The graph shows the amount of water that remains in a barrel after it begins to leak. The variable x represents the number of days that have passed since the barrel was filled, and y represents the number of gallons of water that remain in the barrel.

What is the slope of the line?
A. -2
B. -1/2
C. 7/16
D. 39/30

Answer:

The constant of proportionality is the constant value of the ratio of two proportional quantities x and y, typically the equation is Y=KX. ... The constant of proportionality does is, the value of Y is dependent on how the given value of X is effected by the constant of proportionality.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Constant of proportionality means slope which can be represented as y=mx+b, y=kx and a ton of other stuff I don't know.

But lets take it as y=kx because it's easier. Constant of proportionality/slope is k so its C, 5.5.

Answer:

\(\boxed{\tt a=9}\)

Step-by-step explanation:

We are given the equation:

\(-5a+7= -38\)

We want to solve for a, so we must isolate a on one side of the equation.

7 is being added to -5a. The inverse of addition is subtraction. Subtract 7 from both sides of the equation.

\(-5a+7-7=-38-7\)

\(-5a=-38-7\)

\(-5a=-45\)

a is being multiplied by -5. The inverse of multiplication is division. Divide both sides of the equation by -5.

\(\frac{-5a}{-5} =\frac{-45}{-5}\)

\(a=\frac{-45}{-5}\)

\(a=9\)

Let's check our solution. Plug 9 in for a.

\(-5a+7=-38\)

\(-5(9)+7=-38\)

\(-45+7=-38\)

\(-38=-38\)

This checks out, so we know our solution a=9 is correct.

-5a +7 =-38

-5a +7 (-7) = -38 (-7)

-5a= -45

-5a (÷-5)= -45 (÷-5)

a= 9

Answer:

A

Step-by-step explanation:

You can didvide 0.006 by 0.00002 to get 300 then convert it into scientific notation which would be 3 * 10^2

\(0.006/0.00002=300\)

\(300 = 3 * 10^{2}\)

Answer:

Answer A is correct

Step-by-step explanation:

To find the answer for that you have divide the new diameter by old diameter.

Let us solve now.

0.006m ÷ 0.00002m

6 × 10⁻³ ÷   2 × 10⁻⁵

( 6 ÷ 2) × ( 10 ⁻³⁻⁽⁻⁵⁾)

3 × 10 ⁻3⁺⁵

3 × 10²

Answer A is correct

Hope this helps you :-)

Let me know if you have any other questions :-)

The rate of constant for the above-given first-order reaction is b.) 8.77 × 10–3 h–1.

The half-life of a first-order reaction can be calculated using the equation t1/2 = ln(2)/k, where t1/2 is the half-life and k is the rate constant.

In this case, we know that the reaction goes to half completion in 79 hours. Therefore, the half-life is also 79 hours.

Plugging this into the equation, we get:

79 = ln(2)/k

Solving for k, we get:

k = ln(2)/79

Using a calculator, we can evaluate this expression to get:

k = 8.77 × 10–3 h–1

Therefore, the correct answer is b) 8.77 × 10–3 h–1.

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The correlation is a significant non-zero value.

The number of samples is n.

n = 25

The correlation of the coefficient is r.

r = -0.40

When correlation is significant,

\(H _{0} : p = 0\)

When correlation is non-zero,

\(H _{ \alpha } : p ≠0\)

The test statistic is,

\(TS = \frac{r \times \sqrt{n - 2} }{ \sqrt{1 - r {}^{2} } } \)

\( = \frac{0.4 \times \sqrt{25 - 2} }{ \sqrt{1 - ( - 0.4) ^{2} } } \)

\( = \frac{ - 1.918 }{ \sqrt{0.84} } \)

= -2.093

The test statistic is -2.093.

The correlation is,

\(H _{ \alpha } : - 2.93 ≠0\)

The correlation is not equal to zero and is significant.

Therefore, the correlation is a significant non-zero value.

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Answer:10.5

Step-by-step explanation: I hope this helps

The height, x, of the right trapezoidal prism is 10.5 ft.

Given that, the volume of this right trapezoidal prism is 341.25 ft³.

We need to find the height x, of the prism.

The formula to find the volume of this right trapezoidal prism is Volume=BH.

Where B=Area of the Base and H=Height.

Area of the Base(Trapezium)=1/2(a+b)×h

Where a and b are parallel sides of the trapezium and h= height of the trapezium.

Now, the area of the Base=1/2(8+5)×5=32.5 ft²

The volume of the right trapezoidal prism=32.5×x

⇒341.25=32.5×H

⇒x=10.5 ft

Therefore, the height, x, of the right trapezoidal prism is 10.5 ft.

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Answer:

1.50

Step-by-step explanation:

To find the mean of the probability distribution, we need to multiply each value of hours studied by its corresponding probability, then add up the products.

Mean = (0.5 x 0.07) + (1 x 0.2) + (1.5 x 0.46) + (2 x 0.2) + (2.5 x 0.07)

Mean = 0.035 + 0.2 + 0.69 + 0.4 + 0.175

Mean = 1.5

Therefore, the mean of the probability distribution is 1.5.

Answer:

D

Step-by-step explanation:

1.50 on edge (if that guys right)

The polynomial equation is P(x) = (x - 1)³(x² -2x - 10)

From the question, we have the following parameters

The expression 1 + 3i is a complex number

This means that its conjugate must also be a root

The conjugate is represented as 1 - 3i

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

So, we have

P(x) = (x - 1)^3 * (x - (1 + 3i)) * (x - (1 - 3i))

This gives

P(x) = (x - 1)^3 * (x^2 - (1 +3i)x - (1 - 3i)x -(1 - 3i)(1 + 3i))

P(x) = (x - 1)^3 * (x^2 -2x - 10)

So, we have

P(x) = (x - 1)³(x² -2x - 10)

Hence, the equation of the polynomial equation is P(x) = (x - 1)³(x² -2x - 10)

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Answer:

2nd answer

Step-by-step explanation:

4x^3+2

4*(-1)^3+2

4*(-1)+2

-4+2

-2

Answer: -2

Step-by-step explanation:

Replacing x for -1 would make the equation \(4(-1^3)+2\). Knowing PEMDAS, we know that the parentheses goes first. \(-1^3\) means that we need to multiply -1 by itself 3 times (\(-1*-1*-1\),  * equals "times"). \(-1*-1=1\) so \(1*-1=-1\). Now our equation is \(4(-1)+2\).    \(4*-1=-1\) and -4 + 2 = -2. Hope this explanation helps :)

This year the choir has 96 members.

An ensemble of singers known as a choir performs together, usually singing choral music. Choirs frequently sing in harmony and might include singers in a variety of vocal ranges.

To find out how many members the choir has this year, we need to calculate 120% of the number of members two years ago.

First, let's calculate 120% of 80:

120% of 80 = (120/100) * 80 = 1.2 * 80 = 96

Therefore, this year the choir has 96 members.

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Answer:

16,17,18,19

Step-by-step explanation:

one guy guessed. probably using a calculator

another guy took the 4th root of 100,000 and rounded down a number

(a third way started like this

n*(n+1)*(n+2)(n+3)=100000

Answer: the answer is 72

Step-by-step explanation:

if 50% of a number is 120 then that means its only half of that number so to find out the whole number multiply 120 by 2 which gives you the answer of 240

Now we need to determine 30% of 240 and the procedure explaining it as such

Step 1: In the given case Output Value is 240.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 240 = 100%.

Step 4: In the Same way, x = 30%.

Step 5: On dividing the pair of simple equations we got the equation as under

240 = 100% (1).

x = 30% (2).

(240%)/(x%) = 100/30

Step 6: Reciprocal of both the sides results in the following equation

x%/240% = 30/100

Step 7: Simplifying the above obtained equation further will tell what is 30% of 240

x = 72%

Therefore, 30% of 240 is 72

I hope this helps

Answer:

  72

Step-by-step explanation:

You want 30% of a number, given that 50% of it is 120, and 80% of it is 192.

The 30% you want will be the difference between 80% and 50%:

  80% -50% = 30%

  192 -120 = 72

30% of the same number is 72.

The quadratic equations are solved and the value of x are 1 and -7 respectively

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

a)

x² + 6x = 7

Adding 9 on both sides of the equation , we get

x² + 6x + 9 = 16

On simplifying the equation , we get

( x + 3 )² = ( 4 )²

Taking square roots on both sides , we get

x + 3 = ±4

Subtracting 3 on both sides , we get

x = 1 and x = -7

Therefore , the value of x are 1 and -7 respectively

Hence , the quadratic equations is solved

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y=-4/7

7*(-4/7)=-4

-4-4=-8

-8/6=-4/3

Answer:

Area of Plane Shapes-

1. Triangle Area = ½ × b × h b = base h = vertical height

2. Square Area = a2 a = length of side

Step-by-step explanation:

The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces), for which the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration. Surface area is the total amount of space that all of the surfaces of an object take up. It is the sum of the area of all the surfaces of that object.[1] Finding the surface area of a three-dimensional shape is moderately easy as long as you know the correct formula. Each shape has its own separate formula, so you'll first need to identify the shape you’re working with. Memorizing the surface area formula for various objects can make calculations easier in the future. Here are a few of the most common shapes you might encounter.

1

Define the formula for surface area of a cube.

2

Measure the length of one side.

3

Square your measurement for a.

4

Multiply this product by six.

The overhead cost for the insurance company to insure the driver is approximately $919.63.

To calculate the overhead cost, we need to first determine the expected value of the cost of accidents for the driver. This can be found by multiplying the probability of getting into an accident by the average cost of an accident:

Expected cost of accidents = 0.068 * $28,750 = $1952.50

Next, we subtract the expected cost of accidents from the premium paid by the driver to get the overhead cost:

Overhead cost = $2205.00 - $1952.50 = $252.50

Finally, we need to adjust the overhead cost for any additional expenses or profit margins for the insurance company. One way to do this is to multiply the overhead cost by a factor, such as 1.5 or 2. Using a factor of 1.5, we get:

Adjusted overhead cost = $252.50 * 1.5 = $378.75

Adding the adjusted overhead cost to the expected cost of accidents, we get:

Total cost to insure driver = $1952.50 + $378.75 = $2331.25

Therefore, the overhead cost for the insurance company to insure the driver is approximately $919.63.

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(a) To find the curl of the vector field F(x, y, z), we first find its component functions:

F(x, y, z) = (5ex sin(y), 9ey sin(z), 2ez sin(x))

Then, we use the formula for the curl of a vector field:

curl F = (∂Fz/∂y - ∂Fy/∂z, ∂Fx/∂z - ∂Fz/∂x, ∂Fy/∂x - ∂Fx/∂y)

Plugging in the component functions of F(x, y, z), we get:

curl F = (2ez cos(x), -5ex cos(y), 9ey cos(z))

(b) To find the divergence of the vector field F(x, y, z), we use the formula for the divergence of a vector field:

div F = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z

Plugging in the component functions of F(x, y, z), we get:

div F = 5e^x sin(y) + 9e^y sin(z) + 2e^z sin(x)
(a) To find the curl of the vector field F(x, y, z) = (5e^x sin(y), 9e^y sin(z), 2e^z sin(x)), we need to compute the cross product of the del operator (∇) and F:

curl F = ∇ x F

curl F = ( (∂/∂y)(2e^z sin(x)) - (∂/∂z)(9e^y sin(z)), (∂/∂z)(5e^x sin(y)) - (∂/∂x)(2e^z sin(x)), (∂/∂x)(9e^y sin(z)) - (∂/∂y)(5e^x sin(y)) )

After computing the partial derivatives, we get:

curl F = ( 0, 5e^x cos(y) - 2e^z cos(x), 9e^y cos(z) - 5e^x cos(y) )

(b) To find the divergence of the vector field F(x, y, z), we need to compute the dot product of the del operator (∇) and F:

div F = ∇ ⋅ F

div F = (∂/∂x)(5e^x sin(y)) + (∂/∂y)(9e^y sin(z)) + (∂/∂z)(2e^z sin(x))

After computing the partial derivatives, we get:

div F = 5e^x sin(y) + 9e^y sin(z) + 2e^z sin(x)

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Answer:

:Coefficient

Step-by-step explanation:

It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

Here, we have,

given that,

min t_i

x₁ = x₂-u

x₂ = u

-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.

and origin  (0,0) be the begging of the coordinate.

also given that, (x₁, x₂)→ (0,0)

so, min t_i at origin (0,0) = t

Therefore, the generality condition of the situation does not met.

so, we get,

The given system can be represented by the following equations:

x₁' = x₂ - u

x₂' = u

To analyze the behavior of the system, we can examine the dynamics of each variable separately.

For x₁:

x₁' = x₂ - u

The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.

For x₂:

x₂' = u

The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.

Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).

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The inradius of the triangle of the given dimensions will be equal to the value 2.

To find the inradius of a triangle, we need to know the semi perimeter of the triangle, which is half of the perimeter. The perimeter of a triangle is the sum of the lengths of its sides. So, the semi perimeter of triangle ABC is (6+8+10)/2 = 12.

Now that we know the semi perimeter, we can use the formula for the inradius of a triangle:

inradius = √(s-a)(s-b)(s-c)/s

where a, b, and c are the lengths of the sides of the triangle and s is the semi perimeter.

Plugging in the values for a, b, c, and s, we get:

inradius = √(12-6)(12-8)(12-10)/12 = √(6)(4)(2)/12 = √48/12} = √4 = 2

Therefore, the inradius of triangle ABC is 2.

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A)The probability of exactly four buses arriving in the next 2 hours is\($P(X=4)=e^{\wedge}(-2)\left(2^{\wedge} 4 / 4 !\right)=0.090$\) ≈ 0.090.

B) The probability of at least two buses arriving in the next 2 hours is =0.865

C)  The probability of no buses arriving in the next 2 hours is =0.135

d) The probability that it will be between 30 and 90 minutes before the next bus arrives is ,0.185

a) Let \($X$\) be the number of buses that arrive in a 2-hour period. Since the time between arrivals of buses follows an exponential distribution with a mean of 60 minutes, the arrival rate λ is given by\($\lambda=1 / 60$\) 0 buses per minute.

Therefore, the number of buses that arrive in a 2-hour period is a Poisson distribution with parameter \(\mu=\lambda t=(1 / 60) \times 120=2$.\). Thus, X has a Poisson distribution with parameter μ = 2.

The probability of exactly four buses arriving in the next 2 hours is\($P(X=4)=e^{\wedge}(-2)\left(2^{\wedge} 4 / 4 !\right)=0.090$\) ≈ 0.090.

b) The probability of at least two buses arriving in the next 2 hours is

\($P(X \geq 2)=1-P(X=0)-P(X=1)=1-e^{\wedge}(-2)\left(2^{\wedge} 0 / 0 !\right)-e^{\wedge}(-2)\left(2^{\wedge} 1 / 1 !\right)=0.865$.\)

c) The probability of no buses arriving in the next 2 hours is

\(P(X=0)=$ $e^{\wedge}(-2)\left(2^{\wedge} 0 / 0 !\right)=0.135$\)

d) Let Y be the time between the first and second bus arrivals. Then Y follows an exponential distribution with a mean of 60 minutes. We want to find the probability that \($30 \leq Y \leq 90$\).

This is equivalent to finding \(P(Y \leq$ $90)-P(Y \leq 30)$,\), which is equal to F(90) - F(30), where F is the cumulative distribution function of the exponential distribution with \($\lambda=1 / 60$\)

Therefore, the probability that it will be between 30 and 90 minutes before the next bus arrives is\(F(90)-F(30)=\left(1-e^{\wedge}(-90 / 60)\right)-(1$ $\left.e^{\wedge}(-30 / 60)\right)=e^{\wedge}(-1.5)-e^{\wedge}(-0.5)=0.185$\)

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More information is needed to properly answer the question!

Step-by-step explanation:

(x+12)+(6x-4)+(3x+2)=180

10x+10=180

10x=170

x=17

m<W =17+12

=29

Answer:

D. The graph shows the cost in dollars, Y, of a muffin delivery and number of muffins, X, ordered. The slope of the line is 2.

Step-by-step explanation:

Ok done that's the answer

Answer:

9

Step-by-step explanation:

\(x=2\\12/4+3(8-x)-12\\=12/4+3(8-2)-12\\=3+24-6-12\\=27-6-12\\=21-12\\=9\)

Answer:

See below

Step-by-step explanation:

each term is the sum of the two before it

2 3 5 8 13 21 34

The length and the width vary inversely.

A variation is a relation between a set of values of one variable and a set of values of other variables.

In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.

If first rectangle length = 72cm and width = 56cm

Then, area = length x width = 72 x 56 = 4032\(cm^{2}\)

If length of second rectangle = x

and width = 21

Area of second rectangle = 21x

so both areas are equal, which means

21x = 4032

x = 4032/21

x = 192cm

Since the first rectangle had a width of 56cm and length, 72 and second rectangle has a reduced width 21 cm and an increased length 192cm. it means that the length and the width vary inversely since the reduction in width led to an increase in length.

In conclusion, the two quantities length and width vary inversely.

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Answer:

y = 2/3x - 2

Step-by-step explanation:

I'm pretty sure this is asking about the slope intercept form, since you didn't give us the actual answers. If not, comment below. Slope intercept form follows the y = mx + b form, where m is the slope and b is the y-intercept. By plugging your givens in, you get y = 2/3x - 2

The rate of change of concentration with respect to time at t=12 minutes is -1/1029 units/m in.

So, the correct answer is A.

To find the rate of change of concentration with respect to time at t=12 minutes, we need to take the derivative of the equation C(t) = 1/6(4t +1)^-1/2 with respect to time.

This will give us the instantaneous rate of change of concentration at t=12 minutes.

The derivative of C(t) is given by -1/12(4t+1)^-3/2(4), which simplifies to -2/(3(4t+1)^3/2).

Plugging in t=12 minutes, we get -2/(3(4(12)+1)^3/2), which simplifies to -1/1029 units/m in.

Hence the answer of the question is A.

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Answer:

i think that is 2 i only guess