Simon's photo album has 8 photos of his car and some photos of his motorbike
He replaced some of the photos of his motorbike with some more photos of his car.
The number of photos of his car became 12. The ratio of the number of photos of his car to his motorbike became 3:5. How many photos of Simon's bike was there in the album ORGINALLY?

We have lcm(2, 3, 5) = 30, but none of 30/2 = 15, 30/3 = 10, nor 30/5 = 6 are divisible by 2, 3, and 5, respectively.

To account for this, take the square of 30, 30² = 900. Then 900/2 = 450, 900/3 = 300, and 900/5 = 180 are respectively divisible by 2, 3, and 5.

Multiply this by 2 to get a 4-digit number. It follows that [tex]\boxed{a=1800}[/tex].

There are [tex]\frac{30!}{(3!)^{10} }[/tex] ways for the teacher to decide which student she will teach during each lesson time if she must teach each student exactly 3 times. Here, "!" represents the factorial.

A number's factorial is the result of multiplying the integer by each natural number below it. Factorial can be symbolized by the letter "!". Thus, n factorial is denoted by n! and is the result of the first n natural numbers.

A whole number's "n" factororial is the sum of that number and each whole number up to one.

When a question asks you to determine how many different ways you can arrange or order a given number of items, you use a factorial.

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Answer: 37.92

Step-by-step explanation: We know that 3202 / 5 = 640.4.

We subtract that by 830 to get (830 - 640.4  =) 189.6. Then we do / by five again to get 37.92. That is the answer.

When you are bisecting AB using a string and you have secured the strong at point A to be more than half of AB, the next step is to C. Make an arc on AB from point A and another arc from point B .

If you are using a string, the first step is the secure that string at point A because the string will be used for the bisecting.

After the string is secured, take the length to just a little more than half of line AB.

Once that is done, use the string to make an arc on line AB from the top to bottom.

Unsecure the string and take it to point B. Once secured in point B, repeat the process done with point A.

This would bisect the line using a string.

In conclusion, option C - Make an arc on  AB from point A and another arc from point B is correct.

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Answer:

Step-by-step explanation:

Answer:

35.7 megabytes

Step-by-step explanation:

Let's first find 10% of the percent needed. If it is 234 megabytes and 10% has downloaded so far, we conclude that 10% of the download is 23.4 megabytes (since we move the decimal point one spot to the left to find ten percent).

To get to 15% of the percent needed, let's split 10% in half to get the amount of megabytes per every 5%.

23.4/2 = 11.7

We can now conclude that 5% = 11.7. Therefore, 15% will equal (23.4 + 11.7) 35.1 megabytes.

To find the remaining 3.5% left of the percent needed, we use a calculator.

3.5% x 18 = 0.63.

We will add that to the 35.1 megabytes, but we need to round to the nearest tenth, as the question stated. Therefore, we round to 0.6, add it to 35.1, to get a total of 35.7 megabytes.

For 18.5% of the download, it will be 35.7 megabytes.

Answer:

(f - g)(x) = [tex]3^{x}[/tex] + 8x + 4

Step-by-step explanation:

(f - g)(x)

= f(x) - g(x)

= [tex]3^{x}[/tex] + 10x - (2x - 4) ← distribute parenthesis by - 1

= [tex]3^{x}[/tex] + 10x - 2x + 4 ← collect like terms

= [tex]3^{x}[/tex] + 8x + 4

The composition of the functions f(x) and g(x) gives the equation:

[tex]f(g(x)) = 4x^2 + 6x - 3[/tex]

Here we want to get the composition of the two functions:

[tex]f(x) = x^2 + 3x - 3\\\\g(x) = 2x[/tex]

f(x) is a quadratic and g(x) is a linear equation.

Now we want to get the composition:

[tex]f(g(x))[/tex]

This means that we need to evaluate function f(x) in g(x), so we can replace all the "x" in the function f(x) by the notation "g(x)"

[tex]f(g(x)) = g(x)^2 + 3*g(x) - 3[/tex]

Now we replace all the "g(x)" by the actual function g(x) = 2x, we wll get:

[tex]f(g(x)) = g(x)^2 + 3*g(x) - 3 = (2x)^2 + 3*(2x) - 3[/tex]

finally, we can simplify this to get the composition, which is a quadratic function just like f(x).

[tex]f(g(x)) = 4x^2 + 6x - 3[/tex]

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Answer:

[tex]the \: answer \: is \: choice \: b \: \frac{ - 2 \sin(x) }{1 + \cos(x) } [/tex]

will give you an explanation if you want tag me on comment.

Answer:

1/2=20/40 19/20=38/40

Step-by-step explanation:

so the first option

The mistake that Shawn made in his definition of a reflection is that D. Shawn didn't make a mistake.

It should be noted that reflection simply means ten transformation of the shape of an object.

In this case, for any point R on the line of reflection L, the image R’ is at the same point as R. Furthermore, for any point P not on the line of reflection L, the image P’ is on the other side of L such that P and P’ are the same distance from L.

Therefore, Shawn is right as no mistake was made.

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Answer:

PP' must be perpendicular to the line of reflection. Whatever the distance is between P and L, there are infinitely many points on the other side of L that are the same distance from L.

Step-by-step explanation:

The curve passes through the point (3, 3), so [tex]y=3[/tex] when [tex]x=3[/tex]. Then

[tex]y = ax^2 + bx \implies 3 = 9a + 3b \implies 3a + b = 1[/tex]

The tangent line to the curve at (3, 3) has gradient [tex]\frac{dy}{dx}[/tex] at [tex]x=3[/tex]. Compute the derivative.

[tex]y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b[/tex]

Then when [tex]x=3[/tex], the gradient is 4, so

[tex]2ax + b = 4 \implies 6a+b=4[/tex]

Solve for [tex]a[/tex] and [tex]b[/tex]. Eliminating [tex]b[/tex], we find

[tex](6a+b) - (3a+b) = 4-1 \implies 3a = 3 \implies \boxed{a=1}[/tex]

and it follows that

[tex]3 + b = 1 \implies \boxed{b = -2}[/tex]

Answer:

8.8

Step-by-step explanation:

If DEF///ABC

AB=4.4

Using the probability concept, the correct statement is:

B. P(hibiscus|red) = P(hibiscus).

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For item a, the probabilities are:

Same probabilities, hence the statement that they are different is false.

For item b, the probabilities are:

Equal, hence this is the correct statement.

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Answer:

  (c)  (28/3)√6

Step-by-step explanation:

Side ratios of "special triangles" are used to solve this problem.

  30-60-90° triangle — 1 : √3 : 2

  45-45-90° triangle — 1 : 1 : √2

We need to apply these ratios a few times:

  CD : CE = √3 : 2   ⇒   CE = (7√3)(2/√3) = 14

  CE : BE = 1 : √2   ⇒   BE = 14(√2) = 14√2

  BE : AE = √3 : 2   ⇒   AE = (14√2)(2/√3) = (28√2)/√3

The fraction can be simplified by multiplying by (√3)/(√3):

  ((28√2)/√3)×(√3)/(√3) = (28√6)/3

  AE = (28/3)√6

The correct option is Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction

Emanuel did a mistake in her first step by taking negative sign twice.

Positive results are obtained if the sign are same. If the signs disagree, the outcome is adverse. Addition: Keep in mind that a signed number's magnitude and absolute value are the same.

Multiplication and division appear to be more difficult than addition and subtraction, but they are actually far less challenging. The result of multiplying two positive or two negative numbers with the same sign, according to the rule, will always be positive.

For instance:

According to question,

= [tex]\left(\frac{3}{5}\right)\left(\frac{4}{9}\right)\left(-\frac{1}{2}\right)[/tex]

Emanuel found the solution, but she erred in the first step. She incorrectly distributes the negative sign with both 1 and 2, as she should. We can write negative sign with either 1 or 2 but not both.

Correct steps are:

Step 1:

[tex]\frac{(3)(4)(-1)}{(5)(9)(2)}[/tex]

Step 2:

[tex]\frac{-12}{90}[/tex]

Step 3:

[tex]-\frac{2}{15}[/tex]

Therefore, the step 1 was miscalculated by Emanuel.

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The complete question is -

Emanuel used the calculations below to find the product of the given fractions. (Three-fifths) (StartFraction 4 over 9 EndFraction) (Negative one-half)

Step 1 StartFraction (3) (4) (negative 1) over (5) (9) (negative 2) EndFraction Step 2 StartFraction negative 12 over negative 90 EndFraction

Step 3 StartFraction 12 over 90 EndFraction

Step 4 StartFraction 2 over 15 EndFraction

In which step did his first error occur?

Answer:

Step-by-step explanation:

The triangle would end up back where it started.  It is hard to explain without a graph.  If you have graph paper, you might want to try drawing this out.  Say that the original points are at A (1,2) B (2,0) and C(0,0).  Now, when we reflect the points over the x axis, they will be the same distance below the x that the points original were about the x axis.  Since A was 2 units above the axis, it will now be 2 units below at (1, -2).  Points B and C will stay on the x axis and will remain in place at B(2.0) and C(0,0).  Since these points are on the line, they were not above the x axis, so they will now not be below the x axis.

Now, we are going to reflect the triangle over the y axis.  Since C (0,0) is already on the y axis, it will not move.  It will remain there.  Since B(2,1) is two units to the right of the y axis, when we flip it, it will now be 2 units to the left of the y axis B (-2,0).  Point C will move one unit to the left of the y axis to become (-1,2).

The last thing left it to rotate this final triangle 180 degrees.  Since a circle is 360 degrees and 180 is half of a circle, it does not matter if we rotate clockwise or counter-clockwise.  If you could trace our new triangle and put a plus sign at the origin (0,0).  You would put your pencil on the origin  and rotate the two turns at the plus sign.  This would put your triangle right back to the beginning.  So the original value of B would be the same.  In this case C ((2,0)

The point B' would be at point B. The position of point won't change.

A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.

Given:

Triangle ABC is reflected over the x‐axis, reflected over the y‐axis, and rotated 180 degrees.

Let (x, y) be the coordinates of B.

To find B':

If a figure reflected over x-axis, then

(x, y) → (x, -y)

So, let point B₁ is  (x, -y).

If a figure reflected over y-axis, then

(x, y) → (-x, y)

So, (x, -y) → (-x, -y)

So, let point B₂ is  (-x, -y).

If a figure rotated 180 degrees about the origin, then

(x, y) → (-x, -y)

(-x, -y) → (x, y)

So the B' is (x, y).

Therefore, the position of point won't change.

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Answer:

1.320000

2. 0.057

Step-by-step explanation:

Answer:

300 gallons

Step-by-step explanation:

A saline solution is a solution of salt in water.

The percent is the percent of salt in the total amount of solution.

A 40% saline solution has 40% of salt out of the total volume.

Let the amount of pure water needed = x.

The amount of existing 40% solution is 500 gal.

Let the total amount of 25% saline solution made = y.

Equation of volumes of solutions:

500 + x = y

y = x + 500          Eq. 1

Equation of volume of salt:

500 gal of 40% saline solution has 0.4 × 500 gal = 200 gal of salt

Pure water has 0% salt.

The final product is a solution that is 25% saline. Its volume is y.

The volume of salt in the y gallons of 25% saline solution is 25% of y = 0.25y

The equation of salt content is:

200 + 0 = 0.25y

y = 800       Eq. 2

Eq. 1 and Eq. 2 form a system of equations.

y = x + 500

y = 800

Substitute 800 for y in Eq. 1.

y = x + 500

800 = x + 500

x = 300

Answer: 300 gallons of pure water

Using its concept, it is found that the probability that the lawyer will flip to a page number that is not a multiple of 4 is given by:

p=19/25

Probability is a field of mathematics that deals with the numerical description of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the impossibility of the event and 1 indicating certainty.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 50 numbers, of which 50 - (48/4) = 38 are not multiples of 4, hence the probability is given by:

p=38/50 = 19/25

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Since the ratio of their similar sides are equal hence the triangles are similar

Two figures are are known to be similar if the ratio of their similar sides are equal to a constant known as the scale factor.

For the triangles given, take the ratio of the sides;

12/2 = 6

30/5 = 6

36/6 = 6

Since the ratio of their similar sides are equal hence the triangles are similar

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The option A is correct, the linear equation x + y = 34. and 10x + 15y = 410 represent the the statement.

According to the statement

we have given that the

Jody earns $10 per hour babysitting And jody earns $15 per hour doing yardwork.

And she worked 34 hours and earned $410

and we have to express in the linear equation terms.

So, For this purpose,

Let x represents the number hours she babysat

Let y represents the number of hours she did yardwork

And the equations become

x + y = 34.

10x + 15y = 410

And with the help of these linear equations we find the hours which are x and y.

So, The above written equations perfectly express the given conditions in the statement.

The option A is correct, the linear equation x + y = 34. and 10x + 15y = 410 represent the the statement.

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The centre angle of circular sector is n = 90 degrees (approximately).

A sector is referred to as a component of a circular made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radius of the circle at its ends.

A piece of pizzas can be used as an analogy for the form of a circle's sector.

The formula for finding the angle formed at the circular sector in radian is;

Let 'n' be the centre angle.

Let 'l' be the slant height of the cone which is equal to radius of circular sector.

Let 'r' be the radius of the cone.

First, calculate the total length of the circular sector say 'L' which is equal to the circumference of the circular base of the cone.

circumference = 2[tex]\pi[/tex]r

                        = 2×3.14×1

                        = 6.28

Now,

centre angle = length of circular sector/radius of circle

n = L/l

n = 6.28/4

n = 1.57 radian

Convert radian in degree as;

n = (1.57×180)/[tex]\pi[/tex]

n = 89.95

n = 90 degrees (approximately)

Therefore, the angle made by the circular sector is 90 dergees.

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The correct question is-

The slant height and radius of a cone are 4 and 1, respectively. Unrolling the curved surface gives a circular sector with center angle n degrees. Find n.

**Disclaimer** Hi there! I assumed the question to be finding the "y-intercept", "x-intercept", and "slope/gradient" of the equation "y = 3x - 9". The following answering will be according to this understanding. If it is incorrect, please tell me and I will modify my answer.

Answer:

y-intercept = (0, -9)

x-intercept = (3, 0)

slope (m) = 3

Step-by-step explanation:

What is being asked: to find the corresponding values

Given equation

y = 3x - 9

Concept

The y-intercept of a line is on the coordinate of (0, a), where [ a ] is a constant.

Substitute values into the equation

y = 3x - 9

y = 3 (0) - 9

y = 0 - 9

y = -9

Therefore, the y-intercept is [tex]\Large\boxed{(0, -9)}[/tex]

Concept

The x-intercept of a line is on the coordinate of (a, 0), where [ a ] is a constant.

Substitute values into the equation

y = 3x - 9

0 = 3x - 9

Add 9 on both sides

0 + 9 = 3x - 9 + 9

9 = 3x

Divide 3 on both sides

9 / 3 = 3x / 3

x = 3

Therefore, the x-intercept is [tex]\Large\boxed{(3,0)}[/tex]

Concept

In the linear formula, y = mx + b, [ m ] is the slope and [ b ] corresponds to the y-intercept.

Determine the slope

Given the equation, y = 3x - 9, when corresponds to the general linear equation formula:

                                                  y = mx + b

                                                  y = 3x - 9

Therefore, the slope is [tex]\Large\boxed{m=3}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

5 students like hockey more than football.

To find out How many more students like hocket than football:

Refer to the given table -

Students who do not like football and like hockey = a = 30

Students who like football and do not like hockey = b = 25

Now,

[tex]=a-b\\=30-25\\=5[/tex]

Therefore, 5 students like hockey more than football.

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The question you are looking for is shown below:

The two-way table shows the number of students in a school who like hockey and/or football. like hockey does not like hockey total like football 50 25 75 do not like football 30 45 75 total 80 70 150.

How many more students like hocket than football?

Answer:

x>-2

Step-by-step explanation:

x>-2 is the answer since we are looking for x values that the graph takes.

The line x=-2 looks like an asymptote so x>-2 must be the answer

Answer: x>-2

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

volume = side³

v = 3³

v = 27

i dont know how to convert to whatever h is so this is the best answer i can give

Answer:

x=5

h = 5 sqrt 2

Step-by-step explanation:

isosceles right triangles are always 45-45-90, ratio of those triangles are always x:x:x*sqrt 2

The Time taken by Jacob to run the dash race is (80 - t) seconds

We are told that;

Total distance for the dash race = 500 yards

Time taken by Jacob to run the dash race = 80 seconds

Now, we are told that Juan ran the same dash race but used t less seconds than Jacob. Thus;

Time taken by Jacob to run the dash race = (80 - t) seconds

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The value of the expression 6x+3y is 33

System of equations consists of two or more equation with unknown variables.

Given the equation below

8x + 4y = 44,

Factor out 4 from the equation to have:

4(2x+y) = 44

Divide both sides by 4

2x+y = 11

Determine the value of 6x+3y

6x+3y = 3(2x+y)

6x+3y = 3(11)

6x+3y =33

Hence the value of the expression 6x+3y is 33

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Answer:

[tex]\sf t_{20}= 0[/tex]

Step-by-step explanation:

      [tex]\sf \boxed{\bf n^{th} \ term = a + (n-1)d}\\\\\text{Here, a is the first term ; d is the common difference }[/tex]

6th term is 14 ⇒ [tex]\sf t_6 = 14[/tex]

                a + (6 - 1)d = 14

                    a  +  5d = 14  --------------(I)

14th term is 6 ⇒[tex]\sf t_{14} = 6[/tex]

             a + (14-1)d = 6

                  a + 13d = 6 ----------------(II)

Subtract equation (II) from equation(I)

        (I)          a + 5d = 14

        (II)         a + 13d = 6

                    -    -          -

                            -8d = 8

                               d  = 8 ÷(-8)      

                              [tex]\sf \boxed{\bf d= (-1)}[/tex]

Plugin d = -1 in equation (I)

a + 5(-1) = 14

      a -5  = 14

             a = 14 + 5

             [tex]\sf \boxed{\bf a = 19}[/tex]  

20th term:

 [tex]\sf t_{20}= 19 + 19*(-1)[/tex]

       = 19 - 19

   [tex]\sf \boxed{\bf t_{20} = 0}[/tex]

Answer:

0

Step-by-step explanation:

The number of terms of an Arithmetic progressions has the formular.

Tn = a + ( n - 1 ) d

From the question,

6th term = 14

14th term = 6

Therefore,

a + 5d = 14 -----------(1)

a + 13d = 6 ----------(2)

subtracting

-8d = 8

dividing bothsides by -8

[tex] \frac{ - 8d}{ - 8} = \frac{8}{ - 8} \\ d = - 1[/tex]

Therefore,

common difference= -1

substituting the value of d into equation (1)

a + 5 ( -1) = 14

a - 5 = 14

a = 14 + 5 = 19

First term = 19

For the 20th term

T 20 = a + 19d

19 + 19 ( -1 )

19-19 = 0

Therefore,

20th term = 0