Lin wrote a proof to show that diagonal EG is a
line of symmetry for rhombus EFGH. Fill in the
blanks to complete her proof.

The rate of change of the functions are: I. -3 II. -1/4.

Therefore, C. Both functions are decreasing and have different rates of change.

The rate of change of any function can be calculated as = change in y / change in x.

If the rate of change is a negative number, the function is decreasing. If it is a positive number, the function is decreasing:

Rate of change of the line that passes through (3, 3) and (4, 0):

Rate of change = (0 - 3) / (4 - 3)

= -3/1

= -3 [this means the function is decreasing].

Rate of change of the function represented by the table, using two pairs of the table values, (0, -1) and (-4, 0):

Rate of change = (0 -(-1)) / (-4 - 0)

= 1/-4

= -1/4 [this shows the function is decreasing]

Therefore, the answer is: C. Both functions are decreasing and have different rates of change.

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The number 1000 can be written in its expanded form as

1000 = 1×10³ + 0×10² + 0×10 + 0

Given, a number 1000

we have to write the given number in its expanded form

so, 1000 can be written in its expanded form as

1000 = 1×10³ + 0×10² + 0×10 + 0

and it is the expanded form of the number 1000

where, the place value of 1 is thousand.

So, the number 1000 can be written in its expanded form as

1000 = 1×10³ + 0×10² + 0×10 + 0

Hence, the number 1000 can be written in its expanded form as

1000 = 1×10³ + 0×10² + 0×10 + 0

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Answer:

Yes, the yellow triangles are similar.

Step-by-step explanation:

Angle-Angle similarity states that if any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

If angle x is 71° then both yellow triangles have two angles of equal measure (28° and 71°), which means they are similar triangles.

1.Regression line is given by:

  y = 4.14 - 0.04 x

2. When explanatory variable is 0, y = 4.14

3.For each increase of 1 in explanatory variable, there can be a decrease of 0.04 in response variable.

4. The value of y is 4.28

5.  The value of r is -0.04

What is regression line?

A regression line is a line that in statistics best depicts the behavior of a set of data. It is, in other words, a line that best fits the trend of the data at hand.

Simple linear regression results:

Dependent Variable: Y

Independent Variable: X

Y = 4.1428571 - 0.035714286 X

Sample size: 7

From above equation:

1. Regression line is given by:

  y = 4.14 - 0.04 x

2. When explanatory variable is 0, y = 4.14

3. For each increase of 1 in explanatory variable, there can be a decrease of 0.04 in response variable.

4. when x = -3.5:

substitute this into the equation of regression line

y = 4.14 - 0.04*(-3.5) = 4.28

It is an example of extrapolation

5. r = -0.04

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A group of two or more equations containing the same variables but with at least one non-linear equation is a non-linear system of equations.

What is a non-linear equation?

What is a nonlinear equation example?

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The cost of 6 boxed lunches is 62.7

A company orders 19 boxed lunches from a deli for $198. 55.

We need to calculate the price of 6 lunch boxes.

This can be found by using unitary method

Number of lunch boxes =  19

Total price = 198.55

If 19 lunch boxes cost 198.55

Cost of 1 lunch box is 198.55/19

Cost of 1 lunch box is 10.45

Cost of 6 lunch boxes is 10.45 x 6

Cost of 6 lunch boxes  is 62.7

Therefore, If a company orders 19 boxed lunches from a deli for $198. 55 the cost of 6 boxed lunches is 62.7

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The steps to construct the bisector of angle A are- draw an arc across both rays of the angle. From each arc, draw another pair of arcs that intersect each other. Draw a line to the intersection point to form the angle bisector.

Detailed steps to construct the bisector of angle A using compass are:

1. Give name to  the intersection of the arcs in the interior of the angle as point M.

2. Without changing the width of the compass, place the point of the compass at point O and draw another arc in the interior of the angle.

3. Place the point of the compass on point N and again draw an arc in the interior of the angle.

4. Use the straight ruler to draw a line.

5. Place the point of the compass at point A and draw an arc that intersects the sides of ∠A. Label the points of intersection as points N and O.

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Median for the given data 17, 2 ,7 is  12.

What is median?

The median is that the value that’s precisely within the middle of a dataset once it's ordered. It’s a live of central tendency that separates the bottom 50% from the very best 50% of values.

Main body :

First of all to find the median data should be arranged in ascending order.

Aranging data in ascending order

2, 5 , 7 , 7 , 8 , 8 , 10 , 10 , 14 , 15 , 17 , 18 , 24 , 27 , 28 , 48

Now there are even number of terms i. e 16

So,

M1 = n / 2 and M2 = ( n / 2 ) + 1

= 16 / 2 = 8 + 1

= 8th term = 9th term

M1 = 10 M2 = 14

Median, M = ( M1 + M2 ) / 2

= ( 10 + 14 ) / 2

= 24 / 2

= 12

Hence median of observation is 12.

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It takes Ahby a total of 9.5 minutes to run a mile.

What is a total?

The sum of two or more numbers is known as the total in mathematics. It is the total of the figures added up. When we add two or more numbers, amounts, or items, the total sum is obtained. The sum can also be expressed as the total, aggregate, or tally in this example, where the sum of 3 and 7 is 10.

Solution Explained:

Given in the question,

Total time taken to run 6 miles = 57

So,

Total time taken to run 1 mile = 57/6 = 9.5 minutes

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The minimum sample size would be 953.

What is the confidence interval?

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally used.

The given sample space is n = 300.

x = 101 plan to vote

P = x/n = 101/300 = 0.3367

95% confidence = [tex]P\pm Z_\frac{\alpha}{2}=1.96[/tex]

Confidence Interval:

                         [tex]CI=P\pm Z_\frac{\alpha}{2}\sqrt{\frac{P(1-P)}{n}}\\\\CI=0.3367\pm 1.96 \times \sqrt{\frac{0.3367(1-0.3367)}{300}}\\\\CI=(0.2832, 0,3902)[/tex]

Margin of error = 3%

The margin of Error = [tex]Z_\frac{\alpha}{2}\sqrt{\frac{P(1-P)}{n}}[/tex]

                   [tex]3 \% = P\pm Z_\frac{\alpha}{2}\sqrt{\frac{P(1-P)}{n}}[/tex]

                  [tex]\frac{1}{\sqrt{n}}=\frac{0.03}{1.96\sqrt{(0.3367)(1-0.3367)}}\\\\\sqrt{n} = 30.875\\\\n = 953[/tex]

Hence the minimum sample size = 953.

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(a) The demand function assuming it is linear is  P(x) = -x/3000 + 19   .

(b) The ticket price to maximize the revenue should be $9.5    .

In the question ,

it is given that ,

the number of spectators that baseball stadium can hold = 53000

the ticket price = $10

the average attendance = 27000 ,

when ticket price lowered to $8 , average attendance rose to 33000 .

So , the points are represented as

for $10 the attendance is 27000 ,

for $8 the attendance is 33000 ,

the points are (27000 , 10) and (33000 , 8) .

the slope = (change in price)/(change in attendance )

= (8-10)/(33000 - 27000)

= -2/6000

= -1/3000

So ,the equation is

(y - 10) = (-1/3000)(x - 27000)

y - 10 = -x/3000 + 27000/3000

y - 10 = -x/3000 + 9

y = -x/3000 + 19

the demand function is P(x) = -x/3000 + 19   ,

the revenue function , R(x) is x.P(x)

R(x) = x.P(x)

So , R(x) = x(-x/3000 + 19)

= -x²/3000 + 19x

to maximize the revenue function , we differentiate with respect to "x" ,

we get ,

R'(x) = 19 - 2x/3000

= 19 - x/1500

for critical value , R'(x) = 0 ,

w get ,

19 - x/1500 = 0

x/1500 = 19

x = 28500

again Differentiating R′(x) with respect to x,

R″(x) = -1/1500 < 0

So , for 28500 spectators, the revenue will be  maximum .

the ticket price for 28500 spectators will be ,

P(28500) = 19 - 28500/3000

= 19 - 9.5

= 9.5

Therefore , (a) The demand function assuming it is linear is  P(x) = -x/3000 + 19   .

(b) The ticket price to maximize the revenue should be $9.5    .

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The estimate of number of cars with speed more than 85 is 25

In the table, the frequency shows the number of cars with the range of speeds as in the first column

The number of cars with speed more than 85 will fall in the interval 80 < s ≤ 100, the number with speed more than 85 is 85 < s

The frequency of this interval 80 < s ≤ 100 is 25 and this is the estimate of  the number of cars with speed ore than 85

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Answer:

1km= 1000m

[tex]\frac{650}{1000}[/tex]

=[tex]\frac{13}{20}[/tex] (simplified)

Answer:

Step-by-step explanation:

78

The number line we can see that 1.5 is less than 1.75.

Mark two points 1.75  and 1.5 on number line  and make a number line from -1 to 2 where each point is 0.25 units away

Then compare 1.75  and 1.5 on number line

Given :

Nico wants to use a horizontal number line to compare 1 3/4 and 1.5

Lets write the fraction in decimal form to compare and mark it on number line [tex]1\frac{3}{4}[/tex] = 1.75

Now mark two points 1.75  and 1.5 on number line

Make a number line from -1 to 2 where each point is 0.25 units away

Mark a number line that are 0.25 units away using below numbers

-1, -0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2

On the number line ,

1.5 comes first

1.75 is next to 1.5

From this number line we can see that 1.5 is less than 1.75.

1.5 <       [tex]1\frac{3}{4}[/tex]

Hence the answer is the number line we can see that 1.5 is less than 1.75.

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for the following gear train, tooth numbers are n2 = 12, n3 = 16, and n4 = 12 the speed of the arm is 426.67 rev/min.

The angular velocity of an item as it rotates around an axis or centre is quantified as the speed of rotation. Usually, it is expressed in terms of degrees,   per minute (RPM). The angular velocity of an object is a measure of how rapidly the object rotates around a central point and is connected to the linear velocity of the object around the perimeter of its path of revolution. In physics, the idea of It is used to explain the motion of things ranging from tiny particles to large celestial bodies, and it is an important aspect in understanding object behaviour. for the following gear train, tooth numbers are n2 = 12, n3 = 16, and n4 = 12

How to solve?

n1/n2 = n3/n4. In this case, the gear ratio for the first set of gears (gears 1 and 2) is 12/12 = 1. For the second set of gears (gears 3 and 4), the gear ratio is 16/12 = 4/3.

Since internal gear 5 is fixed, it must have the same number of teeth as gear 1, which is 12. Therefore, the number of teeth on internal gear 5 is 12.

To determine the speed of the arm, we need to use the equation for speed of rotation: speed of rotation = (speed of input shaft) x (gear ratio of gears 3 and 4) = 320 rev/min x (4/3) = 426.67 rev/min.

Therefore, the speed of the arm is 426.67 rev/min.

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The number of combinations of a president, vice president, secretary and a treasurer can be chosen from a group of 12 students is 11,880.

Given: we have group of 12 students.

we are asked to determine the number of combinations of a president, vice-president, secretary, and treasurer can be chosen from a group of 12 students.

nPr = n!/(n-r)!

12P4 = 12!/(12 - 4)!

12P4 = 12!/8!

9 × 10 × 11 × 12

= 11,880

Hence the number of combinations are 11,880.

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The statement is false. It is always necessary for an agent to disclose the identity of the principal to any third person with whom he is contracting; else the contract becomes void.

Given that,

Any third party with whom an agent enters into a contract must always be informed of the identity of the principal; otherwise, the contract is null and void.

By speaking to the third party or carrying out an approved act, the principle reveals his or her identify and existence.

If the principle's identity is unknown and the third party has learned enough details to guess it, the principal is deemed to have been disclosed. The principal is in this case responsible to the third party; the agent is not. Contracts or other agreements between agents and third parties are regarded as agreements between the main and the third party.

Despite the fact that the agent is not a party to the contract, in the event that the principal breaches it, the agent is not personally liable for any damages that follow from the breach.

So, the statement is false.

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Greater inputs only result in the leading term becoming more and more positive if the leading coefficient is positive. The graph will incline rightward. Larger inputs will simply make the leading term more and more negative if the leading coefficient is negative. The rightward descent of the graph is planned.

The coefficient of the leading term is the leading coefficient in a polynomial. Because of the negative leading coefficient, the graph slants to the right. To ascertain the behavior, consider the function's degree and the sign of the leading coefficient.

The term with the largest power of x is the leading term in a polynomial. As an illustration, the leading word in 7+x3x2 is 3x2. A polynomial's leading coefficient is the coefficient of the leading term. The leading coefficient in the aforementioned illustration is 3.

The numbers placed in front of the variable with the largest exponent are known as leading coefficients. They can be whole numbers, fractions, or decimals, as well as positive, negative, real, or imaginary, just like regular coefficients.

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The distance from (0, -4) to the line x + 5y = 10 is approximately 6 units.

To find the distance from a point to a given line, recall the following:

Step 1: Find the slope of the line, x + 5y = 10:

Rewrite the equation, x + 5y = 10 as y = mx + b, to find the value of the slope (m)

5y = -x + 10

y = -x/5 + 10/5

y = -1/5x + 2

The slope (m) = -1/5.

Step 2: Find an equation of the perpendicular line to the line x + 5y = 10 that passes through the point (0, -4):

Slope (m) = 5 [negative reciprocal of -1/5]

y-intercept (b) = -4

Substitute m = 5 and b = -4 into y = mx + b:

Equation of the line:  y = 5x - 4

Step 3:  Find the point of intersection of the lines y = 5x - 4 and y = -1/5x + 2:

Therefore, the lines intersect when 5x - 4 = -1/5x + 2

5x - 4 = -1/5x + 2

5x + x/5 = 4 + 2

26x/5 = 6

26x = 30

x = 30/26

x ≈ 1.2

Substitute x = 1.2 into y = 5x - 4:

y = 5(1.2) - 4

y = 2

Point of intersection is: (1.2, 2)

Step 4:  Find the distance between (0, -4) and (1.2, 2) using the distance formula:

d = √[(1.2 − 0)² + (2−(−4))²]

d = √[(1.2)² + (6)²]

d = √37.44

d ≈ 6 (nearest whole number)

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Answer:

Yes

Step-by-step explanation:

As long as 3 can multiply into 15, then 15 is a multiple of 3.

Multiples of 3 are: 3,6,9,12,15 and so on.

For this combination can be used , the answer would be  639450 ways

What is combination?

In arithmetic, a combination may be a choice of things from a group that has distinct members, such the order of choice doesn't matter.

Main body:

Given, the total number of members in the chorus are 30.

Also, it is given that 6 members from the chorus have to be

chosen for a special performance.

The number of ways of choosing r people out of given n people

is given by the expression

nCr

= n!/r!(n-r)!

So the number of ways of choosing 6 members out of 30 are

³⁰C₆

=  30!/24!6!

= 639450 ways

But since only the expression to represent the number of ways

was asked not the exact number of ways we can leave the

answer as ³⁰C₆ .

Hence total number of ways is 639450 ways.

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Answer:

12 y 42

Step-by-step explanation:

Let x and y represent the two numbers:

(1)  x+y=54 and (2)  x-y=30

Solve for x:

x-y=30

x=30-y

Substitute into equation (1):

(30-y)+y=54

2y+30=54

2y=24

y=12

Substitute into equation (2):

x-12=30

x=42

Answer:

First, know that [tex]csc(x)=\frac{1}{sin(x)}[/tex]:

[tex]\frac{1}{sin^{2}(x)} *cos^{2}(x)=\frac{cos^{2}(x)}{sin^{2}(x)}[/tex]

Remember that cos²(x) + sin²(x) = 1, so cos²(x) = 1 - sin²(x):

[tex]\frac{cos^{2}(x)}{sin^{2}(x)} =\frac{1-sin^{2}(x)}{sin^{2}(x)} =\frac{1}{sin^{2}(x)} -\frac{sin^{2}(x)}{sin^{2}(x)} =csc^{2}(x)-1[/tex]

Step-by-step explanation:

this might be the answer

Answer: Your answer should be  294 cm2.

Answer:

294 cm²

Step-by-step explanation:

A cube has 6 congruent square faces. The surface area is the sum of the area of the 6 faces.

area of one face = 7 × 7 = 49 cm²

surface area = 6 × 49 = 294 cm²

The cat's weight in grams will be 1450 grams.

According to the question,

We have the following information:

A cat weighs 82 ounces. There are about 28.3 grams in 1.6 ounces.

Now, we can easily find the weight of the cat in grams by following the given steps:

1.6 ounces = 28.3 grams

We will find the weight in grams in 1 ounce using division.

1 ounce = 28.3/1.6 grams

Now, the weight of 82 ounces in grams:

82 ounces = (28.3*82)/1.6 grams

82 ounces = 1450.375 grams

After rounding it off to the nearest whole gram, we have 1450 grams.

Hence, the cat's weight in grams will be 1450 grams.

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The total number of sides of the given polygon is 16.

What is the interior and exterior angle of a regular polygon?

In a regular polygon, all internal angles and exterior angles are equal. The formula for determining the amount of an interior angle is given:

Interior angle of a polygon = sum of interior angles/number of sides  

A polygon's exterior angles add up to 360°.

Given, each interior angle of a regular polygon = 157.5°

Then, each exterior angle of a regular polygon = 180° - 157.5° = 22.5°

the sum of the exterior angles of any n-gon = 360°

So, the total number of sides = 360°/22.5° = 16 sides

Hence, the total number of sides of the polygon is 16.

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Answer:

0.10 or 10%

Step-by-step explanation:

Think about it, 20% of 50 = 10

You could also do 0.20 x 0.50 to get 0.10

return(int(a+b)) is the way to determine the integer floor of the sum of two floating point numbers.

Here is an example program:

int main(void){

double a,b,c;

a=1.001;

b=2.243;

c=a+b;

return(int(c));

}

where, a and b are floating points we need addition of that as an integer which means removing the decimal part.

hence, we use return(int(c)), it is also called as parsing integer.

What is parseInt()?

The function parseInt(int I produces an integer when given a textual representation of a number that is either decimal, binary, octal, or hexadecimal (radix equals 10, 2, 8, or 16 correspondingly).

Example in java program:

public class Test {

  public static void main(String args[]) {

     int x =Integer.parseInt("9");

     double c = Double.parseDouble("5");

     int b = Integer.parseInt("444",16);

     System.out.println(x);

     System.out.println(c);

     System.out.println(b);

  }

}

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The probaility of non smokers is 0.3

One prominent physician claims that 70% of those with lung cancer are chain smokers

use binomial formula, where probability x successes in n tries where each try has probability p:

P(x successes) =  C(n,x) * p^x * (1-p)^(n-x)

n is sample size

p is the probability of success

here n = 10, p = 0.7

a)   more than have is P(x = 6) + P(x=7) + P(x = 8) + P(x = 9) + P(x = 10)

b)  exactly 4 are heavy-smokes is P(x = 4)

c)  probability non-smoker is 1 - 0.7 = 0.3

P(x < 2) = P(x = 0) + P(x = 1), and P = 0.3

Therefore, the probaility of non smokers is 0.3

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Disclaimer,

the question given by you is incomplete,

a similar question is

One prominent physician claims that 70% of those with lung cancer are heavy smokers. If his assertion is correct, find the probability that out of 10 such patients recently admitted to a hospital

(a) more than half are heavy smokers

(b) exactly 4 are heavy smokers

(c) less than 2 are non- smokers