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Yes, the correlation coefficient is statistically significance

The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient. In a correlation report, the r stands for the coefficient.

Given,

Sample size, n = 4

Where ρ is the population correlation.

Then the number of degrees of freedom is, df = n-2 = 4-2 = 2

The corresponding critical correlation value re for a significance level of a 0.01, for a two-tailed test is た= 0.254

Here,

The null hypothesis, [tex]H_{0}[/tex] = ρ - 0 is rejected

Suppose lr> re 0.254

Because on the sample correlation provided, we know that lrl = 0.835>=0.254.

Here, it is clear that the null hypothesis is rejected.

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Answer:

Step-by-step explanation:

1/3 + 1/3 x 1/3 / 1/3 - 1/3

= 1/3 + 1/3 x 1/1 -1/3

= 1/3 + 1/3 - 1/3

= 2/3 - 1/3

= 1/3

Answer:

5/9.

Step-by-step explanation:

1/3 + 1/3 * 1/3 / 1/3 - 1/3 * 1/3

= 1/3 + 1/3 * 1 - 1/3 * 1/3

= 1/3 + 1/3 - 1/3 * 1/3

= 2/3 - 1/9

= 5/9.

Answer:

25

Step-by-step explanation:

The results of subtraction of functions are listed below:

There three fundamental binary operators (addition, multiplication, composition) and two secondary binary operators (subtraction, division) for functions. The subtraction is operation derived from addition, defined by the following expression:

(h - f) (x) = h(x) - f(x)       (1)

Now we proceed to develop each expression:

i) (h - f) (x):

ii) m(x) = (g - j) (x):

iii) m(3):

m(3) = 3² + 10 · 3 + 5

m(3) = 9 + 30 + 5

m(3) = 44

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Answer:

b=67.5°

Step-by-step explanation:

hope it helps!!!

Answer:

m = F / a is the answer

Step-by-step explanation:

F = ma

m = F / a

2x + 2y = 42

2w + q = 35

2w + v = 29

x + q + y - v = ?

x = 7

y = 14

w = 3

q = 29

v = 23

7 + 29 + 14 - 23 =

The answer is 27

Answer: [tex]\Large\boxed{27}[/tex]

Step-by-step explanation:

Given information converted into a mathematical statement

[tex]a = icecream\\b=cookie\\c=brownie\\d=cake\\e=creamed cake[/tex]

[tex]1)~a+b+a+b=42[/tex]

[tex]2)~c+d+c=35[/tex]

[tex]3)~c+c+e=29[/tex]

[tex]4)~a+d+b-e=\mbox{?}[/tex]

Simplify each equation

[tex]1)~2a+2b=42[/tex]

[tex]2)~2c+d=35[/tex]

[tex]3)~2c+e=29[/tex]

[tex]4)~(a+b)+(d-e)=\mbox{?}[/tex]

Factorize 2 out of the 1) equation

[tex]2a+2b=42[/tex]

[tex]2(a+b)=42[/tex]

Divide 2 on both sides

[tex]2(a+b)\div2=42\div2[/tex]

[tex]a+b=21[/tex]

Current system

[tex]1)~a+b=21[/tex]

[tex]2)~2c+d=35[/tex]

[tex]3)~2c+e=29[/tex]

[tex]4)~(a+b)+(d-e)=\mbox{?}[/tex]

Subtract 3) equation from the 2) equation

[tex](2c +d)-(2c+e)=(35)-(29)[/tex]

Expand the parenthesis

[tex]2c+d-2c-e=35-29[/tex]

Combine like terms

[tex]2c-2c+d-e=6[/tex]

[tex]d-e=6[/tex]

Current system

[tex]1)~a+b=21[/tex]

[tex]2)~d-e=6[/tex]

[tex]3)~(a+b)+(d-e)=\mbox{?}[/tex]

Substitute values into the 3) equation to determine the final value

  [tex](a+b)+(d-e)[/tex]

[tex]=(21)+(6)[/tex]

[tex]\Large\boxed{=27}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The minimum cost to produce the product is $7.

What are functions?

To determine the minimum cost:

We have to determine the minimum cost of producing this product.

Since [tex]f(x) = 5x^{2} -70x+258[/tex].

Now, consider the equation [tex]5x^{2} -70x+258= 0[/tex].

Dividing the above equation by 5, we get

[tex]x^{2} -70x/5+258/5=0\\x^{2} -14x+258/5=0[/tex]

Now, considering the coefficient of 'x', dividing it by '2' and then adding and subtracting the square of the number which we got after dividing.

Since the coefficient of 'x' is 14, and half of 14 is '7'.

So, adding and subtracting from the above equation.

[tex]x^{2} -14x+(7)^{2} -(7)^{2}+258/5=0\\x^{2} -14x+49 -49+258/5=0\\(x-7)^{2} -49+258/5=0\\(x-7)^{2} +258-245/5=0\\(x-7)^{2} +13/5=0\\5(x-7)^{2} +13=0[/tex]

Now, we have to determine the minimum cost to produce the product.

Since [tex]f(x) = 5x^{2} -70x+258[/tex].

[tex]f'(x) = 10x-70[/tex]

Now, let f'(x)=0

[tex]10x-70=0\\10x=70[/tex]

Therefore, x=7

Now, consider which is greater than 0.

Therefore, x= 7 is the minimum cost.

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Answer: The minimum cost to produce the product is $13.

I apologize for the late answer, hope this helps in the future!

Step-by-step explanation:

To complete the square, we need to rewrite the given function in the form:

f(x) = a(x - h)^2 + k

where (h, k) is the coordinates of the vertex of the parabola defined by the function, and a is a positive constant that determines the shape of the parabola.

We start by factoring out the coefficient of x^2:

f(x) = 5(x^2 - 14x + 51.6)

To complete the square, we need to add and subtract a constant inside the parentheses that will allow us to write the expression inside the parentheses as a perfect square. The constant we need to add and subtract is half of the coefficient of x, squared:

f(x) = 5(x^2 - 14x + 51.6 + (7)^2 - (7)^2)

= 5((x - 7)^2 + 13)

Now we have the function in the desired form, with a = 5, h = 7, and k = 13. Since a is positive, we know that the vertex of the parabola is a minimum. Therefore, the minimum cost of producing the product is $13. So the correct answer is:

5(x − 7)2 + 13

The maximum possible area would have a length of 24 feet and width of 12 feet.

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Let x represent the length and y represent the width, hence:

Since beth has 48 ft fencing and cover 3 sides, hence:

x + 2y = 48  

x = 48 - 2y     (1)

Also:

Area (A) = xy

A = (48 - 2y)y

A = 48y - 2y²

The maximum area is at A' = 0, hence:

A' = 48 - 4y

48 - 4y = 0

y = 12 feet

x = 48 - 2(12) = 24

The maximum possible area would have a length of 24 feet and width of 12 feet.

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Answer:

12 sqrt (10)

Step-by-step explanation:

S = (12 + 11 + 7) / 2 = 15

A = sqrt (s(s-a)(s-b)(s-c))

= sqrt (15(15-12)(15-11)(15-7))

= sqrt (15*3*4*8)

= sqrt (1440)

= 12 sqrt (10)

Answer:

Number = 12

Step-by-step explanation:

2n-7=n+5 (+7 to both sides)

2n=n+12 (-n to both sides)

n=12

Answer: 260 m

Step-by-step explanation:

Let's say the length of NR is x m, using the similarity rule, we get the equation

175/130 = (175+175)/x

x = 260

So NR is 260 m

The correct option is option(A) (5x-1)(x+6).

The factors of the given equation are (5x-1)(x+6).

An algebraic expression or number that divides another expression or number equally, leaving no remainder is known as factor.

The quadratic equation [tex]ax^{2} +bx+c=0[/tex]  can be expressed as the product of its linear factors as (x - k)(x - h), where h, k are the roots of the equation. This is known as factoring quadratics.

Dividing the middle term into two factors is used in quadratic factorization in this method. In splitting of the middle term, where x is the product of two factors and last term is the sum of the two factors.

Use the splitting middle term formula

[tex]5x^{2} +29x-6[/tex]

=[tex]5x^{2} +30x-x-6[/tex]

=5x(x+6)-1(x+6)

=(5x-1)(x+6)

The factors of the given equation are (5x-1)(x+6).

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Answer:

11.8 units

Step-by-step explanation:

The circle equation is given as:

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2Where

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2r

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we have

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sides

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 2

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 22r = 11.8

The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 22r = 11.8Hence, the diameter of the circle is 11.8 units

Answer: 8,9.

Step-by-step explanation:

[tex](x-2)^2+(y+6)^2=20\\Circle \ equation\\\boxed {(x-a)^2+(y-b)^2=r^2}\\r^2=20\\r*r=\sqrt{20}*\sqrt{20}\\ r=\sqrt{20}\\ r=\sqrt{4*5}\\ r=2\sqrt{5} \\ D=2r\\D=2*2\sqrt{5}\\ D=4\sqrt{5}\\ D\approx8,9.[/tex]

Answer:

In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer.

Answer:

Side AB = [tex]9\sqrt{2}[/tex]

Side AB = [tex]9\sqrt{2}[/tex]

Side CB = 36

Step-by-step explanation:

This is a special right triangle and it's also an isosceles triangle

therefore the measure of AC = AB and they are both = [tex]9\sqrt{2}[/tex]

for this special triangle the measure of hypotenuse (CB in here) is represented with [tex]x\sqrt{2}[/tex] and the legs are represented with x, each

since legs' lengths are given as = [tex]9\sqrt{2}[/tex] then x = [tex]9\sqrt{2}[/tex]

replace the x in front of [tex]x\sqrt{2}[/tex] with  [tex]9\sqrt{2}[/tex]

[tex]9\sqrt{2}[/tex] *  [tex]\sqrt{2}[/tex] = 36

The car speed measurements that represent the same level of accuracy compared to the speed limit sign is 64mph (option D).

Accuracy is the exact conformity to truth or the degree of conformity of a measure to a true or standard value.

Accuracy is different from precision as precision deals with the closeness of an observed value with a true value.

According to this question, a highway sign shows a speed limit of 65 miles per hour. This suggests that a car speed measurement that will represent the same level of accuracy compared to the speed limit sign is 64mph.

64mph is the closest speed measurement to 65mph that does not exceed this speed limit. However, 66 mph is also close but exceeds the true value for the speed limit.

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Answer:

Yes.

Step-by-step explanation:

This would be an isosceles triangle - with 2 equal sides both 20 long with a base of length 6.

A triangle can be formed from 3 line segments as long as the sum of  the length of any 2 sides exceeds the length of the third side.

The 2nd term exists 12 and 7th term exceeds the 4th by 15 exists AP : 7,12,17,....

Given : The second term exists 12th and the 7th term exceeds the 4th term by 15

The formula of the nth term :

[tex]$a_{n}=a+(n-1) d[/tex]

Where d exists a common difference

n be the number of terms

a be the first term

Substitute the value of n = 2

[tex]$a_{2}=a+(2-1) d=a+d[/tex]

Let, the second term exists 12

So, a + d = 12 ..........(1)

Substitute the value of n = 7

[tex]$a_{7}=a+(7-1) d=a+6 d[/tex]

Substitute n = 4

[tex]$a_{4}=a+(4-1) d=a+3 d[/tex]

We are given that the 7th term exceeds the 4th term by 15

So, a+6d-a-3d = 15

3d = 15

d = 5

Substitute the value of d in (1)

So, a+5 = 12

a = 12-5

a = 7

AP : a,a+d,a+2d,.... = 5, 7+5, 7+2(5),....=7,12,17,....

Therefore, AP : 7,12,17,....

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Answer:

1.8 tonne

Step-by-step explanation:

sum the parts of the ratio, 2 + 3 = 5 parts

divide the total mix by 5 to find the value of one part of the mix

3 tonne ÷ 5 = 0.6 tonne , then

3 parts = 3 × 0.6 = 1.8 tonne ← amount of gravel in the mix

Answer:

y=-5x-12/5

Step-by-step explanation:

First you need to find y intercept

y=mx+b

plug in the points (0,12)

12=mx+0

now plug in -5

12=-5x+0

subtract 0 from both side

12=-5x

divide -5 from both side.

x=12/-5

The correct simplification of 8x2(5x 2x2 − 3) is [tex]16x^{4} +40x^{3} -24x^{2}[/tex]

The correct simplification of 8x2(5x 2x2 − 3).

[tex]8x^{2} (5x+2x^{2+1} -3)=8*2x^{2+2} -8*3x^{2}[/tex]

                                [tex]=40x^{3} +16x^{4} -24x^{2}[/tex]

Rearranging the above expression in descending order of power, we get:[tex]16x^{4} +40x^{3} -24x^{2}[/tex]

The correct simplification of 8x2(5x 2x2 − 3) is [tex]16x^{4} +40x^{3} -24x^{2}[/tex]

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√64 is rational.

Hope this helps :)

❄ Hi there,

let us consider this –

Is [tex]\sqrt{64}[/tex] a rational or irrational number?

Well, to answer that we need to work out [tex]\sqrt{64}[/tex].

And we know that

[tex]\sqrt{64} =8[/tex]

and 8 is a rational number.

That's it!

❄

If there was just one of each animal, the outcome would be that of 1 cow and 1 dog.

Option(B) is correct.

The average cost, or how much it generally costs to produce a unit, can be discovered using the cost function.

If you own two cats worth $100 each and a cow worth $2,500. One dog, though, is worth $7000.

Cost of 1 cow = $2500

Cost of 2 cats = $100

Thus, cost of 1 cat = $100/2 = $50

Cost of 1 dog = $7000

If there was only 1 of each animal, total cost = $(2500+50+7000) = $9550.

This outcome resembles the situation of having 1 cow and 1 dog.

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Answer:

1241

Step-by-step explanation:

∴

L.C.M. of 28, 36 and 45 = 2 × 2 × 3 × 3 × 5 × 7 = 1260

∴

the required number is 1260 - 19 = 1241

Hence, if we add 19 to 1241 we will get 1260 which is exactly divisible by 28, 36 and 45.

Answer:

Option 2

Step-by-step explanation:

There is an amplitude of 1/2, a period of pi, and a non-zero y-intercept.

Answer:

  12 in, 7 in

Step-by-step explanation:

The area of a rectangle is the product of length and width. Here, you are given the area, and an additional relation between length and width.

The two relations between length and width described by this problem are ...

  A = LW . . . . . . . dimensions are of a rectangle

  L = W +5 . . . . . . length is 5 inches more than width

  A = 84 . . . . . . . . area in square inches

Substituting for L and A in the area formula, we have ...

  84 = (W +5)(W)

We can solve this as a quadratic in any of several ways. One of those ways is by factoring.

Essentially, we're looking for factors of 84 that differ by 5. We can consider different factorizations of 84 to see what we get:

  84 = 84×1 = 42×2 = 28×3 = 21×4 = 14×6 = 12×7

The differences between the factors in these pairs are 83, 40, 25, 17, 8, 5.

This means the last pair, with a difference of 5, is the one we're looking for.

 W+5 = 12, W = 7

The rectangle is 12 inches long and 7 inches wide.

__

Additional comment

As a quadratic in standard form, we would have ...

  W² +5W -84 = 0   ⇒   (W +12)(W -7) = 0   ⇒   W = {7, -12}

If you were to solve this by completing the square, you would have ...

  (W +2.5)² = 90.25   ⇒   W = -2.5 ±9.5 = {7, -12}

Answer: Midpoint=(−6 ,3.5)

Step-by-step explanation:

=(1+22,1+22)M=(x1+x22,y1+y22)=(−1+−112,−3+102)M=(−1+−112,−3+102)=(−122,72)M=(−122,72)=(−6,312)

Answer:

(-6,3.5)

Step-by-step explanation:

x = [tex]\frac{-1-11}{2}[/tex] = [tex]\frac{-12}{2}[/tex] = -6

y = [tex]\frac{-3+10}{2}[/tex] = [tex]\frac{7}{2}[/tex] = 3.5

Answer:

16m^2 + 72m + 81

Step-by-step explanation:

you expand it, by (9+4m)(9+4m), using distributive property you get

81 + 36m + 36m + 16m^2, simplifying you get the answer