Answer: I- 81 pints, II-9 pints
Step-by-step explanation:
Given
The first type of juice has 30% pure Juice
The second type of juice has 80% pure Juice
The final mixture has 95 pints of 35% pure juice
Suppose we take x pints from the first Juice
So, the second Juice contributes 90-x
for 35% content
[tex]\Rightarrow 35=\dfrac{x\times 30+(90-x)80}{90}\\\\\Rightarrow 3150=30x+7200-80x\\\\\Rightarrow 50x=4050\\\Rightarrow x=81\ \text{pints}[/tex]
First contributes 81 pints. second contributes 9 pints
Yoko received a $90 gift card for a coffee store. She used it in buying some coffee that cost $8.23 per pound. After buying the coffee, she had $40.62 left on her card. How many pounds of coffee did she buy?
Answer: 6
Step-by-step explanation:
Step 1: Set up equation:
90=40.62+8.23p
^ the 'p' represents pounds.
Step 2: Subtract 40.62 from both sides
49.38 = 8.23p
Step 3: Divide both sides by 8.23 (We do this to get the variable "p" by itself)
6=p
Trust Milky. Milky Smart
Solve for x
HELP ME PLEASEEEE
Answer:
x = 9
Step-by-step explanation:
5x + 7 = 52
5x = 52-7
5x = 45
x= 9
Find with proof the sum from i = 1 to n of 2^i for each n >= 1. Find with proof the sum from i = 1 to n of 1/(i(i+1)) for each n >= 1. Prove that n! > 2^n for each n >= 4.
Prove sqrt(2) is irrational.
Find with proof the sum of the first n odd positive integers.
If A is the set of positive multiples of 8 less than 100000 and B is the set of positive multiples of 125 less than 100000, find |A intersect B|.
Find |A union B|.
There are 7 students on math team, 3 students on both math and CS team, and 10 students on math team or CS team. How many students on CS team?
The sum from i = 1 to n of 2^i is 2(2^n - 1), the sum from i = 1 to n of 1/(i(i+1)) is n/(n+1), n! > 2^n for n ≥ 4, and therefore, sqrt(2) is irrational. The intersection of sets A and B has |A ∩ B| elements, the union of sets A and B has |A ∪ B| elements, and the number of students on the CS team is 6.
Let's break down the questions and provide the proofs and solutions step by step:
Sum of powers of 2: We want to find the sum from i = 1 to n of 2^i for each n ≥ 1. We can use the formula for the sum of a geometric series to simplify the expression:
The sum of a geometric series is given by the formula Sn = a(r^n - 1)/(r - 1), where a is the first term, r is the common ratio, and n is the number of terms. In this case, a = 2, r = 2, and we need to find Sn.
Plugging in the values, we get Sn = 2(2^n - 1)/(2 - 1) = 2(2^n - 1).
Therefore, the sum from i = 1 to n of 2^i is 2(2^n - 1).
Sum of fractions: We want to find the sum from i = 1 to n of 1/(i(i+1)) for each n ≥ 1. We can rewrite the expression as follows:
1/(i(i+1)) = 1/i - 1/(i+1).
Now, we can observe that the terms cancel out in pairs when we sum them. The first term 1/1 remains, and the last term 1/(n+1) remains as well.
Therefore, the sum from i = 1 to n of 1/(i(i+1)) is 1 - 1/(n+1) = n/(n+1).
Proof of n! > 2^n: We will prove this by induction. The base case is n = 4: 4! = 24 > 2^4 = 16.
Now, assume the inequality holds for some k ≥ 4, i.e., k! > 2^k.
We need to prove it for k + 1: (k + 1)! = (k + 1) * k! > (k + 1) * 2^k (since k! > 2^k by the induction hypothesis).
It suffices to show that (k + 1) * 2^k > 2^(k + 1), which simplifies to k + 1 > 2.
Since k ≥ 4, the inequality holds.
Therefore, by induction, we can conclude that n! > 2^n for each n ≥ 4.
Proof that sqrt(2) is irrational: We will prove this by contradiction. Assume that sqrt(2) is rational, i.e., sqrt(2) can be expressed as a ratio of two integers p and q in its simplest form, where q ≠ 0.
sqrt(2) = p/q.
Squaring both sides, we get 2 = p^2/q^2.
Rearranging, we have p^2 = 2q^2.
This implies that p^2 is even, and thus p must be even.
Let p = 2k, where k is an integer.
Substituting back, we have (2k)^2 = 2q^2, which simplifies to 4k^2 = 2q^2.
Dividing by 2, we get 2k^2 = q^2.
This implies that q^2 is even, and thus q must be even.
However, if both p and q are even, then p/q is not in its simplest form, contradicting our initial assumption.
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Given that a^b=x, evaluate the following: a^26 PLS HELP NOW
Answer:
Step-by-step explanation:
Find the log of both the equation and the expression:
b log a = log x this can be solved for log a in terms of log x:
log x
log a = ------------
b
"Name" the second expression "y." Then y = a^26 and log y = 26 log a.
log x
Then log y = 26--------------
b
and the expression a^26 is found by taking the antilog of both sides of log y:
log y log x
10 = y = 10^(26----------)
b
Please double check to ensure that you have copied this problem down correctly.
A long straight wire carrying a 4-A current is placed along the x-axis as shown in the figure. What is the direction of the magnetic field at a point P due to this wire? Q Tap image to zoom 0 along the +x-axis 0 out of the plane of the page 0 along the -x-axis 0 into the plne of the page into the plane of the page 0 along the ty-axis
The direction of the magnetic field at P is perpendicular to both the current direction and the direction of the curl of our fingers.
The direction of the magnetic field at point P due to the current-carrying wire can be determined using the right-hand rule. If we point our right thumb in the direction of the current (which is along the positive x-axis), and curl our fingers toward the point P, then the direction of the magnetic field at P is perpendicular to both the current direction and the direction of the curl of our fingers.
In this case, since the wire is straight and lies in the x-y plane, the direction of the magnetic field at point P will be perpendicular to the plane of the page, and will either be pointing into or out of the page. To determine which direction, we need to know the orientation of point P relative to the wire. If point P is above the wire, then the magnetic field will be pointing into the page, and if it is below the wire, then the magnetic field will be pointing out of the page.
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Can someone help me with this question. Will Mark brainliest.
Answer:
Step-by-step explanation:
Plz help me we are almost done
Answer:
1) D
2) B
Step-by-step explanation:
Hope this Helps!
:)
Plsssss helps 50 points
Answer:
2000.2 cm³
Step-by-step explanation:
Finding the volume of a cylinder is quite simple if you under what pi (3.14) is. You can watch khan academy. It has some useful videos on solving for volume. It also explains very well. Hope this helps!
1. The three year discount factor is 0.7773 and the one year discount factor is 0.9434. Calculate the two year discount factor if the three year annuity factor is 2.6065 a. 0.9623 b. 0.8758 c. 0.9132
After considering the given data we conclude that the generated two year discount factor is 0.9132, under the condition that three year annuity factor is 2.6065.
Applying the formula for the annuity factor, we can find the two year discount factor:
[tex]annuity factor = (1 - discount factor^n) / r[/tex]
Here,
n = number of years
r = annual interest rate.
We are given that the three year discount factor is 0.7773 and the one year discount factor is 0.9434. We are also given that the three year annuity factor is 2.6065.
Applying the formula for the annuity factor, we can evaluate the annual interest rate:
[tex]2.6065 = (1 - 0.7773^3) / r[/tex]
r = 0.1
Now, we can evaluate the two year discount factor:
[tex]annuity factor = (1 - discount factor^2) / 0.1[/tex]
[tex]2.6065 = (1 - discount factor^2) / 0.1[/tex]
[tex]discount factor^2 = 0.89335[/tex]
discount factor = [tex]\sqrt(0.89335)[/tex]
discount factor = 0.9132
Therefore, the two year discount factor is 0.9132.
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WHat do u do with the brainly credits or whatever
Answer:
You basically grow rep
Step-by-step explanation:
Brainly points you need for asking questions and people are more likely to trust you with their questions if you have alot!
Answer:
i actually dont know
Step-by-step explanation:
QUESTION 45
What is the value of x?
3x
Answer:
1/67
Step-by-step explanation:
Complete question
If X+2/3x is equal to 45. find the value of x
Given the equation
x+2/3x = 45
Cross multiply
x+2 = 3x(45)
x+2 = 135x
x - 135x = -2
-134x = -2
x = 2/134
x = 1/67
Hence the value of x is 1/67
The sum of two numbers is 48. The second number is twice the first
Write and solve a system of equations to find the numbers.
Answer:
The equations are
X + Y = 48 ----Eq (1)
Y = 2 X -----Eq (2)
Solution of the equations and the two number are
X = 16, Y = 32
Step-by-step explanation:
Let the two numbers be X and Y
Given -
The sum of two numbers is 48.
Thus, X + Y = 48 ----Eq (1)
The second number is twice the first
Thus, Y = 2 X -----Eq (2)
Substituting the value of Y in equation (1), we get -
X + 2X = 48
3 X = 48
X = 16
Y = 2 X = 32
d = 18 in. Fine the radius or diameter of each circle with the given dimensions.
Answer:
r= 9
Step-by-step explanation:
radius (r) = diameter (D)/2
= 18/2
= 9
HELPP I WILL GIVE YIU BRAINLIEST!! i think the answer is 42x + 12 but not entirely sure!!!
Answer:
yes your answer is correct
Step-by-step explanation:
Use Rouché's Theorem to find the number of (complex) roots, counting multiplicities, of 2z8 + 3z5 - 9z³ + 2 = 0 in the region 1 < |z| < 2.
To apply Rouché's Theorem, we consider two functions: f(z) = 2z⁸ + 3z⁵ - 9z³ + 2 and g(z) = 2z⁸. We want to analyze the number of roots of f(z) = 0 inside the region 1 < |z| < 2.
First, let's examine the behavior of f(z) and g(z) on the boundary of the region. When |z| = 1, the term 2z⁸ dominates over the other terms in f(z), so |f(z)| < |g(z)|. On the other hand, when |z| = 2, the term 2z⁸ is still dominant, and again |f(z)| < |g(z)|.
Since |f(z)| < |g(z)| on the boundary of the region, Rouché's Theorem guarantees that f(z) and g(z) have the same number of roots inside the region, counting multiplicities. In this case, g(z) = 2z⁸ has exactly eight roots, counting multiplicities.
Therefore, by Rouché's Theorem, we can conclude that the equation 2z⁸ + 3z⁵ - 9z³ + 2 = 0 has eight roots, counting multiplicities, inside the region 1 < |z| < 2.
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Which angles are supplementary to 16? Select all that apply.
Answer:
Step-by-step explanation:
15,13,11,9,1,3,5,7
Answer:
13
Step-by-step explanation:
Supplementary angles add up to 180 and angles on a straight line add up to 180 so 13
PLEASE HELP ASAP A glass stand to display a doll is in the shape of a right triangular pyramid. The area of the base is 40.5 square inches with a height of 15 inches. What is the volume of the glass stand
Answer: [tex]202.5\ in.^3[/tex]
Step-by-step explanation:
Given
The area of the base is [tex]A=40.5\ in.^2[/tex]
height of the triangular prism is [tex]h=15\ in.[/tex]
The volume of a triangular prism is [tex]V=\dfrac{1}{3}Ah[/tex]
The volume of given Prism is
[tex]V=\dfrac{1}{3}\times 40.5\times 15=202.5\ in.^3[/tex]
The volume of the triangular prism is [tex]202.5\ in.^3[/tex]
Help ASAP I’ll give brainliest how do u find this out or how do u think we could find this out
Answer:
9526/87
Step-by-step explanation:
87·x=9,526
x=9526/87
HELPP I WILL GIVE YOU BRAINLIEST!! i think the answer is 42x + 12 but i am not sure!!
Write down the vectors along the lines representing those pipes, find the cross product between them from which to create the unit vector n, define a vector that spans two points on each line, and finally determine the minimum distance between the lines. (Take the origin to be at the lower corner of the first pipe.) Similarly, you may also develop the symmetric equations for each line and substitute directly into your formula.
Vectors along the lines:
To find vectors along the lines, we need two points on each line. Let's denote the points on Line A as A₁ and A₂, and the points on Line B as B₁ and B₂.
Vector along Line A: v₁ = A₂ - A₁
Vector along Line B: v₂ = B₂ - B₁.
Define the vectors along the lines:
Let's say we have two lines represented by the following equations:
Line 1: r₁(t) = a₁ + t * u₁
Line 2: r₂(t) = a₂ + t * u₂
Here, a₁ and a₂ are points on the lines, and u₁ and u₂ are the direction vectors of the lines.
Find the cross product:
To find the unit vector n, we can take the cross product of the direction vectors:
n = u₁ × u₂
Note: × represents the cross product operator.
Define a vector spanning two points on each line:
Let's choose two points on each line, which we'll call b₁ and b₂. The vector spanning these points on Line 1 is given by:
v₁ = b₁ - a₁
Similarly, the vector spanning the points on Line 2 is given by:
v₂ = b₂ - a₂
Determine the minimum distance:
The minimum distance (d) between the lines can be found using the formula:
d = |(v₁ × u₂) · n| / |n|
In this formula, · represents the dot product operator, and | | represents the magnitude or length of the vector.
Alternatively, if you prefer using symmetric equations, you can substitute the equations of the lines directly into the formula to find the minimum distance.
Remember to substitute the appropriate values for a₁, a₂, u₁, u₂, b₁, and b₂ based on the specific problem you are solving.
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On a map, 1 inch equals 5.2 miles. Two house are 3.5 inches apart on the map. What is the actual distance between the house?
Answer:
18.2 miles
Step-by-step explanation:
simple multiplication:
We know that 1 inch of distance on the map is equal to 5.2 miles.
Using this knowledge we can multiply the amount of inches by the miles per inch.
5.2*3.5=18.2 miles apart
Hope this helps!!
In a class of 30 students, 6 play an instrument and 17 play a sport. There are 9
students who do not play an instrument or a sport. What is the probability that a
student chosen randomly from the class plays neither a sport nor an instrument?
Answer:
9/30
Step-by-step explanation:
what value would make the set of points a function. (9, -2) (4,
3) (8,10) (? , 8)
Answer:
Any x-value other than 4, 8, or 9 would make this set of points a function.
What nominal interest rate compounded monthly is equivalent to
2.50% compounded quarterly? Round to two decimal places
Rounding this to two decimal places, the equivalent nominal interest rate compounded monthly is approximately 2.53%.
To determine the equivalent nominal interest rate compounded monthly for a given nominal interest rate compounded quarterly, we can use the formula for nominal interest rate conversion.
The formula is:
r = (1 + i/n)^n - 1
Where:
r is the nominal interest rate compounded annually (we're looking for this),
i is the nominal interest rate compounded quarterly (2.50% in this case),
n is the number of compounding periods per year (4 for quarterly compounding).
Plugging in the values, we have:
r = (1 + 0.025/4)^4 - 1
Calculating this expression, we find:
r ≈ 0.025335
Rounding this to two decimal places, the equivalent nominal interest rate compounded monthly is approximately 2.53%.
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HELP ASAP!!! find the lines of symmetry. Select all that apply
Answer:
B. and D.
Step-by-step explanation:
If you folded that shape along the lines o and m, it would match up.
There are two lines of symmetry m and o. Options B and D are correct.
From the given figure we have to determine the axes of symmetries.
A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.
Here,
As of the given figure,
There are 2 axes of symmetry first line m and the other is line o.
Line l and line n are not symmetrical lines because the reflection of one portion will not be superimposed with the other.
Thus, there are two lines of symmetry m and o. Options B and D are correct.
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Help me please I will give points
NO FAKE ANSWERS
Answer: 2,3,4
Step-by-step explanation:
Apple’s is represented by 8 and oranges is represented by 5. So the ratio 8:5 means every 8 apples their are 5 oranges
I need help on this question
sheri’s cab fare was $32, with a 20% gratuity and no taxes. sheri's write a check to the cab driver for $40. is this a reasonable amount? explain.
In a case whereby sheri’s cab fare was $32, with a 20% gratuity and no taxes. sheri's write a check to the cab driver for $40, this can be considered as being reasonable amount because it is $1.60 more to the cab driver.
How can we know if it is reasonable?A gratuity is a sum of money that customers typically give to specific service sector employees, including those in the hotel industry, in addition to the service's base charge for the work they have completed.
Given ; Sheri’s cab fare was $32 and the percentage of gratuity is 20%
amount of gratuity = 20% 0f 32 = 6.40
The fare of the cab + gratuity = 32 + 6.40 = 38.40
Check to the cab driver for $40 , implies ($40 - $38.40)= $1.60 more to the cab driver.
Hence, it is reasonable.
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True or False: When conducting a survey of a group of people, you must interview every person in that population A Truc B False
Porportion equation and solution: a punch recipe calls for 3 liters of ginger ale and 1.5 liters of tropical fruit juice how many quarts of punch will the recipe make (1 Liter = 1.6 quarts)
Answer:
The recipe will make 7.2 quarts of punch.
Step-by-step explanation:
A punch recipe calls for 3 liters of ginger ale and 1.5 liters of tropical fruit juice.
Then the recipe will make 4.5 liters of punch, obtained by the sum of ginger ale and tropical fruit juice.
The ration is the comparison of two quantities and is measured from the division of two values, then: [tex]\frac{a}{b}[/tex].
The proportion is the equality between two or more ratios. That is, [tex]\frac{a}{b}=\frac{c}{d}[/tex] equals a proportion.
In this case, being 1 L= 1.6 quarts, you have:
[tex]\frac{1.6 quarts}{1 L}=\frac{x}{4.5 L}[/tex]
Solving:
[tex]x=4.5 L*\frac{1.6 quarts}{1 L}[/tex]
x= 7.2 quarts
So, the recipe will make 7.2 quarts of punch.