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Zielflug [23.3K]

3 years ago

6

A tennis racket in Sport City costs $180 and is discounted by 15%. The same model racket costs $200 at Tennis World and is on sa

le for 20% off. Which store is offering the better deal?

1 answer:

scZoUnD [109]3 years ago

5 0

Sport City is the better deal.

Sport City = 180 - (180 x .15) = $153
Tennis World = 200 - (200 x .20) = $160

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In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning. a2b3; a5b3; ab8; b8;

Fiesta28 [93]

We have to find the expansion of $(3a+4b)^{8}$

We will use binomial expansion to expand the given expression, which states that the expression $(a+b)^{n}$ is expanded as :

$(a+b)^{n}=^{n}C_{0}a^{n}+^{n}C_{1}a^{n-1}b+^{n}C_{2}a^{n-2}b^{2}+........^{n}C_{n}b^{n}$

Now expanding $(3a+4b)^{8}$ we get,

$(3a+4b)^{8}=^{8}C_{0}(3a)^{8}+^{8}C_{1}(3a)^{7}(4b)+^{8}C_{2}(3a)^{6}(4b)^{2}+^{8}C_{3}(3a)^{5}(4b)^{3}+^{8}C_{4}(3a)^{4}(4b)^{4}+^{8}C_{5}(3a)^{3}(4b)^{5}+^{8}C_{6}(3a)^{2}(4b)^{6}+^{8}C_{7}(3a)(4b)^{7}+^{8}C_{8}(4b)^{8}$

$(3a+4b)^{8}=^{8}C_{0}(3)^{8}a^{8}+^{8}C_{1}(3)^{7}(4)(a^{7}b)+^{8}C_{2}(3)^{6}(4)^{2}(a^{6}b^{2})+^{8}C_{3}(3)^{5}(4)^{3}(a^{5}b^{3})+^{8}C_{4}(3)^{4}(4)^{4}(a^{4}b^{4})+^{8}C_{5}(3)^{3}(4)^{5}(a^{3}b^{5})+^{8}C_{6}(3)^{2}(4)^{6}(a^{2}b^{6})+^{8}C_{7}(3)(4)^{7}(ab^{7})+^{8}C_{8}(4)^{8}(b^{8})$

So, the variables are $a^{5}b^{3}$ , $b^{8}$ , $a^{4}b^{4}$ , $a^{8} , [tex] ab^{7}$

5 0

3 years ago

What is 252781937463620 x 4636272985518390382?<br><br>

eimsori [14]

Answer:

$1.1719661e+33$

Step-by-step explanation:

$252781937463620 * 4636272985518390382$

Multiply.

$1.1719661e+33$

Hope this helps!

4 0

3 years ago

Find the following list of data calculate a demean be the maid in and see the mouth or mothers of the numbers from

Lelechka [254]

Given:

A fair die is rolled.

It pays off $10 for 6, $7 for a 5, $4 for a 4 and no payoff otherwise.

To find:

The expected winning for this game.

Solution:

If a die is rolled then the possible outcomes are 1, 2, 3, 4, 5, 6.

The probability of getting a 6 is:

$P(6)=\dfrac{1}{6}$

The probability of getting a 5 is:

$P(5)=\dfrac{1}{6}$

The probability of getting a 4 is:

$P(4)=\dfrac{1}{6}$

The probability of getting other numbers (1,2,3) is:

$P(\text{Otherwise})=\dfrac{3}{6}$

$P(\text{Otherwise})=\dfrac{1}{2}$

Now, find the sum of product of payoff and their corresponding probabilities to find the expected winning for this game.

$E(x)=10\times P(6)+7\times P(5)+4\times P(4)+0\times P(\text{Otherwise})$

$E(x)=10\times \dfrac{1}{6}+7\times \dfrac{1}{6}+4\times \dfrac{1}{6}+0\times \dfrac{1}{2}$

$E(x)=\dfrac{10}{6}+\dfrac{7}{6}+\dfrac{4}{6}+0$

On further simplification, we get

$E(x)=\dfrac{10+7+4}{6}$

$E(x)=\dfrac{21}{6}$

$E(x)=3.5$

Hence, the expected winnings for this game are $3.50.

5 0

3 years ago

Which of these numbers has the highest value? -22 0.0099 0 -1 |-1|

Ivan

|-1| because the the two lines on the outside of -1 make it positive. Hope this helps.

5 0

3 years ago

Read 2 more answers

The wavelength of a radio wave varies inversely as its frequency. A wave with a frequency of 720 kilohertz has a length of 500 m

LenaWriter [7]

Answer:

800 meters

Step-by-step explanation:

y is inversely proportional to x is the same as y is inversely proportional to $\frac{1}{x},$ that means

$y=\dfrac{k}{x}.$

If a wave with a frequency of x=720 kilohertz has a length of y=500 meters, then

$500=\dfrac{k}{720}\\ \\k=500\cdot 720=360000.$

Hence, the length of a wave y with a frequency of x=450 kilohertz is

$y=\dfrac{360000}{450}=800$

4 0

3 years ago