in price.
A building contractor buys 7070% of his cement from supplier A and 3030% from supplier B. A total of 9595% of the bags from A arrive undamaged, while 7070% of the bags from B arrive undamaged. Find the probability that anan undamagedundamaged bag is from supplier Upper AA.
Title:
The answer is [tex]\frac{133}{174}[/tex].Step-by-step explanation:
Let the building contractor bought 1000 cement in total.
70% of 1000 = 700 cements were from A and (1000 - 700) = 300 cements were from B.
The number of undamaged bag from A was 95% of 700 = [tex]\frac{95}{100} \times700 = 7\times95 = 665[/tex] and the number of undamaged bags from B was 70% of 300 = [tex]\frac{70}{100} \times300 = 210[/tex].
Total undamaged bags were (665 + 210) = 870.
The probability that an undamaged bag is from A is [tex]\frac{665}{870} = \frac{133}{174}[/tex].
Which equation is the inverse of y = 9x2 – 4? y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 9 EndFraction y = plus-or-minus StartRoot StartFraction x Over 9 EndFraction + 4 EndRoot y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 3 EndFraction y = StartFraction plus-or-minus StartRoot x EndRoot Over 3 EndFraction + two-thirds
The inverse of the equation y = 9x² − 4 is found by switching x and y and solving the equation for the new y. The correct inverse function after simplification is y = ±√(x / 9 + 4).
Explanation:To find the inverse of the equation y = 9x2 − 4, you need to switch the roles of x and y and then solve for y once again. Here is a step-by-step explanation:
Replace y with x and x with y to get x = 9y2 − 4.Add 4 to both sides to isolate the perfect square term: x + 4 = 9y2.Divide both sides by 9 to get (x + 4) / 9 = y2.Take the square root of both sides note that there are always two solutions when taking a square root, a positive and a negative: y = ±√((x + 4) / 9).Finally, simplify to express y: y = ±√(x / 9 + 4/9).Comparing the result with the choices given, we find that y = ±√(x / 9 + 4) is the correct inverse function.
Which table shows a proportional relationship between a and b?
Answer:
B
Step-by-step explanation:
I first went through starting with A and took 3-9 (since it’s in the first box) I got -6 . You then divide 3 and 9 by -6 and report your answer.
I got 3/-6 = -.5 and And 9/-6 = -1.5
I then moved onto 4 and 12, I took the difference 4-12 and got -11.
4/-11 = -0.36 and 12 /-11 = -1.09
Since these answers are not the all the same I moved onto B
I took 20-25 = -5
20/-5 = -4 and 25/-5 = -5
Next numbers
24-30 = -6
24/6 = 4 and 30/6= 5
Next number
32-40= -8
32/-8 = -4
40/-8 = -5
( when putting this in fraction form it would be -4/-5 and that turns positive.) making this table proportioned unlike the other ones
Answer: option B is the correct answer.
Step-by-step explanation:
If two variables are proportional, a change in the value of one variable would cause a corresponding change in the value of the other variable. This means that both variables are related by a constant of proportionality, k.
Looking at the given tables,
For table A,
9/3 = 12/4 but not equal to 20/5
The relationship is not proportional.
For table B,
25/20 = 30/24 = 40/32 = 1.25
The relationship is proportional.
For table C,
12/4 = 15/5 but not equal to 24/6
The relationship is not proportional.
For table D,
4/3 = 16/12 but not equal to 9/6
The relationship is not proportional.
Graph the relation. Is the relation a function? Why or why not?
{(–1, 1), (–2, 1), (–2, 2), (0, 2)}
No; a range value has two domain values.
Yes; there is only one range value for each domain value.
No; a domain value has two range values.
Yes; there is only one domain value for each range value.
Answer:
No; a range value has two domain values.
Step-by-step explanation:
Output has to be unique for all inputs.
Output for -2 is not unique
Answer:
No; a range value has two domain values
Step-by-step explanation:
CAN I GET SOME HELP AND NOT SKIPPED?
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-2, 2) and point (4, 4) rounded to the nearest tenth?
1 unit
5.7 units
4 units
6.3 units
Answer:
The last one: 6.3 units.
Answer: 6.3 units
Step-by-step explanation:
The formula for determining the distance between two points on a straight line is expressed as
Distance = √(x2 - x1)² + (y2 - y1)²
Where
x2 represents final value of x on the horizontal axis
x1 represents initial value of x on the horizontal axis.
y2 represents final value of y on the vertical axis.
y1 represents initial value of y on the vertical axis.
From the graph given,
x2 = 4
x1 = - 2
y2 = 4
y1 = 2
Therefore,
Distance = √(4 - - 2)² + (4 - 2)²
Distance = √6² + 2² = √36 + 4 = √40
Distance = 6.3 units
According to a study published by a group of University of Massachusetts sociologists, approximately 60% of the Valium users in the state of Massachusetts first took Valium for psychological problems. Find the probability that among the next 8 users from this state who are interviewed, (a) exactly 3 began taking Valium for psychological problems;(b) at least 5 began taking Valium for problems that were not psychological.
Answer:
(a) 0.124
(b) 0.174
Step-by-step explanation:
We are given that 60% of the Valium users in the state of Massachusetts first took Valium for psychological problems.
The Binomial distribution probability is given by;
P(X = r) = [tex]\binom{n}{r}p^{r}(1-p)^{n-r}[/tex] for x = 0,1,2,3,.......
Here, n = number of trials(samples) which is 8 in our case
r = no. of success
p = probability of success which is probability of users who take
Valium for psychological problems of 0.60 in our case
(a) Let X = users taking Valium for psychological problems
So, P(X = 3) = [tex]\binom{8}{3}0.6^{3}(1-0.6)^{8-3}[/tex]
= [tex]56 * 0.6^{3}*0.4^{5}[/tex] = 0.124
(b) Since, it is given that 60% of the Valium users in the state of Massachusetts first took Valium for psychological problems which means 40% of the Valium users in the state of Massachusetts take Valium for problems which are not psychological.
i.e., in this case p = 0.40
So, P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)
= [tex]\binom{8}{5}0.4^{5}(1-0.4)^{8-5} + \binom{8}{6}0.4^{6}(1-0.4)^{8-6} + \binom{8}{7}0.4^{7}(1-0.4)^{8-7} + \binom{8}{8}0.4^{8}(1-0.4)^{8-8}[/tex]
= [tex]56 * 0.4^{5} * (0.6)^{3} + 28 * 0.4^{6} * (0.6)^{2} + 8 * 0.4^{7} * (0.6)^{1} + 1 * 0.4^{8}[/tex]
= 0.174
Using the binomial probability formula, we can determine the probabilities requested in the question. For example, the probability that exactly 3 of the next 8 users began taking Valium for psychological problems is computed using the formula for binomial probability with n=8, k=3, and p=0.60, and the probability that at least 5 began taking Valium for other reasons is computed analogously with p=0.40.
Explanation:This question relates to the concepts of binomial probability and combinatorics. It asks about the probability that certain conditions are met among a specific set of Valium users.
First, to find the probability that exactly 3 of the next 8 users began taking Valium for psychological problems, we would use the formula for binomial probability: P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k)). Here, n=8 (the total number of trials), k=3 (the number of successful trials we're looking for), and p=0.60 (the probability of a single successful trial).
Calculating, we get P(X=3) = C(8, 3) * (0.60^3) * ((1-0.60)^(8-3))
For the second part of the question, we want to find the probability that at least 5 out of the 8 users began taking Valium for reasons other than psychological issues. This is equivalent to 1 - the probability that 4 or fewer of the 8 users took it for non-psychological reasons.
The same binomial probability formula can be used, with n=8, p=0.40 (since the probability of a single user taking Valium for non-psychological reasons is 1 - 0.60 = 0.40), and k taking values from 0 to 4. The probabilities are computed for each k and then summed. The result is then subtracted from 1 to get our desired probability, given by: P(X>=5) = 1 - Σ [P(X=k) from k=0 to 4]
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This is the correct method of recording numerical information from an experiment.
Answer:
Data-table is the correct approach of recording numerical information from an experiment
Step-by-step explanation:
A data-table is a group of related facts arranged in labeled rows and columns and is used to record information. Its purpose is to help sort, analyze and compare data gathered from a science experiment or research project. Knowing how to create a data table demonstrates skills in organizing information in a meaningful way and provides a learning base to progress to more sophisticated ways to track data.
Please help dont skip
What is the distance between point (6, -1) and point (5, 3) rounded to the nearest tenth?
4.1 units
17 units
4.6 units
1.4 units
Answer:
1.4 units
Step-by-step explanation:
x + 4y – 12 = 0 x = 3y – 7 Which of the following is the resulting equation?
-7y – 19 = 0
y – 5 = 0
7y + 19 = 0
7y – 19 = 0
Answer:
The answer to your question is 7y - 19 = 0
Step-by-step explanation:
Data
Equation l x + 4y - 12 = 0
Equation ll x = 3y - 7
Process
1.- Substitute equation ll in equation l
3y - 7 + 4y - 12 = 0
2.- Group like terms
(3y + 4y) + (-7 - 12) = 0
3.- Simplify like terms
7y - 19 = 0
4.- Result
7y - 19 = 0
Please Help !!!!!!
How long (in years) would it take $9,900 to grow into $22,800 if it's compounded continuously at 4% interest per year?
Answer= ____ years (Round your answer to 2 decimal places.)
Answer:
21.27 years
Step-by-step explanation:
22800 = 9900(1.04^t)
22800/9900 = 1.04^t
76/33 = 1.04^t
ln(76/33) = t×ln(1.04)
t = 21.27
Answer: it will take 20.83 years.
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
P = 9900
A = 22800
r = 4% = 4/100 = 0.04
Therefore,
22800 = 9900 x 2.7183^(0.04 x t)
22800/9900 = 2.7183^0.04t
2.3 = 2.7183^0.04t
Taking ln of both sides, it becomes
Ln 2.3 = 0.04t ln2.7183
0.833 = 0.04t
t = 0.833/0.04
t = 20.83 years
PLEASE HELP URGENT MY MOM WILL GROUND ME IF I DONT FINISH THIS LOL
What coordinates on the unit circle are associated with the angle measure?
Drag coordinates into each box to match the angle measure.
Step-by-step explanation:
Hope it helps you in your learning process.
[tex]\frac{23\pi}{3}[/tex] corresponds to [tex]\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)[/tex].
[tex]-\frac{3\pi}{4}[/tex] corresponds to [tex]\left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)[/tex].
-150 degree corresponds to [tex]\left(-\frac{\sqrt{3}}{2},\frac{1}{2}\right)[/tex].
Rewrite as:
[tex]\frac{23\pi}{3}=\frac{18\pi+5\pi}{3}=6\pi+\frac{5\pi}{3}[/tex].
We know that [tex]\frac{5\pi}{3}[/tex] corresponds to [tex]\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)[/tex]. So [tex]\frac{23\pi}{3}[/tex] also corresponds to [tex]\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)[/tex].
[tex]-\frac{3\pi}{4}[/tex] has same position as: [tex]-\frac{3\pi}{4}+2\pi=\frac{5\pi}{4}[/tex].
So the corresponding point to it is [tex]\left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)[/tex].
From unit circle 150 degree corresponds to [tex]\left(-\frac{\sqrt{3}}{2},\frac{1}{2}\right)[/tex].
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Find the missing side length BM. Round your answer to the nearest tenth.
Length of side BM is 30 yd
Step-by-step explanation:
Step 1: Find the value of ∠S using the property that sum of angles of a triangle is 180°⇒ ∠B + ∠M + ∠S = 180°
⇒ 35° + 102° + ∠S = 180°
∴ ∠S = 180° - 137° = 43°
Step 2: Use the law of sines to find the length of BM.Law of sines ⇒ a/sin A = b/sin B = c/sin C
Here, let BM be a then, sin A = sin S = sin 43° = -0.83
Also, b = 18 yd, then sin B = sin 35° = -0.43
⇒ BM/-0.83 = 18/-0.43
⇒ BM = -0.83 × 18/-0.43 = 14.94/0.43 = 34.74 yd = 30 yd (rounded to nearest tenth)
Answer:
Step-by-step explanation:
Looking at the triangle, to determine BM, we would apply the sine rule. It is expressed as
a/SinA = b/SinB = c/SinC
Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. From the triangle, m∠S = 180 - (102 + 35) = 43°
Therefore, applying the rule,it becomes
18/Sin35 = BM/Sin43
Cross multiplying, it becomes
BM × Sin 35 = 18 × Sin 43
BM × 0.5736 = 18 × 0.6820
0.5736BM = 12.276
Dividing the left hand side and the right hand side of the equation by 0.5736, it becomes
0.5736BM/0.5736 = 12.276/0.5736
BM = 21.4
Brandy set her watch 4 seconds behind and it falls behind another 1 second every day. How many days had it been since brandy last set her watch if the watch is 22 seconds behind?
Answer:
18 days
Step-by-step explanation:
Let x represent number of days.
We have been given that Brandy's watch falls 1 second every day. So Brandy's watch will fall [tex]1x[/tex] seconds behind in x days.
We are also told that Brandy set her watch 4 seconds behind, so Brady's watch will be behind by total [tex]x+4[/tex] seconds in x days.
Since Brady's watch is 22 seconds behind, so we will equate [tex]x+4[/tex] by 22 to solve for x as:
[tex]x+4=22[/tex]
[tex]x+4-4=22-4[/tex]
[tex]x=18[/tex]
Therefore, Brandy set her watch 18 days ago.
Answer:
Its been 19 days since brandy last set her watch as the watch is 22 seconds behind.
Step-by-step explanation:
We are given the following in the question:
Brandy set her watch 4 seconds behind and it falls behind another 1 second every day.
Thus, this forms an arithmetic progression.
4, 5, 6, 7, ...
First term, a = 4
Common difference, d = 1
The [tex]n^{th}[/tex] terms is 22. We have to find the value of n.
The [tex]n^{th}[/tex] terms of A.P is given by
[tex]a_n = a + (n-1)d[/tex]
Putting values, we get,
[tex]22 = 4 + (n-1)1\\18 = n-1\\n = 19[/tex]
Thus, its been 19 days since brandy last set her watch as the watch is 22 seconds behind.
Evaluating each geometric series described. Find the sum A1=-3, An=-196608, r=4 Answer choices: A) 1 B)-285886 C)-262143 D)-339855 S=
Answer:
(C)-262143
Step-by-step explanation:
For a geometric series, the nth term
[tex]A_n=ar^{n-1}[/tex] where a= first term, r=common ratio.
If [tex]A_1=a=-3[/tex] , r=4 and [tex]A_n=-196608[/tex]
then from [tex]A_n=ar^{n-1}[/tex]
-196608=-3 X [tex]4^{n-1}[/tex]
[tex]4^{n-1}=\frac{-196608}{-3} =65536\\4^{n-1}=4^8[/tex]
Since the bases are the same, the powers are equal
n-1=8
n=8+1=9
Therefore the Sum of the geometric series
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex] (This form is used because r>1)
[tex]S_n=\dfrac{-3(4^{9}-1)}{4-1}[/tex]
[tex]S_n=\dfrac{-3(262144-1)}{3}=\dfrac{-3(262143)}{3}=-262143[/tex]
At a convention, there are 8 mathematics instructors, 13 computer science instructors, 4 statistics instructors, and 6 physics instructors. If an instructor is selected, fint the probability of getting a physics or a statistics instructor.
Answer:
0.323
Step-by-step explanation:
Number of mathematics instructors=8
Number of Computer Science instructors=13
Number of Statistics instructors=4
Number of Physics instructors=6
Total Attendance = 8+13+4+6=31
Probability of Getting a Physics Instructor=6/31
Probability of Getting a Statistics Instructor=4/31
Pr (Getting a Physics OR Statistics Instructor)
=Probability of Getting a Physics Instructor+
Probability of Getting a Statistics Instructor
=6/31+4/31=10/31=0.323
giving out brainliest !!
Three runners Dave, Edith, and Foley all start at the same time for a 24 km race, and each of them runs at a constant speed. When Dave finishes the race, Edith is 8 km behind, and Foley is 12 km behind. When Edith finishes the race, how far behind is Foley, in km?
Answer:
4 Km behind.
Step-by-step explanation:
1. Draw a graph
2. make Dave Edith and Foley
3. 8-0 is 8 and 12-8 is 4
The speed is the distance covered by an object at a particular time. When Edith finishes the race, the distance by which Foley is behind is 6 km.
What is speed?The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Let the time in which Dave finishes the race be represented by t. Therefore, in time t Dave completed 24 km.
Given that When Dave finishes the race, Edith is 8 km behind. Therefore the distance that Edith will cover in time t is 16 km. Now, the speed of Edith will be,
Speed of Edith = 16 km /t
Also, When Dave finishes the race, Foley is 12 km behind. Therefore the distance that Edith will cover in time t is 12 km. Now, the speed of Edith will be,
Speed of Edith = 12 km /t
Now, the time it will take for Dave to finish the rest of 8 km distance is,
Time = 8 km / (16 km/t)
= 0.5 t
Further, the distance that Edith will cover in time 0.5t is,
Distance = 0.5t × 12km/t
= 6 km
Therefore, the distance that will be left for Foley is 6 km.
Hence, When Edith finishes the race, the distance by which Foley is behind is 6 km.
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A person’s blood pressure is monitored by taking 3 readings daily. The probability distribution of his reading had a mean of 132 and a standard deviation of 5. Each observation behaves as a random sample. Find the mean of the sampling distribution of the sample mean for the three observations each day.
Answer:
The mean of the sampling distribution of the sample mean for the three observations each day is 132.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 132
Standard Deviation, σ = 5
Each observation behaves as a random sample.
a) Mean of the sampling distribution
[tex]\bar{x} = \mu = 132[/tex]
b) Standard deviation of the sampling distribution
Sample size,n = 3
[tex]s = \dfrac{\sigma}{\sqrt{n}} = \dfrac{5}{\sqrt{3}} = 2.887[/tex]
Thus, the mean of the sampling distribution of the sample mean for the three observations each day is 132.
Using the distributive property to find the product (y - 4x)(y ^ 2 + 4y + 16) results in a polynomial of the form y ^ 3 + 4y ^ 2 + ay - 4x * y ^ 2 - axy - 64x . What is the value of a in the polynomial?
Answer:
a=16
Step-by-step explanation:
The distributive property states that
[tex]a(b+c)=ab+ac[/tex]
Therefore using the distributive property
[tex](y - 4x)(y ^ 2 + 4y + 16)[/tex]
=[tex]y(y ^ 2 + 4y + 16) - 4x(y ^ 2 + 4y + 16)[/tex]
Expanding the brackets
[tex]y ^ 3 + 4y^2 + 16y - 4xy ^ 2 - 16xy - 64x[/tex].....(i)
Comparing with the form
[tex]y ^ 3 + 4y ^ 2 + ay - 4x y ^ 2 - axy - 64x[/tex]-----(ii)
The coefficient of y in (i) is 16 which corresponds to a and the likewise the coefficient of xy
Therefore, a=16
Answer:
C.) 16
Step-by-step explanation:
A school wishes to form three sides of a rectngular playground using 480 meters of fencing. The playground borders the school building, so the fourth side does not need fencing.
Answer:
Step-by-step explanation:
If you were talking about how many meters of fencing the school would need it would be 160 meters. The reason i say this is because if you were to divide the 3 sides of the playground by 48o meters of fencing you would get 160 meters of fencing. If this is not the answer your looking for than please state the question next time. THANK YOU
The function of area will be A(x) = x( 480 - 2x)
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The perimeter is given P = 480 meters
Since the one of the sides does not need fencing, the perimeter would be:
P = 2x + y
Make y the subject;
y = P -2x
Substitute 480 for P;
y = 480 - 2x
The area of a rectangular fence is:
Area = xy
Substitute ;
A = x( 480 - 2x)
Express as a function
A(x) = x( 480 - 2x)
Hence, the function of area will be A(x) = x( 480 - 2x)
Read more about areas at:
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A country has 50 million people, 30 million of whom are adults. Of the adults, 5 million are not interested in working, another 5 million are interested in working but have given up looking for work, and 5 million are still looking for work. Of those who do have jobs, 5 million are working part time but would like to work full time, and the remaining 10 million are working full time. What is this country's labor force participation rate? 83.3% 75% 50% 66.7%
Answer:
66.7%
Step-by-step explanation:
Given that
Total population = 50 million
Adults = 30 million
Those not interested in working = 5 million
Those interested in working but given up on searching = 5 million
Those searching = 5 million
Those working part time = 5 million
Those working full time = 10 million
Recall that
Labour force participation rate = (number of people actively participating in labour ÷ total number of people eligible) × 100
Number of people actively participating in labour = employed + unemployed
Employed = 10 million full time + 5 million part time
= 15 million
Unemployed = 5 million. Those searching.
Thus,
People actively participating in labour = 15 + 5= 20 million.
Total number of eligible people = total number of adults = 30 million
Therefore
Labour participation rate = (20/30) × 100
= 0.66667 × 100
= 66.6667
Approximately 66.7%
If the standard deviation of a set of data is zero, what can you conclude about the set of values? The sum of the deviations from the mean is zero. All values are identical. All values are equal to zero. The sum of the values is zero
Answer:
All values are identical.
Step-by-step explanation:
We are given the following in the question:
If the standard deviation of a set of data is zero.
Then, all the values in data are identical.
This can be shown as:
Let all the terms in data be x.
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{nx}{n} = x[/tex]
Sum of squares of differences =
[tex]\displaystyle\sum (x_i - x)^2 = 0[/tex]
[tex]\sigma = \sqrt{\frac{0}{n}} = 0[/tex]
Thus, the correct answer is
All values are identical.
The correct conclusion about the set of values when the standard deviation is zero is that all values are identical.
The standard deviation is a measure of the amount of variation or dispersion in a set of values. A standard deviation equal to zero means that there is no variation at all in the data set. This can only occur if all the values in the set are exactly the same.
To understand why this is the case, let's consider the formula for standard deviation (for a population):
[tex]\[ \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}} \][/tex]
Here, [tex]\( \sigma \)[/tex] is the standard deviation, [tex]\( x_i \)[/tex] represents each value in the data set, [tex]\( \mu \)[/tex] is the mean of the data set, and [tex]\( N \)[/tex] is the number of values in the data set.
Now, let's address the other options:
The sum of the deviations from the mean is zero: This statement is true for any data set, regardless of whether the standard deviation is zero or not. The positive and negative deviations from the mean always sum to zero.All values are equal to zero: This is not necessarily true. The standard deviation can be zero if all values are the same non-zero number.The sum of the values is zero: This is also not necessarily true. The standard deviation is concerned with the variation of the values around the mean, not the sum of the values themselves.