Geometry
Surface area and volume

Calculations:

Normal pop has mean of 20.0

standard deviation = 4.0

XNN(20.0, 4.0)

a).

[tex]z=\frac{x-h}{z}[/tex]

[tex]=\frac{25-20}{4.0} =\frac{5}{4} =1.25[/tex]

Z = 1.25

b).

The proportion between 20 and 25 is P(20 <x<25.0)

[tex]=p(\frac{20-20}{4} < z < \frac{25-0}{4} )[/tex]

[tex]=P(0 < z < 1.25)[/tex]

[tex]=P(Z < 1.25)-P(z < 0)[/tex]

[tex]=0.8944-0.5000[/tex]

P(20 < x < 25)=0.3944

c).

The proportion value is less than 18 when

[tex]P(x < 18)=p(\frac{x--4}{6} < \frac{18-20}{4}[/tex]

[tex]=P(z < \frac{-2}{4})[/tex]

[tex]=P(z < -0.5)[/tex]

P(x<18) = 0.3085

Step-by-step explanation:

arithmetic operations with functions just means to do these operations with the function expressions. and the result is the resulting function.

so,

(f - g)(x) = f(x) - g(x) = (2x² + 3) - (x² - 7) =

= 2x² + 3 - x² + 7 = x² + 10

Answer:

-2

Step-by-step explanation:

To find slope, we need to use the formula

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

Substituting your coordinates (-1,8) and (5,-4) , we get -2 as a result.

Hope this helped!!

Answer:

slope = - 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 8 ) and (x₂, y₂ ) = (5, - 4 )

m = [tex]\frac{-4-8}{5-(-1)}[/tex] = [tex]\frac{-12}{5+1}[/tex] = [tex]\frac{-12}{6}[/tex] = - 2

The most accurate statement about progress monitoring is progress monitoring is a useful way to ensure children are participating in targeted, purposeful, and meaningful math instruction and allows for the teacher to identify the skills children may need additional support in. Option A

Progress monitoring can be defined as a standard process of evaluating or checking progress toward a performance target on the basis of level of improvement from frequent assessment of a skill.

Thus, the most accurate statement about progress monitoring is progress monitoring is a useful way to ensure children are participating in targeted, purposeful, and meaningful math instruction and allows for the teacher to identify the skills children may need additional support in. Option A

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Answer: D. all negative and positive angle measures.

The missing values of x² column of the table are; 9 and 16 respectively and the value of ΣX² is; 47.

If follows from the table that the three columns of the table record values x, y and x².

On this note, if fill that the first missing value in which case, x = 3 and y = 2 is; 3² = 9. And in the second case where, x = 4 and y = 3 is; 4² = 16.

Hence, the value of ΣX² = 9 + 9 +9 + 4 +16 = 47.

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A percentage is a way to describe a part of a whole. The percetage decrease in the price of CD is 33.33%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

The price of the CD decreases from $18 to $12. Therefore, the percentage decrease is,

Percentage Decrease = ($18-$12)/$18 × 100% = 33.33%

Hence, the percetage decrease in the price of CD is 33.33%.

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Answer:

A = 1.16d

Step-by-step explanation:

Multiplying by 1 + the percentage value is equivalent to adding the percentage.

The correct option is the second one:

We know that:

We have the operation:

x - y + (-z)

Notice that because y is negative, then -y is positive.

Because z is positive, -z is negative.

Then we have:

positive + positive + negative

Or, in the number line:

right, right, left.

Second question:

Can we conclude the sign of the outcome?

No, we can't, the sign will depend on the values of x, y, and z.

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Answer:The correct option is the second one:i) right, right, left.ii) Undefined.

Step-by-step explanation:

Answer:

A 256/3

Step-by-step explanation:

1/3 * 4^4 =

1/3 * (4*4*4*4) =

1/3 * 256 = 256/3

Answer:

A = 256/3

Step-by-step explanation:

F(x) = 1/3 × 4ˣ = 4ˣ/3

F(4) = 4⁴/3 = 256/3

Answer:

(x-{-2})^2+(y-{4})^2={36}

Equation:

x^2+y^2=r^2

r=radius

Blank following x/y is flipped center(of circle) coordinate for x/y

By using the given distances and directions, we have;

Part A: 1083.5 feet

Part B: 1921.37 feet

Part C: 58.05°

The distance between David and Lacey = 2000 feet

David's angle to the boat = 70°

Lacey's angle to the boat = 32°

Part A

The distance of the boat from David is found as follows;

Imaginary lines drawn from the boat to David and then to Lacey form a triangle.

In the triangle, let A = 70°

B = 32°

Therefore by the sum of angles in a triangle, we have;

C = 180° - (70° + 32°) = 78°

By using sine rule we have;

[tex] \frac{a}{sin(A)} = \frac{b}{sin( B )} = \frac{c}{sin(C)}[/tex]

David's distance from the boat, b, is therefore;

[tex] \frac{b}{sin( 32 )} = \frac{2000}{sin(78)}[/tex]

The angle subtended by the coastline, C, is therefore;

[tex] b = \frac{2000}{sin(78)} \times sin( 32 ) = 1083.5 [/tex]

Part B

The distance between the boat and Lacey is found as follows;

[tex] \mathbf{ \frac{a}{sin( 70)} }= \frac{2000}{sin(78)}[/tex]

[tex] a = \frac{2000}{sin(78)} \times sin( 70 ) = 1921.37 [/tex]

Part C

When b = 1200 feet, we have;

Finding the vertical distance of the boat from the coastline, we have;

1083.5 × sin(70) = 1018.17

We have;

[tex] \frac{1200}{sin(90)} = \frac{1018.17}{sin( B' )} [/tex]

[tex] {sin( B' )} = \frac{sin(90)}{1200} \times 1018.17 [/tex]

The angle between the coastline and his view to the boat, B', is therefore;

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Answer:

90

Step-by-step explanation:

slope

Answer:

formula is equal to rice run is equal to y 2 -y 1 X2 minus X1

0.16 = 0.16161616... as a ratio of integers is 16 : 99

The equation is given as:

0.16 = 0.16161616...

The above is a non-terminating decimal.

It can be represented as:

a/b - 1

Where

a = 16

b = 100

So, we have:

16/100 - 1

Evaluate the difference

16/99

Express as ratio

16 : 99

Hence, 0.16 = 0.16161616... as a ratio of integers is 16 : 99

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The measure of an interior angle of a regular nonagon (9-sided polygon) is 140°

The formula for sum of interior angles of a polygon is given as;

= ( n -2) × 180

Recall that a nonagon has nine sides, so , n = 9

Substitute the value into the formula

= ( 9 -2) × 180

= 7× 180

= 1260°

Since the sum of the angles =  1260°

One of the angles = 1260/ 9 = 140°

Therefore, the measure of an interior angle of a regular nonagon (9-sided polygon) is 140°

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The yield to maturity best defined by the option c. The overall return the investor makes if they purchase a bond today and hold to maturity.

It is the total return of rate that will have been incomed by a bond when it makes all liability payments and repays the principal amount.

Since, as per the definition of yield to maturity, investor would get the original price of bond plus and the rate of interest that  finalized (at the time of bond purchase) when the maturity period will over.

Thus, the overall return the investor makes if they purchase a bond today and hold to maturity. Best describes yield to maturity.

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The correct information based on the equation is that the functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.

From the graph of f(x):

⇒ Axis of symmetry will be at x = 2

⇒ The maximum value of f(x) = 4

From the table of g(x):

⇒ Axis of symmetry will be at x = 2

⇒ The maximum value of g(x) = 3

The graph is attached.

The functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.

Here is the other part of the question:

Which statement is true?

The functions f and g have the same axis of symmetry, and the maximum value of f is less than the maximum value of g.

The functions f and g have the same axis of symmetry, and the maximum value of f is greater than the maximum value of g.

The functions f and g have different axes of symmetry and different maximum values.

The functions f and g have the same axis of symmetry and the same maximum values.

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Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

[tex](f-g)(x)=4x^2+5x-3-(4x^3-3x^2+5)\\\\=-4x^3+7x^2+5x-8[/tex]

Hence B is correct.

The volume of the cone is 4775.94 cu.cm

A cone is a three dimensional shape which has a circular base and then tapers down to a point called as Vertex.

It is given that the cone has

Height = 27 cm

Radius = 13 cm

The volume of the cone is given by

V = (1/3)πr²h

Volume = (1/3) * 3.14 * (13)² * 27

Volume = 4775.94 cu.cm

Therefore the volume of the cone is 4775.94 cu.cm

The complete question is

Find the volume of the cone of height = 27 cm and radius is 27 cm.

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The length of XY on the line segment WY is 6 units.

The full line segment is WY.

Point X is on the line segment WY.

Therefore,

WY = 16 units

WX = 10 units

XY = WY - WX

Hence,

XY = 16 - 10 = 6 units.

Therefore, the length of XY on the line segment WY is 6 units.

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Using the hypergeometric distribution, it is found that there is a 0.0002 = 0.02% probability that exactly 6 patients will die.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters for this problem are:

N = 25, k = 6, n = 8.

The probability that exactly 6 patients will die is P(X = 6), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 6) = h(6,25,8,6) = \frac{C_{6,6}C_{19,2}}{C_{25,8}} = 0.0002[/tex]

0.0002 = 0.02% probability that exactly 6 patients will die.

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The type of table that has the largest area is circular table

area of a square = l²

where

Therefore,

area of the square table = 39² = 1521 inches²

area of a rectangle = lw

where

Therefore,

area of the rectangular table = 23 × 71 = 1633 inches²

area of a circle = πr²

where

Therefore,

area of a circular table = π × (48 / 2)² = 576π = 1808.64 inches²

Therefore, the table that has the largest area is the circular table.

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An appropriate viewing rectangle is the set of minimum and maximum values of x and y on which all important attributes of the graph are clearly displayed.

We have been given a rational function:

[tex]f(x)=\frac{x^{2} -81}{x^{2} -11x+18}[/tex]

And we are required to determine an appropriate viewing rectangle for the graphing calculator.

Hence, An appropriate viewing rectangle is the set of minimum and maximum values of x and y on which all important attributes of the graph are clearly displayed.

For the given function, an appropriate viewing rectangle will be [-20,20,2]  by [-20,20,2].

This function, when graphed using a graphing calculator on the said viewing rectangle, it appears as attached.

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Answer:

C.

Step-by-step explanation:

The boundary of a circle is the circle itself.

The radius of a circle is a segment from the center of the circle to any point of the circle.

In a circle, every radius has the same length.

Answer: C.

This is a very simple transformation problem and can be solved by observation. The correct answer is Option D where g(x) = f(x-3) + 6. See the attached graph for the full question.

In mathematics, transformation is the process of converting one figure, expression, or function into another of equivalent value.

Note that on an x-axis, moving past zero to the left gets you into the negative, and vice versa.

On the y-axis moving upwards past zero gets you into the positive.

Recall that g(x) is a transformation of f(x). This means that the original image is f(x).

Notice that F(x) is transformed three degree beyond 0 on the -axis and 6 degrees beyond zero on the y-axis. Hence the correct equation is:

g(x) = f(x-3) + 6.

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Answer:16.67

Step-by-step explanation:

880 of 5280 can be written as:

880

5280

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

880

5280

×

100

100

= (

880 × 100

5280

) ×

1

100

=

16.67

100

Therefore, the answer is 16.67%

If you are using a calculator, simply enter 880÷5280×100 which will give you 16.67 as the answer.

Answer:

option D. DE = 11

Step-by-step explanation:

The line DF is equivalent in length to the blue line,

(x + 7) + 7 = 4x + 2

Solve:

x + 14 = 4x + 2

subtract 14 from both sided to get x alone,

x + 14 - 14 = 4x + 2 - 14

x = 4x - 12

subtract 4x from both sided,

x - 4x = 4x - 4x - 12

-3x = -12

divided both sides by -3,

-3x / 3 = -12 / -3

x = 4

Plug in x into DE equation:

x + 7: (4) + 7 = 11

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Given that the AC and BC are perpendicular, their slopes are the negative inverse of each other which gives that the product of the slopes of AC and BC is -1

The completed proof is presented as follows;

The slope of AC or GC is GF/FC by definition of slope. The slope of BC or CE is DE/CD by definition of slope.

<FCD = <FCG + <GCE + <ECD by angle addition property <FCD = 180° by the definition of a straight angle, and <GCE = 90° by definition of perpendicular lines. So by substitution property of equality 180° = <FCG + 90° + <ECD. Therefore 90° - <FCG = <ECD, by the subtraction property of equality . We also know that 180° = <FCG + 90° + <CGF by the triangle sum theorem and by the subtraction property of equality 90° - <FCG = <CGF, therefore <ECD = <CGF by the substitution property of equality. Then <ECD ≈ <CGF by the definition of congruent angles. <GFC ≈ <CDE because all right angles are congruent. So by AA ∆GFC ~ ∆CDE. Since the ratio of corresponding sides of similar triangles are equal then GF/CD = FC/DE or GF•DE = CD•FC by cross product. Finally, by the division property of equality GF/FC = CD/DE. We can multiply both sides using the slope of using the multiplication property of equality to get GF/FC × -DE/CD = CD/DE × -DE/CD. Simplify so that GF/FC × -DE/CD = -1. This shows that the product of the slopes of AC and BC is -1.

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