find the area of the region bounded by the three lines below. [hint: you will have to split up the integral into two parts.] y

The z score is -0.18 and 57 % of all Atlantic cod have more than 49.23 cm in length and

The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.

The Z-score is calculated using the formula:

z = (x - μ)/σ

where z: standard score

x: observed value

μ: mean of the sample

σ: standard deviation of the sample

Given data ,

Let the probability that a randomly selected Atlantic cod has a length of 53.68 cm or less be represented as P

Now , the equation will be

The observed value of be x

The mean of the sample μ = 49.9 cm

The standard deviation of the sample σ = 3.74 cm

Now , z-score is calculated using the formula:

z = (x - μ)/σ

And , the length of 57% of all Atlantic cod have more than is calculated by

Now , the z score with a p value of 0.43 is

z = -0.18

Substituting the values in the equation , we get

-0.18 = ( x - 49.9 ) / 3.74

Multiply by 3.74 on both sides of the equation , we get

-0.6732 = x - 49.9

Adding 49.9 on both sides of the equation , we get

x = 49.2268 cm

Hence , 57 % of all Atlantic cod have more than 49.2268 cm in length and the z score is -0.18

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The formula for the sum of cubes of the first n natural numbers is:

(1³+2³+3³+ ... + n³) = (1 + 2 + 3 + ... + n)²

Let us consider:

A(n)=1³+2³+⋯+n³--------(1)

B(n)=(1+2+⋯+n)²---------(2)

Now plug the numbers in the above equations(1)&(2) then,we get:

A(1)=B(1)=1

A(2)=B(2)=9

A(3)=B(3)=36

A(4)=B(4)=100

A(5)=B(5)=225

So both A and B are polynomials of degree at most 4 on n, and they coincide at 5 points.

Hence A(n) = B(n) for all n.

In general, p(n) is a polynomial of degree d on n,

∑kn=1 P(k)

is defined as a polynomial of the degree of d+1 on n. This trick will help solve every single issue involving the summation of polynomials, and then find the value on d+2 points, and we will determine the sum for all n.

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Solve for x in one of the equations and substitute it into the other equation.

To solve the system of equations 3x + 5y = 25 and x - 2y = -6 using substitution, we first solve for x in one of the equations. Let's solve for x in the second equation: x = 2y + 6. Next, we substitute this expression for x into the first equation: 3(2y + 6) + 5y = 25. This gives us 6y + 18 + 5y = 25, which simplifies to 11y + 18 = 25. Finally, we subtract 18 from both sides to obtain 11y = 7, and divide both sides by 11 to find y = 7/11. Now that we have y, we can substitute it back into either equation to find x.

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An equation of the best-fit line of data can be used to estimate untested values. Graphical data can be used to show relationships between variables, but those relationships do not have to be linear and do not always have a positive relationship.

Graphical data is a way of visually representing information in a way that can be easily understood. It is often used to determine relationships between variables, such as the relationship between prices and sales. Graphical data can be used to show correlations, even if the relationship is not linear. An equation of the best-fit line of data can be used to estimate untested values, which can be useful in predicting future values. The x-values and y-values of a graph can both be estimated based on the data presented, and do not necessarily need to start at the origin. Graphical correlations can have both positive and negative relationships, depending on the data presented. Graphical data can be a powerful tool for understanding relationships between data points.

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After resolving [tex](c+3)^{2}[/tex] , c = -3, and the approach is an example of the distributive property of equations.

Its simplest form has been thought to be the figure is probably smallest equivalent fraction. How or when to determine the basic form. Look for shared factors throughout the denominator and numerator. A fractional number can sometimes be checked to discover if it is a power of 2. A statement having two equal sides and an equal sign in the middle is referred to as a mathematical equation. Every variable's degree courses are listed in descending order as in general form of any equation. The formula for a linear equation is x + b = 0. The general form of a three separate linear equation is an x + b y + c = 0. (or something similar). Either conditioned equations or identities are categories for mathematics. An identity holds true for whatever value of the variables.

Given,

[tex](c+3)^{2}[/tex]

= by using formulas of [tex](a+b)^{2}[/tex]

by distributive property

[tex]c^{2}[/tex] + [tex]3^{2}[/tex] + 6c

= [tex]c^{2}[/tex] + 9 + 6c

= [tex]c^{2}[/tex] + 6c + 9 = 0

[tex]c^{2}[/tex] + 3c + 3c + 9 = 0

= c ( c + 3 ) + 3 ( c + 3)

= (c + 3 )(c+ 3)

c = - 3

After resolving [tex](c+3)^{2}[/tex], c = -3, and the approach is an example of the distributive property of equations.

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The likelihood that a stranger on the street has an IQ below 98 is 0.4470, or 44.70%.

The probability that an event will happen or a claim will be correct is measured by statistical mechanics, a branch of mathematics. The possibility of an occurrence is a positive integer and 1, where about 0 represents how likely the event is to occur and value of 1 indicates certainty. A probability is a numerical illustration of the possibility that a specific activity will take place. Probabilities can also be expressed using percentages extending from 0% to 100% or from 0 to 1. the ratio of the number of outcomes to the proportion of occurrences in a comprehensive set of equally likely choices that lead to a specific occurrence.

given

This is Z's pvalue for X = 98. So

Z = 98 -100 / 15

Z = -0.133

Z = -0.133 pvalue of 0.4470

The likelihood that a stranger on the street has an IQ below 98 is 0.4470, or 44.70%.

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Answer: 3y + 2

Step-by-step explanation: First, you can organize the equation into -3y + 6y + 4 - 2. Then, you get 3y + 2. :)))))

l=7m

Step-by-step explanation:

here us the answer of the solution

The total surplus received by both Patricia and Cecilia is $55.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

Patricia decides to buy a pair of boots for $90.00. She was willing to pay $120.00.

And, Her friend Cecilia sees the boots, she loves them and thinks they are worth $170.00. So she offers Patricia $145.00 for the boots, and Patricia accepts.

Hence, Consumer surplus is the difference between the willingness to pay of a consumer and the price of the good.

Consumer surplus = willingness to pay – price of the good

Consumer surplus received by Patricia = $120 - $90 = $30

Consumer surplus received by Cecilia = $170 - $145 = $25

Thus, Sum of the surpluses = $30 + $25 = $55

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A group of students and adults are going to the museum and have spent a total of $115 on tickets. Adult tickets cost $5 each and student tickets cost $3 each. There are 25 more students than adults in the group therefore the number of students are in the group are 35 and the number of adults in the group are 5.

This is referred to as the value of money that has been used up to produce something or deliver a service.

Since we were told that  Adult tickets cost $5 each and student tickets cost $3 then  $5 × 5 = $25 and $3 × 30 = $90. Therefore the total is $115.

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The simplified expression for this problem is given as follows:

[tex]43\sqrt{5} - 6[/tex]

The expression for this problem is defined as follows:

[tex]30\sqrt{5} + 13\sqrt{5} - 6[/tex]

To simplify the expression, we combine the like terms, which are the terms that have the same rational, thus:

[tex]30\sqrt{5} + 13\sqrt{5} = 43\sqrt{5}[/tex]

Combining along with the subtraction by 6, the complete simplified expression is given as follows:

[tex]43\sqrt{5} - 6[/tex]

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ac is congruent to pr because those sides correspond

Answer: 4.8

Step-by-step explanation:

6.4 - 1.6 = 4.8

Answer:

If we subtract 14 from both sides of the equation for RU, we get 6p = RU - 14, or 6p = RU - 14. We can then substitute this expression for 6p into the equation for ST to get:

ST = p + 31

ST = (RU - 14) + 31

Expanding RU, we get:

ST = RU - 14 + 31

ST = RU + 17

Since RU = 6p + 14, we can substitute this expression into the above equation to solve for p:

ST = 6p + 14 + 17

ST = 6p + 31

Finally, we can subtract 31 from both sides of the equation to find p:

ST - 31 = 6p + 31 - 31

ST - 31 = 6p

ST - 31 = 6p

p = (ST - 31) / 6

So, to find the value of p, we need to know the value of ST.

As a result, the original discounted price is $1 while the weekly normal price is $9.

The fundamental formula for calculating a reduction is to increase the initial price by the provided percentage rate in decimal form. We must deduct the reduction from the initial price to determine the item's sale price.

From the given information, we have:

d + 6x = 55 (discounted price for 7 weeks)

d + 11x = 100 (discounted price for 12 weeks)

We can solve this system of equations by eliminating d. Subtracting the first equation from the second, we get:

5x = 45

Dividing both sides by 5, we get:

x = 9

Substituting x = 9 into one of the equations, we can solve for d. Using the first equation, we get:

d + 6(9) = 55

d + 54 = 55

d = 1

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Answer:

7cm²

Step-by-step explanation:

volume of a triangular prism=1/2×b×h×l

1/2×b×h=cross sectional area

84cm³=C.A×12

C.A=84/12

base area=7cm²

Answer:

the number is 78

Step-by-step explanation:

call x is the tens digit (0<x<9)

y is the unit digit (0[tex]\leq[/tex]y[tex]\leq[/tex]9)

we have:

10y+x=[tex]\oveline{yx}[/tex] (1)

10x+y= [tex]\overline{xy}[/tex] (2)

acording (1),(2) and the topic we have: (10y+x)-(10x+y)=9 ⇔9y-9x=9

⇔y-x=1 (3)

and x+y=15 (4)

from (3), (4) we have a system of equation

[tex]\left \{ {{y-x=1} \atop {x+y=15}} \right.[/tex]

⇔[tex]\left \{ {2y=16} \atop {x+y=15}} \right.[/tex]

⇔[tex]\left \{ {{y=8} \atop {x+8=15}} \right.[/tex]

⇔[tex]\left \{ {{y=8} \atop {x=7}} \right.[/tex] (conditions are satified)

the number is 78

Answer:

5,4,2,0

Step-by-step explanation:

f(g(4))=5

g(f(3))=4

f(f(2))=2

g(g(5))=0

The value of composition function is:

1. f(g(4)) = 5

2. g(f(3)) = 4

3. f(f(2)) = 2

4. g(g(5)) = 0

To find the value of function focus on the graph of the function.

1. f(g(4))

From the graph of g(x), when x= 4 the value of y is 2.

So, g(4) = 2

Now, the value of f(g(4))

f(g(4))= f(2)

        = 5.

2. g(f(3))

From the graph of f(x), when x= 3 the value of y is 0.

So, f(3) = 0

Now, the value of g(f(3))

g(f(3))= g(0)

        = 4.

3. f(f(2))

From the graph of f(x), when x= 2 the value of y is 5.

so, f(2)= 5

Now, the value of f(f(2))

f(f(2)) = f(5)

        = 2

4. g(g(5))

From the graph of g(x), when x= 5 the value of y is 3.

so, g(5)= 3

Now, the value of g(g(5))

g(3) = 0

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The unit rate for the games per loss are:

Jules’ Rules unit rate = 3 or 3/1

Pink sox unit rate = 4 or 4/1

Go - Girl unit rate = 4 or 4/1

High- 5s unit rate = 9 or 9/1

Unit rate = Games/Losses

Jules’ Rules unit rate = 36/12

Jules’ Rules unit rate = 3 or 3/1

Pink sox unit rate = 68/17

Pink sox unit rate = 4 or 4/1

Go- Girls unit rate = 52/13

Go - Girl unit rate = 4 or 4/1

High-5s unit rate = 72/8

High- 5s unit rate = 9 or 9/1

Therefore the Jules’ Rules unit rate 3, Pink sox unit rate 4, Go - Girl unit rate 4, High- 5s unit rate 9.

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The eigenvalues of a matrix are roots of its characteristic polynomial using this we prove  that a square matrix and its transpose have the same characteristic polynomial.

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital applications as well.

Recall that the eigenvalues of a matrix are roots of its characteristic polynomial.

Hence if the matrices A and A Transpose have the same characteristic polynomial, then they have the same eigenvalues.

So we show that the characteristic polynomial pA(t)=det(A−tI) of A is the same as the characteristic polynomial p[tex]A^T[/tex] (t)=det(A ^T−tI)of the transpose [tex]A^T[/tex].

We have,

p[tex]A^T[/tex](t)=det([tex]A^T[/tex] −tI) =det([tex]A^T[/tex] −tI T )

=det((A−tI) [tex]A^T[/tex] )

=det(A−tI)

=pA(t)

Since I ^T =I

Since det([tex]B^T[/tex] )=det(B)for any square matrix B

Therefore, we obtain p[tex]A^T[/tex] (t)=pA(t), we conclude that the eigenvalues of A and [tex]A^T[/tex] are the same.

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Answer:y=5/3 x-5

Step-by-step explanation: first find the y-intercept, when the x value is 0 that is the y intercept, then the equation becomes -3x=15, there you get

x=-5, then do the same to the other to get the x value so you get the points (0,-5), and (3,0) there you find the slope and plug in

Answer: $14.22

Step-by-step explanation: 237*0.06

Answer:

the inequality y ≥ 0.8x + 1.5 accurately describes the relation between the duration of the hike (x) and the amount of water needed (y). This inequality means that for any duration of the hike (x), the amount of water needed (y) must be greater than or equal to 0.8x + 1.5.

Answer:

Step-by-step explanation:

3 liters of water for 4 hours of hiking.

Answer:

[tex]y=x-2[/tex]

Step-by-step explanation:

The slant, or oblique asymptote, is found by taking the quotient of the two polynomials and disregarding the remainder:

-3 |  1  1  2

____  -3_6

      1 -2 | 8

Hence, our slant asymptote is [tex]y=x-2[/tex]

Answer:

[tex]6 {}^{3x} [/tex]

Step-by-step explanation:

Given expression to us is ,

2^{-x} . 3^{-x} . 6^{2x} . 3^{2x} . 2^{2x}

We can rewrite it as ,

[2^{-x} . 2^{2x} ] [ 3^{-x} . 3^{2x}] . 6^{2x}

we know a^m . a^n = a^{m+n} , so ;

2^{-x +2x} . 3^{-x+2x} . 6^2x

simplify,

2^x . 3^x . 6^{2x}

we know a^m . b^m = (ab)^m , so ;

(2*3)^x . 6^{2x}

6^x . 6^2x

6^{x+2x}

6^{3x}

And we are done!

Answer:

[tex]6^{3x}[/tex]

Step-by-step explanation:

Given exponential expression:

[tex]2^{-x} \cdot 3^{-x} \cdot 6^{2x} \cdot 3^{2x} \cdot 2^{2x}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^n \cdot c^n=(a \cdot c)^n:[/tex]

[tex](2\cdot 3)^{-x} \cdot 6^{2x} \cdot (3 \cdot 2)^{2x}[/tex]

Multiply the numbers:

[tex]6^{-x} \cdot 6^{2x} \cdot 6^{2x}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]6^{(-x+2x+2x)}[/tex]

Therefore:

[tex]6^{3x}[/tex]

The factor of 1 - 2.25x⁸ is (1 + 1.5x⁴) (1 - 1.5x⁴).

The correct option is C.

Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.

Given:

An expression,

1 - 2.25x⁸.

Simplifying to the factored form.

1² - (1.5x⁴)²

= (1 + 1.5x⁴) (1 - 1.5x⁴)

Therefore, (1 + 1.5x⁴) (1 - 1.5x⁴) is the factored form.

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]Answer:

The area of a rectangle is calculated by multiplying its length by its width. If the length of the rectangle is 7 and its width is 4x, the area can be found by performing 7 * 4x. The answer would be 28x square units, where x represents the unit of measurement.

This means that the average sale price for a home in this sample was "$773" and that half the sales were for less than the median price of "$577", while half were more than the median price of "$577".

(a) To calculate the sample mean, we add up all the values and divide by the number of values:

x = (592 + 817 + 577 + 608 + 353 + 1,281 + 412 + 535 + 550 + 679)/10 = 7,727/10 = $773

The sample median is the middle value when all the values are ordered from smallest to largest:

353, 412, 535, 550, 577, 608, 592, 679, 817, 1,281

The median is 577.

This means that the average sale price for a home in this sample was $773 and that half the sales were for less than the median price of $577, while half were more than the median price of $577.

(b) If the 6th observation had been 985 rather than 1,281, the new mean would be calculated as:

x = (592 + 817 + 577 + 608 + 353 + 985 + 412 + 535 + 550 + 679)/10 = 7,610/10 = $761

The new median would still be $577.

(c) To calculate a 20% trimmed mean, we first need to find the two smallest and two largest observations, then remove them and take the average of the remaining values:

Two smallest: 353, 412

Two largest: 1,281, 817

Remaining values: 535, 550, 577, 608, 592, 679

The trimmed mean is (535 + 550 + 577 + 608 + 592 + 679)/6 = $592

(d) To calculate a 15% trimmed mean, we first need to find the three smallest and three largest observations, then remove them and take the average of the remaining values:

Three smallest: 353, 412, 535

Three largest: 817, 1,281, 679

Remaining values: 550, 577, 608, 592

The trimmed mean is (550 + 577 + 608 + 592)/4 = $576.

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Step-by-step explanation:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. If a line is parallel to another line, it means they have the same slope. To find the slope of the line 7x - y = 3, we can rearrange it into slope-intercept form: y = 7x - 3. So, the slope of the line 7x - y = 3 is 7.

Since the line we want to find is parallel to 7x - y = 3 and has a slope of 7, the equation of the line can be written as y = 7x + b, where b is the y-intercept. To find b, we use the point (6, 3) as a solution:

y = 7x + b

3 = 7 * 6 + b

3 = 42 + b

b = -39

So, the equation of the line that passes through (6, 3) and is parallel to 7x - y = 3 is y = 7x - 39.