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matrenka [14]
3 years ago
10

A plane has 360 total seats, which are divided into economy class and business class. For every 13 seats in economy class, there

are 5seats in business class.How many seats are there in each class?
Mathematics
1 answer:
wlad13 [49]3 years ago
8 0
260 seats in economy class, 100 in business class
The ratio of economy class to business class is 13:5
13+5 = 18 (total seats in the ratio)
360/18 = 20 (to see how many multiples of the ratio there are)
20*13 economy = 260 economy
20*5 business = 100 business
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The temperature T of an object in degrees Fahrenheit after t minutes is represented by the equation T(t) = 69e−0.0174t + 79. To
Papessa [141]

Answer: T(90) = 93.413 F

Step-by-step explanation:

The temperature T of an object in degrees Fahrenheit after t minutes is represented by the equation

T(t) = 69e−0.0174t + 79.

T is the dependent variable while t is the independent variable. To determine any value for Temperature, we will input the corresponding value for time into the function.

We want to determine the temperature of the object after one and a half hours. This means that we have to convert one and a half hours to minutes

1f 1 hour = 60 minutes

Then 1.5 hours = 1.5 × 60 = 90 minutes.

We would substitute t = 90 minutes into the equation, it becomes

T(90) = 69e−0.0174×90 + 79

T(90) = 69e−1.566 + 79

T(90) = 14.413 + 79

T(90) = 93.413 F

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3 years ago
Graph each of the equations and then determine which one represents the rank catcher that is elevated
Tanya [424]
We have two functions that are Parabolas. A parabola is a type of quadratic function which is a special type of “U”-shaped curve called. So let's solve this problem for the first parabola and then for the second one.

1. Graph of the first equation

We have that:

y=x^2-2x+3

So if we graph this equation, the parabola that matches it is shown in Figure 1.

1.1 Direction of Parabola

In general, a parabola or quadratic function is given by the following way:

y=ax^2+bx+c \\ \\ where \ "a" \ is \ called \ the \ leading \ coefficient

Given that our leading coefficient is positive, then the direction of the parabola is upward, that is, it opens upward.

1.2 Location of vertex with respect to the x-axis

The vertex a parabola can be found as follows:

(-\frac{b}{2a},f(-\frac{b}{2a}))

But: \\ \\ a=1 \\ b=-2 \\ c=3 \\ \\ Accordingly: \\ \\ -\frac{b}{2a}=-\frac{(-2)}{2(1)}=1 \\ \\ f(1)=1^2-2(1)+3=2 \\ \\ So \ the \ vertex \ is: \\ \\ V(1,2)

So the vertex is located two units above the x-axis.

<span>1.3 Determine if the graph depicts the rain gauge
</span>
A rain gauge is an instrument used by meteorologists and hydrologists to gather and measure the amount of liquid precipitation<span> over a set period of time.
</span>
From Figure 4 we can affirm that this is the parabola that resembles a rain gauge elevated from the ground. 

1.4 Why or why not?

It basically the question asks for the parabola that has a vertex well above the x-axis. From Figure 4, you can see that the elevated parabola is in fact:

y=x^2-2x+3

2. Graph of the second equation

We have that:

y=x^2+4x+4

So if we graph this equation, the parabola that matches it is shown in Figure 2.

2.1 Direction of Parabola

As in the previous problem, given that our leading coefficient is positive, then the direction of the parabola is also upward, that is, it opens upward.

2.2 Location of vertex with respect to the x-axis

The vertex of a parabola can be found as follows:

(-\frac{b}{2a},f(-\frac{b}{2a}))

In \ this \ case: \\ \\ a=1 \\ b=4 \\ c=3 \\ \\ Accordingly: \\ \\ -\frac{b}{2a}=-\frac{4}{2(1)}=-2 \\ \\ f(-2)=(-2)^2+4(-2)+4=0 \\ \\ So \ the \ vertex \ is: \\ \\ V(-2,0)

So the vertex lies on the x-axis.

2.3 Determine if the graph depicts the rain gauge

This parabola does not resembles a rain gauge elevated from the ground.

2.4 Why or why not?

As you can see the parabola touches the x-axis. If the x-axis represents the ground, then the rain gauge is touching it, that is, it is not elevated.

3. Graph of the third equation

We have that:

y=3x^2+21x+30

So if we graph this equation, the parabola that matches it is shown in Figure 5.

3.1 Direction of Parabola

As in the previous parabolas, given that our leading coefficient is positive, then the direction of the parabola is also upward, that is, it opens upward.

3.2 Location of vertex with respect to the x-axis

In \ this \ case: \\ \\ a=3 \\ b=21 \\ c=30 \\ \\ Accordingly: \\ \\ -\frac{b}{2a}=-\frac{21}{2(3)}=-\frac{7}{2} \\ \\ f(-\frac{7}{2})=3(-\frac{7}{2})^2+21(-\frac{7}{2})+30=-\frac{27}{4} \\ \\ So \ the \ vertex \ is: \\ \\ V(-\frac{7}{2},-\frac{27}{4})

So the vertex is shifted \frac{27}{4} units downward the x-axis.

3.3 Determine if the graph depicts the rain gauge

This parabola does not resembles a rain gauge elevated from the ground.

3.4 Why or why not?

The vertex of this parabola lies on the negative y-axis. So it is not elevated from the ground.

5 0
3 years ago
Lisa makes 35 dollars per month babysitting . She spends 25% of what she earns on entertainment. How much does she spend on ente
Musya8 [376]

Answer:8.75$

Step-by-step explanation:hope this helps :)

4 0
3 years ago
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What is the volume of the metal in this heavy-duty pipe? (It is not drawn to scale and the inside of the pipe is empty space.) S
Jlenok [28]
The volume of the pipe is about 282.6 cubic feet.

First, we need to find the area of each circular cross section and subtract them to find the width of the pipe. The area of a circle is pi(r^2).

pi(3^2) - pi(2^2)
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The width of the pipe is 15.7. Now, multiply that by 18 to find the volume.
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Stolb23 [73]

Answer:

14 +15 the answer is this

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