Answer:
a. 31 months
b. $818.32
c. $168.32 interest
Step-by-step explanation:
Given that Joe makes a minimum payment of $21.45 on his credit card purchase of $650 with an APR of 19.85%, you want to know ...
how long until the purchase is paid offthe total amount paidthe cost of using the credit carda. Payoff timeIf the balance is reduced by $21.45 per month, it will take ...
$650/($21.45/mo) ≈ 30.3 months
to pay off the balance.
Joe will be making payments for 31 months.
b. Payoff amountThe total amount Joe pays for his sound system is the sum of its initial cost and the total of interest payments. That sum is ...
cost + interest = total paid
$650 +168.32 = $818.32
Joe will pay a total of $818.32.
c. Credit chargesThe total amount of interest Joe pays is $168.32.
__
Additional comment
If the total payment each month is $21.45, then it will take 43 months to pay off the system, for a total cost of $909.61, of which $259.61 is the cost of the credit. (The finance charge is paid first from this payment amount, so the amount that goes to reduce the balance is less.)
McDonald's has a leaking drink machine. The manager placed a cup under the leak until he
could get it fixed. After 1 1/4 hours, the manager noticed that the cup had collected 1/3 cups of
soda. What is the rate, in cups per hour, at which the drink machine is leaking?
Answer:
4/15 cups of soda per hour
Step-by-step explanation:
1 1/4 = 5/4 and if 5/4 hours yielded 1/3 cups, you would have to multiply 1/3 by the reciprocal to find the hourly rate
1 4 4
- * - = --
3 5 15
You are given the figure below well as the following information.
Answer:
A. 110°
Step-by-step explanation:
according to the theorems,
m∠1=m∠6=m∠9=m∠14=110°;
m∠2=m∠5=m∠10=m∠13=70°;
m∠3=m∠8=m∠11=m∠16=70°;
m∠4=m∠7=m∠12=m∠15=110°.
all the details are in the attachment.
Kim decided that she wanted to go bowling. The bowling alley charges $2.75 per game and $10 for shoes. If Kim has $30, how many complete games can she bowl?
Write an equation and solve it.
Answer: 2 complete games
Step-by-step explanation:
add shoes and game charge
$10.00 + 2.75 = 12.75 <— that’s 1 complete game
subtract it from $30.00
$30.00 - 12.75 = 17.25.
A complete game costs 12.75. so, Kim had enough money for one more game.
17.25 - 12.75 = $4.50 remaining after 2 complete games
Answer: 7 games
Step-by-step explanation: if it charges 10 for shoes, then you already subtract 10 from 30. 30-10=20. then, to find out how many games she can play, divide 2.75 from 20. 20/2.75=7.272727.... Since you can't pay for half of a game, it would be 7 games.
Can someone please explain step by step on how I solve this equation?
-1 - (-0.25) = ?
Answer: -1 - (-0.25) = -0.75
Step-by-step explanation:
The way you would do that is by first pretending as the negative sign (-), isn't present.
Then do "1 - 0.25".
1.00 - 0.25 = 0.75
After you solved the equation, then we can add the negative sign (-), back into the equation = -1 - (-0.25) = -0.75 ✅
Evaluate the expression below for s=3 and t=6.
3st² - s²
For s = 3 and t = 6, 3st² - s² =
The value of the expression is 3st² - s² is 315.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given expression is 3st² - s².
For s = 3 and t = 6, find the value of the expression 3st² - s².
To find the value of the expression, replace s by 3 and t by 6:
3st² - s²
= 3×3×6² - 3²
= (9 × 36) - 9
= 324 - 9
= 315
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Total students in a class are 120. 40% of them are female students. 70 male students passed with 100% pass rate. What is the pass rate of female students at 100 percent rate?
Answer:
Here is the answer
Step-by-step explanation:
If 40% of the students in the class are female, then there are 40/100 * 120 = 48 female students.
If 70 male students passed with a 100% pass rate, then the pass rate for male students is 100%.
If the pass rate for male students is 100%, then the pass rate for female students must also be 100%. This is because the pass rate is calculated as the number of students who pass divided by the total number of students, and if all the male students pass, then the pass rate for male students must be 100%.
Therefore, the pass rate for female students at a 100% rate is also 100%.
You install 538 feet of fencing along the perimeter of a rectangular yard. The width of the yard is 127 feet. What is the length of the yard?
Hey what is 0.18 x 0.02
Answer:
0.0036
Step-by-step explanation:
Answer: 0.0036
Step by step explin
Five acres of land were divided into 4 lots of equal size. How many square feet did each lot measure? (1 acre = 43,560 sq ft)
The number of square feet each lot measure is 54, 450 square feet.
How to find the area in square feet of the lot?Five acres of land were divided into 4 lots of equal size. The number of square feet each lot measure can be calculated as follows:
1 acre = 43,560 square ft
5 acres = ?
cross multiply
number of acres = 5 × 43,560
number of acres = 217800 square feet.
Therefore, the lots is divide into 4 equal lots.
Hence,
measure of each lot = 217800 / 4
measure of each lot = 54, 450 square feet.
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Solve 0=sin1/2x+cosx−1
The value of x = 2nπ, (n ∈ Z) and
[tex]x=2(n\pi+(-1)^{n} \pi /6)[/tex], (n ∈ Z)
What are Trigonometric Identities?
Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. Trigonometric Identities are true for every value of variables being on both sides of an equation. Geometrically, these identities involve certain trigonometric functions( similar as sine, cosine, tangent ) of one or further angles.
According to question
⇒ sin(x/2) + cos(x) - 1 = 0
⇒ sin(x/2) + cos(x) - 1 = 0
{ cos(2x) = 1 - 2sin²(x) }
cos(x) = 1 - 2sin²(x/2)
⇒ sin(x/2) + cos(x) - 1 = 0
⇒ sin(x/2) + 1 - 2sin²(x/2) - 1 = 0
⇒ - 2sin²(x/2) + sin(x/2) + 1 - 1 = 0
⇒ - 2sin²(x/2) + sin(x/2) = 0
⇒ sin(x/2)(- 2sin(x/2) + 1) = 0
⇒ sin(x/2) = 0 , x = 2nπ (n ∈ Z)
and
⇒ sin(x/2) = 1/2 , [tex]x=2(n\pi+(-1)^{n} \pi /6)[/tex] (n ∈ Z)
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MP MODELING REAL LIFE You sell instruments at a
Caribbean music festival. You earn $326 by selling 12 sets
of maracas, 6 sets of claves, and x djembe drums. Find the
number of djembe drums you sold.
The number of djembe drums you sold is 8
How to determine the number of djembe drums you sold.From the question, we have the following parameters that can be used in our computation:
Total = 12 sets of maracas, 6 sets of claves, and x djembe drums.
Earning = $326
Also, we have:
The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.
So, we have
12 * 14 + 6 * 5 + x * 16 = 326
Evaluate the products
198 + 16x = 326
Evaluate the iike terms
16x = 128
So, we have
x = 8
Hence, the number of djembe drums is 8
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Complete question
You sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas, 6 sets of claves, and x djembe drums.
The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.
Find the number of djembe drums you sold.
Which number is a solution of the inequality?
x(7-x) > 8
x(7 - x) > 8
Steps for calculationFirst solve x(7 - x) = 8
x^2 - 7x + 8 = 0
x = 5.56, 1.44
If we plug in these values into the original equation we can see that solution is
1.44 < x < 5.56
Meaning and definition of systems of inequality:The value of the variable(s) that transforms the inequality into a true statement is the solution. Think about the example (x+3>5). If we provide any real value bigger than (2) for this inequality, it will be true (x). (therefore) This inequality's answer is (x>2)A collection of two or more inequalities in one or more variables is referred to as a system of inequalities. Systems of inequalities are utilized when a scenario calls for several solutions but also places multiple restrictions on those answers.The best answer is often found by solving a set of linear inequalities. This response could be as simple as calculating the number of products that need be produced in order to maximize profit or as complex as selecting the ideal medication regimen for a patient. The different kinds of inequalities and how to solve them will be covered in this article.To learn more about Systems of inequalities refer https://brainly.com/question/26119697
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PLEASE HELP
Given that x is a normal variable with mean = 47 and standard deviation = 6.4, find the following probabilities. (Round your answers to four decimal places.)
(a) P(x ≤ 60)
(b) P(x ≥ 50)
(c) P(50 ≤ x ≤ 60)
Given that x is a normal variable with mean = 47 and standard deviation = 6.4, find the following probabilities.
(a) P(x ≤ 60) = 0.9356 (b) P(x ≥ 50) = 0.6744 (c) P(50 ≤ x ≤ 60) = 0.2612What are the probabilities?Generally, To solve these problems, we can use the standard normal distribution table or a computer program to find the desired probabilities.
First, we need to standardize the given values of x by subtracting the mean and dividing by the standard deviation. This gives us a standard normal random variable, denoted by Z, with a mean of 0 and a standard deviation of 1.
(a) P(x ≤ 60) = P(Z ≤ (60 - 47)/6.4) = P(Z ≤ 1.5625). From the standard normal distribution table or a computer program, we find that P(Z ≤ 1.5625) = 0.9356.
(b) P(x ≥ 50) = P(Z ≥ (50 - 47)/6.4) = P(Z ≥ 0.46875). From the standard normal distribution table or a computer program, we find that P(Z ≥ 0.46875) = 0.6744.
(c) P(50 ≤ x ≤ 60) = P(0.46875 ≤ Z ≤ 1.5625) = P(Z ≤ 1.5625) - P(Z ≤ 0.46875) = 0.9356 - 0.6744 = 0.2612.
Therefore, the probabilities are as follows:
(a) P(x ≤ 60) = 0.9356 (b) P(x ≥ 50) = 0.6744 (c) P(50 ≤ x ≤ 60) = 0.2612
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Find the equation of a line that contains the points (−7,2) and (2,−2). Write the equation in slope-intercept form using fraction if necessary.
The required equation of the line which contains the points (−7,2) and (2,−2) is y = -4/9x - 8/9.
What is the equation of the line?A straight line's general equation is y = MX + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.
The equation of the line's general form is:
y = MX + c
Where, m = slope, c = y-intercept and slope = ( y₂ - y₁ ) / ( x₂ - x₁ ).
Determine the line's slope:
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -2-2) / (2+7 )
Slope= -4/9
The y-intercept is determined as follows:
y = MX + c
2 = -4/9x 2+c
c = -8/9
The lines' equation:
y = MX + c
y = -4/9x - 8/9
Therefore, the required equation of the line which contains the points (−7,2) and (2,−2) is y = -4/9x - 8/9.
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which of the following is not a valid property of circles? a rotateangle b none of these c left d width
There is no property named 'left' for the circle. So the answer is 'c'.
What is Circle?Circle is a two dimensional figure which has a round shape. It is formed by joining all the points which are at an equal distance from a fixed point called the center of the circle.
The line formed by joining the center to any point on the boundary of the circle is called radius. Diameter is double of the radius.
Rotate angle is the term defining the angle of rotation of the circle. Angle of rotation of a complete circle is 2π.
Width is another term for diameter of the circle, although it is not commonly used.
Left is the only term which does not have any role in the properties of circles.
Hence, the term 'left' is not a valid property of circles.
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What is the value of p ?
By using the fact that the sum of the internal angles of a triangle is 180°, we will see that p = 80°
What is the value of p?Notice that on the top vertex of the triangle we have a plane angle, then we can write:
p + 49° + A = 180°
So we can solve that really simple linear equation we can find the value of A, the top internal angle of the triangle:
A = 180° - 49° - p
A = 131° - p
Now remember that the sum of the 3 internal angles of a triangle is equal to 180°, so now we can write the equation:
131° - p + p - 16° + p- 15° = 180°
p = 180° - 131° + 16° + 15°
p = 80°
The value of p is 80°.
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Your iron works has contracted to design and build a 500-ft^3, square-based, open-top, rectangular steel holding tank for a paper company. The tank is made by welding thin stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weigh as little as possible. What dimensions do you tell the shop to use?
The dimensions for the base and height that will make the tank weigh as little as possible are 10 feet and 5 feet, respectively
How to determine the dimensions to use?From the question, we have the following parameters that can be used in our computation:
Volume = 500 cubic feet
Base = square base
This means that the volume can be calculated using
V = b²h
Where
b = base length
h = height
So, we have
b²h = 500
Make h the subject
h = 500/b²
The surface area is calculated as
A = 4bh + b²
Substitute h = 500/b² in A = 4bh + b²
A = 4b(500/b²) + b²
Evaluate
A = 2000/b + b²
Differentiate and set to 0
-2000/b² + 2b = 0
So, we have
2b = 2000/b²
Divide by 2
b = 1000/b²
Multiply by b²
b³ = 1000
So, we have
b = 10
Substitute b = 10 in h = 500/b²
h = 500/10²
Evaluate
h = 5
Hence, the height is 5 feet
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What is an equation of the parabola
Answer:
(c) x = -1/11(y -3)²
Step-by-step explanation:
You want an equation of the parabola with directrix x = 11/4 and vertex (0, 3).
EquationThe directrix is a vertical line to the right of the vertex. This means the parabola opens to the left.
The vertex form of the equation is ...
x = 1/(4p)(y -k)² +h . . . . . . . . where (h, k) is the vertex, and p is the distance from the directrix to the vertex (also, the distance from the vertex to the focus)
ApplicationHere, we have ...
p = 0 -11/4 = -11/4 . . . . negative because the vertex is left of the directrix
and
(h, k) = (0, 3)
so the equation is ...
x = 1/(4(-11/4))(y -3)² +0
x = -1/11(y -3)²
At a football game, a vender sold a combined total of 244 sodas and hot dogs. The number of hot dogs sold was 42 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
Answer:
143 sodas101 hot dogsStep-by-step explanation:
Given a total of 244 sodas and hot dogs sold, with sodas numbering 42 more than hot dogs, you want to know the number of each that were sold.
SetupLet s represent the number of sodas sold. Then s-42 is the number of hot dogs sold, and the total sold is ...
s +(s -42) = 244
SolutionAdd 42 and simplify
2s = 286
s = 143 . . . . . divide by 2
hot dogs = 143 -42 = 101 . . . . . figure the number of hot dogs
143 sodas and 101 hot dogs were sold.
What are the domain and range of the function F(x) = 3/4 x + 5?
Domain (-infinite, infinite)
Range (-infinite, infinite)
Domain (3/4, infinite)
Range (-infinite, 5)
Domain (-infinite, 3/4)
Range (5, infinite)
Domain (3/4, infinite)
Range (5, infinite
The domain and range of the provided function are (-infinite, 3/4) and (5, infinite) respectively.
What is function?A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output. A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).
What is domain and range?The domain of a function is the set of values that may be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the collection of values that the function returns when we enter an x value. To acquire the domain and range, just solve the equation y = f(x) to discover the values of the independent variable x. To compute the function's range, just define x as x=g(y) and then discover the domain of g. (y).
Here,
f(x)=3/4x+5
Domain=(-infinite, 3/4)
Range=(5, infinite)
The domain for given function is (-infinite, 3/4) and range is (5, infinite).
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Suppose X varies directly with YX equals 29 when Y equals -87 what is the constant variation and what is the value of x when y = -187
A. Constant variation -1/3, x= 63
B. constant variation -1/3, x= -63
C. Constant variation -3, x= 63
D. Constant variation -3, x = 567
The constant variation and the value of x are (a) Constant variation -1/3, x= 63
How to determine the constant variation and the value of xFrom the question, we have the following parameters that can be used in our computation:
X varies directly with Y
X equals 29 when Y equals -87
This means that
Constant of variation = X/Y
Substitute the known values in the above equation, so, we have the following representation
Constant of variation = 29/-87
Evaluate
Constant of variation = -1/3
From the question, we have
y = -187
This means that
Constant of variation = X/-187
So, we have
X = -187 * Constant of variation
This gives
X = -187 * -1/3
Evaluate
X = 63
Hence, the solution is (a)
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Help me! Can someone please
Answer:
13
Step-by-step explanation:
Divide both sides of the equation by 4.
- At a bake sale, the Math Club raised $225 by selling 300 baked goods. If the amount
raised varies directly with the baked goods sold, how much money will be raised for
selling 450 baked goods?
Record your answer on the answer document.
5x3
The amount of money for selling 450 baked goods will be
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
At a bake sale, the Math Club raised $225 by selling 300 baked goods.
And, The amount raised varies directly with the baked goods sold.
Now,
Let the amount of money for selling 450 baked goods = x
Since, At a bake sale, the Math Club raised $225 by selling 300 baked goods.
And, The amount raised varies directly with the baked goods sold.
Hence, By definition of proportion we get;
⇒ $225/300 = x / 450
⇒ x = 225 × 450 / 300
⇒ x = $337.5
Thus, The amount of money for selling 450 baked goods = $337.5
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An air traffic controller is tracking two planes. To start, plane A is at an altitude of 3500 feet and plane B is at an altitude of 2609 feet. Plane A is gaining altitude at 45.5 feet per second and plane B is gaining 65.75 feet per second. How many seconds will pass before the planes are at the same altitude? What will their altitudes be when they’re at the same altitude?
44 seconds will pass before the planes are at the same altitude.
What do you mean by algebraic expression?
An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.
There are three main types of algebraic expressions:
Monomial Expression
Binomial Expression
Polynomial Expression
An algebraic expression with only one term is called a monomial.
It is given that plane A is at an altitude of 3500 feet and plane B is at an altitude of 2609 feet. Plane A is gaining altitude at 45.5 feet per second and plane B is gaining 65.75 feet per second.
Let x seconds will pass before the planes are at the same altitude.
Plane A, 3500 + 45.5x
Plane B, 2609 + 65.75x
x is number of seconds of time
When altitudes equal
3500 + 45.5x = 2609 + 65.75x
3500 - 2609 = 65.75x - 45.5x
891 = 20.25x
891/20.25 = x
44 = x
Therefore, 44 seconds will pass before the planes are at the same altitude.
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a number has the same digit in its hundreds place and in its hundreds place. how many times greater is the value of the digit in the hundreds place than the value of the digit in the hundreds place
A number has the same digit in its hundreds place and in its hundreds place. 10,000
What is the value of the digit?Generally, Given that a number's hundreds place and its hundredths place both have the same digit, we may assume that the number is perfect.
Let's say that the digit is a 1.
Therefore, the value of the hundreds position in a number is equal to 100.
The value of the hundredth position in a number is equal to 0.01%.
The following formula may be used to determine the number of instances in which the value of the digit in the hundreds place is higher than the value of the digit in the hundredths place:
As a result, the difference between the value of the digit in the hundreds place and the value of the digit in the hundredth place is 10,000 times bigger.
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CQ
A number has the same digit in its hundreds place and its hundredths place. How many times greater is is the value of the digit in the hundreds place than the value of the digit in the hundredths place?
A. 100,00
B. 100
C. 1,000
D. 10,000
Select the number that completes the equivalent fraction.
3/4=9/?
4
8
10
12
x = 1/4. y = 2/3. z = 4*1/5
Work out the value of X x y x z
Give your answer as a fraction in its simplest form.
Answer:
[tex]\frac{7}{10}[/tex]
Step-by-step explanation:
NO LINKS!! Please help me with this problem. Part 3ff
Answer:
a) $48700, b) $305200------------------------------------
GivenStarting salary = $38500,Annual increase = $1700.Part AThe salary during the 7th year is:
38500 + 1700*(7 - 1) = 38500 + 1700*6 = 48700Part BTotal compensation through full 7 years is base salary for 7 years and total of the annual increase:
38500*7 + 1700*(1 + 2 + 3 + 4 + 5 + 6) = 269500 + 1700*6/2*(1 + 6) = 269500 + 1700*21 = 305200Please help me with this question
Answer:
Point of intersection is (13.72, 660)
Step-by-step explanation:
You have to use your graphing tool to answer questions 2 and 3.
Then click on the point of intersection and note the coordinates.
That's it.
This can also be solved mathematically but since the question does not ask I have not given that solution process.
Graph attached
A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Internet. They sort the data by payment plans, as shown below. Plan A: 27 text, 21 Internet Plan B: 13 text, 10 Internet Answer the questions to determine a conditional probability. What is the probability that a randomly selected customer who is on plan B uses the phone most often to text? Give the answer in fraction form.
The probability that a randomly selected customer who is on plan B uses the phone most often to text is; 13/23
How to solve fraction word problems?We are given that;
The data by payment plans are;
Plan A: 27 texts, 21 Internet
Plan B: 13 texts, 10 Internet
Now, the probability is defined as the ratio of the sum of all observations and the total number of observations.
The total number of observations for plan B is; 13 +10 = 23
The number of customers that are on payment plan B = 23 customers are on payment plan B.
The number of customers that are on plan B text is; 13
Thus, the probability that a randomly selected customer who is on plan B uses the phone most often to text is;
Probability = 13/23
The probability that a randomly selected customer who is on plan B uses the phone most often to text is 13/23.
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