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3 years ago

9

Mark took his family out for dinner. He planned to leave a 15% gratuity on the bill. What is the total cost if the bill was 123.

50 and he used a 10% coupon?

1 answer:

valkas [14]3 years ago

3 0

believe its

$127.82 because if you subtract 10% of 123.50 from itself then add a 15% tip you get 127.82

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2. Suppose the temperature that most foods can stay bacteria free in restaurants varies approximately according to a normal dist

vagabundo [1.1K]

Answer:

28.4

Step-by-step explanation:

Given that:

Mean, m = 31.3

Standard deviation, s = 2.8

Since, data is normally distributed :

P(x < 0.15) gives a Z value of - 1.036

Using the Zscore formula :

Z = (x - mean) / standard deviation

-1.036 = (x - 31.3) / 2.8

-1.036 * 2.8 = x - 31.3

-2.9008 = x - 31.3

-2.9008 + 31.3 = x

28.3992 = x

The temperature which correlates to the bottom 15% of the distribution is 28.4

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I have a hard time with fractions and I need help. <br><br> 6 2/3 × 5/6=

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g In R simulate a sample of size 20 from a normal distribution with mean µ = 50 and standard deviation σ = 6. Hint: Use rnorm(20

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Answer:

> a<-rnorm(20,50,6)

> a

[1] 51.72213 53.09989 59.89221 32.44023 47.59386 33.59892 47.26718 55.61510 47.95505 48.19296 54.46905

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Then we can find the mean and the standard deviation with the following formulas:

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[1] 50.72451

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[1] 7.470221

Step-by-step explanation:

For this case first we need to create the sample of size 20 for the following distribution:

$X\sim N(\mu = 50, \sigma =6)$

And we can use the following code: rnorm(20,50,6) and we got this output:

> a<-rnorm(20,50,6)

> a

[1] 51.72213 53.09989 59.89221 32.44023 47.59386 33.59892 47.26718 55.61510 47.95505 48.19296 54.46905

[12] 45.78072 57.30045 57.91624 50.83297 52.61790 62.07713 53.75661 49.34651 53.01501

Then we can find the mean and the standard deviation with the following formulas:

> mean(a)

[1] 50.72451

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[1] 7.470221

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3 years ago

Find the perimeter of the pentagon MNPQR with vertices M(2, 4), N(5, 8), P(8, 4), Q(8, 1), and R(2, 1)

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Answer:

The pentagon MNPQR has a perimeter of 22 units.

Step-by-step explanation:

Geometrically speaking, the perimeter of the pentagon is the sum of the lengths of each side, that is:

$p = MN + NP + PQ + QR + RM$ (1)

$p = \sqrt{\overrightarrow{MN}\,\bullet \, \overrightarrow{MN}} + \sqrt{\overrightarrow{NP}\,\bullet \, \overrightarrow{NP}} + \sqrt{\overrightarrow{PQ}\,\bullet \, \overrightarrow{PQ}} + \sqrt{\overrightarrow{QR}\,\bullet \, \overrightarrow{QR}} + \sqrt{\overrightarrow{RM}\,\bullet \, \overrightarrow{RM}}$ (1b)

If we know that $M(x,y) = (2,4)$ , $N(x,y) = (5,8)$ , $P(x,y) = (8,4)$ , $Q(x,y) = (8,1)$ and $R(x,y) = (2,1)$ , then the perimeter of the pentagon MNPQR is:

$p =\sqrt{(5-2)^{2}+(8-4)^{2}} + \sqrt{(8-5)^{2}+(4-8)^{2}}+\sqrt{(8-8)^{2}+(1-4)^{2}}+\sqrt{(2-8)^{2}+(1-1)^{2}}+\sqrt{(2-2)^{2}+(4-1)^{2}}$ $p = \sqrt{3^{2}+4^{2}} + \sqrt{3^{2}+(-4)^{2}}+\sqrt{0^{2}+(-3)^{2}}+\sqrt{(-6)^{2}+0^{2}}+\sqrt{0^{2}+3^{2}}$

$p = 22$

The pentagon MNPQR has a perimeter of 22 units.

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2 years ago