Three trains are made of identical train cars, so each car has the same number of seats. The first train has 418 seats, the second train has 456 seats, and the third train has 494 seats. How many cars are in each train if no train has more than 25 seats?
In my system the answer format is like this: There were __ cars in the first train, __ cars in the second train and __ cars in the third train
There were _22_ cars in the first train, _24_ cars in the second train, and _26_ cars in the third train
How many cars are on each train?
We know that the trains have 418, 456, and 494 seats. And are made of the same train cars, so the number of seats on each train car is a common factor of 418, 456 and 494.
We also know that no train car has more than 25 seats.
First, let's decompose the given numbers as a product of prime numbers:
418 = 2*11*19
456 = 2*2*2*3*19
494 = 2*13*19
As you can see, the factors 2 and 19 appear in the 3 numbers, 19 is the largest one that is also smaller than 25, so we conclude that each train car has 19 seats.
Then:
The first train, which has 418 seats, has:
418/19 = 22 train cars.
The second train has 456 seats, so it has:
456/19 = 24 train cars
The third train has 494 seats, so it has:
494/19 = 26 train cars.
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7) What does a multiplier of \( 1.2 \) mean?
A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.
A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.
A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.
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Case Study 11 In November 2020, a theme park set the price of their 2021 annual pass at $140, and at that price 26,467 passes were sold. In November 2021, the price of the 2022 annual pass rose to $200, and the number of passes sold dropped to 17,994. 1. What is the elasticity of demand for the park annual pass?
The elasticity of demand for the park annual pass is approximately 1.58.
The formula for calculating the elasticity of demand is:
Elasticity = percentage change in quantity demanded / percentage change in price
Using the given data, we can calculate the percentage change in quantity demanded:
((17,994 - 26,467) / ((17,994 + 26,467) / 2)) x 100% = -26.42%
We can also calculate the percentage change in price:
((200 - 140) / ((200 + 140) / 2)) x 100% = 40.00%
Plugging in these values to the elasticity of demand formula, we get:
Elasticity = -26.42% / 40.00% = -0.66
However, elasticity is typically reported as an absolute value, so we take the absolute value of -0.66 to get:
Elasticity ≈ 1.58
Therefore, the elasticity of demand for the park annual pass is approximately 1.58, indicating that the demand for the pass is relatively elastic. This means that as the price of the pass increases, the quantity demanded will decrease at a faster rate.
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The square root parent function is translated so that the endpoint is located at (-7,7). Write an equation that represents this new function
The square root function is translated so that the endpoint is located at (-7,7), \(g(x)= \sqrt{x+7} +7\) and this can be determined by using the transformation.
The square root parent function is translated so that the endpoint is located at (-7,1).
The following steps can be used to determine the equation that represents this new function:
Write the square root parent function.\(f(x) =\sqrt{x}\)
The graph of the above function is translated by a factor of 7 in the negative x-axis that is in the left direction.Then the graph obtained in the above step is translated by a factor of 7 in the positive y-axis in the upward direction.Write the equation of the function that obtains in step 3.\(g(x)= \sqrt{x+7} +7\)
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bla nnn,,,,,,bs jfbjnf msnjkmfe sjnmf cmmnefnmv fcve
Answer:
Ummmmm ehhhhhh
I need points for a hw
The stopping distance D of a car after the brakes have been applied varies directly as the square of the speed of R. If a car traveling 80 mph can stop in 400ft, How fast can a car travel and still stop in 144ft?
Direct variation equations have the following form:
\(y=kx\)Where "k" is the Constant of variation.
In this case, analyzing the information given in the exercise, you know that the equation for that Direct variation has this form:
\(D=kR^2\)You know that:
\(D=400ft\)When:
\(R=80mph\)So you need to make the conversion from feet to miles. Since:
\(1mi=5280ft\)You get:
\((400ft)(\frac{1mi}{5280ft})\approx0.076mi\)Then, you can find the value of "k" as following:
\(undefined\)In the accompanying diagram, what is sin E?
Please see image below (math)
Answer:
\(\sin E=\dfrac{4}{5}\)
Step-by-step explanation:
To find the value of sin E we can use the sine trigonometric ratio.
\(\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)
From inspection of the given right triangle:
The angle is E, so θ = E.The side opposite angle E is FG, so O = 4.The hypotenuse of the triangle is EF, so H = 5.Substitute these values into the sine ratio:
\(\sin E=\dfrac{4}{5}\)
Find a, b, and c for the following function.
f(x)= 3x² – 2x – 1
Answer:
{3, -2, -1}
Step-by-step explanation:
Since this is a quadratic equation in standard form, we can immediately pick out the coefficients of the x terms: {3, -2, -1}
How many natural numbers between $150$ and $300$ are divisible by $9$?
Answer:
There are 17 natural numbers divisible.
There are 17 natural numbers between 150 and 300 that are divisible by 9.
To find the number of natural numbers between 150 and 300 that are divisible by 9, we need to find the count of multiples of 9 within this range.
The first multiple of 9 greater than or equal to 150 is 153 (9 x 17), and the last multiple of 9 less than or equal to 300 is 297 (9 x 33).
Now, we can calculate the number of multiples of 9 between 153 and 297 (inclusive):
Number of multiples of 9 = (Last multiple - First multiple) / 9 + 1
Number of multiples of 9 = (297 - 153) / 9 + 1
Number of multiples of 9 = 144 / 9 + 1
Number of multiples of 9 = 16 + 1
Number of multiples of 9 = 17
So, there are 17 natural numbers between 150 and 300 that are divisible by 9.
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4. A pizza shop has 12" pizzas with 6 slices and 16" pizzas with slices. Which pizza has bigger slices?
If Abcd is a parallelogram find m
54% as a simplified fraction
Answer:
27/50
Step-by-step explanation:
54 = 54/100
54/100 simplified = 27/50
jasmine is 5 years younger than twice her sister age of jasmine sister 22 year old then how old is jasmine
Answer:
100000000000000000000000000
Step-by-step explanation:
Answer:
Step-by-step explanation:
i think the answer is 12
62 high school students took part in the mathematical olympiad. there were 7 fewer first year students than sophomores, two thirds of the number of third year students, and 5 fourth year students. how many students from each grade took part in the competition?
Answer:a = 17
b = 24
c = 16
d = 5
Step-by-step explanation:
a+b+c+d=62
a = b-7
c = 2/3·b
d = 5
a+b+c+d = 62
a-b = -7
2b-3c = 0
d = 5
Row 2 - Row 1 → Row 2
a+b+c+d = 62
-2b-c-d = -69
2b-3c = 0
d = 5
Row 3 + Row 2 → Row 3
a+b+c+d = 62
-2b-c-d = -69
-4c-d = -69
d = 5
d = 5/1= 5
c = -69+d/-4= -69+5/-4= 16
b = -69+c+d/-2= -69+16+5/-2 = 24
a = 62-b-c-d = 62-24-16-5 = 17
a = 17
b = 24
c = 16
d = 5
Please explain to me how to do this!
I don't have much time to get it in please help!
Answer:
y = mx + b
Step-by-step explanation:
so you first put the points on the graph and connect them with a slanted line.
Next, for your equation start of with y =
then, your going to find your slope, after you find it put it in front of x (slope x) (Ex; if the slope was 3 then it would look like this 3x)
finally you write + and the y intercept (at which point the line goes through the y axis)
the equation together should look like y = slope x + y intercept
HELP DUE IN 10 MINS! Solve for x in the parallelogram below:
x=??
Answer:
x = 10
Step-by-step explanation:
The opposite angles in a parallelogram are congruent, then
5x - 9 = 3x + 11 ( subtract 3x from both sides )
2x - 9 = 11 ( add 9 to both sides )
2x = 20 ( divide both sides by 2 )
x = 10
Help me please, I really don't want to fail
Which system of equations has no solution?
Answer: Top left i'm pretty sure
Step-by-step explanation: Because there isn't a blue line and you need a blue line for it to be an equation
Answer:
Parallel line
Step-by-step explanation:
The parallel line doesn't connect so it a infinite therefore it means its a no solution line
Make p the subject of the formula
y = 3p2 - 4
Answer:
p =√(y+4)/3
Step-by-step explanation:
y=3p^2-4
so 3p^2=y+4
then p^2=(y+4)/3
so p =√(y+4)/3
Answer:
Step-by-step explanation:
y=3p^2-4
so 3p^2=y+4
then p^2=(y+4)/3
so p =√(y+4)/3
Use synthetic division and the Remainder Theorem to find f(4) if f(x) = – 2x3 + 9x2
2x3 + 9.c- 6x + 7
Step-by-step explanation:
Let's see. f(4) makes the divisor x-4
4|-2 9 -6 7
| 8 -68 296
-2 17 -74 2072
The quotient is -2x²+17x-74 with a remainder of 2072
evaluate 9.3p + 8.9r when p=7 and r=8
The value of the expression for the given p and r value is 136.3.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 9.3p + 8.9.
Here, p=7 and r=8
Substitute p=7 and r=8 in 9.3p + 8.9r, we get
9.3×7+8.9×8
= 136.3
Therefore, the value of the expression is 136.3.
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(2, -2) and (0, -1)
Answer:
Step-by-step explanation:
Answer:
-1
Step-by-step explanation:
If ur trying to write in slope- intercept form then its y=-1/2x-1
Emergency! Find the measure of angle A
Answer:
57
CosA = (14/26)
A = Cos⁻¹ (14/26)
A = 57
Find the missing dimension of the prism.
Volume = 60 in ³
Height = 4 in
Width = 2.5 in
Length = ?
What is the length?
7in
4in
6 in.
5 in.
Answer:
volume
Step-by-step explanation:
Answer:
1.5 in
Step-by-step explanation:
To find the missing dimension (length), we can use the formula for the volume of a prism:
Volume = Base Area x Height
We know that the volume of the prism is 60 in³ and the height is 4 in. We also know that the base of the prism is a rectangle with a width of 2.5 in.
Base Area = Length x Width
We can rearrange the formula for volume to solve for the missing dimension:
Length = Volume / (Base Area x Height)
Base Area = Width x Length
Plugging in the given values, we get:
Base Area = 2.5 in x Length
Base Area x Height = 10 in²
Length = 60 in³ / (10 in² x 4 in)
Length = 1.5 in
Therefore, the missing dimension (length) of the prism is 1.5 inches.
HELPPPPPP how do you find the height of a right triangle
Answer:
The height of any right triangle is just simply the many units that are going up but it has to start from the right angle and upwards and that would be your height.
It may already give you a height so there is no need to worry if so.
Here, in this case the side on the very left is my height:
Answer:
Use Pythagorean Theorem
Step-by-step explanation:
a²+b²=c²
You need to find the height, which means you have a and c. You square a and c, subtract a from c, then find the square root of that difference. Now you have b.
EXAMPLE:
a=3, c=6
3²+b²=6²
9+b²=36
-9 -9
b²=27
sqrt of 27 is 5.2. So the side is 5.2
---
hope it helps
Find the quotient of 3/4 and 5/6.
Give your answer as a fraction in its simplest form.
The quotient of 3/4 and 5/6, expressed in its simplest form, is 9/10 .To find the quotient of fractions, we need to divide the numerator of one fraction by the denominator of the other fraction.
To simplify the process, we can convert the division into multiplication by taking the reciprocal of the second fraction. The reciprocal of a fraction is obtained by interchanging the numerator and the denominator. So, the reciprocal of 5/6 is 6/5.
Now, we can multiply the fractions:
3/4 * 6/5 = (3*6)/(4*5) = 18/20
However, we need to simplify the fraction to its simplest form. To do this, we find the greatest common divisor (GCD) of the numerator and denominator, which is the largest number that divides both without leaving a remainder. In this case, the GCD of 18 and 20 is 2.
By dividing both the numerator and denominator of 18/20 by 2, we get the simplest form of the fraction:
18/20 ÷ 2/2 = 9/10
The quotient of 3/4 and 5/6, expressed in its simplest form, is 9/10.
It's important to note that simplifying fractions involves dividing both the numerator and denominator by their greatest common divisor. This ensures that the fraction is in its simplest form, where the numerator and denominator have no common factors other than 1.
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Determine whether the lines are parallel or identical. 6
x−9
= −3
y+2
= 5
z+7
−12
x+9
= 6
y−7
= −10
z+22
The lines are parallel. The lines are identical.
the lines are parallel.
To determine whether the lines are parallel or identical, we can compare the direction vectors of the lines.
For the first line, we have the direction vector:
d₁ = (6, -3, 5)
For the second line, we have the direction vector:
d₂ = (12, 6, -10)
If the direction vectors are proportional, then the lines are parallel. If the direction vectors are equal, then the lines are identical.
To check for proportionality, we can compare the components of the direction vectors:
d₁ = (6, -3, 5)
d₂ = (12, 6, -10)
To check if d₁ and d₂ are proportional, we can see if the ratios of their corresponding components are equal:
6/12 = -3/6 = 5/-10
Simplifying, we get:
1/2 = -1/2 = -1/2
Since the ratios are equal, the direction vectors are proportional, which means the lines are parallel.
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suppose that marv and patricia will each take a covid test, and that the probability that both will test positive is 0.15. what is the probability that one or more of them tests negative? group of answer choices 0.015 0.15 1.5 0.85 it depends on the probability model used
The probability that both Marv and Patricia will test positive is 0.15. Therefore, the answer is 0.85.
Given that the probability that both Marv and Patricia will test positive is 0.15, we can find the probability that one or more of them tests negative using the complement rule.
The complement rule states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring. In this case, the event is both Marv and Patricia testing positive.
Probability of one or more testing negative = 1 - Probability of both testing positive
Probability of one or more testing negative = 1 - 0.15 = 0.85
So, the probability that one or more of them tests negative is 0.85.
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dr. sanchez conducts a simple random sample of 500 men who became fathers for the first time in the past year. he finds that 23% of them report being unsure of their ability to be good fathers, plus or minus 4%. if dr. sanchez increased his sample size to 1,000, which of the following would happen?
If Dr Sanchez increased his sample size to 1,000, it is most certain that the margin of error would become smaller.
Why will be margin of error become smaller?The margin of error is the measure of the amount of random sampling error that exists in a survey's results. The larger the sample size, the smaller the margin of error. This is because a larger sample size reduces the amount of random variation in the data, making the estimates more accurate.
If Dr. Sanchez increases his sample size from 500 to 1,000, the margin of error will become smaller because the sample size is directly proportional to the margin of error.
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Multiply (x²+2x+3)(4x² - 2x + 1).
A. 4x+10x³ + 17x² + 8x+3
B. 5x²2 +4
C. 4x+6x³+9x² - 4x +3
D. 4x4 - 4x² + 3
Answer: C
Step-by-step explanation:
By expanding and combining like terms, you get 4x^4+6x^3+9x^2-4x+3, which is C. (Too complex, I don't want to type all the work I did on paper onto this)
Please help nowww thxx
The water of the cylinder cannot fill the container, since the cylinder has less volume. Lastly, there is no apparent mistakes.
How to determine if two volumes are equivalent?The rectangular container (\(V_{R}\)), in cubic inches, is full whether its volume is equal to the volume of the cylinder (\(V_{C}\)), in cubic inches. The volume formulae for both containers are described below:
Rectangular container\(V_{R} = w\cdot l \cdot h\) (1)
Where:
\(w\) - Width, in inches\(l\) - Length, in inches\(h\) - Height, in inchesCylinder\(V_{C} = \pi\cdot r^{2}\cdot h\) (2)
Where:
\(r\) - Radius, in inches\(h\) - Height, in inchesNow we proceed to determine the volume of each figure:
Rectangular container (w = 3.6 in, l = 3.6 in, h = 5.3 in)\(V_{R} = (3.6\,in)\cdot (3.6\,in)\cdot (5.3\,in)\)
\(V_{R} = 68.688\,in^{3}\)
Cylinder (r = 1.8 in, h = 5.3 in)\(V_{C} = \pi\cdot (1.8\,in)^{2}\cdot (5.3\,in)\)
\(V_{C} \approx 53.947\,in^{3}\)
The volume of the water in the cylinder is approximately 53.947 cubic inches. The water of the cylinder cannot fill the container, since the cylinder has less volume. Lastly, there is no apparent mistakes. \(\blacksquare\)
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