It will take 40.5 minutes for Car 2 to catch up to Car 1 after its 18-minute head start.
To find out how long it will take for Car 2 to catch up to Car 1, we first need to determine the distance Car 1 travels during the 18-minute head start.
Convert 18 minutes to hours.
18 minutes ÷ 60 minutes/hour = 0.3 hours
Calculate the distance Car 1 travels during the 18-minute head start.
Distance = Speed × Time
Distance = 45 mph × 0.3 hours
Distance = 13.5 miles
Now that we know Car 1 has traveled 13.5 miles when Car 2 starts, we need to find out how long it takes for Car 2 to catch up, which is essentially the time needed to cover this distance at the speed difference between the two cars.
Calculate the relative speed of Car 2 compared to Car 1.
Relative Speed = Speed of Car 2 - Speed of Car 1
Relative Speed = 65 mph - 45 mph
Relative Speed = 20 mph
Calculate the time it takes for Car 2 to catch up.
Time = Distance ÷ Relative Speed
Time = 13.5 miles ÷ 20 mph
Time = 0.675 hours
Convert the time from hours to minutes for better understanding.
0.675 hours × 60 minutes/hour = 40.5 minutes
So, it will take 40.5 minutes for Car 2 to catch up to Car 1 after its 18-minute head start.
Two-fifths of the fish in Gary's fish tank are guppies.One-fourth of the guppies are red.What fraction of the fish in Gary's tank are red guppies?Show your work.
Answer:
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
Given: Two-fifths of the fish in Gary's fish tank are guppies.One-fourth of the guppies are red.
To Find: What fraction of the fish in Gary's tank are red guppies.
Solution:
Let total number of fish in tank be [tex]=\text{x}[/tex]
Number of guppies in tank are [tex]=\frac{2}{5}\text{of total fish}[/tex]
Number of guppies in tank are [tex]=\frac{2}{5}\text{x}[/tex]
Number of red guppies in tank are [tex]=\frac{1}{4}\text{of total guppies}[/tex]
[tex]\frac{1}{4}\times\frac{2}{5}\text{x}[/tex]
[tex]\frac{1}{10}\text{x}[/tex]
Now,
fraction of the fish in Gary's tank that are red guppies
[tex]=\frac{\text{red guppies}}{\text{total fish in Gary's tank}}[/tex]
[tex]\frac{\frac{1}{10}\text{x}}{\text{x}}[/tex]
[tex]\frac{1}{10}[/tex]
Hence [tex]\frac{1}{10}[/tex] of total fish are red guppies.
Hypatia has read 13 chapters of a 22 chapter book what percent has she read
Answer:
59.09%
Step-by-step explanation:
We can calculate it with a direct rule of 3. If 22 chapters are the 100% of the book, what percent is 13 chapters?
[tex]\text{22 chapters} -\!\!\!-\!\!\!- 100\%\\ \\\text{13 chapters} -\!\!\!-\!\!\!- x\%[/tex]
We use the formula of the direct rule of 3:
[tex]x = \frac {13* 100}{22} \\ \\ x = \frac {1300}{22}[/tex]
x = 59.09
She has read the 59.09% of the book.
Let hh be the set of all points in the second quadrant in the plane v=ℝ2v=r2. that is, h={(x,y)∣x≤0,y≥0}h={(x,y)∣x≤0,y≥0}. is hh a subspace of the vector space vv?
The set hh, which represents all points in the second quadrant of the Cartesian plane, is not a subspace of the vector space vv, because it does not contain the zero vector and is not closed under scalar multiplication.
Explanation:In vector space theory, a subset of a vector space forms a subspace if it satisfies three key properties: it contains the zero vector of the larger vector space, it is closed under vector addition, and it is closed under scalar multiplication.
In our case, the set hh represents all points in the second quadrant of the Cartesian plane, that is, hh={(x, y)∣x≤0, y≥0}. Since the zero vector is not included in this set of vectors, it does not meet the first requirement. Therefore, hh is not a subspace of the vector space vv.
To illustrate, let's consider the vectors A=(0, 1) and B=(-1, 0) that belong to set hh. The sum of these vectors is A + B = (0 - 1, 1 + 0) = (-1, 1), which also belongs to set hh. However, if we multiply vector A by the scalar -1, the result is -A = (0, -1), a vector that does not belong to set hh. Hence, the set hh is not closed under scalar multiplication.
Learn more about Vector Subspaces here:https://brainly.com/question/30031077
#SPJ2
The point P(8, 6) is on the terminal side of θ. Evaluate sin θ.
list the partial products of 42 x 28
Answer:
The partial product of [tex]42\times 28[/tex] are 800,320,40,16 and their sum is 1176.
Step-by-step explanation:
The given expression is,
[tex]42\times 28[/tex]
In number 42 the place value of 4 is 40 and the place value of 2 is 2. In number 28 the place value of 2 is 20 and the place value of 8 is 8.
To find the partial product, we have multiply the place values of first number with the place values of second number.
Place values of 42 are 40 and 2. Place values of 28 are 20 and 8.
[tex]40\times 20=800[/tex]
[tex]40\times 8=320[/tex]
[tex]2\times 20=40[/tex]
[tex]2\times 8=16[/tex]
Therefore the partial product of [tex]42\times 28[/tex] are 800,320,40 and 16.
To find the total product, we have add all partial products.
[tex]T=800+320+40+16=1176[/tex]
The value of given expression is 1176.
Related Rates Problem: The radius of a spherical watermelon is growing at a constant rate of 2 centimeters per week. The thickness of the rind is always one tenth of the radius. The volume of the rind is growing at the rate __?__ cubic centimeters per week at the end of the fifth week. Assume that the radius is initially zero. ...?
Brian drove 120 miles at a speed of 60 mph. He drove the same distance back home at an average speed of 40 mph. Brian adds the speeds and divides by two to come up with an average speed of 50 mph what is wrong with his reasoning? Find his average speed
The cartesian coordinates of a point are given. (a) (2, −2) (i) find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π.
A restaurant uses 4 pounds of potatoes for a party of 12 people. If they are cooking potatoes for a party of 60 people, what should they do?
A negative correlation between two variables x and y usually yields a negative p-value for r.
a. True
b. False
A bus timetable states that the next bus leaving for holmfirth is at 16:40 what time is this in 12 hours time
Javier rounded to the nearest half to estimate the product of 3 2/5 and -3 7/8. How do the estimate and the actual product compare?
A. The actual product is less than the estimate. The numbers differ by less than one.
B. The actual product is greater than the estimate. The numbers differ by less than one.
C. The actual product is less than the estimate. The numbers differ by more than one.
D. The actual product is greater than the estimate. The numbers differ by more than one.
Answer:
b the answer
Step-by-step explanation:
just did it
Final answer:
The actual product is less than the estimate. The numbers differ by less than one.
Explanation:
Javier rounded to the nearest half to estimate the product of 3 2/5 and -3 7/8.
To estimate the product, we can round both numbers to the nearest half, which gives us 3.5 and -3.5. Multiplying these rounded numbers gives an estimate of -12.25.
The actual product of 3 2/5 and -3 7/8 is -3.4. Therefore, the actual product is less than the estimate. The numbers differ by less than one.
A pine tree grows at a rate of 1.5 feet per year. James plants a 2-foot tall pine tree in his yard. How many years will it take for the tree to be at least 14 feet tall?
There are 1800 gym members in total. 3\4 are aged 25-59 years. 1/5 are over 60 years old and the remainder are under 25 years old. How many members are under 25 years old
5×143=use distributive property
Find the value of the following expression:
(3^8 ⋅ 2^-5 ⋅ 9^0)^-2 ⋅ (2^ -2 / 3^3) ^4 ⋅ 3^28
Write your answer in simplified form. Show all of the steps.
(3^8 ⋅ 2^-5 ⋅ 9^0)^-2 ⋅ (2^ -2 / 3^3) ^4 ⋅ 3^28 =
(6561 * 0.03125 * 1)^2 * (0.00925)^4 * 22876792454961 =
42037.81348 * 0.00000000732094 * 22876792454961 =
7040477235.56798349
round answer as needed
The price of a pair of shoes is $45.90. The sales tax rate is 5%. How much sales tax do you need to pay?
Answer:
The sales tax to be paid for the pair of shoes is $2.29.
Step-by-step explanation:
If the price of a pair of shoes is $45.90, and the sales tax rate for it is of 5%, in order to know the sales tax to be paid we have to do the following calculation:
(45.90 x 5) / 100 = X
229.5 / 100 = X
2.295 = X
So, as we can see, the sales tax to be paid is $2.29
Find the state that has the largest number for the execution variable in 1993. (the variable exec is total executions in 1991, 1992, and 1993.) how much bigger is this value than the next highest value?
The rectangular box shown in the figure has dimensions 8" × 7" × 4" (a = 8, b = 7, c = 4). Approximate the angle θ formed by a diagonal of the base and a diagonal of the 7" × 4" side. (Round your answer to two decimal places.)
Answer:
Rectangle
four
Length and width
Step-by-step explanation:
Step by step ways to solve 3.4 x 4.72
Final answer:
To solve 3.4 x 4.72, multiply the numbers as if they are whole, then place the decimal in the product so that it has the same number of decimal places as the sum of the decimal places in the factors, resulting in 16.048.
Explanation:
To solve the multiplication of 3.4 x 4.72, follow these steps:
Write down the numbers to be multiplied, one below the other, aligning the decimal points: 3.4The final result of multiplying 3.4 by 4.72 is 16.048.
How much work is needed to stretch this spring from x = 3.0 cm to x = 7.0 cm ?
The work done to stretch a spring is calculated using Hooke's Law, denoted by the formula W = 1/2kx², where 'k' is the spring constant and 'x' the displacement. The displacement is the difference between the final and initial lengths of the spring (7.0 cm - 3.0 cm). However, without the spring constant, a specific numerical answer cannot be provided.
Explanation:The problem requires calculating the work done to stretch a spring. This can be done using Hooke's Law in Physics, which states that the force necessary to extend or compress a spring by a distance 'x' from its equilibrium position is proportional to 'x'. The magnitude of the force applied is represented as F = kx, where 'k' is the spring constant. However, the work done, W, against this force is given by 1/2kx².
To calculate, we need to know the value of the spring constant 'k', and the displacement 'x', which is the difference between the final length (7.0 cm) and the initial length (3.0 cm) of the spring. Without the spring constant, we, unfortunately, cannot provide a numerical answer.
Learn more about Work done on a Spring here:https://brainly.com/question/29392391
#SPJ2
Use the graph to find the x-intercept for the equation y + 2 = 2(x + 3). The x-intercept is
Answer:
(-2,0)
Step-by-step explanation:
I just did the assignment
A person standing close to the edge on top of a 56-foot building throws a ball vertically upward. The quadratic function h ( t ) = − 16 t 2 + 104 t + 56 h(t)=-16t2+104t+56 models the ball's height about the ground, h ( t ) h(t), in feet, t t seconds after it was thrown. a) What is the maximum height of the ball?
The maximum height of the ball at a time of 3.25 seconds will be 275 feet.
What are the maxima and minima of a function?For the maximum value of the function if f''(x) < 0 and for the minimum value of the function if f''(x) > 0.
The maximum and minimum value of the function is at f'(x) = 0.
An individual standing near the edge on top of a 56-foot building tosses a ball upward vertically.
The quadratic function is given below.
h(t) = - 16t² + 104t + 56
The value of 't' at which the ball is at its maximum height. Then we have
h'(t) = 0
-32t + 104 = 0
32t = 104
t = 3.25 seconds
Then the maximum height of the ball is given as,
h(t) = - 16(3.25)² + 104(3.25) + 56
h(t) = -16 x 10.5625 + 338 + 56
h(t) = - 169 + 444
h(t) = 275 feet
The maximum height of the ball at a time of 3.25 seconds will be 275 feet.
More about the maxima and minima links are given below.
https://brainly.com/question/12870695
#SPJ3
Maude sees 3 more foxes than Henry. Henry see 4 foxes. How many foxes did Maude see?
Maude sees 3 more foxes than Henry and Henry sees 4 foxes then Maude
sees 7 foxes.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Henry sees 4 foxes and Maude sees 3 more foxes than Henry.
∴ Maude sees (4 + 3) = 7 foxes.
Some more insights:
Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ2
which would not be a step in solving 3x + 1 + 2x = 2+ 4x?
To solve the equation 3x + 1 + 2x = 2 + 4x, you would first combine like terms, then eliminate variable terms on one side of the equation, and finally solve for x.
Explanation:In solving the equation 3x + 1 + 2x = 2 + 4x, the first step would be to combine like terms on both sides of the equation. This means adding or subtracting the same type of terms together. In this case, you would combine the x terms on the left side and the constant terms on the right side. The equation will then be simplified to 5x + 1 = 2 + 4x.
The next step would be to get rid of the variable terms on one side of the equation. To do this, you can subtract 4x from both sides of the equation. This will result in x + 1 = 2.
Finally, you can solve for x by subtracting 1 from both sides of the equation. This gives us the solution x = 1.
Which word best describes the range of a function?
A. input
B. output
C. independent
D. relation
Answer:
It is actually B output
Step-by-step explanation:
Gregg subtracted some number x from 47, then multiplied the result by two, subtracted 15 and got 45. What was Gregg's number?
(PLEASE ANSWER WITH WORK, THANKS)
Write a real-life situation that can be modeled by the expression 1 1/3 x 2.
1 1/3 is a mixed number
which of the following three dimensional objects has a rotational symmetry about a line
Answer choices:
A. a car
B. a set of rectangular stairs
C. a rolling pin
D. a stapler
The answer is C. a rolling pin
Round each addend to the nearest ten thousand,and then find the estimated sum.?
337,961 + 482,746
_+_=_
To find the estimated sum, round each addend to the nearest ten thousand by looking at the digit in the ten thousand places. Then add the rounded numbers together.
Explanation:To round each addend to the nearest ten thousand, look at the digit in the ten thousand places. If the digit is 5 or greater, round up by increasing the number in the ten thousand place by 1. If the digit is less than 5, round down by keeping the number in the ten thousand places the same. For 337,961, the digit in the ten thousand places is 9, so it rounds up to 340,000. For 482,746, the digit in the ten thousand places is 7, so it rounds down to 480,000. Now, you can find the estimated sum by adding the rounded numbers, which would be 340,000 + 480,000 = 820,000.
Learn more about Rounding here:https://brainly.com/question/34045884
#SPJ2