![[need Math Help] Study Buddies Part #2](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/sD6rUY4f04PCwaW98f7HJu0rTcsYfWgx.png)
Answers
Answer:
Part A) The distance between Whitney's house and Anh's house is 6.5 miles.
Part B) The total distance traveled by Whitney during the trip was 9.5 miles.
Step-by-step explanation:
Part A)
Notice that during Whitney's journey to Anh's house, her velocity was negative for some time. So, Whitney was travelling backwards. Hence, the total distance Whitney traveled will be greater than the actual distance from Whitney's house to Anh's.
So, instead, we can calculate Whitney's total displacement. Total displacement is given by:
[tex]\displaystyle \text{Displacement}=\int_a^bv(t)\, dt[/tex]
Where v(t) is the velocity function.
So, the displacement of Whitney when she traveled from her house to Anh's house will be:
[tex]\displaystyle \text{Displacement}=\int_0^{24}v(t)\, dt[/tex]
To calculate the integral, we can split it off at t = 11, t = 16, and t = 24.
The three regions represent three geometric figures, which we can use to calculate the area and then find the integral. Rewriting:
[tex]\displaystyle \text{Displacement}=\int_0^{11}v(t)\, dt+\int_{11}^{16}v(t)\, dt+\int_{16}^{24}v(t)\, dt[/tex]
Now, we can calculate the area of each figure.
The first figure is a trapezoid with a height of 0.8 and two bases of 11 and 3. So, its area is:
[tex]\displaystyle A_1=\frac{1}{2}(0.8)(11+3)=5.6\text{ miles}[/tex]
The second figure is a triangle with a height of 0.6 and a base of 5. So, its area is:
[tex]\displaystyle A_2=\frac{1}{2}(0.6)(5)=1.5\text{ miles}[/tex]
Lastly, the third figure is another triangle will a height of 0.6 and a base of 8. So, its area is:
[tex]\displaystyle A_3=\frac{1}{2}(0.6)(8)=2.4\text{ miles}[/tex]
However, notice that the second figure is below the x-axis. During that interval, Whitney was traveling backwards. Hence, we will subtract the second area from the rest of the areas.
Then the displacement will be:
[tex]\displaystyle \text{Displacement}=5.6-1.5+2.4=6.5\text{ miles}[/tex]
So, the distance between Whitney's house and Anh's house is 6.5 miles.
Part B)
The total distance differs from displacement in that it includes all the distances in both directions. It is given by:
[tex]\displaystyle \text{Distance}=\int_a^b|v(t)|\, dt[/tex]
In other words, all of our values are now positive. We will utilize the same strategy:
[tex]\displaystyle \text{Distance}=\int_0^{11}|v(t)|\, dt+\int_{11}^{16}|v(t)|\, dt+\int_{16}^{24}|v(t)|\, dt[/tex]
Substitute. The only difference is that we will add 1.5 instead of subtracting it. So:
[tex]\displaystyle \text{Distance} =5.6+1.5+2.4=9.5[/tex]
Therefore, in this instance, Whitney traveled a total of 9.5 miles to get to Anh's house.
Related Questions
2
What is the volume of the solid below?
16 m
15 m
17 m
3840 m
1360 m
2040 m
4080 m
Answers
Answer:
Is there supposed to be a picture?
1219 kg of Swiss cheese is packaged in 3 kg bags. Will there be any cheese left over? How do you know?
Answers
Answer:
1 cheese is left over.
Step-by-step explanation:
Given that,
1219 kg of Swiss cheese is packaged in 3 kg bags.
i.e. 3 kg bags = 1219 kg of Swiss cheese
Implies, 1 kg bag = [tex]\dfrac{1219}{3}[/tex] kg of swiss cheese
If we divide 1219 by 3, we get [tex]46\dfrac{1}{3}[/tex]. Here, 46 is the quotient and 1 is the remainder.
It means 1 cheese is left over.
show work , I’ll vote you brainliest if it is correct . Thank you
Answers
Answer:
Whats the question to this problem? Do you want to know if it's correct?
i can help! Just show your work? 1/2 times whatever X is + X+1 over whatever X is = 1/2 i can get the answer if you need it unless what i said helped! :) Your welcome!
Step-by-step explanation:
Have a great week! Hope i helped! Plz dont delete answer i promise i will help and it will be correct!
answer 3+3 for 100 points brainlyist to first answer
(yes i know it's simple I'm not d u m b)
Answers
Answer:
6
Step-by-step explanation:
plz me
Answer:
6
Step-by-step explanation:
can i have brainliesyt
ZA and ZB are vertical angles. If mZA = (3.C – 9)° and m B = (x+3)°, then find the value of x.
Answers
Answer:
x = 6
Step-by-step explanation:
Vertical angles in a geometry are equal. Hence m<A = m<B
Given that
m<A = 3x - 9
m<B - x+3
Then 3x - 9 = x+3
3x - x = 3 + 9
2x = 12
Divide both sides by 2
2x/12 = 12/2
x = 6
Hence the value of x is 6
Solve for t
4/3 = t/7
Answers
Answer:
[tex]\frac{28}{3}=t[/tex]
Step-by-step explanation:
[tex]\frac{4}{3}=\frac{t}{7}[/tex]
Use cross products to simplify the equation. Multiply the denominator of the second fraction by the numerator of the first fraction, and the denominator of the first fraction by the numerator of the second,
[tex](4)(7) = (3)(t)[/tex]
Simplify,
[tex]28=3t[/tex]
Inverse operations,
[tex]\frac{28}{3}=t[/tex]
Can someone help me pls
Answers
Answer:
70°
Step-by-step explanation:
If arc BY is 40, angle BAY is 20.
BAC is 90.
90-20 is 70.
m<YAC=70
Need help on this please
Answers
Answer:
25[tex]\pi[/tex]
Step-by-step explanation:
[tex]\pi[/tex][tex]r^{2}[/tex]=area of circle
[tex]\frac{1}{4}[/tex][tex]\pi[/tex][tex]r^{2}[/tex]=1/4 of the area of a circle
now solve
[tex]\frac{1}{4}[/tex][tex]\pi[/tex][tex]10^{2}[/tex]
[tex]\frac{1}{4}[/tex][tex]\pi[/tex]100
25[tex]\pi[/tex]
Solve the right triangle. Round decimal answers to the nearest tenth.
B
14
6
A
b
С
Answers
Answer:
A^2 + B^2 = C^2
6^2 + 14^2=c^2
36+196=C^2
232=c^2
square root of 232= c
therefore c is equal to 15,23
Step-by-step explanation:
use the Thereom of Pythagoras
Jeremiah conducts a survey and finds that as the first variable in his survey increases, the
second variable in his survey decreases. What type of association is there between the
two variables in his survey?
Answers
Answer:
Negative Association.
Step-by-step explanation:
Association between variables:
Association between variables can be classified as positive or negative.
Positive: Both move in the same direction, that is, either both increase or both decrease.
Negative: The variables move in opposite directions, one increases and the other decreases.
In this question:
As the first increases the second decreases, that is, they move in opposite directions, so it is a Negative Association.
What is the equation of the line that is parallel to the line y = 3x - 4 and passes
through the point (4, -2)?
A. Y= 3x + 2
B. y= 3x - 14
O C. --}x
D. y = 3x + 14
Answers
Answer:
B. y = 3x - 14
Solve using the distributive property:
20 (3 + 8)
Answers
Answer:
60+160
Step-by-step e
Answer:
60+160 or 220
Step-by-step explanation:
20(3+8)
multiple 20 by 3 and 8
60+160
add 60 and 160 which is 220
Which of the following is the equation of the line below?
Pls help
Answers
Answer:
x+y =-6 you can write this equation
Pls help me. My assignment is due in half an hour. Thank you.
A rectangular card has a length 3 inches longer than twice the width. The area is 324 inches squared. What are the dimensions of the card in inches? Order your answer from least to greatest.
Answers
Answer:
w=12 L=27
Step-by-step explanation:
length is twice the width with additional 3 inches
12×2=24+3=27
12×27=324
if f(x)=6x-8, then f^-1(x)=
Answers
Answer:
f(x) is another way to write y.
You have y = 6x - 8.
To find the inverse, switch the x and the y and solve for the new y.
Switching gives you x = 6y - 8.
You add 8 to both sides to give you 6y = x + 8.
Divide both sides by 6 gives you the inverse as y =1/6x + 4/3
Step-by-step explanation:
A study of 420,027 cell phone users found that 133 of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0414% for those not using cell phones. Complete parts (a) and (b). a. Use the sample data to construct a 90% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.
Answers
Answer: (0.00027144, 0.00036176)
Step-by-step explanation:
The sample proportion of cell phone users who develop cancer of the brain or nervous system = [tex]\dfrac{133}{420027}=0.0003166[/tex]
Sample size : 420027
Confidence interval for p: [tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex], where [tex]\hat{p}[/tex]= sample proportion , n= sample size , z* = crirical z value.
For 90% confidence interval , z*= 1.645
Required confidence interval:
[tex]0.0003166\pm (1.645)\sqrt{\dfrac{0.0003166(1-0.0003166)}{420027}}\\\\=0.0003166\pm 0.00004516\\\\=(0.0003166-0.00004516,\ 0.0003166+ 0.00004516)\\\\=(0.00027144, \ 0.00036176)[/tex]
A 90% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system = (0.00027144, 0.00036176)
find the solution of the system of equations.
Answers
Answer:
(-6,-3)
Step-by-step explanation:
solve using substitution or elimination
David wants to test a claim about a population mean. The population standard deviation is unknown, the sample is a simple random sample of size 20, and the population is normally distributed. In this case, the t-test should be used since σ is unknown. If David incorrectly uses the z-distribution instead of the t-distribution, will he obtain a P-value that is too big or too small? Explain your thinking. Will he be more likely or less likely to reject the null hypothesis than if had correctly used the t-distribution?
Answers
Answer:
a)The P-value will be too small
b) He will reject the Null hypothesis
Step-by-step explanation:
a) If David incorrectly uses the z-distribution instead of the t-distribution, he will obtain a p-value that is too small because p-values obtained using Z distribution are smaller when compared to p-values obtained using t-distribution
b) He will reject the Null hypothesis given that the P value he will obtain will be very different from the one he obtained using z-distribution
True or false?
When multiplying fractions, you flip the second fraction to solve.
True - Keep the first fraction the same then flip to solve the MULTIPLICATION problem
True - Only when the second number is a whole number
False - Only when the second number is a whole number
False - You ONLY flip the second fraction when you have a FRACTION DIVISION problem. Keep, change, flip.
Answers
Answer:
True - Keep the first fraction the same then flip to solve the MULTIPLICATION problem
Step-by-step explanation:
Answer:
It would be A, True - Keep the first fraction the same then flip to solve the MULTIPLICATION problem.
Step-by-step explanation:
geometry question pls help!!!
Find measure of angle BPD
A-9 degrees
B- 14 degrees
C- 155 degrees
D- 146 degrees
Answers
Answer:
(C). 155°
Step-by-step explanation:
Choose the number sentence that illustrates the distributive property of multiplication over addition.
8 x (6 + 4) = (8 + 6) * (8 + 4)
8 x (6 + 4) = (8 x 6) + (8 x 4)
8 x (6 + 4) = (8 x 6) + 4
Answers
what is the value of 7|H| + 4G?
Answers
Answer:
a-70
Step-by-step explanation:
28+42=70
Hi!
7|H| + 4G = 7 * |-6| + 4 * 7 =
= 7 * 6 + 4 * 7 = 42 + 28 = 70
Grettings!
solve the system by substitution......
Answers
Answer:
(4,8) is the answer.
Step-by-step explanation:
To solve by substitution, you need to isolate a variable. The bottom equation already has y isolated, so we can just plug that into the other equation:
[tex]2x=-2x+16[/tex]
Add [tex]2x[/tex] to both sides in order to get rid of the [tex]-2x[/tex] on the right side:
[tex]4x=16[/tex]
Now divide by 4 on both sides to get:
[tex]x=4[/tex]
That gives us our x. Now plug in that x into either equation. I will just choose the bottom equation:
[tex]y=2(4)\\y=8[/tex]
Therefore the solution to this problem is (4,8).
Suppose the family wise error rate is 0.05, if there are ten levels of one factor but only 5 comparisons are of importance, what would the individual error rate need to be for each of those 5 comparisons? Group of answer choices 5 0.01 .05 0.10
Answers
Answer:
Individual error rate = 0.01
Therefore, Option b) 0.01 is the correct answer
Step-by-step explanation:
Given the data in the question;
family wise error rate ∝ = 0.05
there are ten levels of one factor but
important comparisons m = 5
the individual error rate need to be for each of those 5 comparisons = ?
we know that;
individual error rate = family wise error rate ∝ / important comparisons m
so we substitute
individual error rate = 0.05 / 5
individual error rate = 0.01
Therefore, Option b) 0.01 is the correct answer
A sports shop has 80 employees. 90% of the employees work
part-time. How many part-time employees does the sports shop
have? If necessary, round to the nearest whole number. (Include
the units)
Answers
Answer:
72
Step-by-step explanation:
90/100 x 80 = 72 employees
What is the factorization of the expression below?
4x^2-9y^2
O A. (2x - 3)(2x + 3y)
B. (2x-3y)(2x-3y)
O C. (4x - 3y)(x + 3y)
D. (4x-3y)(x-3y)
Answers
Answer:
answer will be A. (2x-3)(2x+3y)
A wooden box has the shape of a rectangular prism. The inside of the box is also a rectangular prism. What is the volume of the solid part of the box? Enter your answer below.
Answers
Answer:
1560 cm²
Step-by-step explanation:
4*5*22 = 440 cm²
25*8*10 = 2000 cm²
find the difference between the two numbers to find the volume of the solid part of the box
Brₐinliest plz close to leveling up
Solve the two-step equation.
14 = 31.7 – 3x
What is the solution?
Answers
Answer:
The answer is 5.9
Step-by-step explanation:
1) Subtract 31.7 from both sides.
[tex]14 - 31.7 = - 3x[/tex]
2) Simplify 14 - 31.7 to -17.7
[tex] - 17.7 = - 3x[/tex]
3) Divide both sides by -3.
[tex] \frac{ - 17.7}{ - 3} = x[/tex]
4) Simplify -17.7/-3 to 5.9
[tex]5.9 = x[/tex]
5) Switch sides.
[tex]x = 5.9[/tex]
Therefor, the answer is x = 5.9.
An airplane is flying from Redville to Leek.
The airplane flies 50 miles East and then 180 miles south.
How far is Leek from Redville directly?
Answers
The required distance of Leek from Reidville directly is 186.82 miles.
Given that,
An airplane is flying from Reidville to Leek. The airplane flies 50 miles East and then 180 miles south. How far is Leek from Reidville directly is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
The direct distance can be given as,
x = √[50² + 180²]
x = √34900
x = 186.82
Thus, the required distance of Leek from Reidville directly is 186.82 miles.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
what is 13 times 95 divided by .35?
Answers
Answer:
3,528.57142857
Step-by-step explanation:
Answer:
[tex]3528\frac{4}{7}[/tex]
Step-by-step explanation:
13 × 95 ÷ 0.35
1235 ÷ 0.35
[tex]3528\frac{4}{7}[/tex]
