Gourmet Eatery has a policy of automatically adding an 18% tip to every restaurant bill.

loris [4]

The percent of change is 73.33 percent

4 0

3 years ago

The lengths of the legs of a right triangle are consecutive even integers. The hypotenuse is 58 inches. What is the sum of the l

miskamm [114]

Answer:

82 inches

Step-by-step explanation:

The difference between consecutive even integers is 2, thus

let the legs be n and n + 2

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

n² + (n + 2)² = 58² ← expand and simplify left side

n² + n² + 4n + 4 = 3364 ( subtract 3364 from both sides )

2n² + 4n - 3360 = 0 ( divide all terms by 2 )

n² + 2n - 1680 = 0 ← in standard form

(n + 42)(n - 40) = 0 ← in factored form

Equate each factor to zero and solve for n

n + 42 = 0 ⇒ n = - 42

n - 40 = 0 ⇒ n = 40

But n > 0 ⇒ n = 40

and n + 2 = 40 + 2 = 42

Thus sum of legs = 40 + 42 = 82 inches

3 0

3 years ago

Fifty-five percent of the members of the junior varsity swim team wear glasses. Of the team memebers who do not wear glasses, 30

GarryVolchara [31]

the probability that a randomly chosen member of the JV swim team does not wear glasses and is in the 10th grade is 14%.

Given, the members of the junior varsity swim team wear glasses is 55%.

And the members of junior varsity swim team who do not wear glasses and in 10th grade is 30%.

Let the total no. of members be x.

So, the members of the junior varsity swim team wear glasses (55%),will be

$0.55x$ .

The total number of members not wearing glasses, will be

$x - 0.55 x = 0.45 x$ .

Now, the no. of members not wearing glasses and in 10th grade will be,

$\frac{0.45x\times30}{100} =0.135x$

We know that the probability of an event E, P(E) will be,

$P(E)=\frac{No.\ of Favourable\ outcomes}{total \ no. \ of \ outcomes}$

So, the probability for no. of members not wearing glasses and in 10th grade will be,

$P(E)=\dfrac{0.135x}{x}$

$P(E)=0.135\\\\P(E)=13.5 \%$

Hence the nearest whole percent of probability is 14%.

For more details on probability follow the link:

brainly.com/question/795909

8 0

3 years ago

Confused on number 10. I put one solution, but I don’t know if it’s right. I got

velikii [3]

4(3x + 12) = -6(-8-2x)
12x + 48 = 48 +12x
12x + 18 = 12x + 48
0 = 0
answer is A. infinitely many solutions

4 0

3 years ago

If data for a time series analysis are collected on an annual basis only, which pattern can be ignored? a. horizontal b. seasona

ddd [48]

If data for a time series analysis are collected on an annual basis only, then the option(b) seasonal pattern can be ignored

Time series analysis is a specific way of analyzing a sequence of data points collected over an interval of time

The seasonal pattern is refers to the seasonal characteristics of the time series data. It is the predictable pattern that repeats at a certain frequency within one year, such as weekly, monthly, quarterly, etc.

A horizontal pattern exists when the data fluctuate randomly around a constant mean over time.

A trend pattern exists when there is a long-term increase or decrease in the series.

The cyclical component of a time series refers to fluctuations around the trend, excluding the irregular component, revealing a succession of phases of expansion and contraction

Here, the data for a time series analysis are collected on an annual basis, so the seasonal pattern can be ignored

Learn more about Time series analysis here

brainly.com/question/15411875

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7 0

2 years ago