Alok started a business investing Rs 90, 000. After three
months Prabir joined him with capital of Rs 1,20000
If at the end of 2 years, the total profit made
by them was
Rs 96,000 what will the difference
between Alok and Prabir's share in it?

The irrational number on set B is given by: [tex]\sqrt{5}[/tex]

Irrational numbers are numbers that cannot be represented by fractions. The two most common examples are:

In the set B given in this problem, the only number that is irrational is [tex]\sqrt{5}[/tex], as it is a non-exact root.

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The answers to these questions are:

a. In the question we have the existence of the mean, the mode and the median hence the answer to this question is none.

b. if the measurement 14 is replaced by 2, the data that it is going to have the most effect on is going to be the mean. It would reduce the mean.

c. If the largest measurement is removed, it is going to have the most effects on the mean and the median.

d. If the data is skewed then the mean of the data set is going to be greater.

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Step-by-step explanation:

since the y- axis stands for velocity (and the x-axus for time), speeding up means when the curve goes up (increasing velocity), and slowing down means when the curve goes down (decreasing velocity), all when reading the graph from left to right (small time values to larger time values).

(a)

speeding up

t in [0, 1)

or

0 <= t < 1

I would exclude t = 1, because at that point the slope is 0, there is no speeding up there.

slowing down

t in (1, 3)

or

1 < t < 3

the same argumentation for excluding 1 and 3, because there the slope of the curve turns 0 (just the turning point from one tendency to the other), and there is no speeding up or slowing down at these points.

(b)

speeding up

t in (1. 2)

or

1 < t < 2

slowing down

t in [0, 1) or in (2, infinity)

or

0 <= t < 1 || 2< t < infinity

we could use 3 instead of infinity, as this seems to be the last point of the drawn curve, but normally this kind of drawing tells me "infinity".

Answer:

instruments are very important to the direction of the personal information and concerns about the direction

Answer:

6x⁴ - 2x² +3

Step-by-step explanation:

[tex]\frac{12x^6-4x^4+6x^2}{2x^2}=6x^4 - 2x^2 + 3[/tex]

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 answer choice which correctly draws a comparison between the end behaviours of the functions is; Choice C; They have the same end behavior as x approaches -∞ and same end behavior as x approaches ∞.

As given in the task content; the graph of the exponential function passes through (-4, 9), (0, 1), (1, 0), and (5, -2).

It therefore follows that as; x reduces (approaches -∞), the y value increases.

And, as x -increases (approaches +∞), the y-value decreases.

For the table, the values can be written as coordinates as follows; (-1,2), (0,4), (1,6), (2, 0), (3,-2).

Consequently, as x reduces (approaches -∞), the y- values decrease.

And, as x increases (approaches +∞), the y-values decrease.

Ultimately, the two functions in discuss can be concluded to have; Choice C.

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Step-by-step explanation:

x = a + 7

y = b-a

To prove

x + y = b + 7.

=a+7+b-a

=a-a+7+b

=0 + 7+b

= b+7

Proved ✅

The glass will contain 89.086 milliliters of juice with 7 ice cubes, using the equation of the line of best fit, y =  -29.202x + 293.5.

In the question, we are informed that the equation of the line of best fit, for the, scatter plot with x representing the number of ice cubes and y representing the milliliters of juice is given as y =  -29.202x + 293.5.

We are asked to tell how many milliliters of juice will be in a glass with 7 ice cubes based on the line of best fit.

To find the milliliters of juice in the glass with 7 ice cubes, we substitute x = 7, in the equation of the line of best fit, to get a value of y, representing the milliliters of juice in the glass.

Thus,

y =  -29.202x + 293.5,

or, y =  -29.202(7) + 293.5 {Substituting x = 7},

or, y = -204.414 + 293.5,

or, y = 89.086.

Thus, the glass will contain 89.086 milliliters of juice with 7 ice cubes, using the equation of the line of best fit, y =  -29.202x + 293.5.

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Answer:

Two Equal Angles = 45°

Third Angle = 90°

Step-by-step explanation:

Given information

Two equal angles of an isosceles triangle are half the third angle

Set variables

Let x be the angle of the equal angles of the isosceles triangle

Let 2x be the angle of the third angle

Set equations

x + x + 2x = 180 (Triangle angle sum theorem)

Combine like terms

2x + 2x = 180

4x = 180

Divide 4 on both sides

4x / 4 = 180 / 4

[tex]\Large\boxed{x=45^\circ}[/tex]

Substitute the x value into the expression to find the third angle

Third angle = 2x

                   = 2 (45)

                   = [tex]\Large\boxed{90^\circ}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation:

We can determine whether the change represents exponential growth or decay by seeing whether the number being raised to x is between 0 and 1, or greater than 1.

In the equation [tex]y = 540(1.04)^x[/tex], y will increase every time that x increases, as we are multiplying by a number greater than 1 every time.

Hence, this exponential function represents exponential growth.

The percentage rate of increase for this function would be how much the y-value increases each time. Since we are multiplying by 1.04, each time the new value is 104% the original y-value. Hence, the percentage increase is 4%.

Using the law of cosines and sines, the measure of angle B is: 38.4°.

Law of cosines is: c = √[a² + b² ﹣ 2ab(cos C)]

Law of sines is: sin A/a = sin B/b = sin C/c

Use the law of cosines to find c:

c = √[12² + 18² ﹣ 2(12)(18)(cos 117)]

c ≈ 25.8

Use the law of sines to find angle B:

sin B/b = sin C/c

sin B/18 = sin 117/25.8

sin B = (sin 117 × 18)/25.8

sin B = 0.6216

B = sin^(-1)(0.6216)

B = 38.4°

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[tex] \frac{ \sqrt{x + 8} - \sqrt{x} }{8} \times \frac{ \sqrt{x + 8} + \sqrt{x} }{ \sqrt{x + 8} + \sqrt{x} } \\[/tex]

[tex] \frac{( \sqrt{x + 8} ) {}^{2} - ( \sqrt{x}) {}^{2} }{8( \sqrt{x + 8} + \sqrt{x} ) } \\ [/tex]

[tex] \frac{( \sqrt{x + 8} ) {}^{2} - ( \sqrt{x}) {}^{2} }{8( \sqrt{x + 8} + \sqrt{x} ) } \\ \frac{x + 8 - x}{8 \sqrt{x + 8} + 8 \sqrt{x} } = \frac{8}{8 \sqrt{x + 8} + 8 \sqrt{x} } [/tex]

Answer:

y=

[tex] - \frac{1}{4} x + 6[/tex]

Step-by-step explanation:

Standard form of equation of line: y=mx+c

where m = slope

c = y-intercept

Since we know that slope for all equations , we can find the one with the least steep graph.

To find which one is the least steep graph, we find the lowest value in the slope, m. (Ignoring the +/- sign)

In this case, y=

[tex] - \frac{1}{4} x + 6[/tex]

will give the least steep graph as it has the lowest slope value.

Answer:

[tex]\huge\boxed{\sf v = 45 \ km/hr}[/tex]

Step-by-step explanation:

Distance = S = 162 km

Time = t = 3hr 36/60 min = 3 hr 0.6 hr = 3.6 hr

Average Speed = v = ?

[tex]\displaystyle v = \frac{S}{t}[/tex]

Put the givens in the above formula

[tex]\displaystyle v = \frac{162}{3.6} \\\\v = 45 \ km/hr\\\\\rule[225]{225}{2}[/tex]

The total cost of the materials calculated by the worker on the notebook is $325.52

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

The total cost of materials = 7(43.75) + 2(4.69) + 9.89 = $325.52

The total cost of the materials calculated by the worker on the notebook is $325.52

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The most convenient way to capture [tex]D[/tex] is with the parameterization

[tex]D = \left\{(x,y) \mid -1 \le y \le 3 \text{ and } -\dfrac{y+1}2 \le x \le y+1\right\}[/tex]

so we only need one iterated integral.

[tex]\displaystyle \iint_D e^{x-y} \, dA = \int_{-1}^3 \int_{-(y+1)/2}^{y+1} e^{x-y} \, dx \, dy[/tex]

Compute the integral with respect to [tex]x[/tex].

[tex]\displaystyle \int_{-(y+1)/2}^{y+1} e^{x-y} \, dx = e^{x-y} \bigg|_{x=-(y+1)/2}^{x=y+1} = e^{(y+1)-y} - e^{-(y+1)/2-y} = e - e^{-(3y+1)/2}[/tex]

Compute the remaining integral.

[tex]\displaystyle \int_{-1}^3 \left(e - e^{-(3y+1)/2}\right) \, dy = \left(ey + \frac23 e^{-(3y+1)/2}\right)\bigg|_{y=-1}^{y=3} \\\\ ~~~~~~~~ = \left(3e + \frac23 e^{-(9+1)/2}\right) - \left(-e + \frac23 e^{-(-3+1)/2}\right) \\\\ ~~~~~~~~ = \boxed{\frac{10e}3 + \frac2{3e^5}}[/tex]

If we had chosen the opposite order of variables, we would have used

[tex]D = \left\{(x,y) \mid -2 \le x \le 4 \text{ and } \max\left(-2x-1,x-1\right)\le y\le3\right\}[/tex]

where

[tex]\max(-2x-1, x-1) = \begin{cases} -2x-1 & \text{when } x<0 \\ x-1 & \text{when } x\ge0\end{cases}[/tex]

so we would have needed two iterated integrals,

[tex]\displaystyle \iint_D e^{x-y} \, dA = \int_{-2}^0 \int_{-2x-1}^3 e^{x-y} \, dy \, dx + \int_0^4 \int_{x-1}^3 e^{x-y} \, dy \, dx[/tex]

Answer:

-13

Step-by-step explanation:

First, we will find the value of j(2) first.

j(2) = -2(2) = -4

next, we will solve h[j(2)].

h[j(2)] = h(-4) = 3(-4) - 1 = -12 - 1 = -13

Answer: Madison can travel 2.2 miles less than Anthony on one gallon of gas.

Step-by-step explanation:

The equation y = 39.1[tex]x[/tex] represents the number of miles, [tex]y[/tex], that madison can drive her car for every x gallons of gas.

Question: Madison can travel _ miles _ than Anthony on one gallon of gas.

Lets find how much Madison travels on 1 gallon of gas.

39.1(1) = 39.1

Therefore, Madison travels 39.1 miles on one gallon of gas.

Now lets solve for Anthony

Anthony travels 380.7 miles on 9 gallons of gas.

Therefore we can set up the equation:

9x = 380.7 to show that 9 gallons equates to 380.7 miles

to solve divide 9 from both sides

[tex]\frac{9x}{9} =\frac{380.7}{9}[/tex]

x = 41.3

So, Anthony travels 41.3 miles on one gallon of gas

Now find whether Madison travels more or less than Anthony on one gallon.

39.1 - 41.3 = -2.2

This means that Anthony can travel 2.2 miles more than Madison.

For your answer, this means that:

Madison can travel 2.2 miles less than Anthony on one gallon of gas

Hope this helped and have a nice day :)

Answer:

113

Step-by-step explanation:

first we need to divide 1000 by 8 to get 125.

Our prime number has to be less than 125.

The largest prime number less than 125 is 113.

The dimensions based on the area given are 15cm by 20cm.

From the information given about the rectangle, the area is given as 300cm² and the margins are given as 1.5 and 2.

Therefore, the dimensions will be:

(1.5 × x) × (2 × x) = 300

1.5x × 2x = 300

3x² = 300

x² = 300/3

x² = 100

x = 10

Therefore the dimensions will be:

= 1.5x = 1.5 × 10 = 15

= 2x = 2 × 10 = 20

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We minimize the total area of the sheet

[tex]S = xy[/tex]

constrained by

[tex](x-4)(y-3) = 300[/tex]

Solve the constraint equation for [tex]y[/tex].

[tex](x-4)(y-3) = 300 \implies y-3 = \dfrac{300}{x-4} \implies y = 3 + \dfrac{300}{x-4} = \dfrac{3x+288}{x-4}[/tex]

Substitute this into [tex]S[/tex] and find the critical points.

[tex]S = \dfrac{3x^2+288x}{x-4} = 3x + 300 + \dfrac{1200}{x-4}[/tex]

[tex]\dfrac{dS}{dx} = 3 - \dfrac{1200}{(x-4)^2} = 0[/tex]

[tex]\implies \dfrac{1200}{(x-4)^2} = 3[/tex]

[tex]\implies (x-4)^2 = 400[/tex]

[tex]\implies x-4 = \pm20[/tex]

[tex]\implies x=-16 \text{ or } x = 24[/tex]

Of course [tex]x[/tex] can't be negative, so the page dimensions that minimize [tex]S[/tex] are [tex]x=24[/tex] and [tex]y=18[/tex].

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

On looking for a pattern in the given data set, the quadratic model best describes the data.

2nd option is correct.

A data model represents the type of relationship between the variables of a data set.

Data models are of four types, namely, Linear, Cubic, Quadratic and Exponential data models.

Given data is:

Distance Traveled                      Average Speed(miles per hour)

(miles)

1                                                                7

2                                                               6.3

3                                                              5.67

4                                                              5.103

A quadratic model is the best data model for the given data set.

The pattern observed in the given data set observes the properties of a quadratic function.

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Answer:

Exponential is the correct answer.

Step-by-step explanation:

Answer:

The percentage of the students that can swim is 75%

The percentage of students that can't swim is 25%

Step-by-step explanation:

100÷40=2.5

2.5×30=75

The percentage of the students that can swim is 75%

100-75=25

The percentage of students that can't swim is 25%

Please comment below if you don't understand or want me to clarify. :)

Answer:

a=-54/7

Step-by-step explanation:

-35=5+7(a+2)

by opening the bracket we have

-35=5+7a+14

-35=7a+19

collect like terms

we have:

-35-19=7a

-54=7a

a=-54/7

Answer:

a = -54/7

Step-by-step explanation:

multiply 7 with the number in brackets

-35 = 5 + 7(a + 2)

-35 = 5 + 7a + 14

then add the numbers without symbols

-35 = 19 + 7a

make a the subject

-7a = 19 + 35

-7a = 54

divide the subject with the same number + the answer

-7a ÷ -7 = 54 ÷ -7

a = -54/7 or -7 5/7

hope this helps :)

Using proportions and the markup concept, it is found that the cost to store is of $12.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The markup price of 80% means that the selling price is of 180% = 1.8 of the cost to store of x. The selling price is of $21.60, hence:

1.8x = 21.60

x = 21.60/1.8

x = $12.

The cost to store is of $12.

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Answer:

he is more likely incorrect.

Step-by-step explanation:

Z = (ps - p0)/sqrt(p0(1-p0)/n)

ps = proportion sample

p0 = proportion null hypothesis (NCAA)

n = sample size

ps = 17 / 36/100 = 17/1 / 36/100 = 1700/36 =

= 47.22222222...%

Z = (0.47222... - 0.575)/sqrt(0.575(1 - 0.575)/36) =

= -0.10277777... /sqrt(0.244375 / 36) =

= -0.10277777... / 0.0823905... =

= -1.247446952... ≈ -1.25

p(-1.25) = 0.10565

0.10565 > 0.05

the null hypothesis is therefore likely, or at least cannot be rejected.

so, his claims are not supported, as surprising as this might feel given that the sample result itself is 10 points off the NCCA result, which feels to be a solid difference.

Answer:

40°, 50°, and 90°

Step-by-step explanation:

Let the smallest angle be x.

Then, the other small angle is x+10.

The acute angles of a right triangle are complementary, so x+x+10=90, and thus x=40.

So, the acute angles measure 40° and 50°.

Therefore, the three angles are 40°, 50°, and 90°.

Answer:

221

Step-by-step explanation:

If the diameter is 26, the radius is 13 (which is the same as the perpendicular from P to JH)

So, the area is

[tex]\frac{1}{2}(13)(24+10)=221[/tex]

Answer: x = 50

Concept:

Here, we need to know the idea of alternative interior angles and the angle sum theorem.

Alternative interior angles are angles that are formed inside the two parallel lines, and the values are equal.

The angle sum theorem implies that the sum of interior angles of a triangle is 180°

If you are still confused, please refer to the attachment below or let me know.

Step-by-step explanation:

Given information:

AC ║ DE

∠ABC = 85°

∠A = 135°

Find the value of ∠BAC

∠A + ∠BAC = 180° (Supplementary angle)

(135°) + ∠BAC = 180°

∠BAC = 45°

Find the value of ∠BCA

∠ABC + ∠BAC + ∠BCA = 180° (Angle sum theorem)

(85°) + (45°) + ∠BCA = 180°

∠BCA = 50°

Find the value of x (∠EBC)

∠EBC ≅ ∠BCA (Alternative interior angles)

Since, ∠BCA = 50°

Therefore, ∠EBC = 50°

[tex]\Large\boxed{x=50}[/tex]

Hope this helps!! :)

Please let me know if you have any questions