Find the slope of the line that passes through (1, 14) and (4,9)
Which two numbers in the points represent y values? Select both in the
list

Answer:

Null hypothesis: [tex]\rho =0[/tex]

Alternative hypothesis: [tex]\rho \neq 0[/tex]

The statistic to check the hypothesis is given by:

[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]

And is distributed with n-2 degrees of freedom

And the statistic to check the significance of a coeffcient in a regression is given by:

[tex] t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}[/tex]

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

Always

Step-by-step explanation:

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:

Null hypothesis: [tex]\rho =0[/tex]

Alternative hypothesis: [tex]\rho \neq 0[/tex]

The statistic to check the hypothesis is given by:

[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]

And is distributed with n-2 degrees of freedom

And the statistic to check the significance of a coeffcient in a regression is given by:

[tex] t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}[/tex]

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

Always

Answer:

y = 1.44

Step-by-step explanation:

What are you aiming to do here?  Please share all instructions with each problem.

If you want to solve 4.5/y = 12.5/4 for y:  Multiply both sides by 4y:

18 = 12.5y.  Then y = 1.44

Answer:

d ≈ 8.3

Step-by-step explanation:

This is kind of like the pythagorean theorem, but with one extra value.  Thus, [tex]d^2=l^2+w^2+h^2[/tex].

Plug in the values to get:

[tex]d^2=2^2+7^2+4^2\\d^2=4+49+16\\d^2=69\\d=\sqrt{69} \\[/tex]

Thus d ≈ 8.3

Answer:

Here is the refactored function:

def rectangle_area(base, height):

   area = base * height

   return area    

print("The area is ", rectangle_area(5,6))

Step-by-step explanation:

The above program has a function rectangle_area that takes two variables base and height as parameters. The function then computes the area of rectangle by multiplying the values of base and height. The result of the multiplication is assigned to the variable area. Then the function returns the resultant area.

print("The area is ", rectangle_area(5,6)) statement calls rectangle_area() method by passing values of base and height i.e. 5 and 6 to compute the area. The output of this program is:

The area is 30

Note that the use of rectangle_area function name describes what the function does i.e. it computes the area of rectangle. By naming the parameters as base and height that clearly depicts that in order to compute rectangle are we need the base and height of rectangle. So this makes the code readable.

Answer:

3 pounds

51 ounces

Step-by-step explanation:

Answer:

its 9

Step-by-step explanation:

Answer:

c. 9i.

Step-by-step explanation:

[tex]\sqrt{-81}[/tex]

= [tex]\sqrt{-1 * 9 * 9}[/tex]

= [tex]\sqrt{-1 * 9^2}[/tex]

= [tex]9\sqrt{-1}[/tex]

The square root of -1 is the same thing as i.

= [tex]9i[/tex]

So, your answer is C.

Hope this helps!

obviously 4 is bigger coz 12/7 will yeild you 1.71

Answer:

Max area is 16

Step-by-step explanation:

If A² + B² = C², then A² + B² = 64. The largest triangle area is when both A² and B² are equal to 32, so 32 + 32 = 64.

So equal side of the triangle is √32 or about 5.6568. The area of the triangle is then 1/2(5.6568 × 5.6568) or 16.

The maximal area of a right triangle is 90.496

Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

Given:

let the perpendicular be 'x'

and base be 'y'

Using Pythagoras theorem

x² + y² = 8²

x² + y² = 64

y²= 64- x²

y = √64-x²

Now, Area of triangle

= 1/2* base* height

=xy/2

=x *√64-x²*1/2

On differentiating both side

A' = 64-2x²/√64-x²*1/2

Setting derivative function equal to zero,

64= 2x²

32=x²

x=5.656

So, Area of triangle = x *√64-x²*1/2

= 90.496

Learn more about differentiation here:

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Answer:

If you compute the slope between any two points that must be the same, that's how you can tell if a table represents a linear function.

Remember that the slope between any two points (x1,y1), (x2,y2) is

slope   =  ( y2 - y1 ) / (x2 - x1)

Step-by-step explanation:

If you compute the slope between any two points that must be the same, that's how you can tell if a table represents a linear function.

Remember that the slope between any two points (x1,y1), (x2,y2) is

slope   =  ( y2 - y1 ) / (x2 - x1)

Answer:

It takes 4 seconds for the projectile to hit the ground

Step-by-step explanation:

The height of the projectile after t seconds is given by the following equation:

[tex]h(t) = -16t^{2} + 32t + 128[/tex]

How long will it take the projectile to hit the ground?

It happens when [tex]h(t) = 0[/tex]

So

[tex]h(t) = -16t^{2} + 32t + 128[/tex]

[tex]-16t^{2} + 32t + 128 = 0[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]-16t^{2} + 32t + 128 = 0[/tex]

So [tex]a = -16, b = 32, c = 128[/tex]

[tex]\bigtriangleup = 32^{2} - 4*(-16)*(128) = 9216[/tex]

[tex]t_{1} = \frac{-32 + \sqrt{9216}}{2*(-16)} = -2[/tex]

[tex]t_{2} = \frac{-32 - \sqrt{9216}}{2*(-16)} = 4[/tex]

Time is a positive measure, so:

It takes 4 seconds for the projectile to hit the ground

Answer: 36

Step-by-step explanation:

Simply do 24/(2/3) to get 36 2/3 ounce slices.

Hope it helps <3

Answer:The answer is c

Step-by-step explanation:

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where l is the length

w is the width

The length of the rectangle is 2 feet longer than the width is written as

l = 2 + w

Perimeter = 20feet

So we have

20 = 2( 2 + w ) + 2w

20 = 4 + 2w + 2w

4w = 16

Divide both sides by 4

w = 4

Substitute w = 4 into l = 2 + w

That's

l = 2 + 4

l = 6

Hope this helps you

Answer:

w = 4 and L = 10

Step-by-step explanation:

perimeter of a rectangle = 2(l+w)

p = 20

L = 2 + w

w = ?

20 = 2(2 + w + w)

20 = 2(2 + 2w)

20/2 = 2 + 2w

10 = 2 + 2w

10 - 2 = 2w

8 = 2w

w = 8/2 = 4

L = w + 2

L = 4 +2 = 6

w = 4 and L = 10

Answer: x= 7

Step-by-step explanation:

-2x= -14    Divide both sides by -2

x= 7  

check

-2(7) = -14

-14 = -14

Answer:

x = 7

Step-by-step explanation:

-2x = -14

Divide each side by -2

-2x/-2 = -14/-2

x = 7

Answer:

the real deal is that you mistook if

cos(x)=y/z gives y=zcos(x)

Answer:

[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex]

Step-by-step explanation:

Hey there!

Well the slope of the perpendicular line is -1/5 because that's the reciprocal of 5.

Look at the image below ↓

By looking at the image we can conclude that the equation for the perpendicular line is,

[tex]y=-\frac{1}{5}x\ +\ 5.6[/tex].

Hope this helps :)

Answer:

[tex]\boxed{y=-\frac{1}{5}x+\frac{28}{5}}[/tex]

Step-by-step explanation:

Part 1: Finding the new slope of the line

Perpendicular lines have reciprocal slopes of a given line - this means that the slope you are given in the first equation will be flipped and negated.

Because the slope is 5 in the first line, it gets flipped to become [tex]-\frac{1}{5}[/tex].

Part 2: Using point-slope formula and solving in slope-intercept form

Input the new slope into the slope-intercept equation: [tex]y=mx+b[/tex]. This results in [tex]y=-\frac{1}{5} x+b[/tex].

Then, use the point-slope equation to get b, or the y-intercept of the equation.

[tex](y-y_{1})=m(x-x_{1})[/tex]

[tex](y-5)=-\frac{1}{5}(x-3)\\\\y-5=-\frac{1}{5}x+\frac{3}{5} \\\\y=-\frac{1}{5}x+\frac{28}{5}[/tex]

Answer:

Step-by-step explanation:

From the information given:

mean life span of a brand of automobile = 35,000

standard deviation of a brand of automobile = 2250 miles.

the z-score that corresponds to each life span are as follows.

the standard z- score formula is:

[tex]z = \dfrac{x - \mu}{\sigma}[/tex]

For x = 34000

[tex]z = \dfrac{34000 - 35000}{2250}[/tex]

[tex]z = \dfrac{-1000}{2250}[/tex]

z = −0.4444

For x = 37000

[tex]z = \dfrac{37000 - 35000}{2250}[/tex]

[tex]z = \dfrac{2000}{2250}[/tex]

z = 0.8889

For x = 3000

[tex]z = \dfrac{30000 - 35000}{2250}[/tex]

[tex]z = \dfrac{-5000}{2250}[/tex]

z = -2.222

From the above z- score that corresponds to their life span; it is glaring  that the tire with the life span 30,000 miles has an unusually short life span.

For x = 30,500

[tex]z = \dfrac{30500 - 35000}{2250}[/tex]

[tex]z = \dfrac{-4500}{2250}[/tex]

z = -2

P(z) = P(-2)

Using excel function (=NORMDIST -2)

P(z) = 0.022750132

P(z) = 2.28th percentile

For x =  37250

[tex]z = \dfrac{37250 - 35000}{2250}[/tex]

[tex]z = \dfrac{2250}{2250}[/tex]

z = 1

Using excel function (=NORMDIST 1)

P(z) = 0.841344746

P(z) = 84.14th percentile

For x = 35000

[tex]z = \dfrac{35000- 35000}{2250}[/tex]

[tex]z = \dfrac{0}{2250}[/tex]

z = 0

Using excel function (=NORMDIST 0)

P(z) = 0.5

P(z) = 50th percentile

a.  The z score of each life span should be -0.4444, 0.889, and 2.2222.

b.  The percentile of each life span should be 0.0228, 0.8413 and  0.5000.

Given that,

(a)

The z score should be

[tex]Z1 = \frac{34000-35000}{2250} = -0.4444\\\\Z2 = \frac{37000-35000}{2250} = 0.8889\\\\Z3 = \frac{30000-35000}{2250} = -2.2222\\\\[/tex]

The tire with life span of 30000 miles would be considered unusual

(b)

The percentile should be

[tex]Z1 = \frac{30500-35000}{2250} = -2[/tex]

p(Z1 < -2) = NORMSDIST(-2) = 0.0228

[tex]Z2 = \frac{37250-35000}{2250} = 1[/tex]

p(Z2 < 1) = NORMSDIST(1) = 0.8413

[tex]Z3 = \frac{35000-35000}{2250} = 0[/tex]

p(Z3 < 0) = NORMSDIST(0) = 0.5000

Find out more information about standard deviation here:

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Answer:

[tex]\boxed{\mathrm{Option \ 4}}[/tex]

Step-by-step explanation:

Given that

[tex]y-4 = x[/tex]

Adding 4 to both sides

[tex]y-4+4 = x+4\\[/tex]

[tex]y = x+4[/tex]

Answer:

Ok, we have a total of 26 letters, and we want to select 5 of them.

Of the 26 letters, 21 are consonants and 5 are vowels.

Suppose that we want to have the consonant in the first selection, so the probability of picking a consonant is equal to the quotient between the number of consonants and the total number of letters.

p = 21/26

now a letter has been selected, so in the set, we have 25 letters left.

In the next 4 selections, we must select vowels.

In the second selection the probability is:

p = 5/25

in the third, the prob is:

p = 4/24 (we already selected one vowel before, so now we only have 4 vowels)

The fourth selection:

p = 3/23

and the last selection:

p = 2/22

The total probability is equal to the product of all the individual proabilities, so we have:

P = (2/22)*(3/23)*(4/24)*(5/25)*(21/26)

Now, remember that we said that the consonant must be in the first place, but it can be in any of the five places, so if we add the permutations of the consonant letter we have:

P = 5*(2/22)*(3/23)*(4/24)*(5/25)*(21/26) =  0.0018

Answer:

[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]

Step-by-step explanation:

You can understand the statement from many perspectives, but in terms of proposition logic it is best to understand it as   "negation of a" or "  b" in mathematical terms is written like this

[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]

You can show that they are logically equivalent because they have the same truth table.

Answer:

3906250

Step-by-step explanation:

We can notice that the ratio is 5. 10/2 = 5

Each term gets multiplied by 5 to get the next term.

250 × 5 = 1250 (5th term)

1250 × 5 = 6250 (6th term)

6250 × 5 = 31250 (7th term)

31250 × 5 = 156250 (8th term)

156250 × 5 = 781250 (9th term)

781250 × 5 = 3906250 (10th term)

The 10th term of the geometric sequence is 3906250.

Answer: 1 30/39

Step-by-step explanation:

Because y/x=z and y/z=x are true with the same values, simply do 7 2/3 divided by 4 1/3 to get 69/39.

Hope it helps <3

Hey there! :)

Answer:

m = 4.

Step-by-step explanation:

We are given the formula y = -5 + 4x. Rearrange the equation to be in proper slope-intercept form (y = mx + b)

Where 'm' is the slope and 'b' is the y-intercept. Therefore:

y = -5 + 4x becomes y = 4x - 5

The 'm' value is equivalent to 4, so the slope of the equation is 4.

Answer:

4

Step-by-step explanation:

because of y= mx + b where m is the slope

m= 4 in the equation

Answer:

a simple interest rate of 4.5%

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▹ Answer

Slope = -3

Y-intercept = 8

▹ Step-by-Step Explanation

y = mx + b

mx represents the slope.

b represents the y intercept.

therefore,

y = -3x + 8

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

[tex]\boxed{\mathrm{Slope:}-3 \: \: \: \:\: \mathrm{Y \: intercept:}8}[/tex]

Step-by-step explanation:

The general form of slope-intercept:

[tex]y=mx+b[/tex]

[tex]m:slope\\b:y \: intercept[/tex]

[tex]y=-3x+8[/tex]

[tex]m=-3\\b=8[/tex]

The slope is -3.

The y-intercept is (0, 8) or 8.

Answer:

1 - Correct

2 - incorrect

3- incorrect

4 - incorrect

5 - Correct

Step-by-step explanation:

Notice that

3x  + 5 + 4x -1  =    3x + 4x + 5 -1 = 7x  + 4

therefore the two expressions are equivalent for ANY number, specially x = 4 and x = 6 therefore

1 - Correct

Since that is true for all numbers  

2 - incorrect

3- incorrect

4 - incorrect

The expressions are equivalent for all numbers therefore

5 - Correct

Answer:

108, 324, 972

Step-by-step explanation:

This sequence is multiplying by ✖️3.

4✖️3=12✖️3=36✖️3=108✖️3=324✖️3=972

Hope this helps!

Answer:

3s-4bbb=17

Step-by-step explanation:

brother=4bbb

sister=3s

3s-4bbb=17

Answer:

[tex]Height = x \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]

Step-by-step explanation:

[tex]Volume = Base \ Area\ * Height[/tex]

[tex]Height = \frac{Volume}{Base \ Area}[/tex]

Where [tex]Volume = x^4+4x^3+8x+4[/tex] and [tex]Area = x^3+3x^2+8[/tex]

Putting in the formula

[tex]Height = \frac{x^4 + 4x^3 + 3x^2 + 8x + 4}{x^3 + 3x^2 + 8}[/tex]

Doing long division, we get

[tex]Height = x + \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]

[tex]Height = x \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]

This is the simplifies form and it can't be further simplified.

Answer:

[tex]x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]

Step-by-step explanation:

[tex]volume=base \: area \times height[/tex]

[tex]height=\frac{volume}{base \: area}[/tex]

[tex]\mathrm{Solve \: by \: long \: division.}[/tex]

[tex]h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}[/tex]

[tex]h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}[/tex]

[tex]h=x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]

Answer:

Disks = $4 each and Notebooks = $7 each

Step-by-step explanation:

-4(2D + 3N = 29)

3(5D + 4N = 48)

-8D - 12N = -116

15D + 12N = 144

7D = 28

D = $4

2(4) + 3N = 29

8 + 3N = 29

3N = 21

N = $7