(c) Use a calculator to verify that Σ(x) = 64, Σ(x2) = 1118, Σ(y) = 628, Σ(y2) = 87,982, and Σ(x y) = 9,627.

Compute r. (Enter a number. Round your answer to three decimal places.)

The correlation coefficient is -0.87; strong correlation

The given parameters are:

x = Time spent working out

y = lbs Overweight

Next, we enter the table of values in a graphing tool.

From the graphing tool, we have the following summary:

X Values

Y Values

X and Y Combined

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -114.19 / √((22.569)(778.9))

r = -0.8613

Approximate

r = -0.87

This means that the correlation coefficient is -0.87

Also, the correlation coefficient is a strong correlation, because it is closer to -1 than it is to 0

Read more about correlation coefficient at:

https://brainly.com/question/27226153

#SPJ1

Answer:

45 meters

Step-by-step explanation:

[tex]Area=\frac{1}{2}bh\\ A=\frac{1}{2}(6)(15)\\ A=3(15)\\A=45[/tex]

⊱________________________________________________________⊰

Answer:

A=45 m²

Step-by-step explanation:

The formula for the area of a triangle is, [tex]\bigstar\underline{\boxed{\sf{A=\frac{bh}{2}}}}[/tex].

where :

[tex]\triangleright\sf{A=Area,b=base,h=height}\triangleleft[/tex]

Substitute the values,

[tex]\large\begin{gathered}\sf{A=\frac{6*15}{2} \\ \sf{A=\frac{90}{2}\\\bigstar\underline{\boxed{\sf{A=45 \ m^2}}}} \end{gathered}[/tex]

Done !! Hope this made sense to you :)

[tex]\small\boldsymbol{Calligraphy}[/tex]

⊱______________________________________________________⊰

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}[/tex]

[tex]5000=P\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies 5000=P(1.05)^3 \\\\\\ \cfrac{5000}{1.05^3}=P\implies 4319\approx P[/tex]

The amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.

The annual payments represent the periodic cash outflows invested in accumulating a future value using an interest rate compounded for a period.

This can be achieved using the future value and present value formulas or factors.

We can also use an online finance calculator, as follows:

Future value = $5,000

Investment period = 3 years

Annual compound interest = 5%

N (# of periods) = 3 years

I/Y (Interest per year) = 5%

PV (Present Value) = $0

FV (Future Value) = $5,000 ($4,531.56 + $468.44)

Results:

PMT = $1,510.52

Sum of all periodic payments = $4,531.56 ($1,510.52 x 3_)

Total Interest = $468.44

Thus, the amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.

Learn more about periodic payments at https://brainly.com/question/24244579

If the total cost of two umbrellas and one cap is is $20 the total cost for one umbrella and two caps is $16 then the price of one umbrella is $8 and price of one cap is $4.

Given that the total cost of two umbrellas and one cap is is $20 the total cost for one umbrella and two caps is $16.

We have to find the price of one umbrella and one cap.

We have to form equations first to find the price of umbrella and cap.

Equation of two variables look like ax+by=c. It can be a linear equation, quadratic equation or a cubic equation.

let the price of umbrella be x and price of cap is y.

We know that total cost is equal to price of one unit multiplied by the units.

According to question.

2x+y=20----------1

x+2y=16-----------2

Multiply equation 2 by 2 and then subtract resulted equation from equation 1.

2x+y-2x-4y=20-32

-3y=-12

y=-12/-3

y=4

put the value of y in equation 2 to get the value of x.

x+2y=16

x+2*4=16

x+8=16

x=16-8

x=8

Hence the price of one umbrella is $8 and the price of one cap is $4.

Learn more about equations at https://brainly.com/question/2972832

#SPJ1

Step-by-step explanation:

T = 2×pi × sqrt(L/9.8)

now we know the time the swing should take for a complete back and forth cycle : 3 4 seconds.

the only unknown variable is now L (the length of the rope) :

3.4 = 2×pi × sqrt(L/9.8)

3.4/(2pi) = sqrt(L/9.8)

(3.4/(2pi))² = L/9.8

3.4²/(4pi²) = L/9.8

11.56/(4pi²) = L/9.8

2.89/pi² = L/9.8

9.8 × 2.89/pi² = L = 2.869618563... m ≈ 2.9 m

Then the x-intercept of the inverse is the same as the y-intercept of f(x), this means that the correct statement is the third option.

On the image, we can see two linear equations, such that the orange one is f(x) and the blue one is the inverse.

Then the x-intercept of the inverse is the same as the y-intercept of f(x), this means that the correct statement is the third option.

If you want to learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

You can just replace [tex]u[/tex] with 2:

[tex]2^2 - 4\times2 + 2 = 4 - 8 + 2 = \boxed{-2}[/tex]

Alternatively, you can complete the square.

[tex]u^2 - 4u + 2 = u^2 - 4u + 4 - 2 = (u-2)^2 - 2[/tex]

When [tex]u=2[/tex], the quadratic term vanishes and we again get -2.

When calculating the total area of this unknown figure, you should use (π - r²)/4 for the area of both the semicircle (half circle) and the larger square.

By critically observing this unknown figure, we can logically deduce that it comprises a semicircle, squares, a rectangle and a triangle. Thus, its total area should be calculated by adding the area of each of the geometric figures together.

Total area = A₁ + A₂ + A₃ + A₄

However, you should take note that the diameter of the semicircle (half circle) is equal to the side length of the larger square.

Area of a semicircle = πr²/4

Thus, the total area of both the semicircle (half circle) and the larger square is given by:

Area = πr²/4 - d²

Note: d = 2r

Area = πr²/4 - (2r)²

Area = πr²/4 - 4r²

Area = (π - r²)/4 sq. units.

Read more on area of square here: https://brainly.com/question/8902873

#SPJ1

Claire's measuring stick would make a more precise measurement

The given parameters are:

Claire = 1 cm

Martin = 0.1 cm

The 0.1 cm marking would make a more accurate measurement.

This is so because the length of a slug would most likely be in decimal centimeters

However, this doesn't translate to a precise measurement.

Hence, Claire's measuring stick would make a more precise measurement

Read more about accuracy and precision at:

https://brainly.com/question/15274003

#SPJ1

Using the angle of intersecting tangents theorem, the measure of angle A is: C. 70°

Based on the angle of intersecting tangents theorem, measure of angle A = 1/2(the positive difference of the intercepted arcs).

Measure of one of the intercepted arcs = 250°

The second intercepted arc = 360 - 250 = 110°

Positive difference of the intercepted arcs = 250 - 110 = 140°

Measure of angle A = 1/2(140)

Measure of angle A = 70°

Learn more about the angle of intersecting tangents theorem on:

https://brainly.com/question/1626547

#SPJ1

Answer:

the answer is 70. hope this helps <3

Step-by-step explanation:

The number of number of four-legged and three-legged stools in stock is 38 and 16 respectively.

let

x + y = 54

4x + 3y = 200

From equation (1)

x = 54 - y

4x + 3y = 200

4(54 - y) + 3y = 200

216 - 4y + 3y = 200

216 - y = 200

- y = 200 - 216

-y = -16

y = 16

x + y = 54

x + 16 = 54

x = 54 - 16

x = 38

Learn more about simultaneous equation:

https://brainly.com/question/16863577

#SPJ1

Answer:

Step-by-step explanation:

Okay, so first of all, when a slope is negative, the line goes down from left to right, not up from left to right. Then, plot the Y intercept as -2. Finally, either go up 2 and left 3 or down 2 and right 3.

Answer:

Graph attached.

Step-by-step explanation:

As we have been given the slope and the y-intercept, we can create a linear equation using the slope-intercept form.

Slope-intercept form of a linear equation:

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

where:

Substitute the given values into the formula to create an equation for the line:

[tex]\implies y=-\dfrac{2}{3}x-2[/tex]

Now we have an equation for the line, find at least two points on the line by inputting values of x into the found equation:

[tex]x=0 \implies y=-\dfrac{2}{3}(0)-2=-2 \implies (0,-2)[/tex]

[tex]x=3 \implies y=-\dfrac{2}{3}(3)-2=-4 \implies (3,-4)[/tex]

[tex]x=-6 \implies y=-\dfrac{2}{3}(-6)-2=2 \implies (-6,2)[/tex]

Plot the found points and draw a straight line through them (see attachment).

Learn more about linear equations here:

https://brainly.com/question/27317293

Answer:

320

Step-by-step explanation:

Is the 3 to 2 part to part?  Out of every 5 people, 3 prefer pizza and 2 do not.  We can us this to set up a proportion.

3/5 = 120/x  The 3 represent the part that like pizza over the whole of 5.  The second ratio is showing the actual number of people that liked pizza over the total number of people.

What would be multiply 3 by to get 120? 40.  So, we will multiply 5 times 40 to get the total number of people.  5 x 40 = 200

Using the probability concept, the number of blue balls you need to add is:

D) 5.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

A probability of 0.5 is reached if the number of red balls is the same as the number of blue balls. Current the difference is of 7 - 2 = 5, hence 5 blue balls must be added.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

The chart that best represents the student results from a class assignment is B. Histogram or bar graph.

Both histograms and bar charts are graphic vertical and horizontal bars that visually display frequencies with columns plotted on a graph.

The frequencies are depicted on the Y-axis (vertical axis).

The X-axis (horizontal axis) represents the measured variable.

A. Frequency table

B. Histogram or bar graph

C. Pareto chart

D. Pictogram

E. Pie chart

Thus, the best chart to represent the student results from a class assignment is B. Histogram or bar graph.

Learn more about bar charts at brainly.com/answer expert verified

#SPJ1

From the line theorems explained below and when we apply it to the given image, we have; X║Y, A║B, Z ⊥ A

The perpendicular transversal theorem states that in a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other line.

Now, since we are told that Line X is perpendicular to Line A, then it means that Line X is also perpendicular to line B.

The inverse of perpendicular transversal theorem states that if there are two perpendicular lines to a straight line, they're parallel to each other. Thus, it means that Line X is parallel to Line Y and similarly, line A is parallel to Line B.

Read more about Transverse Line Theorem at; https://brainly.com/question/12834964

#SPJ1

The rotation of the triangle [tex]\left[\begin{array}{ccc}-1&2&2\\-1&-1&3\end{array}\right][/tex] 270° counter-clockwise about the origin gives [tex]\left[\begin{array}{ccc}-1&-1&3\\1&-2&-2\end{array}\right][/tex]

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

If a point (x, y) is rotated 270° counter-clockwise about the origin, the new point is (y, -x)

The rotation of the triangle [tex]\left[\begin{array}{ccc}-1&2&2\\-1&-1&3\end{array}\right][/tex] 270° counter-clockwise about the origin gives [tex]\left[\begin{array}{ccc}-1&-1&3\\1&-2&-2\end{array}\right][/tex]

Find out more on transformation at: https://brainly.com/question/4289712

#SPJ1

No hay ninguno de los nimbers que no pertenezca a la secuencia.

Sabemos que una secuencia tiene que ver con un arreglo de números en un orden definido. Todos los números en una secuencia deben tener la misma razón común o diferencia común.

Si miramos todos los números que están escritos en la secuencia, la diferencia común aquí es seis. Se sigue entonces que todos los números son parte de la sucesión y no hay ninguno de los números que no pertenezca a la sucesión.

Obtenga más información sobre la secuencia: https://brainly.com/question/21961097

#SPJ1

Answer:

3(r + 5)(r - 5)

Step-by-step explanation:

Both 3 and 75 are divisible by 3, so we take out a 3.

3(r^2 - 25)

Next, we can factor r^2 - 25. It's a difference of squares.

3(r + 5)(r - 5)

Brainliest, please :)

The inequality of the graph is y < -1/2(x - 16)^2 + 32

A quadratic function is represented as:

y = a(x - h)^2 + k

The vertex of the graph is

(h, k) = (16, 32)

So, we have:

y = a(x - 16)^2 + 32

The graph pass through the point

(x, y) = (12, 24)

So, we have:

24 = a(12 - 16)^2 + 32

Evaluate the like terms

-8 = a(-4)^2

This gives

16a = -8

Divide by 16

a = -1/2

Substitute a = -1/2 in y = a(x - 16)^2 + 32

y = -1/2(x - 16)^2 + 32

The graph is a less than graph.

So, we have

y < -1/2(x - 16)^2 + 32

Hence, the inequality of the graph is y < -1/2(x - 16)^2 + 32

Read more about inequality at:

https://brainly.com/question/17675534

#SPJ1

Answer:

31 3/4 %

Step-by-step explanation:

There are 100 squares so each square is a percent.  There at 31 full squares colored and it looks like 3/4 of 1 square.

Answer:

0.4

Step-by-step explanation:

4+3+2+1 =10

5m÷10 =0.5

(0.5×4=2, 0.5×3=1.5, 0.5×2=1, 0.5×1=0.5)

2 : 1.5 : 1 : 0.5

longest piece= 2 (2m)

4+1= 5

2÷5= 0.4

(0.4×4=1.6, 0.4×1=0.4)

1.6 : 0.4

so the shortest piece is 0.4!

The best predicted weight of a person that is 156 cm is 285.4kg

y= 106+1.15

When the adult male is 156 cm tall the weight of this person would be calculated as:

y= 106+1.15*156

y = 106 + 179.4

y = 285.4

Hence we can arrive at the conclusion that the best predicted weight of a person that is 156 cm is 285.4kg

Read more on regression equation here:

https://brainly.com/question/26843436

#SPJ1

The value of x to the nearest hundredth is 4.14

The given diagram is a right triangle with the following parameters

Opposite side to 16 degrees = x

Hypotenuse = 15

Using the expression below

sin theta = x/15

sin16 = x/15

x = 15sin16

x = 4.135

Hence the value of x to the nearest hundredth is 4.14

Learn more on triangle here; https://brainly.com/question/2217700

#SPJ1

Answer:

Step-by-step explanation:

In the quadratic form ...

  (x -h)² = 4p(y -k)

The value 4p is the length of the latus rectum. It also tells the distance between the vertex (h, k) and the focus (h, k+p).

The value of 4p is given as 8. This means p = 8/4 = 2.

The length of the latus rectum is 8.

The end points of the latus rectum have the same y-value as the focus:

  y = k +p = -1 +2 = 1

The end points of the latus rectum have x-values that are h±2p.

  x = h ± 2p = -4 ± 2·2 = {-8, 0}

The end points of the latus rectum are (-8, 1) and (0, 1).

Answer:

2635

Step-by-step explanation:

the first two stand for 1000

so

2000

is the first part

the second numeral stands for 100

there are 6 of them

so

600

is the second part

the third numeral stands for 10 and there are 3 of them

thus

30

is the third part

there are 5 lines so the last part is 5

so your answer is 2635

Answer:

it matches with equation a

The area of the equilateral triangle is 110.9 cm

area of a triangle = 1 / 2 bh

where

Therefore,

tan 60 = opposite / adjacent

tan 60 = 8√3 / x

x =  8√3 / √3

x = 8

hence,

b = 8 + 8 = 16

Therefore,

area of a triangle =  1 / 2 × 16 × 8√3

area of a triangle = 64√3

area of a triangle = 110.851251684

area of a triangle = 110.9 cm

learn more on triangle here: https://brainly.com/question/20593575

#SPJ1

The error is that

[tex] {x}^{y} - {x}^{z} \neq {x}^{y - z} [/tex]

Instead, it should be 4⁴ - 4³ = 256 - 64 = 192.

Answer: THE ANSWER IS A) $860

Step-by-step explanation: I GOT A 100 ON THE TEST