What would the equation be for this table? (y=kx) Answer must be in y=kx form *

a) The mean of the data-set is of 2.

b) The range of the data-set is of 4 units, which is of around 4.3 MADs.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.

The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:

Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)

Mean = 2.

The range is the difference between the largest observation and the smallest, hence:

4 - 0 = 4.

4/0.93 = 4.3 MADs.

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Answer:

-2x^3+x^2+5x-5

Step-by-step explanation:

f(x) = 4 - 2x – 2x^3

g(x) = x² + 7x-9

f(x) + g(x)=4 - 2x – 2x^3+ x² + 7x-9

Combine like  terms

f(x) + g(x) = -2x^3+x^2+5x-5

The requreid,
(a) Approximate values of the given numbers are π ≈ 3.1, √6 ≈ 2.4, 2√6 ≈ 4.8, and √7 ≈ 2.6.
(b) √6  < √7 <  π  < 2√6

(a)

π ≈ 3.1 (since π is between 3 and 4, and is closer to 3.1 than to 3.2)

√6 ≈ 2.4 (since 6 is between 4 and 9, and the square root of 6 is closer to 2.4 than to 2.5)

2√6 ≈ 4.8 (since 2√6 is approximately twice the value of √6, which is 2.4)

√7 ≈ 2.6 (since 7 is between 4 and 9, and the square root of 7 is closer to 2.6 than to 2.7)

(b)

Order from least to greatest:

√6  < √7 <  π  < 2√6

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Easy way to do this, divide 24 with 3, you will get 8. That means 8 is 1/3 of 24. To get 2/3 you just add 8+8 which equals to 16

Answer:

0.5555

Step-by-step explanation:

The answer is in decimal form

Answer:

x=10,y=120

Step-by-step explanation:

3x-30=60 CDA

3x=30

x=10

again,

y+60=180 straight line

y = 120

With a constant speed Robert took 20 minutes paddle.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, Robert paddled at a constant speed and travels 3/4 of a mile in 15 minutes.

We know that, Speed = Distance/Time

Speed = 3/4 ÷15/1

= 3/4 × 1/15

= 1/20 miles per minutes

Now, distance = 1 mile and speed =1/20 miles per minutes

1/20 = 1/Time

Time = 20 minutes

Therefore, with a constant speed Robert took 20 minutes paddle.

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Answer:

6.5

Step-by-step explanation:

6.5+(3.5*2)-7/3

6.5+(7-7)/3

6.5+0/3

6.5+0

6.5

Answer:

Its multiplication but if you want the actual answer it is 6.5

Step-by-step explanation:

Answer:

Your car is faster of course

Step-by-step explanation:

100 km would be 100000 meters. Then you would need to know that if Usain bolt ran 100 meters every 9.54 sec then in 100000 meters he would have ran 9540 seconds which is also known has 159 minutes, which is more than 1 hour so your car is faster.

happy first question!!!!

The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

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Answer:

17.32 meters

Step-by-step explanation:

Let’s call the height of the tower H. The distance from the point to the base of the tower is 10 m. The angle of elevation from the point to the top of the tower is 60 degrees.

Using trigonometry, we can calculate that:

tan (60) = H / 10

H = 10 * tan (60)

H = 10 * √3

H = 17.32 m

Therefore, the height of the tower is 17.32 meters.

Let me know if I helped :)

Answer:

170 cm³

Step-by-step explanation:

V = πr²h

= 3.14 * (3)² * 6

= 3.14 * 9 * 6

= 169.56 cm³

= 170 cm³

Answer:

Step-by-step explanation:

Answer:

312

Step-by-step explanation:

Add the area of each face together

Don't forget the units!

Let's start by finding the right face (12 by 3). From your picture, we can tell its 12m long, and 3m tall. To find the aria of any face, we multiply the length, times the width.
12 x 3 = 36.
Now let's look at where it says 8m. Since that face is just as tall as the first one, we can tell its 3m tall.
8 x 3 = 24.

We can continue this for the top face.
Since the width of the second face we did is 8m, and the width of the first one is 12m, we can tell that the top one is 8 x 12. (96).

We can do this again for the other 3 sides.
A shortcut i like to take, is to do 3 of the sides, (Like the ones we did) and add them together, then double the sum.

36+24+96=156.

156x2=312.

This shortcut should work, because by adding the aria of half the sides together, we get exactly half the answer.

When doing this, it only works to do 3 different sides. it will not work if you do the same side twice, or a parallel side.

I encourage you to let me know if this method works for you! I hope this helps!

The height of the arch at a distance of 5 feet from the center is approximately 10. 93 feet

The standard equation of the ellipse centered at origin behind the shape of arch is presented below:

\(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\)

Where:

If we know that x = 6feet , a = 20 feet and b = 12feet, then the height of the arch at this location is:

\(y = b. \sqrt{1 - \frac{x^2}{a^2} }\)

\(y = 12. \sqrt{1 - \frac{6^2}{20^2} }\)

\(y = 10. 92\) feet

Thus, the height of the arch at a distance of 5 feet from the center is approximately 10. 93 feet

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Answer:

128

Step-by-step explanation:

if to substitute y= -6, then

\(\lim_{y \to \ {-6}} \sqrt[3]{(2-y)^7}=\sqrt[3]{8^7}=2^7=128.\)

Option D is the correct answer.

All real numbers greater than or equal to 0 and less than 4.

The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined.

Here, The function of the car value is given as:

V(x) = 20000 X (0.84)ˣ

When the car reaches half its value, we have:

V(x) = 10000

Substitute V(x) = 10000 in V(x) = 20000 * (0.84)ˣ

10000 = 20000 X (0.84)ˣ

Divide both sides by 20000

0.84ˣ = 0.5

Take the logarithm of both sides

x log(0.84) = log(0.5)

Divide both sides by log(0.84)

           x = 4

This means that the maximum value of x is 4.

Thus, all real numbers greater than or equal to 0 and less than 4.

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The solution is:

⇒ 6b = 95.94   (equation to determine cost of one box)

cost of one box 'b' = $`15.99

⇒ 12t = 95.94   (equation to determine cost of per tile)

cost of one tile t = $0.7995.

Given :

Jorge bought a crate of floor tiles for $95.94.

The crate had 6 boxes of floor tiles.

Each box contained 20 floor tiles .

To Find :

Write and solve equation to determine the cost per box'b'.

Write and solve a second equation to determine the cost per tile't'

Solution :

Cost of one box = b

There are 6 boxes

So, cost of 6 boxes = $  6b

Since Jorge bought 1 crate( = 6 boxes) of cost $95.94

⇒     (equation to determine cost of one box)

⇒6b = 95.94

⇒b =15.99

Thus cost of one box = $`15.99

Since 1 box 20 floor tiles

So, 6 boxes (=1 crate) contain tiles = 6*20 = 120 tiles

We are given that cost of 1 crate( = 6 boxes = 120 tiles) is $95.94

Cost of one tile = t

Cost of 120 tiles = $120t

⇒ (equation to determine cost of per tile)

⇒12t = 95.94

⇒t = 0.7995.

Thus cost of one tile t = $0.7995.

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a) Two different ways.

x = ln(32)/ln(2)

2^x = 2^5

b) Only the natural logarithm way can be used.

c) x = 3.58

We want to solve:

2^x = 32

in two ways.

The first way is trivial, apply the natural logarithm to both sides:

ln(2^x) = ln(32)

x = ln(32)/ln(2)

The second way is the next one:

2^x = 32

The right number can be written as:

4*8 = 32

Now we can factorize the left side:

4*8 = (2*2)*(2*2*2) = 2^5

Replacing that we get:

2^x = 2^5

So we know that x = 5.

b) The second way can't be used to solve:

2^x = 12

Because 12 has a factor different than 2.

c) Using the natural logarithm  way:

x = ln(12)/ln(2) = 3.58

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Answer:

Step-by-step explanation:

Set up an equation:

7x + 10x + 13x = 100000 and solve for x:

30x = 100000 so

x = 3333.33

Anna gets 7(3333.33) = 23333.31

Louise gets 10(3333.33) = 33333.33

Lacey gets 13(3333.33) = 43333.29

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

1. C

2. B

Step-by-step explanation:

A. A(-2,5) => A' (-2 + 2, 5) or A' (0,5)

B. A(-2,5) => A' (- -2, 5) or A' (2,5)

Answer:

1/3³

Step-by-step explanation:

\( {3}^{2} \times {3}^{ - 5} \\ = {3}^{[2 + ( - 5)]} \\ = {3}^{ - 3} \\ = \frac{1}{ {3}^{3} } \)

The trapezoid is a form of quadrilateral that has at least one parallel sides. The trapezoid here is given by the mentioned coordinates.

A point is a dot on a sheet of paper or in a plane. There are no lengths, widths, or heights in a point. It establishes a plane's position or location.

It is possible to find any point in a 2D plane or 3D space using coordinates, which are ordered pairs of points. You may have observed the use of grids in mathematics.

Select a point on the graph according to the given coordinates. Connect all the points on the graph using a line segment. The shape formed by joining all the points together is knows as a trapezoid.

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The volume of the solid generated by revolving the regions bounded by the curves and lines about the​ y-axis is  8.90 unit³.

Since the region is the one for  then the intersection we are interested on is x=1 as it can also be seen in the graph.

Where h(x) is the height of the shell which here is the distance between the parabola and the line, so  (since the line is on the top we subtract from it the parabola

Notice the limits of the integral are the x-axis (x=0) and the intersection of the parabola and the line that we found before (x=1)

We want the volume generated when the area bounded by the curves :

v = x2 v = 8 —7x , and

x = 0 for x > 0 is revolved about the y axis using the cylindrical shell method .

The intersection of y = x2 and y = 8 —7x is :

y= x2 = 8 — 7x x2 + 7x —8 = 0

(x + 8)(x — 1) = 0 x = —8 or

x = 1 .

We thus have for x > 0 the two curves intersect at x = 1 and y = 12 = 1 .

The limits for integration are --- 0 <x < 1 .

The upper curve is --- y2 = 8 —7x ,

and the lower curve is --- yi = x2 .

The height of the shell is --- h = y2 -yi = 8 —7x — x2 •

The radius of the shell is --- R = x •

\($$The surface area of the shell is :$$A=2 \pi \mathrm{Rh}=2 \pi x\left(8-7 x-x^2\right)=2 \pi\left(8 x-7 x^2-x^3\right) .$$The differential of volume which is the cylindrical shell is :$$\mathrm{dv}=\mathrm{Adx}=2 \pi\left(8 x-7 x^2-x^3\right) \mathrm{dx}$$\)

\($$We then have the volume of revolution is :$$\begin{aligned}v & =2 \pi \int_0^1\left(8 x-7 x^2-x^3\right) \mathrm{d} x \\& =2 \pi\left(4 x^2-\frac{7}{3} x^3-\frac{1}{4} x^4\right)_0^1 \\& =2 \pi\left[4\left(1^2-0^2\right)-\frac{7}{3}\left(1^3-0^3\right)-\frac{1}{4}\left(1^4-0^4\right)\right] \\& =2 \pi\left(4-\frac{7}{3}-\frac{1}{4}\right) \\& =2 \pi\left(\frac{48-28-3}{12}\right) \\& =2 \pi\left(\frac{17}{12}\right) ; \text { or, we have : } \\v & =\frac{17 \pi}{6} .\end{aligned}$$\)

17π/6 = 8.90 unit³

Thus, The volume of the solid generated by revolving the regions bounded by the curves and lines about the​ y-axis is  8.90 unit³.

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Answer:

I put the answer on the attachment please look

Answer:

Step-by-step explanation:

From the given information:

sample size n = 100

Since the population is assumed to be normal. then:

\(\overline X _{state} - \overline X_{private} \sim N(\overline X _{state}-\overline X _{private, SD^2_{state} + SD^2_private} -2\times Cov(\overline X _{state} - \overline X_{private}})}\)

\(\overline X _{state} - \overline X_{private} \sim N(4.5-4.1, 0.8^2 + 0.2^2 -2\times 0})}\)

\(\overline X _{state} - \overline X_{private} \sim N(0.4, 0.68})}\)

The test statistics:

\(z = \dfrac{\overline X_{state} - \overline X_{private} }{ \sqrt{\dfrac{\sigma^2_{state}}{n } + \dfrac{\sigma^2_{private}}{n } } }\)

\(z = \dfrac{0.4 }{ \sqrt{\dfrac{1.5811^2}{100 } + \dfrac{1^2}{100 } } }\)

z = 2.138

Using the z tables;

P-value = (Z> 2.138)

P-value = 1 - (Z<2.138)

P-value = 1 - 0.9837

P-value = 0.0163

Decision rule: to reject the null hypothesis if the p-value is less than the significance level

Conclusion: We reject the null hypothesis and conclude that there is enough evidence to conclude that the average time it requires for the students to graduate from a private university is lesser than that of the time it takes such student to graduate from the California state university system.