Answer: 18480
i used a calculator :)
What is the distance from the point (15,-21) to the line for which f(4)=-8 and f(8)=-18
The distance from the point (15,-21) to the line is 5.39 units.
What is point slope form?The equation of a line in point-slope form is:
y - y1 = m(x - x1) (x - x1)
where (x1, y1) is a point on the line and m is the slope of the line. When we are unsure of the y-intercept but are aware of the line's slope and a point on the line, we can utilise this form of the equation.
To calculate the equation of a line using the point-slope method, we must first determine the slope of the line using the following formula:
m = (y2 - y1)/(x2 - x1) (x2 - x1)
where the two points on the line are (x1, y1) and (x2, y2). We may enter the slope, along with one of the line's points, into the point-slope form to obtain the equation of the line.
Given that, the line has the following values f(4)=-8 and f(8)=-18.
The coordinates of the line are (4, -8) and (8, -18)
Thus, the slope of the line is:
m = y2 - y1/ x2 - x1
m = -18 + 8 / 8 - 4
m = -10/4 = -5/2
Now the slope intercept form is given as:
y - y1 = m (x - x1)
Substitute the values:
y + 8 = -5/2(x - 4)
2y + 16 = -5x + 20
2y = -5x + 20 - 16
2y = -5x + 4
The distance from the line to point is given as:
Distance = |ax + by + c| / √(a² + b²)
Substituting the values:
Distance = |-5(15) + -2(-21) + 4| √(-5² + -2²)
Distance = |-29|/ 5.38
Distance = 5.39
Hence, the distance from the point (15,-21) to the line is 5.39 units.
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150,000 bonds with a coupon rate of 11 percent and a current price quote of 108; the bonds have 20 years to maturity. 320,000 zero coupon bonds with a price quote of 16 and 30 years until maturity. Both bonds have a par value of $1,000 and semiannual coupons
The total value of both bonds is $704,367,500.
Coupon payment = [tex]\frac{Coupon rate * Par value}{2}[/tex]
Coupon payment = [tex]\frac{11 * $1,000}{2}[/tex]
Coupon payment = $55
PV = [tex]55 * [1 - (1 + 0.04)^{^-40} ] / 0.04 + $1,000 / (1 + 0.04)^40[/tex]
[tex]PV = $1,026.45[/tex]
[tex]Total value = PV * Number of bonds * Par value\\Total value = $1,026.45 * 150,000 * $1,000\\Total value = $153,967,500[/tex]
[tex]PV = \frac{Price}{(1 + r)^n}[/tex]
[tex]PV = \frac{16}{(1 +0.03)^60}\\PV = $1.72[/tex]
[tex]Total value = PV * Number of bonds * Par value\\Total value = $1.72 * 320,000 * $1,000\\Total value = $550,400,000[/tex]
Therefore, the total value of both bonds is:
[tex]Total value = Value of coupon bonds + Value of zero coupon bonds\\Total value = $153,967,500 + $550,400,000\\Total value = $704,367,500[/tex]
A coupon rate is the annual interest rate paid by a bond or other fixed-income security to its bondholders or investors. It is typically expressed as a percentage of the bond's face value, also known as its par value. For example, if a bond has a face value of $1,000 and a coupon rate of 5%, the bond will pay $50 in interest each year to its bondholders. The coupon payments are usually made semi-annually or annually, depending on the terms of the bond.
The coupon rate is set when the bond is issued and remains fixed throughout the life of the bond unless the bond issuer chooses to call the bond or the bond defaults. Coupon rates are determined by a variety of factors, including market conditions, the creditworthiness of the issuer, and the length of the bond's maturity.
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Complete Question: -
The IPO Investment Bank has the following financing outstanding,
Debt: 150,000 bonds with a coupon rate of 11 percent and a current price quote of 108; the bonds have 20 years to maturity. 320,000 zero coupon bonds with a price quote of 16 and 30 years until maturity. Both bonds have a par value of $1,000 and semiannual coupons.
Preferred stock: 240,000 shares of 9 percent preferred stock with a current price of $67, and a par value of $100.
Common stock: 3,500,000 shares of common stock; the current price is $53, and the beta of the stock is.9.
Market: The corporate tax rate is 24 percent, the market risk premium is 8 percent, and the risk-free rate is 5 percent.
What is the WACC for the company? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Define a sample space and count the number of sample points in the sample space for each of the following experiments. a. Select at random a set of 5 questions from a set of 15 questions. b. Form by random selection a committee of 5 from a membership of 20.
There are 15C5 or 3003 possible combinations in the sample space.There are 20C5 or 15504 possible combinations in the sample space.
What is number?A number is a mathematical object used to count, measure, and label. Numbers can be represented in many different forms such as natural numbers, integers, real numbers, and complex numbers. They can also be classified as scalar numbers (which have a magnitude or value only) or vector numbers (which have both magnitude and direction). Numbers can be used to represent many different things, including measurements, distances, money, and quantities.
A) Sample Space: The sample space for selecting a set of 5 questions from a set of 15 questions is the set of all possible combinations of 5 questions from 15 questions. There are 15C5 or 3003 possible combinations in the sample space.
B) Sample Space: The sample space for forming a committee of 5 from a membership of 20 is the set of all possible committees that can be formed from 20 members. There are 20C5 or 15504 possible combinations in the sample space.
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The original price of the pearl was 52 euros.
What is price?Price is the monetary value of a product, service, or asset. It is one of the most important factors in a customer's decision to purchase something. Price also determines the amount of profit a business makes on a particular product or service. Price is a key component of the marketing mix, and it can be used to create a sense of value for customers. Price can also be used to differentiate a product from competitors, as well as to indicate quality levels and to create loyalty.
a) One of the cheapest pearls costs 41 euros.
b) This necklace costs 2153 euros, which is the sum of all the pearls.
c) The pearl with the crack originally cost 52 euros. The price was reduced by 1/5, which is 10.4 euros, making the price of the pearl 41.6 euros. The decrease in price of the necklace was 6.5 euros, which means the reduction in price of the pearl was 6.5 euros. Therefore, the original price of the pearl was 52 euros.
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stive efforts in
Eamples (finding slope in tables and graphs)
termine the slope of each linear equation. You may want to use the slope formula.
X O
1
2
3
y
S5
7
9
11
b)
566
X
-7
-6
-5
-4
y
10
7
4
1
c)
X
-2
0
2
4
y
I
3
5
can't
7
9
The slope of a linear equation is an important skill to have, as it can be used to identify the rate of change of the equation, and can be used to predict future values of the equation.
What is equation?An equation is an expression that states the equality of two things. It typically consists of an equal sign (=) and two expressions on either side of the equal sign that represent the same thing. Equations are used to describe relationships between different variables and can be used to solve mathematical problems. They can also be used to show the relationships between different quantities in physics and chemistry.
a)The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 6, and the run is 2, so the slope is 3.
b) The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 3, and the run is -7, so the slope is -3/7.
c) The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 4, and the run is 6, so the slope is 2/3.
Finding slope in tables and graphs is a common mathematical skill that is used to identify the rate of change of a linear equation. This is determined by finding the change in the dependent variable (the y-axis) divided by the change in the independent variable (the x-axis). This is what is referred to as the slope of the equation. To find the slope in tables and graphs, you must look at the differences between the points on the x-axis and y-axis, and divide the change in the y-axis by the change in the x-axis. This will give you the slope of the equation. Finding the slope of a linear equation is an important skill to have, as it can be used to identify the rate of change of the equation, and can be used to predict future values of the equation.
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What is the answer to this math problem? I can’t seem to figure it out.
Answer:
X
Step-by-step explanation:
We first must check the total amount of breakfast. Y happens to have 130 instead of 125. Now, we see that W and Z have a majority on strawberries with oatmeal, which is not what we are looking for. The last answer we have is X, where there is a majority of oatmeal + blueberries and there is a total of 125 breakfasts.
Hope this helps!
when the expression -3x^5+6x^2-9x^3-x is written with terms in descending order (from highest to lowest), which list represents the coefficients of the term?
a. 6, -9, -3, -1
b. -3, 6, -9, -1
c. 1, 6, -9, -3
d. -3, -9, 6, -1
PLS ANSWER THIS ASAP
In two similar triangles, the ratio of the lengths of a pair of corresponding sides is 7:8. If the perimeter of the larger triangle is 32, find the perimeter of the smaller triangle.
The perimeter of the smaller triangle would be = 28.1
How to calculate the perimeter of the smaller triangle?A triangle can be defined as a three sided polygon that has a total internal angle of 180°.
To calculate the perimeter of the triangle is to find out the scale factor that exists between the two triangles.
The formula for scale factor = original object/new object
Scale factor= 8/7 = 1.14
The perimeter of the smaller triangle = 32/1.14
= 28.1.
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Juanita’s Social Security full monthly retirement benefit is $2,128. She started collecting Social Security at age 65. Her benefit is reduced since she started collecting before age 67. Using the reduction percents from Example 1, find her approximate monthly Social Security benefit to the nearest dollar.EXAMPLE 1Marissa from Example 2. What will her monthly benefit be, since she did not wait until age 67 to receive full retirement benefits?SOLUTION Age 67 is considered to be full retirement age if you were born in 1945. If you start collecting Social Security before age 67, your full retirement benefit is reduced, according to the following schedule.• If you start at collecting benefits at 62, the reduction is about 30%.• If you start at collecting benefits at 63, the reduction is about 25%.• If you start at collecting benefits at 64, the reduction is about 20%.• If you start at collecting benefits at 65, the reduction is about 13.3%.• If you start at collecting benefits at 66, the reduction is about 6.7%.Marissa’s full retirement benefit was $1,130.40. Since she retired at age 65, the benefit will be reduced about 13.3%.Find 13.3% of $1,130.40, and round to the nearest cent.0.133 x 1,130.40Subtract to find the benefit Marissa would receive.1,130.40 x 150.34Marissa’s benefit would be about $980.06.EXAMPLE 2Marissa reached age 62 in 2007. She did not retire until years later. Over her life, she earned an average of $2,300 per month after her earnings were adjusted for inflation. What is her Social Security full retirement benefit?
Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.
What is social security benefits retirement age?The age at which a person is qualified to receive their full retirement payment under Social Security is determined by their lifetime earnings history. The complete retirement age for anybody born in 1960 or later is 67. The complete retirement age is steadily lowered for people born before 1960, and is 65 for those born in 1937 or before.
Given that, Juanita started collecting benefits at age 65.
Thus, her benefits reduced by 13.3%.
0.133 x $2,128 = $283.10
Deducting the reduction amount from the total:
$2,128 - $283.10 = $1,844.90
Hence, Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.
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find bases for the null spaces of the matrices given in exercises 9 and 10. refer to the remarks that follow example 3 in section 4.2.
In summary, to find the null spaces of the matrices given in exercises 9 and 10, use the Gauss-Jordan elimination method and refer to the Remarks that follow example 3 in section 4.2 of the text. This will give the dimension of the null space and the number of free variables.
In exercises 9 and 10, the null space of the given matrices can be found by solving the homogeneous linear system of equations. In order to do this, use the Gauss-Jordan elimination method. Refer to example 3 in section 4.2 of the text for a detailed explanation. Afterwards, use the Remarks that follow the example to determine the dimension of the null space and the number of free variables.
The null space of a matrix is the set of all vectors that produce a zero vector when the matrix is multiplied by the vector. Therefore, to find the null space of a matrix, the homogeneous linear system of equations needs to be solved. The Gauss-Jordan elimination method involves adding multiples of one row to another to get a row with all zeroes. After this is done for all the rows, the equations can be solved for the free variables. The number of free variables will determine the dimension of the null space. Refer to example 3 in section 4.2 of the text for more details.
The Remarks that follow the example are important when determining the dimension of the null space and the number of free variables. In the Remarks, it is mentioned that the number of free variables is equal to the number of columns with a zero row. Therefore, after using the Gauss-Jordan elimination method to get the row with all zeroes, the number of columns with a zero row can be counted. This will give the dimension of the null space and the number of free variables.
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Suppose a single trial experiment results in one of three mutually exclusive events, A, B, or C. It is known that P(A) = 0.3, P(B) = 0.6, and P(C) = 0.1. Find the probability P(ANC) Answer: Question 2 Not yet answered Points out of 2.00 P Flag question Refer to the previous question. Find the probability P(AUB). Answer:
intersection of A and B events, P(A ∩ B) is 0. So, P(A U B) = P(A) + P(B) = 0.3 + 0.6 = 0.9Hence, P(AUB) = 0.9.
Probability of P(ANC)We know that events A, B and C are mutually exclusive.
Therefore, if A, B, and C are mutually exclusive events, then P(A U B U C) = P(A) + P(B) + P(C). Given, P(A) = 0.3,P(B) = 0.6,P(C) = 0.1
Therefore, P(A U B U C) = P(A) + P(B) + P(C) = 0.3 + 0.6 + 0.1 = 1Now, P(ANC) = 1 - P(A U B U C) = 1 - 1 = 0
Probability the intersection of A and B events, P(A ∩ B) is 0. So, P(A U B) = P(A) + P(B) = 0.3 + 0.6 = 0.9
Hence, P(AUB) = 0.9.ility of P(AUB)We know that events A, B and C are mutually exclusive.
Therefore, if A, B, and C are mutually exclusive events, then P(A U B U C) = P(A) + P(B) + P(C)
Now, we need to find P(AUB). If two events A and B are not mutually exclusive events, then the probability of their union P(A U B) can be found as follows; [tex]P(A U B) = P(A) + P(B) - P(A ∩ B)[/tex]We know that events A, B and C are mutually exclusive.
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[LAST QUESTION, OFFERING BRAINLIEST]
??? PTS
Answer:
Step-by-step explanation:
Let h be the height of the trapezoid.
The area of a trapezoid is given by the formula:
Area = (1/2) × (sum of parallel sides) × (height)
In this case, we know that the area is 21 cm², one base length is 5 cm, and the other base length is 9 cm. So we can write:
21 = (1/2) × (5 + 9) × h
Simplifying this equation, we get:
21 = 7h
Dividing both sides by 7, we get:
h = 3
Therefore, the height of the trapezoid is 3 cm.
Answer:
Height of Trapezium is 3 cm.Step-by-step explanation:
Area of Trapezium is 21 cm². Parallel sides are 5 cm and 9 cm .
Shorter parallel side is 5 cm and the Longer Side is 9 cm.
As we know that formula of area of Trapezium is,
Area of Trapezium = ½ (a + b) hWhere,
a and b are Parallel sides and h is the height.On substituting the values of area and the two parallel sides in the above formula we will get the required Height.
Substituting the values,
21 = ½ (5 + 9)h
21 = ½ × 14 × h
21 = 7 × h
h = 21/7
h = 3 cm
Therefore, Height of the Trapezium will be 3 cm respectively.
Put the steps in correct order to prove that if n is a perfect square, then n + 2 is not a perfect square.1).Lets assume m ≥ 1.2) If m = 0, then n + 2 = 2, which is not a perfect square. The smallest perfect square greater than n is (m + 1)^2.3) Hence, n + 2 is not a perfect square4) Expand (m + 1)^2 to obtain (m + 1)^2 = m2 + 2m + 1 = n + 2m + 1 > n + 2 + 1 > n + 2.5) .Assume n = m2, for some nonnegative integer m
The following is the correct sequence of steps to prove that if n is a perfect square, then n + 2 is not a perfect square:
Step 1: Assume n = m², for some non-negative integer m.
Step 2: If m = 0, then n + 2 = 2, which is not a perfect square. The smallest perfect square greater than n is (m + 1)².
Step 3: Expand (m + 1)² to obtain (m + 1)² = m² + 2m + 1 = n + 2m + 1 > n + 2 + 1 > n + 2.
Step 4: Let's assume m ≥ 1.
Step 5: Hence, n + 2 is not a perfect square.
The first step in the sequence involves making an assumption to start the proof. The second step entails the derivation of the smallest perfect square greater than n. In the third step, we expand the (m + 1)² expression to get n + 2m + 1. The fourth step is an important one, as it shows that m must be greater than or equal to 1.
In the final step, we conclude that n + 2 is not a perfect square.
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Proving Triangle Similarity
The proof is completed using two column proof as follows
Statement Reason
QT ⊥ PT Given
∠ QRP ≅ ∠ SRT = 90 definition of perpendicularity
∠ QPR ≅ ∠ STR Given
Δ PQR is similar to Δ TSR AA similarity theorem
What is AA similarity theorem?The AA similarity theorem, also known as the Angle-Angle Similarity Theorem, states that if two triangles have two corresponding angles that are congruent, then the triangles are similar.
In the given triangle, the two angles given to be equal are
∠ QRP ≅ ∠ SRT = 90 and ∠ QPR ≅ ∠ STRHence the triangles are similar
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Answer:
:)
Hopefully this helps you guys :)
good luck :D
Tamarisk company began operations on january 2, 2019. It employs 9 individuals who work 8-hour days and are paid hourly. Each employee earns 9 paid vacation days and 7 paid sick days annually. Vacation days may be taken after january 15 of the year following the year in which they are earned. Sick days may be taken as soon as they are earned; unused sick days accumulate. Additional information is as follows. Actual hourly wage rate vacation days used by each employee sick days used by each employee 2019 2020 2019 2020 2019 2020 $6 $7 0 8 5 6 tamarisk company has chosen to accrue the cost of compensated absences at rates of pay in effect during the period when earned and to accrue sick pay when earned
The total cost of compensated absences for Tamarisk Company for the years 2019 and 2020 was $348 + $1,399 = $1,747.
To calculate the cost of compensated absences for Tamarisk Company, we need to calculate the number of vacation days and sick days earned by the employees in 2019 and 2020, and then calculate the cost of the days earned but not taken.
Each employee earns 9 vacation days per year. As they can be taken after January 15th of the year following the year in which they are earned, the vacation days earned by the employees in 2019 can be taken in 2020. Therefore, in 2019, no vacation days were taken by any employee.
In 2020, the employees took a total of 8 vacation days. As there are 9 employees, the total vacation days taken in 2020 were 9 x 8 = 72.
Sick Days:
Each employee earns 7 sick days per year, and unused sick days accumulate. In 2019, the employees used a total of 5 sick days. Therefore, the unused sick days at the end of 2019 were 9 x 7 - 5 = 58.
In 2020, the employees used a total of 6 sick days, and the unused sick days at the end of 2020 were 58 + 9 x 7 - 6 = 109.
To find the cost of compensated absences. The unused sick days and vacation days must be multiplied to get the hourly wage rate in effect in a year.
In 2019, the cost of compensated absences was 58 x $6 = $348.
In 2020, the cost of compensated absences was (72 + 109) x $7 = $1,399.
Therefore, the total cost of compensated absences for Tamarisk Company for the years 2019 and 2020 was $348 + $1,399 = $1,747.
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HELP. I'm really struggling on this one. My calculus teacher claimed this to be the easiest math problem ever but I still can't understand. Is anyone smart enough to figure this one out. Whats 1 + 1?
Answer:
The answer to 1 + 1 is 2.
Very complicated problem, please mark brainliest!
Answer:
1+1 = 2
Or, 1=2-1
1=1
we know value of one is one
so,
1+1=11
Find m ∠ JKL using the picture
The value of m∠JKL is 34°
How to find the value of m∠JKL?An angle formed by a tangent and a secant intersecting outside a circle is equal to one-half the difference of the measures of the intercepted arcs.
Based on the theorem above, we can say:
m∠JKL = 1/2 * (159 - 91)
m∠JKL = 1/2 * 68
m∠JKL = 34°
Therefore, the value of m∠JKL in the circle is 34°.
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a 12 cm tall and radius of 10 cm cylinder is filled with 10 cm of water. find a) the rotational speed at which the water just touches the bottom of the cylinder and b) the resulting pressure at points a and b.
a 12 cm tall and radius of 10 cm cylinder is filled with 10 cm of water.
a) Rotational speed at which the water just touches the bottom of the cylinder:
We will use the formula for centripetal force for a liquid with the volume of a cylinder to obtain the rotational speed at which the water just touches the bottom of the cylinder.
The formula for centripetal force for a liquid with the volume of a cylinder is as follows:
F = (ρr²πh)ω²WhereF:
Centripetal forceρ: Densityr: Radiush : Heightω: Rotational speed Substituting the given values,
we get: F = (1000 kg/m³ × (0.1m)² × π × 0.12m)ω²F
= 377 Nω
= √(F/m)ω
= √(377 N/ 10 kg)ω
= √37.7ω = 6.14 rad/sb)
Pressure at points A and B:
We will use the formula for hydrostatic pressure for a liquid to calculate the pressure at points A and B. The formula for hydrostatic pressure for a liquid is as follows:
P = ρgh
Where,
P: Pressureρ: Densityg: Acceleration due to gravity: DepthSubstituting the given values for point A,
we get P = 1000 kg/m³ × 9.8 m/s² × 0.1 mP
= 980 Pa
Substituting the given values for point B,
we get P = 1000 kg/m³ × 9.8 m/s² × 0.22 mP
= 2156 Pa
The resulting pressure at point A is 980 Pa and the resulting pressure at point B is 2156 Pa.
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what is the angle of x when the other is 51
Answer:
I'm sorry, your question is not clear. Please provide more information or context so I can better understand what you are asking.
Step-by-step explanation:
which of the following is a characteristic of a reliable scientific poll? choose 1 answer: choose 1 answer: (choice a) small sampling error a small sampling error (choice b) required names for all respondents b required names for all respondents (choice c) entire population surveyed c entire population surveyed (choice d) open-ended questions d open-ended questions
The characteristic of a reliable scientific poll is small sampling error. The small sampling error is a characteristic of a reliable scientific poll.
What is a scientific poll?Scientific polls are surveys that gather and evaluate people's opinions or responses to questions. These surveys are done in a scientific way, implying that pollsters use scientifically proven techniques to gather responses and analyze data.A reliable scientific poll must have a small sampling error. A sampling error is the deviation of the sample mean from the population mean due to random error. The smaller the sample size, the more likely it is that the results will be imprecise. As a result, it's essential to conduct a reliable scientific poll with a sample size that is representative of the population as a whole.The option for the correct answer to this question is; (choice a) small sampling error.
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Marcus bought a booklet of tickets to use at the amusement park. He used 25% of the tickets on rides, 1 2 of the tickets on video games, and the rest of the tickets in the batting cage. Marcus says he used 23% of the tickets in the batting cage. Do you agree? Complete the explanation.
Answer: Do not agree.
Step-by-step explanation:
To determine if we agree with Marcus, we need to verify if the percentages he used on rides, video games, and batting cage add up to 100%.
Marcus used 25% of the tickets on rides and 1/2 on video games. So, the total percentage of tickets he used is:
25% + 1/2 × 100% = 25% + 50% = 75%
This means that Marcus should have used 25% of the tickets in the batting cage. If he said he used 23% of the tickets in the batting cage, then we do not agree with him.
use the formula for the sum of a geometric series to find the sum or state that the series diverges. (use symbolic notation and fractions where needed. enter dne if the series diverges.) (4^3 / 5^3) + (4^4 / 5^4) + (4^5 / 5^5) = ________--
The sum of the geometric series is 3904/3125.
By using the formula for the sum of a geometric series, we'll have to identify the first term, the common ratio, and the number of terms.
Let's identify the first term, the common ratio, and the number of terms in the given series as shown below;
The first term, a = 4³/5³
Common ratio, r = 4/5
The number of terms, n = 3
We have identified the values of a, r, and n, we can now substitute them into the formula for the sum of a geometric series, shown below;
S_n = a(1 - rⁿ) / (1 - r)
S₃ = {(4³/5³) [1 - (4/5)³]} / [1 - (4/5)]
S₃ = {(64/125) [1 - (64/125)]} / [1/5]
S₃ = (64/125) [(125-64)/125] [5/1]
S₃ = (64/125) (61/125) (5)
Therefore, S₃ = 3904/3125.
Thus, the sum of the geometric series (4³/5³) + (4⁴/5⁴) + (4⁵/5⁵) is equal to 3904/3125.
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math question please help
Answer:
Step-by-step explanation:
only the 1st and 5th statements are true
You want to measure the height of an antenna on the top of a 125-foot building. From a point in front of the building, you measure the angle of elevation to the top of the building to be 68° and the angle of elevation to the top of the antenna to be 71°. How tall is the antenna, to the nearest tenth of a foot?
The antenna which is having an angle of elevation 71° from the front of the it is on is 19.67 feet tall to the nearest tenth of foot.
What is an angle of elevationThe angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.
To get the height of the antenna, we subtract the height of the building from the height from the bottom of the building to the top of the antenna.
we shall represent the distance from the point of observation to the building with x and the height from the bottom of the building to the top of the antenna with y. so that;
tan 68° = 125/x {opposite/adjacent}
x = 125/ tan 68° {cross multiplication}
x = 50.5033
tan 71° = y/50.5033
y = 50.5033 × tan 71°
y = 144.6722
height of the antenna = 144.6722 - 125
height of the antenna = 19.6722
Therefore, the antenna which is having an angle of elevation 71° from the front of the it is on is 19.67 feet tall to the nearest tenth of foot.
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Let all of the numbers given below be correctly rounded to the number of digits shown. For each calculation, determine the smallest interval in which the result, using true instead of rounded values, must lie. (a) 1.1062+0.947 (b) 23.46 - 12.753 (c) (2.747) (6.83) (d) 8.473/0.064
An interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.
For each calculation, the smallest interval in which the result, using true instead of rounded values, must lie is as follows:
(a) 1.1062+0.947 = 2.0532 ≤ true result ≤ 2.053
(b) 23.46 - 12.753 = 10.707 ≤ true result ≤ 10.708
(c) (2.747) (6.83) = 18.6181 ≤ true result ≤ 18.6182
(d) 8.473/0.064 = 132.3906 ≤ true result ≤ 132.3907
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In ΔJKL, the measure of ∠L=90°, JK = 7. 3 feet, and KL = 4. 7 feet. Find the measure of ∠J to the nearest tenth of a degree
The measure of ∠J in ΔJKL is approximately 57.5 degrees.
The measure of ∠J in ΔJKL can be found using the trigonometric function tangent, which is defined as the ratio of the opposite side to the adjacent side.
The straight line that "just touches" the plane curve at a given point is called the tangent line in geometry. It was defined by Leibniz as the line that passes through two infinitely close points on the curve.
tan(∠J) = JK/KL
tan(∠J) = 7.3/4.7
∠J = arctan(7.3/4.7)
∠J = 57.5 degrees (rounded to the nearest tenth of a degree)
Therefore, the measure of ∠J in ΔJKL is approximately 57.5 degrees.
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a rectangular swimming pool 50 ft long, 30 ft wide, and 8 ft deep is filled with water to a depth of 6 ft. use an integral to find the work required to pump all the water out over the top. (take as the density of water lb/ft. )
The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.
We have,
To find the work required to pump all the water out of the rectangular swimming pool, we can use the concept of work as the force multiplied by the distance.
First, let's calculate the weight of the water in the pool.
The weight of an object is given by the formula:
Weight = mass x gravitational acceleration
Since the density of water is given as 1 lb/ft³, we need to find the volume of water in the pool.
The volume of the pool is given by the formula:
Volume = length x width x depth
Volume = 50 ft x 30 ft x 6 ft = 9000 ft³
Now, let's calculate the weight of the water:
Weight = density x volume x gravitational acceleration
Weight = 1 lb/ft³ x 9000 ft³ x 32.2 ft/s² ≈ 290,400 lb
To pump all the water out over the top, we need to raise it to the height of the pool, which is 8 ft.
The work required to pump the water out is given by the formula:
Work = weight x height
Work = 290,400 lb x 8 ft = 2,323,200 ft-lb
Therefore,
The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.
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4. What is the solution to 2 + 3(2a + 1) = 3(a + 2)?
Answer:
a=1/3
Step-by-step explanation:
First, expand the brackets by doing multiplication:
2+6a+3=3a+6
Then, move the unknown to the left and the numbers to the right:
3a=6-5
3a=1
a=1/3
The solution to the given equation is -1.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The given equation is 2+3(2a+1)=3(a+2)
2+6a+3=3a+2
6a+5=3a+2
6a-3a=2-5
3a=-3
a=-1
Therefore, the solution to the given equation is -1.
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In each expression below the numbers under the root sign all add to the same number, 10. Determine which expression is greatest. How?
a) √7+ √3
b) √6+ √4
c) √8+ √2
Answer:
Step-by-step explanation:
I think a calculator is the only way to solve this question:
[tex]\sqrt{7} +\sqrt{3} = 2.96\\\\\sqrt{6} +\sqrt{4} = 2.54\\\\\sqrt{8} +\sqrt{2} =3.07[/tex]
So (c) is the greatest.
Problem 1 (3 pts). The nearest neighbor method is used with the following labeled training data in a two class, two feature problem. Show clearly the decision boundaries obtained. Indicate all break points and slopes correctly Class1={(0,0)^T,(0,1)^T}. Class2={(1,0)^T,(0,0.5)^T}
Problem 1 (3 pts). The nearest neighbor method is used with the following labeled training data in a two class, two feature problem. Show clearly the decision boundaries obtained. Indicate all break points and slopes correctly Class1={(0,0)^T,(0,1)^T}. Class2={(1,0)^T,(0,0.5)^T}.
The decision boundary is the line that separates the two classes. When it comes to the nearest neighbour method, the boundary of a class is determined by the closest data point in the other class.What is the nearest neighbour method?The nearest neighbour method (NNM) is a type of lazy learning method in which the data is stored and the computation is deferred until the classification phase.
The goal of the nearest neighbor technique is to use the pattern of the closest data point to classify a new sample. It's also one of the simplest non-parametric classification methods, and it's based on the assumption that the feature spaces used by each class are continuous regions.For Class 1, there are two labeled training data points: (0, 0)T and (0, 1)T. Similarly, for Class 2, there are two labeled training data points: (1, 0)T and (0, 0.5)T.
To generate decision boundaries, follow the steps below:Step 1: Plot the given labeled training data. They are shown in the figure below. Step 2: Label the data points according to their class: Class 1 and Class 2.Step 3: Now, we need to find the nearest neighbors. Find the nearest neighbor for each of the labeled training data points from the opposite class. The distances are calculated as follows:For the Class 1 data points, the nearest neighbor is Class 2's (1, 0)T data point.
For the Class 2 data points, the nearest neighbour is Class 1's (0, 1)T data point.Step 4: Connect the nearest neighbour's labeled training data points with a line. These are the decision boundaries. The red line represents the decision boundary between Class 1 and Class 2. The green line represents the decision boundary between Class 2 and Class 1. The slopes of the decision boundaries are -1 for the red line and 1 for the green line. These slopes are the result of the negative reciprocal of the nearest neighbour's slope. The break point for the red line is 0.5, while the break point for the green line is 0. A break point is the point at which the decision boundary intersects the y-axis.
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A+9 as a verbal expression
Answer:
"9 more than A" is a verbal expression.
