The choice between using the standard deviation and standard error in the denominator of a z-score formula depends on the context of the problem and the type of data being analyzed.
To determine which z-score formula to use, consider the type of data and the context of the problem. If you have a sample with a known population standard deviation, use the first formula. If the data represents a random sample of a larger population, the standard error is typically used to account for the variability in estimating the population mean. On the other hand, if the data represents the entire population, the standard deviation is used as the denominator. It's important to understand the distinction between a sample and a population and to choose the appropriate formula accordingly.
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what is the variance and standard deviation for the number of patients arriving at this hospital with flu-like symptoms between 12:00pm and 12:20pm?
Without any data, we cannot determine the variance and standard deviation for the number of patients arriving at a hospital with flu-like symptoms between 12:00pm and 12:20pm.
To determine the variance and standard deviation for the number of patients arriving at a hospital with flu-like symptoms between 12:00pm and 12:20pm, we would need to know some data about the number of patients arriving during this time period. Without this data, we cannot calculate the variance and standard deviation.
If we were given a sample of data for the number of patients arriving during this time period, we could calculate the sample variance and sample standard deviation using the following formulas:
Sample variance = [(Σx²) - (Σx)² / n] / (n - 1)
Sample standard deviation = √(sample variance)
where Σx² is the sum of the squares of the deviations from the mean, Σx is the sum of the deviations from the mean, n is the sample size.
Alternatively, if we were given the mean number of patients arriving during this time period and the population variance, we could use the following formula to calculate the population standard deviation:
Population standard deviation = √(population variance)
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pls help me i dont understand
Answer:
y+3=-3/4(x+4)
Step-by-step explanation:
the formula is
y-y1=m(x-x1)
y1 is -4 and x1 is -3 and m is slope
when the x or y is a negitive it then is added
Maxine is pre-heating the oven to bake a pie. The temperature of the oven increases at a constant rate.
How long will it take the oven to reach a temperature of at least 375
degrees?
Responses
It will take approximately 12.96 minutes for the oven to reach a temperature of at least 375 degrees.
What is Approximation?
Approximation is the act of estimating or finding a value that is close to the true or exact value, but not necessarily identical to it. In other words, an approximation is a rough calculation or an educated guess that is used when the exact value is not known or is too difficult to calculate. Approximations are commonly used in mathematics, science, engineering, and many other fields where exact values are often difficult to obtain or not required. The level of accuracy of an approximation depends on the method used and the degree of precision needed for the particular situation.
Let's use the information given to find the rate of temperature increase per minute.
Between the first two data points, the temperature increased by 3 degrees in 1 minute. Between the next two data points, the temperature increased by (112.5 - 3) = 109.5 degrees in (5 - 1) = 4 minutes. So the rate of temperature increase is (109.5/4) = 27.375 degrees per minute.
To find out how long it will take the oven to reach 375 degrees, we can use the formula:
time = (final temperature - initial temperature) / rate of temperature increase
In this case, the initial temperature is 3 degrees and the final temperature is 375 degrees. Substituting these values and the rate of temperature increase we calculated earlier, we get:
time = (375 - 3) / 27.375 = 12.96 minutes (rounded to two decimal places)
So it will take approximately 12.96 minutes for the oven to reach a temperature of at least 375 degrees.
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After their soccer game, Mark and his friends eat at their favorite restaurant, the Dancing Meatball. When the bill comes, they divide the cost of a meatball pizza evenly among 5 people. Each person pays $3.25. Which equation can you use to find the cost c of the pizza?
Compare the two ratios by entering >, <, or = in the box. 1:8 3:4
[tex] \frac{1}{8} < \frac{3}{4} [/tex]
If A, B, C, and D, are the only possible outcomes of an experiment, find the probability of D using the table below.
Answer:
D. 8/11
Step-by-step explanation:
why ?
the sum of the probabilities of all possible outcomes of an experiment must always be 1.
because there always has to be an outcome - one of the many possibilities.
the reality has to be part of this list of possibilities, and so, their total sum is 1 : the sure event.
the probability of A is 1/11.
of B is 1/11.
of C is 1/11.
A + B + C + D = 1
1/11 + 1/11 + 1/11 + D = 1
3/11 + D = 1
D = 1 - 3/11 = 11/11 - 3/11 = 8/11
an actress has a probability of getting offered a job after a try-out of 0.15. she plans to keep trying out for new jobs until she gets offered. assume outcomes of try-outs are independent. hint: use a geometric random variable. find the probability she will need to attend more than 5 try-outs.
The probability that the actress will need to attend more than 5 try-outs is approximately 0.478.
Since the outcomes of each try-out are independent,
As per the given information,
Number of try-out is 0.15
probability means the possibilities.
We can model the number of try-outs needed to get an offer as a geometric random variable with the probability of success p = 0.15.
Let X be the number of tryouts needed to get an offer.
Then, X follows a geometric distribution with parameter p=0.15, and the probability of needing to attend more than 5 try-outs is:
[tex]P(X > 5) &= 1 - P(X \leq 5)[/tex]
=[tex]1 - \sum_{k=1}^{5} P(X=k)[/tex]
= 1 [tex]- \sum_{k=1}^{5} P(X=k)[/tex]
= [tex]1 - [(1-p)^0p + (1-p)^1p + (1-p)^2p + (1-p)^3p + (1-p)^4p][/tex]
=[tex]1 - [(1-p)^0p + (1-p)^1p + (1-p)^2p + (1-p)^3p + (1-p)^4p][/tex]
= 0.478
Hence the number of possibility required to attend more than 5 try-outs is approximately 0.478.
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Sue interests $800 in an investment that can be represented by the function m=800(1.08)^t where t is the number of years the money is invested for, and m is the value of the investment in dollars. Enter the average rate or change, rounded to the nearest dollar per year, from year 2 to year 4
[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ m(t)=800(1.08)^t \qquad \begin{cases} t_1=2\\ t_2=4 \end{cases}\implies \cfrac{m(4)-m(2)}{4 - 2} \\\\\\ \cfrac{800(1.08)^4~~ - ~~800(1.08)^2}{2} ~~ \approx ~~ \cfrac{1088.39-933.12}{2}~~ \approx ~~\text{\LARGE 78} ~~ \frac{\$}{year}[/tex]
PLEASE HELP ASAP DUE TODAY
Answer: 1) (0, -3) & 2) (0,0)
Step-by-step explanation:
Can somebody please look at the picture and help me pleaseeeeeeee
The equation 2 and 3 would not present linear functions.
What is linear function?
A linear function is one in which the maximum power of the variables is one.
A linear function is a function that has the form f(x) = mx + b, where m and b are constants. In other words, a linear function is a straight line when plotted on a graph.
Out of the given relationships, the following do not represent a linear function:
2) The ant population for a colony that begins with 5 ants and doubles in number every two weeks.
This relationship is not linear because the rate of change (the number of ants per unit time) is not constant. The number of ants increases exponentially, which results in a curve rather than a straight line when plotted on a graph.
3) A history student's grade on a test that begins at 100 but decreases by 4 points for each question answered incorrectly.
This relationship is not linear because the rate of change (the decrease in points per incorrect question) is not constant. The decrease in points results in a curve rather than a straight line when plotted on a graph.
The other two relationships do represent linear functions.
Therefore, The equation 2 and 3 would not present linear functions.
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Find the area of each part of the figure and the whole figure
1) The area of the first figure is 99 square units, 2) Total area = Area of rectangle + Area of triangle = 30 + 6 = 36 square units, 3) Total area = Area of rectangle + Area of triangle = 13.5 + 10.5 = 24 square units.
i) The first figure is a trapezium with height 9 units, bottom base 9 units and top base 13 units.
To find the area of the trapezium, we can use the formula:
Area of trapezium = h/2[a + b]
where h is the height, a and b are the lengths of the parallel sides.
Substituting the given values, we get:
Area = 9/2[13 + 9] = (9 x 22)/2 = 99 square units
Therefore, the area of the first figure is 99 square units.
ii) The second figure is composed of a rectangle with sides 6 and 5 units and a right-angled triangle with base 3 and height 4 units.
To find the area of the rectangle, we can use the formula:
Area of rectangle = length x breadth
Substituting the given values, we get:
Area of rectangle = 6 x 5 = 30 square units
To find the area of the right-angled triangle, we can use the formula:
Area of right-angled triangle = 1/2 x base x height
Substituting the given values, we get:
Area of right-angled triangle = 1/2 x 3 x 4 = 6 square units
Therefore, the total area of the second figure is:
Total area = Area of rectangle + Area of triangle
= 30 + 6 = 36 square units
iii) The third figure is made up of a rectangle with length 9 and breadth 1.5 units and a right-angled triangle with base 6 (9-3) and height 3.5 (5-1.5) units.
To find the area of the rectangle, we can use the formula:
Area of rectangle = length x breadth
Substituting the given values, we get:
Area of rectangle = 9 x 1.5 = 13.5 square units
To find the area of the right-angled triangle, we can use the formula:
Area of right-angled triangle = 1/2 x base x height
Substituting the given values, we get:
Area of right-angled triangle = 1/2 x 6 x 3.5 = 10.5 square units
Therefore, the total area of the third figure is:
Total area = Area of rectangle + Area of triangle
= 13.5 + 10.5 = 24 square units
Thus, the areas of all three figures have been determined.
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Complete question is in the image provided.
a population of 100 frogs increases at an annual rate of 22%. after how many years will the population of the frogs double?
The population of the frogs will be double after 4 years when the current number of frogs were 100 and the annual rate of increment is 22%.
In the given question,
the current population of frogs are: 100
Annual rate of increase in population of frogs = 22%
Population required = double the current population = 2 x 100
= 200
Using the compound interest formula for amount, we can calculate the number of years in which the population of the frogs will be double:
Amount = principal ((1 + r%)^n) ,
here we will consider the amount to be population required, principal will be the current population, r is the annual rate of increment, and n is the time in years.
200 = 100 ((1 + 0.22) ^ n)
⇒ 200/100 = (1.22)^n
⇒ 2 = (1.22) ^ n
We plug digits in place of n and check for the closest result as 2.
We observe that (1.22)^4 = 2.2153 ≈ 2
Hence, we can say that the population of the frogs will be double after 4 years.
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In a certain college, 40% of the senior class students are taking Physics, 30% are taking calculus and 10% are taking both. If 40 students are enrolled in the senior class, how many students are taking neither Physics nor calculus?
Answer:
16 students are taking Physics and 12 are taking calculus
Step-by-step explanation:
40×40%=16 students taking Physics
40×30%=12 students taking calculus
16+12=28
40-28=12 students are taking both
PLEASE HELP 20 POINTS
unit 9: transformations homework 1: translations
The translation of a function and coordinates are given below..
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
The following functions:
y = x²
y = 2x
The transformation is:
Translate two units to the left.
So,
y = (x - 2)²
y = 2(x - 2)
Translation 5 units up.
y = x² + 5
y = 2x + 5
The following coordinates:
Translate 2 units to the right.
(1, 4) = (1 + 2, 4) = (3, 4)
(5, 8) = (5 + 2, 8) = (7, 8)
Translation 5 units down.
(1, 4) = (1, 4 - 5) = (1, -1)
(5, 8) = (5, 8 - 5) = (5, 3)
Thus,
The translation of a function and coordinates are given above.
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A plumber earned AED 1,075 when he worked 3. 5 hours. He charged the customer an extra AED 200
for materials. What is his hourly rate?
A plumber worked 3. 5 hours for AED 1,075 in total. He added AED 200 for supplies to the customer's bill hourly rate of the plumber is AED 364.29.
How much is charged, paid, or earned for each hour worked?
Instead of paying for the things the advisers try to sell you, you pay a set or hourly charge for their time.
We must first deduct the price of the materials from the plumber's overall profits in order to get his hourly rate:
Income equals AED 1,075 plus AED 200, or AED 1,275.
After that, we may split his total income by the quantity of hours he put in:
Hourly fee is calculated as follows: AED 1,275 / 3.5 hours of work.
Hourly rate is 364.29 AED.
The plumber's hourly charge is therefore AED 364.29.
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How so i graph this ans what is thr solution.
The system of equations has a unique solution. The solution of the system of equations is (-3,4).
What is the system of equations?
Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
Given equations are
y = x + 7 ......(i)
y = -7/3x - 3 ......(ii)
Putting x = 0 in equations (i) and (ii):
y = 0 + 7
y = 7
y = -7/3 × 0 - 3
y = -3
Putting x = 3 in equations (i) and (ii):
y = 3 + 7
y =10
y = -7/3 × 3 - 3
y = -10
Putting x = -3 in equations (i) and (ii):
y = -3 + 7
y = 4
y = -7/3 × (-3) - 3
y = 4
The points in equation (i) are (0,7), (3,10), (-3,4)
The points in equation (ii) are (0,-4), (3,-10), (-3,4)
Plot the points and join the points:
The intersection of the equation is (-3,4).
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miguel spent 1/2 hour riding his bike, as shown on the clockface. He spent 1/3 hour cleaning his room. How much more time did miguel spend riding his bike than cleaning his room? Express the answer as a fraction of an hour. Write numbers in the boxes provided.
Answer: 1/6 of an hour
Step-by-step explanation: multiply the numerator and denominator by 3 of 1/2 and 1/3 to get 3/6 and 2/6. There is 1/6 more
Kofi bought 4 books at an average price of 2500 if the total cost of 3 books was 6500 find the cost of the fourth books
The cost of the fourth book is 3500. To find the cost of the fourth book, we used the formula Average Price = Total Cost / Number of Items and calculated the cost to be 3500.
Formula: Average Price = Total Cost / Number of Items.Calculation: Since Kofi bought 4 books at an average price of 2500, the total cost of the 4 books must be 4 x 2500 = 10000. Since the total cost of 3 books was 6500, the cost of the fourth book must be 10000 - 6500 = 3500.In conclusion, the cost of the fourth book is 3500. To find the cost of the fourth book, we used the formula Average Price = Total Cost / Number of Items and calculated the cost to be 3500.
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triangle abc and triangle def are smillar
which proportion must be true ?
The proportion EF/DF = BC/AC is true. Hence, option A is the accurate answer to this question.
We are given that the two triangles ΔABC and ΔDEF are similar.
According to the definition of a similar triangle, we know that the ratio of the corresponding sides is proportional and the corresponding angles are always congruent.
Since ΔABC and ΔDEF are similar, this implies that -
∠A corresponds to ∠D,
∠B corresponds to ∠E, and
∠C corresponds to ∠F.
Thus we can say -
EF/DF = BC/AC
AB/DF = DE/AC
AB/EF = DE/BC
Only option A satisfies the condition. Hence, the proportion EF/DF = BC/AC is true.
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The complete question is -
The triangle abc and triangle def are similar. Which proportion must be true?
Could someone help me please??
Answer:
0.32958 kilometers per minute
Step-by-step explanation:
Distance covered = 26.219 miles
Step 1: Convert this distance to kilometers using the conversion( 1mi = 1.609 km)
==> 26.219 miles = 26.219 miles x 1.609 km/mile = 42.186371 km
This distance was covered in 128 minutes
Step 2: To find the speed in km/min, divide 42.186371 by 128
= 42.186371/128
= 0.32958 kilometers per minute
------------------------------------------------------------------------------------
We could also solve this problem using the following alternative technique
Step 1 Determine speed in miles/minute = 26.219/128 = 0.2048 m per min
Step 2: Multiply by conversion factor 1.609:
0.2048 x 1.609 = 0.32958 kilometers per minute
There are many ways to save for retirement: putting money away into a treasure chest, purchasing gold nuggets, investing
in real estate, or financial assets. The method that is right for you depends on your income as well as your personal
preferences, such as risk tolerance. You can compare different methods and approximate your savings at retirement to
help you determine the option that best suits your personal needs and preferences. It is a good idea to approximate the
Income you will need at retirement before you start investing. This is where retirement planning becomes important to
consider. How much money do you think you would need to retire by age 67? Which investment options are the most
profitable when saving for retirement?
In this project, you will explore how to construct a retirement plan and consider the various investment options that are
financially beneficial as it pertains to retirement
OBJECTIVES
Construct a retirement plan given a yearly salary.
Compare investment options to determine the most financially beneficial option for a given situation.
VOCABULARY
Inflation rate
the rate of change in prices of a standard basket of consumer products over time
Most profitable investment option for retirement depends on your individual circumstances, such as your risk tolerance, time horizon, and investment goals. It's essential to consult with a financial advisor who can help you create a personalized retirement plan that meets your specific needs and goals.
Why are retirement planning crucial for generating money?Retirement planning is crucial to ensure that you have enough money to live comfortably during your golden years. The amount of money you will need in retirement depends on several factors, including your lifestyle, health, and expected lifespan.
However, a general rule of thumb is that you should aim to have saved 10-12 times your current annual income by the time you retire. Assuming a retirement age of 67, if you earn $50,000 per year, you would need to have saved between $500,000 and $600,000 by the time you retire. This amount may vary depending on your specific circumstances, such as your expected retirement lifestyle, expected lifespan, and anticipated expenses.
Which investment options are the most profitable when saving for retirement?When it comes to investment options for retirement, there are several options that can be financially beneficial. Some of the most profitable investment options for retirement include:
401(k) plans: A 401(k) plan is an employer-sponsored retirement plan that allows employees to contribute pre-tax dollars towards retirement savings. Traditional IRAs: A traditional IRA is an individual retirement account that allows you to contribute pre-tax dollars towards retirement savings. Roth IRAs: A Roth IRA is an individual retirement account that allows you to contribute after-tax dollars towards retirement savings. Mutual funds: Mutual funds are a type of investment that pools money from multiple investors to purchase a diversified portfolio of stocks, bonds, or other securities.Read more about retirement planning
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Find all six trigonometric functions of θ if the given point is on the terminal side of θ. Answer exactly. ( − 4 , − 1 )
The six trigonometric functions of the angle θ for the given point (-4, -1) are sin θ = -1/5, cos θ = -4/5, tan θ = 1/4, cot θ = -4, sec θ = -5/4, and csc θ = -5.
The six trigonometric functions of an angle θ are sine (sin θ), cosine (cos θ), tangent (tan θ), cotangent (cot θ), secant (sec θ), and cosecant (csc θ). These functions can be used to calculate the coordinates of a point on the terminal side of θ when the angle and one coordinate are known.
For example, if you know the angle θ and one coordinate (in this case, -4) of a point on the terminal side of θ, you can use the six trigonometric functions to calculate the remaining coordinate. In this case, the point is (-4, -1). The sine of θ is equal to the y-coordinate (-1) divided by the hypotenuse (distance from the origin). Therefore, sin θ = -1/5. The cosine of θ is equal to the x-coordinate (-4) divided by the hypotenuse. Therefore, cos θ = -4/5. The tangent of θ is equal to the y-coordinate (-1) divided by the x-coordinate (-4). Therefore, tanθ = -1/-4 = 1/4. The cotangent of θ is equal to the x-coordinate (-4) divided by the y-coordinate (-1). Therefore, cot θ = -4/-1 = -4. The secant of θ is equal to the hypotenuse (distance from the origin) divided by the x-coordinate (-4). Therefore, sec θ = 5/-4 = -5/4. The cosecant of θ is equal to the hypotenuse divided by the y-coordinate (-1). Therefore, csc θ = 5/-1 = -5.So, the six trigonometric functions of the angle θ for the given point (-4, -1) are sin θ = -1/5, cos θ = -4/5, tan θ = 1/4, cot θ = -4, sec θ = -5/4, and csc θ = -5.
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What are some similarities between sales tax and hotel tax? Select all that apply
Some of the similarities between sales tax and hotel tax include the following:
B) Both must be paid in advance when you make a hotel reservation.
C) Both are based on a percentage of the original cost.
What is taxation?
Taxation can be defined as the involuntary fees that are levied on individuals or business firms by the government of a particular country, so as to generate revenues that can be used to fund public projects, institutions and activities.
The types of tax.
In Economics, there are different types of tax that are levied on individuals or business firms by the government and these include the following:
Hotel tax
Sales tax
Property tax
Income tax
we can reasonably infer and logically deduce that both sales tax and hotel tax must be paid in advance when making a hotel reservation in the United States of America.
Hence, Some of the similarities between sales tax and hotel tax include the following:
B) Both must be paid in advance when you make a hotel reservation.
C) Both are based on a percentage of the original cost.
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The complete question is given below:
What are some similarities between sales tax and hotel tax? Select all that apply. Multiple select question. cross out A) Both are an additional amount one must pay. cross out B) Both must be paid in advance when you make a hotel reservation. cross out C) Both are based on a percentage of the original cost. cross out D) Both the sales tax and the hotel tax are equal when you stay in a hotel. cross out E) Both represent a guest fee that hotels charge their customers.
Keisha got a prepaid debit card with $30 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 16 cents per yard. If after that purchase there was $23.92 left on the card, how many yards of ribbon did Keisha buy?
Answer:
38 yards of ribbon
Step-by-step explanation:
23.92 +.16x = 30
30-23.92 = 6.08
.16x =6.08
6.08/.16 = x
x =38 yards
in a particular county of our state, it was revealed that 5% of all automobiles did not pass inspection. of the next ten automobiles entering the inspection station, a. what is the probability that none will pass inspection? b. what is the probability that all will pass inspection? c. what is the probability that exactly two will not pass inspection? d. what is the probability that more than three will not pass inspection? e. what is the probability that fewer than two will not pass inspection?
According to the question, it was revealed that 5% of all automobiles did not pass inspection. Of the next ten automobiles entering the inspection station
a. The probability that none will pass inspection is
P(x = 0) = [tex]^{10}C_{0}(0.05)^{0}(0.95)^{10}[/tex]
P(x = 0) = 0.5987
b. The probability that all will pass inspection is
P(x = 10) = [tex]^{10}C_{0}(0.05)^{10}(0.95)^{0}[/tex]
P(x = 10) = 0.5987
c. The probability that exactly two will not pass inspection is
P(x = 2) = [tex]^{10}C_{2}(0.05)^{2}(0.95)^{8}[/tex]
P(x = 2) = 0.0746
a. The probability that none will pass inspection is 0.001%.
b. The probability that all will pass inspection is 59.87%.
c. The probability that exactly two will not pass inspection is 0.27%.
d. The probability that more than three will not pass inspection is 0.0102.
e. The probability that fewer than two will not pass inspection is 6.48%.
In statistics, probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain.
In a particular county of our state, it was revealed that 5% of all automobiles did not pass inspection. This means that the probability of an automobile not passing inspection is 0.05, and the probability of an automobile passing inspection is 0.95.
To find the probability of none of the ten automobiles passing inspection, we need to multiply the probability of an automobile not passing inspection by itself ten times since the events are independent. Therefore, the probability of none of the ten automobiles passing inspection is 0.05¹⁰, which is approximately 0.00001 or 0.001%.
To find the probability of all ten automobiles passing inspection, we need to multiply the probability of an automobile passing inspection by itself ten times since the events are independent. Therefore, the probability of all ten automobiles passing inspection is 0.95¹⁰, which is approximately 0.5987 or 59.87%.
To find the probability of exactly two of the ten automobiles not passing inspection, we need to use the binomial distribution formula. The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose k) is the binomial coefficient. Therefore, the probability of exactly two of the ten automobiles not passing inspection is P(X=2) = (10 choose 2) * 0.05² * 0.95⁸, which is approximately 0.0027 or 0.27%.
The complement rule states that the probability of an event occurring is equal to one minus the probability of the event not occurring. Therefore, the probability of more than three of the ten automobiles not passing inspection is 1 - P(X<=3), where P(X<=3) is the probability of three or fewer automobiles not passing inspection.
To find P(X<=3), we can use the binomial distribution formula with k=0,1,2, and 3. Therefore,
P(X<=3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
=> (10 choose 0) * 0.05⁰ * 0.95¹⁰ + (10 choose 1) * 0.05¹ * 0.95⁹ + (10 choose 2) * 0.05² * 0.95⁸ + (10 choose 3) * 0.05³ * 0.95⁷, which is approximately 0.9898 or 98.98%.
Therefore, the probability of more than three of the ten automobiles not passing inspection is 1 - 0.9898, which is approximately 0.0102.
To find the probability of fewer than two of the ten automobiles not passing inspection, we need to use the complement rule again. The probability of fewer than two automobiles not passing inspection is the same as the probability of one or zero automobiles not passing inspection.
To find the probability of more than two automobiles not passing inspection, we can use the complement rule again:
=> P(X>2) = 1 - P(X<=2) = 1 - (P(X=0) + P(X=1) + P(X=2)) = 1 - [((10 choose 0) * 0.05⁰ * 0.95¹⁰ + (10 choose 1) * 0.05¹ * 0.95⁹ + (10 choose 2) * 0.05² * 0.95⁸]
which is approximately 0.0648 or 6.48%.
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a sample from a refuse deposit near the strait of magellan had 60% of the carbon-14 found in a contemporary living sample. how old was the sample?
The sample is approximately 50,000 years old, as the amount of Carbon-14 in it is lower than that of a contemporary sample.
1) Calculate the ratio of Carbon-14 in the sample compared to a contemporary sample.
Ratio = (60/100) = 0.6
2) Calculate the number of half-lives since the sample was alive.
Number of half-lives = ln(0.6) / ln(0.5) = 0.69897
3) Calculate the age of the sample.
Age of sample = (0.69897 x 5730) = 4020 years
60% of the Carbon-14 identified in a sample taken from a waste site close to the Strait of Magellan was present in the sample from the trash deposit. We must first determine the sample's carbon-14 ratio in relation to a more recent sample in order to determine the sample's age. This ratio is equivalent to the sample's 60% carbon-14 content, or 0.6, when divided by 100. The number of half-lives since the sample has been alive may then be determined by taking the natural log of the ratio and dividing it by the natural log of 0.5, which is 0.69897. By dividing the quantity of half-lives by the 5730-year half-life of carbon-14, we may finally determine the sample's age.
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Jamila approximates the areas of circles
using the equation A = 3r², and records areas
of circles with different radius lengths in a table.
Is the relation a linear function? Explain.
2 − 2n = 3n + 17
CAN SOMEONE HELP ME
[tex] \: [/tex]
[tex] \frak{ - 2n - 3n = 17 - 2}[/tex][tex] \: [/tex]
[tex] \frak{ - 5n = 15}[/tex][tex] \: [/tex]
[tex] \frak{n = \cancel\frac{15}{ - 5} }[/tex][tex] \: [/tex]
[tex] \underline { \boxed{ \frak{ \red{n = - 3}}}}[/tex][tex] \: [/tex]
hope it helps! :)
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Answer:
[tex] \sf \: n = - 3[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of n.
The equation is,
→ 2 - 2n = 3n + 17
Then the value of n will be,
→ 2 - 2n = 3n + 17
→ 2 - 17 = 3n + 2n
→ -15 = 5n
→ 5n = -15
→ n = -15 ÷ 5
→ [ n = -3 ]
Hence, the value of n is -3.
5c−3d+115, c, minus, 3, d, plus, 11 when c=7c=7c, equals, 7 and d=8d=8d, equals, 8.
The value of the expression 5c−3d+11 is 22 when c is 7 and d is 8.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 5c−3d+11
Five c minus three times of d plus eleven.
c and d are the variables in the expression
Given that value of c is seven and value of d is eight
c=7 and d=8
Now we have to find the value of the expression when c is 7 and d is 8
Plug in the value of c and d in expression.
5(7)-3(8)+11
Five times seven is 35 and three times of eight is 24, we get
35-24+11
22
Hence, the value of the expression 5c−3d+11 is 22 when c is 7 and d is 8.
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Complete question is given below,
5c−3d+115, find the value of expression when c=7 and d=8
Armer Brown harvested 245 oranges . He packed them into bags holding 20, 10 and 5 oranges if he used and equal number of each bag jow many bags did he use in all? Show working
If Armer Brown used and equal number of each bag then there will be 21 bags.
What is algebraic expression?
When we use numbers and words to solve a mathematical problem, we are using algebraic expressions.
Let's say that Armer Brown used x bags holding 20 oranges, y bags holding 10 oranges, and z bags holding 5 oranges. We know that he harvested 245 oranges, so we can write an equation:
20x + 10y + 5z = 245
We also know that he used an equal number of each bag, so we can write another equation:
x = y = z
We can use the second equation to substitute y and z with x:
20x + 10x + 5x = 245
Simplifying this equation, we get:
35x = 245
Dividing both sides by 35, we get:
x = 7
So he used 7 bags holding 20 oranges, 7 bags holding 10 oranges, and 7 bags holding 5 oranges.
In total, he used: 7 + 7 + 7 = 21 bags.
Therefore, There will be 21 bags.
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