Unit 10: circles
Homework 8
#2, 4, 6, and & 8

Answer:

y = (x + 2)² + 2

Step-by-step explanation:

a quadratic function in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

y = x² + 4x + 6

using the method of completing the square

add/subtract ( half the coefficient of the x- term)² to x² + 4x

y = x² + 2(2)x + 4 - 4 + 6

 = (x + 2)² + 2 ← in vertex form

Answer:

63.25

Step-by-step explanation:

You need to calculate each figure separately.

The diameter of the circle = 4 + 3 + 3 = 10

=> radius = 5

area of 1/2 circle = 1/2πr^2 = 1/2π(5)^2 = 1/2(3.14)(25) = 39.25

area of the top rectangle = 3 x 6 = 18

area of the bottom rectangle = 2 x 3 = 6

total area = 39.25 + 18 + 6 = 63.25

Answer:Hi

Step-by-step explanation:

The probability of randomly selecting someone who does not believe that some people see the future in their dreams is 39.6%.

Probability is an area of mathematics that deals with the study of chance events.

We have, A poll showed that 60.4% of Americans say they believe that some people see the future in their dreams.

Therefore, the probability of randomly selecting someone who does not believe that some people see the future in their dreams can be calculated as follows:

P(A) = 1 - P(B)

Where,

P(A) = Probability of selecting someone who does not believe that some people see the future in their dreams.

P(B) = Probability of selecting someone who believes that some people see the future in their dreams.

P(A) = 1 - P(B)

⇒ 1 - 60.4/100

⇒39.6/100

⇒ 0.396 or 39.6%

Hence, the probability of randomly selecting someone who does not believe that some people see the future in their dreams is 39.6%.

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Answer:

To find the slope of the line through point B and perpendicular to line k, we need to first find the slope of line k.

If we have the equation of line k in slope-intercept form, y = mx + b, then the slope of line k is simply the coefficient of x, which is m.

Assuming we don't have the equation of line k, we can find its slope by using the slope formula, which is:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are two points on line k.

Let's say line k passes through points P and Q. Then we can write the slope of line k as:

m = (yQ - yP)/(xQ - xP)

Now, we want to find the slope of the line through point B and perpendicular to line k. We know that the product of the slopes of two perpendicular lines is -1. That is:

m1 * m2 = -1

where m1 is the slope of line k, and m2 is the slope of the line through point B and perpendicular to line k.

Therefore, we can write:

m2 = -1/m1

So we just need to find the slope of line k, and then we can use this formula to find the slope of the line through point B and perpendicular to line k.

Once we have the slope of the line through point B, we can write its equation in point-slope form:

y - yB = m2(x - xB)

where (xB, yB) is the point B.

Hope this helps with you with your question (it's not a direct answer, I think?) I'm sorry if it doesn't! If you need more help, ask me! :]

Answer:

45 degrees

Step-by-step explanation:

The first angle of the triangle is 45 degrees. This can be determined by the given information that the second angle is 30 degrees larger than the first and the third angle is 3 times the second. Since the second angle is 30 degrees larger than the first, the first angle must be 15 degrees, and the third angle must be 3x15=45 degrees.

The minimum number οf identical cοntainers Rene wοuld need tο make 2,000 cm³ οf ice is 4. Optiοn b is the cοrrect οptiοn.

A cylinder is a three-dimensiοnal sοlid in mathematics that maintains, at a fixed distance, twο parallel bases cοnnected by a curved surface. These bases typically have a circular shape (like a circle), and a line segment knοwn as the axis cοnnects the centers οf the twο bases.

The base οf a cοntainer is 8 centimeters. The height οf the cοntainer is 10 centimetres.

The radius οf a shape is half οf its diameter.

The radius οf  cοntainer is 8/2 = 4 cm.

The vοlume οf a cylinder is πr²h.

The vοlume οf a cοntainer is π×4²×10

= 160 × 3.14

= 502.4 cm³

Assume that Rene needs x number οf cοntainers.

The vοlume οf x number οf cοntainers is 502.4 x.

Accοrding tο the questiοn:

502.4 x = 2,000

Divide bοth sides by 502.4:

x = 2000/502.4

x = 3.98

x ≈ 4

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The correct answer is:

x + 12 ≤ 5 − y ≤ 2(x − 3)

Explanation:

From the given inequalities:

x + 12 ≤ 5 − y ... (1)

5 − y ≤ 2(x − 3) ... (2)

We can see that 5 - y is common in both inequalities. We can isolate this term by subtracting 5 from both sides of (1) and (2):

x + 7 ≤ -y ... (3)

-y ≤ 2(x - 8) ... (4)

Multiplying (3) by -1, we get:

y - 7 ≥ x ... (5)

Substituting this value of x in (4), we get:

y - 7 ≤ -2(7 - y)

y - 7 ≤ -14 + 2y

y ≤ 7

Substituting this value of y in (5), we get:

0 ≤ x + 7 ≤ 14

Subtracting 7 from all sides, we get:

-7 ≤ x ≤ 7

Therefore, the statement x + 12 ≤ 5 − y ≤ 2(x − 3) is not true, but the statement -7 ≤ x ≤ 7 is true.

The linear function that best fits the data is given as follows:

y = 60x.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

When x = 0, y = 0, hence the intercept b of the line is given as follows:

b = 0.

When x increases by 5, y increases by 300, hence the slope m of the line is given as follows:

m = 300/5

m = 60.

Hence the equation is:

y = 60x.

The points on the scatter plot are given as follows:

(0,0) and (5,300).

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Answer:

d

Step-by-step explanation:

Answer:

Complex or Imaginary solutions

Step-by-step explanation:

In the Quadratic Formula, the discriminant is the part that is inside of the radical (square root symbol).

So there are three cases, the discriminant can be:

-positive, OR

-zero, OR

-negative

If its positive, there are two real solutions.

If its zero, there is one real solution.

If its negative, there are two complex (imaginary) solutions.



The expression for the nth term of the sequence is,  Tn = 3n^2 - 7n - 1

To find an expression for the nth term of a quadratic sequence, we need to find a quadratic function that describes the sequence.

Let the nth term of the sequence be denoted by Tn. We can use the method of finite differences to determine the degree of the quadratic function that describes the sequence.

The first differences between the terms are 6, 10, 14, 18, 22. The second differences between these first differences are all equal to 4. This tells us that the sequence is quadratic, since the second differences are constant.

To find the quadratic function that describes the sequence, we can use the formula for the nth term of a quadratic sequence,

Tn = an^2 + bn + c

where a, b, and c are constants to be determined.

We can use the first three terms of the sequence to form a system of three equations,

T1 = a + b + c = -5

T2 = 4a + 2b + c = 1

T3 = 9a + 3b + c = 11

Solving this system of equations, we get:

a = 3

b = -7

c = -1

Therefore, the expression for the nth term of the sequence is

Tn = 3n^2 - 7n - 1

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Approximately 491351% of the annual moisture at an altitude of 6000 feet falls as snow.

According to the given function, the percent of annual snowfall at an altitude of h feet is given by p(h) = 82 in (h) - 649. To approximate the amount of snow at the altitudes of 3000 feet and 6000 feet, we can simply plug these values into the function and solve for p(h).

At an altitude of 3000 feet, we have:

p(3000) = 82 in (3000) - 649

p(3000) = 246000 - 649

p(3000) = 245351

Therefore, approximately 245351% of the annual moisture at an altitude of 3000 feet falls as snow.

Similarly, at an altitude of 6000 feet, we have:

p(6000) = 82 in (6000) - 649

p(6000) = 492000 - 649

p(6000) = 491351

Therefore, approximately 491351% of the annual moisture at an altitude of 6000 feet falls as snow.

It's important to note that these values represent percentages and not the actual amount of snowfall in inches. To convert these percentages to the actual amount of snowfall, we would need to know the total annual moisture at each altitude. Nonetheless, we can use the given function to approximate the percentage of snowfall at different altitudes in the mountain range of California.

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let's recall that the point of tangency for a tangent line to a radius in a circle is alway a right-angle, also let's notice that ∡AOD as well as ∡ABC are both intercepting the same arc.

Check the picture below.

Answer:

x=-2+-8

Step-by-step explanation:

If you mean (x+2)^2=64

take the sqrt of both sides and get x+2 = +-8

then subtract 2 to get -2+-8 = x

x=12°

so:(2x+1°)°+(5x+5)°+90°=180°

7x=180°-1°-5°-90°

7x=84°

x=84°÷7

x=12°

i don't know if it is x that you wanted but the it is

P(X > 60) = P(Z > 1.7321) = 0.0418

When answering questions on Brainly, it is important to be factually accurate, professional, and friendly. Additionally, answers should be concise and relevant to the question being asked. When possible, provide a step-by-step explanation using the following terms: sample, observation, and probability. In this particular question, the following information is provided:Part a) A sample of n=25 observations is drawn from a normal population with μ=100 and σ=2. Find the following: i) P(X < 96) ii) P(96 < X < 105)Part b) The amount of time university professors devote to their jobs per week is normally distributed with a mean of 52 hours and a standard deviation of 6 hours. Find the probability that a professor works for more than 60 hours per week. Find the probability that the mean amount of work per week for three randomly selected professors is more than 60 hours.Part a) Calculate the value of the test statistic, set up the rejection region, undertake the hypothesis test, and interpret the result.

i) P(X < 96)First, we calculate the z-score as follows:z = (X - μ) / σ = (96 - 100) / 2 = -2P(X < 96) = P(Z < -2) = 0.0228ii) P(96 < X < 105)We first calculate the z-scores for both X values as follows:z1 = (X1 - μ) / σ = (96 - 100) / 2 = -2z2 = (X2 - μ) / σ = (105 - 100) / 2 = 2.5Next, we look up the area between these two z-scores using a standard normal distribution table. We have: P(96 < X < 105) = P(-2 < Z < 2.5) = 0.9944 - 0.0228 = 0.9716b) i) Probability that a professor works for more than 60 hours per weekWe first calculate the z-score as follows:z = (X - μ) / σ = (60 - 52) / 6 = 1.3333Using a standard normal distribution table, we find the area to the right of the z-score as follows:P(X > 60) = P(Z > 1.3333) = 0.0912ii) Probability that the mean amount of work per week for three randomly selected professors is more than 60 hoursLet X be the random variable representing the mean amount of work per week for three randomly selected professors. We know that X ~ N(μ, σ / sqrt(n)), where μ = 52, σ = 6, and n = 3. We calculate the z-score as follows:z = (X - μ) / (σ / sqrt(n)) = (60 - 52) / (6 / sqrt(3)) = 1.7321Using a standard normal distribution table, we find the area to the right of the z-score as follows:P(X > 60) = P(Z > 1.7321) = 0.0418Part a) Calculate the value of the test statistic, set up the rejection region, undertake the hypothesis test, and interpret the result.No information is provided about the hypothesis test in Part a of the question, so it is not possible to provide an answer to this part. Please provide more information or clarify the question if possible.

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Therefore, the maximum value of 17 is not considered an outlier as it falls within the upper limit.

what is  Median?

The median is a statistical measure that represents the central value of a dataset.

To calculate the upper limit for outliers, we can use the interquartile range (IQR) and the formula:

Upper Limit = Q3 + 1.5 * IQR

where Q3 is the third quartile, and IQR is the interquartile range.

First, we need to find the values for Q1, Q2 (median), and Q3:

1, 6, 6, 6, 7, 7, 8, 9, 13, 10, 17

Arranging the data in order:

1, 6, 6, 6, 7, 7, 8, 9, 10, 13, 17

The median is the middle value. Since there are 11 values, the median is the average of the 6th and 7th values:

Median = (7 + 8) / 2 = 7.5

To find Q1 and Q3, we need to find the medians of the lower and upper halves of the data, respectively:

Lower half: 1, 6, 6, 6, 7

Upper half: 8, 9, 10, 13, 17

Q1 is the median of the lower half, which is 6.

Q3 is the median of the upper half, which is 10.

Next, we can calculate the interquartile range:

IQR = Q3 - Q1 = 10 - 6 = 4

Finally, we can calculate the upper limit for outliers:

Upper Limit = Q3 + 1.5 * IQR = 10 + 1.5 * 4 = 16

Any value above 16 can be considered a potential outlier on the high end of the data.

Therefore, the maximum value of 17 is not considered an outlier as it falls within the upper limit.

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0.0002

The required probability can be calculated as follows:Explanation:There are 7 different songs from 7 different artists, thus there are 7! ways of shuffling these songs. In other words, there are 7! = 5040 different playlists in which these songs can be shuffled.We need to calculate the probability of Adam Rickitt's song being played first and Phil Collins' song being played second. This can be done in two steps.Step 1: We place Adam Rickitt's song at the beginning of the playlist. There is only one way to do this. After Adam Rickitt's song has been placed, we are left with 6 remaining songs that can be shuffled. Thus, there are 6! = 720 different playlists.Step 2: We place Phil Collins' song as the second song on the playlist. There is only one way to do this as well.Therefore, the probability that Adam Rickitt's song is played first and Phil Collins' song is played second is given by the product of the probabilities of the two steps as follows:P = 1/5040 × 1 = 1/5040 = 0.000198 rounded to 4 decimal places. Thus, the probability is approximately 0.0002. Therefore, the probability that the first song is by Adam Rickitt and the second song is by Phil Collins is 0.0002.

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Using ratios, we can find that the number of girls in the class are 20.

If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. A proportion is an equation that equalises two ratios.

For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 boy and 3 girls (for every one boy there are 3 girls) There are 3 out of 4 girls and 1 out of 4 guys.

Now in the question, total students in class = 32.

The ratio between the boys and girls is 3:5.

So, total parts from the ratio = 3+5=8

Now 5/8 students in the class are girls.

= 5/8 × 32

= 5 × 4

= 20.

Therefore, the number of girls in the class are 20.

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Answer:

Triangle XYZ is shifted 9 units to the right, then 4 units down.

The best way to design a study to measure the amount of traffic during the morning rush hour along a city street is to make video recordings of the street during rush hour every day for a year and count the number of vehicles that pass a certain point, then calculate the average using the given formula.

The best way to accurately measure the amount of traffic during the morning rush hour along a city street is to make video recordings of the street during rush hour every day for a year. After recording the video, count the number of vehicles that pass a specific point in the video. Then, calculate the average number of vehicles that pass the point each day during one year by using the following formula: Average = (Number of vehicles per day1 + Number of vehicles per day2 + ... + Number of vehicles per dayn) / n, where n is the number of days the video recording was made. This method is the most reliable way to measure the amount of traffic during the morning rush hour since it provides an average based on the data collected over a full year.

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Applying the distance formula, the distance between points N and C in the coordinate plane is calculated as: 5 units.

To calculate the distance between two points on a coordinate plane, the distance formula can be applied which is given as:

d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Given the two points lie on the coordinate plane as the following coordinates:

N = (-8, 9)

C = (-4, 6)

Therefore, we will have:

d = √[(−4 − (−8))² + (6−9)²]

d = √[(4)² + (−3)²]

d = √(16 + 9)

d = √25

d = 5 units

Thus, the distance between points N and C is calculated as: 5 units.

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Therefore, based on the data provided, Oldtown is more popular than Newburg.

To determine which city is more popular, we need to compare their populations for each year.

In 2015, Oldtown had a population of 1518, which is significantly larger than Newburg's population of 100. Therefore, Oldtown was more popular in 2015.

In 2016, Oldtown's population increased to 1643, while Newburg's population increased to 110. Again, Oldtown had a larger population and was more popular.

In 2017, Oldtown's population increased to 1768, while Newburg's population increased to 121. Once again, Oldtown had a larger population and was more popular.

In 2018, Oldtown's population increased to 1893, while Newburg's population increased to 133. Yet again, Oldtown had a larger population and was more popular.

Therefore, based on the data provided, Oldtown is more popular than Newburg.

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The mayors of old town and newborn were having a disagreement about which city was more popular. They made the table below to show the population of their cities for the past several years.

2015 Newburg Population 100. Oldtown Population 1518

2016 Newburg Population 110. Oldtown Population 1643

2017 Newburg Population 121. Oldtown Population 1768

2018 Newburg Population 133. Oldtown Population 1893

Which city is more popular?

Answer:it’s 0

Step-by-step explanation:

Answer:

67.5

Step-by-step explanation:

4 1/2x6= 27 27x2 1/2=67.5

Answer:

Step-by-step explanation:

[tex]\frac{42}{x+5} =7[/tex]

[tex]42=7(x+5)[/tex]

[tex]42=7x+35[/tex]

[tex]7x=-7[/tex]

[tex]x=-1[/tex]

Answer:25 sticks

Step-by-step explanation:

1st=5 sticks

2nd=9 sticks

3rd=13 sticks

4th=17 sticks

5th=21 sticks

6th=25 sticks

Answer:

True answers:

f(x) is an increasing exponential function.

f(x) has a greater y-intercept

Step-by-step explanation:

Option 1:

Both functions have the same y-intercept is FALSE

The y-intercept of f(x) is found by plugging in 0 for x

[tex]f(0) = 5^0 - 3 = 1 - 3 = -2[/tex]

The intercepts are different, so option 1 is FALSE.

Option 2:

f(x) is an increasing exponential function is TRUE

the largest term is positive and exponential.

Option 3:

g(x) has a greater y-intercept. is FALSE

The y-intercept of g(x) is -3, and the y-intercept of f(x) is -2. -2 > -3

Option 4:

f(x) has a greater y-intercept is TRUE

The y-intercept of g(x) is -3, and the y-intercept of f(x) is -2. -2 > -3

x°=46

Step-by-step explanation:

There are two methods of solving this question

Method 1:

x°+90°=136° the theorem states that "the sum of two opposite interior is equal to the exterior"

x°=136°-90°

x°=46°

or

Method 2:

136° is on a straight line which is 180°

so, let the other side of the straight line be a.

therefore, 136°+a°=180° theorem {Angle on a straight line}

a°=180°-136°

a°=44°

so, in the triangle is the sum of 180°

a°+90°+x°=180° theorem {Sum of angles in a triangle}

44°+90°+x°=180°

x=180°-134°

x°=46°