(a) The probability that a randomly chosen vehicle is traveling at a legal speed is 3.01%.
(b) If police are instructed to ticket motorists driving 120 km/h or more, the percentage of motorists targeted would be approximately 15.87%.
What is the likelihood of a vehicle traveling within the legal speed limit and what % of motorist at 120 km/h or more?(a) The mean speed of vehicles on the highway is 115 km/h, with a standard deviation of 9 km/h. We are given that the speed limit is 100 km/h. To calculate the probability of a vehicle traveling at a legal speed, we need to determine the proportion of vehicles that have a speed of 100 km/h or less.
Using the properties of a normal distribution, we can convert the given values into a standardized form using z-scores. The z-score formula is (x - μ) / σ, where x is the observed value, μ is the mean, and σ is the standard deviation.
For a vehicle to be traveling at a legal speed, its z-score should be less than or equal to (100 - 115) / 9 = -1.67. We can consult a standard normal distribution table or use a statistical calculator to find the corresponding cumulative probability.
From the standard normal distribution table or calculator, we find that the cumulative probability for a z-score of -1.67 is approximately 0.0301, or 3.01% (rounded to two decimal places).
(b) To calculate this, we first need to find the z-score for the speed of 120 km/h using the formula: z = (x - μ) / σ, where x is the value we want to calculate the probability for, μ is the mean, and σ is the standard deviation. In this case, we want to find the probability for x ≥ 120 km/h.
Using the formula, we calculate the z-score as follows: z = (120 - 115) / 9 = 0.56.
To find the probability, we need to calculate the area to the right of the z-score of 0.56 in a standard normal distribution table or using statistical software. This area corresponds to the probability that a randomly chosen vehicle is traveling at a speed of 120 km/h or higher. This probability is approximately 0.2939 or 29.39%.
Since the question asks for the percentage of motorists targeted, we subtract this probability from 100% to find the percentage of motorists not adhering to the speed limit. 100% - 29.39% = 70.61%.
Therefore, the percentage of motorists targeted for ticketing by the police would be approximately 15.87%.
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Craig opened a savings account and deposited $600.00 as principal. The account earns 2%
interest, compounded annually. What is the balance after 6 years?
Use the formula A =
1 +
(starting amount), r is the interest rate expressed as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
Answer:
the answer is 675.70 or 4,504.33
Step-by-step explanation:
the right answer is that
Help help please please
Answer:
18
Step-by-step explanation:
This is actually pretty easy. Keep this in mind.
There are 34 total students. 16 of them like bananas and the rest like apples. All you really need to do is count up from 16 to 34 to find the answer.
The simple equation for this is: 34-16
Thus, the answer is 18.
Solve the problem. Round your answer to one decimal place. Human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. Find the temperature that separates the top 7% from the bottom 93%. Round to the nearest hundredth of a degree. Select one: О 99.12°F O 97.28ºF 98.78°F O 98.40°F
The temperature that separates the top 7% from the bottom 93% is 98.78°F.
To solve this problem, we need to use the concept of the normal distribution. In a normal distribution, data is symmetrically distributed around the mean, with the majority of values falling within a certain range determined by the standard deviation. In this case, we are given a normal distribution of human body temperatures with a mean of 98.20°F and a standard deviation of 0.62°F.
To find the temperature that separates the top 7% from the bottom 93%, we need to locate the value on the distribution that corresponds to the 93rd percentile. The 93rd percentile represents the point below which 93% of the data falls. Conversely, the top 7% of the data lies above this point.
Using statistical tables or a calculator, we can determine the z-score corresponding to the 93rd percentile. The z-score measures the number of standard deviations a given value is away from the mean. Once we find the z-score, we can use it to calculate the temperature value.
In this case, the z-score corresponding to the 93rd percentile is approximately 1.475. We can then use the z-score formula: z = (x - mean) / standard deviation. Rearranging the formula to solve for x (the temperature value), we get x = (z * standard deviation) + mean. Plugging in the values, we find x = (1.475 * 0.62) + 98.20 = 98.78°F.
Therefore, the temperature that separates the top 7% from the bottom 93% is approximately 98.78°F. This means that 93% of human body temperatures are below 98.78°F, while the top 7% are above this value.
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A vendor purchase 8 dozen teacups to sell. She packed them into boxes of 4 and each and sold each box for$60. Calculate the amount of the money she earned from the sale of all the teapcups?
Answer: $1440
Step-by-step explanation:
So if we have 8 dozens that is 8*12=96 teacups
boxes of 4 means 96/4= 24 boxes in total with 4 teacups in each
Since she is being paid 60$ for each of the 24 boxes she makes exactly $1440
Please don't go around not answering others questions. We are all trying to pay it forward and help each other :)
In circle a the length of the radius is 24 units what is the length of the arc BC?
Answer:
20pi
Step-by-step explanation:
150/360 = 5/12
5/12 * 2*24*pi = 20pi
==============
Please give brainliest, I really want to rank up, thank you!
8 x 10 inch rectangle.Total area is 168 in^2. Calculate the width of the rectangle. Which of the following quadratic equations would be used when solving this?
A - 2x^2 + 18x = 88
B - 4x^2 + 36x = 88
C - 4x^2 + 18x = 88
D - 2x^2 + 36 = 88
A construction company produces two products (doors and windows) that require two plants (A and B). Management wants to determine how many units of each product should be produced to maximize profit. For each unit of Product 1 (i.E. Door), 2 workers are required in Plant A and 4 workers are required in Plant B. For each unit of Product 2 (i.E. Window), 3 workers are required in Plant A and 4 workers are required in plant B. The company has 40 workers in Plant A and 60 workers in Plant B. Each unit of Product 1 gives a profit of $100. Each unit of Product 2, up to 10 units, gives a profit of $80. Any excess over 10 units of Product 2 brings no profit; so, such excess has to be ruled out.
Answer:
Z max = 1500
x₁ = 15
x₂ = 0
Step-by-step explanation:
From problem statement:
Plant A Plant B Profit $/each
Product 1 (Doors ) x₁ 2 4 100
Product 2 (windows ) x₂ 3 4 80
Product 2 (windows ) x₂ above 10 is scrap
Objective function to maximize
z = 100*x₁ + 80*x₂
Subject to:
Plant A capacity
2*x₁ + 3*x₂ ≤ 40
Plant B capacity
4*x₁ + 4*x₂ ≤ 60
Windows condition:
0*x₁ + x₂ ≤ 10
Model:
Max z = 100*x₁ + 80*x₂
Subject to:
2*x₁ + 3*x₂ ≤ 40
4*x₁ + 4*x₂ ≤ 60
x₂ ≤ 10
x₁ , x₂ ≥ 0 and integers
Afther 6 iterations using Simplex Solver AtomZmath
Z max = 1500
x₁ = 15
x₂ = 0
2. Determine the value of k such that when the given function f(x) = x4 + kx³ - 3x - 5 a) is divided by (x-3) the remainder is -10 b) Determine the remainder when f(x) is divided by x +3.
To determine the value of k in the function f(x) = [tex]x^4[/tex] + k[tex]x^3[/tex] - 3x - 5, we can consider the remainders when f(x) is divided by (x-3) and (x+3).
a) When f(x) is divided by (x-3), the remainder is -10. To find the remainder, we can use the Remainder Theorem, which states that if a polynomial f(x) is divided by (x - a), the remainder is equal to f(a). Plugging in x = 3 into f(x), we get:
f(3) = [tex]3^4[/tex] + k([tex]3^3[/tex]) - 3(3) - 5
= 81 + 27k - 9 - 5
= 27k + 67
Since the remainder is -10, we can set up the equation:
27k + 67 = -10
Solving this equation, we find:
27k = -77
k = -77/27
b) To determine the remainder when f(x) is divided by (x+3), we can follow a similar process. Plugging in x = -3 into f(x), we get:
f(-3) =[tex](-3)^4[/tex] + k[tex](-3)^3[/tex] - 3(-3) - 5
= 81 - 27k + 9 - 5
= -27k + 85
The remainder is given by f(-3), so we can set up the equation:
-27k + 85 = remainder
Hence, the remainder when f(x) is divided by (x+3) is -27k + 85.
In summary, the value of k such that the remainder when f(x) is divided by (x-3) is -10 is k = -77/27. Additionally, the remainder when f(x) is divided by (x+3) is -27k + 85.
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Help will mark brainliest show steps pls
Answer:
at first , you need the sum of both equations . It will be like :
2y= 0 + 2
Y=1
_____
now that you know the value of Y , place it in the one of the equation that you like , forexample i place it in the second equation and find out that the value of x is ( -3/2)
1= 2X+5
-4=2X
X= -2
Hope it helps , good luck ^.^
A local store owner is interested in finding the mean age of her customers. She randomly surveys 82 customers and records their age. Identify the population, sample, variable, type of variable, parameter, and statistic.
Population: The set of all possible customers in the store.
Sample: The 82 customers randomly surveyed.
Variable: Age of the customers Type of variable: Quantitative parameter
Parameter: The mean age of all the customers in the store.
Statistic: The sample mean age of the 82 customers surveyed.
Analysis: The mean age of all customers is a parameter since the store owner is interested in knowing the mean age of all the customers that come to her store.
The store owner will be interested in collecting data on all the customers who come to her store. Since this will be difficult, she will sample some customers instead. The store owner randomly surveyed 82 customers, which is the sample size. The variable of interest is the age of the customers. This is a quantitative variable since it is measured using numerical values. The sample mean age of the 82 customers surveyed is a statistic.
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what is one of the distinctions between a population parameter and a sample statistic?
One distinction between a population parameter and a sample statistic is that the former describes a characteristic of an entire population, while the latter is characteristic of a subset of the population, called a sample.
In statistics, a population parameter is a numerical value that describes a characteristic of an entire population. It is a fixed value and is usually unknown or difficult to determine precisely. Population parameters are typically denoted by Greek letters (e.g., [tex]\mu[/tex] for the population means, σ for the population standard deviation).
On the other hand, a sample statistic is a numerical value that represents a characteristic of a sample, which is a subset of the population. Sample statistics are used to estimate population parameters. Since a sample is a smaller portion of the entire population, sample statistics can vary from one sample to another. Sample statistics are typically denoted by Latin letters (e.g., [tex]\bar{x}[/tex] for the sample mean, s for the sample standard deviation).
The distinction lies in the scope of the information they provide. Population parameters aim to describe the overall characteristics of a population, while sample statistics provide information about a specific subset of the population, which can be used to infer or estimate the population parameters.
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Melanie's dance class was 100 minutes long. If 1/8 of the time was spent
stretching, how many minutes were spent stretching?
Answer:
12.5 minutes
Step-by-step explanation:
Multiply 1/8 by 100. Convert 25/2 to a decimal by dividing 25 by 2. The answer is 12.5 minutes.
Help me pls, tysm! I will give brainly if you give me the right answer, tysm! I need help on number 6 btw
Answer: 96 feet
Step-by-step explanation:
The inverse of the function f(x) = { x + 10 is shown.
h(x) = 2x-0
What is the missing value?
O 1
O 5
O 10
O20
Answer:
D) 20
Step-by-step explanation:
the missing value is 20
the last option
The equation h(x) = 2x - 0 = x - 10 is satisfied by the value x = -10; the omitted integer is 10.
What is a function?A function is a mathematical formula that illustrates the relationship between the dependent and independent variables. The independent variable's value and the dependent variable's value both change in the function.
Determine x in terms of f(x) in order to determine the inverse of the function f(x) = x + 10:
f(x) = x + 10
f(x) - 10 = x
x = f(x) - 10
Since h(x) is the opposite of f(x), replace x with h(x):
h(x) = f⁻¹(x) = x - 10
Since h(x) is the opposite of f(x), replace x with h(x):
To identify the missing value, compare the expression for h(x) to the supplied function, h(x) = 2x-0. We can see that the appropriate expression for h(x) is:
h(x) = 2x - 0 = x - 10
Find the value of x that allows this equation to be solved:
2x - 0 = x - 10
Simplifying and solving for x,
x = -10
Therefore, the missing value is O 10, since x = -10 satisfies the equation h(x) = 2x - 0 = x - 10
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Can someone solve this equation?
2.6x + ? = 2x
Answer:
−1.666667
Step-by-step explanation:
Explain how to solve 4640 divided by 10. use complete sentences!!
Answer:
464
Step-by-step explanation:
the number has one, zero at the end. same for the ten.
4640 10just take zero for zero and you end up with 464
Match the word to its description. The difference between the lowest and highest value 1. mode The middle value 2. mean 3. median The most frequent value PP 4. range The average
Answer:
range
Step-by-step explanation:
The difference between the lowest and the highest number is called the range. The middle value is the median (it's in the "mid"dle, median) The mean is the average. And the mode is the most frequent value.
Write an expression to represent the following:
Two less than the product of five and a number x.?
Step-by-step explanation:
[tex]5x - 2[/tex]
...........
Answer:
2-5x
Step-by-step explanation:
let the number be x, 5 *x = 5x.
2 less means ,2 minus,
>> 2-5x.
An increase in the real interest rate will
A. most likely lower consumer's purchases of durable goods.
B. most likely lower the cost of borrowing.
C. cause consumers to spend more and save less.
D. most likely lower the reward to savings.
An increase in the real interest rate will most likely lower the reward to savings. The correct answer is D.
When the real interest rate increases, it means that the return on savings and investments is higher in real terms, adjusted for inflation. As a result, individuals are incentivized to save more as they can earn a higher return on their savings.
When the reward to savings is lower, it becomes less attractive for individuals to save. Higher interest rates can discourage borrowing and encourage saving, which reduces consumer spending on durable goods and other discretionary purchases.
Option A is incorrect because an increase in the real interest rate would likely lead to a decrease in consumer's purchases of durable goods, as higher interest rates increase the cost of borrowing, making it more expensive to finance large purchases.
Option B is incorrect because an increase in the real interest rate generally makes borrowing more expensive, as it increases the cost of borrowing for individuals and businesses.
Option C is incorrect because an increase in the real interest rate usually encourages individuals to save more and spend less, as the potential return on savings is higher.
The correct answer is D.
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The following data are the amounts of total fat (in grams) in all sweet treats available at your local donut shop
24 16 23 22 17 15 24 24 24 16
Are these population or sample data? _____Population
What is the range for this data set? ______9
What is the variance for this data set? Round your answer to three decimal places, if necessary. ______15.455
What is the standard deviation for this data set7 Round your answer to three decimal places, if necessary. _____3.931
The data set represent a population.
The range for this data set is 9.
The variance for this data set is 14.05.
The standard deviation for this data set is 3.748.
What is a population?In Statistics, a population simply refers to a set of similar items or events that comprises every member of a group i.e the total number of elements.
Based on the given data set, we would calculate the range by using the following formula:
Range = Highest number - Lowest number
Range = 24 - 15
Range = 9.
Next, we would determine the mean as follows;
Mean = ∑fx/n
Mean = (24 + 16 +23+22+17+15+24+24+24+16)/10
Mean = 205/10 = 20.5
Now, we can calculate the standard deviation and variance by using this formula:
Standard deviation, δ = √(1/n × ∑(xi - μ)²)
Standard deviation, δ = √[1/10 × (24 - 20.5)² + (16 - 20.5)² + (23 - 20.5)² + (22 - 20.5)² + (17 - 20.5)² + (15 - 20.5)² + (24 - 20.5)² + (24 - 20.5)² + (24 - 20.5)² + (16 - 20.5)²]
Standard deviation, δ = √140.5/10
Standard deviation, δ = 3.748.
For the variance, we have:
Variance = δ²
Variance = 3.75²
Variance = 14.05
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Need someones help on this!
Answer:
x^3
Step-by-step explanation:
quotient property of exponents
I think the answer is c. x^3
Let G=⟨a⟩ be a cyclic group of order n. Show that, for every divisor d of n there exists a subgroup of G whose order is d
This time I have no approach. I haven't found any relation between the divisors of n
and the order of the subgroups of G. How would approach this?
For every divisor d of the order n of a cyclic group G=⟨a⟩, there exists a subgroup of G whose order is d.
To approach this, we can consider the properties of cyclic groups. A cyclic group G generated by a single element "a" has elements that are powers of "a" in the form of [tex]a^k[/tex], where k takes values from 0 to n-1. The order of an element "a" in G is the smallest positive integer k such that [tex]a^k[/tex] equals the identity element.
Now, let's focus on the divisors of n. Each divisor d divides n evenly, meaning n/d is an integer. We can consider the element "[tex]a^(^n^/^d^)[/tex]" in G. The order of "[tex]a^(^n^/^d^)[/tex]" is d because [tex](a^(^n^/^d^))^d = a^n = e[/tex], where e is the identity element of G.
Hence, the subgroup generated by "[tex]a^(^n^/^d^)[/tex]" has an order of d, since it consists of elements of the form [tex](a^(^n^/^d^))^k[/tex], where k takes values from 0 to d-1. Therefore, for every divisor d of n, there exists a subgroup of G whose order is d.
This demonstrates the relationship between the divisors of n and the order of the subgroups in the cyclic group G.
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is
0.07 and the probability that the flight will be delayed is 0.19. The probability that it
will not rain and the flight will leave on time is 0.75. What is the probability that it is
raining and the flight is delayed? Round your answer to the nearest thousandth.
Step-by-step explanation:
P(rain and flight delayed) = P(rain) x P(flight delayed) = 0.07 x 0.19
= 0.013 (nearest thousandth)
Answer: 0.01
Step-by-step explanation:
the person above did it wrong, this answer is for sure correct.
What is the theoretical probability of rolling anything other than a two on a fair six sided die?
Answer:
5/6 probability
Step-by-step explanation:
Find the perimeter of a rectangle if the length of one side is 9x + 6y and the width is 13x + 2y.
Answer:
perimeter of rectangle = 2 (length + breadth)
= 2(9x + 6y + 13x + 2y)
= 2(22x +8y)
= 44x + 16y
Step-by-step explanation:
9x+6y
9-9x+6-9y both side subtract 9
x+(-3)y
x-3y the answer
13x+2y
13-13x+2-13y
x+(-11)y
x-11y .
follow me
A random experiment involves drawing a sample of 12 data values from a normally distributed population. The random variable is the minimum of the data set. 44 47 49 52 56 61 63 64 67 69 75 76 Give the random variable. (Appropriate rounding rules still apply.) r.v=__
The random variable is given by :
r.v. = 37.51.
Given that a random experiment involves drawing a sample of 12 data values from a normally distributed population. The random variable is the minimum of the data set.44 47 49 52 56 61 63 64 67 69 75 76, we need to find the random variable i.e., minimum of the given data set.
Converting to normal distribution, we get to know that :
µ = (44+47+49+52+56+61+63+64+67+69+75+76) / 12
µ = 60σ
µ = sqrt((44-60)² + (47-60)² + (49-60)² + (52-60)² + (56-60)² + (61-60)² + (63-60)² + (64-60)² + (67-60)² + (69-60)² + (75-60)² + (76-60)²) / 12
µ= sqrt(2018 / 12)σ
µ = 5.29
Hence, the random variable is given by : r.v = 44-5.29(1.15) ≈ 37.51
Therefore, the random variable is 37.51.
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A plan can travel 420 miles in 80 minutes. Find a unit that describes this situation
Answer:
5.25 miles per minute
Step-by-step explanation:
420/80 = 5.25 so it is 5.25 miles per minute as it is 80 minutes
13. What is the positive solution to this equation? 4x2 + 18 x= 162
Answer:8.5 is x but there is an extra 1
Step-by-step explanation:18x8.5=153+8=162 with an extra one is 162
. A rectangle has its base on the x-axis and its upper two vertices on the semi-circle y = V1 - 32. What is the largest area the rectangle can have? 1 6 1
The largest area the rectangle can have is -1024 square units.
To solve the given problem, follow the steps given below:
Step 1: Sketch the given graph on a coordinate plane as shown below:
Step 2: Let's assume that the base of the rectangle is x units and its height is y units.
Step 3: As the base of the rectangle is on x-axis, we have the length of the base as the x-coordinate of the upper two vertices of the rectangle.
Now, the x-coordinate of the upper two vertices of the rectangle lie on the given semicircle whose equation is y = V1 - 32.
So, we can write:
y = V1 - 32x^2 = (y + 32)^2 ⇒ x^2 = y^2 + 64y + 1024
Step 4: Now, we can write the area of the rectangle as: A = base × height= x × y
Using the value of x from equation (1), we get: A = (y^2 + 64y + 1024)1/2 y
So, we have an equation for area in terms of y. Let's differentiate it with respect to y to find the maximum value of A. dA/dy = (y^2 + 64y + 1024)-1/2 (2y + 64)
By equating dA/dy = 0, we get: 2y + 64 = 0y = -32
Substituting the value of y in equation (2), we get:x^2 = 1024 ⇒ x = ±32
The given rectangle lies in the first quadrant.
Hence, the length of the base of the rectangle is x = 32 units.
So, we have the dimensions of the rectangle as length = 32 units and breadth = height = y = -32 units.
However, as the length and breadth of the rectangle cannot be negative, we cannot consider the negative value of y.
Therefore, the maximum area of the rectangle is: A = base × height= 32 × (-32)= -1024 sq. units
Hence, the largest area the rectangle can have is -1024 square units.
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Please answer correctly! I will mark you as Brainleist!
Answer:
1047.2 cubic inches
Step-by-step explanation:
V = 4(pi)(r³/3)
V = 4(pi)(125/3)
V = 523.6 cubic inches (1 ball)
V = 2(523.6) = 1047.2 cubic inches (total)