Answer:
Ayo its Jose is the only one who was trying to get me to do the thank you usa for the support of the joy luck club the story is about a mother that lost every thing in China and whent to America to start a new life but she make her daughter do something that she don't want to be ninja in and she is not sending her
Sandra bikes 1/4 of a trail that is 4 1/2 miles long how many miles does she bike
To find how many miles she bike we multiply the amount she biked by the total length of the track:
\(\begin{gathered} \frac{1}{4}\cdot4\frac{1}{2}=\frac{1}{4}\cdot\frac{9}{2} \\ =\frac{9}{8} \\ =1\frac{1}{8} \end{gathered}\)Therefore she biked 1 1/8 of a mile or 1.125 miles.
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Which phrase matches the expression 2v?
A. v divided by 2
B. twice v
C. 2 decreased by v
D. 2 more than v
Answer:
B) twice v
Step-by-step explanation:
because if there is no any sign between a number and a variable then you know that there is sign of multiplication
angie, a student in an advanced statistics course, was given an algebra test and she scored 80%. is this an accurate predictor of how well students in the algebra class will perform on the test? (2 points) yes, because angie is representative of the population in the algebra class yes, because angie scored high on the test so it must be easy no, because angie is not representative of the population in the algebra class no, because angie scored too high on the test
No, this is not an accurate predictor because angie is not representative of the population in the algebra test.
Here,
Angie, a student in an advanced statistics course, was given an algebra test and she scored 80%.
We have to find is this an accurate predictor.
What is Accurate predictor?
Accurate predictor describes whether the predicted values match the actual values of the target field within the incertitude due to statistical fluctuations and noise in the input data values.
Here,
Angie is the student of an advanced statistics course but she gives the algebra test and scored 80%.
We know that the advanced statistics is the higher level of math so it is not an accurate predictor.
Because, An accurate predictor should be applied when the person is 100% confirmed to the related thing. So in the given situation, the student is not 100% confirm.
Hence, this is not an accurate predictor because Angie is not representative of the population in the algebra test.
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Ben brought two pizzas to a party. He says that since 1/4 of each pizza is left, the same amount of pizza is left. What is his error? (Show your steps) (Giving brainliest for whoever answers good) (40 points)
Answer: 80
Step-by-step explanation: 8/10
In each of Problems 38 through 42, a differential equation and one solution yı are given. Use the method of reduction of or- der as in Problem 37 to find a second linearly independent solution y2. . x2y" + xy' – 9y = 0 (x > 0); yı(x) = x3
A second linearly independent solution of y₂ is \(-\frac{1}{6x^3}\)
The general Equation is y" + P(x)y' + q(x)y = 0 ...............(i)
where P(x), Q(x) are continues in the internal I ≤ R.
If y₁(x) is a solution of equation 1 in I then y₁(x) ≠ 0.
Then y₂(x) = y₁(x)\(\int{\frac{e^{-\intP(x)dx}}{(y_{1}x)^2}}dx\) is another solution.
The differential equation is x²y" + xy' – 9y = 0 where x > 0.
As y₁(x) = x³ is one solution of differential equation.
Divide throughout by (x²) to given differential equation.
1/x² (x²y" + xy' – 9y = 0)
y" + (y'/x) – (9/x²)y = 0 ................(ii)
By comparing equation (i) & (ii) we get:
p(x)=1/x , q(x)= –are continuous for x>0
So, another solution,
y₂(x) = y₁(x)\(\int{\frac{e^{-\intP(x)dx}}{(y_{1}x)^2}}dx\)
Now putting the values of P(x) And Q(x)
y₂(x) = \(x^3\int\limits {\frac{e^{\int(1/x)dx} }{(x^3)^2}} \, dx\)
y₂(x) = \(x^3\int\limits {\frac{\frac{1}{x} }{x^6} }} \, dx\)
y₂(x) = \(x^3\int\limits {\frac{1}{x^7} }} \, dx\)
y₂(x) = \(x^3\int\limits {x^-7} } \, dx\)
y₂(x) = \(x^3\left[\frac{x^{-7+1}}{-7+1}\right]\)
y₂(x) = \(-\frac{1}{6}(x^3\times x^{-6})\)
y₂(x) = \(-\frac{1}{6x^3}\)
So, the answer of this question is \(-\frac{1}{6x^3}\).
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Solve using Gauss-Jordan elimination. 4x₁ + 16x₂-24x3 = 8 5x₁ +20x2 - 30x3 = 10 Select the correct choice below and fill in the answer box(es) within your choice. O A. The unique solution is x₁ = x₂ = , and x3 = O B. The system has infinitely many solutions. The solution is x₁=₁ X₂ =, and x3 = t. (Simplify your answers. Do not factor. Type expressions using t as the variable.) = The system has infinitely many solutions. The solution is x₁, x₂ = s, and x3 = t. (Simplify your answer. Do not factor. Type an expression using s and t as the variables.) O D. There is no solution.
The matrix, we can observe that 0x₁ + 0x₂ + 0x₃ = -30, which is a contradiction. This implies that there is no solution to the system of equations. Therefore, the correct choice is D. There is no solution.
To solve the given system of equations using Gauss-Jordan elimination, we can represent the system as an augmented matrix and perform row operations until we obtain the reduced row-echelon form.
The augmented matrix for the system is:[4 16 -24 | 8]
[5 20 -30 | 10]
We'll use row operations to eliminate the coefficients below the diagonal in the leftmost column. First, we'll multiply the first row by 5 and the second row by 4, and then subtract the second row from the first row:
[20 80 -120 | 40]
[20 80 -120 | 10]
Next, we'll divide the first row by 20 to obtain a leading 1:
[1 4 -6 | 2]
[20 80 -120 | 10]
Now, we'll subtract 20 times the first row from the second row:
[1 4 -6 | 2]
[0 0 0 | -30]
From the last row of the matrix, we can observe that 0x₁ + 0x₂ + 0x₃ = -30, which is a contradiction. This implies that there is no solution to the system of equations. Therefore, the correct choice is D. There is no solution.
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the angle of elevation to the top of a building in new york is found to be 3 degrees from the ground at a distance of 2 mile from the base of the building. find the height of the building. what is this formula of this question? sort
The height of the building is approximately 554.26 feet.
To find the height of the building, you can use the tangent formula in trigonometry. The formula you need is:
height = distance × tan(angle)
where "height" is the height of the building, "distance" is the distance from the base of the building, and "angle" is the angle of elevation.
In this case, the distance is 2 miles and the angle of elevation is 3 degrees. First, convert the angle to radians:
angle (in radians) = angle (in degrees) × (π/180)
angle (in radians) = 3 × (π/180) ≈ 0.05236 radians
Now, plug the values into the formula:
height = 2 miles × tan(0.05236 radians)
To get the height in feet, convert miles to feet (1 mile = 5280 feet):
height = (2 × 5280) × tan(0.05236 radians) ≈ 554.26 feet
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The freezing point of oxygen is –218.790C and hydrogen is –252.80C. A lab is lowering the temperature inside a fridge. Which freezes first? How much colder does it have to be for both to freeze?
Answer:
Oxygen; 34.01°C
Step-by-step explanation:
The oxygen freezes first as it has a higher (warmer) freezing point. For both to freeze, the temperature must drop a further 34.01°C as:
-218.79 - (-252.8)
= 252.8 - 218.79
= 34.01
Right triangle ABC is located at A (-1,-2), B(-1, 1), and C (3, 1) on a coordinate plane. What is the equation of a circle A with radius AC?
Olx + 1)2 + y + 2)2 = 9
O(x + 1)2 + (y + 2)2 = 25
OOX - 3)2 + y - 12 = 16
Ox - 3)2 + (y - 142 = 25
Answer:
(x +1)^2 + (y +2)^2 = 25
Step-by-step explanation:
A diagram of the given triangle shows you it has side lengths of 3 and 4, so the square of the hypotenuse is ...
(AC)^2 = (AB)^2 +(BC)^2 = 3^2 +4^2
(AC)^2 = 25
The center of the circle is at A(-1, -2), so the equation is ...
(x -h)^2 +(y -k)^2 = r^2
for the circle centered at (h, k) with radius r.
We know that the square of the radius (r^2) is 25, so we can write the equation as ...
(x +1)^2 +(y +2)^2 = 25
Answer:
(x + 1)2 + (y + 2)2 = 25
Step-by-step explanation:
Hope this helps :)
The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
The equations that can be used to find the lengths of the legs of the triangle are 0.5(x)(x + 2) = 24 and x² + 2x - 48 = 0 , the correct options are (a) and (d) .
In the question ,
a right angled triangle is given ,
the area of the right triangle = 24 square feet
base of the triangle = x feet
height of the triangle = (x + 2) feet
we know that the formula for the area of the right triangle is written as
Area = (1/2)*base*height
Substituting the values from above , we get
24 = (1/2) * x * (x+2)
0.5(x)(x + 2) = 24 ,.....which is option (a) ,
Solving further , we get
48 = x(x+2)
x² + 2x = 48
x² + 2x - 48 = 0 ,....which is option (d)
Therefore , The equations that can be used to find the lengths of the legs of the triangle are 0.5(x)(x + 2) = 24 and x² + 2x - 48 = 0 , the correct options are (a) and (d) .
The given question is incomplete , the complete question is
The Area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Select all that apply .
(a) 0.5(x)(x + 2) = 24
(b) x(x + 2) = 24
(c) x² + 2x – 24 = 0
(d) x² + 2x – 48 = 0
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Find the missing side of the right
triangle.
7
4
Х
x= [?]
Enter the number that belongs in the green box,
Step-by-step explanation:
using Pythagoras theorem,
(hypotenuse)² = (perpendicular)² + (base)²
given that, hypotenuse =x, perpendicular =7, base =4
(x)² = 7² + 4²
(x)² = 49 + 16
x = √65
Mandy was making 6 pillows, to give to her family. She needed 5/8 of a yard of material for each pillow. How many yards of material does she need
Answer:
3 3/4 yards of material
Step-by-step explanation:
Mandy was making 6 pillows, to give to her family. She needed 5/8 of a yard of material for each pillow. How many yards of material does she need?
From the above question:
1 pillow = 5/8 yard
6 pillows = x yards
Cross Multiply
1 pillow × x yards = 6 pillows × 5/8 yards
x yards = 6 pillows × 5/8 yards/1 pillow
x yards = 3 3/4 yards of material
Therefore, she needs 3 3/4 yards of material to make 6 pillows.
2. What is the range of the set
{13, 5, 8, 9, 15, 9)?
Answer: range is 10 hope it helps
Step-by-step explanation:
If a given probability distribution has a mean of 7, a median of 6, a standard deviation of 3, and a variance of 9, what is the expected value
The expected value is 6.0.
The expected value (or mean) of a probability distribution can be obtained by the formulaµ = E(X) = ∑ xᵢP(xᵢ). The given probability distribution has a mean of 7, a median of 6, a standard deviation of 3, and a variance of 9. Therefore, we can get the expected value using the formulaµ = E(X) = ∑ xᵢP(xᵢ).
Mean = 7Median = 6Standard deviation = 3Variance = 9The formula for variance is:Variance = (Standard deviation)²9 = (3)²Variance = 9The formula for variance can be modified as:
Variance = E(X²) - [E(X)]²Variance + [E(X)]² = E(X²)Substituting the values,9 + 7² = E(X²)E(X²) = 58To find expected value (or mean), the formula is:µ = E(X) = ∑ xᵢP(xᵢ)The median is the value that separates the upper 50% of the distribution from the lower 50%.
The mean is a measure of the central tendency of the distribution. So, the probability distribution is skewed to the right. There are many possible ways to construct a probability distribution with the given mean, median, variance, and standard deviation.
One example of such a probability distribution is shown below:x: 0 1 5 6 9P(x): 0.05 0.1 0.4 0.3 0.15Using the formula µ = E(X) = ∑ xᵢP(xᵢ), the expected value isµ = 0(0.05) + 1(0.1) + 5(0.4) + 6(0.3) + 9(0.15)µ = 0.5 + 2 + 1.8 + 1.35 + 1.35µ = 6.0Thus, the expected value is 6.0.
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DATA EXPLORATION Did Mr. Starnes stack his class? Mr. Starnes teaches APD Statistics, but he also does the class scheduling for the high school. There are two AP® Statistics classes-one taught by Mr. Starnes and one taught by Ms. McGrail. The two teachers give the same first test to their classes and grade the test together. Mr. Starnes's students earned an average score that was 8 points higher than the average for Ms. McGrail's class. Ms. McGrail wonders whether Mr. Starnes might have "adjusted" the class rosters from the computer scheduling program. In other words, she thinks he might have stacked" his class. He denies this, of course. To help resolve the dispute, the teachers collect data on the cumulative grade point averages and SAT Math scores of their students. Mr. Starnes provides the GPA data from his computer. The students report their SAT Math scores. The following table shows the data for each student in the two classes. Note that the two data values in each row come from a single student. la W 28 Starnes GPA McGrail GPA Starnes SAT-M 670 2.9 2.9 2.86 520 2.6 3.6 3.2 McGrail SAT-M 620 590 650 600 620 680 500 502.5 2.71 570 710 600 590 640 570 710 630 630 670 650 660 510 3.1 3.085 3.75 3.4 3.338 3.56 3.8 3.2 3.1 3.3 3.98 2.9 3.2 3.5 2.8 2.9 3.95 3.1 2.85 2.9 3.245 3.0 3.0 640 630 580 590 600 600 2.8 620 580 600 600 2.9 3.2 Did Mr. Starnes stack his class? Give appropriate graphical and numerical evidence to support your
The possible data in the question does not provide sufficient evidence available to support the alternative hypothesis that there is a difference between Mr. Starnes and Ms. McGrail's AP Statistics classes and Mr. Starnes did not stack the class.
What is a hypothesis testing?
In statistics, a hypothesis test is the performance of a test on an assumption made about a population parameter.
The possible data in the question, obtained from a similar online question, using MS Excel, indicates;
The mean of the Starnes GPA ≈ 3.212867
The standard deviation of Starnes GPA ≈ 0.364249
Mean of McGrail GPA ≈ 3.134722
The standard deviation of McGrail's GPA ≈ 0.357995
The null hypothesis is H₀: μ₁ - μ₂ = 0
The alternative hypothesis is Hₐ: μ₁ - μ₂ ≠ 0
The test statistic is found using the following formula;
\(t_0 = \dfrac{(\overline{x_1} - \overline{x_2})-(\overline{\mu_1}-\overline{\mu_2})}{\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2} } }\)
The decision rule is obtained with α = 0.05 and the null hypothesis is rejected t₀ ≤ -1.96 or t₀ ≥ 1.96
Therefore, we get;
\(t_0 = \dfrac{(3.212867 - 3.134722)-0}{\sqrt{\dfrac{0.364249^2}{15}+\dfrac{0.357995^2}{18} } } \approx 0.618\)
The parameter for the degrees of freedom is 15 - 1 = 14
The critical value obtained from the t-table, at t.₉₅ is 1.761 which is larger than 0.618, therefore, we fail to reject the null hypothesis, and the evidence is insufficient to suggest that there is a difference in the average score of the two AP Statistics classes.
Taking the variance to be the same, we get;
\(S_p^2= \dfrac{(n_1-1)\cdot s_1^2+(n_2-1)\cdot s_2^2}{n_1+n_2-2}\)
Therefore;
\(S_p^2= \dfrac{(15-1)\times 0.364249^2+(18-1)\times 0.357995^2}{15+18-2}\approx 0.1302\)
\(t_0 = \dfrac{(\overline{x_1} - \overline{x_2})-(\overline{\mu_1}-\overline{\mu_2})}{\sqrt{s_p^2 \times\left(\dfrac{1}{n_1}+\dfrac{1}{n_2} }\right) }\)
\(t_0 = \dfrac{(3.212867 - 3.134722)-0}{\sqrt{0.1302\times \left(\dfrac{1}{15}+\dfrac{1}{18} }\right) } \approx 0.6195\)
df = 15 + 18 - 2 = 31
From the t-table, the critical value is about 1.697, which is larger than 0.6195, therefore, the null hypothesis cannot be rejected and the evidence available is not enough to suggest that there is a difference between the grade point averages of Mr. Starnes and Ms. McGrail AP Statistics classes and Mr. Starnes did not stack the class
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William can pack 60 toys in 4 hours. Find the unit rate with which he packs
toys.
A.16 toys/hour
B.15 toys/hour
C.14 toys/hour
D.13 toys/hour
Find points A B C, you are given the points in the picture below.
What helps us show inverse variation?
Answer:
Solving an Inverse Variation Problem
-Write the variation equation: y = k/x or k = xy.
-Substitute in for the given values and find the value of k.
-Rewrite the variation equation: y = k/x with the known value of k.
-Substitute the remaining values and find the unknown.
Step-by-step explanation:
yeah
if n is a positive integer, how many integers from 0 through 2n must you pick in order to be sure of getting at least one that is odd? incorrect: your answer is incorrect. how many integers must be picked in order to be sure of getting at least one that is even?
Therefore , the we need to pick n + 2 numbers to be sure of random selection is an odd number.
What is random selection?In statistic, a simple random sample is a subset of people chosen at random from a larger group, all of whom were chosen with the same probability. This procedure involves choosing a sample at random.
Here,
You must choose n + 2 numbers at random in order to guarantee that you will get at least one odd number.
Since n is a positive integer, the following values of n are possible:
{1, 2, 3, 4, ...}
Let's assume n = 1.
Now, in order to guarantee that you choose at least one odd integer from 0 to 2n = 2*1 = 2, how many must you choose (at random)?
There are three numbers from 0 to 2:
0, 1, 2
If you choose these at random, selecting all three digits will guarantee that you receive an odd number.
From 0 to 2*n, there are the following options if n = 2.
0, 1, 2, 3, 4
Five choices.
If you wish to choose at least one odd number for certainty after picking 3 even numbers, you must choose 4 numbers.
From 0 through 2*n, if n = 3, we get:
0, 1, 2, 3, 4, 5, 6
Since 4 of these are even, you must choose 5 of them to guarantee an odd number.
The amount of even numbers is always n + 1, therefore given a random integer n, we will have n + 1 even numbers from 0 to 2n. Therefore, if we want to be certain that we are selecting an odd number at random, we must choose n + 2 numbers.
Therefore , the we need to pick n + 2 numbers to be sure of randomly selecting an odd number.
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Brandon bought snacks for his team's practice. He bought a bag of popcornfor $2.11 and a 6-pack of juice bottles. The total cost before tax was $11.41.Write and solve an equation which can be used to determine x, how mucheach bottle of juice costs?
x represents the cost of each bottle of juice. Given that he bought a pack containing 6 bottles of juice, the cost of the 6 pack juice bottles would be $6x
Given that the total cost of a bag of popcorn which costs $2.11 and a 6-pack of juice bottles is $11.41, it means that
2.11 + 6x = 11.41
6x = 11.41 - 2.11
6x = 9.3
x = 9.3/6
x = 1.55
The cost of each bottle of juice is $1.55
Find the measure of
=======================================================
Explanation:
The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.
Those angles add to the other angles to form a full 360 degree circle.
Let x be the measure of angle SPT and angle TPU.
86 + 154 + 60 + x + x = 360
300 + 2x = 360
2x = 360-300
2x = 60
x = 60/2
x = 30
Each red angle is 30 degrees.
Then,
angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)
angle SPQ = (30) + (30) + (86)
angle SPQ = 146 degrees
--------------
Another approach:
Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:
360 - 214 = 146 degrees
The following are weights in pounds of a college sports team:
165, 171, 174, 180, 182, 188, 189, 192, 198, 202, 202, 225, 228, 235, 240
a. The mean is: _________________
b. The sample standard deviation is: _______________
c. The first quartile is: _____________
d. The median is: ______________
e. The third quartile is: ______________
Answer:
Step-by-step explanation:
a-6
b-165-240
c-165
d-182 and 152
e-174
what's 33 ÷ 33 × 33 - 33 + 33
Answer:
33
Step-by-step explanation:
first we divide 33 by 33 then we have 1 now we have times 33 which is 33 now 33-33 is 0 not we add 33 to 0 now we have 33
Find the range of the graphed function.
The range of the graphed function is -4≤y≤8.
Option (A) is correct.
To find the range of the graphed function.
What is function?A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
Given that:
It is given that the graph shows parabolic.
The "range" is the vertical extent of the graph.
The range of a function refers to the values of y for which x is defined.
The least value of y from the graph is -4.
The reason is that each box is 2 units, therefore tracing down to the third box on the y-axis gives -4.
Similarly the highest value is 9..
So, the range of the graphed function is -4≤y≤9.
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Answer:
A is the correct answer
Step-by-step explanation:
On a coordinate plane, Point C is at (-3,5) and Point D is at (4,9). What is the distance from point C to point D?
Answer:
5\(\sqrt[\\]{3} \\\) or about 8.66
Step-by-step explanation:
To find the distance of any line, you have to use distance formula.
\(\sqrt{(y-y_{1} )^{2} + (x-x_{1} )^{2}\)
So, we insert our points:
\(\sqrt{(5-9 )^{2} + (-3-4 )^{2}\)
Then you solve, and should end up with \(\sqrt{75}\). Either you can simplify it for an exact number, or you can round. It depends on what the directions ask for.
Please find answers of 14 a, b, c and d
Q14)
a) The smallest prime number is 2. The smallest composite number is 4.
b) Rs 720 - 20 [as loss]
=> Rs 790 = SP
c) Rs 500 - 30 [as profit]
=> Rs 470 = CP
d) a° + b° = 180°
Hope it helps you!
Pls HELPPP, BRAINLIEST for best and right answer
Answer:
i think the answer is 5
Step-by-step explanation:
If 3 cars have traveled a total of 180,000 miles and the distance traveled by each car differs by at least 1 mile from the distance traveled by either of the other 2 cars,what is the minimum possible number of miles traveled by the car with the most mileage
Answer:
60001 miles
Step-by-step explanation:
Given
\(Total\ Distance = 180000\)
Let the cars be: \(Car\ A, Car\ B\ and\ Car\ C\)
Assume that Car A has the minimum mileage of x.
\(Car\ A = x\)
The other cars would be:
\(Car\ B = x + 1\)
\(Car\ C = x + 2\)
This implies that Car C has the highest mileage
Required
Determine the possible minimum number of miles
Since the total distance is 180000, then:
\(Car\ A + Car\ B + Car\ C = 180000\)
Substitute values for Car A, B and C
\(x + x + 1 + x + 2 = 180000\)
Collect Like Terms
\(x + x + x = 180000-1-2\)
\(3x = 179997\)
Divide both sides by 3
\(\frac{3x}{3} = \frac{179997}{3}\)
\(x = \frac{179997}{3}\)
\(x = 59999\)
The car with the most mileage is Car C
So:
\(Car\ C = x + 2\)
Substitute 59999 for x in \(Car\ C = x + 2\)
\(Car\ C = 59999 + 2\)
\(Car\ C = 60001\)
The minimum distance travelled by Car C is 60001 miles
A math professor waits at the bus stop at the Mittag-Leffler Institute in the suburbs of Stockholm, Sweden. Since he has forgotten to find out about the bus schedule, his waiting time until the next bus is uniform on (0,1). Cars drive by the bus stop at rate 6 per hour. Each will take him into town with probability 1/3. What is the probability he will end up riding the bus?
The probability that the professor ends up riding the bus is approximately 0.777.
How to find the probability that the professor will end up riding the busThe professor's chances of riding in a car into town are: P(waiting time > t) = e(-6t)
The probability that the professor will catch a ride in a passing car rather than taking the bus is: P(car ride only) = (0 to 1) (1/3) * e(-6t) dt
This integral is evaluated as follows: P(car ride only) = 1/2 - e(-6/3)/6 0.223
We need to calculate the likelihood that the professor does not receive a ride with a car and instead waits for the bus:
P(only bus journey) = (0 to 1) (2/3) * e(-6t) dt
When this integral is evaluated, we get:
P(only bus journey) = 1/2 + e(-6/3)/6 0.777
Therefore, the probability that the professor ends up riding the bus is approximately 0.777.
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Find the constants m and b in the linear function f(x)=mx+b so that f(7)=9 and the straight line represented by f has slope −3.
m=
b=
To find the constants m and b in the linear function f(x) = mx + b, we can use the given conditions f(7) = 9 and a slope of -3.
The value of f(7) represents the y-coordinate of the point on the line when x = 7. So, substituting x = 7 into the equation, we get 9 = 7m + b.
The slope of a linear function is given by the coefficient of x, which in this case is -3. So, we have m = -3.
Now, we can substitute the value of m into the equation obtained from f(7). We get 9 = 7(-3) + b, which simplifies to 9 = -21 + b.
Solving for b, we find b = 30.
Therefore, the constants for the linear function f(x) = mx + b that satisfy the given conditions are m = -3 and b = 30.
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