73 is the rate of the eastbound train while The speed of the westbound train is 59 miles per hour.
What is Speed?speed is described as. the pace at which an object's location changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it just has a direction and no magnitude.
Given, Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 14 miles per hour slower than the westbound train.
Eastbound train:
time = 3 hrs, rate = x mph, distance = 3x miles
Westbound train:
time = 3 hrs ; rate = x-14 ; distance = 3x-42 miles
3x + 3x - 42 = 480
6x = 438
x = 73 (rate of the eastbound train)
To find the rate of the westbound train:
rate = x -14
rate = 73 - 14
rate of westbound train = 59
Therefore, The speed of the westbound train is 59 miles per hour.
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Which of the following statements are true?
The Fire Station and the Worship Center lie on the same side of the transversal and form a linear pair.
The Museum and the Coffee Shop lie on the opposite sides of the transversal and form a pair of alternate exterior angles.
The Bank, the Museum, the Coffee Shop, the Worship Center are interior angles.
O The Day Care and the Park are on the same side of the transversal and form a linear pair.
The Day Care and the Community Center are supplementary angles and on opposite sides of the transversal.
The Bank and the Community Center are on opposite sides of the transversal and form a pair of alternate interior angles.
The Park and the Museum are adjacent angles and form a vertical pair of angles.
The Fire Station and the Community Center are consecutive interior angles lying on the same side of the transversal.
Answer:
*The Museum and the Coffee Shop lie on the opposite sides of the transversal and form a pair of alternate exterior angles
*The Day Care and the Community Center are supplementary angles and on opposite sides of the transversal.
*The Fire Station and the Community Center are consecutive interior angles lying on the same side of the transversal
Step-by-step explanation:
The transversal is the major road that crosses the other two roads shown in the diagram above.
Applying the knowledge of properties of lines, let's consider each statement given, to ascertain which is true and which is untrue:
Statement 1: 'The Fire Station and the Worship Center lie on the same side of the transversal and form a linear pair."
The fire station and the Worship center are on the same side of the transversal, however, they do not form a linear pair. They are corresponding angles.
Statement is NOT TRUE.
Statement 2: "The Museum and the Coffee Shop lie on the opposite sides of the transversal and form a pair of alternate exterior angles."
This statement is TRUE.
The Museum and the Coffee shop form alternate exterior angles pair.
Statement 3: "The Bank, the Museum, the Coffee Shop, the Worship Center are interior angles."
This is NOT TRUE.
They are all EXTERIOR angles.
Statement 4: "The Day Care and the Park are on the same side of the transversal and form a linear pair."
This is NOT TRUE.
They are consecutive interior angles.
Statement 5: "The Day Care and the Community Center are supplementary angles and on opposite sides of the transversal."
This is TRUE.
Statement 6: "The Bank and the Community Center are on opposite sides of the transversal and form a pair of alternate interior angles"
This is NOT TRUE.
They are on opposite side of the transversal but one the bank is an exterior angle while the community center is an interior angle.
Statement 7: "The Park and the Museum are adjacent angles and form a vertical pair of angles."
This is NOT TRUE.
They do not share the same side, so they can't be adjacent angles. They only share the same vertex, which makes them vertical angles.
Statement 8: "The Fire Station and the Community Center are consecutive interior angles lying on the same side of the transversal."
This is TRUE.
Mel drove 432 miles during his trip. He drove an average of 72 miles per hour. How long was his trip?
Answer:
6h
Step-by-step explanation:
If he drove 72 mph and you know how long he drove, just need to divide:
[tex]Distance / Speed = Time[/tex]
Therefore:
[tex]432 / 72mph = 6h[/tex]
Answer:
hi its just like the dood above me said *dude sorry if i was late
Step-by-step explanation:
Find the value of x.
Answer: x=10
Step-by-step explanation:
5x+3=53 subtract 3 from 3 and 53
5x=50 divide both sides by 5
50/5=10
now lets check to be sure
5*10=50+3=53
the solution is correct
hoped this help =)
Is 2|12 true or false
Answer:
true
Step-by-step explanation:
Because it is
Sue has $1.15 in nickels and dimes, a total of 16 coins.
How many nickels and how many dimes does Sue have?
Answer:
9 nickels . 7 dimes
Step-by-step explanation:
i take the same class so i know where u got it from
Identify the independent and dependent variables: The cost to gift wrap an order is $ 3 plus $1 per item wrapped
Answer: Indep. is: $3 and the dependent is $1
Step-by-step explanation:
Every item is $3, but if you add more then you also add $1
Find the value of x
(4x-20)°
Answer:
Bro this has no solution
Answer: 4(x−5)
Step-by-step explanation: I think this is right. If it’s not Im sorry. But if it is hope this helps!
A fruit juice box contains 6% juice how is this percent rent as a decimal
Answer:
0.06
Step-by-step explanation:
6% = 0.06
0.06 as a decimal Hope this helped!
i need your help and to try this out so can you please answer dis
-2(x+6)
Answer:
12x - 12
Step-by-step explanation:
-2(x + 6)
open the parenthesis
-2 * x + -2 * 6
-2x - 12
-2x - 12
Which term describes the relationship between L A and 2 B, if the m LA= 84º and m 2 B = 96º7
A
vertical
В.
adjacent
С
supplementary
D
complementary
Answer:
Supplementary
Step-by-step explanation:
84 plus 96 equals 180 degrees
supplementary angles are angles that add up to 180 so their relationship is supplementary
A right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches.
What are the measures of the angles in triangle ABC?
m∠A ≈ 46.2°, m∠B ≈ 43.8°, m∠C ≈ 90°
m∠A ≈ 73.0°, m∠B ≈ 17.0°, m∠C ≈ 90°
m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°
m∠A ≈ 74.4°, m∠B ≈ 15.6°, m∠C ≈ 90°
Answer:c
Step-by-step explanation:
The measures of the angles in triangle ABC are; m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°
How to find the measures of angles in triangle ABCIt follows that the right angle is between the two shorter sides;
Hence, the angle measure, m∠C ≈ 90°.On this note, the angle, m∠A is opposite side BC;
Therefore, from sine formula;
Sin m∠A ≈ 24/25Sin m∠A ≈ 0.96m∠A ≈ sin-¹(0.96)m∠A ≈ 73.7°
And from sum of angles in a triangle;
m∠A ≈ 16.3°
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3/4 (x + 18) = 15 What is x equal to
Answer:
x=2
Step-by-step explanation:
hope it helps
please mark as Brainliest
Answer:
x = 2
Step-by-step explanation:
For me it's easier to work with decimals than fractions, so I converted 3/4 to .75
.75(x + 18) = 15
.75x + 13.5 = 15
That was just distributing the .75 but here is where it gets a bit confusing.
.75x + 13.5 = 15
-13.5 -13.5
.75x = 1.5
Divide both sides by .75 to isolate the variable.
x = 2
Hope that helps and have a great day!
In Exercises 1–4, use these results from a USA Today survey in which 510 people chose to respond to this question that was posted on the USA Today website: "Should Americans replace passwords with biometric security (fingerprints, etc)?" Among the respondents, 53% said "yes." We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.Number and Proportiona. Identify the actual number of respondents who answered "yes."b. Identify the sample proportion and the symbol used to represent it.
Answer:
The proportion of the population believes that passwords should be replaced with biometric security is not more than 50%.
Step-by-step explanation:
In this case we need to test the claim that more than half of the population believes that passwords should be replaced with biometric security.
Assume that the significance level of the test is, α = 0.05.
The hypothesis can be defined as follows:
H₀: The proportion of the population believes that passwords should be replaced with biometric security is 50%, i.e. p = 0.50.
Hₐ: The proportion of the population believes that passwords should be replaced with biometric security is more than 50%, i.e. p > 0.50.
The information provided is:
[tex]n = 510\\\hat p=0.53[/tex]
Compute the test statistic value as follows:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]=\frac{0.53-0.50}{\sqrt{\frac{0.50(1-0.50)}{510}}}\\\\=1.354991\\\\\approx 1.35[/tex]
The test statistic value is 1.35.
The decision rule is:
The null hypothesis will be rejected if the p-value of the test is less than the significance level.
Compute the p-value as follows:
[tex]p-value=P(Z>1.35)[/tex]
[tex]=1-P(Z<1.35)\\=1-0.91149\\=0.08851\\\approx0.088[/tex]
p-value = 0.088 > α = 0.05.
The null hypothesis will not be rejected at 5% significance level.
Thus, there is not enough evidence to support the claim.
Conclusion:
The proportion of the population believes that passwords should be replaced with biometric security is not more than 50%.
(3.1 · 10² ) (2 · 10³) Write in Scientific Notation.
Answer:6.03*10^3
Step-by-step explanation:
(3.1 *10^2)(2*10^3)
2*10^3=20*10^2
(3.1*10^2)(20*10^2)
(60.3*10^2)=
6.03*10^3
Jose is riding his bicycle. He rides at a speed of 12 kilometers per hour fore 38.4 kilometers. For how many hours does he rides
Answer:
3.2 hours
Step-by-step explanation:
5.) You are working for a car dealership. You are doing an inventory of the lot. You counted 34
trucks. 15 cars, and 8 SUVs. What is the ratio of SUVs to total vehicles on the lot?
Answer: 8 SUVs to 57 total
Step-by-step explanation: You add 34 + 15 + 8 which gives you 57 Then you see there are 8 SUVs. So the answer is 8 to 57.
Sorry. I kinda got ahead of myself and excited. Guess mistakes happen. I was right the first time. I'm just so tired right now
I really need help with this ?
Calculate the area of the triangle: A =
Answer:
27
Step-by-step explanation:
The area of the triangle is 30.9 square units.
We have,
From the figure,
Height = Distance between (-2, 6) and (-2, 0).
Base = Distance between (-2, 0) and (7, -5).
To find the distance between two points in a Cartesian coordinate system, use the distance formula:
Distance = [tex]\sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]
Height:
Distance = √((-2 - (-2))² + (0 - 6)²)
Distance = √(0² + (-6)²)
Distance = √(0 + 36)
Distance = √36
Distance = 6
Base:
Distance = √((7 - (-2))² + (-5 - 0)²)
Distance = √((7 + 2)² + (-5)²)
Distance = √(9² + (-5)²)
Distance = √(81 + 25)
Distance = √106
Distance ≈ 10.3
Now,
The area of the triangle.
= 1/2 x base x height
= 1/2 x 10.3 x 6
= 10.3 x 3
= 30.9 square units
Thus,
The area of the triangle is 30.9 square units.
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If the odds for a certain event are 5 to 12, what is the probability of the event occuring? Write your answer
as a simplified fraction.
Answer:
5/12
Step-by-step explanation:
Isn't this just a ratio?
How do you do this question?
Answer:
a) -7/9
b) 16 / (n² + 15n + 56)
c) 1
Step-by-step explanation:
When n = 1, there is only one term in the series, so a₁ = s₁.
a₁ = (1 − 8) / (1 + 8)
a₁ = -7/9
The sum of the first n terms is equal to the sum of the first n−1 terms plus the nth term.
sₙ = sₙ₋₁ + aₙ
(n − 8) / (n + 8) = (n − 1 − 8) / (n − 1 + 8) + aₙ
(n − 8) / (n + 8) = (n − 9) / (n + 7) + aₙ
aₙ = (n − 8) / (n + 8) − (n − 9) / (n + 7)
If you wish, you can simplify by finding the common denominator.
aₙ = [(n − 8) (n + 7) − (n − 9) (n + 8)] / [(n + 8) (n + 7)]
aₙ = [n² − n − 56 − (n² − n − 72)] / (n² + 15n + 56)
aₙ = 16 / (n² + 15n + 56)
The infinite sum is:
∑₁°° aₙ = lim(n→∞) sₙ
∑₁°° aₙ = lim(n→∞) (n − 8) / (n + 8)
∑₁°° aₙ = 1
Find a and b: (10-4i)-(a+bi)=(6-6i)
Answer:
look at attached image, hope this helps! :)
Carlos cut Start Fraction 5 Over 12 End Fraction of a yard of cloth into 5 pieces of equal length. What was the length of each piece of cloth?
Start Fraction 1 Over 60 End Fraction of a yard
Start Fraction 1 Over 25 End Fraction of a yard
Start Fraction 1 Over 12 End Fraction of a yard
One-fifth of a yard
Answer:
C.1/12
Step-by-step explanation:
Divide 5/12 by 5 since he cut it into 5 equal pieces
Given the linear function 2x - y= 5 what is the slope? And As x increase does y increase or decrease and as x decreases does y increase or decrease
Answer:
The slope is 2. As x increase y is increase and as x decrease y decrease
I will give you branilest!
What does the constant of proportionality represent?
Answer:
The constant of proportionality is the ratio between two directly proportional quantities
Step-by-step explanation:
Two quantities are directly proportional when they increase and decrease at the same rate.
Answer:The constant of proportionality is the constant value of the ratio of two proportional quantities x and y, typically the equation is Y=KX.
Step-by-step explanation:
How do you do this question?
Exact value: [tex]c = \frac{-11+\sqrt{165}}{22}[/tex]
Approximate value: c = 0.08387
Round the approximate value however you need to
==============================================
Work Shown:
Let x = 1+c
[tex]\displaystyle S = \sum_{n=2}^{\infty}(1+c)^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}x^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}\frac{1}{x^n}\\\\\\\displaystyle S = \frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^4}\ldots\\\\\\[/tex]
We have an infinite geometric series here. The first term is a = 1/(x^2). The common ratio is r = 1/x.
Each new term is found by multiplying the previous term by 1/x.
Assuming -1 < r < 1 is true, the infinite geometric sum is
[tex]S = \frac{a}{1-r}\\\\\\S = \frac{1/x^2}{1-1/x}\\\\\\S = \frac{1/x^2}{x/x-1/x}\\\\\\S = \frac{1/x^2}{(x-1)/x}\\\\\\S = \frac{1}{x^2}\div\frac{x-1}{x}\\\\\\S = \frac{1}{x^2}*\frac{x}{x-1}\\\\\\S = \frac{1}{x^2-x}\\\\\\[/tex]
Plug in S = 11 and solve for x
[tex]S = \frac{1}{x^2-x}\\\\11 = \frac{1}{x^2-x}\\\\11(x^2-x) = 1\\\\11x^2-11x = 1\\\\11x^2-11x-1 = 0\\\\[/tex]
Use the quadratic formula to find the two solutions
[tex]x = \frac{11+\sqrt{165}}{22} \approx 1.08387\\\\x = \frac{11-\sqrt{165}}{22} \approx -0.08387\\\\[/tex]
Using these x values, we find that the corresponding r values are
r = 1/x = 1/(1.08387) = 0.92262
r = 1/x = 1/(-0.08387) = -11.92321
The first r value makes -1 < r < 1 true, but the second r value does not. So we will be ignoring the solution x = -0.08387
----------------------------------------------
Using the solution that corresponds to x = 1.08387, we find the value of c is
[tex]x = c+1\\\\c = x-1\\\\c = \frac{11+\sqrt{165}}{22}-1\\\\c = \frac{11+\sqrt{165}}{22}-\frac{22}{22}\\\\c = \frac{11+\sqrt{165}-22}{22}\\\\c = \frac{-11+\sqrt{165}}{22}\\\\c \approx 0.08387\\\\[/tex]
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Describe how to model -3x + 7 = 28 with algebra tiles.
Answer:
-7
Step-by-step explanation:
-3x+7=28
-7=28
-7
-3x/21
x=-7
8 Determine if the product of 32 and 8V 18 is
rational or irrational. Explain your answer.
Answer: It is irrational.
Step-by-step explanation:
√18 is an irational number. Multiplying most rational numbers by an irrational number results in an irrational number.
Find the equation of a line that passes through the points (1, 2) and (5,8).
1: y= 3/2 + 1/2
2: y= 3/2 + 1
3: y= 3/2 + 2
Answer:
1: y = 3/2 + 1/2
Step-by-step explanation:
y1 -y2/x1 - x2
8-2 / 5-1
6/4 = 3/2
y-2=3/2(x-1)
y-2=3/2x - 3/2
y-2 +2= 3/2x - 3/2 +2
y=3/2x + 1/2
Graph y = - 3x + 7 .
Answer:
put your first point at 7 in y axis that point go down 3 to the rights side 1 and your point should be at (1,4) then connect the dots and that's how you graph it
Step-by-step explanation:
The equation of the line y = - 3x + 7 is drawn below.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.
The equation of the line is given below.
y = -3x + 7
Convert the line into intercepts form, then we have
y = - 3x + 7
3x + y = 7
x / (7/3) + y / 7 = 1
The equation of the line is drawn below.
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Kia Read for a total of 60 minutes on Monday and Tuesday. He read for 60 minutes on Tuesday. How many minutes did he read on Monday?