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sdas [7]
3 years ago
15

Which equation represents a linear function? Equation 1: y^3 = 2x +1 Equation 2: y= 3x +1 Equation 3: y= 5x^2 - 1 Equation 4: y=

4x^4 -1
Mathematics
1 answer:
Yuri [45]3 years ago
8 0
the second equation is linear
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Two quantities are related, as shown in the table:
Rashid [163]

Answer:

y = \frac{1}{2} x + 2.

Step-by-step explanation:

From the given table it is clear that x and y are linearly related.

Now, any two points that satisfy the relation between x and y are sufficient to express the equation.

The first two given points are (2,3), and (4,4).

Therefore, the equation is \frac{y - 4}{4 - 3} = \frac{x - 4}{4 - 2}

⇒ y - 4 = \frac{1}{2} (x - 4)

⇒ y - 4 = \frac{1}{2} x - 2

⇒ y = \frac{1}{2} x + 2. (Answer)

6 0
3 years ago
Tell whether the equation has one, zero, or infinitely many solutions.<br>2(x-1/2)=8+2x​
docker41 [41]

Answer: none

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
. upper left chamber is enlarged, the risk of heart problems is increased. The paper "Left Atrial Size Increases with Body Mass
Sonbull [250]

Answer:

Part 1

(a) 0.28434

(b) 0.43441

(c) 29.9 mm

Part 2

(a) 0.97722

Step-by-step explanation:

There are two questions here. We'll break them into two.

Part 1.

This is a normal distribution problem healthy children having the size of their left atrial diameters normally distributed with

Mean = μ = 26.4 mm

Standard deviation = σ = 4.2 mm

a) proportion of healthy children have left atrial diameters less than 24 mm

P(x < 24)

We first normalize/standardize 24 mm

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (24 - 26.4)/4.2 = -0.57

The required probability

P(x < 24) = P(z < -0.57)

We'll use data from the normal probability table for these probabilities

P(x < 24) = P(z < -0.57) = 0.28434

b) proportion of healthy children have left atrial diameters between 25 and 30 mm

P(25 < x < 30)

We first normalize/standardize 25 mm and 30 mm

For 25 mm

z = (x - μ)/σ = (25 - 26.4)/4.2 = -0.33

For 30 mm

z = (x - μ)/σ = (30 - 26.4)/4.2 = 0.86

The required probability

P(25 < x < 30) = P(-0.33 < z < 0.86)

We'll use data from the normal probability table for these probabilities

P(25 < x < 30) = P(-0.33 < z < 0.86)

= P(z < 0.86) - P(z < -0.33)

= 0.80511 - 0.37070 = 0.43441

c) For healthy children, what is the value for which only about 20% have a larger left atrial diameter.

Let the value be x' and its z-score be z'

P(x > x') = P(z > z') = 20% = 0.20

P(z > z') = 1 - P(z ≤ z') = 0.20

P(z ≤ z') = 0.80

Using normal distribution tables

z' = 0.842

z' = (x' - μ)/σ

0.842 = (x' - 26.4)/4.2

x' = 29.9364 = 29.9 mm

Part 2

Population mean = μ = 65 mm

Population Standard deviation = σ = 5 mm

The central limit theory explains that the sampling distribution extracted from this distribution will approximate a normal distribution with

Sample mean = Population mean

¯x = μₓ = μ = 65 mm

Standard deviation of the distribution of sample means = σₓ = (σ/√n)

where n = Sample size = 100

σₓ = (5/√100) = 0.5 mm

So, probability that the sample mean distance ¯x for these 100 will be between 64 and 67 mm = P(64 < x < 67)

We first normalize/standardize 64 mm and 67 mm

For 64 mm

z = (x - μ)/σ = (64 - 65)/0.5 = -2.00

For 67 mm

z = (x - μ)/σ = (67 - 65)/0.5 = 4.00

The required probability

P(64 < x < 67) = P(-2.00 < z < 4.00)

We'll use data from the normal probability table for these probabilities

P(64 < x < 67) = P(-2.00 < z < 4.00)

= P(z < 4.00) - P(z < -2.00)

= 0.99997 - 0.02275 = 0.97722

Hope this Helps!!!

7 0
3 years ago
How many pieces of celery can you fill with peanut butter if you have3\4 cup of peanut an! each piece of celery will hold1\12 cu
Masja [62]
You would be able to fill 9 celery pieces

\frac{1}{12} *  \frac{9}{1} =  \frac{9}{12} which simplifies to \frac{3}{4}
3 0
3 years ago
A winter coat was originally $65 and is now marked up by 2% . What is the price after the markup?
ratelena [41]
It would be 66.3 because 2% Coverts to .02 then you multiply that to 65 and get 1.3 and then you add that to 65
5 0
3 years ago
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