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2 years ago

How many ways can the letters of the word EIGHT be arranged if the first letter must be an E?

Mathematics

1 answer:

Savatey [412]2 years ago

5 0

Answer: C

<u>Step-by-step explanation:</u>

1st letter (E) 2nd letter 3rd letter 4th letter 5th letter

₁C₁ ₄C₁ ₃C₁ ₂C₁ ₁C₁

1 x 4 x 3 x 2 x 1 = 24

₁P₁ x ₄P₃

1 x 24 = 24

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What is 1,000 to the power of 4?

quester [9]

The answer to what is 1,000 to the power of 4 is 1,000,000

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2 years ago

cuanto pagaríamos por un libro cuyo precio es de $25 si le aplicamos un descuento del 25% cuanto dinero ahorramos

kotegsom [21]

Tenemos precio de lista de $25 para el libro.

Si aplicamos un descuento del 25%, este descuento representa:

$D=(\frac{25}{100})\cdot25=0.25\cdot25=6.25$

Ahorramos $6.25.

El precio que pagamos el libro es $18.75.

$P=L-D=25-6.25=18.75$

4 0

6 months ago

iris charges a fee for her consulting services plus an hourly rate that is 1 1/5 times her fee on a 7 hour job and iris charged

Veronika [31]

Based on the given problem above, here is the solution.
Given: Iris's charge: 470
1 1/5 times her fee: additional hourly rate
? = fee for an hourly rate
What we need to do first is divide 470 by 7 hours, so 470/7 = 67.143/hour.
So Iris's per hour is 67.143 without the additional rate.
Now, let's look for the 1 1/5 of 470. 1 1/5 is equal to 1.2. So 470 x 1.2 = 564.
To get the total fee of her hourly rate, we add 67.143 and 564, so Iris's hourly rate then is 631.143 or 631.14.

5 0

3 years ago

The steps below show the incomplete solution to find the value of m for the equation 5m − 2m + 4 = −1 + 12: Step 1: 5m − 2m + 3

Delicious77 [7]

Given:

Consider the equation is:

$5m-2m+3=-1+12$

Some steps of the solution are given.

To find:

The next step of the solution.

Solution:

Step 1: The given equation is:

$5m-2m+3=-1+12$

Step 2: Simplifying right hand side.

$5m-2m+3=11$

Step 3: Simplifying left hand side.

$3m+3=11$

These steps are already given. So, the next step is:

Step 4: Subtracting 3 from both sides.

$3m=8$

Therefore, the correct option is (b).

8 0

2 years ago

Determine which of the sets of vectors is linearly independent. A: The set where p1(t) = 1, p2(t) = t2, p3(t) = 3 + 3t B: The se

defon

Answer:

The set of vectors A and C are linearly independent.

Step-by-step explanation:

A set of vector is linearly independent if and only if the linear combination of these vector can only be equalised to zero only if all coefficients are zeroes. Let is evaluate each set algraically:

$p_{1}(t) = 1$ , $p_{2}(t)= t^{2}$ and $p_{3}(t) = 3 + 3\cdot t$ :

$\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0$

$\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (3 +3\cdot t) = 0$

$(\alpha_{1}+3\cdot \alpha_{3})\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot t = 0$

The following system of linear equations is obtained:

$\alpha_{1} + 3\cdot \alpha_{3} = 0$

$\alpha_{2} = 0$

$\alpha_{3} = 0$

Whose solution is $\alpha_{1} = \alpha_{2} = \alpha_{3} = 0$ , which means that the set of vectors is linearly independent.

$p_{1}(t) = t$ , $p_{2}(t) = t^{2}$ and $p_{3}(t) = 2\cdot t + 3\cdot t^{2}$

$\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0$

$\alpha_{1}\cdot t + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (2\cdot t + 3\cdot t^{2})=0$

$(\alpha_{1}+2\cdot \alpha_{3})\cdot t + (\alpha_{2}+3\cdot \alpha_{3})\cdot t^{2} = 0$

The following system of linear equations is obtained:

$\alpha_{1}+2\cdot \alpha_{3} = 0$

$\alpha_{2}+3\cdot \alpha_{3} = 0$

Since the number of variables is greater than the number of equations, let suppose that $\alpha_{3} = k$ , where $k\in\mathbb{R}$ . Then, the following relationships are consequently found: