a train started from Howrah to Allahabad and another train started from Allahabad for Howrah at the same time. The two trains reached their destinations in 9 hours

The equation in term of p that models the above experience is:
2p + 10 = 0.8p + 20.

Any statement that models or captures the factors of a problem where in an equal sign is present to equate two of the factors or expressions therein is called an equation.

Total cost of baking p pizzas with brick oven = A =  p(cost of one pizza) + cost of baking = p(2) + 10 (in dollars).

Total cost of  baking p pizzas with electric oven = B =  p(cost of one pizza) + cost of baking = p(0.8) + 20 (in dollars).

B = A - 1 (as using electric oven saves $1 per day, as given)

Thus, we get:

2p + 10 = 0.8p + 20

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Answer:

Step-by-step explanation:

....

Step-by-step explanation:

6 and 7 was already answered so I'll do 5 and 8.

5. The point the curve crosses the x axis is the x intercept, to find the x intercept of a rational function, we set y=0, and solve for x.

[tex]0 = \frac{x - 4}{x} [/tex]

Set the numerator equal to 0.

[tex]x - 4 = 0[/tex]

[tex]x = 4[/tex]

So the x intercept is (4,0).

Next, to find gradient, we take the derivative of the function.

[tex] \frac{x - 4}{x} [/tex]

We could use product rule, but for simplicity, serperate the function

[tex] \frac{x}{x} - \frac{4}{x} [/tex]

[tex]1 - \frac{4}{x} [/tex]

Next using exponents rules,

[tex]1 - 4 {x}^{ - 1} [/tex]

Now we take the derivative,

Derivative of a constant is zero.

Derivative of a power function,

[tex]n \times x {}^{n - 1} [/tex]

We move the exponent to the front, then we subtract the exponent by 1.

So, we get

[tex]4 {x}^{ - 2} [/tex]

Now, we plug in. 4,

[tex]4(4) {}^{ - 2} [/tex]

[tex]4 \times \frac{1}{16} = \frac{1}{4} [/tex]

The slope or gradient at the x intercept is 1/4

8. The derivative of ax^2+bx, with respect to x is

[tex]2ax + b[/tex]

When x=2, we have a gradient of 8.

[tex]2a(2) + b = 8[/tex]

[tex]4a + b = 8[/tex]

When x=-1, we have a gradient of -10.

[tex]2a( - 1) + b = - 10[/tex]

[tex] - 2a + b = - 10[/tex]

We have two system of equations,

[tex]4a + b = 8[/tex]

[tex] - 2a + b = - 10[/tex]

Let subtract the system to eliminate b.

[tex]6a = 18[/tex]

[tex]a = 3[/tex]

Plug 3 for a, back in to solve for b.

[tex]4(3) + b = 8[/tex]

[tex]12 + b = 8[/tex]

[tex]b = - 4[/tex]

So a is 3

b is -4

Answer:

The no. of student failed is 36.

Step-by-step explanation:

Given, the number of student enrolled= 216

Let us suppose number of student failed = x

Given,

no. of student passed is 5 times no. of student failed.

Then, no. of student passed = 5x

x +5x = 216

6x = 216

x = 216/6

x = 36

Thus, the no. of student failed is 36.

Answer:

[tex]-8x^2 - 4x + 29 \\[/tex]

Step-by-step explanation:

Second expression evaluates to:

[tex](5 + x -2x)^2 = (5 -x)^2 = (-x+5)^2 = x^2 + 2(-x)(5) +5^2 = x^2 -10x + 25[/tex]  (1)

For (1) We are using the rule [tex](a+b)^2 = a^2 +2ab + b^2\\\\[/tex]

Here [tex]a = -x, b = 5\\\\[/tex]

First expression evaluates to

[tex](3x)^2 -6x - 4 = 9x^2 -6x -4[/tex]    (2)

Subtract (2) from (1)

[tex]x^2 - 10x +25 - (9x^2 -6x -4) = x^2-9x^2 -10x - (-6x) +25 -(-4)\\\\= -8x^2 - 4x + 29 \\[/tex]

The function that is graphed is y = |x -2| + 3. The correct option is D. y = |x -2| + 3

From the question, we are to determine the function for the given graph

From the graph,

When x = 2, y = 3

The equation that satisfy this condition is

y = |x -2| + 3

NOTE: This function satisfies all the points on the graph

Hence, the function that is graphed is y = |x -2| + 3

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Answer: B

Step-by-step explanation:

The horizontal change is 6.

The vertical change is 5.

So, the distance is [tex]\sqrt{6^2 + 5^2}=\sqrt{61}[/tex]

By using the linear function which models the data in the given table, the cost of a textbook with 402 pages is equal to $47.4478.

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the linear function is given by:

y = 0.1057x + 4.9564

If x = 402, then y is given by:

y = 0.1057(402) + 4.9564

y = 42.4914 + 4.9564

y = $47.4478.

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The equivalent expression of -14 - 6 is -14 - (+6)

Equivalent expressions are expressions that have the same value when evaluated

The expression is given as:

-14 - 6

Put the terms of the expression in brackets

-14 - (6)

Rewrite 6 as +6

-14 - (+6)

Hence, the equivalent expression of -14 - 6 is -14 - (+6)

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The interquartile range of 48, 26, 31, 50, 38, 40, 42, 34, 44, 36, is: D. 10.

The interquartile range of a data distribution is determined as: upper quartile (Q3) - lower quartile (Q1).

The upper quartile of a data distribution is the center of the second half of a data distribution while the lower quartile is the center of the first half of a data distribution.

Given the data, 48, 26, 31, 50, 38, 40, 42, 34, 44, 36:

Order the data set as, 26, 31, 34, 36, 38, 40, 42, 44, 48, 50

The first half of the data is: 26, 31, 34, 36, 38.

The center is 34.

Lower quartile (Q1) = 34.

The second half of the data is: 40, 42, 44, 48, 50. The center is 44.

Upper quartile (Q3) = 44.

Interquartile range = 44 - 34

Interquartile range = 10

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The Two sets, A and B, are said to be disjoint sets if A n B=ϕ

The Two sets, A and B, are said to be disjoint sets if A n B=ϕ

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Step-by-step explanation:

that question is fundamentally wrong.

"appropriate" completely depends on the situation and circumstances.

if we are dealing with a weight that a human can feel, lift and distinguish from other weights without any special tool, then we are usually using kg. because then we humans can "connect" with the case, and deal with every day numbers.

if we are dealing with tiny little quantities like dosages of substances in a pill or other medication, then milligram is more than "appropriate".

because then, as humans, we are still dealing with numbers we can understand. like tens or hundreds.

if we kept kg in such situations, we would have to deal with numbers like 0.000008 kg vs. 0.000021 kg, where we could not see the magnitude of difference right away.

Answer:

130

Step-by-step explanation:

let the inside value be,x

x+30°+20°=180°(Being sum of interior angle of triangle)

or,x+50°=180°

or,x=180°-50°

or,x=130°

Now,

let the exterior angle be,a

a=x(VOA)

a=130°

Therefore the value of a is 130°.

Answer:

Step-by-step explanation:

The probability and the parameter

Step-by-step explanation:

The formula for probability  in a binomial distribution is where p is the probability of success (ticket with popcorn coupon), n is the number of trials (tickets bought) and x the number of successes desired. In this case p=0.629 (probability of buying a movie ticket with coupon), n=29,  and x=17,18,19, ...29.

The probability of more than 16 is equal to the sum of the probability of x=17, 17,18,19, ...29.

Answer + Step-by-step explanation:

1) The probability of getting 2 white balls is equal to:

[tex]=\frac{8}{20} \times \frac{7}{19}\\\\= 0.147368421053[/tex]

2) the probability of getting 2 white balls is equal to:

[tex]=C^{2}_{5}\times (\frac{8}{20} \times \frac{7}{19}) \times (\frac{12}{18} \times \frac{11}{17} \times \frac{10}{16})\\=0.397316821465[/tex]

3) The probability of getting at least 72 white balls is:

[tex]=C^{72}_{150}\times \left( \frac{8}{20} \right)^{72} \times \left( \frac{7}{20} \right)^{78} +C^{73}_{150}\times \left( \frac{8}{20} \right)^{73} \times \left( \frac{7}{20} \right)^{77} + \cdots +C^{149}_{150}\times \left( \frac{8}{20} \right)^{149} \times \left( \frac{7}{20} \right)^{1} +\left( \frac{8}{20} \right)^{150}[/tex]

[tex]=\sum^{150}_{k=72} [C^{k}_{150}\times \left( \frac{8}{15} \right)^{k} \times \left( \frac{7}{15} \right)^{150-k}][/tex]

First of all, we would determine the total number of balls in the urn as follows:

Total number of balls = 8 + 7 + 5

Total number of balls = 20 balls.

Next, we would determine the probability of getting two (2) white balls without replacement:

P(2 white balls) = 8/20 × 7/19

P(2 white balls) = 2/5 × 7/19

P(2 white balls) = 0.1474.

When 5 balls are selected without replacement, the probability of getting two (2) white balls would be calculated as follows:

P = [⁵C₂ × (8/20 × 7/19) × (12/18 × 11/17 × 10/16)]

P = [5!/(2! × (5 - 2)!) × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]

P = [5!/(2! × 3!) × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]

P = [20/2 × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]

P = [10 × (2/5 × 7/19) × (2/3 × 11/17 × 5/4)]

P = 0.3456.

When 150 balls are randomly selected with replacement, the probability of getting at least seventy two (72) white balls would be calculated by applying binomial probability equation. Mathematically, binomial probability is given by this equation:

[tex]P =\; ^nC_r (p)^r (q)^{(n-r)}[/tex]

Substituting the given parameters into the formula, we have;

P = [¹⁵⁰C₇₂ × (8/20)⁷² × (8/20)⁽¹⁵⁰ ⁻ ⁷²⁾]

P = [150!/(72! × (150 - 72)!) × (8/20)⁷² × (8/20)⁽¹⁵⁰ ⁻ ⁷²⁾]

P = [150!/(72! × (78)!) × (4/5)⁷² × (4/5)⁽⁷⁸⁾]

P = 0.7948.

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Answer:

3.36 cm

Step-by-step explanation:

24 - 5 1/2 = 18.5

To find the distance on the map, we can set up a proportion:

1 cm / 5.5 miles = x cm / 18.5 miles

5.5 times 37/11 equals to 18.5; 1 times 37/11 is approximately equals to 3.36 cm (rounded to the nearest hundredths).

Answer:

55.4068881439

Step-by-step explanation:

Lets first find the feet they walk per day, multiply the steps by the feet/step:

[tex]10,388*2.5=25970[/tex]

Now lets find the feet/week by multiplying that value by 7:

[tex]25970*7=181790[/tex]

Now lets convert the feet to km:

[tex]181790/3281=55.4068881439[/tex]

Resulting in approximately 55 kilometers

Answer:

IT HAS A SLOPE OF -2

Y INTERCEPT IS 0,0

Step-by-step explanation:

Answer:

Step-by-step explanation:

The perimeter formula and the given relation between length and width can be used to write and solve an equation for the field dimensions.

Let w represent the width of the field. Then (3w-120) is the length of the field, and its perimeter is ...

  P = 2(L +W)

  1040 = 2((3w-120) +w)

Dividing by 2 and simplifying, we have ...

  520 = 4w -120

  130 = w -30 . . . . . . divide by 4

  160 = w . . . . . . . . . add 30

  3w-120 = 3(160) -120 = 360 . . . the field's length

The dimensions of the field are 160 feet long by 360 feet wide.

The equation of the parabola with the given vertex and directrix in vertex form is y = (1/16)( x + 5 )² - 9.

Hence, option C is the correct answer.

Given the data in the question;

To find the equation, we use the equation of the parabola that opens up or down since the directrix ( y = -13 ) is vertical.

The equation is expressed as;

( x - h )² = 4p( y - k )

First, we find the distance from the focus to the vertex.

|p| is the distance rom the focus to the vertex and from the vertex to the directrix.

p = -9 + 13

p = 4

We substitute the values into the equation;

( x - h )² = 4p( y - k )

( x - (-5) )² = 4(4)( y - (-9) )

( x + 5 )² = 16( y + 9 )

Multiply both side by 1/16

(1/16)( x + 5 )² =  y + 9

Make y the subject of the formula

(1/16)( x + 5 )² - 9 =  y

y = (1/16)( x + 5 )² - 9

The equation of the parabola with the given vertex and directrix in vertex form is y = (1/16)( x + 5 )² - 9.

Hence, option C is the correct answer.

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The direct variation function is y = 0.3x

The direct variation from y to x is represented as:

y = kx

When y = 1.5 and x = 5, we have

1.5 = 5k

Divide by 5

k = 0.3

Substitute k = 0.3 in y = kx

y = 0.3x

Hence, the direct variation function is y = 0.3x

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Answer:

c

Step-by-step explanation:

Foreshortening is a technique used in perspective to create the illusion of an object receding strongly into the distance or background.

Foreshortening is a technique used to create the illusion of depth and three-dimensionality in a two-dimensional image.

Option B is the correct answer.

Foreshortening is a technique used in art to create the illusion of depth and three-dimensionality in a two-dimensional image.

It involves distorting the shapes of objects or figures to make them appear closer or farther away from the viewer, often by shortening the lengths of their features or changing the angle from which they are viewed.

Foreshortening is often used in drawing, painting, and other visual arts to create a sense of perspective and realism.

We have,

Foreshortening is a technique used to create the illusion of depth and three-dimensionality in a two-dimensional image.

It involves distorting the shapes of objects and figures to make them appear closer or farther away from the viewer, often by shortening the lengths of their features or changing the angle from which they are viewed.

Foreshortening can be used in drawing, painting, and other visual arts to create a sense of perspective and realism.

Thus,

Foreshortening is a technique used to create the illusion of depth and three-dimensionality in a two-dimensional image.

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Answer:

LHS=2(sin

6

θ+cos

6

θ)−3(sin

4

θ+cos

4

θ)+1

=2{(sin

2

θ+cos

2

θ)

3

−3sin

2

θcos

2

θ(sin

2

θ+cos

2

θ)}−3(sin

2

θ+cos

2

θ)

2

−2(sin

2

θcos

2

θ)}+1

We know, [sin²x+cos²x=1]

=2{1−3sin

2

θcos

2

θ}−3{1−2sin

2

θcos

2

θ}+1

=2−6sin

2

θcos

2

θ−3+6sin

2

θcos

2

θ+1

=0

=RHS

Step-by-step explanation:

The theoretical probability of randomly getting a black counter is P = 2/5.

In this case, we have 8 black counters and 12 white counters, so there is a total of 20 counters.

We assume that all the counters have the same probability of being randomly selected, then the probability of randomly selecting a black counter is just given by the quotient between the number of black counters and the total number of counters.

There are 8 black counters and 20 in total, then the probability is given by:

P = 8/20

Now we can simplify that fraction to get:

P = 2/5

The theoretical probability of randomly getting a black counter is P = 2/5.

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1. Observe that

[tex]\nabla \dfrac{x^2y^2w^2}2 = \langle xy^2w^2, x^2yw^2, x^2y^2w\rangle[/tex]

is a gradient field, so the gradient theorem holds and the integral in question is indeed path-independent. Its value is

[tex]\dfrac{x^2y^2w^2}2\bigg|_{x=1,y=3,w=2}^{x=2,y=4,w=1} = 32 - 18 = \boxed{14}[/tex]

2. [tex]dz[/tex] is an exact differential if we can find a scalar function [tex]z=f(x,y)[/tex] such that

[tex]\dfrac{\partial f}{\partial x} = 3x^2 (x^2+y^2) = 3x^4 + 3x^2y^2[/tex]

[tex]\dfrac{\partial f}{\partial y} = 2y(x^3+y) = 2x^3y + 2y^2[/tex]

Integrating both sides of the first equation with respect to [tex]x[/tex] yields

[tex]f(x,y) = \dfrac35 x^5 + x^3 y^2 + g(y)[/tex]

Differentiating with respect to [tex]y[/tex] gives

[tex]\dfrac{\partial f}{\partial y} = 2x^3y + \dfrac{dg}{dy} = 2x^3y + 2y^2 \\\\ \implies \dfrac{dg}{dy} = 2y^2 \implies g(y) = \dfrac23y^3 + C[/tex]

and we ultimately find

[tex]f(x,y) = \boxed{z = \dfrac35 x^5 + x^3y^2 + \dfrac23 y^3 + C}[/tex]

(We can also use the same method here to determine the scalar function in part (1).)

Then the integral is path-independent, and its value is

[tex]f(2,1) - f(1,2) = \dfrac{418}{15} - \dfrac{149}{15} = \boxed{\dfrac{269}{15}}[/tex]

The margin of error is 1.9%. and the interval that likely contains the true percent of all people who work out 3 or more days a week is: (71.1%, 74.9%)

Margin of error is the critical value (t score or z score) multiplied by the standard error (standard deviation of the sample). Thus;

ME = Critical value × S.E

Since n > 30, we can use the z-score as the critical value.

Assuming 95% confidence level, then z = 1.96

The standard error for a proportion is given by the formula:

s = √(p (1 − p) / n)

We are given;

p = 0.73

n = 2035:

Thus;

s = √(0.73 (1 − 0.73) / 2035)

s = 0.0098

Thus, the margin of error is:

ME = 1.96 × 0.0098

ME = 0.019

The margin of error is 1.9%.  

The interval that likely contains the true percent of all people who work out 3 or more days a week is:

73% ± 1.9% = (71.1%, 74.9%)

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Answer:

Volume=96.7

Step-by-step explanation:

V=πr^2h=

V=π·1.8^2·9.5=

96.69822

Answer:

the height would be around 19.2 cm

Step-by-step explanation:

hyp length = 63

base = 60

length = sqrt(63^2 - 60^2) = sqrt(369)