Find the total area of the composite figure below. SHOW ALL WORK.

Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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Answer:

yes

Step-by-step explanation:

a) The expected number of people who would name chocolate in the sample is approximately 6.30. b) The probability of exactly eight people naming chocolate is given by  \(P(X = 8) = (14 C 8) (0.45^8) (1 - 0.45)^{(14 - 8)\)

c) The probability of eight or more people naming chocolate sum the probabilities of exactly eight, nine, ten, eleven, twelve, thirteen, and fourteen people naming chocolate

(a) To find the expected number of people who would name chocolate in the sample, we multiply the percentage of people who prefer chocolate by the sample size. In this case, 45% is equivalent to 0.45, so we calculate the expected number as 0.45 * 14 = 6.30. Rounding to two decimal places, we expect approximately 6.30 people in the sample to name chocolate.

(b) To calculate the probability of exactly eight people naming chocolate, we use the binomial probability formula. The formula is \(P(X = k) = (n C k) * p^k * (1 - p)^{(n - k)\), where n is the sample size, k is the number of successes (people naming chocolate), p is the probability of success (45% or 0.45), and (n C k) represents the number of combinations. Substituting the values, we have \(P(X = 8) = (14 C 8) * (0.45^8) * (1 - 0.45)^{(14 - 8)\). Evaluating this expression gives us the probability of exactly eight people naming chocolate.

(c) To find the probability of eight or more people naming chocolate, we sum the probabilities of exactly eight, nine, ten, eleven, twelve, thirteen, and fourteen people naming chocolate. Using the same binomial probability formula as before, we calculate the probabilities for each number of successes and add them together to obtain the probability of eight or more people naming chocolate.

Note: Without additional information about the distribution or assumptions, we assume that the survey results are representative of the population and that the responses are independent and identically distributed.

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Answer: 24

Step-by-step explanation:

Let x be the number of newspapers he derlivered on Tuesday.

3.5x+30=114

Then

3.5x=114-30=84

x=24

Answer:

Let ac=ab=5

With this, bc= 5√2

Step-by-step explanation:

So to find ad, Let ad be x

5√2=(2)(x)

(5√2/2)= x

This proves that bc=2ad

The final simplified expression is: -211/7i - 3/7

To simplify the given expression, let's work step by step:

(4 - i)(-3/7i) - 7i(8/2i)

First, let's simplify each multiplication:

(4 * -3/7i - i * -3/7i) - (7i * 8/2i)

Now, simplify further:

(-12/7i + 3/7i^2) - (56/2)

Remember that i^2 is equal to -1:

(-12/7i + 3/7(-1)) - (28)

Simplify the expression:

(-12/7i - 3/7) - 28

Combining like terms:

-12/7i - 3/7 - 28

Now, let's express the terms as a single fraction:

-12/7i - 3/7 - 196/7

Combine the numerators:

(-12 - 3 - 196)/7i - 3/7

Simplify further:

(-211)/7i - 3/7

The final simplified expression is:

-211/7i - 3/7

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the probability that a woman has cancer given that she has a negative test result is 0.964.

A certain form of cancer is known to be found in women over 60 with probability 0.7. A blood test exists for the detection of the disease, but the test is not infallible. In fact, it is known that 10% of the time the test gives a false negative and 5% of the time the test gives a false positive.

For a woman over the age of 60, the probability of having cancer is 0.7.

Let A be the occurrence of a woman having cancer, and let B be the occurrence of a woman receiving a favorable test result. We need to calculate the probability that a woman has cancer given that she has a negative test result.

Using Bayes’ theorem, we can calculate

P(A | B) = P(B | A) * P(A) / P(B).P(B | A) = probability of receiving a favorable test result if a woman has cancer = 0.9 (10% false negative rate).

P(A) = probability of a woman having cancer = 0.7.P(B) = probability of receiving a favorable test result = P(B | A) * P(A) + P(B | ~A) * P(~A).

The probability of receiving a favorable test result if a woman does not have cancer is P(B | ~A) = 0.05.

The probability of a woman not having cancer is P(~A) = 0.3.P(B) = (0.9 * 0.7) + (0.05 * 0.3) = 0.655.P(A | B) = (0.9 * 0.7) / 0.655 = 0.964.

Hence, the probability that a woman has cancer given that she has a negative test result is 0.964.

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The greatest common factor of \(20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}\) is \(10x^{4} y\) .

The greatest common factor of a set of numbers is defined as the largest number that divides all the numbers in that given set and leaves 0 as remainder in each case.

In the given expression

\(20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}\)

Applying Prime Factorization and Writing all the terms in the above expression as

\(20x^{6} y=10x^{4}y *2x^{2}\)

\(40x^{4} y^{2} =10x^{4} y*4y\)

\(10x^{5} y^{5} =10x^{4}y*xy^{4}\)

As we can see that \(10x^{4} y\) is common and greatest in all the terms .

Hence \(10x^{4} y\) is the Greatest common factor.

Therefore , the greatest common factor of \(20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}\) is \(10x^{4} y\) , the correct option is (a)\(10x^{4} y\).

The given question is incomplete , the complete question is

What is the greatest common factor of \(20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}\)

(a)\(10x^{4} y\)

(b)\(5x^{2} y^{5}\)

(c)\(5x^{4} y\)

(d)\(20x^{6} y\)

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The normal vector, f, to the surface of the inner conductor is a unit vector in the radial direction, pointing away from the conductor.

a. The normal vector, f, to the surface of the inner conductor is a unit vector in the radial direction, pointing away from the conductor.

b. The boundary condition at the surface of the conductor (medium 2) is that the normal component of the electric field is equal to the surface charge density.

c. The boundary condition in the dielectric (medium 1) is that the tangential component of the electric field is equal to zero.

d. The surface charge density, Ps, at the surface of the conducting cylinder is P.

The complete question is:

An infinitely long conducting cylinder of radius a (medium 2) has a surface charge density P. The cylinder is surrounded by a dielectric (Er = 4, medium 1) that contains no free charges (that is to say p = 0 inside the dielectric). Defining 2 as the axis of the conducting cylinder, the electric field, E, inside the dielectric medium (whenra) is found as: E = Er*sin(θ)/r.

a. What is the normal vector, f, to the surface of the inner conductor?

b. What is the boundary condition at the surface of the conductor (medium 2)?

c. What is the boundary condition in the dielectric (medium 1)?

d. What is the surface charge density, Ps, at the surface of the conducting cylinder?

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El valor que satisface D es 188.

El modelo matemático será así:

D/d = 12(resto 8)

si escribimos 8 como resto de D, entonces:

(D-8) /d=12

D-8= 12d o se puede escribir D= 12d+8

luego sustituya D= 12d+8 por D+d= 203

D+d= 203

(12d +8) +d= 203

13d= 203-8

13d= 195

re=15

sustituir d=15 en D+d= 203

D+d= 203

D+15=203

D=203-15

D=188

El modelo matemático es una forma de interpretación humana al traducir o formular problemas existentes en forma matemática, de modo que el problema pueda resolverse utilizando las matemáticas.

El uso principal de los modelos matemáticos es ayudar a las personas a comprender los problemas y simplificarlos para que puedan resolverse.

, los siguientes son algunos de los usos que se obtienen al utilizar un modelo matemático, a saber:

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Answer:

16 ft³

Step-by-step explanation:

4ft x 2ft x 2ft = 4ft x 4ft = 16 ft³

Answer:

50.1°

Step-by-step explanation:

An angle is a measure of a turn, measured in degrees or °. Angles are made up of two rays, making the sides of the angle.

For two angles to be complementary, they need to add up to 90°.

If we now know that two complementary angles add up to 90°, we can use this equation to solve for the missing degree:

To check, we can use this equation:

Therefore, the measure of the missing angle is 50.1°.

Answer:

The answer is 30 ROWS.

Step-by-step explanation:

Please give brainlyest

The advantages of the superposition theorem compared to other circuit theorems are its simplicity and modularity in circuit analysis, as well as its applicability to linear circuits.

Superposition theorem is a powerful tool in circuit analysis that allows us to simplify complex circuits and analyze them in a more systematic manner. When compared to other circuit theorems, such as Ohm's Law or Kirchhoff's laws, the superposition theorem offers several advantages. Here are two key advantages of the superposition theorem:

Simplicity and Modularity: One major advantage of the superposition theorem is its simplicity and modular approach to circuit analysis. The theorem states that in a linear circuit with multiple independent sources, the response (current or voltage) across any component can be determined by considering each source individually while the other sources are turned off. This approach allows us to break down complex circuits into simpler sub-circuits and analyze them independently. By solving these individual sub-circuits and then superposing the results, we can determine the overall response of the circuit. This modular nature of the superposition theorem simplifies the analysis process, making it easier to understand and apply.

Applicability to Linear Circuits: Another advantage of the superposition theorem is its applicability to linear circuits. The theorem holds true for circuits that follow the principles of linearity, which means that the circuit components (resistors, capacitors, inductors, etc.) behave proportionally to the applied voltage or current. Linearity is a fundamental characteristic of many practical circuits, making the superposition theorem widely applicable in real-world scenarios. This advantage distinguishes the superposition theorem from other circuit theorems that may have limitations or restrictions on their application, depending on the circuit's characteristics.

It's important to note that the superposition theorem has its limitations as well. It assumes linearity and works only with independent sources, neglecting any nonlinear or dependent sources present in the circuit. Additionally, the superposition theorem can become time-consuming when dealing with a large number of sources. Despite these limitations, the advantages of simplicity and applicability to linear circuits make the superposition theorem a valuable tool in circuit analysis.

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Answer:Ben will roll an even number about 560 times if the number cube is rolled 1,000 times.

Step-by-step explanation:

The row for 20 degrees and the row for 70 degrees in the right triangle table have the same values, but in reverse order.

Specifically, the sine, cosine, and tangent of 20 degrees are the same as the cosine, sine, and tangent of 70 degrees, respectively. The same holds true for their reciprocals, the cosecant, secant, and cotangent.

It should be noted that to complete the row for 35 degrees in the right triangle table, we can use the same ratios as for the complementary angle of 55 degrees, but in reverse order. Specifically:

The adjacent leg ÷ hypotenuse ratio for 35 degrees is equal to the opposite leg ÷ hypotenuse ratio for 55 degrees, which is 0.819.

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Answer:

I want to say that it is E

Step-by-step explanation:

Well in terms of probability there is a 50% chance the coin will land heads and a 50% chance the coin will land tails. Since probability isn't definite you can never really get a precise number of each side. the most you could do is predict/guess

The most likely outcome is: E. They are all equally likely.

Each individual toss of a fair coin has an equal probability of being a heads or tails, regardless of what the previous tosses were. Therefore, all of the outcomes listed are equally likely. The order in which the heads and tails occur does not affect the probability of the overall outcome.

So, even though (i) has an equal number of heads and tails in an alternating pattern and (iii) has all heads, they are both equally likely to occur. The same goes for (ii) and (iv), which have an equal number of heads and tails but in a random order.

Therefore, The most likely outcome is: E. They are all equally likely.

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Answer:

136.99

Step-by-step explanation:

Đây là một câu hỏi dễ chỉ cần sử dụng máy tính

Answer:

Step-by-step explanation:

from the angles we understand that it is an isosceles right triangle, therefore x is also 13, we find y with the Pythagorean theorem

y = √(13² + 13²)

y = √(169 + 169)

y = √338

y = 18.38 (you can round to 18.4)

Answer:

x = 13 , y = 18.38

Step-by-step explanation:

p.s. There is two ways to answer it.

In Triangle,

if there is a right angle, other angles are the same.

It the angles are the same, the two sides are the same.

So, x = 13

By the Converse of the Pythagorean Theorem , these values make the triangle a right triangle.

(hypotenuse)² = (side of right triangle)² + (other side of right triangle)²

(hypotenuse)² = 13² + 13²

(hypotenuse)² = 169 + 169

(hypotenuse)² = 338

hypotenuse = 18.38

so y = 18.38

Among the following, the population mean u = (upper confidence limit) + (lower confidence limit) is not derived from the confidence interval.

A confidence interval is defined as the range of values that we observe in our samples and for which  we expect to find the value that accurately reflects the population.

In frequentist statistic, a confidence interval is a range of estimates for an unknown parameter.    

To find a confidence level for a data set by taking half of the size of the confidence interval, multiplying it by the square root of the sample size and then dividing by the sample standard deviation.

Confidence level refers to the percentage of probability,or certainty, that the confidence interval would contain the true population parameter when you draw a random sample many times. The most common confidence levels are 90%, 95% and 99%.

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The number of non-similar 1000-pointed stars is

\($\frac{1000-600-2}{2}= \boxed{199}.$\)

If we join the adjacent vertices of the regular \($n$\)-star, we get a regular \($n$\)\(-gon\). We number the vertices of this \($n$\)\(-gon\) in a counter clockwise direction: \($0, 1, 2, 3, \ldots, n-1.$\)

A regular \($n$\)-star will be formed if we choose a vertex number m where \($0 \le m \le n-1$\), and then form the line segments by joining the following pairs of vertex numbers:\($(0 \mod{n}, m \mod{n}),$ $(m \mod{n}, 2m \mod{n}),$ $(2m \mod{n}, 3m \mod{n}),$ $\dots,$ $((n-2)m \mod{n}, (n-1)m \mod{n}),$ $((n-1)m \mod{n}, 0 \mod{n}).$\)

If \($\gcd(m,n) > 1$\), then the star degenerates into a regular \($\frac{n}{\gcd(m,n)}$-gon\) or a (2-vertex) line segment if \($\frac{n}{\gcd(m,n)}= 2$\). Therefore, we need to find all $m$ such that \($\gcd(m,n) = 1$.\)

Note that \($n = 1000 = 2^{3}5^{3}.$\)

\(Let $S = \{1,2,3,\ldots, 1000\}$, and $A_{i}= \{i \in S \mid i\, \textrm{ divides }\,1000\}$. The number of $m$'s that are not relatively prime to $1000$ is: $\mid A_{2}\cup A_{5}\mid = \mid A_{2}\mid+\mid A_{5}\mid-\mid A_{2}\cap A_{5}\mid$ $= \left\lfloor \frac{1000}{2}\right\rfloor+\left\lfloor \frac{1000}{5}\right\rfloor-\left\lfloor \frac{1000}{2 \cdot 5}\right\rfloor$ $= 500+200-100 = 600.$\)

\(Vertex numbers $1$ and $n-1=999$ must be excluded as values for $m$ since otherwise a regular n-gon, instead of an n-star, is formed.\)

The cases of a 1st line segment of (0, m) and (0, n-m) give the same star. Therefore we should halve the count to get non-similar stars.

Therefore, the number of non-similar 1000-pointed stars is

\($\frac{1000-600-2}{2}= \boxed{199}.$\)

\(Note that in general, the number of $n$-pointed stars is given by $\frac{\phi(n)}{2} - 1$ (dividing by $2$ to remove the reflectional symmetry, subtracting $1$ to get rid of the $1$-step case), where $\phi(n)$ is the Euler's totient function.\) \(It is well-known that $\phi(n) = n\left(1-\frac{1}{p_1}\right)\left(1-\frac{1}{p_2}\right)\cdots \left(1-\frac{1}{p_n}\right)$, where $p_1,\,p_2,\ldots,\,p_n$ are the distinct prime factors of $n$.\) \(Thus $\phi(1000) = 1000\left(1 - \frac 12\right)\left(1 - \frac 15\right) = 400$, and the answer is $\frac{400}{2} - 1 = 199$.\)

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Answer:

(-1, 6)

Step-by-step explanation:

Midpoint formula:

For G(-7, 3) and H(5, 9) the midpoint:

Answer:

(-1,6)

Step-by-step explanation

use the midpoint formula:

(x 1 + x2 /2 , y1 + y2/2)

(-7+ 5 /2, 3+ 9 /2)

after simplfying

(-1,6)

The equation that justifies why\(27^{(1/3)}\) is equivalent to the cube root of 27 is:\(27^{(1/3)} = (27^{1)^{(1/3)}} = 27^{(1/3)}\)

The cube root symbol is represented by the number "3". In the square root case, only the root symbol—also known as a radical—was employed. Therefore, the cube root of different numbers can be symbolically represented as follows: 5 divided by its cube = 3. 11 has a cube root of 311 and so on.

The cube root of three is the same as the number 1.442224957031. The cube root of three has the radical representations 33 and 31/3. " denotes the square root.

The cube root formula aids in computing the cube root of any given number that is represented by the symbol in radical form. It can be determined by first determining the number's prime factorization and then using the cube root formula. Assume that x is any number such that it equals y, y, and y.

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The polynomial that shows that the left side is rising and the right side is falling is: Option D: -2x⁷ + ¹/₂x⁶ - 8x⁵ + 3x⁴ + 2x³ - 5x² + x - 7

The end behavior of a polynomial function is defined as the behavior of the graph of f(x) as x approaches positive infinity or negative infinity. The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

Now, we are told that the left side is rising and the right side is falling. This means that both beginning and the end terms will have a negative sign attached to them.

The only option that shows both first and last terms having negative numbers is option D.

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1800 lawns were mowed. 800 driveways were shoveled.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Given Data

Let mowed grass be x

Let shoveled snow be y

Last year you mowed grass and shoveled snow for 12 houses

x + y = 12

y = 12 -x

You earned $225 for each lawn you mowed and $200 for each house you shoveled for a total of $2600.

225x + 200y = 2600

Equating value of y

225x + 200(12-x) = 2600

225x + 2400 - 200x = 2600

225x - 200x = 2600 - 2400

25x = 200

x = 8

For value of y,

y= 12 -x

y = 12 - 8

y = 4

Lawn mowed = 225(8)

Lawn mowed = 1800

Shoveled snow = 200(4)

Shoveled snow = 800

1800 lawns were mowed. 800 driveways were shoveled.

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Answer:

7/10 = 10/7

1/2 = 2/1

5 = 1/5

Step-by-step explanation:

The reciprocal is the flip of a fraction. 1/2 = 2/1

For a whole number (like 5) you put it over 1 (5/1) and then flip it (1/5)

Have a nice day! :)

Make me brainliest.

Answer:

number 1: {0,-6)    number 2: f(-2)=25 number 3: x=±10   number 4:B, or x=-2, x=3

number 5:36  i really hope this helps! have a good day!

Step-by-step explanation:

1: 2x^2+12x +0=0

this is how you set it up

next, you have to find the a,b,and c. This is my personal favorite way of doing this.

a=2 b=12, c=0

you plug it in to the quadratic formula which is

-b±√b^2-4ac/2a

(-12)±√(12)^2-4(2)(0)/2(2)

next you have to simplify

-12±√144-0/4

take the square root of 144

-12±12/4-

then, find the solutions of them

-12+12=0

0/4=0

x=0

we are not done yet

-12-12=-24

-24/4

x=-6

your solutions are 0,-6, which is C

2: it is giving us x, which is -2

plug in -2 to the right side of the equation.

2(-2)^2-4(-2)+9

2(4)-8+9

8-8+9

f(-2)=9

3: this one is fairly simple

x^2=100

take the square root of each side

x=±10

4: you have to replace y for 0 in this one

x^2-x-6=0

all you have to do is factor it out, and it turns into

(x+2)(x-3)

then turn these so they equal 0

x+2=0, x-3=0

x=-2     x=3

your answer would be B

5: this one is fairly simple too

the formula to completing the square is (b/2)^2

you plug in b, which is 12

12/2=6

6^2=36

you would add 36 to each side.

Answer:

7) {0, -6}

1) 25

2) x= ±10

3) x= 3, -2

4) 36

5) 225/4

6) x = -3±\(2\sqrt{3}\)

Step-by-step explanation:

1) 2x^2 -4x + 9

2(-2)^2 - 4(-2) + 9

8+ 8 + 9

25