Can someone please help me with this parallelogram proof
prove angle LMN is congruent to NPL ; PLM is congruent to MNP​

If this experiment was performed many times you would expect that the average number of heads is 5.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

From the graph,

The theoretical probability of getting 5 heads in ten flips of a fair coin.

= 0.25

= 25%

And,

The theoretical probability of getting 0 and 10, 1 and 9, 2 and 8, 3 and 7, and 4 and 6 heads is equal.

The average number of heads.

= (0 + 10)/2 = 5

Similarly,

(1 + 9)/2 = 10/2 = 5

(2 + 8)/2 = 10/2 = 5

(3 + 7)/2 = 10/2 = 5

(4 + 6)/2 = 10/2 = 5

So,

If this experiment was performed many times you would expect that the average of heads is 5.

Thus,

The expected average number of heads is 5.

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Answer:

5

Step-by-step explanation:

The answer above is correct.

The division of the given expressions gives quotient as x + 6 and the remainder 42.

Synthetic division is the method of division used to divide a polynomial expression with the binomial.

We have to divide x² + x + 12 by x - 5.

Write the coefficients of the dividend in the order of descending powers and the constant term in the binomial as :

 5 |     1    1    12

Write the leading coefficient in the bottom row and then multiply the 1 written on the bottom row with 5 and write it beneath the next coefficient of the dividend.

 5 |     1    1    12

               5    

          1    

Now add 1 + 5 to get 6 and write in the bottom row.

Repeat the process by multiplying 6 with 5 and adding up.

 5 |     1    1    12

               5   30

          1    6   42

Here, 42 is the remainder and 1 and 6 are the coefficients of the quotient.

Quotient = x + 6

Remainder = 42

Hence the quotient and remainder are x+6 and 42 respectively.

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The expression in simplest form that represents the

total amount that Andrew spent would be = $8d

The simple forms of representation of expression shows that all the values of that expression are in its simplest form.

In Andrew cans of ping pong balls,

Last week he bought = 4 cans

This week he bought = 2 cans

The cost of ping pong balls = d dollars per

can..

The total amount that Andrew spent would be;

= d × ( 4+2)

= $8d

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Nearly 150,000,000 cars were registered in the US as a whole in 2007. China, India, and the United States are the three nations with the largest populations on earth.

Average lifespan and child mortality rate are indeed the two key metrics that most accurately reflect a citizenry's standard of living.

The population of the globe is projected to reach about 10 billion people in 2050. Africa and Asia will see the most expansion in population if indeed the patterns in demographic persist.

Cultural practices, governmental regulations, and monetary support, as well as female employment prospects as well as education levels, all have an impact on the overall birthrate of a community.

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Answer:

20% of 11 is 2.2

Step-by-step explanation:

11 x .20 = 2.2

Answer:

(a) In a school trip the ratio of adults to students is 1:10 , and all of the students are in year 10 or year 11. The ratio of year 10 to year 11 is 1:4, so the fraction of all the people on the trip who are year 11 students is 1/5.

(b) In a cinema the ratio of adults to children is 2:3, and the children are either boys or girls. The ratio of boys to girls is 5:2 , so the fraction of all the people in the cinema who are girls is 2/5.

Answer:

length = 10 inches

Step-by-step explanation:

the perimeter (P) of a rectangle is calculated as

P = 2l + 2w ( l is the length and w the width )

here w = 14 and P = 48 , then

48 = 2l + 2(14)

48 = 2l + 28 ( subtract 28 from both sides )

20 = 2l ( divide both sides by 2 )

10 = l

then length is 10 inches

Answer:

C. $5,993

Step-by-step explanation:

Markdown is an immediate reduction in the price of an item, performed by a merchant during a special sale. A markdown discount is most often a percentage decrease in the original price. The purpose of a markdown sale is to create a demand of a product during the time period of the sale.

The required distance between each pair of numbers on a number line is below in the solution part.

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

1. The distance between 5 and -2 on a number line is |5-(-2)| = 7 units.

2. The distance between -8 and -17 on a number line is |-17-(-8)| = 9 units.

3. The distance between 28 and -12 on a number line is |28-(-12)| = 40 units.

4. The distance between -17 and 15 on a number line is |15-(-17)| = 32 units.

5. The distance between 33 and -2 on a number line is |33-(-2)| = 35 units.

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Standard deviation affects the skewness more.

In data sets containing outliers or skewed distributions, the interquartile range is the most accurate indicator of variability.   It's unlikely to be impacted by outliers because it's based on numbers that come from the center half of the distribution.

A measure of dispersion that demonstrates how closely a set of data's values resemble the mean is called standard deviation.

Outliers in a data set or a skewed data distribution might have an impact on the standard deviation.

Interquartile Range (IQR) is a spread indicator that depicts the variation between a data set's first and third quartiles.

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The three lengths 8, 9 and 10 form a triangle.

In Euclidean geometry stating that any two triangle sides added together must be greater than or equal to the third side; represented by the symbols a + b ≥c. The basic tenet of the theorem is that a straight line connects any two places.

Given:

Sides: 8, 9, 10

As from Triangle Inequality the sum of two sides are greater than the third side of triangle.

So, 8 + 9 > 10

9 + 10 > 8

10+ 8> 9

Since the triangle inequality satisfied.

Thus, the triangle can form using sides 8, 9, 10.

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Answer:

no linear relationship exists between the two variables being compared

Step-by-step explanation:

Together, Lindsay and Lorraine needs to jump 21 more jumps in a row.

Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.

The process of doing addition is also called as finding the sum.

Number of jumps got by Lindsay = 14

Number of jumps got by Lorraine = 13

Total number of jumps gotten by both = 27

Let j be the number of jumps they need to jump more.

j = 48 - 27

j = 21

Hence 21 more jumps would be needed.

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The method that Ross can use to make valid conclusions on the candidate in the lead is C. Put the names of all the students in a hat, and draw 100 names. Ask those students whose names are drawn.

When conducting the survey, it is important the Ross uses a random sample from the classmates who will be the ones to select the class treasurer.

To do this, one method of random sampling Ross can use is to draw 100 names from a hat after placing all the pupils' names inside. Students whose names were drawn can be questioned.

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The full question is :

Ross wants to conduct a survey of his 400 classmates to determine which candidate for class treasurer, Warren or Willa, is in the lead in the upcoming election.

Ross will ask the question, “If the election were today, which candidate would get your vote?”

Which of the following methods of surveying his classmates will allow Ross to make valid conclusions about which candidate is in the lead?

Select all that apply.

*Ask all of Warren's friends.

*Ask the other members of Willa's cheerleading squad.

*Put the names of all the students in a hat, and draw 100 names. Ask those students whose names are drawn.

*Ask every student in the class.

Answer:

63°

Step-by-step explanation:

The sum of the interior angles of a triangle add up to 180.

90 + (12x + 3) + (5x + 2) = 180     now solve for x

17x + 95 = 180

17x = 180 - 95 = 85

x = 85/17 = 5

m∠A = 12(5) + 3 = 63

The vertical height of the kite is 165.5 ft

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled

Given that, a kid is flying a kite and has reeled out his entire line of 150 ft of string, the angle of elevation of the string is 65°

We need to find, the vertical height of the kite,

If we see the figure (refer to the attachment), we can see that, this scene will make a right triangle, where the string of the kite will be the hypotenuse and the vertical height of the kite is the perpendicular,

Since, we need the vertical height, will use trigonometric ratios,

We have, hypotenuse and the references angle and need perpendicular,

We know that, Sine of an angle is the ratio of perpendicular to hypotenuse,

Therefore,

Sin65° = 150 / AB

AB = 165.5

Hence, the vertical height of the kite is 165.5 ft

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The linear function rule for the given data is y = 6x + 6.

A linear function is defined as an equation in which the highest exponent of the variable is always one.

The rule for the data in the given table:

x:  1   2   3   4

y: 12 18 24 30

The linear function rule for the given data can be found using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

Let's use the first and second points: (1,12) and (2,18).

The slope can be found using the formula:

m = (18 - 12) / (2 - 1) = 6

Next, we can use the slope and one point from the table to find the y-intercept:

b = y - mx = 12 - m × 1 = 12 - 6 × 1 = 6

So the linear function rule for the given data is:

y = 6x + 6

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The sine function with the values in the table is defined as follows:

y = 5sin(πx/2) - 1.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are given as follows:

The function has a maximum value of 4 and a minimum value of -6, for a difference of 10 units, hence the amplitude is obtained as follows:

A = [4 - (-6)]/2

A = 10/2

A = 5.

Without vertical shift, a function with amplitude of 2 would oscillate between -5 and 5, while this one oscillates between -6 and 4, hence the vertical shift is given as follows:

D = -1.

The shortest distance between repetitions can be given by 4 - 0, hence the period is of 4 units and the coefficient B is given as follows:

2π/B = 4

B = 2π/4.

B = π/2.

The function is at it's midline at the origin, hence it has no phase shift, and thus the equation is given as follows:

y = 5sin(πx/2) - 1.

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The kind of discontinuous measurement procedure that is used is partial interval recording

Given that,

A client frequently shouts things out loud. You break up the session into shorter timed segments in order to get data on this. You record an event if the behavior happens at any time throughout the interval.

To find : which discontinuous measuring technique are you employing?

An interval recording technique is partial interval recording. An interval recording approach involves watching to see if a behaviour happens or not within predetermined intervals of time. After determining the duration of an observation session, the time is divided into shorter segments that are all of the same length.

So, partial interval recording is the type of discontinuous measuring technique that is applied.

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Hence, the standard deviation is more affected by skewness compared to the IQR.

Skewness is a metric for a distribution's asymmetry. When the left and right sides of a distribution are not mirror reflections, it is asymmetrical. Right (or positive), left (or negative), or zero skewness can all apply to a distribution.

Skewness refers to the degree of asymmetry in a distribution and a skewed distribution has more observations on one side than the other. In a skewed distribution, the standard deviation is a better measure of spread as it takes into account the deviation of each data point from the mean. On the other hand, the interquartile range (IQR),

which is the difference between the 75th and 25th percentile, is less affected by skewness as it only considers the middle 50% of the data. Hence, the standard deviation is more affected by skewness compared to the IQR.

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If a trapezoid has an area of 100 square units, the scale factor that would be required to dilate the trapezoid to have each area is:

sqrt(A / 100)

To find the scale factor required to dilate a shape, you need to determine what ratio of the new area to the original area you want to achieve.

Let's call the scale factor "k". If the original area of the trapezoid is 100 square units, and the new area is "A", the relationship between the two areas can be expressed as:

So to find the scale factor required to achieve a specific new area, you can solve for k by dividing the new area by 100 and taking the square root:

Note that: This equation assumes that the dilation is proportional, meaning that all dimensions of the trapezoid are scaled by the same factor.

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Answer:  x= - 9/4

Step-by-step explanation:

1. Move the variable to the left, and change its sign.

-4x+8+2x=17

2. Collect like terms

-2x=17-8

3. Divide each side by -2

-2x=9

Answer: x= - 9/2

The first step to graph the solution to the system of equations given is option D. Change the inequalities to equalities and solve the resulting system of linear equations.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

1. Given system of inequalities are,

y ≥ x + 3

x < −2

In order to graph the solution, first we have to change the inequality symbols to equality and solve the resulting system of linear equations.

That is, solve y = x + 3 and x = -2

2. The equations of the given line are

y = x - 3

y = -2x

Take the linear equation y = x - 3.

The solution region of both contains the point (-1, 0).

0 = -1 - 3 = -4, correct inequality is 0 ≥ 4.

So the inequality is y ≥ x - 3.

Consider y = -2x

0 = 2, correct inequality is 0 ≤ 2.

So the inequality is y ≤ -2x.

Hence the system of inequalities shown in the graph are option B. y ≥ x - 3 and y ≤ -2x.

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Answer:

80 divded by 10 is c c=8

Answer: 2/3

Step-by-step explanation: 1/3+1/3 is 2/3.

Answer:

Exact form:2/3

decimal form:       _

                           0.6

Step-by-step explanation:

Answer: (1, -1)

Step-by-step explanation:

you would first start out with

5x+2y=3

4x-8y=12

you would then subsitute the value of x

x=3/5-2/5 y

4x-8y=12

you then solve the equation

4(3/5-2/5 y) -8y=12

you then subsitute the vaulue of y

y=-1

then you solve the equation

x=3/5-2/5 x(-1)

A possile solution is

x=1

you should then check the solution

(x,y) = (1,-1)

Given a standardized normal distribution, 1.96 is the value of z if only 2.5 perent of all possible z values are larger.

In a standard normal distribution, 2.5% of all possible z-values are larger than a certain value of z, which is denoted by z*. We can use this information to find the value of z* by using the cumulative distribution function (CDF) of the standard normal distribution. The CDF of the standard normal distribution is given by the equation:

Φ(z) = 1/2 * (1 + erf(z/sqrt(2))) , where erf(z) is the error function.

Since 2.5% of all possible z-values are larger than z*, we can set Φ(z*) = 1 - 0.025 = 0.975. Then, we can solve for z* by finding the inverse of the CDF using the inverse error function:

z* = sqrt(2) * erf^(-1)(2 * Φ(z*) - 1) , where erf^(-1)(z) is the inverse error function.

Using this formula, we find that z* = 1.96, which means that if a standardized normal distribution is given, a z-value of 1.96 corresponds to 2.5% of all possible z-values being larger.

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Answer:

$6.50

Step-by-step explanation:

25 - 6.25 = 18.75

18.75 - 3.75 = 15

15 - 8.50 = 6.50