The amount of shore at a local beach changes an average of -3/4 foot each year. What is the change in the amount of shore after 7 years and 4 months ( 7 1/3)

a. Mean=5 Median=5 Mode= 1

b. Range=9 Variance=10.16 Standard Deviation=3.19 Coefficient of variation=54.83%

c.  Z score 1.34.  no other z-scores as there is no more data set given

d.  skewed to the left

HTML is a markup language. It is used to structure and present content on the web. Therefore, answering the question formatted with HTML is not necessary. Nonetheless, the following are the solutions to the problem provided below.a. Compute the mean, median, and mode:Mean: (9+5+1+10+4) / 5 = 5.8Median: Arrange the numbers in order: 1, 4, 5, 9, 10. Then the median is the middle value. Hence, median = 5.Mode: The mode is the number that appears most frequently in the set of data. Therefore, the mode of the set of data is 1.b. Competo the range, variance, standard deviation, and coefficient of variation:The range is the difference between the largest and smallest numbers in the set of data. Range = 10 - 1 = 9.Variance: s² = [(9-5.8)² + (5-5.8)² + (1-5.8)² + (10-5.8)² + (4-5.8)²] / 5 = 10.16.Standard deviation: s = √(10.16) = 3.19Coefficient of variation: CV = (3.19 / 5.8) × 100% = 54.83%c. Compute the Z-scores. Are there any others?The formula for Z-score is given by: Z = (x - μ) / s where x = raw score, μ = mean, and s = standard deviation.Z-scores for the set of data are:z₁ = (1 - 5.8) / 3.19 = -1.5z₂ = (4 - 5.8) / 3.19 = -0.56z₃ = (5 - 5.8) / 3.19 = -0.25z₄ = (9 - 5.8) / 3.19 = 1.00z₅ = (10 - 5.8) / 3.19 = 1.34There are no other z-scores as there is no more data set given.d. Describe the shape of the data setThe data set is skewed to the left because the tail is longer in the left direction. It can be observed from the Z-scores, mean, and median, as the mean is less than the median.

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Using trigonometric ratios the value for line segment DC is obtained as 30.5 units.

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios. In triangle ABD, the values given are -

∠BDA = 90°,

∠A = 54° and

AB = 20 units

According to the sum property of a triangle.

∠BDA + ∠A + ∠ABD = 180°

Substitute the values into the equation -

90° + 54° + ∠ABD = 180°

144° + ∠ABD = 180°

∠ABD = 180° - 144°

∠ABD = 36°

Now according to trigonometric ratios -

cos θ = Base / Hypotenuse

In triangle ABD -cos 36° = BD / AB

Substitute the values into the equation -

cos 36° = BD / 20BD

= cos 36° × 20BD

= 0.80901 × 20BD

= 16.18

≈ 16.2

Now in triangle BDC, the values given are -

∠BDC = 90°, ∠C = 28° and BD = 16.2

Now according to trigonometric ratios -tan θ = Perpendicular / Base

In triangle BDC -tan 28° = BD / DC

Substitute the values into the equation -

tan 28° = 16.2 / DC

DC = 16.2 / tan 28°

DC = 16.2 / 0.53170

DC = 30.46 ≈ 30.5 units

Therefore, the value for DC is obtained as 30.5 units.

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The cost of 10.0 gallons of gasoline priced at 1.449 per gallon is 14.49.

The cost of 10.0 gallons of gasoline priced at 1.449 per gallon can be determined using the formula Cost = Quantity * Price. To calculate the cost, first multiply 10.0 (the quantity) by 1.449 (the price). This gives the value 14.49, which is the cost of 10.0 gallons of gasoline priced at 1.449 per gallon.

To explain this further, when calculating the cost of an item, we need to take into account both the quantity and the price of that item. The quantity is the amount of the item that we will be purchasing, and the price is the amount that we will be paying for that item. In the case of gasoline, 10.0 gallons is the quantity, and 1.449 is the price per gallon.

To calculate the cost, we need to multiply the quantity by the price. This gives us the cost of the item. In this case, multiplying 10.0 (the quantity) by 1.449 (the price) gives us 14.49, which is the cost of 10.0 gallons of gasoline priced at 1.449 per gallon.

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a) The populations in 1980, 1990, 2000, and 2010 are 157,000, 218,000, 269,000, and 308,000 respectively.

b) the population will reach 390,000 in 270 years

c) No, as t increases, the population increases rapidly

(a) To find the population in 1980, 1990, 2000, and 2010, we substitute the corresponding values of t into the given model and round the answers to the nearest whole number.

Population in 1980: P = 75.9e^(0.0316*10) = 156,604

Population in 1990: P = 75.9e^(0.0316*20) = 217,643

Population in 2000: P = 75.9e^(0.0316*30) = 269,099

Population in 2010: P = 75.9e^(0.0316*40) = 308,227

(b) To find when the population of Horry County will reach 390,000, we need to solve the equation 390 000 = 75.9e^(0.0316t) for t.

Taking the natural logarithm of both sides, we get:

ln(390,000/75.9) = 0.0316t

Simplifying, we get:

t = ln(390,000/75.9)/0.0316 ≈ 270.395

Rounding down to the nearest whole year, we get that the population will reach 390,000 in 270 years

(c) The model assumes that the population growth rate will remain constant over time. However, in reality, population growth rates can be affected by a variety of factors, such as changes in birth and death rates, immigration, emigration, and natural disasters.

Therefore, it is unlikely that the model will be valid for long-term predictions of the population. The model can provide a good estimate of the population for the short-term, but it is not reliable for predictions far into the future.

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The volume of the entire figure composed of a rectangular prism and pyramid is 2816 ft³

The volume of a figure is the amount of space the three dimensional object occupies.

The volume of the rectangular prism = length * width * height = 16ft * 16ft * 5 ft = 1280 ft³

The volume of the rectangular pyramid = (1/3) * length * width * height = 16ft * 16ft * 18 ft = 1536 ft³

The volume of the entire figure = volume of the rectangular prism + volume of the rectangular pyramid

The volume of the entire figure = 1280 ft³ + 1536 ft³ = 2816 ft³

The volume of the entire figure is 2816 ft³

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The total grade for these 37 students is less than 2590.0 is 0.8745.

The distribution of students' grades is not approximately normal(b) If n = 37 students are selected at random, the distribution of the sample mean grade is approximately normal = with a mean of 68 and a standard deviation of 3.2152(c) The probability that the sample mean grade for these 37 students is less than 70.0 is 0.3909 If n = 37 students are selected at random, the distribution of the sample total grade is approximately normal = with a mean of 2516 and a standard deviation of 70.4583 The probability that the total grade for these 37 students is less than 2590.0 is 0.8745 The answer to the question is as follows: The distribution of students' grades is not approximately normal If n = 37 students are selected at random, the distribution of the sample mean grade is approximately normal = with a mean of 68 and a standard deviation of 3.2152.

The probability that the sample mean grade for these 37 students is less than 70.0 is 0.3909(d) If n = 37 students are selected at random, the distribution of the sample total grade is approximately normal = with a mean of 2516 and a standard deviation of 70.4583.

The probability that the total grade for these 37 students is less than 2590.0 is 0.8745. What is unimodal? Unimodal is a term that describes a distribution that has only one mode. A mode is a value that appears most frequently in a dataset, and in a unimodal distribution, there is only one such value.

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To find f(-6), we need to substitute -6 for x in the expression for f(x):

f(x) = 2x^2 + 5x - x/3

f(-6) = 2(-6)^2 + 5(-6) - (-6)/3

f(-6) = 2(36) - 30 + 2

f(-6) = 72 - 30 + 2

f(-6) = 44

Therefore, f(-6) = 44.

The side which clοses tο the acute angle will be the adjacent side tο the acute angle and the lοngest side is the Hypοtenuse.

What are Sides οf a right-angled triangle?  

In a right-angled triangle, there are three sides. One side is called the hypοtenuse and the οther twο sides are adjacent tο the right angle and are called the legs οf the triangle.

In a right triangle, the side οppοsite the right angle is always the lοngest side and is called the hypοtenuse. The twο οther sides are called the legs οf the triangle, and οne οf the legs is adjacent tο each οf the acute angles.

Tο determine which side is adjacent tο a specific acute angle, yοu need tο identify which οf the twο legs is clοsest tο that angle. The side clοsest tο the angle is the adjacent side.

Fοr example, if yοu have a right triangle with acute angles A and B, and leg AB is adjacent tο angle A, then leg BC is adjacent tο angle B.

Alternatively, yοu can use the trigοnοmetric functiοns sine, cοsine, and tangent tο determine the relatiοnship between the sides οf a right triangle and its angles.

The side which clοses tο the acute angle will be the adjacent side tο the acute angle and the lοngest side is the Hypοtenuse.

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Width of the mat is 0.75 m

Answer:Triangle problemGiven a right triangle, perimeter = 198 cm Hypotenuse = 85 cmLet the other sides of the triangle be a and b respectively.To find the value of a and bSolutionWe know that, in a right triangle with sides a and b, and hypotenuse c Pythagoras Theorem can be usedc² = a² + b²Formula for perimeter of a triangle is P = a + b + cFrom the given values, we can substitute the values for P and c.198 = a + b + 85 198 - 85 = a + b 113 = a + bTo get the values of a and b, we need one more equation We can use Pythagoras theorem since it is a right triangle85² = a² + b²7225 = a² + b²a² = 7225 - b²b² = 7225 - a²Substitute b² into the previous equation113 = a + b7225 = a² + (7225 - a²)7225 = 2a²a² = 7225 / 2a = √(7225 / 2) = √(36125 / 8) = 75.59 cmNow that we have found the value of a, we can find b using the Pythagoras Theorem85² = 75.59² + b²b² = 85² - 75.59²b = √(85² - 75.59²) = 49.79 cm Therefore, a = 75.59 cm, b = 49.79 cmWidth of rubber matA square swimming pool has an area of 289 m²The area of the pool can be expressed as (side)²Therefore, side = √289 = 17 mLet the width of the rubber mat be w. Since it is uniform, it will be the same on all sides. Area of the pool and mat = (side + 2w)² - side² = 289From the above equation, we can solve for w:4w(side) + 4w² = 0+ 4w² + 4w(side) - 289 = 04(w + side/2)² - 289 = 0(w + side/2)² = 289 / 4w + side/2 = ±17/2 w + side/2 = 8.5 or w + side/2 = -8.5side/2 can never be negative, therefore we can consider only w + side/2 = 8.5 w = 8.5 - side/2w = 8.5 - 17/2 = 0.75m Width of the mat is 0.75 m

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a)  A(5) = 10 * e^(-0.05*5)

b)  7.776

To solve the given problem, the initial amount of chlorine should be assumed as 'P0' and the exponential function should be written in the form of y = P_0 * e^(kt) where P_0 is the initial amount of chlorine and k is the rate of change. Therefore, for the given problem, the exponential function can be given by: y = P_0 * e^(-0.05t) where P_0 is the initial amount of chlorine and t is the number of hours. This equation will give the amount of chlorine remaining after t hours. The formula for exponential decay is given by:A(t) = A₀ * e^(-kt) Where A(t) is the amount after time t, A₀ is the initial amount, k is the rate of decay, and t is the time elapsed. To calculate the remaining amount of chlorine after a certain number of hours, we'll utilize the formula above .Let's start with the given information: An exponential function that gives the amount of chlorine remaining after t hours is to be found. P₀ = the initial amount of chlorine, which is 10.We can also figure out the rate of decay from the given information. The amount of chlorine is reduced by 5% per hour, which means the rate of decay is 0.05. We need to put a negative sign in front of the rate of decay to indicate that it is decreasing. Let's use the formula to find the amount of chlorine remaining after 5 hours. Then, substitute A₀ = 10, k = -0.05, and t = 5 into the equation above to obtain A(5) = 10 * e^(-0.05*5) = 7.776.So, the amount of chlorine remaining after 5 hours is 7.776.

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Value of Q3 is approximately 114.1 given mean and standard deviation.

We must identify the IQ score that separates the bottom 9% from the top 91% in order to determine P9. The normal distribution of IQ scores has a mean of 100 and a standard deviation of 15, as is well known. The z-score for the 9th percentile can be calculated using a calculator or a typical normal distribution table.

[tex]z = invNorm(0.09) = -1.34[/tex]

The formula for converting a z-score to an IQ score is as follows:

IQ equals z * standard deviation + mean, or -1.34 * 15 + 100, or 79.1.

P9 is therefore roughly 79.1.

We must identify the IQ score that distinguishes the top 25% from the rest in order to determine Q3. Assuming a normal distribution, IQ values have a mean of 105 and a standard deviation of 15. Since the top 25% and the 75th percentile are the same, we can use a calculator or a conventional normal distribution table to determine the z-score that represents the 75th percentile:

[tex]z = invNorm(0.75) = 0.67[/tex]

We can then use the formula for transforming a z-score to an IQ score:

IQ = z * standard deviation + mean = 0.67 * 15 + 105 = 114.05

Therefore, Q3 is approximately 114.1.

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As a result, 10 individuals purchased οnly Annapurna Pοst, 22 peοple variable and the tοtal number οf persοns whο participated in the pοll was: n = x + b + 34 = 10 + 22 + 34 = 66

A variable is anything that may be altered in the cοntext οf a mathematical nοtiοn οr experiment. Variables are frequently denοted by a single symbοl. The letters x, y, and z are οften used as generic variables symbοls. Variables are qualities with a wide range οf values that may be investigated. Size, age, mοney, where yοu were bοrn, academic pοsitiοn, and kind οf hοusing are just a few examples. Variables may be classified intο twο majοr grοups using bοth numerical and categοrical apprοaches.

k = 100 (100 peοple bοught Kantipur) (100 peοple bοught Kantipur)

a + x = 56 (56 individuals did nοt buy Kantipur) (56 peοple did nοt buy Kantipur)

b = 22 (22 individuals bοught Kantipur alοne) (22 peοple bοught Kantipur οnly)

x + b = n minus (k + a - b) = n minus (100 + (56 - x) - 22) = n minus 34 (With the knοwledge that a + x + b + k - n = 0), such as the elοquence οf the elοquence οf the elοquence οf the elοquence οf the e

n = x + b + 34

a + x = 56 x - an x + 22 = n - k - (a - 22)

x + 22 = x + 22 + a - 100 - a + 22 + 34

x = 10

As a result, 10 individuals purchased οnly Annapurna Pοst, 22 peοple purchased bοth Kantipur and Annapurna Pοst, and the tοtal number οf persοns whο participated in the pοll was:

n = x + b + 34 = 10 + 22 + 34 = 66

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0.571

Given data: The accompanying table shows the numbers of male and female students in a certain region who received​ bachelor's degrees in a certain field in a recent year. A student is selected at random. Find the probability of each event listed in parts​ (a) through​ (c) below.Table:Males FemalesTotalsFreshman 12 25 37Sophomore 14 18 32Junior 17 14 31Senior 9 12 21Totals 52 69 121a) A freshman is selected at random.b) A senior male is selected at random.c) A female is selected at random.a) For part a, we have to find the probability of selecting a freshman at random. The total number of students is 121. And the number of freshmen is 37. The probability of selecting a freshman at random is:37/121 = 0.306b) For part b, we have to find the probability of selecting a senior male at random. The total number of seniors is 21. And the number of senior males is 9. The probability of selecting a senior male at random is:9/121 = 0.074c) For part c, we have to find the probability of selecting a female at random. The total number of females is 69. And the total number of students is 121. The probability of selecting a female at random is:69/121 = 0.571Therefore, the probability of each event is:a) 0.306b) 0.074c) 0.571

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Answer:

a) 7/9 * 2

Because 7*2/9 = 1.555556, which is less than 2.

All the other options' products are greater than 2.

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DONT FORGET!!

The steps to construct a parallel line to point C consists of drawing an arc from point C to intersect AB at points D and E and with the same radius, placing the compass at D to draw an arc intersecting the previous one at F. Join C and F to complete the construction of the parallel line to AB.

Please find attached the example drawing of the line CF parallel to AB created with MS Word

Parallel lines are lines that maintain the same distance from each other and do not meet.

A more detailed steps to construct a line parallel to AB passing through point C using only a straightedge and a compass includes;

The line that passes through C and G is parallel to AB

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Answer: 312

Step-by-step explanation:

Estimate: One way to estimate the quotient of 2,496 ÷ 8 is to round 2,496 to the nearest multiple of 8, which is 2,496 rounded to 2,496. Then, we can divide 2,496 by 8, which gives an estimated quotient of 312.

The former bedroom is 8 feet by 8 feet in dimensions.

In mathematics, a dimension is the length or width of an area, region, or space in one direction. It merely involves taking an object's length, width, and height into account.

Assume that the side length of the former bedroom is x.

Hence, the former bedroom had a square footage of x² feet.

The dimensions of the new bedroom are (x+3) and (x+2), respectively, as compared to the old bedroom, which is 3 feet wider and 2 feet deeper.

The new bedroom is (x+3)(x+2) square feet in size.

Since we are aware that the additional area is 46 square feet, we can construct the following equation:

(x+3)(x+2) - x² = 46

Expanding the left side of the equation:

x² + 5x + 6 - x² = 46

Simplifying:

5x + 6 = 46

Subtracting 6 from both sides:

5x = 40

Dividing both sides by 5:

x = 8

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Step-by-step explanation:

Divya is cooking dinner. she goes to the market to buy ingredients. the price per pound of different ingredients is shown in the table below. Diyva recipe calls for 3.25 pounds of beef, 0.65 pounds of onions, 0.2 pounds of potatoes, 0.15 pounds of tomatoes, and 0.33 pounds of asparagus How much will diyva pay for all the ingredients in the recipe?

The sum or difference of [tex]$-2x^2+x+6$[/tex] and [tex]$(5x^2-4x-2)$[/tex] is [tex]3x^2 - 3x + 4$.[/tex]

What is sum?

In mathematics, the term "sum" refers to the result obtained by adding two or more numbers or quantities together. It also be used to refer to the total amount of something, such as the sum of money you have in your bank account, or the sum of the lengths of all the sides of a polygon.

To find the sum or difference of [tex]-2x^2+x+6 + (5x^2-4x-2)[/tex] we need to combine like terms.

[tex]-2x^2+x+6 + (5x^2-4x-2) &\\\\= (-2x^2 + 5x^2) + (x - 4x) + (6 - 2)[/tex]

[tex]&= 3x^2 - 3x + 4[/tex]

Therefore, the sum or difference of [tex]$-2x^2+x+6$[/tex] and [tex]$(5x^2-4x-2)$[/tex] is [tex]3x^2 - 3x + 4$.[/tex]

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According to the given information, 0.97306, 0.02669, and 0.000005.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

a. The probability that a golfer does not score a hole in one on the sixth hole is [tex]$1 - \frac{1}{3,709}$[/tex]. Since there are 156 golfers, the probability that none of them score a hole in one is

[tex]$$\left(1 - \frac{1}{3,709}\right)^{156} \approx 0.97306$$[/tex]

The probability that no one gets a hole in one on the sixth hole is 0.97306

b. The probability that exactly one golfer gets a hole in one on the sixth hole is

[tex]$${156 \choose 1} \cdot \frac{1}{3,709} \cdot \left(1 - \frac{1}{3,709}\right)^{155} \approx 0.02669$$[/tex]

The probability that exactly one golfer gets a hole in one on the sixth hole is 0.02669

c. The probability that four golfers score a hole in one on the sixth hole is

[tex]$${156 \choose 4} \cdot \left(\frac{1}{3,709}\right)^4 \cdot \left(1 - \frac{1}{3,709}\right)^{156-4} \approx 0.000005$$[/tex]

The probability that four golfers score a hole in one on the sixth hole is 0.000005

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If Bill starts work at 8:15, works until 4:45, and has 90 minutes of breaks. Bill works for 36.25 hours in 5 days.

Work per day typically refers to the amount of time or effort expended by an individual during a typical working day.

First, let's find out how many hours Bill works in one day.

        8 hours and 45 minutes - 90 minutes of breaks

           = 7 hours and 15 minutes

           = 7.25 hours of work per day.

       7.25 hours per day x 5 days = 36.25 hours.

Therefore, Bill works for 36.25 hours in 5 days.

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The grouping of data  or sample points is a component of the machine learning process known as clustering.

The task of arranging a set of objects into an identical group in a way that makes them more similar to one another than those found in different groups is known as cluster analysis or clustering.

A scatter plot is an unique type of plot or mathematical diagram that displays data for usually 2 parameters for a collection of data. It uses Cartesian coordinates.

Coordinates, it is a set or group of values that show an exact or accurate position.

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Answer:

K

Step-by-step explanation:

[tex]c + d \: - 2(c + d) \\ = c + d - 2c - 2d \\ = - c - d \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

On solving the question we have that We can see that RS + ST = RT, equation  confirming that S is on segment RT: RT = RS + ST = 5 + 10 = 15

A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.

Because S is on the section RT, we know that RS + ST = RT. As a result, we may construct the following equation:

RS + ST = 3x + 1 + (x + 2) = 15

To simplify this equation, we can combine similar terms:

4x + 3 = 15

Subtraction of 3 from both sides yields:

4x = 12

When we divide both sides by 4, we get:

x = 3

RS = x + 2 = 5 and ST = 3x + 1 = 10 as a result.

We can see that RS + ST = RT, confirming that S is on segment RT:

RT = RS + ST = 5 + 10 = 15

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The two values of b that make the system inconsistent are b = -4.79 (negative) and b = 4.79 (positive). This is found by setting the discriminant of the quadratic equation in x to be negative.

We can solve this problem by substituting y = 4x + b into the first equation:

x² + (4x + b)² = 25

Expanding the square and simplifying, we get:

x² + 16x² + 8bx + b² - 25 = 0

Combining like terms, we get a quadratic equation in x:

17x² + 8bx + (b² - 25) = 0

For the system to be inconsistent, this quadratic equation must have no real solutions (i.e., the discriminant must be negative). Therefore, we need:

(8b)² - 4(17)(b² - 25) < 0

Simplifying and solving for b, we get:

64b² - 4(17b² - 425) < 0

98b² < 1700

b² < 1700/98

b < ±sqrt(1700/98)

b < ±4.79

Therefore, the two values of b that make the system inconsistent are:

b = -4.79 (negative)

b = 4.79 (positive)

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The factored forms of the equations and the intercepts would be:

g(x) = x² - 4x - 21:

h(x) = x² + 8x + 12:

For g(x) = x² - 4x - 21:

To find the factored form, we need to factor the quadratic expression:

g(x) = (x - 7)(x + 3)

To find the x-intercepts, we set g(x) = 0 and solve for x:

(x - 7)(x + 3) = 0

x = 7 or x = -3

To find the y-intercept, we set x = 0 and evaluate g(x):

g(0) = (0 - 7)(0 + 3) = -21

Therefore, the y-intercept of g(x) is (0,-21).

For h(x) = x² + 8x + 12:

h(x) = (x + 2)(x + 6)

To find the x-intercepts, we set h(x) = 0 and solve for x:

(x + 2)(x + 6) = 0

x = -2 or x = -6

To find the y-intercept, we set x = 0 and evaluate h(x):

h(0) = (0 + 2)(0 + 6) = 12

Therefore, the y-intercept of h(x) is (0,12).

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The missing value that completes the frequency table is 100

A frequency table is just a two-column "t-chart" or table that lists all of the potential outcomes and their corresponding frequencies as seen in a sample.

How to solve:

From the graph given,

The battery life(hours) from x = 15  to x= 20 has a frequency of 130

The battery life(hours) from x= 28 to x= 30 has a frequency of 100

It can be inferred that from the battery life of the different models, the missing value is 100 and when you crosscheck the data, you would find this is correct and accurate.

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For given quadratic equation, the company had a profit of 7 million dollars in either its 6th year or its 10th year of operation.

What exactly are quadratic equations?

A quadratic equation is a second-degree polynomial equation of the form:

ax²+ bx + c = 0

where x is the variable and a, b, and c are constants, with a ≠ 0. The term "quadratic" comes from the Latin word "quadratus", which means "square". In other words, a quadratic equation is an equation that involves the square of the variable x.

Now,

We are given that the profit of the company (in millions of dollars) can be represented by the equation y = x² - 16x + 67, where x is the number of years since the company started.

We want to find when the company had a profit of 7 million dollars.

So, we can set y = 7 in the equation:

7 = x² - 16x + 67

Rearranging and simplifying:

x² - 16x + 60 = 0

Now, we can solve for x using the quadratic formula:

x = (-(-16) ± √((-16)^2 - 4(1)(60))) / 2(1)

x = (16 ± √(16)) / 2

x = 8 ± 2

Therefore, the solutions are x = 10 or x = 6.

This means that the company had a profit of 7 million dollars in either its 6th year or its 10th year of operation.

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The equation of the straight line with the same gradient as [tex]y = 3x + 5[/tex] and passing through the point [tex](0, 12)[/tex] is [tex]y = 3x + 12[/tex]

A mathematical equation, such as 6 x 4 Equals 12 x 2, states that two quantities or units are similar. A noun that ranks. When two or more components must be taken into account together in to fully understand or describe the whole scenario, this is known as an equation.

a) To find the equation of the straight line shown, we need to determine its slope (or gradient) and [tex]y-[/tex]intercept. We can do this by choosing two points on the line and using the point-slope formula:

slope [tex]=[/tex] (change in y) / (change in x)

Let's choose the points [tex](1, 3)[/tex] and [tex](4, 7)[/tex] from the line.

slope [tex]= (7 - 3) / (4 - 1) = 4 / 3[/tex]

Now we can use the point-slope formula with one of the points to find the equation:

[tex]y - y1 = m(x - x1)[/tex]

where m is the slope and (x1, y1) is one of the points on the line.

Let's use the point (1, 3):

[tex]y - 3 = (4/3)(x - 1)[/tex]

Simplifying:

[tex]y = (4/3)x + 1[/tex]

So, the equation of the straight line shown is [tex]y = (4/3)x + 1[/tex].

b) To complete the statement "[tex]y = 3x + 5[/tex] passes through [tex](0, -5)[/tex]", we need to substitute [tex]x = 0[/tex] and [tex]y = -5[/tex] into the equation and verify that it is true:

[tex]y = 3x + 5[/tex]

[tex]-5 = 3(0) + 5[/tex]

[tex]-5 = 5 - 5[/tex]

[tex]-5 = -5[/tex]

Since the equation is true, we can say that the point [tex](0, -5)[/tex] is on the line [tex]y = 3x + 5[/tex].

c) We know that the gradient of the line we want to find is the same as [tex]y = 3x + 5[/tex], which is [tex]3[/tex]. We also know that it passes through the point [tex](0, 12)[/tex].

Using the point-slope formula with [tex]m = 3[/tex] and [tex](x1, y1) = (0, 12)[/tex]:

[tex]y - 12 = 3(x - 0)[/tex]

Simplifying:

[tex]y = 3x + 12[/tex]

So, the equation of the straight line with the same gradient as [tex]y = 3x + 5[/tex]and passing through the point [tex](0, 12)[/tex] is [tex]y = 3x + 12[/tex].

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Answer:

3x+5x=8x

-3t+-t=-4t

3p+3p=6p

2n+n=3n

5g+-g=4g

7y+y=8y

4+12=16

Step-by-step explanation: