You are traveling from Milwaukee (9, 17) to St. Louis (7, 10). Each unit on the map is 50 miles. How many miles did you travel? Round your answer to the nearest tenth.

The rate of change of the volume of a spherical ball is equal to the derivative of its volume with respect to time.  The rate of change of the volume of the ball when the radius is 5 cm is given by:dV/dt = 4π(5)²(-3) = -300π cubic cm/s

Given, the radius of a spherical ball is decreasing at a constant rate of 3 cm per second. Find, in cubic centimeters per second, the rate of change of the volume of the ball when the radius is 5 cm.To solve the problem, we need to find the rate of change of the volume of the spherical ball when the radius is 5 cm.The formula for the volume of a sphere is given by V = (4/3)πr³. So, the volume of the spherical ball is proportional to the cube of the radius of the ball.

This means that the rate of change of the volume of the ball is also proportional to the square of the radius. So, if the radius of the ball decreases at a constant rate, then the rate of change of the volume of the ball also decreases at a constant rate.To find the rate of change of the volume of the ball when the radius is 5 cm, we need to differentiate the volume with respect to time. Using the formula for the volume of a sphere, we getV = (4/3)πr³Differentiating both sides of the equation with respect to time, we get:dV/dt = 4πr² (dr/dt)where r is the radius of the sphere and dr/dt is the rate of change of the radius with respect to time. Since the radius of the ball is decreasing at a constant rate of 3 cm/s, we have dr/dt = -3 cm/s. Therefore,dV/dt = 4πr² (-3) = -12πr² cubic cm/sWhen the radius is 5 cm, we have r = 5 cm. Thus,dV/dt = -12π(5)² = -300π cubic cm/sTherefore, the rate of change of the volume of the ball when the radius is 5 cm is -300π cubic cm/s.

Therefore, option (B) -3001 is the correct answer.

To know more about volume of a spherical ball visit:

brainly.com/question/29053535

#SPJ11

Circumference of the circle with the given diameter is 69.08 inches.

Circumference of a circle is defined as the total length of the boundary of the circle.

The concept is same as the perimeter for straight sided figures.

Given,

Diameter of the circle = 22 inches

Radius of the circle = Diameter / 2 = 22 / 2 = 11 inches

Circumference of a circle = 2πr, where r is the radius of the circle and the value of π is 3.14.

Circumference = 2 × 3.14 × 11 = 69.08 inches

Hence 69.08 inches is the circumference of the circle.

Learn more about Circumference here :

https://brainly.com/question/4268218

#SPJ1

Step-by-step explanation:He can only hold 3 because 170 divivded by 50 = 3 Your welcome!!

Based on the given conditions, formulate: 

34÷1 1/3

Find common denominator and write the numerators above common denominator:

34/3/3+1/3

Write the numerators over common denominator:

34/3+1/3

Calculate the sum or difference:

34/4/3

Divide a fraction by multiplying its reciprocal:34×3/4

Cross out the common factor:

17×3/2

Calculate the product or quotient:

51/2

get the result:

25.5 or 25 1/2

=25.5 or 25 1/2

The dimensions of the rectangle are width = 20 centimeters and length = 1 centimeter.

Let's denote the width of the rectangle as "w" centimeters. According to the problem, the length of the rectangle is 19 centimeters less than its width, so the length can be expressed as "w - 19" centimeters.

The formula for the area of a rectangle is length multiplied by width. In this case, the area is given as 20 square centimeter

Area = Length × Width

20 = (w - 19) × w

To solve this equation, we can expand it:

20 = \(w^2\) - 19w

Rearranging the equation to bring everything to one side:

\(w^2\) - 19w - 20 = 0

Now, we can factor the quadratic equation:

(w - 20)(w + 1) = 0

Setting each factor equal to zero and solving for "w":

w - 20 = 0 --> w = 20

w + 1 = 0 --> w = -1

Since a negative width doesn't make sense in this context, we discard w = -1.

Therefore, the width of the rectangle is 20 centimeters (w = 20).

To find the length, we substitute this value back into the expression for length:

Length = w - 19

Length = 20 - 19

Length = 1 centimeter

So, the dimensions of the rectangle are width = 20 centimeters and length = 1 centimeter.

for such more question on dimensions

https://brainly.com/question/13847072

#SPJ11

The answers to the questions below are as follows:

It is an acronym for Confirmatory Factor Analysis, which is a statistical tool that consists of testing a hypothetical factorial structure of a variable conunt. This is a form of modeling of structural equations (without) and is commonly performed using specialized software, whose objective is to test the the quality of the hypothetical factorial structure in relation to the observed data.

Therefore, it is concluded that the false alternative is one that states that the cross-tubulation is used in CFA for test purposes, which is not true, as the cross-tubulation is used in the contingency table.

Find more about Confirmatory Factorial Analysis in:

https://brainly.com/question/28273004

#SPJ1

The value of angle x is 34.992°

According to the question we have been given a right angled triangle with its two sides as 7 units which is the perpendicular and 10 units which is the base.

We need to find the value of x that we need to find the measure of angle x.

For that we will use trigonometry. We know that,

        tanΘ =P/B

where,   P = perpendicular

             B = base

Now we need to find first tan x which is

       tan x = 7/10

       tan x = 0.7

          x = tan⁻¹(0.7)

          x = 34.992°

Hence the value of x is 34.992°

Learn more about trigonometry here : https://brainly.com/question/13729598

#SPJ9

We can see that since the values that multiply each component (x & y) are less than an unit, the transformation rule would be a reduction.

a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

Learn more about subspace

brainly.com/question/30318872

#SPJ11

Answer:

Start at origin (0,0)

Move 1/2 units left

Move 1 and 1/2 units down

Place your point

Step-by-step explanation:

Start at the origin (0,0)

Move 1/2 units to the left

Then move 1 1/2 units down, and place your point.

The first coordinate is locating the position horizontally, or on the x axis

The second coordinate is locating the position vertically, or on the y axis.

If there is a negative number on the x coordinate, the first one, you move left.

If positive, you move right.

If there is a negative number on the y coordinate, the second one, you move down.

If positive, you move up.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

move toward left of the horizontal x axis then plot the point in between o and -1.For next point then move down the vertical y axis and plot the point in between -1 and -2 .

Step-by-step explanation:

Hope this helps u!!

Since the value function places a higher weight on losses than gains, we can conclude that the individual is loss averse.

In prospect theory, loss aversion refers to the tendency for individuals to weigh losses more heavily than gains. The value function provided exhibits this behavior by assigning a higher value to gains and a lower value to losses.

For wealth (w) greater than 20, the value function v(w) = w^(1/2) indicates that gains are valued positively, with the square root function reflecting a concave shape that diminishes the marginal value of additional gains.

On the other hand, for wealth (w) below 0, the value function v(w) = -(-w)^(1/2) reflects the negative value assigned to losses. The square root function applied to negative wealth also exhibits concavity, emphasizing the aversion to losses.

To know more about loss averse,

https://brainly.com/question/28592664

#SPJ11

As per the angle sum property, the measure of the top-left angle in the triangle is 55° and the measure of the top-right angle is 35°

The term angle sum property is defined as the sum of interior angles of a triangle is 180°.

Here we have the  of each acute angle.

(7x + 6)

(6x – 7)

As per the angle sum property, the given angle is written as,

=> (7x + 6)° + (6x - 7)° + 90° = 180°

Now, we have to expand the equation, then we get,

=>  13x° + 89° = 180°

When we simplify the equation, then we get,

=> 13x° = 180° - 89°

=> 13x° = 91°

Then the value of x is 7°

Therefore, the measure of the top-left angle in the triangle is calculated as

=> (7x + 6)°

Apply the value of x on it, then we get,

=> (7 x 7) + 6

=> 55°

and the measure of the top-right angle is calculated as,

=> (6 x 7) - 7

=> 42 - 7

=> 35°

To know more about Angle sum property here.

https://brainly.com/question/4316040

#SPJ4

To guarantee that the 3 team compositions (and team leads) are repeated, the professor would need to form groups a total of 3 times over the course of the semester. Each time the professor forms groups, there would be 3 possible team compositions (since the team lead can change within each group) and after 3 formations, all 3 compositions would have been used and repeated.

To determine the number of possible unique team compositions and team leads that can be formed.
1. First, we'll find the number of ways to choose team leads for each group:
There are 12 students and 3 team leads needed, so there are 12 choose 3 ways to pick the team leads, which is calculated as C(12,3) = 12! / (3! * (12-3)!) = 220.
2. Now, we'll calculate the number of ways to divide the remaining 9 students into 3 groups of 3 students each. We can use the multinomial coefficient formula, which is:
C(9,3,3,3) = 9! / (3! * 3! * 3!) = 1680
3. To find the total number of unique team compositions (including team leads), we multiply the results from steps 1 and 2 Total unique team compositions = 220 * 1680 = 369,600
4. The professor needs to form the groups 369,601 times in order to guarantee that the 3 team compositions (and team leads) will repeat.

Learn more about compositions here: brainly.com/question/5217462

#SPJ11

The simplified form of the given expression, (-7x^5/14x)^-3, is -8x⁻¹²

From the question we are to simplify the given expression

From the given information,

The given expression is

(-7x^5/14x)^-3

This expression can be properly written as:

(-7x⁵/14x)⁻³

The expression can be simplified as shown below:

(-7x⁵/14x)⁻³

(-7x⁵)⁻³ / (14x)⁻³

[1 / (-7x⁵)³] / [1 / (14x)³]

[1 / (-7)³ × (x⁵)³] / [1 / (14)³ × (x)³]

[1 / -343 × (x¹⁵)] / [1 / 2744 × x³]

[1 / -343x¹⁵] / [1 / 2744x³]

= [1 / -343x¹⁵] × [2744x³ / 1]

= 2744x³ / -343x¹⁵

= -2744/343 × x³ / x¹⁵

= -8 × x³ / x¹⁵

= -8x³ / x¹⁵

= -8 × x³ ⁻ ¹⁵

= -8 × x⁻¹²

= -8x⁻¹²

Hence, the simplified expression is -8x⁻¹²

Learn more on Simplifying an expression here: https://brainly.com/question/15775046

#SPJ1

The number of hawks that can be supported by 250,000 kilograms of producers are 500 hawks.

1 hawk ≈ 500 grams

1 kg = 1,000 grams

According to the 10 percent law, only 10% of the energy is transferred to each trophic level from its lower trophic level. So, in this case, if 250,000 kg is available to the producer (grass), then only 25,000 kg will be available to the primary consumer (mice) and only 2,500 kg will be available to the secondary consumer (snakes). Then, for the tertiary consumer (hawks) will be available about 250 kg.

So, 250 kg = 250,000 grams

Since 500 grams ≈ 1 hawk

Thus, 250,000 grams ≈ 500 hawks

Hence, the number of hawks that can be supported by 250,000 kilograms of producers are 500 hawks.

Learn more about trophic level at: https://brainly.com/question/13267084

#SPJ4

Although part of your question is missing, you might be referring to this full question: Grasses are the dominant producers in the prairie ecosystem. Mice eat the grass seed, snakes eat the mice, and hawks eat the snakes. The mass of a hawk is about 500 grams. How many hawks can be fed by 250,000 kilograms of producers in this ecosystem? Remember that 1 kilogram equals 1,000 grams.

There are 28 ways to choose 6 teams for the playoffs if there are 8 college basketball teams in a certain sub-division.

To determine the number of ways to choose 6 teams for the playoffs out of the 8 college basketball teams in a certain Sub-Division, we can use the combination formula. The formula for combinations is given by

nCr = n! / (r! * (n-r)!),

where n represents the total number of teams and r represents the number of teams to be chosen.

In this case, n = 8 and r = 6.

Plugging in these values, we have

8C6 = 8! / (6! * (8-6)!) = 8! / (6! * 2!) = (8 * 7) / (2 * 1) = 28.

Therefore, there are total 28 ways to choose 6 teams.

To know more about ways refer here:

https://brainly.com/question/4318885

#SPJ11

Answer:

2x+y=-2

-9x-3y=18

So what you would do is see which one you would like to get rid of (either x, or y in this situation get rid of y)

multiply y by postive 3

3(2x+y=-2)

6x+3y=-6

-9x-3y=18          (both y's cross out since 3y+-3y is equal to zero)

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

-3x=-24 (divide both sides by -3)

---     ---

-3      -3

x= 8 (neg/neg=positive)

Then figure out the x so use either the first or second equation

so in this case I will use the first equation (plug in the x for 8)

2(8)+y=-2

16+y=-2

-16    -16

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

y=-18

Check:

2x+y=-2

2(8)+y(-18)=-2

16+-18=-2

-2=-2 (therfore you know that you are right)

Ansers:

y=-18

x=8

Hope this helps!

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

We have,

Let's analyze each of the given statements to determine whether they are identities:

tan x = sin x / cos x:

This is an identity.

It is known as the fundamental identity of trigonometry, as it holds true for all values of x (except when cos x is equal to 0).

tan x cos x = sin x:

This is not an identity.

It is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

cos x = tan x sin x:

This is not an identity.

Similar to the previous statement, it is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

sin x / tan x = cos x:

This is an identity.

It can be derived from the fundamental identity by dividing both sides by cos x, resulting in sin x / cos x = cos x / cos x, which simplifies to sin x / tan x = cos x.

Thus,

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ1

Answer:

= 3

/3 + 5a/12 = 9/4

In order to find the values of x and y, consider that the triangles are similar. Then, the proportion between similar sides of the triangles are equal.

In triangles ABC and DEF you have:

EF/BC = ED/BA

by replacing the values of such sides you obtain:

x/28 = 7/14 multiply by 28 both sides

x = (7/14)(28)

x = 14

Hence, the value of x is x = 14

Next, for the same triangles use the following proportion:

AC/DF = BC/EF

by replacing the values of such sides you obtain:

y/10 = 28/14 multiply by 10 both sides

y = (28/14)(10)

y = 20

Hence, the value of y is y = 20

The percentage by which the orangutan population has changed is 92.23%

We know that the formula for the relative change.

R = |x2 - x1| ÷ x1

where x2 is the final value

and x1 is the initial value

R is the relative change

Here, the orangutan population has changed from 1900 when there were 85,000 orangutans to the present day when there are about 6,600 orangutans.

This means, x1 = 85000 and x2 = 6600

So, the relative change would be,

R = |6600 - 85000| ÷ 85000

R = 78400 / 85000

R = 0.9223

and the percentage change would be,

P = R × 100

P = 0.9223 × 100

P = 92.23%

Therefore, the percentage change = 92.23%

Learn more about the percentage here:

https://brainly.com/question/16797504

#SPJ4

According to the question, the work done in stretching the spring from 3 ft. beyond its natural length to 7 ft. beyond its natural length is 8 lb·ft.

To calculate the work done, we need to use the formula:

\(\[ \text{Work} = \text{Force} \times \text{Distance} \]\)

Given that a force of 2 lb is required to hold the spring stretched 3 ft. beyond its natural length, we can consider this as the force applied to stretch the spring from 0 ft. to 3 ft. beyond its natural length.

Therefore, the work done in stretching the spring from 0 ft. to 3 ft. beyond its natural length is \(\(2 \, \text{lb} \times 3 \, \text{ft}\)\).

To find the work done in stretching the spring from 3 ft. beyond its natural length to 7 ft. beyond its natural length, we need to subtract the work done in stretching from 0 ft. to 3 ft. beyond its natural length.

Hence, the work done in stretching the spring from 3 ft. beyond its natural length to 7 ft. beyond its natural length is:

\(\[ \text{Work} = (2 \, \text{lb} \times 7 \, \text{ft}) - (2 \, \text{lb} \times 3 \, \text{ft}) \]\)

Simplifying the equation:

\(\[ \text{Work} = 14 \, \text{lb} \cdot \text{ft} - 6 \, \text{lb} \cdot \text{ft} \]\)

Therefore, the work done in stretching the spring from 3 ft. beyond its natural length to 7 ft. beyond its natural length is:

\(\[ \text{Work} = 8 \, \text{lb} \cdot \text{ft} \]\)

So, the answer is that the work done in stretching the spring from 3 ft. beyond its natural length to 7 ft. beyond its natural length is 8 lb·ft.

To know more about Work Done visit-

brainly.com/question/33117676

#SPJ11

Answer:

132 square units

Step-by-step explanation:

We are to find the surface area of a square pyramid.

From the diagram above, we are given:

Slant height = 6 units

Base = 8 units

The formula is given as:

= 2bs + b²

= 2 × 8 × 6 + 6²

= 96 + 36

= 132 square units

Answer:

The coordinates of the center of this circle is (-1, -3).

Step-by-step explanation:

As we know that \(A = (-4,2)\) and \(B = (2,-8)\) are points lying on circle T, the center is the midpoint of the segment AB, whose location can be obtained from Midpoint formula:

\(C = \frac{1}{2}\cdot A + \frac{1}{2}\cdot B\)

\(C = \frac{1}{2}\cdot (-4,2)+\frac{1}{2}\cdot (2,-8)\)

\(C = (-2, 1)+(1,-4)\)

\(C=(-2+1,1-4)\)

\(C=(-1,-3)\)

The coordinates of the center of this circle is (-1, -3).

Answer:

He ran one mile in 20 minutes

Step-by-step explanation:

Answer:

1. area = pi*r^2

herein, dia = 20 inch

radius = 10 inch

area = 22/7*10*10

        = 314.2 square inch

Step-by-step explanation:

Answer:

85

Step-by-step explanation:

5×9=45

8×5=40

add it

85

Answer:

answer is 20%!

Step-by-step explanation:

i took a test

Answer:

b. 20%

Step-by-step explanation:

You can do division to find the answers to questions like this.

Just ask how many times does 60 go into 300, and your answer is 5.

So it is 1/5 or 20%