5- When the equation x²- 6x + 9 = 49 is transformed into the equation
(x - p)² = q, what are the values for p and q?
A. -3 and 40
B. -3 and 49
C. 3 and 40
D. 3 and 49

The small two above the radical symbol indicates that the square root of a mathematical number or expression is being taken, which means that the number under the radical must be squared to obtain the original number

Therefore,the correct answer is True.

An expression is a mathematical phrase that combines numbers, variables, and operations to create a value. It can include arithmetic, algebraic, or trigonometric operations and may contain parentheses, exponents, or radicals.

The square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √ and is a type of radical.

According to the given information:

The correct answer is True.

The radical symbol, which looks like a division bar with a dot on top, is used to denote a root operation in mathematics. The index or degree of the root indicates the number of times the root must be multiplied by itself to obtain the number under the radical. In the case of the square root, the index is 2, which means that the number under the radical must be squared to obtain the original number.

Therefore, when the radical symbol has a small two above it, it is indicating that the square root of the number or expression below the radical is being calculated. The result of the square root operation is always a positive number, since the negative sign is indicated separately outside the radical symbol.

For example, the square root of 25 is written as √25 = 5, since 5 squared is equal to 25. Similarly, the square root of 4 is written as √4 = 2, since 2 squared is equal to 4.

In summary, the small two above the radical symbol indicates that the square root of a mathematical number or expression is being taken, which means that the number under the radical must be squared to obtain the original number.

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The radian measure of the central angle which intercepts the arc is 6.2 radians.

We can use the formula relating the arc length to the angle and radius of the circle:

arc length = radius x central angle in radians

Plugging in the given values, we get:

148.8 = 24 x central angle in radians

Solving for the central angle, we have:

central angle in radians = 148.8/24

central angle in radians = 6.2 radians

Therefore, the radian measure of the central angle which intercepts the arc is 6.2 radians.

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Answer:

Answers down below!

Step-by-step explanation:

Mean: 38.2

Median: 34

Range: 56

Mode: 13 and 34

Hope this helps!

In "Pointed Roofs," Dorothy Richardson makes use of conversation and stream of consciousness to improve her writing. Using stream of consciousness, in the given expert.

An excerpt is indeed a quotation from that other resource that the author introduces with fresh language in a sentence. This phrase is taken from Thomas Jefferson's 1801 inaugural speech: As he warned his audience, "I may often go wrong by defect of judgement," Jefferson admitted the fallibility of human nature. "I shall frequently err through lack of judgement" is the excerpt.

In "Pointed Roofs," Dorothy Richardson makes use of conversation and stream of consciousness to improve her writing. Using stream of consciousness, the author lets readers peek inside the protagonist, Miriam, to understand her feelings and thoughts as they happen. For instance, readers can feel Miriam's mild dizziness 

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The density of the milk is 1031.25 kg/m³.

Density refers to the mass of a unit volume of a material substance.

Density (ρ) = mass (m) / volume (V)

Given:

Volume (V) = 320cm³ = 0.00032m³

Mass (m) = 330g = 0.33kg

The Density (ρ) of the milk wll be:

= 0.33kg / 0.00032m³

= 1031.25 kg/m³

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The calculated value of the percent error of the measurement is 18.7%.

Percent error is calculated by subtracting the measured value from the actual value, dividing the result by the actual value, and then multiplying by 100 to get a percentage.

Using this formula, we have:

Error = Actual Value - Measured Value = 13.4 - 10.9 = 2.5

So, we have

Percent Error = (Error / Actual Value) * 100 = (2.5 / 13.4) * 100 ≈ 18.7%

Therefore, the percent error of the measurement is approximately 18.7%.

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Answer:

Step-by-step explanation: Multiplication first 7x1 = 7, Take 7 and divide it by 10 which gives you 0.7, Do the same but for the other 2 questions,

(9x1/100 = 0.09)

(9x1/1000 = 0.009)

(7x1/10 = 0.7)

Now take the answers and add them up

0.09 + 0.009 + 0.7 = 0.799

Answer: 0.799

The probability of having at least one faulty component in your selection is 0.41 or 41%.

The probability of having at least one faulty component in a selection of 5 can be found by calculating the probability of having no faulty components and then subtracting this from 1.

The probability of having no faulty components in a selection of 5 is:

P(no faulty) = (0.9)^5 = 0.59

Therefore, the probability of having at least one faulty component in a selection of 5 is:

P(at least one faulty) = 1 - P(no faulty) = 1 - 0.59 = 0.41

So the probability of having at least one faulty component in your selection is 0.41 or 41%.

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--The complete Question is, You randomly pick 5 components from the bag of 30. What is the probability that you have at least one faulty component in your selection? --

The Central Limit Theorem is an important tool that provides the information you will need to use sample means to make inferences about a population mean.

The Central Limit Theorem (CLT) is a fundamental theorem in statistics that states that if we take repeated random samples of size n from any population with a finite mean and variance, then the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the original population distribution.

This means that if we take a large enough sample size from a population, the distribution of the sample means will be approximately normal, even if the population distribution is not normal. This is important because the normal distribution is well understood and has many useful properties that make it easier to work with in statistical analyses.

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The probability of landing on a blue section on the spinner is 10/16, which simplifies to 5/8.

The probability of landing on a green section is 0/16, which simplifies to 0.

The probability of landing on a red section is 4/16, which simplifies to 1/4.

The probability of any event occurring is calculated by finding the total number of possible outcomes that would result in that event occurring, and then dividing that number by the total number of possible outcomes.

In this case, the total number of possible outcomes is 16, since there are 16 sections on the spinner.

The total number of outcomes that would result in a blue section being chosen is 10, since there are 10 blue sections on the spinner.

Dividing 10 by 16 gives us the probability of landing on a blue section, which is 5/8.

The same process is used to calculate the probabilities for green and red sections, with the only difference being that the number of sections for each color is different.

Since there are no green sections, the probability of landing on a green section is 0.

There are 4 red sections, so the probability of landing on a red section is 4/16, which simplifies to 1/4.

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Hence,The equation that models the height of the roller coaster is  [tex]x^{2} +y^{2}=900[/tex]. and solution of y =[tex]\sqrt{(900-x^{2})}[/tex].

A roller coaster, or roller coaster, is a type of amusement ride that employs a form of elevated railroad track designed with tight turns, steep slopes, and sometimes inversions. Passengers ride along the track in open cars, and the rides are often found in amusement parks and theme parks around the world.

We have given that ,

the Center the circle at the origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground.

we know that equation of circle ,

[tex]x^{2} +y^{2}=r^{2}[/tex]

Where r is the radius

From given we can say that the radius =30

since the radius is 30 ft

[tex]x^{2} +y^{2}=30^{2}\\x^{2} +y^{2}=900[/tex]

so, the equation that models the height of the roller coaster. [tex]x^{2} +y^{2}=900[/tex].

We have to find the equation that can be represent the height of the roller coaster so find the value of y

[tex]x^{2} +y^{2}=r^{2}[/tex]

⇒[tex]y^{2}=r^{2}-x^{2}[/tex]

⇒[tex]y^{2}=30^{2}-x^{2}[/tex]

⇒[tex]y^{2}=900-x^{2}[/tex]

⇒y =±[tex]\sqrt{(900-x^{2})}[/tex]

⇒y =[tex]\sqrt{(900-x^{2})}[/tex]   ∵according to question choose positive sign only

Therefore the models the height of the roller coaster y =[tex]\sqrt{(900-x^{2})}[/tex].

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Sampling methods that may be biased for finding the percentage of defective boards in a sawmill production are: selecting 30 consecutive boards, emailing customers and relying on their responses, and selecting every 40th board produced. So, the correct answer is A, B and D.

The biased sampling methods are Examining 30 consecutive boards one hour after production begins may be biased because it only captures a snapshot of the production at that specific time, and the boards selected may not be representative of the entire batch produced during the day.

Emailing customers to ask about defective boards may be biased because the response rate may vary among customers, and customers who experienced a higher or lower number of defective boards may be more likely to respond.

Selecting 20 boards at random each day for 5 days and examining them is less likely to be biased, as long as the selection process is truly random and representative of the entire production.

Selecting every 40th board produced over the course of one week is also less likely to be biased if the production process is consistent and there are no patterns or variations in the production that would affect the quality of every 40th board. So, the correct answer for biased is A, B and D.

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The areas of the composite figures are listed below:

Case 6: A = 134.126 ft²

Case 7: A = 212.5 cm²

Case 8: A = 957.305 m²

Case 9: A = 316.643 in²

In this problem we find four cases of composite figure, that is, figures that are the result of adding and subtracting figures, whose area formulas are introduced below:

Semicircle

A = 0.5π · r²

Circle

A = π · r²

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Where:

Now we proceed to determine the area of each composite figure:

Case 6

A = (25 ft)² - π · (12.5 ft)²

A = 134.126 ft²

Case 7

A = (25 cm) · (14 cm) - 0.5 · (25 cm) · (11 cm)

A = 212.5 cm²

Case 8

A = 0.5π · [(21.6 m)² + (9 m)²] + 0.5 · (21.6 m) · (9 m)

A = 957.305 m²

Case 9

A = 0.5 · (20 in) · √[(25 in)² - (20 in)²] + (17 in) · √[(25 in)² - (20 in)²] - 0.5π · 0.25 · [(25 in)² - (20 in)²]

A = 316.643 in²

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The area of the plot of land that has a top view as shown on a map above is calculated as: C. 112 square meters

The shape of the plot of land can be decomposed into two different triangles and 1 rectangle.

Area of triangle 1 = 1/2 * base * height

base = 8 m

height = 5 m

Area of triangle 1 = 1/2 * 8 * 5 = 20 square meters

Area of triangle 2 = 1/2 * base * height

base = 8 m

height = 7 m

Area of triangle 2 = 1/2 * 8 * 7 = 28 square meters

Area of the rectangle = length * width = 8 * 8

= 64 square meters.

Therefore, we have:

Area of the plot of land = 64 + 28 + 20

= 112 square meters.

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The coordinates of point U are (-h, 0).

To find the coordinates of point U in the parallelogram RSTU, we can use the properties of parallelograms. In a parallelogram, opposite sides are parallel, and hence they have the same slope.

Given that point S is at (0, 0), we can calculate the slope of RS as follows:

Slope of RS = (y2 - y1) / (x2 - x1)

= (0 - g) / (0 - (-f)) (Substituting coordinates of R and S)

= g / f

Since RS and TU are opposite sides of the parallelogram, they must have the same slope. Thus, the slope of TU is also g / f.

Given that point T is at (h, 0), we can calculate the equation of the line TU in point-slope form using the slope we just found:

y - y1 = m(x - x1) (Point-slope form of a line)

where;

Plugging in the values, we get:

y - 0 = (g / f)(x - h)

Simplifying, we get:

y = (g / f)x + gh / f

Now, we can substitute the coordinates of point U, which are (x, y), into the equation we just found:

y = (g / f)x + gh / f

y = (g / f)x + gh / f

Since U lies on the x-axis (i.e., y = 0), we can set y = 0 in the equation and solve for x:

0 = (g / f)x + gh / f

(g / f)x = -gh / f

x = -h

So, the x-coordinate of point U is -h.

Now, we can substitute the value of x = -h into the equation we found earlier to get the y-coordinate of point U:

y = (g / f)x + gh / f

y = (g / f)(-h) + gh / f

y = -gh / f + gh / f

y = 0

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Answer:

Step-by-step explanation:

Let X be the number of adults who had their faces painted.

Therefore, the number of kids who had their faces painted is 8*X.

Given that 56 kids had their faces painted, we can write an equation as:

8*X = 56

Solving for X:

X = 7

So, there were 7 adults who had their faces painted and 56 kids who had their faces painted.

Altogether, there were 7 + 56 = 63 people who had their faces painted.

The expression that is equivalent by the Distributive Property is A 3x+12

this is the only answer that actually uses the distributive property.

The Distributive Property is a mathematical rule that applies to operations such as multiplication and addition or subtraction. It states that when you multiply a number by a sum or difference of two or more numbers, you can distribute the multiplication over each of the individual terms in the sum or difference.

3 can be multiplied by both x and 4 to get 3x+12 (which is using the distributive property)

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There are 36 ways to arrange the letters d, i, g, i, t so that the two i's are not next to each other.

To find the number of ways the letters d, i, g, i, t can be arranged so that the two i's are not next to each other, follow these steps:
Consider the four non-i letters: d, g, t.

There are 3! (3 factorial) ways to arrange these letters, which is equal to 3 x 2 x 1 = 6 ways.

Since we want to prevent the two i's from being next to each other, we can think of placing them in the "gaps" between the non-i letters.

There are 4 possible gaps for the i's to be placed: (i) d (i) g (i) t (i).
Since there are two i's, we need to choose 2 of the 4 gaps to place them in.

This can be done in 4C2 ways (combination), which is equal to 4! / (2! x (4-2)!) = 6 ways.
Multiply the number of ways to arrange the non-i letters (step 1) with the number of ways to place the i's (step 3): 6 x 6 = 36.

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There are 72 ways to arrange the letters d, i, g, i, t so that the two i's are not next to each other.

To arrange the letters d, g, i, t, and i so that the two i's are not next to each other, follow these steps:

Step 1: Treat the two i's as one entity for now (denoted as [i]). So, we have 4 entities: d, g, t, and [i].
Step 2: Arrange these 4 entities (d, g, t, and [i]) in any order. There are 4! (4 factorial) ways to do this, which is 4 x 3 x 2 x 1 = 24 ways.
Step 3: Now, we need to separate the two i's. There are 3 spaces between the other letters (d, g, and t) where we can place the second i.
For example: if the arrangement is d-[i]-g-t, the second i can be placed in any of the three spaces indicated by the dashes.
Step 4: For each of the 24 arrangements from Step 2, there are 3 possible ways to place the second i. So, the total number of arrangements is 24 x 3 = 72 ways.

Thus, there are 72 ways to arrange the letters d, i, g, i, t so that the two i's are not next to each other.

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(a) To solve this problem, we need to apply the concept of combinations.  We can find the total number of combinations by using the formula:

nCr = n! / r!(n-r)!

where n is the total number of objects, r is the number of objects we want to select.

Let's assume that we have x pennies, y nickels, z dimes, and w quarters. Since we want to select 25 coins, we can write the equation as x + y + z + w = 25

To find the number of ways to select 25 coins, we need to find the number of solutions to this equation. The total number of combinations is given by: (25 + 4 - 1)C(4 - 1) = 28C3

where we have 25 coins to select and four piles to choose from. Thus, the answer is 28C3.

(b) To solve this problem, we need to use the concept of counting with restrictions. Since we must select at least 5 quarters, we can assume that we have selected 5 quarters and we need to select the remaining 20 coins from the remaining piles. Let's assume that we have x pennies, y nickels, and z dimes. We can write it as x + y + z = 20

To find the number of ways to select 20 coins from the remaining piles, we can use the concept of combinations. The total number of combinations is (20 + 3 - 1)C(3 - 1) = 22C2

Thus, the total number of ways to select 25 coins with at least 5 quarters is given as 10C5 x 22C2

where we have selected 5 quarters from 10 quarters and 20 coins from the remaining piles.

(c)To solve this problem, we need to use the concept of counting with restrictions. Since we can select at most 10 quarters, we need to consider two cases:

(i) We select 10 quarters, and we need to select 15 coins from the remaining piles.

For case (i), we need to select 15 coins from the remaining piles. We can assume that we have x pennies, y nickels, and z dimes. We can write the equation as x + y + z = 15

The total number of ways to select 15 coins is (15 + 3 - 1)C(3 - 1) = 17C2

(ii) We select fewer than 10 quarters, and we need to select the remaining coins from the piles.

For case (ii), To calculate the number of ways, we can use the combination formula to select i quarters out of 10, where i can vary from 0 to 9, and select the remaining (25-i) coins from the remaining piles. We can then sum up the number of ways for all possible values of i to get the total number of ways to select 25 coins with at most 10 quarters.

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Answer:

Mrs. Ades is not being fair. The probability of Elias and Maha getting chosen should be equal, but Elias has a 6/10 chance of being chosen, while Maha only has a 4/10 chance of being chosen. This is because Elias has 6 tiles assigned to him, while Maha only has 4 tiles assigned to her.

Explanation:

To make it fair, Mrs. Ades should assign each person an equal number of tiles, or draw from a bag with the tiles numbered 1 through 5 twice, assigning one to Elias and one to Maha each time, and then draw from a bag with tiles numbered 6 through 10 twice, assigning one to Elias and one to Maha each time.

12) There were about 557 principals in attendance. 13) Option A: The college will have about 480 students who prefer cookies. 14) Option C: bar graph, title favorite sport and the x axis labeled sport and the y axis.

The relationship between two quantities that are measured on the same scale and in the same units is known as a percentage. The relative size or magnitude of one thing in comparison to another is represented by proportions, which are frequently stated as ratios, fractions, or percentages. For instance, if there are 8 girls and 12 boys in a class, the girl-to-boy ratio is 8:12, or 2:3, which indicates that there are 3 guys for every 2 girls. Statistics, geometry, and physics are just a few of the mathematical and scientific disciplines that use proportions. Proportions are frequently used in statistics to describe the distribution of a population or a sample.

12) For the number of principals in conference we set up a proportionality with total people as follows:

We know that, 52 principals out of 70 people thus:

52/70 = x/750

Now,

x = (52/70) * 750

x = 557.14

Hence, we can predict that there were about 557 principals in attendance at the conference.

13) Given that, out of 225 students 27 prefer cookies thus,

27/225 = 0.12

That is 12% students like cookies.

Now, for the total number of students we have:

0.12 * 4000 = 480

Thus, option A: The college will have about 480 students who prefer cookies.

14) For the collected data the best representation is option C: bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44.

15) For the given description of the line plot the median is:

For Bus 47 = 16

For Bus 18 = 13

The faster bus is Bus 47, with a median of 16.

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There are 813 minutes in between 17:53 to 7.26 .

Time can be represented in two formats, that is in a twelve - hour format and in a twenty four - hour format.

Here the time 17:53 and 7:26 is represented in twenty four - hour format where the day is divided in twenty four hours and time runs from midnight and ends at midnight.

(If the time 17:53 and 7:26 was represented in twelve - hour format then it would have AM and PM to denote if the time is from midnight till noon or noon till midnight, which is clearly not the case.)

Thus, from 17:53 to 7.26 there is 13 hours and 33 minutes.

We know one hour has 60 minutes. Therefore by method of conversion of hours to minutes we get,

Number of minutes between 17:53 to 7.26 = {(13*60) + 33} = 780+33 = 813

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If cash is  54 one-dollar bills, 12 five-dollar bills, and 6 ten -dollar bills, the total deposit is $454.00.

To find the total deposit, we need to add up the amounts from the checks and cash, and then subtract the cash received.

First, let's add up the amounts from the checks:

$152.54 + $147.46 = $300.00

Next, let's add up the amounts from the cash:

54 one-dollar bills = $54.00

12 five-dollar bills = $60.00

6 ten-dollar bills = $60.00

Total cash = $174.00

Finally, we need to subtract the cash received:

$174.00 - $20.00 = $154.00

Therefore, the total deposit is $300.00 + $154.00 = $454.00.

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Complete question is:

Find the total deposit if you have: Checks: $152.54 and $147.46: cash: 54 one-dollar bills, 12 five-dollar bills, and 6 ten -dollar bills; less $20.00 as cash received.

Answer:62.5

Step-by-step explanation:

Answer: The answer is 84

The total of the angels of the triangle always equals 180. So 62+34=96 therefor 96-180=84.

There seems to be an error in the expression for P3(x). It appears to be missing an exponent for the second term.

Assuming that the correct expression is P3(x) = x^4 - 21x^2 + 20x, we can analyze its properties.

The degree of the polynomial P3(x) is 4, which means its graph will have at most 4 x-intercepts and at most 3 turning points.

To find the x-intercepts, we set P3(x) equal to zero and solve for x:

x^4 - 21x^2 + 20x = 0

x(x^3 - 21x + 20) = 0

Using the factor theorem or synthetic division, we can find that x = 0 is a root of the polynomial, so (x-0) is a factor. The remaining cubic factor can be factored as (x-1)(x-4)(x+5).

Therefore, the x-intercepts of the graph of P3(x) are x = 0, x = 1, x = 4, and x = -5.

As for the y-intercept, we can find it by setting x = 0:

P3(0) = 0^4 - 21(0)^2 + 20(0) = 0

So the y-intercept is (0,0).

To determine the turning points, we can find the critical points by taking the derivative of P3(x) and setting it equal to zero:

P3'(x) = 4x^3 - 42x + 20

4x^3 - 42x + 20 = 0

Solving this equation yields three critical points: x ≈ -1.23, x ≈ 0.58, and x ≈ 2.65.

We can use the second derivative test to determine the nature of these critical points. The second derivative is:

P3''(x) = 12x^2 - 42

At x ≈ -1.23 and x ≈ 2.65, the second derivative is negative, indicating that these are local maxima. At x ≈ 0.58, the second derivative is positive, indicating that this is a local minimum.

Therefore, the graph of P3(x) has a local maximum at (approximately) (-1.23, P3(-1.23)), a local minimum at (approximately) (0.58, P3(0.58)), and a local maximum at (approximately) (2.65, P3(2.65)).

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The volume of cone as per given figure is 314cm³.

The following mathematical operation must be carried out in order to determine a cone's volume: V = Π(h/3)r². The surface area of the circular portion of a cone is simply πr2. The lateral face wrapping around this base is calculated as πrl, or if you aren't given the slant height, you can use the formula πr√(r2+h2).

To calculate the volume of a cone, we apply the following formula:

, where V = volume

h = height

r = radius

π = pi

(h = height of cone, r= radius of cone)

Given:

Height of cone = 12 cm

Radius of cone = 5 cm

Volume of cone, V =  3.14 * (12/3 )* 5* 5

= 3.14 * 20 * 5

= 3.14 * 100

= 314 cm³

Therefore, The volume of cone as per given figure is 314cm³.

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