Answer:
a
Step-by-step explanation:
The distance between two given coordinate points is 11 units. Therefore, option C is the correct answer.
What is distance formula?The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].
The given coordinate points are (-3, 2) and (2, -8).
Substitute (x₁, y₁) =(-3, 2) and (x₂, y₂)= (2, -8) in the distance formula, we get
Distance = √[(2+3)²+(-8-2)²]
= √[5²+(-10)²]
= √125
= 11.18
≈ 11
The distance between two given coordinate points is 11 units. Therefore, option C is the correct answer.
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Das has two bags of sweets each bag contains only lime and strawberry sweets there is 20 sweets in each bag in the first bag for every one lime there are 3 strawberry in the second bag there are 2 lime for every 3 strawberry how many more lime were in the second bag than in the first
Answer:
3
Step-by-step explanation:
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 90 degrees occurs at 4 PM and the average temperature for the day is 70 degrees. Find the temperature, to the nearest degree, at 9 AM
Answer:
65°
Step-by-step explanation:
Since the high is given, it is convenient to use that value with a cosine function to model the temperature. The function will be ...
T = A + Bcos(C(x-D))
where A is the average temperature, B is the difference between the high and the average, C is π/12, reflecting the 24-hour period, and D is the time at which the temperature is a maximum. "x" is hours after midnight.
We have chosen to use a 24-hour clock with x=16 at 4 pm. Then the value of T at 9 am is ...
T = 70 +20cos((π/12(9 - 16)) = 70 +20cos(7π/12) ≈ 64.824
The temperature at 9 am is about 65°.
Final answer:
To find the temperature at 9 AM, a sinusoidal function is constructed with an amplitude of 20 degrees, a vertical shift of 70 degrees, and a phase shift adjusted for a high at 4 PM. Plugging in the time value of 9 AM into the function, it is determined that the temperature at 9 AM is approximately the same as the average or midline temperature, which is 70 degrees.
Explanation:
To find the temperature at 9 AM using a sinusoidal function, we first identify essential characteristics of the function. The maximum temperature (high) of 90 degrees occurs at 4 PM (which we'll take as 16 hours on a 24-hour clock) and the average temperature for the day is 70 degrees, which is also the midline of the sinusoidal function. Since this is a typical daily temperature cycle, we assume that the minimum temperature occurs 12 hours after the maximum temperature. Thus, the temperature will have a periodicity of 24 hours. The amplitude of the temperature variation will be the difference between the high temperature and the average temperature (which is 20 degrees in this case).
The sinusoidal function can be written in the form:
T(t) = A · sin(B(t - C)) + D
Where:
C is the phase shift (16 hours for 4 PM)
Using this information, the sinusoidal function for temperature throughout the day is:
T(t) = 20 · sin((2π/24)(t - 16)) + 70
We then plug in t = 9 (for 9 AM), and calculate the temperature:
T(9) ≈ 20 · sin((2π/24)(9 - 16)) + 70
Which gives us, to the nearest degree:
Temperature at 9 AM ≈ 70 degrees.
Since the value of the sine function ranges from -1 to 1, at 9 AM (7 hours before the maximum temperature at 4 PM), the sine value would be negative indicating that the temperature is rising from the minimum towards the average. However, due to the characteristics of sine, the temperature at 9 AM will actually be the same as the temperature at 19 hours (7 PM), which is also 70 degrees.
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
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.
For each $n \in \mathbb{N}$, let $A_n = [n] \times [n]$. Define $B = \bigcup_{n \in \mathbb{N}} A_n$. Does $B = \mathbb{N} \times \mathbb{N}$? Either prove that it does, or show why it does not.
Answer:
No, it is not.
Step-by-step explanation:
The set [tex] C = \mathbb{N} \times \mathbb{N}[/tex] contains every ordered pair of Natural numbers, while B only contains those pairs in which both values in each entry are the same. Therefore, C is a bigger set than B, but B is not equal to C because for example C contains [tex][1] \times [2] [/tex] and B doesnt because 1 is not equal to 2.
The first term of the original sequence is 2. The first difference of a sequence is the arithmetic sequence 1,3,5,7,9... Find the first six terms of the original sequence.
Answer:
Step-by-step explanation:
2,2+1,2+1+3,2+1+3+5,...
2,3,6,11,18,27
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
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
(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
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.
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The publisher will sell Carlita's book to bookstores for $26.40 per copy. The retail price for customers to pay will be $48. Carlita expects to sell 225,000 copies. The publisher's expenses will be: • Printing: $3.75 per copy • Editing/Design: $27,500 • Publicity/Advertising/ Administrative: $135,150 • Carlita's Author Fee: 6.5% of the suggested retail price of every book sold Carlita suddenly announces that she wants to insert a kelp bookmark in each copy. The publisher thinks this will guarantee sales, but Carlita must agree to pay for 1/3 of the cost of the kelp. If the publisher expects the total profit on the book with the added expense to be $4,092,100, how much should Carlita expect to pay for her share of the kelp? just so i dont scroll up
Answer:
$151,800
Step-by-step explanation:
For the publisher, the expected revenue is $26.40 per copy. For 225,000 copies, the revenue is [tex]225000\times26.40 = 5,940,000[/tex]
The expenses incurred by the publisher are as follows:
Cost of 1 print = $3.75
Cost of 225,000 prints = [tex]225000\times3.75 = 843,750[/tex]
Editing/Design = $27,500
Publicity/Advertising/Administrative = $135,150
Author's fee = 6.5% of retail price per copy for 225,000 copies = [tex]225000\times26.40\times6.5/100= 386,100[/tex]
Total cost = 843,750 + 27,500 + 135,150 + 386,100 = $1,392,500
Let the cost of kelp for copies be k.
Then the total cost = 1,392,500 + k
If the expected profit is 4,092,100, then
Revenue = total cost + profit
5,940,000 = 1,392,500 + k + 4,092,100
5,940,000 = 5,484,600 + k
k = 5,940,000 - 5,484,600 = 455,400
Since Carlita is paying [tex]\frac{1}{3}[/tex] of k, her share of the kelp =
[tex]\frac{1}{3}\times455400 = 151800[/tex]
Carlita will pay $151,800
Jenna is helping her mom plant new flowers for the spring she has 45 red tulips and 63 yellow tulips if she puts the same number of tulips in each row and only one color per row what is the greatest number of tulips each row can have
Answer:
9
Step-by-step explanation:
Number of tulips per row has to be a factor of the number of available tulips.
Red tulips: 45 = 3×3×5
Yellow tulips: 63 = 3×3×7
Highest no. of tulips each row is 9 (3×3 = 9)
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.
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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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
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, ...).
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.
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
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
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
Sarah described the following situation:
When fertilizer was added to one plant and nothing was added to another plant, there was a noticeable difference in the color of the leaves of the plants.
Which of the following best describes the situation?
This is an example of correlation because the fertilizer causes the plants to change color.
This is an example of causation because the application of fertilizer caused the plant to improve its leaf color.
This is an example of correlation because one plant is being fertilized and the other is not.
This is an example of causation because the leaves on both plants change color.
Answer:
B. This is an example of causation because the application of fertilizer caused the plant to improve its leaf color.
Answer:
B
Step-by-step explanation:
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.
Let f (x )equals x squared and note that Modifying Below lim With x right arrow 2f(x)equals 4. For epsilon equals 1, use a graphing utility to find the maximum value of delta greater than 0 such that StartAbsoluteValue f (x )minus 4 EndAbsoluteValue less than epsilon whenever 0 less than StartAbsoluteValue x minus 2 EndAbsoluteValue less than delta.
Answer:
Step-by-step explanation:
Two sets are equal if they contain the
same elements. I.e., sets A and B are equal if
∀x[x ∈ A ↔ x ∈ B].
Notation: A = B.
Recall: Sets are unordered and we do not distinguish
between repeated elements. So:
{1, 1, 1} = {1}, and {a, b, c} = {b, a, c}.
Answer:
Definition: Two sets are equal if they contain the
same elements. I.e., sets A and B are equal if
∀x[x ∈ A ↔ x ∈ B].
Notation: A = B.
Recall: Sets are unordered and we do not distinguish
between repeated elements. So:
{1, 1, 1} = {1}, and {a, b, c} = {b, a, c}.
Definition: A set A is a subset of set B, denoted
A ⊆ B, if every element x of A is also an element of B.
That is, A ⊆ B if ∀x(x ∈ A → x ∈ B).
Example: Z ⊆ R.
{1, 2} ⊆ {1, 2, 3, 4}
Notation: If set A is not a subset of B, we write A 6⊆ B.
Example: {1, 2} 6⊆ {1, 3}
A hat contains four red marbles, two blue marbles, seven green marbles, and one orange marble. If two marbles are picked out of the hat randomly, what is the probability that one will be orange and one will be blue?
A. 98 percent
B. 1/98
C. 3/14
D. 1/7
E. 3 percent
Answer: B. [tex]\dfrac{1}{98}[/tex].
Step-by-step explanation:
Given : A hat contains four red marbles, two blue marbles, seven green marbles, and one orange marble.
Total marbles = 4+2+7+1 = 14
P(Blue)= [tex]\dfrac{2}{14}=\dfrac{1}{7}[/tex]
P(Orange) = [tex]\dfrac{1}{14}[/tex]
if we randomly select two marbles , then the probability of selecting one will be orange and one will be blue marble = P(Blue) x P(Orange) [both events are independent]
[tex]=\dfrac{1}{7}\times\dfrac{1}{14}=\dfrac{1}{98}[/tex]
Hence, the probability that one will be orange and one will be blue is [tex]\dfrac{1}{98}[/tex].
Therefore , the correct answer is B. [tex]\dfrac{1}{98}[/tex].
Polynomial and rational functions can be used to model a wide variety of phenomena of science, technology, and everyday life. Choose one of these sectors and give an example of a polynomial or rational function modeling a situation in that sector.
Answer:
L = s^2/(30.25Cd)
Step-by-step explanation:
In accident investigation, the speed of a vehicle can be estimated using a polynomial function that relates speed (s) to the length of skid marks (L). The drag coefficient Cd will depend on the condition of the road surface and tires, but might be expected to be between 0.7 and 0.8.
If the skid marks end in a collision, the length of the marks that might have been made can be estimated using this formula, then that length added to the actual length of marks to estimate the original speed. The speed at the point of collision can be estimated by the damage caused, and/or the movement created.
In the above formula, length is in feet, and speed is in miles per hour.
In Physics, a polynomial function such as[tex]y = -gt^2 + v0*t + h0[/tex] can model an object's motion under gravity. A rational function like P = a / (1 + bQ) can model the relationship between supply and demand in Economics.
Explanation:In the field of Physics, polynomial functions are often used to model physical phenomena. For example, the motion of an object under the force of gravity can be represented by a second-degree polynomial, or quadratic function. The equation[tex]y = -gt^2 + v0*t + h0[/tex]is an example of a quadratic function modeling free fall, where g represents the acceleration due to gravity, v0 is initial velocity, t represents time and h0 is initial height.
On the other hand, rational functions are used in various fields too. In Economics for instance, it can model situations like the relationship between supply and demand in market equilibrium. A simple model could be P = a / (1 + bQ) where P represents the price, Q is the quantity of good sold, and a, b are constants.
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There are several ways you might think you could enter numbers in WebAssign, that would not be interpreted as numbers. N.B. There may be hints in RED!!!You cannot have commas in numbers.You cannot have a space in a number.You cannot substitute the letter O for zero or the letter l for 1.You cannot include the units or a dollar sign in the number.You can have the sign of the number, + or -.Which of the entries below will be interpreted as numbers?a. 1.56 e-9b. 1.56e-9c. 3.25E4d. 40O0e. $2.59f. 5,000g. 1.23 inchesh. -4.99i.1.9435
Answer:
-4.99
1.9435
3.25E4
1.56e-9
Step-by-step explanation:
At a certain university, 42% of the students are women and 18% of the students are engineering majors. Of the engineers, 22% are women. If a student at this university is selected at random, what is the probability that the selected person is a woman engineering major?
Answer:
The probability that the selected person is a woman engineering major is 0.0396.
Step-by-step explanation:
The proportion of students at the university who are women is 0.42.
P (W) = 0.42
The proportion of students at the university who are engineering majors is 0.18.
P (E) = 0.18
The proportion of engineering majors that are women is 0.22.
P (W|E) = 0.22
The proportion of students at the university that are woman and engineering major is:
[tex]P (W|E)=\frac{P(W\cap E)}{P(E)} \\P(W\cap E)=P(W|E)\times P(E)\\= 0.18\times0.22\\=0.0396[/tex]
Thus, the probability that the selected person is a woman engineering major is 0.0396.
The probability that a randomly selected student from the university is a woman engineering major is 99/100.
To find this probability, we will use the information given about the percentages of women and engineering majors at the university, as well as the percentage of women among the engineering majors.
First, let's denote the total number of students at the university as T.
According to the information given:
- 42% of the students are women, so the number of women students is 0.42T
- 18% of the students are engineering majors, so the number of engineering students is 0.18T
- Of the engineers, 22% are women, so the number of women engineering students is 0.22 \times 0.18T.
Now, we want to find the probability that a randomly selected student is a woman engineering major. Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcomes are the number of women engineering majors, and the total number of possible outcomes is the total number of students.
The probability P that a randomly selected student is a woman engineering major is:
[tex]\[ P = \frac{\text{Number of women engineering majors}}{\text{Total number of students}} \][/tex]
[tex]\[ P = \frac{0.22 \times 0.18T}{T} \][/tex]
Since [tex]$T$[/tex]is in both the numerator and the denominator, it cancels out, leaving us with:
[tex]\[ P = 0.22 \times 0.18 \][/tex]
[tex]\[ P = 0.0396 \][/tex]
To express this probability as a fraction, we can write it as:
[tex]\[ P = \frac{396}{10000} \][/tex]
Simplifying this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4, we get:
[tex]\[ P = \frac{99}{2500} \][/tex]
Question 1 of 10
2 Points
Which of the following is most likely the next step in the series?
a3z, b6Y, C9X, d12W, e15V, f18U
A. 9211
B. 1211
C. 6241
D. 9210
E. g24t
F. 9240
Answer:
the answer is g21T
Step-by-step explanation:
a3z, b6Y, C9X, d12W, e15V, f18U next step in the series is E. g24t
How do you write a series of numbers?
A mathematical series consists of a pattern in which the next term is obtained by adding the two terms in-front. An example of the Fibonacci number series is: 0, 1, 1, 2, 3, 5, 8, 13, … For instance, the third term of this series is calculated as 0+1+1=2.
What are the types of number series?1) Arithmetic Sequences.
2) Geometric Sequences.
3) Exponent Sequences.
4) Two-Stage Sequences.
5) Mixed Sequences.
6) Alternating Sequences.
7) Fibonacci Sequences.
8) A Combination of Sequences' Types.
What is a series in math?In mathematics, a series is the cumulative sum of a given sequence of terms. Typically, these terms are real or complex numbers, but much more generality is possible
How do you answer a series number?You can find the right answer in number series by taking the difference between consecutive pairs of numbers, which form a logical series. In this example, the differences between succeeding pairs of numbers are 1,2, 4, 8, 16, and 32. So, the next difference must be 64.
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A loan of P500,000 was signed by Liza who promised to pay it at the beginning of each month for 5 years. If money is worth 12% compounded monthly, what will be the total sum paid by Liza?
Answer:
3,604,389
Step-by-step explanation:
Monthly payment P = [tex]\frac{a}{[(1+r)^{n} - 1] / [r(1+r)^{n}] }[/tex]
where a = total loan amount, r = periodic rate, n = number of payment periods
a = 500,000 ; r = 0.12 ; n = (5 x 12) = 60 months
P = [tex]\frac{500000}{[(1+0.12)^{60} - 1] / [0.12 (1+0.12)^{60} ] }[/tex]
P = [tex]\frac{500000}{(896.597) / (107.712)}[/tex]
p = 60,073.151
Total amount paid = 60073.151 x 60 = 3,604,389
Final answer:
Liza will have to pay a monthly amount of P2,997.75 for a loan of P500,000 at a 12% interest rate compounded monthly over 5 years. The total amount paid at the end of the term will be P179,865.
Explanation:
To determine the total sum Liza will pay for a loan of P500,000 with an interest rate of 12% compounded monthly over 5 years, we first need to calculate the monthly payment she would need to make. The problem is essentially asking to find the annuity payment for a present value, which can be calculated using the formula for present value of an ordinary annuity:
PV = PMT * [1 - (1 + r)-n] / r
Where:
PV = Present Value of the annuity (P500,000 in this case)
PMT = Monthly payment
r = Monthly interest rate (12% per year compounded monthly, so 0.12/12 per month)
n = Total number of payments (5 years × 12 months/year = 60 payments)
First, we calculate the monthly interest rate:
r = 0.12 / 12 = 0.01 or 1%
Now, setting up the equation:
500,000 = PMT * [1 - (1 + 0.01)-60] / 0.01
We find that PMT = 500,000 / 166.7916 (Using the present value factor derived from the reference information)
PMT = P2997.752
Therefore, the monthly payment Liza has to make is P2,997.75. To find the total sum paid after 5 years:
Total Sum = Monthly Payment * Number of Payments
Total Sum = P2,997.75 * 60 = P179,865