3x^4 y - 48x^2 y =
3x^2 y ( x^2 - 16 ) =
3x^2 y ( x - 4 )( x + 4 )
Answer:
-45x²y
so basically you subtract the numbers and then the indices
edit: just realised this was the wrong method x
we have two vectors a→ and b→ with magnitudes a and b, respectively. suppose c→=a→ b→ is perpendicular to b→ and has a magnitude of 2b . what is the ratio of a / b ?
A deck of cards contains 10 black cards and 10 red cards. The first card drawn is not replaced before drawing the second card.What is the probability of selecting a red card followed by a red card? 141019519938
Solution:
The probability of an event is expressed as
\(P(event)=\frac{number\text{ of desirable outcome}}{number\text{ of possible outcome}}\)Given:
\(\begin{gathered} number\text{ of black cards = 10} \\ number\text{ of red cards = 10} \\ Total\text{ number of cards = 20} \end{gathered}\)In this case, the number of possible outcomes is 20.
Given that the first card is drawn and not replaced before drawing the second card, the probability of selecting a red card followed by a red card is expressed as
\(P(red\text{ and red\rparen=P\lparen first red\rparen}\times P(second\text{ red without replacement\rparen}\)For the first red, we have
\(\begin{gathered} P(first\text{ red\rparen=}\frac{number\text{ of red cards}}{number\text{ of cards\lparen number of possible outcomes\rparen}}=\frac{10}{20} \\ \Rightarrow P(first\text{ red\rparen=}\frac{1}{2} \end{gathered}\)For the second card, we have
\(\begin{gathered} P(second\text{ red\rparen=}\frac{number\text{ of red cards left}}{number\text{ of cards left}}=\frac{10-1}{20-1} \\ =\frac{9}{19} \end{gathered}\)Thus,
\(\begin{gathered} P(\text{ first red and second red\rparen=}\frac{1}{2}\times\frac{9}{19} \\ \Rightarrow P(\text{ first red and second red\rparen=}\frac{9}{39} \end{gathered}\)Hence, the probability of selecting a red card followed by a red card is evaluated to be
\(\frac{9}{38}\)The fourth option is the correct answer.
Which of the following functions (there may be more than one) are solutions of the differential equation y''?4y'+4y=e^t?
a) y=te^(2t)+e^t
b) y=e^(2t)+te^t
c) y=e^(2t)
d) y=e^t
e) y=e^(2t)+e^t
The functions that are solutions of the differential equation y''?4y'+4y=e^t are: (B) y=e^(2t)+te^t & (E) y=e^(2t)+e^t.The given differential equation is, y''+4y'+4y=e^t ...(1)
We have to find the solutions of the differential equation. Let's solve the differential equation:(1) => r²+4r+4=0Now, solve the quadratic equation using the quadratic formula: r= (-(4)+√((4)²-4(1)(4))) / 2(1)= -2 (repeated)So, the solution of the corresponding homogeneous equation is:(2) yh= (c₁+c₂t)e^(-2t) ---------------(2)Now, we have to find a particular solution of the non-homogeneous differential equation (1).
Let, yp= Ae^t. Now, yp'= Ae^t, yp''= Ae^t. Substitute yp and its derivatives in the equation (1):yp''+4yp'+4yp= e^tAe^t+4Ae^t+4Ae^t= e^t9Ae^t= e^tA= 1/9Therefore, the particular solution is,(3) yp= e^t/9 ------------(3)
Hence, the general solution of the given differential equation is,(4) y= yh+yp= (c₁+c₂t)e^(-2t) + e^t/9Now, substitute the initial conditions in the general solution to get the constants c₁ and c₂:Let, y(0)=0 and y'(0)=0, then,c₁= -1/9 and c₂= 5/9Finally, the solution of the differential equation y''?4y'+4y=e^t is,(5) y= -(1/9)e^(-2t) + (5/9)te^(-2t) + e^t/9 =(e^(2t)+te^(2t))/9+ e^t ...
(Ans)The options that represent the functions that are solutions of the differential equation y''?4y'+4y=e^t are: (B) y=e^(2t)+te^t & (E) y=e^(2t)+e^t.
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Problem 2
The metal rim of a magnifying glass is inches around.
What is the area of the surface of the glass inside?
The area of the glass inside the 10 inches metal rim is 25/π square inches
What is the area of a plane shape?The area of a geometric shape or figure is a measure of the flat surface the shape occupies.
The dimension in the question, obtained from a similar question online are;
The length of the metal rim around the magnifying glass = 10 inches around
Required; The surface area of the glass inside the rim
The metal rim around the magnifying glass indicates the circumference of the glass inside;
Therefore;
The circumference of the glass inside the rim = 10 inches
The formula for the circumference of a circle = 2·π·r
Where;
r = The radius of the circle;
Therefore;
r = Circumference ÷ (2×π)
The radius of the glass inside is therefore;
r = 10 inches/(2·π) = 5/π inches
The area of a circle = π × r²
The area of the glass, A = π × (5/π)² = 25/π
The area of the glass inside is A = 25/π square inches
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a college dean would like to estimate a population mean to within 40 units with 99% confidence given that the population standard deviation is 200. a. what sample size should be used? b. what sample size should be used if the standard deviation is changed to 50? c. what sample size should be used if using a 95% confidence level? d. what sample size should be used if we wish to estimate the population mean to within 10 units?
Sample size required is 333, 42, 97 and 33,285, respectively using confidence level and different parameters of standard deviation.
To estimate a population mean to within 40 units with 99% confidence and a population standard deviation of 200, the sample size required can be calculated using the formula
n = (Zα/2)² * (σ²) / (E²)
where Zα/2 is the z-score corresponding to the desired level of confidence (99% in this case), σ is the population standard deviation, and E is the desired margin of error (40 units).
Plugging in the values, we get
n = (2.576)² * (200)²/ (40)²
n = 332.84
Therefore, a sample size of at least 333 should be used.
If the population standard deviation is changed to 50, the same formula can be used with the new value of σ:
n = (2.576)² * (50)²/ (40)²
n = 41.68
Therefore, a sample size of at least 42 should be used.
If using a 95% confidence level, the z-score changes to 1.96
n = (1.96)² * (200)²/ (40)²
n = 96.04
Therefore, a sample size of at least 97 should be used.
To estimate the population mean to within 10 units, the margin of error (E) is changed to 10 in the formula, and the sample size is recalculated
n = (2.576)² * (200)² / (10)²
n = 33,284
Therefore, a sample size of at least 33,285 should be used.
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The required sample size should be 166 to estimate the population mean within 40 units with 99% confidence, given a population standard deviation of 200.
To determine the required sample size for estimating a population mean with a given level of confidence and margin of error, we can use the formula:
n = (Z * σ / E)^2
Where:
n = Sample size
Z = Z-score corresponding to the desired confidence level (in this case, 99% confidence corresponds to a Z-score of 2.576)
σ = Population standard deviation
E = Margin of error (in this case, 40 units)
Substituting the given values into the formula, we have:
n = (2.576 * 200 / 40)^2
Simplifying further:
n = (12.88)^2
n ≈ 165.6544
Since the sample size must be a whole number, we round up the value to the nearest integer:
n = 166
Therefore, the required sample size should be 166 to estimate the population mean within 40 units with 99% confidence, given a population standard deviation of 200.
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the first 4 terms and the 10th term for 3n+4
Answer:
first 4 terms =7,10,13,16
10th term = 34
Step-by-step explanation:
3n+4
3(1)+4=7
3(2)+4=10
3(3)+4=13
3(4)+4=16
7,10,13,16
10th term = 3(10)+4= 34
The first four terms of the sequence having nth term 3n+4, are 7, 10, 13, 16 and the 10th term is 34.
What is arithmetic sequence ?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence.
Given that,
The nth term of a sequence is given by 3n+4,
To find the first 4 terms, substitute the values of n,
At n=1, the first term = 3(1) + 4 = 3 + 4 = 7
At n=2, the second term = 3(2)+4 = 6 + 4 = 10
At n=3, the third term = 3(3) + 4 = 9 + 4 = 13
At n=4, the fourth term = 3(4) + 4 = 12 + 4 = 16
For 10th term, substitute n=10.
At n=10, the tenth term = 3(10) + 4 = 30 + 4 = 34
The first four terms are 7, 10, 13, 16 and the 10th term is 34.
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the hurwicz criterion is a compromise between the minimax and maximin criteria. a. true b. false
True. In game theory and decision theory, the Hurwicz criterion is a decision-making rule between the minimax and maximin criteria.
The Hurwicz criterion is a hybrid of the minimax and maximin criterion. The minimax criterion is concerned with minimising the most potential loss, whereas the maximin criterion is concerned with maximising the least possible gain. The Hurwicz criterion is expressed as a weighted average of the greatest and worst outcomes:
Decision value = α(best payoff) + (1-α)(worst payoff)
where alpha is coefficient representing the decision-maker's optimism or pessimism. The Hurwicz criterion provides a more versatile decision-making tool than the minimax or maximin criteria alone, allowing for a balance between risk-taking and risk-aversion.
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Water flows from a pipe at a rate of 4 feet per second. How many feet will it flow in 20 seconds?
What is the average of first 50 positive integers?.
Average of first 50 positive integers which starts from 1 and goes till 50, we get as 25.5.
What is positive integers ?Mathematically speaking, positive integers are defined as "Integers that are greater than zero." Three categories of integers exist: negative integers, zero, and positive integers.
AVERAGE =\(\frac{First Number + Last term}{2}\)
50 positive numbers starting from 1 to 50
So,
First number = 1
Lat number = 50
Putting in formula we get,
AVERAGE = \(\frac{1+50}{2}\)
= 25.5
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Can someone explain to me how to get the answer:
-3 |2d| = 12
-3×2d=12
-6d=12
d=12÷(-6)
then d= -2Hope this helps.
A person invest $3000 in a bank the bank pays 6.75% interest compounded semi annually to the nearest 10th of a year how long must a person leave the money in the bank until it reaches $6700
Answer:
It would take 12.1 years.
Step-by-step explanation:
We are given with $3000 invested in bank pays 6.75% interest compounded semi annually to the nearest 10th. We are asked to find the number of years the bank reaches $6700.
Let's use the compound interest formula.
\(A= P(1+\frac{r}{n}) ^{nt}\)
We know A=6700
P=3000
r =0.0675
n=2(because compounded semiannually)
t =?( we need to find it)
Plug in the known values into the formula.
\(6700=3000(1+\frac{0.0675}{2}) ^{2*t}\)
Simplify and solve for 't'
Divide both sides by 3000
\(2.23333= (1.03375)^{2t}\)
Take log on both sides
\(log(2.23333) = 2t log(1.03375)\)
Divide both sides by log(1.03375)
24.2067=2t
Divide both sides by 2.
t=12.10...
To round to nearest 10th, we get t=12.1 years.
Write the equation in spherical coordinates.
(a) 6z² = 5x² + 5y²
(b) x² + 5z² = 5
( a)ρ² = (5/6) sec² θ.
(b) ρ = ±√(5 - 5 cos² θ) / sin θ cos φ.
For part (a) 6z² = 5x² + 5y²
The spherical coordinates for the variables x, y, and z are as follows:
x = ρsinθcosφy = ρsinθsinφz = ρcosθ
Substitute the values of x, y, and z into the given equation:6 (ρ cos θ)² = 5(ρ sin θ cos φ)² + 5(ρ sin θ sin φ)²
Simplify:6ρ² cos² θ = 5ρ² sin² θ (cos² φ + sin² φ)6ρ² cos² θ = 5ρ² sin² θ
Substitute sin² θ = 1 - cos² θ:6ρ² cos² θ = 5ρ² (1 - cos² θ)6ρ² cos² θ = 5ρ² - 5ρ² cos² θ6ρ² cos² θ + 5ρ² cos² θ = 5ρ²6ρ² = 5ρ² / (cos² θ + 5cos² θ)6ρ² = 5ρ² / cos² θ(6/5)ρ² = sec² θρ² = (5/6)sec² θ
The equation in spherical coordinates is ρ² = (5/6) sec² θ.
For part (b) x² + 5z² = 5
The spherical coordinates for the variables x, y, and z are as follows:
x = ρsinθcosφy = ρsinθsinφz = ρcosθ
Substitute the values of x, y, and z into the given equation:
(ρsinθcosφ)² + 5 (ρ cosθ)² = 5ρ²ρ² sin² θ cos² φ + 5 ρ² cos² θ = 5ρ²
Rearrange:ρ² (sin² θ cos² φ + 5 cos² θ - 5) = 0sin² θ cos² φ + 5 cos² θ - 5 = 0sin² θ cos² φ = 5 - 5 cos² θsin θ cos φ = ±√(5 - 5 cos² θ)
The equation in spherical coordinates is ρ = ±√(5 - 5 cos² θ) / sin θ cos φ.
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A caterer made 4 grilled cheese sandwiches, 7 ham sandwiches, and 6 turkey sandwiches. How many sandwiches did the caterer make in all?
Answer: 17
Just add the Numbers together this is a Addition question.
7 + 6 + 4 Or However you want to do it The answer will always be 17 if u do it as 4 + 6 + 7 or however else just don't add different numbers.
May I Have brainliest?
The middle 50% of the distribution for X, the bounds of which form the distance represented by the IQR, lies between what two values
The middle 50% of the distribution for X, the bounds of which form the distance represented by the IQR, lies between the first and third quartiles of the data set.
Specifically, the first quartile (Q1) marks the 25th percentile of the data set, while the third quartile (Q3) marks the 75th percentile.
The difference between Q3 and Q1 is known as the interquartile range (IQR).The IQR is a helpful measure of spread in a data set since it excludes outliers from the calculation. Outliers are any data points that fall outside of 1.5 times the IQR above the third quartile or below the first quartile of the data set. Therefore, the middle 50% of the distribution for X lies between Q1 and Q3, with the IQR representing the range of values between these two quartiles.
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PLZZ HELPPP
Which matrix equation can be used to solve the system?
x+y=21
5x+4y=20
Answer:
\(X= \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \left[\begin{array}{ccc}21\\20\\\end{array}\right] \\\)
Step-by-step explanation:
Given the simultaneous equation
x+y=21
5x+4y=20
To write in matrix form, it must be in the form AX= b
X = A⁻¹b
A⁻¹ is the inverse of matrix A
A is a 2by2 matrix
X is the variables
b is a column matrix
The expression will therefore be written as;
\(A=\left[\begin{array}{ccc}1&1\\5&4\\\end{array}\right] \\\\|A| = 1(4)- 5(1)\\|A| = 4-5\\|A| = -1\\A^{-1} = -\left[\begin{array}{ccc}4&-1\\-5&1\\\end{array}\right] \\\\A^{-1} = \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \\\)
Hence the required product matrix that represent X is;
\(X= \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \left[\begin{array}{ccc}21\\20\\\end{array}\right] \\\)
distance of -6,8 and 1,7
Answer:
d ≈ 7.07 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)
with (x₁, y₁ ) = (- 6, 8 ) and (x₂, y₂ ) = (1, 7 )
d = \(\sqrt{((1-(-6))^2+(7-8)^2}\)
= \(\sqrt{(1+6)^2+(-1)^2}\)
= \(\sqrt{7^2+1}\)
= \(\sqrt{49+1}\)
= \(\sqrt{50}\)
≈ 7.07 units ( to 2 decimal places )
need help due really soon….
Answer:
the answer is A
Step-by-step explanation:
Answer: A
Step-by-step explanation:
You can plug in calc
\(\frac{\sqrt{9} }{3} =1\)
2\(\pi\) = 6.28
a. \(\pi /9 = .35\) this is not between
b. 3.14 this is
c. 3 this is
d. 1.09
can somebody good at math help me with these please I would really appreciate it
Answer:
down below:)
Step-by-step explanation:
sale price discount
1. multiplied by 0.82
2. multiplied by 0.75
3. multiplied by 0.9
1. 18.45
2. 30
3. 23.4
What is the distance between (5,-1) and (5,4)?
A) 1 unit
B) 3 units
C) 4 units
D) 5 units
Answer:
D
Step-by-step explanation:
The first number in each co-ordinate is the same so -1 plus 4 is 5 units
Answer:
5 units
Step-by-step explanation:
The x-coordinates of both coordinates are the same, so you only need to add the absolute values of -1 and 4, which is 5.
what is b when the slope is 7/6 and the points are (10, -9)
Answer:
y = 7/6x - 62/3
Step-by-step explanation:
The equation for slope:
y = mx + b
m is the slope and b is the y-intercept
y = 7/6x + b
-9 = 7/6(10) + b
-9 = 35/3 + b
-62/3 = b
what is the closet time to midnight?
A. 11:55AM
B. 12:06AM
C. 11:50AM
D. 12:03AM
Answer:
11:55 is closest time time to mid night
Option D is correct, 12:03AM is the closet time to midnight.
Midnight is typically defined as the beginning of a new day, precisely at 12:00 AM.
In a 12-hour clock format, AM (ante meridiem) is used to represent the time before noon (from midnight to 11:59 AM), while PM (post meridiem) is used to represent the time after noon (from 12:00 PM to 11:59 PM).
12.06am is 6 minutes past midnight.
11.50am is 10 minutes from midday, or, if you prefer, 11 hours and 55 minutes past midnight.
12.03am is 3 minutes past midnight.
Hence, the closet time to midnight is 12:03 AM.
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32 + -16 =rghhdfhjddff
Answer:
-16
Step-by-step explanation:
(b) Answer problem 82 on p.742. Create a real-world situation where you would need to find the component form of a force vector. Don't include your analysis in your post. Keep this work for later in the discussion and to respond to your classmates. (4pts) (a) Answer problem 92 on p.696. Create a real-world situation where you would need to overlay a polar coordinate system to show an original point and a second point. Don't include your analysis in your post. Keep this work for later in the discussion and to respond to your classmates. (4pts) 92. A gunner on a naval ship sights a target located 2.1mi north and 0.8mi cast of the ship's position. Choose a polar coordinate system with the gunner at the pole and the polar axis extending to the cast. Find the polar coordinates of the target. Find r to the nearest hundredth of a mile and θ in degree measure to the nearest hundredth of a degree.
1. Component form of a force vector: An engineer analyzes forces on a car's suspension system during turns. Breaking down the force vector into components ensures stability and safety.
2. Overlaying a polar coordinate system: Air traffic controllers use polar coordinates to guide aircraft during landings, accurately representing positions relative to a control tower for efficient airspace management and safety.
Let us discuss in a detailed way:
1. To find the component form of a force vector, let's consider the following real-world situation:
Imagine you are an engineer designing a suspension system for a new car model. One of the crucial design factors is ensuring the system can handle forces acting on the wheels during turns. To analyze these forces, you need to break down the resultant force acting on the wheels into its component form.
By breaking down the force vector into its components, you can determine the specific forces acting in the horizontal and vertical directions. This information is vital for calculating the stresses and strains on various suspension components, such as springs and shock absorbers, and ensuring they can handle the load.
Analyzing the component form of the force vector allows you to understand the individual forces acting on the suspension system. It helps you determine the necessary design parameters and select appropriate materials to ensure the system's stability, performance, and safety.
2. Now, let's consider a real-world situation where overlaying a polar coordinate system is useful:
Imagine you are an air traffic controller responsible for guiding aircraft during landing procedures. To efficiently direct the planes, you need to determine the positions of the aircraft relative to a specific reference point, such as the control tower.
In this situation, overlaying a polar coordinate system allows you to represent the positions of the aircraft accurately. By choosing the control tower as the pole and extending the polar axis outward, you can use polar coordinates to specify the distance and direction of each aircraft from the control tower.
This polar coordinate system enables you to quickly identify the location of each aircraft, calculate the distances between them, and provide precise instructions for landing sequences. By using polar coordinates, you can effectively manage the airspace, ensure the safety of incoming aircraft, and prevent any potential collisions.
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suppose that a manager is interested in estimating the average amount of money customers spend in her store. after sampling 36 transactions at random, she found that the average amount spent was $ 41.15 . she then computed a 90 % confidence interval to be between $ 38.01 and $ 44.29 . which statement gives a valid interpretation of the interval? there is a 90 % chance that a randomly selected customer will spend between $ 38.01 and $ 44.29 . the store manager is 90 % confident that the average amount spent by the 36 sampled customers is between $ 38.01 and $ 44.29 . the store manager is 90 % confident that the average amount spent by all customers is between $ 38.01 and $ 44.29 . there is a 90 % chance that the mean amount spent by all customers is between $ 38.01 and $ 44.29 .
The store manager is 99% confident that the average amount spent by all customers is between $32.89 and $42.81.
It's given to us that a director is interested in estimating the average quantum of plutocrat guests spend in her store, after testing 36 deals at arbitrary, she set up that the average quantum spent was$41.15. she also reckoned a 90 confidence interval to be between$38.01 and$44.29.
Confidence intervals Give farther information than point estimates. By establishing a 95- confidence interval using the sample's mean and standard divagation, and assuming a normal distribution as represented by the bell wind, the researchers arrive at an upper and lower bound that contains the true mean 95 of the time.
A confidence interval is a range of values, bounded over and below the statistic's mean, that likely would contain an unknown population parameter. Confidence position refers to the chance of probability, or certainty, that the confidence interval would contain the true population parameter when you draw a arbitrary sample multitudinous times.
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Simplify. 5/12x1/12=
Answer:
Step-by-step explanation:
720
Which describes the process that could be used as the first step in solving this equation? 6x = 4 + 5(x + 8) A) Combine like terms by adding 4 + 5. B) Use distributive property to multiply 5(x + 8). C) Use division property of equality to divide both sides of the equation by 6. D) Use subtraction property of equality to subtract 6x from both sides of the equation.
Answer: B) Use distributive property to multiply 5(x + 8).
Step-by-step explanation:
trust me its right
The first step in solving this equation 6x = 4 + 5(x + 8) is,
⇒ Use distributive property to multiply 5(x + 8).
Option B is true.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ 6x = 4 + 5(x + 8)
Now, We can solve the expression as;
⇒ 6x = 4 + 5(x + 8)
⇒ 6x = 4 + 5x + 40
⇒ 6x - 5x = 44
⇒ x = 44
Thus, The first step in solving this equation is,
⇒ Use distributive property to multiply 5(x + 8).
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How many different ways can 4 children be ordered in a line?.
Answer:
There are approximately 24 ways to order them to form a line
You run a local bakery. You know from experience that muffin sales can be represented by a normal distribution with mean 40 and standard deviation 6. Today you bake 46 muffins. What is the probability you run out of muffins today
The probability of running out of muffins today can be calculated by finding the area under the normal distribution curve beyond the quantity of muffins baked, which is 46 in this case.
In order to determine the probability of running out of muffins, we need to calculate the area under the normal distribution curve beyond the quantity of muffins baked, which is 46. The mean of the distribution is 40, indicating that, on average, 40 muffins are sold each day. The standard deviation is 6, representing the typical variability in daily muffin sales.
To calculate the probability, we need to find the area under the normal curve beyond 46. Since the normal distribution is symmetrical, we can calculate the area beyond 46 by finding the area to the left of 46 and subtracting it from 1.
Using the properties of the standard normal distribution, we can standardize the value of 46 by subtracting the mean (40) and dividing by the standard deviation (6). This standardization process gives us a z-score of 1.
Next, we can consult a standard normal distribution table or use statistical software to find the area to the left of 1, which corresponds to the probability of selling fewer than 46 muffins. Subtracting this value from 1 will give us the probability of running out of muffins today.
Please note that in order to generate an accurate probability, it's essential to assume that the sales of muffins follow a normal distribution and that there are no additional factors or circumstances that might affect the sales on this specific day.
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Select the final coefficient (factor) and radicand after simplifying
372 +39–162 - 372
A) -9
B) 5
C) 16
D)-8
E)-4
F)6
hope it helps
#carry on learning!In AGHI, the measure of ZI=90°, the measure of ZG=46°, and IG = 87 feet. Find the
length of GH to the nearest tenth of a foot.
Answer:
125.2
Step-by-step explanation: