the teacher separated her class of twenty-eight students into two groups. One group has 4 more than twice as many students as the other group. How many students are in each group?
Two buses are traveling to a state park. One bus leaves the terminal at 4:00 p.m. and travels at 40 miles per hour. The second bus leaves the terminal at 5:00 p.m. and travels at 60 miles per hour.
How much time passes until the second bus catches up with the first bus?
Final answer:
The second bus catches up with the first bus in 2 hours.
Explanation:
To calculate how much time passes until the second bus catches up with the first bus, we need to find the distance between them when the second bus starts and the relative speed between the two buses.
When the second bus starts, the first bus has already traveled for 1 hour (from 4:00 p.m. to 5:00 p.m.) at a speed of 40 mph. Therefore, the first bus has covered a distance of 40 miles.
The relative speed between the two buses is the difference in their speeds, which is 60 mph - 40 mph = 20 mph.
Using the formula: t = d / v, where t is the time, d is the distance, and v is the speed, we can calculate the time it takes for the second bus to catch up with the first bus:
t = 40 miles / 20 mph = 2 hours.
Therefore, it takes 2 hours for the second bus to catch up with the first bus.
if 1 inch = 2.54 centimeters how many inches is equal to 254 centimeters
At Taft high school 59% of all students participate in after school sports and 23% participate in both after school sports and volunteer activities. What is the probability that a student participates in volunteer activities given that the student participates in after school sports. A. 82% B. 36% C. 59% D. 39%
The gross income of Abelina Bennett is $215 per week. Her deductions are: $15.16, FICA tax; $29.33, income tax; 2% state tax; 1% city tax; and 3% retirement fund. What is her net income?
To calculate Abelina Bennett's net income, subtract her deductions from her gross income. Her net income is $157.61 per week.
Explanation:To calculate Abelina Bennett's net income, we need to subtract her deductions from her gross income. The deductions include FICA tax, income tax, state tax, city tax, and retirement fund.
Step 1: Add up all the deductions:
FICA tax: $15.16
Income tax: $29.33
State tax: 2% of $215 = $4.30
City tax: 1% of $215 = $2.15
Retirement fund: 3% of $215 = $6.45
Step 2: Calculate the total deductions: $15.16 + $29.33 + $4.30 + $2.15 + $6.45 = $57.39
Step 3: Subtract the total deductions from the gross income: $215 - $57.39 = $157.61
Abelina Bennett's net income is $157.61 per week.
what is the common factor of 24a^3c and 3a
find the median of the data set: -66, -48, -52, -42
1) After striking a pair of arcs from each endpoint of a line segment, what is the next step in constructing the segment's perpendicular bisector?
C) Use a straight edge to draw a vertical line between the points where each pair of arcs intersect.
Question 9
If x is a small negative integer and y is a large positive integer, which of the following expressions must be positive?
A x * y
B y − x
C y ÷ x
D x ÷ y
The length of a rectangle is 5 in. more than twice its width. its area is 102 in2. find the length of the rectangle
what number would you add to both sides of x^2-20x=5 to complete the square
Which expression is equivalent to the given expression?
13x – 29x
A.x(29 – 13)
B.13(x + 29)
C.x(13 – 29)
D.13(x – 29)
What is the y-coordinate of the vertex of the parabola that is given by the equation below?x = -2.5(y - 3)2 + 5?
PLEASE HELP!!!!!!!!!!!
Whats the value of x?
4x=5x-12
x=
Let f (x) = 2x - 1, g(x) = 3x, and h(x) = x2 + 1. Compute the following: f (h(x)) and . g (f (x))
If there are 400 people in a room, what is the probability of at least 2 people sharing the same birthday?
The probability of at least 2 people out of 400 sharing the same birthday is almost certain due to the 'birthday paradox', due to there being only 365 days in the year but 400 people in the room.
Explanation:The probability that at least 2 people out of 400 sharing the same birthday is almost certain due to the 'birthday paradox.' This is because there are only 365 days in a year for birthdays, but we have 400 people in the room.
To calculate this probability, we assume that every person is equally likely to be born on any day of the year (ignoring leap years). The first person can have their birthday on any of 365 days. The second person has a 364/365 chance of not having the same birthday as the first. The third person has a 363/365 chance of not sharing a birthday with the first two, and so on. By the time we reach the 366th person, the probability of them not sharing a birthday with anyone else is zero, since all 365 possible birthdays have been taken.
So, the overall probability of at least 2 people sharing a birthday is 1 minus the probability of all 400 people having unique birthdays. When you calculate it with 400 people, the result is almost 1, which indicates that it's nearly certain at least 2 people share a birthday.
Learn more about Birthday Paradox here:https://brainly.com/question/14554791
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Please check my answer!
Hogan needs to rent a car while on vacation. The cost of the vehicle is $21 per day. He gives the office manager $180 up front. If x represents the number of days and y represents the total cost of the rental, which equation will help Hogan determine if he owes the agency money at the end of his trip or if the agency owes him money?
Answer:
[tex]y=21x-180[/tex]
Step-by-step explanation:
The cost of the vehicle is $21 per day. He gives the office manager $180 up front.
The upfront is a type of advance payment that is deducted from the final amount.
Let x represents the number of days and y represents the total cost of the rental.
So, the correct equation here is :
[tex]y=21x-180[/tex]
Which number below best represents a temperature of 59.18 degrees above zero? A. -69.18 B. 69.18 C. 59.18 D. -59.18
Given the system of constraints, name all vertices of the feasible region. Then find the maximum value of the given object function.
If Jessie is 24 years younger than her mother and if the sum of their ages is 84, how old is Jessie?
Do I solve this by equaling both equations to each other?
Find the solution of the initial value problem. dp/dt=5e^t, p(0)=25
The equation is [tex]p = 5e^{t} +20[/tex].
IntegrationIt is a method of summing up parts to find the whole. It is a reverse process of differentiation.
Given
dp/dt=5e^t
To findThe value of p.
How to get the value of p?dp/dt=5e^t is given
[tex]\begin{aligned} \dfrac{dp}{dt} &= e^{t} \\\int dp &= \int {5e^{t} } \, dt \\\int dp &= 5 \int {e^{t} } \, dt \\p &= 5e^{t} +c\\\end{aligned}[/tex]
It is given that at t=0, p will be 25, then
[tex]p = 5e^{t} + c\\c = p - 5e^{t}\\c= 25 - 5e^{0}\\c= 25 - 5 * 1\\c= 20[/tex]
Hence the equation will be [tex]p = 5e^{t} +20[/tex].
Thus, the equation is [tex]p = 5e^{t} +20[/tex].
More about the integration link is given below.
https://brainly.com/question/18651211
On Saturday,miguel biked 36 kilometers in 2 hours. What was his average rate of speed in kilometers per hour?
The average rate of speed of Miguel when he biked on Saturday given the distance and time is 18 kilometers per hour.
What is the average speed?
Average speed is the rate at which an object moves with respect to time. Average speed is determined by dividing total distance travelled by time.
Average speed = total distance / time
36 / 2 = 18 kilometers per hour.
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n2-14n+49 what’s the answer
Which of the following is NOT equivalent to the ratio: 12/4 A.6/2 B. 36/12 C.24/16 D.240/80
please help i will give a brainlist if you get it right
A digital camera memory card is 1/4 full. The card is 2/3 full when 375 more pictures have been taken. How many pictures can the memory card hold?
Final answer:
The memory card can hold a total of 900 pictures.
Explanation:
The question asks us to find the total capacity of the memory card in a digital camera by using the information that it is 1/4 full before 375 pictures are added, and 2/3 full after these pictures are added.
Let's define the total capacity of the memory card as 'x' pictures.
If 1/4 of the card is full, then it contains x/4 pictures.
After adding 375 pictures, the card becomes 2/3 full, which means:
x/4 + 375 = (2/3)x
To solve for x, we need to get all the x's on one side of the equation and the numbers on the other side:
Multiply both sides of the equation by 12 to get rid of the fractions: 12(x/4) + 12(375) = 12(2/3)xSimplify the equation: 3x + 4500 = 8xSubtract 3x from both sides: 4500 = 5xDivide both sides by 5: 900 = xTherefore, the memory card can hold a total of 900 pictures.
Unknown angle measures?
Evaluate the expression 14.3-2×5^2÷5
A sample of 36 is drawn from your population and a sample mean of 86 is computed. is this sample mean in the extreme 5% or the middle 95 %