Consider a disk D having center as origin and radius 'a', the average distance from point say ( r, θ) to the origin D to the origin is equals to the 2a/3.
The distance of a point to the origin is given by the function d(x, y) = √x²+ y². Denote the disk by D. To compute the average we need to evaluate the integral, for which we use polar coordinates, f(r, θ) = (1/area of region R)∬ f(r,θ)dA.
We have a disk D with center the origin (0,0) and radius 'a'. We have to determine the average distance from points in D to the origin. Since r is defined as the distance from the origin, the distance of any point (r,θ) from the origin is f(r,θ) = r
Integrating f over the region D, with limits r = 0 to a, and 0≤ θ≤2π , dA = r×dr×dθ
[tex]∬f(r,θ)dA = \int_{0}^{a} \int_{0}^{2π} r (rdr)dθ [/tex]
[tex]= \int_{0}^{2\pi} \int_{0}^{a} r^{2} drdθ = \int_{0}^{2\pi}[\frac{{r}^{3}}{3}]_{0}^{a}dθ[/tex]
[tex]= \int_{0}^{2π}[ \frac{a³}{3} ] dθ = \frac{{a}^{3}}{3} \int_{0}^{2π}dθ[/tex]
[tex]= \frac{a³}{3} [θ]_{0}^{2π} = 2\pi(\frac{a³}{3})[/tex]
Area of disk D with radius 'a' = πa²
So, the average distance from point ( r,θ) in D to the origin is = (1/area of region D)∬f(r,θ)dA
= (1/πa²)( 2πa³/3)
= 2a/3
Hence, required distance is 2a/3.
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A fair coin is tossed five times. Explain why the probability of getting exactly three heads is 0.3125.
The value of the probability is 0.3125 and this is proved by the calulations below
How to explain the value of the probabilityThe probability of getting exactly 3 heads in 5 coin tosses can be calculated by multiplying the probability of one specific combination of 3 heads and 2 tails by the number of possible combinations.
The probability of one specific combination, for example HHTTT, is (1/2)^5 = 1/32, because each toss has a 1/2 chance of being a head or a tail.
There are 5C3 = 10 possible combinations of 3 heads and 2 tails in 5 tosses.
For example: HHTTT, HTHTT, HTTHT, HTHHT, TTHHH, etc.
Therefore, the probability of getting exactly 3 heads is:
Probability = 10 * (1/32)
Probability = 10/32
Probability = 0.3125.
Hence, the value of the probability is 0.3125.
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Which expression is equivalent to
*picture shown*
√5 /x²y is equivalent expression to the given question . Then the correct option is C.
What is Expression?
A mathematical expression is a phrase with at least two variables or integers and one arithmetic operation.
According to the given information:a)Constant It has a set numerical value and is a constant.
For instance: 7,45,413,18,5.
b) Variables don't accept any predetermined values. Value is depend on Equation
Like a, p, and z
Constants, variables, or constants multiplied by variables are all acceptable terms (s). The "+" or "" symbol or both separates each term in an expression.
Instance: 5a+12b.
d) Operators: Addition (+), subtraction (-), multiplication (-), and division (-) are the four operations that are used to combine the terms in an expression.
Therfore, √5 /x²y is equivalent expression to the given question . Then the correct option is C.
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The Ford F-150 is the best selling truck in the United States.
The average gas tank for this vehicle is 23 gallons. On a long
highway trip, gas is used at a rate of about 3.2 gallons per hour.
The gallons of gas g in the vehicle's tank can be modeled by the
equation g(t)=23 -3.2t where t is the time (in hours).
a) Identify the domain and range of the function. Then graph
the function.
b) At the end of the trip there are 6.4 gallons left. How long
was the trip?
a) The domain and the range of the function are given as follows:
Domain: [0, 7.1875].Range: [0,23].The graph of the function is given by the image presented at the end of the answer.
b) The trip was 5.1875 hours long.
What are the domain and the range of a function?The function for this problem is defined as follows:
g(t) = 23 - 3.2t.
The domain is the set of input values that can be assumed by the function. The time cannot have negative measures, hence the lower bound of the domain is of zero, while the gas cannot be negative, hence the upper bound of the volume is given as follows:
23 - 3.2t = 0
3.2t = 23
t = 23/3.2
t = 7.1875 hours.
The range is given by the set of all output values assumed the function, which are the values of the gas, hence it is [0,23].
The graph is a linear function between points (0, 23) and (7.1875, 0).
At the end of the trip there were 6.4 gallons left, hence the length of the trip is given as follows:
23 - 3.2t = 6.4
t = (23 - 6.4)/3.2
t = 5.1875 hours.
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If 50% of a number is 170 and 80% of the same number is 272, find 30% of that number.
Answer:
30% of the number is 102.
Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch.
I need help D:please !!!!
If the top of Bria's bookcase has a length-to-width ratio of 3:1, the width of the top should be about 10 inches to provide an area of 300 square inches for her soap carving collection.
How to find the dimension of the top of the bookcaseThe top of the bookcase is a rectangle, the area of the top can be expressed as the product of its length and width:
Area of the top = length × width
Area of the top = 300 square inches
length × width = 300 square inches
width = 300 square inches / length
Assuming that the top of the bookcase is with a length-to-width ratio of
3 : 1
length = 3 × width
substituting the value gives
width = 300 / (3 × width)
Simplifying, we have:
width² = 100 square inches (the polynomial)
Taking the square root of both sides, we get:
width = √100 ≈ 10 inches
Then the length will be = 30 inches
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An initial deposit of $800 is put into an account that earns 5% interest, compounded annually. Each year, an additional deposit of $800 is added to the account.
Assuming no withdrawals or other deposits are made and that the interest rate is fixed, the balance of the account (rounded to the nearest dollar) after the seventh deposit is __________.
The balance of the account after the seventh deposit can be calculated using the formula below:
A = P (1 + r/n)ⁿ
where:
A = the balance of the account
P = The initial deposit of $800
r = the interest rate of 5%
n = the number of times the interest is compounded annually
n = 1
Therefore, the balance of the account after the seventh deposit is:
A = 800 (1 + 0.05/1)⁷
A = 800 (1.05)⁷
A = 800 (1.4176875)
A = 1128.54
Rounded to the nearest dollar, the balance of the account after the seventh deposit is $1128.
HELP ASAP WILL GIVE BRAINLYEST AND 100 POINTS
IF YOU DON"T TRY TO ANSWER THE QUESTION RIGHT I WILL REPORT YOU
Label the Standard Form, the Scientific Notation Form, the Coefficient, the Exponent, and the Base.
Answer:
45,000 is standard form.
4.5 is the coefficient.
4 of 10⁴ is the exponent.
7.6 × 10⁻⁴ is scientific notation.
10 of 10⁻⁴ is the base.
Step-by-step explanation:
Scientific notation is a way of writing very large or very small numbers in a compact and convenient form. It consists of two parts:
The coefficient: a number between 1 and 10.The exponent: an integer that indicates how many times 10 is multiplied by the coefficient.The base of scientific notation is always 10, which means that the number is written in terms of powers of 10.
For example, the number 4,000,000 can be written in scientific notation as 4 x 10⁶. In this case, the coefficient is 4, and the exponent is 6.
The standard form of a number is simply the usual way of writing it, without using scientific notation. For example, the standard form of 4 x 10⁶ is just 4,000,000.
Therefore, for the given problem:
45,000 is standard form.4.5 is the coefficient.4 of 10⁴ is the exponent.7.6 × 10⁻⁴ is scientific notation.10 of 10⁻⁴ is the base.Evaluate the expression.
|-2| – |-1|
Answer:
1
Step-by-step explanation:
We must solve the absolute values first
An absolute value is the numbers distance from zero
So a simplified version of your problem would be
2-1
So your answer is 1
The absolute value of a number is its distance from 0, so |-2| is 2 and |-1| is 1. Substituting these back in, the expression 2 - 1 equals 1.
Explanation:To evaluate the expression |-2| – |-1|, you first need to understand what the absolute value symbol does. The absolute value of a number is its distance from 0 on the number line, regardless of direction. So, both |-2| and |-1| become positive numbers, as distance is always positive.
Therefore, |-2| equals 2 and |-1| equals 1. If we substitute these values back into the original expression, 2 - 1, the result is 1.
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calculate 20 1/3 -7 1/2
Answer: 77/6 or 12 5/6
Step-by-step explanation:
To solve this subtraction problem, we need to first convert the mixed numbers to improper fractions.
20 1/3 can be written as:
20 + 1/3 = 60/3 + 1/3 = 61/3
7 1/2 can be written as:
7 + 1/2 = 14/2 + 1/2 = 15/2
So, the problem becomes:
61/3 - 15/2
To subtract two fractions, we need to have a common denominator. The smallest number that both 3 and 2 divide into is 6. So we will convert both fractions to have a denominator of 6.
61/3 = (61/3) * (2/2) = 122/6
15/2 = (15/2) * (3/3) = 45/6
Now we can subtract the two fractions:
122/6 - 45/6 = 77/6
So, the final answer is:
20 1/3 - 7 1/2 = 77/6 or 12 5/6 (as a mixed number)
1. The population of California was 10,586,223 in 1950 and 23,668,562 in 1980. Assume the population grows exponentially. a) Find an exponential function that models the population, P, in terms of t, the years after 1950. b) Use your model, to predict the population of California in 2020.
An exponential function can model California's population growth from 1950 to 1980. The predicted population in 2020 is around 43.3 million (43,301,300), assuming exponential growth.
To find an exponential function that models the population, we can use the formula:
P(t) = P0 * e^(rt)
where P0 is the initial population, r is the growth rate, and t is the time in years. We can use the information given to find P0, r, and then plug in t = 0 to find the exponential function.
P0 = 10,586,223 (initial population in 1950)
P(30) = 23,668,562 (population in 1980, 30 years later)
t = 30
P(0) = P0 * e^(0*r) = P0 (population in 1950)
So we have:
23,668,562 = 10,586,223 * e^(30r)
Dividing both sides by 10,586,223:
e^(30r) = 2.234
Taking the natural logarithm of both sides:
30r = ln(2.234)
r = ln(2.234)/30
Now we can use this value of r to find the exponential function:
P(t) = 10,586,223 * e^(t*ln(2.234)/30)
To predict the population in 2020, we can plug in t = 70 (since 2020 is 70 years after 1950) into the function we just found:
P(70) = 10,586,223 * e^(70*ln(2.234)/30) ≈ 43,301,300
Therefore, the predicted population of California in 2020 is approximately 43,301,300.
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X and Y are independent exponential RVs with parameters 1 and 2, respectively. What is the joint CDF of X and Y? OFxy (a,b) = -4e-26, a > 0,6> 0 OFxy (a, b) = 2e-e-2 , a > 0,6 > 0 O Fxy (a,b) = (1 - e-a) (1 - e-26), a > 0, 6 > 0
The joint CDF of X and Y, two independent exponential random variables with parameters 1 and 2, respectively, is Fxy(a,b) = (1 - e^(-a))(1 - e^(-2b)), where a > 0 and b > 0. The correct answer is C).
Since X and Y are independent, the joint CDF of X and Y is the product of their marginal CDFs:
FXY(a,b) = FX(a)FY(b)
where FX and FY are the CDFs of X and Y, respectively.
The CDF of an exponential distribution with parameter λ is given by:
FX(x) = 1 - e^(-λx)
Therefore, the marginal CDFs of X and Y are:
FX(a) = 1 - e^(-a), λ = 1
FY(b) = 1 - e^(-2b), λ = 2
Taking the product, we get:
FXY(a,b) = FX(a)FY(b) = (1 - e^(-a))(1 - e^(-2b))
Therefore, the answer is:
Fxy (a,b) = (1 - e^(-a))(1 - e^(-2b)), a > 0, b > 0.
The correct option is C).
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Do X4 and 15+ X have the same value when X is 5
Decrease R450 in the ratio 9:8
The value of R500 decrease to ratio 9:8 is x = 400.
What is cross multiplication?By using the cross multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa. Using the mathematical rule of three, we may determine the answer based on proportions. The best illustration is cross multiplication, where we may write in a percentage to determine the values of unknown variables.
Given that, decrease R450 in the ratio 9:8.
Let 9 = 450
Then 8 will have the value = x.
That is,
9 = 450
8 = x
Using cross multiplication we have:
9x = 450(8)
x = 50(8)
x = 400
Hence, the value of R500 decrease to ratio 9:8 is x = 400.
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The functions a ( t ) = 8.75 ⋅ ( 1 + 0.01 ) t and b ( t ) = 8.75 ⋅ e ( 0.01 t ) each model the population of a city, in thousands, t years after 2010. Describe how each model predicts that the population in the town will grow.
Using the functions, we can predict that the population in the town will grow 't' times as t is directly proportional to the function.
Define a function?A function in mathematics is a connection between two x and y values that come from different sets. These four types of correspondence are all possible. Yet not every correspondence serves a purpose.
The following are the results of a survey conducted by the National Institute of Standards and Technology (NIST) on the effectiveness of the standardised testing process. So, we state that a function can only have one input and one output. If we are given any x, the only y that can be coupled with that x is the one and only y. Two outputs cannot be connected to the same function.
Here in the given question,
The functions a(t) = 8.75 × (1+0.01) t and
b(t) = 8.75 × e × (0.01t) here are dependent on the variable t, where t is the time in years after 2010.
So, as t will increase after 2010, the value of a(t) and b(t) will increase with t.
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Using your favorite statistics software package, you generate a scatter plot which displays a linear form. You find a regression equation and the standard deviation for both variables. The standard deviation for x is 1.67, and the standard deviation for y is 3.76. The regression equation is reported as
y = 3.3 + 1.13x
What fraction of the variation in y can be explained by the variation in the values of x? (Enter your answer as a decimal between 0 and 1.)
A fraction of the variation in y that can be explained by the variation in the values of x is equal to 0.25189186354.
What is a regression equation?In Mathematics, the standard form of the equation of a regression line is represented or modeled by the following mathematical expression;
y = bx + c
Where:
b represent the gradient, slope, or rate of change.x and y represent the data points.c represents the y-intercept, vertical intercept, or initial value.How to determine the fraction of the variation?In Mathematics and Statistics, the value of slope can be calculated by using the following mathematical expression;
[tex]b=r(\frac{S_y}{S_x})[/tex]
where:
r is correlation coefficient.Sy represent the sample standard deviation of the y-values.Sx represent the sample standard deviation of the x-values.By rearranging, we have:
[tex]r=b(\frac{S_x}{S_y})[/tex]
r = 1.13(1.67/3.76)
r = 0.50188829787
By taking the square of both sides, we have:
r² = 0.25189186354.
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Fred and George share some money. If Fred gets 3/11 of the money,in what ratio did they share it?
Answer:
Step-by-step explanation:
If they had $11: Fred gets $3, George gets $8.
So the ratio is: 3:8
How do you apply perimeter, area, and circumference in real world applications (One Paragraph)
Perimeter, area, and circumference are important mathematical concepts that have numerous real-world applications.
How to apply?
For example, in construction and architecture, these concepts are used to measure and design buildings, rooms, and other structures. Knowledge of perimeter is important when determining how much material is needed for a fence or wall, while understanding area is crucial for calculating how much paint or flooring material is needed for a room.
Circumference is important for designing circular objects such as wheels, pipes, and round tables. In addition to construction and design, these concepts are also used in various fields such as engineering, science, and finance.
For instance, understanding area and circumference is important in calculating the surface area and volume of 3D objects in science, while in finance, perimeter and area can be used to calculate the cost of goods or real estate. Overall, the applications of perimeter, area, and circumference are numerous and essential in many aspects of our daily lives.
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PLS HELP FAST 20 POINTS + BRAINLIEST
Answer:
£22
Step-by-step explanation:
50% of 88=88/100 ×50=44
44÷2=25%=22
75% of £88 is deducted, so that 88-66=£22
Don't forget my Brainliestƒ and g, ƒ(2) = −3 and g( − 3) = 10. Find g(f(2)) .
Answer:
To find g(f(2)), we first need to find f(2) and then use that result as the input for g.
We are given that f(2) = -3, so we substitute that value into g(x) to get:
g(f(2)) = g(-3)
We are also given that g(-3) = 10, so we substitute that value in:
g(f(2)) = g(-3) = 10
Therefore, g(f(2)) = 10.
Solve the equation
(down)
5+50
2/3/4/5/6
The value of x in the equation that is given as 2/3x + 4/5x = 6 will be 4.
How to calculate the equationBased on the information given, one should note that an equation has to do with the statement in a question which depicts the variables given. In this case, one should note in an equation, one will need to consider two or more components are to be able to illustrate the scenario.
In this case, it is important to note that an equation simply depicts the mathematical statement which can be made up of two expressions which are simply connected by an equal sign.
The equation is explained thus:
2/3x + 4/5x = 6
10/15x + 12/15x = 6
22/15x = 6
1.467x = 6
x = 6 / 1.467
x = 4
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Solve the equation
2/3x + 4/5x = 6
Find the missing side in each triangle using any method.
AC has a length of ____ units. DE has a length of ____ units.
HELP ME ASAPPP!!! Ill mark you brasinlisest
Step-by-step explanation:
Theoretical probabilities can be calculated using the concept of probability. Each student has a 0.5 chance of selecting either List A or List B. Therefore, the probability of getting 27 heads and 33 tails can be calculated as:
P(27 heads and 33 tails) = (60 choose 27) * (0.5)^27 * (0.5)^33 where (60 choose 27) is the number of ways to select 27 students out of 60.
Using a calculator, we can compute the above probability as approximately 0.109. This means that if we were to repeat this experiment many times, we would expect to get 27 heads and 33 tails about 10.9% of the time.
Comparing this theoretical probability to the experimental results, we see that the observed proportion of heads (27/60 = 0.45) is lower than the expected proportion of heads (0.5) and the observed proportion of tails (33/60 = 0.55) is higher than the expected proportion of tails (0.5).
However, it is important to note that due to the random nature of the experiment, we would not expect the exact theoretical probabilities to match the experimental results exactly. In other words, there is always some amount of variation expected in the results. Nonetheless, the experimental results are consistent with the theoretical probabilities, and we can conclude that there is no significant deviation from what we would expect by chance.
The average cost of a lost laptop using information from various industries is $49,246. This average includes laptop replacement, data breach cost, lost productivity cost, and other legal and forensic costs. A separate study of 30 cases from the health care industry produced a mean of $67,873. Given these figures, is there sufficient evidence to support the claim that health care laptop replacement costs are higher in general? Use a .01 level of significance and a standard deviation of = $25,000. Perform your hypothesis testing using a one tail “P-value probability” concept.
Answer:
The claim that healthcare laptop replacement costs are higher than in other industries.
Uniform Distribution: Suppose that the random variable X follows a uniform distribution that takes on values from -2 to 3.
(3 points) Draw the graph of this uniform density function. I do not need a title for this one – but do want to see the scaling.
(3 points) What is P (-1.25 < X < 1.3)?
A company produces ceramic floor tiles that are supposed to have a surface area of 16 square inches. Due to variability in the manufacturing process, the actual surface area has a normal distribution with a mean of 16 square inches and a standard deviation of 0.008 square inches.
(5 points) What percent of the tiles have an area that is between 15.975 and 16.01 square inches?
(5 points) What is the probability that a tile will have an area that is more than 16.025 square inches?
i. Is this unusual? (1 point) How do you know?
(7 points) If 10,000 tiles are produced, how many can be expected to have a surface area less than 15.985 square inches?
(7 points) How many tiles must be produced to ensure that the manufacturer has 70,000 tiles that are between 15.98 and 16.02 square inches?
1. Graph is attached below. 2. 0.51 3. the percent of tiles with an area between 15.975 and 16.01 square inches is 82.78%. 4. 0.08% 5. 304 tiles 6. 0.4938x tiles.
Describe uniform density function?A uniform density function is a type of probability distribution that assigns equal probability to all values within a specified range. It is also known as a rectangular distribution because the graph of the probability density function appears as a rectangle with a constant height over the interval of possible values.
The probability density function of a uniform distribution is defined by two parameters: a minimum value (a) and a maximum value (b). The function assigns a probability of 1/(b-a) to each value within the range [a, b], and a probability of 0 to any value outside this range.
1. The graph of the uniform density function that takes on values from -2 to 3 is mentioned below
2. To find P(-1.25 < X < 1.3), we need to find the area under the uniform density function between -1.25 and 1.3. Since the density function is uniform, the area is simply the rectangle with base (1.3 - (-1.25)) = 2.55 and height 1/5 (since the range of values is 5). Therefore,
P(-1.25 < X < 1.3) = (2.55 * 1/5) = 0.51
3. To find the percent of tiles that have an area between 15.975 and 16.01 square inches, we need to standardize the values using the z-score formula and then find the area under the normal curve between those two values:
z1 = (15.975 - 16) / 0.008 = -3.125
z2 = (16.01 - 16) / 0.008 = 1.25
Using a standard normal table or calculator, we find the area between these two z-scores to be approximately 0.8278.
Therefore, the percent of tiles with an area between 15.975 and 16.01 square inches is 82.78%.
4. To find the probability that a tile will have an area that is more than 16.025 square inches, we again need to standardize the value using the z-score formula and then find the area under the normal curve to the right of that value:
z = (16.025 - 16) / 0.008 = 3.125
Using a standard normal table or calculator, we find the area to the right of this z-score to be approximately 0.0008.
Therefore, the probability that a tile will have an area that is more than 16.025 square inches is 0.08%.
i. Yes, this is unusual because the probability is very low, indicating that it is highly unlikely for a tile to have an area greater than 16.025 square inches.
5. To find the number of tiles that can be expected to have a surface area less than 15.985 square inches, we first need to standardize the value using the z-score formula:
z = (15.985 - 16) / 0.008 = -1.875
Using a standard normal table or calculator, we find the probability to the left of this z-score to be approximately 0.0304.
Therefore, out of 10,000 tiles, we can expect approximately 0.0304 * 10,000 = 304 tiles to have a surface area less than 15.985 square inches.
6. To find the number of tiles that must be produced to ensure that the manufacturer has 70,000 tiles that are between 15.98 and 16.02 square inches, we need to find the z-scores for the lower and upper bounds of this range:
z1 = (15.98 - 16) / 0.008 = -2.5
z2 = (16.02 - 16) / 0.008 = 2.5
Using a standard normal table or calculator, we find the probability between these two z-scores to be approximately 0.4938.
Therefore, out of x tiles, we can expect approximately 0.4938x tiles to have a surface area between 15.
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1. The graph of the uniform density function that takes on values from -2 to 3 is attached below.
2. P(-1.25 < X < 1.3) = (2.55 * 1/5) = 0.51
3. The percent of tiles with an area between 15.975 and 16.01 square inches is 82.78%.
4. The probability that a tile will have an area that is more than 16.025 square inches 0.08%.
5. Number of tiles that can be expected to have a surface area less than 15.985 square inches
6. To find the number of tiles that must be produced to ensure that the manufacturer has 70,000 tiles that are between 15.98 and 16.02 square inches, 0.4938x tiles.
Describe uniform density function?A uniform density function is a type of probability distribution that assigns equal probability to all values within a specified range. It is also known as a rectangular distribution because the graph of the probability density function appears as a rectangle with a constant height over the interval of possible values.
1. The graph of the uniform density function that takes on values from -2 to 3 is mentioned below:
2. To find P(-1.25 < X < 1.3), we need to find the area under the uniform density function between -1.25 and 1.3. Since the density function is uniform, the area is simply the rectangle with base (1.3 - (-1.25)) = 2.55 and height 1/5 (since the range of values is 5). Therefore,
P(-1.25 < X < 1.3) = (2.55 * 1/5) = 0.51
3. To find the percent of tiles that have an area between 15.975 and 16.01 square inches, we need to standardize the values using the z-score formula and then find the area under the normal curve between those two values:
z1 = (15.975 - 16) / 0.008 = -3.125
z2 = (16.01 - 16) / 0.008 = 1.25
Using a standard normal table or calculator, we find the area between these two z-scores to be approximately 0.8278.
Therefore, the percent of tiles with an area between 15.975 and 16.01 square inches is 82.78%.
4. To find the probability that a tile will have an area that is more than 16.025 square inches, we again need to standardize the value using the z-score formula and then find the area under the normal curve to the right of that value: z = (16.025 - 16) / 0.008 = 3.125
Using a standard normal table or calculator, we find the area to the right of this z-score to be approximately 0.0008.
Therefore, the probability that a tile will have an area that is more than 16.025 square inches is 0.08%. Yes, this is unusual because the probability is very low, indicating that it is highly unlikely for a tile to have an area greater than 16.025 square inches.
5. To find the number of tiles that can be expected to have a surface area less than 15.985 square inches, we first need to standardize the value using the z-score formula:
z = (15.985 - 16) / 0.008 = -1.875
Using a standard normal table or calculator, we find the probability to the left of this z-score to be approximately 0.0304.
Therefore, out of 10,000 tiles, we can expect approximately 0.0304 * 10,000 = 304 tiles to have a surface area less than 15.985 square inches.
6. To find the number of tiles that must be produced to ensure that the manufacturer has 70,000 tiles that are between 15.98 and 16.02 square inches, we need to find the z-scores for the lower and upper bounds of this range:
z1 = (15.98 - 16) / 0.008 = -2.5
z2 = (16.02 - 16) / 0.008 = 2.5
Using a standard normal table or calculator, we find the probability between these two z-scores to be approximately 0.4938.
Therefore, out of x tiles, we can expect approximately 0.4938x tiles to have a surface area between 15.
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The number of people who took I-45 to Houston in one day was 31,426. The number of people who took the bus was one and a half times the number of people who took the highway. How many more people took the bus?
Answer:
Bus vs Highway: Houston
Let's start by finding out how many people took the bus.
If the number of people who took the highway is x, then the number of people who took the bus is 1.5x (since it's one and a half times the number of people who took the highway).
We know that the total number of people who traveled to Houston is 31,426, so we can write an equation:
x + 1.5x = 31,426
Simplifying the equation:
2.5x = 31,426
Dividing both sides by 2.5:
x = 12,570.4
Since we can't have a fraction of a person, we can round this down to 12,570.
Now we can find the number of people who took the bus:
1.5x = 1.5(12,570) = 18,855
To find out how many more people took the bus, we can subtract the number of people who took the highway from the number of people who took the bus:
18,855 - 12,570 = 6,285
Therefore, 6,285 more people took the bus.
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can you find the following limits?
1=?
2=?
3=?
The first limit, [tex]\lim_{x\to \→-2^- } -3(x+2)/x²+4x+4[/tex] , evaluates to negative infinity, while the second limit, [tex]\lim_{ x\to \-2^+}-3(x+2)/x²+4x+4[/tex] , evaluates to positive infinity.
What is function?Function in maths is a relation between two sets of values. It is a type of mathematical equation in which each input value has a unique output value. In a function, each input value must correspond to only one output value. This means that for any input value, the output must be the same.
This indicates that the function has a vertical asymptote at x=-2.
In order to understand why this is the case, we can first rewrite the function as follows:
f(x) = -3(x+2)/(x+2)(x+2)
The denominator of the function is (x+2)(x+2), which has a double root at x=-2. This means that the denominator is equal to zero when x=-2. As a result, the function f(x) will have a vertical asymptote at x=-2, since the denominator will be equal to zero and the function will approach negative or positive infinity. This is why the two limits mentioned above both evaluate to either negative or positive infinity.
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The limit of the given functions are:
[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4 = positive infinity
[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4 = negative infinity
[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4 = Undefined
What is function?Function is a relation between two sets of values. In a function, each input value must correspond to only one output value. This means that for any input value, the output must be the same.
[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4
= -3(-2+2)/(-2)²+4(-2)+4
= -3/0 + 8 + 4
= +∞ (infinity)
[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4
= -3(-2+2)/(-2+2)²+4(-2+2)+4
= -3/4 + 0 + 4
= -∞
[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4
= -3(-2+2)/(-2+2)²+4(-2+2)+4
= -3/0 + 0 + 4
= Undefined
Therefore, the limit of the functions given are:
[tex]\lim_{x \to \--2^-}[/tex]-3(x+2)/ x²+4x+4 = +∞
[tex]\lim_{x \to \--2^+}[/tex] -3(x+2)/ x²+4x+4 = -∞
[tex]\lim_{x \to \--2[/tex] -3(x+2)/ x²+4x+4 = Undefined
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Finding limits of piecewise functions!
Check the picture below.
btw, we could have used the f(4) for both subfunctions just the same.
i need help with the question please
The equation 32 - 3x + 13 = 0 can be rewritten as 3x = 19. Therefore, x = 19/3. Because x is a real number, the solution to the equation is x = 19/3.
What is real number ?Real numbers are any number that can be expressed as a decimal number or a fraction. This includes the natural numbers (1,2,3,4, etc.), the negative numbers (-1,-2,-3, etc.), the rational numbers (fractions, such as 1/2, 3/4, etc.), and the irrational numbers (numbers that cannot be expressed as a fraction, such as pi, square root of 2, etc.). Real numbers can be manipulated with basic arithmetic operations such as addition, subtraction, multiplication, and division. Real numbers have an infinite number of decimal places, making them useful for measuring physical quantities such as time, distance, and temperature.
Expressing this answer in the form a + bi, where a and b are real numbers, gives the solution a = 19/3 and b = 0. Therefore, the answer is 19/3 + 0i = 19/3.
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Given that x is a positive integer less than 100, how many solutions does the congruence x+13=55 (mod 34) have?
The congruence x + 13 ≡ 55 (mod 34) simplifies to x ≡ 12 (mod 34). There are three solutions for x less than 100 that satisfy this congruence.
The given congruence is x + 13 ≡ 55 (mod 34). Simplifying this, we get x ≡ 12 (mod 34).
We need to find the number of solutions for x that are less than 100 and satisfy this congruence.
The general solution for the congruence x ≡ 12 (mod 34) is x = 12 + 34k, where k is an integer.
The solutions that are less than 100 are obtained when k = 0, 1, or 2.
Thus, the number of solutions is 3.
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she earned $480 in one week. If she worked 40 hours, how much did she earn per hour?
Answer:
12 dollars
Step-by-step explanation:
480 / 40 = 12
12 dollars