A small car has a tire with a 15-inch diameter. A mountain bike has a tire with a 27-inch diameter. How much father than the small car does the mountain bike have to drive for its tire to complete one revolution?
Answers
Answer:
The mountain bike will travel 37.7 inches farther than the small car in one complete revolution.
[tex]37.7\text{ inches}[/tex]Explanation:
The distance a tire travel in one complete revolution is equal to the circumference of the tire.
The circumference can be calculated using the formula;
[tex]C=2\pi r=\pi d[/tex]Where;
C = Circumference
r = radius of tire
d = diameter of the tire
For the small car with tire of diameter 15 inches, the distance travelled in one revolution is;
[tex]\begin{gathered} C_1=\pi d_1=\pi(15)=15\pi \\ C_1=47.12\text{ inches} \end{gathered}[/tex]For the mountain bike with tire of diameter 27 inches, the distance travelled in one revolution is;
[tex]\begin{gathered} C_2=\pi d_2=\pi(27)=27\pi_{} \\ C_2=84.82\text{ inches} \end{gathered}[/tex]The difference between the distance travelled in one complete revolution is;
[tex]\begin{gathered} \Delta C=C_2-C_1=84.82-47.12 \\ \Delta C=37.70\text{ inches} \end{gathered}[/tex]Therefore, the mountain bike will travel 37.7 inches farther than the small car in one complete revolution.
[tex]37.7\text{ inches}[/tex]Related Questions
Take away 5 from p????????????????
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Answer:
p - 5
Step-by-step explanation:
5 - p = p - 5
Really need help solving this practice from my ACT prep guide It’s a trig practice
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Given:
- The amplitude of the Sine Function:
[tex]A=10[/tex]- The midline:
[tex]y=4[/tex]- And the period:
[tex]Period=2[/tex]- You know that the function does not have a Phase shift.
• You need to remember that, by definition, the General Equation for a Sine Function has this form:
[tex]y=Asin\mleft(B\mleft(x+C\mright)\mright)+D[/tex]Where "A" is the amplitude, "C" is the phase shift, "D" is the vertical shift and this is the period:
[tex]Period=\frac{2\pi}{B}[/tex]Since the midline is given by the vertical shift, you can identify that, in this case:
[tex]D=4[/tex]And, knowing the period, you can set up that:
[tex]2=\frac{2\pi}{B}[/tex]Solving for "B", you get:
[tex]\begin{gathered} 2B=2\pi \\ \\ B=\frac{2\pi}{2} \\ \\ B=\pi \end{gathered}[/tex]• It is important to remember the following Transformation Rule for Functions:
When:
[tex]-f(x)[/tex]The function is reflected over the x-axis.
Therefore, knowing all the data, you can set up this equation:
[tex]f(x)=-10\sin (\pi x)+4[/tex]Hence, the answer is: First option.
1f(x) =X-24g(x)ХFind: (fog)(x) =
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We have the functions:
[tex]undefined[/tex]s
The measure of the supplement of an angle exceeds twice the measure of the complement of the angle by 20. Find the measure of half of the complement
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The supplement is when two angles add up to 180° and complement is when two angles add up to 90°
let:
x = the angle.
180 - x = its supplement.
90 - x = its complement
then x = 2(90-x) + 20 means the measure of the supplement of an angle exceeds twice the measure of the complement of the angle by 20
Graph the equation after rewriting it in slope-intercept form. Y-3x=4
Answers
We have this equation
[tex]y-3x=4[/tex]The following is the slope intercept form
[tex]y=mx+b[/tex]add 3x on both sides of the equation
[tex]y-3x+3x=4+3x[/tex]simplify
[tex]y=4+3x[/tex]rearrange
[tex]y=3x+4[/tex]So, the above is the equation in slope-intercept form
Now, let's graph the equation
since this is a linear equation, we need to find 2 points and plot them in the chart
let's find point 1. Let's say x = 0 and replace: y = 3x+4 = 3*0 + 4 = 0 + 4 = 4
so, when x=0, then y = 4 , so our 1st point is (0,4)
now, let's suppose, y=0 , in that case, y = 3x + 4 = 0 , then 3x = -4 , so the value of x is -4/3 = -1.3333
in that case, our seconds point is (-4/3 , 0)
just to make sure, we can also plot a 3rd point, let's say we make x = 2, then y = 3*2 + 4 = 6 + 4 = 10
so, our 3rd point is (2, 10)
using the points above, we can plot something like this...
How many different regrestation codes are possible. And also what is the probability that all the first three digits of the code are not even numbers.
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a) Consider the 7-digit registration code to be an arrangement of 7 cells to be filled using the given digits.
In the first cell, one can write any of the digits; on the other hand, there are only 6 digits available to fill the second cell (no number can be used more than once). Therefore, there are 5 digits that can be used in the third cell and so on; thus, there is a total of
[tex]7*6*5*4*3*2*1=7!=5040[/tex]5040 different registration codes.b) The 5040 different combinations found above are equally probable.
There are only 3 available even numbers (2, 4, and 6); therefore, we need to find the number of combinations such that none of the first three digits is equal to 2, 4, or, 6.
Thus, using a diagram,
There are 4 possible numbers that one can fit in the first cell (1,5,7, or 9), in the second cell, one can fit 3 numbers (any of the remaining ones from cell 1), and so on.
In the fourth cell (first cell in blue), one can fit any even number plus a remaining odd number from cell 3.
Therefore, the total number of codes such that their first three digits are not even are
[tex]4*3*2*4*3*2*1=576[/tex]Then, the corresponding probability is
[tex]P=\frac{576}{5040}=\frac{4}{35}[/tex]The answer to part b) is 4/35Any math tutors available to help me ? I need help
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Hello!
First of all, let's write the initial temperature:
• 6am: 58ºF
In next 5 hours, the temperature rose 1ºF per hour, so:
• 7am: 59ºF
,• 8am: 60ºF
,• 9am: 61ºF
,• 10am: 62ºF
,• 11am: 63ºF
In the next 3 hours, it rose 3ºF per hour:
• 12pm: 66ºF
,• 1pm: 69ºF
,• 2pm: 72ºF
The temperature stayed steady until 6pm:
• In this part, we'll have a constant line until 6pm (it will be 72ºF in all).
In the next 4 hours, the temperature dropped 2ºF per hour:
• 7pm: 70ºF
,• 8pm: 68ºF
,• 9pm: 66ºF
,• 10pm: 64ºF
Dropped steadily until 63ºF at midnight
• 12am: 63ºF
Now, let's make the graph!
8. MOVIE TICKETS Tickets to a movie cost $25 for adults and 5.50 formodents A group of friends purchased 8 tickets for $52.75 a Write a system of equations to represent the station
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Tickets for adults --> $25
Tickets for formodents --> $5.50
The equations that would represent the number of adults and formodents in th group of friends:
Let x be adults
Let y be formodents
$25x+$5.50y=$52.72
x+y=8
I need help on this equation. It’s algebra. SAT PREP.
Answers
Answer:
r = 1.14
Explanation:
The value of a product (A) over time with an increasing rate "i" can be calculated as follows:
A = C(1+i)^t
where:
C is the value of the product at time 0;
A is the value of the product at time t;
i is the increasing rate.
If we compare the expression V=300r^t with A = C(1+i)^t. We can observe that:
r = 1+i
r = 1+0.14
r = 1.14
Christina's purchasing a new TV. She was approved to finance the TV with zero interest. If Christina gives a one-time payment of $300 and pays $65 per month, how much has she paid in 5 months? (show work)
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Given:
One time payment, p = $300
Payment per month, q = $65
Number of months paid, n = 5
The objectiv is to find the amount she paid in 5 months.
Let x be the amount she paid in 5 months. Then the the formula is,
[tex]x=p+nq[/tex]Let's substitute the values.
[tex]\begin{gathered} x=300+5(65) \\ x=300+325 \\ x=625 \end{gathered}[/tex]Hence, total amount paid in 5 months is $625.
Find the x-intercept and the y-intercept without graphing. Write the coordinates of each intercept. When typing the point (x,y) be sure to include parentheses and a comma between your x and y components. Do not put any spaces between your characters. If a value is not an integer type your answer rounded to the nearest hundredth.3x+8y=24the x-intercept is Answerthe y-intercept is Answer
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We want to find the x and y-intercepts of
[tex]3x+8y=24[/tex]The x-intercept is where the graph cuts the x-axis, when y = 0. To find this in our equation, we just need to evaluate it at y = 0.
[tex]\begin{gathered} 3x+8\times0=24 \\ 3x=24 \\ x=\frac{24}{3}=8 \end{gathered}[/tex]Then, the x-intercept is (8, 0).
The y-intercept is where the graph cuts the y-axis, when x = 0. To find this in our equation, we just need to evaluate it at x = 0.
[tex]\begin{gathered} 3\times0+8y=24 \\ 8y=24 \\ y=\frac{24}{8}=3 \end{gathered}[/tex]The y-intercept is (0, 3).
5) Francisco practiced playing his violin for 2 1/3 hours on Sunday. He practiced for 5/6 hour on Monday. How much time did Francisco spend playing his violin?(C)1 hours 3 (A)1 hours (B) hour (D) 3-hours, 10 min
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Answer:
D
Francisco spent 3 hours, 10 minutes playing his violin
Explanation:
Given that:
Francisco practised playing his violin for
2 hours on Sunday
5/6 hours on Monday
The total number of time he spends playing his violin is obtained by adding the number of hours he spends each day.
[tex]\begin{gathered} 2\frac{1}{3}+\frac{5}{6} \\ \\ =\frac{7}{3}+\frac{5}{6} \\ \\ =\frac{19}{6} \\ \\ =3\text{ }\frac{1}{6} \end{gathered}[/tex]This is 3 hours, 10 minutes.
Simplify f(x) = 2x^5 for x = 0, 1, 3, 5
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f(0) = 0, f(1) = 2, f(3) = 486, f(5) = 6250
Explanations:The given function is:
[tex]f(x)=2x^5[/tex]To get the value of f(x) for x = 0, 1, 3, and 5, it means we are going to find f(0), f(1), f(3), and f(5).
[tex]\begin{gathered} f(0)=2(0)^5 \\ f(0)\text{ = 2(0)} \\ f(0)\text{ = 0} \end{gathered}[/tex][tex]\begin{gathered} f(1)=2(1)^5 \\ f(1)\text{ = 2(1)} \\ f(1)\text{ = 2} \end{gathered}[/tex][tex]\begin{gathered} f(3)=2(3)^5 \\ f(3)\text{ = 2 (}243) \\ f(3)\text{ = 486} \end{gathered}[/tex][tex]\begin{gathered} f(5)=2(5)^5 \\ f(5)\text{ = 2(}3125) \\ f(5)\text{ = }6250 \end{gathered}[/tex]If 2 dogs cross over a road and 1 dog disappear in the road how did the other dog made it
Answers
Answer:
he was quick???
Step-by-step explanation:
Mark me brainliest!
7(-a-3)=3(2a-6) I have the answer but I need help checking it.
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SOLUTION:
Step 1:
In this question, we are meant to solve the following:
[tex]7\text{ ( - a - 3 ) = 3 ( 2a - 6 )}[/tex]Step 2:
Simplifying, we have that:
[tex]\begin{gathered} -7a\text{ - 21 = 6a - 18} \\ \end{gathered}[/tex]collecting like terms, we have that:
[tex]\begin{gathered} -21\text{ + 18 = 6 a + 7a} \\ 13\text{ a = -3} \\ \text{Divide both sides by 13, we have that:} \\ a\text{ = }\frac{-3}{13} \end{gathered}[/tex]Step 3:
To verify that:
[tex]a\text{ =}\frac{-3}{13}[/tex]is a solution, we have that:
[tex]7\text{ ( - a - 3 ) = 7 \lbrack -(}\frac{-3}{13}\text{ ) - 3 \rbrack}[/tex][tex]7\lbrack\text{ }\frac{3}{13}\text{ - 3\rbrack = 7 \lbrack }\frac{3}{13}\text{ - }\frac{39}{13}\text{ \rbrack = 7 x }\frac{-36}{13}\text{ = }\frac{-252}{13}\text{ ( Left Hand Side)}[/tex]Next,
[tex]3\text{ ( 2 a - 6 ) = 3 \lbrack{}2(}\frac{-3}{13})\text{ - 6 }\rbrack\text{ = 3 \lbrack}\frac{-6}{13}\text{ - 6\rbrack= 3\lbrack}\frac{-6}{13}\text{ - }\frac{78}{13}\rbrack[/tex][tex]=\text{ 3 \lbrack }\frac{-84}{13}\text{ \rbrack = }\frac{-252}{13}\text{ ( Right Hand Side)}[/tex]CONCLUSION:
From the solution and from the verification of the answers, we can see that the correct answer is:
[tex]a\text{ = }\frac{-\text{ 3}}{13}[/tex]can someone please help me solve and graph this the past few have been incorrect and this is my homework and i really need help
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step 1
Solve the inequality
[tex]\begin{gathered} 3x+8\leq11 \\ 3x\leq11-8 \\ 3x\leq3 \\ x\leq1 \end{gathered}[/tex]the solution for the first inequality is the interval
(-infinite, 1]
step 2
Solve the inequality
[tex]\begin{gathered} 3x+8\text{ > 20} \\ 3x\text{ > 20-8} \\ 3x\text{ > 12} \\ x\text{ > 4} \end{gathered}[/tex]the solution for the second inequality is the interval
(4, infinite)
step 3
the general solution for the first inequality or the second inequality is
(-infinite, 1] U (4, infinite)see the attached figure to better understand the problemWhat is the surface area of the solid that this net can form?8 mm25 mm8 mm5 mm5 mm8 mm8 mm5 mm5 mm8 mm8 mm25 mmO 730 square millimetersO 875 square millimeters0 1,000 square millimetersO 1,444 square millimeters
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The solid is formed by 6 rectangles.
Calculate the area of each one and then add them to obtain the surface area (SA),
Area of a rectangle: Length x width
A1 = 8 x 5 = 40 mm2
A2= 25x5 = 125 mm2
A3 = 8 x 5= 40 mm2
A4 = 25 x 8 = 200 mm2
A5 = 25x5 = 125 mm2
A6 = 25 x 8 = 200mm2
SA = A1+A2+A3+A4+A5+A6 = 40 + 125 +40 +200 +125+ 200 = 730 mm2
I know this is easy and i should know but im actually stumped on this one
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For the given triangles:
There are 3 pairs of congruent angles
the triangles can not be proved using the congruent angles
the congruent angles used to prove the similarity of the triangles
So, the answer will be:
For the given triangle, we can not prove they are congruent.
what is the equation of a line that passes through point (-1,5) and has the slope of m=4
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The general equation of a line is given as;
[tex]y=mx+b[/tex]In this question, the slope (which is m) is given as 4. Also we have the points x and y, given as (-1, 5). That is;
[tex]x=-1,y=5[/tex]Therefore the next step is to find the y-intercept (that is b in the equation).
We substitute for the known values as follows;
[tex]\begin{gathered} y=mx+b \\ 5=4(-1)+b \\ 5=-4+b \\ \text{Add 4 to both sides} \\ 5+4=-4+4+b \\ 9=b \end{gathered}[/tex]Now we know the value of b and m, we can substitute them as follows;
[tex]\begin{gathered} y=mx+b \\ m=4,b=9 \\ y=4x+9 \end{gathered}[/tex]3. Square SQRE has coordinates S(2, 2) Q (5,2)R (5. – 1). Find the coordinates of E. I gotta turn it in tomorrow
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Given:
Square SQRE has coordinates S(2, 2) Q (5,2), and R (5. – 1).
To find:
The coordinates of E.
Explanation:
Let (x, y) be the coordinates of E.
Using the midpoint formula,
[tex]p=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]As we know,
The diagonals of the square are intersected by its midpoint.
So, the Midpoint of SR and QE is the same in a given square SQRE.
[tex]\begin{gathered} Midpoint\text{ of SR = Midpoint of QE} \\ (\frac{2+5}{2},\frac{2-1}{2})=(\frac{5+x}{2},\frac{2+y}{2}) \\ (\frac{7}{2},\frac{1}{2})=(\frac{5+x}{2},\frac{2+y}{2}) \end{gathered}[/tex]Equating the coordinates we get,
[tex]\begin{gathered} \frac{7}{2}=\frac{5+x}{2} \\ 7=5+x \\ x=2 \\ \frac{1}{2}=\frac{2+y}{2} \\ 1=2+y \\ y=-1 \end{gathered}[/tex]Therefore, the coordinate of E is (2, -1).
Final answer:
The coordinate of E is (2, -1).
the parent function name for y=|x|
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This function is an absolute type of function
May I please get help with this math problem please I have tried so many times but still could not get the right answers
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We know that the sum of interior angles of a triangle equals 180, then, in this case we have the following:
[tex]90+2x+17+3x+28=180[/tex]solving for x, we get:
[tex]\begin{gathered} 90+2x+17+3x+28=180 \\ \Rightarrow135+5x=180 \\ \Rightarrow5x=180-135=45 \\ \Rightarrow x=\frac{45}{5}=9 \\ x=9 \end{gathered}[/tex]therefore, x = 9
cole is studying ceramics and he was asked to submit 5 vessels from his collection to exhibit at the fair. he has 15. vessels that he thinks are show worthy. in how many ways can the vessels be chosen
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Since he has 15 vessels and needs to choose 5, we can use a combination of 15 choose 5 to calculate the number of possible ways, since the order of the vessels inside the group of 5 is not important.
The formula to calculate a combination of n choose p is:
[tex]C(n,p)=\frac{n!}{p!(n-p)!}[/tex]Then, for n = 15 and p = 5, we have:
[tex]\begin{gathered} C(15,5)=\frac{15!}{5!(15-5)!}=\frac{15!}{5!10!}=\frac{15\cdot14\cdot13\cdot12\cdot11\cdot10!}{5\cdot4\cdot3\cdot2\cdot10!} \\ =\frac{15\cdot14\cdot13\cdot12\cdot11}{5\cdot4\cdot3\cdot2}=3003 \end{gathered}[/tex]So there are 3003 ways to choose the 5 vessels.
For the problem below, find the reference angle, to the nearest 10th (if necessary), and also the two possible quadrants in which θ could lie.tan(θ)=−3
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The two possible quadrants are the second and the fourth
What is the solution to 2x + 2(x – 5)=6,explainhow you solved the equation.explain with words
Answers
Answer
The solution to the equation is x = 4.
Explanation
We are told to find the solution to the equation
2x + 2(x - 5) = 6
The first step is to open the bracket by multiplying through by the number outside the bracket, that is, 2.
2x + 2x - 10 = 6
4x - 10 = 6
Add 10 to both sides to leave only 4x on the Left Hand Side.
4x - 10 + 10 = 6 + 10
4x = 16
Divide both sides by 4 to obtain the value of x.
(4x/4) = (16/4)
x = 4
Hope this Helps!!!
A state sales tax of 6% and a local sales tax of 1% are levied in Tampa, Florida. Suppose the price of a particular car in Tampa is $15,000, and an oil change at a certain auto center is $29.Which statement is true another total cost of the car and the oil change after sales tax has been calculated?Select the correct answer
Answers
We have the following:
What we must do is calculate the total cost of the car by adding its original value plus the cost of taxes, 6% and 1%
We know that the initial value is $15000, if to that we add 6% of those $15000 and equal 1%, we have
[tex]15000+15000\cdot0.06+15000\cdot0.1=15000+900+150=16050[/tex]We do the same procedure for the oil change
[tex]29+29\cdot0.06+29\cdot0.01=29+1.74+0.29=31.03[/tex]Therefore the correct statement is the last
Larry answered 8 out of every 10 questions correctly. The test had 70 questions. How many correct answers did Larry give?---What represents the "x" or unknown in this problem?
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Representation of fractional numbers
Larry's rate of succesful questions is 8/10.
Then must find how many times is divided 70 in 10 questions
70/10 = 7
if there were a 100% succesful then 70 rresulted
but the rate is 8/10 , then multiply 8x 7 = 56 succesful questions for Larry.
Select all the pairs that represent alternate interior angles.See image for instruction
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Alternate means on the opposite side of the transversal, or line n
interior means inside of the parallel lines l and m
The alternate interior angles are 4 and 5
and 3 and 8
Check the boxes for both pairs
Hello for this particular problem can I change the final results to a whole number? or it is not possible?
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We are asked which of the given combinations will produce a number that is less or equal to 25.
For A we have:
[tex]A=3(8\frac{3}{4})[/tex]Let's remember that for a mixed fraction we have:
[tex]a\frac{b}{c}=a+\frac{b}{c}[/tex]Therefore, we can change the mixed fraction and we get:
[tex]A=3(8\frac{3}{4})=3(8+\frac{3}{4})[/tex]Solving the operations:
[tex]A=26.25[/tex]Since we get a number greater than 25 this is not a trail he can ride.
For B we have:
[tex]B=2(10\frac{1}{4})[/tex]Changing the mixed fraction:
[tex]B=2(10\frac{1}{4})=2(10+\frac{1}{4})[/tex]To solve the operation we will apply the distributive property:
[tex]B=20+2\times\frac{1}{4}[/tex]Now, we simplify the fraction:
[tex]B=20+2\times\frac{1}{4}=20+\frac{1}{2}[/tex]Now, we use the fact that 1/2 = 0.5:
[tex]B=20+\frac{1}{2}=20+0.5=20.5[/tex]Since we get a number that is less than 25 this is a train he can ride.
For C we have:
[tex]C=2(7\frac{1}{2})+10\frac{1}{4}[/tex]Changing the mixed fraction:
[tex]C=2(7+\frac{1}{2})+10+\frac{1}{4}[/tex]Now, we apply the distributive property:
[tex]C=14+1+10+\frac{1}{4}[/tex]Solving the operations. We use the fact that 1/4 = 0.25:
[tex]C=25+0.25=25.25[/tex]Since we get a number greater than 25 this is not a trail he can ride.
For D.
[tex]D=7\frac{1}{2}+2(8\frac{3}{4})[/tex]Now, we change the mixed fractions:
[tex]D=7+\frac{1}{2}+2(8+\frac{3}{4})[/tex]Now, we use the distributive property:
[tex]D=7+\frac{1}{2}+16+2\times\frac{3}{4}[/tex]Simplifying the fraction:
[tex]D=7+\frac{1}{2}+16+\frac{3}{2}[/tex]Now, we add the fractions, we have into account that when fractions have the same denominator we can add the numerators and use the common denominator, like this:
[tex]D=7+\frac{4}{2}+16[/tex]Simplifying the fraction we get:
[tex]D=7+2+16[/tex]Solving the operations:
[tex]D=25[/tex]Since we get 25 this is a trail that he can ride.
There are 27 students in Mr. Mello's class. Find the total number of pages the students
read by the end of November.
WILL GET 100 POINTS AND BRAINLIST.
Answers
Answer:
No solution.
Step-by-step explanation:
Why I say this problem has no solution is due to the fact that the amount of pages is unclassified. This leads you to guessing how many pages there might be for each chapter of the students' individual books, and guessing would not be an effective method as it could lead you to thinking of any random number between 1 - 60 at the most. Therefore, this problem has no solution. If you have further concerns about this problem, I recommend addressing them to your teacher. Otherwise, have a great day. :)