T/F : System developers can initiate a formal project as early as the preliminary investigation stage, or later on, as analysis, design, and implementation activities occur.

Part A

we have the equation

(x-13)^2+(y-4)^2=16

Rewrite as

(x-13)^2+(y-4)^2=4^2

so

The center of the circle is the point (13,4)

The radius of the circle is 4 units

using a graphing tool

Part B

Remember that

If an ordered pair lies on the circle, then the ordered pair must satisfy the equation of the circle

so

Verify each ordered pair

Hunter (11,4)

For x=11 and y=4

substitute in the equation of the circle

Is not true

so

Hunter is not in the spotlight

Joe (8,5)

x=8 and y=5

Is not true

so

Joe is not in the spotlight

Mason (15,5)

x=15 and y=5

Is not true

Mason is not in the spotlight

Answer: It is .............. A or C but I can't see the question you're trying to answer

Step-by-step explanation:

First the 9

Then the 5:

The answer is x = 65 (option C)

A one-tailed test's p-value is half that of a two-tailed test.

Whether it is positive or negative, when you find your test statistic, you also find a tail probability to the right or left of that test statistic. What is the likelihood that, if the null hypothesis is correct, you will obtain a value that is more extreme (far out in the tail) than the observed test statistic? If the test is two-tailed, the phrase "probability...more extreme" applies to both tails, beyond the positive and negative values of your test statistic. Your calculations will fall either on the right or left, but if the test is two-tailed, it will also apply to both tails.

Two possibilities sharing similarities is the null hypothesis. That the observed discrepancy is solely the result of chance is the null hypothesis. Calculating the probability that the null hypothesis is correct using statistical testing is achievable.

To know more about Null Hypothesis visit:

https://brainly.com/question/22657316

#SPJ4

Applying the vertical angle theorem, the measure of the missing angles are:

e = 31

f = 72

d = 77

The vertical angles theorem states that two angles that are vertically opposite to each other have equal measures.

Angle e and 31 degrees are vertical angles. Therefore, based on the vertical angles theorem,

e = 31 degrees.

Also, d = 77 degrees [vertical angles theorem].

e + 77 + f = 180 degrees [straight line angles have a sum of 180 degrees].

Substitute the value of e into the equation

31 + 77 + f = 180

108 + f = 180

Subtract 108 from both sides

108 + f - 108 = 180 - 108

f = 72 degrees.

Learn more about the vertical angle theorem on:

https://brainly.com/question/24839702

#SPJ1

The BN structure model with more than 10 nodes can be established. The structure refers to the way the variables are related.

A Bayesian Network (BN) is a probabilistic graphical model that illustrates a set of variables and their probabilistic dependencies. A BN structure is made up of nodes and edges. Nodes represent variables, and edges represent the connections between the variables. The BN structure model can be established by using various algorithms, including structure learning and parameter learning.The BN structure with more than 10 nodes is a complex model with numerous variables and their dependencies. The structure's meaning is how the variables are interrelated, allowing us to estimate the probabilities of certain events or scenarios. The nodes in the structure represent various factors that affect the outcome of an event, and the edges between them demonstrate how these factors are related.The BN structure model is used in many fields, including medical diagnosis, fault diagnosis, and decision making.

The Bayesian Network structure model with more than 10 nodes is a powerful tool for analyzing complex systems. It helps to understand the interrelationships between variables and estimate the probabilities of different events or scenarios. This model is useful in various fields and provides insights into many complex phenomena.

To know more about Nodes visit:

brainly.com/question/32227668

#SPJ11

Therefore, m = 7.5454... (rounded to four decimal places) and n = 0.5455...

What is Simultaneous Equations?

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

1) 3p + 4q = 23

10p + 12q = 74

Subtracting 3 times the first equation from the second equation, we get:

10p + 12q - 3(3p + 4q) = 74 - 3(23)

10p + 12q - 9p - 12q = 5

p = 5

Substituting p = 5 in the first equation, we get:

3(5) + 4q = 23

4q = 8

q = 2

Therefore, p = 5 and q = 2.

2) 4s + 2t = 20

11s + 4t = 49

Multiplying the first equation by 2 and subtracting it from the second equation, we get:

11s + 4t - 2(4s + 2t) = 49 - 2(20)

11s + 4t - 8s - 4t = 9

3s = 9

s = 3

Substituting s = 3 in the first equation, we get:

4(3) + 2t = 20

2t = 8

t = 4

Therefore, s = 3 and t = 4.

3) 3a + 4b = 34

12a + 5b = 59

Multiplying the first equation by 3 and subtracting it from the second equation, we get:

12a + 5b - 3(3a + 4b) = 59 - 3(34)

12a + 5b - 9a - 12b = 17

3a - 7b = 17

Multiplying the first equation by 5 and subtracting it from the second equation, we get:

12a + 5b - 5(3a + 4b) = 59 - 5(34)

12a + 5b - 15a - 20b = -61

-3a - 15b = -61

a + 5b = 20

Adding the equations 3a - 7b = 17 and a + 5b = 20, we get:

4a = 37

a = 9.25

Substituting a = 9.25 in the equation a + 5b = 20, we get:

9.25 + 5b = 20

5b = 10.75

b = 2.15

Therefore, a = 9.25 and b = 2.15 (rounded to two decimal places).

4) 6m + 5n = 48

18m + 4n = 78

Multiplying the first equation by 3 and subtracting it from the second equation, we get:

18m + 4n - 3(6m + 5n) = 78 - 3(48)

18m + 4n - 18m - 15n = -6

-11n = -6

n = 0.5455...

Substituting n = 0.5455... in the first equation, we get:

6m + 5(0.5455...) = 48

6m = 45.2727...

m = 7.5454...

Therefore, m = 7.5454(rounded to four decimal places) and n = 0.5455.

To know more about Simultaneous Equations visit,

https://brainly.com/question/148035

#SPJ1

True, recording the time it takes for each student to complete a one-mile run is an example of measuring a continuous variable.

A continuous variable is a variable that can take on any value within a given range, without any gaps or interruptions. In the case of measuring the time it takes for students to complete a one-mile run, the time can vary from student to student and can take on any value within a continuous range, such as 4.52 minutes, 6.25 minutes, or 8.87 minutes, without any gaps or interruptions.

The time it takes for each student to complete the run can be measured with precision using a stopwatch or a timer, and it can be recorded as a decimal or a fraction, indicating the exact amount of time taken.

Therefore, recording the time it takes for each student to complete a one-mile run is an example of measuring a continuous variable

To learn more about continuous variable here:

brainly.com/question/13339063#

#SPJ11

The unit rate refers to the slope of the line which passes through the given points. So, we need to find the slope with the following formula

We are going to use points (4,5) and (8,10).

Therefore, the unit rate is 5/4.

An interpretation of this unit rate is: while the vertical coordinate varies 5 units, the horizontal coordinate varies 4 units.

The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b. This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

To find the equation for the tangent plane to the graph of the function f(x, y) = 2e^x - y at a given point (x0, y0), we need to calculate the partial derivatives of f with respect to x and y at that point.

The partial derivative of f with respect to x, denoted as ∂f/∂x or fₓ, represents the rate of change of f with respect to x while keeping y constant. Similarly, the partial derivative of f with respect to y, denoted as ∂f/∂y or fᵧ, represents the rate of change of f with respect to y while keeping x constant.

Let's calculate these partial derivatives:

fₓ = d/dx(2e^x - y) = 2e^x

fᵧ = d/dy(2e^x - y) = -1

Now, we have the partial derivatives evaluated at the point (x0, y0). Let's assume our point of interest is (a, b), where a = x0 and b = y0.

At the point (a, b), the equation for the tangent plane is given by:

z - f(a, b) = fₓ(a, b)(x - a) + fᵧ(a, b)(y - b)

Substituting fₓ(a, b) = 2e^a and fᵧ(a, b) = -1, we have:

z - f(a, b) = 2e^a(x - a) - (y - b)

Now, let's substitute f(a, b) = 2e^a - b:

z - (2e^a - b) = 2e^a(x - a) - (y - b)

Rearranging and simplifying:

z = 2e^a(x - a) - (y - b) + 2e^a - b

The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b.

This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

Learn more about tangent here:

https://brainly.com/question/10053881

#SPJ11

Answer:

224

Step-by-step explanation:

1/2x+4=1/8x+88

1/2x-1/8x+4=88

1/2x-1/8x=88-4

4/8x-1/8x=84

3/8x=84

x=84/(3/8)

x=(84/1)(8/3)

x=672/3

x=224

Please mark me as Brainliest if you're satisfied with the answer.

Therefore, the mass of the region bounded by y=5-x and with the density function p(x,y)=5xy is 125/4.

To find the mass of the region bounded by y=5-x, we need to integrate the density function p(x,y) over the region. We can express the region as the integral:

M = ∫∫R p(x,y) dA

where R is the region bounded by y=5-x.

To integrate over R, we can use the limits of integration for x and y:

0 ≤ x ≤ 5

0 ≤ y ≤ 5-x

Substituting the limits of integration and the density function, we get:

M = ∫0^5 ∫0^(5-x) 5xy dy dx

Evaluating the inner integral first, we get:

M = ∫0^5 [5x/2 * (5-x)^2] dx

Simplifying, we get:

M = 125/4

To know more about function,

https://brainly.com/question/14340978

#SPJ11

A cylindrical tank standing upright has radius 20cm. If the water is being drained at rate  25 cm³/s the tank level drops at rate 0.02 cm/s.

Recall the formula for the volume of a cylinder:

V = πr². h

Where:

r = radius of the base

h = height of the cylinder

Take the derivative with respect to t

dV/dt = πr². dh/dt

Substitute dV/dt = 25 cm³/s and r = 20 cm:

25 = π x 20² x dh/dt

dh/dt = 25 / (400π) = 0.02 cm/s

Therefore, the level of the cylindrical tank drops at rate 0.02 cm/s

Complete question:

A cylindrical tank standing upright has radius 20cm. How fast does the water level in the tank drop when the water is being drained at 25 cm³/s?

Learn more about volume here:

https://brainly.com/question/18011570

#SPJ4

Answer:

3=-2x-14+5x+12-8x

3+14-12=-2x+5x-8x

5=-5x

x=(-1)

Missing part of the question

Hayley bakes zucchini bread and banana bread. Some ingredients Hayley uses for each type of  bread are shown in the tables

Zucchini Bread

2 eggs        2 cups of flour       1.5 cups of sugar        0.5 stick of butter

Banana Bread

1 egg          3 cups of flour        2 cups of sugar          0.25 stick of butter

Answer:

\(2z + b \le 9\)

\(2z + 3b \le 15\)

Step-by-step explanation:

Given

\(Flour = 15\)

\(Egg =9\)

Since there are enough of other ingredients, we will only consider the amount of eggs and cups of flour.

So, we have:

Zucchini Bread

\(Egg = 2\)

\(Flour = 2\)  

Banana Bread

\(Egg = 1\)

\(Flour = 3\)

For the eggs

The ratio of eggs to use in the Zucchini bread to Banana bread is:

\(Egg = 2\) (z) : \(Egg = 1\) (b)

This gives:

\(2z + 1b\)

The total number of eggs cannot exceed 9.

So, the inequality is:

\(2z + 1b \le 9\)

\(2z + b \le 9\)

For the flours

The ratio of flours to use in the Zucchini bread to Banana bread is:

\(Flour = 2\) (z) :    \(Flour = 3\) (b)

This gives:

\(2z + 3b\)

The total cups of flours cannot exceed 15.

So, the inequality is:

\(2z + 3b \le 15\)

Hence:

The system of inequalities is:

\(2z + b \le 9\)

\(2z + 3b \le 15\)

Answer:

u = 10 ft

Step-by-step explanation:

cuboid volume = w × h × l

width * hight * length

560 = 7 × 8 × u

u = 10 ft

Answer:

u = 10 ft

Step-by-step explanation:

Volume of a rectangular prism = lwh

where:

Given:

Substitute the given values into the formula and solve for h:

⇒ 560 = 8 × 7 × u

⇒ 560 = 56u

⇒ 56u ÷ 56 = 560 ÷ 56

⇒ u = 10 ft

Therefore, the height of the prism is 10 ft.

The frequency of a given allele, g, in the population is defined as the ratio of the number of copies of that allele to the total number of copies of all alleles.

The proportion of homozygous dominant (GG), heterozygous (Gg), and homozygous recessive (gg) individuals in a population can be calculated using the following equations:
GG = p2
Gg = 2pq
gg = q2
Where p is the frequency of the G allele, q is the frequency of the g allele, and p + q = 1.Since g is recessive, the frequency of white (gg) moths in the population is q2. The frequency of the g allele can be calculated using the following formula:
p = 1 - q

Given that the population was in Hardy-Weinberg equilibrium for the g locus, we can assume that the allele frequencies remained constant over time.

As a result, we can use the frequency of the g allele in 1980 to estimate its frequency in 1962. Using the frequency of the g allele in 1980 as p, we can use the Hardy-Weinberg equations to determine the frequency of the g allele in 1962:
p = 0.54q = 0.46
Using these frequencies, we can calculate the proportion of white moths in the population in 1962:
q2 = 0.46 x 0.46 = 0.2116 = 21.16%
Therefore, the percentage of moths in the natural population that was white in 1962 was approximately 21.16%.Option E is correct (64%).

To know more about frequency refer here:

https://brainly.com/question/5102661

#SPJ11

Answer:

x- 2

Step-by-step explanation:

The solutions to the equation 3x^2 - 9x - 12 = 0 are x = 4 and x = -1.

To solve the quadratic equation 3x^2 - 9x - 12 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a),

where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 3, b = -9, and c = -12. Substituting these values into the quadratic formula, we have:

x = (-(-9) ± √((-9)^2 - 4 * 3 * (-12))) / (2 * 3)

= (9 ± √(81 + 144)) / 6

= (9 ± √(225)) / 6

= (9 ± 15) / 6.

We have two possible solutions:

For the positive root:

x = (9 + 15) / 6

= 24 / 6

= 4.

For the negative root:

x = (9 - 15) / 6

= -6 / 6

= -1.

The solutions to the equation 3x^2 - 9x - 12 = 0 are x = 4 and x = -1.

for such more question on equation

https://brainly.com/question/17145398

#SPJ8

the function is f(x) = 3 (x⁴+243)/4

a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

f'(x) = 3x³

So that, f(x) = ∫3x³dx + C

⇒ f(x) = 3x⁴/4 + C

⇒ 81x + y  is tangent to the graph of f

⇒ slope at point of tangency = -81 = f'(x)

so, that 3x³ = -81

⇒ x³ = -27

⇒ x = -3

Now from 81x + y = 0

⇒ 81 *-3 +y = 0

⇒ -243 +y = 0

⇒ y = 243

f(x) passes through (-3, 243)

So that,

⇒ 243 = 3 * 81/4 + C

⇒ C = 243 - 243/4

⇒ C = 729/4

So that, f(x) = 3x⁴/4 + 729/4

⇒ f(x) = 3 (x⁴+243)/4

to learn more about function visit:

brainly.com/question/19424752

#SPJ1

we need to multiply this number by 100 to get the  as a percentage:

0.1806 * 100 = 18.06%

The probability of choosing a senior can be calculated using the formula:

P(senior) = (102/562) * 100

P(senior) = 18.06%

This means that there is an 18.06% chance of choosing a senior if a student is randomly selected from the school.

First, we need to calculate the total number of students in the school by adding together the number of students in each class:

Total = 165 + 145 + 114 + 102 = 562

Next, we need to calculate the probability of choosing a senior by taking the number of seniors enrolled in the school (102) and dividing it by the total number of students in the school (562).

102/562 = 0.1806

Finally, we need to multiply this number by 100 to get the probability as a percentage:

0.1806 * 100 = 18.06%

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

Note that the proof that ΔABC ≅ ΔEDC is given as follows:

According to the ASA rule, if any two angles and sides included between the angles of one triangle are comparable to the corresponding two angles and sides included between the angles of the second triangle, the two triangles are said to be congruent.

Thus, given the above statements, it is clear that ΔABC ≅ ΔEDC

Learn more about ASA Congruence Theorem:
https://brainly.com/question/13671709
#SPJ1

Full Question:

Angle BAC is congruent to Angle DEC: Given

C is the midpoint of AE: Given

Prove triangle ABC is congruent to triangle EDC

What are the statements and reasons for this proof?

Answer:

Move the variables to one side and the constants to the other through subtraction/additions to BOTH SIDES. Then, divide/multiply to get x = some constant.

Step-by-step explanation:

Try Khan Academy.

9514 1404 393

Answer:

  an=12−1.5n

Step-by-step explanation:

The first term is 10.5.

The common difference is ...

  9 - 10.5 = -1.5

The n-th term can be described by ...

  an = a1 +d(n -1)

  an = 10.5 -1.5(n -1) = 10.5 -1.5n +1.5 . . . . eliminate parentheses

  an = 12 -1.5n

Answer:

scale factor = 2.5

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, polygon P to N

scale factor = \(\frac{20}{8}\) = 2.5

The required volume of the given solid is (√16 - r²) -(-√16 - r²).

The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.

Volume and the notion of length are connected.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface.

The cubic meter (m3), a derived unit, is the SI unit of volume.

So, the integrand often takes the form z upper z lower, where z stands for the solid's lower and upper borders.

We are treating the sphere as a hemisphere as of right now, with the XY-plane serving as its lower boundary. Consequently, you must multiply by 2.

The solid's volume is (√16 - r²) -(-√16 - r²).

Therefore, the required volume of the given solid is (√16 - r²) -(-√16 - r²).

Know more about volume here:

https://brainly.com/question/29665831

#SPJ4

Correct question:

Use polar coordinates to find the volume of the given solid: Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.

Answer:

C.10

Step-by-step explanation:

x=10

You can enter it into the calculator to check it.

Hope this helped! ;)

Answer:

x^2+4-5

Step-by-step explanation:

the first box multiply the next box

x^2-1x+5x-5

x^2+4x-5

Hi! Let's get solving. :D

Okay.. This is a double bracket, so use the '' Waves '' method to expand the bracket. I don't mean to be lazy, but it's kinda hard to explain the working here, so here's a brilliant video that explains this method:

https://youtu.be/Dvo1Q-yBBhk

(Cognito is a brilliant source for KS3, KS4 revision!)

Answer:

X^2+4−5

Stay safe! :)

Note: I'm not a maths expert, please double check your answer.