Answer:
$587.13
Step-by-step explanation:
Monthly Payment Formula
[tex]\sf PMT=\dfrac{Pi(1+i)^n}{(1+i)^n-1}[/tex]
where:
PMT = monthly paymentP = loan amounti = interest rate per month (in decimal form)n = term of the loan (in months)Given:
P = $25,000i = 0.005n = 48To calculate i, divide the interest rate per annum by 12 and convert to decimal form:
[tex]\implies \sf i=\dfrac{6\%}{12}=\dfrac{0.06}{12}=0.005[/tex]
Substitute the given values into the formula and solve for PMT:
[tex]\implies \sf PMT=\dfrac{25000 \cdot 0.005(1+0.005)^{48}}{(1+0.005)^{48}-1}[/tex]
[tex]\implies \sf PMT=\dfrac{125(1.005)^{48}}{(1.005)^{48}-1}[/tex]
[tex]\implies \sf PMT=587.1257262...[/tex]
Therefore, the monthly repayment required to pay this loan off in 48 equal installments is $587.13 (nearest cent).
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If side b measures 5√3, what is the length of side c?
Answer:
10
Step-by-step explanation:
cos(30) = b / c
c = b / cos(30)
c = 5xsqrt(3) / 0.866
c = 10
Select the correct answer.
Consider function f.
f(x) = 2x²
What is the value of (ƒ•ƒ)(x)₂
O A.
8x4
OB. 16x4
OC. 4x4
4x2
D.
Step-by-step explanation:
[tex]f(x) = 2 {x}^{2} [/tex]
[tex] \: [/tex]
[tex] = (f \circ f)(x)[/tex]
[tex] = f(f(x))[/tex]
[tex] = 2 {x}^{2} [/tex]
[tex] = 2 {(2 {x}^{2} )}^{2} [/tex]
[tex] = 2(4 {x}^{4} )[/tex]
[tex] = 2.4 {x}^{4} [/tex]
[tex] = 8 {x}^{4} [/tex]
The answer is A.
The distance on a map between a student’s house and her job is 6 cm. On the same map, the distance between her house and her school 8 cm. The actual distance from her house to school is 12 km. If d represents the approximate distance in km between her house and her job, what is d? A. 4 km B. 9 km C. 48 km D. 16 k
The approximate distance in km between her house and her job is 9 km.
What is the approximate distance?The map is a scale drawing of the places mentioned. A scale drawing is a smaller image of a larger place or diagram.
The scale of the map = 8cm : 12km
Distance between the house and the job = (12 x 6) / 8 = 9m
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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 Question 8(Multiple Choice Worth 1 points) (04.06 MC) In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB. Graph of two intersecting lines. One line g of x is solid and goes through the points negative 3, 0, negative 4, negative 1 and is shaded in below the line. The other line f of x is solid, and goes through the points 1, 1, 2, negative 1 and is shaded in below the line. The graph represents which system of inequalities? y ≤ −2x + 3 y ≤ x + 3 y ≥ −2x + 3 y ≥ x + 3 y ≤ −3x + 2 y ≤ −x + 2 y > −2x + 3 y > x + 3 Question 9(Multiple Choice Worth 1 points) (04.06 LC) Choose the graph that represents the following system of inequalities: y ≤ −3x + 1 y ≤ 1 over 2x + 3 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB. Graph of two intersecting lines. Both lines are solid. One line f of x passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line g of x passes through points 0, 1 and 1, negative 2 and is shaded above the line. Graph of two lines intersecting lines. Both lines are solid. One line g of x passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded above the line. Graph of two intersecting lines. Both lines are solid. One line passes g of x through points negative 2, 2 and 0, 3 and i
The graph that represents the system of inequalities will be y ≤ −2x + 3; y ≤ x + 3
How to depict the graph?The equation of the line will be:
y = mx + b
In this case, we can observe that both lines have the same y intercept and that the lines are solid.
Hence, graph that represents the system of inequalities will be y ≤ −2x + 3; y ≤ x + 3. The graph is attached.
When the coordinate grid shows points A through, the point that is a solution to the system of inequalities is negative 6 point G at negative 3, negative 10 point H at negative 4.
Finally, the graph that represents the following system of inequalities: y ≤ −3x + 1 y ≤ 1 over 2x + 3 is the graph of two intersecting lines where both lines are solid.
One line of x passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line g of x passes through points 0, 1 and 1, negative 2 and is shaded above the line.
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The line contains the point (5,0) and is parallel to the line defined by "-3x=4y"
Answer:
Step-by-step explanation:
The vertex of the parabola below is at the point (2, 4), and the point (3,6) is
on the parabola. What is the equation of the parabola?
10
(3,6)
(2,4)
-10
10
-10
O A. y=2(x-2)² +4
OB. x= 4(y-3)² +1
O C. y= 6(x-2)2 +4
OD. y=3(x-4)2 +2
← PREVIOUS
The equation of the parabola is y = 2(x - 2)^2 + 4
How to determine the parabola equation?The given parameters are:
Vertex, (h,k) = (2,4)Point (x,y) = (3,6)A parabola is represented as:
y = a(x - h)^2 + k
Substitute (h,k) = (2,4)
y = a(x - 2)^2 + 4
Substitute (x,y) = (3,6)
6 = a(3 - 2)^2 + 4
Evaluate the difference
6 = a(1)^2 + 4
This gives
6 = a + 4
Subtract 4 from both sides
a = 2
Substitute a = 2 in y = a(x - 2)^2 + 4
y = 2(x - 2)^2 + 4
Hence, the equation of the parabola is y = 2(x - 2)^2 + 4
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When a range of values is used to estimate a population parameter, it is called a. A point estiamte b. A range estimate c. A statistical parameter d. An interval estimate.
[tex] \: \huge \underline \mathbb{ \green{Answer}} \\ \\ \: \: \tt \boxed{\blue{d. \: \: an \: \: interval \: \: estimate}}[/tex]
Please help asap
What is the domain and range of T
Answer:
Domain = {-3, -2}Range = {-4, -3, 4}Step-by-step explanation:
The domain is the set of x-values, and the range is the set of y-values.
Area of a sector
Find the perimeter of this sector.
Give your answer rounded to 3 SF.
Pls help
The perimeter of the sector is 96.34 m if the radius of the circle is 48 m and the measure of the central angle is 115 degrees.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have given a part of the circle.
As we know:
s = rθ
s is the arc length
r is the radius of the circle
θ is the central angle in radians
The central angle is 115 degrees which is in radians:
θ = 2.00713
s = 48×(2.00713)
s = 96.34 m
The perimeter of the sector = s = 96.34 m
Thus, the perimeter of the sector is 96.34 m if the radius of the circle is 48 m and the measure of the central angle is 115 degrees.
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the price of an mp3 player is increased by 8%to £52.92
what was the original price?
Answer:
49£Step-by-step explanation:
the price of an mp3 player is increased by 8%to £52.92
what was the original price?
52.92 = 108%
52.92 : 108 = 0.49
0.49 * 100 = 49£
-------------
check
49 * 1.08 = 52.92
the answer is good
Golf balls cost $0.90 each at Jerzy’s Club, which has an annual $25 membership fee. At Rick and Tom’s sporting-goods store, the price is $1.35 per ball for the same brand. Where you buy your golf balls depends on how many you wish to buy. Explain, and illustrate your reasoning with a graph.
Answer:
See attached graph.
Step-by-step explanation:
Each situation can be expressed as an equation:
Jerzy: Total Cost (y1) is the $25 membership fee plus $0.80/golf ball (x):
y1 = $25 + $0.90x
Rick and Tom's: Total Cost (y2) is $1.25 per golf ball, x.
y2 = $1.25x
See the attached graphs of these two equations. Jerzy's cost less after 56 balls are purchased.
Which two points on the number line represent numbers that can be combined to make zero?
B and D
A and B
C and D
A and C
387 kilograms = x grams
Answer:
a. 387,000g
b. 38,700g
c. 387g
d. 3.87g
Answer:
a
Step-by-step explanation:
I kilogram is 1000 grams
What is m2?
What is m<1?
Answer:
∠ 2 = 75° , ∠ 1 = 105°
Step-by-step explanation:
∠ 2 and 75° are alternate angles and are congruent , then
∠ 2 = 75°
∠ 1 and ∠ 2 are a linear pair and sum to 180° , that is
∠ 1 + ∠ 2 = 180°
∠ 1 + 75° = 180° ( subtract 75° from both sides )
∠ 1 = 105°
Today an electronics store took
5% off the price of a computer,
and for the next two days, it will
take 5% off the previous day's
price. if the price of the
computer yesterday was
$2000.00, what will be the price
of the computer two days from
now?
Answer:
$ 1805
Step-by-step explanation:
2000 × 95%
= 1900
1900 × 95%
= 1805
Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and roots of 1-√6 , 1+ √6 , and 7-i
Step-by-step explanation:
Use this algebra 2 theorem:
If r and q are roots of a polynomial function then
the polynomial function can be expressed as
[tex](x - r)(x - q)[/tex]
Here the roots are
1- root of 6, 1+ root 6, and. 7-i so our. function can be expressed as
[tex](x - (1 - \sqrt{6} ))(x - (1 + \sqrt{6} ))(x - (7 - i))[/tex]
The first two binomials are difference off squares so the we have
[tex] {x}^{2} + x( - 1 + \sqrt{6} ) + x( - 1 - \sqrt{6} ) + ( - 5)[/tex]
[tex] {x}^{2} - 2x - 5[/tex]
The other root is (7-i).
Also note since (7-i) is a root, then (7+I) is also a root.
So
[tex](x - (7 - i)(x - (7 + i)( {x}^{2} - 2x - 5)[/tex]
[tex]( {x}^{2} - 14x + 50)( {x}^{2} - 2x - 5)[/tex]
Simplify and it gives us
[tex] {x}^{4} - 16 {x}^{3} + 73 {x}^{2} - 30x - 250[/tex]
I need help!!!!
True OR False
------------------------
m - 63 = 37, m = 100?
Answer:
The answer is true!!!
Step-by-step explanation:
If m=100, 100-63=37 which is true.
Step 4: Make a prediction with your data.
a) Using your equation from step 2d, ( y=0.14x+0.75 ) estimate the GPA of a student who studies for 15 hours a
week. Justify your answer.
Answer:
estimated gpa: 2.85
Step-by-step explanation:
Evaluate y=0.14x+0.75 at x = 15 (hours):
y = 0.14(15 hours) + 0.75
= 2.1 + 0.75
y = 2.85 = estimated gpa corresponding to 15 houirs of study
How to do proportional relationships in math 7th grade ?? Please explain ?!!
Answer:
Try searching online
Step-by-step explanation:
go to your browser then search up
How to do proportional relationships in math 7th grade ?? Please explain ?!!
the average height of 10 pupils is 140cm if a new pupil joined the group the average height of 11 pupils become 148
cm find the height of new pupils
Answer:
228 cm
Step-by-step explanation:
the average is calculated as
average = [tex]\frac{sum}{count}[/tex] , then
[tex]\frac{sum}{10}[/tex] = 140 ( multiply both sides by 10 to clear the fraction )
sum = 1400
let the height of new pupil be x , then
[tex]\frac{sum+x}{11}[/tex] = 148 ( multiply both sides by 11 )
sum + x = 1628 , that is
1400 + x = 1628 ( subtract 1400 from both sides )
x = 228
height of new pupil is 228 cm
What is the median of the data?
Answer:
The median is 3.
Step-by-step explanation:
Since, most of the values presented are 0-8 and median is the middle of any data set. It has to be 3.
Look at the pattern.
What is the next image in the pattern?
By following the pattern the next image in the pattern is (b) since the correct option is (b).
A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers is arranged in a particular way, the arrangement is referred to as a pattern.
From the pattern given: In pattern one, the first column contains 2 blocks and the second column contains 1 block. In pattern second, the first column contains 3 blocks, the second column contains 2 blocks and the third column contains 1 block. In pattern third, the first column contains 4 blocks, the second column contains 3 blocks, the third column contains 2 blocks and the fourth column contains 1 block.
∴ You can observe that block the ks are arranged in descending numbers.
Hence, option (b) is correct.
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please help this is so confusing
Answer:
f(x)=f(6)= 6^2 - 2*6=36-12= 24
Step-by-step explanation:
This is a function, so we replace x with 6. When we do this, we use it to replace x in the above equation, so instead of having x^2-2x, we have 6^2 -2x. Then we just solve the equation, leaving us with the final solution of 24.
What is the inverse of the function g(x)=-3(x + 6)?
Please help me ASAP
Answer:
Inverse g(x) = -x/3-6
Step-by-step explanation:
To understand this just think g(x) as y so
we got y= -3(x+6) after that we change the minus three to left
so we got -y/3 because -3 is multiply. After that plus 6 came and become minus 6.
After all,you have to replace x in y place.
y = -3(x +6)
-y/3 = x +6
-y/3 -6 = x
-x/3 -6 = g(x)
50 people were asked if they speak French or German or Spanish. Of these people, 31 speak French 2 speak French, German and Spanish 4 speak French and Spanish but not German 7 speak German and Spanish 8 do not speak any of the languages all 10 people who speak German speak at least one other language How many people only speak Spanish?
The number of people that speak only spanish = 6
How to Interpret Venn Diagrams?We are given;
Total number of people surveyed = 50
31 speak French 2 speak French, German and Spanish.
4 speak French and Spanish but not German.
7 speak German and Spanish.
8 do not speak any of the languages.
All 10 people who speak German speak at least one other language.
Thus;
From the Venn diagram;
Number of people that speak only French and German = 10 - 5 - 2 - 0 = 3
Number that speak only spanish = 50 - 22 - 3 - 2 - 4 - 5 = 6
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The graphs of the functions f (x) = 2x+ 7 and g(x) = x2 -1 intersect in t
xy-coordinate plane. What are the points of intersection?
Answer:
See below
Step-by-step explanation:
This is a line and a parabola......where they intersect the two equations are equal :
2x+7 = x^2 - 1
x^2 - 2x -8 = 0
(x-4)(x+2) = 0 shows the x-coordinate for intersections at x = 4 and -2
sub these x values into one of the equations to calculate the y coordinate
y = 2(4) + 7 = 15 so one point is 4,15
y = 2(-2) + 7 = 3 the other point is then -2, 3
Which inequality defines the shaded region graphed below?
Answer:
Every ordered pair within this region will satisfy the inequality y ≥ x. Incorrect. The boundary line here is y = x, and the correct region is shaded, but remember that a dotted line is used for < and >. The inequality you are graphing is y ≥ x, so the boundary line should be solid.
Solve the equation
This is a question from a mock exam I could not answer
Reflect shape A in the x-axis.
I have 20 min to complete this
Answer:
Step-by-step explanation:
PLEASE HELP ILL GIVE BRAINLIEST PLEASE PLEASE PLEEEEEEEAAAAASE
Write the recursive formula for the arithmetic sequence.
A(n)=(-1)+(n-1)(-5)
The recursive formula is [tex]a_n= a_{n-1} -5[/tex].
What is Arithmetic Progression?A set of numbers is an arithmetic progression (AP) or an arithmetic sequence such that the difference between successive words is unchanged.
Given:
A(n)=(-1)+(n-1)(-5)
A(n) = -1 - 5n + 5
A(n) = 4-5n
n=1
A(1)= 4-5= -1
n=2,
A(2) = -6
n=3
A(3)= -11
Hence, the recursive formula is [tex]a_n= a_{n-1} -5[/tex].
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