Ask question

Ask question

All categories

Keith_Richards [23]

3 years ago

14

The British Queen is to receive 4 foreign dignitaries. The digni- taries are sensitive to the order in which they are received.

In how many ways can the Queen receive them? Give your answer in terms of per- mutations or combinations and explain your choice. You do not have to evaluate.

1 answer:

Readme [11.4K]3 years ago

4 0

Answer:

Number of Ways = ₄P₄ = 24

Step-by-step explanation:

Given that there are going to be 4 dignitaries, and that they are sensitive to the order (i.e the order of the dignitaries matter), hence the total number of ways they can be arranged can be found by permutating 4 dignitaries.

i.e

Number of Ways = ₄P₄ = 24

You might be interested in

Enter a phrase for the expression. 49s

Rainbow [258]

I don’t get this explain it better

5 0

2 years ago

nathan has 15m dollars. he buys 2 bags and 3 books. each bag costs 2m dollars. each book costs $10. how much money does nathan s

Hitman42 [59]

well, if Nathan has 15 million dollars and buys 2 bags and 3 books and if each bag is 2 million you would do 15 minus 2 and when you get the answer you would minus 10 dollars off of that and then do 10 times that number.

I hope you understand what I'm saying if not pls ask for help.

4 0

2 years ago

Wittaler [7]

i have no idea what question you need answered

7 0

2 years ago

Read 2 more answers

FYI I thank to everyone and give brainliest!!!!!!!!!

Kobotan [32]

To find (f+g)(x), add the equations and simplify by combining like terms.

(x/2)-2+2x^2+x-3
2x^2+ (x/2) +x -5
2x^2 + (1/2)x+x -5
2x^2+ (3/2)x -5

Final answer: C

Remember that (x/2) is the same as (1/2)x. They both represent half of x.

4 0

2 years ago

NO LINKS!!! What is the equation of these two graphs?

S_A_V [24]

Answer:

$\textsf{1.} \quad y=-\dfrac{1}{30}x^2+\dfrac{1}{2}x+\dfrac{68}{15}\:\:\textsf{ where}\:\:x \geq \dfrac{15-\sqrt{769}}{2}\\\\\quad \textsf{or} \quad y=2\sqrt{x+5}$

$\textsf{2.} \quad y=-|x+1|+5$

Step-by-step explanation:

<h3><u>Question 1</u></h3>

<u>Method 1 - modelling as a quadratic with restricted domain</u>

Assuming that the points given on the graph are points that the <u>curve passes through</u>, the curve can be modeled as a quadratic with a limited domain. Please note that as the x-intercept has not been defined on the graph, I am not including this in this first method.

Standard form of a quadratic equation:

$y=ax^2+bx+c$

Given points:

(-4, 2)
(-1, 4)
(4, 6)

Substitute the given points into the equation to create 3 equations:

<u>Equation 1 (-4, 2)</u>

$\implies a(-4)^2+b(-4)+c=2$

$\implies 16a-4b+c=2$

<u>Equation 2 (-1, 4)</u>

$\implies a(-1)^2+b(-1)+c=4$

$\implies a-b+c=4$

<u>Equation 3 (4, 6)</u>

$\implies a(4)^2+b(4)+c=6$

$\implies 16a+4b+c=6$

Subtract Equation 1 from Equation 3 to eliminate variables a and c:

$\implies (16a+4b+c)-(16a-4b+c)=6-2$

$\implies 8b=4$

$\implies b=\dfrac{4}{8}$

$\implies b=\dfrac{1}{2}$

Subtract Equation 2 from Equation 3 to eliminate variable c:

$\implies (16a+4b+c)-(a-b+c)=6-4$

$\implies 15a+5b=2$

$\implies 15a=2-5b$

$\implies a=\dfrac{2-5b}{15}$

Substitute found value of b into the expression for a and solve for a:

$\implies a=\dfrac{2-5(\frac{1}{2})}{15}$

$\implies a=-\dfrac{1}{30}$

Substitute found values of a and b into Equation 2 and solve for c:

$\implies a-b+c=4$

$\implies -\dfrac{1}{30}-\dfrac{1}{2}+c=4$

$\implies c=\dfrac{68}{15}$

Therefore, the equation of the graph is:

$y=-\dfrac{1}{30}x^2+\dfrac{1}{2}x+\dfrac{68}{15}$

$\textsf{with the restricted domain}: \quad x \geq \dfrac{15-\sqrt{769}}{2}$

<u>Method 2 - modelling as a square root function</u>

Assuming that the points given on the graph are points that the <u>curve passes through</u>, and the x-intercept should be included, we can model this curve as a <u>square root function</u>.

Given points:

(-4, 2)
(-1, 4)
(4, 6)
(0, -5)

The parent function is:

$y=\sqrt{x}$

Translated 5 units left so that the x-intercept is (0, -5):

$\implies y=\sqrt{x+5}$

The curve is stretched vertically, so:

$\implies y=a\sqrt{x+5} \quad \textsf{(where a is some constant)}$

To find a, substitute the coordinates of the given points:

$\implies a\sqrt{-4+5}=2$

$\implies a=2$

$\implies a\sqrt{-1+5}=4$

$\implies 2a=4$

$\implies a=2$

$\implies a\sqrt{4+5}=6$

$\implies 3a=6$

$\implies a=2$

As the value of a is the same for all points, the equation of the line is:

$y=2\sqrt{x+5}$

<h3><u>Question 2</u></h3>

<u>Vertex form of an absolute value function</u>

$f(x)=a|x-h|+k$

where:

(h, k) is the vertex
a is some constant

From inspection of the given graph:

vertex = (-1, 5)
point on graph = (0, 4)

Substitute the given values into the function and solve for a:

$\implies a|0-(-1)|+5=4$

$\implies a+5=4$

$\implies a=-1$

Substituting the given vertex and the found value of a into the function, the equation of the graph is:

$y=-|x+1|+5$

7 0

1 year ago