what is the exact volume of this cylinder? 4in 8in
The volume of the cylinder is; 128π in3
Base area(πr^2)*height
Π = 3.14
Therefore; 3.14 * 4^2 * 8
3.14 * 128
= 401.92 in3
A video sharing website starts with 20,000 members. Each year it loses 25% of the members, but adds 10,000 new members after the reduction. Write a recursive rule to find the number of members for any year.
Final answer:
To find the number of members for any year on the video sharing website, use the recursive rule with a base case of 20,000 initial members and apply the recursive step Mₙ = 0.75 × Mₙ₋₁ + 10,000 for each subsequent year.
Explanation:
The situation described can be modeled with a recursive rule where each year's membership is based on the previous year's membership.
To write such a rule, we'll use Mn to denote the number of members in year n, and Mn-1 to denote the number of members in the previous year.
The recursive rule is as follows:
Base case: M0 = 20,000 (initial number of members)Recursive step: Mₙ= 0.75 × Mₙ₋₁ + 10,000 for n > 0This means that for any year n, the number of members is equal to 75% of the previous year's members plus an additional 10,000 new members.
Fill in the table and guess the value of the limit: \lim\limits_{x \to 3} f(x), where f(x)= \frac {x^3 - 27} {x^2 - 9}
Final answer:
To find the limit of f(x) as x approaches 3, factor the numerator and denominator as differences of squares, cancel common terms, and substitute x = 3 into the simplified fraction to get the limit, which is 4.5.
Explanation:
The student's schoolwork question involves calculating the limit of a function as x approaches a certain value. Specifically, the function in question is f(x) = (x^3 - 27) / (x^2 - 9) and the limit to be computed is limx → 3 f(x). To solve this, first recognize that directly substituting x = 3 would result in a 0/0 indeterminate form. To find the limit, we'll use algebraic manipulation.
Since both the numerator and the denominator are differences of squares, factoring them would give (x-3)(x^2+3x+9) for the numerator and (x-3)(x+3) for the denominator. The x-3 terms cancel out, leaving us with x^2+3x+9 over x+3. Now, substituting x = 3 into the simplified fraction will provide the value of the limit.
Calculating the limit step by step:
Original function: f(x) = (x^3 - 27) / (x^2 - 9)
Factor both numerator and denominator: f(x) = [(x-3)(x^2+3x+9)] / [(x-3)(x+3)]
Cancel out (x-3) terms: f(x) = (x^2+3x+9) / (x+3)
Substitute x = 3: f(3) = (3^2+3*3+9) / (3+3) = (9+9+9) / 6 = 27 / 6 = 4.5
the sales of lawn mowers t years after a particular model is introduced is given by the function y= 5500 in (9t+4) where y is the number of mowers sold how many mowers will be sold 3 years after a model is introduced
The Chang's neighbor owns a ready-mix company. The company receives an order for 12.5 cubic yards of concrete. This mixture of concrete contains sand, cement, gravel, and water. For each pound of water, there are 5.5 pounds of sand, 2 pounds of cement, and 7.5 pounds of gravel. Determine how many pounds of cement must be used. Assume a cubic yard of concrete weighs 4,000 pounds.
a motorboat travels 432 kilometers on 6 hours going upstream and 384 km in 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current.
please help slove and steps
Answer:
the answer is 12
hope i helped
Step-by-step explanation:
A single gram of a certain substance has 0.52 gram of copper and 0.26 gram of zinc. The remaining portion of the substance.is nickel.Ben estimated that 0.2 gram of nickel is in 1 gram of the subtance.he used this estimate the amount of nickel in 35 grams of the substance.find the result of bens estimation strategy.then find the exact amoumt of nickel in 35 grams of the subtance
A baseball team has three different pitchers. Randy pitched 333 innings and allowed 222 runs, Felix pitched 555 innings and allowed 444 runs, and Johan pitched 777 innings and allowed 555 runs.
Which pitcher has the lowest number of runs allowed per inning?
Answer: the andswer is randy
Step-by-step explanation:
a chord of length 24cm is 13cm from the centre of the circle. caculate the radius of the circle
Determine whether the variable is qualitative or quantitative. number of flights
An airline sells all tickets for a certain route at the same price. if it charges 250 dollars per ticket it sells 5000 tickets. for every 5 dollars the ticket price is reduced, an extra 500 tickets are sold. it costs the airline a hundred dollars to fly a person. what price will generate the greatest profit for the airline?
Answer:
Scenario II i.e. when the price of ticket is $[tex]$245[/tex] will generate the greatest profit for the airline
Step-by-step explanation:
Scenario I
[tex]5000[/tex] tickets are sold at $ [tex]250[/tex] per ticket
The total money earned by the flight agency is
Number of tickets x price of each tickets
[tex]= 5000 * 250\\[/tex]
[tex]= 1250000[/tex] dollars
Scenario II
The price of each ticket is reduced by $[tex]5[/tex]
The price of new ticket is
[tex]250 -5[/tex]
[tex]= 245[/tex] dollars
The new number of tickets sold after reducing the price is
[tex]5000+ 500\\[/tex]
[tex]5500[/tex]
The total money earned by the flight agency is
Number of tickets x price of each tickets
[tex]5500 * 245\\[/tex]
[tex]1347500[/tex] dollars
Scenario II i.e. when the price of ticket is $[tex]$245[/tex] will generate the greatest profit for the airline
In a lot (collection) of 100 light bulbs, there are 5 defective bulbs. an inspector inspects 10 bulbs selected at random. find the probability of finding at least one defec- tive bulb. hint: first compute the probability of finding no defectives in the sample.
To determine the probability of finding at least one defective bulb in the lot of 100 bulbs, one must calculate the complementary event, picking no defective bulbs, and subtract its probability from 1.
Explanation:This problem involves Probability and Combinatorics, fundamental branches in Mathematics to calculate the possible outcomes in an event. Here, to calculate the probability of finding at least one defective bulb, we can begin by calculating the complementary event, that is, finding no defective bulbs in a sample.
The total number of ways to pick 10 bulbs from 100 is the combination C(100, 10). Likewise, the total number of ways to pick 10 non-defective bulbs from the 95 non-defective bulbs in the lot is C(95, 10). The probability of picking 10 non-defective bulbs then is C(95, 10)/C(100, 10).
Since the event of finding 'at least one defective bulb' is the complementary of 'finding no defective bulbs', we can subtract this probability from 1. So, the probability of finding at least one defective bulb is 1 - (C(95, 10)/C(100, 10)).
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What are the solutions of the equation x4 + 95x2 – 500 = 0?
Answer:
C
Step-by-step explanation:
x = plus-or-minus StartRoot 5 EndRoot and x = ±10i
ED 2021
Helpp! Find the area. The figure is not drawn to scale. https://courses.jmhs.com/content/enforced/8012-MA042_20_1/group/45b8c516-1008-46d7-aa1d-bb9b62c786ff/geometry_exam_10_files/mc001-1.jpg?_&d2lSessionVal=vtelKg4rpW3IHn6Wnb7kcJRAw
A 56.24 cm2
B 3.9 cm2
C 11.3 cm2
D 28.12 cm2
A shipment of 20tvs contains 5 that are defective. if 10 of them are randomly chosen for inspection, what is the probability that 2 out of 10 will be defective?
Final answer:
Using the hypergeometric distribution, the probability that exactly 2 out of 10 TVs randomly chosen from a shipment of 20 are defective is approximately 34.81%.
Explanation:
To find the probability that exactly 2 out of 10 randomly chosen TVs are defective, we can use the hypergeometric distribution. This distribution applies because we are dealing with a scenario where we have a finite population (20 TVs) and a non-replacement condition (once a TV is chosen for inspection, it is not put back).
The probability formula for the hypergeometric distribution is:
P(X = k) = [(C(g, k) * C(N-g, n-k)) / C(N, n)]
Where:
C(a, b) is the combination of a items taken b at a time.N is the total number of items in the population (20 TVs).g is the number of defective items in the population (5 defective TVs).n is the number of items chosen (10 TVs inspected).k is the number of defective items we're interested in finding within the chosen items (2 defective TVs).Plugging the numbers into the formula, we have:
P(X = 2) = [(C(5, 2) * C(15, 8)) / C(20, 10)]
P(X = 2) = [(10 * 6435) / 184756]
P(X = 2) = [64350 / 184756] ≈ 0.3481
So, the probability that exactly 2 out of 10 TVs inspected will be defective is approximately 0.3481 or 34.81%.
What ratio can be used to covert meters to kilometers A.100km/1m B.1000km/1m C. 1km/1000m D. 1km/10m
The three-dimensional figure shown consists of a cylinder and a right circular cone. The radius of the base is 10 centimeters. The height of the cylinder is 16 centimeters, and the total height of the figure is 28 centimeters. The slant height of the cone is 13 centimeters. Which choice is the best approximation of the surface area of the figure? Use 3.14 to approximate pi.
This is an incomplete question, here is the complete question.
The three-dimensional figure shown consists of a cylinder and a right circular cone. The radius of the base is 10 centimeters. The height of the cylinder is 16 centimeters, and the total height of the figure is 28 centimeters. The slant height of the cone is 13 centimeters. Which choice is the best approximation of the surface area of the figure? Use 3.14 to approximate pi.
(1) 1727 cm²
(2) 2355 cm²
(3) 2041 cm²
(4) 6699 cm²
Answer : The surface area of the figure is, 1727 cm²
Step-by-step explanation :
The formula for curved surface area of triangle is:
[tex]A=\pi \times r\times l[/tex]
where,
r and l are radius and slant height of triangle.
The formula for curved surface area of cylinder is:
[tex]A=2\pi \times r\times h[/tex]
where,
r and h are radius and height of cylinder.
The formula for area of circle is:
[tex]A=\pi r^2[/tex]
where,
r is radius circle.
Now we have to calculate the surface area of total figure.
Surface area of total figure = Surface area of triangle + Surface area of cylinder + Area of circle
Surface area of total figure = [tex]\pi \times r\times l+2\pi \times r\times h+\pi r^2[/tex]
Surface area of total figure = [tex]\pi \times r(l+2h+r)[/tex]
Given:
r = 10 cm
h = 16 cm
l = 13 cm
Now put all the given values in this formula, we get:
Surface area of total figure = [tex]3.14\times 10\times (13+2\times 16+10)[/tex]
Surface area of total figure = 1727 cm²
Thus, the surface area of the figure is, 1727 cm²
The trapezoid below has an area of 1575 cm. What equation could you solve to find the height of the trapezoid
Answer:
A
Step-by-step explanation:
At the Golden Gopher Mall , 1,300 People Took the Coke/Pepsi Challenge, 55% Of those challenged preferred Coke. how many people selected coke?
bank discount look at the file please to answer questions
A body oscillates with simple harmonic motion along the x-axis. its displacement varies with time according to the equation x(t) = a sin(ω t + φ). if a = 5 m, ω = 3.444 rad/s, and φ = 1.0472 rad, what is the acceleration of the body at t = 3 s? note: the argument of the sine function is in radians rather than degrees. answer in units of m/s 2 .
The acceleration of the body at t = 3 seconds is approximately [tex]\( -58.58785 \, \text{m/s}^2 \).[/tex]
To find the acceleration of the body at ( t = 3 ) seconds, we need to find the second derivative of the displacement function [tex]\( x(t) \)[/tex] with respect to time t.
Given that[tex]\( x(t) = a \sin(\omega t + \phi) \)[/tex] , where [tex]\( a = 5 \) m, \( \omega = 3.444 \) rad/s, and \( \phi = 1.0472 \)[/tex] rad, the acceleration a(t) is the second derivative of of x(t) with respect to t:
First, let's find the first derivative of of x(t) with respect to t:
[tex]\[ v(t) = \frac{dx}{dt} = a \omega \cos(\omega t + \phi) \][/tex]
Now, let's find the second derivative of x(t) with respect to t:
[tex]\[ a(t) = \frac{d^2x}{dt^2} = -a \omega^2 \sin(\omega t + \phi) \][/tex]
Now, substitute the given values:
[tex]\[ a(t) = -5 \times (3.444)^2 \sin(3.444 \times 3 + 1.0472) \][/tex]
Now, calculate:
[tex]\[ a(t) = -5 \times (3.444)^2 \sin(10.332 + 1.0472) \]\[ a(t) = -5 \times (3.444)^2 \sin(11.3792) \][/tex]
Now, compute:
[tex]\[ a(t) = -5 \times (11.858736) \sin(11.3792) \]\[ a(t) \approx -5 \times (11.858736) \times 0.97989 \]\[ a(t) \approx -58.58785 \, \text{m/s}^2 \][/tex]
Therefore, the acceleration of the body at t = 3 seconds is approximately [tex]\( -58.58785 \, \text{m/s}^2 \).[/tex]
Cedric has $0.45 in his pocket which fraction of a dollar does Cedric have
Cedric has 9/20 of a dollar.
Explanation:To find the fraction of a dollar that Cedric has, we need to convert $0.45 into a fraction with a denominator of 100, which represents cents. Since 1 dollar is equal to 100 cents, we can write $0.45 as 45 cents. So, Cedric has 45/100 of a dollar, which can be simplified to 9/20.
What is the volume of the coffee in a can if the can has a radius of 4 inches and a height of 9 inches? (Use 3.14 for π.)
Answer:
452.16 is the answer
Step-by-step explanation:
If $8,500 is deposited in a compound interest account paying 3.9% interest annually, how much will be in the account after 12 years? Round your answer to the nearest cent.
The formula for amount is given by:
[tex] A=P(1+\frac{r}{n})^{nt} [/tex]
Now we are given ,
Principal (P) =$8500
rate (r) =3.9% = 0.039
period of interest (n) =1 for compounded annually
time (t) = 12 years
Plugging these values in the formula,
[tex] A=8500(1+\frac{0.039}{1})^{1*12} [/tex]
Amount =$13452.5773053
Answer : There will be $13452.5773053 in the account after 12 years.
You borrow $3200 to buy new kitchen appliances. The simple interest rate is 5%. You pay the loan off after 4 years.
The total amount paid = $3840
What is simple interest formula?"A = P(1 + rt)
Where A = Total Amount (principal + interest)
P = Principal Amount
I = Interest Amount
r = Rate of Interest in decimal
R = Rate of Interest as a percent
[tex]r=\frac{R}{100}[/tex]
t = Time Period"
For given question,
P = $3200
t = 4 years
R = 5%
[tex]\Rightarrow r=\frac{5}{100}\\\\ \Rightarrow r=0.05[/tex]
Using the formula of simple interest,
[tex]A=P(1+rt)\\\\A=3200(1+(0.05\times 4))\\\\A=3200(1+0.2)\\\\A=3200\times 1.2\\\\A=\$ 3840[/tex]
Therefore, the total amount paid = $3840
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The diagram is a hat box that is designed with the shape of a regular octagon inside and a rectangle outside. Find the value of x. Please explain.
Which function represents a vertical stretch of an exponential function? A. f(x)=3(1/2)^x B. f(x)=1/2(3)^x C. f(x)=(3)^2x D. f(x)=3^(1/2x)
Answer:
A. f(x) = 3*(1/2)^x
Step-by-step explanation:
We know that, a function can be stretched or shrinked both horizontally and vertically.
Now, according to our question we are required to look at the vertical stretch of an exponential function.
The general form for a vertical stretch of a function f(x) is k*f(x) where k>1.
So, we compare this form with the options provided.
We see that in option A the exponential function is multiplied by 3 and so the function will be stretched vertically.
Hence, option A is correct.
(A) A bag of trail mix weighs 2 lb. By weight, 20% of the bag is oats. How many pounds is the oats portion of the trail mix? Write an equation for the situation and label the “part,” “whole,” and “percent.”
(B) What is the weight of the oats in the trail mix? Show your work!
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Whats the sum 3/x + 4/x^2
Answer:
[tex]\frac{3x+4}{x^2} [/tex]
Step-by-step explanation:
sum of [tex]\frac{3}{x} + \frac{4}{x^2}[/tex]
To find the sum of two fractions we need to make the denominator same
LCD is x^2. we need to get x^2 in the denominator of both fractions
Multiply the first fraction with x
[tex]\frac{3 \cdot x}{ \cdot x} + \frac{4}{x^2}[/tex]
[tex]\frac{3x}{x^2} + \frac{4}{x^2}[/tex]
Denominators are same , now we add the numerators
[tex]\frac{3x+4}{x^2} [/tex]
The function h(t) = -2 (t-3)^2 +23 represents the height in feet, t seconds after a volleyball is served which of the following statements are correct
A. the volleyball reached it's maximum height of 3 sec
B. The maximum height of the vollybal was 23 ft
C. If the vball is not returned by the opposing team it will hit the ground in 5.5 sec
D. The graph that models the volleyball height over time is exponential
E. The vball was served from a height of 5 ft
Answer:
A. the volleyball reached it's maximum height of 3 sec
B. The maximum height of the vollybal was 23 ft
E. The vball was served from a height of 5 ft
Step-by-step explanation:
h(t) = -2 (t-3)^2 +23
Given equation is in the form of [tex]f(x)= a(x-h)^2 + k[/tex]
(h,k) is the vertex
Now we compare f(x) with h(t)
h(t) = -2 (t-3)^2 +23
h = 3 and k = 23
Vertex is (3,23)
h=3 . this means the volleyball reaches its maximum height in 3 seconds
k = 23. this means the volleyball reaches the maximum height of 23 ft
When ball reaches the ground the height becomes 0. so plug in 0 for h(t) and solve for t
0= -2 (t-3)^2 +23
Subtract 23 on both sides
-23 = -2(t-3)^2
Divide both sides by -2
[tex]\frac{-23}{-2} = (t-3)^2[/tex]
Take square root on both sides
[tex]+-\sqrt{\frac{23}{2}}= t-3[/tex]
Add 3 on both sides
[tex]+-\sqrt{\frac{23}{2}}+3= t[/tex]
We will get two value for t
t=-0.39 and t= 6.39
So option C is not correct
Given h(t) is a quadratic function not exponential
To find initial height we plug in 0 for x and find out h(0)
h(0) = -2 (0-3)^2 +23 = -2(-3)^2 + 23= -18+ 23= 5
The volleyball was served from a height of 5 ft