Exercise science researchers collecting data within their state noticed that teens who spend more time streaming videos spend less time exercising.


What are the explanatory variable and response variable for this relationship?


Explanatory variable: time spent exercising

Response variable: state of teen’s residence

Explanatory variable: time spent streaming videos

Response variable: time spent exercising

Explanatory variable: time spent exercising

Response variable: time spent streaming videos

Explanatory variable: state of teen’s residence

Response variable: time spent streaming videos


I think it is (B):
Explanatory variable: time spent streaming videos
Response variable: time spent exercising

Answer:

y2-y1/x2-x1

y2: 1050

y1:600

x2:75

x1:30

1050-600=450

75-30=45

450/45=10

slope is 10

Answer:

let:

A(30, 600)=(x1,y1)

B((75, 1050)=(x2,y2)

now,

[tex]slope(m) = \frac{y2 - y1}{x2 - x1} [/tex]

[tex] = \frac{1050 - 600}{75 - 30} [/tex]

[tex] = \frac{450}{ 45} [/tex]

[tex] = \frac{10}{1} [/tex]

You're looking for a solution of the form

[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n[/tex]

Differentiating twice yields

[tex]\displaystyle y' = \sum_{n=0}^\infty n a_n x^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n[/tex]

[tex]\displaystyle y'' = \sum_{n=0}^\infty n(n-1) a_n x^{n-2} = \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n[/tex]

Substitute these series into the DE:

[tex]\displaystyle (x-1) \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n - x \sum_{n=0}^\infty (n+1) a_{n+1} x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]

[tex]\displaystyle \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^{n+1} - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=0}^\infty (n+1) a_{n+1} x^{n+1} + \sum_{n=0}^\infty a_n x^n = 0[/tex]

[tex]\displaystyle \sum_{n=1}^\infty n(n+1) a_{n+1} x^n - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=1}^\infty n a_n x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]

Two of these series start with a linear term, while the other two start with a constant. Remove the constant terms of the latter two series, then condense the remaining series into one:

[tex]\displaystyle a_0-2a_2 + \sum_{n=1}^\infty \bigg(n(n+1)a_{n+1}-(n+1)(n+2)a_{n+2}-na_n+a_n\bigg) x^n = 0[/tex]

which indicates that the coefficients in the series solution are governed by the recurrence,

[tex]\begin{cases}y(0)=a_0 = -7\\y'(0)=a_1 = 3\\(n+1)(n+2)a_{n+2}-n(n+1)a_{n+1}+(n-1)a_n=0&\text{for }n\ge0\end{cases}[/tex]

Use the recurrence to get the first few coefficients:

[tex]\{a_n\}_{n\ge0} = \left\{-7,3,-\dfrac72,-\dfrac76,-\dfrac7{24},-\dfrac7{120},\ldots\right\}[/tex]

You might recognize that each coefficient in the n-th position of the list (starting at n = 0) involving a factor of -7 has a denominator resembling a factorial. Indeed,

-7 = -7/0!

-7/2 = -7/2!

-7/6 = -7/3!

and so on, with only the coefficient in the n = 1 position being the odd one out. So we have

[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n \\\\ y = -\frac7{0!} + 3x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots[/tex]

which looks a lot like the power series expansion for -7eˣ.

Fortunately, we can rewrite the linear term as

3x = 10x - 7x = 10x - 7/1! x

and in doing so, we can condense this solution to

[tex]\displaystyle y = 10x -\frac7{0!} - \frac7{1!}x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots \\\\ \boxed{y = 10x - 7e^x}[/tex]

Just to confirm this solution is valid: we have

y = 10x - 7eˣ   ==>   y (0) = 0 - 7 = -7

y' = 10 - 7eˣ   ==>   y' (0) = 10 - 7 = 3

y'' = -7eˣ

and substituting into the DE gives

-7eˣ (x - 1) - x (10 - 7eˣ ) + (10x - 7eˣ ) = 0

as required.

9514 1404 393

Answer:

  67.0 square units

Step-by-step explanation:

The formula for the area is ...

  Area = 1/2ab·sin(C)

  Area = (1/2)(14)(28)sin(20°) ≈ 67.036 . . . . square units

The area of the triangle is about 67.0 square units.

Answer:

Step-by-step explanation:

Answer:

the answer would be (7,5)

Answer:

The unknown is 100

Step-by-step explanation:

A straight line is 180 degrees

We have two angles x, and 80

x+80 = 180

x = 180-80

x= 100

Answer:

15/17

Step-by-step explanation:

sinA = CB/CA =15/17

Answer:

Step-by-step explanation:

Hey there!

First,  divide 5,000 by 10. You will get 500.

Now, 500 ÷ 10, and you will get your answer, 50.

Hope this helps! Have a great day!

Answer:

y = 25x + 40

Step-by-step explanation:

The electrician charges $25 per hour.

The number of hours is x.

Therefore after x hours the electrician will charge $25x. (multiply the charge by the number of hours $25 * x)

Therefore fee(y) charged by the electrician = $40 + $25x

Hence y = 25x + 40

Answer:

Not a function

Domain: {3,4}

Range: {4,5}

Step-by-step explanation:

A function is a relation where each input has its own output. In other words if the x value has multiple corresponding y values then the relation is not a function

For the relation given {(3, 4), (3, 5), (4, 4), (4, 5)} the x value 3 and 4 have more than one corresponding y value therefore the relation shown is not a function

Now let's find the domain and range.

Domain is the set of x values in a relation.

The x values of the given relation are 3 and 4 so the domain is {3,4}

The range is the set of y values in a relation

The y value of the given relation include 4 and 5

So the range would be {4,5}

Notes:

The values of x and y should be written from least to greatest when writing them out as domain and range.

They should be written inside of brackets

Do not repeat numbers when writing the domain and range

Answer:

The answer is "0.07404893".

Step-by-step explanation:

Applying the binomial distribution:

[tex]n = 22\\\\p= 82\%=0.82\\\\q = 1-0.82 = 0.18\\\\[/tex]

Calculating the probability for not enough seats:

[tex]=P(X>20)\\\\= P(21) + P(22)\\\\[/tex]

[tex]= \binom{22}{21} (0.82)^{21}(0.18)^1+ \binom{22}{22} (0.82)^{22}(0.18)[/tex]

[tex]=0 .06134598+ 0.01270295\\\\=0.07404893[/tex]

Answer:

a) Everyone on the team talks until the entire team agrees on one decision.

Step-by-step explanation:

Option B consists of voting and not everyone would like the outcome. Option C is making an outsider the decision maker, which can't be helpful since he / she won't have as strong opinions as the team itself. Option D is just plain wrong as it defeats the purpose of team work and deciding as one team. So, I believe option A makes the most sense

Answer:

W=7 and L=11

Step-by-step explanation:

We have two unknowns so we must create two equations.

First the problem states that  length of a rectangle is 10 yd less than three times the width so: L= 3w-10

Next we are given the area so: L X W = 77

Then solve for the variable algebraically. It is just a system of equations.

3W^2 - 10W - 77 = 0

(3W + 11)(W - 7) = 0

W = -11/3 and/or W=7

Discard the negative solution as the width of the rectangle cannot be less then 0.

So W=7

Plug that into the first equation.

3(7)-10= 11 so L=11

Answer:

a. 16 slug b. 3.2 ft

Step-by-step explanation:

a. Total mass of the rod

Since the linear density at a point of the rod,λ varies directly as the third power of the measure of the distance of the point form the end, x

So, λ ∝ x³

λ = kx³

Since the linear density λ = 2 slug/ft at then center when x = L/2 where L is the length of the rod,

k = λ/x³ = λ/(L/2)³ = 8λ/L³

substituting the values of the variables into the equation, we have

k = 8λ/L³

k = 8 × 2/4³

k = 16/64

k = 1/4

So, λ = kx³ = x³/4

The mass of a small length element of the rod dx is dm = λdx

So, to find the total mass of the rod M = ∫dm = ∫λdx we integrate from x = 0 to x = L = 4 ft

M = ∫₀⁴dm

= ∫₀⁴λdx

= ∫₀⁴(x³/4)dx

= (1/4)∫₀⁴x³dx

= (1/4)[x⁴/4]₀⁴

= (1/16)[4⁴ - 0⁴]

= (256 - 0)/16

= 256/16

= 16 slug

b. The center of mass of the rod

Let x be the distance of the small mass element dm = λdx from the end of the rod. The moment of this mass element about the end of the rod is xdm =  λxdx = (x³/4)xdx = (x⁴/4)dx.

We integrate this through the length of the rod. That is from x = 0 to x = L = 4 ft

The center of mass of the rod x' = ∫₀⁴(x⁴/4)dx/M where M = mass of rod

= (1/4)∫₀⁴x⁴dx/M

= (1/4)[x⁵/5]₀⁴/M

= (1/20)[x⁵]₀⁴/M

= (1/20)[4⁵ - 0⁵]/M

= (1/20)[1024 - 0]/M

= (1/20)[1024]/M

Since M = 16, we have

x' =  (1/20)[1024]/16

x' = 64/20

x' = 3.2 ft

Answer:

y=-1/7x + 12/7

Step-by-step explanation:

Start by finding the slope

m=(1-0)/(-5-2)

m=-1/7

next plug the slope and the point (-5,1) into point slope formula

y-y1=m(x-x1)

y1=1

x1= -5

m=-1/7

y- 1 = -1/7(x - -5)

y-1=-1/7(x+5)

Distribute -1/7 first

y- 1=-1/7x + 5/7

Add 1 on both sides, but since its a fraction add 7/7

y=-1/7x + (5/7+7/7)

y=-1/7x+12/7

Answer:

Step-by-step explanation:

(-5,1) (2,0)

m=(y-y)/(x-x)

m = (0-1)/2- -5)

m = -1/7

(2,0)

y-0= -1/7 (x-2)

y = -1/7x + 2/7

Base case (n = 1):

• left side = 1×2² = 4

• right side = 1×(1 + 1)×(3×1² + 11×1 + 10)/12 = 4

Induction hypothesis: Assume equality holds for n = k, so that

1×2² + 2×3² + 3×4² + … + k × (k + 1)² = k × (k + 1) × (3k ² + 11k + 10)/12

Induction step (n = k + 1):

1×2² + 2×3² + 3×4² + … + k × (k + 1)² + (k + 1) × (k + 2)²

= k × (k + 1) × (3k ² + 11k + 10)/12 + (k + 1) × (k + 2)²

= (k + 1)/12 × (k × (3k ² + 11k + 10) + 12 × (k + 2)²)

= (k + 1)/12 × ((3k ³ + 11k ² + 10k) + 12 × (k ² + 4k + 4))

= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)

= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)

On the right side, we want to end up with

(k + 1) × (k + 2) × (3 (k + 1) ² + 11 (k + 1) + 10)/12

which suggests that k + 2 should be factor of the cubic. Indeed, we have

3k ³ + 23k ² + 58k + 48 = (k + 2) (3k ² + 17k + 24)

and we can rewrite the remaining quadratic as

3k ² + 17k + 24 = 3 (k + 1)² + 11 (k + 1) + 10

so we would arrive at the desired conclusion.

To see how the above rewriting is possible, we want to find coefficients a, b, and c such that

3k ² + 17k + 24 = a (k + 1)² + b (k + 1) + c

Expand the right side and collect like powers of k :

3k ² + 17k + 24 = ak ² + (2a + b) k + a + b + c

==>   a = 3   and   2a + b = 17   and   a + b + c = 24

==>   a = 3, b = 11, c = 10

Answer:

x is 5

Step-by-step explanation:

[tex] \frac{4x - 5}{9x - 5} = \frac{3}{8} \\ \\ 8(4x - 5) = 3(9x - 5) \\ 32x - 40 = 27x - 15 \\ 5x = 25 \\ x = \frac{25}{5} \\ \\ x = 5[/tex]

Step-by-step explanation:

as you can see as i solved above. all you need to do was to rationalize the both equations

Answer and Step-by-step explanation:

First, we need to set this equation equal to y, which means we need to get y by itself, and all other terms equal to y.

x = [tex]2y^2 + 1[/tex]

Subtract 1, then divide by 2 on both sides.

[tex]x - 1 = 2y^2\\\\\frac{x-1}{2} = y^2[/tex]

Now, take the square root of both sides.

[tex]y=\sqrt{\frac{x-1}{2}}[/tex]

We see that the value with the x (1) is positive, and that we have a square root function, which means the parabola would open to the right.

(If the x value was negative, the square root function's parabola would open to the left)

So, C (Right) is the correct answer.

#teamtrees #PAW (Plant And Water)

I hope this helps!

Answer:

384 cars

Step-by-step explanation:

To find the total number of spaces in the carpark, we must multiply the number of rows by how many cars they can accommodate:

34 ⋅ 40 = 1360

As you can see, we have 1360 total spaces. Since there are 976 cars parked, and we want to find out how many spaces are left, we have to subtract the amount of cars parked from the total spaces.

1360 - 976 = 384

Therefore, our answer is 384, specifically, 384 cars.

Answer:

384 cars.

Step-by-step explanation:

40 * 34 - 976

= 1360 - 976

= 384.

Answer:

A) area decreases

Step-by-step explanation:

Example: we have a 2 by 3 rectangle with area of 2*3 = 6. If we cut the first dimension in half, then we have a 1 by 3 rectangle that has area 1*3 = 3. The area has decreased. To keep the area the same, we would have to increase the other dimension some specific amount.

HOPE THIS HELPS

HAVE A GOOD DAY :)

ITS RASPUTIN002

Answer:

18

Step-by-step explanation:

The diameter is equal to twice the length of the radius

So if the radius is 9 then the diameter is 9 * 2 = 18

Answer:

BC^2=10^2+30^2

Step-by-step explanation:

Using pythagorean theorem

[tex]\\ \sf\longmapsto BC^2=10^2+30^2[/tex]

[tex]\\ \sf\longmapsto BC^2=100+300[/tex]

[tex]\\ \sf\longmapsto BC^2=400[/tex]

[tex]\\ \sf\longmapsto BC=\sqrt{400}[/tex]

[tex]\\ \sf\longmapsto BC=20[/tex]

Answer:

93.6

Step-by-step explanation:

The easiest way for me to complete this was to break it up into parts. I Separated the small triangle and the big triangle. I turned them both into squares and multiplied the dimensions. I then divided those by two and added them together.

Answer:

b. The solution is a non empty set.

Step-by-step explanation:

There are no common elements.

Answer:

Slope is 5/2

y-intercept is 2

Step-by-step explanation:

Turn the equation into slope intercept form [ y = mx +  b ].

2y = 5x + 4

~Divide everything by 2

y = 5/2x + 2

Remember that in slope intercept form, m = slope and b = y-intercept.

Best of Luck!

Answer:

slope: 2.5

y-intercept: 2

Step-by-step explanation:

First isolate the y variable which changes the equation to y=2.5x+2

The equation of a line is mx + b where m is the slope and b and the

y-intercept. Leading us to conclude that 2.5 is the slope and 2 is the y-intercept.

Answer:

[tex]56[/tex] choices

Step-by-step explanation:

We know that we'll have to solve this problem with a permutation or a combination, but which one do we use? The answer is a combination because the order in which the child picks the candy does not matter.

To further demonstrate this, imagine I have 4 pieces of candy labeled A, B, C, and D. I could choose A, then C, then B or I could choose C, then B, then A, but in the end, I still have the same pieces, regardless of what order I pick them in. I hope that helps to understand why this problem will be solved with a combination.

Anyways, back to the solving! Remember that the combination formula is

[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex], where n is the number of objects in the sample (the number of objects you choose from) and r is the number of objects that are to be chosen.

In this case, [tex]n=8[/tex] and [tex]r=3[/tex]. Substituting these values into the formula gives us:

[tex]_8C_3=\frac{8!}{3!5!}[/tex]

[tex]= \frac{8*7*6*5*4*3*2*1}{3*2*1*5*4*3*2*1}[/tex] (Expand the factorials)

[tex]=\frac{8*7*6}{3*2*1}[/tex] (Cancel out [tex]5*4*3*2*1[/tex])

[tex]=\frac{8*7*6}{6}[/tex] (Evaluate denominator)

[tex]=8*7[/tex] (Cancel out [tex]6[/tex])

[tex]=56[/tex]

Therefore, the child has [tex]\bf56[/tex] different ways to pick the candies. Hope this helps!