Using the formula of average distance = total distance traveled / total time taken, we find that Phaelon had the fastest average speed of 10.86 mi/hr.
Explanation:To find out who had the fastest average speed, we'll need to calculate the average speed for each person. We can do this by dividing the total distance traveled by the total time taken.
Serra's average speed: 15 mi / 1.5 hr = 10 mi/hr
Phaelon's average speed: 38 mi / 3.5 hr = 10.86 mi/hr
Justice's average speed: 22 mi / 2.25 hr = 9.78 mi/hr
So, by comparing these speeds, we can conclude that Phaelon had the fastest average speed of 10.86 mi/hr.
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PLZ HELP
Lakita has 65 water bottles for the 5K race participants. In addition, she is considering buying boxes of water bottles that have 16 water bottles each. All of the boxes cost the same. Lakita can buy up to 5 boxes of water bottles given the amount of money she has. Let x represents the number of boxes of water bottles Lakita buys. Write a function rule to describe how many water bottles Lakita will have based on the number of boxes she buys. Find a reasonable range for the function.
A - f(x) = 65x + 16
{145}
B - f(x) = 16x + 65
{65, 81, 97, 113, 129, 145}
C - f(x) = 65x + 16
{81, 97, 113, 129, 145}
D - f(x) = 16x + 65
{65, 81, 97, 113, 129}
The function rule representing the total number of bottles Lakita will have based on the number of boxes she buys would be f(x) = 16x + 65. The reasonable range for this function, considering she can buy up to 5 boxes, is {65, 81, 97, 113, 129, 145}.
Explanation:In this problem, we want to find out the total number of water bottles Lakita will have based on the number of boxes she buys. We know that Lakita already has 65 water bottles and each box she buys contains 16 water bottles. The function rule to represent this would be: f(x) = 16x + 65. Here, x is the number of boxes she buys.
The range of the function is the possible values that f(x) can have based on the scenario. Since Lakita can buy up to 5 boxes, the range would be the number of bottles she will have if she buys 0 through 5 boxes, which is: {65, 81, 97, 113, 129, 145}.
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The function rule to describe the number of water bottles is f(x) = 16x + 65. The range for the function is {65, 81, 97, 113, 129, 145}, which represents the total water bottles counts depending on the number of boxes Lakita buys.
Explanation:The function that will describe how many water bottles Lakita will have based on the number of boxes she buys is f(x) = 16x + 65. To explain, x represents the number of boxes, each with 16 water bottles (16x), and the 65 represents the water bottles she initially has. The total number of water bottles is the sum of these two amounts.
A reasonable range for the function is the set of all possible total water bottles counts, depending on the number of boxes bought. As she can buy up to 5 boxes, we substitute values from 0 to 5 into the function to find the range. So the range will be {65, 81, 97, 113, 129, 145}, corresponding to Lakita buying 0, 1, 2, 3, 4, or 5 boxes (respectively).
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When is the sum of two complex numbers a real number? When is the sum of two complex numbers an imaginary number?
The sum of two complex numbers resulting in a real or imaginary number depends on the cancellation of their real or imaginary components upon addition.
When the sum of two complex numbers is a real number: For the sum of two complex numbers to be a real number, their imaginary parts must cancel each other out. This happens when the imaginary parts have equal magnitude but opposite signs, resulting in the cancellation upon addition.
When the sum of two complex numbers is an imaginary number: The sum of two complex numbers is an imaginary number when the real parts cancel each other out. This occurs when the real parts have equal magnitude but opposite signs, leading to the elimination of the real components.
Which shows the best path to find the number of centimeters in 1 yard?
To find the number of centimeters in 1 yard, convert yards to feet, then feet to inches, and finally, inches to centimeters. 1 yard is equal to 91.44 centimeters after applying the conversion factors 1 yard = 3 feet, 1 foot = 12 inches, and 1 inch = 2.54 centimeters.
To find the number of centimeters in 1 yard, we need to follow a two-step conversion process. First, we convert yards to feet, knowing that 1 yard equals 3 feet. Then, we convert feet to inches, since we know that 1 foot equals 12 inches. Finally, we convert inches to centimeters, using the conversion factor that 1 inch is equivalent to 2.54 centimeters.
So the path would look like this:
Convert yards to feet: 1 yard = 3 feet.
Convert feet to inches: 1 foot = 12 inches.
Convert inches to centimeters: 1 inch = 2.54 centimeters.
Applying these conversions to 1 yard:
1 yard * 3 feet/yard = 3 feet
3 feet * 12 inches/foot = 36 inches
36 inches * 2.54 centimeters/inch = 91.44 centimeters
Therefore, 1 yard is equivalent to 91.44 centimeters.
Determine the range of this set of data.
89,73,84,91,87,77,94
Solve the inequality 0>-3×-2×.
what is the value of x?
Solve the following for y: 9x − 3y = 18
y = −3x − 6
y = 3x − 6
y = −3x + 6
y = 3x + 6
What is the value of g? 3g + 4 5 = 4g - 8 4?
Answer: g=7
Step-by-step explanation:
ASAP HELP FOR NUMBER 13!!
13a, b, c, and d!!
CORRECT ANSWERS PLS
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dora gets paid an hourly wage, which increases if she works over 40 hours per week. she worked a total of h hours last week, and the number of dollars she got paid was 30 ×40+45 ×(h-40). what does 45 represent in this situation?
A. the number of dollars per hour she got paid for all hours under 40
B. the number of dollars per hour she got paid for all hours over 40
C. the number of hours she worked over 40
D. the total number of hours she worked
When Angela begins her drive, she is 400 mi from home. She drives at an average of 50 mph until she gets home. Graph the situation.
Mitchell has a balance of $1,200 in his first state bank checking account. he deposits a $387.89 pay check, a $437.12 dividend check, and a personal check for $250 into his account. He wants to receive $400 in cash. How much will he gave in his account after the transaction ????
The total present money in his account after all the $400 withdrawals is $1875.01.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Total present money initially = $1200
Deposits check = 387.89 + 437.12 + 250 = $1075.01
Total money after deposit = 1200 + 1075.01 = $2275.01
Money remains after withdrawals of $400
⇒ $2275.01 - $400 = $1875.01.
Hence "The total present money in his account after all the $400 withdrawals is $1875.01".
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A storage tank for propane gas is to be constructed in the shape of a right circular cylinder of altitude 20 feet with a hemisphere attached to each end. determine the radius x so that the resulting volume is 216π ft3.
To determine the radius x of the storage tank, we need to break down the shape into smaller parts. We can set up a cubic equation to find the value of r, and then calculate the radius x.
To determine the radius x of the storage tank, we need to break down the shape into smaller parts. First, let's consider the cylinder. The volume of a cylinder is given by V = πr^2h, where r is the radius and h is the altitude. In this case, the altitude is 20 feet. So, the volume of the cylinder is Vcylinder = πr^2(20).
Next, let's consider the hemispheres attached to each end. The volume of a hemisphere is given by V = (2/3)πr^3. Since there are two hemispheres, the total volume of the hemispheres is Vhemispheres = (2/3)(2)(πr^3) = (4/3)πr^3.
Given that the resulting volume is 216π ft3, we can set up the equation:
216π = Vcylinder + Vhemispheres = πr^2(20) + (4/3)πr^3
Simplifying and rearranging the equation, we get:
3r^3 + 60r^2 - 216 = 0
By solving this cubic equation, we can find the value of r. Once we have the value of r, we can determine the radius x by subtracting the radius of the hemispheres (r) from the total radius of the tank (x+r).
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If a rider stops 15 mile to take a break and Another stops at 25 miles at what distance will they stop at the same time
multiples of 15: 15,30,45,60,75
multiples of 25: 25, 50, 75
they will stop together at 75 miles
The height of a triangle is 4 feet more than four times the length of the base. The area is 24 square feet. Find the base and the height. Show your work and explain the steps you used to find the solution in order to receive full credit.
Tracy deposited $59 into a bank account that earned 3.5% simple interest each year. If no money was deposited into or withdrawn from the account, how much money was in the account after 112 years?
What is the product of the roots of the equation x^3-4x^2+x+6=0?
The product of the roots of the equation x³ - 4x² + x + 6 = 0 will be - 6.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ x³ - 4x² + x + 6 = 0
Now,
We know that;
If u, v, w are the roots of the equation ax³ + bx² + cx + d = 0
Then, The product of roots (uvw) = - d / a
Here, The equation is,
⇒ x³ - 4x² + x + 6 = 0
Let the three roots of the equation = a, b, c
Then, We get;
⇒ a × b × c = (-6) / 1
⇒ abc = - 6
Thus, The product of the roots of the equation x³ - 4x² + x + 6 = 0
will be - 6.
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30 points to who answers this first and will get brainliest answer
In which quadrant of the coordinate graph does point J lie?
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV
An interior decorator bought 12 1/2 yards of material to make drapes. He used 8 2/3 yards on one pair of drapes. How much material does he have left?
List the following numbers from least to greatest -5/3, 7/3, -3/4, 7/5.
How is a rational number that is not an integer different from a rational number that is an integer?
1. ABCD is a trapezoid with midsegment EF. If AB = 12 and CD = 24, what is the length of EF?
2. ABCD is a trapezoid with midsegment EF. If AB = 21 and CD = 35, what is the length of EF?
3. ABCD is a trapezoid with midsegment EF. If AB = 7 and EF = 9, what is the length of CD?
4. ABCD is a trapezoid with midsegment EF. If CD = 32 and EF = 22, what is the length of AB?
5. The length of the midsegment of a trapezoid is the _____ of the length of the two bases.
PLEASE HELP ME, SERIOUS ANSWERS ONLY PLEASE
Answer:
5
Step-by-step explanation:
PLESSE HELP!! this question is super hard. it’s due tomorrow and i’m not understanding.
Which one describes the translation of f(x) to g(x) ?
Answer:
a
Step-by-step explanation:
HELP ASAP 30 POINTS GIVEN
The coordinates of the vertices of quadrilateral JKLM are J(−3, 2), K(4, −1), L(2, −5), and(−5, −2). Drag and drop the choices into each box to correctly complete the sentences.
Answer:
[tex]-\frac{3}{7}[/tex],[tex]2[/tex],[tex]-\frac{3}{7}[/tex],[tex]2[/tex],is,both pairs of opposite sides are parallel
Step-by-step explanation:
Given two points
[tex]A=(a1,a2)[/tex] and
[tex]B=(b1,b2)[/tex]
We define the slope ''m'' between this points as :
[tex]m=\frac{b2-a2}{b1-a1}[/tex] or either
[tex]m=\frac{a2-b2}{a1-b1}[/tex]
The slope between the points J and K is
[tex]m=\frac{-1-2}{4-(-3)}=-\frac{3}{7}[/tex]
The slope between the points L and K is
[tex]m=\frac{-1-(-5)}{4-2}=2[/tex]
The slope between the points M and L is
[tex]m=\frac{-2-(-5)}{-5-2}=-\frac{3}{7}[/tex]
The slope between the points M and J is
[tex]m=\frac{-2-2}{-5-(-3)}=2[/tex]
We find all the slopes between the points.
For the quadrilateral JKLM the side JK is opposite to the side ML and the side KL is opposite to the side JM
The definition of parallelogram is :
A figure with 4 sides in which their opposite sides are parallel.
The side JK is parallel to the side ML because they have the same slope.
The side JM is parallel to the side KL because they have the same slope.
We answer that JKLM is a parallelogram because both pairs of opposite sides are parallel.
if five more than three times x is equal to 32, find the value of x.
it also says to show all work so that would really be appreciated!!
What surprised or impressed Xuanzang on his visit to India? What features of Indian life might seem most strange to a Chines visitor?
Actually what surprised Xuanzang the most was the way how Indians ran things and their way of life because this is completely unlike to Chinese cultures. The strangest thing he found was that how everyone in India practiced Buddhism and how structured it was. Because back in China at that time, Buddhism was still much unorganized and not very popular.
the senior classes at high school A and high school B planned separate trips to the indoor climbing gym. the senior class at high school A rented and filled 13 vans and 5 buses with 353 students. high school b rented and filled 9 vans and 5 buses with 309 students. each van and bus carried the same number of students. find the number of students in each van and in each bus.
(04.07)the balance in two separate bank accounts grows each month at different rates. the growth rates for both accounts are represented by the functions f(x) = 2x and g(x) = 4x 12. in what month is the f(x) balance greater than the g(x) balance?
The balance in two separate bank accounts grows each month at different rates. the growth rates for both accounts are represented by the functions f(x) = 2x and g(x) = 4x 12. in what month is the f(x) balance greater than the g(x) balance?
Answer:
6 months
If growth rates for both accounts are represented by the functions f(x) = 2x and g(x) = 4x 12 thn in 6 months the f(x) balance is greater than the g(x) balance.
What type of financial institution account grows?excessive-yield financial savings accounts stand out from conventional financial savings bills in that they praise you with a better interest rate, permitting your cash to grow even quicker as it sits on your account. The interest charge that these debts provide is noted as APY or annual percentage yield.
What account grows the most cash?fees and minimal balance: CDs tend to pay the very best hobby prices of the 3 varieties of savings bills. They commonly require around $1,000 to open, but there are CDs without a minimum beginning balance requirement. CDs typically don't rate a month-to-month rate.
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A veterinary office takes out a loan to purchase a new set of digital animal scales that costs $12,250. The interest rate is 6.5%, and the total interest paid is $2,388.75. How many years is the loan for?
The loan is for approximately 3 years.
Explanation:To find the number of years for the loan, we can use the formula for simple interest:
Interest = Principal * Rate * Time
Given that the principal is $12,250, the rate is 6.5%, and the total interest paid is $2,388.75, we can rearrange the formula to solve for time:
Time = Interest / (Principal * Rate)
Plugging in the values, we get:
Time = 2,388.75 / (12,250 * 0.065)
Simplifying the expression, we have:
Time ≈ 3 years