Using a system of equations, it is found that there are 5 dimes and 9 quarters in his pocket.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: number of dimes in his pocket.Variable y: number of quarters in his pocket.He has a total of 14 coins, hence:
x + y = 14 -> y = 14 - x.
They are worth $2.75, hence, considering the value of each coin(dimes $0.1 and quarters $0.25), we have that:
0.1x + 0.25y = 2.75
Since y = 14 - x:
0.1x + 0.25(14 - x) = 2.75
x = (0.25*14 - 2.75)/0.15.
x = 5.
y = 14 - x = 14 - 5 = 9.
There are 5 dimes and 9 quarters in his pocket.
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Knowing that sin 30° = 1, what is a?
OA. 3.5
OB. 14
OC. 12.12
OD. 7
30⁰
7
a
60⁰
Answer:
B
Step-by-step explanation:
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{a}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
a = 7 × 2 = 14
Wen is factoring the polynomial, which has four terms. 6x3 – 12x2 7x – 14 6x2 (x – 2) 7(x – 2) which is the completely factored form of his polynomial?
Completely factored form of Wen's polynomial is (6x² + 7) (x-2).
What is a polynomial?
An algebraic expression called a polynomial includes coefficients and variables. Indeterminates are another name for variables. For a polynomial expression, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents, but division by variable is not possible. Although a polynomial can have multiple number of terms, it can't be infinite.
Factorizing the polynomial
Complete factorization of a polynomial results in products-of-sums
Given polynomial is,
6x³ - 12x² + 7x - 14
This polynomial can be factorized as follows,
6x² (x - 2) + 7(x - 2)
Now, we can factor out the common term (x-2) form each term on either side of the plus operator. thus, we get the following factors,
(6x² + 7) (x-2)
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Answer:
Answer is A :)
Step-by-step explanation:
Triangle GHI is rotated 90Degrees clockwise and then reflected over the y-axis. Which congruency statement is true?
On a coordinate plane, triangle G H I is rotated 90 degrees clockwise and then is reflected over the y-axis.
Angle G is congruent to angle H is congruent to angle I
Angle G double-prime is congruent to angle H double-prime is congruent to angle I double-prime
Triangle G H I is congruent to triangle G double-prime H double-prime I double-prime
Triangle G H I is congruent to triangle I H G
The congruency statement which is true among the answer choices is;
On a coordinate plane, triangle G H I is rotated 90 degrees clockwise and then is reflected over the y-axis.Triangle G H I is congruent to triangle G double-prime H double-prime I double-prime.Which congruency statement is true?According to the task content, the initial transformation is; Triangle GHI is rotated 90Degrees clockwise and then reflected over the y-axis.
On this note, the congruency which are true regarding the transformation are;
On a coordinate plane, triangle G H I is rotated 90 degrees clockwise and then is reflected over the y-axis.Triangle G H I is congruent to triangle G double-prime H double-prime I double-prime.This follows from the fact that the transformation.does not involved dilation by means of a scale factor and hence, size remains equal and all angle measures remain the same.
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What does it mean for an event to be unusual? why should the cutoff for identifying unusual events not always be 0. 05?.
An unusual event is an occurrence that has a low probability of happening. The cutoff for identifying unusual events not always be 0.05, because it is not always a good idea to utilize the same cutoff to spot unexpected occurrences.
What is an unusual event?An unusual event is an occurrence that has a low probability of happening.
If an event is improbable, its likelihood is zero. If an occurrence is unavoidable, its probability is one.
The probability of an event happening increases as it gets closer to 1. An occurrence that has a probability of 0.375, for instance, is more likely to happen than one with a probability of 0.125.
The less likely an event is to occur, the closer the probability is to 0. An unusual event is what this kind of event falls under. A probability of 5%, or 0.05, is typically regarded as unusual event.
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The jones family and the Connor family both bought the same boxed package of sugar cubes at the store, in which the cubes were arranged in 5 layers. After drinking of 61 cups of tea, the Joneses found that they were out of sugar. The Connors' sugar box was enough to last them thought 88 cups of tea. Both families put either 2 or 3 pieces of sugar per cup. How many sugar cubes were in the box
The number of sugar cubes in the box is 180
How to determine the number of sugar cubes?The given parameters are:
Layers = 5Pieces = 2 or 3Cups of tea = 61 and 88Multiply 61 and 88 by 2 and 3
61 * 2 = 122
61 * 3 = 183
88 * 2 = 176
88 * 3 = 264
The number of sugar cubes cannot be 122 and 264, because they are out of the range
So, we have:
183 and 176
There are 5 layers.
This means that the number of sugar cubes is divisible by 5.
The only number between 176 and 183 that is divisible by 5 is 180
Hence, the number of sugar cubes is 180
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The coordinate grid shows points A through K. What point is a solution to the system of inequalities? y < −2x + 10 y < 1 over 2x − 2 coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3 I B A F
The point that is a solution to the system of inequalities on the coordinates grid is A.
How to illustrate the information?It should be noted that form the information given, the expression is y < −2x + 10. In this case, draw the solid line y = -2x + 10.
Shade the region below the like for x = 5.
y = -2(5) + 10
= -10 + 10
= 0
For x= 0
y = -2(0) + 10
= 0 + 10
= (0, 10)
The diagram is attached.
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Functions and Transformations
The new translated function will be more towards the origin , as the value of length is decreased , Option C is the right answer.
What is a Function ?A function is a mathematical statement used to relate a dependent and an independent variable.
It is given that
Area of a Rectangle is 10 sq. unit
Width of the Rectangle is x unit
Length is given by
l(x) = 10 / x
When the length of the Rectangle is increased by 1 ,
The new function will be
l(x) = 10 /(x+1)
The new translated function will be more towards the origin , as the value of length is decreased ,
This is represented by Graph 3 ,
This can be proved by keeping the value of x
let x = 2
y = 10 /3 = 3.333
This is only in the graph 3 , Therefore Option C is the right answer.
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Abigail poured 8 x 10 milliliters of water into a beaker to use for an experiment. How is 8 x 10 written as a whole number?
Answer:
80?
hshsshjsjsjjsjajjsjsnnsnsnnw
Step-by-step explanation:
hhddussisusuis
Find x
Help me please thank u
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!!Samarium-146 has a half-life of 103.5 million years. after 1.035 billion years, how much samarium-146 will remain from a 205-g sample?
Answer: 0.200 g
Given: Half life of Sm-146 = t1/2 = 103.5 million years
Time period, t = 1.035 billion years = 1035 million years
The original mass of the sample, [A]₀ = 205 g
To determine:
Amount of sample after t = 1035 million years
Explanation:
The rate of radioactive decay is given as:
Answer:
A: 0.200 g.
Step-by-step explanation:
What is the best first step in solving the equation 3+√6x=5?
O Subtract 3 from both sides.
O Find the cube of Vex.
O Cube both sides of the equation.
O Subtract 5 from both sides.
Nathan received $1,500 dollars for his birthday. He saves 3/5 of his money. 6/20 of his money was used to buy a new game. How much money does he have left?
Answer:
$150
Step-by-step explanation:
→ Find 3/5 of 1500
( 1500 ÷ 5 ) × 3 = 900
→ Find 6/20 of 1500
( 1500 ÷ 20 ) × 6 = 450
→ Find the sum of the 2 numbers
900 + 450 = 1350
→ Minus it from the original 1500
1500 - 1350 = $150
If y is inversely proportional to z^4, when y = 16 and z = 3, then 16 = k/81
true or false
Answer: 65
Step-by-step explanation:
1 + 64 = 65
( this is my summer math homework, please help!)
Find the selling price of each item.
1. Original price of a bunny: $46.00
Text: 2%
2. Original price of a CD: $14.99
Tax: 2%
3. Original price of a CD: $16.50
Tax: 4%
4. Original price of a car: $19,500.00
Tax: 4%
Using proportions, the selling prices are given as follows:
1. $46.92.
2. $15.29.
3. $17.16.
4. $20,280.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
To find the selling prices, we have to multiply the original prices by either 1.02(2% sales tax) or 1.04(4% sales tax), hence they are given as follows:
1. 46 x 1.02 = $46.92.2. 14.99 x 1.02 = $15.29.3. 16.50 x 1.04 = $17.16.4. 19500 x 1.04 = $20,280.More can be learned about proportions at https://brainly.com/question/24372153
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what is the midpoint of the line segment that joins -3/4 and 2 1/2
The mid point between the two points is at 13/8 .
What is a Line Segment ?A line segment is a line of fixed measure .
The line segment extends from (-3/4) to [tex]\rm 2 \dfrac{1}{2}[/tex]
i.e the line extends form -3/4 to 5/2
To find the mid point , the total distance needs to be determined
So the distance between the two point is
(5/2) + (3/4) = 13/8
The mid point is at half the distance of this
so it is at 13/8 from both the points
Any point at 13/8 distance from 5/2 towards (-3/4) will be
= (5/2) - (13/8)
= 7/8
So the mid point between the two points is at 13/8 .
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What is the answer, been stuck for 20 minutes.
Answer:
y= -1/2x - 4 ?
Step-by-step explanation:
Which linear function has the same y-intercept as the one that is represented by the graph? On a coordinate plane, a line goes through points (negative 4, 0) and (0, 3). a y = 2 x minus 4 b y = 2 x minus 3 c y = 2 x + 3 d y = 2 x + 4
The line which is having same y intercept as the line which passes through points (-4,0) and (0,3) is y=2x+3.
Given Points through which the line passes through are (-4,0) and (0,3)
We have to find the equation whose y intercept is equal to the y intercept of the line whose points given above.
First of all we have to find the y intercept of the line which passes through (-4,0) and (0,3). Equation of line is :
y-y1=(y2-y1)/(x2-x1)*(x-x1)
y-0=(3-0)/(0+4) *(x+4)
y=3/4(x+4)
y -intercept exists where x=0
put x=0
y=3
So the options are:
y=2x-4y=2x-3y=2x+3y=2x+4By putting the value of x in all options we will find
y=-4
y=-3
y=3
y=4
So the third option is correct.
Hence the line whose y-intercept matched with the given line is y=2x+3.
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Answer:
a
Step-by-step explanation:
After four years of higher education, Julia just graduated with a Bachelor's degree in Engineering from USC where the annual cost of tuition was $22,000. She paid for college by earning $11,000 annually through the work study program and receiving an annual scholarship. She covered the remainder of the costs by taking out $12,000 in student loans. If she didn't fund her education with savings or grant money, what was the amount of Julia's annual academic scholarship?
Answer:
$32,000
Step-by-step explanation:
overall cost for 4 years was $88,000. She made $44,000 after 4 years. After all 4 years she had to take out $12,000 to pay. 88,000-44,000=44,000 44,000-12,000=32,000
Answer:
$8,000
Step-by-step explanation:
Tuition per year: $22,000
Work Study Earnings per year: $11,000
Student Loans per year: $12,000 / 4 = $3,000
Annual Academic Scholarship per year: $x
Per Year Calculations
$22,000 = $11,000 + $3,000 + $x
$x = $22,000 - $11,000 - $3,000
$x = $8,000
The average monthly temperature T(m), in degrees Celsius, in a particular city varies according to the model T of m equals 4 times sine of the quantity pi over 6 times m end quantity plus 2 comma where m represents the months of the year and January begins at m = 0. Between what months will the temperature be below 0°C?
The months with temperature below 0° is August and October.
GIven,
T(m) = 4 sin (π/6 m)₊2
In the above equation, T(m) is the average temperature in a month in degrees Fahrenheit, and m is the month of the year.
T(8) = 4 sin (8π/6 m)₊2
= 4 sin (4π/3 )₊2
= 4 sin (π₊π/3 )₊2
= ₋4 sin π/3 ₊2
= ₋4×√3/2 ₊2
= ₋2√3 ₊ 2 <0
The function for the average monthly temperature, in m months from january is given by
T(0) = 4 sin(10π/6) ₊ 2
= 4 sin(5π/3) ₊ 2
= 4 sin(2π ₋ π/3) ₊ 2
= - 4sin π/3 ₊ 2 = ₋4 × √3/2 ₊ 2
= ₋2√3 ₊2<0
we can notice that after january, from august till october the months will face temperature below 0 degrees.
So the answer is August and October.
Your question is incomplete. Please find the missing content here.
The average monthly temperature T(m), in degrees Celsius, in a particular city varies according to the model T of m equals 4 times sine of the quantity pi over 6 times m end quantity plus 2 comma where m represents the months of the year and January begins at m = 0. Between what months will the temperature be below 0°C?
July and NovemberJuly and OctoberAugust and NovemberAugust and OctoberLearn more about "temperature problems" here-
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Abbot Tools is designing a new toolbox. The length of the toolbox will be three times its width, w, and the length of the diagonal of the top cover will be 30 inches.
Use this information to determine the length, l, of the box. Select the correct answer from the drop-down menu.
The length and width of the toolbox given the diagonal is 45 inches and 15 inches respectively.
TriangleWidth of the triangle = wLength of the triangle = 3wDiagonal = 30 inchesHypotenuse ² = opposite ² + adjacent ²
30² = w² + (3w²)
30² = 4w²
900 = 4w²
w² = 900/4
= 225
w = √225
w = 15
Therefore,
Width of the triangle = w
= 15 inches
Length of the triangle = 3w
= 3(15)
= 45 inches
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Rohan's salary 1200$ per month he spends 75% of it how does he spend in dollars?
Answer:900
Step-by-step explanation:
Identify the term that means the difference of the minimum and maximum values of a data set and the term that means the difference of the first quartile and third quartile of a data set.
Answer:
Range: Difference of minimum and maximum values of a data set
Interquartile Range: Difference of first quartile and third quartile of a data set
Step-by-step explanation:
Answer: what he said
Step-by-step explanation:
Calculate the angle of depression from the
top of the flag pole to point A.
Give your answer to 1 d.p.
A
31 feet
25 feet
The angle of depression from the top of the flag pole to point A is 36.2 degrees.
What is the angle of depression?From trigonometric ratio: cos(θ) = Adjacent / Hypotenuse
Given that;
Adjacent = 25ftHypotenuse = 31ftAngle of depression θ = ?cos(θ) = Adjacent / Hypotenuse
Cos(θ) = 25ft/31ft
Cos(θ) = 0.80645
θ = cos⁻¹( 0.80645 )
θ = 36.2°
Therefore, the angle of depression from the top of the flag pole to point A is 36.2 degrees.
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the answer the answer
Answer:
the answer
Step-by-step explanation:
Answer:
K?
Step-by-step explanation:
The answer of the answer is the answer.
Hope this helped :D
what is the value of 2/3 + 1/2 of (1/2 - 1/6) / 2/3 + 1/4
Answer:
In fraction form: 77/24
In decimal form: 3.20833
Step-by-step explanation:
That took me a while to solve but that’s the correct answer.
Hope that helps! :)
WHICE group of domain-specific words belongs only to math domain
Answer:
The major field of anthroplogy and evolutionary and paleo anthropological perspectives on the origin of humankind
Pedro Fernández es gerente de Avon Chic, Pedro estaba interesado en las tasas de rendimiento de los últimos cinco años de dos diferentes fondos mutuos. Trujix, Inc., mostro un periodo de cinco años, tasas de rendimiento del 12; 10; 3; 9 y 11%, mientras que Fondo Corporation arrojo 13; 12:14:10 y 6%. Un cliente se acercó a Pedro y expreso su interés uno de estos fondos mutuos. ¿cuál debería escoger Pedro para su cliente?
Pedro Fernández should advice his client to go with the second mutual fund named as Fund Corporation. This is because, it showed an higher average return over the five-year period at an average of 11% beating Trujix Inc by 3%.
What is the calculation that supports the above?To get the better fund, Pedro must calculate a simple average of the interest rates of the various funds over the past 5 year period.
Trujix Inc 5-Year Average
(12 + 10+ 3 +9 + 11)/5
= 45/5
=9%
Fund Corporation 5-Year Average
(13 + 12 +14 + 10+ 6)/5
= 55/5
= 11%
Hence, the better investment is the one by Fund corporation.
Full Question
Pedro Fernández is a manager at Avon Chic, Pedro was interested in the rates of return for the last five years of two different mutual funds. Trujix, Inc., showed a five-year period, rates of return of 12; 10; 3; 9 and 11%, while Fund Corporation showed 13; 12:14:10 and 6%. A client approached Pedro and expressed his interest in one of these mutual funds. Which one should Pedro choose for his client?
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A correlation coefficient of 0.08 indicates strong positive correlation. Group startsTrue or False
Since the correlation coefficient has an absolute value that is less than 0.6, it is not a strong relationship, hence the statement is False.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.In this problem, the correlation coefficient is of 0.08, hence:
The coefficient is positive, hence the is a positive correlation.The coefficient is of 0.08, which is less than 0.6, hence the correlation is not strong.Thus, the given statement is False.
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If 9: x= x4, then x=
Answer:
x = ±6
Step-by-step explanation:
9 : x = x : 4
9/x = x/4
Cross multiply.
x² = 9 × 4
x² = 36
x = ±√36
x = ±6
? Question
What are coordinates of the point representing the location of the other end of the string of buoys?
Type the correct answer in each box. Use numerals instead of words.
See below for the explanation on how to determine the coordinates.
How to determine the coordinates?The question is incomplete, and the missing parameters cannot be found.
So, I will give a general explanation on how to determine coordinates.
Assume that the start point of the buoy is
(x, y)
And the length of the buoy is k.
Depending on the position of the bouy on the coordinate plane, the endpoint can be any of the following coordinates (x - h, y), (x + h, y), (x, y + h) and (x, y - h)
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