The standard deviation of a sample of 100 observations equals 64. The variance of the sample equals 10 6400 4096 Question 15 (1 point) The interquartile range is the 50th percentile the difference between the third quartile and the first quartile another name for variance the difference between the largest and smallest values

The variables as length are L and width is W and the system of equations is L = 2W - 3 and 42 = 2(L + W) and the length and width are 13 feet and 8 feet respectively.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

As per the given total fencing = 42 feet

Let's say the length is L and the width is W.

As per the given,

L = 2W - 3

Perimeter = 2(length + width)

42 = 2(L + W)

21 = 2W - 3 + W

21 + 3 = 3W

W = 8 feet

And, L = 2(8) - 3 = 13 feet

Hence "The variables as lengths are L and width is W and the system of equations is L = 2W - 3 and 42 = 2(L + W) and the length and width are 13 feet and 8 feet respectively".

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Answer:

3753.20 ft

Step-by-step explanation:

tan 80° = 3400 ft/x

x = 599.51 ft = distance at ground level from point directly below mountain peek to edge of mountain.

599.51 ft + 990 ft = 1589.51 ft = horizontal distance at ground level from where cable is attached to the ground to the center of the mountain. This is a leg of a right triangle.

3400 ft is another leg of a right triangle.

(1589.51 ft)² + (3400 ft)² = y²

The hypotenuse, y, is the length of the cable.

y = 3753.20 ft

The exponential generating function is,

G(x) = (x¹/1! + x²/2! + ...)(x¹/1! + x³/3! + x⁵/5! +...)(x°/0! + x¹/1! + x²/2! + ...)²

where the first factor describes the pennies, the second describes the quarters, and the last describes nickles and dimes.

We want the coefficient of [tex]x^{r}[/tex]/r!.

Using exponential identities we get,

G(x) = ([tex]e^{x}[/tex] - 1)([tex]\frac{e^{x}-e^{-x} }{2}[/tex]) ([tex]e^{x}[/tex])² = [tex]\frac{1}{2}[/tex] ([tex]e^{4x} - e^{2x} - e^{3x} + e^{x}[/tex]),

and the coefficient is

[tex]\frac{1}{2} (4^{r} - 2^{r}- 3^{r} + 1 )[/tex]

The generating function is

G(x) = (x¹/1! + x²/2! + ...)⁴(x°/0! + x¹/1! + x²/2!+...)²² = ([tex]e^{x}-1[/tex])⁴[tex]e^{22x}[/tex],

and we again want the coefficient of [tex]x^{10}[/tex]/10!.

Multiplying we get,

G(x) = ([tex]e^{4x}-4e^{3x}+2e^{2x}+1[/tex])[tex]e^{22x}[/tex] = [tex]e^{26x}-4e^{25x}+2e^{24x}+e^{22x}[/tex]

so the coefficient of [tex]x^{10}[/tex]/10! is

26¹⁰ - 4 × (25)¹⁰ + 2 × (24)¹⁰ + 22¹⁰

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Step-by-step explanation:

3x+4x+5x=4(x+2)

12x=4x+8

12x-4x=8

8x=8

8/8=x

1=x

x=1

now the length of one side of the square,

3x 5x 4x x+2 x+2

3x1=3 5x1=5 4x1=4 1+2=3 1+2=3

3+5+4+3+3=18

the length of one side of the square is 18 cm.

The relative cumulative frequency of students who earned a score of 20 or lower on the quiz is: B. 68%.

In Mathematics and Statistics, a frequency table can be used to graphically represent the frequencies or relative frequencies that are associated with a categorical variable.

In Mathematics and Statistics, the cumulative frequency of a data set can be calculated by adding each frequency from a frequency distribution table to the sum of the preceding frequency. Thus, the relative cumulative frequency would be calculated as follows;

Cumulative frequency of students = 4 + 8 + 15 + 7 = 34.

Cumulative frequency of students = 34.

Total frequency = 4 + 8 + 15 + 7 + 7 + 3 + 4 + 2

Total frequency = 50.

Therefore, the relative cumulative frequency can now be determined;

Relative cumulative frequency = 34/50

Relative cumulative frequency = 0.68 or 68%

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Answer:

68%

Step-by-step explanation:

Got it right.

The solution of the equation after completing the square of the equation is found as; x = ±√19 + 2.

The given steps are-

x² - 4x = 15.

(b/2)² = (-2)²

x² - 4x + (-2)² = 15 +(-2)²

x² - 4x + 4 = 19

There are various ways to display the outcome.

(x - 2)² = 19

x = ±√19 + 2

Thus, the solution of the equation after completing the square of the equation is found as; x = ±√19 + 2.

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Option (A) ΔDAB ~ΔDAC this similarity statement would be true for the figure.

We know that two triangles are similar if they have the same ratio of corresponding sides and equal of corresponding angles.

The fundamental theorem of similarity states that a line segment splits of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Similar triangles are the triangles that look similar to each other but their sizes might not be exactly the same. Two triangles will be similar if the angles are equal and sides are in the same ratio or proportion. Similar triangles may have different individual lengths of the sides of triangles but their angles must be equal and their corresponding ratio of the length of the sides must be the same.

In Δ DAB and Δ DAC

DA = DA

∠D = ∠D

and AB proportional to AC.

Therefore Δ DAB ~ Δ DAC would be true for the figure.

Given question doesn't provide figure. I have attached figure of triangle to complete the question.

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Answer:

A and C

Step-by-step explanation:

The angles and their images are congruent.

Answer:

The System of inequalities shown is C.

Answer:

77

Step-by-step explanation:

60+128+95+x=360

283+x=360

x=77

Answer: 6 pieces of candy

Step-by-step explanation:

Apply the Binomial Probability Distribution, The Answer is 0.044.

The discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome is known as the binomial distribution with parameters n and p in probability theory and statistics.

The required formula is:

[tex]P(x)= C(n,x) p^{x}q^{n-x}[/tex]

n=10

x=8

p(8)= [tex]C(10,8) * 0.5 ^ {8} *0.5 ^{2}[/tex]

=0.044

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After evaluating the given function using trigonometric identities, we have the resultant answer that is - tan(2t).

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence.

These are identities that, geometrically speaking, involve certain functions of one or more angles.

Pythagorean identities, reciprocal identities, sum and difference identities, and double-angle and half-angle identities are the main trigonometric identities.

We must apply the sine rule and the cosine rule to the non-right-angled triangles.

So, we have the function:

tan (15π - 2t)

Now, evaluate as follows:

(15π - 2t)

Rewrite using trigonometric identities:

- sin(2t)/cos(2t)

Rewrite using trigonometric identities:

- tan(2t)

Therefore, after evaluating the given function using trigonometric identities, we have the resultant answer that is - tan(2t).

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It will take 5.625 hours for both Darryl and Valerie to paint the room if they work together .

In the question ,

it is given that ,

Darryl can paint the room in 9 hours .

So , in 1 hour Darryl can paint 1/9 of the room .

Valerie can paint the room in 15 hours .

So , in 1 hour Valerie can paint 1/15 of the room .

So , the time taken to paint the room together can be calculated using ,

1/t = 1/9 + 1/15

1/t = 5/45 + 3/45

1/t = 8/45

Simplifying further ,

we get ,

t = 45/8

t = 5.625

Therefore , the time taken will be 5.625 hours .

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Answer:

Step-by-step explanation:

2,637

The value fo the numerical expression 2 × (2.5 -|-6|) will be negative 7.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ 2 × (2.5 -|-6|)

We know that the value inside the mode is always positive, then the expression is written as,

⇒ 2 × (2.5 -|-6|)

⇒ 2 × (2.5 - 6)

Simplify the expression, then the value of the expression is given as,

⇒ 2 × (2.5 - 6)

⇒ 2 × (- 3.5)

⇒ - 7

The value fo the numerical expression 2 × (2.5 -|-6|) will be negative 7.

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The (a + 2b + c)(a - c) is the product of the expression (a + b)² - (b + c)² using difference of two squares.

Considering two numbers a and b, the difference of their squares written as a² - b² is equal to the the product of the sum of the numbers and the difference of the numbers, that is (a + b)(a - b).

We have from the question two squares which are (a + b)² and (b + c)² and we shall express their difference as a product as follows:

(a + b)² - (b + c)² = [(a + b) + (b + c)][(a + b) - (b + c)]

open brackets and simplify;

(a + b)² - (b + c)² = (a + b + b + c)(a + b - b - c)

add and subtract like terms;

(a + b)² - (b + c)² = (a + 2b + c)(a + b - b - c)

(a + b)² - (b + c)² = (a + 2b + c)(a - c)

In conclusion, we have that (a + 2b + c)(a - c) is the product of the expression (a + b)² - (b + c)² that is a difference of two squares.

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Answer:

number is 2

Step-by-step explanation:

let the number be n then 6 times the number is 6n , so

6n + 3 = 15 ( subtract 3 from both sides )

6n = 12 ( divide both sides by 6 )

n = 2

the number required is 2

The simplest form in fraction will be 20666667/1000000 that can be find out using decimal and fraction relation.

How to convert decimal to fraction?

Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value.

For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10.

Steps :
1. Write down the decimal divided by 1, like this: decimal/1

2. Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

3. Reduce the fraction.

In given que 2.0666667 ,

7 decimal points are here.

so, equation will be 20666667/10^7

i.e. 20666667/10000000.

As both no. is indivisible to each other

So this is the simplest from.

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Answer:

The difference is

.9

Step-by-step explanation:

In the figure ,angle DEF=Angle DHG=50.prove that

The result after evaluating the expression is: 8

What is equations?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

For this case we have the following expression:

13-0.75w + 8x

We must evaluate for the following values:

w = 12

x = 1/2

Substituting the values we have:

13- 0.75 * (12) + 8 * (1/2) = 8

The result after evaluating the expression is: 8

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The solution of given expression 7×(4-3) - 1+5×1/5 is 5.

The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.

Given that the expression 7×(4-3) - 1+5×1/5.

To solve the above expression we will use PEMDAS;

First, we use the subtraction in brackets and this process is called simplifying parenthesis,

7×(4-3) - 1+5×1/5=  7×(1) - 1+5×1/5.

Now, we use the operation multiplication,

7×(1) - 1+5×1/5 = 7 - 1+1

Now we add the terms and this process is called addition of terms,

7 - 1+ 1 = 7-2

Now, we subtract the numbers and this property is subtraction of numbers,

7 - 2 = 5.

Therefore, the solution of given expression 7×(4-3) - 1+5×1/5 is 5.

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The probability that thickness of coin A will exceed thickness of coin B is 0.3905

Here, we are given that the distribution of x1 is n(1, 0.0004) and the distribution of x2 is n(1.01, 0.0009), that is-

X1 ~ N (1,0.0004) and X1 ~ N(1.01,0.0009)

Now, if a coin battery is selected at random,

The probability that the thickness of coin battery a will exceed the thickness of coin battery b = P(X1 > X2 )

It can be rewritten as follows,

P(X1-X2 > 0)

Let Y = X1-X2

The Y ~ N (1-1.01, 0.0004 + 0.0009)

i.e Y ~ N (-0.01, 0.0013)

= P(Z > 0.278)

= 0.3905

Thus, the probability that thickness of coin A will exceed thickness of coin B is 0.3905

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The solution to the expression 9.1p + 8.9r is 116.9 when p = 6 and r = 7

From the question, the mathematical expression is given as

9.1p + 8.9r

The values of the variables are given as

p = 6 and r = 7

Substitute p = 6 and r = 7 in the given expression 9.1p + 8.9r

So, we have the following representation

9.1p + 8.9r = 9.1 * 6 + 8.9 * 7

Evaluate the products in the above equation

9.1p + 8.9r = 54.6 + 62.3

Evaluate the sum in the above equation

9.1p + 8.9r = 116.9

Hence, the value is 116.9

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(a) If the discrimant is > 0, the quadratic equation has 2 real solutions.

(b) If the discrimant is = 0, the quadratic equation has 1 real solution.

(c) If b^2-4ac is < 0, the quadratic equation has 0 real solution, therefore it has 2 imaginary solutions.

The square root's input (i.e., its contents), which is the phrase b^2 -  4ac, is known as the "discriminant" because using its value, you may "discriminate" between (i.e., be able to distinguish between) the different solution types.

To determine how many possible solutions a quadratic equation has, utilize the discriminant formula.

(a) If the discrimant is > 0, the quadratic equation has 2 real solutions.

Example

x^2 - 5x + 2 = 0

where a = 1, b = -5, c= 2

D=b^2 - 4ac = (-5)^2 - 4 ×1 × 2 = 17

∴ It has two real solutions.

(b) If the discrimant is = 0, the quadratic equation has 1 real solution.

Example

x^2 + 2x + 1 = 0

where a = 1, b = 2, c= 1

D=b^2 - 4ac = (2)^2 - 4 ×1 × 1 = 0

∴ It has one real solution.

(c) If b^2-4ac is < 0, the quadratic equation has 0 real solution, therefore it has 2 imaginary solutions.

Example

3x^2 + 2x + 1 = 0

where a = 3, b = 2, c= 1

D=b^2 - 4ac = (2)^2 - 4 ×3 × 1 = -8

∴ It has two imaginary solutions.

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Answer:

Response bias would be something where answers would be skewed one way or another because of the way you asked. So maybe ask something embarrassing for someone to admit, like asking random students if they pick their nose. Some people will answer truthfully as no, and the people who do will likely also say no because they do not want to tell you that.

The indicated critical value of Z for given significance level, α = 0.04 is 1.75..

The critical Z-value is the point at which the area below the standard normal distribution is cut off. A critical value of z can indicate the probability that a particular variable has. If the absolute value of the test statistic is greater than the critical value, statistical significance is declared and the null hypothesis is rejected. The critical values of Z and t are approximately the same. The critical value test is:

Steps to determine the critical value:

We have given that,

α = 0.04 then α/2 = 0.02

then 1 - 0.02 = 0.98

Using the Z-table,

p-value = 1.7911 4444 ~ 1.75

Hence the critical values z, 0.04, is 1.75

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f(x-3.5) means f(x) is translated 3.5 units left. 3f(x) implies f(x) is vertically stretched by a factor of 3.5.

A function is a relationship between inputs where each input is related to exactly one output. Also, translation means movement on a straight line

In the cartesian plane or graph, movement in the x-axis is either to the left (negative) or right (positive).

Thus, f(x-3.5) implies f(x) is translated 3.5 units left (i.e. -3.5)

For 3.5f(x), when you multiply f(x) by 3.5, you stretch it by 3.5. Thus, f(x) is vertically stretched by a factor of 3.5

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Answer:             5

Step-by-step explanation: because