Answer:
Calculate the arc length according to the formula above: L = r * θ = 15 * π/4 = 11.78 cm. Calculate the area of a sector: A = r² * θ / 2 = 15² * π/4 / 2 = 88.36 cm².
Step-by-step explanation:
help please geometry
Applying similar triangles the length of EB is 14.6
How to find length EBSimilar triangles is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
DE and DF, EB and FC
The solution is worked out using sides BC and FE, then AC and DF
DE / EB = DF / FC
17.5 / EB = 13.1 / 10.9
cross multiplying
17.5 * 10.9 = 13.1 * EB
EB = 14.6
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The equation of a line is given by 3x +4y =12. Solve for y.
Answer:
[tex]y = -\frac{3x}{4} + 3[/tex]
Step-by-step explanation:
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Remember to do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 3x from both sides of the equation:
[tex]3x + 4y = 12\\4y + 3x (-3x) = 12 (-3x)\\4y = -3x + 12[/tex]
Next, divide 4 from both sides of the equation:
[tex]4y = -3x + 12\\\frac{(4y)}{4} = \frac{(-3x + 12)}{4} \\y = \frac{-3x + 12}{4}\\ y = -\frac{3x}{4} + 3[/tex]
[tex]y = -\frac{3x}{4} + 3[/tex] is your answer.
~
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this side lengths of a tringal are 6,8.10. is this a right triangle
Answer:
yes
Step-by-step explanation:
It is a Pythagorean triangle 3-4-5
Hope this helps.
Jason and Piera decide to start a college savings account for their newborn son, Joseph. They want to have $40,000 available for him when he is 18, and they expect the account to have an average return of 7%. How much do they need to deposit each month to reach this goal?
Round answer to 2 decimal places.
Answer:
Step-by-step explanation:
Solve for the value of q
Answer:
-3
Step-by-step explanation:
i hope thisis the right aswrr
144 is 90% what is the other 10 percent
Answer:
To find out what is the other 10%, you can use the following formula:
(100% - 90%) = 10%
So, if 144 is 90% of a value, we can divide 144 by 0.9 to find the total value:
144 / 0.9 = 160
Therefore, the other 10% of 160 is:
0.1 x 160 = 16
Step-by-step explanation:
Two pools are being filled with water. To start, the first pool contains 970 liters of water and the second pool is empty. Water is being added to the firs rate of 20.5 liters per minute. Water is being added to the second pool at a rate of 44.75 liters per minute. After how many minutes will the two pools have the same amount of water? 40 minutes How much water will be in each pool when they have the same amount? liters
The water in the two pools would be the same quantity in 40 minutes.
The amount of water in each pool is 1790 liters.
How much water would be in each pool when they have the same quantity of water?The function that represents the total amount of water in the first pool is:
Water already in the pool + (amount of water added per minute x number of minutes)
970 + (20.5 x t)
970 + 20.5t
The function that represents the total amount of water in the second pool is:
quantity added per minute x number of minutes
44.75 x t
44.75t
When the two pools have the same amount of water, the two functions would be the same.
44.75t = 970 + 20.5t
970 = 44.75t - 20.5t
970 = 24.25t
t = 970 / 24.25
t = 40 minutes
Amount of water in each pool = 44.75 x 40 = 1790 liters
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Make a tree diagram to show all the possible sequences of answers for four multiple-choice questions, each with five possible responses. Assuming that you are guessing the answers so that all outcomes listed in the tree are equally likely, what is the probability that you will guess the one sequence that contains all four correct answers?
Answer: Here's a tree diagram that shows all the possible sequences of answers for four multiple-choice questions, each with five possible responses:
/-- A -- A -- A -- A
/
/ /-- A -- A -- A -- B
/ /-- A -- A -- B -- A
/ /-- A -- B -- A -- A
/ /-- B -- A -- A -- A
/ /
/ / /-- A -- A -- B -- B
/ / /-- A -- B -- A -- B
/ / /-- A -- B -- B -- A
/ / /-- B -- A -- A -- B
/ / /-- B -- A -- B -- A
/ / /-- B -- B -- A -- A
/
/ /-- A -- B -- B -- B
/ /-- B -- A -- B -- B
/ /-- B -- B -- A -- B
/ /-- B -- B -- B -- A
/
/ /-- A -- B -- B -- B
/ /-- B -- A -- B -- B
/-- B -- B -- A -- B
/-- B -- B -- B -- A
Each branch in the tree represents the guess for one of the questions, and the letters A and B represent the possible answers. There are 5 branches coming out of each node in the tree because there are 5 possible answers for each question.
To find the probability of guessing the one sequence that contains all four correct answers, we multiply the probabilities of following the path A-A-A-A:
P(A-A-A-A) = (1/5) * (1/5) * (1/5) * (1/5) = 1/625
Therefore, the probability of guessing the one sequence that contains all four correct answers is 1/625 or about 0.16%.
Step-by-step explanation:
The sum of two numbers is 29. The difference between 4 times the first number and the second number is 6. Find the two numbers.
Answer:
Let's call the two numbers x and y.
From the problem statement, we know that:
x + y = 29 (Equation 1)
4x - y = 6 (Equation 2)
We can solve for one variable in terms of the other by rearranging Equation 1:
y = 29 - x
Substitute this expression for y in Equation 2 and solve for x:
4x - (29 - x) = 6
5x - 29 = 6
5x = 35
x = 7
Now that we know x = 7, we can use Equation 1 to solve for y:
x + y = 29
7 + y = 29
y = 22
Therefore, the two numbers are 7 and 22.
Answer:
the two numbers are x = 7.2 and y = 21.8.
Step-by-step explanation:
Let's call the first number x and the second number y. We can set up two equations based on the information given:
x + y = 29 (equation 1)
4x - y = 6 (equation 2)
We can use these two equations to solve for x and y.
To do so, we can use the method of substitution. Solving equation 1 for x, we get:
x = 29 - y
We can then substitute this expression for x into equation 2:
4(29 - y) - y = 6
Simplifying and solving for y:
116 - 4y - y = 6
115 - 5y = 6
-5y = -109
y = 21.8
So one of the numbers is y = 21.8. To find the other number, we can substitute this value back into equation 1:
x + 21.8 = 29
x = 7.2
Therefore, the two numbers are x = 7.2 and y = 21.8.
1. The fence around the playground costs 90 dollars per 50-foot roll. Laying the grass across the area costs 400 dollars per 500 square feet. How much did the fencing and grass for this playground cost to build?
2. How many kids per square yard can Springfield's playground hold?
3. There's a new playground going up in nearby Wintermeadow. Wintermeadow has a
budget about 3 times greater than Springfield's. Recommend a playground shape
and size that would fit Wintermeadow's budget and hold at least 3 times as many
kids as Springfield's playground at the same density of kids per square yard. How
many kids can your playground hold?
1) We need 2 rolls of grass at a cost of 2 rolls x $400 per roll = $800. 2) Number of kids per square yard: 0.06 kids/ sqyrd. 3) The total cost for this playground would be $3170, which is within the budget of $4290.
How will you solve this question?To find the cost of fencing, we need to know the perimeter of the playground. Let's assume the playground is a rectangle with dimensions 100 feet by 75 feet. The perimeter is then 2(100 ft) + 2(75 ft) = 350 feet. This means we need 7 rolls of fencing (350 ft ÷ 50 ft per roll) at a cost of 7 rolls x $90 per roll = $630.To find the cost of laying grass, we need to know the area of the playground. The area of a rectangle with dimensions 100 feet by 75 feet is 100 ft x 75 ft = 7500 square feet. To convert to square yards, we divide by 9: 7500 sq ft ÷ 9 = 833.33 sq yd. This means we need 2 rolls of grass (833.33 sq yd ÷ 500 sq yd per roll) at a cost of 2 rolls x $400 per roll = $800.
The total cost of fencing and grass for this playground is $630 + $800 = $1430.
To find the number of kids per square yard, we need to know the area of the playground and the number of kids it can hold. Let's assume the playground can hold 50 kids and the dimensions are still 100 feet by 75 feet. We already know the area is 7500 square feet or 833.33 square yards. To find the number of kids per square yard, we divide the number of kids by the area: 50 kids ÷ 833.33 sq yd = 0.06 kids per sq yd.Let's assume the budget for Wintermeadow is three times the cost of Springfield's playground, so the budget is $4290 ($1430 x 3). We want to recommend a playground shape and size that can hold at least 3 times as many kids as Springfield's playground at the same density of kids per square yard.From part 2, we know that Springfield's playground can hold 50 kids in 7500 square feet or 833.33 square yards, which is a density of 0.06 kids per sq yd. To hold three times as many kids, the new playground should be able to hold 150 kids.
Let's assume we want to keep the same density of 0.06 kids per sq yd. To find the area needed for the new playground, we divide the number of kids by the density: 150 kids ÷ 0.06 kids per sq yd = 2500 sq yd.
There are many shapes and sizes that could have an area of 2500 sq yd. One option is a rectangle with dimensions 125 feet by 200 feet. The perimeter of this playground is 650 feet, which would require 13 rolls of fencing at a cost of $1170. The area of the playground is 2500 square yards, which would require 5 rolls of grass at a cost of $2000.
The total cost for this playground would be $3170, which is within the budget of $4290. It can hold at least 3 times as many kids as Springfield's playground, with the same density of 0.06 kids per sq yd.
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Answer:
1. It Should be $ 36039.60
2. Total = 432,00 ft / 3 = 14400/360= 40 kids
3. 443880 ft / 3 = 147960 / 360 = 411 kids
Step-by-step explanation:
The teacher tell me the answers
Can someone help me understand this question.... Thank you
Claude is buying boxes of cinnamon rolls from a bakery. Each box is $6. Which of the following statements are true? (Choose 2 statements.)
A. The independent variable is the number of boxes of cinnamon rolls Claude buys.
B. The dependent variable is the amount of money you spend on the cinnamon rolls.
C. The dependent variable is the number of boxes of cinnamon rolls Claude buys.
D. The independent variable is the amount of money you spend on the cinnamon rolls.
E. None of the above statements are true.
2.Sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a similar sampling probability than others.
correct answer is False
3. Ruben randomly called 100 phone numbers in his town in order to survey them about their shopping habits. 55 people decided to participate in the survey.
This is an unbiased sample.
False
The correct statements are:
A. The independent variable is the number of boxes of cinnamon rolls Claude buys.
B. The dependent variable is the amount of money Claude spends on the cinnamon rolls.
What is independent variable?
The independent variable is the variable that is manipulated or controlled by the experimenter, and in this case, Claude is choosing how many boxes of cinnamon rolls to buy.
1. The dependent variable is the variable that is affected by the independent variable, and in this case, the amount of money Claude spends depends on the number of boxes he buys.
Therefore, statement A and B are correct, while C, D, and E are not true in this context.
2. Sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a similar sampling probability than others. (FALSE)
3. Ruben randomly called 100 phone numbers in his town in order to survey them about their shopping habits. 55 people decided to participate in the survey.
This is an unbiased sample. (FALSE)
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Many matchers we conserved about the number of petentiomers within a certain wes of land besmes of the different represents to serve dumilar mee. What is this
seguentation variable collect
O Missomasin
Poplation
O CRUSA
6.Maleet bety
The population would be the name that is used to refer to the segmentation variables
What is population in research?
In research, population refers to the entire group of individuals or objects that share a common characteristic and are of interest to the researcher. The population is the group to which the researcher wishes to generalize their findings. For example, if a researcher is studying the effects of a new medication on blood pressure in adults, the population would be all adult individuals who have high blood pressure.
It is important to define the population accurately in research because the results of the study can only be generalized to the population being studied. If the population is not defined accurately, the results of the study may not be applicable or generalizable to other groups or populations.
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Oakwood High School is going to select a committee. The committee will have a faculty member, a male student, a female student, a parent, and a school board member.
Here are the positions and the people interested in each.
Position People interested
Faculty member Dr. Choi, Ms. Peterson, Mr. Diaz, Mrs. Lewis
Male student Deandre, Tom, Pablo, Ryan
Female student Amanda, Susan, Latoya, Melissa
Parent Mr. Lopez, Mr. Bailey, Ms. Smith
School board member Mr. Alexander, Ms. Washington, Dr. Anderson, Mrs. Ramirez
Based on this list, how many ways are there to fill the five committee positions?
aleks initial knowledge check
pls help
On solving the question we have that Hence, with the supplied list of equation people, there are 192 methods to form a committee.
What is equation?A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.
We must multiply the number of options for each position to determine the number of ways to fill the five committee posts.
There are four options for the faculty member role.
There are four options for the male student post.
There are four options for the female student post.
There are three options for the parent position.
There are four options for school board members.
As a result, the total number of possible ways to fill the five committee posts is:
4 x 4 x 4 x 3 x 4 = 192
Hence, with the supplied list of people, there are 192 methods to form a committee.
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In 1,024 ways we can fill these five committee positions. we can solve this by using permutation.
What is Permutation?A permutation of a set in mathematics is, broadly speaking or telling , the rearrangement of its elements if the set already has an ordered or arranged structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation" in this context.
Number of faculty members: 4
Number of male students: 4
Number of female students: 4
Number of parents: 4
Number of school board members: 4
4 X 4 X 4 X 4 X 4 = 1,024 , ways to fill the 5 committee positions.
In 1,024 ways we can fill these five committee positions.
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Find the area of the composite shape below.
The area of the composite shape is 63cm²
What is the area of triangle?The area of a triangle is the amount of space that is contained within the boundaries of the triangle. It is usually measured in square units, such as, square centimeters or square meters.
In the figure there are two figures, triangle and rectangle.
first find the area of triangle:
[tex]area of triangle = \frac{ heightXbase }{2}[/tex] = [tex]\frac{5X6}{2} = 15cm^{2}[/tex]
Now, find the area of rectangle:
[tex]area of rectangle= length X width = 8X6 = 48 cm^{2}[/tex]
Total area of the figure is = 15 + 48 = 63cm²
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The function f is defined by the rule that assigns each real number x to 1 more than the opposite of its cube root. Select all the true statements about the function f.
A. The domain is all real numbers.
B. The range is all real numbers.
C. The x-intercept is 0.
D. The y-intercept is 1.
E. The graph is decreasing for all values in the domain of f.
Answer:
A, B, D, E-------------------------------
As per given definition the function is:
[tex]f(x) = -\sqrt[3]{x} + 1[/tex]Verify each statement:A. The domain is all real numbers ⇒ TRUE, as there is no restrictions to the domain.
B. The range is all real numbers ⇒ TRUE, since no domain restrictions, the range has no restrictions.
C. The x-intercept is 0 ⇒ FALSE
It is the point with zero y-coordinate:
[tex]0= -\sqrt[3]{x} + 1[/tex][tex]\sqrt[3]{x} = 1[/tex][tex]x=1[/tex]D. The y-intercept is 1 ⇒ TRUE
It is the point with zero x-coordinate:
[tex]f(0)=-\sqrt[3]{0}+1=0+1=1[/tex]E. The graph is decreasing for all values in the domain of f ⇒ TRUE
The domain has a negative coefficient and the function is cube - root function, hence the odd function, therefore it is always decreasing.
See attached graph to help with answer choices.
Ratios and Proportions (please help on all questions)
36
Step-by-step explanation:
Total ratio 2+6=8
the ratio for glazed doughnuts is 6. divide it by the total ratio and multiply it by the total number of doughnuts
6/8 × 48
= 36
2a. 2+6=8
6/8 × 24
=18
3a. 3+9=12
3/12 × 144
= 36
Min-jun deposited $125 in a bank account earning 19% interest,
compounded annually. How much interest will he earn in 48 months?
Answer: $165.23
Step-by-step explanation:
To solve the problem, we can use the formula for compound interest:
A = P (1 + r/n)^(nt)
where A is the amount, P is the principal (initial amount), r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, P = $125, r = 0.19 (since the interest rate is 19%), n = 1 (since the interest is compounded annually), and t = 48/12 = 4 (since the time is given in months but we need to convert it to years). Plugging in these values, we get:
A = 125 (1 + 0.19/1)^(1*4)
A = 125 (1.19)^4
A ≈ $290.23
So, the total amount after 48 months is approximately $290.23. To find the interest earned, we subtract the principal from the amount:
Interest = Amount - Principal
Interest = $290.23 - $125
Interest = $165.23
Therefore, Min-jun will earn $165.23 in interest in 48 months.
Solve for x and y.this is trig btw
The value of x and y are 8[tex]\sqrt{2}[/tex], we can solve this question by Pythagoras' Theorem.
What is Pythagoras' Theorem?Pythagoras' Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it can be written as: [tex]$a^2 + b^2 = c^2$[/tex]
where 'a' and 'b' are the lengths of the legs (the sides adjacent to the right angle) and 'c' is the length of the hypotenuse. This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery and proof. It has a wide range of applications in geometry, trigonometry, and other areas of mathematics and science.
By using Pythagoras' theorem, we get
[tex]sin 45=\frac{x}{16}[/tex]
[tex]\frac{1}{\sqrt{2} }[/tex] =[tex]\frac{x}{16}[/tex]
[tex]x=8\sqrt{2}[/tex]
[tex]cos 45=\frac{x}{16}[/tex]
[tex]\frac{1}{\sqrt{2} }[/tex]=[tex]\frac{y}{16}[/tex]
[tex]y=8\sqrt{2}[/tex]
So, the values of x and y are 8[tex]\sqrt{2}[/tex]
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What is eight less than the product of two and a number equals four translated into an equation
Answer:
Let's break down the given sentence into an equation.
Let's assume the number is represented by 'x'.
The product of two and a number: 2x
Eight less than the product of two and a number: 2x - 8
Equals four: 2x - 8 = 4
Therefore, the equation is 2x - 8 = 4.
Find the value of the variables or indicated side length in each isosceles triangle.
Using properties of trapezium, x = 7° and y = 10°.
A quadrilateral with at least one set of parallel sides is known as a trapezium. A trapezium has the following characteristics:
Four vertices and four sides make up a trapezium.
The bases of a trapezium are its parallel sides. The legs are the non-parallel sides.
The distance that separates the bases of a trapezium perpendicularly is known as its height (or altitude). It need not be the same as the length of the legs.
The section that joins the midpoints of the legs is known as the mid-segment of a trapezium. It runs parallel to the bases and has the same length as the sum of the bases' lengths.
A trapezium's internal angles add up to 360 degrees.
A = 1/2 x (base1 + base2) x height, where base1 and base2 are the lengths of the two bases and height is the perpendicular distance between them, can be used to compute the area of a trapezium.
These are some of a trapezium's essential characteristics.
The given figure is trapezium,
As, two non - parallel sides are equal and they intersect a parallel line,
⇒ The angle at which they intersect will be equal,
⇒ 7x = 49
x = 7°
The sum of angles on adjacent sides of trapezium equals 180.
⇒ 13y + 1 + 7(7) = 180
⇒ 13 y + 50 = 180
⇒ y = 180 - 50 / 13
⇒ y = 10°
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I really don’t understand please help me
The probability that this person also sailed is 1.
What is probability?
In mathematics, probability is a measure of the likelihood or chance that an event will occur. It is typically expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
Out of 50 people, 40 took part in walking and 18 took part in sailing. However, 3 people did neither activity, which means that 40 + 18 - 3 = 55 people took part in at least one of the activities.
Let's represent the set of people who walked as A, and the set of people who sailed as B. We want to find the probability that a randomly chosen person from A is also in B, which can be represented as P(B|A).
Using the formula for conditional probability, we have:
P(B|A) = P(A and B) / P(A)
We know that P(A and B), the probability that a person took part in both walking and sailing, is 50 - 3 = 47 (since 3 people did neither activity). We also know that P(A), the probability that a person took part in walking, is 40.
Therefore,
P(B|A) = 47 / 40
which simplifies to
P(B|A) = 1.175
probabilities cannot be greater than 1, so the actual probability is 1, meaning that it is certain that a person who walked also sailed.
Hence, The probability that this person also sailed is 1.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
You have two credit cards.
What is your debt ratio? If you budget $375 to payoff your credit card debt and you payoff the highest interest card first while maintaining the interest accrued on the other card, how many months does it take you to pay it off and how much is the payment each time excluding the last payment?
Be sure to include the following in your response:
the answer to the original question
the mathematical steps for solving the problem demonstrating mathematical reasoning
Therefore, the payment for the first card each month excluding the last payment is $163.75, and it takes 10 months to pay it off. The payment for the second card each month excluding the last payment is $186.25, and it will take longer to pay it off completely, depending on the balance and the interest rate.
What is equation?An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.
Here,
To find the debt ratio, we need to divide the total credit card balance by the total credit limit. Let's say the balance on the first card is $1,500 and the credit limit is $5,000, and the balance on the second card is $2,500 and the credit limit is $10,000. Then, the total balance is $1,500 + $2,500 = $4,000 and the total credit limit is $5,000 + $10,000 = $15,000.
Therefore, the debt ratio is:
Debt ratio = Total balance / Total credit limit = $4,000 / $15,000 = 0.2667 or 26.67%
Now, let's look at paying off the credit card debt. We will assume that the first card has a higher interest rate than the second card. Let's say the interest rate on the first card is 18% per year and the interest rate on the second card is 12% per year.
If we budget $375 to pay off the credit card debt, we can determine the payment for the first card and the number of months it will take to pay it off as follows:
Step 1: Determine the interest accrued on the second card
Interest accrued on the second card per month = (12% per year / 12 months) * $2,500 = $25
Step 2: Determine the payment for the first card
Let x be the payment for the first card. Then, the payment for the second card is $375 - x. The total interest accrued on the first card plus the principal must be equal to the total payment:
0.18/12 * $1,500 + x = $375 - x - $25
0.015 * $1,500 + 2x = $350
2x = $350 - $22.50
x = $327.50/2 = $163.75
Therefore, the payment for the first card is $163.75, and the payment for the second card is $375 - $163.75 - $25 = $186.25.
Step 3: Determine the number of months to pay off the first card
Let n be the number of months to pay off the first card. Then, the balance after n months is:
$1,500 * (1 + 0.18/12)*n - $163.75 * ((1 + 0.18/12)*n - 1)/(0.18/12) = $0
Using a spreadsheet or trial and error, we can find that it takes approximately 10 months to pay off the first card.
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I need help with this, please.
The missing side of each right triangle are:
a = 20 m
b = 21 cm
c = 36 cm
How to calculate the missing side of each right triangle?
Trigonometry deals with the study of triangles and the relationships between their sides and angles.
The missing side of each right triangle can be calculated as follow:
No. 1
a = √(12² + 16²) (Pythagoras theorem)
a = 20 m
No. 2
b = √(35² - 28²) (Pythagoras theorem)
b = 21 cm
No. 3
c = √(39² - 15²) (Pythagoras theorem)
c = 36 cm
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pls help i am having a panic attack
The value of cos(2x+y) is -12/65.
Describe cosine ?Cosine, commonly denoted as cos, is a mathematical function that relates the angle of a right triangle to the ratio of the adjacent side to the hypotenuse. In other words, it is the ratio of the length of the adjacent side of an angle to the hypotenuse of the right triangle containing that angle. Cosine is one of the basic trigonometric functions, along with sine and tangent, and is widely used in mathematics, physics, and engineering to model various phenomena.
Cosine is periodic with a period of 2π, and its values range from -1 to 1. When the angle is 0°, the cosine is equal to 1, indicating that the adjacent side of the triangle is equal to the hypotenuse.
We can use the trigonometric identities for cosine to find cos(2x+y), using the values of x and y given:
cos(2x+y) = cos(2x)cos(y) - sin(2x)sin(y)
To find cos(2x), we can use the double angle identity for cosine:
cos(2x) = cos²(x) - sin²(x)
To find cos(x) and sin(x), we can use the fact that x = sin⁻¹(4/5) and the Pythagorean theorem:
sin(x) = 4/5
cos(x) = √(1 - sin²(x)) = √(1 - 16/25) = 3/5
Substituting these values into the double angle identity, we get:
cos(2x) = cos²(x) - sin²(x) = (3/5)² - (4/5)² = -7/25
To find sin(2x), we can use the double angle identity for sine:
sin(2x) = 2sin(x)cos(x) = 2(4/5)(3/5) = 24/25
To find cos(y) and sin(y), we can use the fact that y = tan⁻¹(12/5) and the Pythagorean theorem:
sin(y) = 12/13
cos(y) = 5/13
Substituting these values into the expression for cos(2x+y), we get:
cos(2x+y) = cos(2x)cos(y) - sin(2x)sin(y)
= (-7/25)(5/13) - (24/25)(12/13)
= -60/325
= -12/65
Therefore, cos(2x+y) = -12/65.
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Write a verbal description of the set {a, e, i, o, u}
What is correct regarding a
normal distribution?
The normal distribution has a bell-shaped curve, with the highest point at the mean and a gradual decrease in frequency on either side.
What is Normal Distribution ?
A normal distribution is a continuous probability distribution that is often used in statistics to model a wide variety of phenomena, such as measurements of height, weight, or IQ.
The normal distribution is symmetric. This means that the distribution is mirror-image symmetric around its mean, so that the same proportion of values lie on either side of the mean.
The normal distribution is characterized by two parameters: its mean (μ) and standard deviation (σ). The mean is the center of the distribution, while the standard deviation measures the spread of the distribution.
The total area under the normal distribution curve is equal to 1. This means that the probability of any event occurring is between 0 and 1.
The empirical rule, also known as the 68-95-99.7 rule, applies to normal distributions. This rule states that approximately 68% of the data will fall within one standard deviation of the mean, approximately 95% of the data will fall within two standard deviations of the mean, and approximately 99.7% of the data will fall within three standard deviations of the mean.
Therefore, The normal distribution has a bell-shaped curve, with the highest point at the mean and a gradual decrease in frequency on either side.
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the distance between (3, -6) and (3, -10)
Answer:
4 units
Step-by-step explanation:
Since the x-value is the same in both ordered pairs, you can just figure out the y-step ([tex]y_{2} -y_{1}[/tex]) and get your distance. -10 - (-6) = -4, so a distance of 4 units (negative sign does not matter in this case).
If both the x-values and y-values were different, another way to solve is to figure out the y- and x-steps and plug them into the Pythagoras theorem [tex]A^2+B^2 = C^2[/tex], with A being the horizontal distance (x-step) and B being the vertical distance (y-step).
You can also find the distance between 2 points by using the distance formula, which is [tex]d = \sqrt{(x_{2}-x_{1})^{2} - (y_{2}-y_{1})^{2}[/tex]. After inserting the x- and y-coordinates of your ordered pair you get [tex]d = \sqrt{(3-3)^{2} - (-10-(-6))^{2}[/tex]
Simplifying:
[tex]d = \sqrt{- (-10-(-6))^{2}}[/tex]. [tex](3-3)^{2}[/tex] was eliminated.
Then we distribute the negative signs: [tex]d = \sqrt{- (-10+6)^{2}}[/tex] --> [tex]d = \sqrt{(10-6)^{2}}[/tex].
[tex]d = \sqrt{(4)^{2}}[/tex] --> [tex]d = \sqrt{16}[/tex] --> [tex]d = 4[/tex]
So, the distance between the points is 4 units.
Side note: The distance formula works in the same way as the Pythagoras theorem.
There are 24 people running in a race. 1/4 are wearing green shorts. 1/6 are wearing red shorts. The rest are wearing blue shorts. How many people are wearing blue shorts?
Use a tape diagram to help you answer the question.
Solve. Show or explain your work.
Answer:
First, let's find the fraction of people wearing green or red shorts:
1/4 + 1/6 = 3/12 + 2/12 = 5/12
This means that 5/12 of the people are wearing either green or red shorts. To find the fraction of people wearing blue shorts, we need to subtract this from 1 (since the three options are exhaustive):
1 - 5/12 = 7/12
So, 7/12 of the people are wearing blue shorts. To find out how many people this represents, we can multiply this fraction by the total number of people in the race:
7/12 x 24 = 14
Therefore, 14 people are wearing blue shorts.
Step-by-step explanation:
Answer:
To use a tape diagram, we can start by drawing a rectangle to represent the total number of people in the race. Then, we can divide it into four equal parts to represent the people wearing green shorts and into six equal parts to represent the people wearing red shorts.
Let's use the letter "B" to represent the number of people wearing blue shorts. We know that the total number of people is 24, so we can write:
4 parts + 6 parts + B parts = 24
Simplifying this equation, we get:
10 + B = 24
Subtracting 10 from both sides, we get:
B = 14
Therefore, 14 people are wearing blue shorts.
To double-check our answer, we can add up the number of people in each category:
4 parts out of 24 = 6 people wearing green shorts
6 parts out of 24 = 4 people wearing red shorts
B parts out of 24 = 14 people wearing blue shorts
6 + 4 + 14 = 24, which matches the total number of people in the race.
The state transportation commission counted cars traveling east and west across a toll bridge. The commission counted 7,000 cars, 6,020 of which were traveling east. What percentage of the cars counted were traveling east? Write your answer using a percent sign (%).
To find the percentage of cars that were traveling east, we can use the following formula:
percentage = (part / whole) x 100%
where "part" is the number of cars traveling east, and "whole" is the total number of cars counted.
In this case, we know that 6,020 cars were traveling east, out of a total of 7,000 cars counted. So we can plug these values into the formula:
percentage = (6,020 / 7,000) x 100%
percentage = 0.86 x 100%
percentage = 86%
Therefore, 86% of the cars counted were traveling east across the toll bridge.
For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 33 beats per minute, the mean of the listed pulse rates is 77.0 beats per minute, and their standard deviation is s= 27.6 beats per minute.