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?
40t = 60(t-1)
distribute the right side
40t = 60t-60
subtract 60t from each side
-20t =-60
divide both sides by -20
t = -60 / -20 = 3
3 hours
Clara's suitcase weighs 58 1/4 pounds, but the airline's weight limit for suitcases is 50 pounds. How much weight does she need to remove from her suitcase?
Clara needs to remove 8 1/4 pounds from her suitcase to meet the airline's weight limit.
To find out how much weight Clara needs to remove from her suitcase, we subtract the airline's weight limit from the weight of her suitcase.
First, let's convert 58 1/4 pounds to a proper fraction:
[tex]\[ 58 \frac{1}{4} = \frac{58 \times 4 + 1}{4} = \frac{232 + 1}{4} = \frac{233}{4} \][/tex]
Now, let's subtract the airline's weight limit from Clara's suitcase weight:
[tex]\[ \text{Excess weight} = \frac{233}{4} - 50 \][/tex]
To subtract fractions, we need a common denominator:
[tex]\[ \text{Excess weight} = \frac{233}{4} - \frac{200}{4} \][/tex]
[tex]\[ \text{Excess weight} = \frac{233 - 200}{4} \][/tex]
[tex]\[ \text{Excess weight} = \frac{33}{4} \][/tex]
Now, let's convert this back to a mixed number:
[tex]\[ \text{Excess weight} = 8 \frac{1}{4} \text{ pounds} \][/tex]
So, Clara needs to remove 8 1/4 pounds from her suitcase to meet the airline's weight limit.
Consider the expression 3 * 2 ^ 2 < 16 + 5 andalso 100 / 10 * 2 > 15 - 3. which operation is performed second
A summer baseball league is creating teams of 25 players each from a group of 265 players. How many players will be left over after the teams of 25 players are created?
A. 10
B. 11
C. 15
D. 250
what is the quotient of 6/7 and 3/14
Maggie is having the flooring replaced in her kitchen, living room, and master bedroom. The kitchen is getting slate tile. The tile cost $1.73 per-square-foot plus an installation fee per-square-foot. The area of the kitchen is 120 square feet, and the total cost for the flooring with installation comes to $740.40. The living room is getting hand-scraped hardwood flooring. The hardwood cost $4.98 per-square-foot plus an installation fee per-square-foot. The area of the living room is 200 square feet, and the total cost for the flooring with installation comes to $1,688.00. The master bedroom is getting berber carpet. The carpet cost $2.48 per-square-foot plus an installation fee per-square-foot. The area of the master bedroom is 180 square feet, and the total cost for the flooring with installation comes to $928.80. Place the flooring type in order from the least amount to the greatest amount of cost to install per-square-foot.
Elsa is on the swim team. Each week she swims a total of 2000 meters. How many kilometers does she swim each week?
identify the number in the hundreth(1/100)position 15.386
A meteor crater is 4100 feet in diameter. Approximate the distance around the crater. Use 3.14 for piπ
Which symbol makes the following statement true? 413,115 431,511
If the maximum of 63 years is accidentally recorded as 630 years, how will this affect the mean?
Which expression results in a product that is rational?
(a)square root of 7 times square root of 10
(b)square root of 8 times square root of 10
(c) square root of 9 times square root of 10
(d)square root of 10 times square root of 10
Final answer:
The expression that results in a rational product is √10 times √10, as this simplifies to the rational number 10.
Explanation:
To find which expression results in a product that is a rational number, we need to identify which pair of square roots can be multiplied to produce a non-radical number.
Multiplication of square roots is analogous to the multiplication of exponents. When the same base is multiplied, the exponents are added. Utilizing this property, we know:
√7 × √10 = √(7 × 10) = √70 (which is irrational since 70 is not a perfect square).
√8 × √10 = √(8 × 10) = √80 (which is irrational since 80 is not a perfect square).
√9 × √10 = √(9 × 10) = √90 (which is irrational since 90 is not a perfect square).
√10 × √10 = √(10 × 10) = √100 = 10 (which is rational since 100 is a perfect square).
Therefore, the expression that results in a rational product is √10 × √10, which simplifies to 10.
find the next three terms in the geometric sequence: 2, 4, 8, 16
(3x6÷2)v+10=3²v+9 (Need work)
The student's equation simplifies to 9v + 10 = 9v + 9. Upon further simplification, it becomes apparent that the equation is a contradiction and has no solution.
Explanation:The student is asking about the solution to the equation (3x6÷2)v+10=3²v+9. The first step in solving this equation is to simplify the terms. We start by simplifying the multiplication and division in the first part of the equation (3x6÷2), which equals 9 since 3 times 6 is 18 and 18 divided by 2 is 9. Therefore, the equation simplifies to 9v + 10 = 3²v + 9. Next, we simplify 3², which is 3 raised to the power of 2, meaning 3 times itself, which results in 9. The equation now reads 9v + 10 = 9v + 9.
With the equation simplified, we notice that the terms containing v are equal on both sides of the equation. This indicates that we may be dealing with an identity or a contradiction depending on the constants. Subtracting 9v from both sides yields 10 = 9, which is clearly not true. Therefore, we conclude that the equation is a contradiction, and there is no solution for v that would make the equation true.
Final answer:
To solve the equation (3x6÷2)v+10=3²v+9, we need to follow the order of operations and solve for the variable v. However, the equation is inconsistent and has no solution.
Explanation:
To solve the equation (3x6÷2)v+10=3²v+9, we need to follow the order of operations and solve for the variable v. Let's break it down step by step:
Start by performing the division 3x6÷2 = 18÷2 = 9.
Now rewrite the equation as 9v+10=9v+9.
Subtract 9v from both sides of the equation to isolate the constants: 10 = 9.
Since 10 is not equal to 9, the equation is inconsistent and has no solution.
Therefore, there is no value of v that satisfies the equation.
Help Yaya ASAP Please
Jessica and Marcus each earn the same amount of money every week mowing lawns. Jessica saves 50% of her money and Marcus saves 1/4 of his money.
Which statement is correct?
A. Marcus saves 4/5 as much money as Jessica.
B. Jessica saves 4/5 as much money as Marcus.
C. Marcus saves twice as much money as Jessica.
D. Jessica saves twice as much money as Marcus.
In Seattle, the tax on a property assessed at $570,000 is $12,540. If tax rates are proportional in this city, how much would the tax be on a property assessed at $460,000?
Final answer:
To find the property tax on a $460,000 property, first, find the tax rate by dividing the known tax of $12,540 by the assessed value of $570,000 to get approximately 0.022. Then multiply $460,000 by this tax rate to get an estimated tax of $10,120.
Explanation:
To calculate the property tax on a property assessed at $460,000 in Seattle, given the tax rate is proportional, we can use the tax information from another property as a reference. In this case, we know a property assessed at $570,000 has a tax of $12,540. This allows us to find the tax rate by dividing the tax amount by the assessed value of the property.
Step 1: Determine the tax rate.
Tax Rate = Tax / Assessed Value
Tax Rate = $12,540 / $570,000
Tax Rate ≈ 0.022
Step 2: Calculate the tax for the property assessed at $460,000 using the tax rate.
Tax = Assessed Value × Tax Rate
Tax = $460,000 × 0.022
Tax ≈ $10,120
Thus, the property tax on a property assessed at $460,000 would be approximately $10,120, assuming the tax rates are indeed proportional.
Dave rented a limousine for his wife's birthday. The hourly rate is $60. They used the limousine for 4 hours, plus Dave gave the driver a 10% tip. How much did he spend in total for the hourly charges plus tip?
A Chinese restaurant offers buffet takeout for $4.99 per pound. How much does your takeout meal cost?
Answer:
1.99
Step-by-step explanation:
3.24 repeating as a mixed number in simplest form
A repeating mixed number is a mixed fraction, which after converted to decimal; the numbers after the decimal point repeat without end.
3.23 as a repeating mixed number is [tex]3\frac{23}{99}[/tex]
Given that
[tex]Number = 3.24[/tex]
First, we represent as a fraction
[tex]Number = \frac{324}{100}[/tex]
To represent the number as a repeating mixed number, we simply subtract 1 from the numerator
[tex]Number = \frac{324}{100 - 1}[/tex]
[tex]Number = \frac{324}{99}[/tex]
Represent as a mixed number
[tex]Number = 3\frac{23}{99}[/tex]
Hence, 1.12 as a repeating mixed number is [tex]3\frac{23}{99}[/tex]
Read more about repeating mixed numbers at:
https://brainly.com/question/4693336
Write a number between 1 and 50 that has at least 8 factors. B.) Write the factors.
Answer:
24 has 8 factors with 1,2,3,4,6,8,12,and 24
Step-by-step explanation:
Travis wants to collect 20% more than Jessica. Robin wants to collect 35% more than Travis. If Travis collects $43, how much was collected in all?
What is the greatest possible product of a 2 digit number and a 1 digit number?
Jose is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges $108 and allows unlimited mileage. Company B has an initial fee of $75 and charges an additional $0.60 for every mile driven. For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m .
Final answer:
Jose should rent a truck from Company A if he plans to drive more than 55 miles, as it will charge less than Company B beyond this mileage.
Explanation:
To determine for what mileages Company A will charge less than Company B, we set up an inequality comparing the total cost for each company and solve for m (the number of miles driven).
The cost for Company A is a flat rate of $108, so it does not depend on mileage. The cost for Company B includes an initial fee of $75 plus $0.60 per mile. We set up the inequality as follows:
Company A \< Company B
$108 < $75 + $0.60m
$108 - $75 < $0.60m
$33 < $0.60m
$33 / $0.60 < m
55 < m
Therefore, Company A will charge less than Company B for any number of miles greater than 55. So, if Jose plans to drive more than 55 miles, he should choose Company A for a cheaper rate.
a ramp has a height of 3 foot and a base of 12 feet what is the angle of elevation
HELP PLSSSSS Triangle ABC is an equilateral triangle. The angle bisectors and the perpendicular bisectors meet at D in such a way that CD = 2DE.
The radius of the inscribed circle is____
units, and the radius of the circumscribed circle is___
units.
Answer: For clarification, the answer is 2.9 for the first one and the second is 5.8
Step-by-step explanation: They are correct for PLATO users I got them right.
A rancher has 50,000 linear feet of fencing and wants to enclose a rectangular field and then divide it into four equal pastures with three internal fences parallel to one of the rectangular sides. what is the maximum area of each pasture?
Final answer:
To find the maximum area of each pasture, we can create a rectangular field and divide it into four equal pastures. By using the given linear footage of fencing, we can find the dimensions of the rectangular field and calculate the area for each pasture.
Explanation:
To find the maximum area of each pasture, we can start by creating a rectangular field using the given 50,000 linear feet of fencing. Let's consider the length of the rectangular field as 'x' and the width as 'y', with x being the longer side.
The perimeter of the rectangular field is given by 2x + y = 50,000. Since we want to divide the field into four equal pastures, we can divide the rectangular field into four equal widths, with each width being y/4.
Therefore, the area of each pasture is x * (y/4) = (x*y)/4.
To find the maximum area, we can substitute 2x + y = 50,000 into the formula for the area of each pasture. Solving for y in terms of x gives us y = 50,000 - 2x.
Substituting this value of y into the formula for the area, we get A = x * ((50,000 - 2x)/4).
To maximize the area, we can differentiate the area formula with respect to x and set it equal to zero. Solving this equation will give us the value of x that maximizes the area. Once we have that, we can substitute it back into the area formula to find the maximum area of each pasture.
Suppose one bakery oven at a cookie manufacturer is being used to bake chocolate cookies and vanilla cookies. A batch of chocolate cookies bakes in 8 minutes, and a batch of vanilla cookies bakes in 10 minutes. Let x represent the number of batches of chocolate cookies and y represent the number of batches of vanilla cookies. Write a linear inequality for the number of batches of each type of cookie that could be baked in one oven in an 8-hour shift.
Answer:
The answer is .......D
Step-by-step explanation:
d. 480
You have to remember that The answer is D
If you need to cut 5 pieces of glass from a 14 feet length, how long should each piece be?
14 / 5 = 2.8 feet each
2.8 feet = 2 feet 9.6 inches
2 feet 9 3/5 inches
Solve The Following Question:
5/13t = -9
5/13t=-9
to find t divide both sides by 5/13
t = -9 / 5/13=
-117 /5 =-23.4
t = -23.4
Which colonial power's policy was based on assimilation of native peoples?