Answer:
The total number of bacteria present in the sample after 2 hours is 12.
Step-by-step explanation:
In the function f(2) = 12, 2 represents x, and 12 represents the output when x is equal to 2.
In the context of this problem, this means that f(2) = 12 represents how in 2 hours, there were 12 bacteria present in the sample.
Answer:
The total number of bacteria present in the sample after 2 hours is 12.
Step-by-step explanation:
f(x) is the total number of bacteria, while x is the number of hours. We are given:
f(2)=12
2 is x (the input) and 12 is f(x) (the output).
Since x=2 and x=number of hours, 2 describes the number of hours.
Since f(x)= 12 and f(x)= number of bacteria, 12 describes the number of bacteria.
Therefore, after 2 hours, the total number of bacteria present is 12.
can somebody help me plz
Answer:
126 people
Step-by-step explanation:
9/5 is the ratio tea/coffee
let x be the one who preferred coffee and x+36 preferred tea
9/5=x+36/x
9x=5x+5(36)
9x-5x=180
4x=180
x=180/4=45
x=45 coffee
x+36=45+36=81
45+81=126
check : 81/45= 9/5
Part 1 of 1 -
Question 2 of 50
2 Points
Solve the equation for x. x/3 -1 = -2
Copyright 2010-2020 edtell, LLC. All rights reserved. Portions of this software are copyrighted by other parties as described in the Acknov
Answer:
x = -3
Step-by-step explanation:
When asked to solve the equation for x, it mean that put x only on one side, and everything else on the other side. So....
x/3 - 1 = -2
x/3 = -1 ( add 1 on both side)
x = -3 (x3 on both side)
Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc. Arrange the proof of the given statement in correct order to show that R is an equivalence relation. (Prove the given relation is reflexive first, and then symmetric and transitive.)
Answer:
The given relation R is equivalence relation.
Step-by-step explanation:
Given that:
[tex]((a, b), (c, d))\in R[/tex]
Where [tex]R[/tex] is the relation on the set of ordered pairs of positive integers.
To prove, a relation R to be equivalence relation we need to prove that the relation is reflexive, symmetric and transitive.
1. First of all, let us check reflexive property:
Reflexive property means:
[tex]\forall a \in A \Rightarrow (a,a) \in R[/tex]
Here we need to prove:
[tex]\forall (a, b) \in A \Rightarrow ((a,b), (a,b)) \in R[/tex]
As per the given relation:
[tex]((a,b), (a,b) ) \Rightarrow ab =ab[/tex] which is true.
[tex]\therefore[/tex] R is reflexive.
2. Now, let us check symmetric property:
Symmetric property means:
[tex]\forall \{a,b\} \in A\ if\ (a,b) \in R \Rightarrow (b,a) \in R[/tex]
Here we need to prove:
[tex]\forall {(a, b),(c,d)} \in A \ if\ ((a,b),(c,d)) \in R \Rightarrow ((c,d),(a,b)) \in R[/tex]
As per the given relation:
[tex]((a,b),(c,d)) \in R[/tex] means [tex]ad = bc[/tex]
[tex]((c,d),(a,b)) \in R[/tex] means [tex]cb = da\ or\ ad =bc[/tex]
Hence true.
[tex]\therefore[/tex] R is symmetric.
3. R to be transitive, we need to prove:
[tex]if ((a,b),(c,d)),((c,d),(e,f)) \in R \Rightarrow ((a,b),(e,f)) \in R[/tex]
[tex]((a,b),(c,d)) \in R[/tex] means [tex]ad = cb[/tex].... (1)
[tex]((c,d), (e,f)) \in R[/tex] means [tex]fc = ed[/tex] ...... (2)
To prove:
To be [tex]((a,b), (e,f)) \in R[/tex] we need to prove: [tex]fa = be[/tex]
Multiply (1) with (2):
[tex]adcf = bcde\\\Rightarrow fa = be[/tex]
So, R is transitive as well.
Hence proved that R is an equivalence relation.
The relation R is an equivalence if it is reflexive, symmetric and transitive.
The order to options required to show that R is an equivalence relation are;
((a, b), (a, b)) ∈ R since a·b = b·aTherefore, R is reflexiveIf ((a, b), (c, d)) ∈ R then a·d = b·c, which gives c·b = d·a, then ((c, d), (a, b)) ∈ RTherefore, R is symmetricIf ((c, d), (e, f)) ∈ R, and ((a, b), (c, d)) ∈ R therefore, c·f = d·e, and a·d = b·cMultiplying gives, a·f·c·d = b·e·c·d, which gives, a·f = b·e, then ((a, b), (e, f)) ∈RTherefore R is transitiveFrom the above proofs, the relation R is reflexive, symmetric, and transitive, therefore, R is an equivalent relation.Reasons:
Prove that the relation R is reflexive
Reflexive property is a property is the property that a number has a value that it posses (it is equal to itself)
The given relation is ((a, b), (c, d)) ∈ R if and only if a·d = b·c
By multiplication property of equality; a·b = b·a
Therefore;
((a, b), (a, b)) ∈ R
The relation, R, is reflexive.Prove that the relation, R, is symmetric
Given that if ((a, b), (c, d)) ∈ R then we have, a·d = b·c
Therefore, c·b = d·a implies ((c, d), (a, b)) ∈ R
((a, b), (c, d)) and ((c, d), (a, b)) are symmetric.
Therefore, the relation, R, is symmetric.Prove that R is transitive
Symbolically, transitive property is as follows; If x = y, and y = z, then x = z
From the given relation, ((a, b), (c, d)) ∈ R, then a·d = b·c
Therefore, ((c, d), (e, f)) ∈ R, then c·f = d·e
By multiplication, a·d × c·f = b·c × d·e
a·d·c·f = b·c·d·e
Therefore;
a·f·c·d = b·e·c·d
a·f = b·e
Which gives;
((a, b), (e, f)) ∈ R, therefore, the relation, R, is transitive.Therefore;
R is an equivalence relation, since R is reflexive, symmetric, and transitive.
Based on a similar question posted online, it is required to rank the given options in the order to show that R is an equivalence relation.
Learn more about equivalent relations here:
https://brainly.com/question/1503196
not quite sure of the answer. help me out???
Answer:
C = pi * d
Step-by-step explanation:
C = 2 * pi *r
We can replace 2 * r with d since the diameter is twice the radius
C = pi * 2*r
C = pi * d
An account is opened with $7,595.96 with a rate of increase of 2% per year. After 1 year, the bank account contains $7,746.90. Assuming no deposits or withdrawals are made, which equation can be used to find y, the amount of money in the account after x years
Answer:
y = 7,595.96(1.02)x
Step-by-step explanation:
y = 7,595.96(1.02)x
a normal linear equation is basically y = x + b
in this case,
y = amount of money in the bank accountx = number of yearsb is not required because there are no new deposits or withdrawals from the accountSince the accounts earns 2% interest per year, then you need to multiply the original amount by 1.02. As more years pass, the account will increase by 1.02, so the account increases by 1.02x. Since the original amount is $7,595.96, that will be our starting point.
Answer:
C y = 7,595.96(1.02)x
Step-by-step explanation:
F(x)3x+5/x what is f(a+2)
A: 3a+5/a+2
B:3(a+2)+5/a+2
C:3(f(a))+5/f(a)+2
which linear inequality is represented by the graph?
Can someone help assist me on this Honors Algebra 2 Problem? Challenge Problems #6. The distance from a point on the curve y=√x to the point (2,0) is equal to 2 at what points on the curve? (Hint: Draw a picture.)
Answer: (0, 0) & (3, √3)
Step-by-step explanation:
Since we need a distance of 2, I graphed y = √x and then drew a circle at center (2, 0) and radius of 2 to see where they intersect.
The coordinates of intersection can be determined by solving a system of equations.
Equation 1: y = √x
Equation 2: (x - 2)² + y² = 2²
I will use the Substitution method with Equation 2 to solve for x:
(x - 2)² + (√x)² = 2² substituted y with √x
x² - 4x + 4 + x = 4 expanded binomial
x² - 3x + 4 = 4 added like terms
x² - 3x = 0 subtracted 4 from both sides
x(x - 3) = 0 factored
x = 0 x - 3 = 0 applied Zero Product Property
x = 3
Next, solve for y using Equation 1:
x = 0: y = √0 = 0
x = 3: y = √3
Coordinates of intersection are: (0, 0) & (3, √3)
Answer:
(0, 0) & (3, √3)
Step-by-step explanation:
6TH GRAD LE MATH PLEASE HELP ME
Answer: 6
Step-by-step explanation: I think..... this is a division sign, nvm... so 4 divided by 8/12 is basically 4 x 12/8 which is 48/8 simplified is/equals 6!
Answer:
6
Step-by-step explanation:
4 / 8/12 = 4 * 12/8 = 4 * 3/2 = 6
Helppp!!!! please!!!
Answer:
A) 52.5 inches²
Step-by-step explanation:
The equation for the area of a trapezoid is a=1/2h(b1+b2). This basically means that you take the height of the trapezoid, multiply it by the top base plus the bottom base and divide that by 2. When you do this, you take 8.5 plus 6.5, which equals 15, and multiply that by 7 to get 105. After you get this, you divide it by 2 to get 52.5 inches².
What is the volume of the cylinder to the nearest whole number? a) 942 cm3 b) 3,534 cm3 c)471 cm3 d) 9,420 cm3
Answer:
V = 3534 cm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
the radius is 7.5 and the height is 20
V = pi ( 7.5)^2 * 20
V =1125 pi cm^3
Using the pi button for pi
V =3534.291735 cm^3
Rounding to the nearest whole number
V = 3534 cm^3
Answer:
b)3534 cm^3
Step-by-step explanation:
To find the area of a cylinder, you first have to find the area of the base which is in the shape of a circle. The area of a circle is given by the equation πr^2. In this case r, the radius, is 7.5 cm. So plugging in 7.5 for r you get 7.5^2 × π. Plugging in 3.1415 for π you get ~176.671. Now all you do is multiply this by the height, 20cm, and get the answer of ~3534 cm^3.
the tax rate is 3.9%. What is the tax on $42?
Answer:
$43.64
Step-by-step explanation:
Answer:
1.64
Step-by-step explanation:
To find the tax, multiply the cost by the tax rate
42 * 3.9%
Change to decimal form
42 *.039
1.638
Round to the nearest cent
1.64
what's the product of 9 (-8)
Answer:
-72
Step-by-step explanation:
I googled it.
Answer:
-72
Step-by-step explanation:
You take the 9, multiply by the -8, and boom. You get -72.
And when you multiply two opposite signs together, it equals to a negative number.
Boom bam boom you became a bit smarter
Tublu buys a cylindrical water tank of height 1.4m and diameter 1.1m to catch rainwater off his roof. He has a full 2 litres tin of paint in his store and decides to paint the tank (not the base). If he uses 250 ml to cover 1 2 , will he have enough paint to cover the tank with one layer of paint? [take = 3.142]
Answer:
He will have enough paint to cover the tank with one layer of paint
Step-by-step explanation:
To calculate the area of the surface that has to be painted, we will have to calculate the lateral surface of the cylinder
Lateral surface of the cylinder is given by
A=2πrh
Where,
π=3.142
r=1.1/2m=
h=1.4m
A=2πrh
=2*3.142*1.1/2*1.4
=4.84m^2
He uses 250ml to cover 1m^2
To cover 4.84m^2, he will use
4.84m^2 × 250ml of paint
=1,210ml of paint is needed
He has 2 litres of paint
2litres =2000ml
Tublu has 2000ml of paint but needs 1210ml of paint
Therefore,
He has an excess of 2000-1210
=790ml
The answer is yes, he will have enough paint to cover the tank with one layer of paint.
If x - 10 is a factor of x2 - 8x - 20, what is the other
factor?
X +
Answer:
(x + 2)
Step-by-step explanation:
When we factor the expression x² - 8x - 20, we should get (x + 2)(x - 10).
Alternatively, we can use synthetic division or long division to get our answer.
Answer:
x + 2
Step-by-step explanation:
got it right edg '22
Factor x2 – 3x – 28. An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression a x squared + b x + c. Identify the values that should be written to complete the X diagram. On the top: On the bottom: On the sides: Rewrite the expression using the numbers on the sides of the X diagram. Use double grouping to factor the four terms. x2 – 3x – 28 =
Answer:
(x - 7)(x + 4)
Step-by-step explanation:
Note that 4 times 7 is 28, and that -7x + 4x = -3x.
Therefore, x^2 - 3x - 28 factors into (x - 7)(x + 4)
The factors of the quadratic equation x² – 3x – 28 is (x - 7)(x + 4).
What is a quadratic equation?
It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Writing a number or any mathematical object as the result of several factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.
The factorization will be done as below:-
x² – 3x – 28
Split the middle term as 7 and 4.
x² – 7x + 4x – 28 = 0
x ( x - 7 ) + 4 ( x -7 ) = 0
Take x-7 common from the whole equation.
( x - 7 ) ( x + 4 ) = 0
Therefore, the factors of the quadratic equation x² – 3x – 28 is (x - 7)(x + 4).
To know more about quadratic equations follow
https://brainly.com/question/1214333
#SPJ2
use
tiles
Algebra
factor for X^2-2x-3
Answer:
I hope it's correct
Mrs. Sing invests $12,876 for her business at an annual interest rate of 7 percent for 3 years. Which number will Mrs. Sing substitute for r in the simple interest formula? I = p r t
Answer:
she wills substitute r with 7%.
Step-by-step explanation:
Just did it.
Answer:
R = 7%
Principal (P)
Rate (R)
Time (t)
Step-by-step explanation:
The full intrest rate formula is i=prt
You are looking for r
R is the interest rate 7%
So i = 12,876*7%*3years will be the full equation.
In a school the the duration of primary section is 40 min and senior section is hour if the bell rings at 9 am together when will the next bell ring together
Answer:
11 a.m.
Step-by-step explanation:
Duration of Primary Period = 40 min
Duration of Senior Section =1 hour = 60 min
To find out when the next bell will ring together, we first determine the LCM of 40 and 60.
Multiples of 40 are: 40,80,120,160,...
Multiples of 60 are: 60, 120, 180, 240...
From the above, we observe that the bell will ring together exactly 120 Minutes after 9 a.m.
Therefore:
9+120 Min =9 +2 Hours =11 a.m.
Therefore, the bell of the primary section and senior section will ring together at exactly 11 am.
A car travels the first 50 km of its journey at an average speed of 25 m/s and the next 120 km at an On his outward journey, Ali travelled at a speed of s km/h for 2.5 hours. On his return journey, he increased his speed by 4 km/h and saved 15 minutes. Find Ali's average speed for the whole journey. Speed of 80 km/h. The car completes the last part of its journey at an average speed of 90 km/h in 35 minutes. Find the average speed for its entire journey, giving your answer in km/h.
Answer:
The car's average speed for the entire journey = 84.315 km/h
Step-by-step explanation:
Correct Question
A car travels the first 50km of its journey at an average speed of 25m/s and the next 120 km at an average speed of 80km/h. the car completes the last part of its journey at an average speed of 90km/h in 35 minutes. Find the average speed for its entire journey, giving your answer in km/h.
Solution
Average speed is given as total distance travelled divided by total time taken.
So, we will compute the distance covered for each part of the journey and the corresponding time it takes to cover each of these distances.
- The car travels the 50 km first part of the journey at a speed of 25 m/s.
25 m/s = 90 km/h
We have the distance covered in the first part of the journey, now, we need the time taken to cover the distance.
Speed = (Distance/Time)
Time = (Distance/Speed)
Distance = 50 km, Speed = 90 km/h
Time = (50/90) = 0.5556 hr
- The next part, the car covers 120 km at a speed of 80 km/h
Time = (Distance/Speed) = (120/80) = 1.5 hr
- For the last part of the journey, the car travels with an average speed of 90 km/h for 35 minutes.
35 minutes = (35/60) hr = 0.5833 hr
Here, we need to calculate the distance covered for the last part.
Speed = (Distance/Time)
Distance = (Speed) × (Time) = 90 × 0.5833 = 52.5 km
Total distance covered = 50 + 120 + 52.5 = 222.5 km
Total time taken = 0.5556 + 1.5 + 0.5833 = 2.6389 hr
Average Speed = (222.5/2.6389) = 84.315 km/h
Hope this Helps!!!
55=2.7[tex]55=2.7\sqrt{x} +14[/tex] what is the value of x
Answer:
230.59
Step-by-step explanation:
55 = 2.7sqrt(x) + 14
41 = 2.7sqrt(x)
15.185=sqrt(x)
x = 15.185^2
x=230.59
At the deli, Alberto paid $24.33 for 7.4
pounds of sliced ham. What was the
price of one pound of sliced ham?
Answer:
About $3.28
Step-by-step explanation:
Divide 24.33 by 7.4
Answer:
3.28783783784...
Step-by-step explanation:
You're description could turn into 24.33 : 7.4.
You turn 7.4 into 1, and divide 7.4 / 1.
(It is 7.4)
Then, you divide 24.33 / 7.4.
It is 3.28783783784.......
or, If you want you're answer close to an natural number, It is 3.
3. In the polygon below, what kind of
angle is P?
A Acute
B Obtuse
C Right
D Straight
Answer:a
Step-by-step explanation:
Which answer needs to be true to be able to use the SSS Congruence Postulate to prove △ABC≅△DBC? AB¯¯¯¯¯¯¯¯≅DB¯¯¯¯¯¯¯¯ and ∠ACB≅∠DCB ∠ACB≅∠DCB and ∠A≅∠D AB¯¯¯¯¯¯¯¯≅DB¯¯¯¯¯¯¯¯ and AC¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯ AB¯¯¯¯¯¯¯¯≅DB¯¯¯¯¯¯¯¯ or AC¯¯¯¯¯¯¯¯≅DC¯¯¯¯¯¯¯¯
Answer:
The correct option is;
[tex]\overline{AB}\cong \overline{DB}[/tex] and [tex]\overline{AC}\cong \overline{DC}[/tex]
Step-by-step explanation:
The steps to prove that ΔABC ≅ ΔDBC with the SSS Congruence postulate
We have;
Statement, Reason
BC ≅ BC, Reflexive property
[tex]\overline{AB}\cong \overline{DB}[/tex], Option selected
[tex]\overline{AC}\cong \overline{DC}[/tex], Option selected
ΔABC ≅ ΔDBC, SSS Congruency Postulate
Therefore, whereby all three sides of the triangles ABC and DBC are congruent, then ΔABC is congruent to ΔDBC.
Answer:
AC≅DF
AB≅DE
Step-by-step explanation:
took the test :)
Which statement explains how the lines x+y=2 and y=x+4 are related?
(1) They are parallel.
(2) They are perpendicular.
(3) They are the same line.
4) They are not related.
Answer:
(2)They are perpendicular.
Step-by-step explanation:
I don't understand???? I'll give the brainliest!!!!!
Answer:
37Option A is the correct option.
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} - 2ab \: \cos \: c \: = {c}^{2} \\ a = 4 \\ b = 5 \\ c = 2 \\ \\ 2ab \: cos \: c = {a}^{2} + {b}^{2} - {c}^{2} \\ \: \: \: \: \: \: \: \: = {(4)}^{2} + {(5)}^{2} - {(2)}^{2} \\ \: \: \: \: \: \: \: \: = 16 + 25 - 4 \\ \: \: \: \: \: \: = 41 - 4 \\ \: \: \: \: \: \: = 37[/tex]
Hope this helps...
Good luck on your assignment...
How many times would you have to cross the Golden Gate Bridge in order to travel the exact distance between Wolverhampton and Birmingham?
Answer:
Hey!
Well...the distance from Birmingham to Wolverhampton in about 12 miles (19km)
The length of the Golden Gate bridge is 2,737m OR 2.737 km...in miles it's 1.701
So you will have to cross it about 11.2 times (3 sf)
Step-by-step explanation:
19 km / 1.701km = 11.16990005878895
Rounded up to a degree of accuracy = 3 sf
= 11.2
Hope this helps!
10. 80 machines can produce 4800 identical pens in 5 hours. At this rate
a) how many pens would one machine produce in one hour?
b) how many pens would 25 machines produce in 7 hours?
Answer:
a) 12 (Simply divide 4800/5 to get 960. Then divide 960/80 to get 12)
b) 2100 (Simply multiply 12 by 25 by 7)
Hope it helps <3
here are the ingredients for making pineapple sorbet for 6 people. 800 g pineapple 4 egg whites 1/2 lemon 100 g caster sugar Dan makes pineapple sorbet. he uses 2 and a 1/2 lemons How many people does he make pineapple sorbet for?
Answer:
30 people
Step-by-step explanation:
If you start off with 1/2 a lemon for 6 people, then 1 whole would be 12. 1 1/2 would be 18 people and 2 whole lemons would be 24. so 2 1/2 is 30 people.
Caroline, Colin & Sarah share some money in the ratio 1 : 9 : 1.
In total, Caroline and Sarah receive £28.
How much does Colin get?
Answer:
Colin got £126
Step-by-step explanation:
Here we want to know how much Colin got from the sharing.
We can collapse the ratio to mean;
Colin : Caroline + Sarah
= 9:1 + 1 = 9:2
So total ratio is 9 + 2 = 11
If Caroline and Sarah got £28 we need to find the total money shared
Let the total money shared be £x
Thus;
2/11 * x = 28
2x = 11 * 28
x = (11 * 28)/2
x = 11 * 14 = £154
So the amount of money Colin got would be;
£154 - £28 = £126