The candy store owner should use 37.5 pounds of the candy costing $1.25 a pound.
Given:
Candy costing $1.25 a pound is to be mixed with candy costing $1.45 a poundThe resulting mixture should be 50 pounds of candyThe resulting mixture should cost $1.30 a poundTo find: The amount of candy costing $1.25 a pound that should be mixed
Let us assume that the resulting mixture should be made by mixing 'x' pounds of candy costing $1.25 a pound.
Since the total weight of the resulting mixture should be 50 pounds, 'x' pounds of candy costing $1.25 a pound should be mixed with '[tex]50-x[/tex]' pounds of candy costing $1.45 a pound.
Then, the resulting mixture contains 'x' pounds of candy costing $1.25 a pound and '[tex]50-x[/tex]' pounds of candy costing $1.45 a pound.
Accordingly, the total cost of the resulting mixture is [tex]1.25x+1.45(50-x)[/tex]
However, the resulting mixture should be 50 pounds and should cost $1.30 a pound. Accordingly, the total cost of the resulting mixture is [tex]1.30 \times 50[/tex]
Equating the total cost of the resulting mixture obtained in two ways, we get,
[tex]1.25x+1.45(50-x)=1.30 \times 50[/tex]
[tex]1.25x+72.5-1.45x=65[/tex]
[tex]0.2x=7.5[/tex]
[tex]x=\frac{7.5}{0.2}[/tex]
[tex]x=37.5[/tex]
This implies that the resulting mixture should be made by mixing 37.5 pounds of candy costing $1.25 a pound.
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[tex]\to \bold{ 1.25x+1.45(50-x)= 1.30 \times 50}\\\\ \to \bold{ 1.25x+72.5-1.45x= 65}\\\\ \to \bold{ -0.2x= -7.5}\\\\ \to \bold{ x=\frac{7.5}{0.2}}\\\\ \to \bold{ x=37.5}\\\\[/tex]
It implies that [tex]\bold{37.5\ pounds}[/tex] of candy at [tex]\bold{\$1.25}[/tex] a pound must be used to make the final concoction.Learn more:
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there are 10 marbels in a bag, 4 are multi colored and 6 are solid. what is the probability of picking a solid marble and then another solid marble without replacing the first marble?
Answer:
(2/5) * (3/4) = 3/10 = 0.3
The slope of the line below is -0.25. Write the equation of the line in point-
slope form, using the coordinates of the labeled point. Do not use parenthesis
on the y side.
Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ?
f(x)= x3 - 2x2 - 3x + 6
f(x)= x3 - 2x2 + 3x + 6
f(x)= x3 + 2x2 - 3x + 6
f(x)= x3 + 2x2 - 3x - 6
Using the factor theorem, it is found that the polynomial is:
[tex]f(x) = x^3 - 2x^2 - 3x + 6[/tex]
Given by the first option
---------------------------
Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] using the factor theorem it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.
---------------------------
In this question:
[tex]x_1 = 2[/tex][tex]x_2 = \sqrt{3}[/tex][tex]x_3 = -\sqrt{3}[/tex]By the options, leading coefficient [tex]a = 1[/tex]Thus:
[tex]f(x) = (x - 2)(x - \sqrt{3})(x + \sqrt{3})[/tex]
[tex]f(x) = (x - 2)(x^2 - 3)[/tex]
[tex]f(x) = x^3 -2x^2 - 3x + 6[/tex]
Which is the polynomial.
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Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 11, 7, 3, ... This is_ sequence and the _ is equal to_
the sequence is arithmetic because it's incrementing by a constant ratio of -4
The sequence 11,7,3,... is arithmetic because there is a constant increase of (-4)
Must click thanks and mark brainliest
answer please lol so uh yeah
Answer:
5x=20
5x/5=20/5
x=4
Step-by-step explanation:
substitute the 5x
divide both sides by 5 it will be 20 divide by 5
answer is x =4
What is a negative rational number times a positive integer?
A) A negative integer
B) A positive rational number
C) A negative rational number
D) An irrational number
Answer:
C
Step-by-step explanation:
The product of a negative rational number and a positive integer is a negative rational number
Answer: C (A Negative Rational Number)
Step-by-step explanation
A Negative number mutiplied by a positive number is a negative number.
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[tex]Evaluate \: the \: following \\ (1) \: log1000 \: \\ (2) ( \frac{128}{625} ) \\ (3) log {x}^{2} {y}^{3} {z}^{4} \\ (4) log \frac{ {p}^{2} {q}^{3} }{r} \\ (5) log \sqrt{ \frac{ {x}^{3} }{ {y}^{2} } } [/tex]
[tex]If \: {x}^{2} + {y}^{2} = 25xy. \\ Then \: prove \: that \: \\ 2 log(x + y) = \\ 3 log3 + logx + logy. \: [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \:I \: need \: the \: answer \\ \: \: \: \: \: \: \: \: \: \: \: \: Plz \: fastly \: [/tex]
I need ans !!!!!
Step-by-step explanation:
log1000= log 10³= 3 log10 =3log(128/625)= 7 log 2+ 4 log 5log x²y³z⁴= 2 logx + 3 log y + 4 log zlog p²q³/r= 2 log p +3 log q - log rlog√(x³/y²)=3/2[ log (x)] - log yx²+y²=25xy
(x+y)²-2xy=25xy
(x+y)²= 2xy +25 xy
=27xy
Take log on both sides
2 log(x+y) =log 27 + log x + log y
=log 3³+ log x + log y
2 log(x+y)=3 log 3 + log x + log y
Answer:
(1)
log 1000 = log 10³ = 3 log 10 = 3(2) It should be with log? If yes ignore log x and consider the right side
(128/625) = xlog x = log (128/625)log x = log 128 - log 625log x = 7 log 2 - 4 log 5(3)
log (x²y³z⁴) = log x² + log y³ + log z⁴ = 2 log x + 3 log y + 4 log z(4)
log (p²q³/r) = log p² + log q³ - log r = 2 log p + 3 log q - log r(5)
log [tex]\sqrt{\frac{x^3}{y2} }[/tex] = 1/2 log [tex]x^3y^{-2}[/tex] = 3/2 log x - log y(6)
x² + y² = 25xyx² + 2xy + y² = 27xy(x + y)² = 27xylog (x + y)² = log (27xy)2 log (x + y) = log 3³+ log x + log y2 log (x + y) = 3 log 3 + log x + log yProvedIt's estimated that 330 billion photographs are taken each year. If there are 6.9
billion people in the world, how many photos on average is that per person?
37/50 of a number is what percentage of that number?
Answer:
74% percentage of 37/50
Answer:
74%
Step-by-step explanation:
37/50 * 100 = 74%
When you want to obtain percentages, in most of the cases you multiply by 100.
The figure below is a square. Find the length of side x in simplest radical form with a rational denominator.
9514 1404 393
Answer:
x = (√2)/2
Step-by-step explanation:
The diagonal is √2 times the side length (x), so ...
1 = x√2
√2 = 2x . . . . . multiply by √2
(√2)/2 = x . . . . divide by 2
The side length x is (√2)/2.
Find the length of the third side. If necessary, round to the nearest tenth.
16
12
Answer:
Submit Answer
PLS HELP ASAP
Answer:
I think 16.
Step-by-step explanation:
because 12 is impossible and last answer is 16.
Answer:
the third side will be √500
Step-by-step explanation:
[tex]\sf{}[/tex]
using PGT
(16)²+(12)²=H²
=> 256+144 = H²
=> 500 = H ²
=> √500 = H
EFGH is an isosceles trapezoid and EFGI is a parallelogram. If m∠IEF = 36°, then m∠HGI = ° (Blank 1).
The base angles of an isosceles trapezoid are equal; For EFGI to be a parallelogram, the measure of [tex]\angle HGI[/tex] is: 108 degrees
Given that:
[tex]\angle IEF = 36^o[/tex]
IEF and GHI are the base angles of the trapezoid.
So:
[tex]\angle GHI = \angle IEF = 36^o[/tex]
Also:
[tex]\triangle GHI[/tex] is an isosceles triangle.
This means that:
[tex]\angle GHI = \angle HIG = 36^o[/tex] --- base angles of an isosceles triangle
So:
[tex]\angle GHI + \angle HIG + \angle HGI = 180[/tex] --- sum of angles in a triangle
Substitute known values
[tex]36 + 36+ \angle HGI = 180[/tex]
[tex]72 + \angle HGI = 180[/tex]
Collect like terms
[tex]\angle HGI = 180-72[/tex]
[tex]\angle HGI = 108[/tex]
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please help me Find DE.
Answer:
DE = 11
Step-by-step explanation:
DF = DF +EF
4x+2 = x+7 + 7
Combine like terms
4x+2 = x+14
Subtract x from each side
4x+2-x = x+14-x
3x+2 = 14
Subtract 2 from each side
3x+2-2 =14-2
3x=12
Divide by 3
3x/3 = 12/3
x = 4
DE = x+7 = 4+7 =11
Answer:
DE is 11
Step-by-step explanation:
[tex]DE = DF - EF \\ DE = (4x + 2) - 7 \\DE = 4x - 5 [/tex]
But for x:
[tex]4x + 2 = (x + 7) + 7 \\ 4x + 2 = x + 14 \\ 3x = 12 \\ x = 4[/tex]
Therefore:
[tex]DE = (4 \times 4) - 5 \\ = 16 - 5 \\ = 11[/tex]
Segment overline BD bisects angle ABC . Solve for Round to the nearest tenth, if necessary (Image not necessarily to scale.)
Answer:
Hello,
Answer 52/3
Step-by-step explanation:
using the theorem of the bissector :
[tex]\dfrac{x}{13} =\dfrac{20}{15 } \\\\x=\dfrac{20*13}{15} \\\\x=\dfrac{52}{3}[/tex]
The value of x to the nearest tenth is 18.5
Pythagoras theoremTo get the value of x, we first need to get the height of the triangle.
[tex]h^2=20^2-15^2\\h^2=400-225\\h^2=175\\h=13.23[/tex]
Next is to get the value of x
[tex]x^2=13^2+13.2^2\\x^2=343.24\\x=18.52[/tex]
Hence the value of x to the nearest tenth is 18.5
Learn more on pythagoras theorem: https://brainly.com/question/343682
PLEASE HELP!!!
What is the overlap of Data Set 1 and Data Set 2?
A.) high
B.) moderate
C.) low
D.) none
Step-by-step explanation:
Step by step explanation, The answer is C
PLS HELP ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE QUESTION!!
Which of the following statements is true?
A. A data set will always have exactly one mode
B. A data set can have multiple modes
C. A data set will always have at least one mode
D. A data set will never have a mode
Answer:
Step-by-step explanation:
The mode is the most number of times a number appears in a set of data points.
If there is at least one entry in the data set, then there is at least 1 mode. You can have more than 1 mode.
3, 3, 3, 5, 6, 6, 6 has 2 modes. (3 and 6)
3 has 1 mode.
[ ] set has no modes because this is the empty set.
Conclusion
A is not true. See the example above
B is true. It can have more than 1 mode
C is true for everything but the empty set.
D is simply false.
I think you are intended to pick C, but B is also true. I can't give you just 1 answer. It is a faulty question.
I can't figure this out, please help! I'll give a brainliest
Answer:
u can use pythagoras or sine rule
Step-by-step explanation:
cos-1(9/11)
Find the error in the student's work. Which of the following steps is where the first error occurred?
f(x) = -3x^2 - 2x
Step 1: f(-2) = -3(2)^2 - 2(-2)
Step 2: f(-2) = -3(4) + 4
Step 3: f(-2) = -12 + 4
Step 4: f(-2) = -8
Step 3 should be 12 + 4.
Step 2 should be -3(-4).
O Step 1 should have a -2 substituted for both values.
Answer:
Step 1 should have a -2 substituted for both values.
What is the difference of the rational expressions below?
Answer:
in the pic
Step-by-step explanation:
answer A
.....
Evaluate 29.4 - 33.85.(round to the hundredths place) -4.45 260.15 4.45 63.25
URGENT!!!!
The value of a12 is:
2
0
1
can't be done
it's 1 beacuse the exponent has no power so its 1
The correct answer from the given matrix shows that the value of a12 is 1
What is a Matrix?This refers to a rectangular array of numbers that is arranged in rows and columns to indicate a mathematical property.
Hence, we can see that from the matrix given, we can see that there are different values for each one and to find a12, we can see that because there is no power in the exponent, the answer is 1.
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Given the function f(x) = -2c + cx - x^2? and f^-1(5) = -1, find c.
Answer:
c = - 2
Step-by-step explanation:
Given inverse function
[tex]f^{-1}[/tex] (5) = - 1 , then
f(- 1) = 5 , that is
- 2c + c(- 1) - (- 1)² = 5
- 2c - c - 1 = 5
- 3c - 1 = 5 ( add 1 to both sides )
- 3c = 6 ( divide both sides by - 3 )
c = - 2
1. 108 identical books have a mass of 30 kg. Find
(i) the mass of 150 such books
(ii) the number of such books that have a mass of 20 kg
Answer:
i) around 41.7 kg
ii) 72 books
Step-by-step explanation:
i) if 108 books are 30 kg then how much is the mass for 150? You cross multiply so 150 multiply by 30 and 108 multiply by x (the unknown mass). you will get 4500=108x and then 4500/108 is the unknown mass.
ii) use the same way as above.
Review the graph of function g(x).
Which point is on the graph of the inverse function g^-1(x)?
O (-3,0)
O (0,-3)
O (2,3)
O (3,4)
Answer:
A
Step-by-step explanation:
I did the wrong thing. I inverted the graph. That's not the question. The question is which one of the following is on the inverse of the graph. That means that x and y are interchanged. The answer you gave was the second best answer. The answer is (-3,0) which is A.
Calculus!
The volume of a substance, A, measured in cubic centimeters increases according to the exponential growth model dA/dt = 0.3A, where t is measured in hours. The volume of another substance, B, also measured in cubic centimeters increases at a constant rate of 1 cm^3 per hour according to the linear model dB/dt = 1. At t = 0, substance A has a volume A(0) = 3 and substance B has size B(0) = 5. At what time will both substances have the same volume?
Would it be correct to write the growth model of substance B as x + 5? And how could I write the growth model of substance A? Thank you in advance, and sorry for the poor formatting.
Answer:
The two substances will have the same volume after approximately 3.453 hours.
Step-by-step explanation:
The volume of substance A (measured in cubic centimeters) increases at a rate represented by the equation:
[tex]\displaystyle \frac{dA}{dt} = 0.3 A[/tex]
Where t is measured in hours.
And substance B is represented by the equation:
[tex]\displaystyle \frac{dB}{dt} = 1[/tex]
We are also given that at t = 0, A(0) = 3 and B(0) = 5.
And we want to find the time(s) t for which both A and B will have the same volume.
You are correct in that B(t) is indeed t + 5. The trick here is to multiply both sides by dt. This yields:
[tex]\displaystyle dB = 1 dt[/tex]
Now, we can take the integral of both sides:
[tex]\displaystyle \int 1 \, dB = \int 1 \, dt[/tex]
Integrate. Remember the constant of integration!
[tex]\displaystyle B(t) = t + C[/tex]
Since B(0) = 5:
[tex]\displaystyle B(0) = 5 = (0) + C \Rightarrow C = 5[/tex]
Hence:
[tex]B(t) = t + 5[/tex]
We can apply the same method to substance A. This yields:
[tex]\displaystyle dA = 0.3A \, dt[/tex]
We will have to divide both sides by A:
[tex]\displaystyle \frac{1}{A}\, dA = 0.3\, dt[/tex]
Now, we can take the integral of both sides:
[tex]\displaystyle \int \frac{1}{A} \, dA = \int 0.3\, dt[/tex]
Integrate:
[tex]\displaystyle \ln|A| = 0.3 t + C[/tex]
Raise both sides to e:
[tex]\displaystyle e^{\ln |A|} = e^{0.3t + C}[/tex]
Simplify:
[tex]\displaystyle |A| = e^{0.3t} \cdot e^C = Ce^{0.3t}[/tex]
Note that since C is an arbitrary constant, e raised to C will also be an arbitrary constant.
By definition:
[tex]\displaystyle A(t) = \pm C e^{0.3t} = Ce^{0.3t}[/tex]
Since A(0) = 3:
[tex]\displaystyle A(0) = 3 = Ce^{0.3(0)} \Rightarrow C = 3[/tex]
Therefore, the growth model of substance A is:
[tex]A(t) = 3e^{0.3t}[/tex]
To find the time(s) for which both substances will have the same volume, we can set the two functions equal to each other:
[tex]\displaystyle A(t) = B(t)[/tex]
Substitute:
[tex]\displaystyle 3e^{0.3t} = t + 5[/tex]
Using a graphing calculator, we can see that the intersect twice: at t ≈ -4.131 and again at t ≈ 3.453.
Since time cannot be negative, we can ignore the first solution.
In conclusion, the two substances will have the same volume after approximately 3.453 hours.
find the product using formula (a+b) (a-b) = a square + b square a.61×59. Note: Solve by using formula.
Answer:
[tex]\huge\boxed{\sf 3599}[/tex]
Step-by-step explanation:
= 61 × 59
You can write 61 = 60 + 1 and 59 = 60 - 1
Hence,
= ( 60 + 1 ) ( 60 - 1 )
According to the formula:
[tex](a+b)(a-b) = a^2-b^2[/tex]
= (60)² - (1)²
= 3600 - 1
= 3599
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Peace!Does 8in to 1ft reduce it or enlarge it
Answer:
enlarge it
Step-by-step explanation:
I ft = 12 inches
Thus 8 in → 12 in makes the transformation larger.
Thus going from 8 in to 12 in is an enlargement
The length of a rectangular field is 6 metres longer than its width. If the area of the field is 72 square metres, What are the width and the length of the field?
Answer:
Let's call the length of the field "l", and the width of the field "w".
If the area of the field is 72 square meters, then we have:
l x w = 72
And if the length is 6 meters longer than the width, we have:
l = w+6
So looking at the first equation (l x w = 72), we can substitute the l for a w+6.
And we obtain:
(w+6) x (w) = 72
Which simplifies to w^2 + 6w = 72.
This quadratic equation is pretty easy to solve, you just need to factor it.
w^2 + 6w - 72 = 0
(w-6)(w+12)
This leaves the roots of the quadratic equation to be 6 and -12, but in this case, a width of -12 wouldn't make sense.
So, the width of the rectangular field is 6, and the length of the field is 12.
Let me know if this helps!
Answer:
we assume one side is x and other side must be x+6 and when we multiple it together we can find x²+6x =72
Step-by-step explanation:
one side is 6 and. other is 12 so the lenght= 12 the width=6
Find the missing value.
Hint: Use the number line to find the missing value.
了。
-(-2)
{
开
-10
-5
→
15
0
5
10
-15
Answer:
-5
Step-by-step explanation:
-5 -(-2)
=-7
I hope this helped!Help pls ?? I really don’t know what to do
Answer:
The answer is "C" f(x)= x+ 4 and g(x)= x^3 - 1
Step-by-step explanation:
all you have to do is replace the x in "G" with the "F" function
F(x) = x+4 and G(x) = x^3-1
===========================================================
Explanation:
Let's try choice A to see if it works or not
G(x) = (x+4)^3
G( F(x) ) = ( F(x)+4 ) ^3 .... replace every x with F(x)
G( F(x) ) = ( x-1+4 ) ^3 .... plug in F(x) = x-1
G( F(x) ) = (x+3)^3
This isn't the same as (x+4)^3 - 1. You can confirm this with a graph or a table of values. We cross choice A off the list.
------------
Let's try choice B
G(x) = x+4
G( F(x) ) = F(x)+4
G( F(x) ) = x^3-1 + 4
G( F(x) ) = x^3 + 3
Similar to choice A, this isn't the same as (x+4)^3-1. We can cross this off the list as well.
--------------
Now choice C
G(x) = x^3 - 1
G( F(x) ) = ( F(x) )^3 - 1
G( F(x) ) = (x+4)^3 - 1
We found the final answer.
