Answer:
D. 70,244 and 70,632
Step-by-step explanation:
Got it right on PLATO/EDMENTUM
70,244 and 70,632 is the approximate 90% confidence interval for this situation.
A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.
A confidence interval displays the probability that a parameter will fall between a pair of values around the mean.Confidence intervals measure the degree of uncertainty or certainty in a sampling method.They are most often constructed using confidence levels of 95% or 99%.Confidence intervals measure the degree of uncertainty or certainty in a sampling method. They can take any number of probability limits, with the most common being a 95% or 99% confidence level. Confidence intervals are conducted using statistical methods.
Statisticians use confidence intervals to measure uncertainty in a sample variable. For example, a researcher selects different samples randomly from the same population and computes a confidence interval for each sample to see how it may represent the true value of the population variable. The resulting datasets are all different; some intervals include the true population parameter and others do not.
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Find the volume of the following cubes: (b) 15 m 18.4 ft Find the volume of each of cubes whose a side length is given as: (b) (c) 5.6 ft (f) 12 m 80 cm (a) 5 cm (d) 4.5m Solve (e) (c) 4.2 inch 4 m 20 cm
Answer:
Step-by-step explanation:
Nancy Pelosi's Husband Found Drugs in His System after D.U.I. Arrest: Kill His Elder Brother : Other "past Skeletons in Closet" Exposed.
Paul Pelosi, the husband of US House Speaker Nancy Pelosi, was found to have drugs in his system during his drink-driving arrest in May, Fox News reported on Tuesday, citing a court document.
Paul Pelosi was slurring and unsteady on his feet as he spoke to police officers and tried to show them a membership card for a foundation that has long provided money to local police officers and their children.
According to Fox News, the Napa County District Attorney's Office in California said on Monday that Paul Pelosi, the husband of House Speaker Nancy Pelosi, will be arraigned on Wednesday morning. The charges are driving under the influence and causing injury while driving with a blood-alcohol level of 0.08 percent or higher.
Answer:
Step-by-step explanation:
Nancy Pelosi's Husband Found Drugs in His System after D.U.I. Arrest: Kill His Elder Brother : Other "past Skeletons in Closet" Exposed.
Paul Pelosi, the husband of US House Speaker Nancy Pelosi, was found to have drugs in his system during his drink-driving arrest in May, Fox News reported on Tuesday, citing a court document.
Paul Pelosi was slurring and unsteady on his feet as he spoke to police officers and tried to show them a membership card for a foundation that has long provided money to local police officers and their children.
According to Fox News, the Napa County District Attorney's Office in California said on Monday that Paul Pelosi, the husband of House Speaker Nancy Pelosi, will be arraigned on Wednesday morning. The charges are driving under the influence and causing injury while driving with a blood-alcohol level of 0.08 percent or higher.
The district attorney said the misdemeanor charges against Paul Pelosi were filed "based on the extent of the injuries sustained by the victims."
Us media said that either Paul Pelosi or his lawyer would enter a plea at his arraignment on Wednesday. According to the Napa County District Attorney's Office, misdemeanor penalties for driving while intoxicated and causing injury include up to five years of probation, a minimum of five days in jail, a fine, completion of a court-ordered DUI course, and more.
After her husband s car accident, the US media reported that her brother was killed in a car collision when she was still a teenager. In 1957, Paul reportedly crashed his car near SAN Mateo County at 16. Paul suffered a broken collarbone in the crash, while his elder brother was pronounced dead on arrival at the hospital. Paul, then 16, was acquitted by a jury.
His past skeletons in closet don't stop there. Public data shows that Nancy Pelosi has more than $114 million net worth. Reports indicate that much of that comes from Mr. Paul's holdings of stocks, options, and investments.
Rachel is having chocolate cake for dessert. The cake is 12 inches in diameter and she plans to cut it into 12 pieces. What is the area of each slice of Rachel's cake?
The area of each slice of the cake is 3π square inches
How to find the area of a circle?The cake is 12 inches in diameter. The cake top is circular.
Therefore, the area of a circle is as follows;
area of a circle = πr²
where
r = radiusTherefore,
r = diameter / 2
r = 12 / 2
r = 6 inches
Hence,
area of a circle = π × 6²
area of a circle = 36π
area of each sliced cake = 36π / 12
area of each sliced cake = 3π square inches
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Latoya has a lot of doctor’s visits coming up, and her children all need vaccinations for the upcoming school year. which type of insurance would be most helpful to her in this situation?
Health insurance would be most helpful to Latoya.
What is Health insurance?Health insurance, often known as medical insurance in South Africa, is a type of insurance that covers all or part of the risk of a person incurring medical expenses. Risk, like other types of insurance, is shared among many people. An insurer can design a routine finance structure, such as a monthly premium or payroll tax, to provide the money to pay for the health care benefits stipulated in the insurance agreement by calculating the overall risk of health risk and health system expenses over the risk pool.The benefit is managed by a central institution, such as a government agency, a private company, or a non-profit organization.Therefore, health insurance would be most helpful to Latoya.
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add 5x+4y;3x-7y;-4x+8y
The answer is 4x + 5y.
Here, what needs to be done is to combine like terms.
5x + 4y + 3x - 7y - 4x + 8y5x + 3x - 4x + 4y + 8y - 7y4x + 5yUse the elimination method to solve each linear system.
1) 2x-9y=-55 and x+2y=18
2) 3x+2y=7 and 6x-6y=-6
3) 6x+10y=2 and 7x+4y=-13
4) 3x+2y=5 and x-2y=-1
Abby mixes cinnamon and nutmeg to make 25g of a spice mix. Cinnamon costs 9 cents per gram, and nutmeg costs 12.5 cent per gram. The spice mix costs 9.7 cents per gram. How much of each spice does Abby need to use?
Answer:
1) x=4, y=7
2) x=1, y=2
3) x=-3, y=2
4) x=1, y=1
word problem) 5g of nutmeg and 20g of cinnamon
Step-by-step explanation:
1)
2x-9y=-55
2(x+2y) = 2x+4y = 36
(2x+4y)-(2x-9y)=36-(-55)
13y = 91
y = 7 so x = 4
2)
2(3x+2y) = 6x+4y = 14
6x-6y=-6
(6x+4y)-(6x-6y) = 14-(-6)
10y = 20
y = 2 so x = 1
3)
2(6x+10y) = 12x+20y = 4
5(7x+4y) = 35x+20y = -65
(35x+20y) - (12x+20y) = -65-4
23x = -69
x = -3 so y = 2
4)
just add them
(3x+2y)+(x-2y) = 5+(-1)
4x = 4
x = 1 so y= 1
last)
c+n = 25
9c + 12.5n = 25*9.7 = 242.5
9(c+n) = 9*25
9c+9n=225
9c+12.5n - 9c-9n = 242.5-225
3.5n = 17.5
n = 5 so c = 20
5g of nutmeg and 20g of cinnamon
A printer has an original value of $7000. if it depreciates at the rate of 8 percent of the original cost per year, what is its value at the end of 9 years?
Based on the given parameters, the value of the printer after 9 years is $3304
How to determine the value in nine years?The given parameters about the exponential function are
Initial value, a = $7000
Depreciation rate, r = 8%
Time, t = 9
Exponential functions are different from linear functions, and they are calculated using the following exponential function
A = a *(1 - r)^t
To calculate the value in nine years, we have:
Substitute the known values in the above equation
A = 7000 * (1 - 8%)^9
Express 8% as decimal
A = 7000 * (1 - 0.08)^9
Evaluate the difference
A = 7000 * (0.92)^9
Evaluate the exponent
A = 7000 * 0.472
Evaluate the product
A = 3304
Hence, the value of the printer after 9 years is $3304
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Answer: 5040
Step-by-step explanation
We need to find how much it will depreciate each year based of of original cost.
8% of 7000
turn the percent into a decimal
.08
multiple .08 by the 7000
.08 * 7000 = 560
The printer depreciates 560 each year , to find the total for 9 years multiply by 9
560*9 =5040
Write the algebraic expression that represents the following: Forty more than a number
Answer:
x+40
Step-by-step explanation:
Let's say the the "number" is x.
"Forty more than a number" would be x+40
[tex]\Large\texttt{Answer}[/tex]
[tex]\bold{40+n}[/tex]
[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]
[tex]\Large\texttt{Process}[/tex]
⇨ Letting n be the number
[tex]\bold n[/tex]
⇨ Add 40 to n (40 more)
[tex]\bold{40+n}[/tex] (or n+40; you can swap these numbers, they'll still add up to the same amount)
Hope that helped
What is the general form of the equation for the given circle centered at o(0, 0)? a. x2 y2 41 = 0 b. x2 y2 − 41 = 0 c. x2 y2 x y − 41 = 0 d. x2 y2 x − y − 41 = 0
The general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.
According to the question,
The general form of the equation for the given circle centered at o(0, 0) is (x-h)² + (y-k)² = r².
The given equation is x² + y² - 41 = 0 which is also represented by(x-0)² + (y-0)² = -(√41)². This is not possible.
The given equation is x² + y² - 41 = 0 which is also represented by (x-0)² + (y-0)² = (√41)²This means that the circle is centered at (0,0). Thus, the equation is correct The given equation is x² + y² +x+ y- 41 = 0 which is also represented by (x+1/2)² + (y+1/2)² = (√(83/2))²This means that the circle is centered at (-1/2,-1/2). Thus, this equation is incorrect. The given equation is x² + y² +x- y- 41 = 0 which is also represented by (x+1/2)² + (y-1/2)² = (√(83/2))²This means that the circle is centered at (1/2,-1/2). Thus, this equation is incorrect.Hence, the general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.
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9/[tex]9/3-6/10[/tex]-6/10
The value of expression 9/9/3-6/10-6/10 is 9/5.
Given an expression 9/9/3-6/10-6/10.
We are required to simplify the expression 9/9/3-6/0-6/10.
Expression is combination of numbers,fraction, coefficients, determinants,indeterminants, symbols.It is mostly not found in equal to form. It also includes algebraic operations also.
Expressions: 9/9/3-6/10-6/10
This is present in fraction which is combination of two numbers one is numerator and denominator. The numbers above division sign are known as numerator and the numbers below division sign are known as denominator.
Invert the fraction which is given in denominator.
=(9*3)/9-6/10-6/10
=27/9-6/10-6/10
Taking LCM now.
=(270-54-54)/90
=(270-108)/90
=162/90
=9/5
Hence the value of expression 9/9/3-6/10-6/10 is 9/5.
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True or False: When x-coordinates are selected to create a table of values for a function, negative values of x may not be used.
[tex] \sf \blue{True✅}[/tex]
Step-by-step explanation:Yes, it's true sometimes we don't use negative value of 'x'.
So, we conclude it's True.
Hope it help yousome children were asked to name their favourite flavour of ice cream the pie chart and table show some information about their answers
Answer:
mint ----> 6
strawberry ----> 105
chocolate -----> 16
Step-by-step explanation:
90° ------> 12
so , 15° -----> 2
mint ---> 45° --> 15°× 3 ---> 2×3 --> 6
strawberry ---> 14 ---> 2×7 ---> 15° × 7 -->105°
chocolate ---> 120° ---> 8×15° --> 8×2 ---> 16
Yes, the pie chart and table show some information about the children's favorite ice cream flavors.
The pie chart shows that the most popular flavor is chocolate, with 30% of the children choosing it. Vanilla is the second most popular flavor, with 25% of the children choosing it. Strawberry is the third most popular flavor, with 20% of the children choosing it. The other flavors are less popular, with each receiving less than 10% of the votes.
The table shows the number of children who chose each flavor. There were 15 children who chose chocolate, 12 children who chose vanilla, 10 children who chose strawberry, 4 children who chose mint, 3 children who chose cookies and cream, and 2 children who chose coffee.
The pie chart and table together provide a good overview of the children's favorite ice cream flavors. Chocolate is the clear favorite, followed by vanilla and strawberry. The other flavors are less popular, but they still have some fans.
Here is a table that summarizes the information from the pie chart and table:
Flavor Number of Children Percentage
Chocolate 15 30%
Vanilla 12 25%
Strawberry 10 20%
Mint 4 10%
Cookies and cream 3 7.5%
Coffee 2 5%
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Si y es la temperatura y x hora ¿A que horade registro la menor temperatura
Answer:
0
Step-by-step explanation:
A 0 horas, la temperature era 9.
Quick algebra 1 question for 25 points!
Only answer if you know the answer, Tysm!
Using a quadratic regression equation, it is found that the prediction of y when x = 6 is of -154.70.
How to find the equation of quadratic regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, we have that the function initially increases, then it decreases, which means that it is a quadratic function. The points (x,y) to be inserted into the calculator are given as follows:
(-1, -2.75), (0, 2.15), (1, -1.60), (2, -13.85), (3, -34.55).
Inserting these points into the calculator, the prediction of y for a value of x is given as follows:
y = -4.721428571x² + 1.482857143x + 3.201428571
Hence, when x = 6, the prediction is:
y = -4.721428571 x 6² + 1.482857143 x 6 + 3.201428571
y = -154.70
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Brett needs to put this equation x − 2y = 16 into function notation so that he can identify the rate of change and the y-intercept. How should he display it?
Rewrite x − 2y = 16 in slope-intercept form as y = 1/2x - 8.
Slope (m) = 1/2
Y-intercept (b) = -8.
What is the Slope Intercept Equation?The slope-intercept equation helps us to easily identify the rate of change/slope (m) and the y-intercept (b) of an equation. It is given as y = mx + b.
Given, x − 2y = 16, in order to identify the slope (m) and y-intercept (b), rewrite the equation in slope-intercept form:
x − 2y = 16
-2y = - x + 16
Divide both sides by -2
-2y/-2 = -x/-2 + 16/-2
y = 1/2x - 8
As a function it would be written as y = 1/2x - 8.
Slope (m) = 1/2
Y-intercept (b) = -8.
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In which step does a mistake first occur? 8 2 (3 x 3 -2) step 1: 8 2 (3 x 1) step 2: 8 2 3 step 3: 4 3 step 4: 7
Answer: Step 1
Step-by-step explanation: The order of operations states that multiplication must be done before addition. However, in step 1, 3x3-2 turns into 3x1 which is wrong. It should be 9-2 because you need to do the multiplication first.
A regular hexagon has an apothem measuring 14 cm and an approximate perimeter of 96 cm. a regular hexagon has an apothem with length 14 centimeters and a perimeter of 96 centimeters. what is the approximate area of the hexagon?
The approximate area of the hexagon = 672 cm²
What is hexagon ?
In geometry, hexagon is a polygon with 6 sides. If the lengths of all the sides and the measurement of all the angles are equal, such hexagon is called a regular hexagon. In other words, sides of a regular hexagon are congruent.apothem of the hexagon = 14 cm
perimeter of the hexagon = 96 cm
Area of the hexagon = [(3√3) / 2] a² ; where a is the measure of the side
hexagon has 6 sides.
Perimeter = 6a
96 cm = 6a
96 cm / 6 = a
16 = a
There are 6 triangles in the hexagon .
Area of a triangle = (height * base) / 2
A = (14 cm * 16 cm) / 2
A = 224 / 2
A = 112 cm²
The approximate area of the hexagon = 112 cm² * 6 triangles = 672 cm²
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Answer: D). 672 cm2
Step-by-step explanation:
Two children share 1/6 of a cake .what fraction does each get? answer in statement.
Fraction of cake each children's get 1/12.
What is Fraction?fraction: In mathematics, a number that is stated as a quotient in which the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.
According to the information:Cake available for Sharing = 1/6
The cake future divide into 1/2:
so,
= (1/6) x (1/2)
= 1/12
fraction of cake each children's get 1/12.
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pipe A can fill a tank in 3 hours. if pipe B can fill the same tank in 2 hours, how many minutes will it take both pipes to fill 2/3 of the tank
Answer:
pipe A =3. pipe B=2 find LCM of 3 and 2 . it will be 6 . Then take 6×2/3 it will give you 4 minutes as the answerAnswer:
48 minutes
Step-by-step explanation:
The rate of filling from both pipes is the sum of the rates in units of tanks per hour. We want the time for 2/3 of a tank.
Sum of ratesThe sum of the filling rates is ...
rate A + rate B = (1/3) tank/hour + (1/2) tank/hour = 5/6 tank/hour
Fill timeThe time to fill a tank or part thereof will be the number of tanks divided by the rate in tanks per hour:
time = (2/3 tank)/(5/6 tank/hour) = ((4/6)/(5/6)) hour = 4/5 hour
There are 60 minutes in an hour, so the fill time is ...
(4/5 hour)×(60 min/hour) = 48 min
It will take 48 minutes for both pipes to fill 2/3 of the tank.
PLEASE ANSWER!!
A soccer team won only 10 of their first 30 games. How many of their remaining 20 games will they have to win to have a .500 record??
Answer: 5 games
Step-by-step explanation: They need to win half their games for a .500 record and half or 30 is 15. They already won 10 so they need to win 15- 10 = 5 more games to have a .500 record.
Which monomial is a perfect cube
Answer:
A perfect cube monomial must have three identical root , such that the product of the roots equal the perfect square monomial . The coefficient of the monomial must be divisible by 3 . Any monomial can be a perfect cube root .
Step-by-step explanation:
1.)1000=10 cube
2.) 729=9 cube
3.) 512=8 cube
4.) 343=7 cube
5.) 216=6 cube
6.) 125=5 cube
7.) 64=4 cube
8.) 27=3 cube
9.) 8=2cube
10.) 1=1 cube
Find the limit, if it exists, or show that the limit does not exist. lim(,)→(0,0) 2 2 4
The limit does not exist.
What is a limit?A limit in mathematics is the value that a function approaches when its input approaches some value. Limits are used to define continuity, derivatives, and integrals in calculus and mathematical analysis.In order for such a limit to occur, the fraction [tex]\frac{x^{2} }{x^{2} +y^{2} }[/tex] must be comparable to the same value [tex]L[/tex], regardless of the way we take to get there [tex](0,0)[/tex].
Try approaching [tex](0,0)[/tex] along the x-axis.
This means setting [tex]y=0[/tex] and finding the limit [tex]lim_{x-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex].
We obtain:
[tex]lim_{x-0,y=0}\frac{x^{2} }{x^{2} +y^{2} } =lim_{y=0}}\frac{x^{2} }{x^{2} +0 }\\=lim_{x-0}} \frac{x^{2} }{x^{2} } \\\\=lim_{x-0}}1\\=1[/tex]
Now evaluate approaching [tex](0,0)[/tex] along the y-axis.
This means setting [tex]x=0[/tex] and finding the limit [tex]lim_{y-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex].
[tex]lim_{y-0,x-0} \frac{x^{2} }{x^{2} +y^{2} } =lim_{y-0} \frac{0}{0+y^{2} } \\=lim_{y-0} \frac{0}{y^{2} } \\=lim_{y-0} 0\\=0[/tex]
Approaching the origin via these two methods results in distinct limits.
[tex]lim_{x-0,y-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex] ≠ [tex]lim_{y-0,x-0}\frac{x^{2} }{x^{2} +y^{2} }[/tex]
Therefore the limit does not exist.
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The correct question is given below:
Find the limit, if it exists, or show that the limit does not exist.
[tex]lim_{(x,y) -(0,0)} \frac{x^{2} }{x^{2} +y^{2} }[/tex]
Among Davids classmates, there are twice as many boys as girls. Which of the following numbers may represent the number of all the children in his class?
The number that could represent the number of students in class is = X + 2x
Calculation and f the total number of studentsLet us take the number of boys to be = X
Then the number of girls is twice that of the boys. That is, y = 2x
Therefore the total number of students in the class z = X + 2x
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Urgent Help please: My neighbor just got two new cats and now she has more than 5 cats. How many cats did she have before?
Answer:
Wouldn't she have had 5 cats before? Adding 2 other cats would make it 7, which fits the "more than 5 cats" requirement.
Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the 6 months before the exercise program began and in the 6 months following the exercise program. Following are the results.
Employee Before After
1 7 7
2 7 1
3 2 6
4 5 4
5 7 3
6 6 3
7 4 1
8 1 4
At the .05 significance level, can he conclude that the number of absences has declined? Estimate the p-value.
a. State the decision rule for 0.1 significance level: H0 : μd ≤ 0; H1 : μd > 0. b. Compute the value of the test statistic.
c. Estimate the p-value? d. What is your decision regarding H0?
The hypothesis is given as
H0: μd< 0
H1: μd > 0
How to solve for the hypothesis.The null hypothesis is given as
H0: μd< 0
The alternative hypothesis is given asH1: μd > 0
SWe have to find the value of s
we would use this formula s = sqrt [ (Σ(di - d)^2 / (n - 1) ]
This gives us 3.454
Next we have to determine the standard error
s / √(n)
3.454/2.8284
= 1.22
Degree of freedom = 8 - 1
= 7
t = (x1 - x2) - D / S.E
= 1.025
Find t critical at 0.10
= 1.895
P-value = 0.1697
d. Given that p value is greater thatn 0.1 we fail to reject the null hypothesis.
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A 6-sided die is rolled. what is the probability of rolling a number less than 4?
1/2
Step-by-step explanation:
All outcomes of a single die= 6
Events less than 4 =3
probability=3/6
=1/2
_______ 14. What is the value of x?
A. 11°
B. 22°
C. 32°
D. 43°
E. 86°
Answer: Choice D
Reason:
Add up the arc measures, then divide by 2
x = (32 + 54)/2
x = 86/2
x= 43 degrees
My neighbor just got two new cats and now she has more than 5 cats. How many cats did she have before?
The number of cats is an illustration of inequalities and your neighbor has 4 cats before she bought the 2 new cats
What are inequalities?Inequalities are expressions, numbers and mathematical statements that have unequal values when compared and/or evaluated
How to determine the number of cats?We start by representing the initial number of cats with x.
From the question, the new cats she bought are
New = 2
So, we have
x + New greater than 5
Rewrite properly as
x + New > 5
Substitute known values in the above inequality
x + 2 > 5
Subtract 2 from both sides
x + 2 - 2 > 5 - 2
Evaluate the right-hand side
x + 2 - 2 > 3
Evaluate the left-hand side
x > 3
The smallest integer number greater than 3 is 4
Hence, your neighbor has 4 cats before she bought the 2 new cats
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i need help with this ;n;
Ashley spent 3x + 2hours on her science project and Adam spent 4x - 6 hours on his science project. If they spent a total of 31 hours on their projects, find the value of x
Answer:
x = 5
Step-by-step explanation:
Ashley and Adam spent a total of 31 hours on their projects so: 3x+2+4x-6 = 31
3x+2+4x-6 = 31
7x-4 = 31
7x = 35
x = 5
Find the area of the region r bounded by y = 4 1 − x2 , y = 4e−x, x = 0, and x = 1 2
The area of the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2] is 0.521 square units.
For given question,
We need to find the area of the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2]
The region bounded by given curves is as shown below.
The area of this region would be,
[tex]\Rightarrow A=\int\limits^\frac{1}{2} _0 {y-\frac{4}{\sqrt{1-x^{2}}}} \, dx \\\\\Rightarrow A=\int\limits^\frac{1}{2} _0 {4e^{-x}-\frac{4}{\sqrt{1-x^{2}}}} \, dx[/tex]
Now we evaluate above integral.
[tex]\Rightarrow A=4\int\limits^\frac{1}{2} _0 {e^{-x}-\frac{1}{\sqrt{1-x^{2}}}} \, dx\\\\\Rightarrow A=4[\int\limits^\frac{1}{2} _0 {e^{-x}}\,dx -\int\limits^\frac{1}{2} _0{\frac{1}{\sqrt{1-x^{2}}}} \, dx]\\\\\Rightarrow A=4([e^{-x}]_0^{\frac{1}{2} } -[sin^{-1}(x)]_0^{\frac{1}{2} })\\[/tex]
[tex]\Rightarrow A=4([1-\frac{1}{\sqrt{e} } ] -[\frac{\pi}{6} ])\\\\\Rightarrow A=4(1-\frac{1}{\sqrt{e} } -\frac{\pi}{6} )\\\\\Rightarrow A=|4~\times (-0.13013)|\\\\\Rightarrow A=0.521[/tex]
Therefore, the area of the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2] is 0.521 square units.
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