how to check 2(a+3)=-12

Answer:

  (a, b) alternate interior angles at M and N, and at A and B are congruent

  (c) the triangles are congruent by SAS and by ASA (and MX = NX)

  (d) angles are no longer congruent, so the triangles are not congruent. The radii are given as congruent, but the chords cannot be shown congruent.

Step-by-step explanation:

Given same-size circles A and B, externally tangent to each other at X, each with chords MX and NX, you want to know what can be concluded if AM║BN, and what is unprovable if those segments are not parallel.

The circles being the same size means all the radii are congruent. This is shown by the single hash marks in the attached diagram.

Alternate interior angles where a transversal crosses parallel lines are congruent. If AM║BN, this means the angles marked with a single arc are congruent, and the angles marked with a double arc are congruent. These are the alternate interior angles at transversal MN and at transversal AB.

If AM║BN, in addition to the given congruences, we also know ...

∆AMX ≅ ∆BNX by SAS or ASA (take your pick).

If AM and BN are not parallel, MN is not a straight line through X, the angles at A and B are not congruent, and the angles at M and N are not congruent. (We assume segment AB still goes through X.)

__

Additional comment

Triangles MAX and NBX are isosceles, so their base angles are congruent. If X lies on MN, then AM and BN must be parallel, since the vertical angles at X will be congruent along with the other base angles at M and N. If AM and BN are not parallel, point X cannot lie on segment AB.

the variance of X is 9. b) Determine E [2X² - 20X +5]:

Using linearity of expectation, we can find E [2X² - 20X +5] as:

E [2X² - 20X +5] = 2E[X²] - 20E[X] + 5

by the question.

The number of ways to select the first 2 white chips is given by:

Number of ways = (6C2) (5C0) (3C0) = 15

The number of ways to select the third chip as blue given that the first 2 chips were white is given by:

Number of ways = (3C1) = 3

Therefore, the probability of selecting the third chip as blue given that the first 2 chips were white is:

P(The third chip is blue the first 2 were white) = Number of ways / Total number of ways = 3 / 350 = 0.0086 (rounded to 4 decimal places)

c) P(The fourth chip is blue the first 2 were white):

The number of ways to select the first 2 white chips is given by:

Number of ways = (6C2) (5C0) (3C0) = 15

The number of ways to select the third chip as non-white given that the first 2 chips were white is given by:

Number of ways = (8C1) = 8

The number of ways to select the fourth chip as blue given that the first 2 chips were white, and the third chip was non-white is given by:

Number of ways = (3C1) = 3

Therefore, the probability of selecting the fourth chip as blue given that the first 2 chips were white is:

P(The fourth chip is blue the first 2 were white) = Number of ways / Total number of ways = 8*3 / 350 = 0.0686 (rounded to 4 decimal places)

Suppose we have a random variable X such that E[X]= 7 and E[X²] =58.

a) Determine the variance of X:

The variance of X is given by:

Var[X] = E[X²] - (E[X]) ²

Substituting the given values, we get:

Var[X] = 58 - (7) ² = 9

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Answer: $318/mo

Step-by-step explanation:

First, we get the remainder, which is the difference between $9, 632 and $2,000. That gives us $7, 632.

Then, since we know she will pay in 24 months, we assume she pays the same amount each month and divide $7, 632 by 24 = $318/mo

The expressions that are equivalent to (x-2)² is x² - 4x + 4. (option B)

Now, let's look at the expression (x-2)². This is a binomial expression that can be simplified by applying the rules of exponents. Specifically, we can expand this expression as follows:

(x-2)² = (x-2) * (x-2)

= x * x - 2 * x - 2 * x + 2 * 2

= x² - 4x + 4

So, the expression (x-2)² is equivalent to x² - 4x + 4.

However, the problem asks us to identify other expressions that are equivalent to (x-2)². To do this, we can use the process of factoring. We know that (x-2)² can be factored as (x-2) * (x-2). Using this factorization, we can rewrite (x-2)² as:

(x-2)² = (x-2) * (x-2)

= (x-2)²

So, (x-2)² is equivalent to itself.

Hence the correct option is (B).

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Complete Question:

Which expressions are equivalent to (x−2)²?

Select the correct choice.

A. (x + 2) (x - 2)

B. x² - 4x + 4

C. x² - 2x + 5

D. x² + x - 2x

(a)The distribution of X (the average of the 49 races) follows a normal distribution with mean 146 minutes and standard deviation 11 minutes. (b)The probability of the average of the sample being between 144 and 149 minutes is 0.5854.(c)The 80th percentile for the average of these 49 marathons is 157.2 minutes.(d) The median of the average running times is 146 minutes.

Part(a) The distribution of X (the average of the 49 races) follows a normal distribution with mean 146 minutes and standard deviation 11 minutes. Part (b) The probability that the average of the sample will be between 144 and 149 minutes in these 49 marathons can be calculated using the z-score formula: z = (x - mean)/standard deviation
For x = 144, z = (144 - 146)/11 = -0.18
For x = 149, z = (149 - 146)/11 = 0.27,using the z-score table, the probability of the average of the sample being between 144 and 149 minutes is 0.5854 (0.4026 + 0.1828).

Part (c) The 80th percentile for the average of these 49 marathons can be calculated using the z-score formula: z = (x - mean)/standard deviation, For the 80th percentile, z = 0.84 (from z-score table). Therefore, x = 146 + (0.84 * 11) = 157.2 minutes. Part (d) The median of the average running times is 146 minutes. The median is the midpoint of the data which means half of the data is above the median and half of the data is below the median. Therefore, the median of the average running times is equal to the mean.

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The answer is 250 kilometers. Peter and his mother traveled a total distance of 250 kilometers on their mail delivery.

Distance is a numerical measurement of how far apart two objects or points are. It is a scalar quantity, meaning that it is only expressed as a magnitude, or numerical value, without any direction.

1 centimeter is equal to 0.01 kilometers, so 50 kilometers would be equal to 5,000 centimeters. The total distance between the four cities is 5,000 centimeters, which is equal to 50 kilometers.

Charltc to Thornton is 1,000 centimeters, Thornton to Avon is 1,500 centimeters, Avon to Ashton is 1,000 centimeters, and Ashton to Charltc is 1,500 centimeters. This gives us a total of 5,000 centimeters, or 50 kilometers.

This can be calculated by multiplying the total distance between the four cities (50 kilometers) by the number of times they traveled the route (5 times, since they flew from Charltc to Thornton, then to Avon, then to Ashton, and then back to Charltc). This gives us 250 kilometers, which is the answer to the question.

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Peter and his mother traveled a total distance of 250 kilometers on their mail delivery. The answer is 250 kilometers.

Distance is a numerical measurement of how far apart two objects or points are. It is a scalar quantity, meaning that it is only expressed as a magnitude, or numerical value, without any direction.

1 centimeter =  0.01 kilometers,

so 50 kilometers = 5,000 centimeters.

Charlton to Thornton= 1,000 centimeters,

Thornton to Avon= 1,500 centimeters,

Avon to Ashton= 1,000 centimeters,

and Ashton to Charlton= 1,500 centimeters.

Total distance= 1,000+1,500+1,000+1,500

= 5,000 centimeters, or 50 kilometers.

The total distance between the four cities is 5,000 centimeters, which is equal to 50 kilometers.

This can be calculated by multiplying the total distance between the four cities (50 kilometers) by the number of times they traveled the route (5 times.

=50*5

=250

Since they flew from Charlton to Thornton, then to Avon, then to Ashton, and then back to Charlton.

250 kilometers is the answer to the question.

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Question:

Peter's mother is a pilot. She often makes deliveries near their community. Peter and his mother flew from Charlton to Thornton to make a mail delivery. Then they continued on to Avon and Ashton and returned to Charlton. How many kilometers did Peter and his mother travel in all?

Construct a triangle PQR with sides PQ=8cm, PR=5cm, and QR=6cm, then draw a circle passing through P, Q, and R. This circle is called the circumcircle of triangle PQR.

We draw a line segment PQ = 8 cm long. From point P, we draw a line segment PR = 5 cm long at an angle of 60 degrees to PQ. Then, we draw a line segment QR = 6 cm long joining points Q and R to complete the triangle. Next, we use a compass to draw a circle passing through points P, Q, and R. This circle is called the circumcircle or circumscribed circle of the triangle, which is the unique circle that passes through all three vertices of the triangle. The circumcircle has a special property that its center is equidistant from the three vertices of the triangle.

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Answer: x = 6

Step-by-step explanation:

(7x+3)+85+50 = 180

(7x+3)+135 = 180

7x+3 = 180 - 135 = 45

7x = 45-3 = 42

x = 42 / 7 = 6

x = 6

In Rosettenville, a suburb of Johannesburg, South Africa, Robert Brozin and Fernando Duarte acquired the Chicken Land restaurant in 1987, launching Nando's.

The eatery was renamed Nando's in honor of Fernando. The restaurant incorporated influences from former Mozambican Portuguese colonists, many of whom had relocated to Johannesburg's southeast after their country gained independence in 1975. Expansion was an essential component of their vision from the beginning. Nando's had already grown from one restaurant in 1987 to four by 1990. It became increasingly difficult to implement a common strategy and decision-making became inefficient as new outlets were maintained as separate businesses.

In 1995, Nando's International Holdings (NIH) was established as a new international holding because managing this growingly complex global structure had become extremely challenging. The South African branch of Nando's Group Holdings (NGH) was successfully listed on the Johannesburg Stock Exchange on April 27, 1997. NGH was 54% owned by NIH, with the remaining 26% available to the general public and former joint venture partners. The main goals of the share offer and listing were to broaden the group's capital base and enable group restructuring.

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Question: The heights of adult men can be approximated as normal, with a mean of 70 and a standard deviation of 3, the probability that a man is shorter than 65 inches is approximately 0.0475 or 4.75%.

Let X be the height of an adult man, which follows a normal distribution with mean μ = 70 and standard deviation σ = 3. Then, we need to find the probability that a man is shorter than some height, say x₀. We can write this probability as P(X < x₀).To find P(X < x₀), we need to standardize the random variable X by subtracting the mean and dividing by the standard deviation. This yields a new random variable Z with a standard normal distribution. Mathematically, we can write this transformation as:Z = (X - μ) / σwhere Z is the standard normal variable.

Now, we can find P(X < x₀) as:P(X < x₀) = P((X - μ) / σ < (x₀ - μ) / σ) = P(Z < (x₀ - μ) / σ)Here, we use the fact that the probability of a standard normal variable being less than some value z is denoted as P(Z < z), which is available in standard normal tables.

Therefore, to find the probability that a man is shorter than some height x₀, we need to standardize the height x₀ using the mean μ = 70 and the standard deviation σ = 3, and then look up the corresponding probability from the standard normal table.In other words, the probability that a man is shorter than x₀ can be expressed as:P(X < x₀) = P(Z < (x₀ - 70) / 3)We can now use standard normal tables or software to find the probability P(Z < z) for any value z.

For example, if x₀ = 65 (i.e., we want to find the probability that a man is shorter than 65 inches), then we have:z = (65 - 70) / 3 = -1.67Using a standard normal table, we can find that P(Z < -1.67) = 0.0475. Therefore, the probability that a man is shorter than 65 inches is approximately 0.0475 or 4.75%. Thus, P(X < 65) = 0.0475 or 4.75%. Therefore, the probability that a man is shorter than 65 inches is approximately 0.0475 or 4.75%.

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The answer is: A) r=0.04; R=0.96 B) 8% C) 92.16%.

The Hardy-Weinberg equilibrium is a method for determining the frequency of certain genetic traits in a population. The following are the frequencies of the red hair (r) and non-red hair (R) alleles in the Norwegian population, according to the question: A) The total frequency of alleles is 1. If red hair (r) is found in approximately 4% of the people in Norway, then the frequency of the R allele must be 0.96 or 96%. R = 0.96 r = 0.04 B) The frequency of hetero zygotes in a population can be determined by multiplying the frequency of the R allele by the frequency of the r allele and then multiplying that number by 2.

Heterogeneous genotype = 2pq Here, p represents the frequency of the R allele, and q represents the frequency of the r allele. p = R = 0.96 q = r = 0.04 Therefore, 2pq = 2(0.96 x 0.04) = 0.077, or approximately 8%. C) In order for a child to have red hair, both parents must carry the r allele. If both parents are homozygous for the R allele, there is no chance that their child will have red hair. This means that the proportion of matings that cannot result in a child with red hair is (0.96 x 0.96) = 0.9216 or 92.16%.

Therefore, the answer is: A) r=0.04; R=0.96 B) 8% C) 92.16%.

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The probability that x is less than 2 is approximately 0.4866. The probability that x is greater than 3 is approximately 0.3528. The probability that x is less than 5 is approximately 0.6321. The probability that x is between 2 and 5 is approximately 0.1455.

The given probability density function is an exponential distribution with a rate parameter of λ = 1/3. The formula for P(x < x_0) is the cumulative distribution function (CDF) of the exponential distribution, which is given by:

F(x_0) = ∫[0,x_0] f(x) dx = ∫[0,x_0] 1/3 * 4 * e^(-x/3) dx

a. Write the formula for P(x < x_0):

Using integration, we can solve this formula as follows:

F(x_0) = [-4e^(-x/3)] / 3 |[0,x_0]

= [-4e^(-x_0/3) + 4]/3

b. Find P(x < 2):

To find P(x < 2), we simply substitute x_0 = 2 in the above formula:

F(2) = [-4e^(-2/3) + 4]/3

≈ 0.4866

Therefore, the probability that x is less than 2 is approximately 0.4866.

c. Find P(x > 3):

To find P(x > 3), we can use the complement rule and subtract P(x < 3) from 1:

P(x > 3) = 1 - P(x < 3) = 1 - F(3)

= 1 - [-4e^(-1) + 4]/3

≈ 0.3528

Therefore, the probability that x is greater than 3 is approximately 0.3528.

d. Find P(x < 5):

To find P(x < 5), we simply substitute x_0 = 5 in the above formula:

F(5) = [-4e^(-5/3) + 4]/3

≈ 0.6321

Therefore, the probability that x is less than 5 is approximately 0.6321.

e. Find P(2 < x < 5):

To find P(2 < x < 5), we can use the CDF formula to find P(x < 5) and P(x < 2), and then subtract the latter from the former:

P(2 < x < 5) = P(x < 5) - P(x < 2)

= F(5) - F(2)

= [-4e^(-5/3) + 4]/3 - [-4e^(-2/3) + 4]/3

≈ 0.1455

Therefore, the probability that x is between 2 and 5 is approximately 0.1455.

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The analysis of the data to obtain the confidence interval of the difference in the means indicates;

99% confidence interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂

The correct options are;

Name of Procedure

Random

10%

Normal/Large Sample

99% CI = (-0.302, 2.301)

Conclude;

We are 99% confident that the interval give in the previous step captures -0.301 to 2.301 = the true difference in mean heart height for all subject like these who listen to love songs versus classical music.

A confidence interval is a range of value that is likely to contain the true value of a population parameter with a certain degree of confidence.

The two-sample t-test can be used to construct the 99% confidence interval as follows;

([tex]\bar x[/tex]₂ - [tex]\bar x[/tex]₁) ± t(α/2, df) × √(s₁²/n₁ + s₂²/n₂)

Where;

[tex]\bar x[/tex]₂ and [tex]\bar x[/tex]₁ = The sample means of the love song and classical music groups

s₁, and s₂ = The sample standard deviations

n₁ and n₂ = The sample sizes

df = The degrees of freedom

t(α/2, df) = The value from the t-distribution table with a significance level of 0.01 and df = n₁ + n₂ - 2

The data indicates;

n₁ = n₂ = 15

[tex]\bar x[/tex]₁ = 5.07, s₁ = 1.63

[tex]\bar x[/tex]₂ = 4.07, s₂ = 1.13

Therefore, we get;

([tex]\bar x[/tex]₂ - [tex]\bar x[/tex]₁) ± t(α/2, df) × √(s₁²/n₁ + s₂²/n₂)

= (5.07 - 4.07) ± t(0.005, 28) × √(1.62²/15 + 1.13²/15)

= 1 ± 2.763 × 0.469

= 1 ± 1.301

The 99% confidence interval for the difference in the true mean heart for subjects who listen to a love song versus classical music is; (-0.301, 2.301).

The correct statement is; 99% confidence interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂

The correct statements, placed in the box are;

Name of Procedure;

Two sample interval for [tex]\bar x[/tex]₁ - [tex]\bar x[/tex]₂

Random

The volunteers are randomly selected

The random condition is met

We have a random sample of 15 subjects who listen to a love song

We have a random sample of 15 subjects who listen to classical music

10%

The 10% condition is met

15 < 10% of all subjects like these who listen to love songs

15 < 10% of all subjects like these  who listen to classical music

Normal/Large Sample

The Normal/Large condition is met

The stemplot of the classical music sample data shows no strong skewness or outliers

The stemplot of the love song music sample data shows no strong skewness or outliers

Therefore;

99% CI = (-0.301, 2.301)

Conclude;

We are 99% confident that the interval given in the previous step captures -0.301 to 2.301 = the true difference in mean heart height for all subject like these who listen to love songs versus classical music.

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Answer: There are 10 students who are in both the hockey and football teams.

Step-by-step explanation: We can use the principle of inclusion-exclusion to find the number of students who are in both the hockey and football teams.

The total number of students in both teams is the sum of the number of students in the hockey team and the number of students in the football team, minus the number of students who are in both teams (to avoid double-counting):

Total = Hockey + Football - Both

Substituting the given values, we get:

100 = 40 + 70 - Both

Simplifying, we get:

Both = 40 + 70 - 100

Both = 10

Therefore, there are 10 students who are in both the hockey and football teams.

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer: 15

Step-by-step explanation:

13--2 = 13 + 2 = 15

The value of the unknown lengths in these similar triangles is FH is 6.67 units and EG is 27 units.

A triangle is a polygon with three sides and three angles. It is a two-dimensional shape that is commonly studied in mathematics, geometry, and other fields. The sum of the angles in a triangle is always 180 degrees, and the lengths of the sides can vary. Triangles can be classified based on the lengths of their sides and the measures of their angles. Common types of triangles include equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles have many important properties and are used in various applications, including construction, engineering, and physics.

Here,

1. Let x be the length of FH. We have:

AB/EF = BD/FH

12/8 = 10/x

Cross-multiplying, we get:

12x = 80

x = 80/12

x ≈ 6.67

Therefore, FH ≈ 6.67.

2. Let y be the length of EG. We have:

AC/BD = FH/EG

15/9 = 5/y

Cross-multiplying, we get:

5y = 135

y = 135/5

y ≈ 27

Therefore, EG ≈ 27.

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The point that partitions segment AB in a 1:4 ratio is (-1/2, -1).

What is Segment?

In geometry, a segment is a part of a line that has two endpoints. It can be thought of as a portion of a straight line that is bounded by two distinct points, called endpoints. A segment has a length, which is the distance between its endpoints. It is usually denoted by a line segment between its two endpoints, such as AB, where A and B are the endpoints. A segment is different from a line, which extends infinitely in both directions, while a segment has a finite length between its two endpoints.

To find the point that partitions segment AB in a 1:4 ratio, we need to use the midpoint formula to find the coordinates of the point that is one-fourth of the distance from point A to point B. The midpoint formula is:

((x1 + x2)/2, (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the segment.

So, let's first find the coordinates of the midpoint of segment AB:

Midpoint = ((-3 + 7)/2, (2 - 10)/2)

= (2, -4)

Now, to find the point that partitions segment AB in a 1:4 ratio, we need to find the coordinates of a point that is one-fourth of the distance from point A to the midpoint. We can use the midpoint formula again, this time using point A and the midpoint:

((x1 + x2)/2, (y1 + y2)/2) = ((-3 + 2)/2, (2 - 4)/2)

= (-1/2, -1)

So, the point that partitions segment AB in a 1:4 ratio is (-1/2, -1).

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Answer:

Y intercept is (0,2) Answer D.

Step-by-step explanation:

I included a graph for equation y=2/3 x + 2.

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

0.005

Step-by-step explanation:

When a data line on a graph slopes down as it goes to the right, it is depicting that the relationship between the variables on the graph is inverse.

An inverse relationship is a kind of correlation between two variables, in which one variable decreases while the other increases, or vice versa. An inverse relationship happens when one variable increases while the other decreases, or when one variable decreases while the other increases.

On a graph, when a data line slopes down as it goes to the right, this is an indication that the relationship between the variables on the graph is inverse. As the values of x increase, the values of y decrease. Therefore, we can conclude that there is an inverse relationship between x and y.

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The 41st term of the sequence is 121.

In mathematics, a sequence is a list of numbers or objects that follow a certain pattern or rule. A sequence's terms are typically identified by subscripts, like a1, a2, a3,..., an, where n denotes the number of terms in the sequence.

Sequences can be arithmetic, geometric, or neither, depending on terms follow a static difference, constant ratio, or neither of these series, respectively. Algebra uses geometric sequences to represent exponential development or decay whereas arithmetic sequences are frequently employed to model linear connections.

The given sequence is 2 , 5 , 8 , ...

The common difference is:

d = 5 - 2 = 3

The nth term of a sequence is given as:

an = a1 + (n-1)d

Substituting the value we have:

an = 2 + (n-1)3

an = 3n - 1

a41 = 3(41) - 1 = 122 - 1 = 121

Hence, the 41st term of the sequence is 121.

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Answer:

x=15

Step-by-step explanation:

use the side splitter theorem

(x-6)/x = 3/5 (cross-multiply)

3x=5(x-6) distributive property

3x=5x-30

2x = 30

x = 15

Answer:

yes

Step-by-step explanation:

The mean (also called the arithmetic mean or average) is a measure of central tendency that represents the typical or average value of a set of data. The mean is calculated by summing up all the values in the data set and dividing by the number of values.

The mean of x is calculated by the following formula:

mean of x = ∑(x * P(x))

Where, ∑ = Summation operator

            x = Value of random variable  

            P(x) = Probability of the corresponding value of x.

Let's calculate the mean of x using the formula provided above.

mean of x = (-1 × 0.3) + (0 × 0.4) + (1 × 0.3)

                = -0.3 + 0 + 0.3  

                = 0

Therefore, the mean of x is 0.

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The probability of a bulb lasting for at most 540 hours is 0.7521, rounded to four decimal places.

The life of light bulbs is distributed normally. The variance of the lifetime is 225 and the mean lifetime of a bulb is 530 hours. Find the probability of a bulb lasting for at most 540 hours. Round your answer to four decimal places.

Using the z-score formula z = (x - μ) / σ, where x is the value in question (540 hours in this case), μ is the mean (530 hours in this case) and σ is the standard deviation (15 hours in this case), we can calculate the z-score:
z = (540 - 530) / 15
z = 10 / 15
z = 0.67
Using a z-table, we can look up the probability of a value being less than or equal to 0.67, which is 0.7521.
Therefore, the probability of a bulb lasting for at most 540 hours is 0.7521, rounded to four decimal places.

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Answer:

Step-by-step explanation:

You can’t solve this equation as none of the numbers have the same coefficient to solve. If you wanted to solve for x and y, you will need two equations as there are two unknown variables in the equation and the only way to solve for x and y is to use simultaneous method which includes two equations.

Answer:

if it is perpendicular to eacha other I e 0