Given the linear correlation coefficient r and the sample size n​, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r=0.767, n=25

Answer:

y = -3/4 x + 25/2

Step-by-step explanation:

x² + y² = 100

Take derivative with respect to x.

2x + 2y dy/dx = 0

2y dy/dx = -2x

dy/dx = -x/y

Evaluate at (6, 8).

dy/dx = -6/8

dy/dx = -3/4

Use point-slope form to write equation:

y − 8 = -3/4 (x − 6)

Simplify.

y − 8 = -3/4 x + 9/2

y = -3/4 x + 25/2

Answer:

22 and 23

Step-by-step explanation:

Step 1: Solve the square root

[tex] \sqrt{100 \times 5} [/tex]

[tex] \sqrt{ {10}^{2} \times 5 } [/tex]

We can move the 10² out because it matches the index of the root

[tex]10 \sqrt{5} [/tex]

Step 2: Input into calculator to find decimals

[tex]10 \sqrt{5} = 22.36[/tex]

Therefore the square root of 500 lies between 22 and 23

22 and 23

Because 5000 is between 222

(484) and 232 (529), the square root of 500 is in between 22 and 23..

Answer:

0

Step-by-step explanation:

We can use the slope formula to find the slope

m = (y2-y1)/(x2-x1)

    = ( -2 - -2)/( 4 -1)

    = (-2+2)/( 4-1)

    = 0/3

   = 0

Answer:

Step-by-step explanation:

[tex](1, -2) , (4, -2)\\m = ?\\x_1 =1\\y_1 =-2\\x_2 =4\\y_2 =-2\\\\m = \frac{y_2-y_1}{x_2-x_1} \\\\m = \frac{-2-(-2)}{4-1} \\m = \frac{-2+2}{3}\\ m = \frac{0}{3}\\ m = 0[/tex]

Answer:

Rushmont

Step-by-step explanation:

Trenton can be ruled out due to its constant increase rate of 1.5. Rushmont can be ruled out because it goes from an increase rate of ~1.8 to an increase rate of 1.4 to an increase rate of 1.3 (exponential decay, not growth, so possibly...). Springville has a rate of ~1.9, then 1.475, then 1.3, also exponential decay. However, y\ =\ x\frac{38}{10}-185 goes through all of springville's points (or close to it), so Rushmont must be the answer.

The town that has growth that follows an exponential model is Town B, Rushmont where the population increases or decreases at a consistent rate over time.

In this case, analyze the population data from the three towns to determine which one exhibits exponential growth.

Let's go through each option briefly:

A. Springville:

B. Rushmont:

C. Trenton:

Based on the analysis above, the town that shows growth following an exponential model is Rushmont (B). It exhibits a consistent increase in population over time, suggesting exponential growth.

Learn more about population models here:

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Answer:

[tex]\frac{-27b^{6}}{c^{18}}[/tex]

Step-by-step explanation:

first distribute the ^3, -3^3=-27, for the variables, (x^y)^3=x^(3y) so (b^2)^3=b^6 and (c^-6)^3=c^-18. now we have [tex]-27b^{6}c^{-18}[/tex]. Next we have to get rid of the negative in c^-18. x^-y=1/x^y so c^-18=[tex]\frac{1}{c^{18}}[/tex], plug it in and you get [tex]\frac{-27b^{6}}{c^{18}}[/tex]

Answer:

The x coordinate of P is [tex]\frac{4}{3}[/tex].

Step-by-step explanation:

Let is find the rate of change of the equation in time, which consists in a composite differentiation. That is:

[tex]\frac{dy}{dt} = 2\cdot x \cdot \frac{dx}{dt} -2\cdot \frac{dx}{dt}[/tex]

According to the statement of the problem, these variables are known:

[tex]\frac{dx}{dt} = 6[/tex] and [tex]\frac{dy}{dt} = 4[/tex]

Hence, the x coordinate of P is found by direct substitution:

[tex]4 = 2\cdot x \cdot (6)-2\cdot (6)[/tex]

[tex]4 = 12\cdot x -12[/tex]

[tex]x = \frac{4}{3}[/tex]

The x coordinate of P is [tex]\frac{4}{3}[/tex].

Answer:

a = 84°

Step-by-step explanation:

∠ QPR and ∠ TPR are adjacent and supplementary, thus

∠TPR = 180° - 123° = 57°

Given there are parallel lines , then

∠ PTR = 27° ( alternate angle )

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ TRS is an external angle , thus

∠ TRS = a = 57° + 27° = 84°

Answer:

84 degrees.

Step-by-step explanation:

m < R + m < T = 123  (External angle of a triangle theorem)

m < T =  27 degrees (alternate angle to 27 degrees).

So m < R = 123 - 27 = 96 degrees.

Finally m < a = 180 - 96 = 84 degrees  ( as it is adjacent to < R)

Answer:

Step-by-step explanation:

The length of the edge = x

Surface area:

Answer:

34.7

Step-by-step explanation:

First Step: Multiply.

3 × 10 = 30

4 × 1 = 4

7 × 1/10 = 7/10

Second step: Add.

30 + 4 + 7/10= 347/10

Final step: Make it a decimal.

347 ÷ 10 = 34.7

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[tex]3\times 10+4\times 1+7\times 1/10[/tex]

[tex]= \frac{347}{10}[/tex] (Decimal: 34.7)

Step by Step Explanation.

[tex](3) (10) + (4) (1) + \frac{(7)(1)}{10} \\= 30 + (4) (1) + \frac{(7)(1)}{10} \\= 34 + \frac{(7)(1)}{10} \\= 34 + \frac{7}{10} \\= \frac{347}{10}[/tex]

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If this helped you, could you maybe give brainliest..?

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Answer:

it will take her 79.76 minutes to rise to the surface

Step-by-step explanation:

Total distance to the surface = 40 yards

speed of rising = 1 foot per seconds

1 foot = 1 second

since the total distance is in yards, let's convert from foot to yards:

1 yard = 3 feet

1 foot = 1/3 yards = 0.333 yards

0.33 yards = 1 second

Next, let's convert from seconds to minutes

60 seconds = 1 minute

∴ 1 second = 1/60 minute

1 second = 0.0167 minute

Therefore the speed at which she rose:

speed

0.333 yards = 0.0167 minutes

Now for a distance of 40 yards:

[tex]1\ yard = \frac{0.0333}{0.0167} minutes\\\therefore\ 40\ yards = \frac{0.0333}{0.0167} \ \times\ \frac{40}{1} \\= \frac{1.332}{0.0167} \\= 79.76\ minutes[/tex]

Answer:

4 minutes

Step-by-step explanation:

Answer:

6 questions

Step-by-step explanation:

Take the total number of questions and divide by the number of days

150/28

5.357142858

You would need to round up to make sure that the packet is completed in time

6 questions

Step-by-step explanation:

1%2F5n + 51%2F5 = 302%2F5 - 1%2F6n

make the 3rd term an improper fraction

1%2F5n + 51%2F5 = 152%2F5 - 1%2F6n

multiply equation by 30, cancel the denominators, resulting in:

6n + 6(51) = 6(152) - 5n

6n + 306 = 912 - 5n

6n + 5n = 912 - 306

11n = 606 is the number

n = 606/11

n = 55 1/11

Answer:

68

Step-by-step explanation:

let unknown number be x

⅕x + 5½= 30⅖ - ⅙x

⅕x + 11/2= 152/5 - ⅙x

collect like terms

⅕x+⅙x= 152/5 - 11/2

[tex] \frac{11}{30}x = \frac{249}{10} [/tex]

cross multiply

30 * 249=(11 * 10)x

7470=110x

x=7470/110

x= 68

Answer:

169.74

Step-by-step explanation:

this problem is like a triangle, the sun, mars, and earth are the three points, so you just use a^2 + b^2 =  c^2 so basically

93^2 + 142^2 = c^2

8649 + 20164 = 28813

28813 square root = 169.74

We simply list all of the letters mentioned as they are the possible outcomes. We can only pick one item from the sample space. The event space is the set of outcomes where we want to happen (picking either an 'a' or 'c').

Hey There!!

To this Question, This answer going to had A Explanation to this: Sample space--

A sample space is a set which contains the set of all the possible outcomes or results that could occur while performing an experiment.

i.e. the sample space while flipping a coin is: {H,T}

The sample space while tossing a six-sided die is: {1,2,3,4,5,6}

Here it is given that:

A bag has six balls labeled: A,B,C,D,E,F

One ball will be randomly picked, and its letter will be recorded as the outcome.

This means that the sample space is given by:

Sample space={ A,B,C,D,E,F}

Now, when the event is choosing a letter from D to F.

Then the sample space is:

Sample space= {D,E,F}

Hope It Helped!~ ♡

ItsNobody~ ☆

Answer:

Step-by-step explanation: hope this helps

Answer:

B is related to the last term of trinomial

Last term on the left hand side of the equation = Last term on the right hand side of the equation.

The last term on the right hand side is gotten by multiplying all the terms on the right of the two expression.

-32y²=  2*-8y*By

-32y² = -16By²        Compare both

32 = 16B

16B = 32

B = 32/16

B = 2.

Answer:

B = 2

Step-by-step explanation:

2x^2 − 12xy − 32y^2

Factor out a 2

2 ( x^2 -6xy -16y^2)

Factor inside the parentheses

What two numbers multiply to -16 and add to -6

-8 * 2 = -16

-8+2 = -6

2( x-8y) ( x+2y)

B = 2

Answer:

Astrid needs 280 tons of wood to build ships that can accommodate 2100 sailors

Step-by-step explanation:

Here, in this question, we want to know the amount of wood needed by Astrid to accommodate 2100 sailors.

From the question, we can see that 40 tons are needed to build a ship that can accommodate 300 sailors.

Now, we want to make a calculation for the amount of wood needed for 2100 sailors.

Let’s have it this way;

40 tons = 300 sailors

x tons = 2100 sailors

So mathematically,

x * 300 = 2100 * 40

x = (2100 * 40)/300

x = 280 tons of wood

We can see that 280 tons of wood are needed to build ships that can accommodate 2100 sailors

Answer:

280 tons of wood

Step-by-step explanation:

Khan

Answer:

[tex]\huge\boxed{\sf 3599}[/tex]

Step-by-step explanation:

= 61 × 59

You can write 61 = 60 + 1 and 59 = 60 - 1

Hence,

= ( 60 + 1 ) ( 60 - 1 )

According to the formula:

[tex](a+b)(a-b) = a^2-b^2[/tex]

= (60)² - (1)²

= 3600 - 1

= 3599

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Greetings from Brasil...

2X/(X + 2) = 6/(X + 4)

2X(X + 4) = 6(X + 2)

2X² + 2X - 12 = 0     ÷2

2X²/2 + 2X/2 - 12/2 = 0/2

Δ = 25

S = {-3, 2}

By using factorization,  [tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex] , values of x are -2, 3.

Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number. These numbers are broken down into factors or divisors.

Given

[tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex]

⇒ 2x(x + 4) = 6(x + 2)

⇒ [tex]2x^{2} +8x = 6x + 12[/tex]

⇒ [tex]2x^{2} +8x-6x-12=0[/tex]

⇒ [tex]2x^{2} +2x -12=0[/tex]

Divide above equation by 2, we get

⇒ [tex]x^{2} +x -6=0[/tex]

⇒ [tex]x^{2} +2x-3x-6=0[/tex]

⇒ [tex]x(x+2)-3(x+2)=0[/tex]

⇒ [tex](x+2)(x-3)=0[/tex]

⇒ x = -2, 3

By using factorization,  [tex]\frac{2x}{x+2} =\frac{6}{x+4}[/tex] , values of x are -2, 3.

Find out more information about factorization here

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Answer:

Step-by-step explanation:

To find the length of a we use the cosine rule

That's

a² = b² + c² - 2bc cos A

We have

a² = AB ² + AC ² - 2(AB)(AC) cos A

From the question

AB = 6

AC = 5

A = 20°

Substituting the values into the above formula we have

a² = 6² + 5² - 2(6)(5) cos 20

a² = 36 + 25 - 60cos 20

a² = 61 - 56.38

a² = 4.62

Find square root of both sides

a = √4.62

We have the final answer as

Hope this helps you

Answer:

I think 5

Step-by-step explanation:

5u^2

just count the no. of squares

if they allocate sides or an area for the small square then:

sides

(side^2 • 5)

eg.  the side is equal to 2cm, then

(2^2 • 5) = 4(5)

              = 20 cm^2

allocated area for small square

square area • 5

eg. one square has an area of 4 cm^2

4 • 5 = 20 cm^2

There is no one set answer because there are many ways to estimate here.

35 rounds to 40

9 rounds to 10

She got rid of 10 shirts out of 40, so 10/40 = 1/4 = 0.25 = 25% is the estimated percentage of shirts she got rid of. This is one possible estimate.

Using a calculator, the actual percentage is 9/35 = 0.2571 = 25.71% approximately. So our estimate isn't too bad. Our estimate is an underestimate.

Answer:

112°

Step-by-step explanation:

By inscribed angle theorem:

[tex] m\widehat {BCD} = 2\times m\angle BAD\\

\therefore m\widehat {BCD} = 2\times 129\degree \\

\therefore m\widehat {BCD} = 258\degree\\\\

\because m\widehat{CD} = m\widehat {BCD}-m\widehat{BC} \\

\therefore m\widehat{CD} = 258\degree - 146\degree \\

\huge \red {\boxed {\therefore m\widehat{CD} = 112\degree}} [/tex]

Answer:

21.7 m

Step-by-step explanation:

The question above is a right angle triangle and we would be using the trigonometric function of tangent to solve for it.

tan θ = Opposite/ Adjacent

Opposite side = Height = unknown

Adjacent = 20sqrt(3) m

θ = Angle of Elevation = 30°

Hence, we have:

tan 30° = Opposite/ 20√3

Opposite = tan 30° × 20√3m

Opposite = 20m

Height of the tower = Height of the observer + Height (Opposite side)

Height = 20m

Height of the the observer as given in the question is = 1.7m

Height of the tower = 20m + 1.7m

= 21.7m

Therefore, the height of the tower = 21.7m

Answer:

3x

Step-by-step explanation:

If Kapila's age =x.

Then Sasha's age would be =2x.

Their total age would be 3x.

Because 2x+x adds up to be 3x.

Answer:

1,3,5

Step-by-step explanation:

81 is a perfect square so it can be written as an integer

11.8 is rational because it can be written as a fraction (107/9)

sqrt(6) isn't a perfect square so it is irrational

3/7 is a fraction so it is rational

8.57 is a terminating decimal so it is rational

Step-by-step explanation:

–17–12q=–17+10q

–17+17=10q+12q

0/22=22q/22

q=0