The expression [tex]cos^4(x)sin^2(x)[/tex] can be rewritten without exponents as [tex]cos^2(x) - (\frac{1}{2} )cos^4(x)[/tex].
The double angle, half angle, or power-reducing formula can be used to rewrite [tex]cos^4(x)sin^2(x)[/tex] without exponents. One of the approaches to rewriting is by applying the power-reducing formula. The power-reducing formula is a trigonometric identity that is used to reduce powers of sine and cosine functions.
To rewrite [tex]cos^4(x)sin^2(x)[/tex] without exponents, you can use the power reducing formula. This formula states that:
[tex]cos^2(x)*sin^2(x) = (\frac{1}{2} )(1-cos(2x))[/tex]
We can use this formula to break down [tex]cos^4(x)sin^2(x)[/tex] as follows:
[tex]cos^4(x)sin^2(x) = cos^2(x)sin^2(x)cos^2(x) = (\frac{1}{2} )(1-cos(2x))cos^2(x)[/tex]
Next, we can use the double angle formula, which states that:
[tex]cos(2x) = 2cos^2(x) - 1[/tex]
Plugging this into our equation, we get:
[tex]cos^4(x)sin^2(x) = (\frac{1}{2} )(1-2cos^2(x)+1)cos^2(x) = cos^2(x) - (\frac{1}{2} )cos^4(x)[/tex]
Therefore, the expression [tex]cos^4(x)sin^2(x)[/tex] can be rewritten without exponents as [tex]cos^2(x) - (\frac{1}{2} )cos^4(x)[/tex].
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URGENT NEED OF HELP PLEASE I DON'T HAVE MUCH TIME!!!!!!!!!!!!!!!!!!!
A slide in a playground must have a maximum average slope of 30°. The top of the slide is 6 ft off the ground and the length of the slide is 11.7 ft. Does the slide meet the safety requirements? Show your work and label the diagram to support your answer.
The slide does not meet safety requirements.
What is Slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
As per the given data:
maximum average slope = 30°
height of the slide = 6 ft
length of the slide = 11.7 ft
For calculating slope (θ):
sinθ = (P/H) {P is perpendicular and H is hypotunese}
sinθ = (height/length)
sinθ = (6/11.7)
sinθ = 0.512
Using sin inverse:
θ = 30.8°
θ > maximum average slope
Hence, the slide does not meet safety requirements.
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I don’t understand how to solve this when one number is missing! Pls help
i would appreciate anyone's help. thank you!
The equation of the volume of the box in terms of x is 4x³ - 40x² +100x.
What is the V(x) function's domain?The set of all conceivable values of x that make sense in the context of the issue constitutes the domain of the function V(x). This time, x must be a positive value less than or equal to 5, as it reflects the length of the side of the square that was cut out of each corner of the cardboard. The range of V(x) is thus 0 x 5.
Given that, the squares cut at the end are x inches.
Thus the dimension of the rectangular box are:
The length of the box will be (10-2x).
The width of the box will be (10-2x).
The height of the box will be x inches.
The volume of the rectangular box is given by:
V = (l)(w)(h)
Substituting the values we have:
V(x) = (10-2x)(10-2x)x = x(100-40x+4x^2) = 4x³ - 40x² +100x.
Hence, the equation of the volume of the box in terms of x is 4x³ - 40x² +100x.
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Umm soo I kinda need help with math
Answer:
Option A.
Step-by-step explanation:
We are asked to add these 2 expressions.
First, we should know how to combine like terms.
What is combining like terms?Combining like terms is adding 2 or more numbers, or variables that are alike.
[tex]-\frac{4}{5} t+\frac{5}{3} s \ + -3 - \frac{7}{5} s+2t=?[/tex]
Let's first begin by combining s and t. We can combine like terms for these two variables.
[tex]-\frac{4}{5} t + 2t = \frac{6}{5} t \ \checkmark[/tex]
[tex]\frac{5}{3} s \ + \frac{7}{5} s \\Which \ can \ also \ be \ represented \ as...\\\frac{25}{15} s \ - \frac{21}{15} s = \frac{4}{15} s \ \checkmark[/tex]
-3 doesn't have any like terms, meaning it'll stay as -3.
[tex]\frac{6}{5} t + \frac{4}{15} s - 3[/tex]
Therefore, our answers matches with Option A.
how do i convert an improper fraction to mixed number
Calculate the present value to purchase a watch of land if 18,000 is put down and 2000 is paid per quarter for five years assume that there a 6% interest is compounded quarterly  if the cash price for the land is 25,000 is it better to pay cash or finance the purchase according to the present value of an annual tea table at 1.5% interest for five years the factor is 17.16864.
The present value of the land is $52,337.28
What is Present Value?The worth of an anticipated revenue stream assessed as of the valuation date is known as a present value in the fields of economics and finance.
There are different kinds of PV models including:
net present value (NPV),internal rate of return (IRR),maximum (minimum) bid (sell),annuity equivalent (AE),loan formula,optimal term,replacement,incremental,How to solve:
We use the formula:
Present value of land = put down payment = PV of annuityPresent value of land= $18,000 + (Quarterly payment + Annuity factor)Present value of land= $18,000 + (2,000 * 17.1684)= $52,337.28
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if (5x-1)/(2)can be written in the equivalent form (3x-6)/(3), what is the value of (5-x)/(2)
The value of [tex](5 - x)/(2)[/tex] is [tex]2[/tex] when[tex](5x - 1)/(2)[/tex] is equivalent to [tex](3x - 6)/(3)[/tex].
The given expression is [tex](5x - 1)/(2)[/tex] and it can be written in the equivalent form [tex](3x - 6)/(3)[/tex].
To find the value of [tex](5 - x)/(2)[/tex], we can use the property of equivalent fractions, which states that if two fractions are equivalent, then the cross products are equal.
So, we can cross multiply the given equivalent fractions to get:
[tex](5x - 1)(3) = (3x - 6)(2)[/tex]
Simplifying the equation, we get:
[tex]15x - 3 = 6x - 12[/tex]
[tex]9x = 9[/tex]
[tex]x = 1[/tex]
Now, we can substitute the value of x into the expression [tex](5 - x)/(2)[/tex] to find the value of the expression:
[tex](5 - 1)/(2) = 4/2 = 2[/tex]
Therefore, the value of [tex](5 - x)/(2)[/tex] is 2 when [tex](5x - 1)/(2)[/tex] is equivalent to [tex](3x - 6)/(3)[/tex].
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30,4 Find the value of x and y to the nearest tenth
In the given triangle of attached figure , the required value of x and y is given by option d. x=24.0,y=46.4 ( nearest tenth ).
Let us consider triangle name of the attached figure be ABC,
From vertex A perpendicular line intersect BC at point D.
From the attached figure,
Measure of ∠B = 45°
Measure of ∠C = 30°
Side length AC = 34 units
Side length AB = x units
Side length BC = y units
In triangle ADC,
sin C = AD / AC
Substitute the value we have,
⇒ sin 30° = AD / 34
⇒ AD = ( 1/2 )× 34
⇒ AD = 17
And cos C = CD / AC
Substitute the value we have,
⇒ cos 30° = CD / 34
⇒CD = 34 × cos 30°
⇒ CD = 34 × (√3 /2 )
⇒ CD = 29.45 units
In triangle ADB,
sin B = AD/ AB
⇒ sin 45° = 17 / x
⇒ x = 17 / sin 45°
⇒ x = 17 / ( 1/√2)
⇒ x = 17√2
⇒ x= 24.038 units
⇒ x= 24.0 units ( nearest tenth )
Now in triangle ABD,
cos B = BD/ AB
⇒ cos 45° = BD / 24.0
⇒ BD = 24 × cos 45°
⇒ BD = 24× (1/√2)
⇒ BD = 16.97units
y = BD + CD
= 16.97 + 29.45
= 46.42
= 46.4 units ( nearest tenth )
Therefore , the value of x and y from the attached figure is equal to option d. x=24.0,y=46.4.
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The above question is incomplete, the complete question is:
Find the value of x and y to the nearest tenth.
a. x=48.1,y=46.4
b. x=48.1,y=139.3
c. x=24.0,y=139.3
d. x=24.0,y=46.4
Figure is attached.
9. A box contains three blue bulbs, four green bulbs and five red bulbs. Four bulbs taken out of the box at random and without replacements. What is the probability that: (1) are the first two are of the same colour and the last two are of different colours.
The probability that the first two bulbs are of the same colour and the last two are of different colours is 25/48.
The probability that the first two bulbs are of the same colour and the last two are of different colours is calculated as follows:
Given:
n(B) = 3 (Number of blue bulbs)
n(G) = 4 (Number of green bulbs)
n(R) = 5 (Number of red bulbs)
Formula: P(A) = n(A) / n(S)
Where,
P(A) = Probability of event A
n(A) = Number of favorable outcomes
n(S) = Number of possible outcomes
The probability of selecting two bulbs of the same colour is calculated as:
P(SS) = n(B) * n(B) / n(S)
= 3 * 3 / 12
= 1/4
The probability of selecting two bulbs of different colour is calculated as:
P(DD) = n(B) * n(G) * n(R) * n(R) / n(S)
= 3 * 4 * 5 * 5 / 12
= 25/12
Therefore, the required probability is calculated as:
P(SSDD) = P(SS) * P(DD)
= 1/4 * 25/12
= 25/48
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_________are the most powerful computers
Answer: Supercomputers
Step-by-step explanation: Supercomputers are high-performance computing systems that are designed to perform complex and demanding tasks at incredibly fast speeds. They are capable of processing massive amounts of data and performing calculations at a rate that far exceeds that of conventional computers.
Supercomputers are used for a variety of purposes, including scientific research, weather forecasting, modeling and simulation, data analysis, and artificial intelligence. They are especially valuable in fields that require extensive computational power, such as astrophysics, molecular modeling, climate studies, and cryptography.
One key characteristic of supercomputers is their parallel processing capability. They are designed with multiple processors or cores that work together to execute tasks simultaneously, allowing for faster and more efficient computation. This parallel architecture enables supercomputers to tackle large-scale problems by breaking them down into smaller tasks that can be processed concurrently.
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Exercise 12. Let X and Y be independent random variables satisfying E|X+Y|^n < [infinity] for some a > 0. Show that E|X|^n < [infinity].
E|X|n < ∞
Let X and Y be independent random variables satisfying E|X+Y|n < ∞ for some a > 0. We can show that E|X|n < ∞ using the triangle inequality.
Let b = a/2. Since E|X+Y|n < ∞, we know that E|X+Y| < ∞. Then by the triangle inequality, we have E|X| < |X+Y| + |Y| < ∞.
Raising both sides of the inequality to the nth power gives us E|X|n < (|X+Y| + |Y|)n < ∞.
Therefore, E|X|n < ∞.
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etermine whether the equation is condi 10[4-(3-2x)]+4x=3(8x+4)-2 s the equation a conditional, an identity, or
10[4-(3-2x)]+4x=3(8x+4)-2 is an identity equation.
To determine whether the equation is a conditional, an identity, or a contradiction, we need to simplify the equation and see if it is true for all values of x, true for some values of x, or false for all values of x.
First, let's simplify the equation:
10[4-(3-2x)]+4x=3(8x+4)-2
10[4-3+2x]+4x=24x+12-2
10[1+2x]+4x=24x+10
10+20x+4x=24x+10
24x-24x=10-10
0=0
Since the equation is true for all values of x, it is an identity equation. An identity equation is an equation that is true for all values of the variable.
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Statistics question, please explain what type of problem it is and how to do it
In a group of 60 students; 30 go for extra help and 22 study at home only. Find the probability that a person picked from this group at random is either going for extra help or only studying at home?
The probability that a person chosen at random from this group will either seek further assistance or merely study at home is 5/6, or roughly 0.833. (rounded to three decimal places).
What is the probability formula?Typically, the probability is defined as the ratio of favourable events to all other outcomes in the sample space. The formula for probability of an occurrence is P(E) = (Number of favourable outcomes) (Sample space).
The formula is as follows:
P(AorB) = P(A)+P(B)-P(AandB)
where A and B are two events.
Then, we have:
P(A) = 30/60 = 1/2 (since 30 out of 60 students go for extra help)
P(B) = 22/60 (since 22 out of 60 students study at home only)
Using the formula, we can then find:
P(AorB) = P(A)+P(B)-P(AandB)
= 1/2 + 22/60 - 0
= 5/6
Hence, the probability that someone chosen at random from this group will either seek further assistance or merely study at home is 5/6, or roughly 0.833. (rounded to three decimal places).
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PLEASE HELP A GIRL OUTTTT ITS DUE FOR TMR
Answer:
8x^2-4x-15
Step-by-step explanation:
To find the sum of the functions, we add them together:
f(x) + g(x) = (5x + 4) + (3x² - 9)
Simplifying, we get:
f(x) + g(x) = 3x² + 9x - 5
Therefore, the sum of the functions is 3x² + 9x - 5, which is option D.
Comparing and Building Functions: Functions That Fit
Answer:
i do not know
Step-by-step explanation:
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Answer:
What i arithmetic property is stated as a multiply by (b+c) =(a multiply by b) +(a multiply by c)Which expression represents the volume, in cubic units, of the composite figure
Answer: The second option
Step-by-step explanation:
To find the total area, add the areas of the shapes together
Area of the cylinder = πr²h
Area of the cone = 1/3(πr²h)
Area of the full shape = πr²h + 1/3(πr²h)
The height of the cylinder is 12.
Hope this helps!
Asanji wants to buy a wagon for $93.26. He gives the cashier $100. How much change does he receive?
Answer:
6.74
Step-by-step explanation:
100 - 93.26
Answer:
$6.74
Step-by-step explanation:
100.00 - 93.26 = 6.74
Helping in the name of Jesus.
YO CAN I HAVE SOME HELP FOR THIS LAST TWO THANK YALL I HAVE BEEN AT SCHOOL FOR HOURS AND I JUST CANT DO IT ANYMORE
Answer:
429 m³
Step-by-step explanation:
The volume of right rectangular = Length x Width x Height
The volume of right rectangular prism = 12 x 5 1/2 x 6 1/2
= 12 x 11/2 x 13/2
= 3 x 11 x 13
= 429 m³
Mathe question 2 help
Answer:
Option B
See below
Step-by-step explanation:
Two simultaneous equations:
[tex]7x - 4y - 8 = 0[/tex] —————- (equation i)
[tex]2x^{2} + x + 4y + 8 = 0[/tex] ——- (equation ii)
Step 1:
Rearrange (equation i):
[tex]7x - 4y = 8[/tex] ———- updated (equation i)
Step 2:
Substitute the updated (equation i) into (equation ii) and bring like terms together to simplify them in reduced forms:
[tex]2x^{2} + x + 4y + (7x - 4y) = 0[/tex]
[tex]2x^{2} + x + 4y + 7x - 4y = 0[/tex]
[tex]2x^{2} + x + 7x + 4y - 4y = 0[/tex]
[tex]2x^{2} + 8x = 0[/tex]
Step 3:
Factorize:
[tex]2x(x + 4) = 0[/tex]
Either [tex]2x = 0[/tex]
∴ [tex]x = 0[/tex]
Or [tex]x + 4 = 0[/tex]
∴ [tex]x = -4[/tex]
Step 4:
Substitute these values of x in (equation ii) to determine their corresponding values of y:
For x = 0:
[tex]2(0)^{2} + 0 + 4y + 8 = 0[/tex]
[tex]4y + 8 = 0[/tex]
[tex]4y = -8[/tex]
[tex]y = \frac{8}{-4}[/tex]
∴[tex]y = -2[/tex]
For x = -4:
[tex]2(-4)^{2} + (-4) +4y + 8 = 0[/tex]
[tex]2(16) - 4 + 4y + 8 = 0[/tex]
[tex]32 - 4 + 4y + 8 = 0[/tex]
[tex]32 - 4 + 8 + 4y = 0[/tex]
[tex]36 + 4y = 0[/tex]
[tex]4y = -36[/tex]
[tex]y = \frac{-36}{4}[/tex]
∴ [tex]y = -9[/tex]
∴The values of y are [tex]-2[/tex] and [tex]-9[/tex]
∴Option B
can some body help me
A garden has width √√13 and length 7√√13. What is the perimeter of the garden in simplest
radical form?
014 √√13 units
016√√13 units
091 units
08√√13 units
Add or subtract these rational expressions. Show your common denominators and numerators on this sheet or separate paper. Factor denomunators when possible. 1. 5/8 - 3/8x
2. 9/15x + 2/15x
3. 5x/7 - 2x/7
1). 1/4
2). 11/15x
3). 3x/7
1. To add or subtract the rational expressions 5/8 and 3/8x, we need a common denominator. The smallest common denominator is 8x, so we can rewrite each expression with a denominator of 8x:
5/8 = 5x/8x
3/8x = 3/8 * 1/x = 3x/8x
Now we can combine the numerators and simplify:
5x/8x - 3x/8x = (5x - 3x)/8x = 2x/8x = 1/4
Therefore, 5/8 - 3/8x = 1/4.
2. To add or subtract the rational expressions 9/15x and 2/15x, we again need a common denominator. The smallest common denominator is 15x, so we can rewrite each expression with a denominator of 15x:
9/15x = 3/5x
2/15x = 2/15 * 1/x = 2/15x
Now we can combine the numerators and simplify:
3/5x + 2/15x = (9 + 2)/15x = 11/15x
Therefore, 9/15x + 2/15x = 11/15x.
3. To add or subtract the rational expressions 5x/7 and -2x/7, we already have a common denominator of 7. We can simply combine the numerators:
5x/7 - 2x/7 = (5x - 2x)/7 = 3x/7
Therefore, 5x/7 - 2x/7 = 3x/7.
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A particles average speed is modeled by the equation
s(t)=T^2-6T+35, determine the average rate of the speeds increase
or decrease from t=2 to t=5
To determine the average rate of the speed's increase or decrease from t=2 to t=5, we need to find the slope of the line connecting the points (2,s(2)) and (5,s(5)) on the graph of the equation s(t)=T^2-6T+35. The slope of a line is given by the formula:
slope = (y2-y1)/(x2-x1)
In this case, x1=2, x2=5, y1=s(2), and y2=s(5).
Plugging in the values of x1 and x2 into the equation s(t)=T^2-6T+35, we get:
y1=s(2)=2^2-6(2)+35=4-12+35=27
y2=s(5)=5^2-6(5)+35=25-30+35=30
Now we can plug in the values of x1, x2, y1, and y2 into the slope formula:
slope = (30-27)/(5-2) = 3/3 = 1
Therefore, the average rate of the speed's increase or decrease from t=2 to t=5 is 1. This means that the speed is increasing at a constant rate of 1 unit per unit of time from t=2 to t=5.
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Container a holds 750ml of liquid container b holds 1. 25 how much from container b must be poured into container a so they can be equal?
We need to pour 250 ml of liquid from container B to container A so they can be equal in volume.
To make container A and B equal in volume, we need to pour some liquid from container B into container A. Let's call the amount of liquid that we need to pour from container B to container A as "x" ml.
After pouring x ml of liquid from container B to container A, the total volume of liquid in container A will be (750 + x) ml, and the total volume of liquid in container B will be (1250 - x) ml.
Since we want the volumes of both containers to be equal, we can set up the equation:
750 + x = 1250 - x
Solving for x:
2x = 500
x = 250
Therefore, we need to pour 250 ml of liquid from container B to container A so they can be equal in volume.
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Austin is 6 years older than Roya. In 3 years the sum of their ages will be 54 . How old is Austin now?
Austin is currently 27 years old.
Explanation:
To find out how old Austin is now, we need to use algebra. Let's start by assigning variables to represent their ages. Let A be Austin's current age and R be Roya's current age.
According to the question, we know that:
A = R + 6 (since Austin is 6 years older than Roya)
In 3 years, their ages will be:
A + 3 (for Austin)
R + 3 (for Roya)
And the sum of their ages in 3 years will be 54:
A + 3 + R + 3 = 54
Simplifying the equation gives us:
A + R = 48
Substituting the first equation into the second equation gives us:
R + 6 + R = 48
Combining like terms gives us:
2R = 42
Dividing both sides by 2 gives us:
R = 21
Now that we know Roya's current age, we can use the first equation to find Austin's current age:
A = R + 6
A = 21 + 6
A = 27
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Prove for the simple decision sapling (sure thing of value r vs. risky gamble), that EVPI > 0. Also prove that if the random payoff of the gamble, call it G, is replaced by the random variable G+Y where Y is independent of G and EY = 0 (so G’ = G+Y is a noisy, or more variable, version of the original gamble G), then the EVPI will be larger. a
To prove that EVPI > 0 for the simple decision sapling, we need to understand what EVPI is. EVPI stands for Expected Value of Perfect Information, and it is the difference between the expected value of the decision with perfect information and the expected value of the decision without perfect information.
For the simple decision sapling, we have two options: a sure thing of value r, and a risky gamble with a random payoff G. The expected value of the decision without perfect information is simply the maximum of the two options:
EV = max(r, EG)
The expected value of the decision with perfect information is the maximum of the two options, knowing the outcome of the gamble:
EVPI = max(r, G) - max(r, EG)
Since we know that G is a random variable, the expected value of G is simply the average of all possible outcomes. Therefore, the expected value of the decision with perfect information is simply the maximum of the two options, knowing the average outcome of the gamble:
EVPI = max(r, EG) - max(r, EG) = 0
Therefore, EVPI > 0 for the simple decision sapling.
To prove that the EVPI will be larger if the random payoff of the gamble is replaced by a noisy version of the original gamble, we need to understand how the expected value of the decision changes with the addition of the noise variable Y. The expected value of the decision without perfect information is now:
EV = max(r, EG + EY) = max(r, EG)
Since EY = 0, the expected value of the decision without perfect information does not change. However, the expected value of the decision with perfect information now becomes:
EVPI = max(r, G + Y) - max(r, EG)
Since Y is a random variable with mean 0, the expected value of Y is 0. However, the variance of Y is not necessarily 0, which means that the addition of Y adds variability to the decision. This means that the expected value of the decision with perfect information is now larger, because we have more information about the possible outcomes of the gamble. Therefore, the EVPI will be larger when the random payoff of the gamble is replaced by a noisy version of the original gamble.
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In a survey of 300 members of a local sports club, 150 members indicated that they plan to attend the next Summer Olympic Games, 90 indicated that they plan to attend the next Winter Olympic Games, and 60 indicated that they plan to attend both games. How many members of the club plan to attend (a) At least one of the two games? members (b) Exactly one of the games? members (c) The Summer Olympic Games only? members (d) None of the games? members
a) At least one of the two games? - 300 members
b) Exactly one of the games? - 240 members
c) The Summer Olympic Games only? - 150 members
d) None of the games? - 60 members
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help me what is it i need urgent help
Answer:
#1 is equivalent
#2 is not equivalent
#3 is not equivalent
#4 is not equivalent
#5 is not equivalent
Hope this helps!
Please help me if you can and Shows steps thank you :)
In the above problem, note that the percent powdered sugar in mixture B was approximately 25.81%. See table attached.
What is the rationale for the above response?
The last column shows the amount of powdered sugar in each mixture, which we can calculate using the percent powdered sugar and the pounds of mixture.
To find the percent powdered sugar in mixture B, we can use the fact that the total amount of powdered sugar in the final mixture is the sum of the amounts of powdered sugar in each of the original mixtures. So we have:
1 + 0.11x = 3.84
Solving for x, we get:
0.11x = 2.84
x = 25.81
Therefore, the percent powdered sugar in mixture B was approximately 25.81%.
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I need help! ty !!!! I gatta pass math class
The answer should be D.