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The shaded region of the rectangle is 242.9 cm² and the shaded region of the sector is 7.1 square units.

Question 17) is a figure of a rectangle and two inscribed circles.

The area of a rectangle is expressed as: A = length × width

The area of a circle is expressed as: A = πr²

Where r is the radius.

To determine the area of the shaded region, we simply subtract the areas of the two circles from the area of the rectangle.

Area = ( Length × width ) - 2( πr² )

Area = ( 40 × 10 ) - 2( π × 5² )

Area = ( 400 ) - 2( 25π )

Area = 400- 50π

Area = 242.9 cm²

Area of the shaded region is 242.9 squared centimeters.

Question 18) is the a figure a sector of a circle and a right triangle.

The area of a sector is expressed as: A = (θ/360º) × πr²

The area of a triangle  is expressed as: A = 1/2 × base × height

To determine the area of the shaded region, we simply subtract the areas of the triangle from the area of the sector.

Hence:

Area = ( (θ/360º) × πr² ) - ( 1/2 × base × height )

Plug in the values:

Area = ( (90/360º) × π × 5² ) - ( 1/2 × 5 × 5 )

Area = 25π/4 - 12.5

Area = 7.1

Therefore, the area of the shaded region is 7.1 square units.

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Answer:

x ≥ 1.5

Step-by-step explanation:

2x - 3 ≥ 0 ( add 3 to both sides )

2x ≥ 3 ( divide both sides by 2 )

x ≥ 1.5

Answer:

Step-by-step explanation:

Given that:

The mean μ = 310

The standard deviation σ =  40

Using the empirical rule to determine the following :

a. About 95 % of organs will be between what weights?

At 95% data values lies within 2 standard deviations of mean.

Thus, the  required range is :

= μ ± 2σ

= ( 310 - 2 (40) ,  310 + 2(40) )  

= (230, 390)

b. What percentage of organs weighs between 270 grams and 350 grams

Here:

μ ± σ = (310 - 40,  310 + 40)

μ ± σ = (270, 350)

Using empirical rule, 68% data values is in the range within 1 standard deviation of mean. This implies that 68% data values lie between (270, 350).

c. What percentage of organs weighs less than 270 grams or more than 350 grams?

The complement theorem can be use to estimate the  percentage of organs that weighs less than 270 grams or more than 350 grams,

This can be illustrated as :

= 100 % - 68 %

= 32 %

d. What percentage of organs weighs between 230 grams and 430 grams?

Using the empirical rule:

The percentage of organs weighs between 230 grams and 430 grams is:

u - 2σ  and  u + 3σ respectively.

Answer:

note ;sum of two no. is not 1.

let no. be x and y.

we have

x+y=11.......(1)

x-y=5........(2)

adding equation 1&2

x+y+x-y=11+5

2x=16

x=16/2=8

again

8-y=5

y=8-5=3

:.

x=8,y=3

Answer:

7 seconds that Hannah runs on the side walk

Step-by-step explanation:

let's A is the second that Hannah runs on the side walk.
and B is the second that Hannah runss on the cross street. Base on the information we have 2 equations for 2 unknowns .
A + B = 12
16 A + 3 B =  127  simply to add/subtract column we have
=> 16A + 3B  = 127 (1)
      3A + 3B = 36  (2)  runs on the side walk.
And 12-7 =5 seconds is the time that Hannah runs on the cross street.

Hannah spend 7 seconds for running on the sidewalk.

Here,

Hannah runs down the street to catch her bus.

She runs for a total of 12 seconds.

On the sidewalk, she runs 16 feet per second. When she crosses the street, she runs 3 feet per second.

Hannah runs a total distance of 127 feet.

We have to find, How many seconds did Hannah spend running on the sidewalk.

What is Linear equation in two variables?

Linear equations in two variables is defined as, If a, b, and r are real numbers then ax + by = r is called a linear equations in two variables.

Now,

Let X is the second that Hannah spend running on the sidewalk.

And, Y is the second that Hannah runes on the cross the street.

Since, She runs for a total of 12 seconds.

⇒ X + Y = 12 .... (i)

And,  On the sidewalk, she runs 16 feet per second. When she crosses the street, she runs 3 feet per second and Hannah runs a total distance of 127 feet.

⇒ 16 X + 3 Y = 127 ....(ii)

By solving equation (i) and (ii), we get;

⇒ X = 7 and Y = 5

Hence, Hannah spend 7 seconds for running on the sidewalk.

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Answer:

C. 1/4

hopes this helped

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

\((\stackrel{x_1}{-8}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{(-8)}}} \implies \cfrac{3 +1}{8 +8} \implies \cfrac{ 4 }{ 16 } \implies \cfrac{1 }{ 4 }\)

The required number of different distances possible is given as 36.

Given that,
In a board game, the distance a player travels is equal to the sum of the numbers shown when two 6-sided dice are tossed.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,
1 dice have 6 outcomes
2 dice have 6 outcomes,
Number of possible combination = 6 × 6 = 36

Thus, the required number of different distances possible is given as 36.

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The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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The equation of the set of algebra tiles is x + 8 = 12.

Algebra tiles are mathematical manipulatives that help students comprehend the principles of algebra and strategies to think algebraically. For introductory algebra pupils at the level of elementary school, middle school, high school, and college, these tiles have been demonstrated to offer solid examples.

Given set,

x 1 1 1 1 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1

the set has one positive x and eight positive units,

the equation is x + 8.

and on the right side of the equation, there are 12 positive units,

equation is x + 8 = 12

Hence the equation s x + 8 = 12.

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Answer:

x + 8 = 12.

Step-by-step explanation:

in case you need it (x=4)

Answer:

-53, f(n) = -6(n-1) + 13

Step-by-step explanation:

given the equation to this linear/arithmetic sequence for the nth term: f(n) = -6(n-1) + 13

f(12) = -6(12-1) + 13

f(12) = -6(11) + 13

f(12) = -66 + 13

f(12) = -53

*substitute and simplify*

______________

f(n) = f(1) + d(n-1)

given f(1) = 13, f(2) = 7, and f(3) = 1

7-13 = 1-7 = -6 = d

= f(1) + d(n-1)

f(1) = 13 so

the equation must be f(n) = 13 - 6(n-1) or -6(n-1) + 13

\((\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{8}}} \implies \cfrac{ 3 }{ -3 } \implies - 1\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{8}) \\\\\\ y-5=-x+8\implies {\Large \begin{array}{llll} y=-x+13 \end{array}}\)

Answer:

20y - 20

Step-by-step explanation:

We multiply the first term and the second term in the parentheses by the 4. That means we do:

4(5y) + 4(-5)

And we simplify to get:

20y - 20

Answer:13/25

both 52 and 100 can be divided by 4

Step-by-step explanation:

Answer:

The simplest form of 52/100 is 13/25

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 52 and 100 is 4

Divide both the numerator and denominator by the GCD

52 ÷ 4

100 ÷ 4

Reduced fraction:

13

25

Therefore, 52/100 simplified to lowest terms is 13/25.

Step-by-step explanation:

Hope it helps!

Answer: 3.76 meters

Step-by-step explanation:

Answer:

3.76

Step-by-step explanation:

Answer:

------------------------

Find the slope of AB:

Use point-slope form and point A(2, 4) to determine the line:

Multiply both sides by 9 to clear fraction:

Open parenthesis and convert the equation into ax + by + c = 0:

Answer: Answer choice B

Step-by-step explanation:

The number she'd have is:

Explanation:

First, let's see which number is in the tens place and which number is in the ones place (the units place).

In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).

So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :

550

That's not all, since we also add 1 to the tens:

560

The body surface area is given by the equation A = 1.6865 m²

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the body surface area be represented as A

Now , the equation will be

A = ( HW / 3600 )^1/2

A = √( HW / 3600 )   be equation (1)

where H is the height in centimeters and W is the weight in kilograms

Now , the value of H = 160 cm

The value of W = 64 kg

Substituting the values in the equation , we get

A = √ [ ( 160 x 64 ) / 3600 ]

On simplifying the equation , we get

A = √ ( 10240/3600 )

A = √ ( 2.8444 )

A = 1.6865 m²

Therefore , the body surface area is 1.6865 m²

Hence , the equation is A = 1.6865 m²

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The ways to pack are

This is further explained below.

Generally, The science, art, and technology of packaging involves confining or safeguarding goods for distribution, storage, sale, and usage. The process of creating, analyzing, and designing packages is sometimes referred to as packaging.

In conclusion,

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Answer:4.5

Step-by-step explanation:

Answer:

Absolute value means any value but always positive. So |-4.5|=4.5

Problem

\( \frac{1}{6} (x + 12) = - 4\)

Solution

For this case we have the following equation given:

We can multiply both sides by 6 and we got:

Now we can subtract 12 in both sides and we got:

And the solution for this case would be x=-36

Answer:   A≈380.13ft²

Step-by-step explanation:

Answer:

5 1/4

Step-by-step explanation:

7 days = 1 week, so 3/4 x 7 = 5 1/4

The circumcenter theorem states that the circumcenter of a triangle is the point of intersection of the perpendicular bisectors of the sides of the triangle. In other words, the circumcenter is the center of a circle that passes through all three vertices of the triangle.

The circumcenter theorem is a fundamental theorem in geometry and is used in the construction of the circumcenter of a triangle. The circumcenter is the point of intersection of the perpendicular bisectors of the sides of the triangle, and its coordinates can be determined by the coordinates of the triangle's vertices.

This theorem is useful in many applications, such as in: the construction of a triangle from its circumcenter, or in determining the distance between two points. It can also be used to determine the area of a triangle from its three vertices. The circumcenter theorem has been studied for centuries, and it is still an important tool for geometers and mathematicians today.

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In given fractions 8/9 is 1/36 large than 31/36

Finding the larger and smallest fraction in between two or more fractions is known as comparing fractions.

We need to change fractions with unlike denominators into fractions with similar denominators in order to compare them. For this, we will find the denominators' Least Common Multiple (LCM).    

If the denominators are the same then it is easy to compare the fractions.

Here we have

31/36 and 8/9

To find the largest fraction convert both denominators into the same  

Here LCM(36, 9) = 36  

Now multiply both numerator and denominators of fractions with a number to change the denominators  

=> \(\frac{31}{36} \times \frac{1}{1} = \frac{31}{36}\)  

=> \(\frac{8}{9} \times \frac{4}{4} = \frac{32}{36}\)  

From the above calculations given fractions are 31/36 and 32/36

Difference = \(\frac{32}{36} - \frac{31}{36} = \frac{1}{36}\)  

Therefore,

In given fractions 8/9 is 1/36 large than 31/36

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