Answer: E
Step-by-step explanation: The line going up has a slope of one and the y intercept is 2. The first equation should be y=x+2. The next one has a downwards slope with a y intercept of -4. y=-x-4. Ths means it would be E
ssume that the failure strength of a beam can be represented by a normal distribution where the population standard deviation is 4 psi. if you need the width of the 95% confidence interval to be 3 psi, how large of a sample do you need?
The failure strength of a beam can be represented by a normal distribution where the population standard deviation is 4 psi, we get a test measure of 7. Subsequently, we would require a test of at slightest 7 pillars to attain a 95% certainty interim with a width of 3 psi...
To discover the test measure required to realize a 95% certainty interim with a width of 3 psi, we ought to utilize the equation:
n = [ (z*σ) / E ][tex]^{2}[/tex]
where:
n is the test measure
z is the z-score related to the specified level of certainty (in this case, 95% compares to a z-score of 1.96)
σ is the populace standard deviation
E is the specified edge of blunder (in this case, 3 psi)
n = [ (1.96 * 4) / 3 ][tex]^{2}[/tex]
n = [ 2.61 ][tex]^{2}[/tex]
n = 6.82
we get a test measure of 7. Subsequently, we would require a test of at slightest 7 pillars to attain a 95% certainty interim with a width of 3 psi.
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Ms. Sanhez works as a salesperson in a computer store. She earns $72 per
week plus $15 for every computer she sells. Next week, she would like to earn at least $120. Write an inequality using “c” for the number of computers Ms. Sanchez must sell.
Since 132 is greater than or equal to 120, the inequality is satisfied.
Let's start by defining some variables:
Let "c" be the number of computers that Ms. Sanchez sells next week.
Let "E" be her total earnings for the week.
We know that she earns $72 per week plus $15 for every computer she sells, so we can write the expression for her total earnings as:
[tex]E = 72 + 15c[/tex]
Now we need to write an inequality using "c" for the number of computers she needs to sell in order to earn at least $120 next week. That is, we want to find the value of "c" that makes her earnings at least $120:
E ≥ 120
Substituting the expression for E, we get:
[tex]72 + 15c \geq 120[/tex]
Simplifying this inequality, we can start by subtracting 72 from both sides:
[tex]15c \geq 48[/tex]
Then, we can divide both sides by 15 (keeping in mind that we need to reverse the inequality direction when dividing by a negative number):
[tex]c \geq 3.2[/tex]
Therefore, Ms. Sanchez needs to sell at least 4 computers next week (since she can't sell a fraction of a computer). We can check this by plugging in c = 4 into the expression for E:
[tex]E = 72 + 15(4) = 132[/tex]
Since 132 is greater than or equal to 120, the inequality is satisfied.
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I need help with this math, I forgot how to do it over spring break and we're virtual this week im sobbing
Answer:
if they are similiar then a is 4.9
b is 2.8 and c is 4.1
Step-by-step explanation:
if the the shapes are similiar then match up then sides of the shape and they should have equal lengths.
hope this helps :)
A science class is doing an experiment with a model rocket. The rocket shoots straight up in the air, and the students record the time it takes for the rocket to hit the ground. The height of the rocket at time t, in seconds, is given by the equation y = -2(t – 2)2 + 12, where y is in meters.
If the initial height of the rocket is the height of the rocket at time t = 0, what is the initial height of the rocket?
Answer:
To find the initial height of the rocket, we need to determine the height of the rocket when t = 0, since that is the initial time.
Substituting t = 0 into the given equation, we get:
y = -2(0 – 2)2 + 12
y = -2(-2)2 + 12
y = -2(4) + 12
y = 8
Therefore, the initial height of the rocket is 8 meters.
Step-by-step explanation:
A school has members of 6000 out of which 1200 are girls find the probability of people who are boys
Answer: 80% are boys and 20% are girls
Step-by-step explanation: Take 1200 ÷ 6000 = 0.2 , to find the percentage multipy 0.2 x 100 = 20%, then subtract 20% from 100 giving you 80%. This means 80% of the members are boys.
Alex has a bag of stuffed animals containing nine bears, six lions, and three monkeys. The probability that Alex will randomly pull out a bear and then a lion is .
Using this probability, determine if the event of pulling out a bear and the event of pulling out a lion was independent, dependent, both, or neither.
A.
both independent and dependent
B.
neither independent nor dependent
C.
dependent
D.
independent
The chances of bringing out a lion and a bear are dependent on one another since the actual likelihood (3/17) is not equal to the sum of the individual probabilities (1/6). As a result, the response depends on C.
what is probability ?The potential that an incident will happen is gauged by probability. The most common way to express it is as a value between zero and 1, where 0 denotes an impossibility and 1 denotes a certainty. The number of favourable outcomes is divided by the entire assortment of potential outcomes to get the likelihood of a particular occurrence. To create predictions and choices based on uncertain events, probability is widely utilised in disciplines including statistics, mathematics, physics, and engineering.
given
The likelihood of removing a bear first, followed by a lion, is given by the formula: P(bear and lion) = P(bear) * P(lion|bear not replaced) = (9/18) * 6/17)
= 3/17
The likelihood of both occurrences happening would be the sum of their individual probabilities if the events of taking out a bear and a lion were independent:
P(lion and bear) = P(lion) * P(bear) = 9/18 * 6/18 = 1/6
The chances of bringing out a lion and a bear are dependent on one another since the actual likelihood (3/17) is not equal to the sum of the individual probabilities (1/6). As a result, the response depends on C.
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help! i need help on this :(
Answer: 10 miles
Step-by-step explanation:
a = (P - 2b) / 2
a = (42 - 22) / 2
a = 20/2
a = 10
Answer:
i think its 10
Step-by-step explanation:
in a parallellogram opposite sides are equal so if the top is 11 then the bottom must be 11. 11 plus 11 is 22. 42 - 22 equals to 20. since opposite sides are the same you can divide 20 by 2 which equals to 10.
hope this helps :)
A deli wraps its cylindrical containers of hot food items with plastic wrap. The containers have a diameter of 5.5 inches and a height of 3 inches. What is the minimum amount of plastic wrap needed to completely wrap 8 containers? Round your answer to the nearest tenth and approximate using π = 3.14.
If a deli wraps its cylindrical containers of hot food items with plastic wrap. the minimum amount of plastic wrap needed to completely wrap 8 containers is: 785.4 square inches.
What is the minimum amount of plastic wrap needed?The area of each circular end is:
A = πr^2
where r is the radius of the end. The diameter of each container is given as 5.5 inches, so the radius is half of that, or 2.75 inches. Using π = 3.14, we get:
A = 3.14 * (2.75in)^2
A = 23.68in^2 (rounded to two decimal places)
The area of the rectangular side is:
A = h * circumference
where h is the height of the container and circumference is the distance around the circular end. The circumference is equal to the diameter times π, so we have:
circumference = 5.5in * π
circumference = 17.27in (rounded to two decimal places)
Using the given height of 3 inches, we get:
A = 3in * 17.27in
A = 51.81in^2 (rounded to two decimal places)
Therefore, the total surface area of each container is:
A = 2 * 23.68in^2 + 51.81in^2
A = 98.17in^2 (rounded to two decimal places)
To wrap 8 containers, we need to multiply the surface area of each container by 8:
total surface area = 8 * 98.17in^2
total surface area = 785.36in^2 (rounded to two decimal places)
Therefore, we need a minimum of 785.36 square inches of plastic wrap to completely wrap 8 cylindrical containers of hot food items. Rounding to the nearest tenth, the answer is 785.4 square inches.
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If a deli wraps its cylindrical containers of hot food items with plastic wrap. the minimum amount of plastic wrap needed to completely wrap 8 containers is: 785.4 square inches.
The measure of an angle is 12º. What is the measure of its complementary angle?
If 2 angles are complementary, then they add up to 90 degrees. Therefore, you can find the measure of the complementary angle by subtracting 12 from 90, which is 78 degrees.
You are conducting a study to see if the accuracy rate for fingerprint identification is significantly less than 0. 16.
With H1 : p < 0. 16 you obtain a test statistic of z=−2. 683.
Use a normal distribution calculator and the tet statistic to find the P-value accurate to 4 decimal places. It may be left-tailed, right-tailed, or 2-tailed.
P-value =
The p-value for the given hypothesis test is 0.0037 (accurate to 4 decimal places)
To find the p-value, we need to use the standard normal distribution table or a calculator. Since the alternative hypothesis is left-tailed, we are interested in finding the area under the curve to the left of the observed test statistic z.
Using a standard normal distribution calculator, we find that the area to the left of z = -2.683 is 0.0037 (rounded to 4 decimal places). This represents the p-value for the hypothesis test.
Therefore, we can conclude that there is strong evidence to reject the null hypothesis at a significance level of 0.05, since the p-value of 0.0037 is less than the chosen significance level. The evidence suggests that the accuracy rate for fingerprint identification is significantly less than 0.16.
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Using trig to find angles.
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
x ≈ 39.5°
Step-by-step explanation:
using the cosine ratio in the right triangle
cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{OP}{NP}[/tex] = [tex]\frac{64}{83}[/tex] , then
x = [tex]cos^{-1}[/tex] ( [tex]\frac{64}{83}[/tex] ) ≈ 39.5° ( to the nearest tenth )
pyriamid a square base that measures 140 m on each side. the height is 91 m. what is the volume of the pyramid?
The volume of the pyramid is approximately 574,533.33 cubic meters.
To find the volume of a pyramid, you use the formula: V = (1/3) × base area × height, where B is the area of the base and h is the height of the pyramid.
Given that the side length of the square base is 140 m and the height is 91 m.
Since the base of the pyramid is a square with a side length of 140 m, we can find its area by multiplying the side lengths: B = 140m x 140m = 19,600 square meters.
By calculating this expression, you'll find the volume of the pyramid.
Now we can plug in the values for B and h into the formula: V = (1/3)(19,600 square meters)(91 meters) = 574,533.33 cubic meters.
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Please help! Will give Brainliest!
The perimeter of figure ABCD is determined as 55.2 units.
What are congruent triangles?
Congruent triangles are two triangles that have the same shape and size. In other words, they are identical in shape and size, and all their corresponding angles and sides are equal.
When two triangles are congruent, they can be superimposed on each other such that all their corresponding parts coincide.
We will use the principle of congruent triangles to find the length of the smaller triangle.
base length of the smaller triangle = 13/2 = 6.5
let the height of the smaller triangle = h
h/6.5 = (h + 8)/13
13h = 6.5(h + 8)
13h = 6.5h + 52
6.5h = 52
h = 52/6.5
h = 8
The hypothenuse side of the smaller triangle is calculated as follows;
y = √(8² + 6.5²)
y = 10.3
The hypothenuse side of the bigger triangle is calculated as follows;
Y = √((8+8)² + 6.5²)
Y = 17.3
The perimeter of ABCD is calculated as follows;
P = (17.3 x 2) + (10.3 x 2)
P = 55.2
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Find the circumference of each circle with a radius of 5.4 mi . Use 3.14 for the value of Pi. Round your answer to the nearest tenth. IM IN 7TH
The circumference of the circle with a radius of 5.4 miles is approximately 34.0 miles.
Describe Radius?In geometry, a radius is a straight line segment that connects the center of a circle or sphere to any point on its circumference. It is the distance from the center of the circle to any point on the circle.
The term "radius" can also be used in other contexts, such as in the context of cylinders and cones. In these cases, the radius refers to the distance from the center of the circular base to any point on the circumference of the base.
The radius of a circle is an important measurement because it determines the size of the circle. It is also used in various geometric formulas to calculate the area, circumference, and other properties of a circle or sphere. For example, the formula for the circumference of a circle is C = 2πr, where r is the radius, and π (pi) is a mathematical constant that is approximately equal to 3.14159.
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, π is the mathematical constant π (approximated as 3.14), and r is the radius of the circle.
Substituting the given value of radius, we get:
C = 2 × 3.14 × 5.4
C ≈ 33.98
Rounding to the nearest tenth, we get:
C ≈ 34.0
Therefore, the circumference of the circle with a radius of 5.4 miles is approximately 34.0 miles.
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6 Explain A video game company will make
a new game. The manager must choose between a role-
playing game and an action game. He asks his sales staff
which of the last 10 released games sold the most copies.
Explain why this is a statistical question.
The question is statistical because it requires data analysis, statistical methods, and interpretation of results to make a decision.
What is a Statistical question:A statistical question is a question that can be answered by collecting and analyzing data. It is a question that involves variability, uncertainty, or randomness and cannot be answered with a single definitive answer.
Instead, it requires the use of statistical methods to analyze and summarize data to make informed decisions.
Here we have
A video game company will make a new game. The manager must choose between role-playing the game and an action game. He asks his sales staff which of the last 10 released games sold the most copies.
This is a statistical question because it involves collecting and analyzing data to make an informed decision.
The manager is seeking information from the sales staff about the last 10 released games to determine which type of game - role-playing or action - is more likely to sell well.
By analyzing the sales data, the manager can make a data-driven decision about which game to develop, rather than relying solely on intuition or personal preferences.
To answer the question, the sales staff would need to collect data on the sales figures of each of the last 10 released games, which involves using statistical methods to analyze and summarize data.v
Therefore,
The question is statistical because it requires data analysis, statistical methods, and interpretation of results to make a decision.
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what is the degree and leading coefficient
Answer: The degree of the polynomial is the highest power of the variable that occurs in the polynomial.
Step-by-step explanation:
The hour marks on a clock face are 30° apart. What is the angle a line from the four o'clock mark to the twelve o'clock mark makes with a horizontal line?
Answer:
The hour marks on a clock face are evenly spaced, 30° apart. To find the angle a line from the four o'clock mark to the twelve o'clock mark makes with a horizontal line, we need to count the number of hour marks between the two positions and multiply by 30°.
Starting from the four o'clock mark and moving clockwise to the twelve o'clock mark, we count 8 hour marks, including the one at the twelve o'clock mark. Multiplying 8 by 30°, we get:
8 x 30° = 240°
Therefore, the angle between the line from the four o'clock mark to the twelve o'clock mark and a horizontal line is 240°.
Find the 6th term of geometric sequenceB whose ratio is 2/3 and whose first term is 2
As a result, the geometric sequence's sixth term, which has a ratio of 2/3 and a first term of 2, is 32/243.
What is geometric succession?A mathematical series known as a geometric sequence is one in which each term following the first is obtained by multiplying the previous term by a constant, non-zero quantity known as the common ratio2. To put it another way, it is a sequence in which each term (aside from the initial term) is multiplied by a fixed amount to obtain the subsequent term1.
For instance, the geometric sequence 1, 2, 4, 8, 16,... has a common ratio of 2, since each item after the first is derived by multiplying the previous term by 2.
Aₙ = a₁× r(n-1) is the formula for the nth term of a geometric series, where a1 is the first term and r is the common ratio.
The common ratio in this instance is 2/3, and the first term is 2.
As a result, the sequence's nth term is represented by the formula
a = 2 × (2/3)(n-1).
We change n = 6 in the formula to get the sixth term in the sequence.
A₆ = 2× (2/3)⁵
= 2 × (2/3)⁵ = 32/243 as a result.
As a result, the geometric sequence's sixth term, which has a ratio of 2/3 and a first term of 2, is 32/243.
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patricia hill collins's concept of a matrix of domination is best described as
Patricia Hill Collins' concept of a Matrix of domination is a theoretical framework.
The matrix of domination is based on the idea that society is characterized by multiple, intersecting systems of power and oppression, including those based on race, gender, class, sexuality, and other social categories.
These systems of power and oppression are interconnected and mutually reinforcing, creating a complex web of domination that shapes social life.
According to Collins, the matrix of domination is a useful tool for understanding how power operates in society and how different groups experience and resist oppression.
It allows us to see how different forms of inequality intersect and interact, producing unique experiences of oppression and privilege for individuals who occupy different social positions.
The matrix of domination is not a simple hierarchy of oppression, where one form of oppression is more important than others.
Rather, it is a complex, intersecting system that creates unique experiences of power and oppression for individuals and groups based on their social identities and positions in society.
Overall, the concept of a matrix of domination highlights the complexity of social inequality and the importance of intersectionality in understanding how power operates in society.
It helps us to see how different forms of oppression are interconnected and reinforces each other and underscores the need for holistic and intersectional approaches to social justice and liberation.
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PLEASE HELP
If triangle PQR is has a right angle at Q and m<R is 45°, what is the length of PR is PQ is 3?
1. 3
2. 2
3. 2√3
4. 3√2
The value of the side length PR using Trigonometric ratio is: PR = 3/√2
How to use trigonometric ratios?The primary trigonometric ratios are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
Thus:
We are given that:
∠Q = 90°
∠R = 45°
PQ = 3
Thus:
PR is calculated as:
3/PR = sin 45
PR = 3 * sin 45
PR = 3 * 1/√2
PR = 3/√2
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the mean daily production of a herd of cows is assumed to be normally distributed with a mean of 30 liters, and standard deviation of 8.2 liters. a) what is the probability that daily production is between 32.3 and 36.9 liters? do not round until you get your your final answer.
There is a 21.19% chance that the daily production falls within 32.3 and 36.9 liters.
To find the probability that the daily production of a herd of cows is between 32.3 and 36.9 liters, we need to use the normal distribution properties.
Given that the mean daily production of the herd of cows is 30 liters and the standard deviation is 8.2 liters, we can standardize the distribution and use the standard normal distribution table or calculator. We calculate the z-scores for the values 32.3 and 36.9, which tells us how many standard deviations away from the mean each value is.
Using a standard normal cumulative distribution function, we can find that the probability of the daily production falling between 32.3 and 36.9 liters is approximately 0.2119. This means that there is a 21.19% chance that the daily production falls within this range.
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The probability that daily production is between 32.3 and 36.9 liters is 0.18949 or 18.9%.
To determine the probability that the herd's daily production will be between 32.3 and 36.9 liters, we must compute the z-scores for each number and use a standard normal distribution table to calculate the area under the curve between those z-scores.
To find out the z - scores we need use z-score formula:
Z = X−μ / σ
where μ is the mean, σ is the standard deviation and X is the observed value. In the problem μ is 30 liters, X₁ = 32.3 liters & X₂ = 36.9 liters and σ = 8.2 liters.
Substituting the values in the equation to find the z-score for 32.3 liters is:
z₁ = (32.3 - 30) / 8.2 = 0.2804
z₁ = 0.28049
Substituting the values in the equation to find the z-score for 36.9 liters is:
z₂ =( 36.9 - 30) / 8.2 = 0.8414
z₂ = 0.8414
We can determine the area under the curve between these two z-scores using a conventional normal distribution table. The area between z = 0.28049 and z = 0.8414 and the probability is approximately 0.1894.
As a result, the probability that the herd's daily output is between 32.3 and 36.9 liters is about 0.1894.
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If y=3, then -3+y2 =
Answer:
The answer is 6
Step-by-step explanation:
y=3
-3+y²
-3+(3)²
-3+6=6
Two friends, Julieta and Camila, had just bought their first cars. The equation
y = 38.8x represents the number of
miles, y, that Camila can drive her car for every a gallons of gas. Julieta uses 10 gallons of gas to drive 333 miles in her
car.
Julieta can travel 5.5 miles than Camila on one gallon of gas.
How to find how many miles more Julieta can travel than Camila on one gallon of gas?To find out how many miles more Julieta can travel than Camila on one gallon of gas, we need to compare their respective rates of miles per gallon.
According to the equation y = 38.8x, Camila can drive y miles for every x gallons of gas. Therefore, her rate of miles per gallon is:
y/x = 38.8
On the other hand, Julieta can drive 333 miles on 10 gallons of gas, so her rate of miles per gallon is:
333/10 = 33.3
To find out how many more miles per gallon Julieta can drive than Camila, we can subtract Camila's rate from Julieta's rate:
33.3 - 38.8 = -5.5
This means that Camila can drive 5.5 more miles per gallon than Julieta.
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Complete Question
Two friends, Julieta and Camila, had just bought their first cars. The equation
y = 38.8x represents the number of
miles, y, that Camila can drive her car for every a gallons of gas. Julieta uses 10 gallons of gas to drive 333 miles in her car.
Julieta can travel ____ miles than Camila on one gallon of gas
PLS HELP DUE TODAY LOOK AT SS
Answer:
y = -4.3x + 23.8
Step-by-step explanation:
To find the equation for g(x), we need to first understand what it means for g(x) to be parallel to f(x). Two lines are parallel if they have the same slope, but different y-intercepts. The slope of f(x) is -4 3/10, which can be written as -43/10 in fraction form and -4.3 in decimal form. Therefore, the slope of g(x) is also -4.3.
Now we need to use the fact that g(x) passes through the point (6, -2) to find its y-intercept. We can use the point-slope form of a linear equation to do this: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Plugging in our values, we get:
y - (-2) = (-4.3)(x - 6)
Simplify the left side
y + 2 = (-4.3)(x - 6)
Next, simplify the right side
y + 2 = -4.3x + 25.8
Subtracting 2 from both sides, we get:
y = -4.3x + 23.8
Therefore, the equation for g(x) is y = -4.3x + 23.8 in simplified slope-intercept form.
Pollyomial Roller coaster project! HELP PLEASE
please show all work, below is an example, rubric, and what's needed in this graph.
please show the graph and Factored form
Thank you
The description of the polyomial roller coaster project is shown below
Solving the polyomial roller coaster projectProposal for the "Imaginary Rush" Roller Coaster:
Coaster name: Imaginary RushFactored form of polynomial: 1/10(x + 1)(x - 2)(x - 4)(x + 5i)(x - 5i)Standard form of the polynomial: f(x) = 1/10[x⁵ - 5x⁴ + 27x³ - 117x² + 50x + 200]The polynomial's graph is attached
Description of how client specifications are met:
The coaster starts on ground level, as the graph of the polynomial crosses the x-axis at x = -1.The coaster goes underground, as the graph dips below the x-axis at x = 4.The coaster includes the imaginary root, as the polynomial has two complex roots at x = 5i and x = -5i.The coaster "grazes" the ground, as the graph of the polynomial touches the x-axis at x = 2.Interpretation of the practicality of the design:
The design of Imaginary Rush is both exciting and practical. The coaster meets all the client's specifications while also providing a thrilling ride for coaster enthusiasts.
The dips and peaks of the coaster follow the behavior of the polynomial, providing a unique experience for riders.
The use of the imaginary root adds an additional level of excitement to the ride, making it stand out from other roller coasters.
Overall, the design of Imaginary Rush is both fun and practical, making it an excellent addition to any theme park.
Discussion of the polynomial's behaviors:
Tail Behavior: As x approaches negative infinity, the value of the function approaches negative infinity. As x approaches positive infinity, the value of the function approaches positive infinity.Relative Maxima/Minima: The polynomial has a relative maximum at x = 2 and a relative minimum at x = 4.Intervals of increasing/decreasing behavior: [tex]\mathrm{as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:-\infty \:[/tex], [tex]\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:-\infty \:[/tex]Read more about polynomial at
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Find the inverses of the functions and confirm using compositions.
1. The inverse of the function f(x) is ±√((x + 10)/2). 2. The inverse of the function f(x) is y = (x - 5)² + 3.
1. The inverse of the function f(x) is ±√((x + 10)/2). 2. The inverse of the function f(x) is y = (x - 5)² + 3.
What is one on one function?A one-to-one function is one in which every input (x-value) and every output (y-value) have an exact corresponding relationship. Therefore, there aren't any outputs that are repeated. A one-to-one function geometrically passes the horizontal line test if no horizontal line crosses the function graph more than once.
Contrarily, a many-to-one function is one in which different inputs (x-values) result in the same output (y-value). A many-to-one function geometrically fails the horizontal line test if there is a horizontal line that crosses the function's graph more than once.
1. Replace f(x) with y in the given function:
y = 2x² - 10
Now, swap the values of x and y and isolate the value of y:
x = 2y² - 10
x + 10 = 2y²
(x + 10)/2 = y²
y = ±√((x + 10)/2)
The inverse of the function f(x) is ±√((x + 10)/2).
2. Replace f(x) with y in the given function:
y = √(x - 3) + 5
Swap the values of x and y and isolate y:
x = √(y - 3) + 5
x - 5 = √(y - 3)
(x - 5)² = y - 3
y = (x - 5)² + 3
The inverse of the function f(x) is y = (x - 5)² + 3.
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what is the term of loan where birr 600 was borrowed at simple interest of 8% and the interest paid on the loan was birr 156?
The term of the loan is 32.5 years
How to determine the term of the loan?
To determine the term of the loan, we need to use the formula:
[tex]Simple \: Interest = \frac{ (Principal \times Rate \times Time)}{ 100}[/tex]
where Principal is the amount borrowed
Rate is the interest rate per year
Time is the length of the loan in years
In this case, we know that:
Principal = Birr 600
Rate = 8%
Simple Interest = Birr 156
Substituting these values into the formula,
[tex]156 = \frac{ (600 \times 8 \times Time)} { 100}[/tex]
Simplifying the equation,
[tex]15600 = 480 \times Time[/tex]
Dividing both sides by 480,
[tex]Time = \frac{15600 }{ 480}[/tex]
Time = 32.5
Therefore, the term of the loan is 32.5 years.
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Kiran swims z laps in the pool. Clare swims 18 laps, which is 95
times as many laps as Kiran. How many laps did Kiran swim?
Answer:
Therefore, Kiran swam approximately 0.189z laps in the pool.
Step-by-step explanation:
Let's assume the number of laps Kiran swims to be "x".
From the given information, we know that Clare swims 95 times as many laps as Kiran. Therefore, we can write an equation:
18 = 95x
To solve for x, we can isolate it by dividing both sides of the equation by 95:
x = 18/95
x = 0.189
Find the surface area and volume of a prism with height 15ft whose base is a rhombus with sides of length 20ft and one diagonal of 24ft
Answer:
3600
Step-by-step explanation:
So you find the area of a rhombic prism by multiplying the sides together and dividing by 2, so 15*20*24 would be 7200, and that divided by 2 is equivalent to the final answer, which is 3600.
Compare the function f(x)=-x^2+2x+5 to f(x)=-2x^2-8x-11 which of the following are true?
The correct statements are c and d i.e. the vertex of f(x) = -x² + 2x + 5 is a maximum, while the vertex of f(x) = -2x² - 8x - 11 is a minimum & the graph of f(x) = -x² + 2x + 5 has a higher y-intercept than the graph of f(x) = -2x² - 8x - 11.
What is a function?
A function is a mathematical rule that distributes a unique output value to each input value. It describes the relationship between the input (also called the independent variable) and the output (also called the dependent variable).
To compare the two functions, let's first find their vertices:
The vertex of f(x) = -x² + 2x + 5 can be found by completing the square:
f(x) = -(x - 1)² + 6, so the vertex is (1, 6).
The vertex of f(x) = -2x² - 8x - 11 can be found by using the formula x = -b/2a (where a is the coefficient of x² and b is the coefficient of x) for the axis of symmetry: x = -(-8)/(2*(-2)) = 2. Then, plugging in x = 2, we get f(2) = -23, so the vertex is (2, -23).
a. The absolute value of the leading coefficient of f(x) = -2x² - 8x - 11 is greater than the absolute value of the leading coefficient of f(x) = -x² + 2x + 5. This means that the graph of f(x) = -2x^2 - 8x - 11 is narrower than the graph of f(x) = -x² + 2x + 5. So, this statement is false.
b. The maximum value of f(x) = -x² + 2x + 5 occurs at the vertex, which is (1, 6). The maximum value of f(x) = -2x² - 8x - 11 also occurs at its vertex, which is (2, -23). These vertices have different y-coordinates, so the two functions do not have the same maximum value. So, this statement is false.
c. Both functions share the same x-coordinate for their vertices, which is x = 1. However, their y-coordinates are different: f(1) = 6 for f(x) = -x² + 2x + 5, and f(2) = -23 for f(x) = -2x² - 8x - 11. Since the leading coefficient of the quadratic term is negative for both functions, the vertex of f(x) = -x² + 2x + 5 is a maximum, while the vertex of f(x) = -2x² - 8x - 11 is a minimum. So, this statement is true.
d. To find the y-intercept of f(x) = -x² + 2x + 5, we can plug in x = 0: f(0) = 5. So, the y-intercept is (0, 5). To find the y-intercept of f(x) = -2x² - 8x - 11, we can set x = 0: f(0) = -11. So, the y-intercept is (0, -11). Since 5 > -11, the graph of f(x) = -x² + 2x + 5 has a higher y-intercept than the graph of f(x) = -2x² - 8x - 11. So, this statement is true.
Therefore, the correct statements are c and d.
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