The table shows data collected on the relationship between time spent playing video games and time spent with family. The line of best fit for the data is ý = -0.3694.5.
Video Games (Minutes) Time with Family (Minutes)
40 80
55 75
70 69
85 64
A) According to the line of best fit, the predicted number of minutes spent with family for someone who spent 36 minutes playing video games is 81.54.
B) Is it reasonable to use this line of best fit to make the above prediction?
1) The estimate, a predicted time of 81.54 minutes, is reliable but unreasonable.
2) The estimate, a predicted time of 81.54 minutes, is unreliable but reasonable.
3) The estimate, a predicted time of 81.54 minutes, is both unreliable and unreasonable.
4) The estimate, a predicted time of 81.54 minutes, is both reliable and reasonable.

Step-by-step explanation:

Since x² + kx + (k + 3) is tangent to the x-axis, the quadratic function has a repeated root.

The discriminant is zero, so b² - 4ac = 0.

=> k² - 4(1)(k + 3) = 0

=> k² - 4k - 12 = 0

=> (k - 6)(k + 2) = 0

Hence k = 6 or k = -2.

The value of k is -2 and 6.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

x² + kx + (k + 3) is tangent to the x-axis.

This means,

The equation has roots.

Now,

The determinant of the equation is equal to zero.

D = b² - 4ac

x² + kx + (k + 3) is in the form of ax² + bx + c.

a = 1

b = k

c = k + 3

Now,

D = 0

k² - 4(k + 3) = 0

k² - 4k - 12 = 0

k² - (6 - 2)k - 12 = 0

k² - 6k + 2k - 12 = 0

k(k - 6) + 2(k - 6) = 0

(k + 2) (k - 6) = 0

k + 2 = 0

k = -2

k - 6 = 0

k = 6

Thus,

k = -2 and 6.

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Step-by-step explanation:

[tex]\bullet\hookrightarrow\sf 7 (x+4)=21 [/tex]

[tex]\bullet\Rrightarrow\sf 7x+28=21 [/tex]

[tex]\bullet\rightarrowtail\sf 7x=21-28 [/tex]

[tex]\bullet\twoheadrightarrow\sf 7x=-7 [/tex]

[tex]\bullet\looparrowright\sf x=\dfrac{-7}{7}[/tex]

[tex]\bullet\rightharpoonup\sf x=-1 [/tex]

Answer:

polygon

Step-by-step explanation:

A polygon is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons. A rhombus has 4 sides.

Hope this helps:) Have a great day!

Answer:

the answer is D

Step-by-step explanation:

A. √123 = 11.09

11.09-11 = 0.09

B. √115 = 10.72

11-10.72 = 0.28

C. √118 = 10.86

11-10.86 = 0.14

D. √120 = 10.95

11-10.95 = 0.05 ( the smallest difference )

Answer:

this doesnt make sense is there any type of picture or more explanation on the question? i'll still help :)

Step-by-step explanation:

==================================================

Explanation:

We basically mix red and blue to get purple. The ratio needed is 2 parts red, and 3 parts blue. We can shorten this by writing 2:3

Note how we can double both parts of the ratio to get 4:6, showing that 4 drops of red correspond to 6 drops of blue, which is the answer we want.

------------------

Another approach:

x = some positive real number

(2 parts red)/(3 parts blue) = (4 parts red)/(x parts blue)

2/3 = 4/x

2x = 3*4 .... cross multiply

2x = 12

x = 12/2 .... divide both sides by 2

x = 6

So 6 drops of blue go with 4 drops of red.

Answer:

a. Angel has a greater flat fee

b. Difference = $130

Step-by-step explanation:

Given

Rose:

[tex]Flat\ Fee = \$50[/tex]

[tex]Rate = \$12[/tex]

Angel

Guests --- Charges

10 -------- $180

15 -------- $255

25 -------- $405

30 -------- $480

Solving (a): Who charges the greater flat fee?

We have that the flat fee of Rose is:

[tex]Flat\ Fee = \$50[/tex]

For Angel, we need to determine the equation of the given table

Start by calculating the slope (m) of the table

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where x and y represent any two corresponding values of the guests and the charges.

[tex](x_1,y_1) = (10, 180)[/tex]

[tex](x_2,y_2) = (30, 480)[/tex]

So: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes

[tex]m = \frac{480 - 180}{30 - 10}[/tex]

[tex]m = \frac{300}{20}[/tex]

[tex]m = 15[/tex]

Next, we calculate the equation using:

[tex]y - y_1 = m(x - x_1)[/tex]

Where

[tex]m = 15[/tex]

[tex](x_1,y_1) = (10, 180)[/tex]

[tex]y - 180 = 15(x - 10)[/tex]

[tex]y - 180 = 15x - 150[/tex]

Add 180 to both sides

[tex]y - 180 + 180 = 15x - 150 + 180[/tex]

[tex]y= 15x + 30[/tex]

From the equation above:

The slope = 15 --- This represents the hourly rate

and

y intercept = 30 --- This represents the flat fee

This is better represented as:

Angel

[tex]Flat\ Fee = \$30[/tex]

[tex]Rate = \$15[/tex]

and

Rose:

[tex]Flat\ Fee = \$50[/tex]

[tex]Rate = \$12[/tex]

By comparison, Angel has a greater flat fee

Solving (b): Difference between total charges of 50 guests for both caterers.

For angel, the equation is:

[tex]y= 15x + 30[/tex]

and x = 50.

So:

[tex]y = 15 * 50 + 30[/tex]

[tex]y = 750 + 30[/tex]

[tex]y = 780[/tex]

For Rose,

First, we need to determine the equation.

[tex]Flat\ Fee = \$50[/tex]

[tex]Rate = \$12[/tex]

The equation is:

[tex]y = Flat\ Fee + Rate * x[/tex]

[tex]y = 50 + 12 * x[/tex]

So, the total charges for 50 guests is:

[tex]y = 50 + 12 * 50[/tex]

[tex]y = 50 + 600[/tex]

[tex]y = 650[/tex]

The difference is then calculates as:

[tex]Difference = 780 - 650[/tex]

[tex]Difference = \$130[/tex]

Answer:

Answer is 9 Broski mark as brainliest

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

kinetic energy

Step-by-step explanation:

When a person runs, their body must convert potential energy into kinetic energy.

Answer:

8/15= 0.533

Step-by-step explanation:

8 divided by 15 isn't possible so according to the rules of division we introduce a (0.) then we add a (0) to the back of (8) to make it (80) which is bigger than (15) so we now have (80/15) which is (5) remaining (5) then we add the back of the (0.) it then becomes (0.5) we then step down the remaining (5) and also add a (0) at the back to make it (50) which is also bigger than (15) (50/15) which gives us (3) and a remaining (5) add (3) to the back of (0.5) to become (0.53) also still step down the remaining (5) add a zero to it to become (50) still divide by (15) gives (3) and remains (5) and it gives the same answer so it is a reoccurring decimal.

Thank you hope I was of help!!

Answer:

(105 x 30) + (105 x 5) + m

Step-by-step explanation:

Answer:

(105 x 30) + (105 x 5) + m

Step-by-step explanation:

Hope this helped have an amazing day!

Answer:

9.3

Step-by-step explanation:

6.2 x 15/10= 9.3

Answer:

Scientific notation is 1.6 x 10^16 and in regular format is:

160000000000000000

Answer:

The value is [tex]UCL = 10.8[/tex]  

Step-by-step explanation:

From the question we are told that

    The sample mean is  [tex]\= x = 9 \ ounce[/tex]

    The sample size is  n =  25

    The standard deviation is  [tex]\sigma = 3 \ ounce[/tex]

Given that the sample size is not large enough i.e  n<  30  we will make use of the student t distribution table  

From the question we are told the confidence level is  99.7% , hence the level of significance is    

      [tex]\alpha = (100 -99.7 ) \%[/tex]

=>   [tex]\alpha = 0.003[/tex]

Generally the degree of freedom is  [tex]df = n- 1[/tex]

=>  [tex]df = 25 - 1[/tex]

=>  [tex]df = 24[/tex]  

Generally from the student t distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of [tex]df = 24[/tex]   is  

   [tex]t_{\frac{\alpha }{2} , 24 } = 3.0 [/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = t_{\frac{\alpha }{2} , 24} *  \frac{\sigma }{\sqrt{n} }[/tex]

=>     [tex]E = 3.0 *  \frac{3 }{\sqrt{25} }[/tex]

=>     [tex]E =1.8 [/tex]

Gnerally the  upper control chart limit  for 99.7% confidence is mathematically represented as

         [tex]UCL = \= x + E[/tex]

=>      [tex]UCL = 9 + 1.8[/tex]  

=>      [tex]UCL = 10.8[/tex]  

Answer:

3

Step-by-step explanation:

Step-by-step explanation:

formula to fine slope

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

Answer:

2.755778

Step-by-step explanation:

Just search how much pounds is 1.25 kg?

Answer:

-6.28576e+81

Step-by-step explanation:

Answer:

721

Step-by-step explanation:

dog you in elementary school

Answer:

42

Step-by-step explanation:

uih

Answer:

y=x-2

Hope this helps.

Answer:

1000

Step-by-step explanation:

Answer:

(-3*6.3x)+(-3*1.5y)

(-18.9x)+(-4.5y)

Answer: I think it is (D)

Step-by-step explanation: Its hard to explain but I hope this helps anyways!

Answer:

I think its D to so I would go with that

Answer:

U GO TO DHS

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

a2+b2=c2

3^2+4^2=c^2

9+16=25

25^2=625

Sqrt of 625 = 25

Answer:

x = 5

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² = 4² + 3² = 16 + 9 = 25 ( take the square root of both sides )

x = [tex]\sqrt{25}[/tex] = 5

Answer:

21

Step-by-step explanation:

you plug in 5 for a and 6 for b and solve.

The value of the expression 3 + (a + 4)(8 - b) when a = 5 and b = 6 is 21

3 + (a + 4)(8 - b)

when,

a = 5 and b = 6

= 3 + (5 + 4) (8 - 6)

= 3 + 9 (2)

= 3 + 18

= 21

Therefore, the value of the expression 3 + (a + 4)(8 - b) when a = 5 and b = 6 is 21

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Answer:

See below for Part A.

Part B)

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

Step-by-step explanation:

Part A)

The parabola given by the equation:

[tex]y^2=4ax[/tex]

From 0 to h is revolved about the x-axis.

We can take the principal square root of both sides to acquire our function:

[tex]y=f(x)=\sqrt{4ax}[/tex]

Please refer to the attachment below for the sketch.

The area of a surface of revolution is given by:

[tex]\displaystyle S=2\pi\int_{a}^{b}r(x)\sqrt{1+\big[f^\prime(x)]^2} \,dx[/tex]

Where r(x) is the distance between f and the axis of revolution.

From the sketch, we can see that the distance between f and the AoR is simply our equation y. Hence:

[tex]r(x)=y(x)=\sqrt{4ax}[/tex]

Now, we will need to find f’(x). We know that:

[tex]f(x)=\sqrt{4ax}[/tex]

Then by the chain rule, f’(x) is:

[tex]\displaystyle f^\prime(x)=\frac{1}{2\sqrt{4ax}}\cdot4a=\frac{2a}{\sqrt{4ax}}[/tex]

For our limits of integration, we are going from 0 to h.

Hence, our integral becomes:

[tex]\displaystyle S=2\pi\int_{0}^{h}(\sqrt{4ax})\sqrt{1+\Big(\frac{2a}{\sqrt{4ax}}\Big)^2}\, dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax}\Big(\sqrt{1+\frac{4a^2}{4ax}}\Big)\,dx[/tex]

Combine roots;

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax\Big(1+\frac{4a^2}{4ax}\Big)}\,dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax+4a^2}\, dx[/tex]

Integrate. We can consider using u-substitution. We will let:

[tex]u=4ax+4a^2\text{ then } du=4a\, dx[/tex]

We also need to change our limits of integration. So:

[tex]u=4a(0)+4a^2=4a^2\text{ and } \\ u=4a(h)+4a^2=4ah+4a^2[/tex]

Hence, our new integral is:

[tex]\displaystyle S=2\pi\int_{4a^2}^{4ah+4a^2}\sqrt{u}\, \Big(\frac{1}{4a}\Big)du[/tex]

Simplify and integrate:

[tex]\displaystyle S=\frac{\pi}{2a}\Big[\,\frac{2}{3}u^{\frac{3}{2}}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[\, u^\frac{3}{2}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

FTC:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[(4ah+4a^2)^\frac{3}{2}-(4a^2)^\frac{3}{2}\Big][/tex]

Simplify each term. For the first term, we have:

[tex]\displaystyle (4ah+4a^2)^\frac{3}{2}[/tex]

We can factor out the 4a:

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

Simplify:

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

For the second term, we have:

[tex]\displaystyle (4a^2)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =(2a)^3[/tex]

Hence:

[tex]\displaystyle =8a^3[/tex]

Thus, our equation becomes:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[8a^\frac{3}{2}(h+a)^\frac{3}{2}-8a^3\Big][/tex]

We can factor out an 8a^(3/2). Hence:

[tex]\displaystyle S=\frac{\pi}{3a}(8a^\frac{3}{2})\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Hence, we have verified the surface area generated by the function.

Part B)

We have:

[tex]y^2=36x[/tex]

We can rewrite this as:

[tex]y^2=4(9)x[/tex]

Hence, a=9.

The surface area is 1000. So, S=1000.

Therefore, with our equation:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

We can write:

[tex]\displaystyle 1000=\frac{8\pi}{3}\sqrt{9}\Big[(h+9)^\frac{3}{2}-9^\frac{3}{2}\Big][/tex]

Solve for h. Simplify:

[tex]\displaystyle 1000=8\pi\Big[(h+9)^\frac{3}{2}-27\Big][/tex]

Divide both sides by 8π:

[tex]\displaystyle \frac{125}{\pi}=(h+9)^\frac{3}{2}-27[/tex]

Isolate term:

[tex]\displaystyle \frac{125}{\pi}+27=(h+9)^\frac{3}{2}[/tex]

Raise both sides to 2/3:

[tex]\displaystyle \Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}=h+9[/tex]

Hence, the value of h is:

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

You seem to have left out that 0 ≤ x ≤ h.

From y² = 4ax, we get that the top half of the parabola (the part that lies in the first quadrant above the x-axis) is given by y = √(4ax) = 2√(ax). Then the area of the surface obtained by revolving this curve between x = 0 and x = h about the x-axis is

[tex]2\pi\displaystyle\int_0^h y(x) \sqrt{1+\left(\frac{\mathrm dy(x)}{\mathrm dx}\right)^2}\,\mathrm dx[/tex]

We have

y(x) = 2√(ax)   →   y'(x) = 2 • a/(2√(ax)) = √(a/x)

so the integral is

[tex]4\sqrt a\pi\displaystyle\int_0^h \sqrt x \sqrt{1+\frac ax}\,\mathrm dx[/tex]

[tex]=\displaystyle4\sqrt a\pi\int_0^h (x+a)^{\frac12}\,\mathrm dx[/tex]

[tex]=4\sqrt a\pi\left[\dfrac23(x+a)^{\frac32}\right]_0^h[/tex]

[tex]=\dfrac{8\pi\sqrt a}3\left((h+a)^{\frac32}-a^{\frac32}\right)[/tex]

Now, if y² = 36x, then a = 9. So if the area is 1000, solve for h :

[tex]1000=8\pi\left((h+9)^{\frac32}-27\right)[/tex]

[tex]\dfrac{125}\pi=(h+9)^{\frac32}-27[/tex]

[tex]\dfrac{125+27\pi}\pi=(h+9)^{\frac32}[/tex]

[tex]\left(\dfrac{125+27\pi}\pi\right)^{\frac23}=h+9[/tex]

[tex]\boxed{h=\left(\dfrac{125+27\pi}\pi\right)^{\frac23}-9}[/tex]

Answer:

Step-by-step explanation: