Similar triangles ABE and BCD are shown on the coordinate plane

a) A function f is a rule that assigns to each element x in a set A exactly one element called f(x) in a set B.

b) Both tables define y as a function of x, but they have different domains and ranges

Both tables represent functions because they assign each value of x in the domain to a unique value of y in the range.

First table

f(1) = 5

f(2) = 7

f(3) = 6

f(4) = 8

Second table

f(1) = 5

f(2) = 1

f(3) = 7

f(4) = 6

f(5) = 8

So both tables define y as a function of x, but they have different domains and ranges. The first table has a domain of {1, 2, 3, 4} and a range of {5, 6, 7, 8}, while the second table has a domain of {1, 2, 3, 4, 5} and a range of {1, 5, 6, 7, 8}.

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Let's simplify the given equation step by step to solve for b:

2(b + 5) / (6b² - 3) = 5 + 7b - 1

First, we can simplify the right-hand side by combining like terms:

2(b + 5) / (6b² - 3) = 7b + 4

Next, we can cross-multiply to get rid of the fraction:

2(b + 5) = (7b + 4)(6b² - 3)

Expand the right-hand side using the distributive property:

2(b + 5) = 42b³ + 19b - 12

Simplify the left-hand side by distributing the 2:

2b + 10 = 42b³ + 19b - 12

Move all the terms to one side of the equation:

42b³ - 2b + 19b - 12 - 10 = 0

Combine like terms:

42b³ + 17b - 22 = 0

We can solve for b using numerical methods, such as the Newton-Raphson method or the bisection method. However, there is no exact algebraic solution for b in this case.

If A (3, 5), B (-2, 6), and C (0, 16) are the vertices of a triangle, then the slope of the segment AC is -11/3

To find the slope of segment AC, we need to calculate the change in the y-coordinates divided by the change in the x-coordinates of the two endpoints A and C.

The change in the y-coordinates between A and C is

yC - yA = 16 - 5 = 11

The change in the x-coordinates between A and C is

xC - xA = 0 - 3 = -3

Therefore, the slope of segment AC (mAC) is

mAC = (yC - yA) / (xC - xA) = 11 / (-3) = -11/3

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The causes of variation which are large in magnitude and are not part of the normal variation are known as Outliers.

What is an Outlier? An outlier is a value that is far greater or less than the majority of other values in a given dataset. These may be due to a variety of factors, including statistical errors or data entry mistakes, but they may also represent actual phenomena that have an impact on the overall results. These causes are not typically part of the normal variation of the process. Thus, outliers are not considered a part of the normal variation.

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Each term in the second sequence is one-third of the corresponding term in the first sequence and is the statement that correctly describes the relationship between these two sequences: 18, 21, 24, 27, 30 and 6, 7, 8, 9, 10.

Each term in the second series is one-third of the equivalent term in the first sequence, which is the right way to characterize the relationship between the two sequences.

This means that for each term in the second sequence (6, 7, 8, 9, 10), the corresponding term in the first sequence (18, 21, 24, 27, 30) is three times larger. For example, the first term in the second sequence (6) is one-third of the first term in the first sequence (18), and the second term in the second sequence (7) is one-third of the second term in the first sequence (21), and so on.

It is important to note that the statement "Each term in the first sequence is double the corresponding term in the second sequence" is not correct, as this relationship does not exist between the two sequences.

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Answer:

the probability of the complement of rolling a number less than 5 by using a six-sided die is 1/3.

Step-by-step explanation:

Given that a fair die is rolled. We know there are six numbers in a fair die.On rolling a die, the Sample space of the given event E = {1, 2, 3, 4, 5, 6}Sample space of numbers less than 5 = {1, 2, 3, 4}Clearly we can see that the number of favorable outcomes = 4Hence, P(values less than 5) = 4/6 = 2/3.To find the complement of rolling a number less than 5, we use the formula P' = 1 - P, where P' is the complement of P.So, let P' be the complement probability of getting numbers less than 5Now, P'(numbers less than 5) = 1 - P(numbers less than 5)= 1 - 2/3= 1/3.Hence, the probability of the complement of rolling a number less than 5 by using a six-sided die is 1/3.

Answer:

1/3

Step-by-step explanation:

This means that, the dice can be rolled at value from 1-4 and there are 6 numbers so it would be 4/6 simplified 2/3. Now subtract that value from 1 and you get 1/3

Eequation of the tangent line (b) at the given point P.

y + 5¹/² = (1/2) * (-5)⁻¹/² * (x + 5)

To find the slope of the curve at the given point P, we'll first differentiate the function y with respect to x.

Given function: y = x¹/²

Step 1: Differentiate y with respect to x.
dy/dx = (1/2) * x¹/²

Step 2: Plug in the x-coordinate of the point P into the derivative to find the slope at P.
P = (-5, -5¹/²)

dy/dx at P = (1/2) * (-5)⁻¹/²

Slope (a) = (1/2) * (-5)⁻¹/²

Now, we will find the equation of the tangent line at P.

Step 3: Use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point P.

y - (-5¹/²) = (1/2) * (-5)⁻¹/²(x - (-5))

Step 4: Simplify the equation.

y + 5¹/² = (1/2) * (-5)⁻¹/² * (x + 5)

This is the equation of the tangent line (b) at the given point P.

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Check the picture below.

[tex]\cfrac{\sin(15^o)}{9}=\cfrac{\sin(B)}{12}\implies \cfrac{12\sin(15^o)}{9}=\sin(B)\implies \sin^{-1}\left( \cfrac{12\sin(15^o)}{9} \right)=B \\\\\\ 20.19^o\approx B\hspace{12em}\stackrel{180-20.19-15}{C\approx 144.81^o} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(15^o)}{9}=\cfrac{\sin(144.81^o)}{c}\implies c=\cfrac{9\sin(144.81^o)}{\sin(15^o)}\implies \boxed{c\approx 20.0}[/tex]

A number whose value increases from 15 to 60, the percentage by which the number increases is equal to 300 percent.

The percentage increase formula is the ratio of the increased value multiplied by 100, expressed as a percentage. If the value of something increases, the percentage increases. Mathematically, Percentage increase = (Increase in number/Original number)×100

We have a number value which increased from 15 to 60. We have to determine percentage increase. Now, the original number = 15

final number = 60

Increase in number value = Final Value - Initial Value = 60 - 15 = 45

So, Percentage increase in number value

= (45/15) × 100

= 3 × 100 = 300

Hence, required value is 300%.

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Answer:

1,460

Step-by-step explanation:

Option D will result in an image that is rotated 180 degrees equation counterclockwise about the origin and then reflected across the y-axis, which will not map the image onto itself.

Counterclockwise, also known as anticlockwise, is a direction of rotation that is opposite to the direction in which the hands of a clock move. It is the direction that is typically associated with the rotation of objects in the Northern Hemisphere.

counterclockwise rotation is the positive direction of rotation in a coordinate system, where the x-axis increases to the right and the y-axis increases upwards.

Option B, "Reflect over the y-axis, and then reflect again over the y-axis," will result in an image that maps onto itself.

When you reflect an image over the y-axis, the left and right sides of the image switch places. If you then reflect the already reflected image over the y-axis again, the left and right sides switch places once more, effectively returning the image to its original orientation.

Option A will result in an image that is rotated 180 degrees counterclockwise about the origin and then reflected across the x-axis, which will not map the image onto itself.

Option C will result in an image that is reflected over the y-axis and then reflected over the x-axis, which will produce an image that is flipped both horizontally and vertically and therefore not map the image onto itself.

Option D will result in an image that is rotated 180 degrees counterclockwise about the origin and then reflected across the y-axis, which will not map the image onto itself.

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Answer:

Option B i think

Step-by-step explanation:

hope this helps

The predicted sales for spending $275,000 on advertising is $65,250. This linear regression shows a positive correlation between the advertising dollars spent and the sales.

It is used to predict the value of a dependent variable based on the values of the independent variables.

The equation for the regression line is y = 0.15x + 24,000, where x is the advertising dollars spent and y is the sales.

Substituting $275,000 for x, we get

y = 0.15(275,000) + 24,000

= 41,250 + 24,000

= 65,250.

Therefore, the predicted sales for spending $275,000 on advertising is $65,250.

This linear regression shows a positive correlation between the advertising dollars spent and the sales. This means that as the advertising dollars increase, the sales will increase as well. The regression line also shows that if the company were to double its advertising dollars, the sales would also double. This indicates that the company is getting a good return on investment for their advertising dollars.

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Answer:

It is 2 units

Step-by-step explanation:

If the difference between the number of dots in each term is 8, it means that the number of dots in each successive term is increasing by 8.

If you have a sequence or pattern in which the difference between the number of dots in each term is 8, it means that the number of dots in each successive term is increasing by 8.

For example, if the first term has 5 dots, the second term would have 5 + 8 = 13 dots, the third term would have 13 + 8 = 21 dots, and so on. The difference between the number of dots in each term is always 8 because the pattern or sequence is increasing by 8 dots each time.

It is important to note that this is just one example of a pattern in which the difference between the number of dots in each term is 8. There can be many different patterns or sequences that exhibit this property, and the specific details will depend on the problem or context.

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The number of total kids at Lincoln's school, considering the proportions, is given as follows:

775 kids.

The total number of kids at the Lincoln school is obtained applying the proportions in the context of the problem.

40% of all the Lincoln students participated in the St. Baldrick's event, and this percentage is equivalent to a total of 310 kids.

Hence the number of total kids at Lincoln's school is obtained applying the proportion as follows:

0.4n = 310

n = 310/0.4

n = 775 kids.

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(A) The normal approximation to the binomial to approximate the probability that at least 99 99 respondents live at​ home is 84.21%

(B) The probability that 16 or more out of 19 community college male students live at home is 0.0037.

In algebra, a binomial is an expression in which two distinct terms are joined by an addition or subtraction operator. For example, 2xy + 7y is a binomial because there are two terms. Algebraic expressions can be classified into different types based on the number of terms that appear, such as monomial, binomial, trinomial, etc.

(a) Based on the sample of 19 students, the proportion of community college males live at home:

p = 16/19= 0.8421 or 84.21%.

(b) the probability that 16 or more out of 19 community college male

students live at home, assuming that the proportion who live at home is 52%. Using binomial distribution with parameters

n = 19, p = 0.52, q = 1-p = 0.48,

The probability that 16 or more out of 19 community college male students live at home is

P (16 or more) = P19 (16)+ P19 (17)+ P19 (18)+ P19 (16)=

= C₁₉ ¹⁶P Q³ + C₁₉ ¹⁷P Q² + C₁₉ ¹⁸P Q¹ + C₁₉ ¹⁸P Q⁰= 0.0037.

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The price of a ticket for a matinee movie is $9.

Let's use the variable "e" to represent the price of an evening movie ticket, and "m" to represent the price of a matinee movie ticket.

We know that the evening ticket is 1.5 times more expensive than the matinee ticket, which means

e = 1.5m

We also know that the cost of an evening ticket is $13.50, so we can substitute that value into our equation

13.50 = 1.5m

Now we can solve for m

m = 13.50 / 1.5

Divide the numbers and find the value of m

m = $9

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Answer:

85 - 4x < 40

12 cars

Step-by-step explanation:

He starts with 85 wheels, so the inequality starts with 85.

85 -

He then subtracts 4 wheels for each car he builds.

He builds x cars, and each car uses 4 wheels, so he subtracts 4x from 85.

85 - 4x

The number of wheels he has after building x cars, is

85 - 4x

He orders more wheels when the number of wheels is less than 40.

85 - 4x < 40   <------------ This is the inequality

Now we solve the inequality for x, the number of cars.

85 - 4x < 40

Subtract 85 from both sides.

-4x < -45

Divide both sides by -4. Remember that when you multiply or divide an inequality by a negative number, the inequality sign changes direction.

-4x/(-4) > -45/(-4)

x > 11.25

Since the number of cars must be a whole number, we round up to 12.

Check:

After he builds 12 cars, he uses 4 × 12 = 48 wheels.

85 - 48 = 37

That is the highest number of wheels less than 40 that he can have before ordering ore wheels.

12 is correct.

[tex]\displaystyle\large\sf\mapsto{ CP = ₹60000 }[/tex]

[tex]\displaystyle\large\sf\mapsto{ Total \: CP = ₹ 60000 + 5000 }[/tex]

We know that,

[tex]\displaystyle\large\sf\mapsto{CP = CP + Overhead \: expenses}[/tex]

[tex]\displaystyle\large\sf\mapsto{ Total \: CP = ₹ 65000}[/tex]

Now,

[tex]\displaystyle\large\sf\mapsto{ SP = CP × \frac{(100 - loss \% )}{100} }[/tex]

[tex]\displaystyle\large\sf\mapsto{ \: ₹ 65000 \times \frac{(100 - 30)}{100} }[/tex]

[tex]\displaystyle\large\sf\mapsto{ \: ₹ 650 \cancel{00 } \: \times \frac{70}{1 \cancel{00}} }[/tex]

[tex]\displaystyle\large\sf\mapsto{ \: ₹ 650 \times 70} \\ \\ \displaystyle\large\sf\mapsto{ \: = ₹ 45500}[/tex]

Thus,

[tex]\displaystyle\large\bf\red{ \mapsto{selling \: price \: = ₹ 45500}}[/tex]

[tex] \green {\rule{200pt}{4pt}}[/tex]

28.26 inches of wax is needed to make a candle.

What is the volume of a cylinder?

The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula πr2h where r is the radius of the circular base and h is the height of the cylinder determines the volume of a cylinder.

Here, we have

Given: Sean uses a candle mold to make candles that are perfect cones. the diameter of the cone is 6 inches with a height that is half as long as the diameter.

The volume of cylinder =  π · r² · h

r = 3 inches

h = 3 inches

= π  (3)² · 3

= 27π

Volume of sphere = 4/3πr³

= 4/3π(3)³

= 36π

Total volume = 36π - 27π

= 9π  = 9×3.14 = 28.26

Hence, 28.26 inches of wax is needed to make a candle.

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The number of ounces per golf ball is 1.6

The number of golf balls per ounce is 0.625

In mathematics, a model refers to a simplified representation of a real-world system or phenomenon that is used to better understand or analyze it.

Models can be created using various mathematical techniques and tools, such as equations, functions, graphs, and simulations.

Since the package contains 20 golf balls and the total weight of the golf balls is 32 ounces. We can say:

The number of ounces per golf ball = 32/20 = 1.6

The number of golf balls per ounce = 20/32 = 0.625

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The best way to ensure that conclusions can be generalized to the whole is random sampling; population in survey research. The correct answer is c. Random sampling; population

Random sampling means that a representative sample of the population is chosen and the results of the study can be applied to the population as a whole.
Random sampling is a sampling technique that is used to create a sample from a larger population. Each member of the population has an equal chance of being selected in random sampling.

Survey research is a quantitative research technique that collects information from a representative sample of a population. This research technique can be used to collect data from respondents by asking questions on a pre-determined topic or topics.

In survey research, random sampling is one of the best ways to ensure that conclusions can be generalized to the whole population. In this process, each member of the population is given an equal opportunity to be included in the sample. This approach lowers the possibility of sampling error and ensures that the results are more accurate and reliable.

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Answer:

To find the equation of the linear function, we need to find the slope and y-intercept of the line passing through the given points. The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:

slope = (y2 - y1)/(x2 - x1)

Using the given points (0,12) and (1,3), we can calculate the slope as:

slope = (3 - 12)/(1 - 0) = -9

To find the y-intercept, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is one of the given points. Using the point (0,12), we get:

y - 12 = -9(x - 0)

Simplifying, we get:

y = -9x + 12

Therefore, the equation of the linear function that passes through the points (0,12) and (1,3) is:

y = -9x + 12

Exponential function:

To find the equation of the exponential function, we can use the general form of an exponential function:

y = a*b^x

where a and b are constants. We can use the given points to form a system of equations to solve for a and b.

Using the point (0,12), we get:

12 = ab^0

12 = a1

a = 12

Using the point (1,3), we get:

3 = 12b^1

3 = 12b

b = 1/4

Therefore, the equation of the exponential function that passes through the points (0,12) and (1,3) is:

y = 12*(1/4)^x

The numbers that correctly complete the table about the experimental probability and number of pairs are 0.5, 25, 0.17, and 8.

Experimental probability for the black socks:

We know that in a total of 12 attempts 6 pairs were black, let's calculate the probability:

x = 6 x 1 /12 = 0.5

This number also indicates the total number of attempts was 10.

The number of brown pairs:

Total attempts x probability: 100 x 0.25 = 25

Experimental probability for the white socks:

x = 2 x 1/12 = 0.166 which can be rounded as 0.17

The number of striped pairs:

100 x 0.08 = 8

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Answer:

according to my equation it is 61.6

Step-by-step explanation:

The percentage by which the price of chicken parmesan will increase is 153.76%.

Food cost is defined as the cost of ingredients and raw materials that are required to make a dish. Food cost is also known as menu cost or recipe cost.

Menu pricing strategy determines the selling price of a dish or menu item. To price the menu, the food cost is usually divided by the desired percentage of profit. Let's solve the problem using the following formula:

Menu Price = (Food Cost ÷ Desired Percentage Markup) + Food Cost

Given, Price for chicken parmesan = $11.99

Food cost for this item = $4.31

New menu price will be 30% of the food cost.

Menu Price = (30% × 4.31) + 4.31= 1.293 + 4.31= 5.6033 ≈ $5.60

The percentage increase in the price of chicken parmesan is given by the following formula:

Percentage increase = (New Price - Old Price) / Old Price × 100%

Percentage increase = (5.60 - 11.99) / 11.99 × 100%

Percentage increase ≈ -53.76%

This is a negative value which implies that the price is decreased instead of increasing. So we have to add the absolute value of the percentage increase to 100% to get the actual percentage increase.

Percentage increase = 53.76% + 100%

Percentage increase = 153.76%

So, the percentage by which the price of chicken parmesan will increase is 153.76% rounded to two decimal places .

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When a figure is rotated counterclockwise about the origin, its original coordinates of point P [tex](x,y)[/tex] will now be positioned as P' [tex](-y,x)[/tex].

[tex]\text{X} \ (1,-1) \longrightarrow \text{X'} \ (1,1)[/tex]

[tex]\text{Y} \ (3,4) \longrightarrow \text{Y'} \ (-4,3)[/tex]

[tex]\text{Z} \ (5,-1) \longrightarrow \text{Z'} \ (1,5)[/tex]

The correct set of image points for triangle [tex]\text{X'Y'Z'}[/tex] is [tex]\text{X'}(1,1)[/tex], [tex]\text{Y'}(-4,3)[/tex], and [tex]\text{Z'(1,5)}[/tex].

Answer: 5188.04 miles (2 d.p.)

Step-by-step explanation:

Work out how many kilometres she travels in 5 hours

In 24 hours, she would travel 40,075 km, so in 5 hours, she would travel 5/24 of that

5/24 × 40075 = [tex]8348\frac{23}{24}[/tex]

Now work out how many miles that is

[tex]8348\frac{23}{24}[/tex] × 0.6214 = 5188.04 miles (2 d.p.)

A person at the equator would travel approximately 5,187.7 miles in five hours.

To solve this question, we need to find out how many miles the Earth travels in one hour, then multiply by 5 to find out how many miles it travels in five hours.

Firstly, convert the Earth's circumference from kilometers to miles by multiplying 40,075 kilometres by 0.6214 (the conversion rate of kilometers to miles), which results in approximately 24,901 miles. This is the distance the equator travels in one day.

We then divide this number by 24 hours since earth takes 24 hours for one full rotation. This equals approximately 1,037.54 miles per hour.

Last step is to multiply this value by 5 hours. This would result in 5,187.7 miles. So, a person standing at the equator would travel approximately 5,187.7 miles in five hours.

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The values of the sides PQ and QR are 2 and 2√3 respectively using the trigonometric ratio of cosine and sine 60° for the right triangle PQR.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

recall that cos 60° = 1/3 and sin 60° = √3/2

cos 60° = PQ/4 {adjacent/hypotenuse}

1/2 = PQ/4

PQ = 4 × 1/2 {cross multiplication}

PQ = 2.

sin 60° = QP/4 {opposite/hypotenuse}

√3/2 = QP/4

QP = 4 × √3/2

QP = 2√3

Therefore, the values of the sides PQ and QR are 2 and 2√3 respectively using the trigonometric ratio of cosine and sine 60° for the right triangle PQR.

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Answer:

(-1;5)

Step-by-step explanation:

I added a photo with my solution