Step-by-step explanation:
The wheel has a diameter of 250 feet, so its circumference is:
C = 2πr = πD
C = 250π feet
It makes one revolution in 30 seconds, or half a minute, so the linear speed of the passenger is:
v = d / t
v = 250π / 0.5
v = 500π ft/min
v ≈ 1571 ft/min
This is about the same as 17.9 mph.
Final answer:
The linear speed of a passenger on the original Ferris wheel with a diameter of 250 feet, making one revolution every 30 seconds, was approximately 1570.8 feet per minute.
Explanation:
The question asks to calculate the linear speed of a passenger on the edge of the first Ferris wheel, which was 250 feet in diameter, and made one revolution every 30 seconds. To find the linear speed, we first need to determine the circumference of the Ferris wheel, which can be done by using the formula for the circumference of a circle, C = πd, where d is the diameter.
For the first Ferris wheel:
Diameter (d) = 250 feet
Circumference (C) = π * 250 feet = 785.398163 feet (approximately)
Time for one revolution = 30 seconds
Since the question requires the speed in feet per minute, we need to convert the time for one revolution to minutes:
30 seconds = 0.5 minutes
The linear speed (v) can be found using the formula v = C / time. Substituting our values in:
v = 785.398163 feet / 0.5 minutes = 1570.79633 feet per minute
Therefore, the linear speed of a passenger at the edge of the Ferris wheel was approximately 1570.8 feet per minute.
A die is rolled. What is the probability of rolling the following?
a multiple of 2 or a multiple of 5
Answer:
2/3 chance (67%)
Step-by-step explanation:
Multiples of 5:
(5)
Multiples of 2:
(2)
(4)
(6)
This is a 4/6 chance or 2/3
[tex]|\Omega|=6\\|A|=3+1=4\\\\P(A)=\dfrac{4}{6}=\dfrac{2}{3}\approx67\%[/tex]
6th grade-Write an inequality to represent the situation: The temperature stayed above -15 degrees. Thanks guys!
Let temperature = T
"The temperature stayed above -15 degrees. " means that the temperature is always greater than -15 degrees.
Therefore,
-15 degrees < T
In a city of 35,000 homes a survey was taken to determine the number with WiFi access. Of the 500 surveyed 400 had WiFi access estimate the number homes in the city that have WiFi access.
Answer:
Ste-by-step explanation
400/500 = 0.8 x 35.000 = 28.000
28.000 homes will have wifi access.
Answer:
Estimated .70%2A25000 = 17,500 homes in the city will have wifi access
Step-by-step explanation:
What is the measure of arc AC? Enter your answer in the box. AC is (7x-2) degrees. ABC is inscribed with (2.5x + 4) degrees
Answer:
The measure of arc AC is equal to 33°
Step-by-step explanation:
we know that
The inscribed angle measures half that of the arc comprising
so
∠ABC=(1/2) arc AC
substitute the values
(2.5x+4)=(1/2)(7x-2)
solve for x
5x+8=7x-2
7x-5x=8+2
2x=10
x=5
Find the measure of arc AC
arc AC=(7(5)-2)=33°
Final answer:
The measure of arc AC can be calculated by using the inscribed angle theorem and solving the equation 2×(2.5x + 4) = 7x - 2, which represents the relationship between the inscribed angle and its intercepted arc.
Explanation:
To determine the measure of arc AC, we need to consider the relationship between the inscribed angle of a circle (ABC in this case) and the corresponding arc (arc AC).
By the inscribed angle theorem, the measure of an inscribed angle is half the measure of its intercepted arc. This relationship allows us to set up the equation (2.5x + 4) degrees = 0.5×((7x-2) degrees).
By solving this equation, we can find the value of x, and consequently, the measure of arc AC.
substitute the values
(2.5x+4)=(1/2)(7x-2)
solve for x
5x+8=7x-2
7x-5x=8+2
2x=10
x=5
Find the measure of arc AC
arc AC=(7(5)-2)=33°
The areas of two circles are in the ratio 49:64. Find the ratio of their circumferences.
Answer:
7 : 8
Step-by-step explanation:
Given 2 similar figures with circumference ratio a : b
Then the ratio of the corresponding areas = a² : b²
Here the ratio of areas = 49 : 64
Taking the square root of both gives ratio of circumference
ratio of circumference = [tex]\sqrt{49}[/tex] : [tex]\sqrt{64}[/tex] = 7 : 8
Which of the symbols correctly relates the two numbers ?
Answer:
C. >
Step-by-step explanation:
The answer is C. because 65 is greater than 56!
subtract the polynomials (3x^2-11x-4)-(x-2)(2x+3)
Answer:
[tex]x^2-10x+2[/tex]
Step-by-step explanation:
Multiply out the two monomials first because of PEMDAS.
[tex](-x + 2) * (2x + 3)=-2x^2+x+6[/tex]
Now add them together.
[tex]3x^2-11x-4-2x^2+x+6=x^2-10x+2[/tex]
Which point is an x-intercept of the quadratic function f(x)=(x-4)(x+2)
Answer:
x = - 2 or x = 4
Step-by-step explanation:
To find the x- intercepts let f(x) = 0, that is
(x - 4)(x + 2) = 0
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 2 = 0 ⇒ x = - 2
The x- intercepts are at x = - 2, x = 4
Consider a graph of the equation y = 2x - 1. What is the y-intercept?
Answer:
[0, -1]
Step-by-step explanation:
According to the Slope-Intercept Formula y = mx + b, b is your y-intercept, and in the above raisin, you have your answer in place of that b.
Answer:
[0, -1], or just -1
What is the next step in this construction?
A. Measure the distance from point R to point E using a compass.
B. Use a straightedge to connect point R with the arc below the line.
C. Place the compass on point Rand draw a small arc above the line.
D. Place the compass on point E and draw a small arc below the line and beneath point R.
Answer:
D. Place the compass on point E and draw a small arc below the line and beneath point R.
Step-by-step explanation:
According, to given construction we need to draw the a perpendicular on a line m from a point R above the line.
According to given figure, we have given a line m and R is a point above the line then they placed the compass on point R and draw the an arc by cutting line m at the points E and F. In next step we need to
D. Place the compass on point E and draw a small arc below the line and beneath point R.
If f(x) = 3x - 9 and g(x) = x?, what is (gºf)(5)?
We have been given the following functions:
f(x) = 3x - 9
g(x) = x
(G*f) means to multiply the function of g and f together:
x(3x - 9)
3x^2 - 9x
Now multiply the product of the solution above by 5:
5(3x^2 - 9x)
15x^2 - 45x
So, (g*f)(5) = 15x^2 - 45x
Answer:
6
Step-by-step explanation:
Substitute x = 5 into f(x) then substitute the value obtained into g(x)
f(5) = (3 × 5) - 9 = 15 - 9 = 6, then
g(6) = 6
Hence (g ￮ f)(5) = 6
Which expression represents the amount of punch Milena will need for her party?
g + 20
3g
3g + 20
3(20)
Answer:3g+20 on edg
Step-by-step explanation:
Since the guests equals g and 3 cups per guest it would be 3g+ extra 20 so the answer would be 3g+20
URGENT!!!!
Lionel Cooper paid for a new mechanic's tools with an installment loan of $6,000 at 8% for 36 months with a monthly payment of $187.80. After 20 payments, the balance is $2,849.08. He pays off the loan when the next payment is due.
a.) What is the CURRENT month's interest?
b.) What is the final payment?
c.) How much is saved by paying off the loan early?
Answer:
a) Current month's interest is: $40
b) The final payment is $7,440
c) Amount saved by paying off loan early is: $600
Step-by-step explanation:
Principal = $6,000
Interest rate = 8% or 0.08
Time = 36 months or 3 years
After 20 payments, the payment is $2,849.08.
a) What is the CURRENT month's interest?
The formula used to find the interest is:
I = P*r*t
Where P= Principal Amount
r = interest rate
and t = time in years
Putting the given values:
I = 6,000 * 0.08 * 3
I = 1440
Total Interest = $1440
Current Month interest = 1440/36
Current Month interest = 40
So, Current month's interest is: $40
b) What is the final payment?
The formula used is:
A = P(1+r*t)
A = 6,000(1+0.08*3)
A = 6000*(1.24)
A = 7,440
So, the final payment is $7,440
c) How much is saved by paying off the loan early?
The current balance paid is $2,849.08
The loan is paid when next payment is due.
So, remaining amount to be paid is:
Remaining Amount = Final Payment - Current balance paid
Remaining Amount = 7,440 - 2,849.08
Remaining Amount = 4,590.92
Remaining months in which amount is to be paid: 36-20 = 16 months
The loan is paid off next month so interest rate of remaining 15 months = 15*40 = 600
The amount paid on next payment = 4590.92 - 600 = $3990.9
So, amount saved by paying off loan early is: $600
Final answer:
Lionel Cooper saved $136.63 by paying off his loan early. The current month's interest on his loan was $19.09, making his final payment $2,868.17 after paying off the remaining balance of $2,849.08.
Explanation:
Lionel Cooper paid for new mechanic's tools with an installment loan of $6,000 at 8% annual interest rate for 36 months, with monthly payments of $187.80. After 20 payments, he decides to pay off the remaining balance of $2,849.08.
a.) What is the CURRENT month's interest?
First, calculate the monthly interest rate, which is 8% annually, or 0.08/12 per month = 0.0067. The current month's interest is the balance multiplied by the monthly interest rate: $2,849.08 * 0.0067 = $19.09.
b.) What is the final payment?
The final payment is the sum of the current month's interest plus the remaining balance: $19.09 (interest) + $2,849.08 (balance) = $2,868.17.
c.) How much is saved by paying off the loan early?
Normally, Lionel would pay $187.80 for 16 more months, totaling $3,004.80. By paying off early, he only paid $2,868.17, so he saved $136.63.
WILL MARK BRAINLIEST
Answer:
[tex]110.5\pi \ in^2[/tex]
Step-by-step explanation:
Given
Slant height = l = 17 in
Diameter = d = 13 in
We are given diameter of the circular base. We have to find radius first to calculate lateral area.
Radius = r = d/2
= 13/2
= 6.5 in
The formula for lateral area is:
[tex]LA = \pi rl\\Putting\ the\ values\\\LA = \pi *6.5*17\\= 110.5\pi in^2[/tex]
Hence, second option is correct ..
Answer:
Pls mark me brainliest because other guy is a genius
Step-by-step explanation:
Which is equivalent
Answer:
[tex]x^\frac{5}{3} y^\frac{1}{3}[/tex]
Step-by-step explanation:
This question is on rules of rational exponential
where the exponential is a fraction, you can re-write it using radicals where the denominator of the fraction becomes the index of the radical;
General expression
[tex]a^\frac{1}{n} =\sqrt[n]{a}[/tex]
Thus [tex]\sqrt[3]{x} =x^\frac{1}{3}[/tex]
Applying the same in the question
[tex]\sqrt[3]{x^5y} =x^\frac{5}{3} y^\frac{1}{3}[/tex]
=[tex]x^\frac{5}{3} y^\frac{1}{3}[/tex]
Answer: Second option
[tex](x^5y)^{\frac{1}{3}} = x^{\frac{5}{3}}y^{\frac{1}{3}}[/tex]
Step-by-step explanation:
By definition we know that:
[tex]a ^{\frac{m}{n}} = \sqrt[n]{a^m}[/tex]
In this case we have the following expression
[tex]\sqrt[3]{x^5y}[/tex]
Using the property mentioned above we can write an equivalent expression for [tex]\sqrt[3]{x^5y}[/tex]
[tex]\sqrt[3]{x^5y} = (x^5y)^{\frac{1}{3}}[/tex]
[tex](x^5y)^{\frac{1}{3}} = x^{\frac{5}{3}}y^{\frac{1}{3}}[/tex]
Therefore the correct option is the second option
Solve the equation log4(x + 20) = 3
Answer:
x = 44
Step-by-step explanation:
log4(x + 20) = 3
Raise each side to the power of 4
4^ log4(x + 20) = 4^3
x+20 = 4^3
x+20 = 64
Subtract 20 from each side
x+20-20 = 64-20
x = 44
Find each product or quotient. Use significant digits.
0.0505 m X 665 m
Beth rented a bike from Julia’s Bike. It cost $19.60 plus $6 per hour. If Beth rented the bike for two and half hours, how much did she pay ?
Answer:
She payed $34.60.
Step-by-step explanation:
It cost $19.60, just to rent the bike.
Then multiply $6 × 2 (hours) = 12
Now 6 ÷ 2 = 3 (half hour)
Add 12 + 3 = 15
Add everything together
19.60 + 15
You then get $34.60.
She paid $34.60.
What is the unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given
It cost $19.60, just to rent the bike.
Then multiply $6 × 2 (hours) = 12
Now 6 ÷ 2 = 3 (half hour)
Add 12 + 3 = 15
Add everything together
19.60 + 15
You then get $34.60.
To know more about the unitary method refer to :
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Rewrite the function by completing the square.
f(x) = x2 – 10x + 44
+
f(x) = (x+
Answer:
[tex]f(x)=(x-5)^{2}+19[/tex]
Step-by-step explanation:
we have
[tex]f(x)=x^{2}-10x+44[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)-44=x^{2}-10x[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]f(x)-44+25=x^{2}-10x+25[/tex]
[tex]f(x)-19=x^{2}-10x+25[/tex]
Rewrite as perfect squares
[tex]f(x)-19=(x-5)^{2}[/tex]
[tex]f(x)=(x-5)^{2}+19[/tex]
The vertex of this parabola is at (-3, -2). Which of the following could be its equation?
Answer:
y = a(x + 3)² - 2 where a is any real number except 0.Step-by-step explanation:
The vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex]
(h, k) - vertex
We have the vertex at (-3, -2) → h = -3 and k = -2.
Substitute:
[tex]y=a(x-(-3))^2+(-2)=a(x+3)^2-2[/tex]
The equation of parabola is , [tex]y= -2(x+3)^{2} - 2[/tex]
What is a parabola?Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.What are the 4 types of parabola?There are three types of parabolas. The three forms are: vertex form, standard form and intercept form. Each form provides you a different key feature for the graph.What is parabola and examples?A parabola is nothing but a U-shaped plane curve. Any point on the parabola is equidistant from a fixed point called the focus and a fixed straight line known as the directrix. Terms related to Parabola.What is equation of parabola?[tex]y = a(x- h)^{2} + K[/tex].
According to the question:
Applying value in equation gives.
[tex]y= -2(x-(-3))^{2} -2\\[/tex]
[tex]y= -2(x+3)^{2} - 2[/tex]
Learn more about parabola here:
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What is the inverse of y=^x3
Answer:
Inverse of y=x^3 is f^-1(x) = ∛x
Step-by-step explanation:
We need to find the inverse of y=x^3
Step 1:
Interchange the variables:
x= y^3
Step 2: Now solve to find the value of y
=> y^3 = x
taking cube root on both sides of the equation
∛y^3 = ∛x
y=∛x
Step 3: Replace y with f^-1(x)
f^-1(x) = ∛x
So inverse of y=x^3 is f^-1(x) = ∛x
Which polygon has an interior angle sum of 1080°?
Step-by-step explanation:
The sum of the interior angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees. Because the octagon is regular, all of its sides and angles are congruent.Answer:
Octagon
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides, so
180° (n - 2) = 1080° ( divide both sides by 180° )
n - 2 = 6 ( add 2 to both sides )
n = 8 ← octagon
The product of the polynomials (2ab + b) and (a2 – b2)
Answer:
= 2a³b - 2ab² + a²b - b³
Step-by-step explanation:
We multiply the each term in the first polynomial by each in the other as follows.
2ab(a² - b²) + b(a² - b²)
We then open the brackets and get the following.
2a³b - 2ab² + a²b - b³
We can not simplify the product further than this since it has no like terms.
Answer:
First is C
Second is 2
Step-by-step explanation:EDGE 2021
Write the real number 12 as a complex number in form of a+bi
[tex]12+0i[/tex]
.....................
Answer:
12+0i
Step-by-step explanation:
Evaluate b^2 for b=9
Answer: It's 81
Step-by-step explanation:
So, if B= 9 then it's 9^2 which is 9 x 9 = 81
Hope my answer has helped you and if not i'm sorry.
Compute the permutation. 8 P 4 32 1,680 6,720
ANSWER
[tex]^8P_4=1680[/tex]
EXPLANATION
The given permutation is
[tex]^8P_4.[/tex]
Recall the formula for permutation
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]
We substitute n=8, and r=4 to obtain:
[tex]^8P_4=\frac{8!}{(8-4)!}[/tex]
[tex]^8P_4=\frac{8!}{4!}[/tex]
Recall the factorial expansion
[tex]n! = n \times (n - 1) \times (n - 2)...3 \times 2 \times 1[/tex]
We apply this expansion to get:
[tex]^8P_4=\frac{8 \times 7 \times 6 \times 5 \times 4!}{4!}[/tex]
[tex]^8P_4=8 \times 7 \times 6 \times 5[/tex]
[tex]^8P_4=1680[/tex]
The four folded parts of an envelope are opened up to create this figure. What is the surface area of one side of the unfolded envelope?
A. 25 square centimeters
B. 37 square centimeters
C. 50 square centimeters
D. 64 square centimeters
Answer:
Option C. 50 square centimeters
Step-by-step explanation:
we know that
The surface area is equal to the area of four triangles plus the area of rectangle
so
[tex]SA=2[\frac{1}{2}(4)(2)]+2[\frac{1}{2}(6)(3)]+(6)(4)[/tex]
[tex]SA=8+18+24[/tex]
[tex]SA=50\ cm^{2}[/tex]
Answer:
C
Step-by-step explanation:
The total area comprises of the rectangle (area is base * height) and the 4 triangles (area = 1/2 * base * height).
Area of rectangle = 6 * 4 = 24
Area of top triangle = 1/2 * 6 * 3 = 9
Area of bottom triangle = 1/2 * 6 * 3 = 9
Area of rightside triangle = 1/2 * 4 * 2 = 4
Area of leftside triangle = 1/2 * 4 * 2 = 4
Let's add them up and find the correct answer:
Area = 24 + 9 + 9 + 4 + 4 = 50
Shirts cost $20 each and ties cost $12 each. Write an expression for the cost of s shirts and t
ties.
20 + 12
Find the quotient. Simplify your answer.
y-4/y ÷ 6/y
Answer: [tex]\frac{y-4}{6}[/tex]
Step-by-step explanation:
To find the quotient asked, you need to make the division indicated.
You can follow these steps:
1. Find the reciprocal of [tex]\frac{6}{y}[/tex]. You need to turn it upside down. Then you get that the recriprocal is:
[tex]\frac{y}{6}[/tex]
2. Now you must multiply [tex]\frac{y-4}{y}[/tex] by [tex]\frac{y}{6}[/tex]:
[tex](\frac{y-4}{y})(\frac{y}{6})=\frac{(y-4)(y)}{(y)(6)}[/tex]
3. Simplifying, you get that the quotient is:
[tex]=\frac{y-4}{6}[/tex]
Determine if the two figures are congruent and explain your answer.
Answer:
They can be congurent depending on which two figures you are using
Step-by-step explanation: