The maximum occupancy of the commuter train is 568 passengers
How to determine the maximum occupancy of the commuter train?The given parameters can be represented using the following table of values
1 2
Passenger 56 40
Cars 8 3
The maximum occupancy of the commuter train is then calculated as
Maximum occupancy = Sum of (Passengers * Cars)
So, we have
Maximum occupancy = 56 * 8 + 40 * 3
Evaluate the products in the above equation
So, we have
Maximum occupancy = 448 + 120
Evaluate the sum in the above equation
So, we have
Maximum occupancy = 568
Hence, the maximum occupancy of the commuter train is 568 passengers
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need help with this question, pls
Colton is 1.55 meters tall. At 1 p.m., he measures the length of a tree's shadow to be 44.35 meters. He stands 39 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
If Colton is 1.55 meters tall. At 1 p.m., he measures the length of a tree's shadow to be 44.35 meters. the height of the tree to the nearest hundredth of a meter. is 12.85 meters.
HeightFirst step is to find the distance that he is horizontally from the top of the shadow
Distance = 44.35 meters - 39 meters
Distance = 5.35 meters
Second step is to make use of equal proportion and find the height
5.35/ 1.55 = 44.35/x
5.35x = 1.55 × 44.35
x= 1.55 × 44.35 /5.35
x= 12.849
x= 12.85 meters (Approximately)
Therefore If Colton is 1.55 meters tall. At 1 p.m., he measures the length of a tree's shadow to be 44.35 meters. the height of the tree to the nearest hundredth of a meter. is 12.85 meters.
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Seven times the sum of 23 and a number
Answer: 161+7n
Explanation: Let the number be n.
7(23+n)
=161+7n
Hope this helps you! Have a great day!!!!! :) :D
HELP HELP HELP HELP HELPPPPPPPPPPPPPPPP!!!!!!!!!!
x=3.4
Im writing this bc the app says the answer is too short
what is 3 (3/8) * -7/3
Answer:
-21/8
Step-by-step explanation:
3 (3/8) * -7/3
= 9/8 * -7/3
= 3/8 * -7
= -21/8
Simplify. 4√32 + 4√128
The answer after simplification is 48[tex]\sqrt{2}[/tex]
We are required to simplify two values in square root form
Given values are :
4[tex]\sqrt{32}[/tex]+4[tex]\sqrt{128}[/tex]
4([tex]\sqrt{32}[/tex]+[tex]\sqrt{128)}[/tex]
Now we know that
32= [tex]2^{5}[/tex]
128=[tex]2^{7}[/tex]
Putting these values inside the square root,
we know that square root is to the power 1/2
our equation becomes
4([tex]\sqrt{2^{5} } +\sqrt{2^7[/tex])
removing the square root,
4([tex]2^{5/2}+2^{7/2}[/tex])
Now we know that 4 is 2 to the power 2 , and taking 2^5/2 as common, we get:
[tex]2^{2}*2^{5/2}(1+2^{2/2})[/tex]
16[tex]\sqrt{2}[/tex](3)
=48[tex]\sqrt{2}[/tex]
The answer after simplification is 48[tex]\sqrt{2}[/tex]
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Write an inequality that represents the graph.
A number line from negative 0 to 5. There are 9 evenly spaced marks between negative 0 and 5. The number line is shaded left of a closed circle at negative 4.5.
Inequality:
Answer: x ≤ 4.5
Step-by-step explanation:
Since the inequality goes left and has a closed circle it would be x ≤ 4.5
re arrange the equation
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[tex]\displaystyle\\Answer:\ I=\sqrt{\frac{M}{7} }[/tex]
Step-by-step explanation:
How would I solve an absolute value this:
|2m+3/5|=|1-3m/6|
I’m really stuck on how to remove the 5 and 6 from the equations separately.
m = [tex]\frac{4}{25}[/tex] 0r m = [tex]-\frac{16}{15}[/tex]
|2m+3/5|=|1-3m/6|
Split into two equations
⇒[tex]2m + \frac{3}{5} = 1 - \frac{3m}{6}[/tex] or
⇒[tex]2m + \frac{3}{5} =-( 1 - \frac{3m}{6})[/tex]
[tex]2m + \frac{3}{5} = 1 - \frac{3m}{6}[/tex]
multiply both side of the equation by the common denominator
⇒2m × 30 + [tex]\frac{3 * 30}{5}[/tex] = 30 - [tex]\frac{3 m * 30}{6}[/tex]
⇒2m×30 + 18 = 30 -15m
⇒60 m + 18 = 30 -15m
⇒60m + 15m = 30 - 18
⇒75m = 12
⇒m = [tex]\frac{12}{75}[/tex]
⇒m = [tex]\frac{4}{25}[/tex]
[tex]2m + \frac{3}{5} =-( 1 - \frac{3m}{6})[/tex]
reduce the fraction
⇒[tex]2m + \frac{3}{5} =-( 1 - \frac{m}{2})[/tex]
remove brackets
⇒[tex]2m + \frac{3}{5} = - 1 + \frac{m}{2}[/tex]
multiply both side of the equation by the common denominator
⇒2m × 10 + [tex]\frac{3 * 10}{5}[/tex] = -10 + [tex]\frac{ m * 10}{2}[/tex]
⇒2m × 10 + 6 = -10 + 5m
⇒20 m + 6 = - 10 + 5m
⇒20m - 5m = - 10 -6
⇒15m = -16
⇒m = [tex]-\frac{16}{15}[/tex]
we get,
m = [tex]\frac{4}{25}[/tex] 0r m = [tex]-\frac{16}{15}[/tex]
Equations with fractions involve solving equations where the unknown variable is part of the numerator and/or the denominator of the fraction.
To solve equations with fractions we need to work out what the value of the unknown variable. We solve equations by using the “balancing method” by applying the inverse operation to both sides of the equation.
The inverse operation of addition is subtraction.
The inverse operation of subtraction is addition.
The inverse operation of multiplication is division.
The inverse operation of division is multiplication.
How to solve equations with fractions
In order to solve equations with fraction:
Identify the operations that are being applied to the unknown variable.
Apply the inverse operations, one at a time, to both sides of the equation.
Write the final answer, checking that it is correct.
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What’s the answer!!!!!!!!!
Answer: 26
Step-by-step explanation:
(-4)(-2)-6(2-5)=
-(-8)-6*2-6*(-5)=
-(-8)-12-(-30)=
8-12+30=
30+8-12=
38-12=26
Y=-4x-2 fill in the table using this function rule
What are the domain and range of the function the quantity of x squared minus 4 x minus 12, all over x plus 2? domain is x is all real numbers where x does not equal negative 2 comma range is y is all real numbers where y does not equal negative 8 domain is x is all real numbers where x does not equal 4 comma range is y is all real numbers where y does not equal negative 2 domain is x is all real numbers where x does not equal 2 comma range is y is all real numbers where y does not equal 8 domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal 2
The domain is all real numbers where x does not equal -2 and the range is all real numbers where f(x) does not equal -8
What is the domain and the range of a function?The domain of the function is the set of input values of the graph while the range of a function is the set of output values of the graph.
How to determine the domain and the range of the function?The given parameter is:
f(x) = (x^2 - 4x - 12)/(x + 2)
Based on the definition above, the range of a function is the set of y values of the graph while the domain is the set of x values of the graph
Set the denominator not equal to 0
So, we have
x + 2 ≠ 0
Evaluate
x ≠ -2
This means that the domain is all real numbers where x does not equal -2
For the range, we use a graphing calculator
From the graphing calculator, we have
f(x) ≠ -8
This means that the range is all real numbers where f(x) does not equal -8
Hence, the domain is all real numbers where x does not equal -2 and the range is all real numbers where f(x) does not equal -8
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Complete question
What are the domain and range of the function f(x) = (x^2 - 4x - 12)/(x + 2)
Solve each equation. Round to the nearest ten-thousandth. Check your answers.
2x=3
After solving the equation, x = 3/2 is the value of x in 2x = 3.
⇒ 2x = 3
⇒ x = 3/2
How to solve an equation?
To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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1/4(4)-5(6)-2 solve step by step.
Answer:
[tex] \rightarrow \sf \: −31[/tex]
Step-by-step explanation:
[tex] \rightarrow \sf \frac{1}{4} (4)-5(6)-2[/tex]
[tex] \rightarrow \sf \: \frac{1}{4} \times \frac{4}{1} - 30 - 2[/tex]
[tex] \rightarrow \sf \: 1 - 30 - 2[/tex]
[tex] \rightarrow \sf \: - 31[/tex]
Select the expression that matches the scenario correctly. On January 1, the high temperature was 81 F in Kona, Hawaii the low temperature was -29 F in Barrow, Alaska. What was the difference between the two temperatures?
A. -29 + 81
B. |89 - 21|
C. |81 - (-29)|
D. 36 divided 6
Option c is correct i.e., |81 - ( -29)|
On January 1, the high temperature was 81 F in Kona and the low temperature was - 29 F in Barrow.
We have to find the difference between the two temperatures.
So the difference between is
= 81 - (- 29)
= 81 + 29
= 110
Therefore the difference the two temperatures is 110.
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a book weighs 4 3/8 pounds. a store needs to mail 5 copies of the book.
create an equation to find how many pounds the books weigh in all.
Graham drove 423 miles in 13 hours.
a. How many miles did he drive in one hour?
Bron
b. How many hours did he take to drive one mile?
Graham drove 32.58 miles in one hour and it took 1.84 minutes to drive a mile
Miles Graham drove in 13 hours = 423 miles
Unitary method: A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. It is a technique that we employ for the majority of math calculations.
Part a:
Miles driven in one hour = Total miles driven/Total no. of hours taken
= 423/13 = 32.58 miles
Part b:
Hours took to drive a mile = Total no. of hours taken/ Total miles driven
= 13/423 = 0.030 hours or 1.84 minutes
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HELP ILL GIVE U A LOT OF POINTS
Answer/Step-by-step explanation:
f(6) = 3x² - 5
f(6) = 3(6)² - 5
f(6) = 3(36) - 5
f(6) = 108 - 5
f(6) = 103
(x, y) = (6, 103)
I hope this helps!
What is the decimal equivalent to 2/9
Answer: The decimal equivalent to 2/9 = 0.22
Step-by-step explanation:
Define Decimal equivalent :
The decimals with the same number of decimal places are called like decimals. Equivalent decimals are decimal numbers that have the same value. For example, 3.42, 6.05 are like decimals as they have two decimal places. For example, 0.3 and 0.30 are equivalent decimals as they present the same value.
How do you find the equivalent decimal?
To find the decimal equivalent of a fraction, divide the numerator by the denominator. Because the number in the numerator is smaller than the number in the denominator, you have to place the decimal point after it and add zeros. Then complete long division.
Given data,
Find the decimal equivalent to 2/9.
To get a fraction into a decimal you have to divide the fraction. I was taught since the 2 is the numerator, it gets divided out of and the 9 is what you're dividing the 2.
so, we can write,
x = 2/9
where, numerator = 2
denominator = 9
Then, x = 2/9 = 0.22
Therefor, the decimal equivalent to 2/9 = 0.22
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Three orders are placed at a sandwich shop. Four sandwiches, two beverages, and
one salad costs $40; two sandwiches, one beverage, and two salads costs $26; and
three sandwiches, three beverages, and two salads costs $38. How much does each
item cost?
The respective prices are given below as
The price of the sandwich is 20/3 dollars.
The salad may be purchased for a price of $16/3.
There is a fee of $2 for the drinks.
How can you build equations that are simultaneous?Let's say that the price of the sandwich is x.
Allow the price of salad to equal y.
Allow the price of drinks to equal z.
The new total for this meal is $46. It includes three sandwiches, three beers, and two salads. Thus;
3x + 3y + 2z = 40 ——- (eq 1)
The price of $29 covers two sandwiches, two drinks, and one salad.
Thus;
2x + 2y + z = 26 ——-(eq 2)
It will cost you $54 for four sandwiches, one drinks, and three salads. Thus;
4x + y + 3z = 38 ———-(eq 3)
The following are the results of concurrently solving the three equations:
x = 20/3
y = 16/3
z = 2
Therefore, the following is how much each item costs:
There is a charge of $20/3 for the sandwich.
The salad may be purchased for a price of $ 16/3.
There is a fee of $2 for the drinks.
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what 30x30x1,000 bydb3yuehwu
The question is 0.65 into a fraction can anyone help me figure this out?
Answer:
If 0.65 is a decimal, then as a fraction it would be 65/100. This can be simplified though. 65 and 100 are both divisble by 5.
100 divided by 5 is 20 and 65 divided by 5 is 13. This is as simplified as it can go, so the answer is 13/20.
For clarification the answer is
13/20
Step-by-step explanation:
fill in the boxes please (gradients)
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Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the gradient and c the y- intercept )
y = 7x , that is y = 7x + 0 ← in slope-intercept form
with gradient 7 and y- intercept (0, 0 )
--------------------------------------------------------------
y = 6x - 8 ← is in slope- intercept form
with gradient 6 and y- intercept (0, - 8 )
The length of a rectangular garden is 5 feet less than twice its width. If the total distance around the garden is 44 feet, what are the length and width of the garden?
Answer: 78
Step-by-step explanation: multiply 44 by 2 because there are two sides on the rectangle and then you add 5 and 5 because yet again there are two sides so when you get your answer subtract 10 from the 88 and then you get 78 there is your explanation and equation
Rectangle with perimeter 44 ft has its length and breadth 13 ft and 9 ft respectively.
Dimension of rectangle : 13 × 9
Given, that perimeter of rectangle is 44 ft .
Now, perimeter of rectangle is given by:
P = 2(l + b)
l = Length of rectangle .
b = Breadth of rectangle.
Let the breadth of rectangle be 'x' m.
Then length will be (2x -5) ft.
Substitute the values in the perimeter formula,
[tex]44 = 2(x + 2x -5)\\22 = 3x -5\\x = 9[/tex]
Thus the breadth of rectangle is 9 ft .
Length of rectangle is 5 ft less than twice its breadth.
Length = 2(9) - 5
Length = 13 .
Therefore the dimensions of rectangle is 13 × 9.
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10) Your friend has a play tepee. The tepee
has a radius of 4 feet and a height of 6
feet. What is the volume of the tepee?
The volume of the tepee is 100.48 feet³
The formula for the volume of tepee is same as the volume of cone which is given as :
V = 1/3 πr²h (1)
where V = volume
r = radius of the tepee
h = height of the tepee
According to the question we have been given that
radius = 4 feet
height = 6 feet
Putting the required values in equation (1) we get
V = 1/3 π (4)²(6)
= 1/3 (3.14)(96)
= 301.44/3
= 100.48 feet³
Hence the volume of the tepee is 100.48 feet³
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-64-32+83-13???!!!!
Answer:20
Step-by-step explanation:
Find the amount in a continuously compounded account for the given conditions.
principal: $ 6000 ; annual interest rate: 6.8 % ; time: 10 years
The amount after 10 years is $11,842.43
In continuous compounding the number of times by which compounding occurs tends to infinity.
In order to calculate the amount use the following formula
A= Pe^rt
where P represents the initial amount, e is the mathematical constant having value 2.7182, r is the rate of interest and t is the time period
Here the principal amount is $6000, r is 6.8 and time period t is 10 years
A = $6000 x 2.718⁽¹⁰ ˣ ⁶·⁸ %⁾
A = 6000 x 2.718⁽¹⁰ ˣ ⁶·⁸÷¹⁰⁰⁾
A = 6000 x 2.718 x 0.68
A = $ 11,842.43
Therefore the total amount calculated after 10 years is $ 11,842.43
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408 x 291 show work pls
Answer: 118728
Step-by-step explanation:
You can just simply find this answer using a calculator.
The endpoints of CD are C(-8, -1) and D(2,4). Find the coordinates of midpoint M
Answer:
M(-3;3/2)
Step-by-step explanation:
substitute in this formula of finding midpoint coordinate:M(x1+x2÷2;y1+y2÷2)
+
Using Double Numberlines for Ratios
Use the double numberline to solve the problems.
1)
At a school fundraiser for every 6 boxes of
chocolate sold you earn 4 points. If you were
to sell 42 boxes, how many points would you
have earned?
boxes
points
Name:
1.
M
Answers
Answer:
28 points
Step-by-step explanation: