Answer:
280
Step-by-step explanation:
Give me a moment, I am still gathering my explanation
freight train cars in a train yard there are tank cars, boxcars, and flatcars. how many ways can a train be made up consisting of tank cars, boxcars, and flatcars? (in this case, order is not important.)
The number of ways can a train made up consisting of tank cars, box cas and flat cars is 166320
Total number of tank cars = 4
Total number of Box cars = 112
Total number of flat cars = 5
Here we have to apply the concept of combinations
Number of ways of selecting 2 tank car from 5 = [tex]4C_2[/tex]
= 4! / 2!( 4-2) !
= 6
Number of ways of selecting 5 Box cars from 12 = [tex]12C_5[/tex]
= 12! / 5!(12-5)!
= 792
Number of ways of selecting 3 flat cars from 7 = [tex]7C_3[/tex]
= 7! / 3!(7-3)!
= 35
Number of possible ways can a train be made up = 6 × 792 × 35
Multiply the numbers
= 166320
Therefore, the number of possible ways is 166320
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The given question is incomplete, the complete question is :
Freight Train CarsIn a train yard there are 4 tank cars. 12 boxcars, and 7 flatcars. How many ways can a train be made up consisting of 2 tank cars, 5 boxcars, and 3 flatcars?
32 children voted for thier favorite ice cream chocolate 3/8 so how may children voted for chocolate explanation
Multiplying the total number of children by the fraction that like chocolate yields [tex]32(3/8)=12[/tex]
question 17 suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. after hours of burning, a candle has a height of centimeters. after hours of burning, its height is centimeters. what is the height of the candle after hours? clears your work. undoes your last action.
For the required linear function , the height of the candle when the amount of time for burning a candle is 16 hours is equal to 18.8 centimeters.
Let 'h' be the height of the candle.
And 't' be the amount of time used for burning.
Required linear function is :
h = mt + c
When t = 8 hours , h = 20.4centimeters
20.4 = 8m + c ___(1)
When t = 19 hours , h = 18.2centimeters
18.2 = 19m + c ___(2)
Subtract (2) from (1) we get,
20.4 = 8m + c
18.2 = 19m + c
2.2 = -11m
⇒ m = -2.2 / 11
⇒ m = -0.2
Substitute in (1) we get,
20.4 = 8( -0.2 ) + c
⇒ c = 20.4 + 1.6
⇒ c = 22
Now , h = -0.2t + 22
When t = 16 hours
⇒ h = -0.2(16) + 22
⇒ h = -3.2 + 22
⇒ h = 18.8 centimeters
Therefore, the height of the candle when amount of time of burning is 16 hours is equal to 18.8 centimeters.
The above question is incomplete, the complete question is:
Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 8 hours of burning, a candle has a height of 20.4 centimeters. After 19 hours of burning, its height is 18.2 centimeters. What is the height of the candle after 16
hours?
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−3 + 5 + 6g = 11 − 3g
TYSM YALL
[tex] \: [/tex]
[tex]\frak{2 + 6g = 11 - 3g} [/tex][tex] \: [/tex]
[tex] \frak{6g + 3g = 11 - 2} [/tex][tex] \: [/tex]
[tex] \frak{9g = 9} [/tex][tex] \: [/tex]
[tex]\frak{ \: g = \frac{9}{9} } [/tex][tex] \: [/tex]
[tex] \frak{ \: g = \cancel\frac{9}{9} } [/tex][tex] \: [/tex]
[tex] \underline{ \boxed{\bold{ \red{\frak{g = 1}}}}}[/tex][tex] \: [/tex]
hope it helps!:)
Brian wants to buy some back to school clothes. He has $78 to spend. He buys 5 t-
shirts and has $25.50 left. How much does each shirt cost?
The answer is 10.5
First you need to subtract the ending cost (25.50) giving you $52.5
With that 52.5 just divide by the amount of shirts bought (5) and you get 10.5 per shirt.
Answer:
10.50
Step-by-step explanation:
you take 78 and subtract that by 25.50 which gives you how much money he spends on the 5 t-shirts. that will 52.50
now you know that he spends 52.50 on 5 t-shirts, so you divide that by 5 which gives you 10.50
hope it helps
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At the balloon dart booth, players are charged $1 for the chance to throw 3 darts, Prizes worth $4 each are awarded to players who pop at least 2 balloons. Last year, 4 out of 12 players popped 2 balloons, and 1 out of 12 players popped 3 balloons.
If the ratio of winners to players remains the same as last year, the balloon dart booth can expect to have 85 winners among 204 players and lose $136.
A ratio compares two quantities or values. In this case, the ratio we are interested in is the ratio of winners to players.
Last year, out of 12 players, 4 popped 2 balloons and 1 player popped 3 balloons. Therefore, the total number of players who won prizes was 4+1=5. The ratio of winners to players is 5/12.
To calculate the number of winners this year, we can use the same ratio. If we assume that the ratio of winners to players is constant, we can set up the following proportion:
(winners/players) = (5/12)
Let's solve for the number of winners among 204 players:
(winners/204) = (5/12)
winners = (5/12) * 204
winners = 85
Therefore, we can expect 85 winners among 204 players if the ratio of winners to players remains the same as last year.
Now let's calculate the potential earnings or losses for the booth. Each player pays $1 for three darts, so the booth will earn 204*1 = $204.
Out of the 204 players, we expect 85 winners. Each winner receives a prize worth $4, so the total cost of prizes is 85*4 = $340.
The booth earns $204 and spends $340 on prizes, resulting in a loss of $136.
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Complete Question:
At the balloon dart booth, players are charged $1 for the chance to throw 3 darts. Prizes worth $4 each are awarded to players who pop at least 2 balloons. Last year, 4 out of 12 players popped 2 balloons, and 1 out of 12 players popped 3 balloons.
If the ratio of winners to players is the same this year and 204 people play the game, how much money will the booth earn or lose?
Please help, I’ll give brainliest!!!!!!!!!!!!
The solution to the given system of equation is (-2,7) and (2, -1).
What is system of equation?A system of equations are the set of equations where the solution for these equations are the intersecting point between the equations.
The graph denotes the two equations in which one is line and another one is parabola.
These system equation has two solutions.
That is, the point where the curve and line intersect is the solution for the system.
In this graph, the line and the curve intersects at two points,
i.e., (-2,7) and (2, -1).
Hence, the solution to the given system of equation is (-2,7) and (2, -1).
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Which equations are true for the values of x, y, and z? Select three options.
2 lines intersect to form 4 angles. Clockwise, from top, the angles are: 65 degrees, x, y, z.
The equations that are true of the values x, y, and z are :
x degrees + 65 degrees = 180 degreesx degrees = z degreesy degrees = 65 degreesHow to find the equations ?The line that x degrees and 65 degrees is on, is a straight line which means that they will both add up to 180 degrees :
x degrees + 65 degrees = 180 degrees
x and z are congruent angles which means they are both the same angle measure.
y would be equal to 65 degrees because, just like x and z, y and 65 degrees are congruent.
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Options include:
x degrees + 65 degrees = 180 degreesx degrees = z degreesy degrees = 65 degreesx degrees= 65 degreesx degrees + y degrees + z degrees = 115 degrees2. Find the number of ways in which 9 different computer games can be shared out between Wendy, Jim and Hannah so that each person receives an odd number of computer games.
Using combinatorics, there are 1926 ways to distribute 9 different computer games among Wendy, Jim, and Hannah so that each person receives an odd number of games.
What is the number of ways the game is shared between themIf each person receives an odd number of games, then the number of games must be 1, 3, 5, or 7. There are four odd numbers to choose from.
We can use combinatorics to find the odd number in each turn.
Let's consider each odd number in turn.
If each person gets 1 game, then we are looking for the number of ways to choose 3 games out of 9 to distribute. This is simply the number of combinations of 3 things taken from a set of 9 things, which is 9C3, or (9!)/(3!6!) = 84.
If each person gets 3 games, then we are looking for the number of ways to choose 3 games out of 9 to distribute to one person. Once those games have been chosen, we are left with 6 games to distribute to the other two people. The number of ways to choose 3 games out of 9 is again 84, but we must multiply this by the number of ways to choose 3 games out of the remaining 6. This is 6C3, or (6!)/(3!3!) = 20. Therefore, the total number of ways to distribute 9 games with each person getting 3 games is 84*20 = 1680.
If each person gets 5 games, then we are looking for the number of ways to choose 5 games out of 9 to distribute to one person. Once those games have been chosen, we are left with 4 games to distribute to the other two people. The number of ways to choose 5 games out of 9 is 126, and the number of ways to choose 4 games out of the remaining 4 is 1. Therefore, the total number of ways to distribute 9 games with each person getting 5 games is 126*1 = 126.
If each person gets 7 games, then we are looking for the number of ways to choose 7 games out of 9 to distribute to one person. Once those games have been chosen, we are left with 2 games to distribute to the other two people. The number of ways to choose 7 games out of 9 is 36, and the number of ways to choose 2 games out of the remaining 2 is 1. Therefore, the total number of ways to distribute 9 games with each person getting 7 games is 36*1 = 36.
Adding up the number of ways to distribute the games in each case, we get 84 + 1680 + 126 + 36 = 1926.
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Write an expression to display a loss of 42 yards on the football field
Answer:
Step-by-step explanation:
An expression to display a loss of 42 yards on the football field would be: -42 yards.
The negative sign in front of the number 42 indicates a loss or a decrease in the yards, which represents a loss of 42 yards on the football field.
The instructions on a carton of chemicals call for mixing 144 fl oz of water, 24 fl oz of chemical No. 1, and 56 fl oz of chemical No. 2. How many quarts are
contained in the final mixture?
The final mixture contains 7 quarts.
What is Mixture?
A mixture is generated when more than one chemical is mixed. A mixture can be created in a variety of ways, including using a liquid, solid, or gaseous medium.
First, let's add up the amount of the three ingredients to find the total volume of the mixture:
144 fl oz + 24 fl oz + 56 fl oz = 224 fl oz
Now, we can convert fluid ounces to quarts:
1 quart = 32 fluid ounces
So, we can divide the total volume in fluid ounces by 32 to find the total volume in quarts:
224 fl oz / 32 fl oz/quart = 7 quarts
Therefore, The final mixture contains 7 quarts.
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please help asap thankyou
Answer:
A = 648π cm²
Step-by-step explanation:
the area (A) of a semicircle is half the area of a circle , then
A = [tex]\frac{1}{2}[/tex] πr² ( r is the radius ) , then
A = [tex]\frac{1}{2}[/tex] × π × 36² = [tex]\frac{1}{2}[/tex] × π × 1296 = 648π cm²
8x^{2}-8x8x
2
−8x from -6x^{2}-10x+4−6x
2
−10x+4.
The value of the equation 8x² - 8x + 2 -( 6x² - 10x + 4) is 2x² + 2x - 2.
How to illustrate the equationIt should be noted that an equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that
two or more components are considered in order to be able to describe the scenario.
It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.
The equation can be illustrated thus:
8x² - 8x + 2 -( 6x² - 10x + 4)
8x² - 8x + 2 - 6x² + 10x - 4
= 2x² + 2x - 2
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Differentiate: y = 2 + ln(3-2x)
Here are 2 points in the plane.
B
Explain how to construct a line segment that is half the length
of segment AB .
O Construct a new point and create an angle bisector.
Create two circles centered at each point to the other and make a line through their intersections to
cut it in half.
O
Link them with a segment, make a new point on it and make a circle centered at A and B to the new
point.
To construct a line segment that is half the length of segment AB, follow the steps below.
What is the intersection points of the circle?
The intersections of two circles determine a line known as the radical line. If three circles mutually intersect in a single point, their point of intersection is the intersection of their pairwise radical lines, known as the radical center.
Draw a straight line passing through points A and B.
Bisect the line segment AB at point C.
Draw a circle centered at point C with a radius equal to AC or BC.
The intersection points of the circle and the line passing through A and B will be points D and E.
The line segment DE will be half the length of segment AB.
Therefore, To construct a line segment that is half the length of segment AB, follow the steps above.
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Find the slope of the line graphed below.
Answer:
the slope is -6/-5
Find the sum of 2√5 and 3√7
Answer:
the sum of 2rude 5 is 4.47-(answer)and the sum of 3 rude 7 is 7.79-(answer).
Hi there, here's your answer:
Given the question [tex]2\sqrt{5} + 3\sqrt{7}[/tex]
Since these two roots have no common factors, we can either leave the expression as it is, or simplify using the values of the roots.
In which case, [tex]\sqrt{5} = 2.236[/tex] and [tex]\sqrt{7} = 2.645[/tex]
On simplifying, we get
[tex]2\sqrt{5}[/tex] = 2 × 2.236 = 4.472
And
[tex]3\sqrt{7}[/tex] = 3 × 2.645 = 7.935
Thus, the sum will be 4.472 + 7.935 = 12.407
Hope it helps! Please mark as Brainliest!
3
Type the correct answer in each box. Use numerals instead of words.
Consider this expression.
The equivalent expression to -4x² + 2x - 5(1 + x) is given as follows:
-4x² - 3x - 5.
How to obtain the equivalent expression?The expression for this problem is defined as follows:
-4x² + 2x - 5(1 + x)
To obtain the equivalent expression, we apply the distributive property to -5(1 + x) as follows:
-5(1 + x) = -5 - 5x.
Then the expression is given as follows:
-4x² + 2x - 5 - 5x.
Combining the like terms, we have that the expression is given as follows:
-4x² - 3x - 5.
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Can someone help me please?
Answer:
JGK = 29 degrees
Step-by-step explanation:
i hope this helped :)
An experiment consists of tossing a coin and casting a die then observing the outcomes. Describe an appropriate sample space for this experiment.
A fair coin and a fair six-sided die, the sample space can be represented as:
{ (H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6) }
where H represents heads and T represents tails for the coin toss, and the numbers 1 through 6 represent the numbers on the die.
The sample space for this experiment can be described as the set of all possible outcomes of the coin toss and die cast. One way to represent the sample space is to use the Cartesian product of the sample space for the coin toss and the sample space for the die cast.
where H represents heads and T represents tails for the coin toss, and the numbers 1 through 6 represent the numbers on the die.
Each element in this sample space represents a possible outcome of the experiment, where the first element represents the outcome of the coin toss and the second element represents the outcome of the die cast. This sample space contains 12 possible outcomes, each with an equal probability of 1/12.
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Three friends, Martin, Tyreese, and Braydon, are collecting donations to help in their community's clean-up initiative. Their total contribution goal is represented by the expression 8x2 − 4xy + 9. The friends have already collected the following amounts: Martin: 3xy + 17 Tyreese: x2 Braydon: 2x2 − 6 Which expression represents the amount of money the friends still need to collect to meet their goal? 11x2 −xy + 20 5x2 − xy + 20 5x2 − 7xy − 2 3x2 + 3xy + 11
The expression that represents the amount of money the friends still need to collect to meet their goal is 5x² - 7xy + 20. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
The four fundamental mathematical operations that can be used to express any real number are referred to as "arithmetic operations" in mathematics. The four operations are addition, subtraction, division, and multiplication.
We are given the total contribution goal as 8x² - 4xy + 9
Amounts collected by:
Martin = 3xy + 17
Tyreese = x²
Braydon = 2x² - 6
So, the total amount collected till now is
(3xy + 17) + x² + (2x² - 6) = 3x² + 3xy - 11
Amount left to be collected is
⇒(8x² - 4xy + 9) - (3x² + 3xy - 11)
⇒8x² - 4xy + 9 - 3x² - 3xy + 11
⇒5x² - 7xy + 20
Hence, the expression is 5x² - 7xy + 20.
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Como puedo resolver esto?
- x - y = 4
The points on the graph of the equation represent the solution set to the equation.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is the equation as -
- x - y = 4
The given equation is -
- x - y = 4
x + y = 4
The graph of the given equation will represent a straight line. All the points on the line represent the solution set to the equation.
Therefore, the points on the graph of the equation represent the solution set to the equation.
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{Question in english -
How can i solve this?
- x - y = 4}
the diameter of a colorado blue spruce tree that is years old is inches. what is the average diameter of a colorado blue spruce in its first ten years (that is, from to )? give your answer to two decimal places. just give the number, don't type the units.
A Colorado blue spruce's first ten years have an average diameter of 0.62 inches.
Measure the diameter of the tree in its first ten years and divide it by 10 to determine the average diameter of a Colorado blue spruce in its first ten years. The outcome is the tree's average diameter during its first ten years. Measure the diameter of the tree in its first ten years and divide it by 10 to determine the average diameter of a Colorado blue spruce in its first ten years. The outcome is the tree's average diameter during its first ten years. For instance, if a Colorado blue spruce is five years old, you would calculate its diameter and multiply it by 10. You will then know the tree's typical diameter for the first ten years. Any age of Colorado blue spruce tree can use the same calculation. Depending on the age of the tree, a Colorado blue spruce's first ten years' average diameter will vary. The average diameter will be greater if the tree is older than ten years. The average diameter will be less, however, if the tree is less than 10 years old. In general, a Colorado blue spruce's first ten years have an average diameter of 0.62 inches.
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A water tower is 16 meters tall. Close by, there is a crane that is 24 meters tall. If the water tower's shadow is 30 meters long, how long is the crane's shadow?
Answer:
Tje answer is 36
Step-by-step explanation:
16-30=14
24+14=-36
What is the sum of 3 of the interior angles of a regular pentagon?
540° is your answer!
Use substitution to solve the system. +3x5y = 7 y = +2x4
Answer: To solve the system of equations using substitution, we'll start by rearranging one of the equations so that one of the variables can be expressed in terms of the other. In this case, we'll rearrange the second equation to find y in terms of x.
y = 2x + 4
Next, we'll substitute this expression for y into the first equation:
+3x + 5(2x + 4) = 7
Expanding the right-hand side:
+3x + 10x + 20 = 7
Combining like terms:
13x + 20 = 7
Subtracting 20 from both sides:
13x = -13
Dividing both sides by 13:
x = -1
Finally, we'll use the expression we found for y in terms of x to find the corresponding value of y:
y = 2x + 4
y = 2(-1) + 4
y = -2 + 4
y = 2
So the solution to the system is (x, y) = (-1, 2).
Step-by-step explanation:
lily is saving up to buy a cellphone. she needs to save at least $300 before she is able to buy the phone. her grandfather gives her $40, and she earns $65 tutoring after school each week. write an inequality for the number of weeks lily will need to save to have at least $300, and describe the solutions.(2 points)
Inequality for the number of weeks lily will need to save to have at least $300 is 40 + 65*x >= 300 and 4 week needed to buy the cellphone.
The phenomenon of an unfair and/or unequal distribution of opportunities and resources among the people who make up a society is referred to as inequality. To different people and in various contexts, the word "inequality" may mean different things. Additionally, inequality has distinct yet overlapping social, economic, and geographic dimensions. The conflict between the normative concept of "deservingness" and the moral ethics of equity and social justice, on the one hand, and on the other, further complicates discussions about inequality. Inequalities that can be seen both within and between social groups have come to the forefront of public consciousness in recent years. The growing realization that inequality is systemic and ingrained in various socioeconomic and political structures is the result of this awareness. The contributions of geographers to the subject.
she needs to save at least $300 before she is able to buy the phone and
her grandfather gives her $40 so she need 300 - 40
and she earns $65 tutoring after school each week so until she will not have 260 she not able to buy.
40 + 65*x >= 300
65x >= 260
x >= 260/65
x >= 4
4 week needed.
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A tree that is 18 feet tall is growing at a rate of 2 feet each year. A different tree that is 20.5 feet tall is growing at a rate of
3/4
feet each year. At this rate, when will the trees be the same height? What will
the height of the trees be?
The trees will be the same height in 2 years and the height of these trees will be 22 ft.
Linear Expression
A linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=x+10. Where:
m= the slope.
b= the constant term that represents the y-intercept
For the given example: m=1 and b=10.
For solving the question you should convert the given text into an algebraic expression.
Tree01= 18+2*y
Tree02= 20.5+0.75*y (Note that 3/4=0.75)
y= number of years
Therefore,
18+2*y=20.5+0.75*y
2y-0.75*y=20.5-18
1.25y=2,5
y=2
Thus, at 2 years the trees will be the same height.
When y=2, you have:
Tree01= 18+2*y= 18+2*2=18+4=22
Tree02= 20.5+0.75*y =20.5+1.5=22
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Which collection of three side lengths WILL NOT form a triangle?
10 in, 12 in, 15 in
10 in, 15 in, 6 in
4 in, 5 in, 10in
9in, 16 in, 8 in
The collection of 4 in, 5 in, and 10in of three side lengths will not form a triangle.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.
Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know, A triangle has a property that the sum of any two sides is always greater than the third side and the difference between any two sides is smaller than the third side.
From the given options if we observe the third option,
4 + 5 should be greater than 10 but it is not therefore, It is the correct option.
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Question 7(Multiple Choice Worth 1 points)
(06.02 MC)
Three friends, Martin, Tyreese, and Braydon, are collecting donations to help in their community's clean-up initiative. Their total contribution goal is represented by the expression
7x²-4xy+8. The friends have already collected the following amounts
Martin: 5xy + 16
Tyreese: x²
Braydon: 4x²-7
Which expression represents the amount of money the friends still need to collect to meet their goal?
A.2x²-9xy-1
B.2x² + xy +17
C.5x²+5xy+9
D.12x² + xy + 17
The algebraic expression that represents the amount that they still need to raise is given as follows:
A. 2x² - 9xy - 1.
How to obtain the algebraic expression?The total amount that the three friends want to raise is defined as follows:
7x² - 4xy + 8.
The total amount raised is obtained adding the amounts raised by each of the friends, as follows:
5xy + 16 + x² + 4x² - 7 = 5x² + 5xy + 9.
Then the remaining amount to be raised is obtained by the subtraction of the total amount by the amount raised, as follows:
7x² - 4xy + 8 - (5x² + 5xy + 9) = 7x² - 5x² - 4xy - 5xy + 8 - 9
7x² - 4xy + 8 - (5x² + 5xy + 9) = 2x² - 9xy - 1.
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