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3 years ago

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5 Mr. McClellan is hosting a barbeque at his house for his family. When he went to buy charcoal for the grill, he saw that a 4-p

ound bag of charcoal costs $5.00 and a 7-pound bag of charcoal costs $9.00. If Mr. McClellan want to buy the bag that gives him the best deal, which bag of charcoal would you tell him to buy?

1 answer:

galina1969 [7]3 years ago

7 0

Answer:

4 pounds

Step-by-step explanation:

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A circle has a radius of 3. An arc in this circle has a central angle of 60°.

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Emilia is shopping for fresh produce at a farmers' market. She bought a watermelon for $5 and she also wants to buy peppers. Eac

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$0.75n + $5 = t

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A limited-edition poster increases in value each year.after 1 year,the poster is worth $20.70 after 2 years,it’s worth $23.81.wh

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Answer: Every year the worth of the painting goes up by $3.11 so just add i guess?

Step-by-step explanation:

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3 years ago

Show work and explain with formulas.

vova2212 [387]

Answer:

$\large\boxed{4.\ S_{13}=260}$

$\large\boxed{5.\ \sum\limits_{k=1}^7(2k+5)=91}$

$\large\boxed{6.\ a_1=17,\ a_2=26,\ a_3=35}$

Step-by-step explanation:

4.

We have:

$a_6=18,\ a_{13}=32$

These are the terms of the arithmetic sequence.

We know:

$a_n=a_1+(n-1)d$

Therefore

$a_6=a_1+(6-1)d\ \text{and}\ a_{13}=a_1+(13-1)d\\\\a_6=a_1+5d\ \text{and}\ a_{13}=a_1+12d\\\\a_{13}-a_6=(a_1+12d)-(a_1+5d)\\\\a_{13}-a_6=a_1+12d-a_1-5d\\\\a_{13}-a_6=7d$

Substitute a₆ = 18 and a₁₃ = 32:

$7d=32-18$

$7d=14$ <em>divide both sides by 7</em>

$d=2$

$a_6=a_1+5d$

$18=a_1+5(2)$

$18=a_1+10$ <em>subtract 10 from both sides</em>

$8=a_1\to a_1=8$

The formula of a sum of terms of an arithmetic sequence:

$S_n=\dfrac{a_1+n_1}{2}\cdot n$

Substitute a₁ = 8, a₁₃ = 32 and n = 13:

$S_{13}=\dfrac{8+32}{2}\cdot13=\dfrac{40}{2}\cdot13=20\cdot13=260$

===========================================

5.

We have

$\sum\limits_{k=3}^7(2k+5)\to a_k=2k+5$

Calculate $a_{k+1}$

$a_{k+1}=2(k+1)+5=2k+2+5=2k+7$

Calculate the difference:

$a_{k+1}-a_k=(2k+7)-(2k+5)=2k+7-2k-5=2$

It's the arithmetic sequence with first term

$a_1=2(1)+5=2+5=7$

and common difference d = 2.

The formula of a sum of terms of an arithmetic sequence:

$S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n$

Substitute n = 7, a₁ = 7 and d = 2:

$S_7=\dfrac{2(7)+(7-1)(2)}{2}\cdot7=\dfrac{14+(6)(2)}{2}\cdot7=\dfrac{14+12}{2}\cdot7=\dfrac{26}{2}\cdot7=(13)(7)\\\\S_7=91$

===========================================

6.

We have:

$a_1=17,\ a_n=197,\ S_n=2247$

The formula for the n-th term of an arithmetic sequence:

$a_n=a_1+(n-1)d$

The formula of the sum of terms of an arithmetic sequence:

$S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n$

Substitute:

$(1)\qquad 197=17+(n-1)d\\\\(2)\qquad2247=\dfrac{(2)(17)+(n-1)d}{2}\cdot n$

Convert the first equation:

$197=17+(n-1)d$ <em>subtract 17 from both sides</em>

$180=(n-1)d$ Substitute it to the second equation:

$2247=\dfrac{34+180}{2}\cdot n\\\\2247=\dfrac{214}{2}\cdot n$

$2247=107n$ <em>divde both sides by 107</em>

$21=n\to n=21$

Put the value of n to the equation (n - 1)d = 180:

$(21-1)d=180$

$20d=180$ <em>divide both sides by 20</em>

$d=9$

Therefore we have the explicit formula for the nth term of an arithmetic sequence:

$a_n=17+(n-1)(9)\\\\a_n=17+9n-9\\\\a_n=9n+8$

Put n = 1, n = 2 and n = 3:

$a_1=9(1)+8=9+8=17\qquad\text{CORRECT :)}\\\\a_2=9(2)+8=18+8=26\\\\a_3=9(3)+8=27+8=35$

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3 years ago

a spinner is divided into 11 equal sections from 0 to 10. you spin the spinner once. what is p(even)?

erica [24]

It is given in the question that

A spinner is divided into 11 equal sections from 0 to 10. you spin the spinner once.

And number of even numbers in 0 to 10 is 6.

Total number of possibilities is 6 and total number of sample space is 11.

So the probability of getting an even number is

$p(even) = \frac{6}{11}$

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3 years ago

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