Based on the calculated z-score of 17.07, and a corresponding p-value, the process would be considered out of control at the 0.05 significance level.
To determine whether the process is in control or out of control, we can use a hypothesis test with a significance level of 0.05. The null hypothesis (H0) is that the process is in control, and the alternative hypothesis (Ha) is that the process is out of control.
We can calculate the z-score as follows:
z = (x - μ) / (σ / sqrt(n))
where x is the observed value (118), μ is the mean (104), σ is the standard deviation (8.2), and n is the sample size (1).
Plugging in the values, we get:
z = (118 - 104) / (8.2 / sqrt(1)) = 17.07
The corresponding p-value for this z-score is virtually zero. Since the p-value is less than 0.05, we reject the null hypothesis and conclude that the process is out of control.
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I need a step by step process for to find out what, "x" is in this problem. y = -3x +5
when y = 5 in the equation y = -3x + 5, the value of variable x is 0.
Define equationAn equation is a statement of equality between two mathematical expressions that contain variables and mathematical operations. The goal of solving an equation is to determine the value(s) of the variable(s) that make the equation true.
the steps to find out what x is in the equation y = -3x + 5 for y = 5:
Substitute y = 5 in the equation: y = -3x + 5Replace y with 5: 5 = -3x + 5Subtract 5 from both sides of the equation: 5 - 5 = -3x + 5 - 5Simplify: 0 = -3xDivide both sides by -3: 0/-3 = -3x/-3Simplify: 0 = xTherefore, x = 0 when y = 5 in the equation y = -3x + 5.To know more about Divide, visit:
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The complete question is:
I need a step by step process for to find out what, "x" is in this problem. y = -3x +5 for y=5
could someone explain this to me so I can do it? It's dividing decimals by whole numbers.
First thing you need to do is raise the decimal. Once you've raised the decimal then you should continue through the problem as if it were a standard long division question.
Start with the first number which is 6.
6 divided by 3 is 2. That means you can subtract 6 from the first number.
Then, you bring down 3 and do the same thing.
3 divided by 3 is 1. Subtract 3 from 3 and then bring down the next number.
Finally, 3 divided by 9 is three.
By following this process, you should get 2.13 as your final answer.
Look at the image below for more reference.
Offering 30 points.
Describe the transformation of f(x) = represented by g (x). Then, choose one
of the functions below and graph them.
a. g(x) = -1/x
b. g(x)= 3/x+2
c. g(x) = 1/-x+5
Therefore there is graph below and whole process of graph
g(x) = -1/x (x).
g(x) = 1/(-x + 5).
Describe equation?
A mathematical equation is a formula that uses the equals symbol (=) to denote the equality of two expressions.
A formula would be 3x - 5 = 16,
for instance. We may determine the value of the variable x by solving this equation: x = 73.
We can apply a number of transformations on f to convert f(x) to g(x) (x).
A . Starting with the graph of f(x) = 1/x for function a, we can perform a vertical reflection to obtain the graph of g(x) = -1/x (x).
B . Starting with the graph of f(x) = 1/x, we can apply a horizontal shift to the function b's graph, g(x) = 3/(x + 2).
We can apply a number of transformations on f to convert f(x) to g(x) (x).
For instance, we can use the following transformations to change f(x) = x2 into g(x) = (x - 3)2 + 2:
- Replace x with to move the graph 3 units to the right (x - 3)
- Apply a horizontal shift to the left of two units and a vertical stretch of three factors to f f(x) = 1/x.
Starting with the graph of f(x) = 1/x, we may apply a horizontal shift to the right by 5 units and a vertical reflection to obtain the graph of function c, g(x) = 1/(-x + 5).
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Select the expression that makes the equation true.
13.5 x (1.2 + 4) = ___.
40 ÷ (5 x 2) x 17.55
36 ÷ (4.8 − 2.6) x 3
22 x (3.6 − 1.2) + 4
18 ÷ (3 x 3) x 35.2
The expression that makes the equation true is A)40 ÷ (5 x 2) x 17.55.
What is expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Here first solve given expression then,
=> 13.5 x (1.2 + 4) = 13.5×1.2+13.5×4 = 70.2
Now solving option expressions then,
A) 40 ÷ (5 x 2) x 17.55 = 40÷10×17.55 = 4×17.55 = 70.2
B) 36 ÷ (4.8 − 2.6) x 3 = 36÷2.4×3 = 45
C) 22 x (3.6 − 1.2) + 4 = 22×(2.4)+4 = 56.8
D) 18 ÷ (3 x 3) x 35.2 = 18÷ 9×35.2 = 2×35.2 = 70.4
Hence the expression that makes the equation true is A)40 ÷ (5 x 2) x 17.55.
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Opposite vertices of a rectangle in the standard (x, y) coordinate plane have coordinates (6, 38) and (18, 8) respectively. What are the coordinates of the center of this rectangle?
(12, 23) are the coordinates of the center of the rectangle with coordinates (6, 38) and (18, 8).
To find the coordinates of the center of the rectangle in the standard (x, y) coordinate plane, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are:
((x₁ + x₂) / 2, (y₁ + y₂) / 2)
In this case, the opposite vertices of the rectangle have coordinates (6, 38) and (18, 8). We can use these coordinates to find the midpoint of the rectangle as follows:
The x-coordinate of the midpoint is (6 + 18) / 2 = 12.
The y-coordinate of the midpoint is (38 + 8) / 2 = 23.
Therefore, the coordinates of the center of the rectangle are (12, 23)
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according to benford's law, 5 will be the first digit of a random number set: a. more often than 1. b. more often than 3. c. about the same as 6. d. less often than 4.
According to Benford's law, 5 will be the first digit of a random number set is d. less often than 4.
According to Benford's law, which is an empirical law about the frequency distribution of leading digits in many real-life collections of numerical data, the digit 5 is actually the second least frequent leading digit after 1 and is less common than 4 as a first digit. In actuality,
Benford's rule states that the likelihood of a number having four as its first digit is nearly thirty percent, whereas the likelihood of a number having 5 as its first digit is approximately 25%. This is due to the fact that numbers with smaller starting digits are more common than those with bigger leading digits in many naturally occurring datasets.
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how can we simplify algebric expressions?
There are various techniques to simplify algebraic expressions, including:
1. Combining like terms: In an algebraic expression, like terms are terms that have the same variable raised to the same power. To simplify the expression, we can combine these like terms. For example, in the expression 3x + 2y + 5x - 4y, we can combine the x terms and the y terms to get 8x - 2y.
2. Distributing: When a number or variable is outside a set of parentheses and is being multiplied by a sum or difference inside the parentheses, the number or variable can be distributed to each term inside the parentheses. For example, in the expression 3(x + 2), the 3 can be distributed to both x and 2, resulting in the simplified expression 3x + 6.
3. Simplifying exponents: When an expression contains exponents, rules of exponentiation can be used to simplify the expression. For example, in the expression x^2 * x^3, the exponents can be added to give x^(2+3) = x^5.
4. Factoring: When an expression contains common factors, those factors can be factored out. For example, in the expression 2x^2 + 4x, both terms have a factor of 2 and a factor of x, so these factors can be factored out to give 2x(x + 2).
What are the values of x and y?
We can therefore find the other angle of right angle triangle by
Pythagoras , then x = 142 - y and y = 142 - x
What is the Pythagoras ?A fundamental theorem in geometry that deals with the sides of a right triangle is known as the Pythagorean theorem. In it, it is said:
a+ b² = c²
where the lengths of the right triangle's legs are a, b, and c, and the length of the hypotenuse (the side across from the right angle) is c
Nevertheless, if we know the other two, we can use the fact that the total of the angles in a triangle is always 180 degrees to determine one of the angles. We are aware that angle C in this situation is 38 degrees.
We thus have:
x + y + 38 = 180
Calculating x and y results in:
x = 142 - y
y = 142 - x
We can therefore find the other angle if we know the value of one. To determine the real figures, we still want further details.
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When flying out of a place your expected to fly to 1500 feet before leaving the airspace in a pilots plane their distance measuring equipment says they have traveled 2 miles before they reached this altitude what angle was the pilot flying as they took off from the runway?
Answer: To solve this problem, we can use trigonometry and the relationship between angle, distance, and altitude in a right triangle.
Let's denote the angle the pilot was flying at takeoff as θ. We can then use the tangent function to find θ, since:
tan(θ) = opposite/adjacent
In this case, the opposite side is the altitude the pilot reached (1500 feet), and the adjacent side is the distance the pilot traveled before reaching that altitude (2 miles = 10560 feet). So we can plug in these values and solve for θ:
tan(θ) = 1500/10560
θ = tan⁻¹(1500/10560)
θ ≈ 7.67 degrees
So the pilot was flying at an angle of approximately 7.67 degrees at takeoff from the runway.
Step-by-step explanation:
You’ve been making student loan payments consistently for the past year, and your credit score has increased. Now, your APR is lower, 18%. If you owe $777, what is the amount of interest you will owe?
To find the amount of interest you will owe, we need to calculate the interest using the formula:
Interest = Principal * Rate * Time
Where:
- Principal = $777 (the amount you owe)
- Rate = 18% per year (expressed as a decimal, or 0.18)
- Time = 1 year (since you have been making payments for a year)
Plugging in these values, we get:
Interest = $777 * 0.18 * 1
Interest = $139.86
So, the amount of interest you will owe is approximately $139.86.
suppose that the bac of students who drink five beers varies from student to student according to a normal distribution with mean 0.07 and standard deviation of 0.01. show your work. a. the middle 99.7% of students who drink five beers have bac between what two numbers? b. what is the range for the 16% of lowest bacs? c. what percent of students have a bac above 0.09?
a. The middle 99.7% of students between 0.04 and 0.10.
b. The range for the 16% of lowest BACs is 0.06 or below.
c. 2.28% of students have a BAC above 0.09.
a. How to find range?To find the range, use the properties of the normal distribution and the given mean (0.07) and standard deviation (0.01).
99.7% of the data lies within 3 standard deviations from the mean in a normal distribution.Calculate the lower bound: mean - 3 * standard deviation = 0.07 - 3 * 0.01 = 0.07 - 0.03 = 0.04Calculate the upper bound: mean + 3 * standard deviation = 0.07 + 3 * 0.01 = 0.07 + 0.03 = 0.10The middle 99.7% of students between 0.04 and 0.10.
To find the range use the z-score corresponding to the 16th percentile (z ≈ -1).
Calculate the BAC value corresponding to the z-score: BAC = mean + z * standard deviation = 0.07 + (-1) * 0.01 = 0.07 - 0.01 = 0.06The range for the 16% of lowest BACs is 0.06 or below.
c. How to find percentage?To find the percentage, find the z-score for 0.09 first.
Calculate the z-score: z = (BAC - mean) / standard deviation = (0.09 - 0.07) / 0.01 = 2Look up the area under the curve to the left of the z-score in a z-table (which is about 0.9772).Calculate the percentage of students above 0.09: 100% - 97.72% = 2.28%Approximately 2.28% of students have a BAC above 0.09.
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Help. By the way Ochako is a W no not from the anime. But on Brainly.
The range interval of the given data is {73,80]
and range for term 2 is [74,80]
You may have studied the techniques for determining a representative value for the provided data in statistics, or the measure of central tendency. Remember that there are three ways to measure central tendency: mean, median, and mode.
Spatial Statistics
Due to the fact that the measurements of central tendency do not provide sufficient detail about a given set of data. Another factor that must be investigated in statistics is variability. We require a single number to characterize variability, much like measures of central tendency. This one number has demonstrated a certain amount of dispersion. You will discover more about range, one of the dispersion measures, in this post.
According to the given problem
the range of any date is equal to the interval of lower and upper limits,
So
Form term 1
Our data start from 73, 74,,75,76,78,79,80
So according to the given data 73 is the lower limit and 80 is the upper limit
The range interval of the given data is {73,80]
and range for 2
in term 2 the lower limit is 74 so our range is [74,80]
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Distributive property
3(r+2)+5(r+t-2)?
1. 3r+6+5r+t-10
2. 3r+2+5r+5t-10
3. 3r+6+5r+5t-10
4. 3r+6+5r+t-2
Answer:
Step-by-step explanation:
Using the distributive property, we can simplify the expression as follows:
3(r+2) + 5(r+t-2)
= 3r + 3(2) + 5r + 5t - 5(2)
= 3r + 6 + 5r + 5t - 10
= 8r + 5t - 4
Therefore, the simplified expression is:
8r + 5t - 4
30 points to whoever solves
Answer:
(a) = 0.92
(b) = 0.7613
Step-by-step explanation:
Here are some information to help us answer these problems:
Given That:
P(A) = 0.69
P(B) = 0.23
Then,
Problem (a): P(A ∪ B) when, A ∩ B = ∅:
P(A ∪ B) = 0.69 + 0.23 - 0 = 0.92
Problem (b): P(A ∪ B) when, A ∩ B ≠ ∅:
P(A ∪ B) = 0.69 + 0.23 - (0.69 × 0.23) = 0.7613
I hope you find this easy to understand....
Have any questions? Write in the comments.
give me brainliest if you found this answer useful
Please help me I don't know this ?
1. the equation of the quadratic function is: y = (8/65)(x + 5)(x - 13)
2. The axis of symmetry is the line x = 0 (the y-axis).
What is quadratic function?
The quadratic equation with roots -5 and 13 can be written as:
y = a(x + 5)(x - 13)
where a is a constant that depends on the coefficient of the quadratic term.
To find the value of a, we can use the fact that the coefficient of the quadratic term is the sum of the roots, multiplied by -1:
a = -(sum of roots) / (product of roots)
a = -(-5 + 13) / (-5 * 13)
a = 8 / 65
Therefore, the equation of the quadratic function is:
y = (8/65)(x + 5)(x - 13)
What is symmetry?
2. The axis of symmetry is the line x = 0 (the y-axis).
To find the axis of symmetry, we can use the formula:
x = -(b / 2a)
where a and b are the coefficients of the quadratic function. In this case, a = 8/65 and b = 0, since there is no linear term.
Substituting these values, we get:
x = -(0 / (2 * (8/65)))
x = -0
Therefore, the axis of symmetry is the line x = 0 (the y-axis).
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Write the slope-intercept form of the equation of the line through the given point with the given slope.
Point: (-1,4) , Slope=3/4
Answer:
[tex]y-y_1=m(x-x_1)\\\y-4=\frac{3}{4} (x-(-1))\\\\y-4=\frac{3}{4} x+\frac{3}{4} \\y=\frac{3}{4} x+\frac{19}{4}[/tex]Jared is building a tree house. He pays $75 for materials and pays his friend $12 per hour to help him. If Jared spends a total of $129 on building his tree house, for how many hours did his friend work on it?
Equation for line of best fit
correlation positive/negative
r=
Therefore , the solution of the given problem of equation comes out to be y = -0.9x + 5.5 is the equation for the line of best fit, and r = -0.83 is the correlation value.
What is correlation?
Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It's a common tool for describing simple relationships without making a statement about cause and effect
What is an equation?
Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this case, leveling generates b + 7 rather than another algorithm that could divide 12 into two parts, evaluate the information provided by y + 7, and generate y + 7.
Here,
The least squares technique can be used to determine the equation of the line, presuming that the line of best fit is a linear regression line.
The findings that we get using a calculator or statistical software are as follows:
=> y = -0.9x + 5.5 is the equation of the line of best fit.
=> R = -0.83 is the correlation coefficient (r).
We can infer that there is a negative link between the two variables because the correlation coefficient (r) is negative.
This implies that the value of y tends to decline as the value of x rises.
As a result, y = -0.9x + 5.5 is the equation for the line of best fit, and r = -0.83 is the correlation value.
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hi i need help checking i already know the answer!!
x/7 - 4 = 4
Answer:
x=56
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Answer:
x = 56
Step-by-step explanation:
Given that-
x/7 - 4 = 4
x/7 - 4 + 4 = 4 + 4 >> Add 4 to both sides
x/7 = 8
7x/7 = 8 × 7 >> Multiply both sides by 7
x = 56
Check Answer-
Substitute x in the equation the check.
56/7 - 4 = 4 >> 56/7 = 8
8 - 4 = 4 >> 8 - 4 = 4
4 = 4 >> Correct
RevyBreeze
help with question pls due tmrw
Answer:
vertex= 4,-25
y coordinate of vertex = (x+4)2-25
x coordinate of vertex= x2-8x-9
Step-by-step explanation:
two math classes took the same quiz. The scores of 20 randomly selected students from each class are listed below. Based on the medians of the scores for each class, what inferece would you make about the quiz scores of all the students in class a compared to all the students in class b?
We can't make any inferece of any definitive conclusions about the entire populations of students in the two classes.
What is population in Mathematics?
In mathematics, population refers to a group of individuals, objects, or events that share a common characteristic or feature. This group is the target of a study, and the goal is to make generalizations about the entire population based on a sample from that population.
For example, in a study on the average height of adult males in a particular country, the population would be all adult males in that country. However, it is not practical to measure the height of every single adult male in the country, so a sample is taken instead. The sample is a subset of the population and should be chosen in such a way that it is representative of the entire population.
To make an inference about the quiz scores of all the students in class A compared to all the students in class B, we can compare the medians of the two classes. The median is the middle score when the scores are arranged in order.
The scores of the 20 students in class A are
85, 86, 88, 89, 90, 90, 91, 92, 93, 94, 94, 94, 95, 96, 97, 98, 99, 99, 100, 100
And the scores of the 20 students in class B are
75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94
To find the median score for each class, we need to find the middle score. For class A, the middle score is 94 (since there are an even number of scores, we take the average of the middle two). For class B, the middle score is also 87.
Comparing the medians of the two classes, we see that the median score for class A (94) is higher than the median score for class B (87). This suggests that the quiz scores for class A may be higher overall than the quiz scores for class B. However, it's important to note that this is only based on a sample of 20 students from each class, so we can't make any definitive conclusions about the entire populations of students in the two classes.
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Correct question is "Two math classes took the same quiz. The scores of 20 randomly selected students from each class are listed below. Based on the medians of the scores for each class, what inference would you make about the quiz scores of all the students in class a compared to all the students in class b?
Here the scores of the 20 students in class A are 85, 86, 88, 89, 90, 90, 91, 92, 93, 94, 94, 94, 95, 96, 97, 98, 99, 99, 100, 100
And the scores of the 20 students in class B are
75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94"
in this expression, assume that y=0.
4y^2•2y^4
which is an equivalent expression?
A.)6y^6
B.)6^8
C.)8y^6
D.)8y^8
Answer:
If y=0, then 4y^2•2y^4 = 4(0)^2•2(0)^4 = 0.
Therefore, any of the options that involve y, such as A) 6y^6 or C) 8y^6, would also be equal to 0.
The only option that is still a valid answer is B) 6^8, which is simply 6 to the 8th power, or 1679616.
Hope This Helps!
find the 5th term of this sequence: 3/2,4/3,5/4,6/5
a container is shaped like a triangular prism. each base of the container is an equilateral triangle with the dimensions shown. image the container has a height of 15 centimeters. what is the lateral surface area of the container in square centimeters?
The lateral surface area of the triangular prism container is 270 cm².
We will begin with the calculation of perimeter of equilateral triangle.
Perimeter = 3 × sides
Perimeter = 3 × 6
Perimeter = 18 cm
Now calculating the lateral surface = perimeter of base × height
Keep the values in formula
Lateral surface of equilateral triangle prism = 18 × 15
Performing multiplication again
Lateral surface area = 270 cm²
Thus, the lateral surface area of the container is 270 cm².
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The picture is added of equilateral triangle with dimensions.
a group of rats ran faster after receiving a steroid drug supplement compared to a group of rats that received no steroid drug supplement. which type of statistical test should be used to report these results?
An independent samples t-test would be appropriate to analyze the difference in running speed between rats that received a steroid drug supplement and those that did not.
The appropriate statistical test to analyze the difference in running speed between two groups of rats (one receiving a steroid drug supplement and one not receiving it) would be a t-test. Specifically, an independent samples t-test would be suitable for this type of comparison, assuming that the data meets the assumptions for parametric testing.
This test would compare the means of the two groups and assess the probability that the observed difference is due to chance alone. A significant result would indicate that the difference in running speed is unlikely to be due to chance and is instead likely to be a true effect of the steroid drug supplement
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how many different committees with 4 members can be formed from a group of 10 people? (order is not important.)
The number of committees with 4 members can be formed from a group of 10 people are 210 different committees
To find the number of different committees with 4 members that can be formed from a group of 10 people we can use the combination formula which is,
nCr = n!/r!(n-r)!
where:
nCr = number of combinations
n = total number of objects in the set
r = number of choosing objects from the set
from the given data:
n = 10
r = 4
From the above formula, we can write the equation as:
= 10C4
=C(10,4)
= 10! / (4! * 6!)
= (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)
= 210
Therefore, 210 different committees with 4 members can be formed from a group of 10 people.
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Given: ​quadrilateral abcd​ is inscribed in circle o. prove: m∠a m∠c=180° a quadrilateral is inscribed in a circle o. the vertices of the quadrilateral lie on the edge of the circle and are labeled as a, b, c, and d. drag an expression or phrase to each box to complete the proof. put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse. statements reasons ​quadrilateral abcd​ is inscribed in circle o. given mbcdî…î…‘î…"î…"î…"î…"=2(m∠a) response area response area inscribed angle theorem mbcdî…î…‘î…"î…"î…"î…" mdabî…î…‘î…"î…"î…"î…"=360° response area 2(m∠a) 2(m∠c)=360° substitution property ​​response area division property of equality
The angle m∠A + m∠C = 180° in the inscribed quadrilateral ABCD.
To prove that m∠A + m∠C = 180° in an inscribed quadrilateral ABCD with circle O, follow these steps:
1. Statement: Quadrilateral ABCD is inscribed in circle O.
Reason: Given.
2. Statement: m∠BCD = 2(m∠A) and m∠DAB = 2(m∠C).
Reason: Inscribed Angle Theorem
3. Statement: m∠BCD + m∠DAB = 360°.
Reason: The sum of the measures of the angles in a circle is 360°.
4. Statement: 2(m∠A) + 2(m∠C) = 360°.
Reason: Substitution Property (from steps 2 and 3).
5. Statement: m∠A + m∠C = 180°.
Reason: Division Property of Equality (divide both sides of the equation in step 4 by 2).
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1. When you turn on the hot water tap in your kitchen, the temperature T of the
water depends on how long the water has been running. If we want to model T as
a function of time t, what do you think a rough graph of T would look like? You
can sketch T on a piece of paper if you like, scan and then insert the image as the
answer to this question
A rough graph of T as a function of time t for hot water running from a tap would likely show an exponential decay curve.
Initially, the temperature of the water will be close to the temperature of the hot water supply in the house. However, as the water continues to flow, the temperature will gradually decrease due to heat loss through the pipes and the ambient temperature of the surrounding air. This decay will likely be exponential, with a relatively steep initial drop in temperature followed by a more gradual decrease over time. The graph would show an asymptotic approach towards room temperature as the water continues to flow. The exact shape of the curve will depend on a variety of factors, such as the length and material of the pipes, the ambient temperature, and the temperature of the hot water supply.
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the tensile strength of a certain metal component is normally distributed with a mean of 10,000 kilograms per square centimeter and a standard deviation of 100 kilograms per square centimeter. a) what proportion of these components exceed 10,200 kilograms per square centimeter in ten- sile strength? b) what is the probability that a randomly chosen metal component has a tensile strength of less than 9,500 kilograms per square centimeter?
The probability calculation resulted in (a) 2.28% (b) zero.
a) To find the proportion of components that exceed 10,200 kilograms per square centimeter in tensile strength, we need to find the area to the right of 10,200 under the normal distribution curve. Using the z-score formula, we have:
z = (x - mu) / σ
z = (10,200 - 10,000) / 100
z = 2
Looking up the area to the right of z = 2 in a standard normal distribution table or using a calculator, we find this to be approximately 0.0228. Therefore, about 2.28% of the components exceed 10,200 kilograms per square centimeter in tensile strength.
b) To find the probability that a randomly chosen metal component has a tensile strength of fewer than 9,500 kilograms per square centimeter, we need to find the area to the left of 9,500 under the normal distribution curve. Using the z-score formula, we have:
z = (x - mu) / σ
z = (9,500 - 10,000) / 100
z = -5
Looking up the area to the left of z = -5 in a standard normal distribution table or using a calculator, we find this to be approximately 0.
Therefore, the probability that a randomly chosen metal component has a tensile strength of fewer than 9,500 kilograms per square centimeter is essentially 0.
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according to the u.s. department of agriculture, the mean yield of corn per acre in the u.s. is 107 bushels with a standard deviation of 15 bushels. suppose 80 one-acre plots of corn are selected at random. (a) what is the probability that the mean yield of the 80 one-acre plots chosen will be between 104 and 111 bushels? (b) what is the probability that the mean yield of the 80 one-acre plots chosen will be greater than 105 bushels? (c) what is the probability that a randomly selected one-acre plot has a yield less than 100 bushels? (2) the average age of millionaires in the us is to be determined. twenty us millionaires are randomly selected to find a mean age of 58.5 years. assume the standard deviation of all us millionaires is 12.8 years. assume the population of ages of us millionaires is normally distributed. find a 95% confidence interval for the mean age of all millionaires. round your answer to 2 decimal places if necessary. interpret your answer in a sentence.
The probability that the mean yield of the 80 one acre plots chosen will be within 2 bushels of the population mean is 0.9332. The assumptions made to answer part (a) are that the population standard deviation is known, the sample is randomly selected, and the sample size is large (n>=30)
a) We can use the central limit theorem to approximate the distribution of the sample mean. The distribution of the sample mean can be approximated as a normal distribution with a mean of 107 bushels and a standard deviation of 12/√80=1.34 bushels. Therefore, we can find the probability that the sample mean falls within 2 bushels of the population mean using the standard normal distribution.
P(105 ≤ X ≤ 109) = P(Z ≤ (109-107)/1.34) - P(Z ≤ (105-107)/1.34)
= P(Z ≤ 1.49) - P(Z ≤ -1.49)
= 0.9319 - 0.0681
= 0.8638
Therefore, there is an 86.38% probability that the mean yield of the 80 one acre plots will be within 2 bushels of the population mean.
b) Assumptions made:
The sample of 80 one acre plots is selected at random.
The one acre plots are independent of each other.
The population standard deviation is known and remains constant.
The distribution of the yield of corn per acre is approximately normal.
The sample size is large enough (n≥30) to apply the central limit theorem.
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