10. Chelsea had completed 2/3 ofa 5-mile race when
her shoelace came untied. How many miles had
Chelsea completed at that point?

X intercept: 10/5 = 2

Y intercept: 10/-2 = -5

The x intercept is the point where the line crosses the x-axis and the y intercept is the point where the line crosses the y-axis.

To find the x-intercept, set y = 0 and solve for x. To find the y-intercept, set x = 0 and solve for y.

In this question,

1. To find x intercept, set y = 0

  5x - 2(0) = 10

  5x = 10

  x = 2

2. To find y intercept, set x = 0

  5(0) - 2y = 10

  -2y = 10

 y = -5

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Answer:

605

Step-by-step explanation:

11x55=605

According to the given information, we have

To find the vertex form, we have to find a

The standard form is obtained by developing the square power

Answer:

D = (x+6)² = 13

Step-by-step explanation:

In the attached file

The probability that either event will occur is P ( C ) = 0.89

Given data ,

Let the probability that either event will occur  be P ( C )

P ( A ) = 20/36

P ( B ) = 12/36

where P ( A or B ) = P ( C )

P ( C ) = P ( A ) + P ( B )

P ( C ) = 32/36

P ( C ) = 0.88888

Hence , the probability is P ( C ) = 0.89

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The equivalent expression to the sentence "9 more than the quotient of x and 5" is given as follows:

x/5 + 9.

The sentence in the context of this problem is defined as follows:

"9 more than the quotient of x and 5"

The quotient of x and 5 is given by the division of x by 5, as follows:

x/5.

9 more means that 9 is added to the quotient of x and 5, hence the equivalent expression to the sentence "9 more than the quotient of x and 5" is given as follows:

x/5 + 9.

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Answer:

1/4+1/3+1/8

=17/24

Step-by-step explanation:

1-17/24

=7/24

7/24×240

=70

Answer:

Your answer would be 13

Step-by-step explanation:

Answer:

56 but i could be wrong

Step-by-step explanation:

Answer:

\(\huge \boxed{2}\)

Step-by-step explanation:

\(8^\frac{1}{3}\)

Apply rule : \(a^\frac{1}{3}=\sqrt[3]{a}\)

\(8^\frac{1}{3}=\sqrt[3]{8}\)

8 is a perfect cube. Evaluate the cube root of 8.

\(\sqrt[3]{8}=2\)

Answer:

Radical expression

\( \sqrt[3]{2} \)

Evaluation

\( {8}^{ \frac{1}{3} } = 2\)

Step-by-step explanation:

8^(⅓) = ³√8

=³√(2×2×2)

=³√(2³)

= 2

BRAINLIEST PLEASE

Answer: 2048

Step-by-step explanation: 1. Write the exponential growth model.

The population of the town doubles every year, so the growth factor is 2. The initial population is 112, so the equation is: P(t) = 112(2)^t where P(t) is the population in year t and t is the number of years since 2014.

2. Estimate the population of the town in 2023. To estimate the population of the town in 2023, we can set t=9, since 2023 is 9 years after 2014. Plugging this into the equation, we get: P(9) = 112(2)^9 = 2048

Therefore, the estimated population of the town in 2023 is 2048.

It would take a total of 20 days to produce the batch of pens.

Let's calculate the work done by the 3 machines for the first 8 days:

Work done by 3 machines in 8 days = (3/12) * 8 = 2 days' worth of work

The remaining work that needs to be done by all 12 machines is:

Remaining work = 1 - (2/20) = 0.9

Now, we can use the work formula to find the total number of days needed to complete the remaining work with 12 machines:

Total work = 0.9

Work done by 12 machines in one day = 12/20 = 0.6

Total number of days needed = 0.9/0.6 = 1.5

Therefore, the total number of days needed to produce the batch of pens is:

8 (days with 3 machines) + 1.5 (days with 12 machines) = 9.5 days

However, we also need to add the 10.5 days it would take for all 12 machines to complete the batch from the beginning:

10.5 + 9.5 = 20 days

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Answer:

If you are writing a seesya let me help you

Step-by-step explanation:

Make sure to hilight key info

Also use grammarly to correct past tense and sentences

Make sure to make sense

The total time that should be taken by him to finish the book is 3.9 hours.

Given that,

Based on the above information, the time taken should be

\(= 375 \times 20 \div 32\)

= 234.375 minutes

Now in hours it should be

\(= 234.375 \div 60\)

= 3.9 hours

Therefore we can conclude that the total time that should be taken by him to finish the book is 3.9 hours.

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Answer:

20

Step-by-step explanation:

Just write down the answer.

The rational number - 91 / 200 is a number between the decimal numbers - 0.45 and - 0.46.

In this problem we find two decimal numbers, of which we need to find a rational number between these numbers. Please notice that the decimal numbers are also rational numbers. First, we transform each decimal number into rational numbers:

- 0.45 = - 45 / 100

- 0.46 = - 46 / 100

Second, find a possible rational number between the two ends by the midpoint formula:

x = (1 / 2) · (- 45 / 100) + (1 / 2) · (- 46 / 100)

x = - 45 / 200 - 46 / 200

x = - 91 / 200

Then, the rational number - 91 / 200 is a number between - 0.45 and - 0.46.

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Answer:

the following points would make a trapezoid

Answer:

The polygon is a rectangle

Explanation

If you subtract the y-values of the coordinates that have the same x-values, you will get one of the sides of polygon. Then, if you subtract the x-values of the coordinates that have the same y-values, you will get the other side of the polygon. Since this has only 4, sides with a right angle. It must be a rectangle or square. but seeing that the sides are different, the polygon must be a rectangle

If you have any questions, let me know in the comments! If you could mark this answer as the brainliest, I would greatly appreciate it!

\(\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}\)

Let the no. of students be x

total cost = y

Then the first equation will be

8x + 20 = y

And the second equation will be

3x + 40 = y

A system of two equations where each equation models the total cost y to take x students on each field trip is;

8x + 20 = y

3x + 40 = y

The total cost y is 48 to take x = 4 students on each field trip.

In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same set of variables.

A science teacher is planning a field trip to either the aquarium or the science center.

The aquarium charges $20 for the class tour guide and also charges $8 per student.

The science center charges $3 per student and has a class lab fee of $40.

Let the total cost y to take x students on each field trip.

The aquarium charges $20 for the class tour guide and also charges $8 per student.

8x + 20 = y

The science center charges $3 per student and has a class lab fee of $40.

3x + 40 = y

On solving both the equation

Substitute the value of y in the equation 2

3x + 40 = y

3x + 40 = 8x+20

8x - 3x = 40-20

5x = 20

x = 20/5

x = 4

Substitute the value of x in the equation 1

3x + 40 = y

2(4) + 40 =y

8 + 40 = y

y = 48

Hence, the total cost y is 48 to take x = 4 students on each field trip.

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Answer:

Step-by-step explanation:

Speed upstream is reduced:

Time to travel 20 miles:

Answer:

20/9 hours

Step-by-step explanation:

Note: I'm assuming 'upstream' means against the current.

If the boat flows against the current, it's speed is 13 - 4 = 9 mph.

\(\frac{20m}{9mph} =\frac{20}{9} hours\)

That means our answer is 20/9 hours.

If it is travelling with the current, its speed is 13 + 4 = 17 mph.

Therefore, 20/17 would be our answer if that were the case

The equation of Celia's exponential model is \(y = 9.4 * 0.75^x\)

The table that completes the question is added as an attachment

The y-intercept is given as:

(0,9.4)

The ratios of successive data values are calculated as:

\(r_1 = \frac{6.0}{10}= 0.6\)

\(r_2 = \frac{5.4}{6.0}= 0.9\)

\(r_3 = \frac{3.9}{5.4}= 0.72\)

\(r_4 = \frac{3.7}{3.9}= 0.95\)

\(r_5 = \frac{2.3}{3.7}= 0.62\)

\(r_6 = \frac{1.4}{2.3}= 0.61\)

\(r_7 = \frac{1.0}{1.4}= 0.71\)

\(r_8 = \frac{0.9}{1.0}= 0.9\)

\(r_9 = \frac{0.8}{0.9}= 0.89\)

\(r_{10} = \frac{0.5}{0.8}= 0.63\)

The average of the above values is

\(b = \frac{0.6 + 0.9 + 0.72 + 0.95 + 0.62 + 0.61 + 0.71 + 0.9 + 0.89 + 0.63}{10}\)

Evaluate

b = 0.75

An exponential function is represented as:

\(y = ab^x\)

Where

a = 9.4 as in the y-intercept (0,9.4)

b = 0.75

Substitute these values in \(y = ab^x\)

\(y = 9.4 * 0.75^x\)

Hence, the Celia's exponential model is \(y = 9.4 * 0.75^x\)

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Thanks for the update. "Irrotational" means curl = zero, so we compute the curl, set it equal to zero, and solve for the constants.

\(\vec f(x,y,z) = (axy+z^3) \, \vec\imath + (3x^2-z) \, \vec\jmath + (bz^2-y) \, \vec k\)

\(\nabla \times \vec f(x,y,z) = \left(\dfrac{\partial(bz^2-y)}{\partial y} - \dfrac{\partial(3x^2-z)}{\partial z}\right) \, \vec\imath - \left(\dfrac{\partial(bz^2-y)}{\partial x} - \dfrac{\partial(axy+z^3)}{\partial z}\right) \, \vec\jmath \\ ~~~~~~~~~~~~ + \left(\dfrac{\partial(3x^2-z)}{\partial x} - \dfrac{\partial(axy+z^3)}{\partial y}\right) \, \vec k\)

\(\nabla \times \vec f(x,y,z) = 3z^2 \, \vec\jmath + (6-a)x \, \vec k\)

At this point, all we can conclude is that a = 6 to make the k-component vanish. Unfortunately there's no zeroing out the j-component, so the field as given is *not* irrotational.

As I mentioned in comments, if the i-component had instead been \(axy+bz^3\), we would have ended up with

\(\nabla \times \vec f(x,y,z) = 3bz^2 \, \vec\jmath + (6-a)x \, \vec k\)

in which case we would have b = 0.

I'll continue working with this "fixed" field to find Φ, if only to give you an idea of how to proceed. We want a scalar function Φ(x, y, z) such that the given vector field is the gradient of f. This would entail solving the partial differential equations,

\(\dfrac{\partial\Phi}{\partial x} = axy+bz^3 = 6xy\)

\(\dfrac{\partial\Phi}{\partial y} = 3x^2 - z\)

\(\dfrac{\partial\Phi}{\partial z} = bz^2-y = -y\)

Let's start with the last equation. Integrating both sides with respect to z yields

\(\Phi(x,y,z) = \displaystyle \int (-y) \, dz = -yz + g(x,y)\)

Now differentiate both sides with respect to y :

\(\dfrac{\partial\Phi}{\partial y} = -z + \dfrac{\partial g}{\partial y} = 3x^2 - z \implies \dfrac{\partial g}{\partial y} = 3x^2\)

Integrate both sides of the latter PDE with respect to y to solve for g :

\(g(x,y) = \displaystyle \int 3x^2 \, dy = 3x^2y + h(x)\)

Now we differentiate Φ with respect to x :

\(\Phi(x,y,z) = -yz + 3x^2y + h(x) \\\\ \dfrac{\partial\Phi}{\partial x} = 6xy + \dfrac{dh}{dx} = 6xy \implies \dfrac{dh}{dx} = 0\)

Integrate to solve for h :

\(h(x) = \displaystyle \int 0 \, dx = C\)

where C is an arbitrary constant.

So the scalar function whose gradient is our "fixed" field f is

\(\Phi(x,y,z) = -yz + 3x^2y + C\)

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Answer:

8 and 6

Step-by-step explanation:

Two numbers are such that their difference, their sum, and their product are to

each other as 1:7:24. Their product must equal what number?

:

Two numbers a & b

Let x = the multiplier

:

a - b = 1x

a + b = 7x

a * b = 24x

:

Add the 1st two equations

a - b = x

a + b = 7x

2a = 8x

a = 4x

or

x = .25a

:

a * b = 24x

Replace 24x; a = 4x therefore:

a * b = 6a

b = 6

;

Using the 1st equation

a - b = 1x

Replace b with 6 and x with .25a

a - 6 = .25a

a - .25a = 6

.75a = 6

a =

a = 8

:

Find the multiplier

a - b = x

8 - 6 = 2

:

Check this

a - b = 2 (1*2)

a + b = 14; (7*2)

a * b = 48: (24*2)

:

The numbers are 8 and 6; their products = 48

Answer: 144

Step-by-step explanation: it's so EZ just add all the sides.

The ratio of EG = 36.

Let's assign variables to the lengths of the line segments:

EF = x

FG = 5x

GH = 3x

We know that EH = EF + FG + GH.

Substituting the given values, we have:

54 = x + 5x + 3x

Combining like terms, we get:

54 = 9x

To isolate x, we divide both sides of the equation by 9:

54/9 = x

Simplifying, we find:

6 = x

EF = 6, FG = 5(6) = 30, and GH = 3(6) = 18.

Since EG is the sum of EF and FG, we can calculate it as follows:

EG = EF + FG = 6 + 30

= 36

EG = 36.

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We want to calculate the volume of the spherical shell of chocolate.

The chocolate shell is spherical with a thickness of 0.5cm

Volumes of spherical shells can be calculated with the formula;

The outer diameter is 8cm. The outer radius is therefore 4cm

The inner diameter is 8-2(0.5)=7cm. The inner radius is therefore 3.5cm

Therefore, we can find the volume of the chocolate shell as;

Therefore,

Answer:

first option

Step-by-step explanation:

It's up by 4 units because because the +4 is outside of the exponent and also, it is a +4 not -4 which indicates that the translation is up.

The implicit derivative is given as follows:

dx/dt(x = 4)  = 1/12.

The function in this problem is given as follows:

y = 3x² + 1.

The implicit derivative, relative to the variable t, is given as follows:

dy/dt = 6x dx/dt.

(the derivative of the constant 1 is of zero).

The parameters for this problem are given as follows:

x = 4, dy/dt = 2.

Hence the derivative is obtained as follows:

2 = 6(4) dx/dt

dx/dt = 2/24

dx/dt = 1/12.

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