Answer:
2
Step-by-step explanation:
4 -2f
Let f =1
4 - 2(1)
Multiply and divide first
4 -2
2
For what values of x and y must the figure have in order to be a parallelogram
Given:
Given that the parallelogram with the lengths 5x, 3x + 1, 2y - 5 and y.
We need to determine the values of x and y.
Values of x and y:
We know the property that the opposite sides of a parallelogram are congruent.
Thus, we have;
[tex]5x=2y-5[/tex] ------- (1)
[tex]3x+1=y[/tex] ------- (2)
The value of x and y can be determined using the substitution method.
Substituting equation (2) in equation (1), we have;
[tex]5x=2(3x+1)-5[/tex]
[tex]5x=6x+2-5[/tex]
[tex]5x=6x-3[/tex]
[tex]-x=-3[/tex]
[tex]x=3[/tex]
Thus, the value of x is 3.
Substituting x = 3 in equation (2), we have;
[tex]3(3)+1=y[/tex]
[tex]9+1=y[/tex]
[tex]10=y[/tex]
Thus, the value of y is 10.
wyatt bought a jacket that cost 12 dollers and a scarf that costs 18 dollers he recived a discount at the counter if he only paid 21 dollers total how many dollers was the discount?
Answer:
$9
Step-by-step explanation:
12 + 18 = $30 Total
30 - 21 = $9 Discount
30 - 9 = $21 After discount
I need help ASAP please
Answer:
A. (2, 7), (1, 4)
Step-by-step explanation:
The first equation tells you that y cannot be negative. (Both terms are positive.) So, the only viable answer choice is A.
A researcher studying reaction time of drivers states that, "A 95% confidence interval for the mean time (8.1) it takes for a driver to apply the brakes after seeing the brake lights on a vehicle in front of him is 1.2 to 1.8 seconds. What are the point estimate and margin of error for this interval?
Answer:
For this case we know that the confidence interval is given by (1.2 , 1.8) and the point of estimate for [tex]\mu[/tex] would be:
[tex]\bar X = \frac{1.2+1.8}{2}= 1.5[/tex]
And the margin of error is given by:
[tex] ME = \frac{1.8-1.2}{2}= 0.3[/tex]
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
For this case we know that the confidence interval is given by (1.2 , 1.8) and the point of estimate for [tex]\mu[/tex] would be:
[tex]\bar X = \frac{1.2+1.8}{2}= 1.5[/tex]
And the margin of error is given by:
[tex] ME = \frac{1.8-1.2}{2}= 0.3[/tex]
Todd wants to buy a new video game for $43.31. He has $55.50. The sales tax is 8.5% of the total purchase. Does Todd have enough money to purchase the game?
Answer:
yes
Step-by-step explanation:
We can estimate* that the total price including tax of the game will be less than ...
$43.31 +10% of 43.31 = $43.31 +4.33 = $47.61
Todd easily has enough to pay for the game, including tax.
_____
You can work this more exactly a couple of ways.
1. Price + tax = 1.085×$43.31 = $46.99 . . . less than Todd's budget
2. Most Todd can afford: $55.50/1.085 = $51.15 . . . more than the game price
_____
* For estimating purposes, we like to use numbers that are easy to compute with. 10% is one such number, as it only requires moving the decimal point.
Use the system of equations to answer the questions.
2x + 3y = 3
y = 8 – 3x
The value of y from the second equation is substituted back into the first equation. What is the resulting equation?
2(8 – 3x) + 3x = 3
2x + 3(8 – 3x) = 3
2x + 3y = 8 – 3x
What is the value of x?
–3
–1
3
What is the value of y?
–1
1
3
Answer:
2x + 3(8 - 3x) = 3
x = 3
y = -1
Step-by-step explanation:
2x + 3y = 3
y = 8 – 3x
2x + 3(8 - 3x) = 3
2x + 24 - 9x = 3
7x = 21
x = 3
y = 8 - 3(3)
y = -1
Answer:
✔ 2x + 3(8 – 3x) = 3
What is the value of x?
✔ 3
What is the value of y?
✔ –1
mark me brainiest plz thank you
Step-by-step explanation:
The area of a regular polygon is 216cm2. The perimeter is 48cm, what is the
length of the apothem?
Answer:
The answer to your question is Apothem = 9 cm
Step-by-step explanation:
Data
Area = 216 cm²
Perimeter = 48 cm
Formula
Area = Perimeter x apothem / 2
Perimeter = length of the side x number of sides
Process
Substitute the values in the area formula and simplify it.
1.- Substitution
216 = 48a/2
-Solve for a
216 x 2 = 48a
432 = 48a
a = 432 / 48
-Result
a = 9 cm
An airplane is at a location 800 miles due west of city X. Another airplane is at a distance of 1,200 miles southwest of city X. The angle at city X created by the paths of the two planes moving away from city X measures 60°. What is the distance between the two airplanes to the nearest mile? Assume that the planes are flying at the same altitude. A. 894 miles B. 1,058 miles C. 646 miles D. 1,251 miles
Answer:
The distance between the two airplanes (to the nearest mile) is 1058 miles.
Step-by-step explanation:
Use Law of cosines
d = √(800^2 + 1200^2 - 2·800·1200·COS(60°)) = 1058 miles
Answer:
1058
Step-by-step explanation:
Plato
What is the slope of the line that passes through the points (5, -10) and (11,−12)? Write your answer in simplest form.
Answer:
[tex]slope=-\frac{1}{3}[/tex]
Step-by-step explanation:
Use the slope formula for two points:
[tex]\frac{y(2)-y(1)}{x(2)-x(1)}=\frac{rise}{run}[/tex]
Insert values
[tex]\frac{-12-(-10)}{11-5}[/tex]
Simplify
[tex]\frac{-12+10}{11-5} \\\\\\\frac{-2}{6} \\\\-\frac{2}{6}[/tex]
Simplify
[tex]-\frac{1}{3}[/tex]
The slope of the linear equation will be negative 1/3.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The points are given below.
(5, -10) and (11,−12)
The equation of the line that passes through (5, -10) and (11,−12) will be given as,
(y + 10) = [(-12 + 10) / (11 - 5)](x - 5)
y + 10 = - (1/3)x + 5/3
y = -(1/3)x + 5/3 - 10
y = -(1/3)x - 25/3
The slope of the linear equation will be negative 1/3.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ3
Find the median, range, and interquartile range of both sets:
Set 1: 65, 66, 77, 79, 81, 93, 104, 105
Set 2: 56, 1, 29, 72, 67, 59, 74, 60
Which is true about the two sets?
Set 1 has a range of 40 and a median of 85.
Set 2 has a range of 74 and a median of 62.
Both sets have an interquartile range of 27.
Set 2 has data that is closer to its median than Set 1.
Answer:
C) Both sets have an interquartile range of 27.
Step-by-step explanation:
Sorted data
Set 1: 65, 66, 77, 79, 81, 93, 104, 105
Set 2: 1, 29, 56, 59, 60, 67, 72, 74
Median position: (8+1)/2 = 4.5th value
Ranges:
Set 1: 105 - 65 = 40
Set 2: 74 - 1 = 73
Medians:
Set 1: (79+81)/2 = 80
Set 2: (59+60)/2 = 59.5
IQR:
Set 1: (93+104)/2 - (66+77)/2
= 27
Set 2: (67+72)/2 - (29+56)/2
= 27
Answer:
c
Step-by-step explanation:
One angle of an isosceles triangle measures 50º. Which other angles could be in that
isosceles triangle? Choose all that apply.
Answer:
50° , 80°, 65°
the sum of the angles in a triangle is 180°
=>180-50=130
def: in an isosceles triangle two angles measure the same
case 1: if two angles measure 50°
180-2*50=80
=> angles: 50, 80
case 2: if the other 2 angles measure the same
(180-50)/2=130/2=65
=> angle: 65
Create a list of steps, in order, that will solve the following equation.
5(x-3)^2+4=1295(x−3)
2
+4=129
Answer:
subtract 4 from both sides
divide both sides by 5
take the square roots of both sides
add 3 to both sides
Step-by-step explanation:
Who knows the answer?
Answer:
t
Step-by-step explanation:
Line [tex] \purple{\boxed{\bold{t}}} [/tex] is the transversal.
Researchers studying the acquisition of pronunciation often compare measurements made on the recorded speech of adults and children. One variable of interest is called "voice onset time" (VOT), the length of time between the release of a consonant sound (such as "p") and the beginning of an immediately following vowel (such as the "a" in "pat"). For speakers of English, this short time lag can be heard as a period of breathiness between the consonant and the vowel. Here are the results for some randomly selected 4-year-old children and adults asked to pronounce the word "pat". VOT is measured in milliseconds and can be either positive or negative.
Children: n = 10, mean = 60.67, standard deviation = 39.89
Adults: n = 20, mean = 88.17, standard deviation = 24.74
You are interested in whether there is a difference in the VOT of adults and children, so you plan to test H0:μa−μc=0 against Ha:μa−μc≠0, where μa and μcare the population mean VOT for adults and children, respectively.
A. What additional information would you need to confirm that the conditions for this test have been met?
B. Assuming the conditions have been met, calculate the test statistic and p-value for this test.
C. Interpret the p-value in the context of this study and draw the appropriate conclusion at
α = 0.05.
D. Given your conclusion in part C, which type error, Type I or Type II, is it possible to make? Describe that error in the context of this study.
Answer:
(A) The additional information that is needed to confirm about the conditions for this test have been met is ‘Population is approximately normal.
(B) The test statistic = 1.9965
(C1) P-value = 0.0556
(C2) There is no significant difference between mean VOT for children and adults.
D1) It is possible to make type II error.
(D2) There should be a difference in the VOT of adults and children.
Step-by-step explanation:
Let na be the number of adults = 20
xa mean VOT for adults = 88.17
sa standard deviatiation of VOT for adults = 24.74
Let nc be the number of children = 10
xc mean VOT for children =60.67
sc standard deviatiation of VOT for children = 39.89
(A) From the information the population variances are unknown and the two sample are assumed to be independent and the sample the sample size are smaller that is (n<30).
This indicates that the additional information that is required for the conditions of the test to be satisfied is 'distribution of the population'. the addition assumption to be made is, that the population distribution is normal.
(b) Calculating the test statistics using the formula;
t = (xa -xc)/SE - d
where SE = standard deviation , d= hypothesized difference = 0
But SE = √sa²/na +sc²/nc
= √24.74 ²/20 + 39.89²/10
= √189.72559
= 13.774
Substituting into test statistics equation, we have
t = (xa -xc)/SE - d
= (88.17 - 60.67/13.774
= 1.9965
Therefore the test statistic is 1.9965
(c) Calculating the p-value, we have;
Degree of freedom = na + nc -2
= 10+ 20 -2
= 28
The p-value for t=1.9965 at 28 degrees of freedom and 0.05 level of significance is 0.0556.
The p-value 0.0556 is greater than given level of significance 0.05 hence we fail to reject the null hypothesis and conclude that there is no significant difference between mean VOT for children and adults.
(D1) From the information in part (C) the null hypothesis is not rejected.
Since the null hypothesis is not rejected, there might be a chance that not rejecting null hypothesis would be wrong. In this type of situation the error that can occur would be type II error.
(D2) The type of error describe in the context of this study is obtained by the concept of the type II error which tells that the null hypothesis is not rejected when it is actually false.
70 points- help ASAP, please.
1. Is a^2 - 39 prime...
a. Over the set of polynomials with rational coefficients?
b. over the set of polynomials with real coefficients?
c. Explain your answers to Parts a and b
2. The Discriminant Theorem Factoring Quadratics applies to quadratics with ___ coeffecients.
Answer:
1) a) yes
b) no
c) a² - 39
(a)² - (sqrt(39))²
(a - sqrt(39))(a + sqrt(39))
This quadratic can be split into real factors, but not rational
sqrt(39) is a real number, but not rational
2) real
The equation h(t)=-16t^2+32t+12 gives the height of a baseball, in feet, t seconds after it is thrown from a platform. What is the height of the platform? What is the initial velocity when the baseball is thrown?
Answer:
(a) 12 m
(b) 32 m/s
Step-by-step explanation:
(a) The height of the platform is h(0) i.e. the height, h, at time t = 0 secs, since the ball would not have been thrown at that time.
Therefore, h(0) is:
[tex]h(0) = -16(0^2) + 32(0) + 12\\\\\\h(0) = 0 + 0 + 12\\\\\\h(0) = 12 m[/tex]
The height of the platform is 12 m.
(b) The initial velocity when the baseball is thrown will be v(0) that is velocity when t = 0 secs.
We obtain velocity, v, by differentiating height, h, with respect to time:
[tex]v(t) = \frac{dh}{dt} = -32t + 32[/tex]
Therefore, at time t = 0 secs:
[tex]v(0) = -32(0) + 32\\\\\\v(0) = 32 m/s[/tex]
The initial velocity of the baseball when it is thrown is 32 m/s.
A shipping container holds 40 tissue boxes the dimensions of a tissue box are 4 inches by 6 inches by 3 inches what is the volume of the shipping container
Answer:
The volume of shipping container is 2880 cubic inches.
Step-by-step explanation:
We are given the following in the question:
Dimensions of tissue box =
4 inches by 6 inches by 3 inches
Volume of tissue box =
[tex]V = l \times w\times h\\V = 4\times 6\times 3\\V = 72\text{ cubic inches}[/tex]
Number of tissue box in shipping container, n = 40
Volume of shipping container =
[tex]V = n\times \text{Volume of tissue box}\\V = 40\times 72\\V = 2880\text{ cubic inches}[/tex]
Thus, the volume of shipping container is 2880 cubic inches.
This question is based on volume of cuboid. Therefore, the volume of the shipping container is 2880 cubic inches.
Given:
A shipping container holds 40 tissue boxes the dimensions of a tissue box are 4 inches by 6 inches by 3 inches.
We need to calculating the volume of the shipping container.
According to this question,
It is given that, dimensions of tissue box = 4 inches by 6 inches by 3 inches
As we know that,
Volume of tissue box = [tex]length \times breadth \times height[/tex]
[tex]= 4 \times 6 \times 3\\= 72 \, inch^3[/tex]
As it is given that, number of tissue box in shipping container, n = 40.
[tex]Volume \,of \,40\, tissue \,box = n \times 72\\\\Volume \,of \,40 \,tissue \,box = 40 \times 72\\\\Volume \,of \,40 \,tissue \,box = 2880 \, inch^3[/tex]
Therefore, the volume of the shipping container is 2880 cubic inches.
For more details, prefer this link:
https://brainly.com/question/24904892
Hurry late work! Consider the reduction of the rectangle. Rounded to the nearest 10th, what is the value of X?
Answer:
0.6 feet
Step-by-step explanation:
The first rectangle to scaled down. Therefore, the scale factor will be less than 1.
[tex]\frac{4.5}{16.8}=\frac{15}{56}[/tex]
Therefore, the scale factor is [tex]\frac{15}{56}[/tex].
[tex]\frac{15}{56}*2.3=\frac{69}{112}[/tex]
[tex]\frac{69}{112}[/tex] ≈ 0.6, so the value of x is 0.6 feet.
how do you do surface area? and this question
Answer:
you take all the point from around then multiply and do the same with the base
Step-by-step explanation:
take 2 times 2.812 times 44 times 4add them allA company has determined that when x hundred dulcimers are built, the average cost per dulcimer can be estimated by C(x)=0.3x^(2)-2.7x+7.775, where C(x) is hundreds of dollars. What is the mimimum average cst per dulcimer and how many dulcimers should be built to achieve that minimum?
Answer:
4.5 hundreds dulcimers should be build to achieve the minimum average cost per dulcimer $ 1.7 hundreds.
Step-by-step explanation:
The average cost per dulcimer can be estimated by
C(x)=0.3x² -2.7x+7.775
where C(x) is hundreds of dollar, x hundred dulcimers are built.
C(x)=0.3x² -2.7x+7.775
Differentiating with respect to x
C'(x)=0.6x-2.7
Again differentiating with respect to x
C''(x)=0.6
For maximum or minimum C'(x)=0
0.6x-2.7=0
⇒0.6x=27
[tex]\Rightarrow x=\frac {2.7}{0.6}[/tex]
⇒ x= 4.5
Now [tex]C''(x)|_{x=4.5}= 0.6>0[/tex]
Since at x= 4.5 , C''(x)>0, So, the average cost per dulcimer is minimum.
C(4.5)= 0.3(4.5)²-2.7×4.5 +7.775×
=1.7
4.5 hundreds dulcimers should be build to achieve the minimum average cost per dulcimer $ 1.7 hundreds.
If a bike is $125 how much will it be when its discounted by 20%
Answer:
160 pages.
Step-by-step explanation:
That is 125 - 0.20 * 125
= 125 - 25
= 160 pages.
Answer:
The answer is you saved $25.00 and the new total is $100.00
Step-by-step explanation:
so first you set up the equation of is over of = percent over 100
[tex]\frac{a}{125}=\frac{20}{100}\\\\[/tex]
then simplify the [tex]\frac{20}{100}=\frac{1}{5}[/tex]
then you see if 5 can go into 125. It can so you divide 125 by 5=25
so you multiply the [tex]\frac{1}{5}=\frac{25}{125}[/tex]
so now you just [tex]\frac{a}{125}=\frac{25}{125}[/tex]
then you just subtract the 25 because that is how much you are saving and your total will be $100.00
The vertex form of a function is g(x)=(x-3)^2+9. How does the graph of g(x) compare toe the graph of the function f(x)=x^2
The graph of g(x) compare to the graph of the function[tex]f(x)=x^2[/tex] is; identical.
What is a solution to a system of equations? (SOLUTION GRAPHICALLY)For a solution to be the solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, the solution to a system is the intersection of all its equation at a single point.
We are given that;
[tex]g(x)=(x-3)^2+9[/tex] and [tex]f(x)=x^2[/tex]
The vertex form of a quadratic function is given by:
[tex]g(x) = a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola.
Now Comparing [tex]g(x)=(x-3)^2+9[/tex] to [tex]f(x)=x^2[/tex]we can see that g(x) is the result of translating the graph of f(x) horizontally by 3 units to the right and vertically by 9 units upward.
The vertex of g(x) is (3, 9), that is obtained by shifting the vertex of f(x) at the origin (0, 0) to the right by 3 units and up by 9 units.
Since the coefficient is positive in both functions, both parabolas open upwards.
The shape of the parabolas is the same since both have the same coefficient [tex]x^2[/tex].
Therefore, the graph of g(x) is identical to the graph of f(x), its shape, but it is shifted horizontally and vertically with respect to f(x).
Learn more about finding the solution graphically here:
https://brainly.com/question/26254258
#SPJ6
what is the hardest math question
Answer:
Goldbach’s Conjecture precipitated from letters in 1742 between German mathematician Christian Goldbach and legendary Swiss mathematician Leonhard Euler, considered one of the greatest in math history. As Euler put it, “I regard [it] as a completely certain theorem, although I cannot prove it.”
Euler may have sensed what makes this problem counterintuitively hard to solve. When you look at larger numbers, they have more ways of being written as sums of primes, not less. Like how 3+5 is the only way to break 8 into two primes, but 42 can broken into 5+37, 11+31, 13+29, and 19+23. So it feels like Goldbach’s Conjecture is an understatement for very large numbers.
Still, a proof of the conjecture for all numbers eludes mathematicians to this day. It stands as one of the oldest open questions in all of math.
Answer:
dividing and multiplying decimals
Step-by-step explanation:
Each wall in Keith's room is 12 meters long and seven and 7 7/8 meters wide. He plans to paint one wall blue. Each can of paint covers 15 square meters. How many cans of paint does kids need to cover the bedroom wall?
Answer:
7 cans
Step-by-step explanation:
6 cans of paint kids need to cover the bedroom wall.
What is area of a rectangle?The formula for calculating the area of a rectangle with dimensions l and w is: A = lw (rectangle). In other words, the length times the width equals the area of a rectangle.
Given
length = 12 m
width = 7.875 m
area = 12 * 7.875 = 94.5 sq. m
area 1 can can fill = 15 sq. m
no. of cans that can fill 94.5 = 6
therefore, 6 cans of paint kids need to cover the bedroom wall.
To learn more about area of rectangle refer to :
https://brainly.com/question/25292087
#SPJ2
An electronic company makes educational apps for 5 subjects including math. The app has 10 versions, with a different avatar in each version. One version has an avatar that looks similar to a lion. The company is randomly giving free apps to its customers. Find the probability of randomly receiving a math app with a lion avatar. How likely is the probability of receiving the app at random?
Answer:
2%, low probability
Step-by-step explanation:
In this case we have that the avatars are distributed as follows:
5 subjects and 10 versions of the application for each subject, therefore they are a total of:
5 * 10 = 50
In total there are 50 avatars.
To know the probability that I get 1 in specific, in this case that of a lion is:
1/50 = 0.02
The probability is 2%, that is to say a really low probability, that is to say that the most probable thing is that you do not receive it.
Answer:
2%
Step-by-step explanation:
The frequency of the musical note C4 is about 261.63 Hz.
What is the frequency of the note a perfect fifth below C4?
130.82 Hz
174.42 Hz
256.63 Hz
392.44 Hz
The frequency of the note a perfect fifth below C4, which is F3, is calculated by multiplying the frequency of C4 (261.63 Hz) by 2/3, resulting in 174.42 Hz.
Explanation:The frequency of the musical note C4 is about 261.63 Hz. A perfect fifth below a note is 7 half-steps below on the chromatic scale, which corresponds to a frequency ratio of approximately 2/3. Therefore, to find the frequency of the note that is a perfect fifth below C4, we multiply the frequency of C4 by 2/3.
Calculating this, 261.63 Hz × (2/3) = 174.42 Hz which is the note F3. Hence, the frequency of the note a perfect fifth below C4 is 174.42 Hz.
A random poll of 800 working men found that 11% had taken on a second job to help pay the bills. a) Estimate the true percentage of men that are taking on second jobs by constructing a 95% confidence interval. b) A pundit on a TV news show claimed that only 8% of working men had a second job. Use your confidence interval to test whether his claim is plausible given the poll data.
Answer:
a) 95% Confidence Interval = (8.832%, 13.168%)
b) The 8% claim for the pundit falls outside the range of the confidence interval, hence, it isn't a very plausible claim given the poll data.
Step-by-step explanation:
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Sample proportion = 11% = 0.11
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the sample proportion)
Critical value will be obtained using the z-distribution. This is because the sample size is large enough for the t-distributoon valur to approximate the z-distribution value
Critical value for 95% confidence = 1.960 (from the z-tables)
Standard error = σₓ = √[p(1-p)/n]
where
p = sample proportion = estimated to be 11% = 0.11
n = Sample size = 800
σₓ = √[p(1-p)/n]
σₓ = √[0.11×0.89/800]
σₓ = 0.0110623234 = 0.01106
95% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]
CI = 0.11 ± (1.960 × 0.01106)
CI = 0.11 ± 0.02168
95% Confidence Interval = (0.08832, 0.13168)
95% Confidence Interval = (8.832%, 13.168%)
b) The 8% claim for the pundit falls outside the range of the confidence interval, hence, it isn't a very plausible claim given the poll data.
Hope this Helps!!!
*ignore selected answer haha* just need help answering
Answer:
[tex]x^2+8x+15[/tex]
Step-by-step explanation:
[tex]f(x)=x+4\\g(f(x))=g(x+4)\\g(x+4)=(x+4)^2-1\\(x+4)^2-1=x^2+8x+15[/tex]
The velocity function for a particle is v(t) = 2t - 5 ft/sec. Find the displacement for the particle from t = 0 to t = 4 sec. (Give answer with units)
Answer: The displacement is -4 ft.
Step-by-step explanation:
The velocity is:
v(t) = 2t - 5ft/s
If we want to find the displacement between t = 0s and t = 4s, we need to find the difference between the position at t = 0s and at t= 4s
The equation for the position is obtained by integrating over time:
P(t) = (2t^2)/2 - 5*t + c
where c is the initial position, then we have:
P(t) = t^2 - 5t
P(4) - P(0) = 4*4 - 5*4 - 0 = 16 - 20 = -4
The total displacement is -4 feet
Answer:
Displacement, d = - 4ft
Step-by-step explanation:
Given,
The velocity function for a particle v(t) = 2t - 5 ft/sec.
To obtain the displacement for the particle from t = 0 to t = 4 sec
We integrate v(t) with respect to t
: Displacement, d = ∫₀⁴ ( 2t - 5) dt
= t² - 5t |₀⁴ = (4² - 5(4)) - 0² - 5(0)
=16 - 20 = - 4ft
Find the unit price of 60lbs of honey for $123.99. Round your answer to the nearest cent if necessary.
Answer:
$2.07 per pound
Step-by-step explanation:
price divided by amount will get you the unit price. $123.99/60 equals 2.0665.