Hello,
In prime decomposition:
180=2²*3²*5
140=2²*5*7
lcm(180,140)=2²*3²*5*7=1260
Proof: 1260/180=7 and 1260/140=9
The number of pounds of one-dollar-a-pound
coffee needed to mix with 80 pounds of 70¢ a
pound coffee to make a mixture worth 84¢ a
pound is
(A) 70
(B) 80
(C) 95
(D) 65
Answer:
A
Step-by-step explanation:
Let's say we need x pounds of one-dollar-a-pound coffee . The coffee must average out to 84 cents a pound, and the formula for average is
sum of cost of coffee / number of pounds of coffee, so we have
0.84 = total cost of coffee / (x+80) . The total cost of coffee can be found to be the sum of the cost of $1 coffee and 70 cent coffee, so we have
0.84 = (cost of $1 coffee + cost of 70 cent coffee) / (x+80)
The cost of $1 coffee can be found by adding $1 for each pound of one dollar coffee, or $1 * x. Similarly, the cost of 70 cent coffee is equal to 0.70 * 80, so we have
0.84 = (1*x+0.7*80)/(x+80)
0.84 = (x+56)/(x+80)
multiply both sides by (x+80) to remove a denominator
0.84(x+80) = x+56
0.84x + 67.2 = x+56
subtract both sides by 56 and 0.84x to isolate the x and its coefficients
11.2 = 0.16 x
divide both sides by 0.16 to isolate x
11.2/0.16 = x = 70
The number of pounds of a constituent in a mixture given the cost of the
mixture and the cost and mass of the other constituent can be calculated
by using an equation to model the system
The correct option for the number of pounds of one-dollar- pound coffee needed is option A
(A) 70 pounds
The procedure for arriving at the correct option is as follows:
The given parameters are;
The cost of the the coffee for which the mass in the mixture is to be determined = One-Dollar a pound = 100 ¢ a pound
The mass of the coffee 70¢ a pound coffee to be mixed = 80 pounds
The cost per pound of the mixture = 84 ¢ a pound
The required parameter;
The number of pounds of the one-dollar-a-pound (100 ¢ a pound) coffee in the mixture
Method:
Let x (pound) represent the number of pounds of the one-dollar-a-pound coffee in the mixture, we have;
Mass of mixture = Mass of the one-dollar-a-pound in the mixture, x + Mass of 70 ¢ a pound in the mixture, 80
∴ Mass of mixture in pounds = x + 80
Cost = Cost per pound × Number of pound
Find solution by applying the equation;
Cost of the constituents = Cost of the mixture
Where;
Cost of the constituents = $1 × x + 70 ¢ × 80 = 100 ¢ × x + 70 ¢ × 80
Cost of the mixture = 84 ¢ × (x + 80)
Therefore;
100 ¢ × x + 70 ¢ × 80 = 84 ¢ × (x + 80)
The above can be expressed as 100·x + 70×80 = 84 × (x + 80)
Expanding, evaluating and collecting like terms gives;
100·x + 5,600 = 84·x + 6,720
100·x - 84·x = 6,720 - 5,600 = 1,120
16·x = 1,120
x = 1,120/16 = 70
The number of pounds of one-dollar- pound coffee needed, x = 70 pounds
Learn more about equation modelling here;
https://brainly.com/question/14102741
a grocery store buys boxes of cereal for $ 2.00 each and sells them for 50% more. what does the grocery store charge its customers for each box of cereal?
Answer:
$3.00
Step-by-step explanation:
First find the markup
2.00 * 50%
2 * .5
1
Add this to the original price
2+1 =3
The store sells the cereal for $3.00
Answer:
$3
Step-by-step explanation:
The grocery store pays $2.00 for each box of cereal bought.
First, find 50% of the cost of each box:
2.00 x 0.50 = 1.00
Next, add the additional amount to the starting price:
2.00 + 1.00 = $3.00
$3.00 is your answer.
~
(-9) + (-4) =
(+3) - (-5) =
(+2)x(+2) =
(+36) + (+4)
(+5) X (+7) =
(+8) (+9) =
(-4) + (-2) =
(+3) -(-6) =
(-6)*(-3) =
(-4) + (-4)
(+5) X (+7)
(+4)-(-5) =
(+4) - (+3) =
(+10) + (+5)
(+3) (+8)
[tex]\\ \bull\sf\longmapsto -9+(-4)=-9-4=-13[/tex]
[tex]\\ \bull\sf\longmapsto +3-(-5)=3+5=8[/tex]
[tex]\\ \bull\sf\longmapsto 2\times 2=4[/tex]
[tex]\\ \bull\sf\longmapsto 36+4=40[/tex]
[tex]\\ \bull\sf\longmapsto 5\times 7=35[/tex]
[tex]\\ \bull\sf\longmapsto 8(9)=72[/tex]
[tex]\\ \bull\sf\longmapsto -4+(-2)=-4-2=-6[/tex]
[tex]\\ \bull\sf\longmapsto 3-(-6)=3+6=9[/tex]
[tex]\\ \bull\sf\longmapsto -6(-3)=18[/tex]
[tex]\\ \bull\sf\longmapsto -4+(-4)=-4-4=-8[/tex]
[tex]\\ \bull\sf\longmapsto 5(7)=35[/tex]
[tex]\\ \bull\sf\longmapsto 4-(-5)=4+5=9[/tex]
[tex]\\ \bull\sf\longmapsto 4-3=1[/tex]
[tex]\\ \bull\sf\longmapsto 10+5=15[/tex]
[tex]\\ \bull\sf\longmapsto 3(8)=24[/tex]
Select two choices that are true about the function f(x)=23x+14/x
Answer:
There is an asymptote at x = 0
There is an asymptote at y = 23
Step-by-step explanation:
Given the function:
(23x+14)/x
Vertical asymptote is gotten by equating the denominator to zero
Since the denominator is x, hence the vertical asymptote is at x = 0. This shows that there is an asymptote at x = 0
Also for the horizontal asymptote, we will take the ratio of the coefficient of the variables in the numerator and denominator
Coefficient of x at the numerator = 23
Coefficient of x at the denominator = 1
Ratio = 23/1 = 23
This means that there is an asymptote at y = 23
20 is 15% of what number?
PLEASE ANSWER ILL GIVE BRAINLIESTTTT
Answer:
133.33
Step-by-step explanation:
Answer:
133 1/3 or 133.33
Step-by-step explanation:
So first let's turn 15% into a decimal. For me personally, its less intimidating that way.
15%=0.15
now, let's say the number we are trying to find is x.
A trick I use for these questions is to look at the words. "Of" is used when something is multiplied. "Is" is used for equal signs. So if 20 is 0.15 of x, our formula is easy to figure out!
20=0.15x
x=133.33333...
x=133 1/3
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]
Convert 13pi/6 to a degree measure
A=390
B=2450.44
C=30
D=780
Answer:
390 degrees
Step-by-step explanation:
The conversion factor is 180/pi
13 pi /6 * 180/pi
13/6 *180
390
can someone please help me solve this?
Answer:
-15
Step-by-step explanation:
df(x, y) / dy = lim (f(x, y+h) - f(x, y)) / h =
lim (e^x^2 - 15y - 15h - e^x^2 ‐ 15y) / h = lim -15h / h = -15
so, the first derivative of f(x,y) by y is simply a constant : -15
fy (x, y) = -15 for any and every values of x and y.
the fast track would be derivative calculation :
the derivative by y makes x a constant. and every constant is eliminated for derivation.
so, e^x^2 goes away (= 0 in the derivative).
that leaves -15y = -15×y¹. its derivative simply is
1×-15×y⁰ = -15
Write an equation of the line. What is the equation of the line?
Answer:
y=-1
Step-by-step explanation:
As the line is horizontal in nature and pass through (2,-1), the equation is y=-1
PLS HELP ME ASAP!!!!
What is equivalent to 1/6
Answer:
0.16666...
6/36
2/12
3/18
4/24
5/30
There's a lot of things.
Simplify 2m^2 – 2m + 3m^2
Answer:
5m^2-2m
Step-by-step explanation:
2m^2-2m + 3m^2
5m^2-2m
Answer:
5m² - 2m
Step-by-step explanation:
Given
2m² - 2m + 3m² ← collect like terms
= (2m² + 3m²) - 2m
= 5m² - 2m
Find x.
A. √-2
B. 4
C. √2/2
D. √6/2
Answer:
sqrt(2)
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 45 = x/2
2 sin 45 =x
2 (sqrt(2)/2) =x
sqrt(2) =x
Which correlation best describes the data below.
Answer:
Weak negative correlation
The number seventeen and seven thousand in decimal form is
Answer:
17.00 and 17,000.00
this is your answer to ur question
What is the 6th term of this pattern : 0.1, 0.02, 0.12, 0.14, 0.26, ____?
If you will solve i will give brainliest.
Answer:
0.28
Step-by-step explanation:
PLS HELP ASAP PLS PLSPLS
What is the explicit formula for this sequence?
6, 2, -2, -6, ...
Answer:
B
Step-by-step explanation:
this is just common sense. if you would have tried you could have easily answered this yourself.
the sequence starts with 6. that is a1.
so, the formula simply has to add "something" to 6.
therefore, A and D are out.
and then we see immediately that the sequence is built by subtracting 4 (or adding -4) for every step.
so, we need to add multiples of -4.
therefore, only B is correct (C adds multiples of +4).
Please help explanation if possible
Answer:
(1, - 2 )
Step-by-step explanation:
Given the equations
3x - 4y = 11 → (1)
y + 3x = 1 ( subtract 3x from both sides )
y = 1 - 3x → (2)
Substitute y = 1 - 3x into (1)
3x - 4(1 - 3x) = 11 ( distribute and simplify left side )
3x - 4 + 12x = 11
15x - 4 = 11 ( add 4 to both sides )
15x = 15 ( divide both sides by 15 )
x = 1
Substitute x = 1 into (2) for corresponding value of y
y = 1 - 3(1) = 1 - 3 = - 2
solution is (1, - 2 )
An exponential function fx) is reflected across the y-axis to create functiong(x). Which is a true statement
regarding fa) and g(x)?
The two functions have no points in common
The two functions have the same initial value
The two function have opposite output values of each other for any given input value
The graph of the two functions would look exactly the same
Intro
Answer:
The two functions have the same initial value
I
7. The total cost to rent a truck is $100 and $0.20 per km.
a. Determine an algebraic model for the relationship between total cost and distance driven. Use C to
represent total cost (S) to rent the truck and d to represent distance driven (km).
Answer:
C= 100+ d*0.2
Step-by-step explanation:
Give data
Cost of rental = $100
Cost per km= $0.2
Total cost= C
Distance= d
Let us model the expression
Hence the expression is given as
C= 100+ d*0.2
The blue team scored two more than five times the number of points,p, scored by the red team
Write an expression for the problem
Answer:
2 + 5p
Step-by-step explanation:
Hi there!
Let [tex]p[/tex] equal the number of points scored by the red team.
We're given:
The blue team scored two more than five times the number of points scored by the red team.
⇒ blue team points = 2 + (5 × red team points)
⇒ blue team points = 2 + 5p
I hope this helps!
simplify the following
Answer:
1) 11[tex]\sqrt{3}[/tex]
2) 2[tex]\sqrt{2}[/tex]
3) [tex]20\sqrt{3} + 15\sqrt{2}[/tex]
4) [tex]53 + 12\sqrt{10}[/tex]
5) -2
6) [tex]7\sqrt{2} - 5\sqrt{3}[/tex]
Step-by-step explanation:
1) 2[tex]\sqrt{12}[/tex] + 3[tex]\sqrt{48}[/tex] - [tex]\sqrt{75}[/tex]
=(2 × 2[tex]\sqrt{3}[/tex] )+ (3 × 4[tex]\sqrt{3}[/tex]) - 5[tex]\sqrt{3}[/tex]
= 4[tex]\sqrt{3}[/tex] + 12[tex]\sqrt{3}[/tex] - 5[tex]\sqrt{3}[/tex]
= 11[tex]\sqrt{3}[/tex]
2) 4[tex]\sqrt{8}[/tex] -2[tex]\sqrt{98}[/tex] + [tex]\sqrt{128}[/tex]
= (4 × 2[tex]\sqrt{2}[/tex]) - (2 × 7[tex]\sqrt{2}[/tex]) + 8[tex]\sqrt{2}[/tex]
= 8[tex]\sqrt{2}[/tex] - 14[tex]\sqrt{2}[/tex] +8[tex]\sqrt{2}[/tex]
= 2[tex]\sqrt{2}[/tex]
3) 5[tex]\sqrt{12\\}[/tex] - 3[tex]\sqrt{18} + 4 \sqrt{72} +2\sqrt{75}[/tex]
= 5× [tex]2\sqrt{3}[/tex] - 3×[tex]3\sqrt{2}[/tex] + 4×[tex]6\sqrt{2}[/tex] + 2×[tex]5\sqrt{3}[/tex]
= [tex]10\sqrt{3} - 9\sqrt{2} +24\sqrt{2} +10\sqrt{3}[/tex]
= [tex]20\sqrt{3} + 15\sqrt{2}[/tex]
4) [tex](2\sqrt{2} + 3\sqrt{5} )^{2}[/tex]
= [tex]8 + 12\sqrt{10} + 45[/tex]
= [tex]53 + 12\sqrt{10}[/tex]
5) [tex](1+\sqrt{3} ) (1-\sqrt{3} )[/tex]
= [tex]1 - 3[/tex]
= -2
6) [tex](2\sqrt{6} -1) (\sqrt{3} -\sqrt{2} )[/tex]
= [tex]2\sqrt{18}-2\sqrt{12} -\sqrt{3} +\sqrt{2}[/tex]
= 2×[tex]3\sqrt{2}[/tex] - 2×[tex]2\sqrt{3}[/tex] - [tex]\sqrt{3} + \sqrt{2}[/tex]
= [tex]6\sqrt{2} - 4\sqrt{3} -\sqrt{3} +\sqrt{2}[/tex]
= [tex]7\sqrt{2} - 5\sqrt{3}[/tex]
Hope the working out is clear and will help you. :)
Step-by-step explanation:
please I solved the question in the diagram above
rational or irrational? and why
Answer:
Irrational
Step-by-step explanation:
If we evaluate the square root, we realize that the number will not be a perfect square.
Since it is not a perfect square, it will be an unending, never-repeating, decimal.
Therefore, it will be irrational.
Identify the volume and surface area of the hemisphere in terms of pie.
Answer:
it's off topic but which grade are you in
5^-4 over 5^3
simplify
A. 5^7
B. 5^-1
C. 1/5
D. 1/5^7
Answer:
D is the correct answer.
Use the graph to find the constant of proportionality (unit rate)
Answer:
9) 10
10) 5
Step-by-step explanation:
What is the volume of the cone to the nearest whole number?
20,520pi cm3
43,320pi cm3
86,640pi cm3
136,094pi cm3
[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\red{Volume \: of \: Cone \: = \: \pi \: {r}^{2} \: \frac{h}{3} }}}}}\end{gathered}[/tex]
r represents radius of coneh represents height of coneheight of cone is 90 cmradius of cone is diameter / 2 ⇛76/2 = 38
⇛radius = 38 cm
Solution[tex]\bf \Large \longrightarrow \:π \: × \: (38 \: cm)² \: × \: \frac{90 }{3} [/tex]
[tex]\bf \Large \longrightarrow \: \pi \: \times \: \:1444 \: {cm}^{2} \: \times \: \cancel\frac{90}{3} \: \: ^{30 \: cm} [/tex]
⇥ 43,320 π cm³
Option ( B ) is the correct answer
Identify the glide reflection rule in the given figure.
Question 8 options:
Translation: (x,y) → (x – 5,y); Reflection across y-axis
Translation: (x,y) → (x,y – 5); Reflection across y-axis
Translation: (x,y) → (x,y + 5); Reflection across y-axis
Translation: (x,y) → (x,y + 5); Reflection across x-axis
Answer:
B
Step-by-step explanation:
The shape clearly is reflected across y axis and the x coordinates remain the same. We can see a change in the y coordinates and the shape has shifted 5 units down. Hence (x, y) -> (x, y-5) and then reflection across y axis is the answer
Answer:
B
Step-by-step explanation:
Find the measure of one interior angle for the following regular polygon
Can someone help me out
