A train goes from springfield, MA, to boston at 40 mph. On the way back, it returns with a speed 80 mph. If it takes an hour less time to return, what is it's average speed?

Critical values are basically cut-off values that indicate regions where the test statistic is unlikely to lie. The required critical value is 1.31.

Critical values are basically cut-off values that indicate regions where the test statistic is unlikely to lie; for example, if the null hypothesis is true, the critical value is surpassed with probability alpha.

The value of α can be written as,

α = 1 - 0.81 = 0.19

[tex]z_{\frac{\alpha}{2}} = \dfrac{0.19}{2}= 0.095[/tex]

Now, using the z-table the value of z will be,

z = 1.31

Hence, the required critical value is 1.31.

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Factorizing the denominator gives

[tex]\dfrac{x^4}{(x^3+x)(x^2-x+7)} = \dfrac{x^4}{x(x^2+1)(x^2-x+7)} = \dfrac{x^3}{(x^2+1)(x^2-x+7)}[/tex]

Then the partial fraction decomposition would take the form

[tex]\dfrac{x^4}{(x^3+x)(x^2-x+7)} = \dfrac{a_0x + b_0}{x^2+1} + \dfrac{a_1x + b_1}{x^2-x+7}[/tex]

Answer:

No, it does not represent a function

Step-by-step explanation:

A function can be described as a set of points where each x coordinate has 1 corresponding Y coordinate

1 has multiple different Y coordinates

2 has multiple different Y coordinates

-4 has multiple different Y coordinates

Answer:

Only the second one

Step-by-step explanation:

All of the others have multiple values for 'x'

  a function can only have one value for each value of x

     Example: the first one      when x = 2   it has two 'y' values   3 and 9

The perimeter of the actual pool will be option C. 1100 ft.

It's the sum of the length of the sides used to make the given figure.

A scale drawing of a new pool is shown. All the corners are at right angles.

The lengths are 6 in, 2 in, 5 in and 3 in.

Perimeter = 6 + 2 + 5 + 3 + 2 + 4

                 = 22 in

We have given a scale;

1/2 in = 25 ft

So, 1 in = 50 ft

26 in will be

22 x  50 = 1100 ft

Hence, the perimeter of the actual pool will be option C. 1100 ft.

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This transformation requires us to shift 1 unit left and 4 units down.

Step-by-step explanation:

the slope of a line is the factor of x, when the equating looks like

y = ...

so,

x - 3y = 3

x = 3y + 3

3y = x - 3

y = 1/3 x - 1

so, the original slope is 1/3.

a parallel line has the same slope.

having a specific point we can use the point-slope form as equation :

y - y1 = m(x - x1)

with m being the slope, and (x1, y1) being a point on the line.

y - -3 = 1/3(x - 2)

y + 3 = 1/3(x - 2)

simplified that is

y + 3 = 1/3 x - 2/3

y = 1/3 x - 2/3 - 3 = 1/3 x - 2/3 - 9/3 = 1/3 x - 11/3 =

= 1/3 × (x - 11)

Answer:

[tex]y=\frac{1}{3}x - \frac{11}{3}[/tex]

Step-by-step explanation:

We are given the line x-3y=3.

We want to write the equation of the line that is parallel to this line, and that passes through (2, -3).

Parallel lines have the same slope.

Therefore, let's find the slope of x-3y=3.

The line is currently written in standard form, which is ax+by=c, where a, b, and c are free integer coefficients.

In order to find the slope of this line, we can convert it into slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.

To do that, we need to isolate y on one side; this is the same as solving the equation for y.

x - 3y = 3

Start by subtracting x from both sides

-3y = -x + 3

Now divide both sides by -3

[tex]y = \frac{1}{3} x - 1[/tex]

The slope of the line is 1/3, as 1/3 is the coefficient in front of x.

It is also the slope of our new line.

Since the question doesn't specify which format for the equation of the line, we can use any form. However, let's put the equation of the new line into slope-intercept form.

So, substitute 1/3 as m in y=mx+b.

[tex]y = \frac{1}{3} x + b[/tex]

Now we need to find b.

As the equation passes through the point (2, -3), we can use its values to help solve for b.

Substitute 2 as x and -3 as y.

[tex]-3 = \frac{1}{3} (2) + b[/tex]

Multiply.

[tex]-3 = \frac{2}{3} + b[/tex]

Subtract 2/3 from both sides (we can write this as an improper fraction).

[tex]-\frac{11}{3} = b[/tex]

Substitute -11/3 as b in the equation.

[tex]y=\frac{1}{3}x - \frac{11}{3}[/tex]

That is the answer for the 3 questions

Answer:

out of 700 full marks dolma obtained 525 marks in an examination express her marks in percent

The answers include the following:

This is a form of risk management which protects individuals from any form of loss or damage.

Life insurance has different types which are appropriately mentioned and matched above.

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Option (A) one side of a triangle is the object that best describes the term line segment is the correct answer.

What is a line segment?

A line segment is a part of line that is bounded by two distinct end-points. A line segment has a fixed length. Figures such as a triangle, polygon, hexagon, square are made of different numbers of line segments.

For the given situation,

A line segment is a portion or piece of a line that allows you to build polygons, determine slopes, and make calculations.

From the definition of line segment we know that the object that best describes the term line segment is one side of a triangle.

Hence we can conclude that option (A) one side of a triangle is the object that best describes the term line segment is the correct answer.

The fraction of the colored part is 10/12 or 5/6. None of the option is correct

Fractions are written as a ratio of two integers. From the given question;

3 square divided into4 equal parts will have a total of 12 parts. If Kelly colors 10 parts, the fraction of the colored part will be:

Fraction. = 10/12

Fraction = 5/6

Hence the fraction of the colored part is 10/12 or 5/6

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The amount of money left for Mr Ade after deducting his house payment, children allowance and food is #110

Amount given to each child = #2

Number of children = 5

= #10

Balance left = 460 - (50 + 10 + 290)

= 460 - (350)

= #110

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Similar triangles can be used to explain the slope through the right angle.

It should be noted that a triangle refers to a shape that has three sides and angles.

In this case, similar triangles can be used to explain the slope through the right angle. The slope of the hypotenuse is what we are concerned about.

The legs of the triangle will be the horizontal change and the vertical change of the endpoints.

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There are 14,515,200 ways to arrange the people around the table

The given parameters are:

People = 13

Thénardiers = 2 actors

Cosette and Marius = 2 actors

If the married actors must seat together, then the actors must be grouped as 1.

The 2 actors can be arranged in 2! ways each

Now, there are 9 individuals remaining

The 9 people can be arranged in 9! ways

So, the number of ways is

Ways= 2! * 2!* 9!

Evaluate

Ways =14,515,200

Hence, there are 14,515,200 ways to arrange the people around the table

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Answer:

C

Step-by-step explanation:

To be a factor of 16 they need to be numbers that divide into it without remainders.

Answer:

Step-by-step explanation:

its C

The standard error for the distribution of sampling proportions will be 0.0686.

In mathematics, the difference between a data set and the populace's true average is known as primary data deviation from the mean.

According to the National Postsecondary Student Aid Study conducted by the U.S.

Department of Education in 2008, 62% of graduates from public universities had student loans.

We randomly select 50 students at a time.

Then the standard error for the distribution of sampling proportions will be

[tex]\rm Standard\ error = \sqrt{\dfrac{p(1-p)}{n}}\\\\Standard\ error = \sqrt{\dfrac{0.62(1-0.62)}{50}}\\\\Standard\ error = 0.0686[/tex]

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Answer:

You're correct

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]F(2)=\frac{1}[3} \cdot 4^{2}=\frac{16}{3}[/tex]

The product (-3) * (1, 4) is (-3, -12)

The expression is given as:

(-3) * (1, 4)

Rewrite the expression as

(-3 * 1, -3 * 4)

Evaluate the product

(-3, -12)

Hence, the product (-3) * (1, 4) is (-3, -12)

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Flowers/week is the unit of measurement for the composite function s(W(h)).

Given that the function w(h) indicates the number of hours per week that Matthew spends picking flowers and the function s(t) approximates how many flowers he collects every hour.

The process of combining two or more functions into one function is known as the composition of functions. The output of the function enclosed in parenthesis becomes the input of the function outside of them in a composition of functions.

Hours of flowers is the unit of function s(t).

Additionally, consider that W(h) denotes the number of hours per week that Matthew spends gathering flowers.

W(h) = hours/week as a unit.

The unit of the composite function s(W(h)) will be = (Flowershours)(hoursweek) = Flowersweek.

Hence, the units of measurement for the composite function s(W(h))where the function s(t) approximates how many flowers Matthew picks per hour and the function w(h) represents how hours per week Matthew spends picking flowers is flowers/week.

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Answer:

The required cost is $10,612.8

Step-by-step explanation:

Find the value at t = 3.6:

2948t, t=3,6

Substitute t=3,6

Multiply 2948x3,6

Solution = 10612,8

Answer: 26 cards

Step-by-step explanation: Just divide 52 by 2 and you get 26 cards :)

Answer: 745.50

Step-by-step explanation:

49445-41990=7455

7455/10=745.50

The trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ

Since (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]

Using the identity a² - b² = (a + b)(a - b), we have

(cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]

= (cos²θ - sin²θ)(cos²θ + sin²θ)/[(1 - tan²θ)(1 + tan²θ)] =

= (cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] (since (cos²θ + sin²θ) = 1 and 1 + tan²θ = sec²θ)

Also, Using the identity a² - b² = (a + b)(a - b), we have

(cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] = (cosθ - sinθ)(cosθ + sinθ)/[(1 - tanθ)(1 + tanθ)sec²θ]

= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)/cosθ × (cosθ + sinθ)/cosθ × sec²θ]

= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)(cosθ + sinθ)/cos²θ × 1/cos²θ]

= (cosθ - sinθ)(cosθ + sinθ)cos⁴θ/[(cosθ - sinθ)(cosθ + sinθ)]

= 1 × cos⁴θ

= cos⁴θ

So, the trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ

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The iterative rule for each sequence in the table will be to use the slope-intercept form of the equation of a line y=mx+b.

In this situation, x is the week, and y is the amount paid. Basically, you need to find the slope, represented by m, which is the amount the amount paid increases by each week, and the y-intercept, b, which is the "amount paid" at week 0.

The x-coordinate is the week, and the y coordinate is the amount paid. Because the weeks are incrementing by 1, x2-x1=1.

After that, to complete the rule, you need to find the y-intercept. If the amount paid is 200 on week 1, and the amount paid increases by 50 each week.

Another way to think about it is by plugging your points into the incomplete rule. Let b represent the y-intercept. Plug in the values for week 1 and solve for b.

The calculations to convince your friend that both your rules work are:

m=(y2-y1)/(x2-x1)

(x1,y1)=(1,200)

(x2,y2)=(2,250)

m=(250-200)/(2-1)

=50/1 =50

y=50x+b

200=50(1)+b

200=50+b

b=200-50

b=150

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Answer: (8,3)

Step-by-step explanation:

The distance from (2,3) to (5,3) is 3. The only other point that is 3 units away from (5,3) where y=3 is (8,3).

Answer:

Your answer should be D. $48,856.11

Step-by-step explanation:

This formula is for Compound Continuously.

[tex]A=P*e^{rt}[/tex]

P = 40,000

e = 2.71...

r = 2.5% = 0.025

t = 8 years

Plug in our variables and solve for the money of the account within 8 years.

A = 40,000*e^(0.025*8)

A = 40,000*e^(0.2)

A = 48,856.11033

A = $48,856.11

Answer:

a)

density = mass/volume

density = 320/128

density = 2.5 g/cm3

b)

mass = density x volume

mass = 65 x 26

mass = 1690g

Answer:

a) d = 2.5g/cm3

b) m = 1690g

Step-by-step explanation:

density equals mass between volume

a) [tex]d=320g/128cm^{3} =2.5g/cm^{3}[/tex]

mass equals density by volumen

b)[tex]m=(26g/cm^{3} )(65cm^{3} )=1690g[/tex]

Hope this helps

The true statement about a ladder is; the ladder has parallel line segments and perpendicular line segments.

Parallel lines are lines that never meet on the same plane which have equal distance apart from each other.

They are lines that intersect each other to form a right angle.

Therefore, the ladder has parallel line segments and perpendicular line segments.

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The graph we need is [tex]y=-3^x[/tex], which is shown in the attached image.