The ratio of the amount of money alice has to the amount bob has 31:9.
Assume the following:
Alice's amount = P
Bob's amount = Q
Amount received = n
If Alice receives $n$ dollars from Bob ;then she will have $4$ times as much money as Bob.
P + n = 4(Q - n)
P + n = 4Q - 4n
P = 4Q - 4n - n
P = 4Q - 5n - - - - (1)
If, on the other hand, she gives $n$ dollars to Bob, then she will have $3$ times as much money as Bob
P - n = 3(Q + n)
P - n = 3Q + 3n
P = 3Q + 3n + n
P = 3Q + 4n - - - - - - (2)
Equating both equations - (1) and (2)
4Q - 5n = 3Q + 4n
4Q - 3Q = 4n + 5n
Q = 9n
Express P in terms of n, use either equation (1) or (2)
From equation 2:
P = 3Q + 4n
Substituting Q = 9n
P = 3(9n) + 4n
P = 27 + 4n
P = 31n
Alice's amount = P, Bob's = Q
Ratio = P:Q
31 : 9
Hence, the ratio of the amount of money alice has to the amount bob has 31:9.
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n interval estimation, as the sample size becomes larger, the interval estimate remains the same, because the mean is not changing. gets closer to 1.96. becomes narrower. becomes wider.
In interval estimation, when the sample size have become larger then the interval estimate then it will becomes narrower. Option (c) is correct.
A large sample of pattern length or decrease variability will bring about a tighter self belief c program interval with a smaller margin of error. A smaller pattern length or a better variability will bring about a much wider self belief c program interval with a bigger margin of error. The stage of self belief additionally impacts the c program interval width. The large your pattern, the greater certain you may be that their solutions genuinely mirror the population.
This suggests that for a given self belief stage, the bigger your pattern length, the smaller your self belief c program language period. The width of the self belief c program interval for an character observe relies upon to a massive volume at the pattern length. Larger research generally tend to provide greater unique estimates of effects (and therefore have narrower self belief intervals) than smaller research.
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Correct Question:
In interval estimation, as the sample size becomes larger, the interval estimate
a). remains the same, because the mean is not changing.
b). gets closer to 1.96.
c). becomes narrower.
d). becomes wider.
Aphids are discovered in a cherry orchard. The Department of Agriculture has determined that the population of aphids t hours after the orchard has been sprayed is approximated by N(t)=1500−3tln(0.1t)−t where 0
Step 2 of 2 :
What is the maximum number of aphids in the cherry orchard? Round to the nearest whole number.
The maximum number of aphids in the cherry orchard is 1508.
What is population growth?
Population growth is the term used to describe the relative increase in population over a period of time. The growth rate is defined as growth per unit of time.
Given, N(t) = 1500-3t*ln(0.1t)-t
For maximum/minimum, [tex]\frac{dN}{dt} =0[/tex]
or, -3*ln(0.1t) - [tex]\frac{3t}{0.1t} *0.1[/tex] - 1 = 0
or, -3*ln(0.1t) = 4
or, ln(0.1t) = -4/3
or, t = 2.64
Then, [tex]\frac{d^{2} N}{dt^{2} } = \frac{-3*0.1}{0.1t} = \frac{-3}{t}[/tex] at t = 2.64
= -1.1381 < 0
Hence, it is maximum.
For the maximum number of Aphids put t = 2.64, we get
N = 1508
Hence, the maximum number of aphids in the cherry orchard is 1508.
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a dog of this breed weighs 48 pounds. what is the dog's z-score? round your answer to the nearest hundredth as needed. z
If the dog has a z-score of -1.09, his weight is 48.46kg but if the dog has a z-score of 1.09, his weight is 61.54kg according to given standard deviation.
What is standard deviation?
Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.
Main body:
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = x- υ/σ
Given that μ = 55, σ = 6;
For x = 49:
z = 49 - 55/6
z = -1
If the dog has a z-score of -1.09, his weight is:
-1.09 = x -55/6
x - 55 = -6.54
x = 48.46
If the dog has a z-score of 1.09, his weight is:
1.09 = x - 55/6
x -55 = 6.54
x = 61.54
Hence ,If the dog has a z-score of -1.09, his weight is 48.46kg but if the dog has a z-score of 1.09, his weight is 61.54kg
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what is the equation of the line on the graph?
Answer:y=2x+-1
Step-by-step explanation:
y= slopex + y-intercept, the y-intercept is at the point (0,-1) as the y-intercept is when the x coordinate is 0 and the y coordinate gets touched by the y axis, therefore 2x+-1
while watching a basketball game of lakers in a cafe near l.a. live, you observe someone who is clearly supporting lakers in the game. what is the probability that they were actually born within 30 miles of l.a. downtown ?
The probability that the people came for the match live were born within 30 miles be, 0.197
Given, while watching a basketball game of lakers in a cafe near L.A live, we observe someone who is clearly supporting lakers in the game.
we have to find the probability that the person we observed born within 30 miles of L.A downtown.
As, the area of L.A downtown is 15.13 km².
1.6 km = 1 mile
2.56 km² = 1 miles
15.13 km² = 5.91 miles
Probability that the person was born within 30 miles be,
P = favorable area / total area
P =5.91/30
P = 0.197
Hence, the probability that the people came for the match live were born within 30 miles be, 0.197
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PLS HELP WILL MARK BRAINIEST!!!
Joan has a collection of quarters and nickels worth $2.50. There are 14 more nickels than quarters. How many coins of each type does Joan have?
Answer: 20 nickels and 6 quarters.
Step-by-step explanation:
Let q be equal to quarters and n be equal to nickels. We will write a system of equations to help us solve.
First, we know each quarter is $0.25 and each nickel is $0.05.
0.25q + 0.05n = 2.5
Next, we know there are 14 more nickels than quarters.
n = q + 14
We will plug the second equation into the first and solve.
0.25q + 0.05n = 2.5
0.25q + 0.05(q + 14) = 2.5
0.25q + 0.05q + 0.7 = 2.5
0.3q = 1.8
q = 6
Joan has 6 quarters. We know he has 14 more nickels than quarters, so we will use addition.
6 + 14 = 20 nickels
Let A be the set of all statement forms in the three variables p, q, and r, and let R be the relation defined on A as follows.For all S and T in A, S R T ⇔ S and T have the same truth table.Prove that R is an equivalence relation. Show that it satisfies all the properties you selected in part (a), and submit your proof as a free response.
We have proved the statement that S≅W by 3 properties reflexive property, symmetric property, and transitive property.
Given that,
Let R be the relation defined on A as follows, and let A be the set of all statement forms in the three variables p, q, and r. S R T⇔ S and T have the same truth table for all S and T in A. substantiate the equivalence of R.
We have to demonstrate that it satisfies each of the properties you choose.
We know that,
By reflexive property,
S ≅ S means that S has the same truth table as S.
T≅ T denotes that T and T have the same truth table.
By symmetric property,
S ≅T denotes that S and T share the same truth table.
At that time, T and S share the same truth table.
So, T ≅ S
By transitive property,
S≅T and T≅V and V≅W
S shares a truth table with S. Truth table between T and T W's truth table is the same for V and V.
S, T, V, and W all have the same truth table as a result.
S specifically has the same truth table as W.
Then S≅T≅V≅W ---> S≅W
Therefore, We have proved the statement that S≅W by 3 properties reflexive property, symmetric property, and transitive property.
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if a flock of 45 turkeys shows a constant growth rate of 2.3%, how many turkeys will be in the population after 10 years? show your work. how long would it take the flock of turkeys in the above problem to double in population?
By using the concept of growth, it can be calculated that
Number of turkeys after 10 years = 57
It took 10 years for the number of turkeys to double
What is growth?
Growth is the increase in the value of an asset or cost or population at a certain rate over a certain period of time.
Original number of turkeys = 45
Rate of growth = 2.3 %
Time = 10 years
Number of turkeys after 10 years = [tex]45 \times (1 + \frac{2.3}{100})^{10}[/tex]
= 57
Now,
New number of turkeys = 45 [tex]\times[/tex]2 = 90
[tex]90 = 45 \times (1 + \frac{2.3}{100})^n[/tex]
[tex](1 + \frac{2.3}{100})^n = \frac{90}{45}\\\\1.023^n = 2\\n\ ln (1.023) = ln( 2)\\n \times 0.023 = 0.693\\n = \frac{0.693}{0.023}\\n = 30.1 \ years[/tex]
It took 10 years for the number of turkeys to double
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A gym employee is paid monthly. After working for 3 months,he had earned $4,500. To determine how much money he will make over a six-month period,he created the table below.
1. If he continues to earn at the same rate, how much will he have earned after working 5 months?
2) After how many months will the gym employee have made $19,500?
3) Write an equation to represent the constant of proportionality.
1. The amount that the employee make in 5 months will be $7500.
2. The number of months that the gym employee have made $19,500 is 13 months.
3. The equation to represent the constant of proportionality is C = 1500m
What is the constant of proportionality?The constant of proportionality simply shows the ratio of two proportional values that possess a constant value.
Since after working for 3 months, he had earned $4,500. The amount per month will be:
= $4500 / 3
= $1500
The amount in 5 months will be:
= $1500 × 5
= $7500
The number of months that the gym employee have made $19,500 will be:
= $19500 / $1500
= 13 months.
The equation to represent the constant of proportionality is c = 1500m. In this case, c = total amount earned and m = number of months.
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11. the measures of the four angles in a quadrilateral have a ratio of 2:3:6:7.2:3:6:7. what is the measure, in degrees, of the largest of these angles?
The measure of the largest angle of quadrilateral is 140°.
We have given that,
the ratio of angles of a quadrilateral is 2:3:6:7.
And we have to find the largest angle of quadrilateral.
We know that the sum of all the interior angles of quadrilaterals 360°.
Let the common multiple of angles be x,
therefore
2x + 3x + 6x + 7x = 360°
18x = 360°
x = [tex]\frac{360}{18}[/tex]
x = 20°
so the angles becomes,
2(20°) = 40°
3(20°) = 60°
6(20°) = 120°
7(20°) = 140°
Hence the largest of these angles is 140°.
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PLEASE HELP 15 POINTS 1. A balloon has a volume of 5.0 L and a temperature of 200 K. What will the volume of the balloon be if the pressure temperature is raised to 373 K? Formula: v1/t1 = v2/t2
2. What was the volume in my tire this morning if I knew the pressure was 80 KPa and now in the afternoon the pressure is 250 KPa and the volume is 3.5 Liters? Formula: p1v1=p2v2
The volume of the balloon will be 9.3 L and the volume of the tire in the morning will be 10.93 L.
What is heat?Heat is the result of the movement of kinetic energy within a material or an item, or from a power source to a material or an object. Three ways exist for such transfer of energy to take place: Convection, radiation, and conduction
As per the given information in the question,
1.
Volume, V1 = 5 L
Temperature, T1 = 200 K and,
Temperature, T2 = 373 K
V1/T1 =V2/T2
5/200 = V2/373
V2 = 9.3 L
2.
Pressure, P1 = 80 KPa
Pressure, P2 = 250 KPa
Volume, V2 = 3.5 L
P1V1 = P2V2
80(V1) = 250(3.5)
V1 = 10.93 L
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how many integers must a set s contain to be certain that at least 35 integers in s have the same remainder when divided by 4?
Set S should contain 137 number of integers so that at least 35 integers in S have same remainder when divided by 4.
What is pigeonhole principle?According to the pigeonhole principle in mathematics, at least one container must hold more than one item if n things are placed into m containers, where n > m. As an illustration, if one has three gloves (none of which are ambidextrous or reversible), at least two of them must be right-handed or left-handed as there are three items but only two categories of handedness to classify them into. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.
Equating pigeonhole principle :Given: Set S = {}, least number of integers having same remainder when divided by 4=35
To find: Number of integers in set S so that at least 35 of the integers in set S have same remainder?As we know, any number when divided by 4 has following remainder = 0, 1, 2, 3.
Least number of integers having same remainder when divided by 4 = 35.
∴ Number of integers in set S = 35×4
= 140
but 3 is to be subtracted from 140 as it is the last different remainder after which the remainders repeat in manner 0, 1, 2 & 3.
∴ Total number of integers in set S = 140-3
= 137
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Does someone know this ?
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=8\pi \\ r=2 \end{cases}\implies 8\pi =\cfrac{\pi (2)^2 h}{3}\implies 8\pi =\cfrac{4h\pi }{3} \\\\\\ 24\pi =4h\pi \implies \cfrac{24\pi }{4\pi }=h\implies 6=h[/tex]
what is the even function?
Reason:
Every exponent shown for choice A is an even number, which by extension points us to an even polynomial function.
Choice D has all odd exponents (think of [tex]\text{x}[/tex] as [tex]\text{x}^1[/tex]), which means choice D is an odd polynomial function.
Choices B and C have a mix of even and odd exponents for their terms. This means B and C are neither even nor odd.
Hugo is going on vacation and taking his dog Pickles along. Pickles eats 4 cups of Hungry Hound dog food each day. Hugo wants to know how many days he can feed Pickles from a 24-cup bag of Hungry Hound. Which equation can Hugo use to find the number of days d he can feed Pickles from the bag.
The equation that Hugo can use to find the number of days d he can feed Pickles from the bag is 4d = 24.
Which equation can Hugo use to find the number of days?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this situation, Hugo is going on vacation and taking his dog Pickles along. Pickles eats 4 cups of Hungry Hound dog food each day. Hugo wants to know how many days he can feed Pickles from a 24-cup bag of Hungry Hound.
Therefore, the equation to illustrate this will be:
(4 × d) = 24
4d = 24
d = number of days
d = 24/4
d = 6
The number of days is 6.
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Multiple Choice
1. Write the following ratio in simplest form: 32 min:36 min
08:9
08:36
032:9
128:144
The following ratio is the simplest form of 32 min: 36 min is 8: 9. The correct option is a.
What is the simplest ratio in maths?If two quantities of a ratio (i.e., antecedent and consequent) have no common factor (i.e., antecedent and consequent are co-prime), the ratio is said to be in its simplest form or in the lowest term.
The simplest form of the fraction is also known as the reduced form of a fraction. For instance, 34 is the simplest form of a fraction with a common component of one.
32/36 = 8:9. It is divided by 2.
Therefore, the correct option is a. 8:9.
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Answer:
The answer is D
Step-by-step explanation:
I hope it helps!
A pentagon is made up of an equilateral △ABC of side length 2cm on top of a square BCDE. Circumscribe a circle through points, A,D and E. The radius of the circle is
A1+√32
B5−2√3
C 2
D 1+√3
The circle's radius circumscribed through points, A,D and E are 2 units.
Look at the image of the figure attached below for a better understanding of the solution :
From the given figure, we can conclude the following data:
AP = √3/2(a) → 1 length of the median for the triangle of side a.
by putting the value of a. we get:
AP = √3/2(2) = √3
AQ = AP + PQ = √3 + 2
Area of triangle AEΔ = 1/2 × EΔ × AQ = 1/2(2) (√3+2)
AE = AD = √(EQ)² + (AQ)²
= √(1)² + (2+√3)² = √1+4+3+4√3 = √8+4√3
= 2√2+√3
We know that,
R = abc/4Δ
R = 2(2×√2+√3) (2√2+√3) / 4{1/2×2×(√3+2)}
R= 2{4(2+√3)} / 4(√3+2)²
On solving the above equation we get ,
R = 2 units.
As a result, the radius of the circle is 2 units when it is defined by the points A, D, and E.
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Veronica's birthday was coming up. Her mother bought six packages of cupcake mix. Each package could make 12 cupcakes. 24 people had planned to attend Veronica's party. How many cupcakes would be available for each guest?
Answer:
3 cupcakes per person
Step-by-step explanation:
first we need to find the total number of cupcakes so in order to do that we need to multiply the number of mixes and the number of cupcakes each mix would make so:
total number of cupcakes = 6 * 12 = 72
now we can divide it by the total number of people who attended the party so:
72/24 = 3 cupcakes per person
A survey of all beings on planet Boondin found that 75% preferred alaber juice to all other juices. If 12 beings were surveyed altogether, how many of them preferred alaber juice?
The number of people who preferred alaber juice is 9 people
How many of them preferred alaber juice?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, the survey of all beings on planet Boondin found that 75% preferred alaber juice to all other juices. If 12 beings were surveyed altogether
Those who preferred alaber juice will be:
= 75% × 12
= 0.75 × 12
= 9
The number of people is 9.
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please help me with my homework Find the values of the variables assuming the figures are parallelograms
Adjacent angles of a parallelogram are supplementary.
[tex]3x+10+8x+5=180 \\ \\ 11x+15=180 \\ \\ 11x=165 \\ \\ \boxed{x=15} \\ \\ \\ \\ 5y+3(15)+10=180 \\ \\ 5y+55=180 \\ \\ 5y=125 \\ \\ \boxed{y=21}[/tex]
Estimate the solution to the system of equations. You can use the interactive graph below to find the solution. \begin{cases} y=-2x-5 \\\\ y=2x-2 \end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ y=−2x−5 y=2x−2
The solution to the system of equation (x, y) is -3/4 and -7/2
System of Linear EquationsThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.
The equations given are
y = -2x - 5 ...eq(i)
y = 2x - 2 ..eq(ii)
Solving this equation,
x = -3/4, y = -7/2
Using a graph to solve this problem, the point of intersection (x, y) is the solution to the equation.
Kindly find attached graph below
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How many baseballs are in the next picture in this pattern?
A. 64
B. 30
C. 32
D. 24
E. 25
Find f (5)
quick can someone answer meee
Answer:
f (5) = 4
Step-by-step explanation:
First we need to find f(x)
To do this we can find the gradient of the line then plug it into the formula for an equation of a line.
using the points on the line, (3,0) (0,-6)
gradient, m :
[tex] \frac{y1 - y2}{x1 - x2} [/tex]
[tex] \frac{0 - ( - 6)}{3 - 0} = \frac{6}{3} = 2[/tex]
therefore the gradient was found to be 2.
Equation of a line:
y - y1 = m( x - x1)
y - 0 = 2( x - 3)
y = 2x - 6
Therefore the function of the line was found to be:
f(x) = 2x -6
so to find f(5) we substitute 5 in the place of x:
f(5) = 2(5) - 6
f(5) = 10 - 6
f(5) = 4
A truck delivers 568 oranges to grocery stores each week. How many oranges will it deliver in 25 weeks?.
-19 2/9 - 4 1/9 - (-3 4/9)
Answer:
= –179/9
or –19 ^8/9
Step-by-step explanation:
–19²/9 –4¹/9 –(–3⁴/9)
–(173/9) –37/9 + 31/9
=L.c.m = 9
–173–37+31/9
= –210+31/9
= –179/9
or –19 ^8/9
i hope i was able to helped
which needs to occur on a consistent basis and at regular intervals to determine whether execuatin of goals
Exercise needs to be consistent and done at regular times. The body can adjust more effectively and swiftly when there is consistency. Exercise should ideally be performed 3-5 times per week.
What is Exercise ?Exercise is any physical activity done to increase one's physical or mental fitness.
Exercise and physical activity not only aid to enhance physical health but also help to promote mental health.
A healthy mind follows from a healthy body.
By lowering body weight, frequent physical activity lowers the risk of developing serious conditions like heart attack, cardiovascular disease, diabetes, and high blood pressure. Regular exercise revitalizes the body and the mind.
Additionally, it raises energy levels, mood, and sleep quality.
Hence, Exercise must be performed consistently and at regular intervals. When there is consistency, the body can adjust more quickly and efficiently. The ideal number of times to exercise per week is three to five.
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Colleen took out a $48,000 student loan with a fixed interest rate to pay for college. Colleen did not make payments on her loan for a period of 7 years. After this time period interest had accrued, resulting in the loan balance increasing to $78,000. a. What is is the 7-year growth factor for the amount that Colleen owes on the loan? Preview b. What is the 7-year percent change for the amount that Colleen owes on the loan? % Preview c. What is is the 1-year growth factor for the amount that Colleen owes on the loan? Preview d. What is the 1-year percent change for the amount that Colleen owes on the loan? % Preview Submit
a)The 7-year growth factor for the amount on the loan is $4285.71.
b) 7-year percentage change for the amount is 6.25%.
c) 1-year growth factor for the amount $612.244.
d) 1-year percent change for the amount is 0.894%.
a)We know very well that growth factor is ratio of difference of principal amount and loan amount to the time taken, or
Growth factor=(Final loan amount-Initial loan amount)/Total time
=>Growth factor=(78,000-48,000)/7
=>Growth factor=30,000/7=$4285.71
b)To find the percentage change in amount, we need to use initial loan amount and the difference between two amounts, or
percentage change=((78000-48000)/48000)×100
=>percentage change=[(30000)/48000)]×100
=>percentage change=300/48=6.25%
c)Now, we have already find the growth factor for 7 years, we need to find growth rate in 1 year. So, we use unitary method to find it
=>In 7 years growth factor is=$4285.71
∴In 1 years growth factor is=$4285.71/7=$612.244
d)In 7 years percentage change for the given amount is =6.25%
∴In 1 year percentage change for the given amount=6.25/7=0.894%
Hence, answers are a)$4285.71 b)6.25% c)$612.244 d)0.894%
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a random sample of size 81 is taken from an infinite population with a mean of 50 and a standard deviation of 9. find an approximate probability that the sample mean is within 48 and 51 (round off to second decimal place).
The approximate probability that the sample mean is within 48 and 51 is 0.82.
How to calculate probability?n = sample size = 81
σ = standard deviation = 9
μ = population mean = 50
Probability is a chance of something event can occur, for this case the probability measure of the chance of sample mean is between 48 and 51 can occur. So, the probability of the sample mean is between 48 and 51 is,
P(48 ≤ x ≤ 51) = P([tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex] ≤ z ≤ [tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex])
= P([tex]\frac{48-50}{\frac{9}{\sqrt{81}}}[/tex]≤ z ≤ [tex]\frac{51-50}{\frac{9}{\sqrt{81}}}[/tex])
= P(-2 ≤ z ≤ 1)
= P(z ≤ 1) - P(z ≤ -2)
using z table and we get,
= 0.8413 - 0.0228
= 0.8185
= 0.82
Thus, the probability is 0.82 for the sample mean is within 48 and 51.
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Brainlist + 100 points if correct and well explained:
Graph the line 2x − 3y = 12.
a: The graph shows a line through the points 0 comma 4 and 6 comma 0.
b: The graph shows a line through the points 0 comma negative 4 and 6 comma 0.
c: The graph shows a line through the points 0 comma 4 and negative 6 comma 0.
d: The graph shows a line through the points 0 comma negative 4 and negative 6 comma 0.
Pretty sure it's C!!! :))))))))))))
find the equation of the line that contains the point (1,-1) and is perpendicular to the line x=4 write the line in slope intercept form