A passenger train traveled 240 miles in the same amount of time it took a freight train to travel 160 miles. The rate of the freight train was 20 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train.

Answer: The correct system of linear inequalities that represents this situation is:

X + Y ≤ 32 (to represent the maximum number of hours you can work)

7X + 8Y ≥ 256 (to represent the minimum amount of money you need to earn)

X ≥ 0, Y ≥ 0 (to represent that you can only work a non-negative number of hours at each job)

Where X represents the number of hours you spend tutoring and Y represents the number of hours you spend babysitting. The first inequality represents the maximum number of hours you can work, and the second inequality represents the minimum amount of money you need to earn. The last two inequalities represent that you can only work a non-negative number of hours at each job.

Step-by-step explanation:

The graph shows a positive association. There is a nonlinear association shown. There is no correlation shown on the scatter plot.

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The echelon form of the given augmented matrix with 1's on the diagonal is:

1 -1 0 1000

0 1 0 1100

0 0 1 300

To find the echelon form of the given augmented matrix with 1's on the diagonal, we perform row operations to eliminate the entries below the diagonal. The goal is to get the matrix in row echelon form. Here are the steps:

Step 1: Subtract the first row from the second and third rows to eliminate the 1's in the first column below the diagonal:

1 -1 2 400

0 1 -2 500

0 -2 5 -700

Step 2: Add twice the second row to the third row to eliminate the -2 below the diagonal:

1 -1 2 400

0 1 -2 500

0 0 1 300

Step 3: Add 2 times the third row to the first row and add 2 times the third row to the second row to eliminate the entries above the diagonal:

1 -1 0 1000

0 1 0 1100

0 0 1 300

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Answer : 61.60

Step-by-step explanation:

Answer:61.60

Step-by-step explanation:

i just typed it in

The value for the variable x in the parallelogram is equal to 7.

The parallelogram LMNO have two pairs of parallel sides hence LO = MN and LM = ON.

We shall evaluate for variable x as follows:

5x + 9 = x + 37

5x - x = 37 - 9 {collect like terms}

4x = 28

x = 28/4 {divide through by 4}

x = 7

Therefore, the value for the variable x in the parallelogram is equal to 7.

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The value of the variable x is 7

It is important to note that the opposite sides of a parallelogram are congruent or equal in length.

Then, for the parallelogram LMNO

NM is parallel to OL

Now, substitute the values, we get;

NM = OL

x + 37 = 5x + 9

collect like terms

x - 5x = 9 - 37

subtract the like terms

-4x = -28

Make 'x' the subject

x = 7

Hence, the value is 7

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Answer:

5 seconds

Step-by-step explanation:

d = vt + 16t² , that is

vt + 16t² = d

substitute d = 480, v = 16 into the equation

16t + 16t² = 480 ( divide through by 16 )

t + t² = 30 ( subtract 30 from both sides )

t² + t - 30 = 0 ← in standard form

(t + 6)(t - 5) = 0 ← in factored form

equate each factor to zero and solve for t

t + 6 = 0 ⇒ t = - 6

t - 5 = 0 ⇒ t = 5

t > 0 , then t = 5

the object will hit the ground 5 seconds later

Answer:

-------------------------

As per given we have:

Substitute these into given equation and solve for t:

The first value of t is discarded as time can't be negative, so the answer is 5 seconds.

A) The rate of change in this situation is -$100 per week.

B) She will have $300 left in her account after five weeks.

The set of numbers for which the statement that the square root of a number is greater than the square of the number is true, is equals to (0,1). So, right choice is option (a).

In mathematics, when we multiplying the number by itself, the result is called square of number. This is usually equivalent to raising a number to the power of 2. For example, square of 4 is 4² = 16. The square root of a number is that factor of a number which when multiplied by itself the original number. Square root of number is usually equivalent to raising a number to the power of 1/2. It is represented using the symbol '√'. Now, we have to check the options and determine where square root of a number is greater than the square of the number.

a) (0, 1), if we plug f(x) = √x , x∈(0,1) and g(x) = x² , x∈(0,1) on calculator then we get, the value of f(x) is greater than g(x), i.e, x = 1/2 , f(1/2) = 0.70 and g(1/2) = 0.25.

b) [0, 1], if we plug x = 0 then f(0) = 0 , g(0) = 0

that is f(x) is greater than and equal to g(x). But we have to consider only greater than not equal.

c) [1,∞), closed bracket again represents equality which is not consider. So, statement is false for it.

d) (1,∞), here number inbetween 1 and infinite but not for all reals it is true that square root of a number is greater than the square of the number, for example x = 2 , f(2) =1.414, g( 2) = 4 implies f(x)< g(x) for x = 2. So, the statement is false for it.

Hence, required option is option (a).

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Complete question :

The square root of a number is greater than the square of the number. For what set of numbers is this true?

a) (0, 1)

b) [0, 1]

c) [1, ∞ )

d) (1,∞)

The statistical measurement known as the Z-score describes the connection between a value and the mean of a set of values and the required z-score to the three decimal places is −2.714.

The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score.

Standard deviations from the mean are used to measure Z-score.

A Z-score of zero means the data point's score is the same as the mean score.

Your observed value is 2.5 standard deviations from the mean if your Z-score is 2.5, and so on.

Your value is more closely aligned with the mean the closer your Z-score is to zero.

Your value is further from the mean the farther your Z-score is from zero.

So, let's say Rosetta wins the game on Thursday with 110 points.

When x=110, the z-score is -2.714.

The average is 148.

You can see from this z-score that x=110 is 2.714 standard deviations away from the mean.

This formula can be used to determine the z-score:

z = x−μ/σ

=110−148/14

=−38/14

≈−2.714

Therefore, the required z-score to the three decimal places is −2.714.

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The shape of the distribution of the number of clase friends for the males is best characterized as Skewed to the higher values (right or positively skewed).

Construction of closed geometric shapes involves the usage of points, line segments, circles, and curves. These shapes are all around us. Circles, rectangles, triangles, and other shapes are examples of geometric shapes. Triangle-shaped slices make up the shape of a pizza

The basic shapes include the square, circle, triangle, and other simple shapes that cannot be further subdivided into the simpler shapes by general standards.

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At x=2, the function in the graph is approaches to infinity. This is satisfied by equation 1 that models the rational function, hence option 1 is the correct answer.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

From given graph we can see that

At x=2, the function in the graph is approaches to infinity.

It means function is not defined at x=2

We know that a rational function is undefined when denominator is equal to zero.

For equation 1:

f(x)= 2(x+2)/(x-2)

Equating the denominator:

x-2=0

x=2

It means function is not defined at x=2

The y-intercept is: y= -2

The function is passing through the point (1,-6).

When we substitute x=1

Hence, option 1 is true.

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The equation of the rational function with the given features is given as follows:

F(x) = [4(x² + 5x + 4)]/(x² - x - 6).

A rational function is a fraction, in which both the numerator and the denominator contain instances of the variable x.

Considering the x-intercepts, the numerator of the function is defined as follows:

y = a(x + 4)(x + 1)

y = a(x² + 5x + 4).

Considering the y-intercept at (0,4), the leading coefficient a is given as follows:

a = 4.

The vertical asymptotes determine the zeros of the denominator, which is given as follows:

(x + 2)(x - 3) = x² - x - 6.

Hence the function is defined as follows:

F(x) = [4(x² + 5x + 4)]/(x² - x - 6).

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The value of each variable in the quadrilateral can be found such that :

Angle 107 degrees and z degrees will add up to 180 degrees which means that the value of z is:

= 180 - 107

= 73 degrees

Using this value of z as 73 degrees, we can then solve for y because the sum of the interior angles of a quadrilateral need to add up to 360 degrees.

The value of y variable  is therefore:

= 360 - 83 - 103 - 73

= 101 degrees

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the displacement is 23.14m and the velocity is 21.28m/s

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The given equation y  = 25t - 1.86t²

at t =  1

So the displacement y = 25-1.86 = 23.14

to find velocity dy/dt = 25- 2(1.86)t

v = 25 - 3.72 = 21.28m/s

Hence the displacement is 23.14m and velocity is 21.28m/s

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The solution set of the inequality is [3, ∝)

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

2x + 4 < 10

Subtract 4 from both sides of the inequality

So, we have the following representation

2x + 4 - 4 < 10 - 4

Evaluate the like terms

2x < 6

Divide both sides by 2

x < 3

When represented as an interval notation, we have

[3, ∝)

See attachment for the inequality of the solution set

Hence, the solution is [3, ∝)

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Answer:

Step-by-step explanation:

To determine the percentage increase between 2017 and 2018, we need to calculate the difference between the two years and then divide by the 2017 value and multiply by 100. So, the calculation would be:

(9960,000 - 9640,000) / 9640,000 * 100 = 3.125%

So, the number of households increased by 3.125% from 2017 to 2018.

To find the number of households in 2019, we need to find the increase from 2018 to 2019. We can do this by multiplying the number of households in 2018 by the percentage increase, and then add that to the 2018 value. So, the calculation would be:

9960,000 * (3.125 / 100) + 9960,000 = 10,298,800

Therefore, there would be approximately 10,298,800 households in 2019, rounded to the nearest ten thousand.

The average hourly wage for police officers is $30.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

The U.S. Bureau of Labor Statistics is a government agency that collects information about jobs in the U.S.

In 2018, the Bureau reported that Wisconsin police officers had a mean yearly salary of $62,040.

Assume that police officers generally work 40 hours a week.

There are 52 weeks in the year.

The average hourly wage for police officers is,

= 62040 ÷ (52 x 40)

= 62040 / 2080

= 29.8

≈ $30

Therefore, $30 is the hourly wage.

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The system of equations that can be used to find the length of each workout and the duration of each workout are as follows;

(a) 5·x + 3·y = 10

2·x + 6·y = 10

(b) Length of each Plan A workout: 1.25 hours

Length of each Plan B workout: 1.25 hours

A linear system of equation consists of two or more linear equations that share common variables.

(a) The number of Plan A workouts Mary trained on Wednesday = 5

Number of Plan B workouts she trained on Wednesday = 3

The total time (in hours) Mary trained both workouts on Wednesday = 10

Where x represents the length (in hours) of each of the Plan A workout, and B represents the time in hours of each of the Plan B workout, we get;

5·x + 3·y = 10

Similarly, the number of Plan A workouts trained on Thursday = 2

Number of Plan B workout trained on Thursday = 6

The duration of training of all workouts on Thursday = 10 hours

Therefore, we get;

2·x + 6·y = 10

The system of equations that could be used to find the length (in hours) of each type of workout can be presented as follows;

(b) The first equation from the system of equations indicates that we get;

5·x + 3·y = 10

3·y = 10 - 5·x

Plugging the value of y above into the second equation from the system of equations, we get;

2·x + 6·y = 10

2·x + 6 × ((10 - 5·x)/3) = 10

2·x + 2·(10 - 5·x) = 10

2·x + 20 - 10·x = 10

20 - 8·x = 10

8·x = 20 - 10 = 10

x = 10/8 = 1.25

y = (10 - 5·x)/3,

x = 1.25, therefore;

y = (10 - 5 × 1.25)/3 = 1.25

y = 1.25

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The length of the side is 12 units in simplest radical form with a rational denominator.

A triangle is said to be equilateral if all of its sides and angles are equal. An equilateral triangle is also known as an equiangular triangle since each of its angles has a value of 60 degrees.

Given:

The triangle given in the image is an equilateral triangle.

That means the angle measure of the triangle is 60° each.

And all the sides are equal.

To find the value of x:

Sin(60/2)° = opposite/ hypotenuse.

Sin30° = x/6

x = 6/Sin30°

[tex]x = \frac{6}{1/2}[/tex]

x = 6(2)

x = 12

Therefore, the value of x is 12 units.

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The complete question:

The triangle below is equilateral. Find the length of the side in simplest radical form with a rational denominator.

The image is given below.

Answer:

---------------------------

According to picture we observe:

The segment connecting the midpoints is the midsegment.

As per property of the midsegment, it is parallel to opposite side and is half of its measure.

It tells us that WB is parallel to AE and:

Answer: I do not have the capability to create a graph. However, I can tell you how to graph the parabola h(x) = -x^2 + 3.

A parabola is defined by its equation in the form y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = -1, b = 0, and c = 3.

The vertex of the parabola is the highest or lowest point on the graph and is given by the coordinates (-b/2a, c - b^2/4a). For this parabola, the vertex is (0, 3), since b = 0 and a = -1.

To find another point on the parabola, you can plug in any x-value and use the equation of the parabola to find the corresponding y-value. For example, if you plug in x = -2, you get:

h(-2) = -(-2)^2 + 3

h(-2) = 4 + 3

h(-2) = 7

So the point (-2, 7) is also on the parabola.

With the vertex and one other point on the parabola, you can now graph the parabola.

Step-by-step explanation:

Answer:

(a)

smaller value = 125 ft

larger value = 250 ft

(b)

31250 ft²

Step-by-step explanation:

(a)

In total, the farmer used 875ft worth of fencing.

In terms of x, the total fencing used is: 2x + x + x + x + 2x = 7x

This means 7x=875ft. Dividing both sides by 7, we find x=125ft

The dimensions of the rectangular enclosure in terms of x are "x and 2x". Subbing in 125ft for x, these dimensions become "125ft and 2(125ft)" or "125ft and 250ft".

(b)

Since we know the enclosure is 125ft long and 250ft wide, and since the area of a rectangle is its length times its width, the are of the enclosure is:

125ft * 250ft = 31250 ft²

Answer:

(a)

smaller value =125 ft

larger value = 250 ft

(b)

31250 ft?

Answer:

Step-by-step explanation:

22

According to the given information the lateral surface area of given cylinder is 725.34 in².

In mathematics, a cylindrical is indeed a three-dimensional solid that retains two parallel bases spaced apart by a curving surface. These bases frequently have a circular shape (like a circle), and also an axis links their respective centers.

A cylinder is a three-dimensional form having two parallel, round sides on either end, one side that curves, no vertices or edges.

As we know that the lateral surface area of cylinder (A) = 2πrh

Given

D = [tex]16\frac{1}{2}[/tex]in

h = 14in

r = D/2

 = 33/4 in

A = (2 × 3.14 × 33 × 14) / 4

   = 2901.36 /4

   = 725.34 in²

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The statements are (a) False, (b) True and (c) False

Right angles are angles whose measure is 90 degrees.

In the figure, AE, BF, DG, and HC intersect at point H, and FHG is a right angle.

(a) ∠AHB and ∠AHG are vertical angles.

Vertical angles are angles which are formed on the opposite sides of two intersecting lines.

∠AHB and ∠AHG are not formed on the opposite sides, but are adjacent to each other.

So the statement is false.

(b) ∠EHF and ∠DHE are adjacent angles.

∠EHF and ∠DHE are two angles which are adjacent to each other. So they are adjacent angles.

So the statement is true.

(c) The measure of ∠FHG is equal to the measure ∠DHF.

We know that DG is a straight line.

∠FHG and ∠DHF are linear pair of angles.

So, ∠FHG + ∠DHF = 180°

Given that ∠FHG is right angle.

90° + ∠DHF = 180°

∠DHF = 180° - 90°

∠DHF = 90°

So the statement is true.

Hence the statements (a), (b) and (c) are false, true and true respectively.

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Your question is incomplete. The complete question with the figure is given below.

The number of widgets that Justin can make in 36 minutes is given as follows:

y = 36k.

In which the constant k is the number of widgets that can be made per minute, and is obtained dividing a value of y by it's respective value of x from the table.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

The constant is obtained as follows:

k = y/x.

For a time of 36 minutes, we have that x = 36, hence the number of widgets is given as follows:

y = 36k.

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Answer:

The coordinates of the remaining vertices are (1, -1) and (3, 1).

Step-by-step explanation:

A square is a quadrilateral with with four sides of equal length. It has two sets of parallel sides and its interior angles are all right angles.  Therefore, each vertex shares its x-coordinate with one adjacent vertex, and its y-coordinate with the other adjacent vertex.

If AC with vertices A(1, 1) and C(3, -1) is the diagonal of a square, the coordinates of the remaining vertices will be:

The statement that are true are :

a. Z is an element {y,z}

b. {6,7,8 } is a subset of {1,2,3,4......}

c. 3 is an element of {2,3}

d. r is not an element of {s,t,u}

What is set?

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

The objects in a set are called the elements (or members ) of the set; the elements are said to belong to the set (or to be in the set), and the set is said to contain the elements.

The following statements are true about the set

a. Z is an element {y,z}

b. {6,7,8 } is a subset of {1,2,3,4......}

c. 3 is an element of {2,3}

d. r is not an element of {s,t,u}

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Answer:

3% increase

Step-by-step explanation: