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The binomial (x+5) is a factor of x² + 8x + 15 then the other factor is x+3.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

Given that binomial  (x+5) is a factor of x² + 8x + 15.

We need to find the other factor.

Let us solve x² + 8x + 15=0

x² + 5x +3x+ 15=0

x(x+5)+3(x+5)=0

(x+3)(x+5)

So the other binomial factor is x+3.

Hence, the binomial (x+5) is a factor of x² + 8x + 15 then the other factor is x+3.

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a) (f ∘ g)(4) = 2

b) (g ∘ f)(4) = √2 + 5

c) (h ∘ g ∘ g)(-5) = 2 - 1/ (√(2√5) + 5)

d) (g ∘ f)(x) = √(x + 5) + 5.

e) (f ∘ g)(x) = √(√x + 5) + 5

f) (h ∘ f)(x) = 2 - 1/ (√x + 5)

What is Function?

A function is an expression or relationship that involves one or more variables. It has several inputs and outputs.

a) (f ∘ g)(4) means plugging in the value of 4 into g(x) and then plugging the result into f(x). So we have:

g(4) = √4 + 5 = √9 = 3

f(g(4)) = f(3) = √3 + 5 = 2

Therefore, (f ∘ g)(4) = 2.

b) b) (g ∘ f)(4) means plugging in the value of 4 into f(x) and then plugging the result into g(x). So we have:

f(4) = √4 = 2

g(f(4)) = g(2) = √2 + 5

Therefore, (g ∘ f)(4) = √2 + 5.

c) (h ∘ g ∘ g)(-5) means plugging in the value of -5 into g(x) twice, and then plugging the result into h(x). So we have:

g(-5) = √(-5) + 5 = √(20) = 2√5

g(g(-5)) = g(2√5) = √(2√5) + 5

h(g(g(-5))) = h(√(2√5) + 5) = 2 - 1/ (√(2√5) + 5)

Therefore, (h ∘ g ∘ g)(-5) = 2 - 1/ (√(2√5) + 5).

d) (g ∘ f)(x) means plugging in the function f(x) into g(x), which gives:

g(f(x)) = √(x + 5) + 5

Therefore, (g ∘ f)(x) = √(x + 5) + 5.

e) (f ∘ g)(x) means plugging in the function g(x) into f(x), which gives:

f(g(x)) = √(√x + 5) + 5

Therefore, (f ∘ g)(x) = √(√x + 5) + 5.

f) (h ∘ f)(x) means plugging in the function f(x) into h(x), which gives:

h(f(x)) = 2 - 1/ (√x + 5)

Therefore, (h ∘ f)(x) = 2 - 1/ (√x + 5).

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The value of correlation cofficient between the number of people who complete successfully complete each jump, y and height of jump, x is equals to the - 0.091.

We have a table which consists height ( in feet ), x and completions, y present above figure. We have to calculate the correlation coefficient for variables x and y. Correlation coefficients are used to measure how strong the relationship is between two variables. The commonly used cofficient in linear regression is Pearson's correlation (also called Pearson's R) coefficient . Formulas return a value between -1 and 1, where,

Formula used to determine the cofficient is r = (n∑ xy - (∑x)(∑y))/√[ n∑x² - (∑x)²][n∑y² - (∑y)²]

Here, n = 6, ∑xy = 375.8 , ∑ x =22.4, ∑y

= 102, ∑ x² = 96.5, ∑y² = 1978

so, r = 6×(375.8) - 102(22.4))/√[(6×96 - (22.4)²)(6×1978 - 102²)]

= -30/329.68

= - 0.091

Hence, required value of r is - 0.091.

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Complete question:

The above table shows the heights (in feet) of a high jump bar and the number of people who successfully complete each jump. Identify the correlation of coefficient. Round your answer to three decimal places.

The completed flowchart proof is that ΔΑΒΕ =  ΔCDE

Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, and dimensions of objects in space. It is concerned with the properties of points, lines, curves, surfaces, and solids, as well as the relationships between them.

How to prove this:

<ABD = <BDC

(alternate angles)

<BAC = <ACD

(alternate angles)

Hence, BE = ED (given)

So, ΔΑΒΕ =  ΔCDE

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The total cost of the aquarium that Arlington bought after markdown and including sales tax is $42.

What is meant by the markdown of the price?

The markdown is the price that separates an item's current, lowered price from its original, full price. Typically, a percentage is used to express it. Retailers can offer their products at a discount thanks to markdown.

Discounts are distinct from markdowns. Markdowns give everyone the chance to buy products for a lower price. However, some customers may only be eligible for discounts, such as students.

Markdown = (difference of prices / actual selling price) x 100

Given,

Original Cost of aquarium = $100

Marked down price = 100 - 0.60 * 100= 100 - 60 = $40

Sales tax = 5%

Sales tax is the percentage of the price at which the aquarium was bought i.e the markdown price.

Sales tax = 5% of $40 = 0.05 * 40 = $2

Total cost = marked down price + sales tax = $40 + $2 = $42

Therefore the total cost of the aquarium that Arlington bought after the markdown and including sales tax is $42.

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After adding and subtracting the rational expressions , the simplified rational expression is 4x - 4/x² - 5/x³ + 9  .

We first simplify each expression inside the parentheses :

that means :

⇒ (2x + 5/x² -3x) = (2x - 3x + 5/x²) = (-x + 5/x²) ;

⇒ (3x + 5/x³ - 9x) = (-6x + 5/x³)  ;

⇒ (x + 1/x² - 9) = (-9 + x + 1/x²)  ;

Now we substitute these expressions into original equation/expression :

we get ; (-x + 5/x²) - (-6x + 5/x³) - (-9 + x + 1/x²)

Simplifying further ,

we get ;

⇒ -x + 5/x² + 6x - 5/x³ + 9 - x - 1/x²  ;

On Combining the like terms, we get ;

⇒ 4x - 4/x² - 5/x³ + 9

Therefore, the simplified rational expression is 4x - 4/x² - 5/x³ + 9.

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The given question is incomplete , the complete question is

Adding and subtracting rational expressions, Simplify the rational expression  (2x + 5/x² -3x) - (3x + 5/x³ - 9x) - (x + 1/x² - 9)  .

Answer:

there are 276 + 276 + 5680 = 6232 different ways for Jane to choose her meal.

Step-by-step explanation:

First, we need to find the number of different combinations of a starter dish and a main dish. This is simply the number of combinations of 2 items from 8 starters and 15 main dishes, which can be calculated using the formula for combinations:

C(8 + 15, 2) = C(23, 2) = (23 * 22) / (2 * 1) = 276

Similarly, the number of different combinations of a main dish and a dessert dish is:

C(15 + 9, 2) = C(24, 2) = (24 * 23) / (2 * 1) = 276

Finally, the number of different combinations of a starter dish, a main dish, and a dessert dish is:

C(8 + 15 + 9, 3) = C(32, 3) = (32 * 31 * 30) / (3 * 2 * 1) = 5680

In total, there are 276 + 276 + 5680 = 6232 different ways for Jane to choose her meal.

The amount of money that the items will cost you to send through United States Postal Service would be = $13.3

The dimensions of the first envelope = 20 L, 10°H and 4"W

The weight of the first envelope = 10 ounce.

The first envelope is a parcel because the dimensions are larger than 11.5 L, 6.125" H, 0.25"W.

The price per ounce = $1.22

10 ounce = 1.22×10 = $12.2

The dimensions of the second envelope = 8 L, 5" H and 0.20 W.

The weight of the second envelope = 2.5 ounce.

The second letter is of normal letter size because of the dimensions (min. dimension: 5" L, 3.5" H, 0.007" W; max. dimension: 11.5 L, 6.125" H, 0.25 W, max. weight 3.5 oz)

The price per ounce = $0.44

2.5 ounce = 2.5× 0.44 = $1.1

The total price = 12.2+1.1 = $13.3

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Answer:

x + y = -9

Step-by-step explanation:

let x = -8, y = -1

the equation that passes through the point (-8,-1) is x + y = -9

The expression that will give the distance between points is option D i.e. √(2 - 4)² + (3 + 3)². The solution has been obtained by using distance formula.

What is the distance formula?

The distance between two locations on a coordinate plane can be calculated using the distance formula. The distance equation is written as d = √(x₂ - x₁)² + (y₂ - y₁)².

We are given two points as (2,3) and (4,-3).

So, x₁ = 2, y₁ = 3, x₂ = 4, y₂ = -3

Now, substituting these values in the distance formula, we get

d = √(2 - 4)² + (3 + 3)²

Hence, the expression that will give the distance between points is option D.

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Full question has been attached below

Answer:  TRUE  Flóki reportedly released three ravens, and then sailed in the general direction that they flew, eventually discovering Iceland.

Step-by-step explanation:

The required probability that X is less than 16 is approximately 0.15866 or 15.86%.

A Z-score is stated as the fractional model of data point to the mean using standard deviations.

Here,
We can use the standard normal distribution to find the probability that a normally distributed random variable, X, is less than a certain value. To use the standard normal distribution, we need to standardize X by subtracting the mean and dividing by the standard deviation:

Z = (X - μ) / σ

In this case, X has a mean of 25 and a standard deviation of 9,

Z = (16 - 25) / 9
z = -1

To find the probability that X is less than 16, we need to find the corresponding value of Z using the standard normal distribution table or a calculator.

P(Z < -1) ≈  0.15866

Therefore, the probability that X is less than 16 is approximately 0.15866 or 15.86%.

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Answer:

12 ways

Step-by-step explanation:

the mother and father can either stand at the front/back or back/front respectively (2 ways)

that leaves 3 children in the middle -- there are 3 choices for the first child to go, 2 for the second, and 1 for the third = 3! = 6

6 ways for the children * 2 ways for the parents = 12 ways

Answer:

Step-by-step explanation:

The LAD method minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line, making it more robust to the presence of outliers in the data.

Regression analysis is a powerful statistical tool used to estimate the relationship between two or more variables. The ordinary least squares (OLS) method is the most commonly used regression method. However, the OLS method is sensitive to outliers in the data.

LAD regression is a robust alternative to OLS regression because it minimizes the sum of the absolute vertical differences between the regression line and the data points. This method is also known as L1 regression.

Let's consider an example of a simple linear regression model with n observations, where Y is the dependent variable and X is the independent variable.

The OLS method estimates the parameters of the regression line by minimizing the sum of the squared vertical differences between the observed data points and the predicted values of the regression line.

In mathematical terms, the OLS method can be represented as follows:

minimize the sum of squared vertical differences,

min(β₀, β₁) ∑ (yₐ - β₀ - β₁ xₐ)²

However, if the data contains outliers, the OLS method may produce biased estimates of the parameters of the regression line, leading to incorrect predictions. On the other hand, LAD regression minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line.

In conclusion, the LAD regression is an alternative to OLS that reduces the sensitivity to outliers. The LAD method minimizes the sum of the absolute vertical differences between the observed data points and the predicted values of the regression line, making it more robust to the presence of outliers in the data.

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QUESTION 4: m∠A = 53 degrees

QUESTION 7: Area of triangle PQR is 23.6 unit²

QUESTION 8: Using cosine law, JK = 3.1 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

QUESTION 4

tan A = 9.6/7.2

A = arctan(9.6/7.2)

A = 53 degrees

QUESTION 7

Area of ΔPQR = 1/2 * 6 * 8 * sin 80

Area of ΔPQR = 23.6 unit²

QUESTION 8

JK = √(6² + 8² - 2*6*8*cos 20°)    (cosine law)

JK = 3.1 units

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A histogram would be the most appropriate graphical display to present data by grouping the results into groups of 25 cm.

A histogram is a graphical representation of data that shows the distribution of a set of continuous data by dividing the data into bins (or intervals) and showing the frequency of observations within each bin. The histogram provides a visual representation of the distribution of data, showing the shape, central tendency, and spread of the data.

In this case, the farmer has measured the height of every tree in a large orchard in centimeters and wants to present the data in groups of 25 cm. To create a histogram for this data, the first step would be to divide the data into bins, or intervals, of 25 cm.

Once the bins are created, the next step is to count the number of observations (tree heights) that fall within each bin. This information can be represented as a bar graph, where the height of each bar represents the frequency of observations within the corresponding bin.

By presenting the data in this way, the farmer can easily see the distribution of tree heights in the orchard. The shape of the histogram can indicate whether the data is symmetrical, skewed, multimodal, or uniform.

The central tendency of the data can be determined by looking at the peak of the histogram, which represents the most frequent range of tree heights. The spread of the data can be determined by looking at the width of the histogram and the range of tree heights represented.

In conclusion, a histogram is the most appropriate graphical display to present the results of the tree heights in groups of 25 cm because it provides a visual representation of the distribution of the data and allows the farmer to see the shape, central tendency, and spread of the tree heights in the orchard.

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The length of the original piece of fabric, given the proportion cut by Yu Yan and the amount cut in total, is 75 .75 inches

Assume that the original length of fabric was denoted as x, this means that the first cutting by Yu Yan took out :

= 1 / 3 x

The equation would then be :

x - 1 / 3 x - 10 - 5 = 35 + 1 / 2

x - 1 / 3 x - 10 - 5 = 35 . 5

The length of the original fabric is:

2 / 3x  = 35. 5 + 10 + 5

x = 50. 5 ÷ 2 / 3

x = 50. 5 x 3 / 2

x = 75 .75 inches

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Answe[tex]3\sqrt{2)[/tex]

Step-by-step explanation:

A reflection over the x-axis.

A vertical stretch by 11 units.

A translation left by 5 units.

A translation up 4 units.

The reflection of a function across the x- or y-axis is another transformation that may be used. In contrast to a horizontal reflection, which reflects a graph horizontally across the y-axis, a vertical reflection reflects a graph vertically across the x-axis.

An illustration of a transformation is a reflection, which flips a shape (referred to as the pre image) over a line (referred to as the line of reflection) to produce a new shape (called the image). Imagine what would happen if you flipped the form over the line in order to graph a reflection.

Here, f(x) = 1/x²

Now, reflect the graph over the x-axis to obtain the graph of:

f(x) = -1/x²

Now, stretch the graph vertically by 11 units to get the graph of:

f(x) = -11/x²

Again, translate the graph left by 5 units to obtain the graph of:

f(x) = - 11 / (x + 5)²

Now, translate the graph up by 4 units to obtain the graph of:

f(x) = 4 - {11 / (x + 5)²}

Hence,

A reflection over the x-axis. A vertical stretch by 11 units. A translation left by 5 units. A translation up 4 units.

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Step-by-step explanation:

2y+57=180

2y=180-57

2y=123

y=123/2=61.5°

y=61.5

Answer:

61.5

Step-by-step explanation:

As the lines are parallel you can use the alternate angle rule.

So within the triangle you have 57 + x + x ( y is equal to the other angle because the lines are the same length and angle highlighted by the double lines )

And so...

180 - 57 = 123

123/2 = 61.5

Answer:

1.  2^n + 1.

2. (n +1)/(n + 4)

Step-by-step explanation:

1. 3 5 9 17....

3 = 2^1 + 1

5 = 2^2 + 1

9 = 2^3 + 1

17 = 2^4 + 1

Therefore the nth term is

2^n+ 1 .

2. Looking at the fractions we see that:

Numerators are 2, 3, 4 ,5..

and denominators are  5, 6, 7, 8

So the nth term is

(n + 1) / (n + 4)

When the cost of 7 books is equal to Rs 300 more than the 5 same books then the cost of a single book is equal to Rs 150.

Let us consider Rs 'x' be the cost of a single book .

Equation to represents the given expression 7 books is equal to Rs 300 more than the 5 same books is :

⇒ 7x = 300 + 5x

Subtract 5x from both the side of the equation we get,

⇒ 7x -5x = 300 + 5x - 5x

⇒ 2x = 300

Divide both the side by 2 we get,

⇒ 2x / 2 = 300 / 2

⇒ x =  Rs. 150

Therefore, the cost of a single book as per the given condition of 7 books is equal to Rs 300 more than the 5 same books is given by          Rs 150.

The above question is incomplete, the complete question is:

If 7 books cost Rs. 300 more than 5 books, find the cost of a book.​

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Answer:

8 to 2

Step-by-step explanation:

because u have 8 cocca and 2 sugar

The missing side is [tex]5\sqrt{3}[/tex].

What are basic Trigonometric functions?

The angles of sine,  cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.

In a Right-angled triangle, the tangent of an angle is equal to the opposite side/adjacent side.

from the given figure,

tan 60° = x/5

[tex]\sqrt{3}=\frac{x}{5}\\ x=5\sqrt{3}[/tex]

Therefore, The missing side is [tex]5\sqrt{3}[/tex].

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Based on the information, Wendy will need to purchase 48 quarts of paint

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

Wendy is told ahead of time that she will need to purchase about 12 gallons of paint in order to cover the entire house.

The amount of paint needed will be:

= 4/1 × 12

= 48 quarts

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Wendy is told ahead of time that she will need to purchase about 12 gallons of paint in order to cover the entire house. a. Write equivalent ratios to determine the amount of green and white paint she will need to purchase. b. If there are 4 quarts in 1 gallon, how many quarts of paint does she need to purchase

A 24.8% of babies have a head circumference greater than 14 inches.

The circumference of a circle is the length of the curved boundary or the perimeter of the circular shape. It is a measurement of the distance around the circle and is equal to the arc length of the circle if it were opened up and straightened out into a line segment. The circumference of a circle is related to its diameter by the formula: C = π * d

To calculate the percentage of babies with a head circumference greater than 14 inches, we need to find the area under the normal distribution curve to the right of 14 inches.

First, we need to convert 14 inches to the standard units (z-score). We can do that using the following formula:

z = (14 - 13.5) / 0.75 = 0.67

Next, we can use a standard normal distribution table to find the area to the right of z = 0.67. The value from the table is approximately 0.752.

Therefore, approximately 75.2% of babies have a head circumference less than or equal to 14 inches, and 24.8% of babies have a head circumference greater than 14 inches.

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The missing number in the sequence is 64

From the question, we have the following parameters that can be used in our computation:

1, 4, 16, ____, 256, 1024, ...​

Using the above as a guide, we have the following:

To obtain the next term, we can multiply the previous term by 4:

So, we have

Next term = 16 * 4

Next term = 64

Therefore, the next term in the sequence is 64.

The completed sequence is: 1, 4, 16, 64, 256, 1024, ...

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Answer:

1. $1900

2. $9

Step-by-step explanation:

Part a:

‘If she doesn’t sell any copies of History is Fun’ means x = 0:

[tex]y = 1900 + 9(0)[/tex]

∴ y = Melissa’s total pay = $1900

Part b:
Rearranging the equation:

[tex]y = 9x + 1900[/tex]

∴m = slope of equation = positive 9

  c = y-intercept = 1900

The shape of the graph would be increasing or ascending. And since the Number of copies (x) can never be negative, this means that the amount of pay CANNOT be less than $1900. The amount of $1900 is her minimum pay

The value of m for this equation indicates the change in Melissa’s total pay for every copy she sells.

∴Change in Melissa’s total pay = 9 dollars