Answer:
Total distance = 536 m
Total displacement = 24 m
Step-by-step explanation:
Distance and Displacement
A moving object constantly travels for some distance at defined periods of time. The total moved distance is the sum of each individual distance the object traveled. It can be written as:
dtotal=d1+d2+d3+...+dn
This sum is obtained independently of the direction the object moves.
The displacement only takes into consideration the initial and final points of the path defined by the object in its moving. The displacement, unlike distance, is a vectorial magnitude and can be even zero if the object starts and ends the movement at the same point.
For the question at hand, it's not known if the requirement is about the distance or the displacement, so we will compute both.
To compute the distance, we just add all the distances:
dtotal= 218 m + 72 m + 62 m + 184 m = 536 m
To compute the displacement, we must establish a positive direction as desired. Let's choose the east as the positive direction. Any movement eastward is considered positive and any movement westward is negative. We mentioned the displacement is a vector, but since we only have movement in the x-axis, we can only manage the signs. Thus, the total displacement is:
xtotal = 218 m - 72 m + 62 m -- 184 m = 24 m
Since the result is positive, the jogger stopped 24 meters eastward form the original point.
really need this, it will help alottt
Answer:
[tex]\huge\boxed{m = \frac{y-b}{x}}[/tex]
Step-by-step explanation:
In order to solve for [tex]y=mx+b[/tex] and we want to solve for [tex]m[/tex], we want to get m on one side of the equation.
[tex]y = mx+b[/tex]
Let’s subtract b from both sides.
[tex]y - b = mx[/tex]
Now we can divide both sides by x so we have m on one side of the equation.
[tex]\frac{y-b}{x} = m[/tex]
Hope this helped!
Is the square root of 21 a rational number
Answer:
No
Step-by-step explanation:
But as we've stated, these prime factorizations are unique, so this can't be right. Therefore 21≠a2 , so a≠√21 , meaning that our earlier assumption of √21 being rational turns out to be wrong, therefore √21 is irrational.
Question 6 (0.5 points)
Find the midpoint of the line segment with endpoints (9, -8) and (-6, -3)
0 (0.5, -4.5)
(1.5.-5.5)
0 (7.5, -2,5)
O(-21, 2)
Question 710 5 noints)
Answer:
Step-by-step explanation:
(9-6)/2 = 3/2 = 1.5
(-8-3)/2 = -11/2 = -5.5
(1.5, -5,5)
Pentagon ABCDE was enlarged:
What is the ratio of enlargement to the original? Convert the ratio to a percent.
Answer/Step-by-step explanation:
The ratio of the enlargement to the original = A'E' to AE = A'E':AE = A'E'/AE
AE = 2.5
A'E' = 4
Ratio of the enlargement to the original = 4:2.5 = 1.6:1
To convert to percentage, divide 4 by 2.5 and multiply by 100.
[tex] = \frac{4}{2.5}*100 [/tex]
[tex] = 1.6*100 [/tex]
[tex] = 160 percent [/tex]
solve for X: 5X +2 = 4X -9
Answer:5X+2=4X-9\quad :\quad X=-11
Step-by-step explanation:
5X+2=4X-9
5X+2-2=4X-9-2
5X=4X-11
5X-4X=4X-11-4X
X=-11
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ \: \: X \: = - 11}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{5 \: X + 2 = 4 \: X - 9}[/tex]
Move 4 X to left hand side and change it's sign
Similarly, move 2 to right hand side and change it's sign
[tex] \longrightarrow{ \sf{5 \: X - 4 \: X = - 9 - 2}}[/tex]
Collect like terms
[tex] \longrightarrow{ \sf{X = - 9 - 2}}[/tex]
The negative and positive integers are always subtracted but posses the sign of the bigger integer
[tex] \longrightarrow{ \sf{X = - 11}}[/tex]
Hope I helped!
Best regards! :D
What is the product of Three-fourths and Negative StartFraction 6 over 7 EndFraction?
Answer:
-9/14
Step-by-step explanation:
product of Three-fourths and Negative StartFraction 6 over 7 EndFraction
[tex] = \frac{3}{4} \times \bigg( - \frac{6}{7} \bigg) \\ \\ = \frac{3 \times ( - 6)}{4 \times 7} \\ \\ = - \frac{18}{28} \\ \\ = - \frac{9}{14} \\ [/tex]
Answer:
-9/14 so the answer is B
Step-by-step explanation:
Hope this helps
4/5 × 2 3/8 - 2 × 3/5
Sickle-cell disease is a painful disorder of the red blood cells that in the United States affects mostly African-Americans. To investigate whether the drug hydroxyurea can reduce the pain associated with sickle-cell disease, a study by the National Institutes of Health gave the drug to 150 sickle-cell sufferers and a placebo to another 150. The researchers then counted the number of episodes of pain reported by each subject. What is the response variable in this study
Answer:
The response variable is the episodes of pain reported
Step-by-step explanation:
A response variable, also known as the dependent variable or explanatory variable, is the variable that is not under the direct control of the researcher, but whose value varies with the changing of the independent variable. The response variable is the focus of the experimental question.
In this example, the effect of the drug hydroxyurea is to be tested on sickle-cell patients, hence the drug used is the independent variable, because the experimenter can choose to give the subjects either hydroxyurea or a placebo, hence it is under the direct control of the experimenter. However, the result ( differences in episodes of pain) is a response to the administered drug or placebo.
Jonathon has 3/4 pound of grapes. How many 1/8 pound servings can Jonathon make from his grapes? Do not include units. *
Answer:
This would be 6 of 1/8 pound of serving
Answer:
6 out of 1/8
Step-by-step explanation:
There are only a few roller coasters in the world whose path takes them underground. Suppose a portion of the roller coaster can be modeled by the function f(t) = (t2 − 13t + 40)(t2 − 2t + 3), where t represents the time elapsed in seconds since passing point A on the roller coaster and f(t) represents the height in feet above the ground. What am I supposed to write on the ticket?
Answer:
the blanks are in this order the top two are 5 and 8
then (-,+,+)
then (-,-,+)
then (+,+,+)
last (+,-,+)
Step-by-step explanation:
5√3+3√12 can anyone help me figure this out
Answer:
18.29
Step-by-step explanation:
hope this helped
Please help ive been stuck on this question all weekend long !!
Answer:
The answer is 57.
Step-by-step explanation:
You have to substitute w = 2 into the expression :
[tex]8 {w}^{2} + 8w + 9[/tex]
[tex]let \: w = 2[/tex]
[tex]8 {(2)}^{2} + 8(2) + 9[/tex]
[tex] = 32 + 16 + 9[/tex]
[tex] = 57[/tex]
Answer:
57
Step-by-step explanation:
[tex]8*2^{2}+8*2+9\\8*4+16+9\\32+16+9\\48+9\\57[/tex]
A right rectangular prism has a base area of 2 1/2 square inches and a height of 11 1/2 inches.
What is the volume of the prism?
Answer:14in 3
Step-by-step explanation:
Rhonda had $300 to buy supplies for the animal shelter. She bought 8 bags of dog food and 11 leashes. Each bag of food cost $25.19, and each leash cost $4.65.
How much money did Rhonda have left after her purchases?
A. $11.65
B. $14.29
C. $22.91
D. $47.33
Answer:
47.33
Step-by-step explanation:
Hey there! I'm happy to help!
We have 8 bags of dog food and each costs $25.19
8(25.19)=201.52
And we have 11 leashes each costing $4.65.
11(4.65)=51.15
We add these totals up.
201.52+51.15=252.67
We subtract this from 300 to see how much is left.
300-252.67=47.33
Rhonda had $47.33 left after her purchases.
Have a wonderful day! :D
Answer:
d
Step-by-step explanation:
On a map scale, 2 inches represents 60 miles. Which graph best shows the relationship
between x, the number of inches on the map, and y, the actual distance in miles?
Answer:
c best shows the best relationship
Find the unique solution to the following linear system X = (0 -1 2 3)X + (e' -e')
X(0)=(5 4)
It looks like the system is supposed to be
[tex]\mathbf x'=\begin{bmatrix}0&-1\\2&3\end{bmatrix}\mathbf x+\begin{bmatrix}e^t\\e^{-t}\end{bmatrix}[/tex]
with the initial condition, [tex]\mathbf x(0)=\begin{bmatrix}5&4\end{bmatrix}^\top[/tex].
Compute the eigensystem for the coefficient matrix:
[tex]\begin{vmatrix}-\lambda&-1\\2&3-\lambda\end{vmatrix}=\lambda^2-3\lambda+2=(\lambda-1)(\lambda-2)=0[/tex]
[tex]\lambda_1=1\implies\begin{bmatrix}-1&-1\\2&2\end{vmatrix}\mathbf v_1=\mathbf 0\implies\mathbf v_1=\begin{bmatrix}1\\-1\end{bmatrix}[/tex]
[tex]\lambda=2\implies\begin{bmatrix}-2&-2\\2&1\end{bmatrix}\mathbf v_2=\mathbf 0\implies\mathbf v_2=\begin{bmatrix}1\\-2\end{bmatrix}[/tex]
So we have the characteristic solution,
[tex]\mathbf x_c=C_1e^{\lambda_1t}\mathbf v_1+C_2e^{\lambda_2t}\mathbf v_2[/tex]
[tex]\mathbf x_c=C_1e^t\begin{bmatrix}1\\-1\end{bmatrix}+C_2e^{2t}\begin{bmatrix}1\\-2\end{bmatrix}[/tex]
For the non-homogeneous part, we can guess a particular solution of the form
[tex]\mathbf x_p=te^t\begin{bmatrix}a\\b\end{bmatrix}[/tex]
(We might have started with [tex]e^t[/tex] instead, but that is already accounted for in the first characteristic solution.)
Its derivative is
[tex]{\mathbf x_p}'=e^t\begin{bmatrix}a\\b\end{bmatrix}+te^t\begin{bmatrix}a\\b\end{bmatrix}=e^t\begin{bmatrix}at+a\\bt+b\end{bmatrix}[/tex]
Substitute [tex]\mathbf x_p[/tex] into the system and solve for [tex]a,b[/tex]:
[tex]e^t\begin{bmatrix}at+a\\bt+b\end{bmatrix}=te^t\begin{bmatrix}0&-1\\2&3\end{bmatrix}\begin{bmatrix}a\\b\end{bmatrix}+e^t\begin{bmatrix}1\\-1\end{bmatrix}[/tex]
[tex]\begin{bmatrix}at+a\\bt+b\end{bmatrix}=\begin{bmatrix}-bt+1\\(2a+3b)t-1\end{bmatrix}[/tex]
[tex]\implies a=1,b=-1[/tex]
and so the particular solution is
[tex]\mathbf x_p=te^t\begin{bmatrix}1\\-1\end{bmatrix}[/tex]
The general solution to the system is then
[tex]\mathbf x=\mathbf x_c+\mathbf x_p[/tex]
[tex]\mathbf x=C_1e^t\begin{bmatrix}1\\-1\end{bmatrix}+C_2e^{2t}\begin{bmatrix}1\\-2\end{bmatrix}+te^t\begin{bmatrix}1\\-1\end{bmatrix}[/tex]
Use the given initial conditions to solve for the remaining coefficients.
[tex]\mathbf x(0)=\begin{bmatrix}5\\4\end{bmatrix}[/tex]
[tex]\implies\begin{bmatrix}5\\4\end{bmatrix}=C_1\begin{bmatrix}1\\-1\end{bmatrix}+C_2\begin{bmatrix}1\\-2\end{bmatrix}[/tex]
[tex]\implies C_1=14,C_2=-9[/tex]
Then the solution to the initial value problem is
[tex]\mathbf x=14e^t\begin{bmatrix}1\\-1\end{bmatrix}-9e^{2t}\begin{bmatrix}1\\-2\end{bmatrix}+te^t\begin{bmatrix}1\\-1\end{bmatrix}[/tex]
[tex]\mathbf x=\begin{bmatrix}14e^t-9e^{2t}+te^t\\-14e^t-18e^{2t}-te^t\end{bmatrix}[/tex]
Given F(x)=x-7 and g(x)=x squared find g(f(4))
Answer:
g(f(4)) = -3
Step-by-step explanation:
f(x)=x-7
g(x) = x
g(f(4))
f(4) = 4-7
f(4) = -3
g(-3) = -3
Triangle ABC has coordinates A(-2,0), B(0,2) and C(-4, 3). It is reflected across the line y = 2/5x - 2. About where is B’ located? What is the equation of the line that joins CC’? (2 points)
Answer:
B' is at (2.76,-4.9)
Equation of CC' is 11.38x+4.55y= -31.86
or at its slope-intercept form:
y= (-11.38x - 31.86)/4.55
Step-by-step explanation:
The length of a rectangle is 6 more than its width. The perimeter is 48 inches. What is the length?
Answer:
[tex]15[/tex] inches
Step-by-step explanation:
Let the width be x.
Length = [tex]6+x[/tex]
Perimeter = Length + Length + Breadth + Breadth
Perimeter = [tex](6+x)+(6+x)+x+x=48[/tex]
[tex]6+x+6+x+x+x=48[/tex]
[tex]4x+12=48[/tex]
Subtract 12 from both sides:
[tex]4x+12-12=48-12[/tex]
[tex]4x=36[/tex]
Divide both sides by 4:
[tex]\frac{4x}{4}=\frac{36}{4}[/tex]
[tex]x=9[/tex] (Width)
Length = [tex]9+6=15[/tex] inches.
Answer:
l = 15 inches
Step-by-step explanation:
l = w + 6
p = 2l + 2w
substitute l into equation p
48 = 2(w + 6) + 2w
distribute the 2 into the parentheses
48 = 2w + 12 + 2w
combine like terms
48 = 4w + 12
subtract 12 from both sides
36 = 4w
divide by 4
9 = w
plug w into equation l
(9) + 6 = 15
l = 15 inches
In order to test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom for the critical value of the fare is:___________.
A. 14 and 255
B. 255 and 14
C. 13 and 240
D. 14 and 240
Answer:
C; 13 and 240
Step-by-step explanation:
Here in this question, we are to give the numerator and the denominator degrees of freedom.
Mathematically;
the numerator degrees of freedom = number of variables - 1 = 14 -1 = 13
The numerator degrees of freedom = number of observations- numerator degrees of freedom - 1
= 255 - 14-1 = 255-15 = 240
The critical value of the fare is options c. 13 and 240.
Calculation of the critical value:Since the numerator degrees of freedom should be
= number of variables - 1
= 14 -1
= 13
Now
The numerator degrees of freedom should be
= number of observations- numerator degrees of freedom - 1
= 255 - 14-1
= 255-15
= 240
Therefore, the correct option is c.
learn more about denominator here: https://brainly.com/question/17681702
Robert surveyed 300 of the students in his school about their favorite color. 70% said their favorite color was blue. How many students' favorite color was blue?
Answer:
210
Step-by-step explanation:
We can get 10% of 300 by doing 300 / 10 which is 30. 70 / 10 is 7, so we need 7 lots of 10% to work out 70%. Therefore, 30 * 7 students said that their favourite colour was blue, which is 210.
Answer:
210
Step-by-step explanation:
So 70% OF 300 students said their favorite color was blue
OF means multiply and 70% is equal to .70 so,
.70 x 300 = the number of students that said their favorite color was blue
=210
So, the number of students that said their favorite color was blue is 210 students. :)
POS
In a game, two cards are drawn, and then multiplied. The winner is the person with the largest product. Explain who won the game.
-8
4
-6
-6
SOFIA
Luke
O Luke 36 < 32
O Sofia, 32 36
O Luke. -32 < 36
O Sofia, 32 - 36
Answer:
Luke, -32 < 36
Step-by-step explanation:
The two cards drawn by Sofia has values of -8 and 4 respectively. The product of her cards = -8 × 4 = -32. (Negative × positive = (negative)
The two cards drawn by Luke has values of -6 and -6 respectively. The product of his cards = -6 × -6 = 36 (negative × negative = positive).
36 greater than -32.
Luke had the largest product because -32 < 36.
8.176 divied by 0.56
Answer:
14.6
Step-by-step explanation:
Answer to this is 14.6.
Answer:
14.6 is the answer
Step-by-step explanation:
8.176/0.56 = 14.6
A rectangular piece of paper has an area of 119 square Inches and a perimeter of 48 inches What are the dimensions of the paper?
Answer:
17in by 7in
Step-by-step explanation:
17x7=119
17+17+7+7=48
E = (x + 3)(x + 2)(x + 1) + (x + 2)(x + 1) + (x + 1)
Answer:
U need to copy and paste more of the question
Step-by-step explanation:
Start copy at the top go all the way to the bottem of the question and paste into brainly.
use ctrl c for copy and crtl v for paste
what is the answer for 7.42 ÷ 1.75 = ______
Answer:
4.24
Step-by-step explanation:
In Nebraska, the mean rain-fed corn yield of harvested fields are normally
distributed, produce 147.2 bushels per acre with a standard deviation of 33 bushels per acre.
How many bushels per acre are produced if a field is in the top 25%?
O 180.2
O 125.2
O 155.45
O 169.2
Answer: 169.2 per acre are produced if a field is in the top 25%.
Step-by-step explanation:
Given: The mean rain-fed corn yield of harvested fields are normally distributed, produce 147.2 bushels per acre with a standard deviation of 33 bushels per acre.
Let X denote the mean rain-fed corn yield of harvested fields.
Let x denotes the number of bushels per acre are produced if a field is in the top 25%.
Top 25% on a density curve means , (100-25%)i.e. 75% area lies below x.
I.e.
[tex]P(X<x)=P(\dfrac{X-\mu}{\sigma}<\dfrac{x-147.2}{33})=0.75\\\\\Rightarrow\ P(Z<\dfrac{x-147.2}{33})=0.75\ \ [Z=\dfrac{X-\mu}{\sigma}][/tex].
Z-score for p-value of 0.75 (one tailed)=0.67 [By z-table]
Then, [tex]\dfrac{x-147.2}{33}=0.6744[/tex]
[tex]\Rightarrow\ {x-147.2}=33\times0.67\\\\\Rightarrow\ {x-147.2}=22.11\\\\\Rightarrow\ {x}=22.11+147.2=169.31[/tex]
Here approx value is 169.2 (from options).
So, 169.2 per acre are produced if a field is in the top 25%.
How many three-digit numbers are multiples of neither 5 nor 7?
Answer:
590Step-by-step explanation:
Total 3-digit numbers 100 to 999
999 - 99 = 9003 digit multiples of 5; 100 to 995
smallest one 100 = 5*20greatest one 995 = 199*5number 199 - 4 = 1953 digit multiples of 7:
smallest one 105/7 = 15greatest one 994/7 = 142number 142 - 14 = 128Total multiples of either 5 or 7 :
195 + 128 = 323This number includes multiples of both 5 and 7
We need to exclude half of the multiples of 5*7= 35 as they are counted twice:
smallest one 105 = 35*3greatest one 980 = 28*35number 28 - 2 = 26Half of this is 26/13 = 13
323 - 13 = 310The difference of 900 and 310 is the answer:
900 - 310 = 590A concerned parent wants to determine the amount of time spent on the phone by her child's friends. Which sample is likely to bias the results of the study by reporting less than the actual time? Group of answer choices
Answer: The answers to the questions by 10 of the friends
Step-by-step explanation:
The options to the question are:
a. The answers to the questions by the parents of 10 of the friends.
b. The results of a national poll of 1800 students in the same age group as the child.
c. The answers to the questions by 10 of the friends.
d. The answers to the questions by 10 people from the parents office.
From the question, we are informed that a concerned parent wants to determine the amount of time spent on the phone by her child's friends. The sample that is likely to bias the results of the study by reporting less than the actual time is the answers to the questions by 10 of the friends.
This is because since the questions are being asked from her friends, there'll be bias as the friends won't want to give the exact time used on phone, hence, they'll hold back some information.
Suppose a couple has two children, and you know that at least one is a boy. If the probabilities of having a boy or a girl are both 0.5 for any birth, what is the probability that the couple has two boys in this situation? When calculating this conditional probability, you may want to think of the ordered sample space for two kids as S = {bb, bg, gb, gg} . We can assume that births are independent events.
Answer:
The probability of having two boys = 25%
Step-by-step explanation:
The ordered sample space for two kids is given as S = {bb, bg, gb, gg},
where bb = two boys, bg = a boy and a girl, gb = a girl and a boy, and gg = two girls, in that particular order.
bb occurs 1/4 times
and 1/4 = 0.25 or 25%
Calculating the probability of having two boys is given as the probability of having a boy multiplied by the probability of having a boy
= 0.5 x 0.5
= 0.25
= 25%
This agrees with the ordered sample space given above.
