Answer:
one car at a time
Step-by-step explanation:
For each car in the shorter train* (A) ...
train A leaves one of its cars on the offshootboth trains move until train B can move the car from the offshoot to the portion of track away from train Atrain B moves to allow the cycle to repeatWhen there are no more train A cars in front of train B, both trains can continue on their journey.
We assume cars can be decoupled at any point in the train, so that any required order of cars can be preserved. We further assume that train B can move any one of train A's cars in addition to all of its own.
_____
* The total number of car lengths that must pass the offshoot is (at least) the product of the number of cars in both trains, so it doesn't seem to matter which train makes use of the offshoot. We choose to decouple the cars of train A so that the minimum number of cycles is required--even though each cycle is longer.
A train leaves the station traveling north at 75 mph 2 hours later a second train leaves on a parallel track and travels north at 125 mph how far from the station will they meet
Answer:
At 3 hours, the trains will be equidistant from the station.
Step-by-step explanation:
The first train leaves at 75 miles per hour and has a 2 hour head start. This will put the first train at mile marker 150 (75 * 2) when the second train leaves the station at 125 mph.
To solve when they will be near each other, we set up an equation to solve for t.
150 + 75t = 125t
150 = 50t
3 = t
So given this value, we know the trains will be equidistant from the train station on parallel tracks after 3 hours.
Cheers.
Josephine has a rectangular garden with an area of 2x2 + x – 6 square feet. A rectangle labeled 2 x squared + x minus 6 Which expressions can represent the length and width of the garden? length = x2 – 3 feet; width = 2 feet length = 2x + 3 feet; width = x – 2 feet length = 2x + 2 feet; width = x – 3 feet length = 2x – 3 feet; width = x + 2 feet
Answer:
2x^2 + x - 6 = rectangular garden: length = 2x – 3 feet; width = x + 2 feet
Step-by-step explanation:
(2x - 3)(x + 2) = 2x^2 + x - 6 =
2x^2 + 4x - 3x - 6 = 2x^2 + x - 6 =
2x^2 + x - 6
You get the original equation from the two sides multiplied. :)
Hope this helps, have a good day.
The length and width of the rectangle will be (2x – 3) and (x + 2). Then the correct option is D.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L × W square units
The area is 2x² + x – 6 square feet. Then the factor of the equation is given as,
A = 2x² + x – 6
A = 2x² + 4x – 3x – 6
A = 2x(x + 2) – 3(x + 2)
L × W = (2x – 3)(x + 2)
The length and width of the rectangle will be (2x – 3) and (x + 2). Then the correct option is D.
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The graph of F(x), shown below in pink, has the same shape as the graph of
G(x) = x3, shown in gray. Which of the following is the equation for F(x)?
Greetings from Brasil...
In this problem we have 2 translations: 4 units horizontal to the left and 3 units vertical to the bottom.
The translations are established as follows:
→ Horizontal
F(X + k) ⇒ k units to the left
F(X - k) ⇒ k units to the right
→ Vertical
F(X) + k ⇒ k units up
F(X) - k ⇒ k units down
In our problem, the function shifted 4 units horizontal to the left and 3 units vertical to the bottom.
F(X) = X³
4 units horizontal to the left: F(X + 4)
3 units vertical to the bottom: F(X + 4) - 3
So,
F(X) = X³
F(X + 4) - 3 = (X + 4)³ - 3The transformed function is f ( x ) = ( x + 4 )³ - 3 and the graph is plotted
What happens when a function is transformed?Every modification may be a part of a function's transformation.
Typically, they can be stretched (by multiplying outputs or inputs) or moved horizontally (by converting inputs) or vertically (by altering output).
If the horizontal axis is the input axis and the vertical is for outputs, if the initial function is y = f(x), then:
Vertical shift, often known as phase shift:
Y=f(x+c) with a left shift of c units (same output, but c units earlier)
Y=f(x-c) with a right shift of c units (same output, but c units late)
Vertical movement:
Y = f(x) + d units higher, up
Y = f(x) - d units lower, d
Stretching:
Stretching vertically by a factor of k: y = k f (x)
Stretching horizontally by a factor of k: y = f(x/k)
Given data ,
Let the function be represented as g ( x )
Now , the value of g ( x ) = x³
And , the transformed function has coordinates as A ( -4 , -3 )
So , when function is shifted 4 units to the left , we get
g' ( x ) = ( x + 4 )³
And , when the function is shifted vertically by 3 units down , we get
f ( x ) = ( x + 4 )³ - 3
Hence , the transformed function is f ( x ) = ( x + 4 )³ - 3
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6. Classify the traianle as scalene, isosceles or equilateral. Explain. Leave answers in square root form.
TAL
Answer:
isosceles
Step-by-step explanation:
The point B is located on the perpendicular bisector of AC. No calculation is necessary. AC has a slope of 1, so it is easy to count grid squares to see where the perpendicular bisector goes.
When the altitude of the triangle bisects the side opposite the vertex, it is an isosceles triangle.
_____
Apparently, you're to use the distance formula to determine the lengths of the sides of the triangle. Doing that, you would find ...
AB² = (6-4)² +(1 -6)² = 4 + 25
CB² = (6-1)² +(1-3)² = 25 + 4
At this point, it doesn't require much thought to realize these sides are the same length: √29.
What is the domain of f(x)=2/5x+6
Answer:
Look at that picture
Step-by-step explanation:
Will mark Brainliest! A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?
Answer:
0.16
Step-by-step explanation:
Length = 5 unitsNumber of broken sticks= 3Equal lengths = 5 units/3See the picture attached for reference.
As you see the best points are the green areas which covers 2 out of 5 zones.
Since it is same for both broken points, the probability of this is:
2/5*2/5 = 4/ 25 = 0.16Answer is 0.16
RATIO AND PROPORTION PROGRAM ENHANCEMENT UNIT PAUL IS PAID 473.88 FOR 38 1/4 HOURS OF WORK WHAT AMOUNT SHOULD HE BE PAID FO 40 HOURS
Answer:
495.56 should be p[aid for 40 hours.
Step-by-step explanation:
concept used
In ratio
a:b = c:d
__________________________________________
Given
IS PAID 473.88 FOR 38 1/4 HOURS OF WORK
38 1/4 hour = 38.25 hours
if we get ratio for payment per hour
we have
473.88 / 38.25 or 473.88 : 38.25
___________________________________
now we have to find payment for 40 hours
let that payment be x
thus, ratio for payment per hour in this case will be
x/40 or x:40
since
x:40 and 473.88 : 38.25 is representative of same program enhancement unit both ratio will be equal
thus
x:40 = 473.88 : 38.25
x/40 = 473.88 / 38.25
=> x = 40*(473.88 / 38.25 ) = 495.56
Thus, 495.56 should be p[aid for 40 hours.
Suppose that X; Y have constant joint density on the triangle with corners at (4; 0), (0; 4), and the origin. a) Find P(X < 3; Y < 3). b) Are X and Y independent
The triangle (call it T ) has base and height 4, so its area is 1/2*4*4 = 8. Then the joint density function is
[tex]f_{X,Y}(x,y)=\begin{cases}\frac18&\text{for }(x,y)\in T\\0&\text{otherwise}\end{cases}[/tex]
where T is the set
[tex]T=\{(x,y)\mid 0\le x\le4\land0\le y\le4-x\}[/tex]
(a) I've attached an image of the integration region.
[tex]P(X<3,Y<3)=\displaystyle\int_0^1\int_0^3f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx+\int_1^3\int_0^{4-x}f_{X,Y}(x,y)\,\mathrm dy\,\mathrm dx=\frac12[/tex]
(b) X and Y are independent if the joint distribution is equal to the product of their marginal distributions.
Get the marginal distributions of one random variable by integrating the joint density over all values of the other variable:
[tex]f_X(x)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dy=\int_0^{4-x}\frac{\mathrm dy}8=\begin{cases}\frac{4-x}8&\text{for }0\le x\le4\\0&\text{otherwise}\end{cases}[/tex]
[tex]f_Y(y)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx=\int_0^{4-y}\frac{\mathrm dx}8=\begin{cases}\frac{4-y}8&\text{for }0\le y\le4\\0&\text{otherwise}\end{cases}[/tex]
Clearly, [tex]f_{X,Y}(x,y)\neq f_X(x)f_Y(y)[/tex], so they are not independent.
What is the slope of the line shown below?
A.
B.
C.
-
D.
3
Answer:
D
Step-by-step explanation:
Option D is correct. Slope of the line shown in the graph is 3.
The slope of the line is the ratio of the rise to the run, or rise divided by the run.
It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=(y₂-y₁)/(x₂-x₁)
The line is passing through point (2, 2) and (4, 8).
Lets find the corresponding point values y₂= 8, y₁ = 2, x₂= 4 and x₁ =2.
Plug in the values in slope formula:
Slope = (8-2)/(4-2)
=6/2
=3
Hence, slope of the line shown in the graph is 3. Option D is correct.
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The lower edge of a 5 foot tall painting is 5 feet above your eye level. At what distance should you stand from the wall so your viewing angle of the painting is maximized?
Answer:
x = sqrt(50) = 5sqrt(2) = 7.071 ft (to 3 decimals)
Step-by-step explanation:
referring to the diagram
theta (x) = atan(10/x) - atan(5/x)
differentiate with respect to x
theta'(x) = 5/(x^2+25) - 10/(x^2+100)
For x to have an extremum (max. or min)
theta'(x) = 0 ="
5/(x^2+25) - 10/(x^2+100) = 0
transpose and cross multiply
10(x^2+25) -5(x^2+100) = 0
expand and simplify
10x^2+250 - 5x^2-500 = 0
5x^2 = 250
x^2=50
x = sqrt(50) = 5sqrt(2) = 7.071 ft (to 3 decimals)
Since we know that if x becomes large, theta will decrease, so
x = 5sqrt(2) is a maximum.
A shopping centre wants to examine the amount of space required for parking. Studies indicated that 50% of staff and shoppers use public transportation. A survey of 1002 was taken, and 483 responded that they used public transportation. At 5% level of significance, is it reasonable to conclude that the survey results indicate a change?
Answer:
The survey result doesn't indicate the change
Step-by-step explanation:
Previous study result is 50%
Survey result:
483/1002 = 0.482 = 48.2%Comparing with previous result:
50% - 48.2% = 1.8% < 5%Since this result is within 5% level of significance, it can be concluded that the survey result doesn't indicate the change
will rate you brainliest
Answer:
[tex] \frac{11x}{3y} [/tex]
Step-by-step explanation:
[tex] \frac{7x}{3y} + \frac{12x}{9y} [/tex]
Make both a single fraction by adding together.
[tex] \frac{3(7x) + 1(12x)}{9y} [/tex]
[tex] \frac{21x + 12x}{9y} [/tex]
[tex] \frac{33x}{9y} [/tex]
Simplify
[tex] \frac{3(11)x}{3(3y)} [/tex]
[tex] \frac{11x}{3y} [/tex]
Find the value of NT
A. 4
B. 14
C. 12
D. 16
Answer:
14
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
12*x = 8 * (x+2)
Distribute
12x = 8x+16
Subtract 8x
12x-8x = 8x+16-8x
4x = 16
Divide by 4
4x/4 = 16/4
x = 4
We want NT
NT = 8+x+2
= 10 +x
= 10 +4
= 14
Solve x/2 = 3x/4 + 5 (make sure to type the number only)
Answer:
x= -20
Step-by-step explanation:
x/2=3x/4+5
Multiply both sides of the equation by 4, the least common multiple of 2,4.
2x=3x+20
Subtract 3x from both sides.
2x−3x=20
Combine 2x and −3x to get −x.
−x=20
Multiply both sides by −1.
x=−20
A plan for a dog park has a grassy section and a sitting section as shown in the figure. Which equation can be used to find the area of the grassy section?
Answer:
length times width
Step-by-step explanation:
The mean salary of federal government employees on the General Schedule is $59,593. The average salary of 30 state employees who do similar work is $58,800 with \sigmaσσ= $1500. At the 0.01 level of significance, can it be concluded that state employees earn on average less than federal employees? What is the critical value? Round your answer to the nearest hundredths.
Answer:
Yes it can be concluded that state employees earn on average less than federal employees
The critical value is [tex]Z_{\alpha } = - 2.33[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = \$ 59593[/tex]
The sample size is n = 30
The sample mean is [tex]\= x = \$ 58800[/tex]
The standard deviation is [tex]\sigma = \$ 1500[/tex]
The significance level is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu = \$ 59593[/tex]
The alternative hypothesis is [tex]H_a : \mu < \$ 59593[/tex]
The critical value of [tex]\alpha[/tex] from the normal distribution table is [tex]Z_{\alpha } = - 2.33[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\= x - \mu}{ \frac{ \sigma }{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 58800 - 59593 }{ \frac{ 1500 }{ \sqrt{30} } }[/tex]
=> [tex]t = -2.896[/tex]
The p-value is obtained from the z-table
[tex]p-value = P(t < -2.896) = 0.0018898[/tex]
Since [tex]p-value < \alpha[/tex] , we reject the null hypothesis, hence it can be concluded that state employees earn on average less than federal employees
Which relation is a function?
Answer:
The second graph is a function.
Step-by-step explanation:
This is the only one that passes the vertical line test.
(If there exits a vertical line which passes through more than one point, then the relation is NOT a function).
PLEASE HELP ASAP THANKS IN ADVANCE
Answer:
the answer to the question is "C"
Rob sent an email survey to 2,000 cell phone owners asking about their satisfaction with their current plan. Only 256 people returned the survey and they were predominately 18-24 years old.
Which of the following statements is true?
Rob is ignoring the assumption that all survey participants will want to act independently.
The survey likely has bias because the people who could not answer differ from those who did answer.
Rob included too many people on the survey list, affecting the data collected.
The survey suffers from census issues because only 256 people responded.
Answer:
option B
everyone has different opinions about different things, since we only recorded the survey of a fourth of the total people, the survey will definitely have bias since the people who dont have to answer survey will not be able to record their opinions
i will give brainliest and 5 stars if you help ASAP
Answer:
BC = 13.4
Step-by-step explanation:
its a law of cosines S-A-S
a² = b² + c² - 2bc cosA
a² = 12.6² + 4.6² - ( 2 * 12.6 * 4.6 * cos 90 )
a² = 179.92
a = sqrt (179.92)
a = 13.4
7. The General Society Survey asked a sample of 1200 people how much time they spent watching TV each day. The mean number of hours was 3.0 with a standard deviation of 2.87. A sociologist claims that people watch a mean of 4 hours of TV per day. Do the data provide sufficient evidence to disprove the claim? Use α = .05 to test the hypothesis. a. What are your null and alternative hypotheses? b. What test is appropriate here? Why? c. What is your test statistic? d. What is your critical value? e. What is your final decision: do you reject the null or fail to reject the null?
Answer:
a) and b) Look step by step explanation
c) z(s) = - 12,07
d) z(c) = - 1,64
e) Final decision: Reject H₀
Step-by-step explanation:
We assume Normal Distribution
Data:
Sample population n = 1200
Sample mean μ = 3
Sample Standard deviation 2,87
Claim mean μ₀ = 4
α = 0,05 then from z-table we find z(c) = 1,64 ( critical value )
We need to develop a one tail-test to the left
Test Hypothesis
The General Society developed a survey ( in all cases that is an indication of a sample)
Null hypothesis H₀ μ = μ₀
Alternative hypothesis Hₐ μ < μ₀
To calculate the z(s)
z(s) = ( μ - μ₀ )/ 2,87/√n
z(s) = ( 3 - 4 )/ 2,87/√1200
z(s) = -1 * 34,64 / 2,87
z(s) = - 12,07
To compare z(s) and z(c)
z(s) < z(c) - 12,07 < - 1,64
z(s) is in the rejection region (quite far away) we reject H₀
Data provide enough evidence to disprove the claim
a
A solid metal cone of base radius a cm and height 2a cm is melted and solid
spheres of radius are made without wastage. How many such spheres can be
made?
volume of a cone
.
.
.
volume of sphere
.
.
number of spheres that can be made......
.
.
hence a hemisphere can be formed
please help me in these question ????
A school bag contains 12 pens of which 5 are red and the other are black. 4 pens are selected from the bag.
(a) How many different samples of size 4 pens are possible?
(b) How many samples have 3 red pens and 1 black pen?
(c) How many samples of size 4 contain at least two red pens?
(d) How many samples of size 4 contain
If the average yield of cucumber acre is 800 kg, with a variance 1600 kg, and that the amount of the cucumber follows the normal distribution.
1- What percentage of a cucumber give the crop amount between and 834 kg?
2- What the probability of cucumber give the crop exceed 900 kg ?
Answer:
Step-by-step explanation:
A school bag contains 12 pens of which 5 are red and the other are black. 4 pens are selected from the bag.
(a) How many different samples of size 4 pens are possible?
12C4=12!/(4!*8!)=495
(b) How many samples have 3 red pens and 1 black pen?
5C3*7C1
5C3=5!/(3!*2!)=10
7C1=7!/(1!*6!)=7
=>5C3*7C1=10*7=70
(c) How many samples of size 4 contain at least two red pens?
(5C2*7C2)+(5C3*7C1)+(5C4*7C0)
5C2=5!/(2!*3!)=10
7C2=7!/(2!*5!)=21
5C3=5!/(3!*2!)=10
7C1=7!/(1!*6!)=7
5C4=5!/(4!*1!)=5
7C0=7!/(0!*7!)=1
=>(5C2*7C2)+(5C3*7C1)+(5C4*7C0)=285
(d) How many samples of size 4 contain at most one black pen?
(7C1*5C3)+(7C0*5C4)
7C1=7!/(1!*6!)=7
7C0=7!/(0!*7!)=1
5C3=5!/(3!*2!)=10
5C4=5!/(4!*1!)=5
=>(7C1*5C3)+(7C0*5C4)=(7*10)+(1*5)=75
Independent random samples taken on two university campuses revealed the following information concerning the average amount of money spent on textbooks during the fall semester.
University A University B
Sample Size 50 40
Average Purchase $260 $250
Standard Deviation (s) $20 $23
We want to determine if, on the average, students at University A spent more on textbooks then the students at University B.
a. Compute the test statistic.
b. Compute the p-value.
c. What is your conclusion? Let α = 0.05.
Answer:
The calculated Z= 10/4.61 = 2.169
The P value is 0.975 .
Since the calculated value of z= 2.169 falls in the rejection region we therefore reject the null hypothesis at 5 % significance level . On the basis of this we conclude that the students at University A do not spend more on textbooks then the students at University B.
Step-by-step explanation:
We set up our hypotheses as
H0 : x 1= x2 and Ha: x1 ≠ x2
We specify significance level ∝= 0.05
The test statistic if H0: x1= x2 is true is
Z = [tex]\frac{x_1-x_2}\sqrt\frac{s_1^2}{n_1}+ \frac{s_2^2}{n_2}[/tex]
Z = 260-250/ √400/50 + 529/40
Z= 10 / √8+ 13.225
Z= 10/4.61 = 2.169
The critical value for two tailed test at alpha=0.05 is ± 1.96
The P value is 0.975 .
It is calculated by dividing alpha by 2 for a two sided test and subtracting from 1. When we subtract 0.025 ( 0.05/2)from 1 we get 0.975
Since the calculated value of z= 2.169 falls in the rejection region we therefore reject the null hypothesis at 5 % significance level . On the basis of this we conclude that the students at University A do not spend more on textbooks then the students at University B.
The lengths of two sides of a triangle are 6cm and 8cm.Between what two measures should the length of the third side fall? PLEASE HELP !!!!!!!!
Answer: Search Results
Featured snippet from the web
In triangle sum of 2 sides must be greater than the 3rd side. So, the third > 8 - 6 = 2 and also the third < 8 + 6 = 14. So, the answer is 2 < third side < 14. The third side lies between(2,14).
Step-by-step explanation: Brainlyest please
domain and range A) D: (–7, –2], (–1, 3] R: (–10, 9.2] B) D: [–7, –2], [–1, 3] R: [–10, 9.2] C) D: (–7, 3] R: (–10, 9.2] D) D: (–7, –2), (–1, 3) R: (–10, 9.2)
Answer:
[tex]\Large \boxed{\mathrm{C) \ D: (-7, 3] \ R: (-10, 9.2]}}[/tex]
Step-by-step explanation:
The domain is the set of all possible x values.
The range is the set of all possible y values.
For the domain, we observe the graph, the graph will contain all the x values shown on the x-axis.
[tex]\mathrm{D= (-7,3] }[/tex]
For the range, we observe the graph, the graph will contain all the y values shown on the y-axis.
[tex]\mathrm{R= (-10,9.2] }[/tex]
Need help please! what is the total length of a 20 mm steel coiled like a spring with a 16 turns and an outer diameter of 600 mm. pitch is 300 mm. Show your solution please coz i don't really know how to do it! thanks
Answer:
L = 29,550 mm
Step-by-step explanation:
i think i've done this before.. but anyway Lets make it simple and easy.
Let A = 600mm
Let B = 300mm
Let C = 16 as number turns
Let d = 20mm
L = sqrt ((3.14 * (600 - 20))² + 300³) * 16
L = 29,550 mm
Kenji earned the test scores below in English class.
79, 91, 93, 85, 86, and 88
What are the mean and median of his test scores?
Answer:
mean=87
median=87
Step-by-step explanation:
mean=sum of test score/number of subject
mean=79+91+93+85+86+88/6
mean=522/6
mean=87
Literal meaning of median is medium.
To find the number which lies in the medium, we must rearrange the number in ascending.
79, 91, 93, 85, 86, 88
79, 85, 86, 88, 91, 93
86+88/2=87
Hope this helps ;) ❤❤❤
Let me know if there is an error in my answer.
You run a souvenir store that sells key rings. You can get 50 key rings from your first supplier for $.50 cents each. You can get the same 50 key rings from your second supplier for $30 total, or you can get them from your third supplier for $27.50. How much will you pay if you get the best deal?
Answer:
$25
Step-by-step explanation:
.5 * 50 = 25
25<27.5<30
The cheapest supplier is the first one.
Geometry Help needed Quick!!!!! Will give Brainliest to first answer Solve For X and Y
Answer:
x = 8
y = 2√3
Step-by-step explanation:
Since this is a right triangle
x^2 = (4√3)^2 + 4^2 ➡ x^2 = 64 and x = 8
Using Euclidean theorem
y^2 = (x-6)(x - x - 6) = 6x - 36
y^2 = 6×8 - 36
y^2 = 12
y = 2√3
Answer:
1 ) x = 8,
2 ) y = 2√3
Step-by-step explanation:
Take a look at the outermost triangle. I can tell that this is a 30 - 60 - 90 triangle, as if the leg opposite to the 30 degree angle was x, the other respective leg, opposite to the 60 degree angle, would be x√3. Here this " x " would be 4, but don't let that confuse you with the x we have to solve for.
As this outermost triangle is right, x is present as the hypotenuse and we can solve through Pythagorean Theorem,
( 4√3 )² + ( 4 )² = x²,
48 + 16 = x² = 64,
x = √64 = 8
And an inner triangle, present with y being a leg, has a respective leg length of x - 6, or 8 - 6 = 2. Let's solve for y using Pythagorean Theorem once more,
y² + 2² = 4²,
y² = 16 - 4 = 12,
y = √12 = √2 [tex]*[/tex] 2 [tex]*[/tex] 3 = 2√3
