Answer:
The exact value of x so that the greatest possible amount of light is emitted is 8.96ft.
What is the perimeter of a semicircle?
The perimeter of a semicircle is half that of a circle, that is [tex]\pi r[/tex], where r is the radius of the circle.
Step-by-step explanation:
Given the width of the rectangle is x, let the height of the rectangle be y.
The radius of the semicircle is x/2.
The perimeter of the window is equal to [tex]2y+x+\pi \frac{x}{2} =32[/tex].
The area of the window is [tex]xy+\frac{1}{2}(\pi )(\frac{x}{2})^2=xy+\frac{\pi x^2}{8}[/tex].
We can insert into the formula for the area to obtain the area in terms of only x by solving the equation for the perimeter of y in terms of x.
[tex]2y=32-(1+\frac{\pi }{2} )x=32-(\frac{2+\pi }{2} )x\\y=16-(\frac{2+\pi }{4} )x[/tex].
Now the area of the window in terms of only x is:
Area=[tex]16x-(\frac{2+\pi }{4} )x^2+\frac{\pi x^2}{8}[/tex].
Since it is given in the question that maximum light should be admiitted, we will differentiate the Area and set it to 0.
[tex]16-2(\frac{2+\pi }{4} )x+\frac{\pi x}{4}=0\\ 16=x(1+\frac{\pi }{4})\\ x=\frac{16}{1+\frac{\pi }{4}} \\x=8.96ft[/tex].
Therefore the exact value of x is 8.96ft.
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give two examples of functions from z to z that are one-to-one but not onto. 21. give two examples of functions from z to z that are onto but not one-to-one.
two examples of one-to-one functions from z to z that are not onto
f(x) = x + 4 and f(x) = -x
f(x) = x2 and f(x) = 2x + 1
Example 1:
One-to-one but not onto:
Take the equation f(x) = x + 4 into consideration.This function takes in any integers x and adds 4 to it, resulting in a new integer.
For example, if the input is 7, the output will be 11.
This function is one-to-one because for every input x, there is only one output y. For example, if the input is 7, there is only one output 11.
However, this function is not onto because there are some outputs that cannot be reached. For example, if the input is 0, the output is 4, but there is no input that can give an output of 5.
Example 2:
Onto but not one-to-one:
Let's consider the function f(x) = 2x + 1. This function takes in any integer x and multiplies it by 2, then adds 1 to the result.
For example, if the input is 7, the output will be 15.
This function is onto because for every output y, there is at least one input x that can give the output
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suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of per hour. suppose also that a sample culture of bacteria is obtained from this population. find the size of the sample after two hours. round your answer to the nearest integer.
The size of the sample after two hours would be 682. This is calculated using the formula N(t) = N(0) * e^(rt), where N(t) is the number of bacteria after t hours, N(0) is the initial number of bacteria, r is the growth rate parameter (in this case 0.5 per hour) and t is 2 hours. Therefore, N(2) = 682.
an object at the origin at time has velocity measured in meters per second, when, if ever, does the object return to the origin? t/40 . see example 5 on page 239 of the textbook for a similar problem. hint: you are looking for the time such that .
For the given velocity function , the object will not return to the origin .
In the question ,
it is given that ,
the velocity function is v(t) = { t/35 , 0 ≤ t ≤ 70
{ 2 , 70 ≤ t ≤ 175
{ 7 - t/35 , 175 < t .
So , For t ≤ 175 , velocity is positive ,
So , [tex]\int\limits^T_0 {v(t) } \, dt[/tex] = [tex]\int\limits^{70}_0 {t/35 } \, dt[/tex] + [tex]\int\limits^{175}_{70} {2 } \, dt[/tex] + [tex]\int\limits^{T}_{175} {(7 - t/35) } \, dt[/tex]
On integrating ,
we get ,
x(T) = [t²/70]⁷⁰₀ + [2t]¹⁷⁵₇₀ + [7t - t/70[tex]]^{T} _{175}[/tex]
x(T) = (70 - 0) + (350 - 0) + (7T - T²/70) - (1225 - 875/2)
x(T) = 420 + 7T - T²/20 - 1575/2
x(T) = -T²/20 + 7T - 735/2
x(T) = ( -T² + 140T - 7350)/20
For the object to return to the origin , x(T) = 0
So , (-T² + 140T - 7350)/20 = 0
T² - 140T + 7350 = 0
Therefore , Discriminant (D) = b² - 4ac
= (-140)² - 4(1)(7350)
= 19600 - 29400
= -9800 < 0 .
So , the root is imaginary , hence at no value of T , the object will not return to the origin for the given information .
Therefore , the object will not return to the origin .
The given question is incomplete , the complete question is
An object at the origin at time has velocity
v(t) = { t/35 , 0 ≤ t ≤ 70
{ 2 , 70 ≤ t ≤ 175
{ 7 - t/35 , 175 < t .
measured in meters per second, when, if ever, does the object return to the origin ?
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differentiate of the following w.r.t.
give me this answer i mark u brainlist
Answer:
[tex]\frac{dy}{dx}=\frac{4}{3}x^{1/3}+e^x +\cos x[/tex]
Step-by-step explanation:
[tex]\frac{d}{dx} x^{4/3}=\frac{4}{3}x^{1/3} \\ \\ \frac{d}{dx} e^x=e^x \\ \\ \frac{d}{dx} \sin x=\cos x \\ \\ \therefore \frac{dy}{dx}=\frac{4}{3}x^{1/3}+e^x +\cos x[/tex]
these statements are the congruence statements for right triangles: ha, ll, la, and hl. you will need to use them for congruence statements. match the abbreviation to its description. for right triangles: 1. a hypotenuse and a leg define congruence. hl 2. a hypotenuse and an acute angle define congruence. la 3. a leg and an acute angle define congruence. ll 4. two legs define congruence. ha
Please solve these equations! Ill give brainiest!
Answer:
see explanation
Step-by-step explanation:
1
[tex]\frac{bh}{2}[/tex] = A ( multiply both sides by 2 to clear the fraction )
bh = 2A ( divide both sides by h )
b = [tex]\frac{2A}{h}[/tex]
2
2l + 2w = P ( subtract 2l from both sides )
2w = P - 2l ( divide both sides by 2 )
w = [tex]\frac{P-2l}{2}[/tex]
3
C = 2πd ( isolate d by dividing both sides by 2π )
[tex]\frac{C}{2\pi }[/tex] = d
Help me thank u with these questions I appreciate it
18. not a function
19. not a function
20. the left side graph is a function
18. Any relation to be a function, any x value should have only one y value
this is not a function because when x=7 , y= 9 and 12 (two y values for one x value)
19. x=-1 has two y values
and x=1 also has two y values
20. here, you can use the vertical line test.
the left graph passes the vertical line test which is a function because any vertical line drawn intersects the curve in only 1 point, but the right graph, the vertical line intersects the curve in 2 points, which is not a function.
the ceo of a cable company claims that the mean wait time for callers at the company's customer service center is no more than 7 minutes. a random sample of 36 customers who called the company's customer service center produces the following data:
To test the CEO's claim about the mean wait time we need to conduct a hypothesis test.
The null hypothesis is that the mean wait time is no more than 7 minutes, which we can represent as H0: μ ≤ 7. The alternative hypothesis is that the mean wait time is greater than 7 minutes, which we can represent as Ha: μ > 7. We can use a one-tailed t-test for this situation, with a significance level of alpha = 0.05.
To perform the t-test, we need to calculate the sample mean, sample standard deviation, and the t-statistic. The sample mean is the sum of the wait times divided by the sample size, which is 36 in this case. The sample standard deviation is a measure of the dispersion of the data. The t-statistic is calculated using the sample mean, sample standard deviation, and the hypothesized mean wait time of 7 minutes.
Once we have calculated the t-statistic, we can compare it to the critical value from the t-distribution table to determine the p-value. If the p-value is less than alpha, we can reject the null hypothesis and conclude that the mean wait time is indeed greater than 7 minutes. If the p-value is greater than alpha, we cannot reject the null hypothesis and must conclude that the mean wait time is no more than 7 minutes.
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give an example of a nonabelian group g with the property that every subgroup h of g is a normal subgroup.
Hamiltonian group is an example of a nonabelian group g with the property that every subgroup h of g is a normal subgroup.
To prove that h be a subgroup of g. and suppose h is the only subgroup of g of order(h) h is normal in g is that it is proven by homomorphism .
This is a small contribution, however in reaction to a remark above, you may additionally clear up this with out the use of any homomorphism properties. Assume the subgroup H has order n and select out g∈g.
Since H has order n. The above holds for all h∈H, so the subgroup gHg−1 has order n, so it's miles identical to H through assumption. Then each h∈H has a few h∈H such that ghg−1=h′, implying gh=h′g, so gH=H
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The graph of a linear function is shown on the grid.
#6. Find the slope:
#7. Find the y-intercept:
#8. Write the equation in slope-intercept form:
The slope m = -5/4 , y - intercept is 5 and the equation in slope - intercept form is y = (-5/4)x + 5 .
Given :
The graph of a linear function is shown on the grid.
From the graph :
Take two points ( 0 , 5 ) and ( 4 , 0 )
slope m = 0 - 5 / 4 - 0
= -5 / 4
we know that ,
slope intercept form is y = mx + b
substitute m and ( 0 , 5 )
5 = -5 / 4 ( 0 ) + b
5 = 0 + b
b = 5 ( y - intercept )
substitute b and m value
y = (-5/4)x + 5
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A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:
Salary Education
40 4
73 1
99 7
57 1
83 8
76 4
109 6
49 0
31 4
32 4
91 2
40 4
65 6
71 2
166 5
61 0
88 1
59 4
132 9
25 0
a. Find the sample regression equation for the model: Salary = β0 + β1Education + ε. (Round answers to 3 decimal places.)
Salaryˆ= ? + ? Education
b. Interpret the coefficient for Education.
As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,590.
As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $6,223.
As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $6,223.
As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590.
c. What is the predicted salary for an individual who completed 5 years of higher education? (Round answer to the nearest whole number.)
Salaryˆ $
The linear regression equation between educational attainment (in years of higher education) and annual salary (in $1,000s) be
Salary = 84 - 11×Education
Given, a social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals.
we have to find the sample regression equation for the given model
Salary = β0 + β1Education
On using the different values of salary and education, we get
for salary = 40 and education = 4
40 = β0 + 4β1
for salary = 73 and education = 1
73 = β0 + β1
On subtracting both the equations, we get
33 = -3β1
β1 = -11
On substituting the value of β1, we get
40 = β0 + 4(-11)
β0 = 40 + 44
β0 = 84
So, the regression equation be
Salary = 84 - 11×Education
Hence, the regression equation be
Salary = 84 - 11×Education
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Select the number that matches the power of ten. 105 = 10-3 =
Help quick!! One angle measures 24°, and another angle measures (7d-4)°. If the angles are complementary what is the value of d?
d=80
d=17
d = 10
d=3
Answer:
d = 10°
Step-by-step explanation:
7d - 4 + 24 = 90
7d + 20 = 90
7d = 90 - 20
7d = 70
7/7 d = 70/7
d = 10
Deloitte employment survey asked sample of human resource executives how their company planned to change its workforce over the next 12 months_ categorical response variable showed three options: The company plans to hire and add to the number of employees the company plans no change in the number of emplovees_ or the company plans to lay off and reduce the number of emplovees_ Another categorical variable indicated if the company was private public Sample data for 168 companies are summarized as follows Company Employment Plan Private Public Add Employees No Change Lay Off Employees Conduct test of independence to determine if the employment plan for the next 12 months is independent of the type of company At a 05 level of significance_ Compute the value of the x? test statistic (to 2 decimals). 8.73 The p-value petween 01 and .025 What is your conclusion? Conclude the employment plan not independent of the type of company. Discuss any differences in the employment plans for private and public companies Over the next 12 months_ Private companies are more likely to add employees Public companies are more likely to lay off employees_ of private companies plan on adding employees_ 34.9 % of public companies plan on adding off employees. (to decimal)
As per the chi square test, the variable are dependent to each other.
What is meant by chi-square test?
In math, the chi square test refer a statistical test used to compare observed results with expected results.
From the table in the question; we can see the changes in employees adding, shedding, or not changing their staffing.
Converting the table to chi- squared using the relation.
Here the observed frequency is = 44 and the expected frequency is = 34.8
And the Number Change 0.1421 0.0079 0.15
=> Lay Off 4.8286 2.4083 7.2369
=> Total = 14.657
Therefore, the total chi-square = 14.657;
In order to find the value for p; we need to determine the degree of freedom
=> df = (2-1)(3-1)
Then the result to a degree of freedom of 2
Here from the chi square chart at the chi-square is 14.657 and degree of freedom is 2 ; the p value is between 0.1 and 0.005. Since this makes p-value less than 0.05.
Therefore, the variables are dependent.
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The Variance Inflationary Factor (VIF) measures the: a. correlation of the X variables with the Y variable. b. correlation of the X variables with each other. c. standard deviation of the slope. d. contribution of each X variable with the Y variable after all other X variables are included in the model. e. both a and b.
The X variables have an overall correlation of 0. VIF, or Variance Inflationary Factor, measures the
How much of an inflation variance factor is there?Regression analysis's level of multicollinearity is gauged by a variance inflation factor, or VIF. When several independent variables in some kind of a model with multiple regression correlate with one another, this is known as multicollinearity. The regression findings may be significantly impacted by this.
How high of a VIF is that?Greater correlation between the variable and other variables is indicated by a higher value. With values of Ten or more being considered very high, values greater than 4 or 5 are occasionally considered to be moderate to high.
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Question 11
Toby found a $52 wallet on the clearance rack for 60% off. If sales tax is 6.25%, how much will he pay in total?
A. $ 22.10
B. $ 23.75
C. $ 28.50
D. $ 33.15
A No answer provided
a. A
b. B
c. C
d. D
Question 10
Angela took 56 minutes to take her history test. Bryan took 70% of the time that it took Angela to complete the test. How long did it take Bryan to take his history test?
A. 36.4 minutes
B. 38.5 minutes
C. 39.2 minutes
D. 41.8 minutes
A. No answer provided
a. A
b. B
c. C
d. D
Question 9
What is 95% of 60 ?
(9) The value of 95% of 60 is 57 .
(10) Bryan took the History test in 39.2 minutes ,
(11) Toby will pay $ 22.10 for the wallet .
In the question
[Question 9] ,
we have to find the value of 95% of 60
means⇒ 95% of 60
= 0.95 × 60
= 57
[Question 10] ,
time taken by Angel for the history test = 56 minutes
time taken by Bryan for history test is = 70% of 56
= 0.70 × 56
= 39.2 minutes .
[Question 11] ,
the price of the wallet that Toby found is = $52
discount = 60%
So , the price become = 52 - 60% of 52
= 52 - 31.2
= 20.8
the sales tax is = 6.25%
So , the final amount will be = 20.8 + 6.25% of 20.8
= 20.8 + 1.3
= 22.10
Therefore , (9) the value of 95% of 60 = 57 ,
(10) the correct option is (c)39.2 minutes ,
(11) the correct option is (a) $22.10 .
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for general , the solution . act on this equation with to confirm this is the solution to the original differential equation. remember that acts only on , not . g
To confirm that the solution is correct, we can use the method of substitution. Substitute the solution back into the original differential equation, and if the equation is satisfied, then the solution is correct.
To confirm that the proposed solution is indeed a valid solution to the original equation, we can use the method of substitution. This involves substituting the proposed solution into the original equation and verifying that it satisfies the equation. If the equation holds, then the solution is correct. This method is useful for verifying the correctness of a proposed solution. It can also be used to determine if a proposed solution is the only solution, or if there are other solutions to the equation.
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In September 2020, the University Senate passed a resolution to make the belted kingfisher (a bird with blue, white, and orange markings) the official mascot of the University. One might assume that senators voted as such because a majority of their constituents (more than 50%) are in favor of the resolution. You conduct a random sample of 200 students and find that 94 are in favor of the resolution, 76 are opposed, and 30 do not care at all. (a) Construct a 90% confidence interval for p. (a) [5 pts] (b) Based on your sample, is it plausible within 90% confidence that a majority of students support the resolution: yes or no? Explain the reason for your choice (in one sentence). (b) [5 pts].
On solving the provided question, as Given, n = 200, x = 94, [tex]p^{'} = x/n 94/200 = 0.47[/tex] and the answer is 0.91 < p < 0.53
What is equation?A formula is a statement that the values of two expressions are equal. The formula essentially says that two things are equal. An equals sign or '=' indicates that. 8+2=12-2 is an example equation. According to the above formula, the left side of the formula is equal to the right side. So the equation is the statement "this is equal to that".
Given, n = 200, x = 94, [tex]p^{'} = x/n 94/200 = 0.47[/tex]
[tex]1-\alpha = 0.9\\\alpha =1.\\[/tex]
confidences interval for p :-
(0.47 - 1.695 X [tex]\sqrt{\frac{0.47(1 - 0.47)}{200} }[/tex] , 0.47 + 1.695 X [tex]\sqrt{\frac{0.47(1 - 0.47)}{200} }[/tex])
(0.91 , 0.53 )
0.91 < p < 0.53
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ASAP!! Which one is not an irrational number? I believe it’s A but I just want to double check.
Answer:
Step-by-step explanation:
Je ne sais pas désolé mais si j'obtiens la réponse, je vous le dirai!
Let X and Y be the continuous random variables with the joint probability density function io (2y + 3x2) ) ={th (2) = 0 < x < 2,0 1/5, 1/5 < X < 2/5); (c) P(X2 + 2Y? < 1, X2 +Y? > 1/2, X/4 SY < 2X); (d) Plot the regions Ri = {(x,y) : x2 + y2 = 1,x+y > 1/5,1/5 < x < 2/5} and R2 = {(x, y) : x2 + 2y2 < 1,x2 + y2 > 1, x/2 < y < 2x}; (e) Cov(X, Y); (f) Cov(ex, sin(Y)). - > 2
Let X and Y be random variables that are independent, and their common pdf is f(x) = e x, (x > 0). Find the joint pdf of U = X/(X + Y), V = X + Y. Then, at that point, |J| = v(1 − u) + uv = v(> 0).
How do you determine the joint probability distribution of a continuous random variable?Keep in mind that 0 u 1, 0 v. The joint probability density function (joint pdf) of the continuous random variables X and Y is a piecewise continuous function that satisfies the following if they are defined on the same sample space S. P(Xa and Yb)=baf(x,y)dxdy = F(a,b).
What is the continuous random variable's probability density function?A continuous random variable's probability density function, or PDF, indicates the relative likelihood of any continuum outcome occurring. For a continuous random variable, every outcome has a probability of zero, in contrast to discrete random variables.
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Tipton Tile has seen an increase in tile sales over the last few weeks. They sold 4,212 square feet of tile to 36 customers last week. If they are expecting between 51 and 59 people to buy tile this week, about how many square feet of tile can they expect to sell?
Tipton Tile expected to sell between, 5967 and 6902 square feet of tiles.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given,
Tipton Tile has seen an increase in tile sales over the last few weeks.
They sold 4,212 square feet of tile to 36 customers last week.
That means,
4212 / 36 = 117 square feet of tiles per person.
If they are expecting between 51 and 59 people to buy tile this week.
To find the number of square feet of tiles:
For 51 people,
117 x 51 = 5967 square feet of tiles.
And for 59 people,
117 x 59 = 6903 square feet of tiles.
Therefore, They expected to sell between, 5967 and 6902 square feet of tiles.
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The ultimate goal of muted group theory is to:A. Help men understand the perspective of women. B. Elect women to major leadership positions in Western democracies. C. Change linguistic systems that make it more difficult for women to be heard. D. Predict how women and men will communicate across gender lines.C. Change linguistic systems that make it more difficult for women to be heard.(The feminist dictionary is one attempt to create an alternative vocabulary.)
The question mentions muted group theory, which is a kind of Communication Theory. The answer is option C, which changes linguistic systems that make it more difficult for women to be heard.
A verbal system is a language taken as a combination of its corridor. A verbal system can also relate to a set of choices that druggies of language have in contriving rulings.
Muted group proposition is the introductory idea, articulated by anthropologists Ardener and Ardener, that in every society there are artistic groups who are traditionally muted — given lower access than members of the dominant groups to public converse and to having their individual and community enterprises heard.
Muted group proposition is the introductory idea, that in every society there are artistic groups who are traditionally muted — given lower access than members of the dominant groups to public converse and to having their individual and community enterprises heard.
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a 13 foot ladder is leaning against the side of a house when its base starts to slide away. by the time the base is 12 feet from the house, the base is moving at a rate of 5 feet per second.
If the base of the ladder is moving at 5 ft/s , then the speed of top of the ladder is 12ft/s .
Pythagoras Theorem states that the relation between the square of the longest side is equal to the squares of the other two sides .
the length of the ladder (L) = 13 ft ;
the rate of movement of the base (dx/dt) = 5 m/s ;
By Pythagoras Theorem ,
13 = x + y ....eqn(1)
So , y = √(169 - x)
putting x = 12 , we get ;
y = √(169 - 144) = 5 ft ;
Differentiating eqn(1) , w.r.t. "x" ,
we get ;
0 = 2x(dx/dt) + 2y(dy/dt)
So , dy/dt = (-x/y)(dx/dt)
putting the values ,
we get ;
dy/dt = -12 ft/s .
Therefore , the ladder is sliding down the wall at 12 ft/s .
The given question is incomplete , the complete question is
A 13 foot ladder is leaning against the house when its base starts to slide away. By the time it is 12 feet from the house, the base is moving at the rate of 5 ft/sec.
How fast is the top of the ladder sliding down the wall at that moment ?
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A fair coin is flipped 10 times and the number of heads is counted. The procedure of 10 coin flips is repeated 100 times and the results are place in a frequency table. Which of the frequency tables below is most likely to contain the results from these 100 trials?chart shows number of heads 0-10 and then the following frequencies in order....
0/0/6/9/22/24/18/12/7/2/0 (REMEMBER two zeros at top and just 1 zero at end)
This table illustrates how many trials out of 100 resulted in each number of heads out of ten flips. Because it precisely depicts the possibility of each occurrence, this frequency table is the most likely to include the outcomes of the 100 trials.
The likelihood of receiving any number of heads out of ten flips is the same in a fair coin flip, therefore the table should show a fairly uniform distribution of trials across each number of heads. Overall, the frequency table most likely to capture the outcomes of the 100 trials has the number of heads out of 10 flips as rows and the number of trials out of 100 as columns.
This table may be used to precisely depict the data as well as determine the likelihood of each occurrence.
what is meant by frequancy table?
A frequency table is a way to organize and summarize data in a systematic way. It lists all of the different values (or categories) that appear in a dataset, along with the number of times each value appears. The goal of creating a frequency table is to get a better understanding of the data by seeing how frequently different values occur.
For example, let's say you have a dataset that contains the ages of a group of people. You could create a frequency table to see how many people are in each age range. The table might look something like this:
Age Range Frequency
0-9 5
10-19 8
20-29 12
30-39 10
40-49 7
50-59 4
60-69 3
70-79 2
80-89 1
90+ 1
In this frequency table, you can see that the most common age range is 20-29, with 12 people in that range. You can also see that there are very few people over the age of 80. This type of table can be helpful for understanding the distribution of values in a dataset and identifying patterns or trends.
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. in triangle 4abc, m is the midpoint of the side ab and n is the midpoint of the side ac. find the length of the segment mn if ab =18, bc= 10 and ac= 20
The length of the segment of the MN is 10 units, by using the midpoint formula and distance formula.
Distance FormulaThe algebraic phrase is known as the distance formula, which provides the distances between two places in terms of their coordinates (see coordinate system). The distance formulas for points in rectangular coordinates in two- and three-dimensional Euclidean space are based on the Pythagorean theorem.
Since M is the midpoint of side AB and N is the midpoint of side AC, we can use the midpoint formula to find the coordinates of points M and N.
Midpoint Formula: (x₁ + x₂)/2, (y₁ + y₂)/2
For M:
(A x + B x)/2, (A y + B y)/2
= (18 + 0)/2, (0 + 0)/2
= 9, 0
For N:
(A x + C x)/2, (A y + C y)/2
= (18 + 20)/2, (0 + 0)/2
= 19, 0
Step 4: Now that we have the coordinates of M and N, we can use the distance formula to find the length of the segment MN.
Distance Formula: √((x₂ - x₁)² + (y₂ - y₁)²)
For MN:
√((19 - 9)² + (0 - 0)²)
= √(100)
= 10
Therefore, the length of the segment MN is 10 units.
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I NEED SOME CORRECT ANSWER PLEASE WITH SOLVING!!
A. You need to buy 3eggs cost 8.00, 2 hotdogs cost 10.00 and 3bread cost 5.00 each. How much money you will need to take to the sari-sari store B. Evaluate the following polynomial 4x² + 2x - 3
(i need a reaal math genius please solve it with the right answer and right solving please i'm begging you
89 is the money you will need to take to the sari-sari store and x=-1±√13/4 is the value of polynomial 4x² + 2x - 3.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that need to buy 3 eggs cost 8.00
2 hotdogs cost 10.00
3 bread cost 5.00 each.
We need to find the money you will need to take to the sari-sari store.
3(8)+2(10)+3(15)
24+20+45
89
The given polynomial is 4x² + 2x - 3=0
a=4, b=2 and c=-3
x=-b±√b²-4ac/2a
x=-2±√4-4(4)(-3)/8
x=-1±√13/4
Hence, 89 is the money you will need to take to the sari-sari store and x=-1±√13/4 is the value of polynomial 4x² + 2x - 3.
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Please help define if these triangles are congruent or not and write a statement.
Answer:
11 - not enough information
12 - yes, Angle-Angle-Side (AAS)
13 - yes, Side-Angle-Side (SAS)
14 - yes, Angle-Side-Angle (ASA)
15 - yes, ASA
16 - yes, Side-Side-Side (SSS)
17 - yes, ASA
18 - yes, SSS
19 - no (different from "not enough information")
20 - yes, AAS
Step-by-step explanation:
11 - 1 pair of congruent sides is given; can conclude 1 pair of angles is ≅ by vertical angles; need 3 parts to prove congruence
12 - 1 pair of sides and a pair of angles given ≅; can show vertical angles ≅
13 - the side that's shared by the two triangles is the second ≅ side
14 - in addition to what's given, can show vertical angles ≅
15 - in addition to what's given, can show vertical angles ≅
16 - all given
17 - in addition to what's given, can show shared side ≅
18 - ..., shared side
19 - the congruent parts are not in the same order on each triangle
20 - all given
a. compute the sample mean and sample standard deviation for private and public colleges. round your answers to two decimal places.
The sample mean is = 6.98, the standard deviation is = 4.53 (2) The pint estimate difference is = 20.2 (3) The confidence interval limits are $ 15943.6 and $24456.4
a)
Private Universities
Sample median: 42,500 dollars
Mean = (Σx)/N
where N = Sample size
Σx = sum of all variables
Private colleges
Σx = (52.8+43.2+45.0+33.3+44.0+30.6+45.8+37.8+50.5+42.0) = 425
N = 10
Mean = 425/10 = 42.5 thousand dollars
Standard deviation = S1 = √[Σ(x - xbar)²/N]
Σ(x - xbar)² = (52.8-42.5)² + (43.2-42.5)²
+ (45.0-42.5)² + (33.3-42.5)²
+ (44.0-42.5)² + (30.6-42.5)² + (45.8-42.5)² + (37.8-42.5)² + (50.5-42.5)² + (42.0-42.5)² = 438.56
N = 10
Standard deviation = √[Σ(x - xbar)²/N]
Standard deviation = √(438.56/10) = 6.62 thousand dollars
S1 or the standard deviation equals $6.62k.
b)
The sample means the difference in both circumstances is 42.5 minus 22.3, or 20.2 thousand dollars.
Going to a private college often costs 20.2 thousand dollars more than going to a public institution on average.
c)
A sample distribution's 95% confidence interval for the price difference between private and public colleges is provided as
(15.0, 25.4) dollars in thousands.
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Please help! Confused if the answer is B or D???
Answer:
Step-by-step explanation:
its b
A communication tower (the side CB) is located at the top (the point C) of a steep hill. The angle of inclination of the hill is 58 degrees. A guy wire is to be attached to the top (the point B) of the tower and to the ground (the point A), 104 m downhill from the base of the tower (the side AC). The angle ∠BAC
is 12 degrees.
Find the length of cable (the side AB) required for the guy wire. Your answer is _____m
Using the sine ratio with the angle of depression, the length of the wire is 122.63m
Angle of DepressionThe angle of depression is formed when the observer is higher than the object he/she is looking at. When an observer looks at an object that is situated at a distance lower than the observer, an angle is formed below the horizontal line drawn with the level of the eye of the observer and line joining object with the observer’s eye. Whereas the angle of elevation is the angle formed if a person stands on the ground and looks on the object kept above the ground at a height above the height of the person. This is the basic difference between the two angles. Both the angles are calculated by using the concept of trigonometry.
Using trigonometric ratio;
angle = 58 degreesOpposite = AB = 104mHypothenuse = AC = ?Using the sine angle ratio;
sin θ = opposite / hypothenuse
sin 58 = 104 / AC
AC = 104 / sin 58
AC = 122.63m
The length of the wire is 122.63m
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