There are no points at which the function has its direction of fastest change along the vector i + j. This is because the equations lead to a contradiction.
The exercise asks to find all the points at which the function f(x, y) = x^2 + y^2 - 8x - 16y has its direction of fastest change along the vector i + j.
To find the points, we need to solve the equation:
(2x - 8)i + (2y - 16)j = k(i + j)
where k is a constant. Since the direction of fastest change is along the vector i + j, we know that the left-hand side of the equation represents the gradient vector of f(x, y).
Equating the x and y components of the gradient vector to the corresponding components of the vector i + j, we get:
2x - 8 = k
2y - 16 = k
Equating these two expressions for k, we get:
2x - 8 = 2y - 16
Solving for y in terms of x, we get:
y = x - 4
Substituting this expression for y into the equation of the gradient vector, we get:
2x - 8 = k
2(x - 4) - 16 = k
Simplifying, we get:
2x - 8 = k
2x - 24 = k
Substituting the first equation into the second, we get:
2x - 24 = 2x -
Simplifying, we get:
16 = 0
This is a contradiction, which means there are no points at which the function has its direction of fastest change along the vector i + j.
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when a certain number is doubled and then decreased by 9, the result is not more than 19. Find the range of values of the number
Answer:
The number must be at most 10.
If the number is doubled and then decreased by 9, the result is 2x - 9.
2x - 9 ≤ 19
2x ≤ 28
x ≤ 14
Therefore, the range of values of the number is 0 to 10.
2.4x − 1.5y = 0.3
1.6x + 0.5y = −1.3
The system of equations above is graphed in the xy -plane. What is the x -coordinate of the intersection point (x , y) of the system?
The given system of equations above is graphed in the xy -plane, then the x-coordinate of the intersection point (x, y) is -1.0625.
What is the system of equations?
A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously.
There are different methods to find the solution of a system of two equations in two variables, but one common one is to use elimination or substitution. Here, we will use substitution.
From the first equation, we can isolate x in terms of y by adding 1.5y to both sides and dividing by 2.4:
2.4x - 1.5y = 0.3
2.4x = 1.5y + 0.3
x = (1.5/2.4)y + 0.3/2.4
x = 0.625y + 0.125
Now we substitute this expression for x into the second equation and solve for y:
1.6x + 0.5y = −1.3
1.6(0.625y + 0.125) + 0.5y = −1.3
1.0y = −1.8
y = −1.8/1.0
y = −1.8
Finally, we substitute this value of y back into either equation to find the corresponding x-coordinate:
x = 0.625y + 0.125
x = 0.625(-1.8) + 0.125
x = −1.0625
Therefore, the x-coordinate of the intersection point (x, y) is -1.0625.
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Do not put any punctuation (other than a necessary decimal place) or spaces into your answer.
When Claudia borrowed $6400 at 11% compounded semiannually for three years, the value of the rate per period was
Caludia needs to pay 2917.6128 as a payment of compound interest capital+interest.
What is compound interest?
compound interest is interest on principal + interest and this denotes to the addition of interest to the principal amount of a loan or deposit.
Capital(p) = $6400
Rate of interest(r) = 11%
Years(n) = 3
The general formula of compound interest is [tex]A= p(1+\frac{r}{100}})^n[/tex].
Now
[tex]A= 6400(1+\frac{11}{100}})^3\\A=6400 \times \frac{111}{100} \times \frac{111}{100} \times \frac{111}{100}\\A= 8752.8384[/tex]
The entire amount (Capital+interest) is equal to $8752.8384.
If we take 1 year as a period then Claudia needs to pay [tex]\frac{8752.8384}{3}\\=2917.6128[/tex]
Therefore, Claudia needs to pay 2917.6128 as a payment of compound interest capital+interest.
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At age 39, you start saving for retirement. If your investment plan pays an APR of 4% and you want to have $0.8 million when you retire in 26 years, how much should you deposit monthly?
Answer:
Step-by-step explanation:
type the correct words in the blanks. two radicals are said to be radicals if they have the same and the radicand.
Two radicals are said to be radicals if they have the same indices and the radicand.
In mathematics, a radicand is an expression, a number, or a variable that is enclosed in a root symbol. The factor for which we are determining the root is quantity. As we study exponents and roots, the word "radicand" is utilised. Therefore, the radicand in 2 has a value of 2. Following are some radicand examples:
3√(pq) → pq is the radicand
√(a+b) → a + b is the radicand
4√15 → 15 is the radicand
A radical is a symbol used to represent a number's root. It is symbolised as. The word or phrase that appears after the radical symbol is known as the radicand. Hence, it may be claimed that the radical represents the radicand. Alternatively said, the radicand sign is √.
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Complete question:
Type the correct words in the blanks:
Two radicals are said to be radicals if they have the same and the radicand.
TRUE/FALSE. Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" Ris a linear transformation. If Ic.B = Tç, e then B = E = C.
Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" R is a linear transformation. If Ic.B = Tç, e then B = E = C.
The above statement is True.
In mathematics, and more specifically in linear algebra, a linear map (also called a linear map, a linear transformation, a vector space homomorphism, or in some cases a linear function) is a map between two vector spaces V → W, which performs the conservation of operations on vectors. Addition and scalar multiplication. The same names and definitions are also used for the more general case of modules over rings; see the homomorphism of modules.
A linear map is called a linear isomorphism if it is a bijection. In the case V=W, the linear map is called linear automorphism. Sometimes the term linear operator refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily that V = W, where V is the space of functions, which is a common convention in functional analysis.
Sometimes the term linear function has the same meaning as linear map, but not in analysis.
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Daniel opens a new savings account and makes an initial deposit of $1,200.
If the account earns 2.5%
annual interest, which equation shows how much money is in the account in 9
months?
Responses
A x=1,200+1,200(0.25)(0.75)
x is equal to 1 comma 200 plus 1 comma 200 0 point 2 5 0 point 7 5
B x=1,200+1,200(0.025)(0.75)
x is equal to 1 comma 200 plus 1 comma 200 0 point 0 2 5 0 point 7 5
C x=1,200+1,200(0.25)(9)
x is equal to 1 comma 200 plus 1 comma 200 0 point 2 5 9
D x=1,200+1,200(0.025)(9)
Answer:
D) x = 1,200 + 1,200(0.025)(9)
In this equation, 1,200 is the initial deposit, 0.025 is the decimal representation of the annual interest rate, and 9 represents the time period in months. The multiplication of 0.025 and 9 gives the proportion of interest earned in 9 months, which is then multiplied by the initial deposit and added to it to give the total amount in the account after 9 months.
Simplifying the equation:
x = 1,200 + (1,200)(0.025)(9)
x = 1,200 + 270
x = 1,470
Therefore, there would be $1,470 in the account after 9 months
report error suppose and are isosceles triangles. also suppose that and . what is the sum of all possible lengths for ?
The possible values of TP in isosceles triangle are between 5.5 and infinity.
Let TP = x. Then we have:
TI = TP = x (isosceles triangle)
PI = TP - PI = x - 7 (isosceles triangle)
PO = TP + OP = x + 11 (triangle inequality)
Using the fact that the sum of any two sides of a triangle must be greater than the third side, we have:
x + x > 11 --> x > 5.5
x + 11 > x --> 11 > 0
x + 7 > 5 --> x > -2
Therefore, the possible values of x are between 5.5 and infinity. The sum of all possible values of x is infinity since there is no upper bound on the possible values.
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_____The given question is incomplete, the complete question is given below:
Suppose triangle TIP and triangle TOP are isosceles triangles. Also suppose that TI=5, PI=7, and PO=11. What is the sum of all possible lengths for TP?
Last weekend, Mrs. Nelson earned $132 selling rings. She earned $6 for each ring she sold.
How many rings did she sell?
Hi!
Let's think about this really quick.
Each ring is $6. She made $132.
In order to find the solution, we need to divide the total from the original price of the ring, making the equation: 132÷6.
132÷6= 22.
So, she sold 22 rings. To verify that answer, we'll multiply 6 to 22.
6x22=132.
22 Is your answer.
Hope this helps!
Appreciated if you mark brainliest <3
~~~PicklePoppers~~~
Answer:
22 rings :)
Step-by-step explanation:
By diving 132 by 6 we can determine the number of rings she sold.
After dividing, we get 22 rings!
May I please have a brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!
Use the Law of Cosines to solve the problem. You must solve for BC first. Solve this order
A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it turn when it changed direction? Show you Work.
answer: 175
Step-by-step explanation:
Answer:
71.9 degrees
Step-by-step explanation:
The find the value of x on the given diagram, we must first find the included angle between the two line segments labelled 94 mi and 119 mi in the triangle. To do this, we can use the Law of Cosines.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]
The values to substitute into the formula are:
a = 119b = 94c = 173Solving for the angle C:
[tex]\begin{aligned}173^2&=119^2+94^2-2(119)(94)\cos C\\\\29929&=14161+8836-22372\cos C\\\\29929&=22997-22372\cos C\\\\6932&=-22372\cos C\\\\-\dfrac{6932}{22372}&=\cos C\\\\C&=\cos^{-1}\left(-\dfrac{6932}{22372}\right)\\\\C&=108.0502874...^{\circ}\end{aligned}[/tex]
As angles on a straight line sum to 180°, the value of x can be calculated by subtracting the found value of C from 180°:
[tex]x=180^{\circ}-108.0502874...^{\circ}[/tex]
[tex]x=71.9497125...^{\circ}[/tex]
[tex]x=71.9^{\circ}\; \sf (nearest\;tenth)[/tex]
Therefore, the ship turned 71.9 degrees north of west when it changed direction.
Write a sentence of interpretation for each point given.
When coffee beans sell for p dollars per pound, producers supply q million pounds. (5, 9); (15, 40)
When coffee beans sell for $5 per pound, producers supply 9 million pounds. This indicates that at a higher price, producers are willing to supply a larger quantity of coffee beans.
This means that at a lower price, producers will supply a smaller quantity of coffee beans. Conversely, when the price of coffee beans increases to $15 per pound, producers supply 40 million pounds.
The relationship between price and quantity supplied is a fundamental concept in economics. When prices are lower, producers may not have enough incentive to produce and supply goods. On the other hand, when prices are higher, producers may have more incentive to produce and increase their supply. This is often referred to as the law of supply.
Understanding this relationship is important for businesses and policymakers to make informed decisions about pricing and production. By analyzing market trends and the behavior of producers, they can adjust prices to maintain a balance between supply and demand. For example, if prices are too high, it may lead to a surplus of goods that cannot be sold, while prices that are too low may result in shortages or supply constraints.
In conclusion, the relationship between price and the supply of coffee beans reflects a broader economic principle that is essential for understanding how markets work. By examining the supply curve, we can gain insights into how producers respond to changes in price, and use this information to make informed decisions about pricing and production.
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When a stone is dropped from the top of a tower, the distances metres it falls in t seconds is given by s = 10?. Find how far it falls in 3 seconds?
Answer: 45 meters
Step-by-step explanation:
The given equation is:
s = (1/2) * g * t^2
Where,
g = acceleration due to gravity = 10 m/s^2 (approximate value)
To find the distance it falls in 3 seconds, we can substitute t = 3 in the above equation:
s = (1/2) * g * t^2
s = (1/2) * 10 * 3^2
s = (1/2) * 10 * 9
s = 45 meters
Therefore, the stone falls 45 meters in 3 seconds.
Graph to solve the system: y=-3/2 and y=(1/2) × -1 At what x-values are the equations equal?
the x-value that makes the two equations equal is x = -1. and x=0.
equation defineAn equation consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), connected by an equals sign (=). The LHS and RHS may contain one or more variables, which are values that can change or vary.
The first equation, y = -3/2, is a horizontal line with a y-intercept of -3/2. This means that no matter what x-value we plug in, the corresponding y-value will always be -3/2.
The second equation, y = (1/2) x - 1, is the equation of a line with slope 1/2 and y-intercept -1. To find the x-value(s) where this equation equals -3/2, we can set the two equations equal to each other:
-3/2 = (1/2) x - 1
Adding 1 to both sides, we get:
-1/2 = (1/2) x
Multiplying both sides by 2, we get:
-1 = x
At x=0, two equation satisfy the condition.
Therefore, the x-value that makes the two equations equal is x = -1 and 0.
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26. Paul, Raul, and Saul had a competition to see who could pick the greatest amount of strawberries
in three minutes. Paul picked 1 pounds of strawberries, Raul 1 pounds, and Saul 1 pounds.
Who came in second? Show your work.
There is no second place winner. all three competitors picked the same amount of strawberries, so there is a tie for first place.
What is probability?Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.
According to the given information:The problem states that each of the three competitors picked 1 pound of strawberries. Since all of them picked the same amount, there is no way to determine who came in second. All three competitors can be considered tied for first place. If the problem had given different weights of strawberries picked by each competitor, then we could have compared the weights and determined who picked the second greatest amount of strawberries. But since all three competitors picked the same amount, there is no way to determine a second place winner.
Therefore, there is no second place winner. all three competitors picked the same amount of strawberries, so there is a tie for first place.
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URGENT. PLS HELP ME FILL IN THE CHART. Simplify the given polynomials. Then, classify each polynomial by its degree and number of terms.
The polynomial's value is Degree: 2 (because x has a maximum power of 2), Degree: 2 (since x has a maximum power of 2), and Degree: 1 (since x has a maximum power of 1).
What qualifies as a polynomial?A polynomial is an equation made up of exponents, constants, and variables that is combined using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).
Expanding the provided expression, we obtain: Polynomial 1
6x2 + 2x - 24x - 8 = (x-4)(6x+2) = 6x2 - 22x - 8
When we condense the phrase, we get:
3
(3x² - 11x - 4)
Level: 2
Amount of terms: 1
2nd polynomial:
(7x² + 3x) Degree: (21x2 - 12) = 7x2 + 3x - (21x2 + 12) = -14x2 + 3x + 12 2 (because the maximum power of x is 2)
Polynomial 3: 2(-10x2 + 18x + 13) + 4(5x2 + 9x + 7) = 20x2 + 36x + 28 - 20x2 + 36x + 26 = 72x + 54
Grade: 1
There is one term.
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Let f(x) = 2x2 + 5x -19 and g(x) = x - 1. Perform the function operation and then find the domain.
(f + g)(x)
(Simply your answer.)
Answer:
(f + g)(x) = 2x² + 5x - 19 + x - 1 = 2x² + 6x - 20Domain: all real numbersto calculate the workload of a resource that serves different flow unit types, one must know which of the following?
The workload of the resource is 20.5 units.
To calculate the workload of a resource that serves different flow unit types, one must know the amount of flow units, the processing time for each flow unit, and the number of resources available. This is best calculated using Little's Law, which states that the average number of flow units in a system is equal to the average rate of flow units multiplied by the average time they spend in the system.
For example, if a resource is serving 3 flow unit types, A, B and C, with 10, 8 and 5 units respectively, and a processing time of 2 minutes, 1 minute and 3 minutes respectively, with 2 resources available, the workload can be calculated as follows:
Workload = (10*2 + 8*1 + 5*3) / 2
= 41 / 2
= 20.5 units
Therefore, the workload of the resource is 20.5 units.
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Complete question
What are the flow unit types that the resource is serving?
how many inches are in 1 1/2 yards
Answer:54 inches
Step-by-step explanation:
taking a whole number, how do you know if there is a number that you can multiply by itself to get it
If a whole number has a whole number square root, it means that there exists a number that you can multiply by itself to get that number.
Let us understand this statement by taking example, the whole number 9 has a whole number square root, which is 3. This means that 3 multiplied by itself gives 9: 3 x 3 = 9. Similarly, the whole number 16 has a whole number square root, which is 4. This means that 4 multiplied by itself gives 16: 4 x 4 = 16.
However, not all whole numbers have whole number square roots. For example, the whole number 2 does not have a whole number square root, which means that there is no whole number you can multiply by itself to get 2. In this case, we would say that 2 is an "irrational" number, because its square root is not a whole number or a fraction of whole numbers.
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A sequence is shown as follows:
points at (1,32), (2,8), (3,2), (4,0.5)
Assuming the pattern continues, what is the formula for the nth term?
Answer: an = 128 * (1/4)^n
Step-by-step explanation:
The given sequence is not an arithmetic or geometric sequence, but we can try to find a pattern using algebra. Let's assume that the formula for the nth term is of the form:
an = a * b^n
where a and b are constants to be determined. We can find these constants by using the first two points:
a * b^1 = 32 (when n = 1)
a * b^2 = 8 (when n = 2)
Dividing the second equation by the first, we get:
b^1 = (8/32) / (1/2) = 1/4
Substituting this value of b in the first equation, we get:
a * (1/4)^1 = 32
a = 128
Therefore, the formula for the nth term is:
an = 128 * (1/4)^n
We can check this formula using the other given points:
a2 = 128 * (1/4)^2 = 8
a3 = 128 * (1/4)^3 = 2
a4 = 128 * (1/4)^4 = 0.5
So the formula holds for all the given points.
HELP MEHHHH! I WILL MARK YOU BRAINLIEST! I NEED AN EXPLANATION
This illustrates the rule of large numbers, according to which the sample mean approaches the population mean as the sample size rises.
what is probability ?The likelihood or chance of an occurrence occurring is measured by probability. It is expressed as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of the occurrence. Additionally, probabilities can be stated as percentages, with 0% denoting an improbable event and 100% denoting a specific event. By dividing the number of favourable outcomes by the total number of potential outcomes, the probability of an occurrence is determined.
given
Since there are six potential outcomes and only one of them is a 5, the theoretical probability of rolling a 5 on a fair die is 1/6.
Mya's experimental chance of rolling a 5 after 100 trials is 25/100, which can be expressed as 1/4. Her experimental probability after 200 attempts is 30/200, which can be expressed as 3/20.
This implies that the experimental probability moves closer to the theoretical probability as the number of trials rises.
In other words, Mya's experimental findings get closer to the anticipated theoretical probability the more times she rolls the die.
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The complete question is :- Communicate and Justify Mya rolls a fair die and counts the number of times she rolls a 5. She rolls a 5 on 25 of the first 100 trials. She rolls a 5 on 30 of the first 200 trials. Compare the experimental probability to the theoretical probability after 100 trials and 200 trials. What do you notice? Explain.
Calculate the bearing of G from H.
The bearing of G from H at the given point location is determined as 155⁰.
What is bearing?
Bearing as a direction refers to the direction or angle of an object or location relative to a reference point, usually measured in degrees. For example, a compass can be used to determine the bearing of a landmark or to navigate in a particular direction.
The bearing of G from H is calculated by applying the following principle;
Let the bearing of G from H = θ
θ = 360 - 205 ( sum of angles in a circle )
θ = 155⁰
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A special bag of Starburst candies contains 20 strawberry, 20 cherry, and 10 orange. We will select 35 pieces of candy at random from the bag. Let X = the number of strawberry candies that will be selected. a. The random variable X has a hypergeometric distribution with parameters M= , and N= n= b. What values for X are possible? c. Find PCX > 18) d. Find PX = 3) e. Determine E[X] or the expected number of strawberry candies to be selected. f. Determine Var[X]. The Binomial Distribution input parameters output The mean is The number of trials n is: The success probability p is: Binomial Probability Histogram dev. is: 1 Enter number of trials Must be a positive integer. Finding Probabilities: 0.9 0.8 Input value x fx(x) or P(X = x) Fx(x) or P(X 3x) 0.7 0.6 Input value x fx(x) or P(X = x) Fx(x) or P(X sx) 0.5 0.4 Input value x fx(x) or PCX = x) Fx(x) or P(X sx) 0.3 0.2 0.1 Input value x fx(x) or PCX = x) Fx(x) or P(X sx) 0 0 0 0 0 0 0 0 0 0 0
It involves selecting 35 candies from a bag containing 20 strawberry, 20 cherry, and 10 orange Starburst candies. X is the number of strawberry candies selected. X has a hypergeometric distribution, with possible values from 0 to 20. P(X > 18) is 0.0125, and probability mass function P(X = 3) is 0.0783. The expected value of X is 14, and the variance of X is approximately 5.67.
X has a hypergeometric distribution with parameters M=40 (20+20), N=50 (20+20+10), and n=35.
X can take on values from 0 to 20, since there are only 20 strawberry candies in the bag.
Using the cumulative distribution function for the hypergeometric distribution, we have P(X > 18) = 0.0125.
Using the probability mass function for the hypergeometric distribution, we have P(X = 3) = 0.0783.
The expected value of X is E[X] = np = 35(20/50) = 14.
The variance of X is Var[X] = np(1-p)(N-n)/(N-1) = (35)(20/50)(30/49)(40/49) ≈ 5.67.
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Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch. I need help
D: Please !!!!
Answer:
We can use the formula for the area of a rectangle to solve this problem. Let's assume that the length of the top of the bookcase is L and the width is b. Then, we can write:
L × b = 300
Solving for b, we get:
b = 300 / L
Since we don't know the length L, we cannot find the exact value of b. However, we can use the given information to make an estimate. Let's say that the length of the bookcase is 60 inches. Then, we have:
b = 300 / 60 = 5
So, if the length of the bookcase is 60 inches, the width needs to be at least 5 inches to accommodate Bria's soap carving collection. However, if the length is different, the required width will also be different.
15. In the figure, ABCD is a trapezoid. Given
that length of BE equals to the length
CE, find the area of triangle ADE.
Triangle ADE has a surface area of 75 cm².
What is the triangular area formula?Triangle area determination. Use the equation area = 1/2 * base * height to determine a triangle's surface area. Decide which side will serve as the triangle's base, then calculate the triangle's height from that base.
Using similarity to determine y's value
AD/BD = AE/BE
y/(a-x) = y/x
yx = y(a-x)
x = a/2
This fact can be used to determine the height of the trapezoid:
h = √(BC² - [(AB-DC)/2]²)
= √(10² - [2²]²)
= 8
Now that we know how long MD is, we can:
As a result of the triangles ADE and BDE's resemblance, we can now determine the value of y:
y/BD = AE/BE
y/(a-x) = y/x
yx = y(a-x)
x = a/2
Substituting x = a/2 and BD = AB - DC = 10 - 6 = 4, we get:
y/4 = AE/(a/2)
y = 2AE/a
Substituting y = 2AE/a in the above equation, we get:
(2AE/a)/4 = AE/(a/2)
AE = (a/2)²/2
We may now apply the triangle's area formula, ADE:
Area of ADE = (1/4) x y x (a+b)
= (1/4) x 2AE/a x (a+b)
= (1/8) x (a²/2) x (a+b)
= (1/16) x a² x (a+b)
Substituting a = 10 and b = 6, we get:
Area of ADE = (1/16) x 10² x (10+6)
= 75 cm².
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What is the probability that a 43% free-throw shooter will miss her next free throw?
Answer:
57%
Step-by-step explanation:
Answer:
.57 or 57%
Step-by-step explanation:
If a basketball player has a free-throw shooting percentage of 43%, it means that she makes 43% of her free throws on average. Therefore, the probability that she will miss her next free throw is equal to the complement of her shooting percentage, which is 1 minus 0.43. This simplifies to 0.57 or 57%. So, the probability that she will miss her next free throw is 57%.
please help asap!!!!!!!
To remove the y-term in the given linear equation in two Variable multiply the equation by 4 then add these two equations.
What is linear equation in two Variable;
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable. As a result, this equation has a single solution, x = 5/2. Yet, there are two solutions to a linear equation with two variables.
According to given question;
5X+8y=5 ……..eqn 1.
3x-2y=3 ………eqn 2.
Multiply by 4 in the eqn 2.
We get
12x-8y=12 ……..eqn 3 .
When we add eqn 1 and eqn 3 we get ;
17x =17
X =1
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After eliminating the y-term in the given equations i.e 5x+8y=5 and
3x-2y=3, The solution to the system of equations is x = 1, y = 0.
What is elimination method?The elimination method is the technique used to solve systems of linear equations. It involves adding or subtracting equations in a system to eliminate one variable and find the value of the other variable.
To eliminate the y-term in these equations, you can multiply the second equation by 4, which will give you:
12x - 8y = 12
Now, you can add this equation to the first equation:
5x + 12x + 0y = 5 + 12
Simplifying the left side gives you 17x, and simplifying the right side gives you 17. So, you have the equation:
17x = 17
Solving for x gives you x = 1.
Now that you have found the value of x, you can substitute it into one of the original equations to solve for y. Using the first equation, you get:
5(1) + 8y = 5
Simplifying this equation gives you:
8y = 0
Solving for y gives you y = 0.
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A person invests 5500 dollars in a bank. The bank pays 4.5% interest compounded
annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 6700 dollars?
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
A = the final amount (6700 dollars)
P = the principal amount (5500 dollars)
r = the annual interest rate (4.5% or 0.045)
n = the number of times the interest is compounded per year (once annually)
t = the time period (in years) for which the money is invested
Substituting these values in the formula, we get:
6700 = 5500(1 + 0.045/1)^(1t)
Dividing both sides by 5500, we get:
1.21818181818 = 1.045^t
Taking the logarithm (base 10) of both sides, we get:
t = log(1.21818181818) / log(1.045)
Solving this equation using a calculator, we get:
t ≈ 4.4
Therefore, the person must leave the money in the bank for approximately 4.4 years (to the nearest tenth of a year) until it reaches 6700 dollars.
PLEASEE help!!!! Urgent!!!!!
Answer:
Step-by-step explanation:
Solve for x
(x-14)+(2x+8)= 180
3x-14+8=180
3x-6=180
3x=186
x=62degrees
Solve for y
(7y-15)+62=180
7y+47=180
7y=180-47
7y=133
y=19degrees
g suppoe x follows a distribution with pdf given by...show that the moment generating function of x is mx(t)
The distribution of Z=X+Y is gamma(1,10), which has a probability density function f(z) = 10 × e^(-10z), 0 ≤ z.
The moment generating function (mgf) of Z=X+Y can be found by taking the product of the mgfs of X and Y
Mz(t) = Mx(t) × My(t) = (e^(-4+4t))×(e^(-6+6t)) = e^(-10+10t)
We recognize that Mz(t) is the mgf of the gamma distribution with shape parameter k=1 and rate parameter λ=10. Therefore, Z=X+Y follows a gamma distribution with shape parameter k=1 and rate parameter λ=10.
In summary, the distribution of Z is gamma(1,10), which has a probability density function f(z) = λ^k × z^(k-1) × e^(-λz) / Γ(k) where k=1 and λ=10. Therefore, the probability density function of Z is f(z) = 10 × e^(-10z), 0 ≤ z.
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I have solved the question in general, as the given question is incomplete.
The complete question is:
What is the distribution of Z and the value of the parameter?