The passenger train traveling at 30 mi/hr faster than the freight train and traveling 3 times the distance traveled by the freight train, through the kinematic equations, indicates that the speed of the freight train is 15 mi/hr and the speed of the passenger train is 45 mi/hr.
What is kinematics?Kinematics is the study of the motion of an object without reference to the force that causes the motion.
The speed of the passenger train = 30 + The speed of the freight train
Distance traveled by the passenger train in 6 hours = 3 × The distance traveled by the freight train
Let v represent the speed of the freight train and let d represent the distance traveled by the freight train in 6 hours
From kinematic equations, we get;
Speed of the passenger train = 30 + v
Distance traveled by the passenger train in 6 hours = 3 × d
(30 + v) × 6 = 3•d
6•v = d
Which gives; (30 + v) × 6 = 3 × 6•v
180 + 6•v = 18•v
12•v = 180
v = 180 ÷ 12 = 15
The speed of the freight train is v = 15 mi/hr
The speed of the passenger train = 30 + v
The speed of the passenger train is (30 + 15) mi/hr = 45 mi/hr
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If angle A is (2x) and angle B is (3x+11)° and the sum of angle A and angle B is 66°, find the measure of angle B.
11
22
44
25
The angle B is 66°
Given,
In the question:
If angle A is (2x) and angle B is (3x+11)°
and, the sum of angle A and angle B is 66°
To find the angle of B.
Now, According to the question:
Based on the given condition:
Angle A = 2x
Angle B = (3x + 11)°
The sum of angle A and B is 66°
2x + (3x + 11)° = 66°
5x + 11 = 66°
Calculate the sum or difference
5x = 66 - 11
3x = 55
x = 55/3
The angle B is = 3x + 11
Plug the value of x in angle B
3 × 55/3 + 11
= 66
Hence, The angle B is 66°
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Given the image of the two triangle, which method can you use to show △LHJ≅△KIE
Answer:
ASA
Step-by-step explanation:
As you can see in the picture it is giving us 2 angles, in between those 2 angles are aside. Therefore it is ASA.
We can also eliminate SSS because 2 angles and shown and SAS can also be eliminated because there are 2 angles, not sides.
a. Find the derivative function f' for the function f.
b. Determine an equation of the line tangent to the graph of f at (a,f(a)) for the given value of a.
The derivative function f' for the function f is f'(x) = -10 / (5x+3)^2 and Equation of the line tangent to the graph of f is 5x+2y+7=0.
Given function:
f(x) = 2/5x+3
a.
f'(x) = d/dx(2/5x+3)
According to power rules:
1/u = -1/u^2
= 2(1/(5x+3)^2) d/dx(5x+3)
= 2*5 / (5x+3)^2
= -10/(5x+3)^2
Hence derivative function f' for the function f is f'(x) = -10 / (5x+3)^2.
b.
(a,f(a)) and a = -1
f(-1) = 2/5(-1)+3
= 2/-5+3
= 2/-2
= -1
point (-1,-1)
slope f'(x) = -10/(5x+3)^2
f'(-1) = -10/(5(-1)+3)^2
= -10/(-2)^2
= -10/4
m = -5/2
Equation of the line is y - y1 = m(x-x1)
y - (-1) = -5/2(x-(-1)
2(y + 1) = -5x - 5
5x + 2y + 2 + 5 = 0
5x+2y+7=0.
Equation of the line tangent to the graph of f is 5x+2y+7=0.
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121x
10
6
4
909
-6-5-4-3-2-12- 2 3 4 5 6 x
J
-8-
-10
B
h
Which statement is true regarding the functions on the
graph?
Of(6) = g(3)
Of(3) = g(3)
Of(3) = g(6)
Of(6) = g(6)
Answer:
The Question is not Correct but answer is f 3 and g 3
Nine less than twice the difference between a number and seven
Step-by-step explanation:
9 < 2(x - 7)
hope this helpful
A certain element has a half-life of approximately 15 hours. How long would it take for 500 grams of the element to decay to 299 grams? Leave your answer as an integer or simplified expression.
It would take 11.1 hours to decay from 500 grams to 299 grams.
How long takes to decay?We know that for an element with an half-life T has a decay equation that can be written as:
f(t) = A*e^(-t*ln(2)/T)
Where A is the initial amount, and f(t) is the amount of the element t hours after.
Here we know that:
A = 500g
T = 15h
Then the function is:
f(t) = 500g*e^(-t*ln(2)/15h)
And we want to find the value of t such that f(t) = 299g, then:
299g = 500g*e^(-t*ln(2)/15h)
299/500 = e^(-t*ln(2)/15h)
ln(299/500) = -t*ln(2)/15h
-ln(299/500)*15h/ln(2) = t
11.1h = t
It will take 11.1 hours.
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how many different rectangles are there
Write the equation of the line that perpendicular to y=5/2x + 9/2 that passes through the point (-5,3)
Answer:
y = -2/5 x + 1
Step-by-step explanation:
slope = -2/5
y-3 = -2/5 (x -(-5)
y-3 = -2/5 (x+5)
y - 3 = -2/5 x - 2
y = -2/5 x - 2 + 3
y = -2/5 x + 1
1. Analyze When a fraction with a numerator of 30 and a denominator of 8
is converted to a mixed number and reduced, what is the result?
On average, a banana will last 6 days from the time it is purchased in the store to the time it is too rotten to eat. Is the mean time to spoil less if the banana is hung from the ceiling? The data show results of an experiment with 15 bananas that are hung from the ceiling. Assume that that distribution of the population is normal.
6.3, 3.5, 5.6, 4.2, 4.4, 3.9, 4.5, 5.5, 7.1, 5.6, 6.6, 6.1, 6.3, 7.2, 4
What can be concluded at the the
α
= 0.01 level of significance level of significance?
For this study, we should use
t-test for a population mean
The null and alternative hypotheses would be:
H
0
:
?
Select an answer
H
1
:
?
Select an answer
The test statistic
?
=
(please show your answer to 3 decimal places.)
The p-value =
(Please show your answer to 4 decimal places.)
The p-value is
?
α
Based on this, we should
Select an answer
the null hypothesis.
Thus, the final conclusion is that ...
The data suggest that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is not significantly less than 6 at
α
= 0.01, so there is statistically insignificant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is less than 6.
The data suggest the population mean is not significantly less than 6 at
α
= 0.01, so there is statistically insignificant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is equal to 6.
The data suggest the populaton mean is significantly less than 6 at
α
= 0.01, so there is statistically significant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is less than 6.
Considering the situation described, it is found that:
A t-test for a population mean should be used.The null hypothesis is: [tex]H_0: \mu = 6[/tex]The alternative hypothesis is: [tex]H_1: \mu < 6[/tex]The test statistic is of: t = -1.94.The p-value is of: 0.0364.The conclusion is of: The data suggest the population mean is not significantly less than 6 at α = 0.01, so there is statistically insignificant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is equal to 6.What are the hypothesis tested?At the null hypothesis, it is tested if the mean is of 6 minutes, that is:
[tex]H_0: \mu = 6[/tex]
At the alternative hypothesis, it is tested if the mean is less than 6, hence:
[tex]H_1: \mu < 6[/tex]
What is the test statistic?The test statistic is obtained as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters of the equation are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.Using a calculator from the sample, the values of the parameters are:
[tex]\overline{x} = 5.39, \mu = 6, s = 1.22, n = 15[/tex]
Hence the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{5.39 - 6}{\frac{1.22}{\sqrt{15}}}[/tex]
t = -1.94.
What is the p-value and the conclusion?The p-value is obtained with a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value, with t = -1.94 and 15 - 1 = 14 df, hence it is of 0.0364.
Since the p-value is greater than the significance level of 0.01, the null hypothesis is not rejected and there is not enough evidence that the mean is less than 6 days.
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A store sells barrettes for $2 each and combs for $1. Shelby buys 3 barrettes and a comb. Kendra buys 2 barrettes and 4 combs. Write an expression for the amount the two girls spent all together. Find the total amount spent.
I need help!
Answer:
19
Step-by-step explanation:
add it all up its easy
Step-by-step explanation:
Shelby buys 3 barrettes...
2*3=6
and 1 comb
1*1=1
she spent $7 in total
6+1=7
Kendra buys 2 barrettes...
2*2=4
and 4 combs
1*4=4
so Kendra spent $8 in total
4+4=8
the amount spent from the to girls was...
8+7=15
pls help me asap i dont know the answer
Answer:
96
Step-by-step explanation:
Area of a triangle
A = (1/2) × base × height
A = (1/2) × 12 × 16
A = (1/2) × 192
A = 96 units²
I hope this helps!
Need help please tough question
The value of the investment at the end of 5 years be $ 15,281.012.
Given, 10400 dollars are invested at an interest rate of 8%.
We have to find the value of the investment at the end of 5 years.
Now, on using the compound interest formula, we get
Amount = P(1 + r/100)^t
Amount = 10400(1 + 8/100)^5
Amount = 10400(1.08)^5
Amount = 10400(1.469)
Amount = 15,281.012
Hence, the value of the investment at the end of 5 years be $ 15,281.012.
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Which point is located on the line represented by the equation y + 4 = –5(x – 7)?
(-4, 7)
(-7, 4)
(7, -4)
(4, -7)
Answer:
(7,-4)
Step-by-step explanation:
y + 4 = -5(x-7) Substitute in 7 for x and -4 for y
-4 + 4 = -5 (7-7)
0 = 5(0)
0 = 0 This is a true statement.
5. Jen and Kevin and their children: Jon
(age 14), Beth (age 8), and Joshua
(age 4) are visiting a science museum.
Admission prices are shown below.
Museum Admission
Adult (18-64)
Youth (12-17)
Child (5-11)
Under 5
$22.50
$16.25
$9.75
Free
What will be the total cost of admission
for the family?
?
Answer:
$48.5
Step-by-step explanation:
From the question, we know that Jen and Kevin are definitely adults and the fee for adults
= $22.50
Jon is 14, and any number from 12 to 17 is classified as a youth, so his fee is
= $16.25
Beth is 8, classified as a child, her fee is
= $9.25
Joshua's age which is below 5 is granted free entry without a fee
Hence, the total cost of admission for the family is
$22.50 + $16.25 + $9.75
= $48.5
Round the amount of money to the nearest hundred.
Answer:2,300
Step-by-step explanation:
In a garden club, 90% is ladies. The number of ladies is 12 more than 3 times the number of gentlemen.
How many ladies and how many gentlemen are in the club?
(Note: set up a rational equation and solve)
The number of ladies in the club = 18
and the number of gentlemen in the club = 2
Let x be the number of gentlemen.
So, the number of ladies would be 3x + 12
Total number of people in garden = x + (3x + 12)
= 4x + 12
In a garden club, 90% is ladies.
This means, (3x + 12) is 90 percent of (4x + 12)
We get an equation,
(3x + 12) = 90/100 * (4x + 12)
We solve above equation to find the value of x.
30x + 120 = 36x + 108
6x = 12
x = 2 (number of gentlemen)
So, the number of lades would be:
3x + 12 = 3(2) + 12
= 18
Therefore, the number of ladies in the club = 18 and the number of gentlemen in the club = 2
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How many tiles would it take vanessa to cover 1 square foot
The number of tiles need to cover the closet floor is 180 tiles
The length of the side of the tile = 1/3 feet
The area of the square = Side × Side
The area of the tile = (1/3) × (1/3)
= 1/9 square feet
The width of the closet = [tex]3\frac{1}{3}[/tex] feet
Convert the mixed fraction to simple fraction
[tex]3\frac{1}{3}[/tex] feet = 10/3 feet
The length of the closet = 6 feet
Total area of the closet = 10/3 × 6
= 20 square feet
Number of tiles needed = The area of the closet / The area of the tile
Substitute the values in the equation
= 20 / (1/9)
= 180 tiles
Hence, the number of tiles need to cover the closet floor is 180 tiles
The complete question is
Vanessa wants to cover her closet floor with SRB tiles that are 1/3 foot on each side. The closet is [tex]3\frac{1}{3}[/tex] feet wide and 6feet deep, How many tiles will Vanessa need to cover the closet floor?
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29. Write the equation of the line that passes
through the point (-6, 1) and has a slope
of ½.
Answer:
Step-by-step explanation:
M is slope
B is y intercept
X and y are given
using the equation for the y intercept
b=y1-mx1
B=1−(1/2)⋅(−6)=4
Write in y=Mx+b
=12+4
The general equation of the line is −2+8=0
The speed of a river current is 2 mph. If a boat travels 30 miles downstream in the same that it takes to travel 20 miles upstream, find the speed if the boat in the still water.
Taking into consideration the upstream and downstream speed, and the equal time taken to travel upstream and downstream distance, the speed of the boat in the still water is found out to be 10mph.
It is given to us that -
The speed of the river current = 2mph
Time taken for the boat to travel 30 miles downstream = Time taken for the boat to travel 20 miles upstream --- (1)
We have to find out the speed of the boat in still water.
Let us say that the speed of the boat in still water is x mph.
We know that -
Speed = Distance/Time
=> Time = Distance/Speed ----- (2)
When travelling upstream, the boat is slower and thus, we subtract speed of the current from the speed of the boat.
When travelling downstream, the boat is faster as it goes with the current and thus, we add the speed of the current with the speed of the boat.
From equation (1), we have
Time to travel 30 miles downstream = Time to travel 20 miles upstream
[tex]= > \frac{30}{x-2} =\frac{20}{x+2} \\= > 30(x+2)=20(x-2)\\= > 30x+60=20x-40\\= > 10x=100\\= > x=10[/tex]
Thus, taking into consideration the upstream and downstream speed, the speed of the boat in the still water is 10mph.
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A dog breeder is planning to buy more dog food. He makes a table showing how
many pounds of food he will have after shopping. The table is based on how much he
spends and how much food he already has. Which equation generates the table?
Money Spent (x) $0 $20 $40 $60
Pounds of Food (v) 4 12 20 28
O
x=y-4
y=8x-4
x = 8y +4
Oy=x+4
The equation that generate the table in slope intercept form is y = 2 / 5 x + 4
How to generate equation of a table?The equation of a linear table can be represented in different form such as slope intercept form, point slope form, standard form and general form.
Therefore, let's represent the equation of the table of money spent and pounds of food.
using slope intercept form,
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the slope using (0, 4) and (20, 12)
m = slope = 12 - 4 / 20 - 0
slope = 8 / 20
slope = 2 / 5
Therefore, let's find the y-intercept using (0, 4)
4 = 2 / 5(0) + b
b = 4
Therefore, the equation is y = 2 /5 x + 4
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3 pounds (lbs) = how many grams (g).
Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: −3, ordered pair: (−4,−2)
Answer:
y = - 3x - 14
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 3 , then
y = - 3x + c ← is the partial equation
to find c substitute (- 4, - 2 ) into the partial equation
- 2 = 12 + c ⇒ c = - 2 - 12 = - 14
y = - 3x - 14 ← equation of line
Spencer, a professional golfer, had an average score of 80 points last season. This season, however, his average score has been 5% higher. What is Spencer's current average score?
please
Answer:
84
Step-by-step explanation:
80 x 0.05 = 4
80 + 4 =84
Given the equation F=95C+32 where C is the temperature in degrees Celsius and F is the corresponding temperature in degrees Fahrenheit, and the following ordered pairs:
(−25,F1), (−5,F2)
The values of F1 and F2 are 77 and -22 degrees Fahrenheit respectively.
How to use the equation to convert from degrees Celsius to degrees Fahrenheit?Given that; the equation F=9/5C+32 and ordered pairs are (25, F1), (−30, F2)
To convert the values to degrees Fahrenheit, we have to substitute the given values into the equation to get F1 and F2 respectively:
For (25, F1);
F = 9/5 C+32
Now put C= 25 in the equation;
F1 = 9/5(25) + 32
F1 = 45 +22
F1 = 77 degrees Fahrenheit
For (−30, F2);
F = 9/5 C+32
Now put C= -30 in the equation;
F2 = 9/5(-30) + 32
F2 = -54 + 32
F2 = -22 degrees Fahrenheit
Hence, the values of F1 and F2 are 77 and -22 degrees Fahrenheit respectively.
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A rectangle has an area of 120 square meters and a width of 8 meters. What is the length?
Answer:
Step-by-step explanation:
Ok:
Area's formula is width* length
1. 120 square meters and width of 8 meters. Reversing the formula, divide area by width to get length!
120/8=15 meters
2. Answer: 15 meters
Find The Value Of Tan(M-P)
Given That Sinm=-(4)/(5)
Cosp=-(15)/(17)
Both Mand P Are In Quadrant III.
The value of tan(m - p), where the value of sin(m) = -(4/5), and the value of cos(p) = -(15/17) using trigonometric identities is; [tex]tan(m - p) = \dfrac{36}{77}[/tex]
What are trigonometric identities?Trigonometric identities are equations that involve trigonometric functions which are true for all values of the input variables.
The information in the question are;
[tex]sin(m) = -\dfrac{4}{5}[/tex][tex]cos(p) = -\dfrac{15}{17}[/tex]Therefore;
[tex]cos(m) = \sqrt{1- \left(-\dfrac{4}{5}\right)^2} =\pm\dfrac{3}{5}[/tex]
The location of m is in Quadrant III, therefore;
[tex]cos(m) =-\dfrac{3}{5}[/tex]
[tex]sin(p) = \sqrt{1- \left(-\dfrac{15}{17}\right)^2} =\pm\dfrac{8}{17}[/tex]
The angle p is located in Quadrant III, therefore;
[tex]sin(p) = -\dfrac{8}{17}[/tex]
180° ≤ Angle ∠m ≤ 270°; definition of angles in Quadrant III
180° ≤ Angle ∠p ≤ 270°; definition of angles in Quadrant III
Therefore;
270° - 270° ≤ |∠m - ∠p| ≤ 270° - 180°
0° ≤ |∠m - ∠p| ≤ 90°
The trigonometric identity for tan(m - p) is presented as follows;
[tex]tan(m - p) = \dfrac{tan(m) -tan(p)}{1+tan(m)\cdot tan(p)}[/tex]
[tex]tan(m - p) = \dfrac{\dfrac{sin(m) }{cos(m) } -\dfrac{sin(p) }{cos(p) } }{1+\dfrac{sin(m) }{cos(m) } \cdot \dfrac{sin(p) }{cos(p) } }[/tex]
Therefore;
[tex]tan(m - p) = \dfrac{\left(\dfrac{ -\dfrac{4}{5} }{-\dfrac{3}{5} }\right) -\left(\dfrac{ -\dfrac{8}{17} }{ -\dfrac{15}{17}}\right) }{1+\left(\dfrac{ -\dfrac{4}{5} }{-\dfrac{3}{5} }\right) \times \left(\dfrac{ -\dfrac{8}{17} }{ -\dfrac{15}{17}}\right) } }= \dfrac{36}{77}[/tex]
[tex]tan(m - p) = \dfrac{36}{77}[/tex]
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Answer to each expression
(3 + 9) x 2 dived 4
Answer: [tex]6\\[/tex]
Step-by-step explanation:
[tex]\frac{(3+9) * 2}{4}[/tex]
Add 3 and 9 to get 12.
[tex]\frac{12 * 2}{4}[/tex]
Multiply 12 and 2 to get 24.
[tex]\frac{24}{4}[/tex]
Divide 24 by 4 to get 6.
[tex]6[/tex]
A man deposited $800 in his account at the bank which offers 6% simple interest per annum
a, how much interest would he receive on the $800 after 9 months
b, how long it take for $800 to increase to $992
Answer:
Step-by-step explanation:
after 9 months, the man will have received $836. It would take 4 years to get $992 with a 6% simple interest annually
The function f(x) is graphed below. What is true about the graph on the interval from x = c to x = ∞?
Answer:
It is positive and increasing
Step-by-step explanation:
After the graph, it becomes positive as it passes the y-axis, the line which is where y=0. Also, the graph is headed up and to the right(after c), so as the value of x increase, the value of the function does as well. This would mean the answers is "It is positive and increasing"