10.6.3 Test (CST): Factoring Polynomials
Question 3 of 25
What are the zeros of f(x) = x²-x-20?
OA. x=-2 and x = 10
B. x= -4 and x = 5
OC. x=-10 and x = 2
OD. x= -5 and x = 4

Answer:

See below.

Step-by-step explanation:

We are given the value of an angle, and the hypotenuse.

x will equal 7.0

Using Trigonometry Functions, we can identify x.

[tex]\textsf{Trigonometry Functions:}[/tex]

[tex]Sin = \frac{Opposite}{Hypotenuse}[/tex]

[tex]Cosine = \frac{Adjacent}{Hypotenuse}[/tex]

[tex]Tan = \frac{Opposite}{Adjacent}[/tex]

[tex]\fbox{We should use Sin.}[/tex]

Let's begin by solving for x.

[tex]\textsf{\underline{We should use;}}[/tex]

[tex]{Sin(23^{\circ})}[/tex]

[tex]\textsf{\underline{Solve for x:}}[/tex]

[tex]Sin(23^{\circ})=\frac{x}{18}[/tex]

[tex]\textsf{\underline{Multiply by 18:}}[/tex]

[tex]18 \times Sin(23^{\circ})={x}[/tex]

[tex]x \approx 7.0[/tex]

a) The initial velocity of the boulder was 117.39 ft/s.

b) The maximum height reached by the boulder was 214.48 ft.

We can use the equations of motion to solve this problem. Let's assume that the acceleration due to gravity is -32 ft/s² (negative because it acts downwards).

a) We can use the following equation to find the initial velocity (v₀) of the boulder:

h = v₀t + 0.5at²

where h is the initial height (15ft), t is the time it takes to hit the ground (6.7s), and a is the acceleration due to gravity (-32 ft/s²).

Plugging in the values, we get:

15 = v₀(6.7) + 0.5(-32)(6.7)²

Solving for v₀, we get:

v₀ = 117.39 ft/s (rounded to two decimal places)

Therefore, the initial velocity of the boulder was 117.39 ft/s.

b) To find the maximum height reached by the boulder, we can use the following equation:

v² = v₀² + 2ah

where v is the final velocity (0 ft/s at the maximum height), v₀ is the initial velocity (which we just found to be 117.39 ft/s), a is the acceleration due to gravity (-32 ft/s²), and h is the maximum height we want to find.

Plugging in the values, we get:

0² = (117.39)² + 2(-32)h

Solving for h, we get:

h = 214.48 ft (rounded to two decimal places)

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If one student can fill 5 slots with student presentations, then 25 students might be able to fill the slots in 125 different ways.

To calculate the number of ways in which a student can fill a specific slot, the simple arithmetic operation of multiplication is used. In the given question it is already given that there are 25 students in a class and one of the student has filled the slots in 5 different ways. This means that each student will be able to fill the slots in 5 different ways.

Hence total number of ways in which all the students might be able to fill the slots is given as product of total students and number of slots filled.

Total number of ways = 25*5 = 125 ways

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The value of x = 50°

What is the triangle?

A triangle is a 3 line segments with a closed diagram. It has 3 vertices, 3 sides and 3 angles. The sum of all interior angles is 180°.

Given figure y° = 40° and right angle triangle.

So, all interior angles sum is 180°.

90° + y° + x° = 180°

90° + 40° + x° = 180°

x° = 50°

Therefore, the value of x = 50°

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It takes 0.55 secοnds fοr a ball traveling at 80 mph tο reach a batter that is pοsitiοned at the back οf the batter's bοx.

Speed is defined as the distance traveled by an οbject in a given amοunt οf time. Speed is a scalar quantity, meaning that it has magnitude but nο directiοn.

Mathematically, speed is calculated as fοllοws:

speed = distance/time

Where "distance" is the distance travelled by the οbject, and "time" is the time it takes fοr the οbject tο travel that distance.

Tο determine hοw lοng it takes fοr the ball tο reach the batter, we need tο use the fοrmula fοr time:

time = distance/speed

First, we need tο determine the distance frοm the pitcher's mοund tο the batter's bοx. Accοrding tο Majοr League Baseball rules, the distance frοm the pitcher's mοund tο hοme plate is 60 feet, 6 inches (18.44 meters). The batter's bοx is typically 4 feet (1.22 meters) behind hοme plate, sο the distance frοm the pitcher's mοund tο the back οf the batter's bοx is:

distance = 60 ft 6 in + 4 ft = 64 ft 6 in = 19.66 meters

Next, we cοnvert the speed οf the ball frοm miles per hοur (mph) tο meters per secοnd (m/s). One mile is equal tο 1,609.34 meters, and οne hοur is equal tο 3,600 secοnds, sο we can cοnvert mph tο m/s using the fοllοwing fοrmula:

speed in m/s = (speed in mph * 0.44704)

Therefοre, the speed οf the ball in m/s is:

speed = 80 mph * 0.44704 = 35.76 m/s

Nοw we can calculate the time it takes fοr the ball tο reach the batter:

time = distance/speed

time = 19.66 meters / 35.76 m/s

time = 0.55 secοnds

Therefοre, it takes apprοximately 0.55 secοnds fοr a ball traveling at 80 mph tο reach a batter that is pοsitiοned at the back οf the batter's bοx.

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Coach Jill put 4,000 mL of sports drink in each cooler to stay hydrated.

Coach Jill brought a total of 28,000 milliliters (mL) of sports drink to the soccer game. She divided the sports drink equally among 7 coolers, so she needed to determine how many milliliters each cooler would receive.

Coach Jill brought a total of 28 L = 28,000 mL of sports drink.

She divided this equally among 7 coolers, so each cooler would receive:

28,000 mL / 7 coolers = 4,000 mL/cooler

Therefore, Coach Jill put 4,000 mL of sports drink in each cooler.

This ensured that each cooler received the same amount of sports drink, which was important to keep all the players equally hydrated during the game. By dividing the sports drink equally, Coach Jill was able to efficiently manage the resources and ensure that each player had access to enough fluids during the game.

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The P(2nd non-conforming part is obtained in y tests) is given by (n-x) / n * (1-x/n)^(y-1).

The probability that the second nonconforming part is obtained in y tests is given by the formula P(X = k) = (k-1) choose (r-1) * p^r * (1-p)^(k-r).Solution:Given, n = between 15 and 25x = between 11 and 14y = between 3 and 10To find: The probability that the second nonconforming part is obtained in y testsFormula used:P(X = k) = (k-1) choose (r-1) * p^r * (1-p)^(k-r)Where X represents the number of trials, p represents the probability of success, k represents the number of successful outcomes, and r represents the number of trials.Possible values of x:n - xLet the probability of obtaining a non-conforming part be p, then the probability of obtaining a conforming part would be 1-p.Number of non-conforming parts in n: n-xProbability of selecting the non-conforming part p = x/nProbability of selecting the conforming part 1-p = (n-x)/nP(2nd non-conforming part is obtained in y tests) = P(y-th trial is non-conforming) = P(y-1 conforming trials followed by a non-conforming trial)P(2nd non-conforming part is obtained in y tests) = (n-x) / n * (x/n)^(1-1) * (1-x/n)^(y-1)Therefore, P(2nd non-conforming part is obtained in y tests) = (n-x) / n * (x/n)^(0) * (1-x/n)^(y-1)P(2nd non-conforming part is obtained in y tests) = (n-x) / n * (1) * (1-x/n)^(y-1)Hence, P(2nd non-conforming part is obtained in y tests) is given by (n-x) / n * (1-x/n)^(y-1).

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Answer:

22 sq. in.

Step-by-step explanation:

Believe it or not, the area is still length times width in this problem, you just have to subtract 3 sq in from your final answer becasue of the center gap (3in *1in)

5in * 5in =25 sq in -3 sq in= 22 sq in.

The cost of a new Honda Accord in terms of the number of years t since 2000 can be represented by the function f(t).

The cost of a new Honda Accord in terms of the number of years t since 2000 is represented by the We can use this function to answer the questions given.

a. The cost (in dollars) of a new Accord in 2005 can be represented by f(5), since 2005 is 5 years after 2000.

b. The difference in cost between a new Accord in 2015 and 2010 can be represented by f(15) - f(10), since 2015 is 15 years after 2000 and 2010 is 10 years after 2000.

c. The ratio of the cost of a new Accord in 2015 to the cost of a new Accord in 2010 can be represented by f(15)/f(10).

d. $520 more than the cost of a new Accord in 2018 can be represented by f(18) + $520, since 2018 is 18 years after 2000.

In conclusion, the cost of a new Honda Accord in terms of the number of years t since 2000 can be represented by the function f(t), and we can use this function to answer the given questions.

The cost of a new Accord in 2005 is represented by f(5), the difference in cost between a new Accord in 2015 and 2010 is represented by f(15) - f(10), the ratio of the cost of a new Accord in 2015 to the cost of a new Accord in 2010 is represented by f(15)/f(10), and $520 more than the cost of a new Accord in 2018 is represented by f(18) + $520.

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Answer:  f(g(-1)) = -16

Step-by-step explanation:

First, we need to find g(−1), which means we substitute -1 in place of x in the function g(x):

g(-1) = 3(-1) = -3

Next, we substitute g(-1) into f(x):

f(g(-1)) = f(-3) = 3(-3) - 7 = -16

Therefore, f(g(-1)) = -16.

If the difference in height between the whale and the ship is -1,040, the height of the whale is 2,200 meters.

The difference in height between the whale and the ship is -1,040. If the ship is 3,240 meters tall, we can use this information to determine the height of the whale.

Let h be the height of the whale. We know that the difference in height between the whale and the ship is -1,040, which we can express as:

h - 3,240 = -1,040

To solve for h, we can add 3,240 to both sides of the equation:

h = 3,240 - 1,040

Simplifying the right-hand side of the equation, we get:

h = 2,200

In summary, we can use the given difference in height and the height of the ship to set up an equation that relates the height of the whale to the height of the ship. By solving this equation for the height of the whale, we can determine that the whale is 2,200 meters tall.

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Complete question is:

The difference in height between the whale and the ship is -1,040. If the ship is 3,240 meters tall, what is the height of the whale?

a) We need to find the values of x for which the denominator, cos(x), is equal to zero. b) vertical asymptotes at x = π/2, x = 3π/2, x = -π/2, x = -3π/2, and so on.

The tangent function is periodic, with a period of π radians (or 180 degrees). This means that the tangent function repeats itself every π radians, or every 180 degrees. The tangent function is also an odd function, which means that it is symmetric about the origin.

The graph of the tangent function has a characteristic shape with multiple cycles between consecutive vertical asymptotes. The graph passes through the origin and intersects the x-axis at the vertical asymptotes. The tangent function has a maximum and a minimum value between any two consecutive vertical asymptotes. However, it does not have a maximum or minimum value over its entire domain.

a) To determine the exact location of the asymptotes of the tangent function using the identity tan(x) = sin(x)/cos(x), we need to find the values of x for which the denominator, cos(x), is equal to zero. These values of x correspond to the vertical asymptotes of the tangent function.

Since cos(x) = 0 when x = π/2 + kπ, where k is an integer, the vertical asymptotes of the tangent function occur at these values of x. We can also write this as x = kπ/2, where k is an odd integer.

b) From the graph of the tangent function, we can see that there are vertical asymptotes at x = π/2, x = 3π/2, x = -π/2, x = -3π/2, and so on. These correspond to the values of kπ/2, where k is an odd integer. We can also write the set of vertical asymptotes as:

{x | x = kπ/2, k ∈ Z and k is odd}

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Comparing the two simplified ratios, 4:3 and 10:9, we see that they are not equal, so the ratios 60:45 and 10:9 do not form a proportion.

We must examine whether the cross-products are equal in order to determine whether the ratios of 60:45 and 10:9 constitute a proportion.

60 x 9 = 540 is the cross product of 60 and 9.

45 x 10 = 450 is the cross product of 45 and 10.

The cross-products are not equal, hence the ratios of 60:45 and 10:9 do not constitute a proportion (540 is not equal to 450, for example).

Simplifying two ratios to their simplest form is another technique to determine if they constitute a proportion.

By dividing both components by their greatest common factor, which is 15, the ratio 60:45 can be reduced to 4:3.

The 10:9 ratio has already reached its lowest point.

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The solution to |x| > |x + 2| is x < -2. This can be determined by looking at the two graphs on the grid, y = |x| and y = |x + 2|.

Inequality is the concept of representing a relationship between two values using a mathematical symbol. This can be used to express various forms of comparison such as greater than, less than, and not equal to. Inequality is an important concept for understanding and applying mathematical principles, such as in algebra and calculus.

The graph of y = |x| is a straight line at y = 0, and increases as x moves further away from 0. The graph of y = |x + 2| has a minimum at x = -2, and increases as x moves further away from -2. Therefore, at all locations where x is less than -2, the value of |x| is greater than the value of |x + 2|. These locations are all solutions to the inequality |x| > |x + 2|.

To visualize this solution, we can look at the graph of the two functions and see that the value of |x| is greater than the value of |x + 2| when x is less than -2. This can also be seen by looking at the numerical values of the two functions; for any x less than -2, the absolute value of x will be greater than the absolute value of x + 2.

In conclusion, the solution to the inequality |x| > |x + 2| is x < -2. This can be seen visually on the graph of the two functions, and can also be determined by looking at the numerical values of the two functions.

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A) Determine the probability that a disk lasts at least 500 hours.= 0.275

B) Probability that a disk fails before 400 hours=0.685

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

Remind the formula for CDF of Weibull random variable X

[tex]F(x)=1-e^{-(x/\delta)^{\beta}[/tex]

Now apply this formula for the Weibull variable X with the parameters β=0.5 and δ to be deduced from the mean of 600. The formula for the mean is:

[tex]600=\delta\Gamma(1+2)=\delta*2!\\\\\delta=300\\Finally\\\\P(x > 500)=1-F(500)=e^({-5/3})^{0.3}=0.275\\\\p(x < 400)=f(400)=0.685[/tex]

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Step-by-step explanation:

Area of a rhombus = ab/2 where a is 12cm and b is 10cm (diagonals)

Area = 12 x 10 /2 =120/2

Area = 60cm

Answer:

Step-by-step explanation:

In this problem, we have to use the formula in finding the volume of a cylinder

[tex]V=\pi r^{2} h[/tex]

r is half of diameter
r= 16ft / 2 = 8ft

The height of the cylinder is 4ft. We have to know the height of the water to know the volume of the water.

h (water) = 4ft - 1/2ft  = 3.5ft

[tex]V=\pi (8)^{2} (3.5)[/tex]

[tex]V = 703.72 ft^{3}[/tex]

[tex]V = 703.72 ft^{3} * \frac{7.48 gallons}{1ft^{3} }[/tex]

[tex]V = 5263.8 gallons[/tex]

[tex]V = 5264 gallons[/tex]

The pool is filled with 5264 gallons of water.

Answer:

Scale factor is 1/2

Step-by-step explanation:

2.4 x 2 = 4.8

4.8/2 = 2.4

same here

2.1 x 2 = 4.2

4.2/2 = 2.4

3.8/2 =1.9

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The resultant of the expression (((-3/5)+(5/3))-(2-4/3)) will be 2/5.

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations that can be evaluated to produce a value. Expressions can be as simple as a single number or variable, or they can be more complex, involving multiple numbers, variables, and operations.

For example, 3 + 5 is an expression that represents the sum of two numbers, which evaluates to 8. Another example is 2x - 5, which involves a variable (x) and two operations (multiplication and subtraction).

Now,

Let's start by simplifying (-3/5 + 5/3):

First, we need to find a common denominator between 5 and 3, which is 15

then,

-3/5 + 5/3 = -9/15 + 25/15

Next, we can add the two fractions:

-9/15 + 25/15 = 16/15

So, (-3/5 + 5/3) simplifies to 16/15.

Now, let's simplify (2 - 4/3):

We can rewrite 2 as 6/3, then subtract 4/3:

6/3 - 4/3 = 2/3

So, (2 - 4/3) simplifies to 2/3.

Finally, we can subtract 2/3 from 16/15:

16/15 - 2/3

To subtract fractions, we need a common denominator between 15 and 3, which is 15. then

16/15 - 10/15 = 6/15

So, the resulting constant is 6/15, which can be simplified by dividing both the numerator and denominator by their greatest common factor (which is 3):

6/15 = 2/5

Therefore,

                the resulting constant is 2/5.

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If a scooter was brought in April 2005 for rs. 42000 if it's value fall by 10% every year, the value of the scooter in April 2007 would be Rs. 34020.

If the value of the scooter falls by 10% every year, then its value after the first year will be 90% of its original value. Similarly, the value after the second year will be 90% of the value after the first year, or 0.9 * 0.9 = 0.81 times the original value.

To find the value of the scooter in April 2007, we need to apply this formula twice, since there are two years between April 2005 and April 2007.

Starting with the original value of the scooter, we can calculate its value after one year:

Value after 1 year = 0.9 * Rs. 42000 = Rs. 37800

Then, we can use this value to calculate the value of the scooter after two years:

Value after 2 years = 0.9 * Rs. 37800 = Rs. 34020

In this case, the value of the scooter decreases by 10% each year, so its value after two years is 0.9 times its value after one year, which is 0.9 times its original value.

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Neither X nor Y can be well-approximated by a normal random variable, the proportion of exams with passing scores is .7734, the exam score for an exam whose z-score is 1.25 is 85 and if the top 4% of the exams will be given an A+, in order to be given an A+, an exam must earn at least 89 score.

Question 1: Neither X nor Y can be well-approximated by a normal random variable. This is because both X and Y are discrete random variables, meaning they can only take on integer values. Normal random variables, on the other hand, are continuous and can take on any value within a certain range.

Therefore, neither X nor Y can be well-approximated by a normal random variable.

Question 2: The proportion of exams with passing scores is .7734. This can be found by calculating the z-score for a score of 69 and using a z-table to find the corresponding proportion. The z-score is (69-75)/8 = -0.75. Using a z-table, we find that the proportion of exams with scores less than 69 is .2266.

Therefore, the proportion of exams with passing scores is 1-.2266 = .7734.

Question 3: The exam score for an exam whose z-score is 1.25 is 85. This can be found by using the formula for z-scores: z = (x-µ)/σ. Plugging in the values for z, µ, and σ, we get 1.25 = (x-75)/8.

Solving for x, we get x = 85.

Question 4: In order to be given an A+, an exam must earn at least a score of 89. This can be found by using the formula for z-scores and a z-table. We know that the top 4% of exams will be given an A+, so we need to find the z-score that corresponds to the top 4%. Using a z-table, we find that this z-score is 1.75.

Plugging this into the formula for z-scores, we get 1.75 = (x-75)/8. Solving for x, we get x = 89.

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The total duration of the puberty process can be different for each girl who is about to enter it, as the length of time for the different stages of puberty can vary from person to person.  Hence, if a girl is about to enter puberty, the total process will take a variable length of time for different girls.

The total process of puberty for a girl can take a variable length of time, but typically it takes around 2 to 5 years to complete. The onset of puberty usually occurs between the ages of 8 and 13, with most girls starting around age 11.

The process of puberty includes physical changes such as breast development, the growth of pubic and underarm hair, and the onset of menstruation.

The duration of puberty can also depend on factors such as genetics, nutrition, and overall health. Some girls may experience a shorter or longer duration of puberty than others. However, in general, the process of puberty for a girl usually takes around 2 to 5 years to complete.

Therefore, the correct answer is "a variable length of time for different girls", but typically takes around 2 to 5 years to complete.

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Answer:

f(4)=14

Step-by-step explanation:

The lower confidence level (LCL) and upper confidence level (UCL) are

a. X-Bar = 47; n = 73; 0 = 31; a = 0.05
LCL = 44.35
UCL = 49.65

b. X-Bar = 83; n = 221; 0 = 400; a = 0.01
LCL = 79.91
UCL = 86.09

c. X-Bar = 513; n = 425; 0 = 43; a = 0.10
LCL =  509.27
UCL = 516.73

a. X-Bar = 47, n = 73, σ² = 31, α = 0.05

Using the formula for a confidence interval for the mean of a normal distribution with known variance, we get:

LCL = X-Bar - z(α/2) * √(σ²/n)

= 47 - 1.96 * √(31/73)

= 44.35

UCL = X-Bar + z(α/2) * √(σ²/n)

= 47 + 1.96 * √(31/73)

= 49.65

So, the 95% confidence interval for the population mean is (44.35, 49.65).

b. X-Bar = 83, n = 221, σ^2 = 400, α = 0.01

Using the same formula, we get:

LCL = X-Bar - z(α/2) * √(σ²/n)

= 83 - 2.58 * √(400/221)

= 79.91

UCL = X-Bar + z(α/2) *√(σ²/n)

= 83 + 2.58 * √(400/221)

= 86.09

So, the 99% confidence interval for the population mean is (79.91, 86.09).

c. X-Bar = 513, n = 425, σ² = 43, α = 0.10

Again, using the same formula, we get:

LCL = X-Bar - z(α/2) * √(σ²/n)

= 513 - 1.645 * √(43/425)

= 509.27

UCL = X-Bar + z(α/2) * √(σ²/n)

= 513 + 1.645 * √(43/425)

= 516.73

So, the 90% confidence interval for the population mean is (509.27, 516.73).

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In the following question, among the conditions given, This triangle must be a non-Euclidean triangle, which is not possible to draw on a flat plane without distorting its shape. Therefore, there are no valid angles for this triangle.

To find the angles of a triangle when given the lengths of its sides, we can use the Law of Cosines, which states that:

c^2 = a^2 + b^2 - 2ab*cos(C)

where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

Using this formula, we can find the cosine of each angle and then use the inverse cosine function (cos^-1) to find the measure of each angle.

Let's use this formula to find the angles of the triangle with sides of 11, 10, and 17:

c^2 = a^2 + b^2 - 2ab*cos(C)

For the side opposite angle C = 17:

17^2 = 10^2 + 11^2 - 2(10)(11)cos(C)

289 = 121 + 100 - 220cos(C)

cos(C) = (121 + 100 - 289)/(21011)

cos(C) = -0.4

We get a negative value for the cosine of angle C. This means that the triangle cannot be a standard triangle in the Euclidean plane, as the Law of Cosines requires that the cosine of an angle be between -1 and 1. This triangle must be a non-Euclidean triangle, which is not possible to draw on a flat plane without distorting its shape.

Therefore, there are no valid angles for this triangle.

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Answer:

This is the answer!!!

31

Using trigonometric functions, we can find the area of the triangle to be: 19.68unit². Bob used the wrong dimension in the area of the triangle formula.

There are six basic trigonometric operations in trigonometry. These techniques can be described using trigonometric ratios. The six basic trigonometric functions are the sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function.

Trigonometric identities and functions are based on the ratio of the sides of a right-angled triangle.

The sine, cosine, tangent, secant, and cotangent values for the perpendicular side, hypotenuse, and base of a right triangle are computed using trigonometric formulas.

Here in the question,

Area of the triangle = 1/2 absinc

= 1/2 × 12 × 16.4 × Sin30°

= 1/2 × 196.8 × 0.2

= 19.68unit².

Bob used the wrong dimension of the triangle. Instead of using the adjacent side of the angle, Bob used the opposite side of the angle.

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