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2 years ago

13

Coneys ice cream store records the daily temperature and the number of ice cream cones it sells each day the table shows data fo

r several days a linear function can be used to model the data
what is the best prediction of the number of ice cream cones sold on a day that has a temperature of 90°F?

A) 165 ice cream cones

B) 185 ice cream cones

C) 200 ice cream cones

D) 220 ice cream cones

2 answers:

Katen [24]2 years ago

8 0

Answer:

C) 200 ice cream cones

Step-by-step explanation:

e-lub [12.9K]2 years ago

7 0

Answer:

ITS 185 FOR K12 PPL I JJST TOOK THE TEST TRUSH MEEEEEEEEE

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Binomial Expansion/Pascal's triangle. Please help with all of number 5.

Mandarinka [93]

$\begin{matrix}1\\1&1\\1&2&1\\1&3&3&1\\1&4&6&4&1\end{bmatrix}$

The rows add up to $1,2,4,8,16$ , respectively. (Notice they're all powers of 2)

The sum of the numbers in row $n$ is $2^{n-1}$ .

The last problem can be solved with the binomial theorem, but I'll assume you don't take that for granted. You can prove this claim by induction. When $n=1$ ,

$(1+x)^1=1+x=\dbinom10+\dbinom11x$

so the base case holds. Assume the claim holds for $n=k$ , so that

$(1+x)^k=\dbinom k0+\dbinom k1x+\cdots+\dbinom k{k-1}x^{k-1}+\dbinom kkx^k$

Use this to show that it holds for $n=k+1$ .

$(1+x)^{k+1}=(1+x)(1+x)^k$
$(1+x)^{k+1}=(1+x)\left(\dbinom k0+\dbinom k1x+\cdots+\dbinom k{k-1}x^{k-1}+\dbinom kkx^k\right)$
$(1+x)^{k+1}=1+\left(\dbinom k0+\dbinom k1\right)x+\left(\dbinom k1+\dbinom k2\right)x^2+\cdots+\left(\dbinom k{k-2}+\dbinom k{k-1}\right)x^{k-1}+\left(\dbinom k{k-1}+\dbinom kk\right)x^k+x^{k+1}$

Notice that

$\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!}{\ell!(k-\ell)!}+\dfrac{k!}{(\ell+1)!(k-\ell-1)!}$
$\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(\ell+1)}{(\ell+1)!(k-\ell)!}+\dfrac{k!(k-\ell)}{(\ell+1)!(k-\ell)!}$
$\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(\ell+1)+k!(k-\ell)}{(\ell+1)!(k-\ell)!}$
$\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(k+1)}{(\ell+1)!(k-\ell)!}$
$\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{(k+1)!}{(\ell+1)!((k+1)-(\ell+1))!}$
$\dbinom k\ell+\dbinom k{\ell+1}=\dbinom{k+1}{\ell+1}$

So you can write the expansion for $n=k+1$ as

$(1+x)^{k+1}=1+\dbinom{k+1}1x+\dbinom{k+1}2x^2+\cdots+\dbinom{k+1}{k-1}x^{k-1}+\dbinom{k+1}kx^k+x^{k+1}$

and since $\dbinom{k+1}0=\dbinom{k+1}{k+1}=1$ , you have

$(1+x)^{k+1}=\dbinom{k+1}0+\dbinom{k+1}1x+\cdots+\dbinom{k+1}kx^k+\dbinom{k+1}{k+1}x^{k+1}$

and so the claim holds for $n=k+1$ , thus proving the claim overall that

$(1+x)^n=\dbinom n0+\dbinom n1x+\cdots+\dbinom n{n-1}x^{n-1}+\dbinom nnx^n$

Setting $x=1$ gives

$(1+1)^n=\dbinom n0+\dbinom n1+\cdots+\dbinom n{n-1}+\dbinom nn=2^n$

which agrees with the result obtained for part (c).

4 0

3 years ago

Say that a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse. Find b if a = 21 and c =

maria [59]

When the triangle is a right triangle, you can use the Pythagorean theorem. The formula would be

c^2 = a^2 + b^2

If a = 21 and c=29, thus

b^2 = c^2 - a^2
b^2 = 29^2 - 21^2
b^2 = 400
b = square root (400)
b = 20 units.

Thus, the answer is <span>D) B = 400</span>

5 0

3 years ago

Read 2 more answers

To fill out a sign chart, you will need to use test numbers before and after each of the function's zeros and ___

Vikki [24]

Answer:

C. asymptotes

Step-by-step explanation:

In the figure attached, a sign chart is shown. To fill it out you need to find the function's zeros and asymptotes. The zeros are those x values that makes the function equal to zero, in the example, those are the x values that make the denominator equal to zero (x = -1 and x = 5). In a rational function, the asymptotes are those x values that make the numerator equal to zero (x = -9 in the example)

Function in the example:

$\frac{(-2x-2)(2x-10)}{-9x-81}$

7 0

3 years ago

2. The average daily rainfall in London during April was 3.5 mm. How much rain fell during the month?

Vikki [24]

Answer:

105mm

Step-by-step explanation:

To find the rainfall during the month of April simply multiply the number of days in April times the average daily rainfall

Number of days in April: 30

Average daily rainfall: 3.5mm

Rainfall during the month = 30 * 3.5 = 105mm

7 0

2 years ago

43. Can you place ten lumps of sugar in three empty cups so that

erma4kov [3.2K]

Answer: No.

Step-by-step explanation:

We have 10 lumps of sugar, and we want to divide them into 3 cups, in such a way that there is an odd number of lumps in each cup.

This only can happen if we have 3 odd numbers such that the addition is equal to 10.

Now 10 is an even number, remember that even numbers can be written as:

2*k

where k is an integer number.

And odd numbers can be written as:

2*n + 1

where n is an integer.

Then we have 3 odd numbers, let's call them:

(2*n + 1), (2*k + 1) and (2*p + 1).

Now let's add them:

(2*n + 1) + (2*k + 1) + (2*p + 1).

2*(n + k + p) + 1 + 1+ 1

2*(n + k + p) + 2 + 1 =

2*(n + k + p + 1) + 1.

Now, the number n + k + p + 1 is an integer number, let's call it X, then we have that the addition of the 3 odd numbers is:

2*X + 1

This is an odd number

So for any 3 odd numbers that we add together, the result will always be an odd number.

Then is impossible to add 3 odd numbers and get 10 as the result (Again, 10 is an even number).

Then is not possible to have an odd number of lumps in each cup.

5 0

2 years ago