4n^2 – 15n -25
Factor Completely

The probability of the family having at most one right-handed child is [tex](2/3)^3 + 3 * (2/3)^2 * (1/3) = 0.593[/tex].

The probability of event A can be calculated using the formula P(A) = 1 - P(not A). Since the left-handed:right-handed ratio is 1:2, the probability of a child being right-handed is 2/3 and the probability of a child being left-handed is 1/3. Thus, the probability of the family having children of both handedness is[tex]1 - P(not A) = 1 - (2/3)^3 = 0.741[/tex].

The probability of event B can be calculated using the formula P(B) = P(not A) + P(A and B). Since the left-handed:right-handed ratio is 1:2, the probability of a child being right-handed is 2/3 and the probability of a child being left-handed is 1/3. Thus, the probability of the family having at most one right-handed child is[tex](2/3)^3 + 3 * (2/3)^2 * (1/3) = 0.593.[/tex]

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Answer:

20%

Step-by-step explanation:

45

22 bronze

14 silver

so 45- 22 -14 =9 gold

9/45 = 1/5 =20%

Answer:

1.769 pounds

Step-by-step explanation:

36.269 - 34.5 = 1.769

Yes, the equation 1/4y = 5x represents a direct proportion, and has a constant of proportionality of

A direct proportion is defined by the equation, y = kx, where k is the constant of proportionality.

To check if see the equation is a direct proportion, multiply both sides of the equation by 4:

1/4y * 4 = 4 * 5x

y = 20x

This shows that the ratio of y to x is equal to a constant value of 20, so y and x are directly proportional. The constant of proportionality is 20.

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The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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Answer:

C

Step-by-step explanation:

add each of them all up and you'll see only C 4y = the sum

The number of different possible outcomes when we spin the spinner is; 81

The given parameters are:

Spinner section, n = 3 i.e. Red, Blue, Yellow

Number of spins, r = 4

The number of possible outcomes is calculated using the formula for these type of outcomes is:

Number of outcomes = n^r

So we have:

Outcomes = 3⁴

Outcomes = 81

Hence, the number of outcomes is 81

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(−5, 2) is point lie on a line that passes through the origin with a slope of −2/5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We need to find the points lie on a line that passes through the origin with a slope of −2/5

The line passes through (0, 0) and (x, y) form a slope of -2/5

-2/5=y/x

So y is 2 and x is 5.

Hence, (−5, 2) is points lie on a line that passes through the origin with a slope of −2/5

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When computing the area of a circle, the mathematical constant pi () is required. Pi is the circumference-to-diameter ratio of a circle and is approximately equal to 3.14159.

The area of a circle is calculated by multiplying pi by the radius squared (r2). To estimate the area of a circle, utilize pi in the calculation since it is a vital aspect of the relationship between the circumference and diameter of a circle.

Pi is not required when determining the area of a square, rectangle, or cube since the formulas for these shapes are different.

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The question is -

The mathematical constant pi is needed when calculating the area of a _.

a. circle

b. square

c. rectangle

d. cube

The value of the unknown is 628.57

Percent simply means "per hundred" and the symbol used to express percentage is %. One percent (or 1%) is one hundredth of the total or whole and is therefore calculated by dividing the total or whole number by 100. Example: 1% of 250 = (1 ÷ 100) x 250 = 2.5.

Represent the unknown by x

therefore;

35/100 × x = 220

multiply both sides by 100

35x = 22000

x = 22000/35

x = 628.57

therefore 35% of 628.57 is 220

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$612.50.

Step-by-step explanation:

When x = 6, the value of y is:

y = -5x

y = -5(6)

y = -30

Therefore, when x = 6, y is equal to -30.

Answer:

-30

Step-by-step explanation:

given,

y = -5x

x = 6

Now,

y = -5x

or, y = -5(6)

therefore, y = -30

Answer:

Step-by-step explanation:

Average ROC is [tex]Change=\frac{f(b)-f(a)}{b-a} \\[/tex] so we need to look at the points (0,20) at 0 our y is 6 and at 20 its 12 so we have (0,6) and (20,12) we now use our formula so we have Change=[tex]\frac{12-6}{20-0} =\frac{6}{20} =\frac{3}{10}[/tex] so our answer is 3/10

False. The given statement is not a valid proof of the theorem because it is circular.

The proof starts with the assumption that there exists an integer k such that n < k < n^2 and then uses this assumption to conclude that the theorem is true. However, this does not actually prove the existence of k, it simply restates the theorem. A valid proof would need to start with some other set of premises and use logical deduction to arrive at the conclusion that such a k exists. The given statement is not sufficient to establish the truth of the theorem.

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Answer:

800

Step-by-step explanation:

1/4 =200

200+200 =2/4

200+200+200+200 =4/4 = all = 800

Answer:

Step-by-step explanation:

$800

a) An approximate equation of the line of best fit for the data is,

⇒ y = 18/13 (x - 7)

b) The amount charged per hour by a dog sitter with 10 years of experience is, $54/13

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The scatter plot shows the number of years of experience, x , and the amount charged per hour, y , for each of 24 dog sitters in Texas.

Now, Add a line of best fit (see attached).

Here, The two points on the line are,

⇒  (7, 0) and (20, 18)

Thus, Use these points to find the slope of the line is,

⇒ m = (18 - 0) / (20 - 7)

⇒ m = 18 / 13

Use the found slope and one of the points in the point-slope form of the linear equation to find an equation for the line of best fit:

⇒ y - y₁ = m (x - x₁)

⇒ y - 0 = 18/13 (x - 7)

⇒ y = 18/13 (x - 7)

Substitute x = 10 we get;

⇒ y = 18/13 (x - 7)

⇒ y = 18/13 (10 - 7)

⇒ y = 18/13 × 3

⇒ y = $54/13

Thus, An approximate equation of the line of best fit for the data is,

⇒ y = 18/13 (x - 7)

b) The amount charged per hour by a dog sitter with 10 years of experience is, $54/13

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Answer:

yes

Step-by-step explanation:

working for 2 5/6 hours, she has 5/8 of the fence.

so per hour = 5/8 ÷ 2 5/6 =15/68 per hour

5 hours she'll do: 15/68*5 = 75/68

75 >68

so yes she will finish it

The range of g(x) is all real numbers less than 0.

An easy definition of a function?

As a set of inputs with one output for each, a function is defined as a relationship between them.

                    A function, expressed simply, is an association between inputs where each input is connected to one and only one output.

 The given function is

    f(x) = 1/2(2.5)ˣ

If a graph reflected across x axis, then

     (x,y) ⇒ (x, -y )

The function f(x) reflected across x-axis, so

        g(X) = -f(x)

         g(X) = -1/2(2.5)ˣ

It is an exponential function.

    g(x) ⇒ -∞ as x⇒ ∞

   g(X) ⇒ 0 as x ⇒ - ∞

Since the value of g(x) lies between ∞ and 0, therefore the range of g(x) is all real numbers less than 0.

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Answer:

2

Step-by-step explanation:

Substituting v = 2 and w = 16 in the expression w - 7|v|, we get:

w - 7|v| = 16 - 7|2|

We need to evaluate the absolute value of 2, which is simply 2. Therefore, we can simplify the expression as:

16 - 7|2| = 16 - 7(2) = 16 - 14 = 2

So, w - 7|v| = 2 when v = 2 and w = 16.

we dunno, hmmm let's check for the slope for PQ

[tex]P(\stackrel{x_1}{-8}~,~\stackrel{y_1}{-10})\qquad Q(\stackrel{x_2}{-5}~,~\stackrel{y_2}{-12}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-12}-\stackrel{y1}{(-10)}}}{\underset{\textit{\large run}} {\underset{x_2}{-5}-\underset{x_1}{(-8)}}} \implies \cfrac{-12 +10}{-5 +8} \implies \cfrac{ -2 }{ 3 } \implies - \cfrac{2 }{ 3 }[/tex]

keeping in mind that perpendicular lines have negative reciprocal slopes, then if both are truly perpendicular, then line RS will have a slope of

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-2}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-2} \implies \cfrac{3}{ 2 }}}[/tex]

let's see if that's true

[tex]R(\stackrel{x_1}{9}~,~\stackrel{y_1}{-6})\qquad S(\stackrel{x_2}{17}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-5}-\stackrel{y1}{(-6)}}}{\underset{\textit{\large run}} {\underset{x_2}{17}-\underset{x_1}{9}}} \implies \cfrac{-5 +6}{8} \implies \cfrac{ 1 }{ 8 } ~~ \bigotimes ~~ \textit{not perpendicular}[/tex]

Answer:

Step-by-step explanation:

No they are not perpendicular.

Perpendicular lines have slopes that are negative reciprocals of each other.

PQ slope = -12 - -10/-5 --8 = -2/3

RS slope = -5 - -6/17 -9 = 1/8

Slope are not negative reciprocals - the lines are not perpendicular.

Slope formula is m = y2 - y1/x2 - x1

Use this to determine slope.

For example if the the slope of RS was 3/2 - the lines would be perpendicular.

As a result, f(-2) has a value of -1 by simply substituting the value of x in the function. as Each function is given a domain and a codomain, often known as a scope.

Math deals with numbers with their variants, formulae and adjacent tissues, structures and associated locations, and areas where they might be found. The term "function" refers to the connection between a series of inputs, of which each has a corresponding output. A function is a connection between the inputs and outputs where each input result in a single, unique output. A domain as well as a codomain, or scope, are allocated to each function. Functions are generally symbolized by the letter f. (x). The input is an x. On functions, another functions, many-to-one functions, within operations, and on functions are the four main types of functions that are available.

given

f(x)=2(x)+3=5

= f(-2) = 2(-2) + 3 = 5

= -4 + 3

= -1

As a result, f(-2) has a value of -1 by simply substituting the value of x in the function. as Each function is given a domain and a codomain, often known as a scope.

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The equation is correct and the point (5,-2) is on the line.

The point slope equation of a line with slope 0.25 and a point (5,-2) would be y-(-2) = 0.25(x-5). This equation can be rearranged to y = 0.25x - 1.5.

Calculation:

y = 0.25x - 1.5

Plugging in x = 5

y = 0.25(5) - 1.5

y = -2

The point (5,-2) is on the line.

The point slope equation of a line with slope 0.25 and a point (5,-2) can be written as y-(-2) = 0.25(x-5) which can further be rearranged to y = 0.25x - 1.5. This equation can be further tested by plugging in the x value of the point (5) into the equation and the y value of the point (-2) should be obtained. This proves that the equation is correct and the point (5,-2) is on the line.

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The correct answer is e, none of the above, as a relatively flat, horizontal pattern indicates the absence of a trend or seasonality making it difficult to use any of the mentioned methods for forecasting.

This type of pattern is commonly referred to as a "stationary time series" and may require different forecasting techniques such as moving averages or ARIMA models.

A stationary time series means that the statistical properties of the series, such as the mean and variance remain constant over time. This type of series may still exhibit random fluctuations and noise that need to be accounted for in the forecasting process. Moving averages are commonly used to smooth out the noise and highlight any underlying patterns in the data.

This question should be provided with answer choices, which are;

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Answer:

91.63%

Step-by-step explanation:

The annual interest rate is 1.2% if Stanley invests £7500 for 4 years in a savings account.

percentage, a relative value indicating hundredth parts of any quantity.

We can use the formula for compound interest:

[tex]A = P (1 + r/n)^(^n^t^)[/tex]

where A = the final amount, P = the principal (initial investment), r = the annual interest rate (as a decimal), n = the number of times the interest is compounded per year and t = the time in years

We know that P = £7500, t = 4 years, and A = £7866.53.

Let n is 1

Plugging in the values we know, we get:

£7866.53 = £7500 (1 + r/1)⁴

Simplifying the equation:

(1 + r)⁴ = 1.04887

Taking the fourth root of both sides:

1 + r = 1.012

Subtracting 1 from both sides:

r = 0.012 or 1.2%

Therefore, the annual interest rate is 1.2%.

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Domain and range of the composite function (gof)(x) formed by given f(x) and g(x) is equal to all positive real numbers and y > 6 , y ∈R  respectively.

Function f(x ) is :

f(x) = e^x

Function g(x) is :

g(x) = x + 6

To find the range of composite function (gof)(x) simplify the function .

(gof)(x)

= g ( f(x))

Substitute f(x) = e^x we get

= g ( e^x )

Replace x by e^x in g(x) we get,

= e^x + 6

Domain of the composite function is given by all the value based on e^x that is all positive real numbers.

Range is translated by 6.

y > 6 , y∈ R ( positive real numbers)

Therefore, the domain and range of  composite function (gof)(x) is all positive real numbers and y > 6 , y∈ R ( positive real numbers) respectively.

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The boxplot which is reasonable to the summary of the data used to create the histogram is equals to boxplot A. So, correct answer is option (c).

Histogram is a graph which discribes the distribution of data by using of bars of different heights and same width. In this problem, we'll have a histogram and 3 box plots as box plot A, box plot B and box plot C, and we have to choose here which of these 3 box spots is a reasonable summary of the data. We can see that the histogram in above figure is skewed to left because it's maximum data present on the right end. The box plot C, is representing a normally distributed data, but are data is right side distributed so, it is wrong. Similarly, as we see box plot B shows distribution of data in left end, which is also not right choice. So, boxplot A is correct because it's showing the maximum data and the median where we have. We can see the median line over her median on the right hand. Thus, data is very highly negatively skewed hence boxplot A is appropriate.

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Complete question:

See the above figure, which box plot a, b, or c is a reasonable summary of the data used to create the histogram? there are 16 data points.

a) boxplot C

b) boxplot B

c) boxplot A

The closest solution to this total among the available possibilities is 0.68, indicating that the portfolio is likely to surpass its benchmark in three or fewer quarters over the course of a year.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms.

Here,

The probability that the portfolio outperforms its benchmark in three or fewer quarters over the course of a year is the sum of the probabilities of outperforming the benchmark in exactly 0 quarters, 1 quarter, 2 quarters, and 3 quarters.

Since the probability of outperforming the benchmark in any quarter is 0.75, the probability of not outperforming the benchmark in a quarter is 1 - 0.75 = 0.25.

The probability of not outperforming the benchmark in exactly 0 quarters is 0.25⁰ = 1

The probability of not outperforming the benchmark in exactly 1 quarter is 0.25¹= 0.25

The probability of not outperforming the benchmark in exactly 2 quarters is 0.25² = 0.0625

The probability of not outperforming the benchmark in exactly 3 quarters is 0.25³ = 0.015625

So, the probability of outperforming the benchmark in exactly 0 quarters, 1 quarter, 2 quarters, and 3 quarters is 1 - 0.25⁰, 1 - 0.25¹, 1 - 0.25², and 1 - 0.25³, respectively.

The sum of these probabilities is the probability of outperforming the benchmark in three or fewer quarters over the course of a year:

P(outperform in three or fewer quarters) = 1 - 0.25⁰ + 1 - 0.25¹ + 1 - 0.25² + 1 - 0.25³

This expression can be calculated to get an exact answer, but to get the closest answer to the options given, we can round off the intermediate results to 2 decimal places:

P(outperform in three or fewer quarters) = 1 + 0.75 + 0.94 + 0.98

The closest answer to this sum among the options given is 0.68, so the probability that the portfolio outperforms its benchmark in three or fewer quarters over the course of a year is closest to 0.68.

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On solving the provided question, we can say that the inequality that will be formed is  [tex]1\leq x\leq 1.5 and 6\leq y\leq 8[/tex] and Two possible combinations are (1.25.7). (1.35.7.5)

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

the inequality that will be formed is

[tex]1\leq x\leq 1.5\\6\leq y\leq 8[/tex]

Two possible combinations are (1.25.7). (1.35.7.5)

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The suitable inequality is 8x + 12y < 240

Inequalities are the relationship two expressions which states that the two expressions are not equal. It is denoted by the symbols like < , >, ≤, ≥.

Given that x equal small rugs and y equals medium rugs.

A company needs 8 hours for dyeing small rugs then, 8x.

And it needs 12 hours for dyeing medium rugs then, 12y.

The company must do 22 rugs less than 240 hours.

So the inequality is 8x + 12y < 240, it is paired with x + y ≥ 22.

Hence the suitable inequality is 8x + 12y < 240.

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