The value of k that satisfies the given condition is approximately 0.4041.
In the expansion of (1+kx)⁵, the coefficient of x⁵ is given by the term:
C(5,k) * (kx)⁵ = k⁵ * C(5,k) * x⁵
where C(5,k) is the binomial coefficient or the number of ways to choose 5 items out of k.
So, we have the equation:
k⁵ * C(5,k) = -672
We can use a table of binomial coefficients to find C(5,k) for different values of k, but this can be time-consuming. Alternatively, we can use the fact that C(5,k) = C(5,5-k) and rewrite the equation as:
k⁵ * C(5,5-k) = -672
Expanding C(5,5-k), we get:
k⁵ * C(5,5-k) = k⁵ * C(5,k) = -672
Now, we can use trial and error to solve for k. Using this method, we can find that k = -4 or k ≈ 0.4041. However, since k must be positive (since it appears as a factor in the expansion), the only valid solution is k ≈ 0.4041.
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What is the maximum possible product of two numbers that have a sum of -8?
The maximum possible product of two numbers that have a sum of -8 is 16.
How to find the maximum possible product of two numbers that have a sum of -8Let us name the two numbers "x" and "y".
We are aware of the following: x + y = -8
We're looking for the greatest possible product of x and y.
The number we're looking that are as near together as feasible and have a sum of -8.
-4 and -4 are the two numbers that are as near together as possible and have a sum of -8. As a result, x = -4 and y = -4.
The sum of these two figures is:
x * y = (-4) * (-4) = 16
So, the maximum possible product of two numbers that have a sum of -8 is 16.
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The sum of two even numbers is even. The sum of 6 and another number is even. What conjecture can you make about the other number?
A) The other number is odd.
B) The number is even.
C) Not enough information.
D) The number is 8.
Answer:
B) The other number is even.
can someone help me please
here is the picture is about Row Ops
The result of engaging in the row multiplication operation in a matrix would be [ 1 /2 0 | 3 / 4 ]
[ -1 5 | 4 ].
How to multiply matrices ?First, you should multiply the first row by the value given of 1 / 4 to be:
( 1 / 4 ) x 2 = 1 / 2
( 1 / 4 ) x 0 = 0
( 1 / 4 ) x 3 = 3 / 4
Then you can replace the values found by the values in the matrix to be :
[ 1 / 2 0 | 3 / 4 ]
[ - 1 5 | 4 ]
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Some varsity soccer players are paired with a junior varsity (JV) player for training purposes: 2/3 of the varsity are partnered with 3/5 of the JV. What fraction of the players are partnered for training?
Let's say there are $v$ varsity players and $j$ JV players.
The problem tells us that 2/3 of the varsity players are partnered with 3/5 of the JV players. So the number of varsity players partnered with a JV player is:
$\sf\implies\:(2/3)v$
And the number of JV players partnered with a varsity player is:
$\sf\implies\:(3/5)j$
Since these two numbers represent the same group of paired players, they must be equal:
$\sf\implies\:(2/3)v = (3/5)j$
To find the fraction of players who are partnered, we can divide the total number of paired players by the total number of players:
$\implies\:\frac{(2/3)v}{v} = \frac{2}{3}$ of the varsity players are paired
$\implies\:{\sf{\frac{(3/5)j}{j}} = \frac{3}{5}}$ of the JV players are paired
So the total fraction of players who are paired is:
$\sf\implies\:\frac{2}{3} + \frac{3}{5} - \frac{2}{15}$ (since some players will be counted in both fractions)
Simplifying:
$\sf\implies\:\frac{10}{15} + \frac{9}{15} - \frac{2}{15} = \frac{17}{15}$
Therefore, the fraction of players who are partnered for training is $\frac{17}{15}$, which is greater than 1. This means that the problem may have been set up incorrectly, or there may be additional information missing.
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[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]
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Select the correct answer.
Mary is buying several items that cost $128.25 total. She is using a store coupon for 35% off her purchases. She has to pay 4% sales tax. Calculate the total cost of the items.
A.
$80.03
B.
$83.36
C.
$86.70
The total cost of the several items that originally cost $128.25 with a coupon for 35% off and sales tax of 4% is C. $86.70.
How the total cost is determined:The original cost is discounted by 35% using a discount factor of 0.65 and increased by a sales tax factor of 1.04.
After the multiplications, the product shows the total cost that Mary incurred for buying the items.
Original cost of several items Mary is buying = $128.25
Coupon discount = 35%
Discount factor = 0.65 (100 - 35)
Sales tax rate = 4%
Sales tax factor = 1.04 (100 + 4)
The total cost of the items = $86.70($128.25 x 0.65 x 1.04)
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find cooordinates of point of interection
11x-6y=2
-8x+5y=3
Answer:
To find the coordinates of the point of intersection of the given equations, we need to solve the system of equations simultaneously. We can use the elimination method to do this:
11x - 6y = 2 (multiply both sides by 5)
-8x + 5y = 3 (multiply both sides by 11)
55x - 30y = 10
-88x + 55y = 33
Adding the two equations, we get:
-33x + 25y = 43
Solving for y, we get:
y = (33x + 43)/25
Substituting this expression for y into either of the original equations and simplifying, we get:
x = -1/7
Substituting this value of x into the equation for y, we get:
y = 1/35
Therefore, the coordinates of the point of intersection are (-1/7, 1/35).
4cos45°-2sin45°. Please let me know the answer with thorough steps.
We know that cos(45) = sin(45) = √2/2.
Substituting these values, we can simplify the expression as follows:
4cos(45) - 2sin(45)
= 4(√2/2) - 2(√2/2) (substituting cos(45) and sin(45) values)
= 2√2 - √2
= √2
Therefore, the answer is √2.
Find the probability that
event A or B takes place.
Probability that event A or B takes place is, P(A or B) = 16/21.
Here from the Venn diagram we can obtain that,
Probability of occurring event A = 2/21 + 4/21 = (2 + 4)/21 = 6/21
Probability of occurring event B = 10/21 + 4/21 = (10 + 4)/21 = 14/21
Probability of occurring event A and event B both = 4/21
So, P(A) = 6/21
P(B) = 14/21
P(A and B) = 4/21
We know that the union of events formula,
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 6/21 + 14/21 - 4/21
P(A or B) = (6 + 14 - 4)/21
P(A or B) = 16/21
Hence the value of P(A or B) = 16/21.
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a shape has 3 sides. the bottom edge is 5 inches and the hight is 1 foot. what is the surface area
Answer:
Step-by-step explanation:
You deposit $300 each month into an account earning 2% interest compounded
monthly.
a) How much will you have in the account in 30 years?
b) How much total money will you put into the account?
c) How much total interest will you earn?
a) The future value of the account after 30 years can be calculated using the formula:
FV = P * ((1 + r/n)^(n*t))
where P is the monthly deposit, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, P = $300, r = 0.02, n = 12 (monthly compounding), and t = 30. Plugging these values into the formula, we get:
FV = $300 * ((1 + 0.02/12)^(12*30)) = $150,505.60
So you will have $150,505.60 in the account after 30 years.
b) The total amount of money you will put into the account is simply the monthly deposit multiplied by the number of months in 30 years, which is 30*12 = 360 months. So the total amount of money you will put into the account is:
$300 * 360 = $108,000
c) The total interest earned can be calculated by subtracting the total amount deposited from the future value of the account. So the total interest earned is:
$150,505.60 - $108,000 = $42,505.60
Answer:
a) you will have approximately $133,381.85 in the account in 30 years.
b) a total of $108,000 into the account over 30 years.
c) a total of $25,381.85 in interest over 30 years.
Step-by-step explanation:
Given Circle C, calculate the length of PQ (Thx for any help!)
Answer:
3π
Step-by-step explanation:
Given
Radius=9
Angle=60°
Since PQ is an arc
Perimeter of an Arc =(θ/360)×2πr
60/360×2π(9)
1/6×18π
3π
Find an angle in each quadrant with a common reference angle with 285°, from 0°≤θ<360
The four angles, one in each quadrant, with a common reference angle of with 285° are: 15°, 165°, 195°, 345°
Understanding QuadrantA common reference angle is an angle that is shared by multiple angles in different quadrants when measured from the x-axis. The reference angle for an angle measured in degrees can be found by subtracting the nearest multiple of 90 degrees that is less than the angle.
For the angle 285°, the nearest multiple of 90 degrees that is less than it is 270°. Therefore, the reference angle for 285° is 285° - 270° = 15°.
Using this reference angle, we can find an angle in each quadrant with a common reference angle with 285° as follows:
First Quadrant: An angle in the first quadrant with a reference angle of 15° is 15° itself.Second Quadrant: An angle in the second quadrant with a reference angle of 15° can be found by subtracting the reference angle from 180°. Therefore, an angle in the second quadrant with a common reference angle with 285° is 180° - 15° = 165°.Third Quadrant: An angle in the third quadrant with a reference angle of 15° can be found by subtracting the reference angle from 180° and then adding 180°. Therefore, an angle in the third quadrant with a common reference angle with 285° is 180° + 15° = 195°.Fourth Quadrant: An angle in the fourth quadrant with a reference angle of 15° can be found by subtracting the reference angle from 360°. Therefore, an angle in the fourth quadrant with a common reference angle with 285° is 360° - 15° = 345°.Learn more about quadrant here:
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Show 2 different ways to find the value of x. What do you think is the most efficient method? Explain why.
We can use trigonometric relations or Pythagorean's theorem, we will see that x = 8ft.
How to find the value of x?We can see that x is the hypotenuse of the triangle, and we know the length of one leg and the angle between them, then we can use the cosine trigonometric relation:
cos(60°) = 4ft/x
solving for x:
x = 4ft/cos(60°) = 8ft
Other way to find x is first find the other side and then use the pyhtagorean theorem, to get the other side y we need:
tan(60°) = y/4ft
y = 4ft*tan(60°)
Then using Pythagorean's theorem we get:
x = √( (4ft)² + (4ft*tan(60°))²)
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Find F(7)…………………………………………
Based on the given function conditions of f(x) , the value of f(7) is equal to -6
To find f(7), we need to determine which function definition to use based on the value of x.
Since x = 7 is greater than 5, we know that we'll be using the third definition of the function: f(x) = -x + 1 for 2 < x ≤ 5.
Therefore, we can substitute x = 7 into the third definition of the function:
f(7) = -7 + 1 = -6
So, f(7) = -6.
In summary, to find f(7), we identified which function definition to use based on the value of x. Since x = 7 is greater than 5, we used the third definition of the function, f(x) = -x + 1 for 2 < x ≤ 5, and found that f(7) = -6.
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Singular Savings Bank received an initial deposit of $3000. It kept a percentage of this money in reserve based on the reserve rate and loaned out the rest. The amount it loaned out was eventually all deposited back into the bank. If this cycle continued indefinitely and eventually the $3000 turned into $50,000, what was the reserve rate? And what are the steps to solve?
Tthe reserve rate was approximately 0.9434, or 94.34%.
How to solve for the reserve rateThis is a geometric series with first term 3000r and common ratio (1-r), so we can use the formula for the sum of a geometric series:
sum = a(1 - r^n) / (1 - r)
where a = 3000r is the first term.
As the cycle continues indefinitely, the amount loaned out eventually becomes the final amount of $50,000. Therefore:
3000r/(1-r) = 50,000
Solving for r, we get:
r = (50,000)/(3000 + 50,000) = 0.9434
Therefore, the reserve rate was approximately 0.9434, or 94.34%.
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e) Write a proof to show AABC ~ ACFD.
f) What is the longest cart that can pass through the second doorway?
Explain.
Some of the factory's products are long fragile rods that are carried through
the door by hand. The first door is 72 inches west of the start of the second
door. Assume the rod has zero width and BA = 13 in.
Answer:
Step-by-step explanation:
no
Help pls i dont understand this
The percentage increase in the number of water bottles the company manufactured from February to April is 19%.
How to find the percentage increase ?In March, the company manufactured 7% more water bottles than in February:
Number of water bottles in March = 4,100 + 7% of 4,100
Number of water bottles in March = 4,387
In April, the company manufactured 500 more water bottles than in March:
Number of water bottles in April = 4,387 + 500
Number of water bottles in April = 4,887
To find the percent increase from February to April, we can use the following formula:
percent increase = (new value - old value) / old value x 100%
percent increase = (4,887 - 4,100) / 4,100 * 100%
percent increase = 787 / 4,100 x 100%
percent increase = 19%
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Help with math problems
Answer:
Step-by-step explanation:
15.) [tex]\sqrt{12}[/tex]
[tex]\sqrt{4}[/tex] * [tex]\sqrt{3}[/tex]
Answer: 2[tex]\sqrt{3}[/tex]
17.) Distribute 3[tex]\sqrt{3}[/tex] into both sides of the parentheses
3[tex]\sqrt{3}[/tex] * 4 = 12[tex]\sqrt{3}[/tex]
3[tex]\sqrt{3}[/tex] * -3[tex]\sqrt{5}[/tex] = -9[tex]\sqrt{15}[/tex]
Answer: 12[tex]\sqrt{3}[/tex] - 9[tex]\sqrt{15}[/tex]
19.) Distribute 4[tex]\sqrt{15}[/tex] into both sides of the parentheses
4[tex]\sqrt{90}[/tex] + 4[tex]\sqrt{75}[/tex]
4*[tex]\sqrt{9}[/tex]*[tex]\sqrt{10}[/tex] + 4*[tex]\sqrt{25}[/tex]*[tex]\sqrt{3}[/tex]
4*3*[tex]\sqrt{10}[/tex] + 4*5*[tex]\sqrt{3}[/tex]
12[tex]\sqrt{10}[/tex] + 20[tex]\sqrt{3}[/tex]
21.) Distribute [tex]\sqrt{15}[/tex] into both sides of the parentheses
2[tex]\sqrt{150}[/tex] - 4[tex]\sqrt{90}[/tex]
2*[tex]\sqrt{25}[/tex]*[tex]\sqrt{6}[/tex] - 4*[tex]\sqrt{9}[/tex]*[tex]\sqrt{10}[/tex]
2*5*[tex]\sqrt{6}[/tex] - 4*3*[tex]\sqrt{10}[/tex]
10[tex]\sqrt{6}[/tex] - 12[tex]\sqrt{10}[/tex]
Find a polynomial f(x) of degree 5 that has the following zeros.
0, 1 (multiplicity 2), -6, -3
Leave your answer in factored form.
This polynomial has zeros at 0, 1 (with multiplicity 2), -6, and -3, as required, and is of degree 5.
How to solveA polynomial f(x) of degree 5 with the given zeros can be represented in factored form as:
f(x) = [tex]A(x - 0)(x - 1)^2(x + 6)(x + 3)[/tex]
Since the leading coefficient is not specified, we can leave A as a constant factor. Simplifying the expression, we have:
f(x) = [tex]A(x)(x - 1)^2(x + 6)(x + 3)[/tex]
This polynomial has zeros at 0, 1 (with multiplicity 2), -6, and -3, as required, and is of degree 5.
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find the standard equation of a circle with the points (-18;-5), (-7;-16) and (4;-5)
Answer:
Step-by-step explanation:
To find the equation of a circle given three non-collinear points, we can use the following steps:
Find the equations of the perpendicular bisectors of the line segments connecting the pairs of points.
Find the intersection point of the two perpendicular bisectors. This point is the center of the circle.
Find the distance between the center and any one of the three points. This distance is the radius of the circle.
Let's apply these steps to the given points:
Find the midpoint and slope of the line segments connecting the pairs of points:
Midpoint of (-18, -5) and (-7, -16): ((-18+(-7))/2, (-5+(-16))/2) = (-12.5, -10.5)
Slope of (-18, -5) and (-7, -16): (-16 - (-5))/(-7 - (-18)) = -11/11 = -1
Midpoint of (-18, -5) and (4, -5): ((-18+4)/2, (-5+(-5))/2) = (-7, -5)
Slope of (-18, -5) and (4, -5): (-5 - (-5))/(4 - (-18)) = 0
Midpoint of (-7, -16) and (4, -5): ((-7+4)/2, (-16+(-5))/2) = (-1.5, -10.5)
Slope of (-7, -16) and (4, -5): (-5 - (-16))/(4 - (-7)) = 11/11 = 1
The equations of the perpendicular bisectors passing through the midpoints are:
x + 12.5 = -1(y + 10.5) or x + y + 23 = 0
y + 5 = 0
Find the intersection point of the two perpendicular bisectors:
Solving the system of equations:
x + y + 23 = 0
y + 5 = 0
yields: x = -18, y = -5
So, the center of the circle is (-18, -5).
Find the distance between the center and any one of the three points:
Using the distance formula:
Distance between (-18, -5) and (-18, -5): sqrt(((-18)-(-18))^2 + ((-5)-(-5))^2) = 0
Distance between (-18, -5) and (-7, -16): sqrt(((-18)-(-7))^2 + ((-5)-(-16))^2) = sqrt(221)
Distance between (-18, -5) and (4, -5): sqrt(((-18)-4)^2 + ((-5)-(-5))^2) = 22
The radius of the circle is sqrt(221).
Therefore, the equation of the circle in standard form is:
(x + 18)^2 + (y + 5)^2 = 221
The standard equation of a circle with the points (-18;-5), (-7;-16) and (4;-5) is:
(x + 13)² + (y + 1)² = 41
Standard equation of a circleFrom the question, we are to determine the standard equation of a circle with the given points
The given points are:
(-18;-5), (-7;-16) and (4;-5)
The standard equation of a circle is given by:
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle
and r is the radius.
Using the given points (-18, -5), (-7, -16), and (4, -5), we can find the equation of the circle as follows:
Find the midpoint of the line segments connecting the pairs of points:
Midpoint of (-18, -5) and (-7, -16): ((-18 + -7)/2, (-5 + -16)/2) = (-12.5, -10.5)
Midpoint of (-7, -16) and (4, -5): ((-7 + 4)/2, (-16 + -5)/2) = (-1.5, -10.5)
Midpoint of (-18, -5) and (4, -5): ((-18 + 4)/2, (-5 + -5)/2) = (-7, -5)
Find the equations of the perpendicular bisectors of the line segments:
Perpendicular bisector of the line connecting (-18, -5) and (-7, -16):
Slope of the line: (−16 + 5)/(-7 + 18) = -11/5
Slope of the perpendicular bisector: 5/11
Midpoint: (-12.5, -10.5)
Equation: y + 10.5 = (5/11)(x + 12.5)
Perpendicular bisector of the line connecting (-7, -16) and (4, -5):
Slope of the line: (-5 + 16)/(4 + 7) = 11/7
Slope of the perpendicular bisector: -7/11
Midpoint: (-1.5, -10.5)
Equation: y + 10.5 = (-7/11)(x + 1.5)
Perpendicular bisector of the line connecting (-18, -5) and (4, -5):
Slope of the line: 0
Slope of the perpendicular bisector: undefined (perpendicular bisector is a vertical line)
Midpoint: (-7, -5)
Equation: x + 7 = 0
Find the point of intersection of any two perpendicular bisectors:
Intersection of perpendicular bisectors 1 and 2:
y + 10.5 = (5/11)(x + 12.5)
y + 10.5 = (-7/11)(x + 1.5)
Solving for x and y, we get:
x = -13
y = -1
Thus,
The center of the circle is (-13, -1).
Find the radius of the circle:
Using the center (-13, -1) and one of the given points, say (-18, -5):
r² = (-18 - (-13))² + (-5 - (-1))²
r² = 25 + 16
r² = 41
Hence, the equation of the circle is:
(x + 13)² + (y + 1)² = 41.
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A vehicle purchased for $29800 depreciates at a constant rate of 7% per year. Determine the approximate
value of the vehicle 11 years after purchase.
Round to the nearest whole number.
The exponential value decay equation is solved and the value of the vehicle after 11 years is A = $ 13,413
Given data ,
Let the initial cost of the vehicle be = $ 29,800
Now , the rate of depreciation be r = 7 %
Let the number of years be n = 11 years
And , the exponential decay is given by the equation ,
x ( t ) = x₀ × ( 1 + r )ⁿ
On simplifying , we get
x ( 11 ) = 29800 ( 1 - 0.07 )¹¹
x ( 11 ) = 29800 ( 0.93 )¹¹
x ( 11 ) = 13,413.085
Hence , the cost of the vehicle after 11 years is A = $ 13,413
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Pete has an anvil used for metal working, he models the base as two trapeziums the anvil applied of 834 newton's
The pressure using Pete's model based on the information will be 2.79 N/cm³
What is a trapezium?A trapezium (often known as a trapezoid in some parts of the world) is a four-sided figure with at least one set of parallel lines. These two lines are often referred to as the bases, and the other sides as its legs.
Isosceles Trapezium is a type of trapezium has its legs of equal length, and its base angles possessing an equivalent measure..
Pete has an anvil used for metal working, he models the base as two trapeziums the anvil applied of 834 newton's
The pressure using Pete's model based on the information will be:
= 834 / 299.25
= 2.79 N/cm³
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Answer:
1.54
Step-by-step explanation:
Trapezium=
12+24=36
36 x (length) 15 = 540cm^2
Pressure= force/area
832/540 = 1.54N/cm^2
for question 6 is wax and yau are verticle or not
In the given diagram, angle WAX and angle YAU are vertical angles
What are vertically opposite angles?From the question, we are to determine if angles WAX and YAU are vertical angles or not
Vertically opposite angles are pairs of angles that are opposite each other and formed by the intersection of two straight lines.
When two straight lines intersect, they form four angles at the point of intersection. Vertically opposite angles are the angles that are opposite each other, that is, they are located on opposite sides of the intersection point and are formed by the pair of opposite rays.
Vertically opposite angles are congruent, which means that they have the same angle measure. This property holds true for any pair of vertically opposite angles, regardless of the angle size or the orientation of the lines.
Hence, angle WAX and angle YAU are vertical angles
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If the points A,B and C have the coordinates A (5,2), B (2,-3) and C (-8,3) show that the triangle ABC is a right angled triangle.
Answer:
Step-by-step explanation:
To show that the triangle ABC is a right-angled triangle, we need to prove that one of the angles of the triangle is a right angle, which means it measures 90 degrees.
We can use the Pythagorean theorem to check if the sides of the triangle satisfy the condition for a right-angled triangle. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's find the length of each side of the triangle:
AB = √[(5-2)² + (2-(-3))²] = √(3²+5²) = √34
BC = √[(2-(-8))² + (-3-3)²] = √(10²+6²) = √136
CA = √[(5-(-8))² + (2-3)²] = √(13²+1²) = √170
Now, let's check if the Pythagorean theorem is satisfied:
AC² = AB² + BC²
170 = 34 + 136
Since the Pythagorean theorem is satisfied, we can conclude that the triangle ABC is a right-angled triangle, with the right angle at vertex B.
We know that,
the distance between two points=√(x2-x1)²+(y2-y1)²
∴ The distance between points A and B, AB=√(2-5)²+(-3-2)²
=√(9+25)
= √(34)
∴ The length of side AB = √(34)
Again,
The distance between points B and C, BC= √[(-8-2)²+{3-(-3)}²]
= √(100+36)
= √136
∴ The length of side BC =√136
Also,
The distance between points A and D, AC= √(-8-5)²+(3-2)²
= √(169+1)
= √170
∴ The length of side AC=√170
Now, we get three sides of the triangle as AB = √(34), BC = √136, and AC=√170
Since AC is the longest side, we take it as hypotenuse, and the other sides as base and height in the Pythagoras theorem,
AC²=170
BC²=136
AB²=34
Clearly, 170=136+34
or, AC²=AB²+BC²
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I need help with this please.
1/2 x 3 x 3 = 4.5
I just need help on how 4.5 is the answer.
Answer:
3
Step-by-step explanation:
3 * 3 = 6
1/2 * 6 = 3 not 4.5
Because, when we multiply with 1/2, we are actually dividing the number by 2, and 6/2 = 3.
The 3 x 3 part turns into 9
So we have 1/2 x 9 or 9/2
Use long division to find that 9/2 gives a quotient of 4 and remainder 1
Imagine you had 9 cookies and 2 friends. Each friend would get 4 cookies each, eating 4*2 = 8 cookies overall. Then there's 9-8 = 1 cookie as the remainder.
The "remainder 1" then leads to 1/2 = 0.5
quotient = 4
remainder = 1 ---> decimal portion = 1/2 = 0.5
So that's how we get to 4+0.5 = 4.5
You can use a calculator to see that 9/2 = 4.5
James takes a 150000 mortgage for 20yrs and makes a monthly payment of 915.00. What percent of the total loan does he pay back?
James pays back approximately 82.33% of the total loan in interest over the 20-year period.
To calculate the percentage of the total loan that James pays back in interest, we need to determine how much of the monthly payments go towards interest and how much goes towards paying down the principal.
Using a loan calculator or a formula, we can determine that the monthly interest rate for James' loan is approximately
= 4.25% / 12
= 0.35% (4.25% annual rate divided by 12 months).
The monthly payment of $915.00 is comprised of both principal and interest.
In the first month, the interest portion of the payment would be $531.25 and the remaining $383.75 would go towards the principal. As the loan is paid down over time, the interest portion of each payment decreases while the principal portion increases.
To calculate the total interest paid over the life of the loan, we can multiply the monthly interest by the number of months
20 years x 12 months/year = 240 months
and subtract the original principal amount of $150,000. This gives us a total interest paid of approximately $123,500.
To find the percentage of the total loan that this represents, we can divide the total interest paid by the original principal and multiply by 100:
$123,500 ÷ $150,000 x 100 ≈ 82.33%
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What is the surface area of a triangular prism
Answer:
surface area=bh+2ls+lb
Step-by-step explanation:
If you think it is too long to remember, just find the area of each of the shapes on it and add them together.
Hope this helps :)
A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 2 tables is $25.
The cost of each chair and table is $2.5 and $8.75 respectively.
Given that the total cost to rent 3 chairs and 2 tables is $25 and total cost to rent 5 chairs and 6 tables is $65.
We need to find the cost of each chair and table,
Let the cost of each chair and table be x and y respectively,
3x+2y = 25.......(i)
5x+6y = 65.........(ii)
Multiply the equation (i) by 3 and subtract ii from i,
9x+6y = 75 - (5x+6y = 65)
4x = 10
x = 2.5
Put x = 2.5 in any equation to find the value of y,
3(2.5)+2y = 25
2y = 17.5
y = 8.75
Hence, the cost of each chair and table is $2.5 and $8.75 respectively.
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Can yall help me with this
Answer:
x = 67
Step-by-step explanation:
The two triangles are identail.
Answer:
x = 67
because 67 and x the same
Find the missing side lengths. Leave your answers as radicals in simplest form. I need help quickly!
Answer:
[tex]m = \dfrac{4}{\sqrt{3}} \text{ or, in rational form: } m = \dfrac{4\sqrt{3}}{3}[/tex]
[tex]n = \dfrac{2}{\sqrt{3}} \text{ or, in rational form: } n = \dfrac{2\sqrt{3}}{3}[/tex]
Not sure which form your teacher wants the answers, would suggest putting in both
Step-by-step explanation:
The missing angle of the triangle = 180 - (60 + 90) = 30°
We will use the law of sines to find m and n
The law of sines states that the ratio of each side to the sine of the opposite angle is the same for all sides and angles
Therefore since m is the side opposite 90° and 2 is the side opposite 60°,
[tex]\dfrac{m}{\sin 90} = \dfrac{2}{\sin 60}}\\\\[/tex]
sin 90 = 1
sin 60 = √3/2
So
[tex]\dfrac{m}{1} = \dfrac{2}{\sqrt{3}/2} \\\\m = \dfrac{2}{\sqrt{3}/2} \\\\m = \dfrac{2 \cdot 2}{\sqrt{3}} \\\\m = \dfrac{4}{\sqrt{3}}\\\\[/tex]
We can rationalize the denominator by multiplying numerator and denominator by √3 to get
[tex]m = \dfrac{4\sqrt{3}}{3}[/tex]
(I am not sure what your teacher wants, you can put both expressions, they are the same)
To find n
Using the law of sines we get
[tex]\dfrac{n}{\sin 30} = \dfrac{m}{\sin 90}\\\\\dfrac{n}{\sin 30} = m\\\\\dfrac{n}{\sin 30} = \dfrac{4}{\sqrt{3}}\\\\[/tex]
sin 30 = 1/2 giving
[tex]\dfrac{n}{1/2} = \dfrac{4}{\sqrt{3}}\\\\n = \dfrac{1/2 \cdot 4}{\sqrt{3}} \\\\n = \dfrac{2}{\sqrt{3}}[/tex]
In rationalized form
[tex]n = \dfrac{2\sqrt{3}}{3}}[/tex]