st: Two- and Three-Dimensional Geometry
A solid machine part is to be manufactured as shown in the figure. The part is made by cutting a small cone off the top of a larger cone. The
small cone has a base radius of 3 inches and a height of 5 inches. The larger cone has a base radius of 9 inches and had a height of 15 inches
prior to being cut. What is the volume of the resulting part illustrated in the figure?

Based on the calculations, the area of the shaded region is equal to 22 square foot.

By critically observing the geometric shapes, the area of the shaded region can be calculated by using this formula:

Area of shaded region = Area of square - Area of circle.

Note: The diameter of this circle is equal to the side length of the square because the circumference of this circle lies on the circumference of the square.

Radius = diameter/2 = 10/2 = 5 feet.

For the area of square, we have:

Area of square = S²

Area of square = 10²

Area of square = 100 square foot.

For the area of circle, we have:

Area of circle = πr²

Area of circle = 3.14 × 5²

Area of circle = 78.5 square foot.

Substituting the parameters into the formula, we have;

Area of shaded region = Area of square - Area of circle.

Area of shaded region = 100 - 78.5

Area of shaded region = 21.5 ≈ 22

Area of shaded region = 22 square foot.

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Find the area to the nearest square foot of the shaded region below, consisting of a square with a circle cut out of it. Use 3.14 as an approximation for π.

Answer:

55.2 is the mean

Explanation:

Given data set:  {113, 14, 23, 12, 114}

Mean = sum of the terms/number of terms

Mean = (113 + 14 + 23 + 12 + 114)/5

          = (276)/5

          = 55.2

Answer:

Mean = 55.2

Step-by-step explanation:

Given data set:   113, 14, 23, 12, 114

To find the mean of a data set, divide the sum of all data values by the total number of data values:

[tex]\large \begin{aligned}\sf Mean & = \sf\dfrac{sum\:of\:all\:data\:values}{total\:number\:of\:data\:values} \\\\\implies \sf Mean & = \sf \dfrac{113 + 14 + 23 + 12 + 114}{5}\\\\& = \sf \dfrac{276}{5}\\\\& = \sf 55.2\end{aligned}[/tex]

Answer:

x=1

Step-by-step explanation:

4x=4

(Linear equation)

Solved:-

Transpose 4 from LHS to RHS:

[tex] \rm = > x = \tt \cfrac{4}{4} [/tex]

[tex] \rm = > x = \tt1 [/tex]

The patient would be administered 4 tablets per dose.

In mathematics, solving word problems involves a careful understanding of the content of the problem. This will enable the use of appropriate variables and data representation.

From the given information:

From the standard conversion rate, we know that:

Here, to determine the number of dose to be administered, we have:

(x) /dose = 1000 mg/250 mg

x = 4 dose.

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Option d is the correct answer. All real numbers are greater than or equal to 2.

Domain of a function--The domain of the function is the set or collection of all the x-values for which the function is well defined.

Range of a function--The range of a function is the set of all the values which are attained by a function in its defined domain.

By looking at the graph we observe that the function is continuously increasing and the function takes all the real values greater than as well as equal to 2( since there is a closed circle at (1,2). Hence, the range is: [2,∞).

Thus Option d is the correct answer. All real numbers are greater than or equal to 2.

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Answer:

4 times

Step-by-step explanation:

If the smaller container only holds 2 liters, you would have to divide 8 by 2 which is 4.

Answer:

4 times

Step-by-step explanation:

Its 4 times cause 8/2=4

The value of the next term in the geometric sequence is 16

From the graph, we have the following highlights:

The means that:

Next term = Current term * 2

From the graph, we have:

Current term = 8

So, the equation becomes

Next term = 8 * 2

Evaluate

Next term = 16

Hence, the value of the next term in the geometric sequence is 16

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The mean and standard deviation for the number of boys in the 950 babies are 475 and 15.41, respectively

From the complete question, we have:

P(boy)= 0.5

Sample size = 950

The mean is then calculated as:

[tex]\bar x = np[/tex]

This gives

[tex]\bar x = 950 * 0.5[/tex]

Evaluate

[tex]\bar x = 475[/tex]

The standard deviation is calculated as:

[tex]\sigma = \sqrt{np(1 - p)[/tex]

This gives

[tex]\sigma = \sqrt{950 * 0.5(1 - 0.5)[/tex]

Evaluate

[tex]\sigma = 15.41[/tex]

Hence, the mean and standard deviation for the number of boys in the 950 babies are 475 and 15.41, respectively

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15

Percentages represent a proportion of a number. There are 2 ways to find a percent of a whole number.

Multiple of 10

Since 30% is a multiple of 10%, there is a shortcut we can use. We can find 10% and then multiply by 3 in order to find 30%. First, find 10% of 50. Like always, 10% of any number is that number divided by 10 (move the decimal 1 place to the left).

So, 10% of 50 is 5.0.

Then, to find 30%, multiply 5 by 3.

30% of 50 is 15.

Multiplication

The more consistent method includes multiplication, this can be used with any percentage. To use this method we need to convert 30% to a decimal. To convert any percentage to a decimal divide by 100 (move the decimal 2 places to the left).

Now, we can multiply this decimal by the whole number, 50. This will give us our desired answer.

So, this once again shows that 30% of 50 is 15.

Answer:

68.27%

Step-by-step explanation:

By the Empirical Rule, as 65% and 75% are both one standard deviation apart from the mean of 70%, then this represents 68.27% of the data.

Answer:

h'(z) = 2

Step-by-step explanation:

(b) First, let's expand everything so our equation is easier to look at.
h(z) = (3-4)(8-2z+3)
         (-1)(-2z+11)
         2z-11

Now, let's find the derivative:
h'(z) = 2

Answer:

4,186.67 in³

Step-by-step explanation:

V = (4/3)πr³

V = (4/3)(3.14)(10 in)³

V = (4/3)(3.14)(1,000 in³)

V = 4,186.666667 in³

Answer:

33,75 clients(huh?)

Step-by-step explanation:

75 / 100 = 0,75(1% of all clients)

0,75 * 45 = 33,75(number of business clients)

[tex]20^{\tfrac 52}\\\\=(20^5)^{\tfrac 12}\\\\=\left(20^4 \cdot 20 \right)^{\tfrac 12}\\\\=20^{\tfrac 42} \cdot 20^{\tfrac 12}\\\\=20^2 \sqrt{20}\\\\=400\sqrt{4 \times 5}\\\\=400 \times 2\sqrt 5\\\\=800\sqrt 5[/tex]

Answer:

[tex]800\sqrt{5}[/tex]

Step-by-step explanation:

Given: [tex]\large (20)^\text{$ \dfrac{5}{2} $}[/tex]

Properties of Exponents:

Rational Exponent Property: [tex]\large x^\text{$ \dfrac{m}{n} $} = \large \text{$ \sqrt[n]{x^m} $}[/tex]

Product of Powers Property:

1. Convert into a radical:

[tex]\sqrt[2]{20^5} \implies \sqrt{20^5}[/tex]

2. Simplify the expression:

[tex]\sqrt{20^2\times20^2\times20^1}\\\\\implies \sqrt{20^4\times20}\\\\\implies 20^2\sqrt{20}\\\\\implies 20^2\sqrt{4\times5}\\\\\implies 20^2\times2\sqrt{5}[/tex]

3. Evaluate the power:

[tex]20\times20\times2\sqrt{5}\\\\\implies 400\times2\sqrt{5}[/tex]

4. Multiply:

[tex](400\times2)\sqrt{5}\\\\\implies800\sqrt{5}[/tex]

Answer:

47.1408

Step-by-step explanation:

They gave us the percentage of a number and wants us to find the whole

to do that we will use the following equation:

46.116*100/4.5 = 47.1408 is the number we are looking for.

x²+3x

= x×x+3×x

= x(x+3)

The angle (off of a north-south line) at which a navy carrier needs to travel to sail straight to the submarine is 53.843°.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite the 90° angle.

The Navy carrier, Mercy, is sailing in the Pacific Ocean. The ship is in the sea, 4,365 miles south of a city. On radar, they notice a submarine is 7,390 miles away from them and north-west of their current position.

Therefore, the angle at which the Carrier needs to move to reach the submarine is,

Cosθ = 4365/7390

θ = Cos⁻¹ (0.59)

θ = 53.843°

Hence, the angle (off of a north-south line) at which a navy carrier needs to travel to sail straight to the submarine is 53.843°.

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Answer:

B

Step-by-step explanation:

We can either use sine or cosine, I choose cosine but sine works the same. cos(angle) = adj/hyp. adj = cos(angle) x hyp. adj = cos(30)8, cos(30) = √3/2. √3/2 x 8 = 4√3

Answer:

13

Step-by-step explanation:

a parallelogram has sides that are parallel to the opposite side. This means that y + 7 is going to be parallel to 20.

Two opposing sides of a parallelogram are parallel and equal

You know that the length of both of the sides is equivalent because the other set of opposing lines is also parallel (you can think of it as cutting off the line segment of y+7 and 20 at the same length. )

this means that we can set up the equation to find y as:

y + 7 = 20

then, you can proceed to find y by isolating it:

y + 7 = 20 ; so therefore

y + 7    =    20

   - 7           -7

y           =     13

y = 13

So, the value of y is 13

Answer:

y= -1/5x+5

STEP BY STEP EXPLAINATION:

m = slope = -1/5

c = y-intercept = 5

equation of a straight line:

y=mx+c

so.

y= -1/5x+5

Answer:

Perimeter=150cm

Step-by-step explanation:

25cm×6=150cm

Answer:

436.6

Step-by-step explanation:

3700×0.118=436.6

Answer:

[tex]\text{The quotient is}~ x^2 +2x +5 \\\\\text{The remainder is}~ -3[/tex]

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

1/3 of 90

= 1/3 * 90

= 90/3

= 30

Let the missing number be x.

2/3 of x

= 2/3 * x

= 2x/3

30 = 2x/3

Cross multiply,

2x = 30 * 3

2x = 90

x = 90/2

x = 45

Hence,

the missing number is 45.

Answer:

D

Step-by-step explanation:

The model rocket was 600 feet above the ground at 4.5 seconds and 12 seconds.

"It is a diagram that represents data in an organized manner."

"It is the height of the object above the surface of the ground."

For given question,

The graph shows the altitude, in feet, of a model rocket t seconds after launch.

From the graph we can observe that the model rocket was 600 feet above the ground at 4.5 seconds and 12 seconds.

Therefore, the model rocket was 600 feet above the ground at 4.5 seconds and 12 seconds.

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Answer:

Its A

Step-by-step explanation:

The function f(x) = 2x -14 is a polynomial function

The equation of the function is given as:

f(x) = 2x -14

A polynomial is represented as:

f(x) =ax^n + bx^(n - 1)....... + c

Where n is at least 1.

The function f(x) = 2x -14 is a polynomial with a degree of 1

Hence, the function f(x) = 2x -14 is a polynomial function

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