if the test has 25 questions, the number of multiple choice questions plus the number of short answer questions is 25. The correct answer is c.
To explain, let x be the number of multiple choice questions and y be the number of short answer questions. We know that there are 25 questions in total, so x + y = 25.
We also know that each multiple choice question is worth 2 points, and each short answer question is worth 4 points. If we let M be the total number of points from the multiple choice questions, and S be the total number of points from the short answer questions, we can set up the equation:
M + S = 80
We can also express M and S in terms of x and y:
M = 2x
S = 4y
Substituting these equations into the first equation, we get:
2x + 4y = 80
Dividing both sides by 2:
x + 2y = 40
Now we have two equations with two variables:
x + y = 25
x + 2y = 40
Subtracting the first equation from the second, we get:
y = 15
Substituting this into the first equation, we get:
x + 15 = 25
x = 10
Therefore, there are 10 multiple choice questions on the test.
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If a 35 N block is resting on a steel table with a coefficient of
static friction Hs = 0,40, then what minimum force is required to
move the block.
The minimum force required to move a block of 35 N resting on a steel table with a coefficient of static friction of 0.40 is 14 N.
Friction refers to the force that resists the motion and thus the force acts in the opposite direction of the force applied.
There are the following types of friction:
1. Static Friction
2. Limiting Friction
3. Kinetic Friction
F = μN
where μ is the coefficient of friction
N is the Normal Force
When the object is resting on a table, Normal force is the weight.
N = 35 N
μ = 0.40
F = 0.4 * 35
= 14 N
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If x = yand y = z, which statement must be true?
O A. -x=-z
O B. z=x
O c. x=z
O D. -x=z
Answer:
The answer is C. x=z
Step-by-step explanation:
The correct answer is C. x=z.
Since x = y and y = z, then x = z. This is the transitive property of equality.
Here is a more detailed explanation:
The transitive property of equality states that if a = b and b = c, then a = c.
In this case, x = y and y = z. Therefore, x = z.
Select the statement that best describes the expression 4+3x
A. 4 plus 3plus x
B. The sum of 4 and 3
C. The product of 4 and 3x
D. 4 plus 3 times x
The correct option is D, the statement that best describes the expression 4+3x means "4 plus 3 times x".
An expression is a combination of numbers, symbols, and/or variables that represents a mathematical or logical statement. It can be as simple as a single number or letter, or as complex as a series of operations that involve multiple variables and functions. Expressions can be used to represent equations, inequalities, functions, and other mathematical concepts. They can be evaluated to produce a numerical value or a boolean value (true or false) depending on the values of the variables involved.
Expressions are used to represent calculations or logical conditions. They can be used to assign values to variables, manipulate data, and control the flow of a program. expressions are a fundamental concept in both mathematics and computer science, and play a critical role in solving problems and building complex systems.
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Which expression had a value less than 1
Step-by-step explanation:
[tex] - \infty \: and \: 0[/tex]
or
[tex]x \leqslant 1[/tex]
Briefly discuss the difference between indefinite integral and definite integral. Give an example to provide emphasis. *
A definite integral is defined as the signed area under a function between certain limits (bounds) of integration.
An indefinite integral represents the family of antiderivatives of a function and is also known as its general integral or antiderivative.
The difference between the integralsAn indefinite integral represents the family of antiderivatives of a function and is also known as its general integral or antiderivative. An indefinite integral does not have specific limits of integration; its result includes a constant of integration (usually denoted +C), which accounts for all possible constant shifts within its antiderivative.
A definite integral is defined as the signed area under a function between certain limits (bounds) of integration. The real number that represents its net area between it and x-axis during an interval.
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Two sisters, working together can clean the house in 3 hours. The older sister works 3 times faster than the younger sister when cleaning the house. How long will it take the younger sister to finish the same job by herself? Type just the number don't include words
The time taken by the younger sister to finish the same work by herself is 12 hours.
To solve the problem of how long it will take the younger sister to finish the job by herself, let's use the following terms:
1. Older sister's work rate = O
2. Younger sister's work rate = Y
3. Time taken by the younger sister alone = T
Given that the older sister works 3 times faster than the younger sister, we have: O = 3Y.
Also, the sisters together can finish the job in 3 hours. Therefore, their combined work rate is equal to completing 1/3 of the job per hour. So,
O+Y=1/3.
Now, we can substitute O with 3Y: 3Y+Y=1/3. Combine the terms and simplify:
4Y=1/3
Now, solve for Y:
Y=1/12
Since Y is the work rate of the younger sister, to find the time it takes for her to complete the job alone (T), we can use the following formula:
Work rate × Time = 1 job.
So, Y × T = 1.
Substitute Y with 1/12:
[tex]\frac{1}{12} \times T=1[/tex]
Now, solve for T:
T = 12.
Therefore, it will take the younger sister 12 hours to finish the job by herself.
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Instructors led an exercise class from a raised rectangular platform at the front of the room. The width of the platform is (x+4) meters long and the area of the rectangular platform is 3x^2+10x−8. Find the length of the platform
Length of the platform at the front of the room whose area is 3x² + 10x - 8 and width is (x+4) m is (3x - 2) m
Area of the rectangular platform = 3x² + 10x - 8
Width of the rectangular platform = x+4
Area = length × width
Length = area/width
Length = [tex]\frac{3x^{2} + 10x - 8}{x+4}[/tex]
By splitting the middle term we get
Length = [tex]\frac{3x^{2} + 12x -2x -8 }{x+4}[/tex]
By taking common we get
Length = [tex]\frac{3x(x+4) - 2(x+4)}{x+4}[/tex]
By taking x+4 common we get
Length = [tex]\frac{(3x-2)(x+4)}{x+4}[/tex]
Cutting the x+4 from denominator and numerator we get
Length = 3x-2
Length of the platform at the front of room is 3x-2
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Victoria will deposit $2000 in an account that earns 5% simple interest every year. Her friend Corbin will deposit $1800 in an account that earns 9% interest compounded annually. The deposits are made on the same day, and no additional money will be deposited or withdrawn from the accounts. Which statement about the balances of Victoria and Corbin's accounts at the end of 3 years is true?
Corbin's account will have a higher balance than Victoria's account at the end of 3 years" is true.
How to calculate account balance at the end of 3 years?To calculate the balance at the end of 3 years, we can use the simple interest formula for Victoria's account and the compound interest formula for Corbin's account.
For Victoria's account:
Simple interest = P * r * t
= 2000 * 0.05 * 3
= $300
Balance after 3 years = P + Simple interest
= 2000 + 300
= $2300
For Corbin's account:
Balance after 3 years = [tex]P * (1 + r)^t[/tex]
= 1800 * (1 + 0.09)³
= $2401.40
Therefore, the statement "Corbin's account will have a higher balance than Victoria's account at the end of 3 years" is true.
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1) You want your savings account to have a total of $23,000 in it within 5 years. If you invest your money in an account that pays 6.8% interest compounded continuously, how much money must you have in your account now? 2) You buy a brand new Audi R8 for $148,700 before taxes. If the car depreciates at a rate of 8%, how much will it be worth in 5 years?
After 5 years with 8% depreciation, the Audi R8's value will be around $81,249.36.
To determine how much money you must have in your account now, you can use the formula A = Pe^(rt), where A is the final amount, P is the principal (the initial amount invested), e is the constant 2.71828, r is the annual interest rate expressed as a decimal, and t is the time in years. We will calculate using this formula.Plugging in the given values, we get:
A = $23,000
r = 0.068 (6.8% expressed as a decimal)
t = 5 years
So, $23,000 = P*e^(0.068*5)
Solving for P, we get:
P = $16,376.59
Therefore, you must have $16,376.59 in your account now to reach your goal of $23,000 in 5 years with 6.8% continuous compounding interest. To determine how much the Audi R8 will be worth in 5 years, you can use the formula A = P(1 - r)^t, where A is the final amount, P is the initial amount, r is the annual depreciation rate expressed as a decimal, and t is the time in years. Plugging in the given values, we get:
P = $148,700
r = 0.08 (8% expressed as a decimal)
t = 5 years
So, A = $148,700*(1 - 0.08)^5
Simplifying, we get:
A = $81,249.36
Therefore, the Audi R8 will be worth approximately $81,249.36 in 5 years with 8% depreciation.
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The legs of a right triangle measure 11.4 meters and 15.1 meters. To the nearest tenth, what is the measure of the smallest angle
The measure of the smallest angle is 37.1 degrees
Calculating the measure of the smallest angleFrom the question, we have the following parameters that can be used in our computation:
The legs of a right triangle measure 11.4 meters and 15.1 meters
So, the measure of one of the acute angles is
tan(x) = 11.4/15.1
Evaluate
tan(x) = 0.7550
Take the arc tan of both sides
So, we have
x = 37.1
This means that the measure of the smallest angle is 37.1 degrees
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Can someone help me ASAP please? It’s due tomorrow. Show work please!! I will give brainliest if it’s correct and has work.
The difference in the number of outcomes depending on the coins being replaced is B. 10 outcomes.
How to find the outcomes ?For the first coin, there are 10 possible outcomes (any one of the 10 coins in the jar). For the second coin, there are again 10 possible outcomes, since the first coin is replaced and all 10 coins remain in the jar. Therefore, the total number of outcomes when two coins are selected with replacement is 10 x 10 = 100.
The number of outcomes when two coins are selected without replacement can be calculated as follows:
For the first coin, there are 10 possible outcomes (any one of the 10 coins in the jar). For the second coin, there are only 9 possible outcomes, since one coin has already been removed from the jar. Therefore, the total number of outcomes when two coins are selected without replacement is 10 x 9 = 90.
Difference is:
= 100 - 90
= 10 outcomes
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A population has a proportion of 0. 62 and a standard deviation of sample proportions of 0. 8. A sample of size 40 was taken from this population. Determine the following probabilities. Illustrate each on the normal curve shown below each part.
a. ) The probability the sample has a proportion between 0. 5 and 0. 7
b. ) The probability the sample has a proportion within 5% of the population proportion
c. ) The probability that the sample has a proportion less than 0. 50
d. ) The probability that the sample has a proportion greater than 0. 80
The probability that a) the sample has a proportion between 0.5 and 0.7 is 0.780. b) The probability that the sample has a proportion within 5% is 0.819. c) The probability that the sample has a proportion less than 0.50 is 0.001. d) The probability that the sample has a proportion greater than 0.80 is 0.000.
a) To calculate this probability, we first need to standardize the interval (0.5, 0.7) using the formula: z = (p - P) / (σ / √(n))
where p is the sample b, P is the population proportion, σ is the standard deviation of sample proportions, and n is the sample size. Substituting the values, we get:
z1 = (0.5 - 0.62) / (0.8 / √(40)) = -2.24
z2 = (0.7 - 0.62) / (0.8 / √(40)) = 1.12
Using the standard normal table or calculator, the area between -2.24 and 1.12 is 0.780. Therefore, the probability that the sample has a proportion between 0.5 and 0.7 is 0.780.
b) The probability that the sample has a proportion within 5% of the population proportion is 0.819. We can find the range of sample proportions within 5% of the population proportion by adding and subtracting 5% of the population proportion from it, which gives: P ± 0.05P = 0.62 ± 0.031
The interval (0.589, 0.651) represents the range of sample proportions within 5% of the population proportion. To calculate the probability that the sample proportion falls within this interval, we standardize it using the formula above and find the area under the standard normal curve between -1.55 and 1.55, which is 0.819.
c) The probability that the sample has a proportion less than 0.50 is 0.001. To calculate this probability, we standardize the value of 0.50 using the formula above and find the area to the left of the resulting z-score, which is: z = (0.50 - 0.62) / (0.8 / √(40)) = -4.46
Using the standard normal table or calculator, the area to the left of -4.46 is 0.001. Therefore, the probability that the sample has a proportion less than 0.50 is 0.001.
d) The probability that the sample has a proportion greater than 0.80 is 0.000. To calculate this probability, we standardize the value of 0.80 using the formula above and find the area to the right of the resulting z-score, which is: z = (0.80 - 0.62) / (0.8 / √(40)) = 5.60
Using the standard normal table or calculator, the area to the right of 5.60 is very close to 0.000. Therefore, the probability that the sample has a proportion greater than 0.80 is 0.000.
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Select all of the statements that are true
The [9.7] = -9.7 because the distance from -9.7 to 0 on the number line is 9.7 units.
Numbers with the same absolute value are opposites because they are the same distance from each other.
The [7.1] = 7.1 because the distance from 7.1 to 0 on the number line is 7.1 units.
The [-8.4] = 8.4 because the distance from -8.4 to 8.4 on the number line is 0 units.
Numbers with the same absolute value are opposites because they are the same distance from 0 on the number line.
The [-12.5] = 12.5 because the distance from 12.5 to 0 on the number line is -12.5 units.
The true statements are Numbers with same absolute value are opposites because they are same distance from each other and from 0 on the number line. The |7.1| = 7.1. So, correct options are B, C and E.
b) Numbers with the same absolute value are opposites because they are the same distance from each other. This is true because absolute value is the distance from a number to zero on the number line, and if two numbers have the same distance from zero, then they must be equidistant from zero and therefore, they are opposite in sign.
c) The |7.1| = 7.1 because the distance from 7.1 to 0 on the number line is 7.1 units. This is true because the absolute value of a number is always positive, and it represents the distance of that number from zero on the number line.
d) The |-8.4| = 8.4 because the distance from -8.4 to 8.4 on the number line is 0 units. This is false, as the distance between -8.4 and 8.4 on the number line is 16.8 units. The correct value of the absolute value of -8.4 is 8.4.
e) Numbers with the same absolute value are opposites because they are the same distance from 0 on the number line. This is true because 0 is the midpoint of the number line, and if two numbers have the same distance from 0, then they must be equidistant from zero and therefore, they are opposite in sign.
Therefore, the correct statements are b, c, and e.
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what is the radius of a basketball if the volume is 11488.2 cm? round your answer the the nearest whole number. use 3.14 as π .
Answer:
The radius of the basketball is 20 cm.
Step-by-step explanation:
The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius.
We are given that the volume of the basketball is 11488.2 cm, so we can set up the equation:
11488.2 = (4/3)πr^3Simplifying, we get:
(4/3)πr^3 = 11488.2Dividing both sides by (4/3)π, we get:
r^3 = 11488.2 / (4/3)πr^3 = 7239.79Taking the cube root of both sides, we get:
r ≈ 20Rounding to the nearest whole number, the radius of the basketball is 20 cm.
Bet you can’t solve this
Answer: The answer is (A
Step-by-step explanation:
The answer isB because A is constant, C is irrelevant, and D is dependent.
Taylor would like to have a karaoke deejay at her graduation party. her three sisters volunteered to split the cost of hiring the deejay. they need to rent a tent for $45 and a microphone system for $60 and then pay the deejay $30 an hour for four hours. how much do each of the sisters owe?
write out all the work used to determine the answer to the question.
Each of the three sisters owes $75 to cover the cost of hiring the karaoke deejay for Taylor's graduation party.
To determine how much each sister owes, we need to first calculate the total cost of the party and then divide that cost by three, since there are three sisters splitting the cost.
1. Tent rental: $45
2. Microphone system: $60
3. Deejay cost: $30/hour × 4 hours = $120
Now, we'll add these costs together to find the total cost:
Total cost = $45 (tent) + $60 (microphone) + $120 (deejay) = $225
Finally, we'll divide the total cost by the number of sisters (3) to find out how much each sister owes:
Amount owed per sister = $225 (total cost) ÷ 3 (sisters) = $75
So, each sister owes $75 for the karaoke deejay at Taylor's graduation party.
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how do i find the inverse
Step-by-step explanation:
To solve for inverse, utilize the following steps.
Step 1: let f(x)=y so we get
[tex]y = \sqrt{x - 6} + 5[/tex]
Step 2: Swap y and x
[tex]x = \sqrt{y - 6} + 5[/tex]
Solve for y.
[tex]x - 5 = \sqrt{y - 6} [/tex]
[tex](x - 5) { }^{2} + 6 = y[/tex]
Step 4: Let y =f^-1(x)
[tex](x - 5) {}^{2} + 6 = f {}^{ - 1} (x)[/tex]
Answer: [tex]f^{-1}(x) =[/tex] x²-10x+19
Step-by-step explanation:
Let's replace f(x) for y for now.
[tex]y=\sqrt{x-6}+5[/tex]
To find inverse. make your y into x, and your x into y
[tex]x=\sqrt{y-6}+5[/tex] >Now you solve for y. subtract 5 from both sides
[tex]x-5=\sqrt{y-6}[/tex] >Square both sides to get rid of root
[tex](x-5)^{2} =(\sqrt{y-6})^{2}[/tex] >drop root and square (x-5)
(x-5)(x-5) = y-6 >FOIL
x²-5x-5x+25 = y-6 > combine like terms
x²-10x+25 = y-6 >add 6 to both sides
x²-10x+19=y > this is your inverse now put the y into inverse form
[tex]f^{-1}(x) =[/tex] x²-10x+19
Here are the numbers of calls received at a customer support service during 8 randomly chosen, hour-long intervals.
9, 14, 23, 14, 19, 9,5,7
Send data to calculator
(a) What is the median of this data set? If your answer is not 0
an integer, round your answer to one decimal place.
(b) What is the mean of this data set? If your answer is not an
integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are
their values? Indicate the number of modes by clicking in the
appropriate circle, and then indicate the value(s) of the
mode(s), if applicable.
0
OO
zero modes
O one mode: 0
two modes:
and
a) The median of the dataset is: 11.5
b) The mean of the dataset is: 12.5
c) The mode of the dataset is: 9 and 14
How to find the mean, median or mode?The term average mean is defined as the finding of the average of a sample data. Thus, the average is finding the central value in math, which tells us that mean is finding the central value in statistics.
The numbers arranged in ascending order is:
5, 7, 9, 9, 14, 14, 19, 23
a) The median is defined as the middle term of the distribution when arranged in ascending or descending order. Thus, the median here is:
(9 + 14)/2 = 11.5
b) The mean of the data is expressed as:
(5 + 7 + 9 + 9 + 14 + 14 + 19 + 23)/8
= 12.5
c) The mode is the most frequently occurring term in the data.
In this case, the mode is 9 and 14
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Let F(X) = - 8 - x^2, find the following:
(f(7) - f(3))/ 7 -3
A relation is a set of ordered pairs that define the relationship between two sets. And, a function is a relation in which each element of the domain is connected to a single element of the codomain. The evaluated function is -10.
To find the expression (f(7) - f(3))/ 7 -3, we need to first find f(7) and f(3).
Using the given function F(X) = - 8 - x^2, we can find:
f(7) = -8 - 7^2 = -57
f(3) = -8 - 3^2 = -17
Now, we can substitute these values into the expression:
(f(7) - f(3))/ 7 -3 = (-57 - (-17))/ (7-3) = -40/4 = -10
Therefore, the answer is -10.
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Omar Cuts A Piece Of Wrapping Paper with the shape and dimensions as shown .Find the area of the wrapping paper. Round your answer to the nearest tenth if needed
The area of the wrapping paper would be = 72.5in².
How to calculate the area of the wrapping paper?To calculate the area of the wrapping paper, the figure is first divided into two leading to the formation of a triangle and a rectangle.
For the triangle, the formula use to calculate it's area is given as follows;
Area = 1/2 base × height
base = 15-10 = 5 in
height = 9-4 = 5 in
area = 1/2×5 × 5
= 25/2 = 12.5 in²
Area of a rectangle = length× width
width = 4 in
length = 15 in
area = 4×15 = 60in²
Therefore the area of the wrapping paper = 12.5+60 = 72.5in²
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A student wants to estimate the mean bowling score for all bowlers in a particular bowling league. fifty scores are randomly selected from the league with a
sample mean was 186 with a standard deviation of 22. assume normality.
5. construct a 95% confidence interval for the mean score for all bowlers in the league.
(179.75, 192.25
(177.66, 194.34)
(180.78, 191.22)
(163.83, 208.17)
(179.9, 192.1)
The 95% confidence interval for the mean score for all bowlers in the league is option (E) (179.9, 192.1).
To construct a 95% confidence interval for the mean score for all bowlers in the league, we can use the formula:
CI = X ± z* (σ/√n)
where X is the sample mean, σ is the population standard deviation (unknown), n is the sample size, and z* is the critical value for the desired confidence level (95% in this case).
Since the sample size is 50, we can assume that the population standard deviation is approximately equal to the sample standard deviation, which is 22. The critical value for a 95% confidence interval with a two-tailed test is 1.96.
Substituting the values, we get:
CI = 186 ± 1.96 (22/√50)
= 186 ± 6.44
= (179.56, 192.44)
Therefore, the answer is (B) (177.66, 194.34), which is the closest to the calculated confidence interval.
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Sara collects beads in a jar she weighs the jar every week to see how many grams of beads she has. she as 2.5 grams if blue beads. 4.9 grams of pink beads, 7.1 grams of yellow beads and the rest are white beads
if sara weighs her jar this week and finds out that she has 1.8 grams of beads, how many grams of white beads does she have?
Therefore, Sara has 3.5 grams of white beads in her jar.
Based on the information provided, Sara has 2.5 grams of blue beads, 4.9 grams of pink beads, and 7.1 grams of yellow beads. If she weighs her jar this week and finds out she has a total of 18 grams of beads, we can determine the number of grams of white beads she has by following these steps:
Step 1: Add the weights of the blue, pink, and yellow beads together.
2.5 grams (blue) + 4.9 grams (pink) + 7.1 grams (yellow) = 14.5 grams
Step 2: Subtract the total weight of the blue, pink, and yellow beads from the total weight of the jar (18 grams).
18 grams (total weight) - 14.5 grams (blue, pink, and yellow beads) = 3.5 grams
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The mass of the Rock of Gibraltar is 1. 78 ⋅ 1012 kilograms. The mass of the Antarctic iceberg is 4. 55 ⋅ 1013 kilograms. Approximately how many more kilograms is the mass of the Antarctic iceberg than the mass of the Rock of Gibraltar? Show your work and write your answer in scientific notation
The mass of the Antarctic iceberg is approximately 2.56 × 10¹more kilograms than the mass of the Rock of Gibraltar.
To find out, we can subtract the mass of the Rock of Gibraltar from the mass of the Antarctic iceberg:
4.55 × 10¹³ kg - 1.78 × 10¹² kg = 4.37 × 10¹³ kg
Therefore, the mass of the Antarctic iceberg is about 2.56 × 10¹ (or 25.6) times greater than the mass of the Rock of Gibraltar.
This is because the mass of the Antarctic iceberg is much larger than the mass of the Rock of Gibraltar, as it is a massive block of ice floating in the ocean while the Rock of Gibraltar is a solid rock formation on land.
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John was visiting four cities that form a rectangle on a coordinate grid at A(O.
4), B(4,1). C(3. 1) and D(-1. 2). If he visited all the cities in order and ended up
where he started. What is the distance he traveled? Round your answer to the
nearest tenth
If he visited all the cities in order A(O,4), B(4,1). C(3. 1) and D(-1. 2). then he traveled 12.3 units distance ( nearest tenth).
John visited four cities that form a rectangle on a coordinate grid at A(0, 4), B(4, 1), C(3, 1), and D(-1, 2). If he visited all the cities in order and ended up where he started, the distance he traveled can be found by calculating the perimeter of the rectangle.
Calculate the distance between consecutive points.
AB = √[(4-0)^2 + (1-4)^2] = √[16 + 9] = √25 = 5
BC = √[(3-4)^2 + (1-1)^2] = √[1 + 0] = √1 = 1
CD = √[(-1-3)^2 + (2-1)^2] = √[16 + 1] = √17 ≈ 4.1 (rounded to nearest tenth)
DA = √[(0-(-1))^2 + (4-2)^2] = √[1 + 4] = √5 ≈ 2.2 (rounded to nearest tenth)
Calculate the total distance traveled (perimeter of the rectangle).
Total Distance = AB + BC + CD + DA = 5 + 1 + 4.1 + 2.2 = 12.3
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Unit 7: Right Triangles & Trigonometry Homework 4: Trigonometry Ratios & Finding Missing Sides #13
The value of sides are KL=5.34, JK=16.434, JL=17.29 and ML=22.25.
∵ ΔJLM is a right triangle, as ∠MJL=90°
∴ tan(∠JML)= JL/JM [∵ tan∅=perpendicular/hypotenuse]
⇒ tan(51°)=JL/14
⇒ JL=14×tan(51°)
= 14×1.23
= 17.29
∴ JL=17.29
Again, ΔJKL is a right triangle, with ∠JKL=90°
∴ cos(∠JLK)=KL/JL [∵ cos∅=base/hypotenuse]
⇒cos(72°)= KL/17.29
⇒KL=17.29×cos(72°)
= 17.29×0.309
= 5.34
∴ KL=5.34
Hence, the value of KL is 5.34.
Also, tan(∠JLK)=KJ/KL
⇒tan(72°)=JK/5.34
⇒JK=5.34×tan(72°)
= 5.34×3.077
= 16.434
∴ JK=16.434
And, cos(∠JML)=JM/ML
⇒cos(51°)=14/ML
⇒ML=14/cos(51°)
=14/.629
=22.25
∴ ML=22.25
Hence, the value of sides are KL=5.34, JK=16.434, JL=17.29 and ML=22.25.
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Given: (x is number of items) Demand function: d(x) = 588.7 – 0.4x2 Supply function: 8(x) = 0.322 2 Find the equilibrium quantity: Find the producers surplus at the equilibrium quantity:
The equilibrium quantity is approximately 34.47 items and the producer surplus at the equilibrium quantity is approximately 396.11.
How to find equilibrium quantity and producer surplus?To find the equilibrium quantity, we need to find the quantity at which the demand and supply functions are equal:
Demand function: d(x) = 588.7 – 0.4x^2
Supply function: s(x) = 8(x) = 0.322
Setting these two functions equal to each other, we get:
588.7 – 0.4x^2 = 0.322x
Simplifying this equation, we get:
0.4x^2 + 0.322x - 588.7 = 0
Using the quadratic formula, we get:
x = (-0.322 ± √(0.322^2 + 40.4588.7)) / (2*0.4)
x ≈ 34.47 or x ≈ -43.67
Since we cannot have a negative quantity, the equilibrium quantity is approximately 34.47 items.
To find the producer surplus at the equilibrium quantity, we need to calculate the area between the supply curve and the equilibrium price, which is the price that corresponds to the equilibrium quantity. We can find the equilibrium price by plugging the equilibrium quantity into either the demand or supply function:
s(34.47) = 8(34.47) = 11.58
So the equilibrium price is approximately 11.58.
Now we can find the producer surplus by integrating the supply function from 0 to the equilibrium quantity, and subtracting the result from the area of a rectangle with height equal to the equilibrium price and width equal to the equilibrium quantity. The formula for producer surplus is:
Producer Surplus = (Equilibrium Price * Equilibrium Quantity) - ∫[0, Equilibrium Quantity] Supply Function dx
Plugging in the values we found, we get:
Producer Surplus = (11.58 * 34.47) - ∫[0, 34.47] 0.322 dx
Integrating the supply function, we get:
∫[0, 34.47] 0.322 dx = 0.322 * 34.47 ≈ 11.10
So the producer surplus is:
Producer Surplus ≈ (11.58 * 34.47) - 11.10 ≈ 396.11
Therefore, the equilibrium quantity is approximately 34.47 items, and the producer surplus at the equilibrium quantity is approximately 396.11.
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For questions 1,2, and 3 find intervals of positive and negative r values. 1. r= 1 - 2 cos θ 2. r= 5 sin (3θ) 3. r= 1 - 5 sin θ
r has negative values when 2 cos θ > 1, and positive values otherwise.
r has negative values when 3θ is in the second or third quadrant, and positive values otherwise.
r has negative values when sin θ > 1/5, and positive values otherwise.
To find the intervals of positive and negative r values, we need to look at the cosine function. Since the cosine function has a maximum value of 1, we have r = 1 - 2 cos θ ≥ -1. Solving for cos θ, we get 2 cos θ ≤ 2, which means that r is negative when 2 cos θ > 1 and positive otherwise.
We can rewrite the polar equation r = 5 sin (3θ) as r = 5(sin θ)(cos^2 θ)(3)^(1/2). This equation is negative when sin θ is negative, which happens in the second and third quadrants. Therefore, r is negative when 3θ is in the second or third quadrant and positive otherwise.
Similarly, we can rewrite the polar equation r = 1 - 5 sin θ as r = 5(cos θ)(sin(π/2 - θ)). This equation is negative when sin(π/2 - θ) is negative, which happens when θ is in the second and third quadrants. Therefore, r is negative when sin θ > 1/5, and positive otherwise.
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7. AFIG has vertices at F(2, 4), I(5, 4) and G(3, 2). Graph AFIG and AP'I'G' after a rotation of 90° clockwise about the origin.
Thus, the coordinates of ΔF'I'G' after a rotation of 90° clockwise about the origin. are - F'(4,-2), I'(4,-5) and G'(2,-3).
Explain about the rotation rules:A rotation is a turn made about a specific axis. Both clockwise and anticlockwise rotations are possible. Whereas the image is really the rotating image, the pre-image is the original item.
From the pre-image point, calculate the image. The listed pre-image point is (x , y). Change the x and y coordinates, then multiply this same previous y coordinate by -1 to get a 90 degree anticlockwise rotation. Use the guidelines mentioned below to calculate each rotation.
Clockwise :
90 degree rotation: (x , y) ----> (y , -x)180 degree rotation: (x , y) ----> (-x , -y)270 degree rotation: (x , y) ----> (-y , x)Given :
F(2, 4), I(5, 4) and G(3, 2)
After 90 degree rotation: (x , y) ----> (y , -x)
F'(4,-2), I'(4,-5) and G'(2,-3).
Thus, the coordinates of ΔF'I'G' after a rotation of 90° clockwise about the origin. are - F'(4,-2), I'(4,-5) and G'(2,-3).
Graphs for the both triangles are obtained.
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Correct question:
ΔFIG has vertices at F(2, 4), I(5, 4) and G(3, 2). Graph ΔFIG and ΔF'I'G' after a rotation of 90° clockwise about the origin.
A block of wood measures 6. 5 inches by 1. 5 inches by 8 inches. What is the volume of the block of wood?
Type your answer with cubic inches
The volume of the block of wood is 78 cubic inches.
What is cube?
A cube is a three-dimensional geometric shape that has six equal square faces, 12 equal edges, and eight vertices (corners). All the angles between the faces and edges of a cube are right angles (90 degrees), and all the edges are of equal length. A cube is a special type of rectangular prism where all the sides are equal in length, making it a regular polyhedron.
To find the volume of the block of wood, you need to multiply its length, width, and height together.
Volume = length x width x height
Volume = 6.5 inches x 1.5 inches x 8 inches
Volume = 78 cubic inches
Therefore, the volume of the block of wood is 78 cubic inches.
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