Answer:
[tex]Height= 5cm[/tex]
Step-by-step explanation:
Given
Tank:
[tex]Base =20cm\ by\ 17cm[/tex]
[tex]Depth = 28cm[/tex]
Water:
[tex]Quantity = 1\frac{1}{4}L, 350mL, 100mL[/tex]
Required
Determine [tex]the\ height[/tex] of the water in the tank
First, we calculate the total volume of water added.
[tex]Quantity = 1\frac{1}{4}L+ 350mL + 100mL[/tex]
[tex]Quantity = 1.25L+ 350mL + 100mL[/tex]
Convert all units to Litres
[tex]Quantity = 1.25L+ 0.35L + 0.1L[/tex]
[tex]Quantity = 1.7L[/tex]
Convert to cm^3
[tex]Quantity = 1.7 * 1000cm^3[/tex]
[tex]Quantity = 1700cm^3[/tex]
The volume of the water in the tank is calculated as:
[tex]Volume =Base\ Area * Height[/tex]
i.e. the base area of the tank multiplied by the height of the water in the tank
[tex]Volume =20cm * 17cm* Height[/tex]
[tex]Volume =340cm^2* Height[/tex]
Since the above represents the quantity of water, we can substitute 1700cm^3 for Volume
[tex]1700cm^3=340cm^2* Height[/tex]
Make height the subject
[tex]Height= \frac{1700cm^3}{340cm^2}[/tex]
[tex]Height= \frac{1700cm}{340}[/tex]
[tex]Height= 5cm[/tex]
earth is approximately 9 x 10^7 miles from the sun. neptune is approximately 3x10^9 miles from the sun. neptune is approximately _____ times farther from the sun than earth
Answer:
[tex]33[/tex] times
Step-by-step explanation:
Distance between Earth and the sun [tex](D)[/tex] = 9 × [tex]10^{7}[/tex] miles = [tex]90,000,000[/tex] miles
Distance between Neptune and the sun [tex](d)[/tex] = 3 × [tex]10^{9}[/tex] miles = [tex]3,000,000,000[/tex] miles
Find [tex]\frac{d}{D}[/tex].
[tex]\frac{d}{D}=\frac{3,000,000,000}{90,000,000} =33.3[/tex] ≈ [tex]33[/tex]
Therefore,
Neptune is approximately [tex]33[/tex] times farther from the sun than earth
If EH = 18 and FG 1 EH, solve for the measure of EG.
Answer:
9
Step-by-step explanation:
If its perpendicular, it probably bisects EH, so just split it in half.
Factorise fullyc^3+ c^2
Answer:
c^2( c+1)
Step-by-step explanation:
c^3+ c^2
The greatest common factor is c^2
c^2( c+1)
The ratio of boys to girls in a group is 3:1. If there are 28 more boys than girls, work out how many people there are in total help plz
Answer:
35
Step-by-step explanation:
3x=28
x=7
no.of total students=35
The total profit made by an engineering firm is given by the function p=x^2 - 24x +5000 where x is the number of clients the firm has and p is the profit.
1. Find the maximum profit made by the company.
2. How many clients are necessary to reach the profit outlined in part one?
Answer:
[tex]5144[/tex]
[tex]12[/tex]
Step-by-step explanation:
The function [tex]p=x^2-24x+5000[/tex] is incorrect as its roots are imaginary [tex]b^2-4ac=576-4\times 5000=-19424<0[/tex].
So, the correct function is
[tex]p=-x^2+24x+5000[/tex]
Differentiating with respect to [tex]x[/tex] we get
[tex]p'=-2x+24[/tex]
Equating with zero
[tex]0=-2x+24\\\Rightarrow x=\dfrac{24}{2}\\\Rightarrow x=12[/tex]
Double derivative of the function
[tex]p''=-2<0[/tex]
So, the function is maximum at [tex]x=12[/tex]
Maximum profit is
[tex]p=-x^2+24x+5000=-12^2+24\times 12+5000\\\Rightarrow p=5144[/tex]
The maximum profit made by the company is [tex]5144[/tex]
The number of clients required to make the maximum profit is [tex]12[/tex].
Evaluation 6ab when a = 1/2 and b = 7
Answer:
21
Step-by-step explanation:
6x1/2x7
6 x 1/2=3, 3 x 7=21
I hope this helps and have a nice day!
which expression is equivalent to 7a-8-12a+4
Answer:
-5a-4
Step-by-step explanation:
7a-8-12a+4
7a-12a-8+4
=-5a-4
Which expression is equivalent to 4x - (3x2 + x) + 5 - (2x2 + 1)?
Can someone help me? Thank you!
Answer:
It's C
Step-by-step explanation:
Round to the nearest thousand.
88,651
6th grade mafs
Answer: 89,000
Step-by-step explanation:
Answer:
90,000
Step-by-step explanation:
88 = 90
What would be 82% of 50
Answer:
82% of 50 is 41
Step-by-step explanation:
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A small pump can drain a pool in 9 hours. A large pump could drain the same pool in 3 hours. How long (to the nearest minute) will it take to drain the pool if both pumps are used simultaneously?
Answer: 22.5 hours
Step-by-step explanation:
Let t be the time taken by both of the pumps to drain the pool.
Given: Time taken by pump 1 to drain the pool alone= 9 hours.
Time taken by pump 2 to drain the pool alone= 3 hours.
If both pumps are used simultaneously, then
[tex]\dfrac1t=\dfrac19+\dfrac13\\\\\Rightarrow\ \dfrac1t=\dfrac{1+3}{9}\\\\\Rightarrow\ \dfrac1t=\dfrac49\\\\\Rightarrow\ t=\dfrac94\\\\\Rightarrow\ t=2.25[/tex]
Hence, it will take 22.5 hours to drain the pool if both pumps are used simultaneously.
A water mill grinds corn to make cornmeal. The water wheel has a radius of 18 feet. The wheel is rotating at 8 revolutions per minute. Find the linear speed, in feet per minute, of the water.
Answer:
904.9 feet per minute
Step-by-step explanation:
The Angular distance can be calculated using below expression
S= r θ ..............eqn(1)
Where
θ = angular distance travelled
r= Radius= radius of 18 feet
But angular distance can also be expressed as
θ = wt...................eqn(2)
w= angular speed= 8 rev per minute= (8 × 2π)
t= time
Velocity can also be expressed as
V= s/t............eqn(3)
Where
V= velocity
s= distance
t= time
Substitute eqn(2) into eqn(3)
V=( r θ)/ t................eqn(4)
Substitute eqn(2) into eqn(4)
V=( r w t)/ t
V= r w ..............eqn(5)
V= 18×(8 ×2π)
=288π
= 904.9 feet per minute
Hence, the linear speed, in feet per minute, of the water. is 904.9 feet per minute
Which shows a proportion comparing the rise and run for each of the similar slope triangles,
and the numeric value?
y
Your Answer
?
BC
YZ
YX
b) - B:
d) = 4:2
c) 4 - BA
122
Answer:
1/2 = 3/6
Step-by-step explanation:
Slope = Rise / Run
Rise = change in yaxis = y2 - y1
Run = change in x axis = x2 - x1
For the smaller triangle :
Rise = MO = 1 unit
Run = NO = 2 units
Thus;
slope = 1/2
For the larger triangle :
Rise = PR = 3 unit
Run = QR = 6 units
Thus ;
Slope = 3/6
Smaller = larger
1/2 = 3/6
if JK is the midsegment of triangle GHI, find x
Answer:
C. 11
Step-by-step explanation:
Since JK is a midsegment of ∆GHI, therefore, based in the midsegment theorem:
JK = ½(HI)
HI = 22
Therefore,
JK = ½(22)
JK = 11
Two students on roller skates stand face-toface, then push each other away. Which student will always have the fastest speed
Answer:
The student with lower weight will move faster than the one with higher weight.
Step-by-step explanation:
The students are on roller skates and it is assumed that their wheels are identical. They are on a frictionless flat horizontal ground. According to Newton's Law F=ma
Mass of student 1 is 97 kg
Mass of student 2 is 61 kg
The force magnitude is assumed to be equal and acceleration is same. The student with higher weight will have lesser force exerted than the student with lighter weight.
A tree grows at a rate of 30 cm per year. If the tree is 5 meters tall
now, how tall will it be in 4 years?
Hint: Find the relationship between centimeters and and meters.
Answer:
Step-by-step explanation:
30 cm per year
now the tree is 5m
in 4 years the tree grew 4*30=120cm=1m 20 cm
the tree is 5+1.20 cm=6.20m tall
PLEASE HELP! i have by the end of the day to turn this in. PLEASE DONT GUESS
Answer: See step by step
Step-by-step explanation: Angle 2 and 3 are vertical angles since they both share a vertex and has cross intersecting lines. Angle 6 and 7 are supplementary angles because they forma linear pair.
Answer:
I have multiple answers for this.
Verticle Angles: 2 &4, 3&1, 6&8, 7&5
Supplementary Angles: 2&1, 2&3, 3&4, 1&4, 6&7, 7&8, 6&5, 5&8
Step-by-step explanation:
Verticle angles are aross from one another, not next to each other, while the Supplementary angles ARE next to each other and not across from one another. I hope this helps you :)
While selecting candy for students in his class, Professor Murphy must choose between gummy candy and licorice nibs. Gummy candy packets come in five sizes, while packets of licorice nibs come in two. If he chooses gummy candy, he must select gummy bears, gummy worms, or gummy dinos. If he chooses licorice nibs, he must choose between red and black. How many choices does he have
Answer and explanation:
First Prof. Murphy has to choose between two alternatives: gummy candy or licorice nibs
To find total choices, we only need to multiply number of sizes for each alternative and then add totals for each alternative together
So if Prof Murphy chooses gummy candy. He has sizes= 5 choices and types =3 choices, therefore he has 5×3= 15 choices for gummy candy
If he chooses licorice nibs, he has sizes = 2 choices and types= 2 choices, therefore he has 2×2= 4 choices for licorice nibs
Total choices: 15+4=19
He has 19 different options for selecting candy.
Since while selecting candy for students in his class, Professor Murphy must choose between gummy candy and licorice nibs, and gummy candy packets come in five sizes, while packets of licorice nibs come in two, and if he chooses gummy candy, he must select gummy bears, gummy worms, or gummy dinos, while if he chooses licorice nibs, he must choose between red and black, to determine how many choices does he have, the following calculation must be performed:
Number of sizes x number of options = X Gummy candy = 5 x 3 = 15 Licorice nibs = 2 x 2 = 4 15 + 4 = 19
Therefore, he has 19 different options for selecting candy.
Learn more in https://brainly.com/question/238045
Chris and Maddie share in the ratio 3:5 How much do they each receive?
first down, a football team lost 16 yd. After two
downs, the team had an overall gain of 5 yd. How
many yards were gained on second down?
Answer: +21
Step-by-step explanation:
Based on the information given, we are informed that at first down, a football team lost 16 yd and they after two downs, the team had an overall gain of 5 yd.
The number of yards that were gained on second down can be represented by x. We can then form the question as an equation as:
x - 16 = 5
x = 5 + 16
x = 21
The team gained 21 yards.
2. Using the ruler below, construct a triangle that has side lengths of 3 cm, 4 cm, and 5 cm.
triangle does this appear to be? Verify by using your protractor to measure angles.
What type of
Step-by-step explanation:
if to apply the Piphagorean theoreme, then one of the angles is 90° (opposite to the side with the length 5):
3²+4²=5²; ⇔ 9+16=25.
Help help help help please this is due soon
Answer: (2,-1)
Step-by-step explanation:
Answer:
A'(1, -2)Step-by-step explanation:
The rule for a rotation by 270° about the origin is:
(x, y) → (y, - x)Apply the rule to the point A, which has coordinates of (2, 1)
A(2, 1) → A'(1, -2)what are composite numbers out of 49, 35, 32, 41, and 47
Step-by-step explanation:
Composite numbers are 32,35,and 49 .
I hope it's helpful!
Find the slope of the line that passes through (7, 5) and (4, 1).
ILL GIVE BRAINLIEST TO FIRST PERSON TO ANSWER
Answer:
Slope=-4/-3
Step-by-step explanation:
x1=7, x2=4, y1=5, y2=1
m=y2-y1/x2-x1
m=1-5/4-7
m=-4/-3
Two students are reading a novel. Ashley reads 2 pages per day. Carly reads 1 page per day, but she starts early and is already on page 5. When will the two students read on the
same page?
Ashley:p=2d
Carly:p=d+5
Solve the equation3/5G - 1/3= -10/3
G=
Answer:
g = 5/59
Step-by-step explanation:
Write the number in standard form and expanded form. Three million four hundred eighty- seven thousand six hundred fifty-one
Answer:
down below
Step-by-step explanation:
3,487, 651
(3 x 1,000,000) + (4 x 100,000) + (8 x 10,000) + ( 7 x 1,000) + (6 x 100 ) +
(5 x 10) + (1 x 1)
what is the value of the y coordinate of point A
Answer:
E on Edge
Step-by-step explanation:
When Michael was 10 years old, Sam was 14. Sam is now 28 and Michael is 24.
Answer:
4 years difference
Step-by-step explanation: