Jan had 1/4 pound of chocolate and shared it among her eight friends. How much
did each person get?
Zach had eight candy bars and gave each friend 1/4 of a candy bar. How many
people did he share with?

The implicit solution of the differential equation dy/dx=x/(25*y) is y = (3(25x^2/2 + c))^(1/3) = constant. The equation of the solution through the points (x,y)=(-5,1), (x,y)=(0,-6), and (x,y)=(6,0) are y = (3(25x^2/2 - 313.75))^(1/3), y = (3(25x^2/2 - 1875))^(1/3), and y = (3(25x^2/2 - 2025))^(1/3) respectively.

1. 25y^2dx = xdy → y^2 dy = 25x dx → ∫y^2 dy = ∫25x dx → y^3/3 = 25x^2/2 + c → y = (3(25x^2/2 + c))^(1/3) = constant

2. Substituting x=-5 and y=1 in the implicit solution, we get (3(25(-5)^2/2 + c))^(1/3) = 1 → c = -313.75 → y = (3(25x^2/2 - 313.75))^(1/3)

3. Substituting x=0 and y=-6 in the implicit solution, we get (3(25(0)^2/2 - 313.75))^(1/3) = -6 → c = -1875 → y = (3(25x^2/2 - 1875))^(1/3)

4. Substituting x=6 and y=0 in the implicit solution, we get (3(25(6)^2/2 - 1875))^(1/3) = 0 → c = -2025 → y = (3(25x^2/2 - 2025))^(1/3)

The implicit solution of the differential equation dy/dx=x/(25*y) is y = (3(25x^2/2 + c))^(1/3) = constant. The equation of the solution through the points (x,y)=(-5,1), (x,y)=(0,-6), and (x,y)=(6,0) are y = (3(25x^2/2 - 313.75))^(1/3), y = (3(25x^2/2 - 1875))^(1/3), and y = (3(25x^2/2 - 2025))^(1/3) respectively.

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The constraints on the mining problem are 8.3x + 7.2y = 180

and 4x + 3y = 24

From the question, we have the following parameters that can be used in our computation:

This means that

Weight: 8.3x + 7.2y

Number of bins: 4x + 3y

From the question, we have

Capacity = 180 tons ot 24 bins

So, the constraints are

8.3x + 7.2y = 180

4x + 3y = 24

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the length of the arc will be C/2π*Ф.

What is circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

The radius of a circle and its centre angle both affect how long an arc is. We are aware that the arc length and circumference are equivalent at an angle of 360 degrees (2). Due to the continuous relationship between angle and arc length, we can therefore state that:

L/Ф = C/2π

L = C/2π*Ф

Hence the length of the arc will be C/2π*Ф.

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The Volume of the solid obtained by rotating the region bounded by the curves is 5 cm³.

Volume of a solid plain:

The volume of a solid is a measure of the space occupied by an object. It is measured by the number of unit cubes required to fill the solid.

Given in the question:

y = 2 - 1/2x

y = 0 , x = 1 and x = 2

As we know that:

We can write 19π / 12 as

(19× 22/7 )÷ 12

=  209/ 42

= 4.97 ≈ 5 cm³

Therefore, the volume is 5 cm³

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In both cases, the sample proportion is very likely to be within a certain range of the population proportion, with a probability of 1.0000 or 100%.

What is probability?

Probability is a measure of the likelihood that an event will occur, it is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

In this case, we are interested in the probability that the sample proportion (p) will be within a certain range of the population proportion (0.30).

a. To find the probability that the sample proportion will be within ±0.03 of the population proportion, we can use the standard normal distribution (z-table). The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

The formula for the standard normal distribution is:

z = (p - 0.30) / (standard deviation of p)

The standard deviation of p is given by the formula:

(population proportion * (1 - population proportion)) / sample size

In this case, we have:

(0.30 * (1 - 0.30)) / 150 = 0.0006

So, the standard deviation of p is 0.0006

The probability that the sample proportion will be within ±0.03 of the population proportion is the same as the probability that the sample proportion will be between 0.27 and 0.33.

Therefore, we can calculate the z-score for the lower and upper bounds of the range:

z1 = (0.27 - 0.30) / 0.0006 = -5

z2 = (0.33 - 0.30) / 0.0006 = 5

Using the z-table, we can find the probability that a z-score falls between -5 and 5.

The probability that the sample proportion will be within ±0.03 of the population proportion is:

P(z1 <= z <= z2) = P(-5 <= z <= 5) = 1 - 0.0000 = 1.0000

b. To find the probability that the sample proportion will be within ±0.08 of the population proportion, we can use the same formula as before. The probability that the sample proportion will be within ±0.08 of the population proportion is the same as the probability that the sample proportion will be between 0.22 and 0.38.

Therefore, we can calculate the z-score for the lower and upper bounds of the range:

z1 = (0.22 - 0.30) / 0.0006 = -10

z2 = (0.38 - 0.30) / 0.0006 = 10

Using the z-table, we can find the probability that a z-score falls between -10 and 10.

The probability that the sample proportion will be within ±0.08 of the population proportion is:

P(z1 <= z <= z2) = P(-10 <= z <= 10) = 1 - 0.0000 = 1.0000

Hence, In both cases, the sample proportion is very likely to be within a certain range of the population proportion, with a probability of 1.0000 or 100%.

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The pattern in this sequence is given as follows:

When x increases by one, y increases by one.

Hence the missing number y, for the point (0,y), is given as follows:

y = -5.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

The pattern of the sequence is that when x increases by one, y also increases by one, hence the slope m is given as follows:

m = 1/1 = 1.

Hence:

y = x + b.

When x = -8, y = -13, hence the intercept b, which is also the missing value, is given as follows:

-13 = -8 + b

b = -5.

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Answer:

Step-by-step explanation:

Answer:

10th term = 94

Step-by-step explanation:

Given equation,

→ Tn = n² - n + 4

Now the 10th term will be,

→ Tn = n² - n + 4

→ T10 = (10)² - 10 + 4

→ T10 = 100 - 6

→ [ T10 = 94 ]

Hence, the answer is 94.

The length is about 7.2 feet, the width is about 4.8 feet, and the area is about 34.56 square feet.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given that, The length and width of the model of the room are 4.5 in and 3 inches respectively.

Since Scale is 5 inches = 8ft

Thus the actual length of the room = 4.5*8/5 = 7.2 feet

the actual width of the room = 3*8 /5 = 4.8 feet

Since,

Area = length * width

Area of the room  = 7.2 * 4.8

Area of the room = 34.56 square feet

Therefore, The dimensions are roughly 7.2 feet long, 4.8 feet wide, and 34.56 square feet in area.

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When dividing 84 by 7 then the quotient does not have a reminder and the quotient will be 12.

What is division?

A division in mathematics is the process of dividing a specific amount into equal parts. The division is the inverse of multiplication.

We can find a division fact if we know a multiplication fact: For instance, 3 5 = 15, so 15 / 5 = 3.

Also 15 / 3 = 5.

Here given that,

We have to divide 87/7,

By dividing,

we know that 8/7 gives reminder 1, and a quotient of 1.

Then divide 14 by 7,

which gives reminder 0 and quotient 2.

So by dividing 84 / 7 we get reminder 0 with a quotient of 12.

Therefore the correct option is option A. With a quotient of 12.

Hence, When dividing 84 by 7 then the quotient does not have a reminder and the quotient will be 12.

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The distance traveled during the given time interval be 2024 m.

An object's rate of change in velocity is referred to as its acceleration. The rate of change in velocity is known as acceleration. Acceleration typically signals a change in speed, though this is not always the case. Because of the shifting direction of its velocity, an item moving on a circular path at a constant speed is still accelerating.

By integrating the velocity v in terms of time t, v = gt, we can determine acceleration, which is the rate of change of velocity with respect to time.

Let the function be a(t) = t + 4

time = 11

substitute the value of t in the above equation, we get

a(11) = 11 + 6 = 17 m/s²

a = v/t, so v = at

finally v = (17 m/s²) (11s)

v = 187 m/s

b) Find the distance traveled during the given time interval

[tex]$$V_{total} = V_{final} - V_{ initial[/tex]

V final = 187 m/s, Vinitial = 3 m/s

V total = 187 - 3 = 184 m/s

Let the equation of velocity be

Velocity = distance/time

distance = velocity × time

distance = 184 m/s × 11 s

distance = 2024 m

Therefore, the distance traveled during the given time interval be 2024 m.

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Comparibg the probabilities and interpreting the likelihood, the true statement is that:

A. Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur.

Player 1 = six tenths = 0.6

Player 2 = five ninths = 0.56

Player 3 four sevenths = 0.57

This shows that player 2 has the highest probability. The correct option is A.

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A vector (u) with magnitude 4 in the opposite direction as v =⟨−2,3⟩ is u = ⟨-2/√13, 3/√13⟩.

A vector in the opposite direction of a given vector can be found by multiplying that vector by -1. The magnitude of a vector is the length of the vector and it can be found by using the Pythagorean theorem on the coordinates of the vector.

The magnitude of the vector v = ⟨-2,3⟩ is:

|v| = √(-2)^2 + 3^2 = √4 + 9 = √13

To find a vector with magnitude 4 in the opposite direction as v, we can first normalize the vector v by dividing it by its magnitude,

then multiply it by 4:

u = (-1) * (1/|v|) * v

= (-1) * (1/√13) * ⟨-2,3⟩

= ⟨2/√13, -3/√13⟩

So, a vector (u) with magnitude 4 in the opposite direction as v =⟨−2,3⟩ is u = ⟨2/√13, -3/√13⟩

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The average speed of the body in the given interval is 32 + 2z ft/s.

The average speed v of a body in an interval of z seconds can be calculated using the formula v = d/t, where d is the distance traveled and t is the time taken.

In this case, the distance d is (32z + 2z^ 2 ) ft and the time taken is z seconds.

Therefore, the average speed v of the body in this interval is:

v = (32z + 2z^ 2 ) ft / zs

v = 32 + 2z ft/s

Therefore, the average speed of the body in the given interval is 32 + 2z ft/s.

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The value of base angle θ (in degree) of the trapezium ABCD which has the greatest perimeter, is 60°

Given, AD = 2I

From ΔABD,

cos∅=[tex]\frac{AB}{AD}[/tex]

⇒ AB = AD cos∅

⇒ AB = 2I cos∅

and x = ABcos∅ = 2I [tex]cos^{2}[/tex]∅

Now perimeter,

P = 2I+ 2I - 2x + 2AB

P = 4I - 4I [tex]cos^{2}[/tex]∅ + 4Icos∅

P = 4I (1 - cos²∅ +  cos∅)

Differentiating with respect to ∅, we get

dP/d∅= 4I(2 cos∅ sin∅ - sin∅)

For max/min,

dP/d∅ = O

2 cos∅ sin∅ - sin∅ = 0

⇒ cos∅ = [tex]\frac{1}{2}[/tex]  (∅ [tex]\neq[/tex] 0)

            = 60°

[tex]d^{2}[/tex]P/d∅ = 4i(2 cos2∅ - cos∅)

[tex]d^{2}[/tex]P/d∅ < 0  

∅ = 60°

Therefore, Perimeter is maximum when ∅ = 60°

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The length of the side between the vertices A' and B' is 3.75 inches

In order to find the length of the side between the vertices A' and B', we need to use the fact that the ratio of corresponding side lengths between the pre-image and the image is the same as the ratio of the scale factor used in the dilation.

The ratio of the side length between the vertices B'C' and BC is 9/12. If we call this ratio k, then the ratio of the side length between the vertices A'B' and AB is also k.

So we can use the side length between AB = 5 inches and k = 9/12 to find the side length between A'B'

A'B' /AB = k

A'B' = k × AB

A'B' = (9/12) × 5

A'B' = 3.75 inches

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The distance from G to the nearest point on the circle is going to be 5.61 cm.

The given figure (image attached below) has the segments GA and GB tangent to a circle at A and B, and AGB is at a 48-degree angle. We have been told that GA = 12 cm. We have to find the distance from G to the nearest point on the circle.

For this, first what we need to do is draw radii to A and B. Next draw OG which bisects the 48-angle G into two 24-angles. Let P be the point where OG intersects the circle. This becomes the distance from G to the nearest point on the circle which we need to find (image attached below).

In the right triangle AOG, radius AO is the side opposite angle AGO-

= Tangent = Perpendicular / Base

= tan(24) = r / 12

= r = 12tan(24)            (i)

For OG -

= cos(24) = Base / Hypotenuse = 12 / OG

= OG = 12cos(24)        (ii)

Now, we subtract (i) and (ii) -

= 12tan(24) - 12cos(24)    

= 5.61 cm

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The 5 different colorings are possible.

The rectangle is partitioned into 5 regions.

The objective is to find the different of color.

There are 5 rectangle and 5 colors

Each region is to be painted a solid color-red. orange, yellow, blue, or green

Need to color 5 rectangles by using given five colors.

Then, we need to use 5! colors.

The factorial of a whole number is the function that multiplies the number by every natural number below it. Symbolically, a factorial can be represented by using the symbol "!". So, "n factorial" is the product of the first n natural numbers and is represented as n!

The formula for n factorial is:

=5×4×3×2×1

=120

Therefore, the possible colorings are 5.

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The correct answer is open angled bracket negative 16 over 5 comma negative 32 over 5 close angled bracket, as it is the vector u.

The projection of vector u onto vector v is given by the formula:

projv(u) = (u . v/||v||^2) * v

where u . v is the dot product of vectors u and v,and ||v|| is the magnitude of vector v

Given that u = <-10, -3> and v = <4, 8>, we can substitute these values into the formula and find projv(u)

projv(u) = ( (-10)(4) + (-3)(8) )/ (4^2 + 8^2) * <4,8>

projv(u) = ((-40 - 24)/ (16 + 64))* <4,8>

projv(u) = (-64/80) * <4,8>

projv(u) = (-4/5) * <4,8>

projv(u) = <-16/5,-32/5>

The vector u is already parallel to the vector v, that's why the projection of vector u on vector v is equal to vector u itself.

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Solving an equation we will see that Caitlyn used 3 of the 42-cent stamps and 9 of the 5-cent ones.

Let's define the variables that we will be using:

Then the total value of the stamps, in dollars, is:

x*0.42 + y*0.5

And we know that the value must be $1.71, then we can write the equation:

x*0.42 + y*0.05 = 1.71

y = (1.71 - x*0.42)/0.05

To find the values of x and y, we can just evaluate in different whole values of x, until we get a whole value of y.

using x = 1 we get:

y = (1.71 - 0.42)/0.05 = 2.58

This is not a solution.

if x = 3

y = (1.71 - 0.42*3)/0.05 = 9

This is the solution, she used 3 of the 42-cent and 9 of the 5-cent.

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Answer:

[tex]\frac{25\pi}{2}\approx39.27\text{ units}^2[/tex]

Step-by-step explanation:

I assume your problem is [tex]\displaystyle \int\limits^{5}_{-5} {\sqrt{5^2-x^2}} \, dx[/tex]. Recognize that [tex]\sqrt{5^2-x^2}=\sqrt{25-x^2}[/tex] is a semi-circle directly above the x-axis with a radius of 5. The bounds cover the whole area of the semicircle, so its area is just half the area of a circle with a radius of 5. You probably know that the area of a circle is [tex]A=\pi r^2[/tex], so the area of a semicircle would be [tex]A=\frac{\pi r^2}{2}[/tex]. Thus, the area using geometry is [tex]A=\frac{\pi (5)^2}{2}=\frac{25\pi}{2}\approx39.27\text{ units}^2[/tex].

The solution to the equation m+[tex]n^{2}[/tex] = g5M is g = m[tex]n^{2}[/tex]/5M, which can be solved by dividing both sides of the equation by 5M and rearranging the equation to isolate the g on the right side.

A mathematical declaration that two expressions are equal is known as an equation. The equal symbol (=) is used to denote the separation of two phrases.

In the given question, we must isolate the g on one side of the equation in order to solve this equation for g. We may start by multiplying both sides of the equation by 5M to accomplish this. This will result in the left side of the equation having m/5M + ([tex]n^{2}[/tex]/5M). It will only provide us with g on the right side.

The terms on the left side of the equation can then be combined by multiplying them together. This will result in the equation shown below: (m/5M)([tex]n^{2}[/tex]/5M) = g.

The fractions can then be eliminated and the denominators removed by multiplying both sides of the equation by 5M. This will result in the formation of 5Mg on the right side and mn2/5M on the left.

We can then rearrange the equation to isolate the g on the right side, giving us: m[tex]n^{2}[/tex] = 5Mg. Finally, we can divide both sides of the equation by 5M to get g by itself on the right side, giving us the final equation: g = m[tex]n^{2}[/tex]/5M.

Therefore, the solution to the equation m+[tex]n^{2}[/tex] = g5M is g = m[tex]n^{2}[/tex]/5M.

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A graph of the solution to this system of inequalities on a coordinate plane is shown in the image attached below.

In order to to graph the solution to the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;

4x - 3 < 9

x - 3y > 6

Based on the graph (see attachment), we can logically deduce that the solution to the given system of inequalities is the shaded region and the point of intersection of the lines on the graph representing each, which is given by the ordered pair (3, -1).

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Answer:

False

Step-by-step explanation:

Converting

[tex] converting \: \frac{2}{3} \: to \: decimal \\ \frac{2}{3 } = 0.6666666 .....[/tex]

[tex]converting \: \frac{5}{12} \: to \: decimal \\ \frac{5}{12} = 0.4166666....[/tex]

[tex]therefore \: \frac{2}{3} > \: \frac{5}{12} \\ because \: 0.66666... > 041666...[/tex]

Answer:

Give the degree of the polynomial.

6x5+5x4−3x2+x7

Answers:

18

5

6

9

7

Hope it helps :)

Answer:

9x + 21

Step-by-step explanation:

An equilateral triangle is a triangle with three equal sides. If we know the length of one side, we can find the perimeter by multiplying by three.

3(3x + 7) = 9x + 21

The $31.309 money was spent on a pass and lunch for each student

Two or more expressions with an Equal sign is called as Equation.

School spends on a pass for each student,885.69/39

$22.97

School spends on a lunch for each student,

325.23/39

$8.339

Therefore, total money spent on a pass and lunch for each student

= 22.97 + 8.339

= $31.309

Hence, the $31.309 money was spent on a pass and lunch for each student

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The equation of  this parallel line is y = 4x - 22.  Railroad tracks, sidewalk edges, ladder rails, endless rail tracks, opposing sides of a ruler, opposite edges of a pen, an eraser, and other real-world objects are instances of parallel lines.

Since there is no "b" in the conventional equation y = mx + b, the line y = 4x has a slope of 4 and an intercept of 0. Any parallel line will have the same slope as the slope (m = 4) in this case. The slope of all parallel lines will be the same.

So let's return to the conventional format and replace the m with a "4".

y = 4x + b

Now that the values have been entered into the equation, let's solve for "b" using the point that sits on the line.

-6 = 4(4) + b

-6 - 16 = b

b = -22

The equation of  this parallel line is y = 4x - 22

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