In this case, it means that the company fails to identify components that absorb too much humidity, leading to a potential safety hazard for customers.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
The consequence of a Type II error in this context is that the company believes the humidity absorbed is not more than 3%, when in fact it is more than 3%.
This means that the company will fail to detect components that absorb a dangerous level of humidity, and these components will be sold to customers, potentially causing a safety hazard. This is because the null hypothesis in this case is that the humidity level absorbed is 3%, and the alternative hypothesis is that it is more than 3%. A Type II error occurs when the null hypothesis is not rejected, even though it is false, and the alternative hypothesis is true.
Therefore, In this case, it means that the company fails to identify components that absorb too much humidity, leading to a potential safety hazard for customers.
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The elongation α
of a planet is the angle formed by the planet, earth, and sun. It is known that the distance from the sun to Venus is 0. 723AU
(see Exercise 65 in Section 6. 2 ). At a certain time the elongation of Venus is found to be 39. 4∘.
Find the possible distances from the earth to Venus at that time in Astronomical Units (AU)
The possible distances from the Earth to Venus at the time of an elongation of 39.4 degrees are 0.709 AU and 1.333 AU.
The elongation of a planet is the angle formed when the planet, Earth, and Sun are in a straight line. At a certain time, the elongation of Venus was found to be 39.4 degrees. To find the possible distances from the earth to Venus at that time in Astronomical Units (AU), the Law of Cosines can be used.
The Law of Cosines states that for a triangle with sides a, b, and c and angles A, B, and C, c2 = a2 + b2 - 2abcosC.
In this case, a is the distance from the sun to Venus (0.723 AU), b is the distance from the Earth to Venus, and C is the elongation (39.4 degrees).
Therefore, b2 = 0.7232 + b2 - 2(0.723)(b)cos39.4.
Solving for b, we get b = 0.709 AU and b = 1.333 AU, so the possible distances from the Earth to Venus are 0.709 AU and 1.333 AU.
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Find the arc length of the shape
Answer:
The arc length of this quarter-circle is 7π/4.
Let U= {q, r, s. t, u, v, w, x, y,z}
A= {q, s, u, w, y}
B= {q, s, u, w, y}
C= {v, w, x, y, z}
12. A∩B'
A.) {r, s, t, u, v, w, x, z}
B.) {t, v, x}
C.) {u, w}
D.) {q, s, t, u, v, w, x, y}
The intersection of A and B' is an empty set because there are no elements that are in both A and B'. The correct answer is (option E) the empty set.
What is a set ?
A set is a collection of distinct objects, called elements or members, that are well-defined and unordered.
We can start by finding the complement of set B, which consists of all the elements in U that are not in B:
B' = {r, t, v, x, z}
Then, A ∩ B' consists of all the elements that are in A and also in B':
A ∩ B' = {u, w, y} ∩ {r, t, v, x, z} = { }
Therefore, The intersection of A and B' is an empty set because there are no elements that are in both A and B', the correct answer is (option E) the empty set.
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Make a the subject of relation in a(n-m)=t.
Answer:
the answer is t/(n-m)
Step-by-step explanation:
a(n-m)=t
divide both sides by (n-m) to make a the subject of formula
a(n-m)/(n-m)=t/n-m)
a=t/(n-m)
Which of the following is an irrational number?
Answer:
52/68
Step-by-step explanation:
idr why
Answer: π
Step-by-step explanation:
An irrational number is a number that cannot be shown as a fraction. Based on this, π is an irrational number, since it goes on forever, and can never be written as a perfect fraction.
Gemme makes a conjecture that the sum of an odd integer and itself is always an even interger
Answer:
It's true - all whole numbers that are odd are going to add up to an even integer. An odd integer can be looked at as an even number plus one. For example, 21 would be 20 (the even number) plus one. So the addition of two odd integers is like saying two even numbers were added to each other (in that example, 20 + 20), and then adding the 1+1 that made them odd (which adds up to 2, an even number). So it would be [20 + 20 + (1 + 1)]
the attendant at a parking lot compared the number of hybrid vehicles to the total number of vehicles in the lot over a weekend. the ratios for the three days were equivalent. complete the table. day hybrids total fri. sat. sun.
The table below shows the number of hybrid vehicles and the total number of vehicles in the parking lot for each day of the weekend:
Day Hybrids Total
Fri x y
Sat x y
Sun x y
Since the ratios for the three days were equivalent, this means that the fraction of hybrid vehicles to total vehicles was the same for each day. In other words:
x/y = x/y = x/y
Therefore, the values of x and y must be the same for each day. This means that the number of hybrid vehicles and the total number of vehicles in the parking lot were the same for each day of the weekend.
In conclusion, the table should be completed with the same values of x and y for each day, as shown below:
Day Hybrids Total
Fri x y
Sat x y
Sun x y
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the system2x-5y=1 -3x+7y=-3 is to be solved by elimination of x
the first equation is multiplied by 3
by which number should the second equation be multiplied
9 Is the value of x in linear equation.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.
2x-5y=1 ..............1
-3x+7y=-3 ..................2
Multiply by 3 in (1) and by 2 in (2)
6x - 15y = 3
-6x + 14y = -6
after substtuting
y = 3
put value of y in 1
2*x - 5*3 = 1
2x = 1 + 15
2x = 16
x = 8
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PLEASE I NEED THE AWNSER IN 2 MIN
Match the situation with the correct ratio. Don't forget that you can write a ratio three ways! Also remember the different ways to find equivalent ratios (simplify, rename, table, graph, tape diagram). Make sure you pay attention to the order!! Only enter CAPITAL letters with no spaces or numbers. (Your answer should look something like this WTYUSR)
*
1. 6:15 has a ratio of 2:5
2. 10:40 has a ratio of 1:4
3. 6:28 has a ratio of 3:14 but it would be 12:56 based on the answer choices
4. 15:25 has a ratio of 3:5 but it would be 15:25 based on the answer choices
Which set of measurements would prove that Δ
ABC and Δ
DEF are similar?
Triangle A B C has side A B of length 9, side A C of length 12, and the angle between them 35 degrees. Triangle D E F has no measures given.
A. DE = 15, EF = 20 and m∠D = 35
B. DE = 16, DF = 21 and m∠D = 35
C. DE = 12, DF = 16 and m∠D = 35
D. DE = 18, EF = 24 and m∠D = 70
Therefore , the solution of the given problem of triangle comes out to be DE = 15, EF = 20, and m∠D = 35, so the solution is A.
What exactly is a triangle?A triangle is a polygon because it has two or more additional parts. It has the simple form of a rectangle. A triangle can only be distinguished from a conventional triangle by its three sides, A, B, but not C. So when borders are still not exactly collinear, Euclidean geometry results in a single area as opposed to a cube. Three edges and three angles are the characteristics of triangles.
Here,
We must demonstrate that the respective sides and angles of two triangles are proportional in order to establish their similarity.
We are aware of the lengths of two of the sides and one of the angles in the triangular ABC. The third side's length can be determined using the Law of Cosines:
=> BC² = AB² + AC² - 2ABACcos(35°)
=> 9² + 12² - 2912*cos(35°) = BC²
=> BC ≈ 8.455
The edges of triangle ABC are therefore AB = 9, AC = 12, and BC 8.455.
=> A. DE=15, EF=20, and m=35
The angle measurement is 35 degrees, which corresponds to the angle in the triangular ABC. If the ends are proportionate, we can verify this:
=> DE/AB = 15/9 = 1.67
=> EF/AC = 20/12 ≈ 1.67
This collection of measurements meets the requirements for the triangles to be similar because the ratios are equal.
=> DE = 15, EF = 20, and m∠D = 35, so the solution is A.
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
(2,1)
Step-by-step explanation:
Molly joined an after-school bowling club. The club members go bowling once a week throughout the school year. The bowling scores are recorded for each game so that they can be analyzed at the end of each week. Which of these is a statistical question that can be answered from the data?
Option C requires the examination of the data on bowling scores to find out what Molly's mean score is, and this constitutes a statistical inquiry that can be resolved with the information that has been gathered.
The statistical question that can be answered from the data is: C) What was Molly's average bowling score?
Option A is not a statistical question because it only concerns Molly's personal feeling towards one of her bowling scores.
Option B is a factual question that does not require statistical analysis.
Option D is also a factual question that does not require statistical analysis.
However, option C involves analyzing the bowling scores data to determine Molly's average score. This is a statistical question that can be answered using the collected data.
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Complete question:
Molly joined an after-school bowling club. The club members go bowling once a week throughout the school year. The bowling scores are recorded for each game so that they can be analyzed at the end of each week. Which of these is a statistical question that can be answered from the data?
A) Which bowling score made Molly the proudest?
B) How many times did the bowling club meet?
C) What was Molly's average bowling score?
D) On what day did the bowling club begin?
major axis 12 units long and parallel to the y-axis, minor axis 8 units long, center at (-2,5)
center is located at (-2,5) is:(x+2)^2 / 36 + (y-5)^2 / 64 = 1
The dimensions of the given ellipse are major axis 12 units long and parallel to the y-axis, minor axis 8 units long, and the center is located at (-2,5).Let us find the standard form equation of the ellipse. The standard form equation of an ellipse is given by:(x-h)^2 / a^2 + (y-k)^2 / b^2 = 1Where (h, k) is the center of the ellipse, a is the distance from the center to either the x-axis or the y-axis, and b is the distance from the center to the other axis. Therefore, for the given ellipse, the equation of the ellipse in standard form is:(x+2)^2 / 36 + (y-5)^2 / 64 = 1Thus, the standard form equation of the ellipse whose major axis is 12 units long and parallel to the y-axis, minor axis 8 units long, and center is located at (-2,5) is:(x+2)^2 / 36 + (y-5)^2 / 64 = 1.
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Please help me desperately need help
Answer:
9) 15
10)22
11)25
Step-by-step explanation:
9)
[tex]area=\frac{bh}{2} \\30=\frac{(2x+1)4}{2} \\\\30=4x+2\\\\28=4x\\x=7\\[/tex]
substitute:
=2x+7
=2(7)+1
=15
10)
[tex]area=\frac{bh}{2} \\114=\frac{12(3x-2)}{2} \\114=18x-12\\126=18x\\7=x[/tex]
substitute:
=3x-2
=3(7)+1
=22
11)
[tex]area=h\frac{b1+b2}{2} \\\\69=\frac{4x-2}{2} \\\\69=\frac{24x-12}{2} \\\\69=12x-6\\75=12x\\x=6.25\\\\=4x\\=4(6.25)\\=25[/tex]
x/5+9=11 so I need to get it solved by using 2 Step Equation with Multiplication
Step 1: Isolate x/5 by subtracting 9 from both sides:
x/5 + 9 -9 = 11 -9
x/5 = 2
Step 2: Isolate x by multiplying both sides by 5:
5 · x/5 = 2 · 5
x = 10
The solution is 10.
Find the expected number of flips of a coin, which comes up
heads with probability 0.5,
that are necessary to obtain either h, h, h or t, t, t.
The expected value of X is given byE(X) = 1/p= 1/(1/4) = 4
To obtain either h, h, h or t, t, t, let's consider the sequence h, h, h, t, t, t. The probability of obtaining h, h, h or t, t, t is (1/2)^3 + (1/2)^3 = 1/4. Also, the probability of the first head or tail occurring on the nth flip is (1/2)^n-1. If X denotes the number of flips of a coin required to get h, h, h or t, t, t, then X has a geometric distribution with parameter p = 1/4. Hence, the expected value of X is given byE(X) = 1/p= 1/(1/4) = 4The expected number of flips of a coin, which comes up heads with probability 0.5, that are necessary to obtain either h, h, h or t, t, t is 4.
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What are the solutions to the system of equations below?
7x - 5y = 38
2x+10y = -12
Answer:
Step-by-step explanation:
To solve this system of equations, we can use either substitution or elimination method.
Let's use the elimination method to eliminate y.
Multiplying the first equation by 2 and the second equation by 5, we get:
14x - 10y = 76
10x + 50y = -60
Now, we can add the two equations to eliminate y:
(14x - 10y) + (10x + 50y) = 76 - 60
Simplifying the left side and right side, we get:
24x = 16
Dividing both sides by 24, we get:
x = 2/3
Now that we have the value of x, we can substitute it back into either of the original equations to find y.
Let's substitute it into the first equation:
7x - 5y = 38
7(2/3) - 5y = 38
Simplifying and solving for y, we get:
-5y = 38 - 14/3
-5y = 100/3
y = -20/3
Therefore, the solution to the system of equations is (x, y) = (2/3, -20/3).
Offering brainliest to whoever gives explanation
Answer:
To find the volume of a rectangular prism, we need to know the length, width, and height of the prism. However, the height is not given in the problem, so we cannot calculate the volume.
We can use the surface area and given dimensions to set up an equation to solve for the height. The surface area of a rectangular prism is given by:
SA = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively. We are given that the surface area is 62 square feet, and the width and length are 2 and 5 feet, respectively. Substituting these values into the surface area equation, we get:
62 = 2(2)(5) + 2(5)h + 2(2)h
62 = 20 + 14h
42 = 14h
h = 3
Now that we have found the height of the rectangular prism, we can calculate its volume. The volume of a rectangular prism is given by:
V = lwh
Substituting the given dimensions and calculated height, we get:
V = (5)(2)(3)
V = 30
Therefore, the volume of the rectangular prism is 30 cubic feet.
Step-by-step explanation:
Answer:
[tex]30ft^3[/tex]
Step-by-step explanation:
Surface area of a rectangular prism is A = 2(wl +hl +hw)
Volume, height, and Width is given now we can solve for l, v
[tex]A = 2(wl + hl + hw)\\62ft^2 = 2(2ft * l + 5ft * l + 5ft * 2ft)\\62ft^2 = 2(2lft + 5lft + 10ft^2)\\62ft^2 = 2(7lft + 10ft^2)\\62ft^2 = 14lft + 20ft^2\\14lft = 42ft^2\\l = 3ft[/tex]
Now that we have the length, we can solve for the volume
Volume of a rectangular prism = Length x Width x Height
[tex]V = 3ft * 2ft * 5ft\\ = 30ft^3[/tex]
Hope this helps!
Brainliest is much appreciated!
Write a vertical motion model in the form ()=−++h of , open t close , equals negative 16 , t squared , plus , v sub 0 , t plus , h sub 0 for each situation presented. For each situation, determine how long, in seconds, it takes the thrown object to reach maximum height.
Initial velocity: 32 ft/s; initial height: 20 ft
Answer:
h(t)=−16t²+v
0 t+h 0
for each situation presented. For each situation, determine how long, in seconds, it takes the thrown object to reach maximum height. Initial velocity: 32 ft/s; initial height: 20 ft
Step-by-step explanation:
The late fee at the library is based on the number of days a book is late. Carter paid $1.08 for a book that was 9 days late. If his sister Sydney had a fee of $1.92 for a late book, how many days late was the book?
Answer:
16 days late
Step-by-step explanation:
[tex]1.08 \div 9 = .12[/tex]
So the overdue book charge is 12¢ per day. Letting d be the number of days, we have:
.12d = 1.92
d = 16
algebra 2 assignment three variable HELPPP 13 points
The team scored 2 field goals, 2 safeties, and 4 touchdowns.
Define the term equation?A statement proving the equality of two mathematical expressions is known as an equation. The goal is frequently to ascertain the values of the variables that make the equation true, and it may have one or more variables.
The football team scored 8 times and a total of 38 points.
Let T be the number of touchdowns, F be the number of field goals, and S be the number of safeties.
We know, T = F + S and F + S = 4
Substituting, T = F + S into the equation for total points,
we get, 7T + 3F + 2S = 38
Solving for F and S, we get F = 2 and S = 2.
Therefore, the team scored 2 field goals, 2 safeties, and 4 touchdowns.
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Solve for F and S then get F = 2 and S = 2.
The team scored 4 touchdowns, 2 field goals, and 2 safeties.
How to calculate DF score?The football group scored 8 times, totaling 38 points.
Let,
T is the no.of touchdowns,
F is the no.of field goals, and
S is the no.of safeties.
Touchdown: The ball is in possession of a runner who has moved from the field of play into the end zone and is on, above, or behind the plane of the opposing goal line (extended).
Field Goal: a three-point goal in football obtained by kicking the ball over the crossbar during normal play.
Safeties: NFL defences can score a safety, worth two points, by tackling the offensive player with the ball behind his own goal line or forcing him to run or throw the ball out of bounds behind his own goal line.
We know that,
T = F + S and
F + S = 4
For total points, put T = F + S into the equation.
We get,
7T + 3F + 2S = 38
Solve for F and S,
we get,
F = 2 and S = 2.
As a result, the team tallied 2 field goals, 2 safeties, and 4 touchdowns.
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Part a) (6 marks) Calculate the value of the test statistic, set up the rejection region, undertaking hypothesis test and interpret the result. H0: μ=20 H1: μ≠20 Given that σ=5, n=25, =21, α=0.05. X Part b) (8 marks) A statistics practitioner is in the process of testing to determine whether is enough evidence to infer that the population mean is different from 180. She calculated the mean and standard deviation of a sample of 200 observations as X=175 and s=22. i) Calculate the value of the test statistic of the test required to determine whether. ii) there is enough evidence to infer at the 5% significance level that the population means is different from 180. ii) Repeat the part i) with the population standard deviation to be 22.
When answering questions on Brainly, you should always be factually accurate, professional, and friendly, be concise and do not provide extraneous amounts of detail, provide a step-by-step explanation in your answer, and use the following terms in your answer, "statistic", "X=175 and s=22", "standard deviation".Part a)Hypothesis: H0: μ=20, H1: μ≠20The sample size n=25Given that α=0.05σ=5The X (sample mean) is 21.The test statistic is given by,\[Z = \frac{{\bar X - \mu }}{{\frac{\sigma }{{\sqrt n }}}} = \frac{{21 - 20}}{{\frac{5}{{\sqrt {25} }}}} = 2\]The rejection region is obtained by finding the Z value that will cut off 2.5% of the area in each tail of the standard normal distribution curve at 0.025.The rejection region is Z< -1.96 and Z > +1.96.Interpretation: Since the calculated Z value 2 lies outside the rejection region, reject the null hypothesis H0 and conclude that there is sufficient evidence to support the alternative hypothesis H1.Part b)Given,Sample size n=200, X=175 and s=22Null hypothesis H0: µ=180Alternative hypothesis H1: µ ≠ 180.Level of significance α=0.05i) The test statistic is given by,\[Z = \frac{{\bar X - \mu }}{{\frac{\sigma }{{\sqrt n }}}} = \frac{{175 - 180}}{{\frac{22}{{\sqrt {200} }}}} = - 5.68\]ii) Since the calculated Z value (-5.68) is less than -1.96, it falls in the rejection region. Reject the null hypothesis H0 and conclude that there is enough evidence to infer at the 5% significance level that the population mean is different from 180.When the population standard deviation is 22, the test statistic is,\[Z = \frac{{\bar X - \mu }}{{\frac{\sigma }{{\sqrt n }}}} = \frac{{175 - 180}}{{\frac{22}{{\sqrt {200} }}}} = - 3.37\]Since the calculated Z value (-3.37) is less than -1.96, it falls in the rejection region. Reject the null hypothesis H0 and conclude that there is enough evidence to infer at the 5% significance level that the population mean is different from 180.
Which ordered pair is the solution to tue system if equations below when using matrix tool 3x+y=17 2x-y=8
The solution of the system of equations is (4, 5).
How to solve the system of equations?Here we have the system of equations:
3x + y = 17
2x - y = 8
We would want tosolve this using matrices, then we need to solve:
[tex]\left[\begin{array}{ccc}3&1\\2&-1\end{array}\right] *\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}17\\8\end{array}\right][/tex]
If we add the first and second equations (or the rows of the first matrix) then we will get:
[tex]\left[\begin{array}{ccc}3&1\\5&0\end{array}\right] *\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}17\\25\end{array}\right][/tex]
Then we have:
5y = 25
y = 25/5
y = 5
And now that we know the value of y we can input it in any of the equations to find x.
3x + y = 17
3x + 5 = 17
3x = 17 - 5 = 12
x = 12/3 = 4
The solution is (4, 5).
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What does constant time mean? Please hurry! :)
Answer:
When the ratio of the output to the input remains constant at every given point along the function, the rate of change is said to be constant. The slope is another name for the constant rate of change.
Step-by-step explanation:
The constant would be 2.
In September 1998 the population of the country of West Goma in millions was modeled by f(x)=16.9e0.001x. At the same time the population of East Goma in millions was modeled by g(x)=13.8e0.019x. In both formulas x is the year, where x=0 corresponds to September 1998. Assuming these trends continue, estimate the year when the population of West Goma will equal the population of East Goma.A. 2009B. 1987C. 2008D. 11
In September 1998, the population of the country of West Goma in millions was modeled by f(x)=16.9e0.001x. The population of East Goma in millions was modeled by g(x)=13.8e0.019x. In both formulas, x is the year, where x=0 corresponds to September 1998.
To find the year when the population of West Goma will equal the population of East Goma, we will use the following method:
$$f(x)=g(x)$$
$$16.9e^{0.001x} = 13.8e^{0.019x}$$
Taking natural logarithms of both sides we have,
$$\ln(16.9) + 0.001x = \ln(13.8) + 0.019x$$
$$0.018x = \ln(16.9) - \ln(13.8)$$
$$x = \frac{1}{0.018}(\ln(16.9) - \ln(13.8))$$
$x \approx 41.06$, which corresponds to September 2039.
Therefore, the year when the population of West Goma will equal the population of East Goma is September 2039. Option E. 2039 is the correct answer.
Note: The growth rate of West Goma is smaller than that of East Goma, hence it will take a longer time to equalize.
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You borrow $2000 from a friend and promise to pay back $3000 in two years. What simple interest rate will you
pay?
someone please help me thank u
Answer:
C, E
Step-by-step explanation:
You want to identify the true statements about the end behavior, symmetry, domain, and range of g(x) = -5x² and f(x) = 5x-10.
End behaviorThe function g(x) is of even degree (the exponent is 2), and the function f(x) is of odd degree (the exponent is 1). An even-degree function cannot have the same end behavior as an odd-degree function.
RangeThe range of any odd-degree polynomial function is (-∞, +∞).
Any even-degree polynomial function will have a global maximum or minimum so cannot have the same range. The range of g(x) is (-∞, 0].
DomainThe domain of any polynomial function is "all real numbers." Both f and g have the same domain.
SymmetryAn even-degree function may have an axis of symmetry. An odd-degree function cannot be symmetrical about any line. The functions cannot have the same symmetry.
Points of intersectionTwo polynomial functions may have a number of points of intersection equal to the highest degree. That means a degree-1 and a degree-2 function may have up to 2 points of intersection. These two functions intersect twice, as the graph in the attachment shows.
Suppose that you deposit $19,000 in an investment account that averages 4.1% growth annually. If the account managers charge a fee of 1% annually, how much money will you have at the end of 5 years? Round your answer to the nearest dollar.
The final amount in the investment account will be:$23,055.09 Hence, the final amount of money will be $23,055 at the end of 5 years.
We need to find the amount of money you will have in the investment account at the end of 5 years if you deposit $19,000 in an investment account that averages 4.1% growth annually and if the account managers charge a fee of 1% annually.The formula to find the final amount of investment with annual compounding is given by:P (1 + r/n)^(n*t)P = $19,000r = 4.1% - 1% = 3.1% (as the account managers charge a fee of 1% annually)r = 0.031n = 1t = 5 Therefore, the final amount in the investment account will be:$23,055.09 Hence, the final amount of money will be $23,055 at the end of 5 years.
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Incorrect Your answer is incorrect. Find the midpoint M of the line segment joining the points C = (0, 8) and D = (-8, -8). D M-D = 00 X
The midpoint of the line segment joining the points C and D is M = (-4, 0).
How to calculate the midpoint MThe coordinates of the midpoint M of the line segment joining the points C = (0, 8) and D = (-8, -8) can be found using the midpoint formula:
M = ((x1 + x2)/2, (y1 + y2)/2)
So, for C = (0, 8) and D = (-8, -8), we have:
M = ((0 + (-8))/2, (8 + (-8))/2)
M = (-4, 0)
Therefore, the midpoint of the line segment joining the points C and D is M = (-4, 0).
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anyone know this , i need help again lol
Check the picture below.