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3 years ago

Write an equation of a line that is parallel to y=-3x+5 that passes through the point (0,-4)

Mathematics

1 answer:

elena55 [62]3 years ago

6 0

Answer:

${ \rm{y = - 3x + 5}}$

Gradient = -3

• Parallel lines have the same gradient, therefore gradient, m is -3

${ \rm{y = mx + c}}$

• At point (0, -4)

${ \rm{ - 4 = ( - 3 \times 0) + c}} \\ \\ { \rm{c = - 4}}$

y intercept is -4

${ \boxed{ \boxed{ \mathfrak{answer : }}{ \rm{\: \: y = - 3x - 4}}}}$

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Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of

jarptica [38.1K]

Answer:

The "probability that a given score is less than negative 0.84" is $\\ P(z$ .

Step-by-step explanation:

From the question, we have:

The random variable is normally distributed according to a standard normal distribution, that is, a normal distribution with $\\ \mu = 0$ and $\\ \sigma = 1$ .
We are provided with a z-score of -0.84 or $\\ z = -0.84$ .

Preliminaries

A z-score is a standardized value, i.e., one that we can obtain using the next formula:

$\\ z = \frac{x - \mu}{\sigma}$ [1]

Where

x is the raw value coming from a normal distribution that we want to standardize.
And we already know that $\\ \mu$ and $\\ \sigma$ are the mean and the standard deviation, respectively, of the normal distribution.

A z-score represents the distance from $\\ \mu$ in standard deviations units. When the value for z is negative, it "tells us" that the raw score is below $\\ \mu$ . Conversely, when the z-score is positive, the standardized raw score, x, is above the mean, $\\ \mu$ .

Solving the question

We already know that $\\ z = -0.84$ or that the standardized value for a raw score, x, is below $\\ \mu$ in 0.84 standard deviations.

The values for probabilities of the standard normal distribution are tabulated in the standard normal table, which is available in Statistics books or on the Internet and is generally in cumulative probabilities from negative infinity, - $\\ \infty$ , to the z-score of interest.

Well, to solve the question, we need to consult the standard normal table for $\\ z = -0.84$ . For this:

Find the cumulative standard normal table.
In the first column of the table, use -0.8 as an entry.
Then, using the first row of the table, find -0.04 (which determines the second decimal place for the z-score.)
The intersection of these two numbers "gives us" the cumulative probability for z or $\\ P(z$ .

Therefore, we obtain $\\ P(z$ for this z-score, or a slightly more than 20% (20.045%) for the "probability that a given score is less than negative 0.84".

This represent the area under the standard normal distribution, $\\ N(0,1)$ , at the left of z = -0.84.

To "draw a sketch of the region", we need to draw a normal distribution (symmetrical bell-shaped distribution), with mean that equals 0 at the middle of the distribution, $\\ \mu = 0$ , and a standard deviation that equals 1, $\\ \sigma = 1$ .

Then, divide the abscissas axis (horizontal axis) into equal parts of one standard deviation from the mean to the left (negative z-scores), and from the mean to the right (positive z-scores).

Find the place where z = -0.84 (i.e, below the mean and near to negative one standard deviation, $\\ -\sigma$ , from it). All the area to the left of this value must be shaded because it represents $\\ P(z$ and that is it.

The below graph shows the shaded area (in blue) for $\\ P(z$ for $\\ N(0,1)$ .

7 0

3 years ago

Michael and Lindsey are saving money. Michael begins with $20 and saves $5 per week. Lindsey begins with no money, but saves $10

True [87]

Let
x----------> number of weeks
y----------> saved money

we now that

Michael begins with $20 and saves $5 per week
so
y=20+5x------> equation 1

and
Lindsey begins with no money, but saves $10 per week
y=10x-------> equation 2

the number of weeks it will take for Lindsey and Michael to save the same amount of money is when equation 1 is equals to equation 2

therefore
20+5x=10x------> 10x-5x=20------> 5x=20-----> x=20/5-----> x=4 weeks

the answer is
4 weeks

3 0

2 years ago

If a,b,c are in arithmetic sequence then a = ...

andriy [413]

Answer:

If a, b and c are in arithmetic progression, that means that a + c = 2b. So a + b, a + c and b + c are also in arithmetic progression.

This might help.

8 0

3 years ago

Read 2 more answers

Which statement describes the end behavior of the exponential function f(x) = 2x – 3?

charle [14.2K]

The correct answer is:

As x→-∞, y→-3.
As x→∞, y→∞.

Explanation:

As our values of x get further into the negative numbers, the value of 2ˣ will approach 0. This is because raising a number to a negative exponent "flips" the number below the denominator and raises it to a power; we end up with smaller and smaller fractions, eventually so small that they nearly equal 0.

This will make the value of the function 0-3=-3.

As x gets larger and larger (towards ∞), the value of y, 2ˣ, continues to grow as well. Since it continues to grow exponentially, we say the value approaches ∞.

3 0

3 years ago

Read 2 more answers

Which explanation correctly solves this problem? A golf club has 85 golfers in a golf tournament. The golfers will ride in golf

Aleksandr [31]

The answer is A. 85/4=21 with 1 left over. They will need 22 golf carts.

5 0

3 years ago