A train is moving at a uniform speed of 80 kilometre per hour.
a) how far will it travel in 15 minutes
b) find the time required to cover a distance of 250 km. { as per direct and inverse propositions}.
Explanation -:a)
Given that the train is moving at a uniform speed of 80 km/h.
Time taken = 15 minutes
First we will convert the time
[tex] \small \sf Time \: taken = 15 min = \dfrac{ \cancel{15}}{ \cancel{60}}hr = \dfrac{1}{4}hr [/tex]
Now we will calculate the distance
We know,
[tex] ✪ \: \small\boxed{ \frak{ {Distance }= {Speed} × Time }}[/tex]
Substituting the values in the given formula
[tex] \small\sf{ Distance = \cancel{ 80} \: \: 20 \: km/ \cancel{ hr} × \dfrac{1}{ \cancel{4}} \cancel{hr} =20km }[/tex]
Distance covered in 15 minutes = 20 km
[tex] \rule {40mm}{2pt}[/tex]
b)
Given that the train is moving at a uniform speed of 80 km/h.
Distance covered = 250 km
Calculating the time
We know,
[tex] ✪ \: \small\boxed{ \frak{ Time = \dfrac{Distance}{Speed}}}[/tex]
Substituting the values in the given formula
[tex] \small\sf{ Time = \dfrac{250 km}{80 km/hr} =3 \: hrs \: 20 \: mins }[/tex]
[tex] \star \: \small\sf{ Final \: Answer }[/tex]
Distance = 20 kmTime = 3 hrs 20 minutes[tex] ••═════════════••══════[/tex]
In Psychology 101, the ratio of the number of girls to the number of boys is $3:1$. After one girl drops the class and three more boys sign up, the ratio of the number of girls to the number of boys becomes $5:2$. How many students are in the class after these changes?
Answer:
There are 68 students in the class after these changes.
Step-by-step explanation:
g = number of girls
b = number of boys
Because the ratio of girls to boys is 3:1, initally the equation was
g = 3b
Finally, we have
g-1 girls because one girl dropped the class
b+3 boys because three more boys signed up
Because the new ratio of girls to boys is 5:2, the new equation is
(g - 1)/(b + 3) = 5/2
Cross multiply.
2(g - 1) = 5(b + 3)
2g - 2 = 5b + 15
2g - 5b = 17
Then, substitute g (which is 3b because the first equation was g = 3b)
2(3b) - 5b = 17
b = 17
g = 3b = 3*17 = 51
g = 51
The final number of students in the class = 17 + 51 = 68
Answer: 68
Question in the photo :) (Please help with my other questions!)
Answer:
a
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]u_{n}[/tex] = u₁ + (n - 1)d
given u₂₀ = 100 and u₂₅ = 115 , then
u₁ + 19d = 100 → (1)
u₁ + 24d = 115 → (2)
subtract (1) from (2) term by term to eliminate u₁
0 + 5d = 15
5d = 15 ( divide both sides by 5 )
d = 3
substitute d = 3 into (1) and solve for u₁
u₁ + 19(3) = 100
u₁ + 57 = 100 ( subtract 57 from both sides )
u₁ = 43
Answer:
a) u₁ = 43, d = 3
Step-by-step explanation:
Given :-
u₂₀ = 100
u₂₅ = 115
To Find :-
u₁ and d
Solving :-
u₂₀ = u₁ + 19d = 100 -(1)
u₂₅ = u₁ + 24d = 115 -(2)
(2) - (1)
5d = 15
d = 3
u₁ + 19(3) = 100
u₁ + 57 = 100
u₁ = 43
Solution :-
a) u₁ = 43, d = 3
A recipe for 12 waffles calls for 112 cups of milk, 214 cups of flour, and 113 cups of other ingredients. 4 pts each/16 pts total A... What is the total number of cups of ingredients needed for 12 waffles?... B... What is the total number of cups of ingredients needed for 36 waffles? .... C... If the milk is reduced to 1 cup and the amount of 'other ingredients' (not including the flour) is increased to 2 cups, would the total amount of ingredients for 12 waffles increase or decrease from the original recipe? Justify your thinking... D... If a baker has a 5 pound bag of flour, which is approximately 17 cups of flour, how many complete recipes for 12 waffles can the baker make?... Justify your thinking...
This question was not written properly
Complete Question
A recipe for 12 waffles calls for 1 1/2 cups of milk, 2 1/4 cups of flour, and 1 1/3 cups of other ingredients.
Answer:
A 5 1/12 cups of ingredients
B 10 1/6 cups of ingredients
C The total amount of ingredients for 12 waffles would increase from the original recipe.
D 7.56 or 7 5/9 recipes
Step-by-step explanation:
A... What is the total number of cups of ingredients needed for 12 waffles?...
The total number of cups of ingredients needed =
1 1/2 cups of milk + 2 1/4 cups of flour + 1 1/3 cups of other ingredients
(1 + 2 + 1) + (1/2 + 1/4 +1/3)
4 + ( 6 + 3 + 4/12)
4 + (13/12)
4 + (1 1/12)
= 5 1/12 cups of ingredients
B... What is the total number of cups of ingredients needed for 36 waffles? ....
If 12 waffles requires = 5 1/12 cups of ingredients
36 waffles =
Cross Multiply
= (36 waffles × 5 1 /12)/12 waffles
= 10 1/6 cups of ingredients
C... If the milk is reduced to 1 cup and the amount of 'other ingredients' (not including the flour) is increased to 2 cups, would the total amount of ingredients for 12 waffles increase or decrease from the original recipe?
Justify your thinking...
Original recipe.
A recipe for 12 waffles calls for 1 1/2 cups of milk, 2 1/4 cups of flour, and 1 1/3 cups of other ingredients = total of 5 1/12 cups of ingredients
Current recipe
1 cup of milk + 2 1/4 cups of flour + 2 cups of other ingredients
1 + 2 + 2 + (1/4)
5 1/4 cups of ingredients
Therefore, total amount of ingredients for 12 waffles would increase from the original recipe. This is because when you subtract 5 1/12 from 5 1/4 you get a difference of 1/6 cups
5 1/4 - 5 1/12 = 1/6
D... If a baker has a 5 pound bag of flour, which is approximately 17 cups of flour, how many complete recipes for 12 waffles can the baker make?... Justify your thinking...
The original recipe has 2 1/4 cups of flour as its quantity for 12 waffles
Hence:
2 1/4 cups of flour = 12 waffles
17 cups =
17 × 12/2 1/4
= 204÷ 2 1/4
= 204 ÷ 9/4
= 204 × 4/9
= 90.666666667 or 90 2/3 Waffles
If = 12 waffles = 1 recipe
90 2/3 waffles =
7.56 or 7 5/9 recipes
Given
Total no. of waffles required = 12
No. of cups of milk = [tex]1\frac{1}{2}[/tex]
No. of cups of flour = [tex]2\frac{1}{4}[/tex]
No. of cups of other ingredients = [tex]1\frac{1}{3}[/tex]
The total number of cups of ingredients needed for 12 waffles =
No. of cups of milk + no. of cups of flour + no. of cup of other ingredients
= [tex]( 1+ 2+ 1 ) ( \frac{1}{2} + \frac{1}{4} + \frac{1}{3} )[/tex]
= [tex](4) + ( \frac{6+3+4}{12} )\\\\= (4) +(\frac{13}{12} \\\\= \frac{48+13}{12} \\\\= \frac{61}{12}[/tex]
The total number of cups of ingredients needed for 12 waffles is [tex]\frac{61}{12}[/tex].
The total number of cups of ingredients needed for 36 waffles=
= The total number of cups of ingredients needed for 36 waffles cups of ingredients.
If the milk is reduced to 1 cup and the amount of 'other ingredients' (not including the flour) is increase or decrease in recipe.A recipe for 12 waffles calls for [tex]1\frac{1}{2}[/tex] cups of milk, [tex]2\frac{1}{4}[/tex] cups of flour, and [tex]1\frac{1}{3}[/tex]cups of other ingredients = total of [tex]5\frac{1}{12}[/tex] cups of ingredients
Current recipe
= 1 cup of 2 milk + cups of flour + 2 cups of other ingredients
= 1 + 2 + 2 + ()
= cups of ingredients
Therefore, total amount of ingredients for 12 waffles would increase from the original recipe. This is because when you subtract [tex]5\frac{1}{12}[/tex] from [tex]5\frac{1}{4}[/tex] you get a difference of [tex]\frac{1}{6}[/tex] cups.
[tex]5\frac{1}{4}[/tex] - [tex]5\frac{1}{12}[/tex] = [tex]\frac{1}{6}[/tex]
The original recipe has [tex]2\frac{1}{4}[/tex] cups of flour as its quantity for 12 waffles
Hence:
[tex]2\frac{1}{4}[/tex] cups of flour = 12 waffles
17 cups =
17 ×
= 204÷ [tex]2\frac{1}{4}[/tex]
= 204 ÷ [tex]\frac{9}{4}[/tex]
= 204 × [tex]\frac{4}{9}[/tex]
= 90.666666667 or 90 [tex]\frac{2}{3}[/tex] Waffles
If = 12 waffles = 1 recipe
90 waffles =
7.56 or recipes.
For more information about Ratio and proportion click the link given below.
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Write a word problem using rational numbers and using at least two of the operations (add, subtract, multiply, divide).
Alicia had - $11.00 in her checking account. She did a few chores and made $44.50. She decided to pay for her and a friend to go to the movies and each ticket costs $6.25. How much money does she have left in her account?
There are 30 students in Mrs.
Woodward’s class and 15 of the class has their own cell phone. Of this group of students, 12 of them
are allowed to use social media. How many of the students have a cell phone and can use social media?
There are two up there
A building that is 300 m
tall casts a 270 m
shadow. At the same
time, a different building
casts an 90 m shadow.
How tall is the building?
Answer:
10m
Step-by-step explanation:
we can use the cross multiply method.
300m = 270m
x m = 90m
270x = 300 x 90
270x = 2700
x = 10
so the buliding is 10m tall
Aline etlea, deux coiffeuses contactent le même. fournisseur . Aline commande 10 lots de champoing à 15,60 l,unite et paie la meme somme que lea qui a commande 2 tondeuses et 2 lots dechampoing. Combien coûte une tondeuse? c,est undm note aidez moi reponse
Answer:
on my screen it sayes its 50938
Step-by-step explanation:
find the missing ratio and explain how you found it
Answer:
5:4
Step-by-step explanation
If your shoes to flip-flops are 10:8 then the starting ratio will be 10:8 but 10 and 8 are both divisible to 2 so you can simplify 10:8 to 5:4
Add. Enter a number only as your answer in the space provided
Please I really need help
Answer:
0 is the answer okay
Step-by-step explanation:
0 is the answer okay
20% of 50 =
help ;)
thanks to whoever helpss
Answer: the answer to your question is
10
Step-by-step explanation:
Answer:
20% of 50 = 10
Step-by-step explanation:
1. Convert the problem to an equation using the percentage formula: P% * X = Y
P is 20%, X is 50, so the equation is 20% * 50 = Y
2. Convert 20% to a decimal by removing the percent sign and dividing by 100: 20/100 = 0.2
3. Substitute 0.2 for 20% in the equation: 20% * 50 = Y becomes 0.2 * 50 = Y
4. Do the math: 0.2 * 50 = 10
5. Final answer: 20% of 50 is 10
Please help with homework
Solve the system using Gaussian elimination. 6x−y+3z=−9 5x + 5y−5z = 20 3x−y+4z = −5 A (2,12,−3)open paren 2 comma 12 comma negative 3 close paren B (2,2,0)open paren 2 comma 2 comma 0 close paren C (−1,6,1)open paren negative 1 comma 6 comma 1 close paren D (−2,6,3)
Answer:
C. (-1,6,1)
Step-by-step explanation:
Given the system of equation
6x−y+3z=−9 ...... 1
5x + 5y−5z = 20 ...... 2
3x−y+4z = −5 ...... 3
Reduce the equations to two variables with 2unknown
Multiply equation 3 by 2 and add to 1.
Equation 3×2; 6x−2y+8z = −10 ...... 4
Subtract 4 from 1
-y-(-2y)+3z-8z = -9-(-10)
-y+2y-5z = -9+10
y-5z = 1 ...... 5
Also multiply eqn 2 by 3 and 3 by 5
Equation 2×3; 15x+15y-15z= 60
Equation 3×5; 15x-5y+20z = -25
Subtract
15y+5y-15z-20z = 60+25
20y-35z = 85
Divide through by 5:
4y-7z = 17 ...... 6
...................................
Solve 5 and 6
y-5z = 1 ...... 5 × 4
4y-7z = 17 ...... 6 × 1
....................................
4y-20z = 4
4y-7z = 17
Subtract
-20z+7z = 4-17
-13z = -13
z = -13/-13
z = 1
Substitute z = 1 into equation 5 to get y:
From 5: y-5z = 1
y - 5(1) = 1
y-5 = 1
y = 1+5
y = 6
Substitute y = 6 and z = 1 into equation 3 to get x;
From 3: 3x−y+4z = −5
3x-6+4(1) = -5
3x -6+4 = -5
3x-2 = -5
3x = -5+2
3x = -3
x = -3/3
x = -1
Hence x = -1, y = 6 and z = 1
The correct answer is (-1, 6, 1)
Match each equation to the situation it represents.
Answer:
I believe you need to switch the equations from the top and middle problems.
Step-by-step explanation:
I hope this helps
which of the following lines are perpendicular to the line y= 3/4x - 8? select all that apply
a. y=4/3x+8
b.y=-4/3x-12
c.y+4/3x=2
d.y-3/4x=1
e.6y=-8x+12
Answer:
B and C that's the answers
1. What is the correct reason for statement #3?
2. What is the correct reason for statement #4?
3.What is the coolest reason for statement #5?
Answer:
1) B. Combine-like terms
2) A. Subtraction Property of Equality
3)D. Division Property of Equality
Step-by-step explanation:
when is the temperature constant?
Answer:
From 11 am until 2 pm
Step-by-step explanation:
The line is straight meaning its constant throughout the time 11pm - 2pm, it is neither rising nor falling like the other two.
Create a word problem using the numbers -6 and 3.
Answer:
Aaron has 3 red cubes and 15 yellow cubes in his bag. If he subtracts six yellow cubes, how many cubes of each color does he have?
Answer:
Jake from state farm lost 3 dollars from buying McDonalds it cost him dollars 6 how much money does he still have to pay
Step-by-step explanation:
Please help me answer this question on congruent triangles. 30 points available.
Answer:
Pair A are not congruent.
To prove two triangles are congruent, 3 equal angles aren't sufficient.
Pair B are not congruent as well.
To prove they are congruent using ASA we have to make sure the given equal side lies between the 2 angles, which it is not.
They are not congruent
please help with question
Answer:
We can assume angles 102° and angles 0 and 42° are alternate interior angles.
So, to solve for 0, we must add this unknown angle to 42° and make it equal to 102°;
Let's make '0', x(our variable we solve for)
x + 42 = 102
-42 -42
x = 60
600 people attended a football game. If 25% of the people who attended were teenagers, how many teenagers attended the game?
Answer:
150 Teenagers would have attended the game
What is the £ to € exchange rate?
what is 2 1/2 divided by 1 5/8
Answer:
2 1/2 divided by 1 5/8 equals to 1.53846153846
The drawing shows how to___?
A. Construct an angle congruent to a given angle
B. construct an equilateral triangle
C. draw an angle bisector
D. draw a perpendicular line through a point on the line
Answer:
C. draw an angle bisector
Step-by-step explanation:
Which is true about the completely simplified difference of the polynomials a3b 9a2b2 − 4ab5 and a3b − 3a2b2 ab5?.
The simplified difference of the polynomials (a³b+9a²b²-4ab⁵) and (a³b-3a²b²+ab⁵) is (12a²b²-5ab⁵).
What are Like terms?Like terms are those terms that are having the same variables, also the variables are of the same order as well.
for example, 25x and 5x are like terms; 30xy and 7xy are like terms, 9x³ and 4x² are not like terms, etc.
Let's simplify the two of the given polynomials, therefore, find the difference between the two given polynomials.
[tex]a^3b+9a^2b^2 - 4ab^5 - (a^3b - 3a^2b^2+ab^5)\\\\= a^3b+9a^2b^2 - 4ab^5 - a^3b + 3a^2b^2-ab^5\\\\\text{Bring Like terms together}\\\\=a^3b - a^3b+9a^2b^2+3a^2b^2 -4ab^5-ab^5\\\\= 12a^2b^2-5ab^5[/tex]
Hence, the simplified difference of the polynomials (a³b+9a²b²-4ab⁵) and (a³b-3a²b²+ab⁵) is (12a²b²-5ab⁵).
Learn more about Like Terms:
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Which equation represents the function notation for the equation y = 5x + 4?
Answer:
f(x) = 5x + 4
Step-by-step explanation:
*
4. Find the measure of each angle
Please help need answers ASAP
Answer:
55°, 125°
Step-by-step explanation:
angle EFG = 180°
angle EFH + angle GFH = angle EFG (Colinearity)
substitute the values,
6x - 5 + 12x + 5 = 180°
18x = 180°
(÷18)
x = 10
substitute values of x in both the requires angles,
angle EFH
= (6 × 10) -5
= 55°
angle GFH
= (12 × 10) + 5
=125°
to check,
55° + 125° = 180°
State if the three side lengths form an acute, obture, or right triangle 3 in 12 in and 13 in
Answer:
The triangle is obtuse.
Step-by-step explanation:
If a² + b² < c² , the triangle is obtuse.
If a² + b² = c² , the triangle is right triangle.
If a² + b² > c² , the triangle is acute.
~~~~~~~~~~~~~~~~
3, 12, 13
3² + 12² < 13²
9 + 144 < 169
153 < 169 ⇒ the triangle is obtuse.
Write the equation y=3/4x-4 in standard form
The equation 3x - 4y = 16 is now in standard form, where A = 3, B = -4, and C = 16.
To convert the equation y = (3/4)x - 4 into standard form, we need to eliminate any fractions and rewrite it in the form Ax + By = C, where A, B, and C are integers.
The given equation is already almost in standard form, but we can proceed with the following steps:
Step 1: Multiply both sides by 4 to eliminate the fraction:
4y = 3x - 16
Step 2: Move all terms to one side of the equation to have zero on the other side:
3x - 4y = 16
The equation 3x - 4y = 16 is now in standard form, where A = 3, B = -4, and C = 16.
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What is the ratio 15 : 24 written in lowest terms? 0 3:4 07:8 0 3:5 c 5:8
Answer 5:8
Step-by-step explanation:
Lucy needs to buy snacks for her soccer team. she only has $25 in her pocket.
if each juice box cost $1.50 and a bag of chips (ost $1.00. how many chips
and drinks can she purchase?
4.678
written to one decimal point would be
Answer:
hello
4.678 = 4 678 / 1000
Step-by-step explanation: