to solve the system of equations below, Becca isolated x^2 in the firs equation and then substituted it into the second equation

The combined capacity is given by (f+g) m = 2m² +32 m +210

An equation is defined as a mathematical statement used to relate a dependent and an independent variable.

The equation that gives the capacity of machine 1 is

f(m) = (m+4)² +100

and

The equation that gives the capacity of machine 2 is

g(m) = (m + 12)² -50

The total capacity of both the machine is given by

f(m) + g(m) =  (m+4)² +100 +(m + 12)² -50

(f+g) m = 2m² +32 m +210

Therefore the combined capacity is given by (f+g) m = 2m² +32 m +210

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Step-by-step explanation:

The equation of a circle is usually in the form: [tex](x-h)^2+(y-k)^2=r^2[/tex] where (h, k) is the center and r is the radius. With the information you provided you would have the equation: [tex](x+3)^2+(y-4)^2=16[/tex]. I'm a bit confused by "solve the equation of a circle" do you mean solve for y? if so you would just do

Original Equation:

[tex](x+3)^2+(y-4)^2=16[/tex]

Subtract (x+3)^2 from both sides

[tex](y-4)^2=-(x+3)^2+16[/tex]

Take the square root of both sides

[tex]y-4 = \pm\sqrt{-(x+3)^2+16}[/tex]

add 4 to both sides

[tex]y=\pm(\sqrt{-(x+3)^2+16})+4[/tex]

and then just change the sign to negative or positive depending on what half of the circle you want

Let's take this problem step-by-step:

I will assume that you want the standard form of the equation of the circle:

      ⇒ standard form: [tex](x-h)^2 +(y-k)^2=r^2[/tex]

LEt's plug in the known values

   [tex](x-(-3))^2+(y-4)^2 = 4^2\\(x+3)^2+(y-4)^2=16[/tex]

Answer: (x+3)² + (y-4)² = 16

Hope that helps!

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Answer:

S = {2, 2, 5, 5, 11}

Step-by-step explanation:

So you can partially build a data set given this information. There is going to be 5 positive numbers and the median is going to be 5 so the data set is going to have 5 in the middle which should look like this

S = {a, b, 5, c, d} where a, b, c, d are the other values. Since it has a mode of 2 and 5 that means that the occurrences of 2 and 5 will be equal, otherwise it would only have 1 mode. and they have to appear at least twice since if they only appeared once, there would either be another mode, or the data set would have 5 modes.

So the data set is going to look like this

S = {2, 2, 5, 5, d}

Now the only thing left to do is calculate d. This is where you use the mean to determine the last value. The mean can be calculated as

(the sum of the data set) / (the amount of values in the data set)

Since we know the mean you can set up an equation to find the value of d

[tex]5 = \frac{2+2+5+5+d}{5}\\5=\frac{14+d}{5}\\25=14+d\\11=d[/tex]

so the last value is 11. This gives you the complete data set of 5 positive integers

S = {2, 2, 5, 5, 11}

We would bid $0 as the expected value of this game is always negative.

I’ll assume that cash means there will not be fractions of a dollar in the box. Let X be the payout of the box and Y be the amount that we pay for the box after bidding. Then we have

P(X)=1.5X−Y, X≤Y

as ur profit function. Since E[P(X)]=1.5E[X]−Y, we first need to find the expected value of X and Y. Each integer between 0 and 1000 is equally likely to be in the box

(P(X=x)={1}/{1001}

Since we only realize the payout of the box if X≤Y we only need to sum up to Y:

E[X]= x=0∑Y1/1001 = Y(Y+1)/2002

To find the expected value of Y, note that we will pay Y dollars for the box if X≤Y and 0 otherwise. Given a Y, the probability that X≤Y is {Y+1}/{1001}

since each potential value of X shy of Y has probability {1}/{1001}

Then{E}[Y] = {Y(Y+1)}/{1001}

It follows that

[tex]\begin{aligned} \mathbb{E}[P(X)] &= 1.5\mathbb{E}[X] - E[Y] = \frac{1.5Y(Y+1)}{2002} - \frac{Y(Y+1)}{1001} \\ &= \frac{-3Y(Y+1)}{4004} \end{aligned}[/tex]

E[P(X)]=1.5E[X]−E[Y]= 1.5Y(Y+1)/2002  − Y(Y+1)​/1001 = −3Y(Y+1)/4004

which is always negative so we should not bid any amount for the box. Our optimal bid then is $0, with expected payoff $0. Note that my original assumption was the impetus for using a summation; should I have assumed that any value was possible in the box, then we would have to approach X as though it were a continuous variable.

So, We would bid $0 as the expected value of this game is always negative.

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​

The data life cycle and the data analysis process are interrelated concepts, with the data analysis process being a key component of the broader data life cycle. Both processes play crucial roles in managing and leveraging data for informed decision-making and insights generation.

The data life cycle and the data analysis process are closely related concepts within the broader field of data management and analytics. They both involve the handling, processing, and utilization of data, but they focus on different stages and aspects of this overall process. Let's explore their relationship, similarities, and differences:

1. Data Life Cycle:

The data life cycle refers to the journey that data goes through from its creation or acquisition to its eventual disposal or archival. It encompasses various stages that data passes through during its lifecycle, including:

Collection: Data is collected from various sources, such as sensors, surveys, databases, or external datasets.

Storage: Data is stored in appropriate data storage systems, which could be databases, data warehouses, or cloud storage.

Processing: Data is cleaned, transformed, and organized to make it suitable for analysis. This may involve data preprocessing, transformation, and integration.

Analysis: Data is analyzed using various techniques to extract insights, patterns, and meaningful information.

Visualization: Results of the analysis are often presented visually using charts, graphs, and dashboards to communicate findings effectively.

Interpretation: Analysts interpret the results of the analysis in the context of the problem or question at hand.

2. Data Analysis Process:

The data analysis process specifically focuses on the steps involved in deriving insights, patterns, and information from the data. It can be thought of as a subset of the data life cycle, concentrating on the stages from data processing through analysis, visualization, interpretation, and decision-making.

Similarities:

Interconnectedness: The data analysis process is a significant part of the data life cycle, as the insights derived from analysis can influence decisions at various stages of the cycle.

Data Preparation: Both processes involve data preparation, transformation, and cleaning to ensure that the data is suitable for analysis and downstream use.

Decision-Making: Both processes contribute to decision-making, with the data analysis process providing insights that inform decisions made within the data life cycle.

Differences:

Scope: The data life cycle covers the entire journey of data, from creation to disposal, while the data analysis process is a narrower focus on deriving insights and information from the data.

Stages: The data life cycle includes stages such as data collection, storage, and archival, which are not part of the core data analysis process.

Purpose: The primary purpose of the data life cycle is to manage data throughout its lifecycle, ensuring data integrity, security, and compliance. The primary purpose of the data analysis process is to extract meaningful information and insights to address specific questions or problems.

Timeframe: The data analysis process typically occurs after the data has been collected and processed, whereas the data life cycle encompasses the entire timeline of data existence.

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The attitude of Taylor in the given scenario can be classified as a; Watchdog

From the given narration about Taylor, we can see that she understood the laws applying to whales and knew what the whaling industry would be doing wrong, when they do so.  

Now, considering the fact that Taylor is not old enough to make a difference, politically, she has to tell others and keep an eye out. Thus, with this attitude, we can classify her to be a watchdog

The complete question is;

Taylor, a seventh grader at Juno Middle School, loves whales. She believes it is her duty to understand all laws that apply to the whaling industry and how this will affect the whales. She spends much time researching how officials are or aren't enforcing those laws. Taylor reports her findings to friends and family who can vote.

Taylor would be considered a;

A) watchdog

B) legal representative

C) leader of an interest group

D) member of the media

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The confidence interval for the mean level of carbon dioxide present in the facility is (806.05,828.91) and the critical value is 2.77 which is used to find out the confidence interval.

Given measurement of carbon dioxide :828.1,812.1,805.9,810,831.3

We have to construct a confidence interval for 95% for the mean level of carbon dioxide present in the facility.

n=5

sample mean=817.48 (calculated in figure)

sample standard deviation=[tex]\sqrt{(x_ -x_{bar} )^{2} /n-1 }[/tex]

=[tex]\sqrt{522.768/4}[/tex]

=11.43

We have to apply t test as n<30

t critical at 95% with degree of freedom=4              (5-1)

=2.77

Confidence interval=X bar ±standard error

Standard error= t*s/[tex]\sqrt{n}[/tex]

=2.77*11.43/[tex]\sqrt{5}[/tex]

=14.13

Lower boundary=817.48-11.43

=806.05

Upper boundary=817.48+11.43

=828.91

Hence the confidence interval is (806.05,828.91).

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Answer:

x = 17deg

Step-by-step explanation:

Let angle y be the unknown angle IN THE TRIANGLE.

Angle y = 180 - 90 - 73

= 17deg

Angle x = Angle y (Alternate angles on 2 parallel lines)

Angle x = 17 deg

Answer:

17° is the answer.

Answer:

x = 32

Step-by-step explanation:

Angle <X and angle <Z is has same measure because they are congruent angles so we can write the following equation:

6x - 60 = 2x + 68 transfer like terms to the same side of the equation

6x - 2x = 68 + 60 subtract/add

4x = 128 divide both sides by 4

x = 32

To find the measure of angle <Z and length of WY replace x with the value we found

WY = 3*32 + 5

WY = 101

m<Z = 2*32 + 68

m<Z = 132

Answer:

250

Step-by-step explanation:

mp=sp+d%of mp

x = 200+20÷100×x

100x-20x = 20000

x= 250

Answer:

x=5

Step-by-step explanation:

these two angles are the same so set both equations equal to each other and solve for x.

[tex]23x-5=21x+5\\23x=21x+10\\2x=10\\x=5[/tex]

1. set equations equal to each other

2. add 5 to both sides

3. subtract 21x from both sides

4. divide both sides by 2 to get x alone

5. x=5

Answer:

300 people.

Step-by-step explanation:

The number of people who like at least one of them is 300 people.

A Venn diagram is defined as a visual representation that makes use of circles to highlight the connections between different objects or limited groups of objects. Circles that overlap share certain characteristics, whereas circles that do not overlap do not.

Given data as :

In a survey conducted among the people

The number of people like to eat green vegetables = 200,

The number of people like fruits = 200 and

The number of people like both of them = 100

According to attached Venn-Diagram,

The number of people who like at least one of them = 100 + 100 + 100

The number of people who like at least one of them = 300

Hence, the number of people who like at least one of them is 300 people.

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The solution of the equation is 5477x + 12y = -56

Given the equation;

-8 -48-4y-8y = -x + 5480x

First, we collect like terms

-56 - 12y = 5477x

Collect the numbers with variables together

-56 = 5477x + 12y

Thus, the solution of the equation is 5477x + 12y = -56

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Answer:

24

Step-by-step explanation:

put one fruit cup and banana in each bag

the teacher can make the greatest number of snack bags, which is 12, while ensuring that all the bags contain an equal number of fruit cups and bananas.

To find the greatest number of snack bags that the teacher can make while ensuring that all the bags are exactly the same, you need to determine the common factors of the quantities of fruit cups (36) and bananas (24). The greatest number of bags will be determined by the greatest common factor (GCF) of these two numbers.

Let's find the GCF of 36 and 24:

1. List the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

2. List the factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Now, identify the common factors from both lists:

Common factors: 1, 2, 3, 4, 6, 12

The greatest common factor among these common factors is 12.

So, the teacher can make the greatest number of snack bags, which is 12, while ensuring that all the bags contain an equal number of fruit cups and bananas.

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Answer: 4

Step-by-step explanation:

Helen is incorrect, the pressure decreases by greater than 20% and percent decrease is 23.80%.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

Pressure before the change:

Area = 20 square cm = 0.002 square meters

P = 70/0.002 = 35000 N/m²

The force is increased by 10 newtons. The area is increased by 10cm²

New pressure = (70+10)/(0.003) = 26,666.667 N/m²

Percent decrease = [(35000 - 26,666.667)/35000]×100

= 23.80% (pressure decrease by 23.80%)

Thus, Helen is incorrect, the pressure decreases by greater than 20% and percent decrease is 23.80%.

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Answer:

30.6

Step-by-step explanation:

The closest shape to a tree trunk is a cylinder.

Area of a cylinder: 1/3πr^2h

1/3πr^2h

1/3π(1.5)^2(13)

1/3π(2.25)(13)

1/3π(29.25)

30.6

Based on the information given, the bisected angle, quadrilateral, and congruent angles will be explained.

It should be noted that a quadrilateral simply means a closed shape that has four sides and four angles. These include square, rectangle, parallelogram, etc.

A bisected angle simply illustrates a line that splits an angle onto two equal angles.

Congruent segments are the segments that have the same length.

The diagrams are attached accordingly.

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Answer: m=n=3

Step-by-step explanation:

Reflecting across the y=0, in other words, the x-axis, means

[tex](x,y) \longrightarrow (x,-y)[/tex]

So, [tex]p(m,5-n) \longrightarrow p'(m,n-5)=p'(2m-3, 2n-8)[/tex]

This gives us the system

[tex]m=2m-3 \longrightarrow \boxed{m=3}\\\\n-5=2n-8 \longrightarrow \boxed{n=3}[/tex]

The three positive integer that has mean of 5 and range of 10 will be 0, 5, 10.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Let the three positive number be (a – d), (a), and (a + d).

Then the mean of the number will be 5. Then we have

5 = (a – d + a + a + d) / 3

5 = (3a) / 3

a = 5

Then the range will be 10. Then we have

(a + d) – (a – d) = 10

   a + d – a + d = 10

                   2d = 10

                     d = 5

Then the three positive integer that has mean of 5 and range of 10 will be 0, 5, 10.

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Answer:

each bush is $23 and each tree is $47

Step-by-step explanation:

Answer:

B. 20

Step-by-step explanation:

Cos a = b/c

Cos 53° = b/25

b = 25 × 0,6 = 15

x = √(25² - 15²)

x = √(625 - 225)

x = √400

x = 20

Parallel lines admit equal slopes.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:y = x + 3 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Calculate slope (m) using two points -

[tex]\qquad \tt \rightarrow \:m = \dfrac{rise}{run} [/tex]

[tex]\qquad \tt \rightarrow \:m = \dfrac{4 - 3}{1 - 0} [/tex]

[tex]\qquad \tt \rightarrow \:m = {1}[/tex]

Y - intercept (c) = 3

[tex] \large\textsf{Equation of line : } [/tex]

[tex]\qquad \tt \rightarrow \:y = mx + c[/tex]

[tex]\qquad \tt \rightarrow \:y = 1(x) + 3[/tex]

[tex]\qquad \tt \rightarrow \:y = x + 3[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

(-1,3)

Step-by-step explanation:

You just need to see how the shape connects

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{4t^2 - 2t - s}[/tex]

[tex]\huge\textbf{Solving:}[/tex]

[tex]\mathbf{4t^2 - 2t - s}[/tex]

[tex]\mathbf{= 4(4)^2 - 2(4) - 5}[/tex]

[tex]\mathbf{= 4(4\times 4) - 2(4) - 5}[/tex]

[tex]\mathbf{= 4(16) - 2(4) - 5}[/tex]

[tex]\mathbf{= 64 - 2(4) - 5}[/tex]

[tex]\mathbf{= 64 - 8 - 5}[/tex]

[tex]\mathbf{= 56 - 5}[/tex]

[tex]\mathbf{= 51}[/tex]

[tex]\huge\textbf{Answer:}[/tex]

[tex]\huge\boxed{\textsf{Option B. 51}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

50 %

Step-by-step explanation:

i think this is the answer

2) [tex]\overline{AG} \cong \overline{GC}[/tex] (a segment bisector divides a segment into two congruent segments)

3) [tex]\overline{EG} \cong \overline{GF}[/tex] (a segment bisector divides a segment into two congruent segments)

4) [tex]\angle AGE \cong \angle FGC[/tex] (vertical angles are congruent)

5) [tex]\triangle AGE \cong \triangle CGF[/tex] (SAS)

6) [tex]\angle FCG \cong \angle GAE[/tex] (CPCTC)

7) [tex]\overline{AE} \parallel \overline{FC}[/tex] (converse of alternate interior angles theorem)

8) [tex]\overline{AB} \parallel \overline{CD}[/tex] (segments collinear with parallel segments are parallel)

9) [tex]\angle DAC \cong \angle ACB[/tex] (alternate interior angles theorem)

10) [tex]\angle DAB \cong \angle DCB[/tex] (congruent angles added to congruent angles form congruent angles)

11) [tex]ABCD[/tex] is a parallelogram (a quadrilateral with two pairs of opposite congruent angles in a parallelogram)

The number which when substituted in a polynomial makes its value zero is called the zero of the polynomial.

The zero of a polynomial can be defined as the points where the polynomial becomes zero as a whole.

In other words, The zeros of a polynomial p(x) are the values of x which satisfy the equation p(x) = 0

For example, the zero of the polynomial f(x) = x³- 12x²+ 20x is  x = 0 or x = 10 or x = 2.

This is because f(x) = o when we substitute those x values.

Therefore, the number which when substituted in a polynomial makes its value zero is called the zero of the polynomial.

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Step-by-step explanation:

A. ______________________$