Answer:
There are 12 nickels, 9 quarters, and 15 dimes.
I hope this turns out useful for you!
Step-by-step explanation:
Reading the problem repeatedly, I found that the nickels were the value that I could change to find out the values of the other coins and to find the answer. I started with the number of nickels as 20, calculating 20 x 5 (5 as the value of the nickel) = 100 ($1.00). Then, I subtracted three from 20 since the number of quarters was 3 less and got 17. 17 x 25 = a value far too big when we were going to add dimes as well, so 8 lowered the number of nickels a reasonable amount and tried again, following the directions in the problem. It took a bit, but I found a value that worked.
Nickel = $0.05
Quarter = $0.25
Dime = $0.10
My work (though I converted a bit using my sense of money)
12 x 5 = $0.60
12 - 3 = 9
9 x 25 = $2.25
9 + 6 = 15
15 x 10 = $1.50
$0.60 + $2.25 + $1.50 = $4.35
Multiply and simplify: (12−y)2
The simplification of the given expression on the basis of identity is given as 144 - 24y + y².
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given expression is (12 - y)².
It can be expanded on the basis of the algebraic identity (a - b)² = a² - 2ab + b² as follows,
(12 - y)²
= 12²- 2×12y + y²
= 144 - 24y + y²
Hence, the given expression can be simplified as 144 - 24y + y².
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Hakeem leans a 26-foot ladder against a wall so that it forms an angle of 72^{\circ} ∘ with the ground. What’s the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
To solve this problem, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side of a right triangle. Since the angle formed by the ladder and the ground is 72 degrees, we can consider the horizontal distance between the base of the ladder and the wall to be the adjacent side of the right triangle, and the height of the ladder to be the opposite side.
We can set up the following equation to represent this relationship:
tan(72^{\circ}) = opposite/adjacent
Substituting the values given in the problem, we get:
tan(72^{\circ}) = 26 feet / adjacent
To find the value of the adjacent side, we can solve for "adjacent" in the equation above. We can do this by dividing both sides of the equation by 26 feet and then taking the inverse tangent (tan^(-1)) of both sides:
adjacent = 26 feet / tan(72^{\circ})
Using a calculator or a table of tangent values, we can find that the value of tan(72^{\circ}) is approximately 3.73. Substituting this value into the equation above, we get:
adjacent = 26 feet / 3.73
Solving this equation, we find that the horizontal distance between the base of the ladder and the wall is approximately 6.99 feet. Rounding this value to the nearest hundredth of a foot, we get an answer of approximately 6.99 feet.
(pls give brainliest
Answer: 8.03
Step-by-step explanation:
. The length of a rectangle is represented by 4x and the width by 2x + 1 Determine the perimeter of the rectangle as a simplified expression in standard form. (hint: perimeter=2w+21)
The perimeter of the rectangle can be expressed as 12x+2
What is perimeter of a rectangle?The perimeter of a rectangle is the total distance covered by its boundaries or the sides. Since there are four sides of a rectangle, thus, the perimeter of the rectangle will be the sum of all four sides.
The perimeter of a rectangle is given as 2(l+w)
where l is the length and w is the width.
If the length is represented by 4x and width by 2x+1, therefore the perimeter of the rectangle = 2(4x+2x+1)
= 2( 6x+1)
= 12x+2
the perimeter can also be found by adding all the four sides, this means that
perimeter = 4x+4x+2x+1+2x+1=8x+4x+2= 12x+2
therefore the perimeter of the rectangle is 12x+2.
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see attached image giving brainliyest if correct
The slope of the line given in the graph will be [m] is - 0.78.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is the graph of a straight line.
The line passes through the coordinates as follows -
(- 1.8, 0) [lying on x-axis]
(0, - 1.4) [lying on y-axis]
The slope of the line can be calculated using the formula -
m = (y₂ - y₁)/(x₂ - x₁)
m = (- 1.4 - 0)/(0 + 1.8)
m = - 1.4/1.8
m = - 0.78
Slope of the line will be -0.78.
Therefore, the slope of the line given in the graph will be [m] = - 0.78.
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please help this is a final
By using arithmetic progression, it can be calculated that
The common difference is 12
Third option is correct
What is arithmetic progression?A series of numbers is called an arithmetic progression if the difference between each term in the sequence is the same.
If there is always the same difference between any two consecutive terms in a series of integers, then progression is known as an arithmetic progression. Simply put, it means that the previous number in the series is added to determine the next number in the series. A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms. One arithmetic progression with a common difference of 2 is the sequence 5, 7, 9, 11, 13, 15,...
This is a problem on arithmetic progression
[tex]a _1 = 5[/tex]
[tex]a_n = a_{n-1} + 12[/tex]
[tex]a_2 = a_1 + 12[/tex]
[tex]a_2 = 5 + 12 = 17[/tex]
[tex]a_3 = a_2 + 12 = 17 + 12 = 29[/tex]
[tex]a_4 = a_3 + 12 = 29 + 12 = 41[/tex]
[tex]a_2 -a_1 = 17 - 5 = 12\\a_3 - a_2 = 29 - 17 =12\\a_4 - a_3 = 41 - 29 =12[/tex]
So the common difference is 12
Third option is correct
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By using arithmetic progression, it can be calculated that, the common difference is 12.
Third option is correct
What is arithmetic progression?If the common difference between each term in the sequence is the same, a group of numbers is referred to as an arithmetic progression.
A progression is referred to as an arithmetic progression if there is consistently the common difference between any two successive terms in a series of integers. To put it simply, it indicates that the series' next number is produced by adding the previous one.
An arithmetic progression or arithmetic sequence, also known as AP, is a set of numbers where the terms are always different from one another. The numbers 5, 7, 9, 11, 13, and 15 make up one mathematical progression with a common difference of 2.
We know that the arithmetic progression, this is based on the same
[tex]\begin{aligned}& a_1=5 \\& a_n=a_{n-1}+12 \\& a_2=a_1+12 \\& a_2=5+12=17 \\& a_3=a_2+12=17+12=29 \\& a_4=a_3+12=29+12=41 \\& a_2-a_1=17-5=12 \\& a_3-a_2=29-17=12 \\& a_4-a_3=41-29=12\end{aligned}[/tex]
So the common difference is 12
Third option is correct
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Find sin2x,cos2x, and tan2x if sin x=12/13 and x terminates in quadrant IV.
sin2x=
cos2x=
tan2x=
Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
sin x= 12/ 13
So, B = √13² - 12² = √169 - 144 = √25 = 5
cos x= 5/ 13
So, sin 2x= 2 sin x cos x =2 (12/13)(5/13) = 120/169
and, cos 2x= 1- 2 sin²x
= 1- 2( 144 / 169)
= -119/ 169
and, tan 2x = sin 2x/ cos 2x = 120/ 169 / (- 119/ 169)= 120/ 119
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olivia wants to have a 90 average in algebra, where tests count for 55%, quizzes count for 30% and homework counts for 15%.If she has a 92 test average and 100% HW average, what must her quiz average be? Let x = the average of the
Olivia's quiz average must be 24.4 to achieve a 90 average in algebra.
How to calculate for the quiz averageTo get the average for the quiz, we first evaluate for the sum of the test average and the homework average, and the subtract the result from 90 average in algebra.
the test average = (92/100) × 55
test average = 50.6
100% homework average implies Olivia got a homework average of 15
Let x be the quiz average, so that
x = 90 - (50.6 + 15)
x = 90 - 65.6
x = 24.4
Therefore, the quiz average of 24.4 is what Olivia needs to achieve a 99 average in algebra.
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A student argues that y= x/9 does not represent a proportional relationship between x and y because we need to multiply one variable by the same constant to get the other one and not divide it by a constamt. Do you agree or disagree with this student
I disagree with the student because y = x/9 represents a proportional relationship
What is proportional relationship?
Proportional relationships are relationships between two variables where their ratios are equivalent
A proportional relationship can we written as follows:-
y = mx
Where 'y' is dependent variable, 'x' is independent variable, and 'm' is the slope or we can say 'm' is constant of proportionality.
'm' can take any value whether negative or positive, decimal or whole number. 'm' is a real number.
The given problem is y = x/9 and student says we can only multiply constant, and not divide. We disagree with this comment because m= 1/9 is correct.
So y = 1/9 x makes sense.
Hence, y = x/9 represents a proportional relationship.
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For a total of 28seconds, a seagull flew east at 11meterspersecond. A sailor watched the seagull fly for one-quarter of that time. How far did the seagull fly while the sailor was watching?
Write your answer as a whole number.
meters
To find out how far the seagull flew while the sailor was watching, you can use the following steps:
Calculate the total distance the seagull flew in 28 seconds. You can do this by multiplying the seagull's speed (11 meters per second) by the time it flew (28 seconds):
Distance = Speed * Time
= 11 meters/second * 28 seconds
= 308 meters
Calculate the time the sailor watched the seagull fly. You can do this by dividing the total time the seagull flew (28 seconds) by 4:
Time = 28 seconds / 4
= 7 seconds
Calculate the distance the seagull flew while the sailor was watching. You can do this by multiplying the seagull's speed (11 meters per second) by the time the sailor watched the seagull fly (7 seconds):
Distance = Speed * Time
= 11 meters/second * 7 seconds
= 77 meters
Therefore, the seagull flew 77 meters while the sailor was watching.
What are conditional problems?
Conditional problems are problems that involve determining the likelihood or probability of an event occurring under certain conditions. They often involve the use of probability and statistics to evaluate the likelihood of different outcomes or to make predictions about future events.
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Find slope between 2 points (4,9) and (1,6)
Answer:
Step-by-step explanation:
PLEASE HELP AWARDING 50 POINTS!
What is the volume of a cylinder with a base radius of 2 and height of 5?
Either enter an exact answer in terms of π or use 3.143.143, point, 14 for π, and enter your answer as a decimal.
Answer:
20π cubic units
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cylinder}\\\\$V=\pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
Given:
r = 2h = 5Substitute the given values into the formula for the volume of a cylinder and solve for V:
[tex]\implies V=\pi \cdot 2^2 \cdot 5[/tex]
[tex]\implies V=\pi \cdot 4 \cdot 5[/tex]
[tex]\implies V=\pi \cdot 20[/tex]
[tex]\implies V=20\pi\;\; \sf cubic \;units[/tex]
A deck of cards contains 52 cards, of which 4 are aces. You are offered the following wager: Draw one card at random from the deck. You win $10 if the card drawn is an ace. Otherwise, you lose $1.
If you make this wager vary many times, what will be the mean amount you win?
The mean amount won based on the expectation formula of probability will be - 2/13.
What is probability?The probability of an event occurring is defined by probability.
Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
Probability of winning = 4/52 = 1/13
Probability of lossing = 1 - 1/13 = 12/13
The mean amount or expectation is given as,
E(X) = 10 × (1/13) + - 1(12/13)
E(X) = 10/13 - 12/13
E(X) = - 2/13
Hence "The mean amount won based on the expectation formula of probability will be - 2/13".
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In how many different ways can we distribute 5 different books among 10 children if any child can get any number of books?
Using the formula of combination and the provided condition that any child can get any number of books, The answer is 637.
What is combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. We use permutation to determine how many possible ways we have to arrange items from a collection system.
What is the formula of combination?The required formula is:
[tex]C(n,r) = \frac{n!}{r!(n-r)!}[/tex]
where, n= total number of objects in the set.
r= number of choosing objects from the set.
from the given data, total number of books = n= 5
number of children we need to distribute, r= 10
total possible ways of distribution= C(10,1)+C(10,2)+C(10,3)+C(10,4)+C(10,5)
=10+45+120+210+252
=637
hence, we have total 637 possible ways to distribute.
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Question
the value of 2 cos x - cos 3x - cos 5x is
not spam
Required Answer -:
16cos³ x sin² x
Let's Begin2cos x - ( cos 3x + cos 5x )
= 2cos x - 2 cos 4x cos x
= 2cos x 2sin² 2x
= 4 cos x ( 2sin x cos x)²
= 16cos³ x sin² x
Thus,, the value of 2 cos x - cos 3x - cos 5x is = 16cos³ x sin² x
q and p of both prime numbers with p < q
they are each less than 15
give an example where p + q is odd but not prime
Answer:
17 and 18 because they are equal
help please and thanks you
Give the quotient and remainder.
355÷8
Answer:
355 ÷ 8 = 44 with remainder 3
Step-by-step explanation:
44
-------------------------
8 | 355
- 32
--------
35
- 32
------
3
Ethan is buying a pair of water skis that are on sale for 2/3 of the original price. The total cost is $115. What was the original price of the skis? Use x as the variable.
Answer:
$345 (PLEASE GIVE BRAINLYEST )
Step-by-step explanation:
1/3x=115
x=345
For each of the lines (A, B, C, and D) in the graph above, determine its relationship to the line y=3/4x and its equation.
Line A :
Line B:
Line C:
Line D:
Relationship to the line y=3/4x and its equation is line B.
What is an equation ?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
y = mx+c
y = 3/4x [which shows that the line B as the points]
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Can anyone solve this? 30 points (no bots, please)
For 3 and 4, find the slope of the line that passes through the given points.
3. (0, 10) and (24, 6)
4. (0, 6) and (20, 14).
5. The graph shows the number of centimeters a particular plant grows over time.
a. What is the slope of the line?
b. Apply Math Models What does the slope mean?
Answer: 4. -1/6, 5. 2/5
Step-by-step explanation:
1. The formula for slope is rise/run. To find the slope, you subtract the y coordinates (it doesnt matter the order, and you divide it by the difference of the x coordinates.
2. The y coordinates for 3 are 10 and 6, and the x coordinates are 0 and 24.
10-6/0-24 is 4/-24 which is -1/6.
3. you do the same thing for #4. The y coordinates are 6 and 14, and the x coordinates are 0 and 20. 14-6/20-0=slope. 8/20 is the slope, and that is equal to 2/5.
4. the slope for 3 is -1/6 and the slope for 4 is 2/5.
A new ramp is being built at the school. It will be two meters long and one meter high. What will the slope of the ramp be?
Answer:
1/2
Step-by-step explanation:
Slope is rise (height)/run(length)
Slope is 1 meter/2 meters
Find an expression which represents the difference when (-x-3y)(−x−3y) is subtracted from (8x-9y)(8x−9y) in simplest terms.
The resulting expression after the expressions are subtracted is 9x - 6y
How to determine the resulting equation after the subtraction?From the question, we have the following parameters that can be used in our computation:
(-x-3y)(−x−3y) is subtracted from (8x-9y)(8x−9y)
Rewrite these expressions properly
So, we have the following representations
(−x−3y) is subtracted from (8x-9y)
When the first equation is subtracted from the second, we have the following representation
8x - 9y - (-x - 3y)
Open the brackets
So, we have
8x - 9y + x + 3y
Evaluate the like terms
9x - 6y
Hence. the solution is 9x - 6y
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Graph the function and select the y-intercept y = 2 times 3 Superscript x
y-intercept of given function is y = 1
How to graph the function?
The collection of ordered pairings with the (x,y). (x,y) sign is known as the graph of a function in mathematics, where f(x)=y. x and f(x) are Cartesian coordinates of points in two-dimensional space, and in the typical scenario where they are real numbers, they constitute a subset of this plane.
Given function , f(x) = 2· [tex]3^{x}[/tex]
Graph of the function is given below:
As the given graph is intersecting the y-axis at y=1 So, y-intercept of given function is y = 1
Therefore, y-intercept is y = 1
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5. Charlie deposits $1000 into his investment account. The account grows at a rate
of 8% per year. How much money total is in the account on the first day on
the 11th year.
Answer:
1100
Step-by-step explanation:
First, we start off by finding 10% which is $100. We divide that by 10 to get $10 which is 10%. Now we need to multiply 10% (which is $10) by 10 which is $100. That gives you this answer
The total amount in the account on the first day of the 11th year is if Charlie deposits $1000 into his investment account. The account grows at a rate of 8% per year is $1880.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given data:
Charlie deposits, P = $1000 into his investment account.
The account grows at a rate, r = 8% per year.
The time, t = 11 year
Calculate the simple interest as shown below,
[tex]SI = (P\times r\times t) / 100[/tex]
SI = (1000 × 8 × 11) / 100
SI = $880
Calculate the total amount by the formula given below,
Amount = A
[tex]A = P + SI[/tex]
A = 1000 + 880
A = $1880
Therefore, the total amount in the account on the first day of the 11th year is if Charlie deposits $1000 into his investment account. The account grows at a rate of 8% per year is $1880.
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SHE IS A GIRL. HER NAME IS CHRIS. CHRIS IS A GIRLS NAME. IS THIS SYLLOGISM OR DETATCHMENT
It is Syllogism. It is an example of a type of reasoning where a conclusion is reached from two given or assumed propositions, each of which shares a term with the conclusion.
A syllogism is what?The Greek term "syllogismos," which means "conclusion, inference," is the source of the English word "syllogism." A logical argument employing assertions and deductive reasoning is known as a syllogism. The most important contribution to the topic of syllogisms is attributed to Aristotle. A major premise, a minor premise, and a conclusion make up a syllogism. One phrase from each of the premises and the conclusion are shared.
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help meeeeeeeeeee pleaseee
(a) After 25 years 47.37g of the initial sample left in the sample. (b) 12.83 years takes the initial sample to decay half of its original amount.
Given:
[tex]A(t) = 200 e^{-0.054t}[/tex]
Substituting 25 for t in the expression, we get:
A(25) = 200e⁰.⁰⁵⁴ × 25
= 47.37 g
Thus, after 25 years, there will be 47.37g of the initial sample left in the sample.
(b.) 12.83 years takes the initial sample to decay half of its original amount.
We want to find t such that
[tex]A(t) = 200e^{0.054} \times t[/tex]
where, t = 100.
Solving for t, we get:
[tex]200e^{0.054} \times t = 100[/tex]
Dividing both sides by 200 and applying the natural logarithm to both sides, we get:
0.054 × t = ln(0.5)
Therefore,
[tex]t = \frac{\ln(0.5)}{0.054}[/tex]
= 12.83 years.
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The rectangle is 82m long and 52m wide. Find the area of the training field. Use the value 3.14 for π, and do not round your answer. BE SURE TO INCLUDE THE UNIT IN YOUR ANSWER
The area of the rectangle training field is 4264 m².
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know the area of a rectangle is (length×width).
So, The area of the rectangle 82m long and 52m wide is,
= (82×52) m².
= 4264 m².
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What are some fractions rules that I need to know about?
Answer:
1. The denominator of a fraction represents the number of equal parts the whole is divided into.
2. The numerator of a fraction represents the number of parts being considered.
3. A fraction is in simplest form when the numerator and denominator have no common factors other than 1.
4. The denominator of a fraction must be greater than zero.
5. The numerator of a fraction must be greater than or equal to zero.
6. When two fractions have the same denominator, the fraction with the larger numerator is greater.
7. When two fractions have the same numerator, the fraction with the smaller denominator is greater.
8. To add and subtract fractions, the denominators must be the same.
9. To multiply fractions, multiply the numerators and denominators separately.
10. To divide fractions, invert the second fraction (flip the numerator and denominator) and then multiply.
Step-by-step explanation:
Answer:
For fractions to be added or subtracted, their denominators must match (the bottom value). It just requires adding or subtracting the numerators if the denominators are already equal (the top value). A common denominator must be determined if the denominators are dissimilar.
Step-by-step explanation:
Find the missing number so that the equation has no solutions
–2x + 11 = x + 21 + __x
a
5
b
-2
c
-3
d
2
Answer:
-3
Step-by-step explanation:
Combining like terms, [tex]x-3x=-2x[/tex]. Since this means the variable terms on both sides combine to have the same coefficient, this means there are no solutions (since the constant terms differ).
Answer:
C.) -3
Step-by-step explanation:
We're looking for an equation with NO SOLUTION.
A.) 5
-2x + 11 = x + 21 + 5x
x = -1.25.
A.) is INCORRECT
B.) -2
-2x + 11 = x + 21 + (-2)x
x = -10
B.) is INCORRECT
C.) -3
-2x + 11 = x + 21 + (-3)x
No solution
C.) is CORRECT
D.) 2
-2x + 11 = x + 21 + 2x
x = (-2)
D.) is INCORRECT