Total thirty-nine months will be take by Johnson family to pay off the balance, $10,000.00.
The monthly payment is the amount paid per month to pay off the principle in the time period of the loan. If your rate is r%, divide r/100 by 12 to calculate your monthly interest rate. Formula for monthly payment is, M = Pr(1+r)ⁿ/{(1+r)ⁿ - 1 }
where, P --> principle
r--> rate of interest in months
n --> number of periods (in months )
In this problem, Johnson family bought the furniture and appliances for a new house that is principle, P = $10,000
Rate of interest, R = 15%
In terms of months, R = 0.15/12
= 0.0125 per month
Monthly payment, M = $325.00
Plugging all known values in above formula we get, $325.00 = {$10,000 × 0.0125(1 + 0.0125)ⁿ}/{(1+ 0.0124)ⁿ - 1 }
=> 325 = 125(1.0125)ⁿ/{(1.0125)ⁿ - 1}
=> 325 {(1.0125)ⁿ - 1} = 125(1.0125)ⁿ
=> 325(1.0125)ⁿ - 325 = 125(1.0125)ⁿ
=> 325(1.0125)ⁿ - 125(1.0125)ⁿ = 325
=> 200 (1.0125)ⁿ = 325
=> (1.0125)ⁿ = 325/200 = 13/8 = 1.6250
Taking natural logarithm both sides
=> ln(1.0125)ⁿ = ln (1.6250)
=> n ln(1.0125) = ln (1.6250) = 0.4855
=> n×0.0124 = 0.4855
=> n = 0.4855/0.0124 = 39.153 ~ 39
Hence, required months are 39.
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5x+20+3x-8 please help!
Answer:
29x+20
Step-by-step explanation:
(6cd-¹)-3
Simplify
The -1 is an exponent that needs to be made positive
The solution of the expression is 216(cd)³.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the exponential expression is (6cd⁻¹)⁻³. The expression will be simplified as below,
E = (6cd⁻¹)⁻³.
Use the property of the exponents to multiply the powers and now solve.
E= (6cd³)
E = 6³ x (cd³)
E = 216(cd³)
Therefore, the simplified value of the expression is 216(cd)³.
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What is the corresponding point on the unit circle for the given radian measure?
0=5pi/3
The corresponding point on the unit circle for the angle θ = 5pi/3 is given by: (0,5, -0.866).
What is the unit circle?
Basically, the unit circle is a circle with a radius of 1. It is used in trigonometry to help define and understand angles and their associated trigonometric values. The unit circle is centered at the origin (0, 0) of the coordinate plane, and each point on the circle is defined by its distance from the origin and its angle from the positive x-axis.
What is area of circle ?
The area of circle can be defined as the product of pi and square of radius of a given circle.
In this problem, we have that θ = 5pi/3 , hence:
cos θ = 0.5
sin θ = -0.866
Thus the point is (0,5, -0.866).
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√54
simplify the square root
Answer:
7.3
Step-by-step explanation:
Does someone mind helping me with this problem? Thank you!
Answer:
the answer to get x = 116 and y=54
Step-by-step explanation:
Helen has 687 acres of corn. She expects a yield of 188 bushels per acre. Estimate the total yield.
Answer:
129,156
Step-by-step explanation:
QUICK!!
How can you use multiplication and division to solve an inequality?
Answer:
If you multiply or divide both sides of an inequality by the same positive number, the inequality remains true.
But if you multiply or divide both sides of an inequality by a negative number, the inequality is no longer true.
Step-by-step explanation:
hope it helps<3Answer:
The multiplication property of inequality states that if one side of the inequality is multiplied or divided by a positive number, we can multiply and divide the other side of the inequality by the same number without changing or disturbing the direction sign of the inequality.
Step-by-step explanation:
PLEASE HURRRY I NEED HELP!
From the given angles of the triangle, it was possible to find the angle x=29°.
TrianglesTriangles are geometric figures with three (3) sides. They present different classifications regarding their sides or angles.
Like a classification for angles, it is possible to cite, a right triangle. A triangle is classified as a right triangle when it presents one of your angles equal to 90º.
For another side, an equilateral triangle whose classification is associated with the sides. An equilateral triangle presents the three equal sides.
Regardless of its classification, the sum of the a triangle's angles will always be 180°.
The question gives two angles: 50° and 101°. And, it asks the value of angle x.
Therefore,
50+101+x=180
x+151=180
x=180-151
x=29°
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Use the distributive property to write an expression that is equivalent to . 6−9x
The distributive property states that for any real numbers a, b and c, the following is true:
a(b + c) = ab + ac
To use the distributive property to write an expression that is equivalent to 6 - 9x, we can factor out the -9x from the second term:
6 - 9x = 6 - 9x + 0 - 0x = 6 - 9x + (-9x) = 6 + (-9x)
Therefore, using the distributive property, we can write an expression that is equivalent to 6 - 9x as:
6 + (-9x)
Answer:
-3 ( 3x - 2 )
Step-by-step explanation:
- 9x + 6
Work out the value of a and the value of n[tex](ax^{6} )^\frac{1}{n} = 7x^{3}[/tex]
In the expression (ax⁶)^(1/n) = 7x³ the values of a and n are
49 and 2 respectivelyHow to solve for a and nThe expression (ax⁶)^(1/n) = 7x³is simplified as follows
Information from the problem
(ax⁶)^(1/n) = 7x³
to make x⁶ to be equal to x³ we use the powers
6 * y = 3
y = 1/2
hence n = 2
substituting n = 2 and solving
(ax⁶)^(1/2) = 7x³
√(a) x³ = 7x³
dividing both sides by x³
√a = 7
squaring both sides of the equation wil result to
√a = 7
(√a)² = 7²
a = 7²
a= 49
We can therefore say that a = 49 and n = 2
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What kind of triangle is this 90 29 61?.
The triangle with angles of 90 degrees, 29 degrees, and 61 degrees is a general right triangle that does not belong to any specific type of triangle and it has no specific ratios between the sides.
The triangle with angles of 90 degrees, 29 degrees, and 61 degrees is not a special type of triangle. It is a general right triangle because it has one right angle (90 degrees) and two acute angles (29 degrees and 61 degrees).
This triangle is not a 30-60-90 triangle because it does not have the specific angle measurements of 30-60-90 degrees. Similarly, it's not a 45-45-90 triangle because the angles don't match the specific angles of 45-45-90 degrees. There are no specific ratios between the sides of this triangle.
In general, right triangles are triangles that have one right angle (90 degrees), and the other two angles can take any value between 0 and 90 degrees. The sides of a right triangle have a relationship known as the Pythagorean Theorem. This theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Therefore, In short, the triangle with angles of 90 degrees, 29 degrees, and 61 degrees is a general right triangle that does not belong to any specific type of triangle and it has no specific ratios between the sides.
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Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.
Outcome Frequency
Green 4
Black 6
Orange 5
Based on the given frequency, determine the experimental probability of selecting an orange marble.
0.27
0.33
0.40
0.67
The probability of selecting an orange marble is 0.33.
Option B is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
The number of times each marble is selected.
Green = 4
Black = 6
Orange = 5
Total number of times all marbles are selected.
= 4 + 6 + 5
= 15
Now,
The probability of selecting an orange marble.
= 5/15
= 1/3
= 0.33
Thus,
The probability of selecting an orange marble is 0.33.
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whats x-8< -2?x−8<−2?
you get 15 points for solving
The solution to the inequality is x < 6
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
x - 8 < -2
Add 8 to both sides of the inequality
So, we have the following representation
x - 8 + 8 < -2 + 8
Evaluate the sum in the expression
x < -2 + 8
Evaluate the other sum
x < 6
Hence, the solution is x < 6
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If 10 people hare 3 brownie o each peron get the ame amount, how much brownie will each peron get
If 10 people share 3 brownies equally, each person will get the same amount. To find out how much each person will get, you can divide the total number of brownies by the number of people.
Unitary Method:
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
3 brownies / 10 people = 0.3 brownies per person
So, each person will get 0.3 of a brownie. Since a brownie is a solid object, it is not possible for each person to get 0.3 of a brownie, It would be best to cut the brownies into 10 equal pieces.
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How do I do this problem?
No, these statements are not needed to prove that ABCD is a parallelogram.
What is parallelogram?A parallelogram is a type of four-sided geometric shape with two pairs of opposite sides that are parallel. Each side of the parallelogram is a line segment, and all four of the interior angles are equal. The opposite sides of a parallelogram are also equal in length. Parallelograms can be found in a variety of applications, including engineering, architecture, and other fields. The most common types of parallelograms are squares, rectangles, and rhombuses.
A parallelogram is defined as a four-sided shape with opposite sides that are equal in length and with opposite angles that are equal in measure.
To prove that ABCD is a parallelogram, it is necessary to show that two of its sides are parallel and that its opposite sides are equal in length.
The statements provided do not show any of these properties, and so are not needed to prove that ABCD is a parallelogram.
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Please help me again, part 3
Answer:
c
Step-by-step explanation:
c
What i the range of the variable x
X 2 4 6 8 10 12
p (x) 0. 10 0. 20 0. 15 0. 10 0. 12 0. 25
A. 2
B. 10
C. 8
D. 12
Answer:
B.10
Step-by-step explanation:
Because it increases by 10
A storage silo for grain can house 18,000 bushels of grain. Answer the following questions using the fact that 1 ton equals to 2000 pounds.
1) Given that one bushel of oats weight 32 pounds, how many tons of oats can be stored in the silo?
2) Given that one bushel of barley weighs 48 pounds, how many tons of barley can be stored in the silo?
3) Given that one bushel of wheat weighs 60 pounds, how many tons of wheat can be stored in the silo?
1. 288 tons of oats can be stored in the silo.
2. 432 tons of barley can be stored in the silo.
3. 540 tons of wheat can be stored in the silo.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, A storage silo for grain can house 18,000 bushels of grain.
1. One bushel of oats weighs 32 pounds which is equal to 32/2000 tons.
= 0.016 tons.
Therefore, The number of tons of oats that can be stored is,
= 0.016×18000.
= 288 tons.
2. One bushel of barley weighs 48 pounds or 48/2000 = 0.024 tons.
Therefore, The number of tons of barley that can be stored is,
= 0.024×18000.
= 432 tons.
3. One bushel of wheat weighs 60 pounds or 60/2000 tons = 0.03 tons.
Therefore, The number of tons of wheat that can be stored is,
= 0.03×18000.
= 540 tons.
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Pleaes help me. The points in the table lie on a line. Find the slope of the line.
0/1/2/3
-1/0/1/2
Answer:
slope = 1
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (3, 2) ← 2 ordered pairs from the table
m = [tex]\frac{2-(-1)}{3-0}[/tex] = [tex]\frac{2+1}{3}[/tex] = [tex]\frac{3}{3}[/tex] = 1
Find An Equation Of The Plane Consisting Of All Points That Are Equidistant From (1, 4, 4) And (-4, 1, 2). Note: You Have To Enter The Full Equation.This problem has been solved!You'll get a detailed solution from a subject matter expert that helps you learn core concepts.See AnswerFind an equation of the plane consisting of all points that are equidistant from (1, 4, 4) and (-4, 1, 2).Note: you have to enter the full equation.
An equation for the plane consisting of all points that are equidistant from the points (1,4,4) and (-4, 1, 2) is 5x+3y+2z-6=0
Given, the points are (1, 4, 4) and (-4, 1, 2).
We have to find an equation for the plane consisting of all points that are equidistant from the given points.
Let the parametric point be (x, y, z) on the plane which is equidistant from the given points.
Using the distance formula:
[tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2+(z_{2}-z_{1} )^2 } }[/tex]
Distance between the points (x, y, z) and (1, 4, 4)
=[tex]\sqrt{(x-1)^2+(y-4)^2+(z-4)^2}[/tex]
Distance between the points (x, y, z) and (-4, 1, 2)
=[tex]\sqrt{(x-(-4)^2+(y-1)^2+(z-2)^2}\\\\ \sqrt{(x+4)^2+(y-1)^2+(z-2)^2}[/tex]
Given, [tex]\sqrt{(x-1)^2+(y-4)^2+(z-4)^2}=\sqrt{(x+4)^2+(y-1)^2+(z-2)^2}[/tex]
By using algebraic identity,
(a-b)² = a²-2ab+b²
(a+b)² = a²+2ab+b²
(x² - 2x + 1)+(y²-8y+16)+(z²-8z+16)=(x²+8x+16)(y²-2y+1)+(z²-4z+4)
x²+y²+z²-2x-8y-8z+1+16+16=x²+y²+z²+8x-2y-4z+16+1+4
By grouping,
-2x-8x-8y+2y-8z+4z+33-21
-10x-6y-4z+12=0
Dividing by -2 into both sides,
5x+3y+2z-6=0
Therefore, the equation of the plane is 5x+3y+2z-6=0
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Answer in simplest radical form if necessary (NO DECIMALS!). Copy and paste this symbol if needed: √
The value of x from the given figure is 16 units.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
From the given figure,
Using Pythagoras theorem to ΔBDC
Now, BC²=8²+4²
BC=√80
In ΔABD,
AB²=BD²+AD²
AB²=8²+x² ------(I)
In ΔABC
AC²=AB²+BC²
(x+4)²=AB²+80
AB²=(x+4)²-80 ------(II)
From equation (I) and (II), we have
64+x²=x²+8x+16-80
8x=128
x=16
Therefore, the value of x from the given figure is 16 units.
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helllo need this due in 5 minutes
The numerical value of the slope and its meaning include the following: C. 312; velocity increases at rate of 312 kilometers per minute as the time increases.
What is the slope-intercept form?Mathematically, the slope-intercept form of a line can be modeled by using this equation:
y = mx + c
Where:
m represents the slope.x and y represents the data points.Based on the information provided above, a function which represents the speed of a spaceship that is been launched from the station is given by:
v(t) = 5,924 + 312t
where:
v represents the velocity measured in kilometers per minute.t represents the number of minutes after the spaceship is launched.By comparison, we can logically deduce that the slope is equal to 312 and it represents the rate of change of velocity with respect to time.
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The Rose department store chain was closing one of its stores so they had to sell most of the inventory in the store. In the final markdown, they
marked all items 1/3
off the ticketed price. How much would a shirt that was ticketed at $24.99 cost?
The cost of the shirt given the ticketed price is $16.66.
What is the cost of the shirt?When the price of an item is marked down, it means that the price of the item is reduced. The item would become cheaper after the mark down. The shirt would become cheaper after it is marked down.
Price of the shirt after the mark down = (1 - fraction of mark down in price) x ticketed price
= (1 - 1/3) x $24.99
= 2/3 x $24.99
= $16.66
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What is the inverse of +9?.
The inverse of the expression +9 is -9.
Expression in math is defined as any mathematical statement which consists of numbers, variables and an arithmetic operation between them.
Here we have the expression +9 and we need to find the inverse for it.
As we all know that the term inverse in math is known as a function or operation which reverses the order or operation of another function or operation
Based on the definition, the given expression is written as,
=> +9
Now, the inverse of the expression is written as in the negative form such that,
=> -9
Therefore, the resulting value is -9.
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How do you find the length of the third side of an acute triangle?.
There are several ways to find the length of the third side of an acute triangle, depending on the information given about the triangle and the sides. Some common methods include:
Using the Pythagorean theorem: If you have a right triangle, you can use the Pythagorean theorem to find the length of the third side. The theorem states that 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.
Using the Law of Cosines: If you know the lengths of two sides and the measure of the angle between them, you can use the law of cosines to find the length of the third side.
Using the Law of Sines: If you know the lengths of two sides and the measure of the angle opposite one of them, you can use the law of sines to find the length of the third side.
It's important to note that you need to know at least 2 sides and an angle or the side opposite to the right angle (if the triangle is a right triangle) in order to find the length of the third side.
How do you graph y <- 2x 4?.
To depict the curve, we will make use of the idea of slope and intercept in linear equations.
A line's slope and y-intercept are represented by the equation y = mx + c, where m represents the slope and c represents the y-intercept.
When y = 2x - 4 is put into comparison with the generic form, we get
The curve has a slope of 2 and a y-intercept of -4.
To assist us plot the graph, let's take two points along the line y = 2x – 4.
The line y = 2x - 4 passes through since its y-intercept is equal to -4. (0, -4)
In the formula y = 2x - 4, replace y with 0.
0 = 2x - 4
2x = 4
x = 2
the line therefore goes through (2, 0).
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Full Question = Which graph represents the function y = 2x - 4?
If a: b = 1:2 and b; c = 3:4, find a : c.
Answer:
Step-by-step explanation:
b:c= 3:6
Answer:
Step-by-step explanation:
We know that:
a : b = 1 : 2 (or a = (1/b)*b)
b : c = 3 : 4 (or b = (3/4)*c)
So, we can substitute the value of b from the second equation into the first equation to get the ratio of a : c:
a = (1/b)*b = (1/((3/4)c))((3/4)c) = (4/3)(1/c)*c = (4/3)*1 = 4/3
So, the ratio of a : c is 4 : 3.
Alternatively, we can use the cross-multiplication method to find the ratio.
a : b = 1 : 2, and b : c = 3 : 4
so a4 = b3, and b4 = c3
so a4 = c3
so a:c = 3:4
In this way also we got the ratio of a:c as 3:4
I need some help on this question please
Answer:
m1 = 4, m2 = 176
Step-by-step explanation:
Using complementary angle rule you know the total angle is 180 thus:
[tex]180 - (x-18) = 8x\\198 - x = 8x\\198 = 9x\\x = 22[/tex]
m1 = (22 - 18) = 4
m2 = 8(22) = 176
how much work is done when a 100 lb rock is lifted to a height of 3 ft?
Work done when a 100 lb rock is lifted to height of 3 ft is 9652.215 ft-lb.
What is meant by work done?
The work done on an object is equal to the force applied to it multiplied by the distance over which the force is applied. In this case, the force applied is the weight of the rock, which is equal to the force of gravity acting on it.
The weight of an object is given by the formula:
W = mg
Where m is the mass of the object (in this case, 100 lb) and g is the acceleration due to gravity (approximately 9.8 m/s^2 or 32.17405 ft/s^2).
So the weight of the rock is:
W = (100 lb)(32.17405 ft/s^2) = 3,217.405 ft-lb
The work done on the rock is equal to the force applied (its weight) multiplied by the distance it is lifted (3 ft), so the work done is:
Work = (3,217.405 ft-lb) x (3 ft) = 9652.215 ft-lb
Therefore, the work done when a 100 lb rock is lifted to a height of 3 ft is 9652.215 ft-lb.
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Complete the ratio table.
145 52
290 104
435 156
580
725
Step-by-step explanation:
since a ratio is a fraction with all calculation and comparison rules (but with a special overall meaning), we need to observe the main rule for transforming fractions : when multiplying one part of the fraction by a factor, we also need to multiply the other part by the same factor to keep the value of the fraction unchanged.
the basic ratio is here
145/52 (or written 145:52 - it has the same meaning)
290/104 is just (145×2)/(52×2)
435/156 is just (145×3)/(52×3)
to complete the table we simply have to keep following that structure :
580 = 145×4
so, 52×4 = 208
and the ratio is
580/208
725 = 145×5
52×5 = 260
and the ratio is
725/260
