Determine, which is the shorter path from A to B is: Around the two small semi circles or around the large semi-circle? Verify your answer by calculating the length of the path in each case.​

The number of each type Mika bought =x = 6.8 rolls; y= 2.2 rolls.

The number of rolls of film Mika  bought =  9 rolls

The number of rolls that had 36 exposures = x

The number of rolls that had 12 exposures = y

The total number of exposures = 36 + 12 = 48

To find the exposure by one roll = 48/9 = 5.3

If one roll = 5.3 exposure

    x roll    = 36 exposure

Make x roll the subject of formula,

x roll = 36/5.3 = 6.8 rolls

    y roll    = 12 exposure

Make y roll the subject of formula,

y = 12/5.3 = 2.2 rolls

Therefore, the number of each type Mika bought = x = 6.8 rolls; y= 2.2 rolls.

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Answer:

  6.  80

  7.  60

  8.  100

  9.  40

  10.  110

Step-by-step explanation:

A box and whisker plot is a visual representation of the 5-number summary of a data set. The features of the plot are, left-to-right, the minimum, first quartile, median, third quartile, maximum.

You are being asked to identify the numerical value associated with each of these features.

__

The left whisker extends to the minimum of 40.

The left end of the box identifies the first quartile as 60.

The line in the middle of the box is the median, 80.

The right end of the box identifies the third quartile as 100.

The right whisker extends to the maximum of 110.

__

Additional comment

We hope you can rearrange the order of these numbers to suit the order in which the questions ask for them.

The equation of the function, g(x) from the task content is; g(x) = -x/25 + 203/25.

From observation of the function, f(x), it follows that the slope of f(x) is 25. Hence, it follows that the slope of g(x) is; -1/25 since both functions are perpendicular to each other.

Therefore, the equation for g(x) is;

-1/25 = (y-8)/(x-3)

25y -200 = -x +3

Hence, y = -x/25 + 203/25.

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An expression is defined as a set of numbers, variables, and mathematical operations. The statements that are true are 1, 3, and 5.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

For the given expression 4x + 9 - y(6x + 7), the following things are can be written,

Thus, the statements that are true are:

Hence, the statements that are true are 1, 3, and 5.

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The correct option is option B :    -4 ≤ x ≤ 1

Increasing and decreasing functions are functions whose graphs go upwards and downwards respectively as we move towards the right-hand side of the x-axis. Increasing and decreasing functions are also called non-decreasing and non-increasing functions.

Here, from graph

as we can observe from x = -4 graph starts increases upto x = 1 and after that graph becomes constant.

Thus, between x belongs -4 to 1 the graph is increasing.

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Answer:

1200 bats

Step-by-step explanation:

78 - 39 = 39

600 x 2 = 1200(bats).

Answer:

47°

Step-by-step explanation:

45+88= 133

180-133=47

the third one

Step-by-step explanation:

Answer:

3x³ + 12x

Step-by-step explanation:

→ Multiply 3x by x²

3x³

→ Multiply 3x by 4

12x

The amount after 2 years will be 855.3248

Interest, in its most simple form, is calculated as a percent of the principal.

Given:

P= £800 , r= 3.4%, t= 2 year

For, compounded annually

=800*(0.034+1)²

=800* 1.034*1.034

=800* 1.069156

=855.3248

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Given the steps used to calculate the interquartile range, Bryan did not make any mistake.

The interquartile range is the difference between the third quartile and the first quartile.

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Answer:

See below ~

Step-by-step explanation:

We need to prove that the figures are similar by applying the various kinds of transformations.

===============================================================

Question A :

⇒ Compare the side lengths of A and B

⇒ 2 : 5 (for all sides)

⇒ 1 : 2.5

⇒ Hence, Shape A has been dilated with a scale factor of 2.5 to form Shape B

=============================================================

Question B :

⇒ Compare the side lengths of A and B

⇒ A : B = 2 : 6

⇒ A : B = 1 : 3

⇒ Shape A has been dilated with a scale factor of 1/3 to form Shape B

Using translation concepts, considering S(2,-1), the x-coordinate of S' is given by 6.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the rule is given by:

(x, y) -> (x+4, y-2).

Considering S(2,-1), 4 is added to the x-coordinate in the translation, hence:

2 + 4 = 6.

The x-coordinate of S' is given by 6.

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I assume you know that there are n total n-th roots for any non-zero complex number.

(If you're looking for "the" principal root, you'll have to specify which branch you're calling the principal branch of the n-th root function.)

Start by writing [tex]1 - i\sqrt3[/tex] in exponential form. We have modulus/magnitude

[tex]|1 - i\sqrt3| = \sqrt{1^2 + (-\sqrt3)^2} = \sqrt4 = 2[/tex]

and [tex]1-i\sqrt3[/tex] lies in the fourth quadrant of the complex plane, so its argument is

[tex]\arg(1-i\sqrt3) = \tan^{-1}\left(-\sqrt3\right) = -\dfrac\pi3[/tex]

Then the exponential form is

[tex]1 - i \sqrt3 = 2 \exp\left(-i\dfrac\pi3\right)[/tex]

(where [tex]\exp(x) = e^x[/tex], if you're not familiar with the notation)

By de Moivre's theorem, we have the fourth roots

[tex]\sqrt[4]{1 - i\sqrt3} = \sqrt[4]{2} \exp\left(i \dfrac{-\frac\pi3+2k\pi}4\right)[/tex]

where [tex]k\in\{0,1,2,3\}[/tex], so that we have a choice of

[tex]\sqrt[4]{1 - i\sqrt3} = \begin{cases} \sqrt[4]{2} \exp\left(-i\dfrac\pi{12}\right) \\\\ \sqrt[4]{2} \exp\left(i\dfrac{5\pi}{12}\right) \\\\ \sqrt[4]{2} \exp\left(i\dfrac{11\pi}{12}\right) \\\\ \sqrt[4]{2} \exp\left(i\dfrac{17\pi}{12}\right) = \sqrt[4]{2} \exp\left(-i\dfrac{7\pi}{12}\right) \end{cases}[/tex]

(I rewrote the exponent to the last root just to be consistent about having each argument between -π and π radians)

If you want these in rectangular form (a + bi), sorry, that's where I draw the line; it can be done with simple trigonometry and algebra, but it's rather tedious, and the exponential forms are far more compact.

Answer:

It's a sech x function

Step-by-step explanation:

Explanation is in attached file

Step-by-step explanation:

[tex]12y^{2} + 4y \\4y( \frac{12y^{2} }{4y} + \frac{4y}{4y} ) \\ 4y(3y + 1)[/tex]

Step-by-step explanation:

12y²+4y

divide both sides by 4

therefore,

3y²+y

y(3y+1)

Answer:

Image included:

Step-by-step explanation:

Answer:

always negative?

Step-by-step explanation:

-2^3=-8

Answer:

It is negative

Step-by-step explanation:

since you are multiplying the negative no. by itself an odd no. of times, your answer will be negative, b/c a negative no. multiplied an odd no. of times will be negative, and if it is multiplied an even no. of times it will be positive.

Answer:

the first option

Step-by-step explanation:

f(c)= 1/3p + 5/3

Answer: A right angle

Step-by-step explanation:

Perpendicular lines form right angles

Answer:

90 degree

Step-by-step explanation:

The sum of 0.89 and 1.11 will be 2. Then the correct option is D.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Two 10 by 10 grids are shown.

In the first grid, 8 columns and 9 squares are shaded brown and 1 column and 1 square is shaded blue.

The second grid is entirely shaded blue

Then the sum of 0.89 and 1.11 will be

⇒ 0.89 + 1.11

⇒ 2.00

Then the correct option is D.

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Answer:

switch the position

1/3πr²h=v

multiply all through by 3

3•1/3πr²h=3•v

3 will cancel out 3

πr²h=3v

divide both sides by πh

r²=3v/πh

root both sides

r=±√3v/πh

Answer:

[tex]13\frac{1}{3} \pi[/tex]

Step-by-step explanation:

First, find the area of the small circle whose radius is 3cm.

[tex]A = \pi r^{2} \\A = \pi (3^{2})\\A = \pi (9)\\A = 9\pi \\[/tex]

Next, find the area of the large circle. First, you need to find the radius of the large circle by adding the 3 and 4.

Radius of large circle.

3 + 4 = 7 cm

Area of large circle:

[tex]A = \pi r^{2} \\A = \pi (7^{2})\\A = \pi (49)\\A = 49\pi \\\\[/tex]

Now subtract the area of the small circle from the large circle since the shaded area doesn't include the small circle.

[tex]49\pi -9\pi =40\pi[/tex]

Finally find the shaded area. To do this first find what degree of the circle is shade by dividing 120 by 360.

120/360 = 1/3

Now multiply the area by 1/3, or you can divide it by 3

[tex]\frac{40\pi }{3} =13\frac{1}{3} \pi[/tex]

Using the permutation formula, it is found that these offices can be filled in 336 ways.

There are different roles, hence the order in which the people are chosen is important, hence the permutation formula is used.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

3 people will be chosen from a set of 8, hence the number of ways is given by:

[tex]P_{8,3} = \frac{8!}{5!} = 336[/tex]

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The operation that should be completed first to find the value of the expression is 6 - 3

The expression is given as:

12 + 30/(6 - 3) + 1

When solving an expression;

All expressions in the bracket must be first evaluated

This means that the operation that should be completed first is 6 - 3

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Answer:

40 Rs per kg.

Step-by-step explanation:

solution

Let the rate of tea be x Rs per kg and that of sugar be y Rs per kg.

When Kantabai bought the items by going to the shop,

3/2x+5y+50=700

⇒3x+10y=1300....(I)

When Kantabai bought the items online then

2x+7y=880......(II)

Multiplying (I) with 2 and (II) with 3 we get

6x+20y=2600......(III)

6x+21y=2640.......(IV)

eq.(IV)−(III)

y=40

Putting the value of y =40 in (II)

2x+7(40)=880

⇒2x=880−280=600

⇒x=300

Thus, tea is at 300 Rs per kg and sugar is 40 Rs per kg.

Answer:

34 degrees

Step-by-step explanation:

Just reverse the cos function   ( you will need a calculator)

arc cos (.8290) = 34 degrees

this is sometimes written as   cos^-1 (.8290)   <====it is the same thing

The given expression is [tex]\dfrac{ r^2-r-6}{(r-2)(r-3)}[/tex]. the option C [tex]\dfrac{ (r+2)}{(r-2)}[/tex]is correct.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

The given expression is

[tex]\dfrac{ r^2-r-6}{(r-2)(r-3)}[/tex]

By solving the numerator

[tex]r^2-r-6\\\\r^2 - (3-2)r- 6\\\\(r-3)(r+2)[/tex]

Put the solution in the above equation

[tex]\dfrac{ (r+2)(r-3)}{(r-2)(r-3)}[/tex]

[tex]\dfrac{ (r+2)}{(r-2)}[/tex]

Therefore, the option C is correct.

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