The job would need to pay $500 to cover Cole's expenses.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
Let's define some variables to represent the unknowns in this problem:
Let x be the number of hours that the server will work at the next job.
Let y be the total amount of money that Cole will make from the next job.
With these variables, we can set up a system of equations:
The cost of the equipment and server hire is $100 plus the server's hourly wage multiplied by the number of hours worked:
100 + 16x = total cost
The amount that Cole will make from the next job is the base pay of $50 plus the server's hourly wage multiplied by the number of hours worked:
y = 50 + 18x
We want to find the value of y that will make up for the $100 expense. In other words, we want to find the value of x that satisfies the equation:
total cost = y
Substituting the second equation into the first equation, we get:
100 + 16x = 50 + 18x
Solving for x, we get:
x = 25
Substituting x = 25 into the second equation, we get:
y = 50 + 18(25) = 500
Therefore, the job would need to pay $500 to cover Cole's expenses.
We can graph the two equations to visualize the solution:
y = 50 + 18x y = 100 + 16x
-------------------- --------------------
x = 0 | 50 | | 100 |
| | | |
| | | |
| | | |
| | | |
-------------------- --------------------
25 25
The point where the two lines intersect is (25, 500), which represents the solution to the system of equations.
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limit (2n)! as n goes to 0.
The limit of (2n)! as n goes to 0 does not exist.
What is Limit?Limits are a fundamental concept in mathematics that describe the behavior of a function as the input variable approaches a certain value, either from one or both sides. They are used to determine values that a function can get arbitrarily close to but not necessarily equal to.
The limit of (2n)! as n goes to 0 does not exist, as the factorial function is not defined for non-negative integers less than 1. The factorial function is defined as the product of all positive integers up to and including the argument. Therefore, for non-negative integers less than 1, the factorial function is undefined. The limit does not exist because the function is undefined for the given value of n.
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Prove that Limit (2n)! as n goes to 0 does not exist.
ASAP JUST ONE QUESTION ASAP ASAP ASAP
Number 5
Answer:
54 degrees
Step-by-step explanation:
Any angle subtended by the angle is twice the angle subtended by the same angle.
Or m<LMP =2m<LNM.
So m<LNM = 108/2 = 54 degrees.
in a hurry need help on these questions
The length of the ramp is approximately 4.95 meters and the angle the ladder makes with the ground is approximately 58.21 degrees.
Solving the equationTo solve x^2 + 8x - 20 = 0 using the Zero Product Property, we first need to factor the quadratic equation into two linear factors:
So, we have
(x + 2)(x - 10) = 0
This gives
x = -2 and x = 10
The length of the rampTo find the length of the ramp, we can use the trigonometric ratio of tangent.
We know that the vertical height (opposite side) of the ramp is 1.8 meters and the angle between the ramp and the ground (angle of elevation) is 20
So, we have
tan(20) = opposite / adjacent
tan(20) = 1.8 / adjacent
This gives
adjacent = 1.8/tan(20)
Evaluate
adjacent = 4.95
Therefore, the length of the ramp is approximately 4.95 meters.
The angle with the groundWe know that the ladder is 20 feet long and reaches a point 17 feet up the wall.
Let the angle the ladder makes with the ground be θ.
Using the trigonometric ratio of sine, we have:
sin(θ) = opposite / hypotenuse
sin(θ) = 17 / 20
Taking the arc sine of both sides, we get:
θ = sin^(-1)(17/20)
Using a calculator, we get:
θ ≈ 58.21 degrees
Therefore, the angle the ladder makes with the ground is approximately 58.21 degrees.
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Calculate the difference between the offensive and defensive
Offensive is 81.8 and defensive is 31.57
Answer:
50.23
Step-by-step explanation:
To calculate the difference between the offensive and defensive values, we simply subtract the defensive value from the offensive value:
81.8 - 31.57 = 50.23
The difference between the offensive and defensive values is 50.23.
What is the measure of DE?
Answer: 20
Step-by-step explanation:
Trigonometry dba
100 points need in 1 hour
Answer: I thank it is 200 point in 2 hour
Step-by-step explanation:
The table shows the relationship between the depth, in meters, of a submarine and the time, in
minutes, since it started a dive.
The relation between time and depth is not prοpοrtiοnal as 2/100 ≠ 4/180 ≠ 6/260 ≠ 8/340.
What is prοpοrtiοnal relation?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality"
To solve questions that involve a table showing the relationship between two variables, such as depth and time in this case, you may want to consider the following steps:
A quick check οf table values shοws the relatiοnship is nοt prοpοrtiοnal:
100/2 = 50 ≠ 45 = 180/4
That is, the ratiοs οf table values are nοt cοnstant.
2/100 ≠ 4/180 ≠ 6/260 ≠ 8/340
Therefore, the relation between time and depth is not prοpοrtiοnal.
When the values are graphed, the line thrοugh the pοints dοes nοt intersect the οrigin. This is further indicatiοn the relatiοnship is nοt prοpοrtiοnal.
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Complete question:
Suppose 31% of women would prefer to drink tea over coffee. In a random sample of 7 women, what is the probability that the number of women that would prefer to drink tea over coffee is within 1 standard deviation of the mean?
Group of answer choices
0.2342
0.500
0.5519
0.6827
0.786
0.2342 is the probability that the number of women that would prefer to drink tea over coffee is within 1 standard deviation of the mean
How to find the probabilityLet's start by finding the mean and standard deviation of the number of women who prefer to drink tea over coffee in a sample of 7 women.
The mean is given by:
μ = np
where n is the sample size and p is the probability of success (the proportion of women who prefer tea over coffee).
So, for this problem, μ = 7 * 0.31 = 2.17
The standard deviation is given by:
σ = sqrt(np(1-p))
where sqrt denotes the square root.
So, for this problem, σ = sqrt(7 * 0.31 * (1 - 0.31)) = 1.22
2.17 - 1.22, 2.17 + 1.22
= 0.95, 3.39
using binomial probability
p^x * 1 - p
= 0.31 * 7 x 0.108
= 0.2342
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The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an
elephant weighs 3300 pounds on Planet A, find the elephant's weight on Planet B.
Multiply and combine like terms to determine the product of these polynomials. (2x – 3)(8 + 3x)( 5 - x)
Answer: [tex]-6x^3+23x^2+59x-120[/tex]
Step-by-step explanation:
(2x – 3)(8 + 3x)( 5 - x)
To multiply this polynomial we can break it down into two steps.
First, lets multiply (2x – 3)(8 + 3x) from the polynomial (2x – 3)(8 + 3x)(5 - x).
Its best to rearrange the x in the parenthesis, so it can look and be much easier: (2x – 3)(8 + 3x) -> (2x – 3)(3x + 8)
Now lets multiply it out: (2x – 3)(3x + 8)
[tex]6x^2+16x-9x-24[/tex]
After multiplying it out, combine like terms:
[tex]6x^2+7x-24[/tex]
Now take this polynomial and multiply the remaining factor, (5 - x)
[tex](-x + 5)(6x^2+7x-24)\\\\-6x^3+-7x^2+24x+30x^2+35x-120[/tex]
Now lets combine like terms!
[tex]-6x^3+23x^2+59x-120[/tex]
So the answer is: [tex]-6x^3+23x^2+59x-120[/tex]
Much help is needed asap!
1. Identify each premise and the conclusion in the following argument. Determine whether the argument is an example of inductive or deductive reasoning.
Our house is made of brick. Both of my next-door neighbors have brick houses. Therefore, all houses in our neighborhood are made of brick.
Premises:
Conclusion:
Inductive or deductive?
2. Use the list of equations and inductive reasoning to predict the next multiplication fact in the list:
37 × 3 = 111, 37 × 6 = 222 , 37 × 9 = 333, 37 × 12 = 444 , ....
Use inductive reasoning to determine the probable next number in the list below. An arithmetic sequence adds or subtracts a fixed amount (the common difference) to get the next term in the sequence.
5, 9, 13, 17, 21, 25, 29, .....
3. Successive Differences
Use the method of successive differences to find the next number in the sequence.
(a) 20, 31, 45, 62, 82, ... (Hint: Start with 31 - 20 = 11, use the subsequent term subtract the previous term)
(b) 8, 6, 3, 1, 2, 8, 21, ... (Hint: start with 6 - 8= -2, use the subsequent term subtract the previous term)
4. Find the sum using the special sum formula.
1 + 2 + 3 + ... + 48
5. Use the formula given on the first section to find
a) the sixth pentagonal number.
b) the eighth triangular number.
6. A vending machine accepts nickels, dimes, and quarters. Exact change is needed to make a purchase. How many ways can a person with four nickels, three dimes, and two quarters make a 30-cent purchase from the machine?
7. Ronnie goes to the racetrack with his buddies on a weekly basis. One week he tripled his money, but then lost $12.
He took his money back the next week, doubled it, but then lost $40. The following week he tried again, taking his money back with him. He quadrupled it, and then played well enough to take that much home, a total of $224. How much did he start with the first week?
8. Use inductive reasoning to determine the units digit (or ones digit):
Example: Use inductive reasoning to determine the units digit of the number
3^55 .
The question is not about giving the exact value, but rather than applying the inductive reasoning to figure out the units digit.
The units digit in base 3 are 3, 9, 7, 1, 3, 9, 7, 1, ... repeating meaning that every power that is divisible by 4 will end in 1. 56 is divisible by 4. Using this inductive reasoning 3 to the 56th power would end in a 1, then moving backward to the 55th power would give you a units digit of 7. This is inductive reasoning because we are using the smaller sample size of 4 repeating unit digits to make broad theories about all powers of 3.
Another similar approach: The units digit in base 3 are 3, 9, 7, 1, 3, 9, 7, 1, ... repeating. If the power is a multiple of four, the units digit is 1. Power 52 is a multiple of 4 and it's close to power 55.
Power 52 ends with units digit of 1, next 53 ends with 3, 54 ends with 9, and 55 ends with 7
(a) The ones digit (also called the units digit) in 2^4000 . The question is not about giving the value to the expression,
but rather than applying the inductive reasoning to figure out the units digit. The answer is just a single digit.
(b) The units digit of the number 3^41
9. Kathy stood on the middle rung of a ladder. She climbed up 2 rungs, moved down 5, and then climbed up 6. Then she climbed up the remaining 4 rungs to the top of the ladder. How many rungs are there in the whole ladder?
10. If you ask Batman’s nemesis, Catwoman, how many cats she has, she answers with a riddle: “Five-sixth of my cats plus seven.” How many cats does Catwoman have?
11. A birdhouse for swallows can accommodate up to 8 nests. How many birdhouses would be necessary to accommodate 58 nests?
12. Use the circle graph below to determine how many of the 140 students made an A or a B.
(see picture of circle graph attached below)
13. The bar graph shows the number of cups of coffee, in hundreds of cups, that a professor had in a given year.
a) Estimate the number of cups in 2004.
b) What year shows the greatest decrease in cups?
(see picture of bar graph below)
14. The line graph shows the average class size of a first grade class at a grade school for years 2001 through 2005. (see picture line graph below)
In which years did the average class size increase from the previous year?
How much did the average size increase from 2001 to 2003?
The premise is that both of my next-door neighbors and I have brick homes. So, all of the homes in our area are brick construction. A good illustration of inductive reasoning is this.
How to use equations to answer the rest?2. Given that the pattern appears to be multiplying by 3, then 6, then 9, then 12, and so on, the next multiplication fact is probably 37 x 15 = 555.
3.
(A) The number 101 comes next in the list.
(b) The following digit in the series is -10.
4. According to the formula n(n+1)/2, the first n positive integers are added together. Hence, 48(48+1)/2 = 1176 is the sum of the first 48 positive integers.
5.
(A) The formula n(3n-1)/2 yields the nth pentagonal number. Thus, 6(3x6-1)/2 = 91 is the sixth pentagonal number.
(b) The expression n(n+1)/2 yields the nth triangular number. Hence, 8(8+1)/2 = 36 is the eighth triangular number.
6. There are ten ways to use the four nickels, three dimes, and two quarters to make a 30-cent purchase from the vending machine.
7. The first week, Ronnie had $12 to his name.
8.a.The ones digit in the number 24000 is 6.
(b) 341's units digit is 3.
9. 19 rungs make up the ladder.
10. Catwoman owns 42 felines.
11. 58 nests would require 8 birdhouses, plus 2 additional nests.
12. A total of 60 pupils received an A or a B.
13.
(a) 550 cups are anticipated to be consumed in 2004.
(b) The year 2003 exhibits the biggest decline in cups.
14. Since 2001, the typical class size has risen.
15. During 2001 and 2002, as well as between 2004 and 2005, the average class size increased. From 2001 to 2003, the average class size grew by two pupils.
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In need of help ! Thank you
Since the two equations represent the same line, there are infinitely many solutions to the system.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, each containing one or more terms, separated by an equal sign. The terms may contain variables, constants, and mathematical operators such as addition, subtraction, multiplication, division, exponentiation, and roots. Equations are used to represent relationships between variables and to solve problems in mathematics, science, engineering, and many other fields. They can be classified based on their degree, number of variables, and the types of functions they involve. Linear equations, for example, involve only first-degree terms and are used to represent straight lines; quadratic equations involve second-degree terms and are used to represent parabolas.
Here,
To determine whether the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point, we can first put the equations in slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept.
10y + 8x = 10
10y = -8x + 10
y = (-4/5)x + 1
5y - 5 = -4x
5y = -4x + 5
y = (-4/5)x + 1
Notice that the two equations have the same slope of -4/5 and the same y-intercept of 1. Therefore, the two lines are identical and intersect at every point on the line.
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Rewrite in simplest rational exponent form √x-4x Show each step of your process.
Answer:
[tex]x {}^{ \frac{5}{8} } [/tex]
Step-by-step explanation:
[tex]1. \: \sqrt{x {}^{ \frac{5}{4} } } \\ 2. \: x {}^{ \frac{5 \times 1}{4 \times 2} } \\ 3. \: x {}^{ \frac{5}{4 \times 2} } \\ 4. \: x {}^{ \frac{5}{8} } [/tex]
Use the graph to answer the question.
Graph of a polygon ABCD with vertices at 6 comma 3, 15 comma 3, 15 comma 9, 6 comma 9 and a second polygon A prime B prime C prime D prime with vertices at 2 comma 1, 5 comma 1, 5 comma 3, 2 comma 3.
Determine the scale factor used to create the image.
3
one third
one half
2
The distance between point A (6,3) and A' (2,1) is half of the original distance between A and B (6,3) and (15,3). Therefore, the scale factor is one half.
To determine the scale factor used to create the image of the second polygon A'B'C'D' from the original polygon ABCD, we can compare the side lengths of the two polygons.
The scale factor used to create the image is one half. This is because the distance between each vertex in the original polygon and the corresponding vertex in the image polygon is half of the original distance. For example,
Let's take the horizontal sides:
Side AB in polygon ABCD has length 15 - 6 = 9 units.
Side A'B' in polygon A'B'C'D' has length 5 - 2 = 3 units.
Now, we can find the scale factor by dividing the side length of A'B' by the side length of AB:
Scale factor = (A'B') / (AB) = 3 / 9 = 1/3
So, the scale factor used to create the image is one third.
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Question 1 of 5
You're putting together a student poetry book and want to create it as an EPUB book that you
can read in the Books app. How can you make an EPUB book and open it in the Books app?
Identify the correct order of the following steps.
1 Create a new document using a book template.
2 Choose Copy to Books.
3 Enter EPUB information, then tap Export.
4 Tap Export, then choose EPUB.
5 Add text to the book, then tap the More button in the upper-right corner
Choose Download as ePub or Download as PDF from the Personal Books screen's export icon. The Apple Ibooks icon will say Transfer to Books when you select Open in.
What, in plain terms, are books?A book is a device for storing data in the form either writing or images. Books are often made up of several pages that are bound together and covered in reeds, parchment, vellum, or paper.
Why are books essential to our lives?Books are important in life, especially for young people. Reading books helps pupils learn more, improves their intelligence, and raises their awareness of the diverse nations and civilizations throughout the world.
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The correct order of the steps is:
1. Create a new document using a book template.
2. Add text to the book, then tap the More button in the upper-right corner.
3. Enter EPUB information, then tap Export.
4. Tap Export, then choose EPUB.
5. Choose Copy to Books to open the EPUB book in the Books app
.Your answer: To create an EPUB book and open it in the Books app, follow these steps in the correct order: 1. Create a new document using a book template. 2. Add text to the book, then tap the More button in the upper-right corner. 3. Tap Export, then choose EPUB. 4. Enter EPUB information, then tap Export. 5. Choose Copy to Books.
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Write the expression as a product
1-(2x-1)^2
Answer: -4x(x-1)
Step-by-step explanation:
Since both are perfect squares just factor.
Remika just got a new job!
• The job pays $8.50 per hour
During the first year, every 4 months there is a 2% raise in hourly pay.
At the end of one year, how much would Remika be paid hourly, to the nearest cent?
●
Do not enter the dollar sign ($).
Answer: 9.01
Step-by-step explanation: 8.5*0.02= 0.17 *3= 0.51+8.5=9.01
Let A={1,2,3,4,5,6,7 } and let R be the “has the same parity as“ relation on A. Write down R in set listing notation.
The answer of the given question based on the relation is R = {(1,1), (3,3), (5,5), (2,2), (4,4), (6,6), (7,7), (1,3), (3,1), (1,5), (5,1), (1,7), (7,1), (2,4), (4,2), (2,6), (6,2), (3,5), (5,3), (3,7), (7,3), (4,6), (6,4), (5,7), (7,5)}.
What is Set listing notation?Set listing notation is a way to represent a set by listing all of its elements between curly braces { }. If a set has a large or infinite number of elements, it may not be practical to list all the elements. In such cases, we can use set-builder notation to describe the set using a condition or a rule.
The "has the same parity as" relation on set A means that any two elements in A are related if they have the same parity (either both even or both odd).
So, we can write the relation R as a set of ordered pairs where each pair consists of two elements that have the same parity.
R = {(1,1), (3,3), (5,5), (2,2), (4,4), (6,6), (7,7), (1,3), (3,1), (1,5), (5,1), (1,7), (7,1), (2,4), (4,2), (2,6), (6,2), (3,5), (5,3), (3,7), (7,3), (4,6), (6,4), (5,7), (7,5)}
In this set, the ordered pair (x, y) indicates that x and y have the same parity. For example, (1, 3) is in R because 1 and 3 are both odd. Similarly, (2, 4) is in R because 2 and 4 are both even.
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With the aid of appropriate diagrams, compare and contrast the demand for several or multiple variable inputs under perfect competitive and imperfect markets?
In a perfectly competitive market, firms are price takers, meaning they have no market power and must accept the market price for their output.
What is market price?A market price is the price at which a good or service is sold in a specific market. The forces of supply and demand determine market price in a competitive market.
Firms in a perfectly competitive market are price takers, which means they lack market power and must accept market prices for their output.
As a result, in a perfectly competitive market, the demand for multiple variable inputs is derived from the marginal product of each input.
The marginal product is the extra output generated by adding one more unit of an input while holding all other inputs constant.
Thus, the value of the marginal product, which is the marginal product multiplied by the market price of the output, is the demand for an input.
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Solve for s.
3s + 1 = 10
S=
Submit
Answer:
S ========================= 9
because 9+ 1= 10
simple
Answer:
s=3
Step-by-step explanation:
3s+1 = 10
To solve for s in this two step equation, we must first subtract 1 from each side.
3s+1-1 = 10-1
3s = 9
Then divide by 3 on each side.
3s/3 = 9/3
s=3
5(2 +2f)
U need to simplify this expression how do I get the answer and what is the answer pls help I’m so stuck on this
Suppose the amount of time it takes a Capt. Rigg, a pilot for a national airline, to land a plane from announcement to touch down is uniformly distributed from 0 to 25 minutes.
a) Find the probability that, for a randomly selected flight, it takes Capt. Rigg at least 5 minutes to land the plane after the announcement. Round to 1 decimal place.
c) What is the probability that it will take Capt. Rigg exactly 15 minutes to land a plane?
A) Let X be the amount of time it takes Capt. Rigg to land a plane from announcement to touch down. We know that X has a uniform distribution from 0 to 25 minutes. The probability that it takes at least 5 minutes to land the plane is equal to the probability that X is greater than or equal to 5:
P(X ≥ 5) = (25-5)/(25-0) = 20/25 = 0.8
So the probability that, for a randomly selected flight, it takes Capt. Rigg at least 5 minutes to land the plane after the announcement is 0.8.
b) Since X has a continuous uniform distribution, the probability that it takes exactly 15 minutes to land a plane is 0.
Given vectors u = (8, 1) and v = (-7, -1), find the sum u + v and write the
result in component form.
According to the solution we have come to find that, The sum of the given vectors u and v is (1, 0).
What is vector?In mathematics, a vector is a mathematical object that has both magnitude (or length) and direction. It is usually represented as a directed line segment, where the length of the segment corresponds to the magnitude of the vector, and the direction of the segment represents the direction of the vector.
A vector can be specified in terms of its components or coordinates, which are typically expressed as a sequence of numbers or symbols. For example, a two-dimensional vector can be written as (x, y), where x and y are the components of the vector along the x-axis and y-axis, respectively.
To find the sum of two vectors, we simply add their corresponding components.
So, for the given vectors u = (8, 1) and v = (-7, -1), their sum u + v can be computed as:
u + v = (8, 1) + (-7, -1) = (8 - 7, 1 - 1) = (1, 0)
Therefore, the sum of the given vectors u and v is (1, 0).
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A manufacturer sells its products to a wholesaler for $73 each. The
wholesaler then marks up those products and sells them to retailers
for $80.43. What is the wholesaler's markup rate? Round to the
nearest hundredth.
The wholesaler's markup is the difference between the selling price and the cost price, which is $80.43 - $73 = $7.43.
The markup rate can be found by dividing the markup by the cost price and multiplying by 100 to get a percentage:
markup rate = (markup / cost price) x 100%
markup rate = ($7.43 / $73) x 100%
markup rate = 10.17%
Therefore, the wholesaler's markup rate is 10.17%, rounded to the nearest hundredth.
Find√b2-4ac when a = 2, b = −5, c = -3.
Hello, I was happy to solve the problem. If you find a bug, post in the comments or click on the report, I will see it and try to fix it as soon as possible.
The answer to this problem: 7
Anna is saving to buy some souvenirs on a family vacation. She has already saved $125, and she saves another $2 from her allowance every day.
Formulate and then graph the equation that models the total amount Anna saves, y, in terms of the number of days she adds to her savings, x.
The equation that models the total amount Anna saves, y, in terms of the number of days she adds to her savings, x, can be represented as y = 2x + 125, where 2x represents the total amount she saves from her allowance and 125 represents the initial amount she saved.
This is a linear equation in slope-intercept form, where the slope of the line is 2, indicating that she saves $2 per day, and the y-intercept is 125, indicating that she had already saved $125 before starting to save from her allowance. To graph this equation, we can plot the y-intercept at (0, 125) and use the slope to find other points on the line. For example, after 5 days, she would have saved y = 2(5) + 125 = 135 dollars, giving us the point (5, 135). Plotting this point and connecting it with the y-intercept will give us a straight-line graph.
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Find the missing side lengths. Leave your answers as radicals in simplest form
Answer:
a = 3√2;
b = 3
Step-by-step explanation:
Use trigonometry:
[tex] \tan(45°) = \frac{b}{3} [/tex]
Cross-multiply to find b:
[tex]b = 3 \times \tan(45°) = 3 \times 1 = 3[/tex]
Use the Pythagorean theorem to find a:
[tex] {a}^{2} = {3}^{2} + {b}^{2} [/tex]
[tex] {a}^{2} = {3}^{2} + {3}^{2} = 9 + 9 = 18[/tex]
[tex]a > 0[/tex]
[tex]a = \sqrt{18} = \sqrt{9 \times 2} = 3 \sqrt{2} [/tex]
The triangle below is equilateral. Find the length of side
�
x to the nearest tenth.
Value of side x in equilateral triangle is 6units.
Define equilateral triangleAn equilateral triangle is a type of triangle in which all three sides are of equal length. Equilateral triangles are also equiangular, meaning all three angles are of equal measure and are each 60 degrees. Because all three sides and angles are equal, equilateral triangles are symmetric about their center point, and their three medians, altitudes, and angle bisectors are all the same line.
Area of equilateral triangle = √3/4×a²
Given side length=12
So, area of equilateral triangle =√3/4×12²=62.35383
We know that
Area of triangle= ½×base×height
Given
Base=12
let height of triangle be=y
Area=½×12×y
62.35383=½×12×y
y=10.39
Using pythagoras' theorem,
c²=a²+b²
122=x²+10.392
x=√144-107.95
x=6
Hence, value of side x in equilateral triangle is 6units.
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find geomatic series for a1
the first term of the geometric series is approximately 105.294.
How to solve the problem?
The formula for the sum of a geometric series is given by:
Sn = a1(1 - rⁿ)/(1 - r)
where a1 is the first term, r is the common ratio, n is the number of terms, and Sn is the sum of the series.
We are given that Sn = 3045, r = 2/5, and An = 120, where An is the nth term of the series. We can use these values to solve for a1.
First, we can use the formula for the nth term of a geometric series:
An = a1 * rⁿ⁻¹
Substituting An = 120 and r = 2/5, we get:
120 = a1 * (2/5)ⁿ⁻¹
We also know that the sum of the series is Sn = 3045. Substituting the formula for Sn and solving for n, we get:
3045 = a1(1 - (2/5)ⁿ)/(1 - 2/5)
12180 - 4(2/5)ⁿ = 5a1
a1 = (12180 - 4(2/5)ⁿ)/5
Now we can substitute this expression for a1 into the equation we obtained for An:
120 = [(12180 - 4(2/5)ⁿ)/5] * (2/5)ⁿ⁻¹
Simplifying and solving for n, we get:
n = log(12/5) / log(2/5)
Substituting this value of n back into the expression for a1, we get:
a1 = (12180 - 4(2/5) power (log(12//log(2/5))) / 5
Using a calculator, we can evaluate this expression to get:
a1 ≈ 105.294
Therefore, the first term of the geometric series is approximately 105.294.
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Colby’s art class is 50 minutes. She spends 21 minutes cutting paper and the rest of the time making a collage. How much time did Colby spend making her collage?
Colby spends 29 minutes making her collage.
50 is the total amount of minutes and 21 minutes is a part of that total.
This means we have to subtract.
50 - 21 = 29.