The second train will catch up with the first train after 5/3 hours.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a train that leaves a train station at 1 p.m. it travels at an average rate of 60 mi/hr. A high-speed train leaves the same station an hour later. it travels at an average rate of 96 mi/hr. The second train follows the same route as the first train on a track parallel to the first.
We have -
Assume that the second train catches the first in x hours. Then, we can write -
60(x + 1) = 96x
60x + 60 = 96x
96x - 60x = 60
36x = 60
x = 60/36
x = 5/3 hours
Therefore, the second train will catch up with the first train after 5/3 hours.
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How would the distance formula be used in real life?
Name the property of real numbers illustrated by the equation.
-3(x+4)=-3x-12
A: Distributive property
B: Associative property of addition
C: Associative property of multiplication
D: Commutative property of addition
how do you divide fractions
Dividing fractions is basically the same thing as multiplying fractions but by the reciprocal.
For example, [tex]\frac{3}{8}[/tex] ÷ [tex]\frac{1}{4}[/tex] you would change this so in the second fraction that is being divided, the numerator and the denominator would switch places. Instead, it would be...
[tex]\frac{3}{8}[/tex] x [tex]\frac{4}{1}[/tex]
Which set of ordered pairs represents a function?
{(0, 0), (2, 3), (1, -4), (2, -2)}
{(5, 6), (2, 6), (-3, 4), (-1, 4)}
{(3, -2), (-4, -1), (0, 3), (0, 5)}
{(-5, 1), (-4, 2), (-5, 3), (-4, 4)}
A ____ is a subset of a given set of elements
Answer:
The correct answer is a COMBINATION
A combination is a subset of given elements.
Step-by-step explanation:
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 108.7-cm and a standard deviation of 0.6-cm. For shipment, 22 steel rods are bundled together.
Find the probability that the average length of rods in a randomly selected bundle of steel rods is less than 109.1-cm.
Round to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.
Let x be the lengths of the steel rods and X ~ N (108.7, 0.6)
To get the probability of less than 109.1 cm, the solution is computed by:
z (109.1) = (X-mean)/standard dev
= 109.1 – 108/ 0.6
= 1.1/0.6
=1.83333, look this up in the z table.
P(x < 109.1) = P(z < 1.8333) = 0.97 or 97%
In the year 2016, the estimated population of Canadian geese in a city was 750. The Canadian geese population is expected to grow at a rate of 12% each year. What is the Canadian geese population in 2022? Round the answer to the nearest whole number.
Keywords:
population, Canadian geese, growth rate
For this case, we must find the population of Canadian geese for the year 2022, taking into account that in 2016 the estimated population of geese was 750 and as additional data, the population of geese has a growth rate of 12% each year.
Then, we started finding the Canadian geese population for 2017, for this we make a rule of three:
750 -----------> 100%
x --------------> 12%
DOnde "x" represents the number of geese that is added to the base population of 2016.
[tex]x = \frac {12 * 750} {100}\\x = 90[/tex]
Thus, the geese population for 2017 is: [tex]750 + 90 = 840[/tex]
We find the population of Canadian geese for the year 2018, following the previous steps since the annual growth rate is constant:
840 -----------> 100%
x --------------> 12%
where "x" represents the number of geese that is added to the base population of the year 2017.
[tex]x = \frac {12 * 840} {100}\\x = 100.8[/tex]
Thus, the geese population for 2018 is: [tex]840 + 100.8 = 940.8[/tex]
We found the population of Canadian geese for the year 2019, following the previous steps since the annual growth rate is constant:
940.8 -----------> 100%
x --------------> 12%
Where "x" represents the number of geese that is added to the base population of the year 2018.
[tex]x = \frac {12 * 940.8} {100}\\x = 112.896[/tex]
Thus, the geese population for 2019 is: [tex]940.8 + 112.896 = 1053.696[/tex]
We find the population of Canadian geese for the year 2020, following the previous steps since the annual growth rate is constant:
1053.696 -----------> 100%
x --------------> 12%
Where "x" represents the number of geese that adds to the base population of the year 2019.
[tex]x = \frac {12 * 1053.696} {100}\\x = 126.44[/tex]
Thus, the geese population for 2020 is: [tex]1053.696 + 126.44 = 1180.12[/tex]
We found the population of Canadian geese for the year 2021, following the previous steps since the annual growth rate is constant:
1180.12 -----------> 100%
x --------------> 12%
Where "x" represents the number of geese that is added to the base population of the year 2020.
[tex]x = \frac {12 * 1180.12} {100}\\x = 141.6[/tex]
Thus, the population of geese for 2021 is:[tex]1180.12 + 141.6 = 1321.7[/tex]
We found the population of Canadian geese for the year 2022, following the previous steps since the annual growth rate is constant:
1321.7 -----------> 100%
x --------------> 12%
[tex]x = \frac {12 * 1321.7} {100}\\x = 158.6[/tex]
Where "x" represents the number of geese that adds to the base population of the year 2021.
Thus, the population of geese for 2022 is: [tex]1321.7 + 158.6= 1480.3[/tex]
ANswer:
The population of Canadian geese by 2022 will be approximately 1480 geese
Please help, I'm stuck on this answer.
True or false? Explain your answer.
The inequality −2(x + 10) ≥ 75 says the same thing as −2x − 20 ≥ 75. I can multiply by -2 on the left side without reversing the inequality symbol.
Answer:True
Step-by-step explanation:
Yes, you don't have to reverse the inequality symbol since the variables are not from the other side (right).
If two angles are complementary to the same angle, then they are
Miko’s restaurant bill was $16. She used the expression 1.18(16) to find the total cost, including an 18% tip.
Which expression is equivalent to the amount Miko paid?
A. (1+0.18)16
B. 16+0.18(16)
C. 16 + 1.18
D. 1+0.18(16)
Please explain your answer
Answer:
D) 16 + 0.18(16)
Step-by-step explanation:
Which expression is equivalent to (3−22)+5 ?
A. 22−5
B. 5−32
C. 32−5
D. 5−22
The expression (3-22)+5 simplifies to -14. None of the provided options: A. 22-5, B. 5-32, C. 32-5, or D. 5-22 are equivalent to the original expression.
Explanation:Let's break this question down for you. The initial expression given is (3−22)+5. In math, operations inside the parentheses are performed first according to the order of operations (PEMDAS/BODMAS), which is followed by addition or subtraction. However, the expression inside the parentheses here results in a negative number, since 3−22 equals -19. Then add 5 to -19 gives you -14.
So, the none of the options A, B, C or D are equivalent to the original expression (3−22)+5.
It's important to understand order of operations in math because it helps to ensure that calculations are done correctly and consistently.
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none of the provided options (A, B, C, or D) match this value.
We start with the given expression (3−22)+5. It can be simplified step-by-step as follows,
Calculate inside the parentheses first: 3 - 22.
Since subtracting 22 from 3 is performed, we get: 3 - 22 = -19.
Next, add 5 to the result: -19 + 5 = -14.
Let's evaluate each of the provided options:
A. 22−5: This evaluates to 17, which does not match -14.
B. 5−32: This simplifies to 5 - 9 = -4, which does not match -14.
C. 32−5: This evaluates to 9 - 5 = 27, which does not match -14.
D. 5−22: This simplifies to 5 - 22 = -17, which does not match -14.
None of the provided expressions are equivalent to (3−22)+5. Therefore, the correct answer is: None of the above.
The set of complex numbers is the set of all numbers of the form a + bi, where a and b are real numbers and i=
Answer:
i = [tex]\sqrt{-1}[/tex]
Step-by-step explanation:
A complex number is that one having two parts:
One called real part, represented by a.And another called imaginary part, represented by bi, where b is also a real number plus i, as it was describe in the answer [tex]i = \sqrt{-1}[/tex].Although [tex]i =\sqrt{-1}[/tex], it is also [tex]i^{2} = -1[/tex], which has some interesting properties like [tex]i^{3}[/tex] = [tex]i * i^{2}= i * -1 = -i [/tex] , and so on.
These numbers came along when it was necessary to take the squared root of negative numbers:
[tex]\sqrt{-4} = \sqrt{-1} * \sqrt{4} = 2i ; -2i[/tex] .
$10,000 is compounded semiannually at 12% interest for t years. what expression represents the amount of money after t years?
The expression that represents the amount of money after t years when $10,000 is compounded semiannually at 12% interest is [tex]10000(1.06)^{(2t)}[/tex].
The amount of money after t years can be represented by the following expression:
[tex]A = P(1 + \frac{r}{n})^{(n*t)}[/tex]
Where:
A is the amount of money after t years
P is the principal amount (initial investment), which is $10,000 in this case
r is the interest rate, which is 12% expressed as a decimal (0.12)
n is the number of times interest is compounded per year, which is semiannually (2 times per year)
Substituting the values into the expression, we have:
[tex]A = 10,000(1 + \frac{0.12}{2})^{(2*t)}[/tex]
Simplifying further, we get:
[tex]A = 10000(1.06)^{(2t)}[/tex]
Therefore, the expression that represents the amount of money after t years when $10,000 is compounded semiannually at 12% interest is [tex]10000(1.06)^{(2t)}[/tex].
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Find the measure of angle x in the figure.
Angle x measures?
Answer:
Measure of angle x is:
119°
Step-by-step explanation:
The sum of all interior angles in a polygon having n sides is:
180°(n - 2)
Now, this polygon has 7 sides.
So the sum of its interior angles will be= 180°(7 - 2)
= 900°
i.e. 129°+129°+123°+122°+x+141°+137°=900°
or 781°+x=900°
or x=900°-781°
or x=119°
Hence, Measure of angle x is:
119°
A point on a coordinate plane is located 3 units to the right of the origin and 7 units above the origin. What are the coordinates of this point? Use the drop-down menus to enter the coordinates below.
The coordinates of the point are
(
( ,
)
)
This question is based on the coordinates of a plane. Therefore, ( 3, 0) and ( 0, 7) are coordinates of this points.
Given:
A point on a coordinate plane is located 3 units to the right of the origin and 7 units above the origin.
We need to determined the coordinates of the points.
According to the question,
It is given that, 3 units to the right of the origin means that, 3 units on positive x - axis.
As we know that,
On x -axis, y is equal to zero.
Therefore, the co-ordinate of this point is located on ( 3, 0).
Now, 7 units to the above the origin means that, 7 units on positive y - axis.
As we know that,
On y -axis, x is equal to zero.
Therefore, the co-ordinate of this point is located on ( 0, 7).
Hence, ( 3, 0) and ( 0, 7) are coordinates of this points.
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What is the domain of the function f(x)=x+3
Logan's only debt obligations are a car loan payment of $512 and a credit card payment of $70 every month. What is the minimum amount of money he must take home every month in order to avoid being in danger of credit overload?
Answer:
$ 2910
Step-by-step explanation:
Can you determine the number of digits in the quotient of 637 divided by 7 without dividing?explain.
How to find the x and y intercepts when given two points and no slope?
Multiply 436.2 × 0.74 = ____
Changes made to your input should not affect the solution:
(1): "0.74" was replaced by "(74/100)". 2 more similar replacement(s)
write two equations for a horizontal line and a vertical line.
One positive integer is 3 less than twice another. the sum of their squares is 233. find the integers.
if angle m acd = 100 and angle m b =60, find angle m a
Answer:
The measure of ∠BAC is 40° .
Step-by-step explanation:
As given the figure in the question be as follow .
∠ACD = 100° , ∠B = 60°
Noe by using the the exterior angle is equal to the sum of the interior angle .
Thus
∠ACD = ∠CBA + ∠BAC
Put all the values in the above
100° = 60° + ∠BAC
∠BAC = 100° - 60°
= 40°
Therefore the measure of ∠BAC is 40° .
Translate the following word phrase into an algebraic expression.
" 3 multiplied by the sum pf a number and 5"
A. 3(x+5)
B. 3x+5
C. x+(3)(5)
D. 5x+3
A long distance phone company charges $1.01 for the first 25 minutes of a call, then $0.09 for each additional minute. A call cost $9.56 how long did it last?
Final answer:
Subtracting the initial charge from the total cost and then dividing the remainder by the cost per additional minute, we find that the call lasted for 120 minutes.
Explanation:
The student is asking how long a phone call lasted based on the cost of the call with a given rate structure. We know that the first 25 minutes cost $1.01 and each additional minute costs $0.09. The total cost of the call was $9.56. To determine the duration of the call, we need to calculate the cost of the additional minutes beyond the first 25, and then find out how many of those minutes were used.
Subtract the initial charge from the total cost: $9.56 - $1.01 = $8.55.
Divide the remaining cost by the cost per additional minute: $8.55 / $0.09 = 95 minutes.
Add the initial 25 minutes to the additional minutes: 25 + 95 = 120 minutes.
Therefore, the call lasted for 120 minutes.
Suppose an isosceles triangle ABC has A = 45° and b = c = 4. What is the length of a^2?
A.22.63
B.54.63
C.9.37
D.3.10
El área de un triángulo es igual a la mitad del producto de la longitud de la base por la longitud de la altura.
La base de un triángulo mide 23 cm y su área es 27 cm2.
You begin solving the equation 4−5x=594-5x=59 by subtracting 44 from both sides. Which is the best choice for Step 22?
Please help! 3 questions, 1. Determine if the ordered pair is a solution of the equation. Is (-1,-30) a solution of y =10x?: a) True b) False
2.The point (5, -1) is a solution of the equation: y = 2x − 11 options: a) True b) False 3.Which ordered pairs are a solution to the equation? y = 8x options: a) (-1,-7) b) (2,16) c) (1,8) d) (-2,-6)
Order the numbers 0.2, 1/5, 0.02, 0.022 from least to greatest.