Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 3 inches, and the larger gear has a radius of 7 inches.
Part 1: What is the angle measure, in degrees and rounded to the nearest tenth, through which the larger gear has rotated when the smaller gear has made one complete rotation?
Part 2: How many rotations will the smaller gear make during one complete rotation of the larger gear?
Show all work.
Answers
B)since the circumference of the larger gear is 14pi in one rotation the smaller gear would have rotated a length of 14pi. Thus 14pi/6pi=2.3 or 7/3 rotations.
Related Questions
Jim’s fundraiser BBQ needs to make at least $1000 in sales on Saturday. He sells hot dogs for $2 each and hamburgers for $3 each, and he wants to sell at least twice as many hamburgers as hot dogs. He brought 300 hot dogs and 800 hamburgers to sell. The graph shows the feasible region, where x represents the number of hot dogs sold and y represents the number of hamburgers sold. Which ordered pairs meet all the constraints for a successful fundraiser and make sense in context of the situation?
Select each correct answer.
(275, 0)
(100.5, 800.5)
(0, 350)
(250, 700)
(200, 350)
Answers
Find (f - g)(x).
f(x) = -3x + 2
g(x) = x3
Answers
Answer:
[tex](f-g)(x) = -x^{3} - 3\cdot x + 2[/tex]
Step-by-step explanation:
The new function is:
[tex](f-g) (x) = -3\cdot x + 2 -x^{3}[/tex]
[tex](f-g)(x) = -x^{3} - 3\cdot x + 2[/tex]
Which property justifies this statement? If 4x=20, then x=5. Division Property of Equality Reflexive Property of Equality Substitution Property of Equality Subtraction Property of Equality
Answers
Answer:
Option 1 - Division Property of Equality
Step-by-step explanation:
Given : If [tex]4x=20[/tex], then x=5.
To find : Which property justifies this statement?
Solution :
The equation is [tex]4x=20[/tex]
To make variable separate we have to remove 4 which is in multiple of variable x.
So, We divide both side by 4,
Applying division property of equality,
We can divide both sides of an equation by the same number and preserve equality.
[tex]\frac{4x}{4}=\frac{20}{4}[/tex]
[tex]x=5[/tex]
Therefore, The property justifies the statement is 'Division Property of Equality'.
So, Option 1 is correct.
Javier wants to inscribe a circle inside of the triangle ABC shown in the following figure. He begins by constructing the angle bisectors of angles A and B and finding their intersection at point D.
If Javier is trying to inscribe a circle inside of triangle ABC in as few steps as possible, which of the following steps would be the best step for him to take next?
1) Construct the perpendicular line from point D to the line BC.
2) Find the altitude from point C.
3) Use the distance from D to any of the triangle's vertices to set the width of the compass.
4) Construct the angle bisector of angle C.
Thank you :)
Answers
All 3 angle bisectors meet at D, so drawing the angle bisector of C is useless. (Thus step 4 is not the one).
Since we have the center of the inscribed circle, we want to open the compass so that it touches all 3 sides at one point only, that is, we want the 3 sides to be tangent to this circle.
The segments joining the tangency points and D are 3 radii of the circle. We know that a radius is perpendicular to the tangent it touches.
Thus, we need to draw an altitude from D to any of the sides.
Answer: 1
A Springer Spaniel weighs 20 kilograms 490grams. A Cocker Spaniel weighs 7,590 grams less than a Springer Spaniel. A Newfoundland weighs 52 kilograms 656 grams more than a Cocker Spaniel. What is the difference, in grams, between the weights of the Newfoundland and the Springer Spaniel?
Answers
To find the difference in weight between the Newfoundland and the Springer Spaniel, subtract the weight of the Springer Spaniel from the weight of the Newfoundland.
Explanation:To find the difference in weight between the Newfoundland and the Springer Spaniel, we need to subtract the weight of the Springer Spaniel from the weight of the Newfoundland. The Newfoundland weighs 52 kilograms 656 grams more than a Cocker Spaniel. So, we first need to find the weight of a Cocker Spaniel by subtracting 7,590 grams from the weight of the Springer Spaniel. We then add this weight to the weight of the Newfoundland to get the final answer. Let's calculate:
The weight of the Cocker Spaniel = Weight of Springer Spaniel - 7,590gThe weight of the Newfoundland = Weight of Cocker Spaniel + 52kg 656gFinally, the difference in weight between the Newfoundland and the Springer Spaniel is the weight of the Newfoundland - weight of the Springer SpanielWe can now substitute the given values into these equations and solve.
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Twice the difference between 6 times h and 3 gives 30
Answers
2(6h-3) = 30
Tristan jogs a route that is 7/10 mile. If he wants to jog between 2 and 3 miles, how many times should he plan to run the route? Circle the letter for all that apply.
A. 2 times
B 3 times
C. 4 times
D. 5 times
Answers
Answer:
B 3 times
C. 4 times
Step-by-step explanation:
For Tristan to jog between 2 and 3 miles, the number of times he would have to jog the route that is 7/10 mile must be such that the product of the number of times and 7/10 miles gives a number between 2 and 3.
Considering the options given
A. 2 * 7/10 = 1.4 miles (this is not within the range)
B. 3 * 7/10 = 2.1 miles (this is within the range)
C. 4 * 7/10 = 2.8 miles (this is within the range)
D. 5 * 7/10 = 3.5 miles (this is not within the range)
Does each function describe exponential growth or decay?
Drag and drop the equations into the boxes to correctly complete the table.
Growth Decay
y=100(1−12)^t
y=0.1(1.25)^t
y=((1−0.03)12)^2t
y=426(0.98)^t
y=2050(12)^t
Answers
A function [tex]f[/tex] from a set [tex]A[/tex] to a set [tex]B[/tex] is a relation that assigns to each element [tex]x[/tex] in the set [tex]A[/tex] exactly one element [tex]y[/tex] in the set [tex]B[/tex]. The set [tex]A[/tex] is the domain (also called the set of inputs) of the function and the set [tex]B[/tex] contains the range (also called the set of outputs).
[tex]We \ denote \ the \ \mathbf{exponential \ function} \ f \ with \ base \ a \ as: \\ \\ f(x)=a^x \\ \\ where \ a>0, \ a\neq 1, \ and \ x \ is \ any \ real \ number[/tex].
1. It isn't an exponential function.
We have the following equation:
[tex]y=100(1-12)^t[/tex]
That can be written as:
[tex]y=100(-11)^t[/tex]
Recall that the definition of exponential functions establishes that:
[tex]We \ denote \ the \ \mathbf{exponential \ function} \ f \ with \ base \ a \ as: \\ \\ f(x)=a^x \\ \\ where \ a>0, \ a\neq 1, \ and \ x \ is \ any \ real \ number[/tex].
That is:
[tex]a \ \mathbf{must} \ be \ greater \ than \ 1[/tex]
In this problem, [tex]a=-11[/tex], therefore this is not an exponential function.
2. Growth.
The function:
[tex]y=0.1(1.25)^t[/tex]
is an exponential function because is a function of the form [tex]f(t)=ka^t \\ \\ where \ a>0 \ and \ k \ constant[/tex]
So [tex]k=0.1 \ and \ a=1.25[/tex]. Since [tex]a \ is \ greater \ than \ 1[/tex] and being raised to the power of [tex]t[/tex], the function increases. This means that [tex]y[/tex] increases as [tex]t[/tex] increases as illustrated in Figure 1. This represents a growth.
3. Growth.
The function:
[tex]y=((1-0.03)12)^{2t}[/tex] can be written as:
[tex]y=11.64^{2t}[/tex]
and is an exponential function because is a function of the form [tex]f(t)=a^{bt} \\ \\ where \ a>0 \ and \ b \ constant[/tex]
So [tex]a=11.64 \ and \ b=2[/tex]. Since [tex]a \ is \ greater \ than \ 1[/tex] and being raised to the power of [tex]2t[/tex], the function increases. As in the previous exercise, this means that [tex]y[/tex] increases as [tex]t[/tex] increases as illustrated in Figure 2. This represents a growth.
4. Decay.
The function:
[tex]y=426(0.98)^t[/tex]
is an exponential function because is a function of the form [tex]f(t)=ka^t \\ \\ where \ a>0 \ and \ k \ constant[/tex]
So [tex]k=426 \ and \ a=0.98[/tex]. Since [tex]a \ is \ less \ than \ 1[/tex] and being raised to the power of [tex]t[/tex], the function decreases. Here this means that [tex]y[/tex] decreases as [tex]t[/tex] increases as illustrated in Figure 3. This represents a decay.
5. Growth.
The function:
[tex]y=2050(12)^t[/tex]
is an exponential function because is a function of the form [tex]f(t)=ka^t \\ \\ where \ a>0 \ and \ k \ constant[/tex]
So [tex]k=2050 \ and \ a=12[/tex]. Since [tex]a \ is \ greater \ than \ 1[/tex] and being raised to the power of [tex]t[/tex], the function increases. So in this function [tex]y[/tex] also increases as [tex]t[/tex] increases as illustrated in Figure 4. This represents a growth.
Answer:
1. isn't an exponential function
2. growths
3. growths
4. decay
5. growths
Step-by-step explanation:
The exponential functions has the form: y = k1*k2^(k3*t), where k1, k2 and k3 are a constants, and k2>0. Graph of exponential functions always decrease or always increase. To know if a function growths or decay just evaluate the function in 2 points, for example t = 0 and t = 1, and compare their results.
1.
y = 100*(1−12)^x = 100*(−11)^x
Since (-11) is negative, then y is not an exponential function
2.
y(0) = 0.1*(1.25)^(0) = 0.1
y(1) = 0.1*(1.25)^(1) = 0.125
y(1) > y(0) -> growths
3.
y(0) =((1−0.03)12)^2(0) = 1
y(0) =((1−0.03)12)^2(1) = 135.4896
y(1) > y(0) -> growths
4.
y(0) = 426(0.98)^(0) = 426
y(1) = 426(0.98)^(1) = 417.48
y(1) < y(0) -> decay
5.
y(0) = 2050(12)^(0) = 2050
y(1) = 2050(12)^(1) = 24600
y(1) > y(0) -> growths
What is the simplified form of the following expression?
(n5)(n2)
Answers
Change each fraction to a decimal. If the division doesn’t end, round your answer to the nearest hundredth. a. 3⁄4 b. 7⁄16 d. 3⁄5 e. 7⁄40 f. 51⁄20
Answers
Answer:
a = 0.75
b= 0.4375
d= 0.6
e=0.175
f= 2.55
Step-by-step explanation:
By simple division method, the following answers can be calculated:
a.
=[tex]\frac{3}{4}[/tex]
=0.75
b.
= [tex]\frac{7}{16}[/tex]
=0.4375
d.
= [tex]\frac{3}{5}[/tex]
=0.6
e.
= [tex]\frac{7}{40}[/tex]
=0.175
f.
=[tex]\frac{51}{20}[/tex]
=2.55
Thus, the answer are :
a = 0.75
b= 0.4375
d= 0.6
e=0.175
f= 2.55
Answer:
A.0.75 B.0.4375 C. 14.4 D. 0.6 E. 0.175 F. 2.55
Step-by-step explanation:
What x-value makes the set of ratios equivalent? Tiles 2 : 3 = 6 : x ,4 : 7 = x : 42 , 2x : 48 = 3 : 12, 12 : 15 = x : 20
Pairs691624
Answers
The missing x-values are 9, 24, 12, and 16, ensuring proportions remain equal in each ratio set.
To find the missing values that make the sets of ratios equivalent, we can use proportions.
1. Tiles 2 : 3 = 6 : x
Cross multiplying, we get: 2x = 18
So, x = 9
2. 4 : 7 = x : 42
Cross multiplying, we get: 7x = 168
So, x = 24
3. 2x : 48 = 3 : 12
Cross multiplying, we get: 12x = 144
So, x = 12
4. 12 : 15 = x : 20
Cross multiplying, we get: 15x = 240
So, x = 16
Therefore, the x-values that make the sets of ratios equivalent are:
1. x = 9
2. x = 24
3. x = 12
4. x = 16
What is 0 to the 0 power?
Answers
The value of 0 to the power of 0 (0^0) is undefined, it may be treated as 1.
Explanation:The value of 0 raised to the power of 0 (0^0) is undefined.
Mathematically, any nonzero number raised to the power of 0 is equal to 1. However, 0^0 is an indeterminate form, meaning that it does not have a well-defined value.
When evaluating expressions involving 0^0, different contexts may assign different values to it. In some cases, it may be treated as 1, while in others, it may be considered as undefined.
What is the remainder of 860 divided by 14?
Answers
7 / 3 = 2.333r or 2 remainder 1, because 3 fits into 7 twice, with 1 left over.
7/4 = 1 remainder 3
8/4 = 2 remainder 0, however we don't say remainder 0, we just say '2'.
So 860 / 14 = 61.428 (3DP). We can then multiply 61 by 14, and that difference will be the remainder.
14* 61 = 854.
860 - 854 = 6.
The remainder of 860 divided by 14 is 6
in triangle RST, m∠R=(2x+10), m∠S=(2x+25), m∠T=(x-5)
what is the value of x
A. 30
B. 28
C. 26
D. 32
Answers
70+85+25=180 which means A.30 is the correct answer
(2(30)+10)+(2(30)+25)+(30-5)= 180
Fresh side grocery sells 7 bagels for $4.41. value mart sells 5 bagels for $3.60. how do the unit rates compare?
Answers
Value Mart : 3.60 / 5 = 0.72 per bagel
Fresh Side bagels are a better buy being that each bagel cost 0.63 compared to the bagels at Value Mart, which cost 0.72 per bagel.
The unit rate for a bagel at Fresh side is $0.09 cheaper than the unit rate at
Value mart for bagels.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Fresh side grocery sells 7 bagels for $4.41.
∴ The cost of one bagel at Fresh side is $(4.41/7) = $0.63.
Value mart sells 5 bagels for $3.60.
∴ The cost of one bagel at Value mart is
= $(3.60/5).
= $0.72
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How many times will he get heads and tails when flipped 8 times?
Answers
Mr. Chen goes to the post office to buy small and large boxes. He needs at least 4 small boxes. Altogether, he will buy no more than 15 boxes. The post office has 10 small boxes and 9 large boxes in stock. The graph shows the feasible region, where x represents the number of small boxes and y represents the number of large boxes. Which ordered pairs meet all the constraints and make sense in context of the situation? Select each correct answer. (6, 9) (7,10) (8,6) (9,8) Graph of lines and a shaded region on a coordinate plane whose axes are labeled x and y. A solid vertical line passes through 4 comma 0. Another solid vertical line passes through 10 comma 0. A solid horizontal line passes through 9 comma 0. A solid diagonal line passes through 0 comma 15, 4 comma 11, 6 comma 9, and 10 comma 5. The polygon whose vertices are at 4 comma 9, 6 comma 9, 10 comma 5, 10 comma 0, and 4 comma 0 is shaded.
Answers
John has six more nickels than dimes in his pocket for a total of 2.25 write an equation to determine the number of dimes, x in his pocket
Answers
Let x = the number of dimes
Let x+6 = the number of nickles
We know that nickles are represented as $0.05 and dimes $0.10...
Together they make $2.25 right? So you have to add them.
0.05(x+6) + 0.10(x) = 2.25 => This is the equation the problem is asking for.
If they ask you how many nickels and dimes does John have in this pocket, then you have to solve for x, like this:
0.05x + 0.3 + 0.10x = 2.25 In this step you apply the ditributive property.
0.15x + 0.3 = 2.25 In this step you combine like terms
0.15x = 2.25 - 0.3 In this step you moved to +0.3 to the other side, but remember to switch the sign!
0.15x = 1.95 In this step you subtract 2.25 and 0.3
x = (1.95) / (0.15) In this step you divide 0.15 in the right because in the left side of the equals sign it was multiplying. You get x by itslef.
x = 13 Latly, you divide and you get 13 as an answer
Now that the value of x is 13. You plug this number into the let statements.
We had:
x and x+6 which would be
x = 13
x+6 = 13+6 = 19
Which means that John has 13 dimes and 19 nickels in his pocket.
If you have $45 and they take 2.1% of it how much do you have left ?
If you have $765 and they take 2.1% of it how much do you have left ?
If you have $1300 and they take 2.1% of it how much do you have left ?
Answers
100-2.1 = 97.9
97.9/100 = 0.979
Then you multiply all the questions by it:
$45 * 0.979 = $44.055
$765 * 0.979 = $748.935
$1300 * 0.979 = $1272.7
Hope this helps! :)
An is planning a birthday party for her younger sister at a skating rink. the cost of admission is $3.50 per adult and $2.25 per child., and there is a limit of 20 people. jan has $50 to spend. how many adults and how many children can jan invite?
Answers
let y be the number of child
3.5 x + 2.25 y = 50
x+ y =20 y = 20 - x
3.5 (20-y ) + 2.25 y = 50
70 - 3.5 y +2.25y =50
70 -1.25 y = 50
y = 16
and x = 4
Fifty randomly selected individuals were timed completing a tax form. the sample mean was 23.6 minutes; the sample standard deviation was 2.4 minutes. a 99% confidence interval for the mean time required by all individuals to complete the form is about:
Answers
n = 50, sample size
[tex]\bar{x} = 23.6 \, min[/tex], sample mean
s = 2.4 min, sample standard deviation.
The confidence interval is
[tex]\bar{x} \pm t^{*} \frac{s}{ \sqrt{n} } [/tex]
At the 99% confidence level, t* (from the student's t-distribution) is
t* = 2.68
Therefore
t*(s/√n) = 2.68*(2.4/√50) = 0.9096
The confidence interval is
(23.6-0.9096, 23.6+0.9096) ≈ (22.69, 24.51)
Answer: (22.7, 24.5)
I need help with this math question!!
Simplify 0.4i−i.
Answers
= i(0.4-1)
= 0.6i
The simplification of the given expression is 0.6i.
What are complex numbers?Complex numbers are those numbers that contain the imaginary and the real part.
A Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.
where r is the modulus of the complex number and θ is the argument
r =√x²+y² and θ = tan⁻¹y/x
Usually the simplification involves proceeding with the pending operations in the expression.
We need to simpify the 0.4i - i
= i(0.4-1)
= 0.6i
Therefore, the simplification of the given expression is 0.6i.
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Which equation could generate the curve in the graph below?y=3x^2-2x+1
Answers
Then, the attached file would be the answer.
To check, b^2 - 4(a)(c), for each equation and use these facts:
If b^2 - 4(a)(c) = 0, there is only one real root meaning, the graph touches the x-axis only in one point.
If b^2 - 4ac > 0, there are two real roots meaning, the graph touches the x-axis in two different points.
If b2 - 4ac < 0, there are no real roots then the graph does not touch the x-axis. This would be the case for y = 3x^2 - 2x + 1.
Solution:
(-2)^2 -4(3)(1) = 4 - 12 = -8 < 0 will result in not real roots.
Find the geometric mean of 6/5 and 120. Show in simplest radical form.
Answers
HELP!!! I GIVE LOTS OF POINTS!! THE ANSWER IS NOT 3!!!!!!!!
In ∆ABC, the median AM (M ∈ BC ) is perpendicular to the angle bisector BK (K ∈ AC ). Find AB, if BC = 12 in.
Answers
the answer would be 6 i did my calculations on paper then misplaced it but checked answer and it said 6
A child rides around on a ferris wheel twice. Click on the graph until the graph that best represents the given statement appears.
Answers
Answer:
The second graph.
Step-by-step explanation:
When the time is 0, the ride has not yet begun. Therefore the height above ground is nearly nothing.
As time increases, the ride goes up until it hits the top. The ride then goes back down nearly to the ground. This is one time around.
The ride then goes back up to the top and back down to the starting point.
This is the motion of the second graph, so the second graph is correct.
The second graph is used to represent A child rides around on a ferris wheel twice.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points
In the given graphs, the relationship between the height above ground and times are represented.
The second graph given is best suited to represent "A child rides around on a ferris wheel twice"
When the time is 0, the ride has not yet begun. Therefore the height above ground is nearly nothing.
As time increases, the ride goes up until it hits the top. The ride then goes back down nearly to the ground. This is one time around.
The ride then goes back up to the top and back down to the starting point.
This is the motion of the second graph, so the second graph is correct.
Hence second graph is used to represent the given situation.
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The apartments in Brian's apartment house are numbered consecutively on each floor. The sum of his number and his next-door neighbor's number is 1419. What are the two numbers?
Answers
(a) and (b) are neighbors , whe have:
a + b = 1419 and b-a = 1;
<=> a + b = 1419 and a = b-1 ;
so we have b-1 + b = 1419 <=> 2b = 1420 <=> b=710 and a = 709
Answer: 710 and 709
Keenan is checking his bicycle’s wheel. The wheel has a radius of 21 cm, and its center is 56 cm above the ground. Keenan is rotating the wheel at a constant speed of 165°/s. The height of a point on the tire as a function of time is given by h = 56 + 21 sin(165t), where h is the height in centimeters and t is the time in seconds. Find h when t = 17 s. Round your answer to the nearest tenth of a centimeter.
Answers
h = 56 + 21 sin(2805) = 64.9872592735... or approximately 65.0 cm when we round up to the nearest tenth of a centimeter.
Over the last 4 years, Michael has earned $240 interest on an initial investment of $2,000. What simple annual interest rate is the bank paying on this account?
Answers
I = interest
P = principal (investment)
R = simple interest rate
T = years
Formula: I = PRT
What information do we have?
I = $240
P = 2000
T = 4 years
R = ?
Plug into formula:
240 = 2000(R)4
Multiply right side 2000*4
240 = 8000R
Divide both sides by 8000.
R = 240/8000
R = .03
The simple annual interest rate was .03 or 3%.
If Michael has earned $240 interest on an initial investment of $2,000. , then simple interest is 3% for paying in bank.
What is simple Interest?Simple interest is a quick and easy method of calculating the interest charge on a loan.
Given that,
I = interest = $240
P = principal (investment)=2000
R = simple interest rate=?
T = years= 4 years
Formula: I = PRT
Plug into formula:
240 = 2000(R)4
Multiply right side 2000×4
240 = 8000R
Divide both sides by 8000.
R = 240/8000
R = 0.03
Now multiply with 100
The simple annual interest rate was .03 or 3%.
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How many degrees are in each interior angle of a regular pentagon? 50 72 108 120
Answers
The answer 108 degrees.
Answer: [tex]108^{\circ}[/tex]
Step-by-step explanation:
The sum of all the angles in a regular polygon with sides n , is given by :-
[tex]S_n=180^{\circ}(n-2)[/tex]
Now, the sum of all the angles in a regular pentagon with 5 sides will be :-
[tex]S_5=180^{\circ}(5-2)=180^{\circ}(3)=540^{\circ}[/tex]
We know that all the interior angles of a regular polygon are equal .
Therefore, the measure of each interior angle in a pentagon is given by :-
[tex]x=\dfrac{540^{\circ}}{5}=108^{\circ}[/tex]
Hence, the measure of each interior angle in a pentagon=[tex]108^{\circ}[/tex]