A rectangular paperboard measuring 29in long and 20in wide has a semicircle cut out of it, as shown below.
Find the area of the paperboard that remains. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Here, we are required to find the area of the paper board given after the semicircle is cut out of it
Area of the paper board that remains is 423 in²
Length = 29 in
Width = 20 in
Area of a rectangle = length × width
= 29 in × 20 in
= 580 in²
Area of a semi circle = πr²/2
π = 3.14
r = diameter / 2 = 20 in / 2 = 10 in
Area of a semi circle = πr²/2
= 3.14 × (10 in)² / 2
= 3.14 × 100 in² / 2
= 314 in²/2
= 157 in²
The semicircle is cut out of the rectangle
Find the area of the paper board that remains after the semicircle is cut out of it by subtracting the area of a semi circle from the area of a rectangle
Area of the paper board that remains = Area of a rectangle - Area of a semi circle
= 580 in² - 157 in²
= 423 in²
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Related Questions
Use parenthesis to make each number sentence true.
124 - 6 x 0 + 15 = 34
Answers
Answer:
12 - 6 x (0 + 15) = 34
How I got my answer
First, how i got my answer was that I had to solve the equation first, ignoring the answer. I got 0 x 6 = 0, then I did 124 - 0 = 124, then I did 124 - 15 = 109, which clearly isn't 34. I figured that we have to put the parentheses around the zero because if we don't, we are going have to multiply something by zero, which always gets zero. After that, I decided that I should put the parentheses around either the 6, or the 15. I did both, and saw which one was correct. If we put it around the 6, we get, 124 - (6 x 0) + 15 = 124 - 0 - 15 = 124 - 15 = 109, which isn't 34. Then I checked 124 - 6 x (0 + 15) = 124 - 6 x 15 = 124 - 90 = 34, and we just got the answer.
P.S. Sorry if it was confusing, I didn't really know how to explain it
9. Write a polynomial function in factored form with zeros at -2, 5, and 6.
F(x) = (x + 2)(x - 5)(x - 6)
+
F(x) = x3 - 9x2 + 8x + 60
O
f(x) = (x - 2)(x + 5)(x + 6)
Flx) = x3 + 9x2 + 8x - 60
Answers
Answer:
f(x) = ( x+2)(x-5)(x-6)
Step-by-step explanation:
We can write the equation with zeros at b1,b2,b3
f(x) =a( x-b1)(x-b2)(x-b3) where a is a constant and b1 b2 b3 are the zeros
f(x) = a( x- -2)(x-5)(x-6)
f(x) = a( x+2)(x-5)(x-6)
We can choose a since we are not given any more information about the function. Let a = 1
f(x) = 1( x+2)(x-5)(x-6)
f(x) = ( x+2)(x-5)(x-6)
limit chapter~ anyone can help me with these questions?
please gimme clear explanation :)
Answers
Step-by-step explanation:
I(S) = aS / (S + c)
As S approaches infinity, S becomes much larger than c. So S + c is approximately equal to just S.
lim(S→∞) I(S)
= lim(S→∞) aS / (S + c)
= lim(S→∞) aS / S
= lim(S→∞) a
= a
As S approaches infinity, I(S) approaches a.
800,000+700 standard form
Answers
Answer:
800700
Step-by-step explanation:
800000 + 00000 + 0000 + 000 + 00 + 0
000000 + 00000 + 0000 + 700 + 00 + 0
------------------------------------------------------------
= 800700
Answer:
Hey there!
800000+700=800700
Hope this helps :)
Given the following three points, find by hand the quadratic function they represent.
(0,6), (2, 16), (3, 33)
(1 point)
f(x) = 4x2 + 3x + 6
f(x) = -42? +212 + 6
f(x) = -472 – 3r +6
f(1) = 4x2 – 3x + 6
Answers
let the function be [tex]y=ax^2+bx+c[/tex]
put $x=0, \, y=6$ , to get $c=6$
put $x=2, \, y=16$ , $16=4a+2b+6\implies 2a+b=5$
put $x=3, \, y=33$ , $33=9a+3b+6\implies 3a+b=9$
subtract the two equation, to get $a=4$
now substitute $a$ in first equation, to get $b=5-2\cdot4=-3$
so, $f(x)=4x^2-3x+6$
Is the relationship shown by the data linear? If so, model the data with an equation.
Answers
Answer:
4th option
Step-by-step explanation:
The relationship is linear,
putting the value of x in the right side of the equation of option 4, you'll get the value of the left side
putting, x=1
y+4=-1/2(x-1)
y=-1/2(1-1)-4
y=-4
putting, x=7
y+4=-1/2(7-1)
y=-1/2(6)-4
y=-6/2-4
y=-3-4
y=-7
Rewrite to make true: The sequence 8,8,8,8,8, ... is neither arithmetic or geometric.
Answers
Answer:
8,8,-8,-8,8, ... is neither arithmetic nor geometric
Step-by-step explanation:
8,8,-8,-8,8, ...
This sequence is neither arithmetic nor geometric
We could also write
8,8,8,8,8, ... this is geometric since we multiply by 1 each time
Oregon State University is interested in determining the average amount of paper, in sheets, that is recycled each month. In previous years, the average number of sheets recycled per bin was 59.3 sheets, but they believe this number may have increase with the greater awareness of recycling around campus. They count through 79 randomly selected bins from the many recycle paper bins that are emptied every month and find that the average number of sheets of paper in the bins is 62.4 sheets. They also find that the standard deviation of their sample is 9.86 sheets. What is the value of the test-statistic for this scenario
Answers
Answer:
The test statistic is [tex]t = 2.79[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 59.3[/tex]
The sample size is [tex]n = 79[/tex]
The sample mean is [tex]\= x = 62.4[/tex]
The standard deviation is [tex]\sigma = 9.86[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 62.2 - 59.3 }{ \frac{ 9.86}{ \sqrt{ 79} } }[/tex]
[tex]t = 2.79[/tex]
Find interval of increase and decrease of f(x) = 8 sin(x) + cot(x), −π ≤ x ≤ π
Answers
Answer:
Given f(x)=8sin(x)+cot(x) for -pi<x<pi :
Note that:
f'(x)=8cos(x)-csc^2(x)
f''(x)=-8sin(x)+2csc^2(x)cot(x)
(1) To find the intervals where f(x) is increasing or decreasing we use the first derivative test; if the first derivative is positive on an interval the functio is increasing, negative implies the functio is decreasing.
Using technology we find the approximate zeros of f'(x) on -pi<x<pi :
x~~-1.443401
x~~-.3752857
x~~.3752857
x~~1.443401
Plugging in test values on the intervals yields:
f'(x)<0 on (-pi,-1.443401)
f'(x)>0 on (-1.443401,-.3752857)
f'(x)<0 on
Plz correct me if wrong
John and mike got paid $40.00 for washing
car. John work one hour, mike worked 1.5 hrs.
How much do they get paid for time worked?
Answers
In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft. For a group of 1013 adults, the mean of those who do not worry about identify theft is closest to ________.
Answers
Answer: 669
Step-by-step explanation:
Given, In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft.
i.e. The proportion of adults said that they worry about identity theft. (p) = 0.66
Sample size : n= 1013
Then , Mean for the sampling distribution of sample proportion = np
= (1013) × (0.66)
= 668.58 ≈ 669 [Round to the nearest whole number]
Hence, the mean of those who do not worry about identify theft is closest to 669 .
The lengths of two sides of a triangle are 6cm and 8cm.Between what two measures should the length of the third side fall? PLEASE HELP !!!!!!!!
Answers
Answer: Search Results
Featured snippet from the web
In triangle sum of 2 sides must be greater than the 3rd side. So, the third > 8 - 6 = 2 and also the third < 8 + 6 = 14. So, the answer is 2 < third side < 14. The third side lies between(2,14).
Step-by-step explanation: Brainlyest please
A 33-m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 37-m.
. Find the length of the shadow.
Answers
Answer:
[tex]\sqrt{280}[/tex] = 2[tex]\sqrt{70}[/tex]
37^2 = 1369
33^2 =1089
1369-1089 = 280
Step-by-step explanation:
A die is rolled 200 times with the following results. Outcome 1 2 3 4 5 6 Frequency 32 36 44 20 30 38 What is the experimental probability of rolling the given result? 3 a. 0.22 c. 0.44 b. 0.78 d. 0.23
Answers
Answer:
.22
Step-by-step explanation:
The number of times a 3 was rolled is 44 out of 200
The experimental probability is 44/200 = .22
The frequency of rolling a 3 was 44.
So... 44/200
After dividing we get 0.22
Therefore, the answer is A
Best of Luck!
Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.
Part II: Exercise 6.16 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they cannot afford it.
#1: Calculate a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it, and interpret the interval in context.
(a) lower bound: ______ (please round to four decimal places)
(b) upper bound: _____ (please round to four decimal places)
#2: Interpret the confidence interval in context:
(A) We can be 90% confident that our confidence interval contains the sample proportion of Americans who choose not to go to college because they cannot afford it
(B) 90% of Americans choose not to go to college because they cannot afford it
(C) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval
#3: Suppose we wanted the margin of error for the 90% confidence level to be about 1.5%. How large of a survey would you recommend?
(a) A survey should include at least ________ people.
Answers
Answer:
(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].
(2) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval
(3) A survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.
Step-by-step explanation:
We are given that a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of Americans who decide to not go to college = 48%
n = sample of American adults = 331
p = population proportion of Americans who decide to not go to
college because they cannot afford it
Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.
So, 90% confidence interval for the population proportion, p is ;
P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level
of significance are -1.645 & 1.645}
P(-1.645 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.645) = 0.90
P( [tex]-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]\hat p-p[/tex] < [tex]1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.90
P( [tex]\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.90
90% confidence interval for p = [ [tex]\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]
= [ [tex]0.48 -1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }[/tex] , [tex]0.48 +1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }[/tex] ]
= [0.4348, 0.5252]
(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].
(2) The interpretation of the above confidence interval is that we can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval.
3) Now, it is given that we wanted the margin of error for the 90% confidence level to be about 1.5%.
So, the margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]
[tex]0.015 = 1.645 \times \sqrt{\frac{0.48(1-0.48)}{n} }[/tex]
[tex]\sqrt{n} = \frac{1.645 \times \sqrt{0.48 \times 0.52} }{0.015}[/tex]
[tex]\sqrt{n}[/tex] = 54.79
n = [tex]54.79^{2}[/tex]
n = 3001.88 ≈ 3002
Hence, a survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.
What is the constant of proportionality between y and x in the graph?
Answers
Answer:
4
Step-by-step explanation:
Constant of proportionality refers to the slope of the line in this case, the slope of the line is (4-0)/(1-0)=4
tan inverse X + tan inverse Y + tan inverse z=pie prove that X+Y+Z=xyz
Answers
Answer:
see explanation
Step-by-step explanation:
Given
[tex]tan^{-1}[/tex]x + [tex]tan^{-1}[/tex]y + [tex]tan^{-1}[/tex] z = π
let
[tex]tan^{-1}[/tex]x = A , [tex]tan^{-1}[/tex]y = B , [tex]tan^{-1}[/tex]z = C , so
x = tanA, y = tanB , z = tanC
Substituting values
A + B + C = π ( subtract C from both sides )
A + B = π - C ( take tan of both sides )
tan(A + B) = tan(π - C) = - tanC ( expand left side using addition identity for tan )
[tex]\frac{tanA+tanB}{1-tanAtanB}[/tex] = - tanC ( multiply both sides by 1 - tanAtanB )
tanA + tanB = - tanC( 1 - tanAtanB) ← distribute
tanA+ tanB = - tanC + tanAtanBtanC ( add tanC to both sides )
tanA + tanB + tanC = tanAtanBtanC , that is
x + y + z = xyz
Find the value of X.
Answers
Answer:
[tex]the \: two \: angles \: are \: equal \: so \: this \\ \: triangle \: is \: issosceless \\ then3x - 6 = 12 \\ 3x = 18 \\ x = \frac{18}{3} \\ x = 6 \\ thank \: you[/tex]
Look at picture pleasee
Answers
Answer:
Point A.
.................
Answer:
It is the Picture B.
Step-by-step explanation:
A customer can pay GH➣900.00 per month on a mortgage payment.
Interest rate is 12% annually compounded continuously, and mortgage
terms is 15 years. Determine the maximum amount the customer can pay within
the period.
Answers
Answer:
$74,748.11
Step-by-step explanation:
In order to make use of the amortization formula, we need to find the equivalent monthly interest rate.
When 12% interest is compounded continuously, the annual multiplier is ...
e^0.12 ≈ 1.127497
The equivalent multiplier when the interest is compounded monthly is the 12th root of this,
(e^0.12)^(1/12) = e^0.01 ≈ 1.0100502 = 1 + r
___
The amortization formula tells us that monthly payment amount A will pay off principal P in n months:
P = A(1 -(1 +r)^-n)/r = $900(1 -1.0100502^-180)/0.0100502
P = $74,748.11
The customer can pay off a 12% loan of $74,748.11 at the rate of $900 per month for 15 years.
An investigator claims, with 95 percent confidence, that the interval between 10 and 16 miles includes the mean commute distance for all California commuters. To have 95 percent confidence signifies that
Answers
Answer:
Hello the options to your question is missing below are the options
A) if sample means were obtained for a long series of samples, approximately 95 percent of all sample means would be between 10 and 16 miles
B.the unknown population mean is definitely between 10 and 16 miles
C.if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians
D.the unknown population mean is between 10 and 16 miles with probability .95
Answer : if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians ( c )
Step-by-step explanation:
95% confidence
interval = 10 to 16 miles
To have 95% confidence signifies that if these intervals were constructed for a long series of samples, approximately 95 percent would include the unknown mean commute distance for all Californians
confidence interval covers a range of samples/values in the interval and the higher the % of the confidence interval the more precise the interval is,
Which of the following is the function for the graph below and shows the end behavior of the function as x>-00?
Answers
Answer:
A
Step-by-step explanation:
I just used a graphing calculator.
Just type in all the functions and pick the graph and function pair that match the picture.
I hope this helps!
pls ❤ and mark brainliest pls!
Assuming you want x to approach negative infinity, you have the correct answer. It is choice A.
=====================================================
Explanation:
The root x = -2 leads to the factor x+2. That means the answer is between A and B.
As x approaches negative infinity, i.e. as we move to the left, we're going down the red curve and y = f(x) is going to approach negative infinity as well.
In terms of symbols, we'd write [tex]x \to -\infty, \ f(x) \to -\infty[/tex]
Informally, we could say "it falls to the left" as a way to describe this left end behavior.
Convert the following:
How many kilometers are in 1 mile? (Hint: Use the answer from the previous problem)
1 mile is equivalent to
ao kilometers (rounded to the nearest hundredth)
Answers
Answer: 1.609344 kilometers.
Step-by-step explanation:
A mile is an English Unit that is used to measure the length of a linear surface.
Even though the kilometre has replaced it to a large extent as the standard measure of length, it is still the main unit of measurement for distances in the United States, the United Kingdom, Liberia and UK and US oversees territories.
Miles are longer than kilometres as a kilometer is equivalent to only 0.621371 miles.
1 mile is therefore;
= 1/0.621371
= 1.609344 kilometers.
find the area of right-andled triangled whose sight-angled
making side are 3cm and 4cm
Answers
Answer:
3*4=12
Step-by-step explanation:
Find the side length, b.
Round to the nearest tenth.
Answers
Answer:
b ≈ 9.2
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
b² = a² + c² = 6² +7² = 36 + 49 = 85 ( take the square root of both sides )
b = [tex]\sqrt{85}[/tex] ≈ 9.2 ( to the nearest tenth )
Answer:
9.22
Step-by-step explanation:
Since it's a 90° triangle [tex]c^{2} =a^{2} +b^{2}[/tex].
In this example they labeled the hypotenuse as b instead of c are equation is still the same just put the correct variables in the right places.
[tex]b = \sqrt{6^{2} +7^{2} }[/tex]
b = 9.22
Help me please I dont know what to do
Answers
Answer:
It's option A. ± √60
Step-by-step explanation:
x^2 = 60
here ^2 will move to the other side and when it does it'll become a square root to 60.
so, x = √60
now, the answer in its simplified form would be 2√15 and -2√15.
The answer of this square root will be negative as well as positive, so, ±√60.
Answer:
±√60
You'll have to remove the square from the x by squaring the 60, hence the ±60 as the answer
PLZ HELPPPPPP. 25 POINTS.
A store sells books for $12 each. In the proportional relationship between x, the number of books purchased, and y, the cost per books in dollars" to "y, the total cost of the books in dollars, the constant of proportionality is 12. Which equation shows the relationship between x and y?
A. y=12/x
B. y=12x
C. y=12+x
D. y=12−x
Answers
Answer:
b
Step-by-step explanation:
because its right dummy
____________ is/are when data is analyzed in order to make decisions about the population behind the data.
A. Experiments
B. Simulations
C. Surveys
D. Statistics
Answers
Answer:
statistics are when data analyzed in order to make decisions about the population behind the data.
The correct answer to the question is Statistics (Option D).
What is statistics?
Statistics is a field of study in mathematics which deals with raw data. It is a tool which refines the data to produce meaningful results and a pathway to better understanding of it.
Some examples of raw data can be population sample which loves to see a particular TV show or a sample of students getting so and so marks in Math test.
Data is analyzed mainly by three different measure of central tendency that is mean, median and mode.
Mean is the average value of given discrete data.Median is the middle value when the data is sorted in ascending or descending order.Mode is the value that has highest frequency.Therefore, Statistics the correct answer.
To know more about statistics refer:https://brainly.com/question/10734660
#SPJ2
Name the indicated geometric figures for the figure shown. Be sure to use correct notation
A Name a point.
B Name a ray through Y.
C Name a line through Z.
D Name a plane.
Answers
9514 1404 393
Answer:
see below
Step-by-step explanation:
[tex]\text{A. point: }X\\\\\text{B. ray through Y: }\overrightarrow{XY}\\\\\text{C. line through Z: }\overleftrightarrow{XZ}\\\\\text{D. plane: plane } XYZ[/tex]
__
Additional comment
When you don't have the benefit of typesetting, you can refer to the geometry by name: ray XY, line XZ,
Can somebody help me with parametric equations?
I do not have a TI-84 at the moment! Thanks!
1. Graph the following set of parametric equations on your calculator and select the matching graph.
2. Transform the given parametric equations into rectangular form. Then identify the conic.
Answers
Answer:
Attachment 1 : Graph B
Attachment 2 : Option B
Step-by-step explanation:
( 1 ) The equation x = t² - 3 is represented by exponential growth, ( t² ) so it's graph will be similar to the first graph, graph 1, in our options. Then again we have to consider the equation y = √t - 2, which will be similar to graph 4, but with a greater slope. This leaves us with a solution of graph b.
( 2 ) We have the following system of equations at hand here.
{ x = 5 cot(t), y = - 3csc(t) + 4 }
Now instead of isolating the t from either equation, let's isolate cot(t) and csc(t) --- Step #1,
x = 5 cot(t) ⇒ x - 5 = cot(t),
y = - 3csc(t) + 4 ⇒ y - 4 = - 3csc(t) ⇒ y - 4 / - 3 = csc(t)
Now let's square these two equations, adding them --- Step #2
We know that csc²θ - cot²θ = 1, so let's subtract the equations
( y - 4 / - 3 )² = (csc(t))²
- ( x - 5 / 1 )² = (cot(t))²
___________________
(y - 4)² / 9 - x² / 25 = 1
And as we are subtracting the two expressions, this is an example of a hyperbola. Therefore your solution is option b.