a cylindral drill with radius 5 cm is used to bore a hole through the center of a sphere with radius 10 cm. find the volume of the ring-shaped solid that remains.

We can solve this problem using a system of linear equations, have in mind the expression for simple interest:

Let x be the principal invested on the first account.

Let y be the principal invested on the second account.

We can solve the system by the method of substitution, isolate the variable y in equation (1):

Now, substitute (1) into equation (2) to get x-value:

Austin invested $16,000 on the first account.

Then, substitute the x-value in the equation (1) to get y-value:

Austin invested $14,000 on the second account.

Answer:

\(y=-3x+10\)

Step-by-step explanation:

y=mx+b is the slope intercept form.

Answer:

m= -1/2

this is the answer

Answer: Y=1 and X=4

Step-by-step explanation: 4x-10=6 can be 10+6=4x which is 16=4x so x=4 and y=x-3 or y=4-3 so y=1

Answer: The given question is solved :

Step-by-step explanation:

correct solution in imaje

Answer:

A

Step-by-step explanation:

If 18 employees completed a large mailing project in 20 days, adding 6 more employees to complete the same project next month would reduce the time required.

Let's assume that the work completed by one employee in one day remains constant. In this case, the total work done by 18 employees in 20 days can be expressed as 18 * 20 = 360 employee-days of work.

To find the number of days required when 24 employees are working, we divide the total work by the number of employees: 360 employee-days of work / 24 employees = 15 days.

Therefore, with 6 additional employees, the project can be completed in 15 days. Adding more employees reduces the time needed to complete the project.

To know more about project completion here: brainly.com/question/3221895

#SPJ11

Answer:

x=y=z=106

Step-by-step explanation:

The upper line is a straight line, so x+74=180, x=106.

y and x are equal in measure as it's a pair of parallel lines and z=y as they are alternate interior angles

Answer: The answer is 12x–9.

Step-by-step explanation: So to combine the like terms or simplify add –3x and 15x.

Standard Deviation: Is a measure of how spread out values are in a data set compared to the mean. It is calculated by finding the square root of the variance, which is the average of the squared differences from the mean.

Mean: The average value of a set of numbers. It is calculated by summing up all the numbers in the set and dividing the result by the total number of numbers in the set.

Distribution Curve: is a bell shaped curve that displays the mean with a line down the center of the curve and standards deviations within standard deviations.

See attached file for model of curve, from: https://commons.wikimedia.org/wiki/File:Standard_deviation_diagram.svg

Given the mean and standard deviation we can use a general rule to determine the population between the given lengths.

Generally in a normal distribution:

176 cm is 1 standard deviation less than the mean and 184 cm is 1 standard deviation greater than the mean. Using the general rules above, 68% of data falls between -1σ and +1σ. Therefore, the answer to this question would be B. 68%

The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.

Answer:

8

Step-by-step explanation:

Answer:

3000000 is needed to meet the goal $84,000,00

Step-by-step explanation:

Divide 84,000,000 by 28

84000000/28

= 3000000

Answer:

A function is a relation that maps elements from one set (the domain, the set of the inputs) into elements from another set (the range, the set of the outputs). Such that each element of the domain can be mapped into only one element of the range.

Now let's analyze the given relations.

1)

Here we can see that the inputs are -3, -1, 1, and 2.

Then the domain (the set of the inputs) is:

D = {-3, -1, 1, 2}

And we can see that the outputs are 0, 2, and 5.

Then the range is:

R = {0, 2, 5}

We also can see that each input is being mapped into only one output, then this relation is a function.

2) In this case the inputs are -2, -3, and 5.

Then the domain is:

D = {-2, -3, 5}

And the outputs are 6, 7, 8

Then the range is:

R = {6, 7, 8}

And we can see that each input is mapped into only one output, then this relation is a function.

3) In this case we can see that the inputs are -4, -2, and 0

Then the domain is:

D = {-4, -2, 0}

And we can see that the outputs are -2, -1, 3, and 4.

Then the range is:

R = {-2, -1, 3, 4}

In this case, we can see that the input -4 is being mapped into two different outputs (3 and -1)

Then this relation is not a function.

The magnitude of the gravitational force exerted on the 5.9-kg rock and the 5.8 x 10^-4-kg pebble near the surface of the Earth is 57.9 N and 0.0579 N, respectively.

To calculate the gravitational force exerted on an object near the Earth's surface, we can use the formula: F = mg, where F is the gravitational force, m is the mass of the object, and g is the acceleration due to gravity. Near the surface of the Earth, the standard value for g is approximately 9.8 m/s^2.

For the rock with a mass of 5.9 kg, the gravitational force can be calculated as follows:

F_rock = (5.9 kg) * (9.8 m/s^2) = 57.9 N.

For the pebble with a mass of 5.8 x 10^-4 kg, the gravitational force can be calculated as follows:

F_pebble = (5.8 x 10^-4 kg) * (9.8 m/s^2) = 0.0579 N.

Therefore, the rock experiences a gravitational force of 57.9 N, while the pebble experiences a gravitational force of 0.0579 N.

To know more about the gravitational force, refer here:

https://brainly.com/question/32609171#

#SPJ11

39 subjects were tested in this simple one-way ANOVA.

We are given that:

F(7 , 31) = 4.78

Step 1: Find the total degrees of freedom.

The treatment df = 7

The error df = 31

\(df_{treatment} &\ +df_{error} &\ = df_{total}\)

Hence, the total df = 7+31 = 38.

Step 2: Find the number of subjects tested.

We know that in a one-way ANOVA test:

df = n-1

⇒ 38 = n-1

⇒ n = 39.

Hence, 39 subjects were tested in this simple one-way ANOVA.

For similar questions on the one-way ANOVA test, visit:

https://brainly.com/question/28206544

#SPJ4

Answer:

\(\dfrac{31}{2}+\dfrac{27}{2}i\)

Step-by-step explanation:

The given complex number is:

\(z=\dfrac{(2+3i)(4-7i)(1+i)}{(1^2-i^2)}\)

Firstly we can solve (2+3i)(4-7i)(1+i)

= 2(8)+2(-7i)+4(3i)+3i(-7i²)× (1+i)

= (16-14i+12i-21i²i)× (1+i)

Since, i² = -1

= (16-14i+12i-21(-1)i)× (1+i)

= (16-14i+12i+21)× (1+i)

= (29-2i)(1+i)

= 31+27i

Denominator : (1-i²)

= (1-(-1))

= 2

\(\dfrac{(2+3i)(4-7i)(1+i)}{(1^2-i^2)}=\dfrac{31+27i}{2}\\\\=\dfrac{31}{2}+\dfrac{27}{2}i\)

Hence, the correct answer is \(\dfrac{31}{2}+\dfrac{27}{2}i\).

Multiple regression analysis is  is applied when analyzing the relationship between  b) A dependent variable and several independent variables .

In a multiple regression analysis, several regression equations are used to predict the value of the dependent variable based on the values of the independent variables. These equations are derived using data from a single sample.

Multiple regression analysis is especially useful in situations where the relationship between variables is complex and cannot be accurately captured by simple linear regression. By considering multiple factors simultaneously, researchers can better identify the true effects of each independent variable on the dependent variable .

In summary, multiple regression analysis involves using several regression equations and a single sample to examine the relationship between one dependent variable and multiple independent variables.

This technique helps researchers better understand the complex relationships between variables and make more accurate predictions based on the combined influence of all factors. The correct answer is b).

Know more about   Multiple regression   here:

https://brainly.com/question/16259704

#SPJ11

Answer:

2800 - 4000

Step-by-step explanation:

40 × 70 = 2800

50 × 80 = 4000

The average rate of change of the function f(x) = x² + 7x + 6 over the interval -4 ≤ x ≤ -1 is -8/3 or about -2.67.

To determine the average rate of change of a function over a specific interval, we use the following formula:

\($$ \frac{f(b) - f(a)}{b - a} $$\)

where a and b are the endpoints of the interval.

In this case, we have the function f(x) = x² + 7x + 6 and the interval -4 ≤ x ≤ -1. To find the average rate of change of the function over this interval, we need to evaluate the function at the endpoints of the interval and substitute these values into the formula.

Therefore:

\($$ \text{Average rate of change} = \frac{f(-1) - f(-4)}{-1 - (-4)} $$\)

We start by evaluating the function at the endpoints of the interval: \($$ f(-1) = (-1)^2+ 7(-1) + 6 = -2 $$\)

\($$ f(-4) = (-4)^2 + 7(-4) + 6 = 6 $$\)

Substituting these values into the formula, we get: \($$ \text{Average rate of change} = \frac{-2 - 6}{-1 - (-4)} = \frac{-8}{3} $$\)

Therefore, the average rate of change of the function f(x) = x² + 7x + 6 over the interval -4 ≤ x ≤ -1 is -8/3 or about -2.67.

To know more about function, visit:

https://brainly.com/question/30721594

#SPJ11

9514 1404 393

Answer:

  30

Step-by-step explanation:

The total price for x employees will be ...

  p(x) = {1000x for x ≤ 25; x(1000 -20(x -25)) for 25 < x ≤ 40; 700x for 40 < x}

We want p(x) = 27000.

We can check the value of x for the three different functions to see if it is in the specified domain.

  1000x = 27000   ⇒   x = 27 (not in the domain of the first segment)

__

  x(1000 -20(x -25)) = 27000

  20x(75 -x) = 27000 . . . . . collect terms, factor

  (x -37.5)^2 = -1350 +1406.25 . . . . . complete the squre

  x = 37.5 ±√56.25 = 37.5 ±7.5 = {30, 45}

  x =  30 is in the domain; x = 45 is not

__

  700x = 27000

  x ≈ 38.57 (not in the domain of the last segment)

__

So, the piecewise cost function will give a total cost of $27000 when the number of employees going for the trip is 30.

a) To find the first three elements of the sequence defined by an = n^2 - 3n + 2, we simply substitute n = 0, 1, 2 into the expression for an and simplify: a0 = 2, a1 = 0, a2 = 0.

b) To show that the sequence satisfies the recurrence relation an = 2an-2 - an-2 + 2 for every n >= 2, we can use mathematical induction. Assume the relation holds for some arbitrary k >= 2. Then we can show that it also holds for k+1 by substituting k+1 into the expression and using the fact that an = (k+1)^2 - 3(k+1) + 2 = k^2 - k + 2 + 2k. After simplification, we arrive at the expression for ak+1 in terms of ak and ak-2, showing that the relation holds for k+1.

a) To find the first three elements of the sequence, we simply substitute n = 0, 1, 2 into the expression for an and simplify:

a0 = (0)^2 - 3(0) + 2 = 2

a1 = (1)^2 - 3(1) + 2 = 0

a2 = (2)^2 - 3(2) + 2 = 0

Therefore, the first three elements of the sequence are 2, 0, 0.

b) To show that the sequence satisfies the recurrence relation an = 2an-2 - an-2 + 2 for every n >= 2, we need to show that the expression for an can be written in terms of the previous two terms of the sequence, a(n-2) and a(n-1), using the given recurrence relation.

We can write:

an = n^2 - 3n + 2

  = (n-2)^2 - 3(n-2) + 2 + 2(n-2)

  = (n-2)^2 - 3(n-2) + 2n

Next, we can substitute n-2 for n in the expression for a(n-2) to get:

a(n-2) = (n-2)^2 - 3(n-2) + 2

Finally, we can substitute n-1 for n in the expression for a(n-1) to get:

a(n-1) = (n-1)^2 - 3(n-1) + 2

Now, we can use these expressions to write an in terms of a(n-2) and a(n-1) as follows:

an = (n-2)^2 - 3(n-2) + 2n

  = a(n-2) + 2(n-1) - (n-1)^2 + 3(n-1)

  = 2a(n-2) - a(n-1) + 2

Therefore, we have shown that the sequence satisfies the recurrence relation an = 2an-2 - an-2 + 2 for every n >= 2.

Learn more about recurrence relation:

https://brainly.com/question/31384990

#SPJ11

3/7 of the posters are hanged in the hallway.

A fraction represents a part of a whole.

Given that Dave spreads out a roll of paper and cuts it into 7 equal-sized posters.

He decorates the posters and takes them to school.

Dave hangs 4 posters on the side of the gym

4/7 of the posters are on the  side of the gym.

The remaining posters are in the hallway.

1-4/7

LCM is 7

7-4/7

3/7

Hence, 3/7 of the posters are hanged in the hallway.

To learn more on Fractions click:

https://brainly.com/question/10354322

#SPJ1

Answer:

"Games played in a workplace environment to achieve status, advancement and money"

Answer:

P= ( 18s + 12 ) + ( 2s + 2 ) or just P = 20s + 14

Step-by-step explanation:

9s + 6 is said twice just add both together and it is. 18s + 12.

Same with s + 1 so it would be 2s + 2.

You can add it all together and its 20s + 14.

P = Perimeter.

The average speed of the runner is 7.09 miles per hour.Average speed is calculated by dividing the distance traveled by the time taken. In this case, we can use the values provided by the runner's smartwatch to find the average speed. The average speed can be expressed in units such as miles per hour or meters per second.

The formula for average speed is given as;average speed = total distance traveled / total time taken. Let's use the values provided to find the average speed of the runner. We are told that the runner traveled 1.49 miles after 12.6 minutes. Therefore, the distance traveled (total distance) is 1.49 miles and the time taken (total time) is 12.6 minutes. We can first convert the time to hours by dividing by 60. Therefore, the time taken in hours is;12.6 minutes = 12.6 / 60 hours = 0.21 hoursSubstituting the values in the formula for average speed, we get;average speed = 1.49 miles / 0.21 hours = 7.09 miles per hourTherefore, the average speed of the runner is 7.09 miles per hour.

Average speed is a measure of how fast an object travels over a period of time. It is calculated by dividing the total distance traveled by the time taken to travel the distance. The formula for average speed is given as;average speed = total distance traveled / total time takenThe average speed can be expressed in different units depending on the context. For example, if the distance is in miles and the time is in hours, then the average speed will be in miles per hour (mph). If the distance is in meters and the time is in seconds, then the average speed will be in meters per second (m/s).Let's apply the formula for average speed to the scenario given in the question. A runner checks her smartwatch during a run and finds she has traveled 1.49 miles after 12.6 minutes. We can use these values to find the average speed. The distance traveled (total distance) is 1.49 miles and the time taken (total time) is 12.6 minutes. We can first convert the time to hours by dividing by 60. Therefore, the time taken in hours is;12.6 minutes = 12.6 / 60 hours = 0.21 hoursSubstituting the values in the formula for average speed, we get;average speed = 1.49 miles / 0.21 hours = 7.09 miles per hour.Therefore, the average speed of the runner is 7.09 miles per hour.

To know more about Average speed visit :-

https://brainly.com/question/13318003

#SPJ11

Answer:

Mean-19

Mode-28

Median-18

Step-by-step explanation:

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

We have,

To arrange the length of the sides of the quadrilateral from longest to shortest, we need to calculate the length of each side of the quadrilateral using the distance formula:

Distance Formula:

If (x1, y1) and (x2, y2) are two points in a plane, then the distance between them is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Using the distance formula, we can calculate the length of each side of the quadrilateral as follows:

AB = √((4 - (-5))² + (5 - 5)²) = 9

BC = √((2 - 4)² + (0 - 5)²) = √(29)

CD = √((-5 - 2)² + (-2 - 0)²) = √(74)

DA = √((-5 - (-5))² + (5 - (-2))²) = 7

Therefore,

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

Learn more about quadrilaterals here:

https://brainly.com/question/29934440

#SPJ1

Let's prove that if A < Rnxn is positive definite,

Then A is non-singular.

Then we'll also prove that tr(A) > 0.

Proving that A is non-singular Positive definite matrices are always non-singular.

It is because, by definition, a positive definite matrix has no negative eigenvalues.

And, we know that only non-singular matrices have non-zero eigenvalues.

Thus, A is non-singular. We can also show this as: Let's suppose that A is singular.

Therefore, there is a non-zero vector v in the null space of A such that Av = 0.

Then, vᵀAv = 0. However, this contradicts the fact that A is positive definite, which requires that for any non-zero vector v, vᵀAv > 0.

Therefore, A must be non-singular.

Proving that tr (A) > 0

We know that the eigenvalues of A are positive.

Thus, tr(A) = sum of eigenvalues of A > 0,

Since all eigenvalues are positive.

This is because if a matrix has positive eigenvalues,

Then the sum of the eigenvalues is always positive.

Therefore, tr (A) > 0 as required.

to know more about eigenvalues visit :

brainly.com/question/29861415

#SPJ11

Answer:

We know that:

2 cubed is 8

So, we can write 8 as 23.

Likewise, 27 can be written as 33

and 125 can be written as 53.  

So far, we have considered numbers that have a group of the same factors. Sometimes, a number has more than one group of the same factors as shown in the following example.

Example 20

Write 200 in simplest index form.

Solution:

In index form, 200 is 2 cubed times 5 squared

Key Term

simplest index formWe know that:

2 cubed is 8

So, we can write 8 as 23.

Likewise, 27 can be written as 33

and 125 can be written as 53.  

So far, we have considered numbers that have a group of the same factors. Sometimes, a number has more than one group of the same factors as shown in the following example.

Example 20

Write 200 in simplest index form.

Solution:

In index form, 200 is 2 cubed times 5 squared

Key Term

simplest index formWe know that:

2 cubed is 8

So, we can write 8 as 23.

Likewise, 27 can be written as 33

and 125 can be written as 53.  

So far, we have considered numbers that have a group of the same factors. Sometimes, a number has more than one group of the same factors as shown in the following example.

Example 20

Write 200 in simplest index form.

Solution:

In index form, 200 is 2 cubed times 5 squared

Key Term

simplest index formWe know that:

2 cubed is 8

So, we can write 8 as 23.

Likewise, 27 can be written as 33

and 125 can be written as 53.  

So far, we have considered numbers that have a group of the same factors. Sometimes, a number has more than one group of the same factors as shown in the following example.

Example 20

Write 200 in simplest index form.

Solution:

In index form, 200 is 2 cubed times 5 squared

Key Term

simplest index formWe know that:

2 cubed is 8

So, we can write 8 as 23.

Likewise, 27 can be written as 33

and 125 can be written as 53.  

So far, we have considered numbers that have a group of the same factors. Sometimes, a number has more than one group of the same factors as shown in the following example.

Example 20

Write 200 in simplest index form.

Solution:

In index form, 200 is 2 cubed times 5 squared

Key Term

simplest index formWe know that:

2 cubed is 8

So, we can write 8 as 23.

Likewise, 27 can be written as 33

and 125 can be written as 53.  

So far, we have considered numbers that have a group of the same factors. Sometimes, a number has more than one group of the same factors as shown in the following example.

Example 20

Write 200 in simplest index form.

Solution:

In index form, 200 is 2 cubed times 5 squared

Key Term

simplest index formWe know that:

2 cubed is 8

So, we can write 8 as 23.

Likewise, 27 can be written as 33

and 125 can be written as 53.  

So far, we have considered numbers that have a group of the same factors. Sometimes, a number has more than one group of the same factors as shown in the following example.

Example 20

Write 200 in simplest index form.

Solution:

In index form, 200 is 2 cubed times 5 squared

Key Term

simplest index form

Step-by-step explanation: