1/4 Marks
a) Complete the prime factor trees for 16 and 40:
16
b)
2
2
8
2
4
17/31 Marks
2
2
40
What is the Lowest Common Multiple of 16 and 40?
82%
5

By using exponent properties, we can see that the equivalent expressions are:

[tex]5*\sqrt{n^4} = 5*n^2[/tex]

Here we need to use some rules for exponents and roots. Remember that:

[tex]\sqrt[n]{x} = x^{1/n}[/tex]

We also will use that:

[tex](a^n)^m = a^{n*m}[/tex]

Now we have the following expression:

[tex]5*\sqrt{n^4}[/tex]

Particularly, the square root is equivalent to an exponent of 1/2, then we can write:

[tex]5*\sqrt{n^4} = 5*(n^4)^{1/2}[/tex]

Using the second property we can rewrite:

[tex]5*(n^4)^{1/2} = 5*n^{4*1/2} = 5*n^2[/tex]

So the equivalent expressions are:

[tex]5*\sqrt{n^4} = 5*n^2[/tex]

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The probability that none of these vehicles requires warranty service is 0.2824

The probability exactly one of these vehicles requires warranty service is

0.3766

The probability that exactly two of these vehicles require warranty service is 0.2301

The mean of this probability distribution is 1.2

Given, n=12, and the probability is 0.1, we use the binomial distribution formula to solve the probabilities:

[tex]P(X=0)=C^{n}_{x} } P^{x} Q^{n-x}[/tex]

The probability that none of these vehicles requires warranty service

[tex]P(X=0)=C^{12}_{0} } (0.1)^{0} (0.9)^{(12-0)}[/tex]

               =0.2824

The probability exactly one of these vehicles requires warranty service

[tex]P(X=1)=C^{12}_{1} } (0.1)^{1} (0.9)^{(12-1)}[/tex]

                =0.3766

The probability that exactly two of these vehicles require warranty service.

[tex]P(X=2)=C^{12}_{2} } (0.1)^{2} (0.9)^{(12-2)}[/tex]

               =0.2301

Compute the mean of this probability distribution

Mean = n*P, where n = 12, P=0.1

          =12*0.1

          =1.2

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The odd function is

y = sin x

y = cos x

A function f is deemed weird if f(-x) Equals -f for any value of x. (x). A function is said to be an even function if f(-x) = f for any value of x. (x).

What do odd functions entail?

The meaning of odd function

T function where the absolute value does not change if the independent variable's sign is reversed but the sign of the function itself does.

If f(-x) = -f for any number x, a function f is considered strange (x). When f(-x) = f for any number x, a function is referred to as an even function (x). Even while most functions are neither odd nor even, some of the most significant functions are.

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Answer:

A. y = sin x

B. y = csc x

C. y = tan x

Step-by-step explanation:

Speed of car is 5 m/sec

What is speed?

In ordinary language and kinematics, an object's speed is defined as the magnitude of its position change over time or the magnitude of its position change per unit of time; it is therefore a scalar number. The distance traveled by an item in a time interval is divided by the duration of the period; the instantaneous speed is the limitation of the average speed as the length of time period tends to zero. Velocity is not the same as speed. Distance divided by time is the dimension of speed. The metre per second (m/s) is the SI unit of speed, while the kilometre per hour (km/h) is the usual unit.

The speed of the car = 1.5/5 km/min = 0.3 km/min

Speed in m/sec = 0.3x1000/60 = 5m/sec

Hence, speed of car = 5 m/sec

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By taking the 20 percent of £85 and adding that to the base salary, we can see that last week Brett earned £95

Here we need to work with percentages. We know that Brett wins a commission of 20% of sales.

So, if he sells a total amount of A (A is in dollars). Then what he gets is:

0.2*A

Where 0.2 is the decimal form of 20%.

Here we know that Brett wins £78 as a base, and last week he sell a total of £85, then the amount he gets by the commission is:

0.2* £85 =  £17

Adding that to the base he already earns each week, we get:

£78 +  £17 =  £95

In this way, we conclude that last week Brett earned £95

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Answer: (6, -5)

Step-by-step explanation:

       The slope 2/3 means that there is a positive change of 2 in the y-value ( + 2) and a positive change in the x-value of 3 (+ 3) for every new point. To find another point on the line, we can add 2 to the y-value and 3 to the x-value.

    ➜ Slope is written as y over x

    ➜ Coordinate points are written as (x, y)

       (3, -7)

       (3 + 3, -7 + 2)

       (6, -5)

       We can also find a point on the line by graphing. See attached.

Base on the given ratio of quantity of sugar to number of cakes, the quantity of sugar needed to bake 4 cakes is 31.6g of sugar

Ratio refers to a number representing a comparison between two named things or quantities. The ratio of sugar and cake is the comparison between the quantity of sugar used to make cake.

Find the ratio of quantity of sugar to number of cakes

Quantity of sugar : Number of cakes

71.1 g : 9 cakes = x : 4 cakes

71.1 / 9 = x / 4

71.1 × 4 = 9 × x

284.4 = 9x

x = 284.4 / 9

x = 31.6g of sugar

In conclusion, the quantity of sugar needed to bake 4 cakes is 31.6g of sugar

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The straight line y-1=-1/3(x-2) is perpendicular to y = 3x + 2 .

The common form for two-variable linear equations is Ax + By = C which is also the general form of a straight line.

For instance, the linear equation 6x+5y=11 uses standard form. Finding an equation's two intercepts (x and y) is fairly straightforward with this procedure.

The cartesian equation for a straight line is Y = mx + c, where m stands for the gradient or slope of the line and c for the point at which it intersects the y-axis.

If two geometrical objects cross at a right angle, they are perpendicular.

We know that when two line are perpendicular the product of their respective slopes equal to -1.

Now in the given options let us find the slope of each line.

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

slope = 1/3

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

slope = 3

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

slope = -1/3

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

slope = -3

Therefore the slope of the third equation is the negative reciprocal of the slope of the given line.

Hence y-1=-1/3(x-2) is perpendicular to y = 3x + 2 .

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Answer:

y = 4x + - 9

Step-by-step explanation:

(3, 3), (4, 7)

(x₁, y₁)  (x₂, y₂)

        y₂ - y₁        7 - 3           4

m = ------------ = ------------ = ------- = 4

        x₂ - x₁         4 - 3           1

y - y₁ = m(x - x₁)

y - 3 = 4(x - 3)

y - 3 = 4x - 12

  +3          +3

----------------------

y = 4x - 9

I hope this helps!

Answer:

[tex]\frac{29}{8}[/tex]

Step-by-step explanation:

3[tex]\frac{3}{8}[/tex] equals to [tex]\frac{27}{8}[/tex], then we can write out the equation:

[tex]\frac{27}{8} + x = 7[/tex]
then subtract [tex]\frac{27}{8}[/tex]on both sides of the equal sign,

[tex]x = 7 - \frac{27}{8}[/tex]

and then we calculate x

[tex]x=\frac{56-27}{8}[/tex]

[tex]x=\frac{29}{8}[/tex]

Thus the answer is [tex]\frac{29}{8}[/tex]

[tex]5x - 2y = 4 \\ 5x = 4 + 2y \\ \frac{5x}{5} = \frac{4 + 2y}{5} \\ x = \frac{4 + 2y}{5} ......(3)equation[/tex]

NOTE I AM SOLVING BY SUBSTITUTION

[tex]8( \frac{4 + 2y}{5} ) + 5y = - 10 \\ \frac{32 + 16y}{5 } + 5 y = - 10 \\ \frac{32 + 16y}{5} (5) + 5y(5) = - 10(5) \\ 32 + 16y + 25y = - 50 \\ 41y = - 50 - 32 \\ \\ \\ \\ 41y = - 82 \\ \frac{ - 41y}{41} = \frac{ - 82}{41} \\ y = - 2[/tex]

[tex]x = \frac{4 + 2( - 2)}{5} \\ x = \frac{4 - 4}{5} \\ x = \frac{0}{5} \\ x = 0[/tex]

ATTACHED IS THE SOLUTION

Answer: (0,-2)

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{5x-2y=4\ \ \ \ \ (1)} \atop {8x+5y=-10\ \ (2)}} \right.[/tex]

Multiply equation (1) by 5, and equation (2) by 2:

[tex]\displaystyle\\\left \{ {{25x-10y=20\ \ \ \ (3)} \atop {16x+10y=-20\ \ (4)}} \right.[/tex]

Add equations (3) and (4):

[tex]41x=0[/tex]

Divide both parts of the equation by 41:

[tex]x=0[/tex]

Let's substitute the value of x into equation (2):

[tex]8(0)+5y=-10\\0+5y=-10\\5y=-10[/tex]

Divide both parts of the equation by 5:

[tex]y=-2[/tex]

Thus, (0,-2)

Rewrite 50% as 1/2

We need a fraction that is equal to 1/2 of 1/6.
-> That fraction equals to 1/2 x 1/6 = 1/12 (or 1/6 : 2)

Answer:

1/12

Step-by-step explanation:

1/6*100/50=1/12.

The variables a and b have a possible value of 7 and 11

The given parameters are

GCF(a, b)• LCM (a, b) = 77

As a general rule, the product of two numbers equals the product of the greatest common factor and the least common multiple of the numbers

This implies that

a * b = GCF(a, b)• LCM (a, b)

So, we have

a * b = 77

Express 77 as 7 * 11

a * b = 7 * 11

By comparison, we have

a = 7 and b = 11

Hence, the possible values are a = 7 and b = 11

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We found the length of the other leg by using Pythagoras’ theorem y is equal to 21.0 centimeters when the length of one of its legs is 20.0 centimeters.

In this question we have to make an equation by using the right triangle's value which is given in the question,

by putting these values in the Pythagoras’ theorem.

As given, the hypotenuse of a right triangle = 29.0 centimeters.

The length of one of its leg = 20.0 centimeters

Now, by using Pythagoras’ theorem we will find the length of the other leg:

hypotenuse^2 = base^2 + perpendicular^2,

We put the value according as given in question:

29^2 = 20^2 + y^2

After finding the square of number of both side:

841 = 400 + y^2

Now we will rearrange this equation:

y^2 = 841 - 400  

y = 21 centimeters is the length of the other leg.

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Answer:

1.5x=9+4.5y

x= [tex]\frac{9+4.5y}{1.5}[/tex]

x = 6 + 3y

3y= x - 6

y = x/3-2

The probability of randomly selecting an order and getting the order that is used in the spelling​ bee is  0.001388888

Given we have the following:

Number of students in the spelling bee = 6

Number of ways selecting a student in the spelling bee = 6!

The probability of randomly selecting an order and getting the order that is used in the spelling bee :

P(selecting the correct spelling bee order) = 1/6!

= 1/6*5*4*3*2*1

= 1/720

= 0.001388888

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Answer:

27x+50

Step-by-step explanation:

How to solve your problem

50 + 108x/4

Simplify

Cancel terms that are in both the numerator and denominator

50+ 108x/4

50+ 27x

Rearrange terms

50 + 27x

27x +50

=27x+50

Answer:

He will only afford to rent the car for 4 days, he will spend 160 dolars to just have the car for 4 days. Since he plan to drive 125 miles, the cost for the miles will be 10 dolars. So if we add 160 (4 days with the car) plus 10 (for the miles) it would give 170.

Step-by-step explanation:

The probability of picking an odd number ball in fraction form is; 6/11

We are told that a bag contains eleven balls labelled 1 through 11. These numbers are;

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. This is a total of 11 numbers.

The even numbers are a total of 5 while the odd numbers are a total of 6.

Now, the probability of selecting an odd number will be;

P(selecting odd number) = Number of possible odd numbers/Number of Total Numbers

Plugging in the relevant numbers gives;

P(selecting odd number) =  6/11

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Answer:

y = (3/2)x + 3

Step-by-step explanation:

Point 1: (0, 3) Point: (2, 6)

            (x₁, y₁)          (x₂, y₂)

        y₂ - y₁        6 - 3            3

m = ------------ = ------------ = --------

        x₂ - x₁         2 - 0           2

y - y₁ = m(x - x₁)

y - 3 = (3/2)(x - 0)

y - 3 = (3/2)x

  +3               +3

------------------------

y = (3/2)x + 3

I hope this helps!

Answer:

A) 2nd graph

Explanation:

The 1st graph shows a radical expression, where:

to find the inverse, replace f(x) with y, switch the x and the y, then solve for y. The only graph showing exponential growth is the 2nd graph (note how at 1 it's 1, at 2 it's 4, at 3 it will be 9, etc.)

Answer:

3/8 barrels / minute.

Step-by-step explanation:

Rate = fraction of barrel filled / time

        = 1/4 / 2/3

        = 1/4 * 3/2

        = 3/8.

Answer:

gradient is 1/2  =  0.5

Step-by-step explanation:

y= 1/2 x−3

Swap sides so that all variable terms are on the left hand side.

1/2 x−3=y

Add 3 to both sides.

1/2 x=y+3

Multiply both sides by 2.

1/2 x = 1/2 y+3

​

Dividing by  1/2 undoes the multiplication by  1/2

x= 1/2 y+3

​

Divide y+3 by  1/2  by multiplying y+3 by the reciprocal of  1/2

​

.

x=2y+6

Answer:

^2¤{{●○|<♤7◇○◇○◇7~♡6°<♤~{¡\ ~announced unbeknownst.fi

∠K , ∠1 and ∠JKL  are the three names of the angle 1 indicated by red color in the figure given in the question.

We need to select three names of the angle 1 indicated by red color in the figure given in the question . We are provided with the following options ∠JLK , ∠K , ∠LJK , ∠1 , ∠JKL and ∠J .  

∠JLK is not similar to ∠1 .  ∠K and  ∠1  are same angle. ∠LJK is not similar to ∠1 . ∠JKL and  ∠1  are same angle.  ∠J and ∠1 are different angles. So, we can finally conclude that the three names of the angle 1 indicated by red color in the figure given in the question are ∠K , ∠1 and ∠JKL .

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The amount which Mr. Jonas will have to repay after 4 years is $13,888 when the interest rate is 3% per year on a loan of $12,400.

According to the question,

We have the following details:

The amount of the loan or the principal amount = $12,400

Interest rate = 3% per year

Time = 4 years

Now, it is given that the interest is not a compound interest. So, the total interest can be found using the formula of simple interest.

Simple Interest (S.I.) = (Principal*rate*time)/100

S.I. = (12400*3*4)/100

S.I. = (12400*12)/100

S.I. = 148800/100

S.I. = $1,488

Now, the total amount Mr. Jonas have to repay will be the sum of the loan he has taken out and the simple interest after 4 years.

Total amount = Principal + S.I.

Total amount = 12400+1488

Total amount = $13,888

Hence, the total amount of loan Mr. Jonas has to repay is $13,888.

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when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{x}{13}~~ = ~~\cfrac{11}{x}\implies x^2=(13)(11)\implies x^2=143\implies x=\sqrt{143}[/tex]

Answer:

1

Step-by-step explanation:

Anything to the power of 0 is 1 except for 0.  If the base is o, the answer is undefined.  It is will dividing by 0.  That is also undefined.

Answer:

-10degree

Step-by-step explanation:

because the 0 is the degree