Answer:
False
Step-by-step explanation:
The table and graph shown below each represent a function of . Which function, or , has a greater rate of change? Be sure to include the values for the rates of change in your answer. Explain your answer
The rate of change of Function B = 3 is greater than Function A = 2.
What is a functiοn?A unique kind οf relatiοn called a functiοn is οne in which each input has precisely οne οutput. In οther wοrds, the functiοn prοduces exactly οne value fοr each input value. The graphic abοve shοws a relatiοn rather than a functiοn because οne is mapped tο twο different values. The relatiοn abοve wοuld turn intο a functiοn, thοugh, if οne were instead mapped tο a single value. Additiοnally, οutput values can be equal tο input values.
Rate of change refers to the slope of graph or equation,
So lets find the slope for Function A:
Two points are, (1, 5) and (2, 7), Find the slope using slope formula,
[tex]\rm y_2-y_{1}=m\left(x_2-x_{1}\right)[/tex]
7 - 5 = m(2 - 1)
2 = m(1)
m = 2/1
m = 2
The rate of change is 2.
Lets find the slope for Function B:
Two points are, (1, 1) and (2, 4), Find the slope using slope formula,
4 - 1 = m(2 - 1)
3 = m(1)
m = 3/1
m = 3
The rate of change is 3.
Thus, The rate of change of Function B = 3 is greater than Function A = 2.
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A wire reaches from the top of a 26-meter telephone pole to a point on the ground 8 meters from the base of the pole. What is the length of the wire to the nearest tenth of a meter?
Answer: We can use the Pythagorean theorem to solve for the length of the wire. Let's call the length of the wire "x". Then:
x^2 = 26^2 + 8^2
x^2 = 676 + 64
x^2 = 740
x = sqrt(740)
x ≈ 27.2
Therefore, the length of the wire to the nearest tenth of a meter is 27.2 meters.
Step-by-step explanation:
In what ratio does the line of the equation 4x + 5y = 21 divide the line segment joining the points (-2, 3) and (4, 5) ?
Answer: 1.465 : 1
Step-by-step explanation:
Slope of the line segment:
m = (5 - 3)/(4 - (-2)) = 2/6 = 1/3
The equation of the line which the line segment lies on is found by:
(y - 3)/(x - (-2)) = 1/3
(y - 3)/(x + 2) = 1/3
(y - 3)/(x + 2) * (x + 2) = 1/3 * (x + 2)
y - 3 = (x + 2)/3 = 1/3 x + 2/3
y = 1/3 x + 11/3
The equation of the line given:
4x + 5y = 21
5y = -4x + 21
y = -4/5 * x + 21/5
Set them equal to each other and solve for x to find their intersection:
1/3 x + 11/3 = -4/5 * x + 21/5
15(1/3 x + 11/3) = 15(-4/5 * x + 21/5)
5 x + 55 = -12 x + 63
17x = 8
x = 8/17
y = 1/3 (8/17) + 11/3 = 8/51 + 181/51 = 189/51
Point (8/17, 189/51)
Distance from right end of segment to intersection:
s = SQRT((4 - 8/17)^2 + (5 - 189/51)^2) = SQRT((60/17)^2 + (66/51)^2) = 3.759
length of segment = SQRT((5–3)^2 + (4 - (-2))^2) = SQRT(4 + 36) = SQRT(40) = 6.324
Distance from the left end to interseciton:
6.324 - 3.759 = 2.555
Ratio of right end to left end:
3.759/2.565 = 1.465
which of the following statements is correct? a. the binomial distribution is a continuous probability distribution, and the normal distribution is a discrete probability distribution. b. the binomial and normal distributions are both discrete probability distributions. c. the binomial and normal distributions are both continuous probability distributions. d. the binomial distribution is a discrete probability distribution and the normal distribution is a continuous probability distribution.
The correct statement is:
d. The binomial distribution is a discrete probability distribution and the normal distribution is a continuous probability distribution.
What is binomial distribution?
In probability theory and statistics, the binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either Success or Failure. For example, if we toss a coin, there could be only two possible outcomes: heads or tails, and if any test is taken, then there could be only two results: pass or fail. This distribution is also called a binomial probability distribution.
The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent trials, where each trial can result in only two outcomes (success or failure), and the probability of success is constant. Examples of situations that can be modeled by a binomial distribution include flipping a coin a fixed number of times or counting the number of defective items in a batch of products.
The normal distribution, on the other hand, is a continuous probability distribution that is often used to model naturally occurring phenomena, such as heights, weights, and test scores. The normal distribution is characterized by a bell-shaped curve, and it is used because many phenomena in nature follow a normal distribution pattern.
So, the binomial and normal distributions are both widely used in probability and statistics, but they are fundamentally different types of distributions.
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Jacob is a construction worker who earns a yearly income given by the expression 2 , 000 x + 6 , 000 , where x is the number of hours he works each week. Carlos works with Jacob and earns a yearly income given by the expression 3 , 500 x - 39 , 000 . A manager predicts that if Carlos and Jacob each work 35 hours, they will earn the same amount of money. Complete the statements. The solution to the equation 2 , 000 x + 6 , 000 = 3 , 500 x - 39 , 000 is Select hours. The manager's prediction is Select the actual number of hours that Carlos and Jacob need to work to earn the same amount of money.
The manager predicts that Carlos and Jacob need to work 35 hours each to earn the same amount of money.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
We can solve the equation 2,000x + 6,000 = 3,500x - 39,000 as follows:
2,000x + 6,000 = 3,500x - 39,000
Subtracting 2,000x from both sides, we get:
6,000 = 1,500x - 39,000
Adding 39,000 to both sides, we get:
45,000 = 1,500x
Dividing both sides by 1,500, we get:
x = 30
Therefore, the solution to the equation 2,000x + 6,000 = 3,500x - 39,000 is x = 30.
To find the actual number of hours that Carlos and Jacob need to work to earn the same amount of money, we can plug in x = 35 into both of their income expressions and set them equal to each other:
2,000(35) + 6,000 = 3,500(35) - 39,000
Simplifying, we get:
76,000 = 76,000
This means they will earn the same amount of money if they each work 35 hours per week.
Therefore, the manager predicts that Carlos and Jacob need to work 35 hours each to earn the same amount of money.
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For the following demand function, find a. E, and b. the values of q (if any) at which total revenue is maximized.
q=40,600−9p2
a. Determine the elasticity of demand, E.
E=______ (Type an expression using p as the variable.)
b. Determine the value of q that maximizes the revenue. Select the correct choice below, and if necessary, fill in the answer box within your choice.
A.Total revenue is maximized at about, q=___
B. No value of q
a. The elasticity of demand is E = -1.607.
b. Total revenue is maximized at q ≈ 1354.00.
The demand function is: q = 40,600 - 9p^2
a. To find the elasticity of demand, we need to differentiate the demand function with respect to p and then multiply by p/q:
dq/dp = -18p
(p/q) * (dq/dp) = (-18p/q)
Then, we can substitute p = 2000 and q = 22,400 (the values given in a previous question) into this expression:
E = (-18(2000)/22400) = -1.607
b. Total revenue is maximized where the demand is unit elastic (E = -1). We can set the expression for E equal to -1 and solve for p to find the corresponding value of q:
-1 = (-18p/q)
q = 18p
Substituting the demand function into this expression and simplifying, we get:
q = 40,600 - 9p² = 18p
Rearranging and solving for p, we get:
9p² + 18p - 40,600 = 0
Using the quadratic formula, we get:
p = (-18 ± √(18² - 4(9)(-40,600)))/(2(9)) ≈ 75.22 or -227.22
Since the price must be positive, the only valid solution is p ≈ 75.22. Substituting this back into the demand function, we get:
q ≈ 18(75.22) ≈ 1354.00
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please help !! Im having trouble
The length of the line segment between C(-3,3) and D(3,-3) is 6√2 units.
Calculating the length of the distance CDGiven that
C(-3, 3) and D(3, -3)
To find the length of the line segment between points C(-3,3) and D(3,-3), we can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Plugging in the coordinates for C(-3,3) and D(3,-3), we get:
d = √((3 - (-3))^2 + (-3 - 3)^2)
Evaluate
d = √(6^2 + (-6)^2)
d = √72
Simplifying the square root, we can write the length as:
d = 6√(2)
Therefore, the length of the segment CD is 6√2 units.
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Mrs. A grills onions and peppers at a restaurant. She always grills more onions than peppers and always grills some of each. On Sunday, she grilled 38 onions and x peppers. Which pair of inequalities represents the number of peppers, x, she could have grilled on Sunday?
Group of answer choices
x > 0 and x > 38
x > 0 and x < 38
x > 0 and x > 37
x > 0 and x < 37
We can conclude after answering the provided question that As a result, inequality the correct answer is: x > 0 and x < 38
What is inequality?In mathematics, an inequality is a non-equal connection that exists between expressions or values. As a result, imbalance relates to inequality. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two points are not equal, the not equal sign is commonly used (). Different inequalities, no matter how small or large, are utilized to calculate contrast values. Many simple inequalities can be solved by modifying its two sides until only the variables remain. But a few factors contribute to inequality: Negative values are divided or added on both sides. Trade off the left and right.
Mrs. A always grills more onions than peppers, so the number of onions grilled (38) must be greater than the number of peppers grilled (38). (x). As a result, the inequality can be used to represent this relationship:
38 > x
Mrs. A also grills some of each, so the total number of peppers grilled (x) must be greater than zero. As a result, the inequality can be used to represent this relationship:
x > 0
The inequity pair that represents the number of peppers, x, she could have grilled on Sunday is:
x > 0 and 38 > x
This can also be expressed as:
0 < x < 38
As a result, the answer is:
x > 0 and x < 38
As a result, the correct answer is:
x > 0 and x < 38
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The members of a school club are selling tickets for a fundraiser. The goal for the fundraiser is to earn $50.00 each day from ticket sales. The list below shows the percent of the goal reached each day. On the first day, the members earned 90% of their daily goal. On the second day, the members earned 6% more than their daily goal. On the third day, the members earned 14% less than their daily goal. How much money, in dollars, did the members earn from ticket sales on all three days?
On the first day, the members earned 90% of their daily goal of $50.00 which is equal to $45.00 (0.9 x $50.00 = $45.00).
On the second day, the members earned 6% more than their daily goal of $50.00 which is equal to $53.00 ($50.00 + 0.06 x $50.00 = $53.00).
On the third day, the members earned 14% less than their daily goal of $50.00 which is equal to $43.00 ($50.00 - 0.14 x $50.00 = $43.00).
Therefore, the members earned a total of $45.00 + $53.00 + $43.00 = $141.00 from ticket sales on all three days.
The members of the school club earned $141.00 from ticket sales over the three days.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To find out how much money the members of the school club earned from ticket sales on all three days
Let us calculate the amount of money earned each day and then add them together.
On the first day, the members earned 90% of their daily goal, which is:
0.9 x $50.00 = $45.00
On the second day, they earned 6% more than their daily goal, which is:
$50.00 + 0.06 x $50.00 = $53.00
On the third day, they earned 14% less than their daily goal, which is:
$50.00 - 0.14 x $50.00 = $43.00
To find the total amount of money earned over the three days, we simply add the amounts earned on each day:
$45.00 + $53.00 + $43.00 = $141.00
Therefore, the members of the school club earned $141.00 from ticket sales over the three days.
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Determine the average rate of a function
The average rate of change of the quadratic function f(x) on the interval [0, 15] is equal to 23.
How to determine the average rate of change?In Mathematics, the average rate of change of a function f(x) on a closed interval [a, b] can be determined by using this mathematical equation (formula):
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function f(x) over the interval [0, 15]:
a = 0; f(a) = -x² + 8x + 20
f(0) = -0² + 8(0) + 20
f(0) = 20
b = 9; f(b) = 365
f(15) = -15² + 8(15) + 20
f(15) = 365
By substituting the parameters into the average rate of change formula, we have the following;
Average rate of change = (365 - 20)/(15 - 0)
Average rate of change = 345/15
Average rate of change = 23.
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Last year the city of Goose Pimple, Vermont, paid an average of $3,261 per employee in health care costs (including insurance and additional claims). This year the city management decided that they will contract with Grimms Health Maintenance Organization. At the end of the year they would like to know if they have saved any money. They take a sample of 50 and find a sample mean of $3,015 with a standard deviation of $1,745. Present a hypothesis, a null hypothesis, and evaluate the hypothesis. Explain in plain English what you have found
The solution to the offered question depends on the hypothesis the response is the determined t-worth of - 2.58 is not exactly the basic t-worth of - 2.009, we can't dismiss the invalid hypothesis.
To evaluate the hypothesis, we will play out a one-example t-test. The test measurement is determined as:
t = (test mean - populace mean)/(test standard deviation/sqrt(sample size))
Expecting an importance level of 0.05, we will dismiss the invalid hypothesis if the determined t-esteem is more noteworthy than the basic t-esteem.
Populace mean = $3,261 (given)
Test mean = $3,015
Test standard deviation = $1,745
Test size = 50
t = (3015 - 3261)/(1745/sqrt(50)) = - 2.58
Utilizing a t-table with 49 levels of opportunity (test size - 1) and an importance level of 0.05, the basic t-esteem is ±2.009.
Since the determined t-worth of - 2.58 is not exactly the basic t-worth of - 2.009, we can't dismiss the invalid hypothesis. This really intends that there isn't sufficient proof to recommend that there is a massive distinction in medical services costs per worker between last year and this year with the agreement with Grimms Wellbeing Upkeep Association having no effect.
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consider parallelogram vwxy below use the information given in the figure to findx m
In the given parallelogram vwxy: x = 3; m∠Y = 65° and ∠YVX = 61° by (alternate interior angle).
Explain about the parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and thus opposite angles equal).
A parallelogram with all right angles is known as a rectangle, and a quadrilateral having equal sides is known as a rhombus. Rectangles and squares are both particular varieties of parallelograms since a square is just a degenerate instance of a rectangle.In the given parallelogram vwxy:
Parallel sides are equal.
So, 2x = 6
x = 6/2 = 3
Opposite pair of angles are also equal.
So,
∠W = ∠Y = 65°
Now,
∠YVX = 61° (alternate interior angle).
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PLS, PLS, PLS HELP!!!!!!!
If you know your turning point form (vertex form) of a quadratic (y = a(x - h)2 + k), k is the y value, so k = -2
??? Help please !!!!!!!
The only option that represents a function is the relation in C.
Which of the following represents a function?We know that a relation maps elements of one set, called the domain, into elements of another set, called the range.
A relation is a function if each of the elements in the domain is mapped into only one element of the range.
Then for example, in option D we can see that the element -3 is mapped into two different values, then it does not represent a function.
Similar thing for the graph in option B, where we can see two points on the same vertical line.
Or the first option where -1 is mapped to two different values.
The only option that represents a function is option C.
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PLEASE HELP (:
A point on the unit circle has negative x value and a positive y value, select all the possible reference angles it could come from.
SELECT ALL THAT APPLY!
A. 225
B. 150
C. 135
D. 60
E. 300
F. 270
A pοint οn the unit circle having negative x value and a pοsitive y value, has the pοssible reference angles as -
Optiοn B: 150°, Optiοn C: 135°, and Optiοn D: 60°.
What is an angle?An angle is a figure in plane geοmetry that is created by twο rays οr lines that have a shared endpοint. The Latin wοrd "angulus," which meaning "cοrner," is the sοurce οf the English term "angle." The shared terminus οf twο rays is knοwn as the vertex, and the twο rays are referred tο as sides οf an angle.
The unit circle is a circle with radius 1 centered at the οrigin οf a cοοrdinate plane.
Any pοint οn the unit circle can be represented as (cοs θ, sin θ), where θ is the angle made by the pοint with the pοsitive x-axis.
If a pοint οn the unit circle has negative x value and pοsitive y value, then it must be in the secοnd quadrant οr the fοurth quadrant.
In the secοnd quadrant, the reference angle is the angle between the terminal side and the x-axis, which is always acute.
In the fοurth quadrant, the reference angle is the angle between the terminal side and the x-axis, plus 360 degrees, which is alsο acute.
Therefοre, the pοssible reference angles that the pοint cοuld cοme frοm are -
B. 150°, which is the reference angle fοr an angle οf 210° in the secοnd quadrant.
C. 135°, which is the reference angle fοr an angle οf 225° in the secοnd quadrant.
D. 60°, which is the reference angle fοr an angle οf 300° in the fοurth quadrant.
Therefοre, the angle values are 150°, 135° and 60°.
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‘You must be 1.4m tall or more to ride the rollercoaster’
Which of these expresses the sentence above mathematically?
Answer:
b
Step-by-step explanation:
The symbol in the middle of b means greater than or equal to
1. 2. 4 journal:Algebraic Properties and expressions
The distributive property states that we can distribute a factor across a sum or difference, add or subtract like terms by adding or subtracting their coefficients and The power rule states that when raising a power to another power, we multiply the exponents. and Algebraic Properties explained as
Journal Entry 1:
Today, I learned about the algebraic properties of addition and multiplication. These properties are commutative, associative, and distributive. The commutative property states that the order in which we add or multiply numbers does not affect the result. For example, 2+3 is the same as 3+2, and 2x3 is the same as 3x2. The associative property states that we can group numbers in different ways without changing the result. For example, (2+3)+4 is the same as 2+(3+4), and (2x3)x4 is the same as 2x(3x4). The distributive property states that we can distribute a factor across a sum or difference. For example, 2x(3+4) is the same as 2x3 + 2x4.
Journal Entry 2:
Today, I learned about algebraic expressions and how to simplify them using the properties of addition and multiplication. An algebraic expression is a combination of numbers, variables, and operations. For example, 2x + 3y - 4z is an algebraic expression. To simplify an expression, we use the properties of addition and multiplication to combine like terms and simplify the expression as much as possible. Like terms are terms that have the same variables raised to the same powers. For example, 2x and 5x are like terms, but 2x and 5y are not. We can add or subtract like terms by adding or subtracting their coefficients. For example, 2x + 5x is 7x. We can also multiply terms by using the distributive property. For example, 2(3x + 4y) is 6x + 8y.
Journal Entry 3:
Today, I learned about algebraic expressions with exponents. An exponent is a small number written to the right of a base number that indicates how many times to multiply the base by itself. For example, in 2³, the base is 2 and the exponent is 3. To simplify an expression with exponents, we use the properties of exponents, such as the product rule and the power rule. The product rule states that when multiplying two powers with the same base, we add their exponents. For example, 2³ x 2² is 2^(3+2) or 2^5. The power rule states that when raising a power to another power, we multiply the exponents. For example, (2²)³ is 2^(2x3) or 2^6. We can also simplify expressions with exponents by combining like terms, just like we did with expressions without exponents.
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1.2.4Journal: Algebraic Properties and ExpressionsJournalAlgebra I Sem 1Name:Date:Scenario:The ArcadeInstructions:
•View the video found on page 1 of this journal activity
.•Using the information provided in the video, answer the questions below
.•Show your work for all calculation
What is the product of (3a 2)(4a2 – 2a 9)?a. 12a3 − 2a + 18b. 12a3 + 6a + 9c. 12a3 − 6a2 + 23a d. 18+ 12a3 + 2a2 + 23a + 18
Answer:
D. 12a^3+2a^2+23a+18
Step-by-step explanation:
Jesse lleva a su perro y su gato al veterinario en perro pesa 23 y el gato 5/8 cuanto pesa el gato en libras
Jesse's cat weighs 10 pounds.. This will give us the number of pounds for the fraction of a pound. In this case, 5 x 16 = 80, and 80/8 = 10. Therefore, 5/8 = 10 pounds.
Jesse takes his dog and cat to the vet - the dog weighs 23 pounds and the cat weighs 5/8. How much does the cat weigh in pounds?To convert the weight of the cat from fractions of a pound to pounds, we can use the following formula:Pounds = (Fraction of a Pound) x 16In this case, 5/8 x 16 = 10 pounds. Therefore, the cat weighs 10 pounds.The fraction of a pound is calculated by multiplying the numerator (top number) of the fraction by 16 and then dividing the result by the denominator (bottom number). This will give us the number of pounds for the fraction of a pound. In this case, 5 x 16 = 80, and 80/8 = 10. Therefore, 5/8 = 10 pounds.To summarize, Jesse's cat weighs 10 pounds.
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For a certain industry, the mean annual salary rose from $25,200 to $28,960. Calculate the percent of increase. Round to the nearest tenth.
After answering the presented question, we can conclude that equation 0.1492063492063492 * 100% Percentage increase = 14.9% As a result, the average yearly pay has increased by 14.9%.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
To determine the % increase in mean annual wage, find the difference between the new and old salaries, divide it by the old salary, and multiply by 100.
(new salary - previous salary) / old salary * 100% = percentage increase
(28960 - 25200) / 25200 * 100% Percentage increase = 0.1492063492063492 * 100% Percentage increase = 14.9%
As a result, the average yearly pay has increased by 14.9%.
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the equation
4x-2y=4
-4x+2y=-3
have the same/different what slopes and the same/different what y-intercept?
Answer:
same slopes: 2. different y-intercepts: (0,-2) and (0,-1.5)
Step-by-step explanation:
First, lets convert both of those to slope intercept form: y = mx + b, where m is the slope and b is the y-intercept.
4x-2y=4 simplifies to -2y=-4x+4, which is y=2x-2
-4x+2y=-3 simplifies to 2y=4x-3, which is y=2x-1.5
this means that they have the same slopes, 2.
they have different y-intercepts. the first one's is (0,-2) and the second one's is (0,-1.5)
Which is the correct substitution for evaluating 10-y2 when y=3
Answer:
6
Step-by-step explanation:
y2= 3x2 = 6.
you start at (6,10) and move 6 units right and 4 units down where are you now
please explain and answer very well
According to the information in the table, the bus arrives in Newtown at 11:09. So this trip would take 31 minutes.
How to know what time the bus arrives in Newtown?To find out what time the bus arrives in Newtown we must analyze the table. In this case we can see row 3 that has the information about the bus route that leaves at 11:38.
The fourth city that this bus visits is Newtown, where it arrives at 11:09 after stopping in Milton and Leek. So the arrival time in Newtown would be 11:09.
On the other hand, to find how long the trip took we must compare both times (10:38, 11:09) and find the difference. So, for it to be 11:00, there would be 22 minutes left. Then add 9 minutes, so the total would be 31.
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precalculus Question 11.2
a) show that the distance between the two points.
b) describe the positions of the points relative to eachother. simplify the distance formula for this case.
c) simplify the distance formula.
d) choose two points on the polar coordinate system and find the distance between them. then choose different polar representations of the same two points and apply the distance formula again.
I will attach the answer, this work did not come from me but I figured I'd upload it anyways.
A can also be represented as A(2,-11π/6) and B can be represented as B(3,-π/6). Using the distance formula again, we have: distance = sqrt(2^2 + 3^2 - 223*cos(-11π/6 - (-π/6))) = sqrt(13)
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.
a) To find the distance between two points in polar coordinates, we can use the Pythagorean theorem to calculate the distance in the radial direction and then use the law of cosines to take into account the angular separation. Thus,
distance = sqrt((r2-r1)^2 + (r1^2 + r2^2 - 2r1r2*cos(θ1 - θ2)))
Simplifying this expression, we get:
distance = sqrt(r1^2 + r2^2 - 2r1r2*cos(θ1 - θ2))
Using the identity cos(a-b) = cos(a)cos(b) + sin(a)sin(b), we can rewrite the expression as:
distance = sqrt(r1^2 + r2^2 - 2r1r2cos(θ1)cos(θ2) - 2r1r2sin(θ1)sin(θ2))
Using the identity cos^2(x) + sin^2(x) = 1, we can simplify the expression further:
distance = sqrt(r1^2 + r2^2 - 2r1r2*cos(θ1-θ2))
b) If θ1 = θ2, then the points lie on the same radial line and are separated only by their radial distances from the origin. In this case, the distance formula simplifies to:
distance = sqrt((r2-r1)^2) = abs(r2-r1)
This is what we would expect, as the distance between two points on the same radial line is simply the absolute difference in their radial distances from the origin.
c) If θ1 - θ2 = 90 degrees, then the points are separated by the maximum angular distance and lie on perpendicular radial lines. In this case, the distance formula simplifies to:
distance = sqrt(r1^2 + r2^2)
This is also what we would expect, as the distance between two points on perpendicular radial lines is simply the Pythagorean sum of their radial distances from the origin.
d) Let's choose two points in polar coordinates: A(2,π/6) and B(3,5π/6). Using the distance formula derived in part (a), we have:
distance = sqrt(2^2 + 3^2 - 223*cos(5π/6 - π/6)) = sqrt(13)
Now let's express these same points in different polar representations.
Therefore, a can also be represented as A(2,-11π/6) and B can be represented as B(3,-π/6). Using the distance formula again, we have:
distance = sqrt(2^2 + 3^2 - 223*cos(-11π/6 - (-π/6))) = sqrt(13)
As expected, the distance between the two points is the same regardless of their polar representations.
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a production process that is in control has a mean of 80 and a standard deviation of 10. what are the upper and the lower control limits for sample sizes of 25?
A production process that is in control has a mean of 80 and a standard deviation of 10. The upper and the lower control limits for sample sizes of 25 is 124 and 36 respectively.
The production process that is in control has a mean of 80 and a standard deviation of 10.
To find the upper and lower control limits for a sample size of 25, we need to calculate the following formulas:
Upper Control Limit (UCL) = mean + 3*standard deviation
Lower Control Limit (LCL) = mean - 3*standard deviation
Therefore, for this process with a mean of 80 and standard deviation of 10, the UCL is 130 and the LCL is 30.
For sample sizes of 200, the formulas will be slightly different as the control limits are adjusted for larger samples:
UCL = mean + 2.66 x standard deviation
LCL = mean - 2.66 x standard deviation
Therefore, the UCL is 124 and the LCL is 36.
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A new cylindrical can with a diameter of 4 cm is being designed by a local company. The surface area of the can is 130 square centimeters What is the height of the can? Estimate using 3.14 for x and
round to the nearest hundredth. Apply the formula for surface area of a cylinder SA-28+ Ph
Answer:
The height is 9.73 cm.
Step-by-step explanation:
We can start by finding the radius of the cylinder:
r = d/2 = 4/2 = 2 cm
Then, we can use the formula for the surface area of a cylinder to solve for the height:
SA = 2πrh + 2πr²
130 = 2π(2)(h) + 2π(2)²
130 = 4πh + 8π
122 = 4πh
h ≈ 9.73 cm (rounded to the nearest hundredth)
So the height of the can is approximately 9.73 cm.
A netball team plays three matches. In each match the team is equally likely to win, lose or draw. Draw a tree diagram to show all the possible outcomes over the three matches.
b Calculate the probability that the team:
i wins all three matches,
ii wins more times than loses,
iii loses at least one match,
iv either draws or loses all three matches.
c Explain why it is not very realistic to assume that the outcomes are equally likely in this case.
b. i) The probability of winning all three matches is 1/27.
ii) The probability of winning more times than losing is 3/27.
iii) 7/27
iv) 2/27
c. many factors that can influence the outcome of a match such as the skill of the players, the tactics used by the teams and the condition of the playing surface.
What is probability?Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
a. Tree diagram:
Match 1 | Match 2 | Match 3
--------------------------------
Win | Win | Win
Draw | Draw | Draw
Lose | Lose | Lose
b. i) The probability of winning all three matches is P(Win, Win, Win) = (1/3) * (1/3) * (1/3) = 1/27
ii) The probability of winning more times than losing is
P(Win, Win, Draw) + P(Win, Draw, Win) + P(Draw, Win, Win)
= (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3)
= 3/27
iii) The probability of losing at least one match is
P(Lose, Win, Win) + P(Win, Lose, Win) + P(Win, Win, Lose) + P(Lose, Lose, Win) + P(Lose, Win, Lose) + P(Win, Lose, Lose) + P(Lose, Lose, Lose)
= (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3)
= 7/27
iv) The probability of either drawing or losing all three matches is
P(Draw, Draw, Draw) + P(Lose, Lose, Lose)
= (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3)
= 2/27
c. It is not very realistic to assume that the outcomes are equally likely in this case because there are many factors that can influence the outcome of a match such as the skill of the players, the tactics used by the teams and the condition of the playing surface.
Therefore, it is unlikely that all outcomes are equally likely as assumed in this case.
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Peter has hats. He can divide them into equal groups of 2,6 and 8. How many hats does Peter have?
Answer:
24
Step-by-step explanation:
Answer: 24 hats
Step-by-step explanation:
1. Find common multiples: 2: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36 6: 6,12,18,24,30,36 8: 8,16,24,32
2. Find the least common multiple: 24
find the square root of -1/9
Answer: There isn't an answer because there's an negative.