Using the monthly payment formula, it is found that the balance of the plan is of $26,731.23.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
A is the monthly payment.P is the total amount.r is the interest rate.n is the number of payments.The parameters for this problem are given as follows:
A = 144, r = 0.06, n = (68 - 24) x 12 = 528.
Then:
r/12 = 0.06/12 = 0.005.
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]144 = P\frac{0.005(1 + 0.005)^{528}}{(1 + 0.005)^{528} - 1}[/tex]
[tex]P = 144\frac{(1 + 0.005)^{528} - 1}{0.005(1 + 0.005)^{528}}[/tex]
P = $26,731.23.
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A cook needs 7 cups of vegetable stock for a soup recipe. How much is this in pints? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer. Ú 08 Explanation Check fl oz qt X values: One... gal pt S .? © 2022 McGraw HilllLS ALL
Answer:
3 1/2 pints
Step-by-step explanation:
A pint is two cups
7 cups / 2cups/pint = 7/2 pint = 3 1/2 pints
You have 20 coins (8 silver dollars, 7 quarters, and 5 dimes) and plan to sell 8 at random. What is the probability that you sell 3 silver dollars, 2 quarters, and 3 dimes?
Answer: 0.01225%
Step-by-step explanation:
[tex]\frac{8}{20} *\frac{8}{20} *\frac{8}{20} *\frac{7}{20} *\frac{7}{20} *\frac{5}{20} *\frac{5}{20} *\frac{5}{20} = \frac{49}{400000} =0.0001225=0.01225[/tex]%
State the restrictions of 1-x-y/x+y
The restriction of the expression as given in the task content is; x +y = 0.
What is the restriction of the expression?The expression in the task content is rational;
(1-x-y)/(x+y).
On this note, the restriction to the expression is the values which render the denominator of the expression equal to 0 and consequently the expression value to undefined.
Hence, the restriction is; x+y = 0.
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Problem
Circles [tex]K[/tex] and [tex]L[/tex] touch externally at point [tex]P[/tex]. Line [tex]ABC[/tex] cuts [tex]K[/tex] at points [tex]A[/tex] and [tex]B[/tex] and is tangent to [tex]L[/tex] at [tex]C[/tex]. The line through [tex]A[/tex] and [tex]P[/tex] meets [tex]L[/tex] at a second point [tex]D[/tex].
Prove that [tex]PC[/tex] bisects angle [tex]BPD[/tex].
Step-by-step explanation:
Using the various theorems relating inscribed and external angles to intercepted arcs, we can write the following relations:
angle A = 1/2(arc BP) . . . . . . . . . . . inscribed angle
angle A = 1/2(arc CD -arc CP) . . . external angle at tangent/secant
angle CPD = 1/2(arc CD) . . . . . . . inscribed angle
angle CPB = 1/2(arc CP) + 1/2(arc BP) . . . . . sum of angles at the mutual tangent
ProofEquating the expressions for angle A, we have ...
1/2(arc BP) = 1/2(arc CD -arc CP)
Adding arc CP gives ...
1/2(arc BP +arc CP) = 1/2(arc CD)
Substituting the last two equations for angles from above, this gives ...
angle CPB = angle CPD
Hence PC bisects angle BPD.
What is the coefficient of [tex]x^7[/tex] in the expansion of [tex](3 - x)^{11}[/tex]?
Answer:
-26730
Explanation:
To find the coefficient of [tex]x^7[/tex] in the expansion of [tex](3 -x)^{11}[/tex]
Use Binomial Expansion:
[tex](x+y)^n = \ ^n C_0 x^n + \ ^n C_1 x^{n-1} y + \ ^n C_2 x^{n-2}y^2 + ...+ \ ^n C_n y^n[/tex]
In this expansion,
[tex](3-x)^{11}[/tex]
The coefficient of [tex]x^7[/tex]
[tex]= 11C_{7} (3)^{11-7} (-x)^7[/tex]
[tex]= (330) (81) (-x^7)[/tex]
[tex]= -26730x^7[/tex]
list three keywords that refer to multiplication ?
Answer:
full list of words from this list
factor anything that contributes causely to a result
multiply the number by which multiplicant is multiplied
multiply the number that is multiplied by a multiplier
project and refer that has been created by someone or some process
You know the area (A = 300 ft^2) and the width (w = 4 ft), but not the length. Rewrite the formula by dividing both sides by the width.
length = Answer
Answer:
Length equals to 75 ft
Step-by-step explanation:
A=l x w Area of a rectangle formula.
A/w=l Solve for length
300=l x 4
300=l x 4
4 4
300/4=l
75=l
?????????????????????????
Answer:
[tex]\sqrt[10]{4}[/tex]
Step-by-step explanation:
Apply power to power rule on the exponents, [tex]\frac{2}{5}*\frac{1}{4} = \frac{1}{10}[/tex] when simplified
[tex]4^\frac{1}{10}[/tex] is also the same as [tex]\sqrt[10]{4}[/tex]
Answer:
[tex]\sqrt[10]{4}[/tex]
Step-by-step explanation:
We know that,
[tex](a^{x} )^y=a^x^y\\\sqrt{x} =x^{\frac{1}{2} } \\x^\frac{1}{y} =\sqrt[y]{x}[/tex]
By following those, let us solve the given expression.
[tex](4^\frac{2}{5} )^\frac{1}{4} \\\\4^\frac{2*1}{5*4} \\\\4^\frac{2}{20} \\\\4^\frac{1}{10}\\\\\sqrt[10]{4}[/tex]
A swimming pool is 3 meters deep, 50 meters long, and 25 meters wide. If it takes 0.25 pounds of chlorine for every 15 cubic meters of water to keep the pool clean and healthy, how many pounds of chlorine are needed?
a. 27.2 pounds
b. 35.7 pounds
c. 45.4 pounds
d. 62.5 pounds
Answer:
D) 62.5 pounds.
Step-by-step explanation:
The volume of the swimming pool = [tex]3\times50\times25 =3750[/tex]
[tex]3750\div15 = 250[/tex] lots of 15
[tex]250\times0.25=62.5[/tex] pounds of chlorine.
Hope this helps, have a nice day!
in your own words , what is drecrete math
Answer:
Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic.
Interest = $42.68, time 7.08%. Find the principal. Round to the nearest hundredth place. = 7 years, rate =
Answer:
trust me its c i did the test on edge for me
Step-by-step explanation:
i did the test on edge
Answer:
$63.83
Step-by-step explanation:
please mark brainliest
please help me asap thank you so so much u are so amazing!!
_____ ÷ ( - 9 ) = ( - 8 )
pls pls answer me question
QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answer: 154 m^3
Step-by-step explanation:
Volume = (5*2*7) + (3*7*4)
= 70 + 84
= 154 m^3
Brainliest please :P
Answer:
154 m^3
Step-by-step explanation:
join my stream for an explanation
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Can i get an answer ASAP
A rectangle has perimeter 92 cm and its length is 1 cm more than twice its width.
Find the dimensions of a rectangle given that its perimeter is 92 cm and its length is 1 cm more than twice its width.
Set up your solution using the variables L for the length, W for the width, and P for the perimeter.
Part a: Using the definition of perimeter, write an equation for P in terms of L and W .
Part b: Using the relationship given in the problem statement, write an equation for L in terms of W .
Solve the equations from parts a and b.
Part c: The width is
Number
cm.
Part d: The length is
Number
cm.
The length and width of the rectangle is 15cm and 31cm respectively
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is expressed as:
P = 2(L + W)
where
L is the length
W is the width
If its length is 1 cm more than twice its width, then;
L = 2W + 1
Substitute
92 = 2(2W + 1 + W)
46 = 3W + 1
3W = 45
W = 15cm
Determine the length
L = 2(15) + 1
L = 31cm
Hence the length and width of the rectangle is 15cm and 31cm respectively
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PLEASE ANSWER AS FAST AS POSSIBLE PLEASE! I WILL MARK BRAINLIEST!
Three equations are listed below.
*y=x(3x+2)
*y= x/3+2
*y=2-3x
IDENTIFY ONE LINEAR EQUATION AND ONE NONLINEAR EQUATION FROM THE LIST. STATE A REASON WHY EACH QUESTION YOU IDENTIFIED IS LINEAR OR NON LINEAR.
1. WHAT IS THE LINEAR EQUATION?
WHY IS THAT THE LINEAR EQUATION
2. WHAT IS THE NONLINEAR EQUATION
WHY IS THAT THE LINEAR EQUATION
please finish this, i hate math.
Answer:
WHAT IS THE LINEAR EQUATION?
y=2-3x and y=x/3+2
WHY IS THAT THE LINEAR EQUATION
Linear functions are those whose graph is a straight line. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y
WHAT IS THE NONLINEAR EQUATION
Y = x(3x+2)
WHY IS THAT THE LINEAR EQUATION
A nonlinear function has more than one independent variable. The independent variable is x.
y= x(3x-2) is non linear equation.
y= x/3 + 2 is linear equation.
y= 3 -2x is linear equation.
What is Linear Equation?Linear equations are the equations of degree 1.
It is the equation for the straight line.
The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.
We know that the linear equation have highest degree 1.
First, y= x(3x-2)
y= 3x² -2x
Here, the highest degree is 2 which is non linear equation.
Now, y= x/3 + 2 have highest degree 1 which is linear equation.
and, y= 3 -2x have highest degree 1 which is linear equation.
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The functions f(x)=x²-1 and g(x) = -x² + 4 are shown on the graph.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
The solution to the given graph is (-√5/2, √5/2)
Quadratic graphGiven the following quadratic graph f(x)=x²-1 and g(x) = -x² + 4
The solution will be the point of intersection of the two curves.
Equate the functions
x²-1 = -x² + 4
Equate to zero
x²+x² - 1- 4 = 0
2x² -5 = 0
2x² = 5
x² = 5/2
x = ±√5/2
Hence the solution to the given graph is (-√5/2, √5/2)
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v = u + 2at
Where v is the final velocity (in m/s), u is the initial velocity (in m/s), a is the acceleration (in m/s²) and t is the time (in seconds).
Find v when u is 19 m/s, a is 3 m/s², and is 21 seconds.
Answer:
145 m/s
Step-by-step explanation:
v = u + 2at
v = 19 + 2(3)(21)
v = 19 + 126
v = 145
answer
V=145
Step-by-step explanation:
V=U+2at
v=19+2×3×21
v=19+126
v=145
Could someone help me out with this question?
The simplified form of the difference quotient of equation [tex]9x^2+5x-1[/tex] . in the form 9x + 9h + 5.
In question for equation [tex]9x^2+5x-1[/tex], simplified to difference quotient in the form of Ax+Bh+C where A, B, C are integers
equation is the relationship between variable and represented as [tex]9x^2+5x-1[/tex] is example of polynomial equation.
We know that,
for difference quotient
[tex]=\frac{f(x+h)-f(x)}{h} \\\frac{9(x+h)^2+5(x+h)-1-9x^2-5x+1}{h}\\\frac{9h^2+9hx+5h}{h}\\9x+9h+5[/tex]
While, compared with Ax+Bh+C
we have A=9, B=9, C=5.
Thus, The required value of difference Quotient in the form Ax+Bh+c where A, B and C is 9, 9 and 5 respectively
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In a parallelogram, two adjacent sides measure 20 cm and 27 cm. The shorter diagonal is 23 cm. Determine, to the nearest degree, the measure of the larger angles in the parallelogram.
If two adjacent sides of parallelogram are 20 cm and 27 cm and the shorter diagonal is 23 cm then the measure of larger angles in the parallelogram is 123.75°.
Given Two adjacent sides are 20 cm and 27 cm. The shorter diagonal is 23 cm. and we need to find the measure of larger angle.
From law of cosines
[tex]c^{2} =a^{2} +b^{2} -2abcos d[/tex]
where c is the opposite side of angle, a and b are other sides and d is the angle.
[tex]23^{2} =20^{2} +27^{2} -2*20*27cos d[/tex]
where 23 is the length of shorter diagonal
529=400+729 - 1080 cos d
1080 cos d=600
cos d=600/1080
cos d=0.55
d=[tex]cos^{-}[/tex]0.55
d=56.25°
Adjacent angle=180-56.25
=123.75°
Largest angle=123.75°.
Hence the larger angle of parallelogram having sides 20 and 27cm is 123.75°.
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Yall I need help asap pls
question 7
You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.
The company's first task is to cast the lead female roles of Fantine, adult Cosette, and Éponine, and the lead male roles of Jean Valjean, Inspector Javert, and Marius. You have received headshots and resumes from 28 women and 22 men who are interested in auditioning for these parts.
A: If no one has been cast yet, how many different ways are there to cast Jean Valjean from the 22 men?
B: If Jean Valjean has already been cast, how many different ways are there to cast Inspector Javert from the remaining men?
C: If Jean Valjean and Inspector Javert have already been cast, how many different ways are there to cast Marius from the remaining men?
Select one answer choice for part A, one answer choice for part B, and one answer choice for part C.
A: 22P3
A: 22!
B: 21!
C: 20P1
B: 21
B: 21P2
C: 20!
A: 22
C: 20
Question 2:
A: Which of the following expressions will calculate the number of ways the three lead male roles could be cast?
B: Evaluate the permutation from part A.
Select one answer choice for part A, and one answer choice for part B.
A: 22P19
B: ≈1.12×1021
B: 9240
A: 3P22
A: 22P3
B: ≈1.87×1020
The permutation illustrates that if no one has been cast yet, the different ways that are there to cast Jean Valjean from the 22 men is 22.
How to compute the value?The ways to cast Jean will be:
= 22!/(22 - 1)!
= 22!/21!
= 22
When Jean Valjean has already been cast, the different ways that are there to cast Inspector Javert from the remaining men will be:
= 21!/(21 - 1)!
= 21!/20!
= 21
When Jean Valjean and Inspector Javert have already been cast, the different ways that are there to cast Marius from the remaining men will be:
= 20!/(20 - 1)!
= 20!/19!
= 20
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Are the expressions –0.5(3x 5) and –1.5x 2.5 equivalent? explain why or why not.
Answer:
not equivalent; signs don't match
Step-by-step explanation:
Apparently, you want to compare the expressions ...
-0.5(3x +5)-1.5x +2.5Distributive propertyThe distributive property allows you to eliminate parentheses by multiplying each term inside parentheses by the factor outside.
ApplicationWhen we do that to the first expression, we get ...
-0.5(3x +5) = (-0.5)(3x) +(-0.5)(5) = -1.5x -2.5
Note that the signs of the terms inside parentheses are the same, and the signs of the terms after removing parentheses are the same. (Both terms have their signs changed by the negative factor multiplying the parentheses.)
The expanded expression -1.5x -2.5 is not equivalent to -1.5x +2.5, which has terms of different signs.
The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
The equations to calculate the legs are 0.5(x)(x + 2) = 24, x^2 + 2x - 48 = 0 and x^2 + (x + 2)^2 = 100
How to determine the legs of the triangle?The complete question is in the attached image
The given parameters are:
Area = 24
Legs = x and x + 2
The area of the triangle is calculated as:
Area = 0.5 * Base * Height
This gives
0.5 * x * (x + 2) = 24
So, we have:
0.5(x)(x + 2) = 24
Divide through by 0.5
(x)(x + 2) = 48
Expand
x^2 + 2x = 48
Subtract 48 from both side
x^2 + 2x - 48 = 0
Hence, the equations to calculate the legs are 0.5(x)(x + 2) = 24, x^2 + 2x - 48 = 0 and x^2 + (x + 2)^2 = 100
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Solve for x in the diagram below.
Vertical angles are congruent, so:
[tex]4x+50=150\\\\4x=100\\\\x=\boxed{25}[/tex]
Find n in this equation: 308P(n,2)=P(16,4)
Answer:
24
Step-by-step explanation:
7x4
Are the grades shown in the math class below normally distributed? Explain your answer.
Since the histogram is not symmetric, the grades shown in the math class below are not normally distributed.
When does a histogram represent a normal distribution?A histogram represents a normal distribution if it symmetric.
In this problem, we have that:
57% of the grades are on the left tail.25% of the grades are on the center.18% are on the right tail.Since the percentages at the tails are different, the histogram is not symmetric, and the grades shown in the math class below are not normally distributed.
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The vertex of this parabola is at (3,-2). When the x-value is 4, the
y-value is 3. What is the coefficient of the squared expression in the
parabola's equation?
O
O
A-1
B. 7
C. 1
D. 5
Answer:
5
Step-by-step explanation:
f(x) = a(x-3)² - 2
When x = 4, y = 3, so:
3 = a(4-3)² - 2
5 = a
The difference between twice a number, x, and a smaller number, y, is 3. The sum of twice the number and the smaller
number is -3. Which equations represent this situation?
Oy=2x-3 and y=-2x-3
Oy-2x-3 and y=-2-2
O y=2x+3 and y=-2x-3
Oy-2x+3 and y=-x-
3. Help meeee
Answer:
y=2x+3 and y=-2x-3
Step-by-step explanation:
First situation:
2x-y=3
making y subject
y=2x+3
Second situation:
2x+y=-3
making y subject
y=-2x-3
The diameter of a wrecking ball used to tear down buildings is 3.5 ft. What is the volume ( to the nearest hundredth) Use 3.14 for pi and round each approximation to the nearest hundredth.
Answer:
22.44 ft
Step-by-step explanation:
The radius is equal to half of the diameter or 1.75 ft (in this case).
The volume of a sphere is defined as the equation:
V = 4/3 * pi * radius ^ 3
V = 4/3 * 3.14 * 1.75 ^ 3
V = 4/3 * 3.14 * 5.36
V = 22.44 ft
18
(cos+ i sin ) ¹8
6
Answer:
-1.
Step-by-step explanation:
1) according to the DeMoivre's theorem:
[tex]1*(cos\frac{ \pi}{6} +isin\frac{ \pi}{6})^{18}=1^{18}(cos(18*\frac{ \pi}{6})+isin(18*\frac{ \pi}{6}))=cos3\pi +isin3\pi =cos\pi +isin\pi ;[/tex]
2) if cos(π)=-1 and sin(π)=0, then cosπ+i*sin(π)=-1.