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3 years ago

Solution of this equation

Mathematics

1 answer:

lara31 [8.8K]3 years ago

5 0

2.5y + 3x = 27
5x - 2.5y = 5

Align the variables to make solving this easier.

2.5y + 3x = 27
-2.5y + 5x = 5

You can see that the 2.5y and -2.5y cancel each other out. Then add the 3x and 5x, and 27 + 5.

3x = 27
5x = 5

8x = 32

Divide both sides by 8.

x = 4

Now input that x into one of the equations to get y.

2.5y + 3(4) = 27
2.5y + 12 = 27
2.5y = 15
y = 6

The answer to this system of equations is x = 4, y = 6. (4, 6)

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Based on a survey, when 1009 consumers were asked if they are comfortable with drones delivering their purchases, 42% said yes

Darina [25.2K]

Answer:

B.The probability 0+ indicates that the probability is a very small positive value. It indicates that the event is possible, but very unlikely.

Step-by-step explanation:

Out of 1009 consumers a sample of 30 consumers is selected and asked the questions. So, the sample size is 30.

n = 30

Based on previous survey, 42% are comfortable with the drone. So in this sample, we can consider the probability of success to be 42%.

p = 42% = 0.42

q = 1 - p = 1 - 0.42 = 0.58

We want to find the probability of getting exactly 24 consumers who are comfortable with drones.

x = 24

Since, the sample size is fixed, the selections are independent and probability of success is constant, we can use the Binomial Probability to answer this problem. All the conditions of a Binomial Distribution are being satisfied.

According to the formula of Binomial Distribution, the probability of getting exactly x success among n trials is given as:

$P( X = x )=^{n}C_{x}(p)^{x}(q)^{n-x}$

Using the values, we get:

$P(X = 24) =^{30}C_{24}(0.42)^{24}(0.58)^{6}= 0.00002$

Thus, the probability of getting exactly 24 consumers from a sample of 30 who are comfortable with drones is 0.00002, which is extremely small.

Since, the value of probability is a very small positive number, it indicates that event is possible but very unlikely. An impossible event has probability equal to 0.

Therefore, option B gives the correct answer.

6 0

3 years ago

Three trigonometric functions for a given angle are shown below. cosecant theta = thirteen-twelfths; secant theta = Negative thi

Kay [80]

Answer:

(–5, 12) is the correct answer.

Step-by-step explanation:

We are given the following values:

$cosec\theta = \dfrac{13}{12}\\sec\theta=-\dfrac{13}{5}\\cot\theta =-\dfrac{5}{12}$

Now, we know the following identities:

$sin \theta = \dfrac{1}{cosec\theta}\\cos \theta = \dfrac{1}{sec\theta}\\tan \theta = \dfrac{1}{cot\theta}$

Now, the values are:

$sin\theta = \dfrac{12}{13}\\cos\theta=-\dfrac{5}{13}\\tan\theta =-\dfrac{12}{5}$

Sine value is positive and cos, tan values are negative.

It can be clearly observed that $\theta$ is in 2nd quadrant.

2nd quadrant means, the value of $x$ will be negative and $y$ will be positive.

Let us have a look at the value of $tan\theta$ :

$tan\theta = \dfrac{Perpendicular}{Base}\\OR\\tan\theta = \dfrac{y-coordinate}{x-coordinate} = -\dfrac{12}{5}\\\therefore y = 12,\\x = -5$

Please refer to the attached image for clear understanding and detailed explanation.

Hence, the correct answer is coordinate (x,y) is (–5, 12)

8 0

3 years ago

Transactions to a computer database are either new items or changes to previous items. the addition of an item can be completed

sashaice [31]

P(<100) = P((new or change) & <100) = P(new & <100) + P(change & <100)

... = P(<100 | new)*P(new) + P(<100 | change)*P(change)

... = 0.90*0.70 + 0.20*0.30

... = 0.63 + 0.06 = 0.69 . . . . probability of completing a transaction in < 100 ms

4 0

3 years ago

Use the following graph to solve the equation 3n + 7 = 52

Tanya [424]

Answer:

$3n + 7 = 52 \\ 3n = 52 - 7 \\ 3n = 45 \\ n = \frac{45}{3} \\ n = 15$

Graph is not inserted.

8 0

3 years ago

Read 2 more answers

For each container of tea, McKenzie uses 16 tea bags and 3 cups of sugar. If McKenzie uses 64 tea bags, how many cups of sugar w

cestrela7 [59]

So tis is a ratio 16 is to 3 or 16:3
if use 64 tea bags then how many cups of sugar so
turn 16:3 into fraction
16:3=16/3 or 3/16, it doesn't matter
then you want to find 64:x or 64/x or x/64

we know that 16/3=64/x because it tis an equivalent ratio
so 16/3=64/x
multiply both sdies by (3 times x)
16 times x times 3/3=64 times 3 times x/x
16 times x=64 times 3
16x=192
divide both sdies by 16
x=12
theanswer is 12 cups of sugar

5 0

3 years ago