Answer:
Average speed during the trip = 24 km/h
Step-by-step explanation:
Given:
Speed of cyclist uphill, [tex]v_1[/tex] = 20 km/hr
Speed of cyclist on flat ground = 24 km/h
Speed of cyclist downhill, [tex]v_2[/tex] = 30 km/h
Cyclist has traveled on the hilly road to Beast Island from Aopslandia and then back to Aopslandia.
That means, one side the cyclist went uphill will the speed of 20 km/h and then came downhill with the speed of 30 km/h
To find:
Average speed during the entire trip = ?
Solution:
Let the distance between Beast Island and Aopslandia = D km
Let the time taken to reach Beast Island from Aopslandia = [tex]T_1\ hours[/tex]
Formula for speed is given as:
[tex]Speed = \dfrac{Distance}{Time}[/tex]
[tex]v_1 = 20 = \dfrac{D}{T_1}[/tex]
[tex]\Rightarrow T_1 = \dfrac{D}{20} ..... (1)[/tex]
Let the time taken to reach Aopslandia back from Beast Island = [tex]T_2\ hours[/tex]
Formula for speed is given as:
[tex]Speed = \dfrac{Distance}{Time}[/tex]
[tex]v_2 = 30 = \dfrac{D}{T_2}[/tex]
[tex]\Rightarrow T_2 = \dfrac{D}{30} ..... (2)[/tex]
Formula for average speed is given as:
[tex]\text{Average Speed} = \dfrac{\text{Total Distance}}{\text{Total Time Taken}}[/tex]
Here total distance = D + D = 2D km
Total Time is [tex]T_1+T_2[/tex] hours.
Putting the values in the formula and using equations (1) and (2):
[tex]\text{Average Speed} = \dfrac{2D}{T_1+T_2}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{D}{20}+\dfrac{D}{30}}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{30D+20D}{20\times 30}}\\\Rightarrow \text{Average Speed} = \dfrac{2D\times 20 \times 30}{{30D+20D}}\\\Rightarrow \text{Average Speed} = \dfrac{1200}{{50}}\\\Rightarrow \bold{\text{Average Speed} = 24\ km/hr}[/tex]
So, Average speed during the trip = 24 km/h
Without using a calculator, convert the fraction to a decimal
Answer:
what's the fraction though?
According to the graph, what is the factorization of x^2-5x+6?
Answer:
(x-3) (x-2)
Step-by-step explanation:
The zeros of the graph are 2 and 3 ( where the graph crosses the x axis)
The factorization is of the form
(x-a) (x-b) where a and b are the zeros
(x-3) (x-2)
Alex makes $20 per hour in her job as a kiental assistant. She works 8 hours per day
and 40 hours per week. How much does Alex make in a day before taxes?
Answer:
160
Step-by-step explanation:
20 dollars per hour * 8 hours per day
160 dollars per day
Answer:
Alex makes $ 160 per day
Step-by-step explanation:
If she earns $20 per hour and works for 8 hours
8 × 20 = 160
6(3+2) please help me if
Answer:
[tex]30[/tex]
Step-by-step explanation:
[tex]6(3 + 2) \\ = 6(5) \\ = 30[/tex]
Hope it is helpful....PLEASE ANSWER QUICKLY ASAP
COMPLETE QUESTION B
Answer:
Sector
Step-by-step explanation:
A sector of a circle is the portion of circle enclosed by two radii and arc
(t)What is the difference between
{2, 3} and {{2, 3}}?
[tex]\{2,3\}[/tex] is a set containing two elements - numbers 2 and 3
[tex]\{\{2,3\}\}[/tex] is a set containing one element - a set [tex]\{2,3\}[/tex]
PLEASE HELP, I'LL MARK BRAINLIEST.. Of the 37 teachers at Francesca's high school, 9 are female. What is the ratio of the number of male teachers to the total number of teachers? Please write in decimal form
what fraction of these houses have seven rooms
Answer:
9/50
Step-by-step explanation:
18 % have 7 rooms
18 % means 18 out of 100
18/100
Divide top and bottom by 2
9/50
betty's bakery calculates the total price d in dollars for c cupcakes using the equation d=2c. What does 2 mean in this situation?
Answer:
2 means dollars per cupcake
Step-by-step explanation:
it makes sense because it says d=2c which is
money = $2 per cupcake
so if their are 2 cupcakes then
d=2*2 = $4
write down atleast five number pairs to solve the equation (r-2) (s+1) = 100
Answer:
1. (52 - 2) (1 + 1) = 1002. (12 - 2) (9 + 1) = 1003. (6 - 2) (24 + 1) = 1004. (3 - 2) (99 + 1) = 1005. (102 - 2) (0 + 1) = 100Step-by-step explanation:
1. let r= 52 and s= 1(52 - 2) (1 + 1) = 10050 × 2 = 1002. let r= 12 and s= 9(12 - 2) (9 + 1) = 10010 × 10 = 1003. let r= 6 and s= 24(6 - 2) (24 + 1) = 1004 × 25 = 1004. let r= 3 and s= 99(3 - 2) (99 + 1) = 1001 × 100 = 1005. let r= 102 and s= 0(102 - 2) (0 + 1) = 100100 × 1 = 100[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
two inches is approximately
Answer:
5.08 cm
Step-by-step explanation: You dont have the choices for answers.
2inches is also 1/6 of a foot, etc
I’m having a lot of trouble, can someone guide me, step by step?
Answer:
Hi hopefully this helps you!
Step-by-step explanation:
To find the area of a circle you can use the formula A = πr^2
The radius of a circle is just the diameter divided by 2. In this case we know the diameter is 3, so the radius is 1.5
A = π(1.5)^2
= 7.07
Because this is a semicircle, divide this area by 2
= 3.53429 in^2
Add up the area of this semi circle with the area of the rectangle
A = (3.53429) + (3x4)
= 15.53429 in^2
To find the circumference/ perimeter of a circle use this formula C = 2πR
C = 2π(1.5)
= 9.42478 inches
Again because this is a semicircle, divide by 2
= 9.42478 / 2
= 4.71239 inches
To find the perimeter of this entire shape add up the circumference of the semicircle and the rectangle's sides and bottom
P = 4.71239 + 4 + 4 + 3
= 15.71239 inches
So the final answer would be
A = 15.53 squared inches
P = 15.71 inches
Hope this helps! Best of luck in your studies <3
A water sprinkler sends water out in a circular pattern. How large is the watered
area if the radius of the watering pattern is 3 feet?
Use 3.14 for pi.
____feet squared
Which of the following is the function for the graph? Choices/graph below.
set x=0 to get insights.
at x=0 to the functions are
-2(0-2)²+3 = -5
-2(0+2)²-3 = -11
-2(0-2)²+3 = -5
-2(0-2)²-3 = -11
weird, for some reason option 1 and 3 seem to be the same, maybe that's an accident by the author.
maybe a + was intended inside the parentheses, dunno.
option 1 and 3 seem fine, although I think there is an error in the options. they shouldn't be exactly the same
3.41 repeating as a fraction?
Answer: the answer is 3 41/99
Step-by-step explanation: got it from khan pls mark me 5 stars
15. A lamp is on sale at £22.05 This is a 10% reduction of the normal price. What was the price of the lamp before the reduction?
Answer:
£24.26 (rounded to 2dp) or full answ £24.255
Step-by-step explanation:
find 1% of 22.05= 0.2205
0.2205*10=2.205(10%)
add this to the 90%(£22.05+2.025)= 24.255
=24.26(rounded to 2dp)
The price of the lamp before the reduction will be £24.5.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
The sale price of the lamp = £22.05
This is a 10% reduction of the normal price.
Now,
Let the price of the lamp before the reduction = x
So, We can formulate;
⇒ x - (10% of x) = £22.05
⇒ x - 10x/100 = £22.05
⇒ (100x - 10x)/100 = £22.05
⇒ 90x / 100 = £22.05
⇒ 90x = £22.05 x 100
⇒ 90x = £2205
⇒ x = £2205/90
⇒ x = £24.5
Thus, The price of the lamp before the reduction will be £24.5.
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20 squared (+5) divided by 100
The answer is 4.05
Step-by-step explanation:
20^2 is 20•20 which is 400 || +5=405 || /100=4.05
A holiday company charters an aircraft to fly to Malta at
a cost of $22 000. It then sells 150 seats at $185 each and a
futher 35 seats at a 20% discount. Calculate the profit made
per seat if the plane has 200 seats.
Answer:
$54.65 profit per seat
Step-by-step explanation:
150(185) + 35(185)(.8) = 27,750 + 5,180 = 32,930 - 22,000 = 10,930
10,930/200 = $54.65 profit per seat
Answer:
$54.65
Step-by-step explanation:
First, we find the total amount made. This is easy:
(150 x 185) + (35 x .8(185)) =
27750 + 5180 =
32930
We then subtract the $22000, so the company makes a profit of 10930. There are 200 seats, so the profit made per seat is $54.65
write down the missing number in the following 1,,4,9,16,25,?
Answer:
36
Step-by-step explanation:
you know the number based on the sequence
the values increase in the form of x+2
e.g. 4-1=3
9-4=5
16-9=7
25-16=9
you can see the number adds 2 for every increased number
and by following this sequence you will get the number 36
Answer:
by the square of 1, 2 ,3 the sequence has been made
Step-by-step explanation:
1 for 1²
4 for 2²
9 for 3²
16 for 4²
25 for 5²
so the later one will be 36 for 6²
so the answer is 36 thats all
What are the possibilities of “AI technology” in various fields of mathematics education.?
Please help fast
Answer:
it could be used to calculate higher deviations of calculus, to measure heights also for optimization algorithms for decision
making under uncertainty
x -12 = 14
---------------
[tex]x - 12 = 14 \\ x = 14 + 12 \\ x = 26[/tex]
it was help to you ❤︎❤︎❣︎❣︎★★★
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{x - 12 = 14}[/tex]
[tex]\huge\text{ADD 12 to BOTH SIDES}[/tex]
[tex]\huge\textsf{x - 12 + 12 = 14 + 12}[/tex]
[tex]\huge\boxed{\bullet}\huge\text{ CANCEL out: 12 - 12 because it gives}\\\huge\text{you 0}[/tex]
[tex]\huge\boxed{\bullet}\huge\text{ KEEP: 14 + 12 because it gives you}\\\huge\text{the RESULT of the x-value}[/tex]
[tex]\huge\textsf{a = 14 + 12}\\\huge\boxed{\rightarrow}\huge\textsf{ 14 + 12 = a}[/tex]
[tex]\huge\textsf{14 + 12 = \bf 26}[/tex]
[tex]\boxed{\huge\textsf{Therefore, your answer is: a = 26}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
4.
Find the inverse of A if it has one, or state that the inverse does not exist.
Answer:
Hello,
[tex]\begin{bmatrix}\dfrac{-1}{5} &0\\\dfrac{-1}{10}&\dfrac{1}{4}\end{bmatrix}[/tex]
Step-by-step explanation:
See jointed file
The inverse of the matrix A is
[tex]A = \left[\begin{array}{cc}-5&-2\\0&4\end{array}\right][/tex]
What is a matrix?A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.
We have,
[tex]A = \left[\begin{array}{cc}-5&0\\-2&4\end{array}\right][/tex]
The matrix A is a square matrix and its determinant is not zero.
So the inverse exist.
The inverse of matrix A.
We will change the rows into columns and columns into rows.
So,
[tex]A = \left[\begin{array}{cc}-5&-2\\0&4\end{array}\right][/tex]
Thus,
The inverse of the matrix A is given above.
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Which number line best shows how to solve −8 − (−2)? A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2. A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to 2. A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 6. A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to 6.
Answer:
A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 6
Step-by-step explanation:
A number line is a straight line with numbers placed at equal intervals. Positive numbers are placed to the right of 0 and negative numbers are placed to the left of zero.
When a number (x) is added x unit is moved to the right while if a number (x) is subtracted x units is moved to the left.
To solve -8 - (-2) = -8 + 2
Given a A number line from negative 10 to 10 with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8 then since 2 is added, we move 2 units right from negative 8 to negative 6.
Answer:
C (3rd option)
Step-by-step explanation:
simplified the top one
Simplify xy-5x+y^2xy−5x+y 2 if x = -3 and y = 5.
The simplification of the expression [tex]xy-5x+y^2xy-5x+y ^2[/tex] gives - 335.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
Given;
[tex]xy-5x+y^2xy-5x+y ^2[/tex]
Substitute x = -3 and y = 5.
[tex]-3\times 5-5\times -3+5^2\times -3\times 5-5\times -3+5 ^2[/tex]
= -15 + 15 - 375 + 15 + 25
= -335
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The winning times (in seconds) in a speed-skating event for men can be represented by the formula T = 46.97 - 0.099x, where x represents the year, with x = 0 corresponding to 1920. (For example in 1992, x would be 1992 - 1920 = 72.) According to the formula, what was the winning time in 1997? Round to the nearest hundredth. * 1 point 40.34 sec 39.35 sec 3609.07 sec 41.33 sec
Answer:
39.35 sec
Step-by-step explanation:
Given that:
The winning time is represented by the function:
T = 46.97 - 0.099x
Where x = year ; x = 0 corresponding to 1920
According to the formula, what was the winning time in 1997?
first find the value of x;
x = 1997 - 1920 = 77 years
Nowing plugging the value of x in the function :
T = 46.97 - 0.099(77)
T = 46.97 - 7.623
T = 39.347 seconds
T = 39.35 s
The conjecture "if n is a whole number then 3n+1 is a prime number" is disapproved by which statement
Answer:
D
Step-by-step explanation:
Simply because 25 is divisible by 5.
Let x be the sum of the following 2000 numbers
Answer:
See attached image for the sum computed using wolfram alpha, raw value is: 49382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382715160
Answer:
Step-by-step explanation:
First, i divide all terms by 4
sequence is 1,11,111,1111,....,1111...1111 (with 2000 digits)
[tex]u_1=1\\\\u_2=11=10+1=\dfrac{10^2-1}{9}\\\\u_3=111=100+10+1=\dfrac{10^3-1}{9}\\\\u_4=1111=1000+100+10+1=\dfrac{10^4-1}{9}\\....\\u_n=\dfrac{10^n-1}{9}\\\\\\\displaystyle \sum_{i=1}^n\ u_1 =\dfrac{10^1-1}{9}+\dfrac{10^2-1}{9}+\dfrac{10^3-1}{9}+...+\dfrac{10^n-1}{9}\\=\dfrac{1}{9} *(10+10^2+10^3+....+10^n+1-1-(1+1+1+1...+1)\ )\\\\=\dfrac{1}{9}*( \frac{10^{n+1}-1}{9} -(n+1)\ )[/tex]
[tex]\boxed{4+44+444+....+444...4=\dfrac{4}{9}*( \dfrac{10^{2001}-1}{9} -2001\ )}\\\\\\\approx{4,9382716049382716049382716049383*10^{1999} }[/tex]
PLEASE HELP ME WORTH 20 POINTS It looks like the graph of the parents function f(x)x^2. However:
- It has been reflected (flipped) over the x-axis
-It has been shifted down 4 units.
-It had been shifted left 1 unit
Step 1: Start with the equation f(x) = x2. Write the equation for the graph of g(x) that has been reflected, or flipped, over the x-axis.
Step 2: Use the equation you wrote in Step 1. Write the equation for the graph of g(x) that has also been shifted down 4 units.
Step 3: Use the equation you wrote in Step 2. Write the equation for the graph of g(x) that has also been shifted left 1 unit.
flipped : [tex]-x^2[/tex]
moving down: [tex] -x^2+4[/tex]
shifting left [tex] -(x+1)^2+4[/tex]
expanding it: [tex] -x^2-2x+3[/tex]
Answer:
1. f(x)=x^2
f(x)=-x^2
2. f(x)=-x^2-4
3. f(x)=-(x+1)^2-4
WILL MARK BRAINLIEST FOR CORRECT ANSWER. <3 <3 The area of the following rectangle is 24 square units. A. Write an equation that can be used to find the value of n. B. Solve the equation to find the value of n. In your answer, show all of your work.
Because area is multiplication lets multiply the sides and make an equation:
A 2(n-3) = 24
n-3=(12)
B n= 15
15-3 = 12
12 x 2 = 24
Answer:
2(n-3)=24
n=15
Step-by-step explanation:
2(n-3)=24
2n-6=24
2n=30
n=15
London answered 20 questions correctly on her multiple choice history final that had a total of 80 problems. What percentage of questions did London answer correctly on the final exam?
Answer:
25%
Step-by-step explanation:
correct/total
20/80
1/4
Changing to a decimal
.25
.25*100%
25%
Answer:
1/4 or 25%
Step-by-step explanation:
1). 20 / 80 = 1 / 4 = 25 %
Hope this helps