Given :
Let, capacity of small bottle is x and large bottle is y.
To Find :
How much does each bottle hold ?
Solution :
For condition 1 :
3x + 4y = 3312 ...1)
For condition 2 :
2x + 4y = 2888 ...2)
Subtracting equation 2) from equation 1), we get :
x = 424
Putting value of x in equation 1) is :
[tex]y = \dfrac{2888 - (2\times 424)}{4}\\\\y = 510[/tex]
Therefore, capacity of small bottle is 424 gram and large bottle is 510 gram.
Describe the behavior of the function ppp around its vertical asymptote at x=-2x=−2x, equals, minus, 2.
Answer:
[tex]x->-2^{-}, p(x)->-\infty[/tex] and as [tex]x->-2^{+}, p(x)->-\infty[/tex]
Step-by-step explanation:
Given
[tex]p(x) = \frac{x^2-2x-3}{x+2}[/tex] -- Missing from the question
Required
The behavior of the function around its vertical asymptote at [tex]x = -2[/tex]
[tex]p(x) = \frac{x^2-2x-3}{x+2}[/tex]
Expand the numerator
[tex]p(x) = \frac{x^2 + x -3x - 3}{x+2}[/tex]
Factorize
[tex]p(x) = \frac{x(x + 1) -3(x + 1)}{x+2}[/tex]
Factor out x + 1
[tex]p(x) = \frac{(x -3)(x + 1)}{x+2}[/tex]
We test the function using values close to -2 (one value will be less than -2 while the other will be greater than -2)
We are only interested in the sign of the result
----------------------------------------------------------------------------------------------------------
As x approaches -2 implies that:
[tex]x -> -2^{-}[/tex] Say x = -3
[tex]p(x) = \frac{(x -3)(x + 1)}{x+2}[/tex]
[tex]p(-3) = \frac{(-3-3)(-3+1)}{-3+2} = \frac{-6 * -2}{-1} = \frac{+12}{-1} = -12[/tex]
We have a negative value (-12); This will be called negative infinity
This implies that as x approaches -2, p(x) approaches negative infinity
[tex]x->-2^{-}, p(x)->-\infty[/tex]
Take note of the superscript of 2 (this implies that, we approach 2 from a value less than 2)
As x leaves -2 implies that: [tex]x>-2[/tex]
Say x = -2.1
[tex]p(-2.1) = \frac{(-2.1-3)(-2.1+1)}{-2.1+2} = \frac{-5.1 * -1.1}{-0.1} = \frac{+5.61}{-0.1} = -56.1[/tex]
We have a negative value (-56.1); This will be called negative infinity
This implies that as x leaves -2, p(x) approaches negative infinity
[tex]x->-2^{+}, p(x)->-\infty[/tex]
So, the behavior is:
[tex]x->-2^{-}, p(x)->-\infty[/tex] and as [tex]x->-2^{+}, p(x)->-\infty[/tex]
In 4 minutes, a conveyor belt moves 800 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 6 minutes. If both belts are used, find how long it takes to move the cans to the storage area.
Answer:
It takes 2 minutes 4 seconds to move the cans to storage area if both the belts are used.
Step-by-step explanation:
Given - In 4 minutes, a conveyor belt moves 800 pounds of recyclable
aluminum from the delivery truck to a storage area. A smaller belt
moves the same quantity of cans the same distance in 6 minutes.
To find - If both belts are used, find how long it takes to move the cans
to the storage area.
Proof -
Given that,
Larger belt take 4 minutes to transfer the aluminium from delivery truck to storage area.
⇒ Time taken by Larger belt = 4 min/ shifting
Also,
Smaller belt take 6 minutes to transfer the aluminium from delivery truck to storage area.
⇒ Time taken by Smaller belt = 6 min/ shifting
Now,
As we know that Time is inversely proportional to time, so
Rate of Larger Belt = [tex]\frac{1}{4}[/tex] shifting/min
Rate of Smaller Belt = [tex]\frac{1}{6}[/tex] shifting/min
Now,
Let us assume that , if both belts used then,
Total time taken = x min/shifting
Then, Rate = [tex]\frac{1}{x}[/tex] shifting/min
Now,
[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{x}[/tex]
⇒[tex]\frac{6 + 4}{24} = \frac{1}{x}[/tex]
⇒[tex]\frac{10}{24} = \frac{1}{x}[/tex]
⇒10x = 24
⇒x = [tex]\frac{24}{10}[/tex] = 2.4 minutes
∴ we get
It takes 2 minutes 4 seconds to move the cans to storage area if both the belts are used.
The scores on a mathematics exam have a mean of 70 and a stadard deviation of 7. Find the x-value that corresponds to the z-score -1.45.
Answer:
59.85
Step-by-step explanation:
The scores on a mathematics exam have a mean of 70 and a stadard deviation of 7. Find the x-value that corresponds to the z-score -1.45.
We solve the above question using z score formula
z = (x-μ)/σ, where
x is the raw score
μ is the population mean = 70
σ is the population standard deviation = 7
z = -1.45
Hence:
-1.45 = x - 70/7
Cross Multiply
-1.45 × 7 = x - 70
-10.15 = x - 70
x = -10.15 + 70
x = 59.85
Raj is 53.56 inches tall. He is 1.3 times as tall as his younger sister. How tall is Raj's younger sister
Answer:
41.2 inches tall
Step-by-step explanation:
53.56 / 1.3 = 41.2
Step-by-step explanation:
Let Raj's sister's height be x
53.56= 1.3x
= 53.56/1.3=x
= 41.2=x
Elia rode her bicycle from her house to the beach at a constant speed of 18 1818 kilometers per hour, and then rode from the beach to the park at a constant speed of 15 1515 kilometers per hour. The total duration of the rides was 1 11 hour and the distances she rode in each direction are equal. Let b bb be the number of hours it took Elia to ride from her house to the beach, and p pp the number of hours it took her to ride from the beach to the park.
Answer: hello your question is not well written but it seems you are asking for the Total distance covered during the rides hence i will give you a general solution
Total distance travelled during rides = 16.36 km
Total duration of rides = 1 hour
Step-by-step explanation:
Given that :
b = number of hours from house to beach
p = number of hours from beach to park
since the total duration of the rides = 1 hour
hence: b + p = 1 ------ ( 1 )
Also ; speed from house to beach = 18 km/hr
speed from beach to park = 15 km/hr
Given that distance covered in both directions are equal and distance = s * t
Hence distance covered : 18b = 15p ------ ( 2 )
determine the total distance travelled
b + p = 1 ------ ( 1 )
18b = 15 p ----- ( 2 )
from equation 1 : b = 1 - p
18 ( 1 - p ) = 15p
18 = 15p + 18p
p = 18 / 33 = 6/11
back to equation 1
b + 6/11 = 1
hence b = 1 - 6/11 = 5/11
Distance covered in one direction
18 ( 5/11 ) = 15 ( 6/11 )
90 / 11 = 90 /11
hence Total distance covered = ( 90 / 11 ) * 2 = 16.36 km
Find the area of the figure shown below:
a
34 square units
b
220 square units
c
480 square units
d
960 square units
Answer:
.................hshs
Need help!!!! PLZ I don't know
Answer:
Step-by-step explanation:
First factor the polynomials and reduce the fractions.
help plz its worth 100 points
Answer:
Step-by-step explanation:
hi, use y=mx+b to help solve
the equation is y= 6x+30, 6 being the cost per t-shirt and 30 being the fee
substitute x for the values on the left in the table. for example, y=0x+30 would give the total cost of 0 t-shirts 30 dollars
for some reson i cant see it
An aquarium has 14 angel fish, 12
clownfish and 18 seahorses. What is the
ratio of seahorses to total number of fish?
Answer:
18 : 26
Step-by-step explanation:
It is very easy, angel fish and clown fish are fish, so once you add them up you get 26. The seahorses are 18 and we are supposed to make them S:F. Therefore you put the seahorses first and the fish second, so you get the answer 18:26
Marty has a driveway that is 200 feet long. The tires on her car have a diameter of 18 inches. What is the fewest number of tire rotations a tire will make tot travel the entire distance of the driveway?
The the fewest number of tire rotations is 42 to travel the entire distance of the driveway.
It is given that the driveway that is 200 feet long and the tire diameter is 18 inches.
It is required to find the fewest number of tire rotations a tire will make to travel the entire distance of the driveway.
What is a circle?It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).
Driveway length = 200 feet
Diameter of the tire = 10 inches
For converting it to feet divide by 12.
Now the diameter of tire = 18/12 = 1.5 feet
Radius of the tire = 0.75 feet
We know the perimeter of the circle:
[tex]\rm P = 2\pi r[/tex]
P = 2(π)(0.75)
P = 4.71 feet ( π =3.14 and P = 0.75)
[tex]\rm number \ of \ tire \ rotations = \frac{Driveway \ length}{Perimeter \ of tire}[/tex]
[tex]= \frac{200}{4.71}[/tex]
Number of tire rotation = 42.462 ≈ 42
Thus, the the fewest number of tire rotations is 42 to travel the entire distance of the driveway.
Learn more about circle here:
brainly.com/question/11833983
someone plssss helpppp
If a =3, b = 2 and c = 5, solve the following algebraic expressions: (3 marks)
a) 3c + 5 - b
b) b(4 - 2) + c
c) 4a - (2c)
Answer:
A) 18
B)9
C)-2
Step-by-step explanation:
Replace the a,b or c with the give number. So let’s say it’s says 2 + a. It would be 2+3.
Pls help what do I put for the answer
Answer this question to get marked as brainliest!!!
Answer:
∠ R = 120°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 angles from 180 , that is
subtract 60 from 180
∠ R = 180° - 60° = 120°
The awnser to a multiplication problem
Answer:
where is the problem?
Step-by-step explanation:
where
To create a pattern with Legos, Jerry uses 5 green Legos for every 3 blue Legos. If he used 35 green Legos in the pattern, what is the TOTAL amount of Legos he used?
A.43 legos in all
B.8 legos in all
C.56 legos in all
D.21 legos in all
Answer:
56 legos in all
Step-by-step explanation:
35/5=7
7*3=21
21+35=56
Answer:
well i have legos in rl so i think the answer is C. or 56 legos in all
Step-by-step explanation:
Please when answering show your full work. Step-by-step process.
Expand using suitable identity ( 3u + 5v )∧3
Answer:
Use symbolab
Step-by-step explanation:
There are 15 counters. One-third of the counters are yellow. How many
counters are yellow? *
Answer:
3
Step-by-step explanation:
15*1/5= 3
Gas from a local station costs $2.85 per gallon (in US dollars). Tara's car gets 13.4 kilometers to the liter.
About how much will it cost Tara to drive 640 kilometers if she buys the gas from that local gas station?
Answer:
$250.8
Step-by-step explanation:
13.4 = $2.85
13.4 x 15 = 111.0
111.0 = $42.75
111.0 x 6 = 666.0
666.0 - 26.0 = 640.0
$42.75 x 6 = $256.5
$2.85 x 2 = $5.07
$256.5 - $5.07 = $250.8
not gona lie this took forever lol
Hope this helps if so don't hesitate to 'Thanks' and/or 'brainliest' this answer!
The total cost of 640 liters of gas is $35.91.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Gas from a local station costs $2.85 per gallon (in US dollars).
We know that, 1 gallon = 3.785 liters
Tara's car gets 13.4 kilometers to the liter.
Number of liters of gas = 640/13.4
= 47.76 liters
Number of gallons = 47.76/3.785
= 12.6 gallons
Total cost = 12.6×2.85
= $35.91
Therefore, the total cost of 640 liters of gas is $35.91.
To learn more about the unitary method visit:
brainly.com/question/22056199.
#SPJ2
Which is the graph of y= 2x-3?
Answer:
(A:
Step-by-step explanation:
EXAMPLE:
in Slope Intercept form, the letter x determines the slope of the line, where 0 makes the line horizontal and 1 makes the line at a 45 degree angle, in this case to go from x to x plus 1 you would climb y two times, so it takes two units to go one unit to the right, so x is multiplied by 2
the addition at the end of the formula resembles how high up or down the line crosses the y axis, if the number is positive, then the line crosses that amount higher then 0, if it were a negative number, it would cross that much lower
hope this makes sence, dont worry, once you understand how slope intercept form works, you will never forget it, good luck with ur studies :)
MEGA CREDITS to MisterZeng for double checking our work, thx m8 :D
A 22.5 cm straw fits diagonally inside an 18 cm high can of soft drink what is the radius of the can
Answer:
6.75cm
Step-by-step explanation:
The straw fits diagonally inside the can so it makes a right angled triangle with height and base of the can ( which is the diameter of the can)
So, hypotenuse = length of straw = 22.5cm
perpendicular = 18cm
base = diameter of can(d)
Using pythagoras theorem
h² = p² + b²
(22.5)² = 18² + d²
506.25 = 324 + d²
d² = 506.25 - 324
d² = 182.25
d = 13.5cm
Now radius = d/2 = 13.5/2 = 6.75cm
In ΔPQR, the measure of ∠R=90°, the measure of ∠P=53°, and QR = 17 feet. Find the length of PQ to the nearest tenth of a foot.
Answer:
21.2863≈21.3 feet
Step-by-step explanation:
Answer:
21.3
Step-by-step explanation:
Help!!
Find the volume. Around to the nearest Hundredth.
1326cm
1026.04mi
1526.82mi
6104.16mi
Answer:
V=1526.82 mi³
Step-by-step explanation:
The formula for the volume of a right circular cone is V=πr²(h/3).
The radius is half of the diameter of 18, so it is 9 mi.
The height is 18 mi.
Plug in your numbers into the formula.
V=π9²(18/3)
V=π81(6)
V=π486
V=1526.82 mi³
The base of a triangular pyramid is 21 inches squared. The volume is 63 inches cubed. What is the height of the pyramid?
Answer:
9
Step-by-step explanation:
So the formula for a triangular pyramid is v=1/3bh
you plug in the values and you get 63=1/3(21)(h) and since you are finding the height, you get h=63*3/21
and then you check answers with
63=1/3(21)(9) which is true so the height is 9
Type your answer in the box provided. Make sure to use complete sentences.
Real World: Choose ONE of the following quadratic equations to solve. State your method of solving, giving your reasoning for why you chose that method. Show all work, and put your final answers in context.
A person walking across a bridge accidentally drops an orange into the river below from a height of 140 ft. The equation 0=−x2+7x+18 gives the relationship between how many seconds, x, have passed when the orange hits the water. In how many seconds will the orange hit the water?
A bird drops a stick to the ground from a height of 80 feet. The equation 0=−16x2+64x+80 gives the number of seconds that have passed when it hits the ground. After about how many seconds did the stick hit the ground?
Things you MUST include: (1 point each for a total of 5 points)
Method of solving the quadratic.
Reasoning for choosing this method.
All work to solve the quadratic equation.
The two mathematical answers to the equation.
The answer to the question asked, based on which answer is reasonable.
You may either type your answer in the text box below OR upload a file, picture, or scan of handwritten answers. All files should be saved using the following template: "Last Name_First Name_Assignment Name_Question Number." Refer to Orientation for help with file uploads.
Answer:
A bird drops a stick to the ground from a height of 80 feet. The equation 0=−16x2+64x+80 gives the number of seconds that have passed when it hits the ground. After about how many seconds did the stick hit the ground?
Step-by-step explanation:
h = -16t^2 + 80 Stick hits the ground when h = 0:
0 = -16t^2 + 80
16t^2 = 80
t^2 = 80/16 = 5
t = POSITIVE root 5 (due to the real world nature of the problem)
t approximately 2.236 seconds.
========================================
Graph is a downward opening parabola with h-intercept of 80, t-intercept(s) of sqrt(5), - sqrt(5)
Symmetric about h-axis, though I would only graph on the right side of the h-axis since
that is where t >= 0.
A Y U D E N P O R F A :(
Answer:
x=2
Step-by-step explanation:
Primero, necesitamos calcular <<a>>
Sabemos que AD=BC y AB=CD porque lados opuestos congruentes
Entonces, vamos a calcular <<a>>.
Usamos AD y BC
2a-1=4a-15
suma 15 a ambos lados
2a+14=4
añada 2 en ambos lados
14=2a
divida
7=a
Ahora, usamos esta información para calcular <<x>>
Usamos CD=AB
2a-8=4x-2
pero sabemos que <<a>> es 7
entonces:
14-8=4x-2
6=4x-2
8=4x
2=x
<<x>> es 2
(¡lo siento mi español no es perfecto!
) The diagram shows a quadrant of a circle . If the curved edge is 15 cm long, what is the length of a straight edge?
Answer:
9.55 cm
Step-by-step explanation:
A quadrant of a circle is 1/4 of a circle.
Since the curved edge is 15 cm, a full circle would be 60 inches.
60/Pi = diameter
diameter = 60/3.14 = 19.11 cm
diameter/2 = radius
radius = 19.22/2 = 9.55 cm which is the length of a straight edge.
What is the value of the expression 20 ÷ 4 + (6 x 2) − 2?
15
17
22
28
Solve the following equation using the quadratic formula.
2x² + 5x – 42 = 0
Select all solutions that apply.
x = 1.5
x= -4
OX= 3.5
x = -6