999999999999999 times 999999999999999

The significance of the slope in regression can be determined by conducting a hypothesis test

The slope of the regression line in a regression analysis shows how  dependent variable changes as the independent variable increases by a unit. A hypothesis test on a slope coefficient, commonly referred to as the beta coefficient or the regression coefficient, can be used to ascertain the significance of the slope. The slope coefficient is compared to a null hypothesis value of zero in the hypothesis test.

The null hypothesis is rejected and it is determined that there is a significant association between the independent and dependent variables if the p-value for the slope coefficient is less than the significance threshold. Therefore, slope is not equal to zero and there is an association amongst changes in the independent variable and those in the dependent variable.

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The equation of the tangent plane to the surface z = x² + y² is: (2a)x + (2b)y - z = a² + b²

Let's choose a point on the surface, say (a, b, c), where a and b are arbitrary values.

Since z = x² + y², we have c = a² + b².

So, any point on the surface can be written as (a, b, a² + b²).

The gradient vector of the function z = x² + y² gives the direction of the normal vector at any point on the surface.

The gradient of z = x² + y² is given by (∂z/∂x, ∂z/∂y) = (2x, 2y).

Therefore, at the point (a, b, a² + b²), the normal vector is (2a, 2b).

The equation of a plane can be written as ax + by + cz = d, where (a, b, c) is the normal vector and (x, y, z) represents a point on the plane. Substituting the values we obtained, we have:

(2a)x + (2b)y + (-1)z = d

Using the point (a, b, a² + b²) on the surface, we can substitute these values into the equation:

(2a)a + (2b)b + (-1)(a² + b²) = d

2a² + 2b² - a² - b² = d

a² + b²= d

Therefore, the equation of the tangent plane to the surface z = x² + y² is: (2a)x + (2b)y - z = a² + b²

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Answer:

x=4

Step-by-step explanation:

We move all terms to the left:

1-(2x+4)-(-4x+5)=0

We get rid of parentheses

-2x+4x-4-5+1=0

We add all the numbers together, and all the variables

2x-8=0

We move all terms containing x to the left, all other terms to the right

2x=8

x=8/2

x=4

To determine a formula for the n-th term of an arithmetic sequence, we need to find the common difference (d) first.

The common difference is the constant value that is added or subtracted to each term to get to the next term.

In this case, we can find the common difference by subtracting the fourth term from the seventh term:

d = a₇ - a₄

d = 31 - 19

d = 12

Now that we have the common difference, we can use it to find the formula for the n-th term of the arithmetic sequence. The formula is given by:

aₙ = a₁ + (n - 1)d

In this formula, aₙ represents the n-th term, a₁ represents the first term, n represents the position of the term, and d represents the common difference.

Since we don't have the first term (a₁) given in the problem, we can find it by substituting the known values for a₄ and d:

a₄ = a₁ + (4 - 1)d

19 = a₁ + 3(12)

19 = a₁ + 36

a₁ = 19 - 36

a₁ = -17

Now we can substitute the values of a₁ and d into the formula to get the final formula for the n-th term:

aₙ = -17 + (n - 1)(12)

Therefore, the formula for the n-th term (aₙ) of the given arithmetic sequence is aₙ = -17 + 12(n - 1).

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Answer:

A whole number, an integer, a rational number and a real number.

Step-by-step explanation:

It is a whole number, which makes it an integer, which makes it rational, which makes it real.

Answer:

5/32

Step-by-step explanation:

5/12 × 3/8 = 5/32

hope it helps :)

Answer:

Why is there a B in there?

Step-by-step explanation:

Answer:

it is commutative properties

L = k/f, where k is the variational constant, is the formula for the inverse variation.

A mathematical relationship between two variables in which they vary in opposing directions is referred to as an inverse proportion, also known as an inverse relationship. When one variable increases while the other decreases, this is known as having inverse proportions.

Using the variables length of violin 'l' and frequency of vibration 'f'

If the length of violin 'l' is inversely proportional to the frequency of vibration 'f', this is expressed as:

l α 1/f

l = k/f

Hence the formula for the inverse variation is l = k/f where k is the constant of variation.

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Answer:

x=2, y=1

Step-by-step explanation:

4x+8y=16

4x-8y=0

Add the two equations together:

8x=16

Divide both sides by 8:

x=2

Plug this back into one of the original equations to find y:

4(2)-8y=0

8-8y=0

y=1

Hope this helps!

Answer:

x, y = (0, 0)

Step-by-step explanation:

photo math broo

Answer:

Its A 61.88ft

Step-by-step explanation:

just took the test edge 2021

Answer: 313.1 feet

Step-by-step explanation:

\tan 82=\frac{x}{44}

tan82=

44

x

​

44\tan 82=x

44tan82=x

x=313.0763\approx \mathbf{313.1}\text{ feet}

x=313.0763≈313.1 feet

Answer:

313.1

Step-by-step explanation:

If the expression is  10x2-18x-4.:

a. The greatest common factor of the expression 10x^2 - 18x - 4 is 2.

b. The expression 10x^2 - 18x - 4 can be factored completely as: 10x^2 - 18x - 4 = 2(5x + 1)(x - 2)

C.  the factoring from Part B is correct.

Part A: To find the greatest common factor of the expression 10x^2 - 18x - 4, we need to find the largest factor that divides all three terms of the expression evenly. One way to do this is to factor out the greatest common factor using the distributive property.

10x^2 - 18x - 4 = 2(5x^2 - 9x - 2)

Now, we need to factor the expression inside the parentheses further to see if we can find any additional common factors.

5x^2 - 9x - 2 can be factored using the quadratic formula, but it does not have any common factors other than 1.

Therefore, the greatest common factor of the expression 10x^2 - 18x - 4 is 2.

Part B: To factor the expression completely, we can start by using the greatest common factor of 2.

10x^2 - 18x - 4 = 2(5x^2 - 9x - 2)

Next, we need to factor the expression 5x^2 - 9x - 2 further. We can use the factoring method of product and sum:

The product of 5 and -2 is -10, and the sum of the factors that multiply to -10 and add to -9 is -10 and 1.

So, we can write 5x^2 - 9x - 2 as:

5x^2 - 10x + x - 2

= 5x(x - 2) + 1(x - 2)

= (5x + 1)(x - 2)

Therefore, the expression 10x^2 - 18x - 4 can be factored completely as:

10x^2 - 18x - 4 = 2(5x + 1)(x - 2)

Part C: To check our factoring from Part B, we can multiply the factors using the distributive property and simplify:

2(5x + 1)(x - 2) = 2(5x)(x) + 2(5x)(-2) + 2(1)(x) + 2(1)(-2)

= 10x^2 - 20x + 2x - 4

= 10x^2 - 18x - 4

Therefore, the factoring from Part B is correct.

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The required equation is VW/UW = YW/XW for the given similar triangles.

The figure is given as shown.

As per the question, given that triangles ΔUVW and ΔXYW are similar.

As we know that similar triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

Therefore, we can be written as follows:

VW/UW = YW/XW

This signifies that the corresponding angles and sides of the two triangles are equal and proportionate.

Therefore, the required equation is VW/UW = YW/XW.

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Answer:

Step-by-step explanation:

step by step explanation

Answer:

P = 9/25

Step-by-step explanation:

yeah-ya........ right?

Angle A is 19 degrees.

Angle C is 90 degrees.

Side a is approximately 7.83.

Side c is approximately 34.50.

To solve the right triangle given that B = 71 degrees and b = 24, we can use the trigonometric ratios sine, cosine, and tangent.

Finding Angle A:

Angle A is the complementary angle to B in a right triangle, so we can calculate it using the equation:

A = 90 - B

Substituting the given value, we have:

A = 90 - 71

A = 19 degrees

Therefore, Angle A is 19 degrees.

Finding Angle C:

Since it is a right triangle, Angle C is always 90 degrees.

Therefore, Angle C is 90 degrees.

Finding Side a:

We can use the sine ratio to find the length of side a:

sin(A) = a / b

Rearranging the equation to solve for a, we have:

a = b * sin(A)

Substituting the given values, we have:

a = 24 * sin(19)

a ≈ 7.83

Therefore, the length of side a is approximately 7.83.

Finding Side c:

Using the Pythagorean theorem, we can find the length of side c:

c^2 = a^2 + b^2

Substituting the given values, we have:

c^2 = 7.83^2 + 24^2

c^2 ≈ 613.68 + 576

c^2 ≈ 1189.68

Taking the square root of both sides to solve for c, we have:

c ≈ √1189.68

c ≈ 34.50

Therefore, the length of side c is approximately 34.50.

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Therefore, the factors of 3x^2 – 5x – 12 are (A) x - 4, (B) x - 3, and (C) x + 3. However, (D) 3x - 4, (E) 3x + 4, (F) 3x - 3, and (G) 3x + 3 are not factors of the given expression. The expressions that are factors of 3x^2 – 5x – 12 are x - 4, x - 3, and x + 3.

To find the factors of 3x^2 – 5x – 12, we can either use the quadratic formula or factorization. The quadratic formula can give us the roots of the equation, which are also the factors. However, factorization can give us the factors directly. Here, we'll use factorization. We need to find two binomials that multiply to give 3x^2 – 5x – 12. The factors will have the form (ax + b)(cx + d), where a, b, c, and d are integers.

We can start by looking for pairs of integers that multiply to give 3*(-12)=-36 and add up to -5. After some trial and error, we can find that -9 and 4 are such integers. So, we can write:

3x^2 – 5x – 12 = (3x + 4)(x - 3)

Therefore, the factors of 3x^2 – 5x – 12 are (A) x - 4, (B) x - 3, and (C) x + 3. However, (D) 3x - 4, (E) 3x + 4, (F) 3x - 3, and (G) 3x + 3 are not factors of the given expression.

In summary, the expressions that are factors of 3x^2 – 5x – 12 are x - 4, x - 3, and x + 3.

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The equation of a circle having endpoints of diameter as (4,9) and (4,-3) is (x - 4)² + (y - 3)² = 36.

The "center" of circle is called as midpoint of diameter.

The "x-coordinate" of "mid-point" is = (4+4)/2 = 4, and

The "y-coordinate" of "mid-point" is = (9+(-3))/2 = 3.

So, center of circle is (4,3),

The radius of circle is half the length of the diameter, which is distance between two endpoints of diameter. We find distance using distance formula:

⇒ distance = √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁,y₁) and (x₂,y₂) are "end-points" of diameter.

⇒ distance = √((4 - 4)² + (9 - (-3))²)

⇒ √(144) = 12.

So, radius is 6.

The equation of circle with center (h,k) and radius "r" is : ⇒ (x - h)² + (y - k)² = r²,

Substituting the values

We get,

⇒ (x - 4)² + (y - 3)² = 6²,

⇒ (x - 4)² + (y - 3)² = 36,

Therefore, the equation of the circle is (x - 4)² + (y - 3)² = 36.

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Answer:

Step-by-step explanation:

Answer: 60 and 82

Step-by-step explanation:

Let the outside angle = angle x

Let inside angle = angle y

Using SATT (sum of angle in a triangle theorem), we know that all angles in a triangle equal to 180°.

Given this information,

y = 180-(38+60)

y=82

Using SAT (supplemantary angle theorom) angles on a straight line equal to 180

x = 180 - (38 + 82)

= 60°

Answer:

Our friend will have two chances to catch the ball: (i) 1.005 seconds after launch, (ii) 1.978 seconds after launch.

Step-by-step explanation:

In this case, we see that ball is launched up in free fall motion, which is an uniform accelerated motion in which ball is accelerated by gravity and effects of air friction and Earth's rotation are neglected. We have to find how many time our friend would need to wait to have a chance to catch the ball. The height of the ball is represented by this equation of motion:

\(y = y_{o}+v_{o}\cdot t + \frac{1}{2}\cdot g \cdot t^{2}\) (Eq. 1)

Where:

\(y_{o}\) - Initial height of the ball, measured in meters.

\(y\) - Final height of the ball, measured in meters.

\(v_{o}\) - Initial velocity of the ball, measured in meters per second.

\(g\) - Gravitational acceleration, measured in meters per square second.

\(t\) - Time, measured in seconds.

If \(y_{o} = 6\,ft\), \(y = 38\,ft\), \(v_{o} = 48\,\frac{ft}{s}\) and \(g = -32.174\,\frac{ft}{s^{2}}\), we solve the resulting expression for \(t\):

\(-16.087\cdot t^{2}+48\cdot t -32 = 0\)

Roots are found by Quadratic Formula:

\(t_{1}\approx 1.978\,s\) and \(t_{2} \approx 1.005\,s\)

First root represents the instant after reaching maximum height, while the second one is for the instant before reaching that height. Hence, our friend will have two chances to catch the ball: (i) 1.005 seconds after launch, (ii) 1.978 seconds after launch.

Answer:

4 units left

Step-by-step explanation:

Since you are changing the x value by negative 4, you move left towards the negatives 4 units.

Answer:

20×20-4

=400-4

=396

hope it helps u....

plz mark as brainliest...

Answer:

Step-by-step explanation:

Using BODMAS rule:

B = Bracket

O = Of

D = Division

M = Multiplication

A = Addition

S = Subtraction

Now, let's solve:

\(20 \times 20 - 4\)

Multiply the numbers

\( = 400 - 4\)

Calculate the difference

\( = 396\)

Hope this helps...

Best regards!!

Answer:

since , 9^x / 9^3 = 9^5

and since there is a law for exponents that says if the bases of the exponent are equal and divided by each other we subtract the exponents

, so 9^x-3 = 9^5

then x-3 =5 , therefore the final answer will be X= 8 .

Answer:

the eagles nest is 30 cm above the ground because as you can see at the bottom of the tree its 30 degrees so since it has equal sides both of thoses sides would be 30, and as we can see it marks the nest exactly where it ends, thus, its 30 cm above the ground. pls mark me brainliest if you want a visual too ;)

a. Scatter plot: we can use the Years as the x-axis and Damage as the y-axis.

b. Regression line equation: y = -2.2909 + 1.3636x.

c. Scatter plot with regression line: [Insert scatter plot with regression line here].

d. Correlation coefficient: r ≈ 0.949.

e. Sum of squared deviations (SSD): SSD ≈ 170.94.

Prediction for a person who has smoked for 30 years: Predicted percentage of lung damage ≈ 38.963%.

a. To create a scatter plot, we can use the Years as the x-axis and Damage as the y-axis. Below is the resulting scatter plot.

b. To determine the equation of the best-fit regression line, we can use the formula y = a + bx, where a is the y-intercept and b is the slope. The values of a and b can be calculated using the following formulas:

b = (n∑xy - ∑x∑y) / (n∑x^2 - (∑x)^2)

a = (∑y - b∑x) / n

Here, n represents the sample size, ∑x, and ∑y are the sums of the x and y values, and ∑xy and ∑x^2 are the sums of the products and squares of the x and y values, respectively.

After performing the necessary calculations, we find:

b = (7(1924) - (173)(262)) / (7(642) - (173)^2) ≈ 1.3636

a = (176/7) - (1.3636/7)(118) ≈ -2.2909

Therefore, the equation of the regression line is y = -2.2909 + 1.3636x.

c. We can plot the regression line on the scatter plot. Here is the updated scatter plot with the regression line:

d. The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and +1 indicates a perfect positive correlation.

The formula for the correlation coefficient is:

r = (n∑xy - ∑x∑y) / √[(n∑x^2 - (∑x)^2)(n∑y^2 - (∑y)^2)]

After performing the calculations, we find:

r = (7(1924) - (173)(262)) / √[(7(642) - (173)^2)(7(2878) - (176)^2)] ≈ 0.949

Therefore, the correlation coefficient is r ≈ 0.949.

e. The sum of squared deviations (SSD) is a measure of the variation around the regression line. The formula for SSD is:

SSD = Σ(yi - yi)^2

where yi is the observed value and yi is the predicted value.

After substituting the values, we find:

SSD = (20 - 15.3)^2 + (14 - 9.1)^2 + (54 - 39.8)^2 + (63 - 59.6)^2 + (17 - 11.8)^2 + (71 - 67.1)^2 + (23 - 18.4)^2 ≈ 170.94

Therefore, the SSD is approximately 170.94.

To predict the percentage of lung damage for a person who has smoked for 30 years, we can substitute x = 30 into the regression equation:

y = -2.2909 + 1.3636(30) ≈ 38.963

Therefore, the predicted percentage of lung damage for a person who has smoked for 30 years is approximately 38.963%.

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Answer:

c) 600,000

Step-by-step explanation:

100,000 centimeters are in a kilometer, it says that Carl ran a 3 kilometer trail 2 times, that is 6 kilometers in total. So if you multiply 6 and 100,000 you will get 600,000

Hope this helps! :)

The required value of b is 64 units.

The perimeter of this triangle is 124 units.

The formula for the perimeter of a triangle is:

Perimeter = a + b + c

Where a, b, and c are the lengths of the sides of a triangle.

Let the values of the sides of the triangle be 4x, 6x and bx units.

So, Perimeter = 4x + 6x + bx124 = 10x + bx

The value of b can be found as:124 - 10x = bx ... (Equation 1)

We are not provided with the value of x in the problem.

Hence, we cannot directly calculate the value of b. But given that the length of the sides of a triangle is a positive value, we can say that b must be greater than 10x.

Let's assume that b = 11x.

Substituting b = 11x in Equation 1,

we get:

124 - 10x

= 11x

⇒ 21x

= 124

⇒ x

= 124/21

The value of x is: x = 124/21The value of b is: b = 11x= 11(124/21)= 64

Therefore, the value of b is 64 units.Hence, the required value of b is 64 units.

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Answer:

48% of students prefer biology

Step-by-step explanation: