Lesson 5 Skills Practice

Draw Three-Dimensional Figures

Draw at, ad, and a front view of each solid

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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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

Answer:

The answer to the problem is c

When you graph it x+2y <-2

y-x<3 you will get c

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

Enola needs to ride 3.2 miles a day

In the given question enola wants to ride her bicycle 23.8 miles this week and she has already ridden 11 miles and if she rides for 4 more days the we have to write and solve an equation which can be used to determine xx, the average number of miles she would have to ride each day to meet her goal.

The target distance of 23.8 miles can be reached in 4 days if the average rate is x and 11 miles are travelled.

This can be expressed as equation:

4x + 11 = 23.8

Solve it for x:

4x = 23.8 - 11

4x = 12.8

x = 12.8/4

x = 3.2

The value of x is 3.2

So, Enola needs to ride 3.2km

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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

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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Answer: The discount is $13.75, which is found by multiplying the original price by the discount percentage, 0.25.

Step-by-step explanation:

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.

Answer:

1.769 pounds

Step-by-step explanation:

36.269 - 34.5 = 1.769

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 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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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 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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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:

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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The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given line equations are y=3x-6 and y=-2x+8.

Here, 3x - 6 = -2x + 8

Add 2x to both sides of the equation.

5x - 6 = 8

Add 6 to both sides of the equation.

5x = 14

Divide both sides of the equation by 5.

x = 14/5  

Find the y-value where these points intersect by plugging this x-value back into either equation.

y = 3(14/5) - 6

Multiply and simplify.

y = 42/5 - 6

Multiply 6 by (5/5) to get common denominators.

y = 42/5 - 30/5  

Subtract and simplify.

y = 12/5

These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.

Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.

Set both equations equal to 0.

(I) 0 = 3x - 6  

Add 6 both sides of the equation.

6 = 3x

Divide both sides of the equation by 3.

x = 2  

Set the second equation equal to 0.

(II) 0 = -2x + 8

Add 2x to both sides of the equation.

2x = 8

Divide both sides of the equation by 2.

x = 4

The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.

The height of the triangle is 12/5 units.

Formula for the Area of a triangle:

A = 1/2bh

Substitute 2 for b and 14/5 for h.

A = 1/2 ×2 × 12/5

Multiply and simplify.

A = 12/5

Therefore, the area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

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Answer:

Step-by-step explanation:

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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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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the probability that he found his dog. alive is 15%.

What is probability?

The chance of an event can be calculated using the probability formula by simply dividing the favourable number of possibilities by the total number of outcomes. The likelihood of an event occurring can be anything between 0 and 1, as the favourable number of outcomes can never exceed the total number of outcomes. Probability theory is a branch of mathematics that focuses on calculating the likelihood that an event will occur. Probability measures how likely something is to happen.

if he searched in a for two days and b for two days

P(A) = 0.4

P(B) = 0.6

P(Dn D-1 F-1)= n n+2

P(FnA, Sn, F-1) = 0.25

P(FB, S, F-1) = 0.15

Hence the probability that he found his dog. alive is 15%.

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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%

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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Answer:

5.3

Step-by-step explanation:

so, to round this up we need to look at the number beside 2

5 is always rounded up

so, 5.3

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

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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The area of the rhombus is 384 cm²

The diagonals of a rhombus are the lines that connect the opposite vertices (corners) in the center of the shape. The diagonals of a rhombus are perpendicular and form four right triangles through their intersection

Area of Rhombus = d₁ x d₂

Area of Rhombus = base x height

Given data ,

Let the area of the Rhombus be represented as A

Now , the value of A is

Let the base of the rhombus be B = 20 cm

Let the height of the rhombus be H = 19.2 cm

Now , the area of the rhombus = base x height

Substituting the values in the equation , we get

Area of Rhombus A = 19.2 x 20

Area of Rhombus A = 384 cm²

Hence , the area of the rhombus is 384 cm²

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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.

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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The probabilities are given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

Each dice has six outcomes, hence the total number of outcomes when two dice are rolled is given as follows:

6² = 36.

The possible outcomes for the pair of dice are given as follows:

We can see a pattern of the sum, even-odd-even-odd and so on, hence the probability of an odd sum is given as follows:

p = 18/36 = 1/2.

For a sum greater than 6, the number of outcomes is given as follows

1 + 2 + 3 + 4 + 5 + 6 = 21.

Hence the probability is of:

p = 21/36

p = 7/12.

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