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3 years ago

Solve c= 8a-3b for a

Mathematics

1 answer:

Vesnalui [34]3 years ago

6 0

Answer:

(c+3b)/8 = a

Step-by-step explanation:

c= 8a-3b

Add 3b to each side

c+3b= 8a-3b+3b

c+3b = 8a

Divide each side by 8

(c+3b)/8 = 8a/8

(c+3b)/8 = a

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La dirección del Colegio Montes y los padres de familia están organizando un viaje cultural a Guanajuato para los alumnos de seg

notsponge [240]

Answer:

x + y = 47 (eqn 1)

x + 2y = 79 (eqn 2)

Solving the simultaneous equation,

The hotel has 15 single rooms and 32 double rooms.

Step-by-step explanation:

English Translation

The management of Colegio Montes and the parents are organizing a cultural trip to Guanajuato for second grade students and their teachers. Students will sleep in double rooms and teachers in singles. The hotel has double rooms (2 beds) and single rooms (1 bed), totaling 47 rooms and 79 beds. To confirm if they can be accommodated, they want to know how many rooms there are of each type. If "x" denotes single rooms and "y" denotes double rooms, Write the system of equations that represents the situation: Equation that represents the number of rooms (1) Equation that represents the number of beds (2)

Solution

The number of single rooms = x

The number of double rooms = y

The number of beds in single rooms = x

The number of beds in double rooms = 2y

Total number of rooms = 47

Total number of beds = 79

Sum of single and double rooms = Total number of rooms

x + y = 47 (eqn 1)

Sum of the beds in the single rooms and the beds in the double rooms = Total number of beds

x + 2y = 79 (eqn 2)

Writing the equations together

x + y = 47 (eqn 1)

x + 2y = 79 (eqn 2)

Solving the equations simultaneously,

x = 15, y = 32

Hence, the hotel has 15 single rooms and 32 double rooms.

Hope this Helps!!!

6 0

3 years ago

Triangle ABC and DEF are right triangles, as shown. Triangle ABC is similar to triangle DEF. which ratios are equal to sin C?

Dafna11 [192]

Answer:

First option and Fourth option.

Step-by-step explanation:

To solve this exercise you need to use the following Trigonometric Identity:

$sin\alpha=\frac{opposite}{hypotenuse}$

In this case you know that:

$\alpha =C$

Since triangle ABC is similar to triangle DEF:

$\angle C=\angle F$

Let's begin with the triangle ABC.

You can identify that:

$opposite=AB\\hypotenuse=AC$

Then, substituing values, you get:

$sinC=\frac{AB}{AC}$

In triangle DEF, you know that:

$opposite=DE\\hypotenuse=DF$

So, substituing values, you get:

$sinF=sinC=\frac{DE}{DF}$

4 0

3 years ago

The weight of a package of mints is believed to be normally distributed with mean 21.37 grams and standard deviation 0.4, i.e. X

nasty-shy [4]

Answer:

$P(21$

And using a calculator, excel or the normal standard table we have that:

$P(-1.85$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the weigths of a population, and for this case we know the distribution for X is given by:

$X \sim N(21.37,0.4)$