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Anarel [89]
3 years ago
14

Which best describes the strength of a model with an r-value of 0.29

Mathematics
2 answers:
olchik [2.2K]3 years ago
5 0
The <u>correct answer</u> is:

It is not a very strong fit.

Explanation:

The r-value, or correlation coefficient, tells us how closely our model fits the data.

The r-values range from -1 to 1.  -1 is a perfect fit of a decreasing model; 1 is a perfect fit of an increasing model.  0 is no fit at all.

Since our r-value is 0.29, this is much closer to 0 than it is to 1 or -1; this means it is not a very strong fit.
Olegator [25]3 years ago
3 0

Answer:

it is A} a weak positive correlation.

Step-by-step explanation:

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A box contains 2 plain pencils and 2 pens. A second box contains 7 color pencils and 3 crayons. One item from each box is chosen
photoshop1234 [79]
In the box containing the 2 plain pencils and 2 pens, there would be a 50% chance of getting a pen. In the other box containing 7 color pencils and 3 crayons there would be a 30% chance of getting a crayon.
8 0
3 years ago
How to solve this trigonometric equation cos3x + sin5x = 0
mrs_skeptik [129]

Answer:

  x = {nπ -π/4, (4nπ -π)/16}

Step-by-step explanation:

It can be helpful to make use of the identities for angle sums and differences to rewrite the sum:

  cos(3x) +sin(5x) = cos(4x -x) +sin(4x +x)

  = cos(4x)cos(x) +sin(4x)sin(x) +sin(4x)cos(x) +cos(4x)sin(x)

  = sin(x)(sin(4x) +cos(4x)) +cos(x)(sin(4x) +cos(4x))

  = (sin(x) +cos(x))·(sin(4x) +cos(4x))

Each of the sums in this product is of the same form, so each can be simplified using the identity ...

  sin(x) +cos(x) = √2·sin(x +π/4)

Then the given equation can be rewritten as ...

  cos(3x) +sin(5x) = 0

  2·sin(x +π/4)·sin(4x +π/4) = 0

Of course sin(x) = 0 for x = n·π, so these factors are zero when ...

  sin(x +π/4) = 0   ⇒   x = nπ -π/4

  sin(4x +π/4) = 0   ⇒   x = (nπ -π/4)/4 = (4nπ -π)/16

The solutions are ...

  x ∈ {(n-1)π/4, (4n-1)π/16} . . . . . for any integer n

5 0
3 years ago
Find equations of the spheres with center(3, −4, 5) that touch the following planes.a. xy-plane b. yz- plane c. xz-plane
postnew [5]

Answer:

(a) (x - 3)² + (y + 4)² + (z - 5)² = 25

(b) (x - 3)² + (y + 4)² + (z - 5)² = 9

(c) (x - 3)² + (y + 4)² + (z - 5)² = 16

Step-by-step explanation:

The equation of a sphere is given by:

(x - x₀)² + (y - y₀)² + (z - z₀)² = r²            ---------------(i)

Where;

(x₀, y₀, z₀) is the center of the sphere

r is the radius of the sphere

Given:

Sphere centered at (3, -4, 5)

=> (x₀, y₀, z₀) = (3, -4, 5)

(a) To get the equation of the sphere when it touches the xy-plane, we do the following:

i.  Since the sphere touches the xy-plane, it means the z-component of its centre is 0.

Therefore, we have the sphere now centered at (3, -4, 0).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, -4, 0) as follows;

d = \sqrt{(3-3)^2+ (-4 - (-4))^2 + (0-5)^2}

d = \sqrt{(3-3)^2+ (-4 + 4)^2 + (0-5)^2}

d = \sqrt{(0)^2+ (0)^2 + (-5)^2}

d = \sqrt{(25)}

d = 5

This distance is the radius of the sphere at that point. i.e r = 5

Now substitute this value r = 5 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 5²  

(x - 3)² + (y + 4)² + (z - 5)² = 25  

Therefore, the equation of the sphere when it touches the xy plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 25  

(b) To get the equation of the sphere when it touches the yz-plane, we do the following:

i.  Since the sphere touches the yz-plane, it means the x-component of its centre is 0.

Therefore, we have the sphere now centered at (0, -4, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (0, -4, 5) as follows;

d = \sqrt{(0-3)^2+ (-4 - (-4))^2 + (5-5)^2}

d = \sqrt{(-3)^2+ (-4 + 4)^2 + (5-5)^2}

d = \sqrt{(-3)^2 + (0)^2+ (0)^2}

d = \sqrt{(9)}

d = 3

This distance is the radius of the sphere at that point. i.e r = 3

Now substitute this value r = 3 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 3²  

(x - 3)² + (y + 4)² + (z - 5)² = 9  

Therefore, the equation of the sphere when it touches the yz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 9  

(b) To get the equation of the sphere when it touches the xz-plane, we do the following:

i.  Since the sphere touches the xz-plane, it means the y-component of its centre is 0.

Therefore, we have the sphere now centered at (3, 0, 5).

Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, 0, 5) as follows;

d = \sqrt{(3-3)^2+ (0 - (-4))^2 + (5-5)^2}

d = \sqrt{(3-3)^2+ (0+4)^2 + (5-5)^2}

d = \sqrt{(0)^2 + (4)^2+ (0)^2}

d = \sqrt{(16)}

d = 4

This distance is the radius of the sphere at that point. i.e r = 4

Now substitute this value r = 4 into the general equation of a sphere given in equation (i) above as follows;

(x - 3)² + (y - (-4))² + (z - 5)² = 4²  

(x - 3)² + (y + 4)² + (z - 5)² = 16  

Therefore, the equation of the sphere when it touches the xz plane is:

(x - 3)² + (y + 4)² + (z - 5)² = 16

 

3 0
3 years ago
find the equation of the linear function which passes through the points (1,-3) and (4,-2) give your answer in y=mx+b form
Tpy6a [65]
To solve this problem, we first have to find the slope of the two given points. To find the slope, we have to use slope intercept form, which is y₂ - y₁ divided by x₂ - x₁. We substitute each variable for its corresponding value, and we'll get -2 - (-3) divided by 4-1. If we simplify the expression, we'll get 1/3. Next, we plug in the slope and one ordered pair into the equation and we get -3 = 1/3 * 1 + b. We should solve for b and we end up with -3 1/3 = b. Therefore, the equation is y = 1/3x - 3 1/3.
5 0
3 years ago
Brandon rode in a taxi that charges a flat fee of $2.25 and an additional $0.40 per mile of his trip. If he paid $6.80 for the c
r-ruslan [8.4K]

Answer:

11 \frac{3}{8} miles.

Step-by-step explanation:

To find how many miles Brandon rode, we can create an equation in slope-intercept form: y = mx + b

$2.25 is the flat fee, or the unchanging variable. This is our y-intercept, or b.

$0.40 is the changing variable, as it changes value depending on the amount of miles ridden. This is our slope, or m.

We know Brandon spent $6.80 on the cab ride. So, this is our y.

We get the equation: 6.80 = 0.40x + 2.25.

To solve, first subtract 2.25 from both sides of the equation:

6.80 - 2.25 = 0.40x + 2.25 - 2.25

We get: 4.55 = 0.40x

Now, just divide by 0.40 on both sides:

4.55 ÷ 0.40 = 0.40x ÷ 0.40

We get: 11.375 = x

So, Brandon rode for 11.375 miles. When converted to a mixed number, we get 11 \frac{3}{8} .

<em>I would appreciate brainliest, if not that's ok!</em>

6 0
2 years ago
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