Using a graphical method, solve the simultaneous equations
X + y = 4
and
y = 2x+ 1

The towers ZQ and ZR are the closest together.

Triangle is a three-sided polygon which has three vertices.

Solution

If the measure of ZP is x,

Then the measure of ZQ is x-10 and the measure of ZR is x-5.

To find the two towers that are closest together, we need to find the minimum value of the difference between any two angles.

ZP and ZQ: x - (x-10) = 10

ZQ and ZR: (x-5) - (x-10) = 5

So, the towers ZQ and ZR are the closest together, with an angle difference of 5°.

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The average speed in the city by the motorist is  45 km/hr.

Velocity is the direction speed of an item in motion as a measure of the rate at which its location is changing as seen from a certain point of view and as measured by a specific unit of time.

Distance is a measurement of how far away two things or locations are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common use.

Calculating average speed involves dividing the whole distance traveled by the total time it takes to cover that distance.

The average speed in the open road is x km/hr (say)

Average speed in the city is x - 42 km/hr

The time taken is same to travel 29 km in open road and 15 km in city then

29/x = 15/(x -42)

⇒29x - 29*42 = 15x

⇒14x = 29*42

⇒x = 87 km/hr

The average speed in the city by the motorist is 87-42 = 45 km/hr.

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Answer:

[tex]2[/tex]

Step-by-step explanation:

Rate of change = [tex]\frac{change}{change} \frac{y}{x}[/tex]

[tex]\frac{change}{change} \frac{y}{x} = slope[/tex]

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

[tex]y2 = 5, y1 =3, x2=1, x1 =0[/tex]

(left of the table is x, right of the table is y)

[tex]\frac{5-3}{1-0}[/tex] [tex]=slope[/tex]

[tex]\frac{2}{1}[/tex] [tex]=slope[/tex]

[tex]2 = slope=rate[/tex] [tex]of[/tex] [tex]change[/tex]

Yes, the entire remaining water will fit in one of the half gallon jugs.

Gallon refers to the measure of the liquid.

A litre of water is equivalent to 0.264172 gallons. As a result, if one full litre of water spilled out, you'd be left with 1.73482 gallons of water. Because a half gallon jug can carry 0.5 gallons of water, the remainder 1.73482 gallons of water will certainly fit into one of the half gallon jugs.

A gallon is a term of liquid measurement equivalent to eight pints. It is approximately 4.546 litres in the United Kingdom. It is about 3.785 litres in the United States.

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True. Body weight is an example of a discrete variable. A discrete variable is a variable that can only take on certain values.

It can only be counted, not measured. Body weight, for example, can be expressed as an integer value such as 150 pounds or 68 kilograms, but not as a fractional value such as 150.3 pounds or 68.1 kilograms. In other words, the number of possible values for body weight is finite and can be listed out, which makes it a discrete variable.

On the other hand, continuous variables can take on an uncountable number of possible values, such as height or temperature, which can be expressed to an arbitrary degree of precision.

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When the y = f(x) and y = g(x) graphs intersect, the x and y values on both graphs are exactly the same.

Both graphs have the exact same x and y values when the y = f(x) and y = g(x) graphs cross. So, by figuring out the solution to the equation f(x) = g, we can determine the point or points of intersection (x). We may find the x value(s) of the intersection point(s) by solving this equation.

The (x,y) coordinate pairings for which the input, x, yields the same output value from both functions are known as the points of intersection of two functions, f(x) and g(x).

If A, B, and C are three sets, then all of the elements that are shared by A, B, and C are contained in the set formed by the intersection of these three sets. This can be illustrated as A, B, and C.

Let the two functions be

y = 2x + 1 and

y = x - 2

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The number of solutions for the system of equations for this problem, from the first to last, is given as follows:

There are three possible number of solutions for each system of equations, and the cases are presented as follows:

For the second system, we have that:

As 4 and 13 are not multiples, then the system has zero solutions.

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Answer:

1260 springs

Explanation:

From 1 pm to 6 pm, the machine will work for 5 hours.

In the first part of the day, the machine made 450 paper clips, which took it:

So, the machine will start making springs at 2:30 pm.

From 2:30 pm to 6 pm, the machine will work for 3.5 hours.

During this time, the machine can make:

Therefore, the machine will make 1260 springs by 6 pm.

________________________________________________________

In one hour a machine can make 300 paper clips 300 paper clips or 360 springs. At 1 pm the machine starts working. It makes 450 paper clips and then changes to making springs. How many springs will the machine make by 6 pm?

The machine will make 1260 springs by 6 pm.

We are given that the machine can make 300 paper clips in one hour or 360 springs in one hour.

Let's first find out how many hours the machine will make paper clips before switching to making springs.

We know that the machine has made 450 paper clips. So,

Hence, the machine will make paper clips for 1.5 hours before switching to making springs.

Now, we need to find out how many hours the machine will make springs. We know that the machine starts working at 1 pm and we need to find out how many hours it will work making springs before 6 pm.

There are 5 hours between 1 pm and 6 pm. However, we need to subtract the 1.5 hours that the machine will work making paper clips.

So, the machine will make springs for:

Now, we can use the information that the machine can make 360 springs in one hour to find out how many springs it will make in 3.5 hours.

Therefore, the machine will make 1260 springs by 6 pm.

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An example of a product-of-sum (pos) expression is X = (A + B)(C + D)

From the four expressions, first we eliminate the expressions which do not have the addition operator.

Then we have three expressions:

X = AB + CD

X = (A + B)(C + D)

X = A + B + C

With the remaining expressions we find the expression which is POS (product-of-sum)

An expression X = AB + CD  is in the form of SOP, Sum of products, which will give the sum of the two different multiplications  AB and CD.

An expression X = (A + B)(C + D) is in the form of POS (product-of-sum), which will give the product of two different additions (A + B) and (C + D).

And the expression X = A + B + C is the sum of three different variables.

Thus, X = (A + B)(C + D) is the required expression.

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The complete question is:

Which answer is an example of a product-of-sum (POS) expression?

X = ABC

X = AB + CD

X = (A + B)(C + D)

X = A + B + C

Answer:

To solve for x in this equation, you will need to use algebraic techniques such as combining like terms, using the distributive property, and applying the properties of exponents. Here are the steps to solve for x:

Start by isolating x on one side of the equation by moving all the other terms to the other side.

Next, use the properties of exponents to simplify the left side of the equation:

1/2 • 2^3x = 1/2 • 8x = 4x

Next, combine like terms on the right side of the equation: 1/24 - 3x

Now you can set the two sides of the equation equal to each other and solve for x:

4x = 1/24 - 3x

4x + 3x = 1/24

7x = 1/24

x = 1/24 * 1/7

x = 1/168

So the answer for solving the variable is x = 1/168

Each function is a rule, hence each function table includes a rule describing the relationship between the inputs and outputs.A function shall be represented by option (a) table.

Check to see if a list of input and output values is a function.

Establish the input and output values.

Check that each input value corresponds to a single output value.

The table then serves as a function.

Each function is a rule, hence each function table includes a rule describing the relationship between the inputs and outputs.

Sometimes the best way to communicate a rule is verbally, and other times the best way is mathematically.

Given the tables,

Choice B

The same input as -2, but two unrelated results.

Choice C

Although there are five different outputs, the input of -5 is not conceivable.

Choice D

Using the same input as 30 but producing two different results is not feasible.

i.e.,while we can have different inputs and the same output, there is only one output for each input.

As a function, Option (A) is the appropriate response.

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True :   The values of x and y shows that for 2 values of x there is only 1 value of y that is the function not linear but can be a function.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it may take as input. After we enter an x value, the function outputs this sequence of values.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it may take as input. After we enter an x value, the function outputs this sequence of values.

The x = 2,4,6,8,10

for y = 1,3,3,4,6

The values of x and y shows that for 2 values of x there is only 1 value of y that is the function not linear.

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The function f possesses the characteristics of injectivity, strict increase, and surjectivity. It lacks the characteristics of rigorously increasing, decreasing, or decreasing.

Because it is one-to-one, or that there is only one matching y-value for each given x, the function f(x) = sinx is injective. Because the associated y-values rise monotonically for any two x-values, it is also strictly increasing. Additionally, it is surjective because the full [-1, 1] range of the function is covered by its range. Since its values don't always fall or rise linearly, it lacks the characteristics of rigorously decreasing, decreasing, or increasing.

The function f:[4, 4][1, 1];f(x)=sinx has a number of significant characteristics. It is one-to-one since it is injective. This implies that there is only one matching y-value for every possible value of x. Additionally, it is strictly growing, which means that the related y-values rise monotonically for any two x-values. This indicates that the function is not always linear in its increase or decrease. The function is also surjective because its range includes the entire [-1, 1] range of the function. This indicates that the function can produce any value between -1 and 1.

Since the values of the function do not necessarily drop or rise linearly, it does not possess the characteristics of strictly decreasing, decreasing, or increasing. This distinguishes the function from others and enables a wide range of applications.

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The minimum number of dots and/or dashes needed so that each letter in the English alphabet can have a unique representation is 4.

We need a code that can handle at least that many characters because there are 26 letters in the alphabet.

One can choose to use one of two symbols in each position, which results in 2^1 = 2 words.

Given two locations and the option to utilize one of two symbols in each, 2^2 = 4 words are produced.

Using one of two symbols in each of the three slots allows for a total of 2^3=8 words.

With 4 positions and the option to use one of two symbols in each, there are 2^4=16 words possible.

The sum of the dots and dashes is

2 + 4 + 8 + 16 = 30

Since there are 26 letters in the English alphabet, 4 dots and/or dashes are required to represent each letter, hence the answer is 4.

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The function f(x) is shifted down by 4 units to get g(x).

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

g(x) = [tex]9^x[/tex] - 4

and, f(x) = [tex]9^x[/tex]

As, we know that transformation where f(x) - a  shows the function f(x) is shifted down by a units.

Here, the function f(x) is shifted down to 4 units to get the function g(x).

Hence, the shifting is 4 units down.

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The percent of women have low values of HDL (40 mg/dl or less) is 1.03%.

High density lipoprotein (HDL) is an important factor in determining the risk of heart disease.

(a) The formula for z-score is (x - mean) / standard deviation. Using this formula, we can calculate the z-score for 40 mg/dl as

=> (40 - 55) / 15.5 = -1.03.

(b) The standard normal table shows that approximately 40% of women have a z-score of 0.32 or higher. Hence, we can conclude that approximately 40% of women have "protective" levels of HDL.

(c) We know that approximately 13.5% of women have a z-score of -1.03 or lower and approximately 40% of women have a z-score of 0.32 or higher. Hence, the proportion of women in the intermediate range is

=> 100% - (13.5% + 40%) = 46.5%.

(d)  We can then convert this z-score back to the HDL level using the formula

=> x = mean + z-score * standard deviation.

Hence, the 75th percentile of the distribution of HDL for women is

=> 55 + 0.94 * 15.5 = 63.3 mg/dl.

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Answer:

139

Step-by-step explanation:

[tex]\frac{138+128+151}{3}[/tex]

[tex]\frac{417}{3}[/tex]

139

The area of this heptagon is equal to 455 square units.

Mathematically, the area of a regular polygon can be calculated by using this mathematical expression:

Area of the regular heptagon = 1/2 × n × s × r

Where:

Substituting the given parameters into the area of a regular polygon formula, we have the following;

Area of the regular heptagon = 1/2 × 7 × 10 × 13

Area of the regular heptagon = 455 square units.

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Step-by-step explanation: To solve the equation 2x(2x-5)=36, we first need to distribute the 2x:

2x(2x-5) = 2x * 2x - 2x * 5 = 4x^2 - 10x

Now that we have the expanded equation, we can set it equal to 36:

4x^2 - 10x = 36

Next, we'll isolate x by subtracting 36 from both sides:

4x^2 - 10x - 36 = 0

This is a quadratic equation, which we can solve using the quadratic formula or by factoring. Here's one way to solve it using factoring:

(2x-9)(2x+4) = 0

We can set each factor equal to zero and solve for x:

2x-9 = 0, so x = 9/2

2x+4 = 0, so x = -4/2 = -2

So x = 9/2 and x = -2 are the solutions to the equation 2x(2x-5)=36.

Using ax.plot(x, y, lw=2), where lw stands for line width and the value represents the desired line width, you can modify the line's width.

Ax.plot(x, y, lw=2), where lw stands for line width and the number after it denotes the desired line width, can be used to alter the line width. This gives you the option to change the line width to suit your tastes. For instance, you can set lw=4 to create a thicker line and lw=1 to create a thinner line. When you want to plot several lines on the same plot, each with a different width, this command is quite helpful. It can sometimes be helpful to make some lines thicker than others in order to emphasis them. Additionally, you can design aesthetically pleasing plots with regular line widths with this command.

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Answer:

52

Step-by-step explanation:

yes

A simple random sample of 500 voters would be an appropriate method for a pollster to use in this situation.

In this method, each voter in the town is assigned a unique identifier and a list of all unique identifiers is created. Then, using a random number generator or a random number table, 500 unique identifiers are selected and those individuals are surveyed.

This method ensures that each voter in the town has an equal chance of being selected, so that the sample is representative of the population of voters. It also eliminates any potential biases that may be introduced if the pollster were to select individuals based on certain criteria (such as age, gender, or location).

By using a random sample, the pollster can have a good estimate of the true population parameter (voter preferences) with a high degree of confidence.

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Answer:

length = 40 ft, width = 15 ft

Step-by-step explanation:

Since both rooms are rectangles, we know each side is the same as it's opposing side. So:

Alvin's bedroom perimeter = x+(x-25)+x+(x-25), which can be simplified to 4x+50

Simon's bedroom perimeter = (x+10)+2x+(x+10)+2x+(x+10), which can be simplified to 6x+20

Because the perimeters of the bedrooms are the same, we can set the equations equal to each other. So: 4x+50=6x+20

Then you solve the equation.

4x+50=6x+20

4x+(50-20)=6x(20-20)

4x+30=6x

(4x-4x)+30=(6x-4x)

30=2x

30/2=2x/2

15=x

Now that we know 15 = x, we can plug that in to the original length and width of Alvin's Bedroom:

Length = (x+25) = (15+25) ft = 40 ft

Width = x ft = 15 ft

Therefore, the length of Alvin's bedroom is 40 feet and the width of his bedroom is 15 feet.

At least 72 footprints to construct a 98% confidence interval with a margin of error of less than ±2.5 centimetres.

a. To construct a 95% confidence interval for the mean foot lengths of the adults who used the cave-dwelling, we can use the formula:

Mean ± Z × (Standard deviation/√n)

Where Z is the Z-score for a 95% confidence level (which is approximately 1.96), and n is the sample size.

So, the 95% confidence interval is:

24.8 ± 1.96 × (7.5/√30) = (23.38, 26.22)

This means that there is a 95% chance that the true mean foot length of the adults who used the cave-dwelling falls within the range of 23.38 cm to 26.22 cm.

The assumptions for constructing a confidence interval are that the sample is randomly selected, the sample is large enough (n > 30 is generally considered large enough), and the data is approximately normally distributed.

b. To calculate the sample size needed for a 98% confidence interval with a margin of error of less than ±2.5 centimetres, we can use the formula:

n = (Z^2 × Standard deviation^2)/margin of error^2

Where Z is the Z-score for a 98% confidence level (which is approximately 2.33), and the standard deviation is 7.5 cm.

So, the sample size needed is:

n = (2.33^2 × 7.5^2)/2.5^2 = 71.48

Since the sample size must be a whole number, we would need to analyze at least 72 footprints to construct a 98% confidence interval with a margin of error of less than ±2.5 centimetres.

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--The given question is incorrect; the correct question is

"Anthropologists have discovered a prehistoric cave dwelling that contains a large number of adult human footprints. To study the size of the adults who used the cave-dwelling, they randomly selected 20 of the footprints from the population of all footprints in the cave and measured the length of those footprints. Some statistics resulting from this random sample are as follows.

a. The anthropologists would like to construct a 95 per cent confidence interval for the mean foot lengths of the adults who used the cave dwelling. Construct that 95% confidence interval and interpret the confidence interval as it relates to the problem. (Hint: List out the steps of PANIC to help you through the process. Briefly list off and check the assumptions since you can use your notes on this assignment.)

b. If we assume that the standard deviation of footprints is, in fact, 7.5 centimetres, and we want to construct a 98% confidence interval with a margin of error of less than +2.5 centimetres, at least how many footprints will we need to analyze?"--

Based on the information on the graph, it can be inferred that the correct equation is y = 0.8x - 0.3, because if we replace the value of x with the different values shown on the graph, the position of the point coincides.

To identify the correct equation we must analyze the information in the graph. Once we analyze this information we can find the correct equation.

However, one way to check which is the correct equation is by substituting the value of x in all the equations until you find the one that gives a result with the correct values. According to this procedure, the correct option would be option B, as shown below:

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Answer:

To get back to sea level, the scientist must now rise a total of 19.2 feet. This is calculated by subtracting the total amount of feet she has descended (37.4 + 8.4 = 45.8 feet) from the total amount of feet she has traveled (37.4 + 19.8 + 8.4 = 65.6 feet). Therefore, 19.2 feet (65.6 - 45.8) must be ascended in order to reach sea level.

The multiplication of the mixed fraction results in 9 3/7.

A mixed fraction consists of a whole number together with its fractional part. It fractional part is known as an improper fraction which has a numerator and a denominator.

To solve the mixed fraction, we need to change the mixed fraction to an improper fraction, we have:

= ( (7*3) + 1)/7 × ((2*2) + 1)/2

= 21 +1)/7 × 5+1)/2

= 22/7 × 6/2

= 11/7 × 6/1

= 66/7

Converting from improper fractions back to whole numbers, we have:

= 9 3/7

Therefore, the multiplication of the mixed fraction results in 9 3/7.

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The Annual Interest is 2%.

Simple interest is the cost of borrowing money that does not take compounding into consideration. In other words, just the principal is affected by simple interest.

Given:

P = $600

As, The difference between the total interest earned after 5 years and the total interest earned after 3 years is $24.

I(5year) - I( 3 year)= 24

R/100 ( 600 x 5 - 3 x 100) = 24

R ( 3000 - 1800) = 2400

R = 2400 / 1200

R= 2%

Thus, the rate is 2%.

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The A ∩ B is = {3, 5, 7, 11, 13}

The correct option is (C)

Now, According to the question:

Prime Numbers:

A prime number is any positive integer greater than one whose factors are one and the number itself. If a number is not prime it is called a composite number or simply composites.

Odd positive integer:

An odd number is an integer which is not a multiple of 2. If these numbers are divided by 2, there will be a remainder left. In the number line, 1 is the first positive odd number.

Now, Solving the problem :

If A is the set of prime numbers less than 15, and g is the set of odd positive integers,

To find the A ∩ B

A = {2, 3, 5, 7, 11, 13}

B = {1, 3, 5, 7, 9, 11, 13, 15 }

Then, Intersection means (∩)

The intersection of a set A with a B is the set of elements that are in both set A and B. The intersection is denoted as A∩B.

A ∩ B = {3, 5, 7, 11, 13}

Hence, The A ∩ B is = {3, 5, 7, 11, 13}

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The new points after the translation are (1, 0) and (1, 4)

A translation of 3 units to the right and 2 units down, applied to a general point (x, y), gives:

(x + 3, y - 2)

Here we know that one line passes through the points (-4, 2) and (-4, 6). (so this is a vertical line)

If we apply the translation, we will get:

(-4 + 3, 2 - 2) = (1, 0)

(-4 + 3, 6 - 2) = (1, 4)

These are the new points of the line.

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The solution is Option A.

The system of equations is solved and the value of y = -5/9

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A is

x + 6y = 10   be equation (1)

Let the second equation be represented as B

Now , the value of B is

-x + 3y = -15   be equation (2)

On simplifying the equations , we get

Adding equation (1) and equation (2) , we get

6y + 3y = 10 - 15

9y = -5

Divide by 9 on both sides of the equation , we get

y = - ( 5/9 )

Substitute the value of y in equation (1) , we get

x - 30/9 = 10

Adding 30/9 on both sides of the equation , we get

x = 10 + 30/9

x = 120/9

Hence , the value of x and y are 120/9 and -5/9 respectively

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