The area of triangle LMN is 49.61 square units.
We have,
To find the area of triangle LMN.
Area = (1/2) x base x height
where the base and height are the sides of the triangle perpendicular to each other.
First, we need to find the length of side L.
We can use the Law of Cosines.
L² = M² + N² - 2MNcos(132°)
L² = 6² + 8.3² - 268.3cos(132°)
L² = 36 + 68.89 + 99.36
L² = 204.25
L = √204.25
L = 14.28
Now that we know the length of the base of the triangle, we can find the height by dropping a perpendicular from vertex M to side LN.
Since triangle LMN is obtuse, the perpendicular will fall outside of the triangle.
Let's call the foot of the perpendicular point P.
Since M∠M is 132°, we can find the measure of the acute angle ∠LMP:
M∠LMP = 180° - M∠M
M∠LMP = 180° - 132°
M∠LMP = 48°
We can use trigonometry to find the length of MP:
tan(48°) = h/6
h = 6 x tan(48°)
h = 6.93
The area of triangle LMN is:
Area = (1/2) x base x height
Area = (1/2) x 14.28 x 6.93
Area ≈ 49.61
Thus,
The area of triangle LMN is 49.61 square units.
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At age 20, someone sets up an IRA (individual retirement account) with an APR of 5%. At the end of each month he deposits $65 in the account. How much will the IRA contain when
←he
retires at age 65? Compare that amount to the total deposits made over the time period.
After retirement the IRA will contain $ 131,718.42
(Do not round until the final answer. Then round to the nearest cent as needed.)
The total deposits made over the time period is $
(Type a whole number)
CETT
Answer:
total deposits: $35,100
Step-by-step explanation:
You have the value of an annuity earning 5% with payments of $65 a month for 45 years as $131,718.42. You want to know the total value of payments.
Payments12 payments per year of $65 for 45 years will have a total value of ...
12·65·45 = 35100
Total deposits will be $35,100.
at irvs cycle rental shop irv rents all kinds of cycles: unicycles, tandem bikes, regular bikes, and even tricycles for little kids. he parks all the cycles in front of his shop with a helmet for each rider strapped to the cycles. this morning irv counted 57 helmets and 115 wheels parked in front of his store. he knows he had an equal number of unicycles and tandem bikes. he also knows that he has 32 regular bikes. how many unicycles, tandem bikes, and tricycles does irv have
The number of unicycles, tandem bikes, and tricycles that IRVS Cycle Rental has are:
unicycles - 8 tandem bikes - 8 tricycles - 9 How to find the items the shop has ?The relevant equations, ( assuming that unicycles as U, tandem bikes as T, and tricycles as R ) are:
U + T + 32 + R = 57
U + 2T + 2 x 32 + 3R = 115
U = T
Using substitution, we get:
U + 2T + 64 + 3R = 115
U + 2T + 3R = 51
U + 2U + 3R = 51
3U + 3R = 51
Solving gives:
2U + R = 25
U + R = 17
U = 8
Solving for R, we have :
8 + R = 17
R = 17 - 8
R = 9
U and T are the same so T is 8 as well.
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A bag has 4 brown marbles and 12 yellow marbles. Half of the yellow marbles are made of glass. A marble is selected at random from the bag. What is the
probability that it is a yellow, glass marble?
Write your answer as a fraction in simplest form.
9
Answer: 3/8.
Step-by-step explanation: f 4 + 12 = 16, 12 / 2 = 6, 6 / 16 = 3 / 8
Andretti Company has a single product called a Dak. The company normally produces and sells 82,000 Daks each year at a selling price of $62 per unit. The company’s nit costs at this level of activity are given below: Direct materials $ 7.50 Direct labor 9.00 Variable manufacturing overhead 2.40 Fixed manufacturing overhead 7.00 ($574,000 total) Variable selling expenses 3.70 Fixed selling expenses 3.50 ($287,000 total) Total cost per unit $ 33.10
There is a financial advantage of $ 1,187,520.
Incremental Costs and Revenues will be as follows
Increment in sales = 82,000 units × 40% = 32,800 units
and, Selling Price
= (32,800 units × $62 per unit)
= $ 2,033,600
Direct materials
= $ 7.50 × 32,800 units
= 246,000
Direct labor
= $ 9.00 × 32800
= $295,200
and, Variable manufacturing overhead
= 2.40 x 32800
= $78, 720
So, the contribution is
= 2,033,600 - (246000 + 285200 + 78720)
= 1,423,680
Now, Variable selling expenses
= 32800 x 3.7
= 121,360
and, Fixed Selling Expenses
= 32800 x 3.5
= 114,800
So, Net income = 1, 187, 520
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Abi takes out a loan that gathers compound interest. The table below shows the value of the loan over time. a) What is the rate of interest per annum? Give your answer as a percentage to 1 d.p. b) Work out the value of the loan 10 years after it starts. Give your answer in pounds (£) to the nearest 1p. Start After 1 year After 2 years £2500.00 £2645.00 £2798.41
As per the given percentage, the value of the loan 10 years after it starts is £4506.32.
We know the values of P and A for the first two years. So, we can use these values to find the value of r. Let's use the formula for the first year:
2645 = 2500(1 + r/1)¹ˣ¹
Simplifying the equation, we get:
1 + r = 2645/2500
1 + r = 1.058
r = 0.058 or 5.8%
Therefore, the interest rate per annum is 5.8% (to 1 decimal place).
Now, let's move on to finding the value of the loan after 10 years. We can use the same formula for compound interest, but we need to substitute the values of P, r, n, and t accordingly. Here's the formula:
A = P(1 + r/n)ⁿˣ
Where:
P = 2500
r = 0.058
n = 1 (as the interest is compounded annually)
x = 10
Substituting these values, we get:
A = 2500(1 + 0.058/1)¹ˣ¹⁰
A = 2500(1.058)¹⁰
A = 4506.32
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How is the greatest common factor of 8x^5, 12x^3, and 20x^2 4x^2 when 2 does not go evenly into 5?
We can factor each of the given terms so that 4x^2 shows up
8x^5 = 4x^2*2x^3
12x^3 = 4x^2*3x
20x^2 = 4x^2*5
This shows how 4x^2 is the GCF of 8x^5, 12x^3, and 20x^2
-----------------
Here's how to find the GCF of terms involving variables.
First, find the GCF of the coefficients 8, 12 and 20.
List the prime factorizations
8 = 2*2*212 = 2*2*320 = 2*2*5Then circle "2*2" since it is found in all three factorizations. Do not circle 3 because it's not found in 8 or 20. Do not circle 5 since it's not found in 8 or 12.
Therefore, the GCF of {8,12,20} is 2*2 = 4.
As for the variable terms, we look for the smallest exponent.
The exponents for x^5, x^3, x^2 are 5,3,2 in that order. The smallest exponent is 2, so x^2 is part of the GCF.
----------------
Summary:
We found the GCF of the coefficients was 4.
The GCF of the variable terms was x^2
That's how we arrive at the GCF of 4x^2
simplify. sqrt 7 / 2square root 11
The answer to the above question is [tex]\sqrt{77}/22[/tex]
understanding surd simplificationA surd is an irrational number, that is, a number that cannot be expressed as a simple fraction or ratio of two integers.
Given the expression:
[tex]\frac{\sqrt{7} }{2\sqrt{11} }[/tex]
Multiply both numerator and denominator by a factor. In this case our factor is [tex]\sqrt{11}[/tex]
Then we have:
= [tex]\frac{\sqrt{7} }{2\sqrt{11} }*\frac{\sqrt{11} }{\sqrt{11} }[/tex]
This gives us:
= [tex]\frac{\sqrt{7} * \sqrt{11} }{2\sqrt{11} * \sqrt{11} }[/tex]
This should give us:
= [tex]\frac{\sqrt{77} }{2*11 }[/tex][tex]\frac{\sqrt{77} }{22 }[/tex]
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X + y = 8
If x = -1 what is y?
Answer: 9
Step-by-step explanation:-1 plus 9 equals 8
Answer: y = 9
Step-by-step explanation:
First of all, you right out your equation
x + y = 8
Secondly, you sub in the values you have
-1 + y = 8
Then you can swap your answer and y
-1 + 8 = y
Work out the answer
-1 + 8 = 9
Answer is y = 9
о
What are three things that your
personality test can tell you?
Choose three answers.
How you prefer to interact with
others
How to break up with a partner
What you might enjoy in a career
1/3
How you rocharge your onoray
The three things that a personality test can tell you are:
A. How you prefer to interact with others.
C. What you might enjoy in a career.
D. How you recharge your energy.
What is personality test?A personality test is a tool used to assess and measure an individual's traits, characteristics, and patterns of behavior.
It may be a series of questions or statements that the individual must respond to.
The results are used to determine the person's strengths and weaknesses, their communication and social interaction (like if they are extrovert or introvert), how they process information and decision-making, etc.
They can also tell of an individual's preferred methods of finding balance in their lives, like spending time alone or with friends and families, being in nature, etc.
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using algebra prove that given any 3 consecutive whole numbers, the sum of the square of the smallest number and the largest number is always 2 more that twice the square of the middle number
Answer:
Let x, x + 1, and x + 2 be the three numbers.
x^2 + (x + 2)^2 = x^2 + x^2 + 4x + 4
= 2x^2 + 4x + 4
= 2x^2 + 4x + 2 + 2
= 2(x^2 + 2x + 1) + 2
= 2(x + 1)^2 + 2
The principal P is borrowed at a simple interest rate r for a period of time t. Find the loans future value A or the total amount due at time t
P= 5000
r=4.5%
t = 6 months
The future value or the total amount due at time t for the loan is $5112.50.
To find the future value or the total amount due at time t for a loan with a principal P, a simple interest rate r, and a period of time t, we can use the formula for calculating simple interest;
A=P + (P × r × t)
where; A = future value or total amount due at time t
P = principal amount
r = simple interest rate
t = time period (in years)
Given the values; P = $5000
r = 4.5% (or 0.045 as a decimal)
t = 6 months (or 0.5 years)
We can substitute these values into the formula and calculate the future value;
A = 5000 + (5000 × 0.045 × 0.5)
A = 5000 + 112.5
A = $5112.50
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ANSWER AS SOON AS POSSIBLE MUST ANSWER BEFORE 10:30-35 TO GET BRAINLYS!!!
Answer:
look at the photo
Step-by-step explanation:
help please, math question Calculate the perimeter
The Perimeter of the given figure rectangle will be 60m. The correct option is 1.
Perimeter refers to the total length of the boundary of a two-dimensional shape or object. It is the distance around the edge of a shape. To find the perimeter of a shape, you add up the lengths of all its sides.
The perimeter of a rectangle is given by the formula:
P = 2(l + w)
where P is the perimeter, l is the length, and w is the width.
Using the values you provided, we can substitute them into the formula:
P = 2(18 + 12) = 2(30) = 60 meters
Therefore, the perimeter of the rectangle with a length of 18 meters and a height of 12 meters is 60 meters.
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a. what is the length y
b. find out the area of the shaded part
The value of length y is,
y = 4 cm
And, The area of the shaded part is, 20 cm²
We have to given that;
A figure is shown in image.
Hence, We get;
The value of y is,
y = 4 cm
And, The area of the shaded part is,
⇒ 4 × 5
⇒ 20 cm²
Thus, The value of length y is,
y = 4 cm
And, The area of the shaded part is, 20 cm²
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Can you help me solve this asap
Based on the equation, we own 100 shares of JP Morgan Emerging Markets Bond Fund and 900 shares of Fidelity Conservative Income bond fund.
How to explain the equationThe portfolio is worth $10,000 in total:
$100x + $10y = $10,000
We can now use elimination to find x:
$1100x + $110y = $110,000 -($100x + $10y = $10,000)
$1000x = $100,000 x = 100
As a result, we own 100 shares of JP Morgan Emerging Markets Bond Fund. To solve for y, we can plug this number back into the original equation:
$100x + $10y = $10,000
$100(100) + $10y = $10,000
$10y = $9,000 y = 900
As a result, we have 900 shares of Fidelity Conservative Income bond fund
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witch values are solutions to the inequlity [tex]x^{2} \leq 8[/tex]
Answer:
x ≤ [tex]\sqrt[2]{2}[/tex]
Step-by-step explanation:
x² ≤ 8
[tex]\sqrt{x^{2} }[/tex] ≤ [tex]\sqrt{8}[/tex]
x ≤ [tex]\sqrt[2]{2}[/tex]
The large solid below is made from small cubes. Each has a side length of 1/5. Answer the questions below. Write your answers in simplest form. (c) What is the volume of the large solid?
The volume of the large solid is equal to 8/25 cm³.
How to calculate the volume of a cube?In Mathematics, the volume of a cube can be calculated by using the following formula:
V = m³
Where:
V represents the volume of a cube.m is the side lengths of a cube.By substituting the given points into the formula for the volume of a cube, we have the following;
Volume of cube, V = m³
Volume of cube, V = (1/5)³
Volume of cube, V = 1/125 cm³.
For the volume of the large solid, we have:
Volume of large solid = 5 × 2 × 4 × 1/125
Volume of large solid = 8/25 cm³.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Canada has a growth rate of
approximately 1%. Calculate the
doubling time.
Doubling time = 70/growth rate
A. 0.014 years
B. 100 years
C. 35 years
D. 70 years
Please help me 10 extra points
The probability of getting hearts or face cards is 25/52.
We know that, Probability of an event = Number of favorable outcomes/Total number of outcomes.
Total number of outcomes = 52 cards
Number of hearts = 13
Number of face cards = 12
Probability getting hearts = 13/52
Probability getting face cards = 12/52
P(Hearts or Face card) = 13/52 + 12/52
= 25/52
Therefore, the probability of getting hearts or face cards is 25/52.
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Please help solve this for me
Answer:
i believe the answer would be option D
Step-by-step explanation:
A building calls for 1 1/2 foot boards. How many can be cut from a 12 foot long board
Answer:
To find out how many 1 1/2 foot boards can be cut from a 12 foot long board, we need to divide the length of the board by the length of each board.
First, we need to convert 1 1/2 feet to an improper fraction.
1 1/2 = (2 x 1 + 1) / 2 = 3/2
So, each board is 3/2 feet long.
Next, we divide the length of the 12 foot long board by the length of each board:
12 / (3/2) = 12 x 2/3 = 24/3 = 8
Therefore, 8 boards of length 1 1/2 feet can be cut from a 12 foot long board.
Step-by-step explanation:
HELP ME PLEASE PICTURE INCLUDED
Answer:
0.67 million miles per day
Step-by-step explanation:
You want the average rate of change of the function d(t) = ∛(6t²) on the interval [4, 8], where d is in millions of miles, and t is in days.
Average rate of changeThe average rate of change of the function on the interval [a, b] is given by ...
rate of change = (d(b) -d(a))/(b -a)
As the table in the attachment shows, this is approximately ...
rate of change = (7.268 -4.579)/(8 -4) ≈ 0.67
The average rate of change on the interval 4 ≤ t ≤ 8 is about 0.67 million miles per day.
__
Additional comment
Mercury has an orbit of about 88 days at a distance of roughly 36 million miles from the Sun. Already at that distance, the General Theory of Relativity comes into play, making predictions from Newtonian physics somewhat problematic. It is unlikely this formula has any relation to reality for t much less than 200.
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Of the people who fished at Clearwater Park today, 72 had a fishing license, and 8 did not. Of the people who fished at Mountain View Park today, 63 had a license, and 27 did not. (No one fished at both parks.)
I NEED HELP RIGHT AWAY WITH 3 4 5 and 6
1. AB is a tangent, the triangle is a right triangle
2. AB is not a tangent, the triangle is not a right triangle and hence not a Pythagorean triple
3. arc RS = 100 degrees
4. arc ST = 80 degrees
5. arc RTS = 260 degrees
6. arc RST = 180degrees
7. x = 3
8. x = 7
How to determine whether AB is a tangentA tangent will obey Pythagorean triple hence we have that
AB^2 = AC^2 + BC^2
1. AB^2 = 24^2 + 10^2 = 676
AB = sqrt (676) = 26. hence AB is a tangent
2. AB^2 = 8^2 + 11^2 = 185
AB = sqrt (185) = 13.6. hence AB is not a tangent
Length of arc
3. arc RS = 100 degrees (central angle equals intercepted arc)
4. arc ST = 180 - arc RS = 180 - 100 = 80 degrees
5. arc RTS = 180 + arc ST = 180 + 80 = 260 degrees
6. arc RST = 180degrees (semicircle)
Value of x
7. x + 8 = 5x - 4
8 + 4 = 5x - x
12 = 4x
x = 3
8. 4x + 5 = 6x - 9
4x - 6x = -9 - 5
-2x = -14
x = 7
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find the awnser to this question as fast as you can and make sure it’s right
The area of the polygon to the nearest tenth is 80.7 in²
What is area of a polygon?A polygon any closed curve consisting of a set of line segments (sides) connected such that no two segments cross. Examples of polygon include ; triangle, quadrilateral, pentagon e.t.c
The area of a polygon is expressed as;
A = 1/2nsa
where n is the number of side
a is the apothem
s is the side length
Side length = apothem × 2tan(180/n)
n = 12
s = 5 × 2tan(180/12)
s = 5 × 2tan15
s = 2.679
Area = 1/2 × 12 × 5 ×2.679
= 80.7 in²(nearest tenth)
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Solve the trigonometric equation for all values 0 <= x < 2pi
sin^2 x -1 = 0
The solution to a trignometric equation sin²x - 1 = 0 is x = { π/2, 3π/2}
Consider a trignometric equation,
sin²x - 1 = 0
We need to solve this trigonometric equation for all values of angle x such that 0≤ x < 2π
Consider equation,
sin²x - 1 = 0
sin²x = 1
Takin square root,
sin(x) = ±1
when sin(x) = 1, then x = π/2
and when sin(x) = -1 then x = 3π/2
Therefore, required values of angle x = { π/2, 3π/2}
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Change 11/5 from an improper fraction to a mixed number
Solution: 11/5 as a mixed number is 2 1/5.
help help help help help help
The coordinates of point B are given as follows:
B(-7, 6).
What is the midpoint concept?The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.
For this problem, we have that M(-6,2) is the midpoint of A(-5,-2) and B(x,y).
Then the x-coordinate of point B is obtained as follows:
(x - 5)/2 = -6
x - 5 = -12
x = -7.
The y-coordinate of point B is obtained as follows:
(y - 2)/2 = 2
y - 2 = 4
y = 6.
Hence the coordinates of B are given as follows:
B(-7, 6).
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A figure has a area of 25 units^2. what will the new area be after a dilation with a scale factor of 4 ?
The new area of the figure after the dilation with a scale factor of 4 will be 400 units²
We have,
When a figure is dilated by a scale factor of k, its area is multiplied by k².
So,
If the original area of the figure = 25 units²
Dilated by a scale factor = 4
The new area.
= (4²)(25 units²)
= 16(25 units²)
= 400 units²
Therefore,
The new area of the figure after the dilation with a scale factor of 4 will be 400 units².
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Probability Skill Check
DOOR Numbers
1
2
3
4
5
Coloured Blue, Red, Yellow and Green
What is the probability you will sit in a yellow seat? Give your answer as a fraction.
1/4
But what is the probability you will enter using an odd numbered door and sit in a green seat? Give your answer as a fraction.