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3 years ago

I need help with this question

Mathematics

2 answers:

denis-greek [22]3 years ago

8 0

The answer is 6 to the power of 4

Furkat [3]3 years ago

7 0

6^4

when divining two exponents with the same base, you subtract the bottom from the top exponent : 7-3 = 4

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(a) How many different 7-place license plates are possible if the first 2 places are for letters and the other 5 for numbers?

Olegator [25]

Answer:

a) 67600000 possible plates

b) 19656000 possible plates where neither digit or letter are repeated

Step-by-step explanation:

The easiest way to solve this problem is seeing how many possibilities and there for each place in the license plate:

We have the following 7 places:

P1 - P2 - P3 - P4 - P5 - P6 - P7

The alphabet has 26 letters and there are 10 digits. So,

a) For each position there are the following possibilites

26 - 26 - 10 - 10 - 10 - 10 - 10

So in all, there are, 26*26*10*10*10*10*10 = 67600000 possible plates

b) Let's do the possibilites for each position again. Now, no letter or number can be repeated, so.

P1 is still 26. Now for P2, the letter in position P1 cannot be repeated, so there are only 25 possibilies. As for the digits, for P3, the first digit, there are still 10 possibilities. For P4, there are 9, since the digit in P3 cannot be repeated. For P5 there are 8, since P3 and P4 cannot be repeated... So there are the following number of possibilities:

26-25-10-9-8-7-6

In all, there are 26*25*10*9*8*7*6 = 19656000 possible plates where neither digit or letter are repeated.

5 0

3 years ago

What is x if f ( x) = 23?

musickatia [10]

In the expression f(x)=23, x is not a variable. f(x) means “a function of x” or “f of x” and is in practice another way of substituting for the variable y, that is, we are saying:

y=23.

That means x is unspecified and could be anything. So on the xy plane, this is a straight horizontal line, 23 units above the x axis. That would be the best way to interpret this, although it is a little ambiguous.

Usually functions of x are expressed in terms of x, such as:

f(x) = x^2

6 0

3 years ago

How are X and Y related?

Mamont248 [21]

<h3>The relationship between x and y is called a linear relationship because the points so plotted all lie on a single straight line. The number 95 in the equation y=95x+32 is the slope of the line, and measures its steepness.</h3>

5 0

3 years ago

Read 2 more answers

A scientist is working with <br> 0.9m<br> of gold wire. How long is the wire in millimeters

Bingel [31]

There is 1000 mm in one meter....
So..... .9 x 1000 = 900 mm

8 0

4 years ago

Find two unit vectors orthogonal to a=⟨−2,−4,−2⟩a=⟨−2,−4,−2⟩ and b=⟨−3,5,2⟩b=⟨−3,5,2⟩ Enter your answer so that the first non-ze

Levart [38]

Answer:

u₁= ⟨1/(7*√3),−5/(7*√3) ,−11/(7*√3)⟩

u₂= ⟨-1/(7*√3),5/(7*√3) ,11/(7*√3)⟩

Step-by-step explanation:

for a=⟨−2,−4,−2⟩ and b=⟨−3,5,2⟩

a vector orthogonal to a and b can be found through the vectorial product of a and b. Thus

c= a x b $c=\left[\begin{array}{ccc}i&j&k\\-2&-4&-2\\-3&5&2\end{array}\right] = \left[\begin{array}{ccc}-4&-2\\5&2\end{array}\right]*i+\left[\begin{array}{ccc}-2&-2\\-3&2\end{array}\right]*j+\left[\begin{array}{ccc}-2&-4\\-3&5\end{array}\right]*k = 2*i -10*j - 22*k$

then c₁=⟨2,−10,−22⟩ and c₂= - c₁= ⟨-2,10,22⟩ are orthogonal to a and b

the corresponding unit vectors are

u₁=c₁/|c₁| = ⟨2,−10,−22⟩ / √(2²+(−10)²+(−22)²) = ⟨2,−10,−22⟩/(14*√3) = ⟨1/(7*√3),−5/(7*√3) ,−11/(7*√3)⟩

then u₂= - u₁= ⟨-1/(7*√3),5/(7*√3) ,11/(7*√3)⟩

then the unit vectors are

u₁= ⟨1/(7*√3),−5/(7*√3) ,−11/(7*√3)⟩

u₂= ⟨-1/(7*√3),5/(7*√3) ,11/(7*√3)⟩

7 0

4 years ago