What is the equation and solution?

The average height of the soccer team is 77.45 inches, and the average height of the basketball team is 79 inches.

To find the average height of each team, we'll sum up the heights and divide by the number of players on each team.

Soccer team average height:

Sum of heights: 60+61+...+87+88 = 2,246 inches

Number of players: 29

Average height: 2246 / 29 = 77.45 inches

Basketball team average height:

Sum of heights: 72+73+...+86+87 = 1,264 inches

Number of players: 16

Average height: 1264 / 16 = 79 inches

So, the average height of the soccer team is 77.45 inches, and the average height of the basketball team is 79 inches.

Read more about dot plots here:

https://brainly.com/question/25957672

#SPJ1

Soccer team heights (in inches):

60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88

Basketball team heights (in inches):

72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87

Jason wants to find more information about the heights of players on his school's soccer team and his school's basketball team. Jason surveys 29 members of the soccer team and 16 members of the basketball team. The heights of the soccer team and basketball team players are given above. What is the average height of the soccer team and the basketball team?

The rate of water flow is 6 gallons per unit of time.

What is slope?

Slope is a measure of the steepness of a line. It is defined as the change in y-coordinate divided by the change in x-coordinate between any two points on the line.

a. To find the rate, we need to calculate the amount of water that flows per unit of time.

Method 1: Using the Graph

First, we can plot the points (5,30), (7,42), and (10,60) on a graph and connect them with a line.

From the graph, we can see that the line passes through the points (5,30) and (10,60), which means that the change in y-values is 60 - 30 = 30, and the change in x-values is 10 - 5 = 5.

So, the slope of the line is:

slope = change in y-values / change in x-values

     = (60 - 30) / (10 - 5)

     = 6

Therefore, the rate of water flow is 6 gallons per unit of time.

Method 2: Using the Table

We can also find the rate by calculating the differences in y-values and x-values in the table.

x    y   Difference in y   Difference in x   Rate (y/x)

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

5    30        -              -                 -

7    42        12             2                6

10   60       18             3                6

From the table, we can see that the rate of water flow is 6 gallons per unit of time.

b. Both the graph and table have the same rate of 6 gallons per unit of time. We know this because we calculated the rate using both methods, and they gave us the same result.

To know more about slopes visit:

brainly.com/question/14548961

#SPJ1

This line is the horizontal line y = 1. Therefore, the correct answer is "Reflection across y = 1".

How to solve the question?

The line of reflection is the line that serves as the mirror for the original polygon such that each point on the original polygon is reflected to a corresponding point on the reflected polygon such that the distance between the line of reflection and each point is the same as the distance between the line of reflection and its reflection.

In this case, we are given two polygons, one original and one reflected. We need to determine the line of reflection that maps each point of the original polygon to its corresponding point on the reflected polygon.

Looking at the two polygons, we can see that the corresponding vertices are equidistant from a line of reflection that passes through the midpoint of the line segment joining V and V prime. Therefore, the line of reflection is the line that passes through the midpoint of the line segment joining V and V prime.

This line is the horizontal line y = 1. Therefore, the correct answer is "Reflection across y = 1". The other options are incorrect because they do not pass through the midpoint of the line segment joining V and V prime and do not produce the corresponding points for the original and reflected polygons.

To know more about polygon visit :-

https://brainly.com/question/26583264

#SPJ1

The volume of the gas at the height (i.e 6.5 Km) is 652 mL

The final volume of the gas can be obtained by using the Boyle's law equation as shown below:

[tex]P_1V_1 = P_2V_2[/tex]

[tex]1 \times 326 = 0.5 \times V_2[/tex]

[tex]326 = 0.5 \times V_2[/tex]

Divide both side by 0.5

[tex]V_2 = \dfrac{326}{0.5}[/tex]

[tex]\boxed{\bold{V_2 = 652 \ mL}}[/tex]

Learn more about gas laws:

brainly.com/question/6844441

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 50000\\ P=\textit{original amount deposited}\dotfill &\$23000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}[/tex]

[tex]50000 = 23000\left(1+\frac{ ~~ \frac{r}{100} ~~ }{4}\right)^{4\cdot 7} \implies \cfrac{50000}{23000}=\left( 1+\cfrac{r}{400} \right)^{28} \\\\\\ \cfrac{50}{23}=\left( \cfrac{400+r}{400} \right)^{28}\implies \sqrt[28]{\cfrac{50}{23}}=\cfrac{400+r}{400} \\\\\\ 400\sqrt[28]{\cfrac{50}{23}}=400+r\implies 400\sqrt[28]{\cfrac{50}{23}}-400=r\implies \stackrel{ \% }{11.25}\approx r[/tex]

The total volume of glass that makes up the snow globe is approximately 1,757.84 cubic centimeters.

What is the inner sphere?

The Inner Sphere is a region of interstellar space surrounding Earth to a radius of roughly 450 - 550 light-years, generally demarcated by the outer borders of the "Great Houses."

The outer sphere has a diameter of 30 cm, so its radius is 15 cm. The volume of the outer sphere is given by the formula:

V outer = (4/3)πr_outer³

V outer = (4/3)π(15 cm)³

V outer ≈ 14,137.17 cm³

The inner sphere has a diameter of 30 cm minus the thickness of the glass on both sides, so its diameter is:

30 cm - 2(0.35 cm) = 29.3 cm

Therefore, the radius of the inner sphere is:

r inner = 29.3 cm / 2 = 14.65 cm

The volume of the inner sphere is given by the formula:

V inner = (4/3)πr_inner³

V inner = (4/3)π(14.65 cm)³

V inner ≈ 12,379.33 cm³

Finally, the volume of glass that makes up the snow globe is the difference between the volumes of the outer and inner spheres:

V glass = V outer - V inner

V glass ≈ 1,757.84 cm³

Therefore, the total volume of glass that makes up the snow globe is approximately 1,757.84 cubic centimeters.

To know more about inner sphere visit:

brainly.com/question/31041676

#SPJ1

Generally, coordinates are a way of specifying the position of something in space, usually using a system of latitude and longitude or x, y, and z axes.

The coordinates of a physical location that serves as a hub for information, such as a data center or a library, then the answer will depend on the specific location you have in mind. To find the coordinates of such a place, you would need to use a mapping tool or geographic information system (GIS) to locate the facility and determine its latitude and longitude.

On the other hand, if you're asking about the "coordinates" of information in a more abstract sense, then this could refer to the ways in which information is organized or classified.

For example, a database might use a system of fields and tables to arrange information in a structured way, while a search engine might use algorithms to determine the relevance and ranking of different pieces of information based on factors like keywords, backlinks, and user behavior.

In conclusion, the coordinates of an information center is dependent on its nature in terms of its structural formation and the set goals to be accomplished by determining such coordinates.

learn more about coordinates: https://brainly.com/question/17206319

#SPJ1

The mass of the triangular region with density function ρ(x,y) = [tex]x^2 + y^2 is 136/375.[/tex]

A triangle is a three-sided polygon made up of three line segments that connect at three endpoints, called vertices. The study of triangles is an important part of geometry, and it has applications in various fields such as engineering, architecture, physics, and computer graphics.

The mass of a 2D region with variable density can be calculated using the double integral formula:

m = ∬R ρ(x,y) dA

where R is the region of integration, ρ(x,y) is the density function, and dA is the area element.

In this case, we have a triangular region with vertices (0, 0), (4, 0), and (0, 2), and the density function is ρ(x,y) = [tex]x^2 + y^2.[/tex]To set up the double integral, we need to determine the limits of integration for x and y.

Since the triangular region is bounded by the lines y = 0, y = 2, and x = (2/5)y, we can set up the integral as follows:

m = ∫0 ∫[tex]0^[/tex](2/5)y ([tex]x^2 + y^2)[/tex] dxdy

Integrating with respect to x first, we get:

m = ∫[tex]0^2 [(x^3/3) + xy^2]_0^(2/5[/tex])y dy

m = ∫[tex]0^2 [(8/375)y^5 + (4/15)y^3][/tex]dy

Evaluating the integral, we get:

m = [tex][(2/1875)y^6 + (2/5)y^4]_0^2[/tex]

m = (64/1875) + (16/5)

m = 136/375

Therefore, the mass of the triangular region with density function ρ(x,y) = [tex]x^2 + y^2 is 136/375.[/tex]

To know more about triangle visit:

https://brainly.com/question/1058720

#SPJ1

The lengths we found are:

LM = 20

JQ = 26

KQ = 800 / 117

Let's call the length of the median from vertex J to the opposite side LM, and the length of the median from vertex L to the opposite side JN. We can use the fact that the centroid divides each median into two parts, with the ratio of the longer part to the shorter part being 2:1.

First, we can find LM:

LM = 2 x QM = 2 x 10 = 20

Next, we can find JQ:

JQ = 2/3 x JN = 2/3 x 39 = 26

Finally, we can find KQ:

To find KQ, we need to use the fact that the three medians of a triangle divide each other into six smaller triangles with equal areas. Let's call the length of the third median KX. We know that the area of triangle JLK is:

1/2 x LM x JN = 1/2 x 20 x 39 = 390

Similarly, the areas of triangles JNQ, LMQ, JKP, LKP, and JLP are all equal to 390. Let's call this common area A. Then we have:

1/2 x KX x LM = A

1/2 x KX x JN = A

Dividing these two equations, we get:

LM / JN = KX / LM

Substituting the values we know, we get:

20 / 39 = KX / 20

Solving for KX, we get:

KX = 20 x (20 / 39) = 400 / 39

Now we can find KQ:

KQ = 2/3 x KX = 2/3 x (400 / 39) = 800 / 117

Therefore, the lengths we found are:

LM = 20

JQ = 26

KQ = 800 / 117

To know more about lines and segments follow

https://brainly.com/question/23253426

#SPJ1

The total miles drive by Suzy in 18 hours when she can drive 53 miles in 1 hour is equal to 954 miles.

If Suzy can drive 53 miles in 1 hour,

Using the formula of speed based on distance and time we have,

Speed = Distance / Time

Substitute the values in the formula we get,

⇒ Speed = 53 miles / 1 hour

⇒ Speed  = 53 miles/hour

Use this information to find out how far Suzy can drive in 18 hours we get,

Now, Speed =  53 miles/hour

Time = 18 hours

Distance = Speed x Time

Substitute the value of speed and time we get,

⇒ Distance  = 53 miles/hour x 18 hours

⇒ Distance = 954 miles

Therefore, Suzy can drive 954 miles in 18 hours.

Learn more about drive here

brainly.com/question/30483538

#SPJ1

According to the informations,  there are 7 different ways a committee of six people can be selected from a group of seven candidates.

In this case, we must use the combination formula, which is expressed by:

Where n is the total number of items in the set, r is the number of items being selected, and ! denotes the factorial function, which means multiplying a number by all the positive integers less than it.

Therefore, from a group of 7 candidates, a committee of 6 people can be selected in 7 different ways using the combination formula. The formula for the combination of n objects taken r at a time is C(n,r) = n!/r!(n-r)!, where n is the total number of objects and r is the number of objects to be chosen. In this case, we have n = 7 and r = 6, so the formula gives us C(7,6) = 7!/6!(7-6)! = 7 ways.

Find out more about mathematical combination at:

https://brainly.com/question/28065038

#SPJ1

Answer:

2.75

Step-by-step explanation:

When you put that equation into a calculator, you get 2.75.

Answer:

Step-by-step explanation:

To solve for x in the equation 11=4x, we need to isolate x on one side of the equation.

We can start by dividing both sides of the equation by 4:

11/4 = (4x)/4

Simplifying the right side of the equation, we get:

11/4 = x

Therefore, x = 11/4 or 2.75.

Answer:

53

Step-by-step explanation:

angle 2 and 3, angle 3 and 4 are both supplementary angle, which means a2+a3=180 degree, a3+a4=180 degree.

Since you know that the angle 2 and 4 are both 29 degree,

you can write

a3+29=180, and a3 is represented as 3x-8

so

(3x-8)+29=180 (<-- answer for b)

3x+21=180

3x+21-21=180-21

3x=159

x=53

The solution set is {(x, y) | x = y + 2}, which represents a straight line with a slope of 1 passing through the point (2, 0).

Therefore, the correct answer is option 2, infinite solutions.

Equations of the form ax2 + bx + c = 0, where a, b, and c are real numbers, and a 0, are known as polynomial equations in the variable x. Any equation that has the formula p(x) = 0, where p(x) is a polynomial of degree 2 with a single variable, is actually a quadratic equation.

The equation has the following form: ax2 + bx + c = 0, where x is the unknown variable and a, b, and c are constants, with "a" not equal to 0.

Numerous strategies, including factoring, completing the square, and the quadratic formula, can be used to solve quadratic equations.

To solve the system of equations:

x - y = 2 ---(1)

-3x + 3y = -6 ---(2)

We can use the first equation to isolate x in terms of y:

x = y + 2

-3(y + 2) + 3y = -6

Simplifying the equation, we get:

-3y - 6 + 3y = -6

Solving for y, we get:

0 = 0

For all values of y this equation is true-

So,the equations has infinite solutions.

To find the solution set, we can substitute the value of y into the expression for x:

x = y + 2

x = y + 2, for all values of y

To know more about polynomial equation visit:

https://brainly.com/question/30194245

#SPJ1

Answer:

I got you

Step-by-step explanation:

c-11=25

c=25+11

c=36

Answer:

216 mi^3

Step-by-step explanation:

First of all you need to find the area of the base (or top, they are the same)

It is a right-angled triangle, you can simply calculate the area of the base by

A = 6*8/2 = 24 mi^2

The volume of prism is (base area)*height

volume = 24*9 = 216 mi^3

10 is redundant anyway

Answer: the volume of the prism is 62.35 mi cube

Step-by-step explanation:

so first we will find the area of triangular base of the prism, using heron formula.

and s(semi-perimeter)= a+b+c/2= 6+8+10/2= 24/2=12

Area of triangle= A = sqrt [s(s-a)(s-b)(s-c)] = sqrt {12*(12-6)(12-8)(12-10)} = sqrt {6*4*2} = sqrt (48)= 6.92 mi square

Volume = Area x Height

V= 6.92 x 9 = 62.35 mi cube.

Thus, the total surface area of the given right triangular prism is found as : 96 sq. in.

The bases of a prism, which can have up to n sides, are joined to one another by parallel lines that create planes. These bases plus planes would create right angles with one another in a right prism if they were perpendicular to one another.

surface area of right triangular prism S:

surface area of right triangular prism  = base area + 2*triangle area + 2* rectangle area

surface area of right triangular prism  = 4*8 + 2*(1/2*8*3) + 2*4*5

surface area of right triangular prism   = 32 + 24 + 40

surface area of right triangular prism  = 96

Thus, the total surface area of the given  right triangular prism is found as : 96 sq. in.

Know more about the right triangular prism;

https://brainly.com/question/31334313

#SPJ1

Therefore, Postman Builders Inc’s new required rate of return is 23.7%1.

Rate might signify two different things. As a noun, it denotes an amount, frequency, or measure that is typically compared to another quantity or measure. Or, it can be used as a verb to indicate "assign a standard or value to" using a specific scale.

Postman Builders Inc. has a necessary return of 10.2% and a beta of 1.5, according to the information given.

We may get the new necessary rate of return as follows if Postman purchases risky assets that increase its beta by 65% and the predicted inflation rate and inflation premium increase by 2 percentage points.

New Required Rate of Return

= Risk-free rate + Beta * (Expected Market Return - Risk-free rate)

= 2% + (1.5 * (6% + 2% + (65% * 6%))) = 23.7%

New Required Rate of Return equals 8% plus 2.47 x (-2%) to 3.85%.

To know more about rate visit:

brainly.com/question/14731228

#SPJ1

Answer: Vertical angles are formed by the intersection of two lines and are always equal in measure. Therefore, to find the angle that is vertical to angle ∠DEB, we need to look for another angle that has the same measure as ∠DEB.

Unfortunately, we do not know the measure of angle ∠DEB, so we cannot determine which angle is vertical to it based on the given information.

Therefore, the correct answer is: None of the angles can be determined as vertical to angle ∠DEB without additional information.

Step-by-step explanation:

Starting with the original equation:

-2p - 17 = 3(p - 5)

Distributing the 3 on the right side:

-2p - 17 = 3p - 15

Subtracting 3p from both sides:

-5p - 17 = -15

Adding 17 to both sides:

-5p = 2

Dividing by -5:

p = -2/5

Now, we can substitute this value of p back into the original equation and check if it is a solution:

-2(-2/5) - 17 = 3((-2/5) - 5)

4/5 - 17 = 3(-27/5)

-136/5 = -81/5

The left side does not equal the right side, so the supplied value of p = -2/5 is NOT a solution to the equation.

Hope this helps :)

The slope-intercept form of a linear equation with given point (-9,-5) and slope -2/3 is y = (-2/3)x - 11.

The slope of a line is a measure of its steepness or incline, represented by the ratio of the vertical change between two points, known as the rise, to the change in horizontal part between the same two points, known as the run. It describes the rate at which the line is increasing or decreasing as it moves from left to right. The slope of a line can be positive, negative, zero, or undefined, and it plays a critical role in many mathematical applications, including calculus, geometry, and physics. It is commonly denoted by the letter m and is defined as m = (y₂ - y₁)/ (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are any two points on the line.

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line and b represents the y-intercept.

To find the equation of a line with a given slope and a point on the line, we can substitute the values into the equation and solve for the y-intercept, b.

Given that the line passes through the point (-9, -5) and has a slope of -2/3, we can substitute these values into the equation to find the value of b:

-5 = (-2/3) × (-9) + b

-5 = 6 + b

b = -11

Now that we know the value of b, we can write the equation of the line in slope-intercept form:

y = (-2/3)x - 11

Therefore, the equation of the line in slope-intercept form is y = (-2/3)x - 11.

To know more about slope visit:

brainly.com/question/19131126

#SPJ1

1/8

(1/2)^3 1^3 2^3 1/8 or:(1/2)^3 (1/2) (1/2)(1/2)1×1×1/2×2×1/8

Mrs. Jenkins could divide each cookie into six equal pieces, giving each son six pieces of cookies, which would add up to 10 cookies in total.

How to solve the question?

If Mrs. Jenkins gifts 10 cookies to her six sons, the number of cookies each son should get can be found by dividing the total number of cookies by the number of sons.

So, if we divide 10 cookies equally among six sons, we get:

10 / 6 = 1.6667

This means that each son should get approximately 1.67 cookies. However, since it is not possible to divide a cookie into fractions, the actual number of cookies each son would get may vary.

To distribute the cookies equally, Mrs. Jenkins can either give each son one cookie and then divide the remaining four cookies equally among the six sons. This would give each son one cookie and each son would get an additional 4/6 or 0.67 cookies.

Alternatively, Mrs. Jenkins could divide each cookie into six equal pieces, giving each son six pieces of cookies, which would add up to 10 cookies in total.

In any case, the important thing is to ensure that each son receives an equal share of the cookies.

To know more about sample visit :-

https://brainly.com/question/1216161

#SPJ1

YOUR COMPLETE QUESTION IS :-

Mrs. Jenkins gifts 10 cookies to her six sons if they share the cookies equally how many cookies should each son get

Answer:

D. Line O

Step-by-step explanation:

We can simply tell which one it is by looking at the picture. A tangent line is a line that intersects at one point only. Line L doesn't even touch the circle. Line M and N touch the circle in more than one place. If we look at O, we can see that it is "scraping" the edge of the circle, which is what pretty much every tangent line looks like.

Therefore, the answer is D.

The closest option among the given options is option B: 120 units².

What is cylinder?

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases.

The formula for the surface area of a right cylinder is:

SA = 2πr² + 2πrh

where r is the radius and h is the height.

Substituting the given values, we get:

SA = 2π(4)² + 2π(4)(11)

SA = 2π(16) + 2π(44)

SA = 32π + 88π

SA = 120π

Using the approximation π ≈ 3.14, we can calculate the surface area to be:

SA ≈ 120(3.14)

SA ≈ 376.8

Therefore, the closest option among the given options is option B: 120 units².

To learn more about cylinders from the given link:

https://brainly.com/question/16134180

#SPJ1

The length of the rectangle is 10 inches and the width is 4 inches.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

Let's assume that the width of the rectangle is "x" inches.

From the given information, we can write an equation for the length "L" in terms of the width "x":

L = 2x + 2

We also know that the area of the rectangle is 40 square inches:

A = L * x = 40

Substituting the expression for "L" in terms of "x" into the area equation, we get:

(2x + 2) * x = 40

Expanding the left-hand side of the equation and simplifying, we get:

2x² + 2x - 40 = 0

Dividing both sides by 2, we get:

x² + x - 20 = 0

This is a quadratic equation that can be factored:

(x + 5)(x - 4) = 0

The solutions are x = -5 and x = 4. Since the width of the rectangle cannot be negative, the only valid solution is:

x = 4

Substituting this value for "x" into the equation for "L", we get:

L = 2x + 2 = 2(4) + 2 = 10

Therefore, the length of the rectangle is 10 inches and the width is 4 inches.

To learn more about the area of the rectangle visit:

brainly.com/question/2607596

#SPJ1

Answer:

630

Step-by-step explanation:

v= pi×radius squared×hight so its 3.14×5 sqared×8 628 and 628 rounded to the nearest tenth is 630 hope this help

The answer of the given question based on the graph coordinate is , the rule for the values in the table is: Y = 7X - 0.

In mathematics, a coordinate is a set of values that specifies the position of a point in space. Coordinates are used to locate points, lines, and other geometric objects in a plane, a three-dimensional space, or even higher dimensions.

X    Y

5    35

1     7

4    28

2    14

One possible way to do this is to calculate the differences between successive pairs of X and Y values, and then see if there is a constant difference or ratio between them.

Taking the first two rows as an example, we have:

X Y

5 35

1 7

The difference between the X values is 5 - 1 = 4, and the difference between the Y values is 35 - 7 = 28. Dividing the difference in Y by the difference in X gives us:

(35 - 7) / (5 - 1) = 28 / 4 = 7

This means that for every increase of 1 in X, the corresponding increase in Y is 7. We can check this for the other pairs of values in the table and see that it holds true:

X Y

5 35

4 28 (decrease of 1 in X, decrease of 7 in Y)

2 14 (decrease of 2 in X, decrease of 14 in Y)

So the rule for the values in the table is:

Y = 7X - 0.

To know more about Ratio visit:

https://brainly.com/question/29543940

#SPJ1

Answer:

The distance between (3, 4.1) and (3, 1.2) is approximately 2.9 units.

Step-by-step explanation:

You're welcome.