To find the surface area C of the birdhouse, we need to find the area of each face and add them together.
First, let's find the area of the square base:
Area of base = side^2 = 16^2 = 256 in^2
Next, let's find the area of each triangular face:
Area of each triangular face = 1/2 * base * height
Since the base is 16 in and the slant height is 10 in, the height can be found using the Pythagorean theorem:
height^2 = slant height^2 - base^2/4
height^2 = 10^2 - 16^2/4
height^2 = 100 - 64
height^2 = 36
height = 6
So the area of each triangular face is:
1/2 * 16 * 6 = 48 in^2
There are four triangular faces, so the total area of the triangular faces is:
4 * 48 = 192 in^2
Finally, we add the area of the base and the area of the triangular faces to find the total surface area:
256 + 192 = 448 in^2
Therefore, the surface area of the birdhouse is 448 square inches, which is closest to option A: 262 in^2.
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Find the area of a trapezoid if base 1 is 10 units and base 2 is 18 units and the height is 5 units.
Answer:
A=7.5
Step-by-step explanation:
A=a+b
2h=1+2
2·5=7.5
What is the value of X?
Answer:
102
Step-by-step explanation:
triangle area = 180 degrees
straight line = 180 degrees
180 - 127 = 53
49
49 + 53 + 3rd angle = 180
3rd angle = 78
180-78 = x
x = 102
On January 1, 2017, the Clutz Company purchased 30% of the 1,000,000 shares of Nancy's common stock for $15,000,000 when 30% of Nancy's net assets totaled $12,000,000. The excess of purchase price over the underlying assets was attributable to undervalued depreciable plant assets with a remaining useful life of ten years. Nancy reported net income of $8,000,000 and paid cash dividends of $2,000,000 during 2017.
Refer to Exhibit 13-2. What should the income reported by Clutz during 2017 from its investment in the Nancy Company be?
a. $2,100,000
b. $2,900,000
c. $2,400,000
d. $ 600,000
The income reported by Clutz during 2017 from its investment in the Nancy Company be $2,100,000. So, the option a is correct.
Acquisition price for 30% of the Stock (A) = $15,000,000
Fair Value of Nancy's Assets, 30% (B) = $12,000,000
Undervalued depreciable assets are to blame for the excess of consideration above fair value (A-B) = $ 3,000,000
Calculation of Nancy's Investing Income for 2017
Dividends that Nancy paid out (a) = $2,000,000 × 30%
Dividends that Nancy paid out (a) = $ 600,000
Clutz's Part of Nancy's Income (b) = ($8,000,000 - $2,000,000) × 30%
Clutz's Part of Nancy's Income (b) = $6,000,000 × 30/100
Clutz's Part of Nancy's Income (b) = $1,800,000
Depreciation calculations for undervalued assets
Value of Assets = $3,000,000
Useful Life = 10 years
Depreciation for 2017 = $3,000,000/10
Depreciation for 2017 = $300,000
Depreciation of Undervalued Assets (c) = $ 300,000
Therefore Income from Investment to be reported by Clutz(a + b - c) = $600,000 + $ 1,800,000 - $ 300,000
Income from Investment to be reported by Clutz(a + b - c) = $21,00,000
So the option a is correct.
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The graph shows the relationship between the number
of cups of flour and the number of cups of sugar in
Angela's brownie recipe.
The table shows the same relationship for Jaleel's
brownie recipe.
Jaleel and Angela buy a 12-cup bag of sugar and divide
it evenly to make their recipes.
If they each use ALL of their sugar, how much FLOUR
do they each need?
Angela's use 6 cups of flour and Jaleel's use 19/3 cups of flour.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The graph shows the relationship between the number of cups of flour and the number of cups of sugar in Angela's brownie recipe.
And, The table shows the same relationship for Jaleel's brownie recipe.
Hence, The equation for Angela's brownie recipe is,
Two points on graph are (4, 2) and (2, 1)
⇒ y - 2 = (2 - 1)/ (4 - 2) (x - 4)
⇒ y - 2 = 1/2 (x - 4)
⇒ y - 2 = 1/2x - 2
⇒ y = 1/2x
And, The equation for Jaleel's brownie recipe is,
Two points on graph are (3/2, 1) and (3, 2)
⇒ y - 1 = (2 - 1)/ (3 - 3/2) (x - 4)
⇒ y - 1 = 2/3 (x - 4)
⇒ y - 1 = 2/3x - 8/3
⇒ y = 2/3x - 8/3 + 1
⇒ y = 2/3x - 5/3
So, For Jaleel and Angela buy a 12-cup bag of sugar.
The equation for Angela's brownie recipe is,
⇒ y = 1/2x
⇒ y = 1/2 × 12
⇒ y = 6
The equation for Jaleel's brownie recipe is,
⇒ y = 2/3x - 5/3
⇒ y = 2/3 × 12 - 5/3
⇒ y = 19/3
Thus, Angela's use 6 cups of flour and Jaleel's use 19/3 cups of flour.
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The Quotient of 5 times a number and 7 is no more than 10.
every polynomial function of odd degree with real coefficients will have at least
Every polynomial function of odd degree with real coefficients will have at least one real root or zero.
This statement is known as the Fundamental Theorem of Algebra. It states that a polynomial of degree n, where n is a positive odd integer, will have at least one real root or zero.
The reason behind this is that when a polynomial of odd degree is graphed, it exhibits behavior where the graph crosses the x-axis at least once. This implies the existence of at least one real root.
For example, a polynomial function of degree 3 (cubic polynomial) with real coefficients will always have at least one real root. Similarly, a polynomial function of degree 5 (quintic polynomial) with real coefficients will also have at least one real root.
It's important to note that while a polynomial of odd degree is guaranteed to have at least one real root, it may also have additional complex roots.
The Fundamental Theorem of Algebra ensures the existence of at least one real root but does not specify the total number of roots.
In summary, every polynomial function of odd degree with real coefficients will have at least one real root or zero, as guaranteed by the Fundamental Theorem of Algebra.
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Consider the given pseudo code. Write the function T(n) in terms of the number of operations, and then give the asymptotic (big Oh) complexity of the algorithm, show all the work you do. [ write the summation formula and solve it, or use the "Look for pattern"method. a. Matrix Multiplication
The function T(n) in terms of the number of operations is:
T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).
To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.
The pseudo code for matrix multiplication may look something like this:
```
MatrixMultiplication(A, B):
n = size of matrix A
C = empty matrix of size n x n
for i = 1 to n do:
for j = 1 to n do:
sum = 0
for k = 1 to n do:
sum = sum + A[i][k] * B[k][j]
C[i][j] = sum
return C
```
Let's break down the number of operations step by step:
1. Assigning the size of matrix A to variable n: 1 operation
2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)
3. Outer loop: for i = 1 to n
- Incrementing i: n operations
- Inner loop: for j = 1 to n
- Incrementing j: n^2 operations (since it is nested inside the outer loop)
- Initializing sum to 0: n^2 operations
- Innermost loop: for k = 1 to n
- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)
- Performing the multiplication and addition: n^3 operations
- Assigning the result to C[i][j]: n^2 operations
- Assigning the value of sum to C[i][j]: n^2 operations
Total operations:
1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1
Therefore, the function T(n) in terms of the number of operations is:
T(n) = 2n^3 + 3n^2 + 2n + 1
To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.
In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).
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When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 7 kg, the acceleration of the object is 8 m/s^2. If the same force acts upon another object whose mass is 4 kg, what is this object's acceleration?
F = m.a
F = 7.8 = 56 N
56 = 4.a
a = 14 m/s²
What types of concurrent constructions are needed to find the centroid of a triangle?
The types of concurrent constructions that are needed to find the centroid of a triangle include the following: B. intersection of the lines drawn to the midpoint of each side of the triangle to its opposite vertex.
What is the centroid theorem?In Mathematics and Geometry, the centroid theorem states that the centroid of a triangle is located at two-third (2/3) of the distance from the vertex to the midpoint of the (opposite) sides.
Generally speaking, the centroid of a triangle simply refers to the point where the three (3) medians of the triangle meet or intersect. This ultimately implies that, a centroid is a point of intersection of the lines from each vertex of a triangle to the midpoint of the opposite sides.
In this context, the types of concurrent constructions would be modeled by answer option B.
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Complete Question:
What types of concurrent constructions are needed to find the centroid of a triangle.
A. intersection of the lines drawn from each vertex of a triangle and perpendicular to its opposite side.
B. intersection of the lines drawn to the midpoint of each side of the triangle to its opposite vertex.
C. intersection of the lines drawn to bisect each vertex of the triangle.
D. intersection of the lines drawn perpendicular to each side of the triangle through its midpoint
Consider a male restroom design with minimum plumbing requirements of 12 water closets and 13 lavatories, which one of the following is closest to the minimum space required with considering urinal substitution? Select one: O a. 222 b. 219 c. 237 d. 249
none of the provided options (a, b, c, d) appear to be accurate or close to the minimum space required.
To determine the minimum space required for a male restroom design with the given plumbing requirements, we need to consider the minimum space required for water closets and lavatories.
The minimum space required for water closets is typically around 30-36 inches per unit, and for lavatories, it is around 24-30 inches per unit.
Since the design requires a minimum of 12 water closets and 13 lavatories, we can estimate the minimum space required as follows:
Minimum space required for water closets = 12 water closets * 30 inches = 360 inches
Minimum space required for lavatories = 13 lavatories * 24 inches = 312 inches
Adding these two values together, we get a total minimum space requirement of 672 inches.
Among the given options, the closest value to 672 inches is option d) 249. However, this value seems significantly lower than the expected minimum space requirement.
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2cos theta=sqrt 3
solve in radians
The solution of the trigonometric equation is θ = π/6 radian
How to solve trigonometric equation?
Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles
2cosθ = √3
Divide both sides by 2:
cosθ = (√3)/2
θ = cos⁻¹[(√3)/2]
θ = 30°
Convert 30° to radian by multiplying it with π/180. That is:
θ = 30 × π/180
θ = π/6 radian
Thus, the solution is θ = π/6 radian
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the soccer field at bianca’s school has a length of 120 yards and a width of 85 yards. if she runs across the diagonal from one corner to another, how far does she run, in yards? round your answer to the nearest tenth.
The distance that she runs from one corner of the field to another is given as follows:
147.1 yards.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
The distance in this problem is the diagonal of a rectangle, which is the hypotenuse of a right triangle in which the length and the width are the sides, hence:
d² = 85² + 120²
d = sqrt(85² + 120²)
d = 147.1 yards.
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Plz help due tomorrow iff correct ill give brailiest
Answer:
so d = 43
and the answer to the question is divide
An item is regularly priced at $75. It is now priced at a discount of 65% off the regular price
Answer:
you pay $26.25
you save $48.75
Step-by-step explanation:
Trust
the average teaching salary in georgia is $48,553 per year. the school districts in the metro atlanta area boast that they pay more. a company that is running a career fair decides to take a random sample of 228 teachers from the metro atlanta area and record their salaries. the sample mean is $49,021, with a standard deviation of $3,127. do the data provide statistically significant evidence at the alpha
To answer this question, we need to perform a hypothesis test with the following null and alternative hypotheses:
- Null hypothesis: The true population mean teaching salary in the metro Atlanta area is equal to the average teaching salary in Georgia, i.e., μ = $48,553.
- Alternative hypothesis: The true population mean teaching salary in the metro Atlanta area is greater than the average teaching salary in Georgia, i.e., μ > $48,553.
We can use a one-sample t-test since we have a sample mean, sample standard deviation, and a sample size of n = 228. We can use a significance level of α = 0.05.
The test statistic for the t-test can be calculated as:
t = (sample mean - hypothesized population mean) / (sample standard deviation / sqrt(sample size))
t = (49,021 - 48,553) / (3,127 / sqrt(228))
t = 4.65
Using a t-distribution table with 227 degrees of freedom (n-1), we can find the critical value for a one-tailed test with α = 0.05, which is 1.645.
Since the calculated t-value of 4.65 is greater than the critical value of 1.645, we reject the null hypothesis.
This means that we have statistically significant evidence to conclude that the true population mean teaching salary in the metro Atlanta area is greater than the average teaching salary in Georgia.
In other words, the school districts in the metro Atlanta area do pay their teachers more than the state average.
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Ellen sells wedges of cheese at the local farmers' market. To make the wedges, she cuts a big 5-pound block of cheese into 16 pieces. How much does each wedge of cheese weigh?
Given :
Ellen sells wedges of cheese at the local farmers' market. To make the wedges, she cuts a big 5-pound block of cheese into 16 pieces.
To Find :
How much does each wedge of cheese weigh.
Solution :
Let , weight of each wedge of cheese is x.
16 pieces of wedge of cheese weight 5 pounds .
So,
\(16x=5\\\\x=\dfrac{5}{16}\\\\x=0.3125\ pounds\)
Therefore, weigh of cheese is 0.3125 pounds.
Hence, this is the required solution.
The value of a piece of property is growing at a rate of 3.5% annually. If the property was worth $125,000 when it was purchased, which equation could be used to determine the value of the property,x , years after it was purchased?
A.Y = 125000(3.5)x B. y = 125000(0.0035)x
C. y = 125000(1.035)x D. y = 125000(0.965)x
C.) Y = 125000(1.035)x
Step-by-step explanation:
I took the test and got it right
find the area under the normal curve to the left of z plus the area under the normal curve to the right of z. the combined area is
One is the sum of the areas under the normal curves to the left and right of z.
For a normal distribution, the total area under the curve is 1. Therefore, if we can find the area to the left of z, we can subtract it from 1 to find the area to the right of z.
The area to the left of z can be found using a standard normal distribution table or a calculator. For example, if z is 1.5, the area to the left of z is 0.9332.
The area under the entire normal curve is 1. Therefore, the area to the left of z plus the area to the right of z must add up to 1.
Visually, we can think of the normal curve as being symmetric about its mean, which is located at \(z = 0\). As a result, the area to z's left and right are equal. Area to the left of z plus Area to the right of z equals
\(1/2 + 1/2 = 1\) as a result.
\(1 - 0.9332 = 0.0668\)
Therefore, the combined area is:
\(0.9332 + 0.0668 = 1\).
This supports the notion that the entire area under the normal curve is 1.
As a result, the area under the normal curve to the left of z plus the area to the right of z together equal one.
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For j(x) = 5^x − 3, find j of the quantity x plus h end quantity minus j of x all over h period
For j(x) = 5^x − 3, find j(x+h) - j(x)/h
If j(x) = 5^(x - 3), using laws of exponents to solve the given expression [j(x + h) - j(x)]/h gives; [j(x + h) - j(x)]/h = [(5^(x - 3))(5^(h) - 1)]/h
How to utilize laws of exponents?We are given the function as;
j(x) = 5^(x - 3)
Now, we want to solve the expression;
[j(x + h) - j(x)]/h
This gives us;
j(x + h) = 5^(x - 3 + h)
Thus, our expression is now;
[j(x + h) - j(x)]/h = [5^(x - 3 + h) - 5^(x - 3)]/h
Now, according to laws of exponents, we know that;
y³ × y² = y³ ⁺ ²
Thus;
5^(x - 3 + h) = 5^(x - 3) × 5^h
Therefore;
[5^(x - 3 + h) - 5^(x - 3)]/h = [(5^(x - 3))(5^(h) - 1)]/h
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85. What is the value of x?والے1040)DDrawing not to scaleA 38°B. 128°C. 76D. 52°
Given:
One of the angle of a triangle is 104°.
The objective is to find the missing angle x.
If two sides of a triangle are equal, then it is an isosceles triangle.
In an isosceles triangle, the angle formed by the equal sides is also equal.
Then, the value of angle x can be calculated angle sum property of triangle.
\(\begin{gathered} x+x+104\degree=180\degree \\ 2x+104\degree=180\degree \\ 2x=180\degree-104\degree \\ 2x=76\degree \\ x=\frac{76}{2} \\ x=38\degree \end{gathered}\)Hence, option (A) is the correct answer.
A poster of area 8640 cm2 has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the sides. Find the dimensions that maximize the printed area. (Use decimal notation. Give your answers as whole or exact numbers.)
Therefore, the dimensions that maximize the printed area are 4 cm × 2156 cm.
Let's first find the dimensions of the printable region of the poster.
The total width of the poster is the sum of the printable width and the margins on the left and right sides:
Total width = Printable width + Left margin + Right margin
We know that the left and right margins are each 6 cm wide, so the total width is:
Total width = Printable width + 6 cm + 6 cm = Printable width + 12 cm
Similarly, the total height is the sum of the printable height and the margins on the top and bottom:
Total height = Printable height + Top margin + Bottom margin
We know that the top and bottom margins are each 10 cm wide, so the total height is:
Total height = Printable height + 10 cm + 10 cm = Printable height + 20 cm
The area of the printable region is:
Printable area = Printable width × Printable height
We want to maximize the printable area, so let's express the printable height in terms of the printable width:
Printable height = Total height - Top margin - Bottom margin
Printable height = (Printable width + 12 cm) - 10 cm - 10 cm
Printable height = Printable width - 8 cm
Substituting into the equation for printable area, we get:
Printable area = Printable width × (Printable width - 8 cm)
Now, we want to find the value of Printable width that maximizes Printable area. We can do this by taking the derivative of Printable area with respect to Printable width, setting it to zero, and solving for Printable width:
d(Printable area)/d(Printable width) = 2Printable width - 8 cm
2Printable width - 8 cm = 0
Printable width = 4 cm
So, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:
Printable height = Printable width - 8 cm
Printable height = 4 cm - 8 cm
Printable height = -4 cm
This is not a valid solution, since the height cannot be negative. Therefore, we made an error somewhere.
Printable width = -b/2a
where a = 1 and b = -8
Printable width = -(-8)/(2×1) = 4
Therefore, the width of the printable region that maximizes the printable area is 4 cm. Substituting this back into the equation for Printable height, we get:
Printable height = Printable width - 8 cm
Printable height = 4 cm - 8 cm
Printable height = -4 cm
Again, this is not a valid solution, since the height cannot be negative. However, we can see that the maximum occurs when Printable width is 4 cm, so the maximum printable area is:
Printable area = Printable width × Printable height
Printable area = 4 cm × (8640 cm / 4 cm - 16 cm)
Printable area = 4 cm × 2156 cm
Printable area = 8624 cm
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Please help
Solve for x
Answer:
x = 32
Step-by-step explanation:
(5x - 43) = (4x - 11) because the angles are vertically opposite
TAKE AWAY 11 FROM BOTH SIDES
(5x - 32) = 4x
SWAP -32 OVER TO +32 BY MOVING IT TO THE OTHER HALF OF THE EQUATION
5x = 4x + 32
SWAP 4x OVER BY DOING SAME THING
4x BECOMES NEGATIVE
5x - 4x = 32
FIND LIKE TERMS
1x = 32
x = 32
If f(x)=7x+3 ,what is f^-1(x)?
Answer:
\(\displaystyle{f^{-1}(x)=\dfrac{x}{7}-\dfrac{3}{7}}\)
Step-by-step explanation:
Swap f(x) and x position of the function, thus:
\(\displaystyle{x=7f(x)+3}\)
Then solve for f(x), subtract 3 both sides and then divide both by 7:
\(\displaystyle{x-3=7f(x)}\\\\\displaystyle{\dfrac{x}{7}-\dfrac{3}{7}=f(x)}\)
Since the function has been inverted, therefore:
\(\displaystyle{f^{-1}(x)=\dfrac{x}{7}-\dfrac{3}{7}}\)
And we can prove the answer by substituting x = 1 in f(x) which results in:
\(\displaystyle{f(1)=7(1)+3 = 10}\)
The output is 10, now invert the process by substituting x = 10 in \(f^{-1}(x)\):
\(\displaystyle{f^{-1}(10)=\dfrac{10}{7}-\dfrac{3}{7}}\\\\\displaystyle{f^{-1}(10)=\dfrac{7}{7}=1}\)
The input is 1. Hence, the solution is true.
2.1Simplifying Expressions: Problem 1 (1 point) Simplify the following expression. 6- 4(x - 5)-
The simplified expression is 26 - 4x.
To simplify the expression 6 - 4(x - 5), we can apply the distributive property and simplify the terms.
6 - 4(x - 5)
First, distribute -4 to the terms inside the parentheses:
6 - 4x + 20
Now, combine like terms:
(6 + 20) - 4x
Simplifying further:
26 - 4x
Therefore, the simplified expression is 26 - 4x.
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i need help somebody please
The last one is equivalent: 2( n - 3 )
CAN SOEMBODYY JUST PLSS IM BEGGIN HEL PMEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
Hi, there
Question 1: B. 6x^3(x-6)
Question 2: A. (8x+3)^2
Question 3: A. (5x+9y)(5x-9y)
Question 4: D.(x-2)(x-3)
Step-by-step explanation:
Hope this helps :)
What is the value of y?
PLEASE HELPP If you place a 21-foot ladder against the top of a building and the bottom of the ladder is 12 feet from the bottom of the building, how tall is the building?
Answer:\(3\sqrt{33}\)
Step-by-step explanation:
a^2+b^2=c^2
12^2+b^2=21^2
144+b^2=441
b^2=297
b=\(3\sqrt{33}\)
Step-by-step explanation:
You are basically doing the Pythagorean Theorem. The answer is estimated so the building is 17.23 feet tall.
Why is i squared equal to 1?
The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.
Given that,
We have to find why i squared is equal to negative 1.
We know that,
The imaginary numbers are denoted as i.
We occasionally obtained negative integers in equations when using the radican (square root) symbol to solve them. When they realized this, some would halt and respond, "no actual solution," which is technically accurate. We can further simplify radicals by using the imaginary number I which is the square root of real numbers. We occasionally even manage to get rid of the fictitious element, which provides us with actual solutions.
The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.
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2x - x = 3x - 12 what does x equal
Answer:
2x-3x- x=-12
-2x= -12
x=6