The graph shows the distance, in feet, required for a car to come to a full stop if the brake is fully applied and the car was initially traveling x miles per hour. Which equation can be used to determine the stopping distance in feet, y, for a car that is traveling x miles per hour?
Answer:
y=[tex]\frac{x^{2} }{18}[/tex]
There are currently 3 students signed up for a trip. The van can transport only 7 students.
Which graph shows all the possible values for the extra number of students that need to sign up so that more than one van is needed to transport them?
You are giving the following amounts: $190,258.50; $152,698.00; $122,753.00; $220,523.00; $231,951.00. What is the average of these five amounts?
Which of the following statements correctly describes the position on the intake of the exhaust valves during most of the power stage in a four cycle gas engine
Final answer:
During the power stage of a four-cycle gas engine, both the intake and exhaust valves are closed, allowing the air-fuel mixture to expand and exert force on the piston, converting fuel's chemical energy into mechanical work.
Explanation:
The question concerns the position of the intake and exhaust valves during the power stage of a four-cycle gas engine, specifically within the context of the Otto cycle. During the power stroke, the intake valves are closed to allow the air-fuel mixture, which was ignited at the beginning of this stage, to expand without escaping. Meanwhile, the exhaust valves also remain closed to ensure that the expanding gases exert maximum force on the piston, driving it down.
This process converts the chemical potential energy of the fuel into mechanical work. The exhaust valve opens only after the completion of the power stroke, during the exhaust stage, to expel the combustion products and prepare the engine for the next cycle.
the length of a rectangle is 3 ft longer than its width if the perimeter of the rectangle is 26 feet find its area
The problem primarily involves the calculation and understanding of the concepts of perimeter and area in Mathematics. Given the length is 3 ft longer than the width, and the perimeter of the rectangle is 26 feet, first, we find that the width is 5 feet and the length is 8 feet. The area is thus, 40 square feet.
Explanation:To solve this problem, we need to understand the formula for the perimeter of a rectangle, which is 2l + 2w, where 'l' stands for length and 'w' for width. Also, the area of a rectangle is calculated by l*w. The problem states that the length is 3 ft longer than the width and that the perimeter is 26 feet. Firstly, we can express the length as 'w + 3' and substitute into the perimeter formula:
2(w + 3) + 2w = 26
After simplifying, we get the width equals to 5 feet. Substituting 5 for width, we get the length as 8 feet, because length is 3 feet longer than the width. Then, the area of the rectangle can be calculated by multiplying the width by the length:
Area = l * w = 8 ft * 5 ft = 40 square feet
Learn more about Area and Perimeter here:https://brainly.com/question/11957642
#SPJ2
Given two parallel lines and a transversal, at what angle do the angle bisectors of two same side interior angles intersect?
The angle bisectors of the same side interior angles, formed by two parallel lines and a transversal, intersect at a 90-degree angle.
Explanation:In geometry, when you have two parallel lines intersected by a transversal, the same side interior angles are those which are in the same position on the two lines. If we bisect these angles (i.e., divide them in two equal parts), the angle bisectors will intersect forming an angle that is 90 degrees.
To understand why, note that the same-side interior angles are supplementary (i.e., they sum up to 180 degrees) because they are on the same side of the transversal. So, if we bisect these angles, each pair of congruent angles will add up to 90 degrees. When these bisectors intersect, they form four right angles. Therefore, the angle at the intersection of the bisectors is 90 degrees.
Learn more about Geometry here:https://brainly.com/question/31408211
#SPJ12
Find the derivative of the function using the definition of derivative. f(x) = 1 5 x − 1 6
To find the derivative of the given function using the definition of derivative, we can start by taking the limit of the expression. By simplifying the expression and canceling out terms, we can find the derivative as -10/(20x√x-√x)(10x-1/2).
The function f(x) = 1/(10x-1/2)
To find the derivative of the function using the definition of derivative, we can start by writing the expression of the derivative:
f'(x) = lim(h->0) [f(x+h) - f(x)] / h
Substituting the function f(x) into the expression, we have:
f'(x) = lim(h->0) [1/(10(x+h)-1/2) - 1/(10x-1/2)] / h
To simplify the expression, we can find a common denominator and combine the fractions:
f'(x) = lim(h->0) [(10x-1/2) - (10(x+h)-1/2)] / h[(10(x+h)-1/2)(10x-1/2)]
Expanding and simplifying the expression, we get:
f'(x) = lim(h->0) -10/(2√x-√(x+h)) / h(10x-1/2)(10(x+h)-1/2)
Now, we can cancel out the h in the denominator:
f'(x) = lim(h->0) -10/(2√x-√(x+h))(10x-1/2)(10(x+h)-1/2)
Taking the limit as h approaches 0, we get:
f'(x) = -10/(2√x-√x)(10x-1/2)(10x-1/2)
Now, we can simplify further:
f'(x) = -10/(20x√x-√x)(10x-1/2)
So, the derivative of the function is f'(x) = -10/(20x√x-√x)(10x-1/2)
complete question given below:
Find the derivative of the function using the definition of derivative.
1 f(x) = 1/10x-1/2
f'(x) =
State the domain of the function, f(x). (Enter your answer in interval notation.)
State the domain of its derivative, f'(x). (Enter your answer in interval notation.)
Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 + 2x +1?
right 1 unit
left 1 unit
right 2 units
left 2 units
Answer:
Option B is correct
Left 1 unit.
Explanation:
According to the graph theory of transformation:
y = f(x+k)=[tex]\left \{ {{k>0 shift graph of y= f(x) left k unit} \atop {k<0} shift graph of y= f(x) right |k| unit} \right.[/tex]
Given the parent function: [tex]f(x)=x^2[/tex]
and the function [tex]g(x)=x^2+2x+1[/tex]
we can write it as:
g(x)= [tex](x+1)^2[/tex] [ ∴[tex](a+b)^2 = a^2+2ab+b^2[/tex] ]
Therefore, vertex of the graph of the function [tex]g(x)=(x+1)^2[/tex] is 1 units to the left of the vertex of the graph of the function [tex]f(x)=x^2[/tex] .
Answer:
Shift 1 unit left
B is correct
Step-by-step explanation:
Given: The vertex of f(x) shift to g(x)
[tex]f(x)=x^2[/tex]
Vertex of f(x): (0,0)
[tex]g(x)=x^2+2x+1[/tex]
Vertex form: [tex]y=a(x-h)^2+k[/tex]
[tex]g(x)=(x+1)^2[/tex]
Vertex of g(x): (-1,0)
[tex](0,0)\rightarrow (-1,0)[/tex]
Only x-coordinate change and y-coordinate remain same.
[tex]0\rightarrow -1[/tex]
Hence, The vertex of f(x) shift 1 unit left to get vertex of g(x)
If you have $90 to start a business and you can’t exceed that amount, how would you write an inequality for this
lily swims a 100-meter race. she swims the first half in 27.8 seconds. she swims the second half in 30.12 seconds. how long does it take lily to swim the whole race?
we know that
1) Lily swims a [tex]100[/tex]-meter race
2) She swims the first half in [tex]27.8[/tex] seconds
3) She swims the second half in [tex]30.12[/tex] seconds
so
To find the total time to swim the whole race sum the time in the first half plus the time in second half
[tex](27.8+30.12)=57.92\ seconds[/tex]
therefore
the answer is
[tex]57.92\ seconds[/tex]
By adding the two given times, we will see that she completes the race in 57.92 seconds.
How to find the time in which she finishes the race?
We know that:
She swims the first half on 27.8 seconds.She swims the second half on 30.12 seconds.Then the time that it took to complete the whole race is just the sum of these two times, we will get:
Total time = 27.8 seconds + 30.12 seconds = 57.92 seconds.
We can conclude that Lily swims the whole race in 57.92 seconds.
If you want to learn more additions, you can read:
https://brainly.com/question/2475734
a rectangular garden has an area of 9 5/24 square yards. The garden is 2 1/6 yards wide. how long is it?
An American green tree frog tadpole is about 0.00001 kilometer in length when it hatches. Write this decimal as a power of 10
The decimal number 0.00001 can be written as a power of 10 as 1 x 10^-5. This is because the decimal is shifted five places to the right.
Explanation:The student is asked to express the number 0.00001 as a power of 10. This can be achieved by understanding that the power (exponent) of 10 is equal to how many places the decimal is shifted. Here, the decimal is shifted five places to the right so we use the negative exponent -5 to denote this shift. Therefore, 0.00001 written as a power of 10 is 1 x 10^-5.
Learn more about Scientific Notation here:https://brainly.com/question/16936662
#SPJ2
5% of the soccer team is on the honor roll. Rewrite this percent as a fraction in simplest form
Connect in Justin's school, 0.825 of the students participate in a school sport. If there are thousand students in Justin school, how many participate in a school sport?
Answer: 825.
Step-by-step explanation:
An employee's annual salary was increased from $22,464.00 to$24,710.40 last year. If it is increased by the same percent this year, what will the employee's salary?
please help ASAP!!!
Fill in the truth table below for the disjunction p ∨ q. Type T for true or F for false.
p q p ∨ q
T T a0
T F a1
F T a2
F F a3
Answer: The filled truth table for p ∨ q is shown below.
Step-by-step explanation: We are given to fill the truth table for the p ∨ q.
We know that
If any one of p or q is true, then p ∨ q is also true. And it is false, only when both p and q are false.
The filled truth table is as follows :
p q p ∨ q
T T T
T F T
F T T
F F F
Thus, a0 = T, a1 = T, a2 = T and a3 = F.
In the general linear equation, y = bx + a, what is the value of b called?
During study hall, 58% of the students are studying for tests, 29% of the students are doing homework, and the remaining students are writing papers. What percentage of the students are writing papers?
The percentage of the students writing papers will be 13%.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio.
During study hall, 58% of the students are studying for tests, 29% of the students are doing homework, and the remaining students are writing papers.
The percentage of the students writing papers will be given by the difference of the 100% and the sum of 58% and 29%. Then we have
⇒ 100% - 58% - 29%
⇒ 100% - 87%
⇒ 13%
The percentage of the students writing papers will be 13%.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ5
Final answer:
The percentage of students writing papers during study hall is 13%.
Explanation:
To find out what percentage of students are writing papers during study hall, we need to find the remaining percentage after accounting for the students studying for tests and doing homework.
Since 58% of the students are studying for tests and 29% of the students are doing homework, the percentage of students writing papers can be found by subtracting the sum of these two percentages from 100%:
Percentage of students writing papers = 100% - (58% + 29%) = 13%
Therefore, 13% of the students are writing papers during study hall.
Anton bakes 36 cookies. He gives cookies to each of his 3 friends.
Let c represent the number of cookies he gives each friend.
Which expression shows how many cookies Anton has left?
the average rate of elevation change in feet per second if a submarine dives 440 feet in 20 seconds?
Find a power series solution to the differential equation at the point x0. (2+x2)y′′-xy′+4y=0
Over the last three evenings, Raina received a total of 83 phone calls at the call center. The first evening, she received 7 more calls than the third evening. The second evening, she received 2 times as many as the third evening. How many phone calls did she receive each evening?
Raina received 19 phone calls on the third evening, 26 phone calls on the first evening, and 38 phone calls on the second evening.
Explanation:Let's consider the number of phone calls Raina received each evening.
Let x represent the number of phone calls on the third evening.
The first evening, Raina received 7 more calls than the third evening, so the number of phone calls on the first evening is x + 7.
The second evening, Raina received 2 times as many calls as the third evening, so the number of phone calls on the second evening is 2x.
Given that Raina received a total of 83 phone calls over the three evenings, we can set up the equation:
x + (x + 7) + 2x = 83
Combining like terms, we have:
4x + 7 = 83
Subtracting 7 from both sides, we get:
4x = 76
Dividing both sides by 4, we find that x = 19.
Therefore, Raina received 19 phone calls on the third evening, 26 phone calls on the first evening, and 38 phone calls on the second evening.
Learn more about Solving Equations here:https://brainly.com/question/14410653
#SPJ2
the distance between the points 5,1 and 5,-6 is the square root of length?
Find the interval of convergence of the series (5x-1)^n
what is the correct way to read this number 6.3078
A bucket holds c liters of water, but a jar holds 8 liters less. How many times as much water can the bucket hold as the jar?
Answer:
The bucket hold 3x the capacity of the jar
Step-by-step explanation:
First we have to write down the amount of both, the jar and the bucket, to make a small equation to see the problem mathematically.
Bucket = c liters of water
Jar = c - 8
so we can say that:
c = c - 8
Now that we have the equation, we can determine that the variable 'c' on the right is substracting to the number 8. So we can pass the 'c' to the left of the equation by adding it to the elements on the left, like this:
c + c = 8
Now, two 'c' are the same, we can add them:
2c = 8
This two on the equation of the left is multiplying the variable 'c', so we can move it to the right by dividing the number 8 with this number:
c = 8/2
If we solve this operation, we'll get:
c = 4
That means that the amount of liters of water a jar can hold is 4 liters
Jar = 4 liters
Now that we have this value, we can solve the problen. If the jar holds 8 liters of water les than a bucket, we can now represent it like this:
Bucket = Jar capacity + 8 liters
Wich can be represented like this as well:
Bucket = 4 + 8
And the result is:
Bucket = 12 liters
If we try to fit the jar's capacity on the bucket, we find that the bucket hold 3x the capacity of the jar
Let me know if you have any doubts :D
The marginal-revenue equation is
Side "a" of a triangle is twice side "b." Side "c" is 2 meters shorter than side "a." The perimeter is 98 meters. Find the lengthy of each side. (show work)
Final answer:
By setting up a system of equations based on the given information and solving for b, we find that side a is 40 meters, b is 20 meters, and c is 38 meters.
Explanation:
To solve for the lengths of the sides of the triangle, we can set up a system of equations based on the information given:
Let b be the length of one side.Side a is twice the length of side b, so a = 2b.Side c is 2 meters shorter than side a, so c = a - 2 = 2b - 2.The perimeter of the triangle is the sum of its sides, which equals 98 meters: a + b + c = 98.Substituting the expressions for a and c into the perimeter equation gives:
2b + b + (2b - 2) = 985b - 2 = 985b = 100b = 20With the value for b, we can now find a and c:
a = 2b = 2(20) = 40 metersc = 2b - 2 = 40 - 2 = 38 metersThe lengths of the sides of the triangle are 20 meters (b), 40 meters (a), and 38 meters (c).
Final answer:
To solve for the lengths of the triangle's sides, we formulate equations based on the given relationships and perimeter. We find that side b is 20 meters, side a is twice b (40 meters), and side c is 2 meters shorter than a (38 meters).
Explanation:
The student's question involves finding the length of each side of a triangle given specific relationships between the sides and the overall perimeter. The problem can be formulated using algebra. Let's denote side b as the baseline. From the question, we know that side a is twice side b (a = 2b), and side c is 2 meters shorter than side a (c = a - 2 = 2b - 2). The perimeter (P) is given as 98 meters, so we have P = a + b + c = 98 meters.
Substituting for a and c in terms of b we have P = 2b + b + (2b - 2) = 98, simplifying to 5b - 2 = 98. Solving for b we add 2 to both sides, 5b = 100, and then divide by 5 to get b = 20 meters. Now we easily find that a = 2(20) = 40 meters, and c = 40 - 2 = 38 meters. Therefore, the lengths of the sides of the triangle are 40 meters for side a, 20 meters for side b, and 38 meters for side c.
blake said 4/5+1/3 =5/8 does his answer make sense explain. please help
Your girlfriend just won the florida lottery. she has the choice of $13,800,000 today or a 20-year annuity of $1,050,000, with the first payment coming one year from today. what rate of return is built into the annuity? disregard taxes.
a. 3.77%
b. 4.38%
c. 3.90%
d. 4.03%
e. 4.12%
The rate of return built into the annuity is approximately 4.38%, calculated using the present value formula and solving for [tex]\( r \).[/tex]
To determine the rate of return built into the annuity, we set the present value of the annuity equal to the lump sum option.
The present value formula for an annuity is used, equating the lump sum amount of $13,800,000 to the present value of the annuity.
The formula is:
[tex]\[ 13,800,000 = 1,050,000 \times \frac{1 - (1 + r)^{-20}}{r} \][/tex]
Solving this equation for [tex]\( r \)[/tex], the annual interest rate (rate of return), requires numerical methods or a financial calculator.
Using trial and error or a financial calculator, we find that [tex]\( r \)[/tex] is approximately 4.38%.
This implies that the annuity offers a rate of return of 4.38% per year over the 20-year period, making it equivalent to receiving $13,800,000 today. Thus, the correct answer is option (b) 4.38%.