POR is a right-angled triangle.
13 cm
5 cm
12 cm
Work out the size of angle POR.
Give your answer correct to 1 decimal place.
+ +
1
Total marks: 3

If total cost of a pair of shoes and jacket is $46 and cost of shoes is $8 more than cost of jacket, cost of shoes is $27 and the system of equations to determine the cost of the shoes are x - y = 8 and x + y = 46.

Let the cost of the shoes be x and the cost of the jacket be y in dollars. As cost of shoes is $8 more than the jacket,

x = y + 8

Therefore, x - y = 8    (1)

Also the total cost of the shoes and jacket is $46, therefore

x + y = 46    (2)

Adding (1) and (2) we get

2x = 54

x = 27

Therefore, cost of shoes is $27.

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Answer: the answer is 16 if i am not mistaken

Step-by-step explanation:

Answer:

Step-by-step explanation:

-3y = -2x + 4

3y = 2x - 4

y = 2/3x - 4/3

perp; -3/2

y + 3 = -3/2(x - 4)

y + 3 = -3/2x + 6

y = -3/2x + 3

Answer:

(9,-5)

I hope this helps!

Answer:

blue is about 31.4

Step-by-step explanation:

orange is about 15.7

Answer: answered :)

Step-by-step explanation:

Answer:

3 5/7

Step-by-step explanation:

2 3/5 * 1 3/7

convert the numbers to mixed fractions

13/5 * 10/7

factor the number 10 = 5*2

13/5 * 5 * 2/7

cancel the common number 5

13/1 * 2/7

apply fraction rule

13/1 * 2/7 = 13 * 2/ 1*7

multiply the numbers

26/7

convert to mixed number

26/7 = 3 5/7

The number of students who study Indonesian only = 10

Total pupils= 110

Study French = 88

Study Indonesian = 65

Study French and German = 40

Study German and Indonesian = 38

Study French and Indonesian = 26

Study German only = 19

Students who study German only = G - F∩G - G∩I + F∩G∩I

                                                     19= 88-40-38 + F∩G∩I

                                                   F∩G∩I = 9

Students who study all three languages = 9

So the students who study only Indonesian = I - F∩I - G∩I + F∩G∩I

                                                                        = 65- 38-26+ 9

                                                                        = 10

Therefore the number of students studying Indonesian only = 10.

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The complete question is:

In a certain school, there are 180 pupils in Year 7. One hundred and

ten pupils study French, 88 study German and 65 study Indonesian.

Forty pupils study both French and German, 38 study German and

Indonesian, and 26 study both French and Indonesian, while 19 study

German only. Find the number of pupils who study Indonesian only.

Answer:

Step-by-step explanation:

\(\frac{480+24(x-40)}{x}\)

The numerator of the rational expression the money he earned for 'x' hours

The rate at which William is paid for each hour in excess of 40 hours 24.

x = 50 hours = (40 + 10 ) hours

The amount paid for excess 10 hours = 24 *10 = 240

Total amount earned for the week = 480 + 240 = 720

The compound event probability of spinning an even number and flipping heads is P ( A ) = 1/4

Given data ,

Let the total number of outcomes in spinning a spinner be = 6

The number of even outcomes = 3

Let the number of outcomes in flipping a coin = 2

So , the probability of landing an even number = 3/6 = 1/2

The probability of landing a heads = 1/2

And , probability of spinning an even number and flipping heads is given by P ( A ) = probability of landing a heads x probability of landing an even number

On simplifying , we get

P ( A ) = 1/2 ( 1/2 )

P ( A ) = 1/4

Hence , the probability is 1/4 or 25 %

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Answer: I calculated the value after 5 years to be 5,734.40 or 5,734

Step-by-step explanation:

Answer:

the empty set  {∅}

Step-by-step explanation:

{x | x < -3} ∩ {x | x > 5} is giving us

(-∞, -3) intersecting (5, ∞).

Since those two intervals do not intersect the solution is the empty set

Exterior Angle property = sum of interior opposite angle is equal to the exterior Angle

x= 48+96

x= 144°

Answer:

144°

Step-by-step explanation:

x is an exterior angle of the triangle.

Angles 96° and 48° are interior angles of the triangle that are not adjacent to angle x. Angles 96° and 48° are called the "remote interior angles" of exterior angle x.

Theorem:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

x = 48 + 96

x = 144

Answer: 144°

Let the unknown number be x;

Two more than the number is expressed as x + 2

Twice of that number is expressed as 2x

Now, if two more than a number is less than twice that number, we can express that as;

Hence the correct inequality that represents the sentence is;

The probability is the ratio of the favorable event to the total number of events. All three show the correct description.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.

The probability of spinning and landing on red is 20% can be written as 1/5 which represents the spinner has five equal sections.

Meg spins the spinner 25 times and lands on red 10 times, or 40% of the time. In this, 40% represents the probability of red occurring 10 times out of 25.

She spins the spinner 80 times and lands on red 18 times or 22. 5% of the time. In this, 22.5 % represents the probability of red occurring 18 times out of 80.

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A stem and leaf plot look like a bar graph when they are turned on its sides.

A stem and leaf plot is defined as the type of display tool that can be used for the representation of results from a data set which shows shape and spread of a continuous data distribution.

A bar graph is also defined as the type of display tool that can be used for the representation of results from a data set with rectangular bars with heights or lengths proportional to the values that they represent.

A stem and leaf plot will take the shape of a bar graph when they are turned by their side.

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Answer:

North?

Step-by-step explanation:

A generic graph would be

Where:

A = amplitude

p = period

φ = phase

D = middle line

First let's evaluate the period of the function, see that x = -1/4 we have y = 5, it will have again at x = 3/4.

The period is

Let's put it in our function already

To find out the amplitude, we take the max value, the minimum value (all in modulus) and take the average, the max value here is 5 and the minimum -3 (in modulus it's 3), the average is

Therefore

And the D value will be the average too, of the maximum two, but here we don't use the modulus on negative values, therefore

Hence.

We know that when x = 0 we have y = 1, then

When cos(φ) = 0? when φ = π/2 for example. Of course, there are other solutions but we just need one. Now we have all the parameters of our cosine

The final answer is:

Answer:

one side is 16, the other is 8\(\sqrt{3}\)

Step-by-step explanation:

30-60-90 angle triangle always give the following sides

1-\(\sqrt{3}\)-2 , which is a-b-c

to label your triangle as such

8= a

other leg =b

hypotenuse = c

so. if a =8, then

c = 8*2 =16

b=8\(\sqrt{3}\)

The "data view" of a dataset with two groups that each contain 40 people will have 80 rows.

A data set is a collection of data that is organized and processed to provide useful information. In a data set, each row represents a single observation or record. In the case where a data set contains two groups, each group represents a separate set of observations or records.

If each group has 40 people, this means that there are 40 separate observations or records in each group. Therefore, the total number of rows in the "data view" of the data set will be equal to the sum of the number of rows in each group, which is 40 + 40 = 80.So, the "data view" of a data set with two groups that each have 40 people will have 80 rows, with each row representing a single observation or record from one of the two groups.

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Answer: 1/5 of the money

Step-by-step explanation:

The ratio shows that Kyle gets 3 parts of the money, Meg gets 2 parts of the money, and Dan gets 7 parts of the money.  Simple addition lets us know there are 10 parts of the money, and because Meg got 2 of them, she has 2/10ths of the money, or 1/5.

Hope it helps :) and let me know if you want me to elaborate.

Isaiah's challenges may manifest themselves in his behavior at school in several ways. Firstly, he may display difficulties in paying attention and staying focused on tasks. This can result in incomplete assignments.

Missed instructions, and a general struggle to keep up with the class. Secondly, Isaiah may exhibit disruptive behavior, such as talking out of turn, interrupting others, or engaging in off-task activities. These behaviors can disrupt the learning environment for both himself and his peers. Lastly, Isaiah may demonstrate a lack of motivation or engagement in school-related activities. He may appear disinterested, withdrawn, or reluctant to participate in class discussions or group work.

These manifestations of Isaiah's challenges in his behavior at school are often indicators of underlying issues, such as learning disabilities, attention difficulties, or emotional struggles. It is important for teachers and caregivers to recognize these behaviors as potential signs of underlying challenges and provide appropriate support and intervention to help Isaiah overcome these obstacles and thrive academically and socially.

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Question:

Write an algebraic statement that represents all the ways your player will win. Be sure to define your variable

Answer:

Erica:

\(0 \leq |x - y| < 10\)

Nita:

\(10 < |x - y| \leq 20\)

Step-by-step explanation:

Given

Players: Erica & Nita

Range: 0 to 20

Represent Erica with x and Nita with y

For Erica to win;

The difference between x and y must be less than 10 but greater than or equal to 0

i.e.

\(0 \leq x - y \leq 10\) or \(0 \leq y - x \leq 10\)

These two expressions can be merged together to be:

\(0 \leq |x - y| < 10\)

For Nita to win;

The difference between x and y must be greater than 10 but less than or equal to 20

i.e.

\(10 < x - y \leq 20\) or \(10 < y - x \leq 20\)

These two expressions can be merged together to be:

\(10 < |x - y| \leq 20\)

Answer:

Standard form: 1

Step-by-step explanation

expanded notation form: 1

expanded factors form: 1x1

expanded exponential for 1x 10^0

The resulting graph looks like as given below

To represent complex numbers on the graph, we use the complex plane. A complex plane is a two-dimensional plane, where the x-axis represents the real part of the complex number, and the y-axis represents the imaginary part of the complex number.

To plot the complex number -3+2i, we first locate the point (-3, 2) on the complex plane. This point represents the complex number -3+2i, where -3 is the real part and 2 is the imaginary part.

Here we have

To represent the sum of the complex numbers -3+2i and -3-i on the complex plane, we first add the real parts and the imaginary parts separately to get the sum:

-3 + 2i + (-3 - i) = -6 + i

This means the sum is the complex number -6+i.

To plot this on the complex plane, we represent the real part -6 as the horizontal axis and the imaginary part i as the vertical axis.

So we draw a coordinate plane with the x-axis labeled -6 and the y-axis labeled 1i.

Then we plot the point (-6,1) on the plane. This point represents the complex number -6+i.

Hence,

The resulting graph looks like as given below

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The complement of set A, denoted by ​ A`, is the collection of all elements that belong to the universal set but are not part of set A. It's not necessary to mention the universe (also known as U) if it's understood which set of elements is being referred to.

The complement of a set A is the collection of all elements that belong to the universal set but not to set A. It is denoted as ​ A` and does not include any elements that are already in set A. The universal set, also known as U, contains all possible elements and is assumed to be known. Therefore, when referring to the complement of a set, it is not necessary to mention the universal set explicitly. The complement of a set is useful in determining the set of elements that are not part of a particular set, and it can be used in various mathematical operations.

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Given:

There are 2,540,160 strings of SALESPERSONS with no consecutive S's.

Explanation:

The number of r-combinations of a set of n distinct objects is C(n,r) = \(\frac{n!}{r!(n-r)!}\)

Multiplication principle : If one event can occur in m ways AND a second event can occur in n ways, then the number of ways that the two events can occur in sequence is then mn.

We want to place the 4S's in the string of the other letters such that there are not consecutive. Since there are 9 positions including spaces between two consecutive letters in the 8-letter string and two positions on either side of the string, we need to place 4 of the 9 positions to contain a single S each.

By the definition of combination, there are ⁹C₄ ways to select 4 of the 9 positions to place the S's (as the order of the positions is not important since a different order of the S's leads to the same string).

By the multiplication principle, there are then ⁹C₄. \(\frac{8!}{2}\) (divided by 2 since , in remaining 8 characters 2E are identical) possible strings of SALESPERSONS with no consecutive S's.

⁹C₄ . \(\frac{8!}{2}\) = \(\frac{9!}{4!(9-4)!}\) \(\frac{8!}{2}\)

           = \(\frac{9!}{4!.5!} . 20,160\)

           = 126.20,160

           = 2,540,160

Thus, there are 2,540,160 strings of SALESPERSONS with no consecutive S's.

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