The age of Julia is 13 years.
Integers are whole numbers, including both positive and negative numbers, that do not have any fractions or decimals. In mathematics, integers are often used to represent real-world quantities such as age, time, and money.
In this problem, Julia is the oldest of three siblings whose ages are consecutive integers. We can represent this using the equation x + (x+1) + (x+2) = 42, where x is Julia's age.
To solve this equation, we can use the distributive property to expand the left side of the equation to 3x + 3 = 42.
We can then subtract 3 from both sides of the equation to get 3x = 39. Finally, we can divide both sides by 3 to get x = 13.
Therefore, Julia's age is 13.
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Complete Question:
Julia is the oldest of three siblings whose ages are consecutive integers. If the sum of their ages is 42, find Julia's age.
solve
5 1/8 + 2 5/8=
Answer:7 3/4
Step-by-step explanation:
(5*8+1)/8+(8*2+5)/8=41/8+21/8=62/8=7 6/8=7 3/4
Please i need help due in 25 minutess
The evaluation of the two more bids Bruno received, and the equations, table and graph obtained from the bids are as follows;
The variables used for the bids are;x = The number of books
y = The total charge based on the pricing
The equations are;
Bid 7: y = 15·x + 3
Bid 8: y = 10·x + 40
Please find the completed table in the following explanation part
Part B;
Please find attached the graph of the two equations, created with MS Excel
What is an equation?An equation is a mathematical statement indicating that the quantity, magnitude or values of two expressions are the same.
The amount Bid 7 charges per book = $15
Amount paid upfront for Bid 7 = $5
Amount Bid 8 charges upfront = $40
Amount Bid 8 charges per book = $10
The variables are;
x = The amount charged per booky = The total amount paidThe equations are;
Bid 7: y = 15·x + 5Bid 8: y = 10·x + 40The table of values can be presented as follows;
Bid 7 [tex]{}[/tex] Bid 8
x [tex]{}[/tex] y = 15·x + 5 y = 10·x + 40
0 [tex]{}[/tex] 5 [tex]{}[/tex] 40
3 [tex]{}[/tex] 50 [tex]{}[/tex] 70
5 [tex]{}[/tex] 80 [tex]{}[/tex] 90
7 [tex]{}[/tex] 110 [tex]{}[/tex] 110
10 [tex]{}[/tex] 155 [tex]{}[/tex] 140
Part B;
Please find attached the required graph of the two equations, showing the legend and the scale for the x and y axis created with MS Excel.
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You are testing the claim that smiling, rather than remaining neutral, during a court proceding will lead to a different punishment from the judge.
A sample of 34 people who smiled during their hearing and 34 people who kept neutral facial expressions during their hearing is taken and each judgment was rated for leniency. Those who smiled (population 1) had a mean leniency rating of 4.9 with a standard deviation of 1.7, while those who did not smile (population 2) had an average leniency rating of 4.1 and standard deviation 1.5. Test the claim using a 10% level of significance.
What are the correct hypotheses?
Based on the hypotheses, find the following:
Test Statistic =
p-value =
Therefore , the solution of the given problem of test statistic comes out to be Using a t-table or calculator, with 66 degrees of freedom (df = n1 + n2 - 2), we find the p-value to be approximately 0.039.
Which test statistic is this?The Z-statistic has been the test statistics for anything resembling a Z-test and it confirms that the ordinary standard neutral hypothesis is true. Consider doing two separate X-y tests with a 0.05 level of significance and getting a 2.5 R-t value from your data (also referred as a Z-value). The p-value associated with this Z-value is 0.0124.
Here,
The hypotheses are:
Null hypothesis: There is no significant difference in punishment between those who smiled and those who remained neutral during a court proceeding.
Alternative hypothesis: There is a significant difference in punishment between those who smiled and those who remained neutral during a court proceeding.
To test this claim, we can use a two-sample t-test since we are comparing the means of two independent samples.
The formula for the test statistic is:
t = (x1 - x2) / sqrt((s1² / n1) + (s2² / n2))
where:
x1 = sample mean of those who smiled
x2= sample mean of those who remained neutral
s1 = sample standard deviation of those who smiled
s2 = sample standard deviation of those who remained neutral
n1 = sample size of those who smiled
n2 = sample size of those who remained neutral
Substituting the given values, we get:
t = (4.9 - 4.1) / sqrt((1.7² / 34) + (1.5² / 34))
t ≈ 2.116
Using a t-table or calculator, with 66 degrees of freedom (df = n1 + n2 - 2), we find the p-value to be approximately 0.039.
Since the p-value (0.039) is less than the significance level (0.10), we reject the null hypothesis. Therefore, we have sufficient evidence to conclude that there is a significant difference in punishment between those who smiled and those who remained neutral during a court proceeding.
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Brad sold a rental house that he owned for $251,500. Brad bought the rental house five years ago for $223,500 and has claimed $50,750 of depreciation expense. What is the amount and character of Brad's gain or loss?
A basketball player makes 39% of her shots from the free throw line. Suppose that each of her shots can be considered independent and that she throws 3 shots. Let x = the number of shots that he makes. What is the probability that she makes 0 shots?.
The probability that the basketball player makes 0 shots out of 3 is 0.343, or 34.3%. This can be calculated by using the binomial probability formula.
To calculate the probability of any outcome of a binomial experiment, use the formula: P(x) = nCx * px * (1-p)n-x, where n is the number of trials, x is the number of successes, and p is the probability of success in any one trial.
The Binomial Probability formula is
P(x) = nCx * [tex]p^x[/tex] * [tex](1-p)^{(n-x)}[/tex].In this case, n = 3, x = 0, p = 0.39, and (1-p) = 0.61. Plugging these values into the formula, we get
P(x) = 3C0 * [tex]0.39^0[/tex] * 0.61³
= 0.343.
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X/-3 is greater or equal to 12
The solution to the inequality is any value of X that is less than or equal to -36
What is Inequality?
An inequality is a relationship that compares two numbers or other mathematical expressions that are not equal. It is most commonly used to compare the sizes of two numbers on a number line.
The inequality X/(-3) ≥ 12 can be solved as follows:
We begin by multiplying both sides of the inequality by -3, which will reverse the direction of the inequality since we are multiplying by a negative number. This gives:
X ≤ -36
Therefore, the solution to the inequality is any value of X that is less than or equal to -36.
In interval notation, we can write the solution as:
(-∞, -36]
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A large grocery store chain pays all workers time and a half on Saturdays and double time on Sundays. If an employee's regular pay is $10.50 per hour, use the expression 10.50(1.5)(x) + 10.50(2)(y) to find their gross income if they worked 5 hours on Saturday and 3.5 hours on Sunday. (4 points)
$160.13
$152.25
$312.38
$143.31
put 7+2 on a number line.
Answer: Shown in screenshot.
Step-by-step explanation: First, let's start at 7. We are adding 2 to seven, so we move to the right two places. When we do so, we get to 9. So, 9 is the answer.
This answer will probably get taken down like SO MANY of my answers for no reason when literally WRONG answers stay on the website.
9 is the answer .When using a number line and you need to add you go to the right or forward
CAN SOMEONE HELP WITH THIS QUESTION?✨
The population after 4 years is 1982.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have.,
Current population = 1652 people
The population triples every 10 years.
This means,
We can make a function for the number of population after m years.
y = 1652 x 3(m/10)
Where M is the number of years.
Now,
Substitute m = 4.
y = 1652 x 3(m/10)
y = 1652 x 3 (4/10)
y = 1652 x 3 x 2/5
y = 1982.4
y = 1982
Thus,
1982 is the population after 4 years.
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The number of petty crimes this year fell to 276 from 349 incidents. Find the percent of decrease. Round to the nearest tenth of a percent.
Answer:
≅20.9%
Step-by-step explanation:
To find the percent decrease, we need to calculate the difference between the old value (349) and the new value (276), divide that by the old value, and then multiply by 100 to express it as a percentage.
The formula for percent decrease is:
percent decrease = ((old value - new value) / old value) x 100%
Substituting the given values, we get:
percent decrease = ((349 - 276) / 349) x 100%
percent decrease = (73 / 349) x 100%
percent decrease = 20.92%
Rounding to the nearest tenth of a percent, we get:
percent decrease ≈ 20.9%
Therefore, the percent decrease in the number of petty crimes this year is [approximately 20.9%.]
Southeast Washington State has a long history of seasonal dust storms. During October 1991 levels were six times greater than the Environmental Protection Agency’s standard. During that year, several researchers conducted studies at three community hospitals to examine the relationship between the amount of dust particles in the air when the storms occur and the number of emergency room visits for respiratory disorders. Using the methods of correlation and regression that you will learn in this module they were able to determine the effect of these dust storms on local residents (Elementary Statistics, fourth edition, Allan Bluman).
For this module you will write a short statistical report based on your linear regression analysis of data collected for two interesting variables that you believe could be linearly correlated. This report should be supported by a scatter plot of the data and a least squares regression line. Here are guidelines for Statistical Report Writing. (Please review the download of the pdf file.)
For your study, you may collect your own data (cite sources!!) or use data that has already been collected. For example, you will find data in the exercises at the end of sections 10.2 and 10.3 of your course text. Use at least 5 pairs of data.
Southeast Washington State has a long history of seasonal dust storms. In October 1991, levels of dust particles in the air were six times greater than the Environmental Protection Agency's standard.
Several researchers conducted studies at three community hospitals to examine the relationship between the amount of dust particles in the air during the storms and the number of emergency room visits for respiratory disorders. Using the methods of correlation and regression, they were able to determine the effect of these dust storms on local residents.
In this module, you will write a short statistical report based on your linear regression analysis of data collected for two interesting variables that you believe could be linearly correlated. Your report should be supported by a scatter plot of the data and a least squares regression line.
To begin, you should collect your own data or use data that has already been collected. You may find data in the exercises at the end of sections 10.2 and 10.3 of your course text. Use at least 5 pairs of data.
Once you have collected your data, you should create a scatter plot of the data and a least squares regression line. You should also calculate the correlation coefficient and the equation of the regression line.
In your report, you should discuss the relationship between the two variables and the strength of the correlation. You should also discuss the equation of the regression line and how it can be used to make predictions.
Finally, you should conclude your report by discussing the implications of your findings and any limitations of your study.
Overall, your statistical report should be factually accurate, professional, and concise. You should also be sure to cite any sources that you use in your report.
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NO LINKS!!! URGENT HELP PLEASE!!! NOT MULTIPLE CHOICE!!!!!
3. You are sitting on the edge of the pool and swim underwater to the other side. Your path through the water can be modeled by the equation d(p) = 1/4p^2 - 2p in feet per second. Use this scenario to answer questions a - c.
a. What is your deepest point underwater?
b. What is your depth when you have held your breath for 22 seconds? (Round your answer to the nearest foot)
c. How long do you hold your breath to make the swim?
Answer:
3.
a.4 feet
b.77 feet
c.8 seconds
Step-by-step explanation:
We can start by noting that the given equation, d(p) = 1/4p^2 - 2p, represents the depth (in feet) at a given point in time as you swim underwater, where p is the time in seconds since you started swimming.
a. To find the deepest point underwater, we need to find the maximum of the function d(p). We can do this by finding the vertex of the parabola. The formula for the x-coordinate of the vertex of a parabola in the form y = ax^2 + bx + c is given by x = -b/2a. In this case, a = 1/4 and b = -2, so the x-coordinate of the vertex is:
x = -b/2a = -(-2)/(2(1/4)) = 4
So the deepest point underwater occurs at p = 4 seconds. To find the depth at this point, we can substitute p = 4 into the equation:
d(4) = 1/4(4)^2 - 2(4) = -4 feet
Therefore, the deepest point underwater is 4 feet below the surface.
b. To find the depth when you have held your breath for 22 seconds, we need to evaluate the function d(p) at p = 22. We can round our answer to the nearest foot.
d(22) = 1/4(22)^2 - 2(22) = 77 feet
Therefore, the depth when you have held your breath for 22 seconds is approximately 77 feet below the surface.
c. To find how long you hold your breath to make the swim, we need to find the time it takes to swim from one side of the pool to the other. We can do this by finding the roots of the equation d(p) = 0, which represent the times when you reach the other side of the pool (i.e., when the depth is zero). We can use the quadratic formula to solve for p:
p = (-b ± sqrt(b^2 - 4ac))/2a
In this case, a = 1/4, b = -2, and c = 0, so the formula becomes:
p = (-(-2) ± sqrt((-2)^2 - 4(1/4)(0)))/(2(1/4)) = 8 or 0
The root p = 0 corresponds to the start of the swim, so the time it takes to make the swim is:
p = 8 - 0 = 8 seconds
Therefore, you hold your breath for 8 seconds to make the swim from one side of the pool to the other.
Guys help!!
Slope of one of the dotted lines:
Slope of the line of reflection:
Multiplying a whole number by a proper fraction, results in a ___
product.
Please help fill In the blank I WILL GIVE 5 STARS PLEASEE
Multiplying a whole number by a proper fraction results in a product which is lesser than the whole number.
What are Proper Fractions?Proper fractions are fractions in which the value of the numerator is less than the value of the denominator.
For example, 1/4, 3/4, 3/8, are all proper fractions.
4/3, 5/2, are all improper fractions.
So, from the definition, it is clear that, proper fractions are all less than 1.
When a whole number is multiplied by 1, we get the number itself.
So logically, when we multiply an whole number with fractions less than 1, then the resulting number will always be less than the whole number.
For example, consider 3 × [tex]\frac{3}{4}[/tex]
Multiplication of fraction is by multiplying numerators together and the denominators together.
3 × [tex]\frac{3}{4}[/tex] = [tex]\frac{3}{1}[/tex] × [tex]\frac{3}{4}[/tex] = [tex]\frac{9}{4}[/tex] = 2.25 < 3
Hence the multiplication of a whole number with a proper fraction is always less than the whole number.
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There are 2.5 times the amount of girls in a class than boys. If there are 35 students in the class, calculate the number of girls in the class.
Answer:
25
Step-by-step explanation:
Let's assume the number of boys in the class is "x". Then, according to the problem, the number of girls in the class is 2.5 times the number of boys, which can be expressed as:
number of girls = 2.5 * number of boys
We also know that the total number of students in the class is 35. Therefore, we can write an equation in terms of "x" as follows:
x + 2.5x = 35
Simplifying the above equation, we get:
3.5x = 35
Dividing both sides by 3.5, we get:
x = 10
This means that there are 10 boys in the class. To find the number of girls, we can use the equation we derived earlier:
number of girls = 2.5 * number of boys
number of girls = 2.5 * 10 = 25
Therefore, there are 25 girls in the class.
The question is in image form. It's about geometry pls help me to solve this question
The area of the shaded region is 104 m².
What is a Triangle ?
The intersection of the two sides of a triangle's three sides, which are known as the vertex, is a sort of polygon. Between two sides, an angle forms. This is among geometry's crucial components.
We know that Area of a triangle = 1/2 × base × height
The area of Big triangle = 1/2 × 30 × 13
= 15 × 13
= 195 m²
Area of Small triangle = 1/2 × 14 × 13
= 91 m²
So, Area of the shaded region
= Area of big triangle - Area of small triangle
= 195 - 91
= 104 m²
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The measures of the exterior angles of a hexagon are x°, 4x°, 5x°, 7x°, 9x°, and 10x°. Find the measure of the largest exterior angle.
The measure of the largest exterior angle of the polygon in discuss is; 100°.
What is the measure of the largest exterior angle of the polygon?It follows from the task content that the measure of the largest exterior angle of the polygon be determined.
Since the sum of all exterior angles of a polygon is equal to 360°;
x° + 4x° + 5x° + 7x° + 9x° + 10x° = 360°
36x° = 360°
x = 10
Therefore, it follows that the measure of the largest exterior angle is; 10x° = 10(10)° = 100°.
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write 1/81 * 27^5 as a power of 3
Answer:
Below
Step-by-step explanation:
1/81 * 27^5 =
1/(3^4) * (3^3)^5 =
3^-4 * 3^(3 *5)
3^-4 * 3^15
3^(-4 + 15)
3^11
The expression 1/81 * 27⁵ can be written as a power of 3 as 3¹¹.
What are Exponents?Exponents are the method of writing numbers, especially large numbers, in terms of a base and an exponent, which is written as the power of base.
Given expression is,
1/81 × 27⁵
We have to write the expression as a power of 3.
Write each term as a power of 3.
81 can be written as 3⁴.
27 can be written as 3³.
1/81 × 27⁵ = (1 / 3⁴) × (3³)⁵
We can use two rules here, 1/aᵇ = a⁻ᵇ and (xᵃ)ᵇ = xᵃᵇ.
1/81 × 27⁵ = 3⁻⁴ × 3¹⁵
Multiplication rule of exponent states that xᵃ × xᵇ = xᵃ⁺ᵇ.
1/81 × 27⁵ = 3⁻⁴⁺¹⁵
= 3¹¹
Hence the expression can be written as 3¹¹.
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Measure the diameter of the tin in mm and write down the real diameter in mm
The required real diameter of the tin is 250 mm.
What is the diameter?Diameter is a measurement of the length of a straight line that passes through the center of a circular object, such as a circle or a sphere. It is the distance between two points on the object's edge that are furthest from each other and that pass through the center of the object.
Here,
If the diameter of the tin in the picture is 10 cm, then the actual diameter of the tin can be calculated as:
Actual Diameter = 2.5 x Picture Diameter
Actual Diameter = 2.5 x 10 cm
Actual Diameter = 25 cm
To convert the actual diameter to millimeters (mm), we can multiply by 10:
Actual Diameter in mm = Actual Diameter x 10
Actual Diameter in mm = 25 cm x 10
Actual Diameter in mm = 250 mm
Therefore, the real diameter of the tin is 250 mm.
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Answer:
⁷
Step-by-step explanation:
questions 1 and
Find the nth term rule for the sequence 3, 4, 7, 12, 19
Answer:
Find the ninth term rule for the sequence 3, 4, 7, 12, 19
28, 39, 52, 67
(the term number) nth term is +increasing odd numbers (+1, +3, +5, +7, etc)
Step-by-step explanation:
You're welcome.
What is the value of n in the figure?
Answer:
n = 14
Step-by-step explanation:
Theorem:
In a triangle, the measure of an exterior angle equals the sum of the measures of the two remote interior angles.
12n - 8 = 8n - 4 + 52
4n = 56
n = 14
Suppose you are designing short walls to go across the front of flower beds. The walls will be built with small concrete blocks in the design shown here. Each block is 1-foot long by 1-foot wide by 1-foot high. Only whole blocks can be used for the walls.
What is not a symbolic representation of the relationship between the number of blocks in each wall, b, and the length of each wall in feet, f?
Answer:
f/ 3 4 5 6
b/ 8 10 12 14
Step-by-step explanation:
the 4th wall has 6×3-4=14
so the relationship is
f/ 3 4 5 6
b/ 8 10 12 14
I am unsure how to do this, please help!
The original number in the given question solved by algebra is 39/7.
What is Algebra?
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
The number is divided 5 times by 7 more than that number.
Let the number be x
Then,
x+7/5x = 8
x+7=40x
7=39x
x=39/7
Therefore, by algebra the answer will be 39/7.
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Find the standard form of the eclipse with end points of Major Axis (2,2) & (8,2) and minor axis (5,3) & (5,1)
Answer:
Step-by-step explanation:
Pour trouver la forme standard de l'équation d'une ellipse à partir des extrémités des grands axes et des petits axes, nous pouvons utiliser les formules suivantes:
Le centre de l'ellipse est le point (h, k), où h est la moyenne des coordonnées x des extrémités des grands axes et k est la moyenne des coordonnées y des extrémités des petits axes. Donc,
h = (2 + 8) / 2 = 5
k = (3 + 1) / 2 = 2
Donc, le centre de l'ellipse est (5, 2).
La distance a est la moitié de la longueur du grand axe, donc
a = (8 - 2) / 2 = 3
La distance b est la moitié de la longueur du petit axe, donc
b = (3 - 1) / 2 = 1
Maintenant, nous pouvons utiliser ces valeurs pour écrire l'équation de l'ellipse en forme standard:
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
En substituant les valeurs trouvées précédemment, nous avons:
(x - 5)^2 / 3^2 + (y - 2)^2 / 1^2 = 1
Ce qui est la forme standard de l'équation de l'ellipse.
This is about Linear equations, please help.
Answer:
Step-by-step explanation:
line a is 5ft
Sno-Cone at the carnival has the shape of a hemisphere on top of an inverted cone. What is the volume of the sno-cone if its radius is 5 cm and the height of the conical portion is 9.6 cm?
The volume of the sno-cone is approximately 774.9 cm³.
Describe Volume of hemisphere?The volume of a hemisphere is the amount of space that a hemisphere (a half-sphere) takes up. A hemisphere is a three-dimensional shape that is half of a sphere, and it is created by cutting a sphere in half along a plane that passes through the center of the sphere.
The formula for the volume of a hemisphere is given by:
V = (2/3)πr³
Where V is the volume of the hemisphere, π is the mathematical constant pi (approximately 3.14), and r is the radius of the hemisphere.
To use this formula, you simply need to know the radius of the hemisphere. To find the radius, measure the distance from the center of the sphere to the edge of the hemisphere. Then, plug this value into the formula and simplify to find the volume.
The volume of the sno-cone can be calculated by finding the volume of the hemisphere and the volume of the cone separately and then adding them together.
Volume of the hemisphere = (2/3)πr³
where r is the radius of the hemisphere
Given r = 5 cm, the volume of the hemisphere is
(2/3)π(5)³ = (500/3)π ≈ 523.6 cm³
Volume of the cone = (1/3)πr²h
Given r = 5 cm and h = 9.6 cm, the volume of the cone is
(1/3)π(5)²(9.6) ≈ 251.3 cm³
The volume of the sno-cone is the sum of the volume of the hemisphere and the volume of the cone, which is
523.6 + 251.3 ≈ 774.9 cm³
Therefore, the volume of the sno-cone is approximately 774.9 cm³.
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Find the general solution of the differential equation.
6y (4) +83y" +100y = 0
y(x) =
Refer to the attached image.
7. Charles is designing a backsplash with a pattern of
diamond-shaped tiles as shown. If m /1 = 65°,
find m2. Explain your reasoning.
The measure of angle m2 is 65°, the reason is interior opposite angles.
What is the sum of all the exterior angles of a regular polygon?For a regular polygon of any number of sides, the sum of its exterior angle is 360° (full angle).
Exterior angle is an measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended. Also, due to polygon being regular, let it be having 'n' sides, all the exterior angles are of same measure, and therefore, their measure is (360/n)°.
We are given that;
The measure of angle 1= 65°
Now,
By interior opposite angle property
Angle 1 = Angle 2
Substituting the value of angle 1
65°= angle 2
Therefore, by interior angle property the answer will be 65°.
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g two small planes start from the same point and fly in opposite directions. the first plane is flying 50 mph slower than the second plane. in 2 h, the planes are 600 mi apart. find the rate of each plane. 600 mi two planes start from the same point and fly in opposite directions. there are six hundred miles between the two planes. slower plane mph faster plane mph
The speed of the slower plane is 125 mph and the speed of the faster plane is 175 mph.
How to calculate the speedLet's call the speed of the slower plane "x" and the speed of the faster plane "x+50".
When two planes are flying in opposite directions, the distance between them increases at a rate equal to the sum of their speeds. So, we can set up the following equation:
2(x + x+50) = 600
Simplifying this equation, we get:
2(2x+50) = 600
4x + 100 = 600
4x = 500
Divide
x = 125
Therefore, the speed of the slower plane is 125 mph and the speed of the faster plane is x+50 = 175 mph.
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A certain market has both an express checkout line and a superexpress checkout line. Let X1 denote the number of customers in line at the express checkout at a particular time of day, and let X2 denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X1 and X2 is as given in the accompanying table. (a) What is P(X1 = 1, X2 = 1), that is, the probability that there is exactly one customer in each line? P(X1 = 1, X2 = 1) = (b) What is P(X1 = X2), that is, the probability that the numbers of customers in the two lines are identical? P(X1 = X2) = (c) Let A denote the event that there are at least two more customers In one line than in the other line. Express A in terms of X1 and X2. Calculate the probability of this event. P(A) = (d) What is the probability that the total number of customers in the two lines is exactly four? At least four? P(exactly four) = P(at least four) =
Required probability P(A)= 0.46. The problem here is a Joint Probability Distribution exercise. See the answers and explanation below.
What is Joint Probability Distribution?Joint Probability Distribution can be simply described as the likelihood of two events (variables) occurring at the same time. These two events are commonly referred to as event A and event B, and their formal names are: p (A and B).
here, we have,
What is the solution to the questions?
A - The likelihood that each line has exactly one customer: The probability relates to the associated row and column.
X₁ = 1 and X₂ = 1
P (X₁ = 1, X₂ =1) = 0.15
B - The sum of the diagonal elements of the joint pmf indicates the likelihood that the amount of clients in both lines is the same:
P(X₁ = X₂) =) p(0,0) + p (1,1) + p(2, 2) + p(3,3
= 0.08 + 0.15 + 0.10 + 0.07
= 0.4
Hence,
C - Let A represent the situation in which there are at least two more clients than the other line: The following are examples of variable combinations:
X₂ =0 ; X₁ = 2,3, 4
X₂ =1 ; X₁ = 3, 4
X₂ =2 ; X₁ = 0, 4
X₂ =3 ; X₁ = 0, 1
The probability is thus computed as follows:
P (A) = p(1, 3) + p (2,2) + p(2, 3) + p(3,1) + p(3,2) + p(3,3) + p(4,0) + p(4,1) + p(4,2) + p(4,3)
= 0.04 + 0.10 +0.06 + 0.03 + 0.04+ 0.07 + 0.00 + 0.01 + 0.05 + 0.06
= 0.46
Hence , P(A)= 0.46
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