Answer:
1/10 of pizza
Step-by-step explanation:
Let x represent size of equal pieces.
We have been given that a pizza is cut into five pieces. Four of the pieces are the same size, and the fifth size is 0.5 the size of each of the others.
This means that size of small piece would be half the size of other pieces, that is [tex]\frac{x}{2}[/tex].
Since the pizza is divided in 5 pieces, so we will divide [tex]\frac{x}{2}[/tex] by 5 as:
[tex]\frac{\frac{x}{2}}{5}=\frac{x}{2\cdot5}=\frac{x}{10}=\frac{1}{10}x[/tex]
Therefore, the smallest piece is 1/10 of the pizza.
Kelly is a salesperson at a shoe store, where she must sell a pre-set number of pairs of shoes each month. At the end of each work day the number of pairs of shoes that she has left to sell that month is given by the equation S=300-15x , where S is the number of pair of shoes Kelly still needs to sell and x is the number of days she has worked that month. What is the meaning of the number 300 in this equation
Answer: The initial number of shoes in the store is 300.
Step-by-step explanation:
Given : Kelly is a salesperson at a shoe store, where she must sell a pre-set number of pairs of shoes each month.
At the end of each work day the number of pairs of shoes that she has left to sell that month is given by the equation
[tex]S=300-15x[/tex] , where S = Number of pair of shoes Kelly still needs to sell.
x = Number of days she has worked that month.
When x= 0 , we get S= 300
i.e. When she started working in that month , she has 300 pairs of shoes to sell.
Therefore , Number 300 means that the initial number of shoes in the store is 300
Calculate the volume of the cylinder, where a = 18 and b = 11. Use 3.14 for pi and round your answer to the nearest tenth.
Answer:
Volume of cylinder [tex]=2797.7[/tex]
Step-by-step explanation:
Let [tex]a[/tex] be diameter and [tex]b[/tex] the height of the cylinder
[tex]Then\ radius(r)=\frac{diamater\ (a)}{2}\\\\r=\frac{18}{2}\\\\r=9[/tex]
Volume of cylinder [tex]=\pi\times(radius)^2\times(height)[/tex]
[tex]=\pi\times(9)^2\times11\ \ \ \ \ \ (\pi=3.14)\\\\=3.14\times9\times9\times11\\\\=2797.74\\\\\approx2797.7[/tex]
An unbiased coin is tossed 15 times. In how many ways can the coin land tails either exactly 8 times orexactly 5 times?
In 15 coin tosses, an unbiased coin can land tails either exactly 8 times or exactly 5 times in 46,683 ways.
Explanation:The question relates to the concept of probability, specifically calculating the number of outcomes in coin tosses. The outcomes in which a coin lands tails exactly 8 times or exactly 5 times can be calculated using the formula for combinations, which is nCr = n! / r!(n-r)!. For n=15 (the number of trials) and r=8 (the number of successful outcomes), the number of ways the coin can land tails 8 times is 15C8 = 15! / 8!(15-8)! = 43,680 ways. Similarly, for the coin to land tails 5 times the number of ways is 15C5 = 15! / 5!(15-5)! = 3,003 ways. Therefore, the coin can land tails either exactly 8 times or exactly 5 times in 43,680 + 3,003 = 46,683 ways.
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The correct answer is that there are [tex]\(\binom{15}{8} + \binom{15}{5}\)[/tex] ways for the coin to land tails either exactly 8 times or exactly 5 times.
To solve this problem, we will use the concept of combinations, which is denoted by the binomial coefficient [tex]\(\binom{n}{k}\)[/tex], where [tex]\(n\)[/tex] is the total number of trials and [tex]\(k\)[/tex] is the number of successful trials. The binomial coefficient calculates the number of ways to choose [tex]\(k\)[/tex] successes from [tex]\(n\)[/tex] trials.
For the first part of the question, where we want the coin to land tails exactly 8 times out of 15 tosses, we calculate the number of combinations using the binomial coefficient:
[tex]\[ \text{Number of ways for 8 tails} = \binom{15}{8} \][/tex]
For the second part of the question, where we want the coin to land tails exactly 5 times out of 15 tosses, we calculate the number of combinations similarly:
[tex]\[ \text{Number of ways for 5 tails} = \binom{15}{5} \][/tex]
To find the total number of ways for either event to occur, we add the two separate probabilities together:
[tex]\[ \text{Total number of ways} = \binom{15}{8} + \binom{15}{5} \][/tex]
Now we calculate each binomial coefficient:
[tex]\[ \binom{15}{8} = \frac{15!}{8!(15-8)!} = \frac{15!}{8!7!} \][/tex]
[tex]\[ \binom{15}{5} = \frac{15!}{5!(15-5)!} = \frac{15!}{5!10!} \][/tex]
We can simplify these expressions by canceling out common factors in the numerator and the denominator:
[tex]\[ \binom{15}{8} = \frac{15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9}{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ \binom{15}{5} = \frac{15 \times 14 \times 13 \times 12 \times 11}{5 \times 4 \times 3 \times 2 \times 1} \][/tex]
After calculating these values, we would add them together to get the final answer. However, since we are not providing numerical calculations here, we leave the answer in the form of the sum of the two binomial coefficients:
[tex]\[ \text{Total number of ways} = \binom{15}{8} + \binom{15}{5} \][/tex]
This is the number of ways the coin can land tails either exactly 8 times or exactly 5 times in 15 tosses.
Donna ate 7 12 box of popcorn jack ate 4 10 box of popcorn the boxes of popcorn are the same size write to explain how to use benchmark fraction to determine who ate more popcorn
Answer:
712/1 410/1
Step-by-step explanation:
theres a fraction for 712 and 410
Donna ate more popcorn than Jack.
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
We have to given that;
Donna ate 7/12 box of popcorn, and Jack ate 4/10 box of popcorn the boxes of popcorn.
Now, By using benchmark fraction we can determine who ate more popcorn as,
Here, Jack ate 4/10 box of popcorn.
⇒ 4/10
⇒ 2/5
And, Donna ate 7/12 box of popcorn.
⇒ 7/12
Take LCM of 5 and 12,
⇒ LCM {5, 12} = 60
Hence, We get;
⇒ 2/5 = 24/60
⇒ 7/12 = 35/60
Clearly, We get;
⇒ 7/12 > 2/5
Hence, Donna ate more popcorn than Jack.
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If we draw some dots on a paper, and connect each one of them to every other one with a single line, how many lines will we draw? Using mathematical induction, prove that the number of lines for n dots is 1, 2, ........., n(n − 1).
Answer:
Step-by-step explanation:
Let us assume that we have n different dots on a paper. We are to connect pairwise by a line. We have to find out how many lines can be formed.
Let us prove by induction.
If there is one dot then we have no line = 1(1-1) =0
Thus n(n-1) is true for 1 dot
Let us assume that for n dots we have n(n-1) lines
Add one more point now total points are n+1.
Already the existing n points are connected by a line.
So the extra point has to be connected to each of n point
i.e. n lines should be added from the new point to the n points and again n lines from the points to the new point(Assuming lines are different if initial and final point are different)
So 2n lines would be added
So total number of lines for n+1 points
[tex]= n(n-1) +n+n= n^2-n+2n \\= n^2+n\\=n(n+1)[/tex]
Thus true for n+1 if true for n. Already true for n =1
So proved by induction for all natural numbers n.
Using mathematical induction, we prove the number of lines connecting pairs of dots for n dots is n(n-1)/2. We confirm the base case for n=1 and then assume the proposition holds for k, leading to it holding for k+1, thus proving it for all natural numbers n.
The question involves calculating the number of lines that can be drawn to connect each pair of dots on a paper. To find this number for n dots, we can use mathematical induction.
Let's denote P(n) as the proposition that for n dots, the number of lines required to connect each pair of dots is n(n-1)/2, which simplifies to the sum of the first n-1 natural numbers.
Base Case
For n=1, there are no lines needed since there is only one dot, and no connections to be made: P(1) holds because 1(1-1)/2 = 0.
Inductive Step
We assume that P(k) is true for some natural number k, meaning that k dots require k(k-1)/2 lines. Now, we consider n=k+1 dots. The new dot must be connected to each of the k existing dots, adding k new lines. Therefore, the total number of lines for k+1 dots is k(k-1)/2 + k, which simplifies to (k+1)k/2, and is exactly P(k+1).
By the principle of mathematical induction, since we have proven the base case and the inductive step, we conclude that P(n) holds for all natural numbers n.
Find an equation for the nth term of the arithmetic sequence. -15, -6, 3, 12, ...
an = -15 + 9(n + 1)
an = -15 x 9(n - 1)
an = -15 + 9(n + 2)
an = -15 + 9(n - 1)
Answer: [tex]t_{n}=-15+9(n-1)[/tex]
Step-by-step explanation:
The formula for finding the nth term of an arithmetic sequence is given as:
[tex]t_{n}=a+(n-1)d[/tex]
[tex]a =[/tex] first term = -15
[tex]d =[/tex] common difference = -6 - (-15) = 9
[tex]n =[/tex] number of terms
substituting into the formula , we have :
[tex]t_{n} = -15+(n-1)9[/tex]
[tex]t_{n}=-15+9(n-1)[/tex]
What is the average rate of change for ƒ(x) = 2x + 2 over the interval −1 ≤ x ≤ 1?
A) 0.50
B) 0.75
C) 1.25
D) 2.50
The average rate of change for the function is 2
Step-by-step explanation:
The average rate of change of a function (also equal to the slope of the function) over a certain interval [tex][x_1,x_2][/tex] is given by
[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
Where f(x) is the value of the function at x.
In this problem, the function is
[tex]f(x)=2x+2[/tex]
And the interval is −1 ≤ x ≤ 1, so we have:
[tex]x_1 = -1\\f(x_1)=f(-1)=2(-1)+2=0[/tex]
And
[tex]x_2=1\\f(x_2)=f(1)=2(1)+2=4[/tex]
Therefore, the average rate of change of the function is
[tex]m=\frac{+4-0}{1-(-1)}=\frac{4}{2}=2[/tex]
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Wśród dziesięciu poniższych pierwiastków jest sześć liczb niewymiernych. Podkreśl je. √64 √0,64 √ 49/81 √ 820 √ 36/83 √ 48/81 √ 111 √ 1,21 √ 17
Answer:
√820
√36/83
√48/81
√111
√17
Step-by-step explanation:
Wszystkie liczby, które nie są wymierne, są uważane za irracjonalne. Liczbę niewymierną można zapisać jako liczbę dziesiętną, ale nie jako ułamek. Liczba niewymierna ma niekończące się powtarzające się cyfry po prawej stronie przecinka dziesiętnego.
mam nadzieję, że to pomoże
(I already did the first half, the Pythagorean theorem part, and the rest is easy I know that for a fact but I don't know how to do it.)
Find CU. If necessary, round answers to 4 decimal places Show all your work for full credit. Hint: Use the Pythagorean Theorem first.
Answer:
3
Step-by-step explanation:
You'll need to use the Angle Bisector Theorem.
CU / ZU = BC / BZ
From the first part of the problem, you used Pythagorean theorem to find that BZ = 10.
Let's say that CU = x. That means ZU = 8 − x. Plugging in values:
x / (8 − x) = 6 / 10
Cross multiply:
10x = 6(8 − x)
Solve:
10x = 48 − 6x
16x = 48
x = 3
Sarah says that you can find the LCM of any two whole numbers by multiplying them together. Provide a counter example to show that Sarah's statement is incorrect
Answer:
4·6 = 24 ≠ 12 = LCM(4, 6)
Step-by-step explanation:
Any pair of numbers with a common factor will refute Sarah's conjecture.
One such pair is 4 and 6, which have a product of 24. The LCM of 4 and 6 is 12, which is that product divided by their common factor of 2.
Sarah's statement is incorrect.
Sarah's statement that the least common multiple (LCM) of any two whole numbers is obtained by merely multiplying them together is incorrect. For example, consider the whole numbers 8 and 12. The product of these two numbers is 8 * 12 = 96. However, the LCM of 8 and 12 is actually 24, since 24 is the smallest number that is divisible by both 8 and 12. To find the LCM of two numbers, you need to list their multiples and find the smallest number that appears on both lists (in this case, the multiples of 8 are 8, 16, 24, 32, ... and the multiples of 12 are 12, 24, 36, 48, ...).
A local factory shut down in 1990 the population of 35,000 in 1991 the population was 24,500 In 1992 it was 17,150 what is expected population in 1999
Answer: the expected population in 1999 is 1412
Step-by-step explanation:
The population is decreasing in geometric progression. This is true because there is a common ratio between consecutive years.
Common ratio = 24500/35000 = 17150/24500 = 0.7
The formula for determining the nth term of a geometric progression is expressed as
Tn = ar^(n - 1)
Where
a represents the first term of the sequence.
r represents the common ratio.
n represents the number of terms.
From the information given,
a = 35000
r = 0.7
n = 10
The 9th term, T9 is
T9 = 35000 × 0.7^(10 - 1)
T9 = 35000 × 0.7^9
T9 = 1412
What is the value of x?
Enter your answer, as a decimal, in the box. Do not round your answer.
x=
The value of x is [tex]5.625[/tex]
Explanation:
Since, from the figure we can see that, a ray bisects the angle of a triangle.
Then, the angle bisector theorem states that, "if a ray bisects an angle of a triangle, then it divides the opposite sides of the triangle into segments that are proportional to the other two sides".
Thus, we have,
[tex]$\frac{A C}{B C}=\frac{A D}{B D}$[/tex]
where [tex]AC=4, BC=7.5, AD=3[/tex] and [tex]DB=x[/tex]
Substituting the values, we get,
[tex]$\frac{4}{7.5}=\frac{3}{x}$[/tex]
Simplifying, we have,
[tex]4x=22.5[/tex]
Dividing both sides by 4,
[tex]x=5.625[/tex]
Thus, the value of x is [tex]5.625[/tex]
Going into the final exam, which will count as two tests, Brandi has test scores of 75, 80, 74, 63, and 92. What score does Brandi need on the final in order to have an average score of 80?
Final answer:
Brandi needs to score an 88 on her final exam, which counts as two tests, to achieve an average score of 80 for the course.
Explanation:
The question involves calculating the score Brandi needs on the final exam to achieve an average of 80 when the final counts as two tests. To solve this, we add the current scores, multiply the desired average by the total number of tests (including the two final exams counted as separate tests), and subtract the sum of the current scores from this product.
Current sum of scores: 75 + 80 + 74 + 63 + 92 = 384
Number of tests, including the final counted twice: 5 + 2 = 7
Desired total of all scores: 80 (average) * 7 (tests) = 560
The score Brandi needs on the final is: 560 - 384 = 176.
Since the final counts as two tests, the necessary score for each portion of the final would be: 176 / 2 = 88.
Therefore, Brandi needs to score an 88 on her final exam to achieve an average score of 80.
Write an equation for the given function given the amplitude, period, phase shift, and vertical shift. attachment below is below, please help with this asap!
The equation of the function is y = 4 sin( [tex]\frac{1}{2}[/tex] t - [tex]\frac{4}{3}\pi[/tex] ) - 2
Step-by-step explanation:
If the equation is y = A sin (B x + C) + D , where
A is the amplitude The period is 2π/B C is the horizontal shift to the left (C is positive) or to right (C is negative)D is the vertical shift (D is positive) or down (D is negative)∵ The amplitude is 4
∴ A = 4
∵ The period is 4π
∴ T= 4π ⇒ T = [tex]\frac{2\pi }{B}[/tex]
∵ The phase shift is [tex]-\frac{4}{3}\pi[/tex]
∴ C = [tex]-\frac{4}{3}\pi[/tex]
∵ The vertical shift is -2
∴ D = -2
Substitute these values in the y = A sin( [tex]\frac{2\pi }{T}[/tex] t + C) + D
∴ y = 4 sin( [tex]\frac{2\pi }{4\pi }[/tex] t - [tex]\frac{4}{3}\pi[/tex] ) - 2
- Simplify it
∴ y = 4 sin( [tex]\frac{1}{2}[/tex] t - [tex]\frac{4}{3}\pi[/tex] ) - 2
The equation of the function is y = 4 sin( [tex]\frac{1}{2}[/tex] t - [tex]\frac{4}{3}\pi[/tex] ) - 2
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y=(x)= (1/4)^x find f(x) when x=(1/2) HELP FAST!!!!
Answer:
1/2
Step-by-step explanation:
(1/4)^x
when x=(1/2)
(1/4)^(1/2)
this can be rewritten in this way
√(1/4)
2 is the radical
then we distribute the root
√1 / √4
and solve
1/2
The number of email responses was twice the number of phone responses. If a person who preferred a picnic is selected at random, what is the probability that the person responded by email? 20% who preferred a picnic responded by phone and 5% responded by email
The probability that a person who preferred a picnic responded by email is 2/3.
Explanation:To find the probability that a person who preferred a picnic responded by email, we need to compare the number of email responses to the total number of responses. Let's assume the number of phone responses is x. Since the number of email responses is twice the number of phone responses, the number of email responses is 2x.
The total number of responses would be the sum of the email and phone responses, which is 2x + x = 3x.
The probability that a person who preferred a picnic responded by email would be the number of email responses divided by the total number of responses, which is 2x/3x = 2/3.
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To find the probability that a person selected at random who preferred a picnic responded by email, you take the 5% who responded by email and divide it by the total response percentage (30%). This results in a probability of 1/6, or approximately 16.67%.
We are given that 20% who preferred a picnic responded by phone and that the number of email responses was twice the number of phone responses. This means that 5% responded by email because twice 5% is 10%, and 10% plus the original 20% for phone responses gives us the 30% of people who responded in total. To find the probability that a randomly selected person who preferred a picnic responded by email, we can use relative frequency probability calculation.
The probability (P) can be expressed by the following equation:
P (Email | Picnic) = Number of people who preferred a picnic and responded by email / Total number of people who preferred a picnic
Given that the number of email responses is twice the number of phone responses, and knowing the percentage that corresponds to each mode of response:
Phone responses: 20%Email responses: 5% (because it's twice the phone responses, hence the total is 20% + (2 * 5%) = 30%)To calculate the probability that the person responded by email, we take the proportion:
P (Email | Picnic) = 5% / 30%
After calculating this, we get: P (Email | Picnic) = 1/6 or approximately 0.1667, which is about 16.67%.
An airplane departs from LA and flies to NY every 30 minutes. The trip takes 3 hours and 5 minutes. An airplane takes off from NY at the same time that one takes of from LA and flies to LA at the same speed. How many planes does it pass going in the opposite direction?
The arrival and departure of the airplanes are arranged according to a
schedule that is sequential.
The number of planes it passes going in the opposite direction is 13 planes
Reasons:
The given parameters are;
The frequency of airplane departure = Every 30 minutes
Time it takes to fly from LA to NY = 3 hours 5 minutes
Required;
The number of planes it passes going in opposite direction.
Solution:
As the airplane takes off from NY, we have that the airplane that took off 3
hours earlier from LA is 5 minutes away from the NY.
The airplane are moving in opposite directions, therefore, the relative
speed of the airplane is twice the speed of each airplane.
The time after takeoff at which the airplane from NY pass the first airplane
from LA is 5 minutes ÷ 2 = 2.5 minutes.
The time after which the airplane passes subsequent airplane is two times
faster or half the normal time which is 30 minutes ÷ 2 = 15 minutes, which
gives;
3 hours 5 minutes = 185 minutes
We have an arithmetic progression with first term, a = 2.5, common
difference = 15, and nth term, aₙ = 185, which gives;
185 = 2.5 + (n - 1)·15[tex]n = \dfrac{185 - 2.5}{15} + 1 = \dfrac{79}{6} = 13\frac{1}{6}[/tex]Given that the number of planes that the airplane passes are whole
number (discrete) values, we have;
The number of planes it passes going in the opposite direction, n = 13 planes
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We want to see how many planes does a plane that flies from NY to LA sees during the travel.
The answer is 6 planes.
We know that every 30 minutes, an airplane departs from LA to NY.
The travel does take 3 hours and 5 minutes (or 185 minutes in total).
At the same time that an airplane departs from LA to NY, one departs from NY to LA, we want to see how many airplanes it will see.
The number of planes that it will see is given by the number of times that 30 minutes (the interval between planes going from LA to NY) enters in 185 minutes (the total time of the flight).
This gives:
185/30 = 6.2
But we can't have a 0.2 of a plane, so we round the result to the nearest whole number, 6.
This means that on the flight from NY to LA, you can expect to see 6 planes going from LA to NY.
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If t represent the number of tickets purchased for a baseball game, which scenario is modeled by the equation, 32.50t + 5 = 28.75t + 20, to determine the number of tickets that result in the same cost for both levels?
Answer:
Replacing t with 4, 32.5*4 + 5 is 135 and 28.75 * 4 + 20 is also 135. Since these two are equal, the equation is verified.
or
If you substitute 4 for t in the equation, you get a true statement. That means it would cost the Burns family $135 for 4 tickets and parking for either lower-level or middle-level seats.
Step-by-step explanation:
Answer:The price for the lower level is $32.50 a ticket, plus $5.00 for a discounted parking pass. The middle-level tickets are $28.75 each, plus $20.00 for a parking pass.
Step-by-step explanation: assigment
if the radius of a sphere is tripled, the surface area of a sphere will increasea) by a factor of 3b) by a factor of 4c)by a factor of 6d)by a factor of 9
Answer:
D
Step-by-step explanation:
The area and the radius of a sphere are related by the formula:
A=4πr^2
Let’s say this is A1 and r1
Now the radius is tripled. This means r2 = 3r1
The new area thus becomes: A = 4 * (3r)^2 * π = 36πr^2
Comparing A1 and A2 , we can see that A2 = 9A1
Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95, but if the first flight is delayed, the probability that the luggage will make it is only 0.65.
A) Are the first flight leaving on time and the luggage making the connection independent events? Explain.
B) What is the probability that her luggage arrives in Denver with her?
Answer:
(A) The two events are Not Independent.
(B) The probability that Leah's luggage arrives in Denver is 0.695.
Step-by-step explanation:
Let F = Leah's first flight leaves on time and C = Leah's luggage will make the connecting flight.
Given:
P (F) = 0.15, P (C|F) = 0.95 and P (C|F') = 0.65
Here F' represents the events that Leash's first flight was not on time.
(A)
The events F and C are not independent.
For the luggage to make the connecting flight Leah's first flight must be on time.
As it is provided that the probability that the the luggage will make the connecting flight provided that the first flight is delayed is 0.65, i.e. there 0.35 probability that the luggage will not make the connecting flight.
Thus, implying that the two events F and C are dependent.
(B)
Compute the probability that Leah's luggage arrives in Denver as follows:
P (D) = P (C|F) × P (F) + P (C|F') × P (F')
[tex]= (0.95\times0.15)+(0.65\times (1-0.15))\\=0.695[/tex]
Thus, the probability that Leah's luggage arrives in Denver is 0.695.
The first flight leaving on time and the luggage making the connection are dependent events. The probability that Leah's luggage arrives in Denver with her is 0.695.
Explanation:A) In order to determine whether the first flight leaving on time and the luggage making the connection are independent events, we need to compare the probability of the luggage making the connection when the first flight is on time (0.95) to the probability of the luggage making the connection when the first flight is delayed (0.65).
If these probabilities are the same, then the events are independent.
However, since the probabilities differ, the events are dependent.
B) To find the probability that Leah's luggage arrives in Denver with her, we need to consider two scenarios:
The first flight leaves on time and the luggage makes the connection (0.15 * 0.95)The first flight is delayed and the luggage makes the connection (0.85 * 0.65)We can then add these probabilities together to get the total probability: (0.15 * 0.95) + (0.85 * 0.65) = 0.1425 + 0.5525 = 0.695
The velocity function, in feet per second, is given for a particle moving along a straight line. Find (a) the displacement and (b) the total distance that the particle travels over the given interval. v(t) = 1/√t, 1 ≤ t ≤ 4
Answer:
(a) 2 feet.
(b) 2 feet.
Step-by-step explanation:
We have been given that the velocity function [tex]v(t)=\frac{1}{\sqrt{t}}[/tex] in feet per second, is given for a particle moving along a straight line.
(a) We are asked to find the displacement over the interval [tex]1\leq t\leq 4[/tex].
Since velocity is derivative of position function , so to find the displacement (position shift) from the velocity function, we need to integrate the velocity function.
[tex]\int\limits^b_a {v(t)} \, dt[/tex]
[tex]\int\limits^4_1 {\frac{1}{\sqrt{t}}} \, dt[/tex]
[tex]\int\limits^4_1 {\frac{1}{t^{\frac{1}{2}}} \, dt[/tex]
[tex]\int\limits^4_1 t^{-\frac{1}{2}} \, dt[/tex]
Using power rule, we will get:
[tex]\left[\frac{t^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}}\right] ^4_1[/tex]
[tex]\left[\frac{t^{\frac{1}{2}}}{\frac{1}{2}}}\right] ^4_1[/tex]
[tex]\left[2t^{\frac{1}{2}}\right] ^4_1[/tex]
[tex]2(4)^{\frac{1}{2}}-2(1)^{\frac{1}{2}}=2(2)-2=4-2=2[/tex]
Therefore, the total displacement on the interval [tex]1\leq t\leq 4[/tex] would be 2 feet.
(b). For distance we need to integrate the absolute value of the velocity function.
[tex]\int\limits^b_a |{v(t)|} \, dt[/tex]
[tex]\int\limits^4_1 |{\frac{1}{\sqrt{t}}}| \, dt[/tex]
Since square root is not defined for negative numbers, so our integral would be [tex]\int\limits^4_1 {\frac{1}{\sqrt{t}}} \, dt[/tex].
We already figured out that the value of [tex]\int\limits^4_1 {\frac{1}{\sqrt{t}}} \, dt[/tex] is 2 feet, therefore, the total distance over the interval [tex]1\leq t\leq 4[/tex] would be 2 feet.
Randy's circular garden has a radius of 1.5 feet.He wants to enclose the garden with edging that costs $0.75 per foot. About how much will the edging cost
Answer:Circumference = 2 \pi r
circumference = 2 \pi (1.5)
circumference = 9.42 feet
The circumference is 9.42 feet, so we need to get fencing for 10 feet (assuming the fence comes in feet, i.e. you cant buy half a foot)
1 feet = $.075
10 feet = $0.75 x 10 = $7.50
I really need help with this. Please help!!
Answer:
the answer would be c)
Step-by-step explanation:
because dy and dx are equal ex10 and that would eventually turn to 5x4 plus 10 x4
but correct me if im incorrect.
If, in equilibrium, the cross-price elasticity between airline tickets and gasoline is 2.2; when the price of the gasoline increases by 4%, the quantity demanded of airline tickets increases by nothing% (enter your response rounded to two decimal places).
Answer:
8.8%
Step-by-step explanation:
Given that,
Cross-price elasticity between airline tickets and gasoline = 2.2
Price of the gasoline increases by 4%.
Therefore,
Cross-price elasticity = Percentage change in the quantity demanded of airline tickets ÷ Percentage change in the price of gasoline
2.2 = Percentage change in the quantity demanded of airline tickets ÷ 4%
2.2 × 4 = Percentage change in the quantity demanded of airline tickets
8.8% = Percentage change in the quantity demanded of airline tickets
The cross-price elasticity of demand, which in this case is 2.2, should theoretically indicate a 8.8% increase in airline ticket demand for a 4% increase in gasoline prices. However, if there is no increase in demand, other factors may be influencing the demand or the elasticity value may be inaccurate.
Explanation:The cross-price elasticity of demand measures the percentage change in quantity demanded for a product (airline tickets in this case) that results from a percentage change in the price of another product (gasoline in this case). If cross-price elasticity is 2.2, it means that a 1% increase in the price of gasoline leads to a 2.2% increase in the demand for airline tickets. So if gasoline price increases by 4%, you'd expect the demand for airline tickets to increase by 8.8% (4% times 2.2). But, in this situation, if the quantity demanded increases by nothing, it could mean that other factors are playing a role and affecting the demand for airline tickets, or it may be that the relationship between the two goods is not as strong as initially determined.
Learn more about Cross-price elasticity of demand here:https://brainly.com/question/33762697
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Laura bought 8 3/10 yard of ribbon. She used 1 2/5 yard to tie a package and 2 1/3 yard to make a bow. Joe later gave her 4 3/5 yard. How much ribbon does she now have?
Answer:
Amount of ribbon remaining with Lara is [tex]10\frac{1}{3}\ yard[/tex].
Step-by-step explanation:
Given:
Amount of ribbon Lara bought = [tex]8\frac{3}{10} \ yard[/tex]
[tex]8\frac{3}{10} \ yard[/tex] can be Rewritten as [tex]\frac{83}{10}\ yard[/tex]
Amount of ribbon Lara bought = [tex]\frac{83}{10}\ yard[/tex]
Amount of ribbon used to tie a package = [tex]1\frac{2}{5} \ yard[/tex]
[tex]1\frac{2}{5} \ yard[/tex] can be Rewritten as [tex]\frac{7}{5}\ yard[/tex]
Amount of ribbon used to tie a package = [tex]\frac{7}{5}\ yard[/tex]
Amount of ribbon used to make bow= [tex]2\frac{1}{3} \ yard[/tex]
[tex]2\frac{1}{3} \ yard[/tex] can be Rewritten as [tex]\frac{7}{6}\ yard[/tex]
Amount of ribbon used to make bow = [tex]\frac{7}{6}\ yard[/tex]
We need to find the amount of ribbon remaining with Lara.
Solution:
Now we can say that;
Amount of ribbon remaining with Lara can be find by subtracting Amount of ribbon used to tie a package and Amount of ribbon used to make bow from Amount of ribbon Lara bought.
framing in equation form we get;
Amount of ribbon remaining = [tex]\frac{83}{10}-\frac{7}{5}-\frac{7}{6}[/tex]
Now we will make the denominator common using LCM.
LCM of 5,6,10 is 30
So we get;
Amount of ribbon remaining = [tex]\frac{83\times3}{10\times 3}-\frac{7\times6}{5\times6}-\frac{7\times5}{6\times5}=\frac{249}{30}-\frac{42}{30}-\frac{35}{30}[/tex]
Now the denominator are common so we will solve the numerator we get;
Amount of ribbon remaining = [tex]\frac{249-42-35}{30}= \frac{172}{30}[/tex]
Now Given:
Amount of ribbon Joe gave = [tex]4\frac{3}{5}\ yard[/tex]
[tex]4\frac{3}{5}\ yard[/tex] can be rewritten as [tex]\frac{23}{5}\ yard[/tex]
Amount of ribbon Joe gave = [tex]\frac{23}{5}\ yard[/tex]
Now we can say that;
Amount of ribbon remaining with her = [tex]\frac{172}{30}+\frac{23}{5}[/tex]
Now again we will make the denominator common using LCM we get;
Amount of ribbon remaining with her = [tex]\frac{172\times1}{30\times1}+\frac{23\times6}{5\times6} = \frac{172}{30}+\frac{138}{30}[/tex]
Now denominators are common so we will solve the numerators we get;
Amount of ribbon remaining with her = [tex]\frac{172+138}{30}=\frac{310}{30}=\frac{31}{3}\ yard \ \ Or \ \ 10\frac{1}{3}\ yard[/tex]
Hence Amount of ribbon remaining with her is [tex]10\frac{1}{3}\ yard[/tex].
Final answer:
To find out how much ribbon Laura now has, we start with her initial amount, subtract the yardage used in two activities, and add the amount received from Joe, combining fractions and whole numbers to reach the final total yardage.
Explanation:
To calculate the amount of ribbon Laura has after her transactions, we need to perform a few steps involving addition and subtraction of mixed numbers, and then convert that number to a single unit if necessary. Here is how we solve this:
Start with the total ribbon Laura bought: 8 3/10 yards.
Subtract the ribbon used to tie a package: 1 2/5 yards.
Also, subtract the ribbon used to make a bow: 2 1/3 yards.
Add the ribbon given by Joe: 4 3/5 yards.
Combine the fractions and whole numbers separately for precision.
Finally, add or subtract the totals to find out how much ribbon Laura now has.
Let's do the math:
Laura's total ribbon after using some and receiving more from Joe is:
8 3/10 (initial amount) - 1 2/5 (package) - 2 1/3 (bow) + 4 3/5 (from Joe) = Laura's current ribbon amount.
Simplify the fractions and calculate:
Step by step:
Convert mixed numbers to improper fractions or work directly with mixed numbers.
Find common denominators for the fractions.
Add and subtract the fractions.
Add and subtract the whole numbers.
Combine the totals.
We'll end up with a total that represents the yardage of ribbon Laura has left.
In the image below, DE || BC. Find the measure of EC. Set up a proportion and solve for the measure. Show your work and label your answer. Please help me -- I will mark brainliest; If your response is inapropriate, or just a way to get points, it will get reported! Thank you so much !
The missing figure is attached down
Answer:
The measure of EC is 1 foot
Step-by-step explanation:
Let us revise the cases of similarity
AAA similarity : two triangles are similar if all three angles in the first triangle equal the corresponding angle in the second triangleAA similarity : If two angles of one triangle are equal to the corresponding angles of the other triangle, then the two triangles are similar.SSS similarity : If the corresponding sides of the two triangles are proportional, then the two triangles are similar.SAS similarity : In two triangles, if two sets of corresponding sides are proportional and the included angles are equal then the two triangles are similar.From the attached figure
∵ DE // BC
∴ ∠ADE ≅ ABC ⇒ corresponding angles
∴ ∠AED ≅ ACB ⇒ corresponding angles
In Δs ADE and ABC
∵ ∠ADE ≅ ABC ⇒ proved
∵ ∠AED ≅ ACB ⇒ proved
∵ ∠A is a common angle in the two triangles
∴ Δ ADE is similar to triangle ABC by AAA postulate
From the results of similarity the corresponding sides of the triangles are proportion
∴ [tex]\frac{AD}{AB}=\frac{DE}{BC}=\frac{AE}{AC}[/tex]
∵ AD = 8 feet
∵ DB = 2 feet
∴ AB = AD + DB
∴ AB = 8 + 2 = 10 feet
∵ AE = 4 feet
By using the proportion statement above [tex]\frac{AD}{AB}=\frac{AE}{AC}[/tex]
∴ [tex]\frac{8}{10}=\frac{4}{AC}[/tex]
By using cross multiplication
∴ 8 × AC = 10 × 4
∴ 8 AC = 40
Divide both sides by 8
∴ AC = 5 feet
∵ AC = AE + EC
∴ 5 = 4 + EC
Subtract 4 from both sides
∴ 1 = EC
∴ The measure of EC is 1 foot
The height of a soccer ball that is kicked from the ground can be approximated by the function:
y = -18x^2 + 54
where y is the height of the soccer ball in feet x seconds after it is kicked.
Find the time it takes the soccer ball to reach its maximum height in seconds
Answer:
[tex]\displaystyle \sqrt{3}\:sec.[/tex]
Step-by-step explanation:
[tex]\displaystyle -54 = -18x^2 → \frac{-54}{-18} = \frac{-18x^2}{-18} \\ \\ 3 = x^2 → \sqrt{3} = x[/tex]
I am joyous to assist you anytime.
Why is the answer E?
Step-by-step explanation:
The only way the answer could be E is if the x² term under the radical is supposed to be t².
f(x) = ∫₄²ˣ √(t² − t) dt
f'(x) = √((2x)² − 2x) (2)
f'(x) = 2√(4x² − 2x)
f'(2) = 2√(4(2)² − 2(2))
f'(2) = 2√12
what does martin luther king jr mean when he said "Freedom at last"
Final answer:
Martin Luther King Jr.'s phrase "Freedom at last" reflects the profound hope and vision for a future of racial equality and the end of segregation and discrimination in America, encapsulating the essence of his iconic "I Have a Dream" speech.
Explanation:
When Martin Luther King Jr. expressed the words "Freedom at last! Freedom at last! Thank God Almighty, we are free at last!", he was encapsulating the immense joy and the culmination of the struggle for civil rights and equality in America. This phrase symbolizes the hope and vision that one day, all people, regardless of race, would live in a society where they are judged by the content of their character and not the color of their skin. The phrase "Freedom at last" conveys a future where segregation, discrimination, and racial prejudice have been eradicated, and all of God's children—black men and white men, Jews and Gentiles, Protestants and Catholics—could join hands as equals.
The background of King delivering his keynote speech at the Lincoln Memorial highlights the reality that, a century after the Emancipation Proclamation, African Americans were still fighting against segregation and discrimination. King's vision was for the nation to truly live out its creed that "all men are created equal." His "I Have a Dream" speech, which included the powerful declaration of "Freedom at last," remains one of the most iconic speeches in American history and a defining moment in the Civil Rights Movement.
Does each equation represent exponential decay or exponential growth? WILL MARK BRAINLIEST [Chart attached]
Answer:
Does each equation represent exponential decay or exponential growth?
Step-by-step explanation:
The best way to know if an equation represents an exponential growth or decay is to look a the base of the exponentiation. If the base is larger than 1, it will be an exponential growth. If the base is smaller than 1, it will be an exponential decay.
Answer:
1
Step-by-step explanation: