1. What is the approximate volume of the sugar container? Show your work. (2 points)
2. What is the approximate height of the rice container? Show your work. (2 points)
3. Compare the heights of the sugar container and the rice container. Next, compare their volumes. How many times as large is the volume of the rice container compared to the volume of the sugar container? Explain your answer. (2 points)
4. In the formula V = Bh, B is the area of the base. Use this formula to calculate the volume of the flour container. (2 points)
5. Compare the volumes of the containers. Which container has the greatest volume? Which has the smallest volume? (2 points)
PLS HELP I WILL GIVE BRAINLIST

We are given the following differential equation, [tex]\frac{dx}{dt}-4x=cos(5t)[/tex], with the initial condition [tex]x(0)=1[/tex]. This is a linear DE in the form, [tex]\frac{dx}{dt}+P(t)x=Q(t)[/tex], where [tex]\mu(t)=e^{\int\ {P(t)} \, dt }[/tex].

First, finding [tex]\mu(t)[/tex].

[tex]\Longrightarrow\mu(t)=e^{\int\ {P(t)} \, dt }\Longrightarrow\mu(t)=e^{\int\ {-4} \, dt }[/tex]

[tex]\mu(t)=e^{-4t }[/tex]

Multiply the DE by [tex]\mu(t)[/tex].

[tex]\Longrightarrow\frac{dx}{dt}-4x=cos(5t)\Longrightarrow e^{-4t} [\frac{dx}{dt}-4x=cos(5t)][/tex]

[tex]\Longrightarrow (e^{-4t}) \frac{dx}{dt}-(e^{-4t})4x=(e^{-4t})cos(5t)[/tex]

[tex]\Longrightarrow e^{-4t} \frac{dx}{dt}-4e^{-4t}x=e^{-4t}cos(5t)[/tex]

Verify that the L.H.S is a product rule of [tex]e^{-4t}x[/tex].

[tex]\Longrightarrow \frac{d}{dt}[e^{-4t}x ] =(e^{-4t}*-4)x+(e^{-4t})(\frac{dx}{dt} )[/tex]

[tex]\Longrightarrow \frac{d}{dt}[e^{-4t}x ] =-4e^{-4t}x+e^{-4t}\frac{dx}{dt}[/tex]

This matches, so we can move forward by integrating both sides of the DE.

[tex]\int\ {[e^{-4t}x ]'} \, =\int\ {e^{-4t}cos(5t)} \, dt[/tex]

The integral on the R.H.S is pretty nasty to do using integration by parts and u-sub. I will use a table of integrals.

[tex]\int\ {e^{ax}cos(bx) } \, dx=\frac{e^{ax}(acos(bx)+bsin(bx))}{a^2+b^2}[/tex]

Let [tex]a=-4[/tex] and [tex]b=5[/tex]

[tex]\int\ {[e^{-4t}x ]'} \, =\int\ {e^{-4t}cos(5t)} \, dt[/tex]

[tex]\Longrightarrow e^{-4t}x = \frac{e^{-4t}(-4cos(5t)+5sin(5t))}{(-4)^2+(5)^2}+C[/tex]

[tex]\Longrightarrow e^{-4t}x = \frac{e^{-4t}(-4cos(5t)+5sin(5t))}{41} +C[/tex]

Now for the initial condition, [tex]x(0)=1[/tex].

[tex]\Longrightarrow e^{-4(0)}(1) = \frac{e^{-4(0)}(-4cos(5(0))+5sin(5(0)))}{41} +C[/tex]

[tex]\Longrightarrow (1)(1) = \frac{(1)(-4(1)+(0))}{41} +C[/tex]

[tex]\Longrightarrow 1 = -\frac{4}{41} +C[/tex]

[tex]\Longrightarrow 1+\frac{4}{41} = C[/tex]

[tex]\Longrightarrow C=\frac{45}{41}[/tex]

Now we have, [tex]e^{-4t}x = \frac{e^{-4t}(-4cos(5t)+5sin(5t))}{41} +\frac{45}{41}[/tex], solve for x.

[tex]\Longrightarrow x = \frac{\frac{e^{-4t}(-4cos(5t)+5sin(5t))}{41}}{ e^{-4t}} +\frac{\frac{45}{41}}{e^{-4t}}[/tex]

[tex]\Longrightarrow x = \frac{(-4cos(5t)+5sin(5t))}{41}} +\frac{45e^{4t}}{41}[/tex]

Thus, the answer to the given differential equation with an initial condition is, [tex]x = \frac{(-4cos(5t)+5sin(5t))}{41}} +\frac{45e^{4t}}{41}[/tex].

Using Compound Interest, The initially invested amount was $5400.

The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You'll have $110.25 after the second year is over.

The formula for compound interest is

[tex]C = P(1 + \frac{r}{n})^{nt}[/tex]

Where C is the compound interest value after n years.

P is the principal amount.

I is interest.

n is the number of years.

It is given that percentage of interest is 5% so I=0.05. C=$5676.27.

n=7.

According to the formula of compound interest,

5676.27 = P(1+0.05)7 P = 5676.27 1.051084

P = 5400

Therefore the amount that was invested initially was $5400.

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Answer:

Hi there! The answer is 3/5

Step-by-step explanation:

The rise is 3 and the run is 5.

Brainiest, please? Can you click on the crown on my answer?

Answer: 3/5

Step-by-step explanation:

Looks at the points (0,1) and (5,4).

Formula: y2-y1/x2-x1

Substitute: 4-1/5-0 = 3/5

m = 3/5

The triangular table that Mrs. Gomez is buying for her classroom is a right triangle table because 3² +4² = 5². That is option C.

A right angle triangle is the type of triangle that has one side of its angle perpendicular to another and the value of the three sides can be calculated through the use of the Pythagorean formula.

The Pythagorean formula is expressed as, c2 = a2 + b2, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs.

Since, 5= c

b= 3

a = 4

Therefore, 3² +4² = 5² shows that the table is a right angle triangle.

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The zeros and their multiplicity are:

Zero: -1, Multiplicity: 1

Zero: 0, Multiplicity: 1

Zero: 1, Multiplicity: 1

Zero: 2, Multiplicity: 1

Zero: 2.5, Multiplicity: 1

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given:

A graph of a polynomial is given in the diagram.

A polynomial is intercepting the x-axis five times.

That means, there are five zeros.

The zeros and their multiplicity are:

Zero: -1, Multiplicity: 1

Zero: 0, Multiplicity: 1

Zero: 1, Multiplicity: 1

Zero: 2, Multiplicity: 1

Zero: 2.5, Multiplicity: 1

Hence, all the required values are given above.

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The value of a that makes u parallel to v is a = 4 and  the value of a that makes u perpendicular to v is -7.

a. For two vectors to be parallel, their direction ratios must be equal. In other words, their components must have the same ratio. For vectors u = (a, 7) and v = (4, 4), we have:

u1/u2 = a/7 = v1/v2 = 4/4

So the value of a that makes u parallel to v is a = 4.

b. For two nonzero vectors to be perpendicular, their dot product must be equal to zero. The dot product of u = (a, 7) and v = (4, 4) is given by:

u · v = a * 4 + 7 * 4 = 4a + 28

To make this equal to zero, we can solve for a:

4a + 28 = 0

4a = -28

a = -7

So the value of a that makes u perpendicular to v is -7.

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The point where the net electric field is equal to zero is located approximately 0.48936m away from q1 and 24m - 0.48936m = 23.51064m away from q2.

Charge is a fundamental property of matter that describes its electrical state. It is a scalar quantity that can be either positive, negative, or neutral, and is measured in Coulombs (C). The concept of charge is used to explain many of the phenomena that occur in electricity and magnetism, such as electric fields, currents, and voltages. Positive and negative charges are thought to be due to the presence or absence of electrons, which are the smallest negatively charged particles in matter. Neutral objects have an equal number of positive and negative charges, resulting in a net charge of zero. The interaction of charges with each other results in many of the electrical and magnetic phenomena observed in the world around us.

The net electric field at a point is equal to zero if the electric field due to one charge is exactly canceled by the electric field due to the other charge.

Since q2 is 49 times greater than q1, the electric field due to q2 will be 49 times greater than the electric field due to q1 at any given point. In order to cancel the electric field due to q1, we need to place q2 at a point that is 49 times closer to q1 than the original separation of 24m.

Let's call the new separation between the charges x. Then, x = 24m / 49, which is approximately equal to 0.48936m.

So, the point where the net electric field is equal to zero is located approximately 0.48936m away from q1 and 24m - 0.48936m = 23.51064m away from q2.

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The correct answer is to Reject the null hypothesis. This is strong evidence that the mean amount of sleep is less than 8 hours.

The test statistic of t = -2.03 and P-value of approximately 0.025 suggest that the mean amount of sleep for students is significantly less than 8 hours.

The P-value of 0.025 is less than the significance level of 0.05, which means that there is enough evidence to reject the null hypothesis that the mean amount of sleep is 8 hours.

Therefore, the appropriate conclusion at the a = 0.05 significance level is that the mean amount of sleep for students is less than 8 hours.

Hence, the correct answer is C.

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About 0.04% percent of quokkas weigh over 15.5 pounds.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Given that, the weights of quokkas can be described by the Normal model N(10, 2.7).

Let Y the weights of quokkas

Given that, Y~N(μ= 10, σ²=2.7)

So, σ=1.643

a) The probability, P(Y＞15.5) denotes chances that quokkas weight over 9.3 pounds, and it is,

P(Y>9.3) = P(Z> (15.5-μ)/σ)

= P(Z> (15.5-10)/1.643)

= P(Z>3.347)

= 0.0004

= 0.0004×100 =0.04%

b) The probability, P(Y＜11.9) denotes chances that quokkas weight under 11.9 pounds, and it is,

P(Y>9.3) = P(Z> (11.9-μ)/σ)

= P(Z> (11.9-10)/1.643)

= P(Z>1.156)

= 0.1250

= 0.1250×100 =12.5%

c) The probability, P(11.9≤Y≤15.5) denotes chances that quokkas weight will be between 11.9 and 15.5 pounds, and it is,

P(11.9≤Y≤15.5) = P((15.5-μ)/σ ≤ Z ≤ (11.9-μ)/σ)

= P((15.5-10)/1.643) ≤ Z ≤ (11.9-10)/1.643)

= P(3.347≤ Z ≤1.156)

= P(Z≤3.347)-PZ ≤1.156)

= 0.0004-0.1250

= 0.1246

= 0.1246×100

= 12.46%

Therefore, about 0.04% percent of quokkas weigh over 15.5 pounds.

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The subsets are {}, {0}.

What is the subset in mathematics?

In mathematics, a subset is a set consisting of elements that are also elements of another set. A set A is said to be a subset of set B if and only if every element of A is also an element of B. In other words, if you have a set A and another set B, and all the elements of set A are present in set B, then set A is considered a subset of set B.

In mathematics, a subset is a collection of elements that belong to a larger set. The elements in a subset can be any type of mathematical objects, such as numbers, vectors, or functions. A set is a subset of itself, and the empty set is a subset of every set.

The subsets of the given set {0} are the empty set {} and the set itself, {0}. So, the subsets of the given set 0 are {}, {0}.

Hence, the subsets are {}, {0}.

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Note that the proof related to the above parallelogram is given as follows:

ΔSVX ≅ ΔUTX                      Given

SV || TU                                 Given

SV ≅ TU                                Corresponding part of congruent triangle

VUTS parallelogram             Definition of parallelogram.

A quadrilateral having two pairs of parallel sides is known as a parallelogram. It is possible to demonstrate that the opposing sides of a parallelogram are congruent.

A parallelogram is any quadrilateral having two pairs of congruent opposing sides. Parallelograms contain two congruent opposing angles, thus a quadrilateral with two congruent opposite angles must be a parallelogram.

A parallelogram's diagonals intersect each other, therefore a quadrilateral with diagonals that bisect each other must be a parallelogram. Finally, if a quadrilateral contains two parallel and congruent sides, it must be a parallelogram.

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I think that answer is yes

Step-by-step explanation:

The answer should be -11

Answer:  -11 (negative eleven)

An integer is a real number. Which includes 0, positive numbers, and negative numbers. Since the temperature outside went down by 11 degrees rather than increased, it is negative. Which means our integer is -11.

I hope this helps & Good Luck <3 !

The area of the tabletop in square inches is 1071 square inches.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

Given that, there are 3 inches between each side of the aquarium and each side of the tabletop.

The length of the tabletop will be:

l = 48 + 3 = 51 inches.

The width of the tabletop will be:

w = 18 + 3 = 21 inches.

The area of the table top will be:

A = (l)(b)

A = (51)(21)

A = 1071 square inches.

The area of the tabletop in square inches is 1071 square inches.

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A calibration curve is a graphical representation of the relationship between the output of a measuring instrument and the actual values of the quantity being measured.

What is the calibration curve?

A calibration curve is typically created by measuring a set of known values of the quantity being measured, and plotting the measured values against the actual values. The curve is used to make adjustments to the measurements obtained with the instrument, so that they more accurately reflect the actual values of the quantity being measured.

A calibration curve can be described as a plot of the relationship between the output of a measuring instrument and the actual values of the quantity being measured. The curve is typically linear, and the slope of the curve represents the sensitivity of the instrument. The y-intercept of the curve represents the offset or bias of the instrument, and any deviations from a straight line represent non-linearity in the measurement.

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The polynomial in standard form is 8x^5 + 4x^4 + 4x^3 + 4

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

4x^3+4x^m+8x^5+4

Express properly

So, we have the following representation

4x^3 + 4x^4 + 8x^5 + 4

Order the powers in decreasing order

This gives

8x^5 + 4x^4 + 4x^3 + 4

Hence, the standard form is 8x^5 + 4x^4 + 4x^3 + 4

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Answer:

Sharpe Ratio?

if you looking for a name for your definition, thats it

good luck!

The correct option regarding the solution of the system of equations is given as follows:

One solution at (-1, 0).

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

For this problem, we have a single equation, hence the solution is obtained when the graph crosses the x-axis.

The graph crosses the x-axis when x = -1 and y = 0, hence the solution is given as follows:

(-1,0).

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AROC formula

(f(b)-f(a))/b-a

f(11)-f(3)    /       11 - 3

-623 -(-47)      / 8

= -72

Hope this helps,

- Jeron :- )

Answer:

28.93 gallons of paint

Step-by-step explanation:

The volume of a sphere can be found using the formula:

V = (4/3)πr^3

We are given that the water tower holds 6,684 cubic feet of water, so we can use this to find the radius:

6684 = (4/3)πr^3

(6684 * 3) / (4 * π) = r^3

r = (6684 * 3 / (4 * π))^(1/3) = 35.73 feet

Next, we need to find the surface area of the sphere. The surface area of a sphere can be found using the formula:

A = 4πr^2

So, the surface area of this water tower can be found as:

A = 4π * 35.73^2 = 4π * 1286.13 = 5071.57 square feet

Finally, we need to find the amount of paint needed to paint the surface area twice. One gallon of paint can cover 350 square feet, so we can divide the surface area by 350 to find the number of gallons of paint needed:

Gallons of paint = (5071.57 * 2) / 350 = (10143.14 / 350) = 28.93 gallons

So, 28.93 gallons of paint are needed to paint the water tower twice.

Answer: The total number of tickets sold (student and adult) cannot exceed 110, so we can write the first inequality as:

r + y ≤ 110

The minimum amount of money needed from ticket sales is $720, so we can write the second inequality as:

4r + 9y ≥ 720

To graph the system of inequalities, we can start by plotting the two lines corresponding to r + y = 110 and 4r + 9y = 720. The solution to the system of inequalities is the area on the graph that is shared by both of the inequalities (i.e., the area above the line 4r + 9y = 720 and below the line r + y = 110).

One possible solution for the number of student tickets (r) and adult tickets (y) is (30, 80). This means that 30 student tickets and 80 adult tickets can be sold to meet the conditions and raise at least $720.

Step-by-step explanation:

The new arc length function for the curve after reparametrization is as follows

[tex]\\\\r(s) = ( 4 - \frac{s}{\sqrt{26}})i + (\frac{4s}{\sqrt{26} } + 4)j+(\frac{3s}{\sqrt{26} } + 3)k[/tex]

What is meant by the arc length of a curve?

The distance between two places along a segment of a curve is known as the arc length.

The formula for arc length is used to determine how far something is along the curved line that makes up an arc. The arc length is, to put it simply, the distance that passes through the curved line of the circle that forms the arc.

Given,

Vector equation of curve  r(t) = (5 - t) i + (4t - 3) j + 3t k

    Given P = (4, 1, 3)

5 - t = 4

So, t = 1

Now differentiate r(t)

 r'(t) = -i + 4j + 3k

Magnitude of r'(t) = |r'(t)| = √[(-1)² + 4² + 3²] = √26

The arc length function for the curve

 [tex]s = \int\limits^t_1 { |r'(t)| } \, dt = \int\limits^t_1 { \sqrt{26} } \, dt = \sqrt{26} (t-1)[/tex]

  [tex]t = \frac{s}{\sqrt{26} } + 1[/tex]

Now to reparametrize the curve with respect to arc length, substitute t with (s/√26) + 1 in r(t).

[tex]r(s) = (5 - ( \frac{s}{\sqrt{26} } + 1)) i + (4( \frac{s}{\sqrt{26} } + 1) - 3) j + 3( \frac{s}{\sqrt{26} } + 1) k\\\\r(s) = ( 4 - \frac{s}{\sqrt{26}})i + (\frac{4s}{\sqrt{26} } + 4)j+(\frac{3s}{\sqrt{26} } + 3)k[/tex]

Therefore the new arc length equation of the curve when  [tex]t = \frac{s}{\sqrt{26} } + 1[/tex] is as follows

[tex]\\\\r(s) = ( 4 - \frac{s}{\sqrt{26}})i + (\frac{4s}{\sqrt{26} } + 4)j+(\frac{3s}{\sqrt{26} } + 3)k[/tex].

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To find the measure of angle G in triangle FGH, we can use the fact that the sum of angles in a triangle is always 180 degrees.

First, we can find the measure of angle H using the fact that the sum of angles in a triangle is 180 degrees:

H = 180 - F - G

H = 180 - 72 - G

H = 108 - G

Next, we can use the Law of Cosines to find the length of side FG:

FG^2 = GH^2 + FH^2 - 2(GH)(FH)cos(F)

FG^2 = 8^2 + 13^2 - 2(8)(13)cos(72)

FG^2 = 169.21

FG ≈ 13.01 ft

Finally, we can use the Law of Cosines again to find the measure of angle G:

cos(G) = (FG^2 + GH^2 - FH^2) / (2(FG)(GH))

cos(G) = (169.21 + 64 - 169) / (2(8)(13))

cos(G) = 0.7686

G ≈ 40.6 degrees

Therefore, the measure of angle G in triangle FGH is approximately 40.6 degrees.

Answer: 44%

Step-by-step explanation:

100 - 49 - 7 = 44 people who preferred Soda B

44 of a 100 = 44%

Answer: 44%

Step-by-step explanation:

Since we have 100 people, each person is one percent.

49 people preferred A, so we can subtract 49 from 100.

100 - 49 = 51

7 people didn't have an opinion, so we can subtract 7 from 51.

51 - 7 = 44

That means that 44 people preferred B, which is 44%

Answer:

F(-2) = -3(-2) - 2 = 6 - 2 = 4

F(-2) + 9 = 4 + 9 = 13

Step-by-step explanation:

F(-2) = -3(-2) - 2 = 6 - 2 = 4

F(-2) + 9 = 4 + 9 = 13

Answer: JD's markup price is $80 * 120% = $96 per bat.

So, the retail price of each bat is $80 + $96 = $176.

The total revenue from the sale of 16 bats is 16 * $176 = $2,816.

He still has 30 - 16 = 14 bats left.

The discount price of each bat is $176 - ($176 * 40%) = $106.40.

The total revenue from the sale of 14 bats at the discount price is 14 * $106.40 = $1,493.60.

The total revenue from all the bats is $2,816 + $1,493.60 = $4,309.60.

The profit JD makes from selling all the bats is $4,309.60 - ($80 * 30) = $1,039.60.

Step-by-step explanation:

The profit which will he make after selling all of the bats is $1,039.60.

This is referred to as the amount of money that you gain when you are paid more for something than it cost you to make, get, or do it.

JD's markup price = $80 ×120% = $96 per bat.

Retail price = $80 + $96 = $176.

Revenue of 16 bats is 16 * $176 = $2,816.

Since 30 - 16 = 14 bats which is what we have left.

The discount price of each bat is $176 - ($176 * 40%) = $106.40.

The total revenue from the sale of 14 bats at the discount price is 14 * $106.40 = $1,493.60.

Therefore the total revenue from all the bats is $2,816 + $1,493.60 = $4,309.60.

The total profit = $4,309.60 - ($80 * 30) = $1,039.60.

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According to the model, the current population of Algeria is 38 million.

The model for the population in t years from now is given by the model P = 38 ( 1 + r ) ^ t.

This means that when given the model, the current population of Algeria is 38 million because the 38 in the model represents the value of population when no years have elapsed.

We can solve for this to get :

= 38 ( 1 + r ) ^ t

= 38 ( 1 + r ) ⁰

= 38 x 1

= 38

= 38 million

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Eric’s gross pay for one year if he earns a salary of $3,500 per month is $42,000.

The total amount of money an employee receives before taxes is referred to as gross pay.

Given  that;

Eric’s gross pay for one year = Eric's salary per month × 12 months

Eric’s gross pay for one year = $3,500 × 12

Eric’s gross pay for one year = $42,000

Therefore, the gross pay is $42,000.

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It is true that if points F and G are contained in a plane, then the line segment FG that connects them is entirely contained in that plane.

A two-dimensional plane, also known as a plane in two dimensions, is a flat surface that has length and width, but no thickness. It is an abstract mathematical concept that can be represented graphically.

Here,
In geometry, if two points are contained in a plane, then any line segment connecting those two points is also contained in that plane. So, if points F and G are contained in a plane, then the line segment FG that connects them is entirely contained in that plane.

Thus, it is true that if points F and G are contained in a plane, then the line segment FG that connects them is entirely contained in that plane.

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