Answer:
[tex]30m^3[/tex] cubic units.
Step-by-step explanation:
Let m represent length of the rectangular prism.
We have been given that the width of a rectangular prism is six times its length, so width of the prism would be [tex]6m[/tex].
We are also told that the height is five times its length, so height of the prism would be [tex]5m[/tex].
We know that volume of rectangular prism is height times width times length.
[tex]\text{Volume of rectangular prism}=lwh[/tex]
[tex]\text{Volume of rectangular prism}=m\cdot 6m\cdot 5m[/tex]
[tex]\text{Volume of rectangular prism}=30m^3[/tex]
Therefore, the volume of the given rectangular prism would be [tex]30m^3[/tex] cubic units.
Brandy set her watch 4 seconds behind and it falls behind another 1 second every day. How many days had it been since brandy last set her watch if the watch is 22 seconds behind?
Answer:
18 days
Step-by-step explanation:
Let x represent number of days.
We have been given that Brandy's watch falls 1 second every day. So Brandy's watch will fall [tex]1x[/tex] seconds behind in x days.
We are also told that Brandy set her watch 4 seconds behind, so Brady's watch will be behind by total [tex]x+4[/tex] seconds in x days.
Since Brady's watch is 22 seconds behind, so we will equate [tex]x+4[/tex] by 22 to solve for x as:
[tex]x+4=22[/tex]
[tex]x+4-4=22-4[/tex]
[tex]x=18[/tex]
Therefore, Brandy set her watch 18 days ago.
Answer:
Its been 19 days since brandy last set her watch as the watch is 22 seconds behind.
Step-by-step explanation:
We are given the following in the question:
Brandy set her watch 4 seconds behind and it falls behind another 1 second every day.
Thus, this forms an arithmetic progression.
4, 5, 6, 7, ...
First term, a = 4
Common difference, d = 1
The [tex]n^{th}[/tex] terms is 22. We have to find the value of n.
The [tex]n^{th}[/tex] terms of A.P is given by
[tex]a_n = a + (n-1)d[/tex]
Putting values, we get,
[tex]22 = 4 + (n-1)1\\18 = n-1\\n = 19[/tex]
Thus, its been 19 days since brandy last set her watch as the watch is 22 seconds behind.
Identify the sample chosen for the study. The number of hours a group of 12 children in Mrs. Smith's kindergarten class sleep in a day. Answer2 Points The 12 children selected in Mrs. Smith's kindergarten class. All children in Mrs. Smith's kindergarten class. The number of hours children sleep.
Answer:
The 12 children selected in Mrs. Smith's kindergarten class.
Step-by-step explanation:
In this case, the population studied are all children in Mrs Smith's kindergarten class, the sample chosen for the study are the 12 children selected in Mrs. Smith's kindergarten class, and the analyzed variable is the number of hours children sleep.
Therefore, since the question asks for the sample, the answer is The 12 children selected in Mrs. Smith's kindergarten class.
Please Help !!!!!!
How long (in years) would it take $9,900 to grow into $22,800 if it's compounded continuously at 4% interest per year?
Answer= ____ years (Round your answer to 2 decimal places.)
Answer:
21.27 years
Step-by-step explanation:
22800 = 9900(1.04^t)
22800/9900 = 1.04^t
76/33 = 1.04^t
ln(76/33) = t×ln(1.04)
t = 21.27
Answer: it will take 20.83 years.
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
P = 9900
A = 22800
r = 4% = 4/100 = 0.04
Therefore,
22800 = 9900 x 2.7183^(0.04 x t)
22800/9900 = 2.7183^0.04t
2.3 = 2.7183^0.04t
Taking ln of both sides, it becomes
Ln 2.3 = 0.04t ln2.7183
0.833 = 0.04t
t = 0.833/0.04
t = 20.83 years
At Sara's birthday party, 15 guests are sharing 3/5 of a gallon of Liquid Soap Bubbles. What fraction of the liquid is available for each guest to use for blowing bubbles?
Answer:
Each guest uses [tex]\frac{1}{25}[/tex] of a gallon of liquid soap bubble at Sara's party.
Step-by-step explanation:
We are given the following in the question:
Number of guests at Sara's party = 15
Amount of liquid soap bubble used by 15 guest =
[tex]\dfrac{3}{5}\text{ of a gallon}[/tex]
Fraction of liquid soap bubble available for each guest =
[tex]=\dfrac{\text{Liquid soap bubble used by 15 guest}}{\text{Number of guest}}\\\\=\dfrac{\frac{3}{5}}{15}\\\\=\dfrac{1}{25}[/tex]
Thus, each guest uses [tex]\frac{1}{25}[/tex] of a gallon of liquid soap bubble at Sara's party.
Answer:
1/25 of the gallon each person will get
Step-by-step explanation:
Please help dont skip
What is the distance between point (6, -1) and point (5, 3) rounded to the nearest tenth?
4.1 units
17 units
4.6 units
1.4 units
Answer:
1.4 units
Step-by-step explanation:
Ms.Perkins needs to order art supplies for the entire school.She would like to get at least 8,000 piece construction paper has 495 pieces , about how many pack will she need!
To find out how many packs of construction paper Ms. Perkins will need, divide the total number of pieces needed by the number of pieces in each pack. Using long division, we find that she will need at least 16 packs of construction paper.
Explanation:To find out how many packs of construction paper Ms. Perkins will need, we can divide the total number of pieces she needs (8,000) by the number of pieces in each pack (495). This will give us the number of packs required.
Using long division, we divide 8,000 by 495:
First, we divide 8,000 by 495 to get 16 with a remainder of 40.We then bring down the next digit, 0, making the new dividend 400.We divide 400 by 495, getting 0 with a remainder of 400.Finally, we bring down the 0, making the new dividend 4000. We divide 4000 by 495, getting 8 with a remainder of 40.Since the remainder is less than 495, we stop here. Therefore, Ms. Perkins will need at least 16 packs of construction paper.
A ball slides up a frictionless ramp. It is then rolled without slipping and with the same initial velocity up another frictionless ramp (with the same slope angle). In which case does it reach a greater height, and why
Answer:
Rolling case achieves greater height than sliding case
Step-by-step explanation:
For sliding ball:
- When balls slides up the ramp the kinetic energy is converted to gravitational potential energy.
- We have frictionless ramp, hence no loss due to friction.So the entire kinetic energy is converted into potential energy.
- The ball slides it only has translational kinetic energy as follows:
ΔK.E = ΔP.E
0.5*m*v^2 = m*g*h
h = 0.5v^2 / g
For rolling ball:
- Its the same as the previous case but only difference is that there are two forms of kinetic energy translational and rotational. Thus the energy balance is:
ΔK.E = ΔP.E
0.5*m*v^2 + 0.5*I*w^2 = m*g*h
- Where I: moment of inertia of spherical ball = 2/5 *m*r^2
w: Angular speed = v / r
0.5*m*v^2 + 0.2*m*v^2 = m*g*h
0.7v^2 = g*h
h = 0.7v^2 / g
- From both results we see that 0.7v^2/g for rolling case is greater than 0.5v^2/g sliding case.
A ball will reach a greater height when it slides up a frictionless ramp and is then rolled without slipping up another frictionless ramp with the same slope angle.
Explanation:A ball will reach a greater height when it slides up a frictionless ramp and is then rolled without slipping up another frictionless ramp with the same slope angle. This is because, when the ball slides up, it gains potential energy which is then converted to kinetic energy as it rolls up the second ramp. The ball will reach a greater height because it retains some of the initial energy it gained from sliding up the first ramp.
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Graph the relation. Is the relation a function? Why or why not?
{(–1, 1), (–2, 1), (–2, 2), (0, 2)}
No; a range value has two domain values.
Yes; there is only one range value for each domain value.
No; a domain value has two range values.
Yes; there is only one domain value for each range value.
Answer:
No; a range value has two domain values.
Step-by-step explanation:
Output has to be unique for all inputs.
Output for -2 is not unique
Answer:
No; a range value has two domain values
Step-by-step explanation:
What is the value of X in the following parallelogram?
Answer: x = 35
Step-by-step explanation:
In a parallelogram, the opposite sides and the opposite angles are equal and parallel.
Also, the consecutive angles in a parallelogram are supplementary. This means that the sum of the consecutive angles is 180 degrees.
Angle (2x - 10) and angle (2x + 50) are consecutive angles. Therefore,
2x - 10 + 2x + 50 = 180
2x + 2x - 10 + 50 = 180
4x + 40 = 180
4x = 180 - 40 = 140
x = 140/4
x = 35
This is the correct method of recording numerical information from an experiment.
Answer:
Data-table is the correct approach of recording numerical information from an experiment
Step-by-step explanation:
A data-table is a group of related facts arranged in labeled rows and columns and is used to record information. Its purpose is to help sort, analyze and compare data gathered from a science experiment or research project. Knowing how to create a data table demonstrates skills in organizing information in a meaningful way and provides a learning base to progress to more sophisticated ways to track data.
Oliver read for 450 minutes this month. His goal is to read for 10% more minutes next month. If Oliver meets his goal,how many minutes will he read in all during the two months
Answer:
Oliver read in two months = 945 minutes
Step-by-step explanation:
Oliver read in this month = 450 minutes
Goal for the next month = 10 % more than this month = [tex]\frac{110}{100}[/tex] × 450
⇒ Oliver read in next month = 495 minute
⇒ Oliver total read in two months = 450 + 495 = 945 minutes
Thus Oliver read in two months = 945 minutes
Answer:
Oliver will read 945 minutes in 2 months.
Step-by-step explanation:
Given:
Number of minutes read this month = 450 mins
Percent of minutes to read next month = 10%
We need to find the number of minutes he read in two months.
Solution:
First we will find the number of minutes he read in next month.
number of minutes he read in next month is equal to Number of minutes read this month plus Percent of minutes to read next month multiplied by Number of minutes read this month.
framing in equation form we get;
number of minutes he read in next month = [tex]450+\frac{10}{100}\times 450 =450+45 =495\ mins[/tex]
Now number of minutes he read in two months is equal to sum of Number of minutes read this month and number of minutes he read in next month.
framing in equation form we get;
number of minutes he read in two months = [tex]450+495 = 945\ mins[/tex]
Hence Oliver will read 945 minutes in 2 months.
Use the polygon tool to draw a rectangle with a length of 4 units and a height of 2 units one of the sides of the rectangle falls on like ef and the rectangle had a vertex of e each segment on the grid represents 1 unit
Answer:
Step-by-step explanation:
Please find the attached photo for your reference how to draw the rectangle.
1. From on point E and draw a segment 2 units long because the height is 2 units and be vertical.
2. Draw horizontally a line 4 units long (the length) to the right
3. Draw a line upwards 2 units long, at that point it must be at the same height than point E.
4. Draw a 4-units line to the left, and you will be back on point E, the rectangle done.
Answer:
Over here
Step-by-step explanation:
If the standard deviation of a set of data is zero, what can you conclude about the set of values? The sum of the deviations from the mean is zero. All values are identical. All values are equal to zero. The sum of the values is zero
Answer:
All values are identical.
Step-by-step explanation:
We are given the following in the question:
If the standard deviation of a set of data is zero.
Then, all the values in data are identical.
This can be shown as:
Let all the terms in data be x.
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{nx}{n} = x[/tex]
Sum of squares of differences =
[tex]\displaystyle\sum (x_i - x)^2 = 0[/tex]
[tex]\sigma = \sqrt{\frac{0}{n}} = 0[/tex]
Thus, the correct answer is
All values are identical.
The correct conclusion about the set of values when the standard deviation is zero is that all values are identical.
The standard deviation is a measure of the amount of variation or dispersion in a set of values. A standard deviation equal to zero means that there is no variation at all in the data set. This can only occur if all the values in the set are exactly the same.
To understand why this is the case, let's consider the formula for standard deviation (for a population):
[tex]\[ \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}} \][/tex]
Here, [tex]\( \sigma \)[/tex] is the standard deviation, [tex]\( x_i \)[/tex] represents each value in the data set, [tex]\( \mu \)[/tex] is the mean of the data set, and [tex]\( N \)[/tex] is the number of values in the data set.
Now, let's address the other options:
The sum of the deviations from the mean is zero: This statement is true for any data set, regardless of whether the standard deviation is zero or not. The positive and negative deviations from the mean always sum to zero.All values are equal to zero: This is not necessarily true. The standard deviation can be zero if all values are the same non-zero number.The sum of the values is zero: This is also not necessarily true. The standard deviation is concerned with the variation of the values around the mean, not the sum of the values themselves.Please assist on these problems
Answer:
a) linear. Cost per minute is a constant.
b) f(x) = 40 -0.15x
d) f(100) = 25. The remaining value is $25 after using 100 minutes.
Step-by-step explanation:
a) Since the cost per minute is a constant, the remaining dollar value of the phone decreases by the same amount for each minute used. The cost as a function of minutes used is a linear function with a constant rate of change.
__
b) The value starts at $40 and decreases by $0.15 for each increment of x (minutes used). The function can be written as ...
f(x) = 40 -0.15x
__
d) Put 100 where x is in the function definition and do the arithmetic.
f(100) = 40 -0.15×100 = 40 -15
f(100) = 25
According to the variable and function definitions, x=100 means 100 minutes have been used; f(x) = 25 means the remaining value of the phone is 25 dollars.
f(100) = 25 means the phone's remaining value is $25 when 100 minutes have been used.
I need help I have no clue
Answer:
The answer to your question is x = 64; y = 20
Step-by-step explanation:
Angles 2x + 2 and 130° are vertical angles so they measure the same.
2x + 2 = 130
- Solve for x
2x = 130 - 2
2x = 128
x = 128/2
x = 64
Angles 3y - 10 and 50° are vertical angles, so they measure the same.
3y - 10 = 50
3y = 50 + 10
3y = 60
y = 60/3
y = 20
giving out brainliest !!
Three runners Dave, Edith, and Foley all start at the same time for a 24 km race, and each of them runs at a constant speed. When Dave finishes the race, Edith is 8 km behind, and Foley is 12 km behind. When Edith finishes the race, how far behind is Foley, in km?
Answer:
4 Km behind.
Step-by-step explanation:
1. Draw a graph
2. make Dave Edith and Foley
3. 8-0 is 8 and 12-8 is 4
The speed is the distance covered by an object at a particular time. When Edith finishes the race, the distance by which Foley is behind is 6 km.
What is speed?The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Let the time in which Dave finishes the race be represented by t. Therefore, in time t Dave completed 24 km.
Given that When Dave finishes the race, Edith is 8 km behind. Therefore the distance that Edith will cover in time t is 16 km. Now, the speed of Edith will be,
Speed of Edith = 16 km /t
Also, When Dave finishes the race, Foley is 12 km behind. Therefore the distance that Edith will cover in time t is 12 km. Now, the speed of Edith will be,
Speed of Edith = 12 km /t
Now, the time it will take for Dave to finish the rest of 8 km distance is,
Time = 8 km / (16 km/t)
= 0.5 t
Further, the distance that Edith will cover in time 0.5t is,
Distance = 0.5t × 12km/t
= 6 km
Therefore, the distance that will be left for Foley is 6 km.
Hence, When Edith finishes the race, the distance by which Foley is behind is 6 km.
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The volume v of any cube with a side length s can be deermind using the formula v=s^3 what is the volume in the cubic cenitermeters of a cube with a side length of 2.3 cenimeters
Answer:
12.167[tex]cm^3[/tex]
Step-by-step explanation:
The volume of any solid shape is the quantity or capacity it can contain. For example, if you have a closed tin of milf that is filled to the brim, the volume of the tin is the quantity of milk that is in the tin.
Given any cube with side length s, the Volume V=[tex]s^3[/tex]
If the cube has a side length of 2.3 centimeters
Volume=[tex]s^3[/tex]= s X s X s = 2.3 X 2.3 X 2.3=12.167[tex]cm^3[/tex]
Volume of the Cube = 12.167[tex]cm^3[/tex]
Answer: 12.167 cubic centimeters
Step-by-step explanation:
Play some pains 1/4 of the area of his living room walls,w, on Monday. On Tuesday, he paints twice as much as he painted on Monday. Write an expression to find the remaining unpainted area
Answer:
X = 1 - (1/4) - 2 * (1/4)
Step-by-step explanation:
The equation to be raised must take into account what is painted on Monday and Tuesday. First consider the wall as a unit, that is to say painting the entire wall (100%) is equivalent to 1. Therefore the equation would be the following:
Let X be the unpainted part:
X = 1 - (1/4) - 2 * (1/4)
X = 1 - (1/4) - (1/2)
Now, if we solve this, we have that 0.25, therefore 25% or 1/4 is left to be painted on the wall.
A TRAFFIC LIGHT IS RED FOR 38 SECONDS YELLOW FOR 10 SECONDS AND GREEN FOR ONE MINUTE AND TWELVE SEONDS. IN A CONSTANTLY REPEATING CYCLE, WHAT IS THE PROBABILITY THAT AT THE MOMENT A PASSING PEDESTRIAN GLANCES AT IT, THE LIGHT WILL BE GREEN
A bookcase has 4 shelves. The bottom shelf has 10 books. Each of the other shelves has 5 more books than the shelf below it. How many books are in the bookcase.
Answer:
70
Step-by-step explanation:
In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?
A) 5
B) 4
C) 3
D) 2
E) 0
Step-by-step explanation:
Below is an attachment containing the solution.
A country has 50 million people, 30 million of whom are adults. Of the adults, 5 million are not interested in working, another 5 million are interested in working but have given up looking for work, and 5 million are still looking for work. Of those who do have jobs, 5 million are working part time but would like to work full time, and the remaining 10 million are working full time. What is this country's labor force participation rate? 83.3% 75% 50% 66.7%
Answer:
66.7%
Step-by-step explanation:
Given that
Total population = 50 million
Adults = 30 million
Those not interested in working = 5 million
Those interested in working but given up on searching = 5 million
Those searching = 5 million
Those working part time = 5 million
Those working full time = 10 million
Recall that
Labour force participation rate = (number of people actively participating in labour ÷ total number of people eligible) × 100
Number of people actively participating in labour = employed + unemployed
Employed = 10 million full time + 5 million part time
= 15 million
Unemployed = 5 million. Those searching.
Thus,
People actively participating in labour = 15 + 5= 20 million.
Total number of eligible people = total number of adults = 30 million
Therefore
Labour participation rate = (20/30) × 100
= 0.66667 × 100
= 66.6667
Approximately 66.7%
CAN I GET SOME HELP AND NOT SKIPPED?
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-2, 2) and point (4, 4) rounded to the nearest tenth?
1 unit
5.7 units
4 units
6.3 units
Answer:
The last one: 6.3 units.
Answer: 6.3 units
Step-by-step explanation:
The formula for determining the distance between two points on a straight line is expressed as
Distance = √(x2 - x1)² + (y2 - y1)²
Where
x2 represents final value of x on the horizontal axis
x1 represents initial value of x on the horizontal axis.
y2 represents final value of y on the vertical axis.
y1 represents initial value of y on the vertical axis.
From the graph given,
x2 = 4
x1 = - 2
y2 = 4
y1 = 2
Therefore,
Distance = √(4 - - 2)² + (4 - 2)²
Distance = √6² + 2² = √36 + 4 = √40
Distance = 6.3 units
Harold catches fish throughout the day at unpredictable intervals. Which reinforcement schedule is this?a. variable interval b. variable ratio c. fixed interval d. fixed ratio
Answer:
The correct answer to the question is
a. variable interval
Step-by-step explanation:
In a variable interval, the time at which reinforcement or reward is gained occurs at an unpredictable time. That is the animal gets a reinforcement on the grounds of an unpredictable time period.
An example of a variable interval is the catching of fish whereby the fisher catches fishes at an unpredictable time throughout the day.
The result of a variable interval is a controlled but stable response rate. In the case in the question, constant monitoring of the fishing device is important
The reinforcement schedule described is a variable interval schedule where the reinforcement occurs at unpredictable intervals of time.
Explanation:The reinforcement schedule described in the question is a variable interval schedule.
Variable interval refers to a schedule in which the reinforcement (in this case, catching fish) occurs at unpredictable intervals of time. Harold catches fish throughout the day, but the intervals between catching fish are inconsistent and unpredictable.
Examples of variable interval schedules include waiting for a bus that arrives at different times or checking your phone for new messages throughout the day.
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A person’s blood pressure is monitored by taking 3 readings daily. The probability distribution of his reading had a mean of 132 and a standard deviation of 5. Each observation behaves as a random sample. Find the mean of the sampling distribution of the sample mean for the three observations each day.
Answer:
The mean of the sampling distribution of the sample mean for the three observations each day is 132.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 132
Standard Deviation, σ = 5
Each observation behaves as a random sample.
a) Mean of the sampling distribution
[tex]\bar{x} = \mu = 132[/tex]
b) Standard deviation of the sampling distribution
Sample size,n = 3
[tex]s = \dfrac{\sigma}{\sqrt{n}} = \dfrac{5}{\sqrt{3}} = 2.887[/tex]
Thus, the mean of the sampling distribution of the sample mean for the three observations each day is 132.
x + 4y – 12 = 0 x = 3y – 7 Which of the following is the resulting equation?
-7y – 19 = 0
y – 5 = 0
7y + 19 = 0
7y – 19 = 0
Answer:
The answer to your question is 7y - 19 = 0
Step-by-step explanation:
Data
Equation l x + 4y - 12 = 0
Equation ll x = 3y - 7
Process
1.- Substitute equation ll in equation l
3y - 7 + 4y - 12 = 0
2.- Group like terms
(3y + 4y) + (-7 - 12) = 0
3.- Simplify like terms
7y - 19 = 0
4.- Result
7y - 19 = 0
Match each function formula with the corresponding transformation of the parent function y = –x 2 – 1. 1. y = –x2 – 1 Translated right by 1 unit 2. y = –(x – 1)2 – 1 Reflected across the x-axis 3. y = x2 + 1 Translated down by 1 unit 4. y = –x2 Reflected across the y-axis 5. y = –(x + 1)2 – 1 Translated left by 1 unit 6. y = –x2 – 2 Translated up by 1 unit
Answer:
1. f₁(x)=-x²+2x-2
2. f₂(x)=-x²+6x-10
3. f₃(x)=-x²-2
4. f₄(x)=-x²+10x-26
5. f₅(x)=-x²-2x-2
6. f₆(x)=-x²
Step-by-step explanation:
1. we have that f(x) is translated right by 1 unit , also
according to the graph f(x) has a vertex P(0,-1) then P₁ ( 1,-1) to f₁(x) therefore y-y₁ = -(x-x₁)² ⇒ y-y₁ = -(x-x₁)² ⇒ y+1 = -(x-1)² ⇒ y=-(x²-2x+1)-1 =-x²+2x-2
2. f(x) is reflected across the x-axis 3, same as in 1., P₂(3,-1) to f₂(x)
y+1 = -(x-3)² ⇒ y=-(x²-6x+9)-1 =-x²+6x-10
3. f(x) is translated down by 1 unit, P₃(0,-2) to f₃(x)
y+2 = -(x)² ⇒ y=-x²-2
4. f(x) is reflected across the y-axis 5, P₄(5,-1) to f₄(x)
y+1 = -(x-5)² ⇒ y=-(x²-10x+25)-1 =-x²+10x-26
5. f(x) is translated left by 1, P₅(-1,-1) to f₅(x)
y+1 = -(x+1)² ⇒ y=-(x²+2x+1)-1 =-x²-2x-2
6. f(x) is translated up by 1 unit, P₆(0,0) to f₆(x)
y+0 = -(x+0)² ⇒ y=-x²
Two trains continuously travel between Washington D.C. and Baltimore which are 120 miles apart. The trains start simultaneously, with train A starting in Washington DC and train B starting in Baltimore, and travel at 30 and 90 mph respectively. If the station turnaround times are negligible, what is the distance between the point where the trains meet for the first time and the point where they meet for the second time?
Answer:
Step-by-step explanation:
Two train traveling in opposite direction
Distance apart the train is 120miles
Train A
Speed =30mph
Train B
90mph
What is common to the train is the same time, they will meet at the same time
Let assume they meet at distance x from from Washington
Then A has travelled x mile distance
Then, B has travelled 120-x mile distance
Time for train A to get to x,, = time for train B to get 120-x
Time=distance/speed
da/Sa=db/Sb
Let da be distance of train A
And db be distance of train B
Sa be speed of train A
Sb be speed of train B
Then,
da/Sa=db/Sb
x/30=120-x/90
Cross multiply
90x=3600-30x
90x+30x=3600
120x=3600
Then, x=3600/120
x=30miles
Then will meet at 30miles from Washington
Second part of the questions
Train B is faster than train A
Train B has already travelled 90miles while train B travels 30 miles
This shows that train A will not get to Baltimore before train B catch up
Then, let train A travel y distance
Then B will have to complete the 30 miles and then with another 30 miles that A has travel and then y
Total distance B travel will be
db=30+30+y
db=60+y
And da=y
Therefore,
da/Sa=db/Sb
y/30=60+y/60
Cross multiply
60y=1800+30y
60y-30y=1800
30y=1800
Then, y=1800/30
y=60miles
That means they will meet at 60miles from both Washington and Baltimore, or they are at mid points
Find the missing side length BM. Round your answer to the nearest tenth.
Length of side BM is 30 yd
Step-by-step explanation:
Step 1: Find the value of ∠S using the property that sum of angles of a triangle is 180°⇒ ∠B + ∠M + ∠S = 180°
⇒ 35° + 102° + ∠S = 180°
∴ ∠S = 180° - 137° = 43°
Step 2: Use the law of sines to find the length of BM.Law of sines ⇒ a/sin A = b/sin B = c/sin C
Here, let BM be a then, sin A = sin S = sin 43° = -0.83
Also, b = 18 yd, then sin B = sin 35° = -0.43
⇒ BM/-0.83 = 18/-0.43
⇒ BM = -0.83 × 18/-0.43 = 14.94/0.43 = 34.74 yd = 30 yd (rounded to nearest tenth)
Answer:
Step-by-step explanation:
Looking at the triangle, to determine BM, we would apply the sine rule. It is expressed as
a/SinA = b/SinB = c/SinC
Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. From the triangle, m∠S = 180 - (102 + 35) = 43°
Therefore, applying the rule,it becomes
18/Sin35 = BM/Sin43
Cross multiplying, it becomes
BM × Sin 35 = 18 × Sin 43
BM × 0.5736 = 18 × 0.6820
0.5736BM = 12.276
Dividing the left hand side and the right hand side of the equation by 0.5736, it becomes
0.5736BM/0.5736 = 12.276/0.5736
BM = 21.4
Nolini says that if the denominator is more than twice the numerator, the fraction can always be replaced with a 0. Is she correct? Give an example in your explanation.
Answer:
yes
Step-by-step explanation:
It depends on how accurate you want your answer to be, but basically yes, imagine we set our numerator to be x, and our denominator to be 2x, if we built our fraction we will get that:
[tex]\frac{x}{2x}=\frac{1}{2}[/tex]
If the denominator of a fraction is exactly twice the numerator, then the fraction will be simplified to 1/2 or 0.5.
Now, the greater the denominator is, the closer the fraction will get to zero.
Take for example I had an fraction like this:
[tex]\frac{3}{6}=0.5[/tex]
which approximates to 0. If we made the denominator bigger, let's say 7, we would get:
[tex]\frac{3}{7}=0.43[/tex]
notice the answer is closer to 0 this time, so it's valid to round it to zero. If we made the denominator greater, let's say 25, we would get:
[tex]\frac{3}{25}=0.12[/tex]
and so on. So it is true that if the denominator of a fraction is greater than twice the numerator, we can always replace the fraction with a 0 (depending on how accurate you want your answer to be).
If the denominator is more than twice the numerator, the number is therefore less than halve, 1/2 but cannot always be replaced with a 0.
An example;
Suppose we have a numerator, 2.
Then, we have a denominator which is more than twice the numerator; say 5
The resulting fraction is therefore;
2/5.The fraction 2/5 is definitely less than 1/2 but cannot always be replaced with a 0.
Read more on fractions:
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