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2 years ago

7

Suppose that a teacher wishes to distribute 25 identical pencils to Ahmed, Barbara, Casper, and Dieter such that Ahmed and Diete

r receive at least one pencil each, Casper receives no more than five pencils, and Barbara receives at least four pencils. In how many ways can such a distribution be made?

1 answer:

MA_775_DIABLO [31]2 years ago

5 0

Answer:

we will change the problem in stages

pre-place 1 in x1 & x4, and 4 in x2, thus guaranteeing their minimum requirements.

now 19 pencils remain to be distributed

when there are no restrictions on distributing n identical objects to k distinct piles, the formula is (n+k-1)C(k-1) which here translates to 22C3

finally, we need to see that x3 = 5, so we place 6 in x3 (guaranteeing that it violates the condition), and subtract such violations, ie (22-6)C3 = 16C3

ans: 22C3 - 16C3 = 980

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URGENT!! Please help Find the values of y=c(x) 3 square x, for x = 0, 0.008, 0.027, 0.064, 0.125, 0.216, 0.343, 0.512, , 0.729 a

mojhsa [17]

Answer:

We have

$y=c(x)=\sqrt[3]{x}$

$\text{for } x = 0, 0.008, 0.027, 0.064, 0.125, 0.216, 0.343, 0.512, 0.729 \text{ and } 1$

We have 10 points to find:

$\text{Point A}(0, 0)$

$\text{Point B}(0.008, 0.2)$

$\text{Point C}(0.027, 0.3)$

$\text{Point D}(0.064, 0.4)$

$\text{Point E}(0.125, 0.5)$

$\text{Point F}(0.216, 0.6)$

$\text{Point G}(0.343, 0.7)$

$\text{Point H}(0.512, 0.8)$

$\text{Point I}(0.729, 0.9)$

$\text{Point J}(1, 1)$

4 0

2 years ago

Mr Chua borrows a sum of money from the bank which charges a compound interest of 4.2% per annum, compounded 6.Given that Mr Chu

Inessa [10]

Answer:

Original sum of money = $2246.51

Step-by-step explanation:

Interest = $96.60

Interest is compounded 6 times in a year ; n = 6

time = 1 year ; Rate of interest (r) = 4.2%

Interest = Future Value - Principal Value ...........(1)

$\text{Future Value = }Principal\cdot (1+\frac{r}{100\times n})^{n\cdot t}\\\\\text{Substituting this value in equation (1) , We get }\\\\Interest=Principal\cdot (1+\frac{r}{100\times n})^{n\cdot t}-Principal\\\\\implies 96.60=Principal[\cdot (1+\frac{4.2}{100\times 6})^{6\cdot 1}-1]\\\\\implies Principal=\$2246.51$

Hence, the original sum of money borrowed = $2246.51

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2 years ago

Louise begins factoring the polynomial, which has four terms.

ad-work [718]

Louise wants to factorize completely the given polynomial $4x^{3}+12x^{2}+5x+15$

Grouping first, second terms together and third, fourth terms together

= $4x^{3}+12x^{2}+5x+15$

Taking $4x^{2}$ common from first and second terms of the given expression and taking 5 common from the third and fourth terms.

= $=4x^{2}(x+3)+5(x+3)$

Taking (x+3) common from the given expression,

= $=(4x^{2}+5)(x+3)$ is the completely factored form.

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2 years ago

To visit his grandmother, Michael takes a motorcycle 3.853.853, point, 85 kilometers and a horse 3.323.323, point, 32 kilometers

liq [111]

Answer: $7.17\ kilometers$

Step-by-step explanation:

<h3> The exercise is: "To visit his grandmother, Michael takes a motorcycle 3.85 kilometers and a horse 3.32 kilometers. In total, the journey takes 50.54 minutes. How many kilometers is Michael's journey in total?"</h3>

To solve this exercise you must pay attention to the data given.

According to the information provided in the exercise, Michael's journey is divided into two parts:

Part 1: $3.85\ kilometers$ (Traveling in a motorcycle)

Part 2: $3.32\ kilometers$ (Traveling in a horse)

Based on the given data, you can conclude that the the total distance in kilometers of Michael's journey to the house to his grandamother, is the sum of those distances ( $3.85\ kilometers$ and $3.32\ kilometers$ )

Therefore, you need to add them in order to solve the exercise.

So, You get that the result is:

$Total=3.85\ kilometers+3.32\ kilometers\\\\Total=7.17\ kilometers$

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2 years ago

Write an equation perpendicular to x-4y=20 that passes through the point 2,-5

marshall27 [118]

Answer:

4x +y = 3

Step-by-step explanation:

Perpendicular lines have slopes that are the negative reciprocals of one another. When the equation of the line is written in standard form like this, the equation of the perpendicular line can be written by swapping the x- and y-coefficients and negating one of them. Doing this much would give you ...

4x +y = (constant)

Note that we have chosen to make the equation read 4x+y, not -4x-y. The reason is that "standard form" requires the leading coefficient to be positive.

Now, you just need to make sure the constant is appropriate for the point you want the line to go through. So, it needs to be ...

4(2) +(-5) = constant = 3

The line of interest has equation ...

4x + y = 3

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2 years ago