Answers
1 revolution or 1 rotation is equivalent to 360 degrees
360 degrees/ 17 minutes = 21.16 rotation per minute or 21.16 rpm.
RPM or rotation per minute is the measure of the number of rotation completed per minute.
The amplitude is the distance from rest until the peak of its wave or crest. Since the rotation is completed in 17 minutes, therefore its amplitude is π/2
Related Questions
A 50 foot ramp makes an angle of 4.9° with the horizontal. to meet new accessibility guidelines, a new ramp must be built so it makes an angle of 2.7° with the horizontal as shown below. what is the length of the new ramp?
Answers
cos theta=[adjacent]/[hypotenuse]
theta=4.9°
hypotenuse=50 ft
adjacent=a
thus;
cos 4.9=a/50
a=50cos4.9
a=49.82ft
thus the new length will be given by:
cos 2.7=49.82/h
h=49.82/cos 2.7
h=49.97
the new length will be 49.97 ft
Which statements about the graph of the function f(x) = 2x2 – x – 6 are true? Check all that apply.
The domain of the function is .
The range of the function is all real numbers.
The vertex of the function is .
The function has two x-intercepts.
The function is increasing over the interval (, ∞).
Answers
we have
[tex] f(x) = 2x^{2}- x -6 [/tex]
using a graph tool
see the attached figure
we know that
1) the domain of the function is all real numbers-------> interval (-∞,∞)
2) The range of the function is the interval [-6.125,∞)
3) The vertex of the function is the point (0.25,-6.125)
4) The function has two x-intercepts-----> ( -1.5,0) and (2,0)
5) The function is increasing over the interval (0.25,∞) and decreasing over the interval (-∞,0.25)
For what values of x and y are the triangles congruent?
a. x=-4. y=-4
b. x=-4, y=4
c. x=4, y=7
d. x=7, y=4
Answers
From the given choices above, it can be seen that only the choice in A will give us this relationship. Thus, the answer is A.
Line m passes through the point (4,1) and has a slope of -1/3. what is the equation of line m in standard form
Answers
an equation is :
y - 1 = (-1/3)(x-4)
y = (-1/3)x +4/3 +1
y = (-1/3)x +7/3
3y = -x +7
is the equation of line m in standard form is : x+3y = 7
Which graph shows the solution set for -1.1x+ 6.4> -1.3
Answers
-1.1x > -7.7
x <7
answer
x is less than 7
What is the quality a design has if it maintains all characteristics when it is rotated about a point lying in its plane?
Answers
Answer:
The answer is rotational symmetry.
Step-by-step explanation:
The Rotational symmetry is the quality a design has if it maintains all characteristics when it is rotated about a point lying in its plane. A shape is said to possess rotational symmetry when it still looks the same after we rotate it.
The city planning committee is discussing making a bike path extension in its city park. They have a $5050 budget for the proposed project. The cost to construct the path is $2.20 per foot. The path would be a straight line from the fountain to the large oak tree. In the right triangle formed, the height is 880 ft and the base is 2112 ft. How much will the path cost? Will this work with the city planning budget?
Answers
[tex] a^2 + b^2 = c^2 [/tex]
[tex] 880^2 + 2112^2 = c^2 [/tex]
[tex] 774400 + 4460544 = c^2 [/tex]
[tex] c^2 = 5234944[/tex]
[tex] \sqrt{c^2} = \sqrt{5234944}[/tex]
[tex] c = 2288 ft[/tex]
$2.20 x 2288 ft = $5033.60
The budget is for $5050 so this will work.
Final answer:
After using the Pythagorean theorem to calculate the length of the bike path as approximately 2287 feet, and multiplying by the cost of $2.20 per foot, the total comes to $5031.40. This total cost fits within the city planning budget of $5050.
Explanation:
The city planning committee needs to determine if their $5050 budget is sufficient for the bike path extension, with construction costs at $2.20 per foot. To calculate the cost of the bike path, we first must find the length of the path, which will be the hypotenuse in a right triangle formed by the height (880 ft) and the base (2112 ft). Applying the Pythagorean theorem (a² + b² = c²), where a is the height and b is the base, the length of the path (c) can be calculated as follows:
c = √(880² + 2112²) = √(774400 + 4456444) = √5230844 ≈ 2287 ft.
Now, we can determine the total cost by multiplying the length of the path by the cost per foot:
Total Cost = 2287 ft × $2.20/ft = $5031.40
Thus, the total cost for constructing the path would be $5031.40, which is within the city planning budget of $5050.
A quadrilateral has two consecutive angles that measure 90° each. Which of the following quadrilaterals could have this property?
i. square
ii. rectangle
iii. parallelogram
iv. kite
v. rhombus
vi. trapezoid
A.
i, ii
B.
i, ii, iii
C.
i, ii, iii, iv
D.
i, ii, iii, v, vi
Answers
Final answer:
A square, rectangle, and certain cases of rhombuses and trapezoids can have two consecutive right angles, while typically a parallelogram and kite do not unless they are special cases of the rectangle or square respectively.
Explanation:
In the context of quadrilaterals with two consecutive right angles, it's important to recognize that certain quadrilaterals have this property by definition. A square and a rectangle both have four right angles, which means they certainly have at least two consecutive right angles.
A parallelogram typically does not have right angles, but a rectangle is a special type of parallelogram with right angles, so it fits this description. A kite generally does not have right angles unless specifically constructed to do so, which is not typical.
A rhombus can have right angles, making it a square, so it fits the criteria too. A trapezoid can also have a pair of consecutive right angles when it is a right trapezoid.
Therefore, the list of quadrilaterals that might have two consecutive right angles is not only the square and the rectangle but extends to include the rhombus and trapezoid as well.
Given these definitions, the correct answer to the question would be:
D. i, ii, iii, v, vi
Final answer:
The quadrilaterals that can have two consecutive angles measuring 90° each are squares, rectangles, and certain parallelograms (when they are squares or rectangles). Therefore, the correct answer to the question is B. This includes a square (i), a rectangle (ii), and some parallelograms (iii).
Explanation:
If a quadrilateral has two consecutive angles measuring 90° each, it could be any of the shapes that inherently contain right angles by definition. These shapes are a square, a rectangle, and certain types of parallelograms, specifically rectangles and squares. Both a square and a rectangle always have four right angles, which makes them valid answers. A rhombus or a general parallelogram may also have right angles, but only in specific cases, such as when a rhombus is also a square. Thus, kites and trapezoids do not necessarily fit this criterion as they do not always have consecutive right angles. Therefore, the correct answer is B, which includes a square, a rectangle, and some parallelograms.
the equation of line AB is y = 1/5x -1 write an equation of a line perpendicular to line AB in slope intercept form that contains point (1, -2)
Answers
y-(-2) = -5(x-1)
y=-5x + 3
find the area of a regular hexagon if a side is 20cm
Answers
Area = 1039.23 square units
Round answer as needed. See picture for equation
A motorcycle with an initial value of $14,000 is decreasing in value at a rate of 3% each year. At this rate, approximately what will the value of the motorcycle be in 9 years?
A) 14,000
B) 10,000
C) 9,800
D) 550
Answers
The value of the motorcycle after 9 years, with a depreciation rate of 3% per year, will be approximately $9,800. This answer has been calculated using the formula for percent decrease applied to the initial value of the motorcycle.
Explanation:This question revolves around the concept of percent decrease, a fundamental topic in mathematics. To estimate the value of the motorcycle after nine years, we need to apply the percent decrease continuously for these years.
The formula is: Final Value = Initial Value * (1 - rate of decrease)number of years
So in this case, the final value will be: $14,000 * (1 - 0.03)^9.
Calculating that gives us approximately $9,855, so the closest answer would be option C, $9,800.
Therefore after 9 years, the motorcycle will have depreciated to around $9,800 in value given a yearly depreciation rate of 3%.
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Four letters to different insureds are prepared along with accompanying envelopes. the letters are put into the envelopes randomly. calculate the probability that at least one letter ends up in its accompanying envelope.
Answers
Final answer:
The probability that at least one of four randomly distributed letters ends up in its correct envelope is 62.5%. This calculation uses the complementary approach, subtracting the probability of no matches (9/24) from 1.
Explanation:
The question asks about the probability that at least one letter ends up in its accompanying envelope when four letters are randomly put into four envelopes.
To solve this, we employ the principle of complementary probability, which suggests that the probability of at least one match is 1 minus the probability of no letters matching their envelopes.
Calculating the probability of no matches directly can be complex due to numerous possible permutations, so using the complementary approach is more efficient.
We can calculate the total permutations of the four letters being distributed into four envelopes as 4!, which equals 24.
To find the probability of no letters matching their envelopes (a derangement of 4 items), we use a specific formula or recognition of known patterns, resulting in 9 derangements. Thus, the probability of no matches is 9/24.
The probability of at least one letter matching its corresponding envelope is then 1 - (9/24), which simplifies to 15/24 or 5/8. Therefore, the probability is 0.625 or 62.5%.
A man travelled 3/8 of his journey by a rail 1/4 by a taxi 1/8 by and the remaining 2km on foot what is the length of his total journey?
Answers
Since all of these travels are equal to 1 whole journey, you can express each travel as a fraction. When you add them up, the answer would be 1. So,
3/8 + 1/4 + 1/8 + x = 1
The variable x here denotes the fraction of his travel by foot. We are only given the exact distance travelled on foot which is 2 km. We have to find the fraction of the travel by foot to determine the length of the total distance travelled. Solving for x,
x = 1 - 3/8 - 1/4 - 1/8
x = 1/4
That means that the travel by foot comprises 1/4 of the whole journey. Thus,
Let total distance be D.
1.4*D = 2 km
D = 8 km
Therefore, the man travelled a total of 8 kilometers.
Mr. Carr has to buy each of his 24 students a flash drive. Each flash drive costs $12. How much will he spend?
Answers
Answer:
Step-by-step explanation:
$228
:) Answers? Thanks,❤
Answers
6) answer: 12?
8) answer: 8?
10+18+18-12=34
6. the answer is 12
10+10+19-12=27
8. the answer is 12
12-10+19+10=31
Solve: 3x-15/2=4x
................
Answers
3x-8x=15 (Subtracted -8x from both sides / Added 15 to both sides)
-5x=15 (shortened equation)
x=-3
3*(-3)-15/2 = 4(-3)
-9-15/2 = -12
-24/2 = -12
-12 = -12
The required solution of the expression is x = -3.
Given that,
To determine the solution of the equation 3x-15/2=4x.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Simplification of 3x-15/2=4x.
3x - 15 = 8x
5x = -15
x = -3
Thus, the required solution of the expression is x = -3.
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The graph below shows the price, y, in dollars, of different amounts of pounds of almonds, x: A graph titled Almond Prices shows Number of Pounds on x axis and Price in dollars on y axis. The scale on the x axis shows numbers from 0 to 12 at increments of 2, and the scale on the y axis shows numbers from 0 to 84 at increments of 14. A straight line joins the ordered pairs 0, 0 and 12, 84 Which equation best represents the relationship between x and y? y = 7x y = x + 7 y = 14x y = x + 14
Answers
slope = (84 - 0) / (12 - 0) = 84/12 = 7
it goes thru the origin (0,0) therefore, the y int = 0
In y = mx + b form, the slope will be in the m position and the y int will be in the b position.
ur equaton is : y = 7x + 0, which can also be written as y = 7x <==
Answer:
my brain has exceeded the limit of cofusion
Step-by-step explanation:
Write two ratios that are equivalent to 3:11
Answers
Hopefully, this helps!
Suppose that F(x) = x^2 and G(x) = 2/3x^2. Which statement best compares the graph of G(x) with the graph of F(x)?
A.) the graph of G(x) is the graph of F(x) compressed vertically.
B.) the graph of G(x) is the graph of F(x) stretched vertically and flipped over the x-axis.
C.) the graph of G(x) is the graph of F(x) stretched vertically.
D.) the graph of G(x) is the graph of F(x) compressed vertically and flipped over the x-axis
Answers
In this case (2/3)^2=4/9 and 4/9<1 so the graph of G(x) is the graph of F(x) compressed vertically.
Answer:
The statement which best compares the function F(x) and G(x) is that the graph of G(x) is the graph of F(x) stretched vertically.
Step-by-step explanation:
Since the difference between the two functions is in the coefficent which multiplies the square function, 1 and 2/3 respectively in F(x) and G(x). So, as the coefficient are positive and is minor for G(x) than for F(x), the values for G(x) will be smaller and thus the graph of G(x) would be below the graph of F(x). Therefore the graph for G(x) is it compressed vertically respect to F(x). The explanation here is ore understandable by looking at the illustration attached.
Calculate the hypotenuse
Answers
[tex] 10^{2} + 14^{2} = c^{2} [/tex]
[tex]100+196= c^{2} [/tex]
[tex]296= c^{2} [/tex]
[tex] \sqrt{296} = \sqrt{ c^{2} } [/tex]
[tex]17.205=c[/tex]
A system of equations is shown below: x + 3y = 5 (equation 1) 7x − 8y = 6 (equation 2) A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof?
Answers
(2) 7x - 8y = 6
Condition: equation (2) is multiplied by 1
If you multiply equation (1) by 1 and add the equation (2), you get
x + 3y = 5
7x - 8y = 6
----------------
8x - 5y = 11
So, if the student proves that the system formed by the new equation and the second equation is the same, he/she will have the proof:
So, the answer is "show that the solution to the system of equations 8x − 5y = 11 and 7x − 8y = 6 is the same as the solution to the given system of equations"
Answer:
The correct answer is B. Show that the solution to the system of equations 8x − 5y = 11 and 7x − 8y = 6 is the same as the solution to the given system of equations"
Step-by-step explanation:
Consider the following sets.
U = {all real number points on a number line}
A = {solutions to the inequality 3x + 4 ≥ 13}
B = {solutions to the inequality x + 3 ≤ 4}
For which values of x is A ⋃ B = Ø?
a 2 < x < 3
b 2 ≤ x ≤ 3
c x ≤ 2 and x ≥ 3
d x < 2 and x > 3
Answers
Answer:
A. 2 < x < 3
Step-by-step explanation:
The values of x which A ⋃ B = Ø is:
A. 2 < x < 3What is a Set?
This refers to the grouping of data which can be graphically represented on a Venn diagram.
With this in mind, we have a set of data which makes use of a general set that contains:
Therefore, the values of x to which A ⋃ B = Ø is:
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Mountain officials want to know the length of a new ski lift from A to C , as shown in the figure below. They measure angle DAC to be 32° . They then move 960 feet to point B and measure angle DBC to be 18° . What is the length of the new ski lift from A to C ? Round your answer to the nearest tenth of a foot.
Answers
sin (32) = CD / 960
CD = 508.72
tan 32 = 508.72 / AD
AD = 814.13
Therefore, the distance would be 814.13 - 508.72 = 305.4 ft.
Knowing if trigonometry knowledge we can say that the distance will be 305.4 ft.
So knowing how sine and tangent work we can write the equals as:
[tex]sin (32) = CD / 960\\CD = 508.72[/tex]
[tex]tan (32) = 508.72 / AD\\AD = 814.13[/tex]
To calculate the distance, we will decrease the two values found, like this:
[tex]814.13 - 508.72 = 305.4 ft[/tex]
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Among the contestants in a competition are 3636 women and 2525 men. if 5 winners are randomly? selected, find the probability that they are all? men? round to five decimal places.
Answers
A contractor records all of the bedroom areas, in square feet, of a five-bedroom house as: 100, 100, 120, 120, 180 What is the variance?
Answers
This can be calculated through the equation,
σ² = summation of X² / N - μ²
where σ² is the variance X's are the data, N is the number of terms, and μ is the mean.
summation of X² = 100² + 100² + 120² + 120² + 180² = 81200
N = 5
μ = (100 + 100 + 120 + 120 + 180) / 5
μ = 124
Substituting these values to the equation for variance,
σ² = (81200/5) - 124² = 864
Thus, the variance is equal to 864.
The variance of the five bedroom house is 864.
The formula varianceσ²
[tex]=\frac{X^2}{N} -u^2[/tex]
To get the value of X²
= 100²+100²+120²+120²+180²
= 81200
The number is N = 5
u = mean
[tex]u = \frac{100+100+120+120+180}{5}[/tex]
u = 124
The values in the variance formula
[tex]\frac{81200}{5} -124^2[/tex]
16240-15376
= 864
The variance is 864
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A rectangle has a length of ∛81 and a width of 3 2/3 inches. Find the area of the rectangle.
A.3 2/3 power inches squared
B.3 8/3 power inches squared
C.9 inches squared
D. 9 2/3 power inches squared
Answers
[tex] \sqrt[3]{81}= 81^{ \frac{1}{3} }= (3^{4}) ^{ \frac{1}{3} }= 3^{ \frac{4}{3} } [/tex]
The area of the rectangle = length*width
=[tex]3^{ \frac{4}{3} } * 3^{ \frac{2}{3} } =3^{(\frac{4}{3} +\frac{2}{3}) }=3^{ \frac{6}{3} }= 3^{2}=9 [/tex] (inches squared).
Answer: 9 inches squared
length = ∛81
width = [tex] 3^{ \frac{2}{3} } [/tex]
Area = [tex] \sqrt[3]{81} [/tex] × [tex] 3^{ \frac{2}{3} } [/tex]
Area = [tex] 81^{ \frac{1}{3} } [/tex] × [tex] 3^{ \frac{2}{3} } [/tex]
Area = [tex] ( 3^{4}) ^{ \frac{1}{3} } [/tex] × [tex] 3^{ \frac{2}{3} } [/tex]
Area = [tex] 3^{ \frac{4}{3} } [/tex] × [tex] 3^{ \frac{2}{3} } [/tex]
Area = [tex] 3^{ \frac{6}{3} } [/tex]
Area = [tex] 3^{2} [/tex]
Area = 9 inches squared
Marla is looking for a new car. She has test-driven two cars but can only purchase one. The probability that she will purchase car A is 0.52, and the probability that she will purchase car B is 0.38. What is the probability that she will not purchase either car A or car B?
Answers
.52 + .38 = .90
1.00 - .90 = .10
Answer: The required probability is 0.10.
Step-by-step explanation: Given that Marla is looking for a new car. She has test-driven two cars A and B but can only purchase one.
We are to find the probability that she will not purchase either car A or car B.
Let, 'C' denotes the event that Marla will purchase car A and 'D' denotes the event that Marla will purchase car 'B'.
Then, according to the given information, we have
[tex]P(A)=0.52,~~~P(B)=0.38.[/tex]
Since Marla cannot purchase both the cars, so the events A and B are disjoint.
That is,
[tex]A\cap B=\phi~~~~~\Rightarrow P(A\cap B)=0.[/tex]
Therefore, the probability that Marla will purchase either car A or car B is given by
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)=0.52+0.38-0=0.90.[/tex]
Hence, the probability that she will not purchase either car A or car B will be
[tex]P^\prime(A\cup B)=1-P(A\cup B)=0-0.90=0.10.[/tex]
Thus, the required probability is 0.10.
The manager at a restaurant keeps track of the number of calzones and slices sold each day and the total money received. On Sunday, a total of 59 calzones and slices were sold, and the money collected was $456. If calzones are sold for $9 and slices are sold for $6, how many calzones and slices were sold?
Answers
c=number of calzones
s=number of slices
total of 59 so
c+s=59
total money was 456
9c+6s=456
we can divide both sides by 3 to simplify
3c+2s=152
use subsitution
c+s=59
minus s both sides
c=59-s
subsitute 59-s for c in other equation
3c+2s=152
3(59-s)+2s=152
177-3s+2s=152
177-s=152
minus 177 both sides
-s=-25
s=25
sub back
c=59-s
c=59-25
c=34
34 calzones
25 slices
The number of baseball cards in Neil's collection is 80 percent of the number in Larry's collection. If Neil has 80 fewer baseball cards than Larry, how many do they have altogether
Answers
N=0.8L
....
N=L-80
Since N=N
0.8L=L-80 subtract 0.8L from both sides
0=0.2L-80 add 80 to both sides
80=0.2L divide both sides by 0.2
400=L, and since N=L-80
N=320
N+L=400+320
So they have 720 baseball cards altogether.
The problem involves setting up an equation based on the given situation to solve for the number of baseball cards Neil and Larry have. By solving the equation, you find that Larry has 400 cards and Neil has 320 cards. So, they have 720 baseball cards together.
Explanation:This is a problem of percentages and of algebra. First, you know that the number of cards Neil has is 80% of what Larry has. This can be set up as an algebraic equation, where N represents Neil’s cards and L represents Larry’s cards: N = 0.8L. You also know that Neil has 80 fewer cards than Larry, which provides a second equation: N = L - 80.
Because both expressions equal N, you can set them equal to each other to solve for L. This leads to 0.8L = L - 80. Solve this equation for L, and you get L = 400. Substituting this into the equation N = 0.8L, you find that N = 320. Therefore, Neil and Larry have 720 baseball cards altogether.
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The quotient of 13 ÷ 24 is a decimal number. Which digit in the quotient is overlined?
1
4
5
6
Answers
13/24 = 0.5416666
since 6 keeps repeating that would be the number that has the line over it.