Answers
The values of x and y are:
x = 3.16
y = 4.47
What is trigonometry?Trigonometry is a topic which deals with the relation between angles and sides of a right angled triangle. It can be used to determine the value of the unknown in a given question. The basic functions in trigonometry are: sine, cosine and tangent.
In the given diagram, we have;
i. To determine the value of x,
Tan θ = opposite/ adjacent
Tan 45 = x/ (10)^1/2
x = Tan 45*(10)^1/2
= 3.16
x = 3.16
ii. To determine the value of y, we have;
Cos θ = adjacent/ hypotenuse
Cos 45 = (10)^1/2 / y
y = (10)^1/2 / Cos 45
= 4.47
y = 4.47
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Related Questions
you lease a car vauled at 23495 for 3 years
at 429.95/month
Answers
The amount of interest paid over the 3-year lease is $4,643.64 for a car.
What is a monthly payment?A monthly payment is a payment made every month to disburse loans or advances.
First, we need to calculate the total amount paid over the 3-year lease.
The monthly payment is $429.95, and there are 36 months in the lease, so:
Total lease payments = 36 x $429.95 = $15,478.20
The down payment of $500 is separate from the lease payments, so we don't include it in this calculation.
Next, we need to calculate the interest paid over the 3-year lease. We are told that interest is 30% of the monthly payment, so:
Monthly interest = 30% of $429.95 = $128.99
To find the total interest paid over the 3-year lease, we can simply multiply the monthly interest by the number of months in the lease:
Total interest paid = 36 x $128.99 = $4,643.64
Therefore, the amount of interest paid over the 3-year lease is $4,643.64.
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The question seems incomplete, the complete question would be as:
You lease a car valued at 23,495 for 3 years at $429.95/month with a $500 down payment. If interest is 30% of the payment, how much interest is paid over the 3 years?
what is 600 hours in days?
Answers
Answer: 25 days
Step-by-step explanation:
Convert the unit for 600 hours
1 day = 24 hours
divide 600 hours with 24 hours as 24 hours = 1 day
600 ÷ 24 = 25
Marco's charges an additional fee for toppings, but all toppings cost the same. Kevin got pepperoni, banana peppers, and black olives on his pizza for a cost of $15.74. Brian ordered mushrooms and eggplant on his pizza and paid $14.49. Using this information, write an equation for the cost of a pizza, C, as a function of the toppings, t, ordered.
Answers
Answer: Let's use x to represent the cost of each topping. Then, the cost of a pizza with t toppings can be expressed as:
C = x * t + 15
We know that Kevin's pizza with 3 toppings cost $15.74, so we can write an equation using this information:
15.74 = 3x + 15
Solving for x, we get:
x = (15.74 - 15) / 3 = 0.74
So, each topping costs $0.74. Now we can use the information about Brian's pizza to check our answer:
14.49 = 2x + 15
Substituting x = 0.74, we get:
14.49 = 2 * 0.74 + 15
Which simplifies to:
14.49 = 1.48 + 15
This confirms that x = 0.74 is the correct cost for each topping. Therefore, the equation for the cost of a pizza as a function of the toppings ordered is:
C = 0.74t + 15
Step-by-step explanation:
Hi can someone help me please and thank you
Answers
Chuck bought 13 pounds of gummy worms.
Each pound cost $1.95. How much did Chuck
spend on gummy worms?
Answers
Answer:
Step-by-step explanation:
1.95 times 13= 25.35
Consider these functions:
f(x)=r² + 4
g(r)=9r - 12
What is the value of g(f(x))?
Answers
The value of g(f(x)) is 9r² + 24.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given are two functions.
f(r) = r² + 4
g(r) = 9r - 12
Composition of two functions f and g is the third function h such that f(g(x)) = h(x).
g(f(x)) = g(r² + 4)
= 9 (r² + 4) - 12
= 9r² + 36 - 12
= 9r² + 24
Hence the new function which is the composition of the two given function is 9r² + 24.
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SOMEONE PLS HELP FASTT
pic below
Answers
Answer:
the correct answer is Tim
Li-Ming has 20 ounces of lettuce, 12 ounces of chopped nuts, and 7 ounces of cranberries. What is the total weight of the salad?
Answers
Answer: 39
Step-by-step explanation: 20 + 12+7
What is truth table in discrete mathematics?
Answers
In discrete mathematics, a truth table is a table that lists all possible combinations of truth values for a given set of logical variables and shows the resulting truth values of a compound proposition.
In discrete mathematics, a truth table is a table that lists all possible combinations of truth values (usually either true or false) for a given set of logical variables and shows the resulting truth values of a compound proposition (a logical expression formed by combining the variables using logical operators such as AND, OR, and NOT). Each row of the truth table represents one possible combination of truth values, and the columns represent the variables and the various intermediate steps of the logical calculation. Truth tables are often used to determine the truth values of complex propositions and to test the validity of logical arguments.
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Consider the distance formula d = rt.
A boat travels 5 hours at a constant speed of 45 km/h. How far does the boat travel? Show your work
i will give brainlyst
Answers
Answer: 225 km/h
Step-by-step explanation: If distance = rate multiplied by time, then you are just multiplying 45 x 5.
45 x 5= 225
In science class, Mr. Brodell's students were directed to weigh a 400- gram mass on the balance scale. Erika weighed the object and reported 420 grams . What is the percent error of the weight of Erika's object
Answers
The percent error of the weight of Erika's object is given as follows:
5%.
How to obtain the percent error?The percent error is obtained applying the proportions in the context of the problem.
A proportion is applied as the percent error is calculated as the division of the error by the actual amount, divided by 100%.
The parameters for this problem are given as follows:
Error: 420 - 400 = 20 grams.Actual amount: 400 grams.Hence the percent error is given as follows:
20/400 x 100% = 5%.
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pls help me i need this answer
solve for p pls
Answers
For the given algebraic expression, the value of p is 0.2 .
Linear Expression
A linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=x+9. Where:
m= the slope.
b= the constant term that represents the y-intercept
For the given example: m=1 and b=9.
The exercise presents the following algebraic expression:
14=p*70 and it asks you the value of p. Thus, you should divide the number 14 by 70. See below.
14=p*70
p=14/70
p=2/10
p=0.2
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Milly bakes cookies to sell for a fundraiser. Her goal is to raise $500. The first day, she reaches 38 of her goal. On the second day, she raises 50% of the remaining money needed to meet her goal. How much money does Milly still need to make to reach her goal?
Answers
Answer:
$231
Step-by-step explanation:
500-38=462
50% of 462= 231
So she needs to make $231 more to reach her goal
Please help with the question in the image
Answers
The measure of arc FB is 68 degrees.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
In the given circle BE is a semicircle
The measure of arc FC is 104 degrees.
We need to find the measure of arc FB
From the figure the measure of arc BC is 36 degrees
FC=FB+BC
104=36+FB
Substitute 36 from both sides
104-36=FB
68 degrees =FB
Hence, the measure of arc FB is 68 degrees.
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Write an equation that represent the linear relationship between x-values and y-values?
X
0
2
4
6 y -1
4
9
14
Answers
Answer: y = 5x - 1 ( look at the image for the solution )
Step-by-step explanation:
What is Math 220 at UIUC?
Answers
Math 220 at UIUC is a calculus course offered at the University of Illinois at Urbana-Champaign.
It is designed to introduce students to the fundamental concepts of calculus, including limits, differentiation, and integration. The course also covers applications of these concepts to real-world problems, such as optimization and modeling.
Students are expected to have a strong foundation in algebra and trigonometry before taking Math 220. The course is typically taken by students in the College of Engineering and the College of Liberal Arts and Sciences.
The textbook for the course is the 8th edition of Calculus: Early Transcendentals by James Stewart. Additionally, Math 220 students must obtain access to the online homework system MyMathLabPlus and a copy of the textbook (hard copy or eBook).
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ASAP PLEASE, WHOEVER ANSWERS ALL 7 CORRECTLY AND QUICKLY WILL GET THANKS, 5 STARS, AND BRANLIEST!!!
Question 1(Multiple Choice Worth 2 points)
(Linear Functions LC)
Which of the following graphs represents a linear function?
coordinate plane with a graph drawn that passes through the points 2 comma negative 2 and 2 comma negative 1 and 2 comma 0
coordinate plane with a graph drawn that passes through the points negative 1 comma 0 and 0 comma negative 2 and 1 comma negative 4
coordinate plane with a graph that passes through the points negative 2 comma 0 and 0 comma negative 4 and 2 comma 0
coordinate plane with a graph that passes through the points negative 3 comma 0 and 0 comma negative 3 and 3 comma 0 and 0 comma 3
Question 2(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the data in the following table represents a linear or nonlinear function?
x y
−4 4
−1 2.5
0 2
4 0
The table represents a nonlinear function because the graph shows a rate of change that is decreasing.
The table represents a linear function because the graph shows a rate of change that is increasing.
The table represents a nonlinear function because the graph does not show a constant rate of change.
The table represents a linear function because the graph shows a constant rate of change.
Question 3(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which of the following tables represents a linear function?
x −2 −1 0 1 2
y 5 2 1 2 5
x −2 −1 0 1 2
y 5 3 1 −1 −3
x 3 3 0 3 3
y −2 −1 0 1 2
x 0 1 2 3 4
y 0 −1 2 −3 4
Question 4(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the following graph represents a linear or nonlinear function?
coordinate plane with a graph that passes through the points negative 4 comma 0 and negative 2 comma negative 1 and 0 comma negative 2
The graph represents a linear function because there is a constant rate of change.
The graph represents a linear function because the rate of change is not constant.
The graph represents a nonlinear function because there is a constant rate of change.
The graph represents a nonlinear function because the rate of change is not constant.
Question 5(Multiple Choice Worth 2 points)
(Linear Functions LC)
Which of the following equations represents a linear function?
2x − 4 = 6
x = −2
y equals one half times x squared
y equals two thirds times x plus 4
Question 6(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the equation y = 3x2 represents a linear or nonlinear function?
The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a linear function because its graph contains the points (−1, 3), (0, 0), and (1, 3), which are on a straight line.
The equation represents a nonlinear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a nonlinear function because its graph contains the points (−1, 3), (0, 0), and (1, 3), which are not on a straight line.
Question 7(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the following table represents a linear or nonlinear function?
x −2 −1 0 1 2
y −4 −2 0 2 4
The table represents a nonlinear function because there is not a constant rate of change in the input values.
The table represents a nonlinear function because there is not a constant rate of change in the output values.
The table represents a linear function because there is a constant rate of change in the input and output values.
The table represents a linear function because there is not a constant rate of change in the input and output values.
Answers
Answer:
Step-by-step explanation:
1) = b im doing the test.
2)=The correct option is C) A coordinate plane is shown with a line crossing through the y axis at negative 3 and the x axis at 2.
3) its a
4)b
Using trigonometric identities to simplify the following expression:
tan(θ)cot(θ)
Answers
Answer:
Step-by-step explanation:
The expression tan(θ)cot(θ) can be simplified using the trigonometric identity:
tan(θ) = sin(θ) / cos(θ)
cot(θ) = cos(θ) / sin(θ)
So,
tan(θ)cot(θ) = (sin(θ) / cos(θ)) x (cos(θ) / sin(θ))
= sin(θ) x cos(θ) / (cos(θ) x sin(θ))
= sin^2(θ) / sin^2(θ)
= 1
Therefore, tan(θ)cot(θ) = 1.
what is 8.75 as a fraction?
Answers
The number 8.75 is equivalent to the fraction 35/4 in its simplest form.
To convert 8.75 to a fraction, we can write it as a fraction with a denominator of 1. We then multiply both the numerator and denominator by 100 to get rid of the decimal point. This gives us:
8.75 = 8.75/1
= 875/100
Next, we want to get rid of the decimal point, which we can do by multiplying both the numerator and denominator by a power of 10 that moves the decimal point of the numerator to the right until it disappears. In this case, we can multiply both the numerator and denominator by 100, which gives us:
8.75/1 x 100/100 = 875/100
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 25. This gives us:
875/100 = (875/25) / (100/25) = 35/4
Therefore, we conclude that 8.75 is equivalent to the fraction 35/4 in its simplest form.
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8 77/80 as a decimal
Answers
Answer: 8.875
Step-by-step explanation:
8 77/88
(77 ÷ 88) + 8
0.875 + 8
8.875
help with this theres a lot of points in it for you
Answers
The measure of angles from the given figure A, B, C, D, E, F, G and H are 61°, 130°, 58°, 50°, 84°, 85°, 146° and 145° respectively.
What is an angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
1) By using the angle sum property of triangle
∠A+58°+61°=180°
∠A+119°=180°
∠A=61°
2) ∠B+50°=180° (Adjacent angles)
∠B=130°
3) ∠A=∠C (Angles of same segment)
∠C=58°
4) ∠D=50° (Vertically opposite angles)
5) 111°+90°+75°+∠E=360° (Sum of interior angles of quadrilateral)
∠E= 84°
6) 111°+84°+130°+130°+x=540° (Sum of interior angles of pentagon)
∠F=x=85°
∠F= 85°
7) 70°+50°+y=180° (angle sum property of triangle)
y=60°
70°+84°+60°+∠G=360° (Sum of interior angles of quadrilateral)
∠G=146°
8) ∠G+∠A+58°+130°+∠H=540°
146°+61°+58°+130°+∠H=540°
∠H=145°
Hence, ∠A=61°, ∠B=130°, ∠C=58°, ∠D=50°, ∠E= 84°, ∠F= 85°, ∠G=146° and ∠H=145°.
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Answer:
Step-by-step explanation:
A: 61°
B:130°
C: 58°
D: 50°
E: 84°
F: 85°
G:146°
H: 145°
How can I find a variable for 20 and 25
Answers
Answer: x/20=25
Step-by-step explanation:
You'll have to take the variable and divide it by 20 to equal 25.
How you do that is by subtracting 20 from 25, then you should get x=5, which would be your answer to the problem itself.
There are 2 questions.
Answers
Answer:
27) #3 --> 12x - 24 = 60
29) 2x^2 + x - 15
Step-by-step explanation:
27) If x represents the number of boxes, and there are 12 cookies in each box, multiplying 12 by x results in the total number of cookies Kendal bought. However, she kept 2 boxes for herself, which is the same as 2(12) = 24 cookies. Kendal ended up with 60 cookies at the party, so subtracting 24 cookies from the total number of cookies (12x) equals 60 cookies.
29) (3 + x)(2x - 5)
3 * 2x = 6x
3(-5) = -15
x * 2x = 2x^2
x(-5) = -5x
6x - 15 + 2x^2 - 5x =
2x^2 + x - 15
B - 2 is greater than equal to -1
Answers
The inequality B -2 ≥ -1 gives the value for B ≥ 1.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
B - 2 is greater than equal to -1
Writing the mathematical inequality is
B -2 ≥ -1
B ≥ -1 + 2
B ≥ 1
So, the value of B should be greater than 1.
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Which of the following is a binomial experiment?
Flipping a coin until it comes up tails
Flipping a coin until 8 heads are recorded
Flipping a coin 10 times and recording if it comes up heads
Flipping a coin by 10 different people and recording the age of each person
Answers
Flipping a coin 10 times and recording if it comes up heads is an example of binomial experiment. Option (c) is correct.
Further Explanation:
Given:
The options are follows,
(a). Flipping a coin until it comes up tails.
(b). flipping a coin until 8 heads are recorded
(c). flipping a coin 10 times and recording if it comes up heads
(d). flipping a coin by 10 different people and recording the age of each person
Explanation:
Conditions for binomial experiment are as follows,
(1). The experiment should be independent means that the probability of successive trial will not be affected by the previous trial.
(2). The experiment should have a finite number of trials.
(3). The probability of success will remain same for each trial.
(4). The experiment should have only two outcomes.
Flipping a coin has only two outcomes head or tail.
Flipping a coin 10 times and recording if it comes up heads is an example of binomial experiment. Option (c) is correct.
Option (a) is not a binomial experiment as the experiment is not for finite number of times.
Option (b) is not a binomial experiment as the experiment is not for finite number of times.
Option (c) is a binomial experiment.
Option (d) is not a binomial experiment as the experiment doesn’t have the same probability of occurrence.
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Answer details:
Grade: College
Subject: Statistics
Chapter: Binomial experiment
Keywords: binomial experiment, flipping a coin, tails, heads, recorded, 10 different people, probability, each person.
This experiment has a fixed number of trials (10), each trial has only two possible outcomes (heads or tails), the probability of success (heads) is the same for each trial (0.5), and there is no interdependence between the trials.
The following features of the binomial experiment apply:
There are a set number of trials in the experiment.In a trial, there are only two possible outcomes: success or failure.The likelihood of success is the same for every trial.The trials run separately from one another.These traits allow us to identify the following characteristics of the binomial experiment:
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I will give brainliest
Answers
The a-value for the quadratic equation x² - 7x - 18.5 = 0 is 1.
The b-value for the quadratic equation x² - 7x - 18.5 = 0 is -7.
The c-value for the quadratic equation x² - 7x - 18.5 = 0 is -18.5.
The a-value for the quadratic equation 2x² + 15x + 12 = 0 is 2.
The b-value for the quadratic equation 2x² + 15x + 12 = 0 is 15.
The c-value for the quadratic equation 2x² + 15x + 12 = 0 is 12.
What is a quadratic equation?In Mathematics, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
Mathematically, the quadratic formula is modeled or represented by this mathematical expression:
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]
For the quadratic equation x² - 7x - 18.5 = 0, we have:
[tex]x = \frac{-(-7)\; \pm \;\sqrt{(-7)^2 - 4(1)(-18.5)}}{2(1)}[/tex]
For the quadratic equation 2x² + 15x + 12 = 0, we have:
[tex]x = \frac{-(5)\; \pm \;\sqrt{(5)^2 - 4(2)(12)}}{2(2)}[/tex]
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A boat traveled 165 miles each way downstream and back. The trip downstream took 11 hours.
The trip back took 15 hours. What is the speed of the boat in still water? What is the speed of
the current?
Answers
The speed of the boat in still water is 20.625 km/hr. and the speed of the current is 66 km/hr.
What is the relation of speed and distance?The speed formula is speed = distance / time.
Consider x= speed of current and y = speed of still water
The speed of the boat in still water can be calculated by dividing the total distance traveled by the total time taken;
(165 km x 2 = 330 km)
(5 hours + 11 hours = 16 hours).
Therefore, the speed of the boat in still water
330 km/16 hours = 20.625 km/hr.
The speed of the current can be calculated by dividing the total distance traveled by the total time taken for the downstream trip ;
(165 km x 2 = 330 km)
(5 hours).
Therefore, the speed of the current = 330 km/5 hours = 66 km/hr.
Hence,
speed of still water = 20.625 km/hr.
speed of current = 66 km/hr
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Ethan has pp pennies and nn nickels. He has no more than 20 coins altogether. Write this situation as an inequality.
Answers
Answer:
P+n<20
Step-by-step explanation:
The given situation can be expressed as an inequality as p + n ≤ 20.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Given that,
Ethan has p pennies and n nickels.
Number of pennies = p
Number of nickels = n
Total number of coins is no more than 20.
This means that the combined total of pennies and nickels does not exceed 20.
sum of p and n is less than or equal to 20.
p + n ≤ 20
Hence the required inequality expression is p + n ≤ 20.
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what is106 inches in feet?
Answers
Converting inches to feet using the given value, we get, 106 inches is equal to 8.83 feet.
To convert inches to feet, we divide the number of inches by 12, since there are 12 inches in a foot.
So, 106 inches divided by 12 gives us:
106 ÷ 12 = 8.83 feet
Therefore, 106 inches is equivalent to 8.83 feet.
It's important to note that in the United States, Liberia, and Myanmar, feet and inches are commonly used units of length for measuring things like height and distance. While other countries may use the metric system, it's always important to make sure you're using the correct units of measurement for the context in which you're working.
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By rounding to one significant figure estimate the answer to 216x876