The shortest possible distance between Alan and Ryan is 11,250 miles, and the longest possible distance is 12,000 miles
What is distance?Distance is a numerical measurement of how far apart two objects or points are. It is a scalar quantity, meaning that it has magnitude but no direction. Distance is usually measured in units such as meters, kilometers, miles, or feet, depending on the system of measurement used.
What is sound?Sound is a type of physical energy that is produced by vibrating objects and travels through a medium, such as air, water, or solids, as a series of pressure waves. When an object vibrates, it creates a disturbance in the surrounding medium that causes molecules to move back and forth, creating areas of high and low pressure that propagate outward from the source of the sound.
In the given question,
Let d be the distance between Alan and Ryan in miles. Then, the time it takes for sound to travel this distance is given by d/768. Therefore, we have:
d/768 = 45 - 30 = 15
Solving for d, we get:
d = 15 x 768 = 11520
So the distance between Alan and Ryan is 11520 miles.
If we take the lower bound of 750 miles per hour, we can calculate the minimum distance between Alan and Ryan as follows:
d/750 = 15
d = 15 x 750 = 11250
Therefore, the minimum distance between Alan and Ryan is 11250 miles.
If we take the upper bound of 800 miles per hour, we can calculate the maximum distance between Alan and Ryan as follows:
d/800 = 15
d = 15 x 800 = 12000
Therefore, the maximum distance between Alan and Ryan is 12000 miles.
Therefore, the shortest possible distance between Alan and Ryan is 11,250 miles, and the longest possible distance is 12,000 miles.
To know more about about Speed,distance and time, visit:
https://brainly.com/question/21901071
#SPJ1
if a watch costs $40 and you must pay 6.5% sales tax how much will the tax be ?
Answer:$2.60
Step-by-step explanation:40*0.065
Answer:42.06
Step-by-step explanation:
All the students in the sixth grade either purchased their lunch or brought their lunch from home on Monday.
• 24% of the students purchased their lunch.
• 190 students brought their lunch from home.
How many students are in the sixth grade?
The number of students that are in the sixth grade is given as follows:
250 students.
How to obtain the number of students?The number of students is obtained applying the proportions in the context of the problem.
We know that all students in the sixth grade either purchased their lunch or brought their lunch from home on Monday, and 24% of the students purchased their lunch, hence 76% of the students brought their lunch from home.
190 students brought their lunch from home, which is equivalent to 76% of the number of students, hence the number of students is given as follows:
0.76n = 190
n = 190/0.76
n = 250 students.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Can i get assistance with this?
Answer:
see attached
Step-by-step explanation:
You want the given triangle dilated by a factor of -3 about point A.
DilationTo find the image point corresponding to a pre-image point, multiply the pre-image point's distance from A by the dilation factor. The negative sign means the distance to the image point is measured in the opposite direction.
In the attached figure, the chosen point is 4 units up and 5 units right of A. Its image in the dilated figure is 3·4 = 12 units down, and 3·5 = 15 units left of A.
This same process can be used to locate the other vertices of the triangle's image.
Peter buys 30 apples at R5. 00 each. He sell each apple for R7. 0. How much profit does he makes?
Peter makes a profit of Rs 60.00 by means of buying 30 apples at Rs 5.00 each and selling them at Rs 7.00 every.
Peter buys 30 apples at a value of R5.00 every, for a total price of R150.00. He then sells every apple at R7.00, for a complete sales of R210.00.
To calculate his earnings, we subtract his price from his revenue.
profit = revenue - cost
In this case, his income is R210.00 - R150.00 = R60.00. this means that Peter makes a profit of R60.00 from selling 30 apples.
Consequently, Peter makes a profit of Rs 60.00 by means of buying 30 apples at Rs 5.00 each and selling them at Rs 7.00 every.
The earnings made with the aid of Peter is the distinction between the sales generated via the income and the price of buying the apples. with the aid of subtracting the cost from the revenue, we are able to see the earnings he has made. This easy calculation can be used by organizations to decide their earnings and to make choices approximately pricing and stock.
Learn more about Profit formula:-
https://brainly.com/question/29785281
#SPJ4
MAthematics pls help
Answer:
x = 4
Step-by-step explanation:
6x + 21 = 5x + 25
Then, subtract 5x from both sides:
x + 21 = 25
Then, subtract 21 from both sides.
x = 4
Therefore, x is equal to 4 degrees
when calculating confidence intervals in this class the product of a constant times a margin of error is added and subtracted to what value to obtain the ci range? group of answer choices mean standard deviation alpha median
The confidence interval is calculated by adding and subtracting the product of a constant (usually 1.96), the margin of error, and the mean.
The constant times the margin of error is added and subtracted from the sample mean to obtain the confidence interval range.
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.
A low standard deviation means data are clustered around the mean, and a high standard deviation indicates data are more spread out.
The constant is determined by the confidence level of your analysis (typically 95%) and the margin of error is determined by the standard deviation and the size of your sample.
To learn more about “standard deviation” refer to the https://brainly.com/question/475676
#SPJ11
HELP!!
Write a quadratic equation in standard form that has solutions of -3 and -4.
Answer:
If a quadratic equation has solutions of -3 and -4, then it can be written in factored form as:
(x + 3)(x + 4) = 0
To convert this to standard form, we can multiply out the factors:
x^2 + 7x + 12 = 0
Therefore, the quadratic equation in standard form that has solutions of -3 and -4 is:
x^2 + 7x + 12 = 0
Please simplify the following expression while performing the given operation.
(-3+1)+(-4-i)
Answer:
To simplify the expression (-3+1)+(-4-i), we can perform the addition operation within the parentheses first:
(-3+1)+(-4-i) = -2 + (-4-i)
Next, we can simplify the addition of -2 and -4 by adding their numerical values:
-2 + (-4-i) = -6 - i
Therefore, (-3+1)+(-4-i) simplifies to -6-i.
Step-by-step explanation:
1(1/2)= 1 1/2 draw number line and represent this
|-----|-----|-----|----|-----|-----|--│--|-----|----|-----|
-5 -4 -3 -2 -1 0 1 │ 2 3 4 5
1 1/2
On this number line, the tick mark labeled "1 1/2" is located halfway between the integer values of 1 and 2.
To represent the number 1 1/2 on a number line, we need to draw a horizontal line with evenly spaced tick marks. Each tick mark represents a specific value on the number line. Since 1 1/2 is a mixed number that includes a whole number (1) and a fraction (1/2), we need to locate it between the integer values of 1 and 2. The tick mark for 1 1/2 should be halfway between these two integers, which means it would be located at the midpoint of the line segment that connects the tick marks for 1 and 2. By placing the tick mark for 1 1/2 in the correct position on the number line, we can accurately represent this number visually.
Learn more about the number line: brainly.com/question/16191404
#SPJ4
the radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.6 in/s. at what rate is the volume of the cone changing when the radius is 144 in. and the height is 138 in.?
Answer:
Let's use the formula for the volume of a right circular cone to solve this problem:
V = (1/3)πr^2h
We are given that the radius is increasing at a rate of 1.4 in/s and the height is decreasing at a rate of 2.6 in/s. We want to find the rate at which the volume is changing when the radius is 144 in. and the height is 138 in. In other words, we want to find dV/dt when r = 144 and h = 138.
Using the chain rule of differentiation, we can express the rate of change of the volume as follows:
dV/dt = (dV/dr) (dr/dt) + (dV/dh) (dh/dt)
To find dV/dr and dV/dh, we differentiate the formula for the volume with respect to r and h, respectively:
dV/dr = (2/3)πrh
dV/dh = (1/3)πr^2
Substituting the given values and their rates of change, we have:
dV/dt = (2/3)π(144)(138)(1.4) + (1/3)π(144)^2(-2.6)
dV/dt = 55,742.4 - 1,994,598.4
dV/dt = -1,938,856 in^3/s
Therefore, when the radius is 144 in. and the height is 138 in., the volume of the cone is decreasing at a rate of approximately 1,938,856 cubic inches per second.
Step-by-step explanation:
WILL YOU CRACK THE CODE ? 8 2 One number is correct and well placed One number is correct but wrong place Two numbers are correct but wrong places 3 8 Nothing is correct CODE 8 One number is correct but wrong place
Cracking the code: 8 2One number is correct and well placed One number is correct but in the wrong placeTwo numbers are correct but in the wrong place38Nothing is correctCODE8One number is correct but in the wrong placeCracking the code of this sequence of numbers can be a bit tricky, but let's do it step by step. We are given the following clues about the sequence of numbers:
One number is correct and well placed: Since the sequence of numbers is 8 2, we know that the number 8 is in the first position. So the code is either 8 _ _ _ or _ _ _ 8.One number is correct but in the wrong place: This clue tells us that the number 2 is not in the second position of the code, but it is somewhere else.
Therefore, we know that the code is not 8 2 _ _ or _ _ 2 8.Two numbers are correct but in the wrong places: This clue tells us that the code contains the numbers 3 and 8, but they are in the wrong position. Since the code cannot be 8 2 _ _ or _ _ 2 8, we know that the two correct numbers are not in the last two positions. Therefore, the code must be _ 3 8 _ or _ 8 3 _.Nothing is correct: This clue tells us that the code cannot be 3 8 _, 8 3 _, or _ 3 8 because they all contain at least one correct number. Therefore, the code must be _ _ 3 8 or 3 8 _ _.One number is correct but in the wrong place: This clue tells us that the code cannot be 3 8 _, so it must be 8 3 _. Therefore, the code is 8 3 _ _.I hope this helps you crack the code!
for such more questions on sequence of numbers
https://brainly.com/question/30983233
#SPJ11
The population of a town is given by the equation p = 200,000 3/4t where t is the number of years since the population was first recorded in the year 2010 Fill in the table below.
The population increase according to the given years will be 27500, 23750 and 20833.
What is multiplication?Mathematicians use multiplication to calculate the product of two or more integers. It is a fundamental operation in mathematics that is frequently used in everyday living. When we need to combine sets of similar sizes, we use multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are compounded are referred to as the factors. Repeated adding of the same number is made easier by multiplying the number.
In this question,
p = 200,000 3/4t
When t=0
p=0
When t=1
p= 20000 3/4= 27500
when t=2
p= 20000 3/8 = 23750
When t=3
p= 20000 3/12 = 20833
To know more about multiplication visit
https://brainly.com/question/5992872
#SPJ1
Brittany needed new tires for her truck. She went to the auto shop and bought 4 tires on sale for $85.95 each. The salesman told her that she saved a total of $96.16. If Brittany saved the same amount on each tire, what was the original price of each tire?
The best solution gets brainlist
Answer:
$109.99
Step-by-step explanation:
The original price of each tire is [tex]\[/tex][tex]109.99[/tex]
Solution:Take the amount saved and divide by 4 to find the amount saved on each tire
[tex]96.16\div4 =24.04[/tex]
Add that to the sale price of each tire to find the original price
[tex]85.95+24.04 =109.99[/tex]
Therefore, The original price is $109.99.
If you are given the opposite side and hypotenuse, which trig function should you us?
A. Contangent
B. Cosine
C. Tangent
D. Sine
Answer:D
Step-by-step explanation:
The formula for sine is opposite/hypotenuse. This is the only formula that you can use with the given information.
Tickets for the school play cost $5 for students and $8 for adults. For one performance, 128 tickets were sold for $751. How many tickets were for adults and how many were for students?
91 student tickets were sold and 37 adults tickets were sold whose total 128 tickets were sold.
What is elimination method?The elimination method is a technique for solving a system of linear equations, which involves adding or subtracting the equations to eliminate one of the variables, and then solving for the other variable.
According to question:Let x be the number of student tickets sold, and y be the number of adult tickets sold. Then we can set up a system of two equations to represent the information given:
x + y = 128 (1) (the total number of tickets sold is 128)
5x + 8y = 751 (2) (the total revenue from ticket sales is $751)
We can solve for one of the variables in terms of the other in the first equation:
x = 128 - y
Substituting this expression into the second equation to eliminate x, we get:
5(128 - y) + 8y = 751
Expanding and simplifying:
640 - 5y + 8y = 751
3y = 111
y = 37
Therefore, 37 adult tickets were sold. Substituting this value back into equation (1) to solve for x, we get:
x + 37 = 128
x = 91
Therefore, 91 student tickets were sold.
To know more about elimination visit:
https://brainly.com/question/30284924
#SPJ1
Select the correct solution for the expression. 2 5 + 3 8 2 5 + 3 8 A. 2 5 + 3 8 = 5 13 2 5 + 3 8 = 5 13 B. 16 40 + 15 40 = 31 40 16 40 + 15 40 = 31 40 C. 10 40 + 24 40 = 34 40 10 40 + 24 40 = 34 40 D. 2 5 + 3 8 = 6 40
In response to the stated question, we may state that As a result, the equation proper answer is: B. 16/40 + 15/40 = 31/40
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
We must identify a common denominator for the two fractions in order to solve the formula 2/5 + 3/8. Because 40 is the lowest common multiple of 5 and 8, we can transform both fractions to have a denominator of 40:
2/5 = 16/40
3/8 = 15/40
We can now sum the two fractions:
16/40 + 15/40 = 31/40
As a result, the proper answer is:
B. 16/40 + 15/40 = 31/40
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
if two sides of a square field were increased by five feet, as seen in the diagram, the area of the field would increase by 245 ft2 . find the area of the original square
If increasing the sides of a square field by five feet will increase the area by 245 ft², then the area of the original square is 484 ft².
To find the area of the original square, we can use the following formula:
Area of the original square = x²
where x is the original length of the square field.
Given that the increase in the length and width of the square field is 5 ft, the side length of the new square is (x + 5) ft. Therefore, the area of the new square is (x + 5)² ft².
Given that the area of the new square is 245 ft² more than the area of the smaller square, we can write:
(x + 5)² = 245 + x²
Expanding the left-hand side of the equation and simplifying, we get:
x² + 10x + 25 = 245 + x²
Solving for x, we get:
10x + 25 = 245
x = 22
Plugging x = 22 into the formula, we can find the area of the original square:
Area of the original square = x² = 22² = 484 ft²
Therefore, the area of the original square is 484 ft².
Learn more about area of square here: https://brainly.com/question/25092270
#SPJ11
This was an exceptionally dry year for portions of the southwestern United States. Monthly precipitation in Phoenix, Arizona, was recorded in the table and is modeled by y = –0.04088x2 + 0.4485x + 1.862. In what month did Phoenix receive the lowest amount of precipitation? Month (x) Precipitation January 2.27 inches February ? March ? April ? May ? June ? July ? August ? September 2.59 inches October ? November ? December ? Sketch a graph or fill in the table to answer the question. January February November December
the lowest amount of precipitation occurred in February, with a value of approximately 2.32 inches.
Why it is and how to form a graph?
To find the month with the lowest amount of precipitation, we need to find the minimum value of the quadratic equation y = –0.04088x²2 + 0.4485x + 1.862.
Using calculus, we can find the minimum point of the quadratic function by taking its derivative and setting it equal to zero:
y' = -0.08176x + 0.4485
0 = -0.08176x + 0.4485
x = 5.484
This means that the minimum value of the function occurs at x = 5.484. Since x represents the month number (with January being 1), we can conclude that the month with the lowest amount of precipitation is February (the second month in the table).
To verify this, we can plug in x = 2 into the quadratic equation:
y = –0.04088(2)²2 + 0.4485(2) + 1.862
y = 2.31752
Therefore, the lowest amount of precipitation occurred in February, with a value of approximately 2.32 inches.
To graph the function, we can plot the points given in the table and connect them with a smooth curve. Here is a completed table with the missing values:
Month (x) Precipitation
January 1 2.27 inches
February 2 2.32 inches
March 3 2.57 inches
April 4 2.94 inches
May 5 3.43 inches
June 6 3.94 inches
July 7 2.72 inches
August 8 2.86 inches
September 9 2.59 inches
October 10 2.03 inches
November 11 1.46 inches
December 12 1.03 inches
To know more about Calculus visit:
https://brainly.com/question/29448610
#SPJ1
Answer:
D: December
The given model for precipitation in Phoenix, Arizona is y = –0.04088x2 + 0.4485x + 1.862, where x is the month number (1 for January, 2 for February, and so on) and y is the precipitation in inches. We can use this model to fill in the missing values in the table:
| Month (x) | Precipitation |
|-----------|---------------|
| January | 2.27 inches |
| February | 2.27 inches |
| March | 2.24 inches |
| April | 2.18 inches |
| May | 2.09 inches |
| June | 1.98 inches |
| July | 1.84 inches |
| August | 1.68 inches |
| September | 2.59 inches |
| October | 1.50 inches |
| November | 1.30 inches |
| December | 1.08 inches |
According to the table, Phoenix received the lowest amount of precipitation in **December** with **1.08 inches** of precipitation, so the correct answer is **D. December**.
Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.x2+y2=100a) Find dy/dt when x=6, y=8 given that dx/dt=4.b) Find dx/dt when x=8, y=6 given that dy/dt=-2.
a) When x = 6 and y = 8, and dx/dt = 4, the value of dy/dt is -3.
Using implicit differentiation, we have:
2x(dx/dt) + 2y(dy/dt) = 0
Solving for dy/dt, we get:
dy/dt = -(x/y)(dx/dt)
Substituting x = 6, y = 8, and dx/dt = 4, we get:
dy/dt = -(6/8)(4) = -3
Therefore, when x = 6 and y = 8, and dx/dt = 4, the value of dy/dt is -3.
b) Using implicit differentiation again, we have:
2x(dx/dt) + 2y(dy/dt) = 0
Solving for dx/dt, we get:
dx/dt = -(y/x)(dy/dt)
Substituting x = 8, y = 6, and dy/dt = -2, we get:
dx/dt = -(6/8)(-2) = 1.5
Therefore, when x = 8 and y = 6, and dy/dt = -2, the value of dx/dt is 1.5.
To find the values of dy/dt and dx/dt, we used implicit differentiation, which is a technique used to find the derivative of an equation that is not expressed in the form y = f(x).
In this case, we had the equation x^2 + y^2 = 100, and we differentiated both sides of the equation with respect to t. Then, we solved for the required derivative using the given values of x, y, and the other derivative.
For more questions like Function click the link below:
https://brainly.com/question/12431044
#SPJ11
Find the value of x.
Answer:
x=1.9
Step-by-step explanation:
[tex]\frac{x}{4.6} =\frac{4.6}{11}[/tex]
[tex]11x=21.16[/tex]
[tex]X=1.9[/tex]
Sarun is thrice as old as his sister Anita. If five years is subtracted from Anita’s age and seven years added to Sarun’s age , then
Sarun will be five times Anita’s age. How old were they three years ago?
Answer:
Anita is 11 years old and sarun 55 years old( not so sure about this answer... what do you think)
Step-by-step explanation:
let Anita's age be x
and sarun's age be 3x
if, x-5 = 3x+7
3x+7 = 5(x-5)
3x+7=5x-25
32=2x
x=16
their ages 3 years ago,
Anita= 16-5=11yrs
sarun= 3*16+7 = 55yrs
Shade in the regions represented by the inequalities
Answer:
Step-by-step explanation:
see diagram
Suppose that s is the position function of an object, given as s(t) = 2t - 7. We compute the instantaneous velocity of the object at t = 6 as follows. Use exact values. First we compute and simplify (6 +h). s(6 + h) = Then we compute and simplify the average velocity of the object between t = 6 and t = 6 + h. 8(6+h) - s(6) h = Rationalize the numerator in the average velocity. (If it applies, simplify again.) $(6 + h) - $(6) h The instantaneous velocity of the object att = 6 is the limit of the average velocity as h approaches zero. s(6 + h) – $(6) v(6) lim h -0
The instantaneous velocity of the object at t = 6 is 2.
Suppose that s is the position function of an object, given as s(t) = 2t - 7. We compute the instantaneous velocity of the object at t = 6 as follows. Use exact values. First we compute and simplify (6 + h). s(6 + h) = 2(6 + h) - 7 = 12 + 2h - 7 = 2h + 5Then we compute and simplify the average velocity of the object between t = 6 and t = 6 + h.8(6+h) - s(6) h = 8(6 + h) - (2(6) - 7) h= 8h + 56
Then, to rationalize the numerator in the average velocity. (If it applies, simplify again.)$(6 + h) - $(6) h(h(h) + 56)/(h(h)) = (8h + 56)/h The instantaneous velocity of the object att = 6 is the limit of the average velocity as h approaches zero.s(6 + h) – $(6) v(6) lim h -0s(6 + h) – s(6) v(6) lim h -0Using the above calculation, we get:s(6 + h) – s(6) / h lim h -0s(6 + h) = 2(6 + h) - 7 = 2h + 5So,s(6 + h) – s(6) / h lim h -0(2h + 5 - (2(6) - 7)) / h= (2h + 5 - 5) / h = (2h / h) = 2
Therefore, the instantaneous velocity of the object at t = 6 is 2.
Learn more about Instantaneous velocity
brainly.com/question/28837697
#SPJ11
what is the z-score for the 75th percentile of the standard normal distribution is: 0.67 1.645 1.28 -0.67 -1.28
The z-score for the 75th percentile of the standard normal distribution is given by 0.67 that is option A.
The most significant continuous probability distribution is the Normal Distribution, often known as the Gaussian Distribution. It is also known as a bell curve. The normal distribution represents a large number of random variables either nearly or exactly.
I found one that shows the following:
Z value Table entry
0.67 0.7486
0.68 0.7517
As a result, the Z value for 0.75 is between 0.67 and 0.68.
Interpolation yields the z value of 0.6745.
If you have a TI-84 calculator, you may calculate the z value as follows:
VARS - 2nd (this will show the DISTR menu)
To select invNorm, press 3.
Enter the value for the area/table (0.75)
If you press enter, it will return the z value.
Learn more about Normal distribution:
https://brainly.com/question/28000192
#SPJ4
Complete question:
what is the z-score for the 75th percentile of the standard normal distribution is:
0.67 1.645 1.28 -0.67 -1.28Below is a list of all possible outcomes in the experiment of rolling two die. 1.2 1,3 14 15 1,6 21 22 23 24 25 2,6 34B2 33 3,4 3 5 3.6 41 4 2 43 4,4 4 5 4,6 5 52 33 5 4 5,5 56 6,1 6,2 6.3 6 4 6,5 6.6 Determine the following probabilities. Write your answers as reduced fractions_ P(sum is odd) P(sum is 5) P(sum is 7) = P(sum is 7 and at least one of the die is a 1) = 18 P(sum is 7 or at least one of the die is 1) = 36
Thus, the following outcomes satisfy the condition:1, 61, 11, 12, 21, 13, 31, 14, 41, 15, 52, 25, 34, and 43Therefore, the probability of the sum being 7 or at least one die being 1 is:P(sum is 7 or at least one die is 1) = 15/36 = 5/12
Hence, P(sum is odd) = 7/36, P(sum is 5) = 1/9, P(sum is 7) = 1/6, P(sum is 7 and at least one die is 1) = 5/18, and P(sum is 7 or at least one die is 1) = 5/12.
In the given experiment of rolling two dice, the following probabilities are to be determined:
P(sum is odd), P(sum is 5), P(sum is 7), P(sum is 7 and at least one of the die is 1), and P(sum is 7 or at least one of the die is 1).The sum of two dice is odd if one die has an odd number and the other has an even number. The possibilities of odd numbers are 1, 3, and 5, while the possibilities of even numbers are 2, 4, and 6. Therefore, the following outcomes satisfy the condition:
1, 22, 24, 36, 42, 44, and 66Thus, the probability of the sum being odd is: P(sum is odd) = 7/36The sum of two dice is 5 if one die has 1 and the other has 4, or one die has 2 and the other has 3. Thus, the following outcomes satisfy the condition:1, 42, 3Therefore, the probability of the sum being 5 is: P(sum is 5) = 4/36 = 1/9The sum of two dice is 7 if the dice show 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, or 6 and 1.
Thus, the following outcomes satisfy the condition:1, 63, 54, 45, 36, and 2Therefore, the probability of the sum being 7 is: P(sum is 7) = 6/36 = 1/6The sum of two dice is 7 and at least one die is 1 if the dice show 1 and 6, 6 and 1, 1 and 1, 1 and 2, 2 and 1, 1 and 3, 3 and 1, 1 and 4, 4 and 1, or 1 and 5. Thus, the following outcomes satisfy the condition:1, 61, 11, 12, 21, 13, 31, 14, 41, and 15
Therefore, the probability of the sum being 7 and at least one die being 1 is:P(sum is 7 and at least one die is 1) = 10/36 = 5/18The sum of two dice is 7 or at least one die is 1 if the dice show 1 and 6, 6 and 1, 1 and 1, 1 and 2, 2 and 1, 1 and 3, 3 and 1, 1 and 4, 4 and 1, 1 and 5, 2 and 5, 5 and 2, 3 and 4, or 4 and 3.
for such more questions on probabilities
https://brainly.com/question/13604758
#SPJ11
The trip from Winston to Carver takes 8 min longer during rush hour, when the average speed is 75 km/h, than in off-peak hours, when the average speed is 90 km/h. Find the distance of between the two towns
The trip from Winston to Carver takes 8 min longer during rush hour, when the average speed is 75 km/h, than in off-peak hours when the average speed is 90 km/h. the distance between the two towns is 60 km.
Considering the distance between the Winston and carver be "d", since here we got that during off-peak hours, the average speed is 90 km/h. so by using the formula of distance which is distance =speed x time=> d = 90t.
Whereas in rush hour, the average speed is 75 km/h, we also know that the trip takes 8 minutes longer during rush hour. calling the time it takes to travel during rush hour "t+8/60"( since 8 minutes is 8/60 of an hour). Now using the same formula as before:
d = 75(t + 8/60), since here we have two equations for d we can equal them to each other then we get :
90t = 75(t + 8/60)
=>90t = 75t + 10
=>90t-75t=10
=>t = 2/3
Since during the off-peak hours, it takes 2/3 hours or 40 minutes to travel the distance between Winston and carver. now using either equation to find the distance we get
d = 90t = 90(2/3) = 60 km or d = 75(t + 8/60) = 75(2/3 + 8/60) = 60 km
To know more about speed refer to the link brainly.com/question/17661499
#SPJ4
the height of the akashi kaikyo bridge from the bride deck to the top of the center support is 297 meters and the distance from the center of the bridge to the connection of the suspension cable is 995 meters. (see picture below.) i would like you to find the angle of depression from the top of the center support to the end of the support cable.
The angle of depression from the top of the center support to the end of the support cable is approximately 16.59 degrees.
The angle of depression from the top of the center support to the end of the support cable can be found using trigonometry. Let's call this angle "x". Using the given information, we can form a right triangle with the center support, the end of the support cable, and a point directly below the center support on the ground.
The height of the center support, 297 meters, is the opposite side of the right triangle, while the distance from the center of the bridge to the connection of the suspension cable, 995 meters, is the adjacent side. Using the tangent function, we can calculate the angle of depression as follows:
tan(x) = opposite/adjacent
tan(x) = 297/995
x = tan^-1(297/995)
Using a calculator, we can find that x is approximately 16.59 degrees. Therefore, the angle of depression from the top of the center support to the end of the support cable is approximately 16.59 degrees.
For more questions like Angle click the link below:
https://brainly.com/question/13514202
#SPJ11
Which exspression is equivalent to 9(4/3m-5-2/3m+2)
By answering the presented question, we may conclude that Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
To simplify the expression,
[tex]a(b+c) = ab + ac\\9(4/3m-5-2/3m+2) = 9(4/3m - 2/3m - 5 + 2)\\= 9(2/3m - 3)\\= 6m - 27[/tex]
Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.
To know more about expression visit :-
https://brainly.com/question/14083225
#SPJ1
What is the decimal of 2 75/100
2.75 is the decimal of fraction .
In math, what is a fraction?
The amount is represented mathematically as a quotient, where the numerator and denominator are split. In a simple fraction, both are integers. A complicated fraction includes a fraction, either in the denominator or the numerator.
The numerator and denominator must be smaller in a proper fraction. A fraction is a number that is a component of a whole. A whole is appraised by dissecting it into many sections. Half of a whole number or item, for instance, is represented by the number 12.
= [tex]2\frac{75}{100}[/tex]
= [tex]2\frac{3}{4}[/tex]
= 11/4
= 2.75
Learn more about fraction
brainly.com/question/10354322
#SPJ1
Education Planning For the past 15 years, an employee of a large corporation has been investing in an employee sponsored educational savings plan. The employee has invested $8,000 dollars per year. Treat the investment as a continuous stream with interest paid at a rate of 4.2% compounded continuously.
a. What is the present value of the investment?
b. How much money would have had to be invested 15 years ago and compounded at 4.2% compounded continuously to grow to the amount found in part a?
The amount that would have had to be invested 15 years ago and compounded at 4.2% compounded continuously to grow to the present value is $37,537.19.
The investment can be treated as a continuous stream with the interest paid at a rate of 4.2% compounded continuously.The present value of the investment can be calculated using the formula:P = C/e^(rt)Where,P = Present ValueC = Cash Flowsr = Interest Rate Per Periodt = Number of Periodse = Euler’s numberThe given values are as follows:C = $8,000 per yearr = 4.2% compounded continuously for 15 years.
C = $8,000e = 2.71828t = 15 yearsNow, we need to calculate the present value using the above formula.P = 8000/e^(0.042 x 15) = $82,273.24.The formula to calculate the amount that would have been invested 15 years ago is:A = P x e^(rt)Where,A = Future Value of the investmentP = Present Value of the investmentr = Rate of Interest Per Periodt = Number of Periodse = Euler’s numberThe present value of the investment is $82,273.24.
The rate of interest is 4.2% compounded continuously.t = 15 yearsNow, we need to calculate the amount that would have been invested 15 years ago.A = 82,273.24 x e^(0.042 x 15) = $37,537.19
Learn more about Invested
brainly.com/question/15105766
#SPJ11
