Answers
For the given problem, a.)The unicycle covers 1.885 meters, in one revolution of wheel. b.) The wheel must rotate 53 times to cover distance of 100 metres.
How to calculate distance covered by wheel in one rotation?a.) The circumference of a unicycle's wheel is determined by
[tex]\qquad \qquad C = \pi d\\ \text {where, d is the diameter of the wheel. }[/tex]
As a result, the unicycle moves C metres when the wheel revolves once.
Now, on substituting d = 60 cm and π= 3.14.
We obtain,
[tex]C\approx 188.5 cm = 1.885 m[/tex] (∵ 1m = 100cm)
As a result, when the wheel revolves once, the unicycle goes 1.885 metres.
How to calculate number of rotation required by wheel?b.) Now, Distance covered in one rotation by wheel = [tex]C = 1.885 m[/tex]
To travel 100 metres, wheel need to rotate = 100/C times.
As a result, the number of full rotations necessary is:
[tex]100/C = 100/1.885 = 53.0504 \;rotations[/tex]
Thus, To traverse 100 metres, the wheel must rotate 53.04 times or 53 times( in nearest whole number )
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Related Questions
Michelle has four credit cards with the balances and interest rates listed below. She would like to consolidate all of her credit cards in a single credit card with an interest rate of 16% and pay off the balance in 36 months. If she did so, what would Michelle’s monthly credit card payment be?
Credit Card
Balance
APR
#1
$4,380
17%
#2
$1,365
19%
#3
$2,480
23%
#4
$5,000
15%
a.
$367.36
b.
$464.95
c.
$685.23
d.
$826.56
Answers
Answer:
mark me brilliant
Step-by-step explanation:
To calculate Michelle’s monthly credit card payment, we need to find the total amount she owes and then divide it by the number of months she has to pay it off.
First, we need to find the total balance on Michelle’s credit cards:
$4,380 + $1,365 + $2,480 + $5,000 = $13,225
Next, we need to find the weighted average interest rate of her credit cards. To do this, we multiply each balance by its corresponding APR and add up the results. Then we divide by the total balance:
($4,380 x 0.17) + ($1,365 x 0.19) + ($2,480 x 0.23) + ($5,000 x 0.15) = $1,038.55
$1,038.55 ÷ $13,225 = 0.0785, or 7.85%
Now we can use the total balance and the weighted average interest rate to calculate Michelle’s monthly payment using the formula for a fixed payment on a loan:
P = (r(PV)) / (1 - (1 + r)^-n)
Where:
P = monthly payment
r = monthly interest rate (as a decimal)
PV = present value of the loan
n = number of payments
r = 0.16 ÷ 12 = 0.01333 (monthly interest rate)
PV = $13,225
n = 36
P = (0.01333(13,225)) / (1 - (1 + 0.01333)^-36) = $367.36
Therefore, Michelle’s monthly credit card payment would be $367.36 if she consolidated all of her credit card debt into a single credit card with an interest rate of 16% and paid it off in 36 months. The answer is (a) $367.36.
match the base and the height
Answers
The key point to remember is
The height is perpendicular to the base
if i was helpful Brainliests my answer ^_^
answerrrrrrrrrrr teh questionnnnnnnn
Answers
The linear function with a slope of 1/2 and passing through the point (4, -2) is given as follows:
y = x/2 - 4.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation shown as follows:
y = mx + b
The coefficients m and b have the meaning presented as follows:
m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.The gradient of the function is given as follows:
m = 1/2.
Hence:
y = x/2 + b.
When x = 4, y = -2, hence the intercept b is obtained as follows:
-2 = 4/2 + b
2 + b = -2
b = -4.
Hence the equation is:
y = x/2 - 4.
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which radian measure is equivalent to 300°?
• 5/3
• 11pi/6
• 5pi/6
• 5pi/3
Answers
The radian measure that is equivalent to 300° is equal to 5π/3. So, correct option is D.
To convert degrees to radians, we use the conversion factor of π/180, which means that one degree is equal to π/180 radians. Therefore, to convert 300° to radians, we multiply 300 by π/180:
300° * π/180 = 5π/3
To understand this conversion, we need to remember that radians are a unit of measurement for angles, just like degrees. However, while degrees divide a circle into 360 equal parts, radians divide a circle into 2π equal parts. One full rotation is equal to 2π radians, which is also equal to 360°.
Since 5π/3 radians is less than one full rotation, it represents an angle that is less than 360°. In fact, 5π/3 radians is equivalent to 300°, which is a well-known angle used in many contexts, such as in geometry, trigonometry, and physics.
In summary, to convert 300° to radians, we multiply it by the conversion factor π/180, which gives us the equivalent angle measure of 5π/3 radians.
So, correct option is D.
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Find the equation of a line parallel to −5x+y=−4that passes through the point (−7,−9).
Answers
The equation of the line is parallel to -5x+y=-4 and passes through the point (−7,−9) is y=5x+26.
Given that, the equation of the line is parallel to -5x+y=-4 and passes through the point (−7,−9).
The given equation can be written as y=5x-4.
Now, compare y=5x-4 with y=mx+c, we m=5
The slope of a line parallel to given line is m1=m2
So, the slope of the line parallel to the given line is 5.
Now, substitute m=5 and (x, y)=(-7, -9) in y=mx+c, we get
-9=5(-7)+c
c=-9+35
c=26
So, the equation is y=5x+26
Therefore, the equation of the line is parallel to -5x+y=-4 and passes through the point (−7,−9) is y=5x+26.
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Does anyone know this answer??
Answers
Step-by-step explanation:
This question uses trigonometry, a subject you may have learnt. Using the functions sin, cos, tan and the abbreviation SOHCAHTOA, you'll need to use sin to find your answer.
sin = opposite/hypotenuse
sin 25 = 112/d
d = 112/sin 25
d = 238.5661004
Answer: 238.6 metres
For questions 23, use a Venn diagram or truth table or common form of an argument to decide whether each argument is valid or invalid.
23. If a person is on this reality show, they must be self-absorbed. Laura is not self-absorbed. Therefore, Laura cannot be on this reality show.
Answers
In the Venn diagram , the statement is Valid.
What is Venn diagram?
Venn diagrams are frequently used in mathematics, statistics, logic, teaching, linguistics, computer science, and business. They are also known as Set diagrams or Logic diagrams.
Here according to the Venn diagram , if person is on the reality show , they must be self absorbed. But Laure is not self absorbed so she cannot be on the reality show.
Hence the statement is valid.
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I don't really get this so this is a big help
Answers
Answer:
what is the problem
Step-by-step explanation:
2c – 4 = 3(4 – 2c) c = –4a + 9 = –2(4 + 5a) – 7 a =
Answers
Answer:
c=7/2, a = 5/34
Step-by-step explanation:
Plot 2 1/2 and 1 5/6 on the number line below.
Answers
Between each of the integers, 0, 1, 2, 3, etc., the space is divided into 6 units. We can use this to our advantage.
Since 1/2 = 2/4 = 5/10 = 3/6 = ....., thus:
2 1/2 = 2 3/6. Now we can easily plot points on the number line.
2 3/6 = 2 units and 3 sub units.
1 5/6 = 1 unit and 5 sub units
Check the attached image to see the graphical solution of the question!
Hope that helps!
Given the matrices.
A = [3 2 1] B= 2 2 3 3
2 B = 2 2 0
2 3 3 4
Find
1. AB
2. CA
Answers
Answer:
To perform the matrix operations, we need to ensure that the dimensions of the matrices match. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix.
A is a row matrix with 1 row and 3 columns, while B is a matrix with 2 rows and 2 columns. Since the number of columns in A does not match the number of rows in B, we cannot calculate AB.
However, we can perform CA since C has 3 rows and 2 columns, which matches the dimensions for left multiplication by A (a 1x3 matrix).
C = 2 2 0
2 3 3
4 0 1
A = 3 2 1
CA = (3)(2) + (2)(2) + (1)(4) (3)(2) + (2)(3) + (1)(0)
(3)(2) + (2)(3) + (1)(0) (3)(2) + (2)(0) + (1)(1)
(3)(0) + (2)(3) + (1)(1) (3)(0) + (2)(3) + (1)(1)
CA = 14 12
12 7
7 9
Therefore, CA = 14 12
12 7
7 9
In a survey conducted by a website, employers were asked if they had ever sent an employee home because they were dressed inappropriately. A total of 2765 employers responded to the survey, with 964 saying that they had sent an employee home for inappropriate attire. In a press release, the website makes the claim that more than one-third of employers have sent an employee home to change clothes.
A button hyperlink to the SALT program that reads: Use SALT.
Do the sample data provide convincing evidence in support of this claim? Test the relevant hypotheses using
= 0.05.
For purposes of this exercise, assume that it is reasonable to regard the sample as representative of employers in the United States. (Round your test statistic to two decimal places and your P-value to four decimal places.)
z =
P-value =
Answers
Using the sample data, the proportion of employers who have sent an employee home for inappropriate attire is:
p-hat = 964/2765 = 0.3493
The sample size is sufficiently large (n = 2765) to assume that the sampling distribution of p-hat is approximately normal.
The test statistic is:
z = (p-hat - p0) / sqrt(p0*(1-p0)/n) = (0.3493 - 1/3) / sqrt((1/3)*(2/3)/2765) = 2.58
Using a one-sided test with a significance level of 0.05, the critical value is 1.645. Since the test statistic (z = 2.58) is greater than the critical value (1.645), we reject the null hypothesis and conclude that there is evidence to support the claim that more than one-third of employers have sent an employee home for inappropriate attire.
The P-value for the test is P(Z > 2.58) = 0.0049. This means that the probability of observing a sample proportion of 0.3493 or more extreme, assuming the null hypothesis is true, is 0.0049. Since this P-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to support the claim that more than one-third of employers have sent an employee home for inappropriate attire.
4. A spinner is divided into four colored sections. that are not of equal size: red blue purple and orange. The arrow on the spinner is spun several times. SPINNER RESULTS Color Number of Times Red 15 Blue 24 Purple Orange 12 B. 9 The arrow on the spinner will be spun one more time. Based on these results, what is the probability that the arrow will land on the purple section? C. 27 D. 1/2
Answers
15 + 24 + 12 + 9 = 60 times
Out of these 60 spins, we know that the arrow landed on the purple section 9 times. Therefore, the probability of the arrow landing on the purple section can be calculated as:
P(purple) = number of times the arrow landed on purple / total number of spins
= 9 / 60
= 3 / 20
Therefore, the probability of the arrow landing on the purple section is 3/20. Answer: B.
Calculate the area of the red triangle to find the area of the garden. Show your work. (2 points)
Answers
Using a metric standard of 2 meters, then the area of the red triangle would be 54m². The area of the garden would be; 500m²
Using typical walkway widths to 6 ft, to calculate the area the red triangle to be 486 square feet and the area of the garden to be about 4400 square feet, rounding up.
Then it is a right triangle and side a is the altitude or height of the triangle and side b is the base.
The measurements of the triangle are approximately in the proportion of 3, 4, 5, a typical "Pythagorean Triple" right triangle.
Estimating from rough measurements of the triangle and the dimensions of the garden as shown, the area of the garden is about 18 times the area of the red triangle.
The area of the triangle is half the area of a rectangle with the same side lengths a & b, therefore, 9 ab is a good estimate of the area of the garden.
Area of the triangle estimate:
A = 36ft × 27ft /2
A = 486 square feet
To estimate 2 meter wide sidewalk, the area of the triangle can be reasonably calculated to be;
A = 9m × 12m /2 = 54 m²
The area of the garden = 9 × 54 = 486m²
Then rounded reasonably to 500m²
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Find P(A')) if P(A) =0.64
Answers
If P(A) is 0.64, then P(A') is 0.36. P(A) is probability of occurrence of event A.
This question pertains to Probability principles. Probability is a measure of the possibility of an event occurring. Many occurrences cannot be foreseen with absolute accuracy. We can only anticipate the likelihood of an event occurring using it.
A is an occurrence in this context. A' denotes the event's complement.
For example, if Event A is getting heads on a coin toss, then Event A' is getting tails.
This demonstrates one thing:
A ∪ A' = U, here U is the universal set.
P ( U) = 1
P (A) + P(A') = 1
0.64 + P (A') = 1
P(A') = 1 - 0.64
P (A') = 0.36
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2. If you know the correlation coefficient between two tests is +.79, you expect a person who gets a
high score on one of the tests to get a _____score on the other test.
Answers
Answer:
"high" should go in the blank. A correlation coefficient of .79 indicates a pretty strong positive correlation.
Which pair has 2 equivalent expressions?
A. 7g +3, g + g + 5g + 2 + 1
B. 3p + 2, 3p + 1 + 1 + 1
C. 6v - 2, 3v + 3v - 3
D. 4z + 2z, 4 + 2 + 2z
Answers
Solve this plsss
Solve for b
Solve for c
Solve for B
Answers
The unknown measurements for the triangle are given as follows:
b = 9.6.c = 3.3. m < B = 38º.What is the law of sines?Suppose we have a triangle in which:
Side with a length of a is opposite to angle A.Side with a length of b is opposite to angle B.Side with a length of c is opposite to angle C.The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
Considering that the sum of the measures of the angles is of 180º, the missing angle is given as follows:
m < B = 180 - (130 + 12)
m < B = 38º.
Then the relation is given as follows:
sin(130º)/12 = sin(38º)/b = sin(12º)/c
Then the length b is given as follows:
sin(130º)/12 = sin(38º)/b
b = 12 x sine of 38 degrees/sine of 130 degrees
b = 9.6.
The length c is then given as follows:
sin(130º)/12 = sin(12º)/c
c = 12 x sine of 12 degrees/sine of 130 degrees
c = 3.3.
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At how many points does the graph of the function below intersect the x-axis y=9x^2-12x+4
Answers
The graph of the function below y = 9x² - 12x + 4 intersect the x-axis at exactly one point (0.667, 0).
What is the x-intercept?In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
In this exercise, we would use an online graphing calculator to plot the quadratic equation in order to determine the x-intercepts as shown in the graph attached below.
Therefore, the x-intercept of the graph of the given quadratic equation y = 9x² - 12x + 4 include the following:
x = (0.667, 0).
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Can someone help This is due today. Thank you!
Answers
(a) The amount of square feet of laminate flooring Samantha need to purchase for her kitchen is 268 ft².
(b) The amount of linear trim of feet Samantha need to purchase for her kitchen 80 ft.
What is a perimeter?Perimeter is the total distance around an plane figure.
(a) To calculate the amount of square feet for laminate flooring, she needed to purchase for her kitchen, we use the formula below.
Formula:
A = LW+lw..................... Equation 1Where:
A = Amount of square feet of laminateL = Length of the bigger rectangleW = Width of the bigger rectanglel = Length of the smaller rectanglew = Width of the smaller rectangleFrom the question,
Given:
L = 20 ftW = 9 ftl = 8 ftw = 11 ftSubstitute these values into equation 1
A = (20×9)+(8×11)A = 180+88A = 268 ft²(b) To calculate the amount of the linear trim of feet needed, we find the Perimeter of the shape
Perimeter = 20+20+9+12+11+8Perimeter = 80 ftHence, The amount of linear trim of feet is 80 ft.
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Find the value of x.
a. 53°
b. 72°
c. 48°
d. 39°
Answers
Answer:
Step-by-step explanation:
yes it is b
Suppose that (1)=−2 , f(4)=5, f'(1)=4 , f'(4)=-7 and f'' is continuous.
Find the value of ∫41″().
Answers
Answer:
integrates by parts:
U = x dV = f''
dU = dx V = f'
The integral becomes:
x f' - integral f' dx
= x f' - f
limit as x->4 : 4 * f'(4) - f(4) = 4 * -3 - 7
= -12-7 = -19
limit as x->1 : 1 * f'(1) - f(1) = 1 * 9 - 8 = 1
subtracting: -19-1 = -20
Step-by-step explanation:
HELPPPP PLSSSSS!!!!! I NEED HELP ASAP
Answers
The estimated cost of sending a letter that weighs 5 ounces is $9.75.
What is estimated cost ?
Estimated cost refers to an approximate or calculated value of the cost of something. It is a value that is based on estimation, rather than being an exact or precise value.
Since the equation given is a linear equation with a slope of 0.25, we can interpret the slope as the cost per ounce of postage. This means that for every additional ounce, the cost of postage increases by $0.25.
To estimate the cost of sending a letter that weighs 5 ounces, we can use the given equation:
y = 0.25x + 8.50
where x = 5 (since the weight of the letter is 5 ounces).
Plugging in x = 5, we get:
y = 0.25(5) + 8.50
= 1.25 + 8.50
= 9.75
So the estimated cost of sending a letter that weighs 5 ounces is $9.75.
Looking at the graph provided, we can also see that the point (5, 9.75) lies on the line, which confirms our estimate.
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9/15
of this figure is shaded.
Select the three figures that represent fractions equivalent to 9/15
Answers
Answer:
Step-by-step explanation:
One of the figures would be 3/5
Another 18/30
or 27/45
What is the distance between the coordinates (2, 9) and (10, 6)? Round your
answer to the nearest tenth.
Answer here
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SUBM
Answers
Answer:
8.54
Step-by-step explanation:
√(6-9)²+(10-2)2
=√(-3)²+8²
=√9+64
=√73=8.54
The answer is 8.54
O is the center of the regular octagon below. Find its area. Round to the nearest tenth if necessary.
Answers
Answer:
Step-by-step explanation:
Rounding to the nearest tenth, the area of the regular octagon is approximately 282.8
Mary is traveling cross country on a road trip. So far, Mary has traveled 200 miles in her car and 200 miles by train. The car traveled at a rate that was 30 miles per hour slower than the train.
Mary modeled the total time for her trip with the following expression.
What does x - 30 represent in this situation?
Answers
Answer:
The answer to your problem is, x-30 is speed of the car.
Step-by-step explanation:
Let the object is moving n miles in one hour.
Let the speed is m miles per hour.
We know that our friend Mary has traveled 200 miles in her car and 200 miles by train. And shown Mary also modeled the total time for her trip;
[tex]\frac{200}{x}[/tex] + [tex]\frac{200}{x-30}[/tex]
The car that was given had traveled at a rate that was 30 miles per hour slower than the train.
speed of the train is x miles per hour
speed of the car = x - 30 miles per hour.
Thus the answer to your problem is, x-30 is speed of the car.
The table represents a quadratic function C(t).
t C(t)
−2 1
−1 4
0 5
1 4
2 1
What is the equation of C(t)?
C(t) = −(x − 5)2
C(t) = (x − 5)2
C(t) = −x2 + 5
C(t) = x2 + 5
g(x) = (x − 4)2 − 3
g(x) = (x − 4)2 + 3
g(x) = (x + 4)2 − 3
g(x) = (x + 4)2 + 3
Answers
From the given table, the equation of C(t) is - t² + 5. that is option C
How to determine the equation of the parabola?The standard form is (x - h)² = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p.
Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The table represents a quadratic function C(t).
t C(t)
−2 1
−1 4
0 5
1 4
2 1
From the table, the coordinate of the vertex will be at (0, 5). Then the equation is given as,
C(t) = a(t - 0)² + 5
C(t) = at² + 5
The equation is passing through the point (1, 4), then we have
4 = a (1²) + 5
4 = a + 5
a = - 1
The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.
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The equation y = 400x represents the relationship between x, the time that a plane flies in hours, and y, the distance the plane flies in miles for Plane A. The table represents the relationship for Plane B. Find the slope of the graph for each plane and the plane's rate of speed. Determine which plane is flying at a faster rate of speed.
Answers
The slope of line is 400 and plane A's rate of speed is 400 mi/h
The slope of line is 475 and plane B's rate of speed is 475 mi/h
Therefore, Plane B is flying faster.
For Plane A the equation y = 400x represents the relationship between x, the time that a plane flies in hours, and y, the distance the plane flies in miles.
We know the equation of line is y =mx + c
m = slope of line
So, on comparing slope of line is 400 and plane A's rate of speed is 400 mi/h
For Plane B
We know the formula for slope = (y₂-y1)/(x₂ - x₁)
= (950 - 475)/(2 - 1)
= 475
So, slope of line is 475 and plane B's rate of speed is 475 mi/h
Therefore, Plane B is flying faster.
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what is the ss total if ss is between 164 and within 70.2
Answers
The value of ss total while ss between is 164 and ss within is 70.2 is given by 234.2.
We know that the sum of square in total is equal to the sum of sum of square in between and sum of squares within.
In mathematical word, ss (total) = ss (between) + ss (within)
Here given that the ss (between) is given by = 164
and ss (within) is given by = 70.2
So the ss(total) is given by,
ss(total) = ss(between) + ss(within) = 164 + 70.2 = 234.2.
Hence the required value of ss total is 234.2.
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