Formulas that may be useful relative to a sphere: V = 43πr3 and SA = 4πr2
The surface area of a sphere is 200.96 square centimeters. What is the approximate volume of the sphere? Use 3.14 for π. Round your answer to the nearest hundredth.

Rate 2 tells us that for every 1 unit of x, we have 2 units of y.

What is double number line?

A double number line is a diagram that shows a proportional relationship between two quantities by representing them as two parallel lines marked with tick marks at regular intervals. The tick marks on one line represent the values of the first quantity, while the tick marks on the other line represent the values of the second quantity.

To write rates for the ratios shown by the double number line, we need to identify two corresponding values on each line and express the ratio between them.

For example, consider the following double number line:

     0         1         2         3         4  

 |-------|-------|-------|-------|-------|

 0      10      20      30      40      50  

 |-------|-------|-------|-------|-------|

          x                y

We can write two rates for the ratio between x and y as:

Rate 1: x units per y units

Rate 2: y units per x units

For example, if x is 15 and y is 30, we can write:

Rate 1: 15/30 = 1/2

Rate 2: 30/15 = 2/1

These rates tell us how much of one quantity is associated with a given amount of the other quantity. For instance, Rate 1 tells us that for every 2 units of y, we have 1 unit of x. Similarly, Rate 2 tells us that for every 1 unit of x, we have 2 units of y.

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Answer:

4.25c + 3.5p = 36.50

c + 6 = p

c = candies and p = pretzels

Step-by-step explanation:

So for the first equation, the prices will be the coefficients of each variable, since for each candy/pretzel it will be that price. We also know that both of these prices together equal 36.50, so that will be on the other side of the equal sign. So the equation representing this info is 4.25c + 3.5p = 36.50

And for the second equation I saw that Mason bought 6 more pretzels than candies. So no matter what number the candies is, the pretzels should always be 6 more than the candies. So the equation representing this information is c + 6 = p

Lastly I just defined the variables that I used to right the system. That is all! Hope this helps you this should be correct :)

A graph of paired (x, y) quantitative data is called a scatterplot. It offers a visual representation of the data plotted as points, assisting in highlighting any patterns in the data. Option B is correct.

Scatter plots are graphs that represent individual points of data and are labeled with quantitative values on both coordinate axes, meaning that there is only one projection on the x-axis and one projection on the y-axis for each point.

A scatterplot is a graph of paired​ (x, y) quantitative data. It provides a visual image of the data plotted as​ points, which helps show any patterns in the data.

Thus, the graph of paired (x, y) quantitative data is called a scatterplot. It offers a visual representation of the data plotted as points, assisting in highlighting any patterns in the data. Option B is correct.

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Answer:

26

Step-by-step explanation: I'm pretty sure its 26 because if k = 7 then 4 times 7 equals 28. Then you subtract 2. That's how I got 26.

Answer:

Step-by-step explanation:

\(4k-2\\k= 7\\\)

Substitute 7 for k into the given equation

\(4(7)-2\\\\=28-2\\\\=26\)

Answer:

10%

The increase of her score would be 7 so 7 over 70 which would = to .10 and .10 as a percent is 10%.

Evan can play 2 games of mini golf and 9 games of kart track.

Given that Evan's mom gave him 11 tickets and left in game zone for 3 hours,

He can spend 1 ticket on one game, and he spend 10 minutes in kart track and a game of mini golf lasts 45 minutes.

We need to find how many games he played of both the games,

So, let he played x games of kart track and y games of mini golf,

So,

x + y = 11

x = 11 - y.............(i)

10x + 45y = 180...........(ii) [ ∵ 3 hours = 180 minutes]

Use the equation i in ii,

So,

10(11-y) + 45y = 180

110 - 10y + 45y = 180

35y = 70

y = 2

Put y = 2 in equation 1,

x = 11-2

x = 9

Hence he played 2 games of mini golf and 9 games of kart track.

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The median of the set of six numbers is 84.5.

The middle number or central value within a set of data is known as the median. The number that falls in the middle of the range is also the median.

To find the median of a set of numbers, we need to arrange the numbers in ascending order and determine the middle value.

The given set of numbers is {87, 85, 80, 83, 84, x}, and we know that the mean of the set is 83.5.

Let's arrange the numbers in ascending order: 80, 83, 84, 85, 87, x.

Since the mean of the set is 83.5, we can calculate the sum of the numbers and subtract the sum of the known values to find the value of x.

Sum of the known numbers = 80 + 83 + 84 + 85 + 87 = 419.

Mean * Number of values = 83.5 * 6 = 501.

Sum of all numbers - Sum of known numbers = x.

501 - 419 = x.

82 = x.

Now that we have the complete set of numbers: {80, 83, 84, 85, 87, 82}, we can determine the median.

The median is the middle value of the set when arranged in ascending order.

In this case, the median is the average of the two middle values, which are 84 and 85.

Median = (84 + 85) / 2 = 169 / 2 = 84.5.

Therefore, the median of the set of six numbers is 84.5.

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The relation 2 represents a function.

In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.

To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.

The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.

If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.

We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.

Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.

Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.

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Answer: 8y=2h

Step-by-step explanation: you have to subtract the first 2 numbers then add the others and then add letters and boom

Answer:

21.5 square units

Step-by-step explanation:

The 4 circles touching eachother have a total combined length of 20.

There are 4 circles. 20/4 = 5. The diameter of each circle is 5 units.

The length ofthe rectangle is 20 units. the width of the rectangle is 5 units.

The area of the shaded region is the area of the rectangle minus the ares of 4 circles.

A = area of rectangle - area of 4 circles

A = LW - 4 × πr²

The radius of each ciorcle is d/2 = 5/2 = 2.5

A = 20 × 5 - 4 × 3.14 × 2.5²

A = 100 - 78.5

A = 21.5

Answer

238π yd^2

Step-by-step explanation:

here's your solution

=> height of cylinder = 10 yd

=> radius of cylinder = 7 yd

=> formula to calculate surface area = 2πr(h + r)

=> putting the value of height and radius in formula

=> SA = 2*22/7*7(10+7)

=>. SA = 2*22*17

=> SA = 748 yd.sq

hope it helps

To find the sum of the vertex angles in various polygons, we need to sketch the polygons and then calculate the sum. For a hexagon, octagon, and dodecagon, the sums of the vertex angles are 720°, 1,080°, and 1,800°, respectively.

a. Hexagon: A hexagon is a polygon with six sides. To find the sum of the vertex angles, we can divide the hexagon into triangles. Since each triangle has an interior angle sum of 180°, the hexagon can be divided into four triangles. Therefore, the sum of the vertex angles in a hexagon is 4 * 180° = 720°.

b. Octagon: An octagon is a polygon with eight sides. Similar to the hexagon, we can divide the octagon into triangles. Dividing it into six triangles, each with an interior angle sum of 180°, the sum of the vertex angles in an octagon is 6 * 180° = 1,080°.

c. Dodecagon: A dodecagon is a polygon with twelve sides. Dividing it into ten triangles, each with an interior angle sum of 180°, the sum of the vertex angles in a dodecagon is 10 * 180° = 1,800°.

Therefore, the sum of the vertex angles in a hexagon is 720°, in an octagon is 1,080°, and in a dodecagon is 1,800°.

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Find the sum of the vertex angles of the following polygons---

a. A hexagon

b. An octagon

c. A dodecagon.

Answer: 7 classes enrolled in

Step-by-step explanation:

200+40n=480

40n = 280

n = 7

The magnitude and the direction of force 592.73 N and 332.748

A force is an effort that changes the state of an object at rest or at motion.

Given:

F1= 308 N, angle = 32

F2= 287 N, angle= 22

F1= < 308 cos 32, 308 sin 32>

F1= <261.198, 163.215>

F2= < 287 cos 22, 287 sin 22>

F2= < 266.101, 107.512>

F1+ F2= <527.299, 270.727>

Now, F= |F1 + F2|

F=√ 527.299² + 270.727²

F=√278044.2354 + 73293.1085

F= 592.73 N

\(\theta\)\(= cos^{-1}\) ( 527.299 / 592.73)

\(\theta\)= 27.252

Now Actual \(\theta\)= 360- 27.252

= 332.748

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A) Yes, the graph represents a proportional relationship because the rate at which the plane's altitude increases is directly proportional to the amount of time that has elapsed since takeoff.

B) The unit rate of change is the number of feet per minute that increases over time, which can be calculated by finding the slope of the line. To do this, we choose two arbitrary points on the line and calculate the change in altitude divided by the change in time for each point. Therefore, if we choose the points (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 12000), then the unit rate of change is (12000 - 0) / (2 - 0).

The unit rate of change is 6000 feet per minute, calculated by (12000 - 0) / (2 - 0).

If you have any additional questions or need further assistance, please let me know.

Answer:

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

Proportional relationship is:

At x = 0, the function gets the value of zero regardless the value of k. Hence the line passes through the origin.

A) The given graph passes through the origin and therefore it is a proportional relationship.

B) The value of y = k when x = 1 is the rate of change.

As per graph it is:

Answer:

j = 38

Step-by-step explanation:

\(\frac{j}{-2} + 7 = -12\)

subtract 7 on both sides:

\(\frac{j}{-2} + 7 - 7 = -12 - 7\)

\(\frac{j}{-2} = -19\)

multiply -2 on both sides:

\(\frac{j}{-2}\) x -2 = -19 x -2

j = 38

Answer

adding 2

Step-by-step explanation:

Median is 8

I don't know if this is correct but I tried.

Peggy's deposit of $350 with 6% interest compounded monthly yields approximately $394.29 after two years, surpassing Larry's $360 deposit with 4% interest compounded quarterly at approximately $389.67.

To determine which method results in more money after two years, we'll calculate the future value for both Larry's and Peggy's deposits using their respective interest rates and compounding frequencies.

For Larry's deposit:

Principal amount (P) = $360

Interest rate (r) = 4% = 0.04 (decimal)

Compounding frequency (n) = 4 (quarterly compounding)

Using the formula for compound interest:

Future value (FV) = P * (1 + r/n)^(n*t), where t is the time in years.

Larry:

FV_Larry \(= \$360 * (1 + 0.04/4)^{(4*2)} = \$360 * (1 + 0.01)^8\)

= $360 * 1.082432 = $389.67 (approx.)

For Peggy's deposit:

Principal amount (P) = $350

Interest rate (r) = 6% = 0.06 (decimal)

Compounding frequency (n) = 12 (monthly compounding)

For Peggy:

FV_Peggy = \(\$350 * (1 + 0.06/12)^{(12*2)}\)

\(= \$350 * (1 + 0.005)^{24}\)

= $350 * 1.127424 = $394.29 (approx.)

After two years, Peggy's method of depositing $350 with a 6% interest rate compounded monthly results in a higher future value of approximately $394.29, while Larry's method of depositing $360 with a 4% interest rate compounded quarterly yields a lower future value of approximately $389.67. Therefore, Peggy's method generates more money after two years.

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Using the divergence theorem we can compute that the outward flux of the vector field is 16π .

The outward flux of F over the solid cylinder and z = 0 is

∫∫F·ds  = ∫∫∫ DivF dv

F = 2xy² i   +  2x²y j + 2xy k

Div F  =  D/dx (2xy²)  +   D/dy (2x²y )

Div F  =  2y²  +  2x²

In cylindrical coordinates   dV = rdrdθdz and as z = 0 the region is a surface ds = r·dr·dθ

Using the parametric form of the surface equation

x = rcosθ        y =  r sinθ      and z = z

Div F  = 2r² sin²θ  + 2r²cos²θ

∫∫∫ DivF dv  =  ∫∫ [2r²sin²θ  + 2r²cos²θ] × rdrdθ

∫∫ 2r² [sin²θ  + cos²θ] × rdrdθdz   ⇒  ∫∫ 2r³ drdθ

Integration limits

0 < r < 2          0 < θ < 2π

2∫₀² r³ ∫dθ

(2/4) × (2)⁴ × 2π

The divergence theorem, commonly known as Gauss' theorem or Ostrogradsky's theorem, is a theorem that connects the flow of a vector field across a closed surface to the field's divergence in the volume enclosed.

In more detail, the divergence theorem states that the surface integral of a vector field across a closed surface, sometimes referred to as the "flux" through the surface, is equal to the volume integral of the divergence over the region inside the surface.

Therefore the flux is 16π .

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Answer:

9+10x

Step-by-step explanation:

Given: g(x)= -3x2 + 5x = -6+5x

    and h(x) = 2x +1

Find: g(h(x+1))

1!

h(x+1)= 2(x+1) +1

        =2x+3

2! substitute h(x+1)in function g(x)

g(h(x+1))= -6 + 5(2x+3)

             = -6+10x+15

             = 9+10x

ps. im not sure (-3x2 + 5x) is -6+5x (-3 multiply 2) or question is not clear

X=5

Step-by-step explanation:

X-5=0. X+2=0

X=5. X=-2

1.85 meters is equal to 6.069 feet.

To convert meters to feet, you can use the conversion factor of 1 meter = 3.28084 feet. To convert 1.85 meters to feet, you would multiply 1.85 by 3.28084. This gives you the result of 6.069 feet. It's important to note that this conversion is an approximation and may not be entirely accurate.

Additionally, there are variations in the definition of a foot.

For example, the international foot is defined as exactly 0.3048 meters, which is roughly equal to 3.28083333 feet. So, depending on the context, the exact conversion of 1.85 m to feet may vary slightly.

It's always best to double check the conversion with a reliable source or use a conversion tool if precision is important.

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Answer: 5/12

Step-by-step explanation:

2/3 - 1/4 = 5/12

Answer:

1.75

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The pattern is adding 130, or multiply the servings by 130.

so if 3x=390, you would divide both sides by 3 and get 130.

This means that x=130

Now plug in 4x=?

You would get 4*130=?

if you do the math through multiplication you would get 520

Answer:

B

Step-by-step explanation:

I got the unit test right on edg 2020

Answer:

1200 m2

Step-by-step explanation:

hope i helped