Answer:
B. LT⁻¹Step-by-step explanation:
The question is incomplete. Here is the complete question,
The equation for the change of position of a train starting at x = 0 m is given by x =(1/2)at² + bt³. The dimensions of b are__
from the equation of motion given, the constant b is the velocity of the body. For us to get the dimension of b, we have to find the dimension of the velocity .
Since velocity is the rate of change of displacement of a body, then;
VELOCITY = DISPLACEMENT/TIME
displacement is measured in metres while time in seconds.
expressing the formula in terms of its fundamental unit,
v = metre/secs
Since the fundamental quantity of the metre is length (L) and that of seconds is the time (T); the dimensions is expressed as;
V = L/T
V = L * 1/T
V = L * T⁻¹
V = LT⁻¹
Hence the dimension of b is LT⁻¹.
Note that the dimension of a body is written in terms of its fundamental quantities.
The dimensions of b from the given equation are; B: LT⁻¹
Dimensional Analysis
The complete question is;
The equation for the change of position of a train starting at x = 0 m is given by x =(1/2)at² + bt³. The dimensions of b are__
Now, in that equation above, b represents the velocity of the motion. Now, the formula for velocity is;
Velocity = Distance/Time
Now, distance is also called Length and represented by L in basic parameters units while Time is represented by T.
Thus, the dimensions of b are; L/T or expressed as LT⁻¹
Read more on dimensional analysis at; https://brainly.com/question/1528136
Please do either 40 or 39
Answer:
y = 1.8
Step-by-step explanation:
Question 39).
Let the operation which defines the relation between a and b is O.
Relation between a and b has been given as,
a O b = [tex]\frac{(a+b)}{(a-b)}[/tex]
Following the same operation, relation between 3 and y will be,
3 O y = [tex]\frac{3+y}{3-y}[/tex]
Since 3 O y = 4,
[tex]\frac{3+y}{3-y}=4[/tex]
3 + y = 12 - 4y
3 + y + 4y = 12 - 4y + 4y
3 + 5y = 12
3 + 5y - 3 = 12 - 3
5y = 9
[tex]\frac{5y}{5}=\frac{9}{5}[/tex]
y = 1.8
Therefore, y = 1.8 will be the answer.
a lottery game has balls numbered 1 through 19. what is the probability selected ball is an even numbered ball or a 4 g
Answer:
Probability ball is an even numbered ball or a 4 [P(A or B)] = 9 / 19
Step-by-step explanation:
Given:
Number of balls = 1 to 19
Find:
Probability ball is an even numbered ball or a 4
Computation:
Total even number = 2, 4, 6, 8, 10, 12, 14, 16, 18
Probability to get even number P(A) = 9 / 19
Probability to get 4 number P(B) = 1 / 19
P(A and B) = 1 / 19 (4 common)
Probability ball is an even numbered ball or a 4 [P(A or B)]
P(A or B) = P(A) + P(B) -P(A and B)
P(A or B) = [9 / 19] + [1 / 19] - [1 / 19]
Probability ball is an even numbered ball or a 4 [P(A or B)] = 9 / 19
what is the 20th term of the arithmetic sequence a(n)=-5+(n-1)3
Answer:
52
Step-by-step explanation:
a(n)=-5+(n-1)3
a(20)=-5+(20-1)3
a(20)=52
The 20th term of the arithmetic sequence is 52.
What is Arithmetic sequence?An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
For example,
In an arithmetic sequence, the difference between consecutive terms is always the same. For example, the sequence 3, 5, 7, 9 ... is arithmetic because the difference between consecutive terms is always two.
The nth term of an arithmetic sequence is given by an = a + (n – 1)d.
Given:
a(n)=-5+(n-1)3
First term,
a(1)= -5 + 0
a(1)= -5
second, a(2)= -5 + 1*3
a(2)= -2
Third, a(3)= -5+6
a(3)= 1
d= 3
So, the 20th term
a(20)= -5+ (20-1)3
a(20)= -5 + 57
a(20)= 52
Hence, the 20th term is 52.
Learn more about Arithmetic Sequence here:
https://brainly.com/question/10396151
#SPJ2
2 (3z-4) <16 Which one of the following values of z is a solution for the inequality
Answer:
z < 4
Step-by-step explanation:
2(3z-4) < 16
Divide by 2 on both sides
3z-4 < 8
Add 4 to both sides
3z < 12
Divide by 3 on both sides
z < 4
A firm just paid an annual dividend of $1.40 and increases that dividend by 2 percent each year. How do you find the price if the firm's stock at year 4 if the discount rate is 13 percent?
Answer:
14.05
Step-by-step explanation:
We have the following:
Current Dividend = D0 = $ 1.40
g = growth rate = 2%
r = discount rate = 13%
Dividend in Year 5
= D5 = D0 * (1 + g) ^ 5
= $ 1.40 * (1 + 2%) ^ 5
= $ 1.40 * (1.02) ^ 5
Firm Stock Price at the end of year 4 = Dividend in Year 5 / (r - g)
= $ 1.40 * (1.02) ^ 5 / (13% -2%)
= $ 1.40 * (1.02) ^ 5 / (0.13 - 0.02)
Therefore, firm stock at the end of year 4 is
P4 = $ 1.40 * (1.02) ^ 5 / (0.13 - 0.02) = 14.05
Which equation is the inverse of y = 16x2 + 1? y = plus-or-minus StartRoot StartFraction x Over 16 EndFraction minus 1 EndRoot y = StartFraction plus-or-minus StartRoot x minus 1 EndRoot Over 16 EndFraction y = StartFraction plus-or-minus StartRoot x EndRoot Over 4 EndFraction minus one-fourth y = StartFraction plus-or-minus StartRoot x minus 1 EndRoot Over 4 EndFraction
Answer:
The inverse is ±sqrt((x-1))/ 4
Step-by-step explanation:
y = 16x^2 + 1
To find the inverse, exchange x and y
x = 16 y^2 +1
Then solve for y
Subtract 1
x-1 = 16 y^2
Divide by 16
(x-1)/16 = y^2
Take the square root of each side
±sqrt((x-1)/16) = sqrt(y^2)
±sqrt((x-1))/ sqrt(16) = y
±sqrt((x-1))/ 4 = y
The inverse is ±sqrt((x-1))/ 4
Answer:
D
Step-by-step explanation:
42.
You were given the four numbers below and were asked to find the sum
of the first two numbers, the difference between the last two numbers,
the quotient when the sum is divided by the difference and the product
when the quotient is multiplied by 8. What is the final answer?
6458 2994
7013
6945
Answer:
1112
Step-by-step explanation:
6458 + 2994 = 9452
7013 - 6945 = 68
9452/68 = 139
139 * 8 = 1112
a sample of bacteria is growing at an hourly rate of 14% according to the exponential growth function.the sa
Answer:
pleasse elaborate more
Step-by-step explanation:
A dress regularly sells for $137. The sale price is $102.75. Find the discount & the percent of the discount
Answer:
Discount : $34.25 off. Percent of the discount : 25%
Step-by-step explanation:
137 - 102.75 = 34.25.
34.25/137 x 100 = 25%
Gena wants to estimate the quotient of –21.87 divided by 4.79. Which expression shows the best expression to estimate the quotient using front-end estimation? Negative 21 divided by 4 Negative 21 divided by 5 Negative 20 divided by 4 Negative 20 divided by 5
Answer:
-21/5 = -4.2
Step-by-step explanation:
-21.87 / 4.79 = -4.5657.....
So, the quotients is -4
Now, Let's see who's quotient is equal to think one:
-21/4 = -5.25
-21/5 = -4.2
-40/4 = -5
-20/5 = 4
Answer:
-21/5 = -4.2
Step-by-step explanation:
-2x(x+3)-(x+1)(x-2)=
Answer:
-3x^2 -5x +2
Step-by-step explanation:
-2x(x+3)-(x+1)(x-2)=
Distribute
-2x^2 -6x -(x+1)(x-2)
Foil
-2x^2 -6x -(x^2 -2x +x -2)
Combine like terms
-2x^2 -6x -(x^2 -x -2)
Distribute the minus sign
-2x^2 -6x -x^2 +x +2
Combine like terms
-2x^2 -x^2 -6x +x +2
-3x^2 -5x +2
Answer:
[tex]\huge\boxed{-2x(x+3)-(x+1)(x-2)=-3x^2-5x+2}[/tex]
Step-by-step explanation:
[tex]-2x(x+3)-(x+1)(x-2)[/tex]
Use the distributive property: a(b + c) = ab + ac
and FOIL: (a + b)(c + d) = ac + ad + bc + bd
[tex]=(-2x)(x)+(-2x)(3)-\bigg[(x)(x)+(x)(-2)+(1)(x)+(1)(-2)\bigg]\\\\=-2x^2-6x-\bigg(x^2-2x+x-2\bigg)=-2x^2-6x-x^2-(-2x)-x-(-2)\\\\=-2x^2-6x-x^2+2x-x+2[/tex]
Combine like terms:
[tex]=(-2x^2-x^2)+(-6x+2x-x)+2=-3x^2+(-5x)+2\\\\=-3x^2-5x+2[/tex]
What is the solution of log3(3x+2)= log3 (4x-6)?
Answer:
x=8 i got it right on my homework on khan academy
Step-by-step explanation:
Answer: Using logarithms to solve you will get x = 8
Safegate Foods, Inc., is redesigning the checkout lanes in its supermarkets throughout the country and is considering two designs. Tests on customer checkout times conducted at two stores where the two new systems have been installed result in the following summary of the data.
System System B
n1=120 n2=100
x1=4.1 minutes x2=3.4 minutes
σ1=2.2minutes σ2= 1.5 minutes
Test at the 0.05 level of significance to determinewhether the population mean checkout times of the two newsystems differ. Which system is preferred?
Answer:
We conclude that the population means checkout times of the two new systems differ.
Step-by-step explanation:
We are given the result in the following summary of the data;
System System B
n1=120 n2=100
x1=4.1 min x2=3.4 min
σ1=2.2 min σ2= 1.5 min
Let [tex]\mu_1[/tex] = population mean checkout time of the first new system
[tex]\mu_2[/tex] = population mean checkout time of the second new system
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex] {means that the population mean checkout times of the two new systems are equal}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex] {means that the population mean checkout times of the two new systems differ}
The test statistics that will be used here is Two-sample z-test statistics because we know about population standard deviations;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1} + \frac{\sigma_2^{2} }{n_2}} }[/tex] ~ N(0,1)
where, [tex]\bar X_1[/tex] = sample mean checkout time of the first new systems = 4.1 min
[tex]\bar X_2[/tex] = sample mean checkout time of the second new systems = 3.4 min
[tex]\sigma_1[/tex] = population standard deviation of the first new systems = 2.2 min
[tex]\sigma_2[/tex] = population standard deviation of the second new systems = 1.5 min
[tex]n_1[/tex] = sample of the first new systems = 120
[tex]n_2[/tex] = sample of the second new systems = 100
So, the test statistics = [tex]\frac{(4.1-3.4)-(0)}{\sqrt{\frac{2.2^{2} }{120} + \frac{1.5^{2} }{100}} }[/tex]
= 2.792
The value of z-test statistics is 2.792.
Now, at 0.05 level of significance, the z table gives a critical value of -1.96 and 1.96 for the two-tailed test.
Since the value of our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the population mean checkout times of the two new systems differ.
helpp me please will give brralinst
Answer:
0
Step-by-step explanation:
the answer is 0
Have a great day
helpppppppppppppppppppppp i will give star thanks bralienst
Answer:
90/x=70/100 that's my answer
[tex]90 \x = 70 \100[/tex]
Answer:
90/x = 70/100
Step-by-step explanation:
Is means equals and of means multiply
90 = 70% *x
Changing to decimal form
90 = .70x
Changing to fraction form
90 = 70/100 *x
Divide each side by x
90/x = 70/100
Translate and solve: 3x less than two times the sum of 2X and one is equal to the sum of 2 and 5
Answer:
The answer is x = 5Step-by-step explanation:
The statement
3x less than two times the sum of 2X and one is written as
2( 2x + 1) - 3x
the sum of 2 and 5 is written as
2 + 5
Equate the two statements
We have
2( 2x + 1) - 3x = 2+5
Expand
4x + 2 - 3x = 7
Simplify
4x - 3x = 7 - 2
We have the final answer as
x = 5Hope this helps you
Find the mean and standard deviation for each binomial random variable:
Answer: a) Mean = [tex]=37.80[/tex]
Standard deviation=[tex]=1.9442[/tex]
b) Mean = [tex]56.00[/tex]
Standard deviation=[tex]4.0988[/tex]
c) Mean = [tex]=24[/tex]
Standard deviation=[tex]2.4495[/tex]
Step-by-step explanation:
To compute Mean and standard deviation , we use following formula:
Mean = [tex]n\pi[/tex]
Standard deviation=[tex]\sqrt{n\pi(1-\pi)}[/tex]
a. [tex]n=42,\ \pi=0.90[/tex]
Mean = [tex]42\times0.90=37.80[/tex]
Standard deviation=[tex]\sqrt{42(0.90)(0.10)}=\sqrt{3.78}\approx1.9442[/tex]
b. [tex]n=80,\ \pi=0.70[/tex]
Mean = [tex]80\times0.70=56.00[/tex]
Standard deviation=[tex]\sqrt{80(0.70)(0.30)}=\sqrt{16.8}\approx4.0988[/tex]
c. [tex]n=32,\ \pi=0.75[/tex]
Mean = [tex]32\times0.75=24[/tex]
Standard deviation=[tex]\sqrt{32(0.75)(0.25)}=\sqrt{6}\approx2.4495[/tex]
Please help. I’ll mark you as brainliest if correct!
Answer:
Step-by-step explanation:
children=c
adults=a
c+a=359
a=359-c
2.75c+6a=1621
2.75 c+6(359-c)=1621
2.75 c+2154-6c=1621
-3.25 c=1621-2154
-3.25 c=-533
[tex]-\frac{325}{100} c=-533\\-\frac{13}{4} c=-533\\c=-533 \times \frac{-4}{13} =41 \times 4=164 \\children=164\\adults=359-164=195[/tex]
Find the length of BC
Answer:
The answer is option AStep-by-step explanation:
To find the length of BC we use tan
tan ∅ = opposite / adjacent
From the question
AC is the opposite
BC is the adjacent
So we have
tan 61 = AC / BC
tan 61 = 47/BC
BC = 47/tan 61
BC = 26.05Hope this helps you
prove identity trigonometric equation
[tex]2 \tan(x) = \frac{ \cos(x) }{ \csc(x - 1) } + \frac{ \cos(x) }{ \csc(x + 1) } [/tex]
Explanation:
The given equation is False, so cannot be proven to be true.
__
Perhaps you want to prove ...
[tex]2\tan{x}=\dfrac{\cos{x}}{\csc{(x)}-1}+\dfrac{\cos{x}}{\csc{(x)}+1}[/tex]
This is one way to show it:
[tex]2\tan{x}=\cos{(x)}\dfrac{(\csc{(x)}+1)+(\csc{(x)}-1)}{(\csc{(x)}-1)(\csc{(x)}+1)}\\\\=\cos{(x)}\dfrac{2\csc{(x)}}{\csc{(x)}^2-1}=2\cos{(x)}\dfrac{\csc{x}}{\cot{(x)}^2}=2\dfrac{\cos{(x)}\sin{(x)}^2}{\cos{(x)}^2\sin{(x)}}\\\\=2\dfrac{\sin{x}}{\cos{x}}\\\\2\tan{x}=2\tan{x}\qquad\text{QED}[/tex]
__
We have used the identities ...
csc = 1/sin
cot = cos/sin
csc^2 -1 = cot^2
tan = sin/cos
PLEASE HELP!! Write the proportion. 120 feet is to 150 feet as 8 feet is to 10 feet. (18 points!!)
Answer:
4 : 5
Step-by-step explanation:
you can divide 120 and 150 by 30 and 8 and 10 by 2.
120/30 = 4
150/30 = 5
8/2 = 4
10/2=5
Answer: 4:5
Step-by-step explanation:
When a survey was conducted among 100 students to find their favorite pizza topping, 45 students voted for pepperoni, 25 for mushrooms, and 30 voted for cheese. If a pie chart were made showing the number of votes for each topping, the central angle for the cheese sector would be __________.
Answer:
The central angle for the cheese sector would be 108 degrees.
Step-by-step explanation:
We know that a pi chart takes the form of a circle so the total angle measure is 360 degrees.
Now we want to find out what ratio of the pie chart that cheese takes up and apply it to the total degree measure.
30 of 100 students voted for cheese:
so the ratio would be 30/100 or 3/10
Now apply that to the total angle measure:
3/10*360 degrees= 108 degrees.
what is 99/00+44(55)99
Answer:
undefined! one cannot divide by 0
Step-by-step explanation:
Answer:
undefined!
Step-by-step explanation:
Find the critical point of the given function and then determine whether it is a local maximum, local minimum, or saddle point.
Answer:
critical point of the given function f(x,y) = x²+y²+2xy is from line y = -x is the critical point of the function f(x0,y0) = 0
and it local minimum.
Step-by-step explanation:
Let the given function be;
f(x,y) = x²+y²+2xy
From above function, we can locate relative minima, maxima and the saddle point
f(x,y) = x²+y²+2xy = (x+y)²
df/dx = 2x+2y = 0 ---- (1)
df/dy =2y+2x = 0 ---- (2)
From eqn 1 and 2 above,
The arbitrary point (x0,y0) from line y = -x is the critical point of the function f(x0,y0) = 0
Then, from f(x,y) >= 0 for arbitrary (x,y) € R^n, the arbitrary point from the line x = -y is local minima of the function f.
Which expression is equivalent to 2m^2 - m^2(7-m)+6m^2?
Answer:
[tex]m^3+m^2[/tex]
Step-by-step explanation:
=> [tex]2m^2-m^2(7-m)+6m^2[/tex]
Collecting like terms and expanding the brackets
=> [tex]2m^2+6m^2-7m^2+m^3[/tex]
=> [tex]8m^2-7m^2+m^3[/tex]
=> [tex]m^2+m^3[/tex]
=> [tex]m^3+m^2[/tex]
(25 points) PLEASE HELP! Gotta get this done before my mom comes home
1. The owner of an organic fruit stand also sells nuts. She wants to mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound. How much of each kind of nut should she include in the mixed bag?
A. Cashews: 0.10 lb.; peanuts: 0.40 1b.
B. Cashews: 0.42 lb.; peanuts: 0.08 1b.
C. Cashews: 0.40 lb.; peanuts: 0.10 1b
D. Cashews: 0.27 lb.; peanuts: 0.23 1b.
E. Cashews: 0.23 lb.; peanuts: 0.27 1b.
F. Cashews: 0.08 lb.; peanuts: 0.42 1b
2. A nursery owner has 288 rose bushes. There are 36 fewer red roses than pink roses. How many of each type of roses are there?
A. Red roses: 162; pink roses: 252.
B. Red roses: 162; pink roses: 126.
C. Red roses: 99; pink roses: 126.
D. Red roses: 126; pink roses: 162
E. Red roses: 126; pink roses: 99
F. Red roses: 252; pink roses: 162
3. The sum of the ages of Stephanie and Heather is 46. Heather is two years younger than Stephanie. Write a system of equations to determine the ages of Stephanie and Heather.
A) S + H = 46
H = S + 2
B) S - H = 46
H - 2 = S
C) S + H = 46
H = S - 2
D) S - H = 2
H = S - 46
E) S + H = 2
H = S - 46
F) 2S – H = 46
4. You want to borrow three rock CDs from your friend. She loves math puzzles and she always makes you solve one before you can borrow her stuff. Here’s the puzzle: Before you borrow three CDs, she will have 39 CDs. She will have half as many country CDs as rock CDs, and one-fourth as many soundtracks as country CDs. How many of each type of CD does she have after you borrow three rock CDs?
A. After borrowing 3 rock CDs, your friend will have 21 rock CDs, 12 country CDs, and 3 soundtracks.
B. After borrowing 3 rock CDs, your friend will have 24 rock CDs, 12 country CDs, and 3 soundtracks.
C. After borrowing 3 rock CDs, your friend will have 25 rock CDs, 10 country CDs, and 4 soundtracks.
D. After borrowing 3 rock CDs, your friend will have 21 rock CDs, 9 country CDs, and 3 soundtracks.
E. After borrowing 3 rock CDs, your friend will have 24 rock CDs, 12 country CDs, and no soundtracks.
F. After borrowing 3 rock CDs, your friend will have 18 rock CDs, 15 country CDs, and 3 soundtracks.
5. Three times the width of a certain rectangle exceeds twice its length by two inches. Four times its length is twelve more than its perimeter. Write a system of equations that could be used to solve this problem. (hint: P = 2L + 2W)
A) 3W = 2L + 2
2L = 2W + 12
B) 3W + 2 = 2L
4L = P – 12
C) 3W = 2L + 2
4L + 12 = P
D) 2W + 2 = 2L
4L = 12 + P
E) 3W + 2 = 2L
4L = 12 + P
F) 2L – 2 = 3W
P = 4L - 12
Thank you!!!!
Which of the following functions best describes this graph ?
Answer:
answer D
Step-by-step explanation:
Lets have a look to the graph and to the each of given functions.
As we can see in graph it intersects X in points (-3;0) and (-6;0) that means the function has the roots x1=-3 and x2=-6
Function A has the roots x1=+3 and x2=+6 => doesn' t fit
Function B has only 1 root x=2 , so can be factorized y=(x-2)^2 => doesn' t fit
Function C has 2 roots x1=4 and x2=-5 => doesn' t fit
Function D can be factotized as y=(x+6)*(x+3) so has 2 roots x1=-6 x2=-3 => exactly what we need!!!
We can also notice that the coefficient near x² is equal to 1 and is positive.
That means the legs of the graph directed up,- this is exactly like in our graph. It gives us extra argument why we choose D.
Imagine working in a freelance developer earning 80 USD per hour how many weeks you will have to take a 12 hour flight on a weekday you can either book a flight for ticket for 11 AM for 900 USD or 11 PM flight or 11 USD there is no Internet boards if you take the day off like you will lose a day of work what would you do
Answer:
pay the 11 AM ticket
Step-by-step explanation:
Note that the flight last for 12 hours, and assuming the freelance developer can still work (have access to the internet) on the airplane throughout the flight, he stand to earn $960 ($80*12), which will still cover the cost of the flight with a profit of $60 ($960-900).
However, if he decides to pay the $11 flight ticket and there is no Internet on boards; there by losing a day of work, he stand to have lost working time which would earn with $900.
Therefore, the best choice is to pay the 11 AM ticket.
A bag of marbles contains 4 green marbles, 3 blue marbles, 2 red marbles, and 5 yellow marbles. How many total possible outcomes are there when choosing a marble from the bag?
Answer:
its 14/C
Step-by-step explanation:
i got i right on edg U^U
Answer:
16
Step-by-step explanation:
i did edge test yea dont be imma fake :***
Assume that y varies directly with
x, then solve.
If y=6 when x=2/3 find x when y=12.
Х=? (It’s a fraction)
Answer:
x = 4/3
Step-by-step explanation:
Direct variation:
y = kx
We use the given x-y point to find k.
6 = k * 2/3
k = 6 * 3/2
k = 9
The equation is
y = 9x
For y = 12,
12 = 9x
x = 12/9
x = 4/3