A 12 cm by 12 cm square piece of paper has 5 holes punched out of it. 4 of the holes are circles of radius 3 cm and 1 of the holes is a circle of radius 1 cm. The paper and punched holes can be visually interpreted as below. Determine the area of paper remaining after the holes have been punched out.
Answers
5 holes have been punched into a 12 cm by 12 cm square piece of paper. The area of remaining paper will be 27.714 cm².
Firstly, we will calculate the area of the square of paper in which the holes are punched.
Side of square = 12 cm
Area of square = side²
= (12) ²
= 144 cm²
Now, we will calculate the area of the bigger punch holes
Radius of big punch hole = 3 cm
Area of 1 big punch = π (radius) ²
= 22/7 × (3)²
22 / 7 × 9
= 198 / 7 cm²
Area of 4 punches = 4 × 198/7
= 792/7 cm²
Now, we will calculate the area of smaller punch whose radius is 1cm
Area = 22/7 × 1²
= 22/7 cm²
Now, we will calculate the total area covered by circles
Total area covered by circles = area of small punch + area of 4 big punch
= 22/7 + 792/7
= 814 /7 cm²
Remaining area = area of square - area of circles
= 144 - 814/7
= (1008 - 814) / 7
= 194 / 7
= 27.714 cm²
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Related Questions
(c) Use a calculator to verify that Σ(x) = 64, Σ(x2) = 1118, Σ(y) = 628, Σ(y2) = 87,982, and Σ(x y) = 9,627.
Compute r. (Enter a number. Round your answer to three decimal places.)
Answers
The correlation based on the computation is 0.97.
How to compute the value?It should be noted that the question is that we should simply calculate the correlation which is r.
The correlation will be:
= Σ(x y) / (Σ(x²) × Σ(y²)
= 9627/✓(1118 × 87982)
= 9627 ✓98363876
= 9627/9917.86
= 0.97
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You need 30 quarts of water based paint to paint the interior of a house. If the price ofa gallon of paint is $22, how much will cost the paint for the interior of the house?
Answers
4 quarts in a gallon
Divide 30 by 4 to get how many gallons you need
Multiply that by 22 to get the price
If in a one tail hypothesis test where H0 is not only rejected in the upper tail, the oval he = 0.0739 and Zstat = + 1.45, what is the statistical decision if the null hypothesis is tested at the .10 level of significance?
What is the statistical decision?
Reject or do not reject?
Answers
Considering the p-value, the decision is described as follows:
Since the p-value is less than [tex]\alpha[/tex], we reject [tex]H_0[/tex].
What is the relation between the p-value and the conclusion of the test hypothesis?Depends on if the p-value is less or more than the significance level:
If it is more, the null hypothesis is not rejected.If it is less, it is rejected.In this problem, we have that:
The p-value is of 0.0739.The significance level is of 0.1.Hence:
Since the p-value is less than [tex]\alpha[/tex], we reject [tex]H_0[/tex].
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Geometry question! Help!
Answers
Answer: [tex]2\sqrt{2}[/tex]
Step-by-step explanation:
The inradius is given by the area of the triangle divided by the semiperimeter.
The semiperimeter is [tex]\frac{12+12+8}{2}=16[/tex].
Thus, by Heron's formula, the area is [tex]\sqrt{16(16-12)(16-12)(16-8)}=32\sqrt{2}[/tex].
Therefore, the radius is [tex]\frac{32\sqrt{2}}{16}=2\sqrt{2}}[/tex]
Josie and Pat are filing jointly as a married couple. Their combined taxable income is $142,800. This places them in the 22% tax bracket, owing $9,235 plus 22% of anything over $80,250. How much income tax do they owe?
Answers
The couple are owning income tax of $22,996.
What is tax?
Tax is the obligatory payment payable to the government on earnings.
In this case, the amount of tax to be paid is the sum of $9,235 plus 22% of the excess of the combined taxable income of the couple over $80,250.
Excess over $80,250=$142,800-$80,250
Excess over $80,250=$62,550
Initial tax amount=$9,235
extra tax amount=$62,550*22%
extra tax= 13,761
total tax amount=initial tax amount+ extra tax
total tax amount=$9,235+$13,761
total tax amount=$22,996
In essence, the couple would pay an initial tax of $9,235 plus an extra tax of $13,761 which gives a total tax liability of $22,996
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Determine the interval(s) on which the given function is decreasing?
Answers
Answer:
(-∞, -1) U (0, ∞)
Step-by-step explanation:
To figure out which parts of the function are decreasing, we need to read the graph left to right.
Given this information, we can figure out that the first part of the graph is decreasing, starts to go up a little bit, and then starts to decrease again.
How do we write this in mathematical terms, however? We simply take the x-values for which parts it decreases.
The graph started on negative infinity, and kept decreasing until -1 on the x-axis. We can write this as (-∞, -1). The graph starts to increase, which is not relevant to the question. As it starts to decrease again, it starts on 0, and slowly decreases to the right, meaning that it is going towards positive infinity. We can write this as (0,∞).
Now that we have both parts of the decreasing function, we can combine them using the union symbol (∪).
Therefore, our final answer is (-∞, -1) U (0, ∞).
Add.
−5/6+(−2 5/8)
Enter your answer as a simplified fraction by filling in the boxes.
pllzzzzz helppppp
Answers
We know we have
-5/6 added to -2 5/8
First we have to make the denominator the same for both fractions. 24 is a number that is divisible by both 6 and 8. See attachment for the math.
Now we have -20/24 and -2 15/24
Combine negative numbers to add them together.
Now we have -2 35/24, you need to reduce to simplest terms. Your fraction -35/24 is an improper fraction so divide -35/24 and you get -1 11/24 so combine that with your -2 for a total of
-3 11/24
Identify a pair of factors of −35 that has a sum of −2.
Answers
Answer:
-7 and 5
Step-by-step explanation:
If you multiply -7 and 5, you get -35
Add them, and you get -2.
Which graph shows the solution to the inequality lx+3l≥2 ?
Answers
When solving absolute value equations, we solve for two conditions, positive and negative.
does this represent quntitites that are proportional
Answers
Answer:
B
Step-by-step explanation:
Not all of the pairs represent the same ratio
PreCalc work, Need help with writing piece wise functions with graphs level 2. Giving branliest.
Answers
The piece-wise linear functions can be written as follows:
[tex]f(x) = -0.5x + 3, x < 5[/tex].[tex]f(x) = -5, x = 5[/tex][tex]f(x) = -x + 9, x > 5[/tex].What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For x less than 5, the y-intercept is of b = 3 and the function also gos through (2,2), hence the slope is:
m = (2 - 3)/(2 - 0) = -0.5.
Hence the rule is:
[tex]f(x) = -0.5x + 3, x < 5[/tex].
When x = 5, the function is constant at -5, hence:
[tex]f(x) = -5, x = 5[/tex]
For x less than 5, the function goes through points (6,3) and (7,2), hence the slope is:
m = (2 - 3)/(7 - 6) = -1.
Then:
y = -x + b
When x = 6, y = 3, hence the y-intercept is given as follows:
3 = -6 + b
b = 9.
Hence the rule is:
[tex]f(x) = -x + 9, x > 5[/tex].
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A cylinder and a cone have the same radius and height. The volume of the
cylinder is 639 ft3. What is the volume of the cone?
Answers
c= 0.99, x= 14.6, s=0.75, n = 13
Answers
Answer:
sorry accidentally posted
Step-by-step explanation:
will update when question comes out
write an inequality to represent the graph:
Answers
Answer:
Step-by-step explanation:
A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by
h(t) = −4.9t(squared) + 20t + 12.
How long does it take to reach maximum height? (Round your answer to three decimal places.)
Answers
The ball takes approximately a time of 2.041 seconds to reach its maximum height.
What time does the ball take to reach maximum height?
The height of the ball as a function of time is modelled by a quadratic equation, the required information can be found by transforming the expression into vertex form:
h = - 4.9 · t² + 20 · t + 12
h = - 4.9 · (t² - 4.082 · t - 2.449)
h + (- 4.9) · (6.615) = - 4.9 · (t² - 4.082 · t + 4.166)
h - 32.414 = - 4.9 · (t - 2.041)²
The ball takes approximately a time of 2.041 seconds to reach its maximum height.
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It took 4 hours for Nancy
Answers
Answer:
for what lol
Step-by-step explanation:
Questions on a statistics exam are considered good questions provided the questions discriminate between students who have
studied for the exam and those who have not studied. Suppose that on a particular statistics exam the students were separated
into two gnpups, Group 1 that studied and Group 2 that had not studied. Data was collected and a 95% confidence interval for
the difference in the proportion of those passing the exam from Group 1 that studied and the proportion of those passing the
exam from Group 2 that had not studied. The confidence interval turned out to be (0.005, 0.125). Select the best answer.
Let P, = the proportion of Group 1 students that passed the exam
Let Py = the proportion of Group 2 students that passed the exam
The data fails to show with 95% confidence that these questions discriminated between those who studied and those who did
not study.
© We are 95% confident that those who studied had a higher passing rate than those who did not study.
We are 95% confident that those who studied had a lower passing rate than those who did not study.
None of the above
Answers
Using the interpretation of the confidence interval, the correct option is:
We are 95% confident that those who studied had a higher passing rate than those who did not study.
What is the interpretation of a x% confidence interval?It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.
The confidence interval of the difference is:
(0.005, 0.125).
Since the entire interval is positive, the correct option is:
We are 95% confident that those who studied had a higher passing rate than those who did not study.
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What is the perimeter of a yard with length = 4 x + 6 2 x + 1 feet and width = x − 3 2 x + 1 feet? 4 x − 3 4 x + 12 feet 4 x − 3 2 x + 6 feet 8 x − 6 4 x + 12 feet 8 x − 6 2 x + 6 feet
Answers
The perimeter of the given yard is P = 10x + 6
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is expressed as:
P = 2(l + w)
where
l is the length
w is the width
Given the following parameters
length = 4x+6
width = x-3
Substitute
P = 2(4x+6+x-3)
P = 2(5x + 3)
P = 10x + 6
Hence the perimeter of the given yard is P = 10x + 6
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Use the graph of the polynomial function to find the factored form of the
related polynomial. Assume it has no constant factor.
Answers
The factored form of the related polynomial is (x - 1)(x - 9)
How to determine the factored form of the related polynomial?In this question, the given parameter is the attached graph
From the graph, we can see that the curve crosses the x-axis at two different points
These points are the zeros of the polynomial function.
From the graph, the points are
x = 1 and x = 9
Set these points to 0
x - 1 = 0 and x - 9 = 0
Multiply the above equations
(x - 1)(x - 9) = 0
Remove the equation
(x - 1)(x - 9)
Hence, the factored form of the related polynomial is (x - 1)(x - 9)
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please help me!! i don’t understand this like at all this is algebra btw
Answers
The length and width of the fence should be made 76.25 feet and 23.75 feet respectively. Also, the expression for the length is L = 3W + 5 and the perimeter is P = 2(4W + 5).
How to determine the fence's dimension?Mathematically, the perimeter of a rectangle can be calculated by using this formula;
P = 2(L + W)
Where:
P is the perimeter of a rectangle.L is the length of a rectangle.W is the width of a rectangle.Since the length of this fence is 5 more than 3 times the width, we have:
L = 3W + 5
Substituting the given parameters into the formula, we have;
200 = 2(3W + 5 + W)
200 = 2(4W + 5)
200 = 8W + 10
8W = 190
W = 190/8
W = 23.75 feet.
For the length, we have:
L = 3W + 5
L = 3(23.75) + 5
L = 76.25 feet.
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According to the graph, what is the value of the constant in the equation
below?
Height =
Constant
Width
A. 0.3
B. 2.2
C. 0.4
D. 1.3
Height
1.8
1.6-
1.4
0.8
0.6 +
0.4+
0.2 +
(0.5, 0.8)
(0.8, 0.5)
(1.6, 0.25)
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Width
(2,0.2)
Answers
Answer: 0.4
Step-by-step explanation:
Consider the point (0.5, 0.8).
Constant = (height)(width), which for this point, is 0.4.
Normandin Inc. has an unfunded pension liability of $575 million that must be paid in 20 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 6.8%, what is the present value of this liability?
Answers
The present value of this unfunded pension liability of $575 million in 20 years at a discount rate of 6.8% is $154,256,257.63.
What is the present value?The present value of an asset or liability refers to its future value discounted from a future period to the present period.
The present value can be computed using the PV table or formula.
We can also use an online finance calculator to determine the present value of the unfunded pension liability, as follows:
Data and Calculations:N (# of periods) = 20 years
I/Y (Interest per year) = 6.8%
PMT (Periodic Payment) = $0
FV (Future Value) = $575,000,000
Results:
PV = $154,256,257.63
Total Interest $420,743,742.37
Thus, the present value of this unfunded pension liability of $575 million in 20 years at a discount rate of 6.8% is $154,256,257.63.
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Find x and simplify completely
Answers
Answer:
x = [tex]6\sqrt{3}[/tex] i
Step-by-step explanation:
We can write the following equation according to Euclidian Theorem to find the value of x:
[tex]x^{2}[/tex] = 12*9 multiply 9 and 12
[tex]x^{2}[/tex] = 108 find the root of both sides
x = [tex]6\sqrt{3}[/tex] is the value of x
You are buying a house and you are financing the purchase with a mortgage of $130,000. The mortgage has a 30 year term and requires monthly payments. The mortgage charges an interest rate of 0.3% every month. What is the total interest payment over the life of the mortgage?
Answers
Answer:
130,000 -:- by 30 x 0.3 x 12 = 15,600.
Step-by-step explanation:
(I hope its right, Im not good at math)
a solid sphere is cut into 12 equal wedges. the volume of each wedge is V=1/9πr^3. solve the formula for r.
Answers
The formula, solved for r is r = ∛(9V/π)
Subject of formulaFrom the question, we are to solve for r is the given formula
The given formula is
V = 1/9πr³
Multiply both sides of the equation by 9 to get
9V = πr³
Now, divide both sides by π
∴ r³ = 9V/π
r = ∛(9V/π)
Hence, the formula, solved for r is r = ∛(9V/π)
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You are training to compete in a 10-kilometer race, and you know the circular running trail at
your park is one mile long. How many times will you need to run this trail in order to run 10
kilometers? (round to the nearest whole number) 1 Kilometer=0.62
.
Answers
Answer:
6.2 rounds
Step-by-step explanation:
since 1 kilometer is 0.62 miles
10 kilometers is 6.2 miles
so about 6 and 1/5 rounds
Howard and Jane are surveying their neighbors about the community garden. Their questions, written on the survey, are below:
Howard: Did you visit the garden this month?
Jane: How many times do you visit the garden in a month?
Who wrote a statistical question and why?
Jane, because there will be variability in the responses collected
Jane, because there can be only one answer to the question
Howard, because every neighbor will give the same answer
Howard, because there can be many answers to the question
Answers
According to the information, it can be inferred that Jane's question is the one that classifies as statistical because there will be variability in the answers (option A).
How to identify the statistical question?A statistical question is a type of question that is used to obtain information about a specific population and its trends or preferences.
In this case the statistical question is Jane's question because there will be variability in the answers, for example you will find that some people go to the garden once and others ten times a month.
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A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 higher than in the first. The tax in the first city was 8%, and the tax in the second city was 5%. The total hotel tax paid for the two cities was $692.50. How much was the hotel charge in each city before tax?
Answers
Step-by-step explanation:
x = hotel charge before tax in 1st city
y = hotel charge before tax in 2nd city
y = x + 1500
x×0.08 + y×0.05 = 692.5
why ?
a% of b = b×a/100
why ?
b = 100%
1% = 100%/100 = b/100
a% = a×1% = a×b/100 = b×a/100
so, e.g. 8% of something is that something multiplied by 8/100 or 0.08
now, we are using the first equation in the second equation :
x×0.08 + (x + 1500)×0.05 = 692.5
x×0.08 + x×0.05 + 1500×0.05 = 692.5
x×0.13 + 75 = 692.5
x×0.13 = 617.5
x = 617.5 / 0.13 = $4,750
y = x + 1500 = 4750 + 1500 = $6,250
the hotel charge before tax in the first city : $4,750
the hotel charge before tax in the second city : $6,250
Here are the gold medal times for the women’s 100-meter freestyle (swimming) in every other Summer Olympics:
Answers
The least-squares regression line equation is y = -0.28x + 610.31
The scatter plot of the dataTo plot the scatter plot of the data, we represent the x-axis with year and we represent the y-axis with time
Next, we plot the scatter plot using the dataset
See attachment for the scatter plot
Describe the relationship between the variables in the graph.From the attached scatter plot, we can see that the relationship between the variables in the graph is approximately linear.
This is so because the points appear to be on a straight line
Find the correlation coefficient.To do this, we make use of a graphing calculator, with the following summary:
X Values
∑ = 21608Mean = 1964.364∑(X - Mx)2 = SSx = 10062.545Y Values
∑ = 686.41Mean = 62.401∑(Y - My)2 = SSy = 842.83X and Y Combined
N = 11∑(X - Mx)(Y - My) = -2806.684R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -2806.684 / √((10062.545)(842.83)) = -0.9638
Hence, the correlation coefficient is -0.9638
Find the least-squares regression line.To do this, we make use of a graphing calculator, with the following summary:
Sum of X = 21608Sum of Y = 686.41Mean X = 1964.3636Mean Y = 62.4009Sum of squares (SSX) = 10062.5455Sum of products (SP) = -2806.6836The least-squares regression line equation is
y = bx + a
Where
b = SP/SSX = -2806.68/10062.55 = -0.27892
a = MY - bMX = 62.4 - (-0.28*1964.36) = 610.30872
So, we have
y = -0.27892x + 610.30872
Approximate
y = -0.28x + 610.31
Hence, the least-squares regression line equation is y = -0.28x + 610.31
The estimated gold medal time for 1924 and for 1976.We have:
y = -0.28x + 610.31
Substitute 1924 and 1976 for x
y = -0.28 * 1924 + 610.31 = 71.59
y = -0.28 * 1976 + 610.31 = 57.03
Are these estimates reliable?
Yes, the estimates are reliable
Are they reasonable?
Yes, the estimates are reasonable
Why are your answers in Question 5 different than the times given in the table?The results are different because the answers in 5 are estimated from the formula while the table are the actual values
Find the estimated gold medal time for 2022 and for 2200.We have:
y = -0.28x + 610.31
Substitute 2022 and 2200 for x
y = -0.28 * 2022 + 610.31 = 44.15
y = -0.28 * 2200 + 610.31 = -5.69
Are these estimates reliable?
No, the estimates are not reliable
Are they reasonable?
The estimate in 2022 is reasonable, while the estimate in 2200 is not reasonable
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Rewrite without parentheses.
−6w x5 (2w³ +7w¹x² – 5x²)
-
Simplify your answer as much as possible.
0
Answers
Step-by-step explanation:
Help me am lost somewhere