a. The probability that the top-selling Red and Voss tire wears out before 60,000 miles can be found by calculating the Z-score and using a standard normal distribution table. The Z-score formula is: Z = (X - μ) / σ, where X is the distance (60,000 miles), μ is the mean (71,000 miles), and σ is the standard deviation (5,000 miles).
Z = (60,000 - 71,000) / 5,000 = -11,000 / 5,000 = -2.2. Using a standard normal distribution table, the probability is approximately 0.0139 or 1.39%.
b. To find the probability that a tire lasts more than 81,000 miles, calculate the Z-score: Z = (81,000 - 71,000) / 5,000 = 10,000 / 5,000 = 2. Using the standard normal distribution table, the probability of a Z-score less than 2 is approximately 0.9772. Since we want the probability of the tire lasting more than 81,000 miles, we need to find the complement: 1 - 0.9772 = 0.0228 or 2.28%.
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The image of the point ( 6 , − 9 ) (6,−9) under a translation is ( 11 , − 4 ) (11,−4). Find the coordinates of the image of the point ( − 3 , − 2 ) (−3,−2) under the same translation
The translation vector is (5, 5). Now we can find the image of point (-3, -2) under the same translation: (-3+5, -2+5) = (2, 3)
What are coordinates?
A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).
Let's denote the translation vector as (a, b), then the image of point (x, y) under the translation is given by (x+a, y+b).
We know that the image of point (6, -9) under the translation is (11, -4), so we can write:
(6+a, -9+b) = (11, -4)
Solving this system of equations for a and b, we get:
a = 5 and b = 5
Therefore, the translation vector is (5, 5). Now we can find the image of point (-3, -2) under the same translation:
(-3+5, -2+5) = (2, 3)
So the image of point (-3, -2) under the given translation is (2, 3).
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PLS help and explain A quadratic function intersects the z-axis at the points (-4, 0) and (2, 0),and passes through the point (-6,-8). Select the equivalent equations for the quadratic function.
Oy=-0.52²-z+4
y=-0.52²+2-4
Oy=(z-4)(1-0.52)
Oy=(z+4)(1-0.5z)
Oy=-0.5(2-2)(=+4)
O y=-0.5(z+2)(z-4)
Previous
Pause Test
Nex
Therefore , the solution of the given problem of function comes out to be Oy=-0.5z²+z+4.
What is function?On the midterm exam, there will be a variety of questions on each topic, including questions about both made-up and actual locations as well as numerical variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.
Here,
We must make use of the data provided in the challenge in order to identify the quadratic function.
=> f(z) = a(z + 4)(z - 2)
where an is a constant we need to figure out.
We can use the position (-6, -8), which is where the function passes through, to determine the value of a:
=> -8 = a(-6 + 4)(-6 - 2)
=> -8 = a(-2)(-8)
=> -8 = 16a
=> a = -1/2
Inputting this number of an into the quadratic function equation yields the following results:
=> f(z) = -1/2(z + 4)(z - 2)
By extending this phrase, we get:
=> f(z) = -1/2(z² - 2z - 8)
Further simplification results in:
=> f(z) = -0.5z² + z + 4
The quadratic function's corresponding equation is thus:
=> Oy=-0.5z²+z+4
The following is the appropriate decision from the options provided:
=> Oy=-0.5z²+z+4
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John worked 35 hours at a rate of $11.50. What is his gross pay this week?
5.
Each table represents a proportional relationship. For each table:
Fill in the missing parts of the table.
Draw a circle around the constant of proportionality.
a.
b.
X
2
7
1
y
10
15
a.(Constant of proportionality: 5)
b.(Constant of proportionality: 5)
Hi! I'm happy to help you with your question. Let's analyze each table and fill in the missing parts.
a.
X | 2
Y | 10
To find the constant of proportionality, divide Y by X:
10 / 2 = 5 (Constant of proportionality)
Now, let's fill in the missing parts for X=7 and X=1 using the constant of proportionality:
For X=7:
Y = 5 * 7 = 35
For X=1:
Y = 5 * 1 = 5
So, the completed table for (a) is:
X | 2 | 7 | 1
Y | 10 | 35 | 5
(Constant of proportionality: 5)
b.
X | 1
Y | 15
To find the constant of proportionality, divide Y by X:
15 / 1 = 15 (Constant of proportionality)
As there are no other values in table (b), we can't fill in any more parts. The constant of proportionality is 15.
Your answer:
a.
X | 2 | 7 | 1
Y | 10 | 35 | 5
b.
X | 1
Y | 15
(Constant of proportionality: 15)
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elijah is simplifying the expression. 4 - 3x 8 10x. 4 - 3x 8 10x. 4 - 8 - 3x 10x -4 7x where did elijah go wrong?
Elijah incorrectly combined the constant terms 4 and 8 to get -8. The correct simplification of the expression should be 4 + 8 - 3x - 10x, which simplifies to 12 - 13x.
To simplify the expression 4 - 3x + 8 - 10x, we first combine the like terms -3x and -10x to get -13x. Then we combine the constant terms 4 and 8 to get 12. So the simplified expression is 12 - 13x.
However, Elijah made a mistake by combining the constant terms 4 and 8 as if they had opposite signs. This resulted in a term of -8 that is not present in the original expression. The rest of his simplification is correct.
Therefore, the correct simplification of the expression is 4 + 8 - 3x - 10x, which simplifies to 12 - 13x.
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Complete Question:
Elijah is simplifying the expression 4 - 3x + 8 - 10x. He arrived at the answer 4 - 8 - 3x + 10x - 4 = 7x,
where did elijah go wrong?
The bell tower of the cathedral in Pisa, Italy, leans 5.6° from the vertical. A tourist stands 105 m from its base, with the tower leaning directly toward her. She measures the angle of elevation to the top of a the tower to be 29.2°. Find the length of the tower to the nearest meter.
the tower leans 5.6° from the vertical, so we can draw a line perpendicular to the ground from the top of the tower to find the height. Let's call the height "h". the length of the tower is approximately [tex]57 meters[/tex] (rounded to the nearest meter).
What is the angle of elevation?We know that the angle of elevation from the tourist to the top of the tower is [tex]29.2^\circ[/tex] , so we can label that angle as 29.2°. We also know that the angle between the perpendicular line and the ground is 5.6°, so we can label that angle as 5.6°.
Using trigonometry, we can find the value of h:
[tex]tan(29.2^\circ) = h/105[/tex]
[tex]h = 105^\circ tan(29.2^\circ)[/tex]
[tex]h \approx 55.05[/tex]
So the height of the tower is approximately [tex]55.05[/tex] meters.
To find the length of the tower, we can use the Pythagorean theorem:
[tex]h^2 + x^2 = (105/cos(5.6^\circ))^2[/tex]
[tex]x^2 = (105/cos(5.6^\circ))^2 - h^2[/tex]
[tex]x \approx 56.67[/tex]
So the length of the tower is approximately [tex]56.67[/tex] meters.
Therefore, the length of the tower is approximately [tex]57[/tex] meters (rounded to the nearest meter).
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solve please help!!!!
The value of angle V which is ∠V is calculated as: 64.01°
How to use trigonometric ratios?The trigonometric ratios are used to find the angles and lengths of a right angle triangle.
Some of the trigonometric ratios are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
The parameters given are:
∠W = 90°
UW = 39
WV = 80
VU = 89
Thus, using trigonometric ratios, we have:
∠V = tan⁻¹(80/39)
∠V = 64.01°
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the ability of a study to detect a difference if one actually exists is called what? group of answer choices beta alpha significance power
The ability of a study to detect a difference if one actually exists is called option (d) power
Power in statistics is the probability of correctly rejecting a false null hypothesis. In other words, it is the ability of a statistical test to detect a difference or effect if one actually exists in the population being studied. A study with high power has a low probability of a Type II error (failing to reject a false null hypothesis) and a high probability of correctly detecting a true difference or effect.
Power is affected by several factors, including sample size, effect size, level of significance (alpha), and variability of the data. Researchers often aim for a power of at least 80% to ensure that their study has a reasonable chance of detecting a meaningful effect.
Therefore, the correct option is (d) power
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Determine the values of the parameter s for which the system has a unique solution, and describe the solution.
5sx1 + 9x2 = -3
5x1 + sx2 = 4
The solution for the given system is x1 = (23/5s - x2)/4s, x2, where s ≠ -360/49 and x2 can be any non-zero
Determine the values of the parameter s?The values of the parameter s
for which the system has a unique solution are s ≠ -45/8. Let's understand how to find the solution and the values of s:
Given equation of the system is,5x1s + 9x2 = -3 ...(1)
5x1 + sx2 = 4 ...(2)
Now, let's solve the given system of equations using the elimination method:
Multiply equation (2) by 5, we get:25x1 + 5sx2 = 20 ...(3)
Now, we'll subtract equation (1) from equation (3) as:
25x1 + 5sx2 = 20- (5x1s + 9x2 = -3)20x1 + 5sx2 = 23 ... (4)
Let's divide equation (4) by 5s, we get:
4x1 + x2/s = 23/5s ... (5)
Multiply equation (2) by 9 and subtract equation (1) from it. We get:40x2 + 9sx2 = 39
Simplifying the above equation, we get:(49s+360)x2 = 39 ... (6)
Now, we have two equations:(5) 4x1 + x2/s = 23/5s(6) (49s+360)
x2 = 39The given system of equations will have a unique solution only if x2 ≠ 0. So, let's consider the value of x2.If x2 ≠ 0, then from equation (6)
we get,49s+360 ≠ 0 or s ≠ -360/49
This means that s ≠ -360/49 is necessary for the given system to have a unique solution.
Now, let's solve the equation (5):4x1 + x2/s = 23/5s
If we multiply both sides of the equation (5)
by s, we get:
4sx1 + x2 = 23/5If x2 ≠ 0, then we can solve this equation for x1 as:
x1 = (23/5s - x2)/4s
Therefore, the solution for the given system is x1 = (23/5s - x2)/4s, x2, where s ≠ -360/49 and x2 can be any non-zero value.
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which of the following correctly compares the t -distribution and z -distribution? responses for small sample sizes, the density curve of the t -distribution is not symmetric, but the density curve of the z -distribution is symmetric. for small sample sizes, the density curve of the t -distribution is not symmetric, but the density curve of the z -distribution is symmetric. for large sample sizes, the density curve of the t -distribution is not symmetric, but the density curve of the z -distribution is symmetric. for large sample sizes, the density curve of the t -distribution is not symmetric, but the density curve of the z -distribution is symmetric. the curves of both distributions are symmetric, but the height of the density curve of the t -distribution is taller than the height of the density curve of the z -distribution. the curves of both distributions are symmetric, but the height of the density curve of the t -distribution is taller than the height of the density curve of the z -distribution. the area under the density curve of the t -distribution is greater than the area under the density curve of the z -distribution, especially for small sample sizes. the area under the density curve of the t -distribution is greater than the area under the density curve of the z -distribution, especially for small sample sizes. the density curve of the t -distribution is more spread out than the density curve of the z -distributi
The correct comparison between the t-distribution and z-distribution is:
The density curve of the t-distribution is more spread out than the density curve of the z-distribution, especially for small sample sizes.
Both t-distribution and z-distribution have symmetric density curves.
However, for small sample sizes, the t-distribution curve is more spread out and has heavier tails compared to the z-distribution curve.
The area under both curves is equal to 1, as they represent probability distributions.
As the sample size increases, the t-distribution curve approaches the z-distribution curve in shape.
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you want to obtain a sample to estimate a population proportion. at this point in time, you have no reasonable estimate for the population proportion. you would like to be 99.5% confident that your estimate is within 4% of the true population proportion. how large of a sample size is required?
The sample size required to estimate a population proportion with a desired level of confidence and margin of error depends on the size of the population and the confidence level desired. In this case, the population proportion is unknown and the desired confidence level is 99.5% with a margin of error of 4%.
To determine the sample size required, we can use the formula:
n = (Z² * p * q) / E²
where n is the sample size, Z is the Z-score corresponding to the desired level of confidence (which for a 99.5% confidence level is 2.81), p is the estimated population proportion (which is 0.5 as we have no reasonable estimate), q is 1-p, and E is the margin of error (which is 0.04).
Plugging in these values, we get:
n = (2.81² * 0.5 * 0.5) / 0.04² ≈ 1381
Therefore, a sample size of at least 1381 is required to estimate the population proportion with 99.5% confidence and a margin of error of 4%.
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A superhero action figure has volume 1700 cubic centimeters. The figure is dilated to create a store display.
The volume of the dilated figure is 25,500 cubic centimeters
What was the approximate scale factor of the dilation? (Round your answer to the nearest tenth, one decimal place ex. 4.2)
Therefore , the solution of the given problem of surface area comes out to be scale factor of the dilation is 15.0, rounded to one decimal point.
What does an area actually mean?By calculating how much space would be needed to fully enclose its exterior, its overall size can be calculated. The surrounding region is considered when selecting a comparable product in the rectangular design. The surface area of something determines its overall dimensions. The number of sides connecting a cuboid's four trapezoidal forms determines how much water it can hold.
Here,
By dividing the volume of the dilated figure by the volume of the initial figure, we can determine the scale factor of the dilation:
volume of dilated figure / volume of initial figure is the scale factor.
Scale factor:
=> 25,500/1700 cm3
=> 15 scale factor
The approximate scale factor of the dilation is 15.0, rounded to one decimal point.
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What is |x-13|+18=-4?
Answer:
No solution
Step-by-step explanation:
Solve for x
[tex]|x-13|+18=-4[/tex]
Subtract 18 on both sides
[tex]|x-13|=-22[/tex]
There is no solution to this problem. Absolute value cannot be less then 0.
the radius of a disk is given as with a maximum error of . use differentials to estimate the relative error in the calculated area of the disk. please enter your answer in decimal format with three significant digits after the decimal point.
Using differentials to estimate the relative error in the calculated area of the disk of disk with radius 15 cm is equals to the 3.192%.
We have, a disk with radius of 15 cm.
Maximum error = 0.25
We have to determine the area of the disk. Area is a two dimensional quantity. It is defined as the space occupied by figure or any two dimensional shape. Here, formula for area of disk, A = πr² --(1)
here, r = 15 cm , dr = 0.25
Relative error is defined as the ratio of absolute error in measurement to the oringnal measurement. Differentating the equation (1) with respect to r, dA = d( πr²)
=> dA = 2πr dr
Substitutes the known values, in above formula, dA = 2× π × 15 ×0.25
=> dA = 7.50 × π = 23.55
So, absoulte error in area = 22.55
Original value of area = π(15)² = 706.5 cm²
Now, relative error % = (∆A/A)×100
= (22.55/706.5)×100
= 0.031917 × 100
= 3.1917 ~ 3.192 %
Hence, required value is 3.192%.
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Complete question:
the radius of a disk is given 15 cm as with a maximum error of 0.25 . use differentials to estimate the relative error in the calculated area of the disk. please enter your answer in decimal format with three significant digits after the decimal point.
Explain how to solve the given equation for "x".
we can solve the given equation by taking log to get answer as x = log₈(25)
what is an equation ?
An equation is a mathematical statement that contains an equal sign, indicating that two expressions have the same value. It is a way of expressing the relationship between different variables or quantities.
In the given question,
Taking the logarithm of both sides with base 8, we get:
log₈(8ˣ) = log₈(25)
Using the logarithmic property that logₐ(b^c) = c logₐ(b), we can simplify the left-hand side to:
x log₈(8) = log₈(25)
Since log₈(8) = 1, we have:
x = log₈(25)
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What additional information is needed to prove Triangle ACE is congruent to Triangle BDE using the ASA postulate?
To prove Triangle ACE is congruent to Triangle BDE using the ASA postulate, we need either ∠A ≅ ∠B or ∠C ≅ ∠D.
To prove two triangle congruent by angle side angle postulate, these triangle must have two sides equal or one angle from these two must be equal and identical to each other.
What are congruent triangle?
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other. The symbol of congruence is’ ≅’.
The meaning of congruence in Maths is when two figures are similar to each other based on their shape and size. There are basically four congruence rules that proves if two triangles are congruent.
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¿Cuál será el fenotipo de un individuo I a
English please I don't unless
A marine biologist was interested in seeing the relationship between a manatee's weight and food consumption. She gathered data and wanted to construct a graph to display the data in order to observe this relationship.
Is a scatter plot or a line graph more appropriate to construct for the data, given the context of the problem? Explain.
A line graph, because it would show the association or relationship between two variables
A line graph, because it would show how a variable changes over time between each data point given
A scatter plot, because it would show the association or relationship between two variables
A scatter plot, because it would show how a variable changes over time between each data point given
Answer:
A line graph, because it would show the association or relationship between two variables
Step-by-step explanation:
The citizens of a city were asked to choose their favorite pet. The circle graph shows how the citizens answered. If 80,000 citizens answered the question, how many chose Fish or Snakes?
fish 12%
dogs 25%
birds 22%
cats 23%
snakes 10%
hamsters 8%
17,600 citizens chose Fish or Snakes.
What is circle graph?
A circle graph, also known as a pie chart, is a type of data visualization used to represent data in a circular format. It is called a pie chart because the graph resembles a pie, which is divided into slices or sectors, where each sector represents a portion of the whole data set. The size of each slice is proportional to the corresponding value it represents in the data set. The circle graph is often used to show relative sizes of different categories or portions of a whole. It is a popular way to display data in business, statistics, and other fields.
According to the given information, the percentage of citizens who chose Fish or Snakes is 12% + 10% = 22%.
It is also given total number of citizens are 80,000.
To find the number of citizens who chose Fish or Snakes, we can first calculate 22% of 80,000,
[tex]22\% \: of \: 80000 \\ = \frac{22}{100} \times 80000 \\ = 0.22 \times 80,000 \\ = 17,600[/tex]
Therefore, 17,600 citizens chose Fish or Snakes.
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rcumference of Circles Extra Practice Question 1 of 22 Question 1 4 3 cm > □ Find the circumference of the bottle cap. Use 3.14 for T. Round to the nearest hundredth if necessary.
The circumference of the bottle cap is nothing but the circumference of a circle and it is 9.42 cm.
What is the circumference of the circle?The circumference of a circle or other curved geometric form refers to the space encircling it. It is a boundary's one-dimensional linear measurement.
The diameter of the circle is given, D = 3cm
Therefore the radius of the circle, r = D/2 = 3/2 cm
Circumference of circle = 2[tex]\pi[/tex]r
= 2 * 3.14 * 3/2
= 3.14 * 3
= 9.42 cm
Therefore the circumference of the bottle cap is 9.42 cm.
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how to solve 132/8 answer should be in whole numbers
Answer:
use long divison ike this
16
-------
8 | 132
8
-----
52
48
-----
4
Step-by-step explanation:
Answer:
Step-by-step explanation:
132/8 = 16 with 4 leftover
32 divided by 8 is 4, 96 divided by 8 is 12, the
extra 4 left over
Pls help and explain
Answer: A (0.5)
Step-by-step explanation:
Determine by dividing total number of popcorn sold by the attendance. Use the plotted points to help you.
In the figure below DB and AC are diameters of circle P. The length of PB is 8 units . What is the length of DC
Thus, the arc length of DC for the given central angle of circle is found as: 16.74 units.
Explain about the arc length:Arc Length Formula: Assume a circle with radius r. If a circle's arc of length s subtends a central angle theta (measured in radians), the formula is as follows: r X theta = s.
Radian Measure: The centre angle must only be expressed in radian measure with in arc length formula above.A novel method of calculating angles in circles is suggested using arc length. Angles can also be measured in radians instead of the previous method of measuring all angles in degrees. The angle of one radian results in an arc whose length is equal to the radius.For the given circle:
Radius r = 8 units.angle APD = 60 degrees.Thus,
∠APD + ∠DPC = 180° (angle sum property of triangle)
60 + ∠DPC = 180°
∠DPC = 180° - 60°
∠DPC = 120°
Using the formula for the arc length:
Arc length = Ф/360 * 2*π*r
Arc length DC = 120/360 * 2*3.14*8
Arc length DC = 16.74 units
Thus, the arc length of DC for the given central angle of circle is found as: 16.74 units.
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Complete question:
In the figure below DB and AC are diameters of circle P. The length of PB is 8 units . What is the arc length of DC.
The figure is attached.
I need to know the missing angle if u can help I’ll give u a lot of points if u keep helping me
Answer:
?=45 degrees
Step-by-step explanation:
All of the angles are congruent.
So the equation is:45+90+?=180
?=45 degrees
Answer: 45 degrees
Step-by-step explanation:
The area of the trapezoid is 42square kilometers. What is the trapezoid's height, h?
the height of the trapezoid is 8.4 kilometers. To find the height, h, of a trapezoid when given the area, A, we need to use the formula:
A = ([tex]b_{1} + b_{2}[/tex])h/2
where b1 and b2 are the lengths of the two parallel bases of the trapezoid.
Given that the area of the trapezoid is 42 square kilometers, we can write:
42 = ([tex]b_{1} + b_{2}[/tex])h/2
We can simplify this equation by multiplying both sides by 2:
84 = ([tex]b_{1} + b_{2}[/tex]) h
Now we need to find the values of b1 and b2. Unfortunately, the problem does not provide us with these values. Without them, we cannot find the exact value of h. However, we can provide an example to show how to solve the problem if we have the values of b1 and b2.
Let's say that b1 = 4 km and b2 = 6 km. We can substitute these values into the equation:
84 = (4 + 6)h
Simplifying:
84 = 10h
Dividing both sides by 10:
h = 8.4 km
So, in this example, the height of the trapezoid is 8.4 kilometers.
In general, to find the height of a trapezoid when given the area, we need to know the values of both bases. Once we have those values, we can use the formula above to solve for the height. If we are not given the values of the bases, we cannot find the exact value of the height.
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a fancy bed and breakfast inn has 5 rooms, each with a distinctive color-coded decor. one day 5 friends arrive to spend the night. there are no other guests that night. the friends can room in any combination they wish, but with no more than 2 friends per room. in how many ways can the innkeeper assign the guests to the rooms?(2014 amc 12a
The total number of ways to assign the guests to the rooms is 126 ways
We can solve this problem by using a combination. We have 5 friends and 5 rooms, so we can think of the friends as stars and the rooms as bars that separate them. The number of ways to assign the friends to the rooms is equal to the number of ways to arrange the 5 stars and 4 bars (since there are 4 spaces between the bars).
We can choose any 4 positions out of 9 (5 stars and 4 bars) to place the bars, so the number of ways to assign the friends to the rooms is equal to the binomial coefficient.
[tex]${9 /\choose 4} = \frac{9!}{4!5!} = 126$.[/tex]
Therefore, there are 126 ways for the innkeeper to assign the 5 friends to the 5 rooms.
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6.4 a bus arrives every 10 minutes at a bus stop. it is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution. what is the probability that the individual waits more than 7 minutes? what is the probability that the individual waits between 2 and 7 minutes?
The probability that the individual waits more than 7 minutes is 0.3 or 30%. The probability that the individual waits between 2 and 7 minutes is 0.5 or 50%.
Let X be the waiting time for a particular individual at the bus stop. As per the given information, X follows a continuous uniform distribution with parameters a=0 and b=10 (as the bus arrives every 10 minutes).
The probability that the individual waits more than 7 minutes can be calculated as follows:
P(X > 7) = (b-7)/(b-a) = (10-7)/(10-0) = 3/10 = 0.3
Similarly, the probability that the individual waits between 2 and 7 minutes can be calculated as follows:
P(2 < X < 7) = (7-2)/(10-0) = 5/10 = 0.5
In summary, the probability that the individual waits more than 7 minutes is 0.3 and the probability that the individual waits between 2 and 7 minutes is 0.5. This means that there is a higher chance that the individual waits between 2 and 7 minutes than waiting for more than 7 minutes.
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Find m < b
Find m < c
The answer of the given figure is ∠B = 72° and ∠C = 108°
What do you understand by the term Corresponding Angle?In geometry, corresponding angles are pairs of angles that have the same relative position and the same degree of rotation, in two different geometric figures that are being compared.
More specifically, when two lines are crossed by another line, the angles on one side of the crossing line that are in the same relative position to each other (i.e., they are on the same side of the crossing line and are either both interior angles or both exterior angles), are corresponding angles.
According to question
∠CFE = 72°
In given diagram
DC ║ EF ║ AB and CB is transversal
∴ ∠CFE + ∠BFE = 180° ( Linear pair )
72° + ∠BFE = 180°
∠BFE = 180 - 72
∠BFE = 108°
∵∠DCF = ∠BFE ( Corresponding equal angle )
∠DCF = 108°
∠C = 108°
∠CFE = ∠B ( Corresponding equal angle )
72° = ∠B
∴∠B = 72°
Hence, the ∠B = 72° and ∠C = 108°
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A rectangle has a length that is 2 units longer than the width, w.
Complete the equation representing the area of the rectangle, in square units.
A= ( )( )
Options: w-2, w, w+2, 2w, 2w+2, 2w+4.
The equation representing the area of the rectangle with width w is A = w² + 2w.
We have a rectangle with a length that is 2 units longer than the width w. Let's refer to the rectangle's length as L. Then we have:
[tex]L = w + 2[/tex]
The product of a rectangle's length and breadth determines its area A. So, to find an equation representing the area of the rectangle, we need to multiply the length L by the width w. Substituting L with the expression we got from the problem statement, we get:
A = L × w
A = (w + 2) × w
A = w² + 2w
This is the final equation representing the area of the rectangle in terms of its width w
This is a quadratic equation in standard form, where the coefficient of the squared term is 1, the coefficient of the linear term is 2, and the constant term is 0. We can use this equation to find the area of the rectangle for any given width w.
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a laboratory scale is known to have a standard deviation of 0.005 in repeated weightings. scale readings in repeated weightings are normally distributed, with the mean of all possible measurements equal to the true weight of the specimen. a specimen weighted 4 times on this scale. the average weight is 4.53 grams. suppose that we needed a 95% confidence interval for this specimen using this data. what would the margin of error be?
The margin of error for a 95% confidence interval for this specimen is 0.008 grams. Then the 95% confident specimen's true weight is 0.008 grams of the sample mean of 4.53 grams.
To find the margin of error for a 95% confidence interval, we need to determine the standard error of the mean. The standard error of the mean formula can be written as:
SE = σ/√n
where:
SE = standard error of the mean,
σ = the standard deviation of the population
n = the sample size.
the standard deviation of the laboratory = 0.005
sample size = 4.
calculating the standard error of the mean:
SE = 0.005/√4
= 0.0025
Next, we need to find the critical value for a 95% confidence interval. the sample size is small (n < 30), then we need to use a t-distribution.
Critical value = 3.182.
The formula for calculating the margin of error is:
ME = t*SE
where :
ME = margin of error
t = critical value = 3.182.
SE = standard error of the mean = 0.0025
By substuting the values, we get:
ME = t*SE
= 3.182*0.0025
= 0.008 grams
Therefore, the margin of error for a 95% confidence interval for this specimen is 0.008 grams. Then the 95% confident specimen's true weight is 0.008 grams of the sample mean of 4.53 grams.
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