Paul has a tack stuck in his four-wheeler tire. If the tire has a diameter of 36 inches, how far does the tack travel in 62° of rotation?

Answers

Answer 1

Given:
Wheel diameter = 36 inches
Rotation = 62°

The radius is diameter/2 = 36/2 = 18 inches
Note that 1 revolution = 360° = 2π radians
Therefore
62° rotation = (62/360)*(2π) = 1.0821 radians.

The distance that the tack travels is
(18 in)*(1.0821 rad) = 19.478 in

Answer: 19.48 inches (approximately 19.5 inches)

Related Questions

There is an average of 3.5×10−2 kilograms of dissolved salt in each liter of seawater.

The Pacific Ocean contains approximately 6.6×1020 liters of seawater.

About how many kilograms of dissolved salt are in the Pacific Ocean?

Enter your answer, in scientific notation, in the boxes.

(blank) x 10(blank) kg

Answers

2.3x10^19 kg This is a matter of multiplication using scientific notation. First, multiply the mantissas 3.5 * 6.6 = 23.1 Then add the exponents -2 + 20 = 18 So we initially have 23.1x10^18 But 23 is too large (the number has to be greater than or equal to 1 and less than 10). So divide the 23.1 by 10 and add 1 to the exponent, getting 2.31x10^19 Then since the least accurate value we have for input has only 2 significant digits, round the result to 2 significant digits, getting 2.3x10^19 kg

IT IS 2.31, I AM TELLING YOU THIS IS 2.31

. Catie is 3 years older than her brother. The sum of their ages is no more than 31. Write an inequality that can be used to represent this situation, where x represents Catie's brother's age. Don’t combine like terms.

Answers

The answer is 17+x=31

Answer: So, the required inequality that can be used to represent this situation is [tex]2x+3\leq 31[/tex]

Step-by-step explanation:

Let the age of Catie's brother be 'x'.

Let the age of Catie be 'x+3'.

According to question, the sum of their ages is no more than 31.

So, it becomes,

[tex]x+x+3\leq 31\\\\2x+3\leq 31[/tex]

So, the required inequality that can be used to represent this situation is

[tex]2x+3\leq 31[/tex]

Trina employer purchased a health insurance plan that's costs $550 per month. Trina pays $85 toward the plan each month. What is the annual value of the employer contribution?

Answers

subtract the amount Trina pays from the total:

550 - 85 = 465 per month employer pays

12 months per year

465 * 12 = $5,580 per year is what the employer pays

Answer: $5580.00

Step-by-step explanation:

Donald baked 77 cookies in the morning and 83 cookies in the afternoon for 14 days how many total cookies did he bake

Answers

77 + 83 = 160, multiply that by 14 days, gives you 2,240

you need to add 77+83 which gives you 160 then multiply by 14 which gives you 1239

Which graph is represented by the following table?

The pictures show the table and graphs. The graphs are what can show which one is the answer.

Answers

the green line
x and y represents the coordinates of points on the line

The sum of the squares of two consecutive even integers is 452. find the integers.

Answers

let me know if you have any questions :-)

How do transformations in m and b effect the graph of y=mx+b

Answers

The equation y=mx+b is called the "slope-intercept" form of the equation of a line.

It is called so because if all the solutions (x, y) of this equation are plotted, they form a line with slope m and y-intercept b.

If m is positive, the line is increasing. So if m is positive, the greater the m, the more steeper the line, in increasing direction.

If m is negative, the line is decreasing. The smaller the m, the steeper the line, in decreasing direction.

b represents the y-intercept. If b is 0, the line passes through the origin. The larger the value of b, the higher the y-intercept. The smaller the value of b, the lower the y-intercept.

A quantity x varies directly with y and inversely with z. Which expression represents the constant of variation,k?

Answers

the answer is xz/y.

Answer:

The expression represents the constant of variation k is [tex]\frac{xz}{y}[/tex].

Step-by-step explanation:

As given

A quantity x varies directly with y and inversely with z.

[tex]x \propto y[/tex]

and

[tex]x \propto \frac{1}{z}[/tex]

Than combined the above equation.

[tex]x \propto \frac{y}{z}[/tex]

[tex]x = k\frac{y}{z}[/tex]

Where k is the constant of variation.

Than

[tex]k = \frac{xz}{y}[/tex]

Therefore the expression represents the constant of variation k is [tex]\frac{xz}{y}[/tex].

A toy manufacturer makes a toy truck, a toy car, and a toy boat. The production spreadsheet is:Toy Time to Produce Cost to Produce Profit for Each Truck 10 minutes $1.00 $1.00 Car 12 minutes $0.75 $1.50 Boat 8 minutes $0.80 $0.60 After accounting for breaks, a worker actually works 400 minutes each day. The manufacturer needs each worker to generate a potential profit of $35 each day. Write a system of inequalities that expresses these constraints

Answers

time profit number
truck 10 min 1.00dollar t
car 12min 1.50 dollar c
boat 8min 0.60 dollar b

let the worker produce t trucks, c cars, and b boats.
10t+12c+8b=400
t+1.5c+0.6b is more than or equal to 35
t is more than or equal to 0
c is more than or equal to zero
b is more than or equal to zero

(this question is kinda wierd. i do not know if i am correct, because mine is not exactly a system of inequalities, but if you really need an answer, you can try this one.)

Find the value of x so that f || g. The diagram is not to scale.

Answers

Lines f and g are parallel with a transversal forming same side interior angles with measures 3x and 5x + 36.

Theorem: If parallel lines are cut by a transversal, then same side interior angles are supplementary.

The angles measuring 3x and 5x + 36 are supplementary, so their measures add up to 180 degrees

3x + 5x + 36 = 180

8x + 36 = 180

8x = 144

x = 18

The answer is x = 18.

Answer:

The answer is 18

Step-by-step explanation:

given the equation -2x-13=8x+7, which order of operations completely solves for x

Answers

We can start by adding 2x to both sides (to put all of the x values on one side), as well as subtracting both sides by 7 to get variables on one side and numbers on the other, ending up with 10x=-20. After that, we can divide both sides by 10 to separate x and get x=-2

if right triangle LMN, L and M are complementary angles and sin (L) is 19/20 what is cos (M)

Answers

the right answer is 19/20 which is A i hope this helps

Answer: Value of cos(M) is

[tex]\cos M=\frac{19}{20}[/tex]

Step-by-step explanation:

Since we have given that

LMN is a right angled triangle where L and M are complementary angles ,

And,

[tex]\sin L=\frac{19}{20}=\frac{Perpendicular}{Hypotenuse}[/tex]

so, we will find base now by using "Pythagorus theorem":

[tex]H^2=B^2+P^2\\\\20^2=B^2+19^2\\\\400=B^2+361\\\\400-361=B^2\\\\39=B^2\\\\\sqrt{39}=B[/tex]

As we know that side opposite to mentioned theta is considered as perpendicular as shown in the figure ,

For M as [tex]\theta[/tex]

NL will be its perpendicular and MN will be its base and to find the cos(M) we use Base and Hypotenuse.

So, now we will find cos(M) i.e.

[tex]\cos M=\frac{Base}{Hypotenuse}=\frac{19}{20}[/tex]

Hence,

[tex]\cos M=\frac{19}{20}[/tex]

Find the Least Common Multiple of these two monomials:
16jk^8m^5 and 20j^9k^4m^6

36j^9k^8m^6
80j^9k^8m^6
4jk^4m^5
80j^10k^12m^11

Answers

lcm 16 & 10 = 80

lcm j^8 & j^9 = j^9

lcm k^8 & k^4 = k^8

lcm m^5 & m^6 = m^6

answer is: 80j^9k^8m^6

50 POINTS!!

What are the missing parts that correctly complete the proof?

Answers

2. ∠JKM≅∠LKM
5. MK≅MK
6. Transitive Property of Congruence
7. Corresponding parts of congruent triangles are congruent.
8. Definition of Equidistant

Answer:- 2. ∠JKM≅∠LKM

5. MK≅MK

6. AAS congruence postulate.

7. Corresponding parts of congruent triangles are congruent.

8. Definition of equidistant.

Therefore the complete proof will be

Proof :- 1. KM is the line bisector of ∠JKL. [Given]

2. ∠JKM≅∠LKM [Definition of bisector]

3. ∠KXM and ∠KYM are right angles [Given]

4. ∠KXM ≅ ∠KYM [All right angles are congruent]

5. MK≅MK [reflexive property of congruence]

6. ΔKXM ≅ ΔKYM [AAS congruence postulate]

7. MX≅MY [Corresponding parts of congruent triangles are congruent]

8. Point M is equidistant from the sides of ∠JKL [Definition of equidistant]

Hence proved.

The scale on a map shows that 2 inches represents 15 miles. Which proportion can be used to find the actual distance, x, represented by 30 inches on the map?

Answers

2 / 15 = 30 / x.....2 inches to 15 miles = 30 inches to x miles

could also be :

15 /2 = x/30...15 miles to 2 inches = x miles to 30 inches

either way, u will get the same answer

Answer:

I think it's 2/15 = 30/x

Step-by-step explanation:

sorry if it's wrong

Twice the sum of a number and 2 is equal to three times the difference of the number and 8. find the number please help

Answers

Answer:

Step-by-step explanation:

Let n represent the number.

Twice the sum of the number and 2 is ...

2(n +2)

Three times the difference of the number and 8 is ...

3(n -8)

The problem statement tells us these quantities are equal, so ...

2(n +2) = 3(n -8) . . . . the given quantities are equal

2n +4 = 3n -24 . . . . . use the distributive property to eliminate parentheses

2n +28 = 3n . . . . . . . add 24

28 = n . . . . . . . . . . . . subtract 2n

The number is 28.

_____

Check

The sum of the number and 2 is 30; twice that is 60.

The difference of the number and 8 is 20; three times that is 60--the same number.

A basketball team played 14 games. the team's mean score was 66 points. how many total points did they score in the 14 games?

Answers

924 is the answer i think

On Wednesday night in St. Petersburg, Russia, the temperature is -11°C. On the same night in Bombay, India, the temperature is 17°C. What is the difference in temperature? Show your work.

Answers

Hello! One number is negative and the other one is positive. In this case, we should find the difference they are from 0 and add the numbers up. -11 is 11 units away from 0. 17 is 17 units away from 0. 11 + 17 = 28. The difference in temperature is 28 degrees Celsius.

Determine the type and number of solutions of −4x^2 − 4x − 1 = 0

Help me please, I'm extremely behind in math

Answers

The question is about types and number of soultions so you must use b^2-4ac which is the experssion under the root in the quadratic formula
so
if
b^2-4ac=0 then there is one real soultion
if
b^2-4ac<0 then there are two imaginary soultions that differ in the sign between them
if
b^2-4ac>0 then there are two real soultions
so a polynomial is written in the form
ax^2+bx+c=0
so a=-4
b=-4
c=-1
so b^2-4ac=16-16=0
so one real soultion is the answer you are looking
type:real
number:1

How many 12ths are equivalent to 1/3?

Answers

multiply 1/3 by 4/4

4/12 is the answer

4/12 is equivalent to 1/3

If i run 5 miles in 38 minutes how many miles can i run in 57

Answers

The way you can solve this is divide 38 by 5 to find out how many miles you run per minute. In this case, it would be 7.6. Now, for each minute you run, add 7.6 to it and you will have ran 7.5 miles.

Decide whether the function is an exponential growth or exponential decay function, and find the constant percentage rate of growth or decay.
f(x) = 2479 ⋅ 0.9948x

Answers

Consider the function f ( x ) = 2479 ⋅ 0.9948x First compare this with f ( x ) po ( 1 + r ) ^ 2 We get po = 2479 And 1 + r = 0.9948 = 1 – 0.0052 r = -0.0052 < 0 Therefore, f is an exponential decay function with a decay rate of 0.0052 x 100 = 0.52%

PLEASE HELP ASAP!! Will give brainliest!

Answers

The first one is the second choice and the third one is the 4 choice. I know this because I had this homework and I got 100

PLEASE HELP!!!!

What is the distance between points M and N?

___ meters.

Answers

Answer:

The distance between points M and N is 9.8m.

Step-by-step explanation:

It is given that JKL is a triangle and M and N are the mid points of the KL and JL respectively.

Now, if we join the mid points together that is MN, then we can see that the basic proportionality holds that is:

[tex]\frac{LM}{MK}=\frac{LN}{NJ}[/tex]

[tex]\frac{10.7}{10.7}=\frac{7.4}{7.4}=\frac{1}{1}[/tex] which holds.

And which also proves that MN is parallel to JK.

Now, if MN is parallel to JK, then the measure of MN will be half the measure of JK, that is:

[tex]MN=\frac{1}{2}JK[/tex]

[tex]MN=\frac{1}{2}(19.6)[/tex]

[tex]MN=9.8 m[/tex]

Thus, the measure of MN is 9.8 meters.

Answer:

yah its 9.8 meters bro

Step-by-step explanation:

best of luck to yall on assignment and happy new year!!!

What is the missing term in the factorization? 18x2−32=2(3x+?)(3x−4)

Answers

Answer:

Step-by-step explanation:

[tex]18x^{2} -32 = 2(9x^{2} -16)[/tex]

we apply difference of squares

2(3x-4)(3x+4)

So, the missing term is 4.

The missing term in the factorization 18x² − 32 = 2(3x + ?)(3x − 4) is 4.

What is Factorization ?

Factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form. Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities.

For an integer, Factorization is decomposition of that integer in terms of smaller integers; when multiplied with each other give back that considered number. Those composing integers are called factors of that considered integers.

WE have given an expression as;

18x² − 32 = 2(3x + ?)(3x − 4)

Now we apply difference of squares;

2(9x² - 16)

2(3x + 4)(3x - 4)

2(3x-4)(3x+4)

Therefore, the missing term is 4.

Learn more about factorization here:

https://brainly.com/question/10454590

#SPJ2

The box plots show male and females grades in mathematics class: Which of the following best describes the information about the interquartile ranges?

Answers

I think the answer is "The interquartile range for females should be higher because the overall mean is higher".

Answer:

The interquartile ranges are quite close in value.

Step-by-step explanation:

We have been given two box-plots and we are asked to choose the correct statement about the interquartile ranges.

Since we know that interquartile range is difference between upper and lower quartile.

[tex]IQR=Q_3-Q_1[/tex]

Let us find IQR for the female grades in math.

We can see from box-plot representing female grades that upper quartile is about 90 and lower quartile is about 75.

[tex]\text{IQR of female grades}=90-75[/tex]

[tex]\text{IQR of female grades}=15[/tex]

Now let us find IQR for the male grades in math.

[tex]\text{IQR of male grades}=85-70[/tex]

[tex]\text{IQR of male grades}=15[/tex]

We can see IQR values for males and females are same, therefore, last statement is true.

How does doubling the side lengths of a triangle affect its area?

Answers

it doubles the area of it

What is the diameter of a dime in inches?

Answers

0.705 inches is the answer

The distributive property to express 48+72

Answers

Answer:

24(2+3)=24.2+24.3=48+72

Step-by-step explanation:

Given form of number is 48+72.

we have to apply the distributive property to express the above number.

The distributive property is

a(b+c)=ab+ac

Multiply the common term with the term inside the parentheses

So to express 48+72 we have to take the highest factor outside

Let us take 24 outside, we get

24(2+3)=24.2+24.3=48+72

Hence applied

The required expression is [tex]24(2+3)[/tex] by using the distributive property.

Given:

The given expression is [tex]48+72[/tex].

To find:

The equivalent expression by using the distributive property.

Explanation:

According to the distributive property:

[tex]a(b+c)=ab+ac[/tex]

We have,

[tex]48+72[/tex]

It can be rewritten as:

[tex]48+72=24\times 2+24\times 3[/tex]

Using the distributive property, we get

[tex]48+72=24(2+3)[/tex]

Therefore, the required expression is [tex]24(2+3)[/tex].

Learn more:

https://brainly.com/question/19652806

Which is an x-intercept of the graphed function?

Answers

The x-intercepts of the graphed function are -2, -1, 1, and 2

How to determine the x-intercept?

The x-intercept is the point where the graph crosses the x-axis

This means that the point on the x-axis where y = 0

From the graph, we have:

x = -2, -1, 1, and 2 when y = 0

Hence, the x-intercepts of the graphed function are -2, -1, 1, and 2