Answer:
Let the weight of Train A be x tons. Then the weight of Train B is 537 - x tons. We know that the difference between their weights is 421 tons, so we can set up an equation to solve for x:
x - (537 - x) = 421
Expanding the right side:
x - 537 + x = 421
Combining like terms:
2x = 958
Dividing both sides by 2:
x = 479
So Train A weighs 479 tons and Train B weighs 537 - 479 = 58 tons.
Step-by-step explanation:
How do I find the value of two numbers if their sum is 12 and their difference is 4?
Answer:
The value of two numbers if their sum is 12 and their difference is 4 are 8 and 4.
Step-by-step explanation:
I hope this helped
what is the answer ?
In the triangle that we have here cos 42 degrees is equal to sin 48
How to solve for the angleThis was simply solved using the calculator
cos 42 = 0.7431
sin 42 = 0.6691
cos 48 = 0.6691
sin 48 = 0.7431
From the above we can see that the value of cos 42 and sin 48 returned the same digits at 0.7431
Hence the value of cos 42 is sin 48 degrees
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Araceli uses 8. 7 pints of blue paint and white paint to paint her bedroom walls. 1/4
of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?
Express your answer in fraction and decimal form. Solve on paper. Then check your work on Zearn
The amount of white paint did she use to paint her bedroom walls is 6 21/40 or 6.525 pints.
To find the amount of white paint used, we first need to find the amount of blue paint used. Since 1/4 of the total amount of paint is blue, we can multiply the total amount of paint by its fraction, 1/4, to find the amount of blue paint:
Blue paint = 8.7 pints × 1/4 = 87/40 = 2.175 pints
Now, to find the amount of white paint used, we can subtract the amount of blue paint from the total amount of paint:
White paint = 8.7 pints - 2.175 pints = 261/40 = 6.525 pints
So, Araceli used 6.525 pints of white paint to paint her bedroom walls.
In fraction form, this can be written as 6525/1000 pints, or 6 21/40 pints.
In decimal form, it is simply 6.525 pints.
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-) Doreen Short was
looking over the
repayment schedule for
a loan of $40,000.00 at
9% interest for 4 years
with a monthly payment
of $995.40. The loan is
paid off with payment
30 with a previous
balance of $17,565.74.
The final payment and amount saved based on the given interest are respectively;
a) $17697.5 and $1215.12
b) $12377.80 and $562.40
How to find the simple Interest?The equation for the interest is mathematically expressed as:
I = balance*percentage/12
Therefore:
I = 17565.74 * 0.09/12
I = 131.7
The final payment is; F = I + B
F = 131.7 + 17,565.74
F = 17697.5
Amount saved
A.S = (19 * 995.40) - 17697.5
A.S = 1215.12
b) For the loan is paid off with payment 36 with a loan balance of $12,285. 66
I= balance*percentage/12
Therefore:
I = (12,285.66 * 0.09)/12I92.142
I = 92.142
Final payment
F = I + B
F = 92.142 + 12377.80
F = 12377.80
Amount saved
A.S = (13 * 995.40) - 12377.80
A.S = $562.40
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The complete question is;
Doreen Short was looking over the repayment schedule for a loan of $40,000. 00 at 9% for 4 years with a monthly payment of $995. 40.
Find the final payment and amount saved if :
A. ) The loan is paid off with payment 30 with a previous balance of $17,565. 74
B. ) The loan is paid off with payment 36 with a loan balance of $12,285. 66
Your friend says, "We will each roll a die. If the highest number out of the two dice is a 5 or a 6, gaberil wins. And if the highest number out of the two dice is a 1, 2, 3, or 4, then justen win. Whoever wins the most out of ten tries, wins the taco. "
what is the that justen wins
The probability that Justen wins is 4/9.
Determine the probabilityThe probability that Justen wins is determined by the likelihood that the highest number rolled on the two dice is a 1, 2, 3, or 4. To find this probability, we can first calculate the probability that the highest number rolled is a 5 or 6, which is what would cause Gaberil to win.
The probability of rolling a 5 or 6 on one die is 2/6, or 1/3. The probability of rolling a 5 or 6 on both dice is (1/3) * (1/3) = 1/9.
However, we also need to account for the possibility that one die rolls a 5 or 6 and the other does not.
This can happen in two ways: either the first die rolls a 5 or 6 and the second does not, or the first die does not roll a 5 or 6 and the second does.
The probability of each of these scenarios is (1/3) * (2/3) = 2/9.
So the total probability of Gaberil winning is 1/9 + 2/9 + 2/9 = 5/9.
Since there are only two possible outcomes (either Gaberil wins or Justen wins), the probability of Justen winning is 1 - the probability of Gaberil winning. So the probability of Justen winning is 1 - 5/9 = 4/9.
Therefore, the probability that Justen wins is 4/9.
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A college student is paying for tuition through private loans. Two lenders have approved the student for a $25,000 loan. Offer 1: 5.99% annual simple interest, with a total account balance of $32,487.50 after a 60-month term Offer 2: 3.75% annual interest compounded monthly for a 66-month term Assuming no payments are made, what is the difference in the account balances at the end of the loan terms? Round your answer to the nearest penny. $1,245.00 $1,770.87 $2,964.36 $3,319.94
Answer:
$1770.87
Step-by-step explanation:
Formula; Simple Interest(I) = P × R × T/100
= $1770.87
If it takes 4 people 6 hours to build a wall how long will it take 3 people to complete the same task
Simplifier chacune des expressions suivantes et identifier la nature du nombre obtenu.
= 2 +
2
3
; =
2
5
+ 7; = (√3 + 1)(√3 − 1) ; = (√5 + 1)²
Answer:its 5
Step-by-step explanation: cuz
how to tell if an integral is convergent or divergent
what is the probability of three or fewer heads on four flips of a fair coin. enter the answer to four decimal places?
The probability of three or fewer heads on four flips of a fair coin is 0.375. This can be determined by calculating the probability of zero, one, two and three heads, which are 0.0625, 0.25, 0.375 and 0.25 respectively. The total of these probabilities is 0.375.
The probability of zero heads on four flips of a fair coin is 0.0625 (1/16).
The probability of one head on four flips of a fair coin is 0.25 (4/16).
The probability of two heads on four flips of a fair coin is 0.375 (6/16).
The probability of three heads on four flips of a fair coin is 0.25 (4/16).
The total probability of three or fewer heads on four flips of a fair coin is 0.375 (1/4).The probability of three or fewer heads on four flips of a fair coin is 0.375. This can be calculated by determining the probability of zero, one, two and three heads. The probability of zero heads is 0.0625, the probability of one head is 0.25, the probability of two heads is 0.375, and the probability of three heads is 0.25. When these probabilities are added together, the total probability of three or fewer heads on four flips is 0.375. This means that the probability of getting three or fewer heads on four flips of a fair coin is 0.375.
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A student is walking to school and sees a mirror on the ground.
She stops a short distance from the mirror to practice her Geometry.
She knows her own height and the height of the school. She also knows
the distance from the mirror to the school from a previous Geometry activity.
She would like to calculate the distance she is standing from the mirror.
The height of the school is 30 ft.
The distance from the school to the mirror is 50 ft.
The height of the student is 5.1 ft.
What is the distance d between the student and the mirror?
Show all your work
The distance between the student and the mirror is apprοximately 29.41 feet.
What do you mean by Distance?Distance is a numerical measurement of hοw far apart or how far away objects or lοcations are from each other. It is a physical quantity that is usually expressed in units such as meters, kilοmeters, miles, οr feet. Distance is a scalar quantity, meaning it οnly has magnitude and nο direction.
To sοlve the problem, we can use the similar triangles prοperty of geometry. Let's denοte the distance between the student and the mirrοr as d. Then, we can set up the follοwing proportion:
(student height + height of mirrοr) / distance frοm student to mirror = height of schοol / distance from mirrοr to school
Plugging in the given values, we get:
(5.1 + 0) / d = 30 / (50 + d)
Simplifying and sοlving for d, we get:
5.1d + 0 = 150
d = 29.41
Therefοre, the distance between the student and the mirrοr is apprοximately 29.41 feet.
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PLEASE HELP NEED SOON!!!!!!!!!!!! WILL GIVE BRAINLIEST TO BEST ANSWER!
do the following calculations
1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9 2. 11 > -2 Add 3 to both sides, then add 3, then add (-4) 3. -2 = -2 Subtract 6 from both sides, then 8, and then 2 4. -4 < 8 Divide both sides by -4, then by -2 5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
The expressions are evaluated below
How to evaluate the expressionsExpression 1: 4 < 7
Multiplying both sides by 3, 2, 4, and 9 respectively:
3 * 2 * 4 * 9 * (4 < 7)
864 < 1515
Expression 2: 11 > -2
Adding 3 to both sides, then adding 3, then adding (-4) respectively:
3 + 3 - 4 + (11 > -2)
13 > 0
Expression 3: -2 = -2
Subtracting 6 from both sides, then adding 8, then adding 2 respectively:
-2 + 6 + 8 + 2 = -2 + 6 + 8 + 2
14 = 14
Expression 4: -4 < 8
Dividing both sides by -4, then by -2 respectively:
-4/(-4 * -2) < 8/(-4 * -2)
-1/2 < 1
The operations performed on the inequalities in each question did not affect the inequality sig.
The truth of the inequality was also not affected by the operations in all cases.
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How much 30000 won to usd ?
The value of 30000 south korean currency is $25.50.
To convert 30000 South Korean Won to US Dollars, we can use the current exchange rate between the two currencies.
1. First, we need to find the current exchange rate between South Korean Won and US Dollars. As of September 9th, 2021, the exchange rate is 0.00085 USD per 1 South Korean Won.
2. Next, we can multiply the amount of South Korean Won we have by the exchange rate to find the equivalent amount in US Dollars.
30000 South Korean Won * 0.00085 USD/South Korean Won = 25.50 USD
3. Therefore, 30000 South Korean Won is equivalent to 25.50 US Dollars.
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help pls
1. Use the relationship PV = nRT to find the number of moles in an amount of gas when the
temperature is 299 K, the pressure is 3 atmospheres, and the volume is 5 liters
(R = 0.0821).
The number of moles is given by the equation n = 0.611 moles
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
PV = nRT be equation (1)
Divide by RT on both sides of the equation , we get
n = PV / RT
Now , when temperature T = 299 K
The value of pressure P = 3 atm
The value of volume V = 5 Liters
The universal gas constant R = 0.0821
Substituting the values in the equation , we get
n = ( 3 x 5 ) / ( 0.0821 x 299 )
On simplifying the equation , we get
n = 15 / 24.5479
n = 0.611 moles
Therefore , the number of moles is 0.611 moles
Hence , the equation is n = 0.611 moles
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What is the intermediate step in the form (x+a)2 = b as a result of completing the square for the following x^2=16x+8
The intermediate step in the form (x+a)2 = b is (x - 8)^2 = 72
How to determine the intermediate stepFrom the question, we have the following parameters that can be used in our computation:
x^2 = 16x + 8
Rewrite as
x^2 - 16x = 8
Take the coefficient of x
k = 16
Divide by 2
= 8
Square the quotient
= 64
So, we add 64 to both sides of the equation
So, we have
x^2 - 16x + 64 = 8 + 64
Express as squares and evaluate
(x - 8)^2 = 72
Hence, the intermediate step is (x - 8)^2 = 72
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PLEASE HELP! And show all steps!
Answer:2y32 is the answer u the graph line and some o f the sqaures to count it
Step-by-step explanation:
Two water balloons were launched into the air at different moments and collided. The water balloons were modeled by the quadratic functions: y = −7x2 + 26x + 3 and y = −6x2 + 23x + 5, where y represents the height in meters and x represents the time in seconds after the launch. What is the time, in seconds, that the balloons collided at the highest point? 2.0 seconds 2.25 seconds 2.5 seconds 2.75 seconds
The time it takes is 2 seconds
What is the time the balloons collided at the highest point?
To find the time that the balloons collided at the highest point, we need to find the vertex of the resulting quadratic function.
First, we can set the two functions equal to each other, since they represent the height of the two balloons at any given time:
-7x^2 + 26x + 3 = -6x^2 + 23x + 5
Simplifying and rearranging terms, we get:
-x^2 + 3x + 2 = 0
Now, we can use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -1, b = 3, and c = 2.
Plugging in these values, we get:
x = (-3 ± sqrt(3^2 - 4(-1)(2))) / 2(-1)
x = (-3 ± sqrt(1)) / (-2)
Simplifying further, we get:
x = (-3 ± 1) / (-2)
So, x can be either 1 or 2. However, we're only interested in the positive value for x since time cannot be negative.
Therefore, the time that the balloons collided at the highest point is:
x = 2 second
So, the correct answer is: 2.0 seconds
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: CC> Chapter 9: Mean> Section Exercises 9.2 > Exercise 13
13
Complete these two different sets of data so that they each have six values and a mean of 21.
20, 20.5, 20.5, 21.5, 21.5,
20, 21, 21, 21, 21,
Answer:
To complete the first set of data so that it has six values and a mean of 21, you can add the following values: 20, 20.5, 20.5, 21.5, 21.5, 21.
The mean of this set is calculated as follows: (20 + 20.5 + 20.5 + 21.5 + 21.5 + 21) / 6 = 21.
To complete the second set of data so that it has six values and a mean of 21, you can add the following values: 20, 21, 21, 21, 21, 22.
The mean of this set is calculated as follows: (20 + 21 + 21 + 21 + 21 + 22) / 6 = 21.
∠A and ∠B are vertical angles. If m∠A=(7x−18) ∘ and m∠B=(6x−8) ∘ , then find the measure of ∠A.
The measure of angle A is 52 degree.
What is the measure of angle A?Vertical angles are angles that are opposite of each other when two lines crosses, they are congruent.
Given that;
Angle A = ( 7x - 18 )∘Angle B = ( 6x - 8)∘Since vertical angles are congruent,
Angle A = Angle B
Plug in the given values
( 7x - 18 ) = ( 6x - 8)
Solve for x
7x - 18 = 6x - 8
7x - 6x = -8 + 18
x = -8 + 18
x = 10
Hence, angle A will be;
Angle A = 7x - 18
Plug in x = 10
Angle A = 7( 10 ) - 18
Angle A = 70 - 18
Angle A = 52°
Therefore, angle A is 52 degree.
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Keith's bookshelf has 5 shelves. If he has 262 books, estimate the number books he can put on each shelf by rounding the larger number to the neare hundred.
Answer:
52.40
Step-by-step explanation:
Given that,
Keith's bookshelf has 5 shelves.
He has 262 books.
To find the number of books he can put on each shelf.
[tex]required \\ number = \frac{Total Books}{Total Shelves}\\\\= \frac{262}{5} = 52.40[/tex]
Hence 52.40 is the right answer.
Answer:
you in BBC FDA's in BBC FDA's in just had not had not had not had on under end
Step-by-step explanation:
no exception
Which picture corresponds to the correct graph of the points A = (-2, -3), B = (4, 1)., C = (-2, 3), and D = (0, -1)?
The second graph given in the figure attached below is a correct representation of the given points.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given, few points on cartesian plane A = (-2, -3), B = (4, 1)., C = (-2, 3), and D = (0, -1)
The xy pairs of a cartesian point are written in parenthesis as follows: (x, y).
To graph a point, first determine where it lies on the x-axis, then determine where it lies on the y-axis, and lastly plot the intersection of these two axes.
Due to its location at the intersection of the x- and y-axes, the origin of the graph, also known as the point (0, 0), is the center of the diagram.
For point A(-2, -3)
Find the negative 2 on the x-axis and the negative 3 on the y-axis, for instance, to draw the point (-2, -3).
The same will go for the remaining three points.
Therefore, The second graph given in the figure attached below is a correct representation of the given points.
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1. Simplify each of the following.
a^4 divided by a^-2 multiplied by a^7
Find the area of the composite figure:
Please hurry!!
SOMEONE PLS HELPP FAST
picture below
The graph representing the association will be a negative linear association. Then the correct option is C.
What is the association?The form, direction, confidence, and outliers of an association (relationship) between two quantitative variables can be used to describe it. • A positive association exists when one variable increases as the other dependent variable.
There is no boundary and all the dots are widely dispersed if there is no association. Variational individuals who are part that the dots are close together but not in a straight line.
From the graph, the slope of the best line will be negative.
The graph representing the association will be a negative linear association. Then the correct option is C.
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A student is walking to school and sees a mirror on the ground.
She stops a short distance from the mirror to practice her Geometry.
She knows her own height and the height of the school. She also knows the distance from the mirror to the school from previous Geometry activity. She would like to calculate the distance she is standing from the mirror.
The height of the school is 30 ft.
The distance from the school to the mirror is 50 ft.
The height of the student is 6.3 ft.
What is the distance d between the student and the mirror?
The distance d between the student and the mirror is given by the similar triangles are d = 10.5 feet
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the triangles be represented as ΔABC and ΔCDE
Now , they are similar triangles
The measure of AB = height of the school = 30 feet
The measure of BC = distance from the school to the mirror = 50 feet
And ,
The measure of DE = height of the student = 6.3 feet
The measure of CD = distance d between the student and the mirror
So , the corresponding sides of similar triangles are in the same ratio
On simplifying the equation , we get
BC / AB = CD / DE
And , 50 / 30 = d / 6.3
Multiply by 6.3 on both sides , we get
d = ( 5/3 ) x 6.3
d = 31.5 / 3
d = 10.5 feet
Hence , the distance d between the student and the mirror is 10.5 feet
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a park in the shape of a rectangle 2.5 miles long and 1.25 miles wide if you walk diagonally across the park how many miles will you walk
Answer: You will walk 2.795 miles
Step-by-step explanation:
You can solve this using the Pythagorean theorem which is a^2 + b^2 = c^2
Plug in your numbers so you have 2.5^2 + 1.25^2 = c^2
Simplify that down to 6.25 + 1.5625 = c^2
Add 7.8125 = c^2
Find the square root of each of them. 2.795 = c
I don't know how you want me to round the answer so I just did it to the nearest thousandths.
Figure ABCD is a square. If AC+BD=56, what is the length of AX?
Figure ABCD is a square. If AC+BD=56, the length of AX is 28.
How did we get the value?Since ABCD is a square, all sides have the same length, let's call it "x".
We know that the sum of the diagonals of a square is equal to twice the length of a side, so AC + BD = 2x.
Therefore, 56 = 2x, and x = 28.
So the length of AX (or any side of the square) is 28 units
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the sensitivity range for an objective function coefficient is the range of values over which the profit does not change.True or False
Answer:The answer to your question “the sensitivity range for an objective function coefficient is the range of values over which the profit does not change.True or False” Is FALSE.
what a unit of measurement equal to one thousand meters?
A unit of measurement equal to one thousand meters is called a kilometer.
A kilometre is a length measurement in the metric system that is equivalent to 1000 metres because the word "kilo" implies "one thousand". Longer distances, such those between cities or nations or the duration of a marathon, are frequently measured in kilometers. The lower length units of the metric system, such as meter's, centimeters, and millimeters, can be used to measure shorter distances.
A length measurement in the metric system that is 1,760 yards or 5,280 feet long. A metric capacity unit is one thousandth of a liter. a length expressed as a thousandth of a meter in meters. a common measure of time that is equal to 60 seconds and 1/60 of an hour.
Therefore, the kilometer is equal to one thousand meter's.
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Find three consecutive even integers such that the sum of the three integers is 90
Unknowns: Let x=first even integer
____= second consecutive even integer
____= third consecutive even integer
Equation:
Solve:
Answer: 28, 30, 32
Step-by-step explanation: The first integer is 28, the second is 30, and the third is 32. The difference from the first integer and the last integer should be 4. x is the first integer, so the equation is:
x+x+2+x+4=90
The first integer plus the second integer(x+2) plus the third integer(x+4) equals 90. Now solve.
x+x+2+x+4=90
3x+6=90
-6 -6
3x=84
/3 /3
x=28
So the first integer is 28, second is 30, third is 32.
Hope this helps!