david+borrowed+$2,500+from+his+local+bank.+the+yearly+interest+rate+is+8%.+if+david+pays+the+full+principle+and+interest+in+the+first+year+of+the+loan,+how+much+money+will+he+pay+to+the+bank?
Answers
To calculate the total amount David will pay to the bank, we need to consider both the principal amount borrowed and the interest accrued over the first year.
The interest can be calculated using the formula:
Interest = Principal * Rate
Where the Principal is $2,500 and the Rate is 8% expressed as a decimal (0.08).
Interest = $2,500 * 0.08 = $200
Therefore, the interest accrued over the first year is $200.
To find the total amount David will pay, we need to add the principal and the interest:
Total payment = Principal + Interest = $2,500 + $200 = $2,700
David will pay a total of $2,700 to the bank if he pays the full principal and interest in the first year of the loan.
David will pay a total of $2,700 to the bank if he pays the full principal and interest in the first year of the loan.
To calculate how much money David will pay to the bank, we need to consider both the principal amount and the interest charged on the loan.
The principal amount borrowed by David is $2,500.
The yearly interest rate is 8%, which means that David will have to pay 8% of the principal amount as interest.
Let's calculate the interest first:
Interest = Principal Amount * Interest Rate
= $2,500 * (8/100)
= $200
So, the interest charged on the loan is $200.
To find out the total amount David will pay to the bank, we need to add the principal and interest together:
Total Payment = Principal Amount + Interest
= $2,500 + $200
= $2,700
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Related Questions
Let us suppose the following profit function for this industry: π(p,w
1
,w
2
)=
8(w
1
+w
2
)
1/2
p
2
where p is the market price of its output, while w
1
and w
2
are the prices of the inputs. Assume further that the firms are identical and that each firm faces the same market prices for both its output as well as inputs. a) Explain whether the firm is operating in the short run or long run and further determine the supply function for each firm. b) Derive the firm's input demand functions, determine their degree of homogeneity as well as the impact of a change in the input prices. c) Derive the market supply function given that there are 40 firms operating in this, market. d) If the market price of output (p) is 5 , the market price of the input (w
1
) is 1 , that of (w
2
) is also 1 and the demand function is given by q=1500/p(p+1). Determine the total market supply.
Answers
(a) The firm is operating in the long run, and its supply function is determined by the profit maximization condition.
(b) The firm's input demand functions can be derived from the profit function, and their degree of homogeneity is 1/2. Changes in input prices will impact the firm's input demand.
(c) The market supply function can be derived by aggregating the supply functions of all 40 firms operating in the market.
(d) Given the market conditions and demand function, the total market supply can be calculated.
(a) The firm is operating in the long run because it has the flexibility to adjust its inputs and make decisions based on market conditions. The firm's supply function is determined by maximizing its profit, which is achieved by setting the marginal cost equal to the market price. In this case, the supply function for each firm can be derived by taking the derivative of the profit function with respect to the price of output (p).
(b) The input demand functions for the firm can be derived by maximizing the profit function with respect to each input price. The degree of homogeneity of the input demand functions can be determined by examining the exponents of the input prices. In this case, the degree of homogeneity is 1/2. Changes in the input prices will affect the firm's input demand as it adjusts its input quantities to maximize profit.
(c) The market supply function can be derived by aggregating the individual supply functions of all firms in the market. Since there are 40 identical firms, the market supply function can be obtained by multiplying the supply function of a single firm by the total number of firms (40).
(d) To determine the total market supply, we substitute the given market conditions and demand function into the market supply function. By solving for the market quantity at a given market price, we can calculate the total market supply.
In conclusion, the firm is operating in the long run, and its supply function is determined by profit maximization. The input demand functions have a degree of homogeneity of 1/2, and changes in input prices impact the firm's input demand. The market supply function is derived by aggregating the individual firm supply functions, and the total market supply can be calculated using the given market conditions and demand function.
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Faisal drives his car a distance of 40 km in half an hour, how many minutes will it take to drive 100 km?
Answers
Answer:
75 minutes
Step-by-step explanation:
To calculate the time it will take for Faisal to drive 100 km, we can use a proportion based on the given information:
\(\sf \dfrac{Time \; 1}{Distance\;1}=\dfrac{Time\;2}{Distance\;2}\)
Given:
Time 1 = 30 minutes (since half an hour is equal to 30 minutes)Distance 1 = 40 kmTime 2 = Unknown (we need to find this)Distance 2 = 100 km (the desired distance)Substitute these values into the proportion:
\(\sf \dfrac{30\;min}{40\;km}=\dfrac{Time\;2}{100\;km}\)
To find Time 2, we can multiply both sides by 100 km:
\(\sf \dfrac{30\;min}{40\;km}\times 100\;km=\dfrac{Time\;2}{100\;km} \times 100\;km\)
\(\sf Time \; 2 = \dfrac{30 \; minutes \times 100 \; km}{40\;km}\)
Solve for Time 2:
\(\sf Time \; 2 = \dfrac{30 \; minutes \times 100}{40}\)
\(\sf Time \; 2 = \dfrac{3000 \; minutes}{40}\)
\(\sf Time\;2=75\;minutes\)
Therefore, it will take Faisal 75 minutes to drive 100 km.
PLEASE HELP. 35 POINTS.
What are the coordinates of B’ in the dilated image?
Answers
Answer:35:4
Step-by-step explanation:
the acts in a talent competition consist of 4 instrumentalists, 10 singers, and 6 dancers. if the acts are ordered randomly, what is the probability that a dancer performs first? provide the answer as a simplified fraction.
Answers
The probability that a dancer performs first in the talent competition can be calculated by dividing the number of favorable outcomes (a dancer performing first) by the total number of possible outcomes (all possible orderings of the acts). The answer is a simplified fraction.
There are a total of 20 acts consisting of 4 instrumentalists, 10 singers, and 6 dancers. Since we want to find the probability of a dancer performing first, we can consider the first act as the dancer, and the remaining acts can be arranged in any order.
The total number of possible orderings of the 20 acts is 20!, which represents the factorial of 20 (20 factorial).
The number of favorable outcomes is 6 * 19!, which means fixing one dancer as the first act and arranging the remaining 19 acts in any order.
Therefore, the probability can be calculated as:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
= (6 * 19!) / 20!
The expression (6 * 19!) / 20! can be simplified by canceling out the common factors:
Probability = 6 / 20
Hence, the probability that a dancer performs first is 6/20, which simplifies to 3/10.
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Volume of Composed Figures-Quiz-Level G
Isaac's grandmother is teaching him how to make an egg casserole. Isaac pours the
mixture into the pan shown. Isaac's grandmother tells him he should stop when the
mixture is inch from the top, to allow room for the casserole to rise in the oven.
2
1
What is the volume, V, of the mixture that
Isaac should pour into the pan?
V = ||
in.³
9 in.
9 in.
2 in
Answers
So, Isaac should pour 81 cubic inches of mixture into the pan.
What is volume?Volume is a physical quantity that refers to the amount of space occupied by an object or a substance. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.
The volume of an object or substance can be determined by measuring its length, width, and height (in the case of a solid object), or by measuring the amount of space it occupies (in the case of a liquid or gas).
In mathematical terms, the volume of an object is given by the formula V = l x w x h, where l is the length, w is the width, and h is the height. For irregularly shaped objects, the volume may be determined by displacement - that is, by measuring the amount of water or other fluid displaced by the object when it is immersed in the fluid.
To find the volume of the mixture that Isaac should pour into the pan, we need to find the volume of the pan itself and subtract the volume of the space that needs to be left empty.
The pan is in the shape of a rectangular prism, so its volume is:
V_pan \(= l *w * h = 9 in. * 9 in. * 2 in. = 162 in^{3}\)
To leave room for the casserole to rise, Isaac should only fill the pan to a height of 1 inch. So, the volume of the space that needs to be left empty is:
V_empty \(= l *w * h = 9 in. * 9 in. * 2 in. = 81 in^{3}\)
Therefore, the volume of the mixture that Isaac should pour into the pan is:
V = V_pan - V_empty\(= 162 in^{3} - 81 in^{3} = 81 in^{3}\)
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plz help me i have been asking this question way too much will give brainiset
Answers
Answer:
A. 5 in= 5/12 ft
B. 13 in= 1 1/12 ft
C. 9 oz = 9/16 Ib
D. 18 oz = 1 1/8 lb
Numeric entry e-tering a numeric answer. These numeit entry fieles can appear with a veriefy of seitings, such as the body sf a paragraph or a teble. Complere rhe following stanemoot to sas numark ancry in actiov. The surn of 1,400 and 3,000 is Can I enter negative numbers and declmals? however, youm need to enter a minus sign to represent a negative nutber, ar a decimal to represent a noninteper. Compiefe fhe fowsing tabie fo see now cecimas and negarive favoers work. How do 1 lanow if 1 got the answer right? Once you have submitted your answers for an entire problem, your individual anseers wil be marked elther cortedt with a green check or lncorrect with a red X. At this point, you msy select the entery fleid to reveal the comect answer; selecting it again will hide the correct answec. True of rase: The cerrect answer ts a numeric entry feid wal a comaccaly be pcputated in the correct faid arter you cpen the enptanations. True False Is entering 20,000,000 the same as entering 20 million? Pay careful astention to the instructions gNen in the prediem for how to enter your answer. Far wampe, if a questicn specines thar yeu give your the field in a paragraph. Complefe fhe foloming fab'e fo demonswafe your enderstwising of chis A case headers. What if my answer doesn't fit In the space I'm glven? If you find yourseif trying to enter a numiar that tha flaid coes not a ow (eithar because thare is not anough space or because it dees not acospt decmal values), eread the inseructisns to make sure yeu are antarng the number in the correct rermar. Complere the following statement to domonstrate your undortanding of in-line unite. The 8um or se0,Ded and so0,000 is milion. What about currency? You do not need to enter the symbois for currency. For exampia, if you enter d doocuo0 inco a numenc antry ceil that daas with currency and than need to enter declmas as well. Complere rhe folkuing staramost no ses now curency warks. If rou sfart out with $2.55 and find an addilonel 54.65 in your pocket, you will have a total of What about percentages? As with che curency symbo, ir a perecarage symbsi 15 recured, It wil autemancaly apsear aisngside your numenc entry after you exil tre numerte zypese as 65%. (Note: Mthouph 65% can also be represented as 0.65, if you were to enter 0.65 into a field that automaticaly comerts to percencages, this would be fomatted as 0.65% and would be graded as incerrect, because 0.65% is not equal to 65%.) Complete the following statement to see how percentages work. As a percentage, \$22.00 ia equal tD of $40.00.
Answers
The sum of 1,400 and 3,000 is 4,400. Can I enter negative numbers and decimals.
Can I enter negative numbers and decimals?When entering a numeric answer, you may encounter different settings such as within the body of a paragraph or a table. To understand how numeric entry works, let's break down the provided information.
The statement mentions completing a table to observe how decimals and negative numbers function. This implies that you will be performing calculations using decimals and negative numbers and recording the results in a table.
To determine if your answers are correct, after submitting your responses for a particular problem, each individual answer will be marked either correct with a green check or incorrect with a red X. You can select the entry field to reveal the correct answer, and selecting it again will hide it.
The statement also discusses whether entering "20,000,000" is the same as entering "20 million." It is important to pay attention to the instructions given in the problem to ensure the correct format for your answer.
In this case, the question aims to assess your understanding of the format by specifically mentioning giving your answer in a paragraph. So, entering "20,000,000" would be the correct format.
If the space provided for entering your answer is insufficient or doesn't accommodate decimal values, carefully review the instructions to ensure you are entering the number correctly. Adjust your approach accordingly, considering the space and format requirements.
Regarding in-line units, you are required to complete a statement that demonstrates your understanding of them. This likely involves performing calculations involving units and providing the resulting value with the appropriate unit.
Currency symbols are not necessary when entering answers. If a question involves currency and decimals, you can enter the numerical value without including the currency symbol. The statement asks you to demonstrate your understanding of how currency works.
Finally, percentages are mentioned, and you are instructed to complete a statement involving them. Keep in mind that when a percentage symbol (%) is required, it will automatically appear alongside your numeric entry after you exit the numerical input field.
To summarize, the explanation covers various aspects of numeric entry, including negative numbers, decimals, correctness assessment, table completion, fitting answers within given spaces, in-line units, currency, and percentages.
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suppose you toss 3 coins at one time. what is the probability that exactly two land with heads facing up?
Answers
The probability of getting heads is 3/8.
Probability:
Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. Probability is a number between 0 and 1, with 0 generally indicating impossibility and 1 indicating certainty. that an event will occur. A simple example is tossing a fair (unbiased) coin. Since the coin is fair, the two outcomes (heads and tails) are equally likely. The probability of heads is the same as the probability of tails. Since no other outcome is possible, the probability of heads or tails is 1/2 (also written as 0.5 or 50%).
Since 3 is a small number, let's list out all possible combinations.
H represents a head while T represents a tail.
3 Heads
HHH
2 Heads
HHT
HTH
THH
1 Head
HTT
THT
TTH
0 Head
TTT
The answer is
3/1+3+3+1=3/8
OR
In general, we will find that the list resembles a particular row of the pascal's triangle.
If you want to know the probability of getting r heads (or tails) from n flips, it is the sum of the rth elements in the n + 1 line. All elements of the series n+1.
\(\left[\begin{array}{ccc}N\\\\R\end{array}\right]\)/ 2ⁿ = \(\frac{n!}{r! * (n - r)!* 2^{n} }\)
n this case,
N =3andR= 2
3!/ 2!×1! × 2³
= 6/ 2× 1 × 8
= 3/8
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How do I do this please
Answers
Answer:
Step-by-step explanation:
substitute p for 8, because p=8
question 1 : 8+4=12 ----Yes
question 2: 8x8 =64-------Yes
question 3 5x8=35, not 8----No
question 4 2+8=10, not 12----No
Dr. Ellison says that the equation y = -3x + 7 has a solution f(2) = 5/3. Is Dr. Ellison right or wrong?
Answers
Dr. Ellison's equation that f(2) = 5/3 is wrong
How to determine if the doctor is right or wrong?From the question, we have the following equation that can be used in our computation:
y = -3x + 7
This equation can be expressed as a function
So, we have
f(x) = -3x + 7
In Dr. Ellison's equation, we have
f(2) = 5/3
This means that
x = 2
So, we have
f(2) = -3 * 2 + 7
Evaluate
f(2) = 1
The calculated value is different from Dr. Ellison's equation
Hence, the solution is wrong
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acellus algebra 2. piece wised functions.
find f(-2) for the piece wised function
Answers
\(f(-2) = -4\) for the given piecewise function by using the equation \(f(x) = x - 2\) if \(x < 3.\)
What is the piecewise function?A piecewise function is a mathematical function that is defined differently on different parts of its domain.
Instead of having a single formula that applies to the entire domain, a piecewise function has multiple formulas, each applying to a specific interval or subset of the domain.
To find f(-2) for the given piecewise function, we need to determine which piece applies to the input value o \(f -2\), which is less than 3. Therefore, we use the first piece of the function, which is\(f(x) = x - 2 if x < 3.\)
Substituting x = -2 into this piece, we get:
\(f(-2) = (-2) - 2 = -4\)
Therefore, f(-2) = -4 for the given piecewise function.
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Smores, a Taste of Multivariate Normal Distribution Smores Company store makes chocolate (Xi), marshmallow (X2), and graham cracker (Xs). Assume that the profit (in millions) for selling these smores materials follow a multivariate uormal ditributim with parameters 1 0.3 0.3 and Σ= 0.31 0 0.3 01 What is the probability that 1. the profit for selling chocolate is greater than 6 millions? 2. the profit for selling chocolate is greater than 6 millions, given the sales of marshmallow is 5 million and the sales of graham cracker is 5 mllion? 3. P(3X1-1X2 + 3X3 > 20)?
Answers
The sales of marshmallow is 5 million and the sales of graham cracker is 5 million is 0.5648 and the probability that 3X1-1X2 + 3X3 > 20 is 0.000005.
The multivariate normal distribution is a probability distribution which describes the joint behavior of multiple random variables. In the given case, the profit (in millions) for selling chocolate (Xi), marshmallow (X2) and graham cracker (X3) follows a multivariate normal distribution with parameters 1, 0.3, 0.3 and Σ = 0.31 0 0.3 01.
1. To calculate the probability that the profit for selling chocolate is greater than 6 millions, we need to calculate the probability that X1>6. Using the given parameters, we can use the formula for calculating the cumulative probability of a standard normal distribution: \(P(X1>6) = 1-P(X1≤6) = 1-0.9999994 = 0.000006.\)
2. To calculate the probability that the profit for selling chocolate is greater than 6 millions, given the sales of marshmallow is 5 million and the sales of graham cracker is 5 million, we need to calculate the conditional probability \(P(X1>6|X2=5, X3=5)\). Using the given parameters, we can calculate this probability using the formula for conditional probability:\(P(X1>6|X2=5, X3=5) = P(X1>6 ∩ X2=5 ∩ X3=5) / P(X2=5 ∩ X3=5) = 0.002207 / 0.003915 = 0.5648.\)
3. To calculate the probability that, we need to calculate the probability that\(X1>7-X2/3-X3/3\). Using the given parameters, we can calculate this probability using the formula for cumulative probability of a standard normal distribution: \(P(3X1-1X2 + 3X3 > 20) = 1-P(3X1-1X2 + 3X3 ≤ 20) = 1-0.9999995 = 0.000005.\)
In conclusion, the probability that the profit for selling chocolate is greater than 6 millions is 0.000006, the probability that the profit for selling chocolate is greater than 6 millions
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The graphs of functions f(x) and g(x) = f(x) + k are shown:
7
6
5
g(x)
4
3
f(x)
2
2
-2
-34
What is the value of k?
+
Answers
Answer:
9514 1404 393
Step-by-step explanation:
k = 2
The point (0, 0) on the graph of f(x) tells you f (0) = 0.
The point (-4, 0) on the graph of g(x) tells you g (-2) = 0.
Now we know that
g(-2) = 0 = f(0) = f(-2+k)
or ...
0 = -2+k
2 = k
The value of k is 2
so the answer to you problem is k=2
which of the following is not an effect of epidermal growth factor (egf) on the epidermis?
Answers
The term "not" indicates that I need to provide an option that is not an effect of epidermal growth factor (EGF) on the epidermis.
Therefore, the option that is not an effect of EGF on the epidermis is "increased production of melanin." EGF primarily promotes cell growth, proliferation, and differentiation in the epidermis, as well as the maintenance of tissue homeostasis and wound healing. It does not directly affect the production of melanin, which is primarily regulated by melanocytes.
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HELP MI PLSSS!!! I WILL GIVE POINTS AND BRAINEST!!!
Answers
Answer:
x≈5.3 feet
Step-by-step explanation:
\(\frac{4}{15} =\frac{x}{20}\)
\(15x=80\)
x≈5.3 feet
Answer:
5.3m tall
Step-by-step explanation:
15/4 = 3.75
20/3.75= 5.3333333
a circle in the xyx, y-plane has center (5,7)(5,7)(, 5, comma, 7, )and radius 222. which of the following is an equation of the circle?
a. (x-5)^2 + (y-7)^2 = 2
b. (x+5)^2 + (y+7)^2 = 2
c. (x+5)^2 + (y-7)^2 = 4
d. (x-5)^2 + (y-7)^2 = 4
Answers
Therefore, the correct equation of the circle is option d: (x - 5)^2 + (y - 7)^2 = 4.
The equation of a circle with center (h, k) and radius r is given by (x - h)^2 + (y - k)^2 = r^2.
In this case, the center of the circle is (5, 7) and the radius is 2.
Plugging these values into the equation, we have:
(x - 5)^2 + (y - 7)^2 = 2^2
Simplifying:
(x - 5)^2 + (y - 7)^2 = 4
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A cylinder has volume of 60 cm3 what is the volume of a cone with the same radius and height
Answers
Answer:
Option A 26cm3
Step-by-step explanation:
have a great day
pls mark brainlist
Graph (–4, 5), (2, 3), (–3, 0), (–4, –5), (–5, 2), and
(–5, 3) and connect the points to form a polygon.
How many sides does the polygon have?
The polygon has
sides.
Answers
Answer:
my bad im so sorry
Step-by-step explanation:
Answer:
The polygon has 6 sides
Step-by-step explanation:
Consider the number 7,123,456.
a. Approximate the number by rounding to the nearest million.
Answers
Approximating 7,123,456 by rounding to the nearest million will be 7,000,000.
What is approximation?Anything similar to something else but not precisely the same is called an approximation. By rounding, a number can be roughly estimated. By rounding the values in a computation before carrying out the procedures, an estimated result can be obtained.
If you want to round to one or two decimal places, look at the digit immediately following the decimal point. To the right of the necessary place value digit, draw a vertical line. Observe the following digit. Increase the preceding digit by one if the following digit is 5 or higher.
Therefore, approximating 7,123,456 by rounding to the nearest million will be 7,000,000.
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Plz help it’s due tonight!!!
Answers
Mabel saved up her money and bought a model train. Each of the 8 cars on the train was the same length. When Mabel put all the cars together, the train was 3 feet long. How long was each car?
Answers
Each car on Mabel's train is a little less than half a foot long i.e., 3/8 feet long, or 0.375 feet long. This is solved by using simple mathematical operations.
To find the length of each car on Mabel's train, we can use the formula:
Total length of train = length of one car × number of cars
We are given that Mabel's train has 8 cars and is 3 feet long, so we can substitute those values into the formula and solve for the length of one car:
3 = x × 8
where x is the length of one car.
To solve for x, we can divide both sides by 8:
3/8 = x
Therefore, each car on Mabel's train is 3/8 feet long, or 0.375 feet long.
In other words, each car is a little less than half a foot long.
To help visualize this, imagine dividing the 3-foot length of the train into 8 equal parts. Each part would be 3/8 feet long, which is the length of one car. So when Mabel puts all 8 cars together, they form a train that is 3 feet long.
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Evaluate the indefinite integral. Use a capital " C " for any constant term. ∫(3ex+4x5−x34+1)dx= TIP Enter your answer as an expression. Example: 3x∧2+1,x/5,(a+b)/c Be sure your variables match those in the question
Answers
The equatiion where C is the constant of integration.To evaluate the indefinite integral ∫(3e^x + 4x^5 - x^3/4 + 1)dx, we can integrate each term separately.
∫3e^x dx = 3∫e^x dx = 3e^x + C₁
∫4x^5 dx = 4∫x^5 dx = 4 * (1/6)x^6 + C₂ = (2/3)x^6 + C₂
∫-x^3/4 dx = (-1/4)∫x^3 dx = (-1/4) * (1/4)x^4 + C₃ = (-1/16)x^4 + C₃
∫1 dx = x + C₄
Now, we can combine these results to obtain the final answer:
∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C
Therefore, the indefinite integral of (3e^x + 4x^5 - x^3/4 + 1)dx is:
∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C
where C is the constant of integration.
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please help me I need to turn this in now
Answers
The volume of a right circular cone that has a height of 3.5 ft and a radius of 18.9 ft is given as follows:
1308.6 ft³.
How to obtain the volume a cone?The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.
V = πr²h/3.
The parameters for the cone in this problem are given as follows:
Radius of r = 18.9 ft.Height of h = 3.5 ft.Hence the volume of the cone is given as follows:
V = 3.14 x 18.9² x 3.5/3
V = 1308.6 ft³.
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lindsay bedford works at the baseball cap shop. she is paid $6.50 per hour plus $0.45 for each cap she embroiders. how many caps must she embroider to earn at least $85 in an 8-hour day? group of answer choices
Answers
Answer:
Step-by-step explanation:
74 caps
Find the sum of the first one hundred terms in the progression. (-6, -2, 2...) (Rigorous) A. B. C. D. 19,200 19,400 -604 604
Answers
Answer:
19,200
Step-by-step explanation:
d = (-2) - (-6) = 4
a_1 = -6
S_n = (n/2)[2a_1 + (n - 1)d]
S_100 = (100/2)[2 × (-6) + (100 - 1)(4)]
S_100 = 50(-12 + 99(4)]
S_100 = 50(384)
S_100 = 19,200
Answer: 19,200
Step-by-step explanation:
The nth term of an arithmetic progression can be found by the formula:
\(a_{n} = a_{1} + (n-1) * d\)
Where:
\(a_{n}\) = nth term
\(a_{1}\) = first term = -6
n = number of terms = 100
d = common difference = 4
The 100th term (\(a_{100}\)) would therefore be:
\(a_{100}\) = -6 + (100-1) * 4 = -6 + 99 * 4 = 390
The sum \(S_{n}\) of the first n terms of an arithmetic sequence can be found using the formula:
\(S_{n} = \frac{n}{2} *(a_{1} + a_{n} )\)
So the sum of the first 100 terms (\(S_{100}\)) would be:
\(S_{100}\) = 100/2 * (-6 + 390) = 50 * 384 = 19200
So, the sum of the first 100 terms of the given arithmetic progression is 19200
give an example of a linear transformation whose kernel is the line spanned by ⎡ ⎣ −1 1 2 ⎤ ⎦ in r3.
Answers
v^T proj_v(x) = 0, so v^T T(x) = v^T x - v^T proj_v(x) = v^T x, which is not zero unless x is on the line spanned by v.
Therefore, the kernel of T is precisely the line spanned by v, as desired.
Let's start with understanding what the kernel of a linear transformation is. The kernel, also known as the null space, is the set of all vectors that get mapped to the zero vector by the transformation.
In this case, the kernel is the line spanned by the vector ⎡ ⎣ −1 1 2 ⎤ ⎦. This means that any vector on this line will get mapped to the zero vector by the linear transformation we're looking for.
One example of a linear transformation that has this kernel is the projection onto the plane orthogonal to ⎡ ⎣ −1 1 2 ⎤ ⎦. This transformation takes any vector in R^3 and projects it onto the plane that is perpendicular to the given vector.
To see why this works, let's call our given vector v = ⎡ ⎣ −1 1 2 ⎤ ⎦. We can find a basis for the plane orthogonal to v by finding the orthogonal complement of v. This is the set of all vectors w in R^3 that satisfy the equation v^T w = 0.
If we solve this equation, we get the set of all vectors of the form ⎡ ⎣ a -a/2 b ⎤ ⎦, where a and b are any real numbers. This is a basis for the plane orthogonal to v.
Now, we can define our linear transformation T as follows: T(x) = x - proj_v(x), where proj_v(x) is the projection of x onto the plane orthogonal to v.
Since proj_v(x) is in the plane orthogonal to v, it is also orthogonal to v. This means that v^T proj_v(x) = 0, so v^T T(x) = v^T x - v^T proj_v(x) = v^T x, which is not zero unless x is on the line spanned by v.
Therefore, the kernel of T is precisely the line spanned by v, as desired.
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In triangle JKLS measure of angle Alice 13 more than measure of angle K and measure of angle J7 more than six times measure anger angle K find the measure of each angle
Answers
Answer: 84
Step-by-step explanation: just need points
I WILL MARK BRAINIEST
please answer question 1 and please also, let me know if I did question 2 right
Answers
Answer:
1. B. it always stays the same length it will just have different points
2. yes you did do number 2 correctly
Step-by-step explanation:
Answer:
Please check the explanation.
Step-by-step explanation:
Question 1)
Please note that when a translate any object on the coordinate plane, we are just sliding a figure on the coordinate plane. The shape, orientation, or size do not change.
Hence, if you translate a line up 4 and to the left 2, its image will look like a line that is the same exact length.
Question 2)
Given the original point C(-1, -4) and its image C'(-6, 3).
It is clear that the coordinates of the image C'(-6, 3) is the result of translating the C(-1, -4) to the left 5 and down 7.
So the rule of the translation to the left 5 and down 7 will be:
(x, y) → (x-5, y+7)
C(-1, -4) → (-1-5, -4+7) = C'(-6, 3)
The map shows a straight highway between two towns. Highway planners want to build two new rest stops between the towns so that two rest stops divided the highway into three equal parts. Find the coordinates of the points at which the rest stops should be built.
Answers
1,1 and -1,0 would be the answer
(-2, -1/3) and (1, 1 1/3) the coordinates of the points at which the rest stops should be built.
What is coordinates point?
A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes.
According to the question,
In given figure,
x from -3 to +3
1/3 would be -2
2/3 would be +1
y from -2 to +3
1/3 would be -2 + 5/3 = -1/3
2/3 would be -2 + 10/3 = 1 1/3
The two coordinates
(-2, -1/3) and (1, 1 1/3)
Hence , (-2, -1/3) and (1, 1 1/3) the coordinates of the points at which the rest stops should be built.
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1. The length of a rectangle is four
times its width. If the area is 100m
what is the length of the rectangle
Answers
Answer:
20m
Step-by-step explanation:
write a equation duh
x * 4x = 100
u can split 100 into 5 x 20
x * 4x = 5 * 20
x = 5
and 4x = 20