Which equation would you use to find the value of x?

Answer:

He would collect 28 cans

Step-by-step explanation:

Ethan = 1/3

84 * 1/3 = 28

Answer:

28 cans were collected by Ethan

Step-by-step explanation:

It says that the total amount of cans collected was 84 cans. Of the 84 total cans, Ethan collected 1/3 of them. To find the number of cans Ethan collected, you would multiply 84 • 1/3. (You could also divide 84 by 3 in this case)

84 • 1/3 = 28

Answer:

2a+50=5a-4

5a-2a=50+4

3a=54

a=18

Answer:

\(a=18\)

Step-by-step explanation:

\(2a+50=5a-4\\\mathrm{Subtract\:}50\mathrm{\:from\:both\:sides}\\2a+50-50=5a-4-50\\Simplify\\2a=5a-54\\\mathrm{Subtract\:}5a\mathrm{\:from\:both\:sides}\\2a-5a=5a-54-5a\\\mathrm{Simplify}\\-3a=-54\\\mathrm{Divide\:both\:sides\:by\:}-3\\\frac{-3a}{-3}=\frac{-54}{-3}\\Simplify\\\frac{-3a}{-3}=\frac{-54}{-3}\\\mathrm{Simplify\:}\frac{-3a}{-3}:\quad a\\\frac{-3a}{-3}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{3a}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1\)

\(=a\\\mathrm{Simplify\:}\frac{-54}{-3}:\quad 18\\\frac{-54}{-3}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{54}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{54}{3}=18\\=18\\a=18\)

Answer:

\(a_n=19+(n-1)(-5)\)

Step-by-step explanation:

The explicit formula for an arithmetic sequence is \(a_n=a_1+(n-1)d\) where \(a_n\) is the \(n\)th term and \(d\) is the common difference.

In this problem, we can see that the first term of the sequence is \(a_1=19\) and the common difference is \(d=-5\) since 5 is being subtracted each consecutive term.

Therefore, the explicit formula that describes the given arithmetic sequence is \(a_n=19+(n-1)(-5)\)

Answer:

option 2

Step-by-step explanation:

Let { a1, a2, a3, a4, ... } be the sequence.

now the 1st term (a1) will have a value when n = 1.

similarly, all the other terms will have the values given when we substitute their respective n values into the explicit formula or fibonacci sequence.

thus, check if the 1st term is 19 by using option 2

an = 19 + (n-1)(-5)

an = 19 + (n-1)(-5) ....n = 1

an = 19 + (n-1)(-5) ....n = 1 a1 = 19 + (1-1)(-5) = 19 + 0 = 19. so it's accurate so far.

next, check a2 where n = 2.

a2 = 19 + (2-1)(-5) = 19 - 5 = 14. ....

n = 3

a3 = 19 + (3-1)(-5) = 19 - 10 = 9.

hence the conclusion from this pattern.

Answer:

-5x^3-23x^2+82x-14

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Cos^-1   = 1/ cos = sec x

Answer: True

Step-by-step explanation:

     When the cos(ine) function is raised to the negative first power, we find the reciprocal. This will be the case for most functions and numbers.

The area of the region bounded by the curves y=x^2 +4, y=x, x=0 and x=3 is 16.5 square units.

Integrate the function using partial fractions:

∫ [(x+1)(x−2)(x+3)] / [2x² + 9x - 35] dx

The area A between the curves y=f(x) and y=g(x) from x=a to x=b is given by:

A = ∫ |f(x) - g(x)| dx, from x=a to x=b

The absolute difference between these two functions on this interval is:

|x² + 4 - x|

x² + 4 - x = x² - x + 4

Therefore, the area A is:

A = ∫ (x² - x + 4) dx, from x=0 to x=3

A = [1/3x³ - 1/2x² + 4x] (from 0 to 3)

= (1/33³ - 1/23² + 43) - (1/30³ - 1/20² + 40)

= 9 - 4.5 + 12

= 16.5 square units

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3. Integrate - \int \frac{(x+1)(x-2)(x+3)}{2x^{2}+9x-35} dx = \frac{54}{7} \ln|x-5| + \frac{5}{12} \ln|2x+7| + C

4. The required area of the region is 27/2.

3. Integrating using partial fractions:

To solve the following integral, we will begin by performing the partial fraction decomposition of the given function. Here, we have a quadratic factor, so we will begin by setting the function equal to the sum of two fractions that have first-degree polynomial denominators like this :

\frac{(x+1)(x-2)(x+3)}{2x^{2}+9x-35} = \frac{A}{x-5}+\frac{B}{2x+7}

Since the denominators are of different degrees, we must find the least common denominator of both sides.

That is (x-5)(2x+7)

Multiplying by this common denominator, we have (x+1)(x-2)(x+3) = A(2x+7) + B(x-5)

Let us now solve for A and B by substituting the values of x:

\begin{aligned}\text{Let }x&=5:\ \ 6 \cdot 8 \cdot 8 = 7A\\A&=\frac{384}{7}\\\\\text{Let }x&=-\frac{7}{2}:\ \ \frac{5}{2} \cdot -\frac{9}{2} \cdot -\frac{1}{2} = -\frac{9}{2}B\\B&=\frac{5}{6}\end{aligned}

Therefore,\begin{aligned}\frac{(x+1)(x-2)(x+3)}{2x^{2}+9x-35} &= \frac{\frac{384}{7}}{x-5}+\frac{\frac{5}{6}}{2x+7}\\\\&=\frac{54}{7} \int \frac{1}{x-5}dx + \frac{5}{6} \int \frac{1}{2x+7}dx\\\\&=\frac{54}{7} \ln|x-5| + \frac{5}{12} \ln|2x+7| + C\end{aligned}

Thus,\int \frac{(x+1)(x-2)(x+3)}{2x^{2}+9x-35} dx = \frac{54}{7} \ln|x-5| + \frac{5}{12} \ln|2x+7| + C

4. Area of the region bounded by the curves:

The area of the region bounded by the curves y=x^2, y=x, x=0, and x=3 is given by\int_0^3 (x^2-x) dx = \frac{1}{3}x^3-\frac{1}{2}x^2 \Bigg|_0^3 = \boxed{\frac{27}{2}}

Hence, the required area of the region is 27/2.

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The surface area of the portion S of the cone z^2 = x^2 + y^2 where z>/ 0 contained within the cylinder y^2 + z^2 < 1 is 8π.

The cone is defined by the equation z^2 = x^2 + y^2.

The cylinder is defined by the equation y^2 + z^2 < 1.

The intersection of the cone and the cylinder is a surface that is part of a cone and part of a cylinder.

The surface area of the cone is given by the formula A = πr^2h, where r is the radius of the base and h is the height of the cone.

The radius of the base of the cone is equal to 1, and the height of the cone is equal to √2. Therefore, the surface area of the cone is π(1)^2(√2) = √2π.

The surface area of the cylinder is given by the formula A = 2πrh, where r is the radius of the base and h is the height of the cylinder.

The radius of the base of the cylinder is equal to 1, and the height of the cylinder is equal to 1. Therefore, the surface area of the cylinder is 2π(1)(1) = 2π.

The surface area of the intersection of the cone and the cylinder is equal to the surface area of the cone minus the surface area of the cylinder. Therefore, the surface area of the intersection is √2π - 2π = 8π.

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Answer:

1 over 20

Step-by-step explanation:

Given that:

a spinner and 4 cards

A Spinner ⇒ 5 equal sectors;Color: Blue,Purple,Yellow,Red,Green

Arrow point at purple

Four cards ⇒ Color : Red,Yellow,Blue,Pink

Jane spins the spinner & selects card without looking.

To Find - Probability spinner stops at purple & select pink card.

Solve:

Multiply 4 (the number of cards) with 5 (The number of equal sectors)

\(\frac{1}{5}\times\frac{1}{4}=\frac{1}{20}\)          {1 × 1 = 1}    {5×4=20}

~lenvy~

Answer:

1 over 20

Step-by-step explanation:

Given the following:

1 spinner and 4 cards

A Spinner which has 5 equal sectors;Color: Green, Blue,Purple,Yellow,Red.

{Arrow point at purple}

Four cards ⇒ which color are Red,Yellow,Blue,Pink

Jane spins the spinner & selects card without looking.

To Find →  Probability spinner stops at purple & select pink card.

Since, purple and pink only has one in each of Spinner/card

Thus,

Spinner (5 equal sectors - 1/5}

Card {4 cards - 1/4}

1/4 × 1/5 = 1/20

Hence, probability spinner stops at purple & select pink card is [A] 1/20

[RevyBreeze]

Answer:

-3y = -8 then you get your answer from that

Step-by-step explanation:

-3y = -8

Answer:

640\(x^{6}\)

Step-by-step explanation:

(5x³)(4x) ³2

(4x) ³ is the same as

4³ * x³ = 64x³

--

(5x³)(64x³)2

5*64*2 = 640

x³ * x³ = \(x^{6}\)

640\(x^{6}\)

The correct option is H. 5. The value of x is 5, which satisfies the given conditions for the congruent triangles Δ ABC and Δ ADC

To solve for x in the given scenario, where two adjacent right-angled triangles label it as Δ ABC and Δ ACD are given with certain angle and side measures, we can utilize the concept of congruent triangles.

Given that ∠ ABC = ∠ CDA = 90°, ∠ BAC = ∠ CAD = 30°, and AC is the common hypotenuse for both triangles, we are also provided with the lengths of BC and CD as BC = 6x + 1 and CD = 7x - 4, respectively.

Consider  Δ ABC and Δ ACD ,

∠ ABC = ∠ CDA = 90°(A),

AC is common side(S)

∠ BAC = ∠ CAD = 30°(A)

Δ ABC ≅ Δ ADC (ASA)

That implies, BC = CD (Corresponding parts of congruent triangles)

Since Δ ABC ≅ Δ ADC, we can equate their corresponding sides. Specifically, we can equate BC with CD.

This gives us the equation 6x + 1 = 7x - 4.

To solve for x, we can start by isolating the x terms on one side of the equation.

Adding 4 to both sides, we have ,

6x + 5 = 7x.

Next, subtracting 6x from both sides, we get

5 = x.

Therefore, x is equal to 5.

By substituting x = 5 back into the given expressions for BC and CD, we find that:

BC = 6(5) + 1 = 31 and CD = 7(5) - 4 = 31.

This confirms that the lengths of BC and CD are indeed equal, as expected for congruent triangles.

In conclusion, by solving the equation 6x + 1 = 7x - 4 and isolating x, we find that x = 5. This value satisfies the given conditions and demonstrates that the triangles ABC and ADC are congruent.

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Step-by-step explanation:

It’s in step one.

Ling subtracted 6.2 to get rid of it on both side but instead they subtracted it from the right side but added it to the left side when Ling was supposed to subtract from both sides.

Answer:

125x^3 + 27/ 64

Step-by-step explanation :

This can be done in man ways. But I recommend solving what is inside the brackets first.

So add 5x/4 and 3/4, which gives 5x+3/4

Now, rewrite the term with simplified brackets

(5x+3/4)^3

Now we have to cube 5x+3/4

5x+3/4^3 = 125x^3 + 27/64

Hope this helps

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There is a significant relationship between the number of cats she owns and the number of times an old widow was married (r = +0.91, p < 0.05, r² = 0.82).

Given, the Pearson correlation coefficient of +0.91,

There appears to be a strong +ve correlation between the number of cats she owns and the number of times an old widow was married.

It suggests that the more times a widow was married,the more cats she tends to own.

Approximately 82% of the variance in the number of cats owned can be explained by the number of times a widow was married is indicated by the coefficient of determination (r²).

Hence, we can say that there is a significant relationship between the number of cats she owns and the number of times an old widow was married (r = +0.91, p < 0.05, r² = 0.82).

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The most effective way to use her 4 hours of study time to get the highest possibility or probability of test scores would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.

From the information given, it is clear that working on multiple-choice problems is the most effective way to improve her test score. Therefore, the highest possibility or probability of test scores would be achieved by spending the most time working on multiple-choice problems.

The available time for studying is 4 hours, so the maximum time that can be spent working on multiple-choice problems is 4 hours. If she spends 4 hours working on multiple-choice problems, she will not have any time left to review lecture notes.

So, the most effective way to use her 4 hours of study time to get the highest possible test score would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.

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The probability that a client owns both stocks and bonds in their retirement portfolio is 0.22.

We know the formula for the probability of the intersection of two events,

P(A and B) = P(A) x P(B|A)

Where P(A) is the probability of event A,

And P(B|A) is the conditional probability of event B given that event A has occurred.

In this case,

We want to find the probability that a client owns both stocks and bonds, so we can let,

A = owning stocks B = owning bonds

According to the problem statement,

P(A) = 0.80 (the probability of owning stocks)

P(B) = 0.40 (the probability of owning bonds)

P(A and B|B) = 0.55 (the probability of owning stocks given that the client already owns bonds)

Using the formula, we can calculate the probability of owning both stocks and bonds as,

⇒ P(A and B) = P(B) x P(A and B|B)

                      = 0.40 x 0.55

                      = 0.22

Therefore, The probability that a client owns both stocks and bonds in their retirement portfolio is 0.22 or 22%.

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Answer:

Yes

Step-by-step explanation:

We know this because the proportion can be used to find another answer.

Example:

How many feet did the elevator ascend in 0.25 minutes?

 750           x

---------- = ----------

    1           0.25

750(0.25) = 1x

187.5 = x

***Sorry about the format. Hope this helps!

The statement true about simple random sampling is that it produces unbiased estimates of a target population's characteristics. (Option A)

A simple random sampling refers to a type of probability sampling where the researcher randomly selects a population subset from the finite target population in a manner that each member of the population has an equal chance of selection. Data is obtained from the random subset to analyze and draw conclusion about the population. As the participants are randomly selected and have equal chances of selection, the advantage of this type of sampling is the production of unbiased estimates of a target population's characteristics.

Note: The question is incomplete. The complete question probably is: Which of the following is true of simple random sampling? A. It produces unbiased estimates of a target population's characteristics. B. It eliminates the need to identify all sampling units. C. It is less costly when compared to systematic random sampling because it can be done quickly. D. It requires that a defined target population be ordered in some way, usually in the form of a customer list, taxpayer roll, or membership roster. E. It does not require the sampling units to be given any special code prior to drawing a sample unlike systematic random sampling.

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After the sale of the chickens from Kan, the ratio of Chalerm's, Kan's and Wach's chickens is 220 : 105 : 275.

We are given that the ratio of the number of chickens reared by Chalerm, Kan and Wach is 4:3:5. We can represent this as:Chalerm's chickens : Kan's chickens : Wach's chickens = 4x : 3x : 5x

We know that the total number of chickens is 660. So we can set up an equation to solve for x:4x + 3x + 5x = 660

12x = 660x = 55

Now we know that the number of chickens reared by Chalerm, Kan, and Wach are:Chalerm's chickens = 4x = 4(55) = 220

Kan's chickens = 3x = 3(55) = 165 Wach's chickens = 5x = 5(55) = 275Kan sells 50 of his chickens to Chalerm and 25 chickens to Wach.

After the sale, Chalerm will have 220 + 50 = 270 chickens, and Wach will have 275 + 25 = 300 chickens.

The new ratio of Chalerm's, Kan's and Wach's chickens after the sale is:Chalerm's chickens : Kan's chickens : Wach's chickens = 270 : 165 : 300

Simplifying this ratio by dividing by 15, we get:Chalerm's chickens : Kan's chickens : Wach's chickens = 18 : 11 : 20

Therefore, after the sale of the chickens from Kan, the ratio of Chalerm's, Kan's and Wach's chickens is 18:11:20.

Given that the ratio of the number of chickens reared by Chalerm, Kan and Wach is 4:3:5. Thus, Chalerm has 4x chickens, Kan has 3x chickens and Wach has 5x chickens, where x is some positive constant. The total number of chickens is 660.

Hence,4x + 3x + 5x = 66012x = 660x = 55Chalerm has 4x = 4 × 55 = 220 chickens.Kan has 3x = 3 × 55 = 165 chickens.

Wach has 5x = 5 × 55 = 275 chickens.

Kan sells 50 chickens to Chalerm, so Chalerm has 220 + 50 = 270 chickens.Kan also sells 25 chickens to Wach, so Wach has 275 + 25 = 300 chickens.

So, the ratio of Chalerm's, Kan's and Wach's chickens after the sale is270:165:300 = 18:11:20

Therefore, the ratio of Chalerm's, Kan's and Wach's chickens after the sale is 18:11:20.

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Answer: Solution

=

−

9

Step-by-step explanation:

Answer:

answer is x = -9

Step-by-step explanation:

2x+2=x-7

x= -9

Answer:

-3/(b-6) = 3/(-b+6) = 3/(6-b)

Step-by-step explanation:

7/(b-6) + 10/(6-b)

= 7/(b-6) + 10/(-b+6)

= 7-10/(b-6)

= -3/(b-6) = 3/(-b+6) = 3/(6-b)

\( {\qquad\qquad\huge\underline{{\sf Answer}}} \)

Let's solve ~

\(\qquad \sf  \dashrightarrow \: \cfrac{7}{b - 6} + \cfrac{10}{6 - b} \)

\(\qquad \sf  \dashrightarrow \: \cfrac{7}{b - 6} + \cfrac{10}{ - (b - 6)} \)

\(\qquad \sf  \dashrightarrow \: \cfrac{7}{b - 6} - \cfrac{10}{ b - 6} \)

\(\qquad \sf  \dashrightarrow \: \cfrac{ - 3}{ b - 6}\:\:\: or \:\:\: \dfrac{3}{6-b} \)

^congruence concept^

ok. i already answer it

(L2) An inscribed circle is one that encompasses a polygon so that it passes by each of the polygon's vertices.

A circumcircle, not an inscribed circle, is a circle that encircles a polygon at each vertex. A circle that is enclosed within a polygon and intersects each side of the polygon exactly once is said to be inscribed. A circumcircle, on the other hand, is a circle that goes through every vertex of the polygon, with its center located at the point where the perpendicular bisectors of the polygon's sides converge. The greatest circle that can be drawn within a polygon is the circumcircle, while the largest circle that can be drawn inside a triangle is the inscribed circle.

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Based on the number of members and the ratio in which they chose the types of film, the number who chose Action in the second week more than the first week is 6 people.

Assuming that the number of members is 99 members, the number who chose Action on the second week were:

= (7 / (5 + 7 + 6)) x 99

= 39 people

The number who chose Action in the first week:

= (5 / (2 + 5 + 8)) x 99

= 33

The difference is:

= 39 - 33

= 6 people

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Answer: 224m^3

Step-by-step explanation:

Since V=B(Base)h(Height)

B=1/2x4x8

8x4=32x1/2=16

V=16h

H=14

V=16(14)=224

So your answer is 224m^3

(^3 means cubed)

I hope this helps!

Answer:

x=-3

y=-4

Step-by-step explanation:

Given:

y=x-1

4x+8=y

Plug in the 1st equation into the 2nd equation

4x+8=x-1

subtract x from both sides

3x+8=-1

subtract 8 from both sides

3x=-9

divide both sides by 3

x=-3

Now that we have the x value, plug it into the first equation:

y=-3-1

simplify

y=-4

So, x=-3, and y=-4.

Hope this helps! :)

The volume of the solid obtained by rotating the region enclosed by the graphs \(x=y^4\) and \(x= y^1/4\) about the y-axis over the interval [0,1] is 4π/7.

\(V = π ∫y^4 - y^1/4 dy\)

 = π ∫\(y^7/4 dy\)

 =\([4π/7*y^(7/4+1)]_0^1\)

 = \(4π/7\)

To find the volume of the solid obtained by rotating the region enclosed by the graphs\(x=y^4\) and \(x= y^1/4\) about the y-axis over the interval [0,1], we first use the formula for the volume of a solid of revolution: V = π ∫\(y^2 - y^1/4 dy.\) Then, we rewrite the upper limit of the integral as \(y^7/4\)and evaluate the integral from 0 to 1. This gives us the volume as 4π/7.

The volume of the solid obtained by rotating the region enclosed by the graphs \(x=y^4\) and \(x= y^1/4\) about the y-axis over the interval [0,1] is 4π/7.

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Answer:

Histogram (Please tell me if you disagree, Have a great day:)