For an object whose velocity in ft/sec is given by v(t) = −t^2 + 4, what is its displacement, in feet, on the interval t = 0 to t = 3 secs?
7.67
−3.00
−0.33
3.00
Answer:
The answer is 3 feet
Step-by-step explanation:
The displacement function is the integration of the velocity formula, so:
[tex]d(t)=\int\limits^0_t \, (-t^{2} +4) dt \\d(t)=\int\limits^0_t{} \, (-t^{2}) dt + \int\limits^0_t{} \, 4 dt \\\\d(t)=(\frac{-t^{3} }{3} + C ) + (4t + C)\\\\\\\ d(t)=frac{-t^{3} }{3} + 4t + C\\[/tex]
if we evaluate the displacement for the upper and lower limit it would be
D = total displacement = d(3) - d(0)
[tex]D=(\frac{-3^{3} }{3} + 12 + C) - (\frac{-0^{3} }{3} + 4*0 + C)\\\\D=(-9 + 12 + C) - (0 + 0 + C)\\\\\\D=(3 + C) - C\\\\\\D=3[/tex]
Answer:
3 feet
Step-by-step explanation:
The relationships between displacement (position), velocity and acceleration are:
[tex]\boxed{\boxed{\begin{array}{c}\textbf{DISPLACEMENT (s)}\\\\\text{Differentiate} \downarrow\qquad\uparrow\text{Integrate}\\\\\textbf{VELOCITY (v)}\\\\\text{Differentiate}\downarrow\qquad\uparrow \text{Integrate}\\\\\textbf{ACCELERATION (a)}\end{array}}}[/tex]
Displacement is an object’s distance from a particular point (often its starting point), measured in a straight line. It’s not necessarily the same as the total distance travelled.
To find the displacement of an object in its first 3 seconds of travel, we need to integrate its velocity function on the interval [0, 3] seconds.
[tex]\begin{aligned}\displaystyle \int^3_0 (-t^2+4)\; \text{d}t&=\left[\dfrac{-t^{2+1}}{2+1}+4t\right]^3_0\\\\&=\left[-\dfrac{t^{3}}{3}+4t\right]^3_0\\\\&=\left(-\dfrac{(3)^{3}}{3}+4(3)\right)-\left(-\dfrac{(0)^{3}}{3}+4(0)\right)\\\\&=-9+12+0-0\\\\&=3\end{aligned}[/tex]
Therefore, the displacement of the object on the interval [0, 3] seconds is 3 feet.
A time-ordered plot of representative sample statistics is called a:
how do you make this equation 13+5y=6x into slope-intercept form?
An appointment lasted from 2:30 pm until 5:15 pm. how long was the appointment?
Final answer:
The total duration of the appointment was 2 hours and 45 minutes.
Explanation:
To determine how long the appointment lasted, we need to calculate the time difference between the start time and the end time. The appointment started at 2:30 pm and ended at 5:15 pm.
First, take note of the start time: 2:30 pm.
Then, take note of the end time: 5:15 pm.
Calculate the hours by subtracting the start hour from the end hour: 5 pm - 2 pm = 3 hours.
Next, calculate the minutes by subtracting the start minutes from the end minutes: 15 minutes - 30 minutes. Since you cannot have a negative number of minutes, you need to borrow an hour from the 3 hours calculated, making it 2 hours, and add 60 minutes to the 15 minutes. Now, 75 minutes - 30 minutes = 45 minutes.
Combine the total hours and minutes: 2 hours and 45 minutes
Quiz/Survey Quiz Week 4 - Unexpected Events A
1. What happens if you don't pay your car insurance premium for your vehicle? Your car payments will increase
You are not insured
You are driving illegally
Any insurance claim isn't processed and your car doesn't get fixed
Your are not insured and are driving illegally
2. Suppose that you only have liability and comprehensive car insurance and you allow your roommate (who doesn't have car insurance) to drive your car to run an errand. What will likely happen if there is a single-car accident causing moderate damage to your car while your roommate is driving?
Your insurance policy will likely not cover the damages to your car.
Your friend will likely go to jail for theft of your car and destruction of property. Your friend will likely receive fines for driving without insurance.
Your insurance will likely pay for the damages and add your friend's accident to your record.
3. John, Alyson and Jared all selected identical new cars at the same price. John bought the car with some of his own money and the rest a car loan. Alyson bought the car with cash. Jared leased the car. What is true about their options for car insurance?
Alyson has the option to choose the less expensive liability-only insurance coverage.
John and Alyson have the option to choose the less expensive liability-only insurance coverage.
Alyson and Jared have the option to choose the less expensive liability-only insurance coverage.
John, Alyson and Jared all have the option to choose the less expensive liability-only insurance coverage.
4. William pays his $500 premium every 6 months for automobile insurance with collision coverage. His deductible is $750. William caused a minor accident that resulted in $700 of damages to his car and $1,100 of damages to the other car. William's car looks and drives fine and he chooses not to file a claim to repair his car. How much will William pay out-of-pocket to have the other car fixed?
$1,550
$750
$0
$1,100
$500
$800
5. When Lisa purchased her house, the mortgage lender required her homeowner's insurance to cover 100% of the loan amount. After many years, Lisa paid off her mortgage. If Lisa decided to comparison shop for homeowner's insurance now, what should the insurance coverage amount be based on…
The market value of the house
The original cost to build the house
The cost to rebuild the house
The appraised value of the house
6. How can understanding risk management topics help in everyday life?
It can help you evaluate the risks involved with situations you might face while driving, hanging out with friends, or being adventurous.
It can help you avoid large medical bills incurred because you have no medical insurance.
It can help safeguard your credit and protect you from lawsuits.
All answers are correct
1. What happens if you don't pay your car insurance premium for your vehicle?
Your are not insured and are driving illegally.
2. Suppose that you only have liability and comprehensive car insurance and you allow your roommate (who doesn't have car insurance) to drive your car to run an errand. What will likely happen if there is a single-car accident causing moderate damage to your car while your roommate is driving?
Your insurance policy will likely not cover the damages to your car.
3. John, Alyson and Jared all selected identical new cars at the same price. John bought the car with some of his own money and the rest a car loan. Alyson bought the car with cash. Jared leased the car. What is true about their options for car insurance?
Alyson has the option to choose the less expensive liability-only insurance coverage.
4. William pays his $500 premium every 6 months for automobile insurance with collision coverage. His deductible is $750. William caused a minor accident that resulted in $700 of damages to his car and $1,100 of damages to the other car. William's car looks and drives fine and he chooses not to file a claim to repair his car. How much will William pay out-of-pocket to have the other car fixed?
$0
5. When Lisa purchased her house, the mortgage lender required her homeowner's insurance to cover 100% of the loan amount. After many years, Lisa paid off her mortgage. If Lisa decided to comparison shop for homeowner's insurance now, what should the insurance coverage amount be based on…
The market value of the house.
6. How can understanding risk management topics help in everyday life?
All answers are correct.
Find the measures of angles x,y, and z
What is 63108 divided by 72
Which is the correct input-output table for the function f(x) = 7 – 4.5x?
Answer:
The function is given to be :
f(x) = 7 - 4.5x
Now, to make a correct input-output table for the given function write the given function in the form of y and x
⇒ y = 7 - 4.5x
Now, in this equation x is independent variable and y is dependent variable.
So, give the input values to the variable x and note down the output values of variable y.
The required table is :
x 0 1 2 3
y 7 2.5 -2 -6.5
Approximately how many times greater is 9.75×106 than 1.25×102 ? 7.8 7800 78,000 780,000
Answer:
78,000
Step-by-step explanation:
9.75 is 7.8 times larger than 1.25.
However, we have powers of 10. In the first number, 10 is raised to the 6th power; in the second number, 10 is raised to the 2nd power. This means that the first number is 10⁴ times bigger than the second one, or 10000 times bigger.
This means in total, the first number is 7.8(10000) = 78000 times larger than the second one.
This can be confirmed by dividing the two; 9.75(10⁶)÷1.25(10²) = 78000
Answer:
78000
Step-by-step explanation:
HEEEEEEEEEEEELP 20 POINTS FOR REAL
Shayla is baking muffins that require 1/2 cup vegetable oil. She only has 1/3 cup left. How much more does she need?
If $2500 is invested at an interest rate of 4.5% per year, compounded daily, find the value of the investment after the given number of years. (round your answers to the nearest cent.)
$2500 is invested at an interest rate of 4.5% per year, compounded daily for 2 years will amount to $5225.
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest is,
A = P(1 + r/100)ⁿ.
Where, A = amount, P = principle, r = rate, and n = time in years.
Given, $2500 is invested at an interest rate of 4.5% per year, compounded daily, and assuming it is for 2 years.
∴ The amount compounded daily will be,
A = P(1 + (r/365)/100)ⁿˣ³⁶⁵ as compounded daily.
A = 2500(1 + (4.5/365)/100)²ˣ³⁶⁵.
A = 2500( 1 + 0.00101)⁷³⁰.
A = 2500(1.00101)⁷³⁰.
A = 2500×2.09 dollars.
A = 5225 dollars.
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To calculate the future value of an investment of $2500 at a 4.5% interest rate compounded daily for 5 years, we use the compound interest formula. Assuming 5 years of growth, the future value would be approximately $3117.14.
Explanation:If $2500 is invested at an interest rate of 4.5% per year, compounded daily, we need to find the value of the investment after a certain number of years. The formula to calculate the future value of an investment with daily compounding is given by:
FV = P × (1 + r/n)^(n×t)
where:
FV is the future value of the investment,P is the principal amount ($2500),r is the annual interest rate (4.5% or 0.045),n is the number of times the interest is compounded per year (365 for daily),t is the time the money is invested for, in years.To calculate the future value, we plug in the values into the formula. However, the number of years, t, has not been specified, so we'll need that to give a final answer. For our purposes, let's assume the student asks for the value after 5 years. Using the formula:
FV = $2500 × (1 + 0.045/365)^(365×t)
FV = $2500 × (1 + 0.00012328767)^(1825)
FV = $2500 × 1.246856823
FV = $3117.14 (rounded to the nearest cent)
After 5 years, the investment would be worth approximately $3117.14.
When is g(x) = 0 for the function g(x) = 5⋅23x + 4?
when x = 0
when x = 1
when x = 4
never
Suppose an airplane climbs 15 feet for every 40 feet it moves forward. What is the slope of this airplane's ascent?
Answer:
D) 3/8
Step-by-step explanation:
How to write an equation of a line in slope intercept form with two points?
There are 18 girls in the school choir. The ratio of girls to boys is 1 to 2. How many boys are in the choir?
There are 36 boys in the school choir.
What is ratio?The numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
Given:
There are 18 girls in the school choir.
The ratio of girls to boys is 1 to 2.
That means,
Girls / boys = 1/2
Substituting the values,
18 / boys = 1/2
Boys = 2 x 18
Boys = 36
Therefore, there are 36 boys.
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To get to work, a commuter must cross train tracks. the time the train arrives varies slightly from day to day, but the commuter estimates that he'll get stopped on about 15% of work days. during a certain 5-day work week, what is the probability that he doesn't get stopped all week long?
The probability that the commuter doesn't get stopped all week long is approximately 0.44.
Explanation:To find the probability that the commuter doesn't get stopped all week long, we need to find the probability of not getting stopped on each day and then multiply those probabilities together. Since the commuter estimates that he gets stopped on about 15% of work days, the probability of not getting stopped on a single day is 1 - 15% = 85%. To find the probability of not getting stopped all week, we raise 85% to the power of 5, since there are 5 work days in a week:
Probability of not getting stopped all week = (85%)5 = 0.85 * 0.85 * 0.85 * 0.85 * 0.85 = 0.44370515625.
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The probability that the commuter doesn't get stopped by the train all week long is 44%.
Explanation:This question falls under the category of probability in mathematics. The commuter estimates he'll get stopped 15% of work days, which implies that he'll have a smooth commute 85% of the time (100% - 15%). In a 5-day work week, the probability that he doesn't get stopped at all can be computed by multiplying the probability of not getting stopped each day. Therefore, the answer is (0.85)^5 or approximately 0.44, which represents 44%.
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If y = 285 when x = 57, what is y when x = 81?
The sum of three consecutive integers is 267. What is the largest integer?
What are five properties preserved under a translation?
Frederick needs to borrow $3000 for a down payment on a new car. His uncle decided to loan him the money as a 4.5% loan. Frederick doesn't want to pay more than $810 in interest. How many years does Frederick have to pay back the loan?
Factor completely 4x5 − 20x4 − 36x3. (1 point)
Answer:
The factored form of given polynomial is [tex]x^3(4x^2-5x-9)[/tex]
Step-by-step explanation:
Given the polynomial [tex]4x^5 - 20x^4 - 36x^3[/tex]
We have to factor the above polynomial completely.
[tex]4x^5 - 20x^4 - 36x^3[/tex]
Take [tex]x^3[/tex] common from each term.
[tex]x^3(4x^2-5x-9)[/tex]
Here, the quadratic polynomial is prime i.e it cannot be factored into lower degree polynomial. It has complex roots.
Hence, the factored form of given polynomial is [tex]x^3(4x^2-5x-9)[/tex]
Answer: 4x^3(x^2 - 5x - 9)
Proof of validity is shown below.
Identify a benefit of applying statistical forecasting methods
One benefit of applying statistical forecasting methods is the ability to make informed predictions and decisions based on historical data.
Statistical forecasting methods utilize historical data and mathematical models to make predictions about future outcomes. By analyzing patterns, trends, and relationships within the data, statistical forecasting methods can provide valuable insights and estimates for various industries and fields.
One key benefit of applying statistical forecasting methods is the ability to make informed decisions and plan for the future. By utilizing historical data and statistical models, organizations can anticipate future demand, sales, or resource needs. This enables them to optimize their operations, allocate resources efficiently, and make strategic decisions.
Statistical forecasting methods also provide a level of objectivity and reliability in the prediction process. These methods are based on rigorous mathematical techniques and statistical principles, ensuring that the forecasts are grounded in sound methodology. This allows decision-makers to have confidence in the accuracy and validity of the forecasts, reducing uncertainty and aiding in effective planning.
Overall, applying statistical forecasting methods provides a systematic and data-driven approach to predicting future outcomes. It enables organizations to anticipate and adapt to changing circumstances, optimize their resources, and make informed decisions, leading to improved efficiency, profitability, and overall performance.
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The law of cosines is used to find the measure of Q.
242 = 202 + 342 – 2(20)(34)cos(Q)
576 = 400 + 1156 – (1360)cos(Q)
576 = 1556 – (1360)cos(Q)
–980 = –(1360)cos(Q)
To the nearest whole degree, the measure of angle Q _____ is
degrees
the right answer is 44.
Answer:
44 degrees.
Step-by-step explanation:
We are asked to find the measure of angle Q using law of cosines.
Law of cosines:
[tex]c^2=a^2+b^2-2ab\times cos(C)[/tex]
Upon substituting our given values in above formula we will get,
[tex]24^2=20^2+34^2-2\times 20\times 34\times cos(Q)[/tex]
[tex]576=400+1156-1360\times cos(Q)[/tex]
[tex]576=1556-1360\times cos(Q)[/tex]
[tex]576-1556=1556-1556-1360\times cos(Q)[/tex]
[tex]-980=-1360\times cos(Q[/tex]
Upon dividing both sides of our equation by -1360 we will get,
[tex]\frac{-980}{-1360}=\frac{-1360\times cos(Q}{-1360}[/tex]
[tex]0.7205882352941176=cos(Q)[/tex]
Now we will use arccos to solve for the measure of angle Q.
[tex]cos^{-1}(0.7205882352941176)=Q[/tex]
[tex]43.896932391182=Q[/tex]
[tex]Q\approx 44[/tex]
Therefore, the measure of angle Q is 44 degrees.
*PLEASE HELP, BRAINLIEST* A salesman must commute 1 hour and 48 minutes from his house to the airport, fly to another city and take a bus to his destination. What is the total travel time one way?
The total travel time one way is 288 minutes.
Explanation:To find the total travel time one way, we need to add up the time spent on each part of the journey. The salesman spends 1 hour and 48 minutes commuting from his house to the airport. Let's convert this to minutes, which gives us 60 + 48 = 108 minutes.
Next, we add the flight time. The question doesn't specify the duration of the flight, so we can't determine that. We'll assume it takes 2 hours, which is 120 minutes. Finally, we add the time spent on the bus. Again, the question doesn't provide this information, so let's assume it takes 1 hour (60 minutes) by bus.
Adding up the commute time, flight time, and bus time, we get 108 + 120 + 60 = 288 minutes. Therefore, the total travel time one way is 288 minutes.
Jack has 2,613 songs saved on his computer. Dexter has 4 times as many songs saved on his computer as Jack has. How many songs does Dexter have saved on his computer?
how would the expression x^3-3sqrt(3) be rewritten using difference of cubes?
Answer:
Correct option is:
C. [tex](x-\sqrt{3})(x^2+3+x\sqrt{3} )[/tex]
Step-by-step explanation:
x^3-3sqrt(3)
= [tex]x^3-3\sqrt{3} \\\\=x^3-\sqrt{3}^3[/tex]
= [tex](x-\sqrt{3})(x^2+3+x\sqrt{3} )[/tex]
(since, [tex]a^3-b^3=(a-b)(a^2+b^2+ab)[/tex])
Hence, the correct option is:
C. [tex](x-\sqrt{3})(x^2+3+x\sqrt{3} )[/tex]
Ronnie cuts 3/4 inch sections of wood to make a birdhouse roof. he cut 12 sections. how many inches did he cut
Ronnie cut a total of 9 inches of wood. This is determined by multiplying the number of sections he cut (12) by the length of each section (3/4 inch).
Explanation:Ronnie cut 12 sections of wood, each measuring 3/4 inch to make his birdhouse's roof. In order to find out the total length of wood he used, we need to multiply the number of sections he cut by the length of each section. This is a basic multiplication problem in fractions.
So, 12 (sections) x 3/4 (inches/section) = 9 inches.
This means Ronnie cut a total of 9 inches of wood to make the birdhouse roof.
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PLEASE HELP! Complete the truth table and determine whether or not the following statement is a tautology, a contradiction, or neither. ∼(∼p∧q)∧(p∨q)∼(∼p∧q)∧(p∨q). I attached an image.
If triangle ABC is congruent to triangle XYZ, then which of the following is congruent to ∠A?
∠C
∠X
∠Y
∠Z
Answer: ∠X
Step-by-step explanation:
If ΔABC is congruent to ΔXYZ then their corresponding parts must be congruent by CPCTC.
To find the corresponding angle to ∠A, just check the position of A in the name of ΔABC,
A is the first letter in the name of ΔABC, thus the angle corresponding to ∠A is ∠X.
CPCTC (congruent parts of corresponding angles are congruent) tells that if two triangles are congruent then the corresponding angles and sides are congruent .Tony bowled 135 and 145 in his first two games. write and solve a compound inequality to find the possible values for a third game that would give him an average between 120 and 130, inclusive.
a.) 120 <= 135 +145+n/3 <=145; 120 <= n <= 140
b.) 135 <= 120 + 140 + n/3 <= 145; 80 <= n <= 85
c.) 120 < 135 + 145 + n/3 < 130; 80 < n < 110
d.) 120 <= 135 + 145 + n/3 <= 130; 80 <= n <= 110