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3 years ago

Commutative property

1 answer:

8 0

Simply put, it says that the numbers can be added in any order, and you will still get the same answer. For example, if you are adding one and two together, thecommutative property<span> of addition says that you will get the same answer whether you are adding 1 + 2 or 2 + 1. This also works for more than two numbers.</span>

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For the linear equation 3x + 7y = 42: a. Determine the slope: b. Determine y- intercept if it exists: c. Express equation in slo

algol13

Answer: The required answers are

(a) the slope of the given line is $-\dfrac{3}{7}.$

(b) y-intercept exists and is equal to 6.

(c) the slope-intercept form of the line is $y=-\dfrac{3}{7}x+6.$

Step-by-step explanation: We are given the following linear equation in two variables :

$3x+7y=42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to :

(a) determine the slope,

(b) determine the y-intercept, if exists

and

(c) express equation in slope-intercept form.

We know that

The SLOPE_INTERCEPT form of the equation of a straight line is given by

$y=mx+c,$ where m is the slope and c is the y-intercept of the line.

From equation (i), we have

$3x+7y=42\\\\\Rightarrow 7y=-3x+42\\\\\Rightarrow y=\dfrac{-3x+42}{7}\\\\\\\Rightarrow y=-\dfrac{3}{7}x+6.$

Comparing with the slope-intercept form, we get

$\textup{slope, m}=-\dfrac{3}{7},\\\\\\\textup{y-intercept, c}=6.$

Thus,

(a) the slope of the given line is $-\dfrac{3}{7}.$

(b) y-intercept exists and is equal to 6.

(c) the slope-intercept form of the line is $y=-\dfrac{3}{7}x+6.$

3 0

4 years ago

How much water should we add to 5 gallons of 18% acid solution to dilute it to a concentration of 10%?

KIM [24]

4 gallons of water is needed to dilute to a concentration of 10%.

<u>Step-by-step explanation:</u>

It is given that,

The 5 gallons of water contains 18% of acid solution.

Now, we are asked to find the gallons of water needed to dilute it to a concentration of 10% acid solution.

We obtain the equation by stating that the amount of acid 10% in the water must dilute up to 18%.

For this, x amount of water should be added.

Therefore, the equation is framed as,

⇒ 0.1 (x+5) = 5 (0.18)

⇒ 0.1x + 0.5 = 0.9

⇒ 0.1x = 0.9 - 0.5

⇒ x = 0.4 / 0.1

⇒ x = 4

∴ 4 gallons of water is needed to dilute to a concentration of 10%.

5 0

4 years ago

How would i solve this the shaded region is the whole inside circle.

rosijanka [135]

Answer:

34.48cm²

Step-by-step explanation:

Assuming the shaded area doesn't contain the triangle:

area of triangle = bh/2

area of triangle = 4(2)/2

area = 4

area of circle = πr²

area = π3.5²

area = 38.48

area of shaded = 38.48 - 4

area = 34.48cm²

6 0

2 years ago

A random variable is normally distributed with a mean of 25 and a standard deviation of 5. If an observation is randomly selecte

ad-work [718]

Answer:

Value of 26.93 will be exceeded 85% of the time.

Step-by-step explanation:

We are given that a random variable is normally distributed with a mean of 25 and a standard deviation of 5.

Let X = a random variable

So, X ~ N( $\mu=25,\sigma^{2} =5^{2}$ )

The z score probability distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean

$\sigma$ = standard deviation

Now, we have to find that value which will be exceeded 85% of the time, i.e.;

P(X > $x$ ) = 0.85

1 - P(X $\leq x$ ) = 0.85

P(X $\leq x$ ) = 0.15

P( $\frac{X-\mu}{\sigma}$ $\leq \frac{x-25}{5}$ ) = 0.15

P(Z $\leq \frac{x-25}{5}$ ) = 0.15

Now, in the z table the critical value of $x$ whose less than area is 0.15 is given as 0.3853, i.e;

$\frac{x-25}{5}$ = 0.3853

$x-25=0.3853 \times 5$

$x$ = 25 + 1.9265 = 26.93

Therefore, value of 26.93 will be exceeded 85% of the time.

4 0

3 years ago

I need help fast fast fast !

goblinko [34]

Answer: i don’t know if I’m correct but I think it’s A

Step-by-step explanation:

4 0

3 years ago