A cylindral drill with radius 5 cm is used to bore a hole through the center of a sphere with radius 9 cm. Find the volume of the ring-shaped solid that remains.

The solution to the system of equation is ( -4.5 , -2)

A system of equation is a set of equations that have a common solution.

The set of equation given are

-2x +4y  = 1

-4x +3y = 12

To find the solution , Elimination Method will be used

Multiplying equation 1 by 2 and then

Subtracting equation 1 by 2

-4x +8y = 2

-4x +3y = 12

+        -       -

5y = -10

y = -2

Substituting this value to determine the value of x

-2x -8 = 1

-2x = 9

x = -4.5

Therefore the solution to the system of equation is ( -4.5 , -2)

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If Jay spends 40 at the store, the number of points he will earn is; 10 points

Let the number of rewards points a customer earns be y

Let the amount of money, in dollars, that the customer spends at the store be x.

Since the number of rewards points a customer earns varies directly with the amount of money, in dollars, that the customer spends at the store, then we can say that;

y ∝ x

Thus;

y = kx

where k is the constant of proportionality.

We are given x = 15 when y = $60. Thus;

60 = 15k

k = 60/15

k = 4

If Jay spends $40, it means the number of points will be;

40 = 4x

40/4 = x

x = 10 points.

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On the first two pairs you need to write 3 and 4, and 6 and 2.

On the second page we have:

1) 4

2) 2 and 7

3) 1

4) 1 and 3

5) 3.

a) Here we just need to use scientific notation.

For the first case, the numbers that go in the exponent boxes are the same ones that go in the example, which are 4 in the first one and 2 on the second one.

Then, if we want the difference to be 29,400, then we can use 3 on the first box and 6 on the second. OR, because this is an absolute value, we can just invert those.

This is:

6 and 2 on the first two squares, and 3 and 4 on the second two squares.

b) Here we want to make perfect squares.

For example, on the first case we have:

x*2*2

We need to find the value of x such that this is a perfect square. Notice that we can rewrite this as:

x*2*2 = x*4

Then it only is a perfect square if x = 4.

For the second case:

14*x*y

This is only a perfect square if x*y = 14

Then we can use x = 2 and y = 7.

With similar reasoning, on the next box we have:

2*8*x

2*8 = 16, is already a perfect square, so x = 1.

The next one is:

x*3*y

Here we can define x = 3 and y = 1, so we get a perfect square.

Finally:

3*x

Here the only possible value of x is 3.

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Answer:

36

Step-by-step explanation:

MC : BC : MB = 1 : √3 : 2

MC : BC = 1 : √3

12 : BC = 1 : √3

BC = 12 : 1/√3

BC = 12 × √3/1

BC = 12 × √3

BC = 12√3

MC : MB = 1 : 2

12 : MB = 1/2

MB = 12 : 1/2

MB = 12 × 2/1

MB = 12 × 2

MB = 24

AB = 2BD

AB = 2CD√3

AB = 2(½BC)√3

AB = 2(½ × 12√3) √3

AB = 2 × 6√3 × √3

AB = 12 × √9

AB = 12 × 3

AB = 36

The equation in point slope form is y-1 = 1/4(x - 12)

The formula for calculating the equation of a line is expressed as;

y = mx + b

m is the slope

b is the intercept

Slope = 1+3/12+4

Slope = 4/16

Slope = 1/4

For the intercept

1 = 1/4(12) + b

b = 1 - 3

b = -2

Hence the equation in point slope form is y-1 = 1/4(x - 12)

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The standard form is:

4y - x = -8

We know that the point-slope equation of the line is:

y - 1 = (1/4)*(x - 12)

Expanding the right side, we get:

y - 1 = (1/4)*x - 3

Now we can move the term with x to the left side:

y - (1/4)*x = +1 - 3

y - (1/4)*x = -2

Now we can multiply both sides by 4:

4y - x = -8

This is the standard form of the linear equation.

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Yes, a point of inflection exists where f''(x) = DNE.

We know that the point of inflection, also known as the inflection point, is where the function's concavity changes. Changing the function from concave down to concave up, or vice versa, means that. In other words, an inflection point is a location at which the rate of slope change from an increasing to a decreasing manner, or vice versa, occurs. There is no doubt that those points are neither local maxima nor minima. They are called stationary points.

Let's take an example [tex]f(x) = x^{\frac{1}{3} }[/tex]

Here, [tex]f'(x)=\frac{1}{3x^{\frac{2}{3} } }[/tex]

and [tex]f''(x)=-\frac{2}{9x^{\frac{5}{3} } }[/tex]

Clearly f''(x) = DNE at x = 0. We are going to check if x = 0 is a point of inflection or not.

At x = -1, (left side of 0), [tex]f''(-1)=-\frac{2}{9(-1)^{\frac{5}{3} } }=\frac{2}{9} > 0[/tex] (concave up)

At x = 1, (right side of 0), [tex]f''(1)=-\frac{2}{9(1)^{\frac{5}{3} } }=-\frac{2}{9} < 0[/tex] (concave down)

Then by the definition, we can conclude that x = 0 is a point of inflection.

Therefore, a point of inflection exists where f''(x) = DNE.

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The additional information needed to prove both triangles are similar are:

A. ∠B ≅ ∠M

C. △ABC was rotated and dilated by a scale factor between 0 and 1

E. ∠C ≅ ∠L

When a triangle is rotated and dilated by a scale factor, the new triangle formed has the same shape but different size of the original triangle. However, all its corresponding angles remains congruent.

Thus, for triangles ABC and NML to be similar to each other, since we already known each have one congruent right angles, the additional information needed are:

A. ∠B ≅ ∠M

C. △ABC was rotated and dilated by a scale factor between 0 and 1

E. ∠C ≅ ∠L

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The number of problems that were on the text was 240 problems.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the total number of problems that were on the text, y represent the time to be spent, hence:

y = x/8

Also:

y - 6 = x/10

x/8 - 6 = x/10

x = 240

The number of problems that were on the text was 240 problems.

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The area of the enlarged picture on the wall is gotten as; D: 486 in²

The formula for Linear scale factor is;

L.S = Image distance/object distance

Thus, from the attached image, we can find the Linear scale factor as;

L.S = OL'/OL

L.S = 54/ 12

L.S = 9/2

Area scale factor is equal to the square of linear scale factor. Thus;

Area scale factor = (9/2)²

Area scale factor = 81/4

Now,

81/4 = Area of larger rectangle/Area of smaller rectangle

Area of the smaller rectangle = 4 ×6 = 24 in²

Thus;

Area of enlarged picture on wall = (81/4) × 24

Area of enlarged picture on wall = 486 in²

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Answer:

Step-by-step explanation:

its D

Answer:

=================

We know that:

So the sum of the 8 exterior angles is:

Sum of both interior and exterior angles of 8 angles:

Sum of those 8 interior angles is:

Step-by-step explanation:

there are 2 main approaches (in their core they are the same, of course, but they look different) :

1. use one equation to express one variable by the second, and then use this in the second equation to solve for the remaining variable. with that you go back into the first equation and solve for the first variable.

2. multiply both equations by certain factors as needed, then add both results, so that there is one summary equation with only one variable, and then solve for it. then use that in one of the original equations and solve for the second variable.

using 1.

3x + 2y = 1

3x = 1 - 2y

x = (1 - 2y)/3

2x + 7y = 3

2(1 - 2y)/3 + 7y = 3

2(1 - 2y) + 21y = 9

2 - 4y + 21y = 9

17y = 7

y = 7/17

x = (1 - 2y)/3 = (1 - 2×7/17)/3 = (1 - 14/17)/3 =

= (17/17 - 14/17)/3 = 3/17 / 3 = 1/17

using 2.

multiply first equation by 2, the second by -3

6x + 4y = 2

-6x - 21y = -9

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

0 -17y = -7

-17y = -7

17y = 7

y = 7/17

and so on (as under 1.).

Step-by-step explanation:

First, you can multiply the both equation by one of the coefficient of either X or Y as shown above.

Secondly, after doing that you can multiply one of the equations by the negative sign in order for one of the coefficient to cancel out.

From there you can find X

After getting X , you can put the answer you get into any equation of your choice. collect like terms and then you'll find Y.

Hope this helps. If you don't understand use the picture if the solving above for better explanation. Thanks

Hello!

Rate of income tax = Tax paid / Monthly income

⇒ Rate = 8,000 / 40,000

⇒ Rate = 0.2

⇒ Rate = 20%

∴ The rate of income tax is 20%.

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What's the equation with a slope of -4 that goes through (-1,1)? find it

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

The equation used, here is [tex]\bf{y-y1=m(x-x1)}[/tex].

[tex]\bf{y-1=-4(x-(-1)}[/tex] | simplify after putting in the information given

[tex]\bf{y-1=-4(x+1)}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

                          [tex]\bf{=y-1=-4(x+1)}[/tex]

[tex]\boxed{\bf{aesthetic\not101}}[/tex]

Answer:

In the question, it is given that the fixed cost is $25000 and the expense to produce each doughnut is $0.25.

It is required to represent the cost C of the company as a function of x, the number of doughnuts produced.

To do so, multiply the expense of each doughnut by the number of doughnuts then add the fixed expenses of the doughnut selling company to find the total cost of the company.

Step-by-step explanation:

The expense of each doughnut is $0.25.

The expenses for x doughnuts are $0.25x.

The fixed cost is $25000.

The total cost of the company is the sum of fixed cost and the expenses for the doughnut, C = 0.25x + 25000.

The total cost of the company is, C = 0.25x + 25000.

Answer:

32

Step-by-step explanation:

To find the mean of the data set, you find the sum of the data set, and divide it by how much data you have in the data set. In this case you have 18 people (amount of data in the data set) and the sum is 35+2+7+33+25+70+75+40+42+12+15+7+44+20+25+3+65+62 = 582. So divide these two values: [tex]\frac{582}{18} = 32.\overline{33} \approx 32[/tex]

Answer:

32.33

Step-by-step explanation:

Answer:

= ax + b ln x - c/x + C

Step-by-step explanation:

Recall:

integral a dx = ax + C

integral 1/x dx = ln x + C

integral x^(n) = [x^(n +1)]/(n + 1) + C

Also:

c = variable in this problem

C = constant you add when you integrate

Separate each term of the numerator and set it over the denominator.

integral (ax^2 + bx + c)/x^2 dx =

integral [(ax^2)/x^2 + (bx)/x^2 + c/x^2] dx

Simplify each term and separate into the sum of 3 integrals.

= integral (a dx) + integral (b/x dx) + integral (c/x^-2) dx

= ax + b ln x + (cx^-1)/(-1) + C

= ax + b ln x - c/x + C

Answer:

  2.36 liters

Step-by-step explanation:

The volume Janet wants is 1/3 of 1/2 of the volume of a sphere with radius 15 cm. The formula for the volume of a sphere is given.

The water volume is ...

  V = (1/3)(1/2)(4/3π)(15 cm)³ = 750π cm³ ≈ 2356 cm³

There are 1000 cm³ in 1 liter, so Janet needs about ...

  2356 cm³/(1000 cm³/L) = 2.356 L

Janet should put about 2.36 liters of water in the fish tank.

Answer:

it is all I could.

Hope it helps

The other equality which must be stated by Jose is that angles BAC and BAE are congruent and their measures are equal.

It follows from the task content that Jose is trying to prove the congruence of both triangles by means of the Side-Angle-Side congruence theorem.

It therefore follows that since, Jose has identified that the ratio of corresponding sides are equal as indicated in the task content, the equality which Jose has to state is the angle congruence equality.

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By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.

The Central Limit Theorem established that, for a normally distributed random variable X, with mean and standard deviation, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean  and standard deviation ;

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

The sample of 112 residents has a mean GPA of 1.7.

By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.

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Answer:

9x ^ 6 -9x ^ 2-2x + 1

Step-by-step explanation:

The second transformation is a rotation about point H.

It should be noted that a congruent triangle simply means when two triangles have the same sides and the same angles.

As two rigid transformations, to map ΔHJK to ΔLMN.

The first is a translation of vertex H to vertex L, and the second transformation is a rotation about point H.

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Answer:

B. a rotation about point H

Step-by-step explanation:

got it correct on my quiz

The sides of the right-angle triangle will be 16 units and 20.30 units. And the missing angle will be 52°.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The side AC will be

tan 38° = 12.5 / AC

      AC = 15.999

      AC ≈ 16 units

Then the side AB will be

AB² = 12.5² + 16²

 AB = 20.30 units

We know that the angle sum is 180 degrees. Then we have

∠A + ∠B + ∠C = 180°

38° + ∠B + 90° = 180°

                  ∠B = 52°

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The slope of line AB, BC, CD and AD are 1, -1/6, 2, -4/6 respectively. Quadrilateral ABCD with the given vertices is not a parallelogram because neither pair of opposite sides is parallel. Option C

Formula for slope is given as;

Slope = [tex]\frac{y2 -y1}{x2 -x1}[/tex]

A(-4 -1)

B(-1 2)

C(5 1)

D(1 -3)

a. Slope of line AB = [tex]\frac{2- (-1)}{-1 (-4)}[/tex] = [tex]\frac{2+ 1}{-1 + 4}[/tex] = [tex]\frac{3}{3}[/tex] = 1

b. Slope of line BC = [tex]\frac{1-2}{5-(-1)}[/tex] = [tex]\frac{-1}{6}[/tex]

c. Slope of line CD = [tex]\frac{-3 - 5}{1-5}[/tex] = [tex]\frac{-8}{-4}[/tex] = 2

d. Slope of line AD = [tex]\frac{-3 (-1)}{1 -(-4)}[/tex] = [tex]\frac{-4}{5}[/tex]

Quadrilateral ABCD with the given vertices is not a parallelogram because neither pair of opposite sides is parallel. Option C

Thus, the slope of line AB, BC, CD and AD are 1, -1/6, 2, -4/6 respectively.

and quadrilateral ABCD with the given vertices is not a parallelogram because neither pair of opposite sides is parallel. Option C

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Answer:

12stickers

Step-by-step explanation:

that's all I could do.have a nice day.hope it helps.

Triangle JHK and GHL are congruent based on the angle-angle-angle congruency theorem.

Two triangles are said to be congruent if they have the same shape and angles. The ratio of their corresponding sides are also to be proportional.

Given triangle JHK and GHL are congruent based on the angle-angle-angle congruency theorem.

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1. if we add something in x then it will also add up in value of y

2.  x by 5 times then y value increases by 3*5 = 15 times

3.  if x is added with 5 then y value increases by 8.

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

As, per the first part

y=x

So, if we add something in x then it will also add up in value of x.

In second part,

y=3x

If x by 5 times then y value increases by 3*5 = 15 times

In third part, if x is added with 5 then y value increases by 8.

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Answer:

-b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

g(x)=(4-4)²

g(x) =0

and f(x)=x²

f(x)=0²

The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome is known as risk analysis

Risk analysis is define as the the process of identifying and analyzing potential issues that could negatively impact key business initiatives or projects. This process is done in order to help organizations avoid or mitigate those risks.

So, The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome is known as risk analysis

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Answer:

The distrubutive property

-9(n-4)

=-9n+36