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Mary drove 355 miles using 17 gallons of gas. At this rate, how many gallons of gas would she need to drive 284 miles?

alexgriva [62]

Answer: 13.60 gallons divide 355 by 17 to get the base miles per gallon then use that and divide it 284 by 20.88

Step-by-step explanation:

5 0

3 years ago

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Find the perimeter of the triangle with vertices A(negative 2,2,3), B(4,negative 4,3), and C(7,6,4).

gayaneshka [121]

Answer:

$P\approx 28.872\,\text{units}$

Step-by-step explanation:

We are given coordinates of each of the vertices of the triangle ABC, hence we can use the distance formula to find the lengths of each of the side.

the distance formula is generally written as:

$r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

for the side AB: A(-2,2,3) and B(4,-4,3)

$AB = \sqrt{(-2-4)^2+(2-(-4))^2+(3-3)^2}$

$AB = \sqrt{(-6)^2+(6)^2+(3-3)^2}$

$AB = \sqrt{72}$

for the side BC: B(4,-4,3) and C(7,6,4)

$BC = \sqrt{(4-7)^2+((-4)-6)^2+(3-4)^2}$

$BC = \sqrt{110}$

for the side CA: C(7,6,4) and A(-2,2,3)

$CA = \sqrt{(7-(-2))^2+(6-2)^2+(4-3)^2}$

$CA = \sqrt{98}$

Now we all the sidelengths:

to find the perimeter we need to just sum the three side lengths:

$P = AB + BC + CA$

$P = \sqrt{72} + \sqrt{110} + \sqrt{98}$

$P\approx 28.872\,\text{units}$

this is the perimeter of triangle ABC

6 0

3 years ago

Find the value of x. Round your answer to the nearest tenth. tan 12 degrees= ten over (x)

Lorico [155]

Tan(12)=-0.6358599287. That means -0.6358599287 = 10/x so you can swap the x to the other side to make x = 10/-0.6358599287 Which equals -15.7 rounded to the nearest tenth.

5 0

3 years ago

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The amount of time it takes Isabella to wait for the bus is continuous and uniformly distributed between 3 minutes and 17 minute

Arturiano [62]

Answer:

P(X>5) = 0.857

Step-by-step explanation:

Let X $\sim$ uniform(3.17)

$f(x) = \dfrac{1}{17-3} ; \ \ \ 3 \le x \le 17$

The required probability that it will take Isabella more than 5 minutes to wait for the bus can be computed as:

$P(X > 5) = \int ^{17}_{5} f(x) \ dx$

$P(X > 5) = \int ^{17}_{5} \dfrac{1}{17-3} \ dx$

$P(X > 5) =\dfrac{1}{14} \Big [x \Big ] ^{17}_{5}$

$P(X > 5) =\dfrac{1}{14} [17-5]$

$P(X > 5) =\dfrac{12}{14}$

P(X>5) = 0.857

6 0

3 years ago

In the sale, jumpers are on the offer "buy 2, save a third of the price". Jeans are also currently 30% off. Jumpers cost £45 eac

Alinara [238K]

Answer:

The total cost is 130

Step-by-step explanation:

Jumpers: 45 x 2= 90

90-33.33%=$60

Jeans:

50 x 2=100

100-30%=70

Add together

70+60=130

3 0

3 years ago

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