A boat traveled 240 miles downstream, then 240 miles back upstream. The trip downstream took 20 hours. The trip back upstream took 60 hours. Use this information to fill in the following blanks. Note: Express your answers as integers.

The speed of the boat in still water is [answer]
miles per hour.

The speed of the current is [answer]
miles per hour.

Answer:

(2,4)

Step-by-step explanation:

Answer:  

(2,4)

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation

An inequality which best models the situation described above is: D. 52 + 3w ≥ 90.

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments (symbols):

In order to solve this word problem, we would assign a variable to the number of weeks and then translate the word problem into algebraic equation as follows:

Let w represent the number of weeks.

Translating the word problem into an algebraic equation, we have;

Next, we would combine the above parameters to form an algebraic equation as follows:

52 + 3w ≥ 90

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Complete Question:

Antonina needs to have worked at least 90 volunteer hours to graduate. She has already volunteered with a housing organization over the summer for 52 hours. Antonina needs to tutor after school for 3 hours per week to complete the remainder of her volunteer hours. If www is the number of weeks that Antonina needs to tutor in order to complete her volunteer hours, which of the following inequalities best models the situation described above?

answer choices

A. 52w + 30w ≥ 90

B. 52w + 30w ≤ 90

C. 52 + 3w ≤ 90

D. 52 + 3w ≥ 90

Answer:

\(x=\pm \sqrt{-c}\)

Step-by-step explanation:

This means the equation is of the form \(x^2+c=0\).

\(x^2=-c \\ \\ x=\pm \sqrt{-c}\)

Answer:

8x^(3/2)

Step-by-step explanation:

We can simplify the expression first:

2sqrt(x)4x^(-5/2)=8x^(-3/2)

Now we can rewrite this in the form kx^2:

8x^(=3/2)=8(x^(-3/2))(x^(5/2))/x^2

=8(x^2/x^3)(x^(1/2))/x^2

=8x^(-1/2)

therefore, 2sqrt(x)4x^(-5/2) is equivalent to 8x^(-1/2), which can be written in the form kx^2 as 8x^(3/2)

I hope this helps!

Answer:

For one inch of rain, it will take 1.5 hours (1:30)

Step-by-step explanation:

6 divided by 4 is 1.5

Answer:

1hr 30min

Step-by-step explanation:

so 6 hours = 4 inches. You can . divide both by 4 to get 1 inch.

1 inch = 1.5 hours.

1.5 hours is 1 hour and 30 min

Answer:

2,000. 90x20 is 1,800 and that is close to 2000.

Step-by-step explanation:

Answer:

90 × 27 = Would be estimated to 2,000-2,500

Step-by-step explanation:

Answer:

The median is 9

Step-by-step explanation:

The median is the number in the middle. The middle of this is 8 and 10, so you plus them and divide by to 2, then it gives 9, so the median is 9.

To evaluate the surface integral of f(x,y,z) dS over the given surface, the first step is to set up the surface integral as a double integral over a region R in the xy-plane. To do this, we can express f(x,y,z) in terms of two parameters, u and v, as f(u,v). Then, the surface integral is expressed as follows:
Integral f(u,v) dS = Integral Integral f(u,v) dA,
where A is the area of the region R in the xy-plane.

For the given surface, we can express the equation of the cone as z2 = (x2 +y2), for 0≤z≤8. To parameterize this equation, we can set u = x and v = y, and express x and y in terms of z as follows:
x = rcosθ and y = rsinθ.
Therefore, the double integral of f(u,v) dA can be expressed as:
Integral Integral f(u,v) dA = Integral Integral f(r cosθ,r sinθ) rdrdθ,
where 0≤r≤5 and 0≤θ≤2π.
Finally, substituting f(x,y,z) with 4x and evaluating the integral, we obtain the surface area of the given cone as A = 80π.
In conclusion, the surface integral of f(x,y,z) dS over the given cone is 80π.

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The maximum height of the projectile is 56.53 meters.

The height of a projectile at time t is represented by the function h (t)= −4.9 t² +18t + 40, where h(t) is the height in meters and t is the time in seconds.

This is a quadratic function of the form h(t) = at² + bt + c, where a = -4.9, b = 18, and c = 40.

To find the maximum height of the projectile, we need to find the vertex of the parabolic graph of the function h(t).

The vertex of the parabola is at the point (t, h(t)) where t = -b/2a. Substituting the values of a and b, we get t = -18/(2(-4.9)) = 1.8367 seconds.

To find the maximum height, we need to substitute t = 1.8367 seconds into the function h(t). h(1.8367) = -4.9(1.8367)^2 + 18(1.8367) + 40 = 56.53 meters.

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Answer:

47/53 or 0.88 or 88%

Step-by-step explanation:

The possible combination for three-course meals to be chosen from given the restriction is equal to 16.

The restriction that can only choose either a dessert or an appetizer,

Have two choices for the first course.

For the second course,

Have 4 choices for the soup.

For the third course,

Have 3 choices for the main course,

And since can only choose one of the remaining two categories (dessert or appetizer),

Have 2 choices for the third course.

Using the multiplication principle of counting,

The total combinations of number of three-course meals possible under these conditions by multiplying the number of choices for each course,

= Number of choices for the first course × Number of choices for the second course × Number of choices for the third course

= 2 × 4 × 2

= 16

Therefore, there are 16 possible combination for three-course meals that can be chosen.

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The variable x, which represents the number of students who receive an offer, is a discrete variable.

The variable can take on one or more exact values, a countable number of values, or values that are finite, such as the number of students in a class, the number of cars in a parking lot, the number of seeds in a bag, and so on, if the variable is a discrete variable. A variable is referred to as continuous if it can take on an infinite number of values (although the values may be restricted to a certain range), and those values are not limited to specific points on a continuum.

For three students who are undergoing interviews at Brookwood Institute, the experimental results are defined in terms of the outcomes of the three interviews. Each interview would yield one of two possible results: either an offer for a job or no offer.

As a result, for each of the three interviews, there are two possible outcomes. If we multiply the possibilities for each of the three interviews, we get a total of eight possible outcomes, which can be listed as follows:

NNN, NNO, NON, NOO, ONN, ONO, OON, and OOO.

Let's assume that an 'O' represents an offer, while an 'N' represents no offer. The variable x represents the number of students who receive an offer. Since the variable can only take on one of four discrete values (0, 1, 2, or 3), it is a discrete variable.

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Answer:

imcomplete question

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the total area of the track, we need to calculate the area of each section and then add them together.

Area of a semi-circle with radius 31m:

A = (1/2)πr^2

A = (1/2)π(31m)^2

A = 4795.4m^2

Area of a rectangle with length 92.7m and width 31m (the straight parts):

A = lw

A = (92.7m)(31m)

A = 2873.7m^2

To find the total area, we need to add the areas of the two semi-circular ends and the two straight sections:

Total area = 2(Area of semi-circle) + 2(Area of rectangle)

Total area = 2(4795.4m^2) + 2(2873.7m^2)

Total area = 19181.6m^2

Rounding this to 1 decimal place, we get:

Total area ≈ 19181.6 m^2

Therefore, the total area of the track is approximately 19181.6 square meters.

The center and vertices of the ellipse x² + 9y² + 16x - 54y + 136 = 0 is

Generally, The standard form of the equation of an ellipse is (x-h)^2/a^2 + (y-k)^2/b^2 = 1, where (h,k) is the center of the ellipse and a and b are the semi-major and semi-minor axes respectively.

To convert the given equation to standard form, complete the square by adding and subtracting constants to both sides: x² + 16x + 81 + 9y² - 54y + 324 = 410

This results in: (x + 8)²/16 + (y - 3)²/9 = 1

Therefore, the center of the ellipse is (h,k) = (-8,3) and the semi-major and semi-minor axes are a = 4 and b = 3.

To find the vertices of the ellipse, substitute the center coordinates into the equation of the ellipse and solve for x and y. Since the semi-major and semi-minor axes are 4 and 3, respectively, the vertices are located at: (h ± a, k) = (-8 ± 4, 3) and (h, k ± b) = (-8, 3 ± 3)

Therefore, the vertices of the ellipse are (-12,3) and (-4,3), (-8,6) and (-8,0).

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The x-coordinates of the left edges of the rectangles are 1,5/4,6/4,7/4.

The area of this region with a Riemann Sum is 0.7595.

A specific type of approximation of an integral by a finite sum in mathematics is known as a Riemann sum. It bears the name of the German mathematician Bernhard Riemann from the nineteenth century. Approximating the area of functions or lines on a graph, as well as the length of curves and other approximations, is a highly typical use.

Given function is f(x) = 1/x on the interval [1,2] is shown.

The four rectangles of width 1/4 are present.

From the figure we can see that the x coordinate of the left edges of the rectangle are:

1,5/4,6/4,7/4

Now we plug these values in the function to find the height of rectangles.

For x=1 ,f(x) = 1

For x=5/4 ,f(x) = 4/5

For x=6/4 ,f(x) = 4/6

For x=7/4 ,f(x) = 4/7

Now, Area = length*width, and width of each rectangle is 1/4

Area of rectangle 1 = 1*1/4 = 1/4

Area of rectangle 2 = 4/5*1/4 = 1/5

Area of rectangle 3 = 4/6*1/4 = 1/6

Area of rectangle 4 = 4/7*1/4 = 1/7

Total Area is = 1/4+1/5+1/6+1/7  = 0.7595

This is an overestimation of ln(2).

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The function of "if ‴−6″ 8′=15" is f(x) = c1 + c2e^(2x) + c3e^(4x).

To find the function of "if ‴−6″ 8′=15," we need to first understand what the notation means.

The triple prime symbol (‴) indicates the third derivative of a function, while the double prime (″) indicates the second derivative and the prime (') indicates the first derivative.

So, we can rewrite the equation as follows: f‴(x) - 6f″(x) + 8f'(x) = 15

Now, we can use techniques from differential equations to solve for f(x).

First, we can find the characteristic equation:

r^3 - 6r^2 + 8r = 0

Factorizing out an r, we get: r(r^2 - 6r + 8) = 0

Solving for the roots, we get: r = 0, r = 2, r = 4

Therefore, the general solution to the differential equation is:

f(x) = c1 + c2e^(2x) + c3e^(4x)

where c1, c2, and c3 are constants determined by initial or boundary conditions.

In summary, the function of "if ‴−6″ 8′=15" is f(x) = c1 + c2e^(2x) + c3e^(4x).

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The probability of 5 people of different ages are sitting in age order is 1/12.

Let the youngest individual take a seat first. If the seats are not designated, this person may occupy any of the five available seats, and each one is equally valuable.

The next senior citizen must then be placed. For this reason, there are two possible placements for the second person: either to the left of the first person or to the first person's right. The two options, ascending order and descending order, are matched by this.

We are unable to place the additional individuals after the second person is set because there is only one spot available adjacent to the first person.

There are only two methods to arrange five persons of different ages sitting at a round table in ascending or descending order.

The number of ways in which we can arrange are 5 people at a round table without any restriction is  4!.

Probability of 5 people in  around table is 2/4! = 1/12.

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Answer:

square root of 3 ,1.84,2.3, square root of 5

Answer:

I think it’s y=50x

Step-by-step explanation:

Cause y(distance) increase by 50 each time do y=50x

The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

a) Here the area of the parallelogram determined by d and e is given as 10. The area of the parallelogram is given as `|d×e|`.

We have,

d=(2,4)

and e=(4k,3k)

Then,

d×e= (2 * 3k) - (4 * 4k) = -10k

Area of parallelogram = |d×e|

= |-10k|

= 10

As we know, area of parallelogram can also be given as,

|d×e| = |d||e| sin θ

where, θ is the angle between the two vectors.

Then,10 = √(2^2 + 4^2) * √((4k)^2 + (3k)^2) sin θ

⇒ 10 = √20 √25k^2 sin θ

⇒ 10 = 10k sin θ

∴ k sin θ = 1

Therefore, sin θ = 1/k

Hence, the value of k is 1.

Part(b) The volume of the parallelepiped determined by vectors a, b and c is given as,

| a . (b × c)|

Here, a=(1,1,2),

b=(5,3,λ), and

c=(4,4,0)

Therefore,

b × c = [(3 × 0) - (λ × 4)]i + [(λ × 4) - (5 × 0)]j + [(5 × 4) - (3 × 4)]k

= -4i + 4λj + 8k

Now,| a . (b × c)|=| (1,1,2) .

(-4,4λ,8) |=| (-4 + 4λ + 16) |

=| 12 + 4λ |

Therefore, the volume of the parallelepiped is 12 + 4λ.

Part(c) The vector component of a + c orthogonal to c is given by [(a+c) - projc(a+c)].

Here, a=(1,1,2) and

c=(4,4,0).

Then, a + c = (1+4, 1+4, 2+0)

= (5, 5, 2)

Now, projecting (a+c) onto c, we get,

projc(a+c) = [(a+c).c / |c|^2] c

= [(5×4 + 5×4) / (4^2 + 4^2)] (4,4,0)

= (4,4,0.5)

Therefore, [(a+c) - projc(a+c)] = (5,5,2) - (4,4,0.5)

= (1,1,1.5)

Therefore, the vector component of a + c orthogonal to c is (1,1,1.5).

Conclusion: The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

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The maximum number of real zeros in a polynomial will same as its degree thus 3 degrees will have 3 zeros.

The roots of an equation are the solution of that equation since an equation consists of hidden values of the variable to determine them by different processes and then the resultant is called roots.

An n degree of a polynomial can have a maximum of n number of variables.

For example, a quadratic equation ax² + bx + c = 0 is a two-degree equation so it has a maximum of two roots or zeros.

As per the given a polynomial is having 3 degrees so it will have exactly 3 roots.

Hence "A polynomial can have as many real zeros as the number of degrees it has, therefore one with three degrees can have up to three of them.".

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The quotient from the given division is 46 and the remainder is 50.

Given that, 3500 divided by 75.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Here, 3500/75

75|3500|46

     300

    _____

       500

       450

   ______

        50

Thus, quotient = 46 and remainder=50

Therefore, the quotient from the given division is 46 and the remainder is 50.

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The figure is decomposed by separating it into three simpler shapes

The area of the complex shape is solved by splitting the shape into simpler shapes.

The splitting is also called decomposition, doing this will result to three shapes which are

Triangle

rectangle and

semicircle

Then are area is solved individually and added up

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Answer: $2.94

Step-by-step explanation:

You do 0.07 x 42

The principal stresses for this stress state are σ_1 = 47.5 MPa and σ_2 = 24.5 MPa, and the magnitude of the maximum in-plane shear stress is |Tmax| = 8 MPa.

To determine the principal stresses and maximum in-plane shear stress for this stress state represented by Mohr's circle, we can use the following equations:

The center of the circle (C, 0) represents the mean stress (σ_avg):
σ_avg = C

Outer edge point A (Ax, Ay) represents the maximum and minimum stresses (σ_max and σ_min):
σ_max = Ax
σ_min = Ay

Principal stresses can be calculated as:
σ_1 = σ_avg + (σ_max - σ_avg)/2
σ_2 = σ_avg - (σ_max - σ_avg)/2

Substituting the given values, we get:
σ_avg = C = 36 MPa
σ_max = Ax = 59 MPa
σ_min = Ay = 43 MPa

σ_1 = 36 + (59-36)/2 = 47.5 MPa
σ_2 = 36 - (59-36)/2 = 24.5 MPa

The magnitude of the maximum in-plane shear stress can be calculated as:
|Tmax| = (σ_max - σ_min)/2
|Tmax| = (59-43)/2 = 8 MPa

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Answer:

12y+3x-24

Step-by-step explanation:

Answer:

It is 8

Step-by-step explanation:

you would do 13-0.75(12)+8(1/2) and that would equal 8.

Answer:

8

Step-by-step explanation:

substitute w = 12 and x = \(\frac{1}{2}\) into the expression

13 - 0.75(12) + 8(\(\frac{1}{2}\) )

= 13 - 9 + 4

= 4 + 4

= 8