Step-by-step explanation:
1. To round $5/11 = 0.\overline{45}$ to the nearest whole number, we look at the digit in the ones place, which is 5. Since 5 is greater than or equal to 5, we round up to the next whole number, which is 1. Therefore, rounded to the nearest whole number, $5/11$ is equal to 1.
2. To round $5/11 = 0.\overline{45}$ to the nearest tenth, we look at the digit in the hundredth place, which is 5. Since 5 is greater than or equal to 5, we round up to the next tenth, which is 0.5. Therefore, rounded to the nearest tenth, $5/11$ is equal to 0.5.
3. To round $5/11 = 0.\overline{45}$ to the nearest hundredth, we look at the digit in the thousandth place, which is also 5. Since 5 is greater than or equal to 5, we round up to the next hundredth, which is 0.46. Therefore, rounded to the nearest hundredth, $5/11$ is equal to 0.46.
4. To round $5/11 = 0.\overline{45}$ to the nearest thousandth, we look at the digit in the ten thousandth place, which is 4. Since 4 is less than 5, we round down to 0.455. Therefore, rounded to the nearest thousandth, $5/11$ is equal to 0.455.
5. To round $5/11 = 0.\overline{45}$ to the nearest ten thousandth, we look at the digit in the hundred thousandth place, which is 5. Since 5 is equal to 5, we round up if the digit in the ten thousandth place is odd, and round down if it is even. In this case, the digit in the ten thousandth place is 4, which is even, so we round down to 0.4550. Therefore, rounded to the nearest ten thousandth, $5/11$ is equal to 0.4550.
6. To round $5/11 = 0.\overline{45}$ to the nearest hundred thousandth, we look at the digit in the millionth place, which is also 5. Since 5 is equal to 5, we round up if the digit in the hundred thousandth place is odd, and round down if it is even. In this case, the digit in the hundred thousandth place is even, so we round down to 0.45499. Therefore, rounded to the nearest hundred thousandth, $5/11$ is equal to 0.45499.
When Tony rounds $0.\overline{45}$ to the nearest hundred thousandth, he gets 0.45499, which he then rounds to 0.4550, and so on, following the same steps we did above. His final answer for question 1 will be 0, since rounding 0.5 to the nearest whole number gives 0. Therefore, Tony's final answers will be:
1. 0
2. 0
3. 0.46
4. 0.455
5. 0.4550
6. 0.45499
In finding the percent of a number, when might you want to use the fraction form of the percent instead of the decimal form?
The percent is easily represented as a fraction (e.g., 25% as 1/4 or 50% as 1/2). Using the fraction form can make calculations easier to understand and perform, especially when dealing with whole numbers.
You might want to use the fraction form of a percent instead of the decimal form when working with fractions or when it is easier to simplify a problem using fractions. For example, if you are trying to find 25% of a number and the number can be easily divided by 4, it may be simpler to write 25% as 1/4 rather than 0.25. Additionally, if you are working with ratios or proportions, it may be more useful to use fractions rather than decimals to keep the numbers in the same format.
In finding the percent of a number, you might want to use the fraction form of the percent instead of the decimal form when working with ratios, simplifying calculations, or when the percent is easily represented as a fraction (e.g., 25% as 1/4 or 50% as 1/2). Using the fraction form can make calculations easier to understand and perform, especially when dealing with whole numbers.
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Can someone please help me answer this question, thank you in advance!
Answer:
[tex]\frac{w^{6} }{9}[/tex]
Step-by-step explanation:
To divide powers that have the same base, subtract the denominator's exponent from the numerator's exponent.
Doing so leaves us with [tex]3^{-2}[/tex] [tex]k^{0}[/tex][tex]w^{6}[/tex].
Next, you need to calculate 3 to the power of −2 to get [tex]\frac{1}{9}[/tex].
Then, calculate k to the power of 0 to get 1.
Multiply [tex]\frac{1}{9}[/tex] and 1 to get [tex]\frac{1}{9}[/tex].
This leaves us with [tex]\frac{1}{9} w^{6}[/tex], which is equivalent to our final answer.
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In 2000, the world population was estimated to be 6. 124 billion people. In 2005, it was 6. 515 billion. Write and exponential growth equation to represent the population y in billions t years after 2000
To represent the world population in billions t years after 2000, an exponential growth equation can be used.
Explanation:
Let y be the world population in billions t years after 2000. Let t be the time elapsed in years since 2000. Let y0 be the world population in billions in the year 2000. Let r be the annual growth rate of the world population as a decimal.
Using the exponential growth equation, we can write:
y = y0 * (1 + r)^t
To find the value of r, we can use the population data from 2000 and 2005. The population growth from 2000 to 2005 can be calculated as:
(6.515 - 6.124) / 6.124 = 0.0638
This means that the world population grew at an annual rate of 0.0638 or 6.38% per year. Therefore, the exponential growth equation for the world population in billions t years after 2000 is:
y = 6.124 * (1 + 0.0638)^t
This equation can be used to estimate the world population in any year t after 2000.
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help me!! in speed of light please whoever answer it and gets it right gets brainiest
solve for y in the following inequality
A.Y⊇ 2.5
B. Y⊆ 2.5
C. Y⊇ 8
D. Y⊆ 8
The solution of the inequality is as follows:
y ≥ 8
How to solve inequality?Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.
Therefore, let's solve the inequality by finding the value of variable y in the inequality.
A variable is a number represented with letter in the inequality.
Therefore,
11 - 4y ≥ -21
subtract 11 from both sides of the inequality
11 - 4y ≥ -21
11 - 11 - 4y ≥ -21 - 11
-4y ≥ - 32
divide both sides of the inequality by -4
y ≥ - 32 / - 4
y ≥ 8
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Answer:
D. y ≤ 8
Step-by-step explanation:
Given inequality:
[tex]11-4y \geq -21[/tex]
To solve for y, begin by subtracting 11 from both sides of the inequality:
[tex]\begin{aligned}11-4y-11 &\geq -21-11\\\\-4y &\geq -32\end{aligned}[/tex]
To isolate y, divide both sides by -4.
As we are dividing by a negative number, we must reverse the direction of the inequality symbol.
[tex]\begin{aligned}\dfrac{-4y}{-4} &\geq \dfrac{-32}{-4}\\\\y&\leq8\end{aligned}[/tex]
Therefore, the solution to the given inequality is y ≤ 8.
a bank manager wants to know the mean amount of mortgage paid per month by homeowners in an area. a random sample of 98 homeowners selected from this area showed that they pay an average of $1510 per month for their mortgages. the population standard deviation of such mortgages is known to be $194. a. [3 pts] find the margin of error for a 98% confidence interval (to 3 decimal places) b. [2 pts] give the 98% confidence interval for the mean amount of mortgage paid per month by all homeowners in this area (rounded to 2 decimal places). [3 pts] if the bank manager wanted to restrict the margin of error to $25, what sample size should the banker use?
The margin of error is approximately $43.51. The 98% confidence interval for the mean amount of mortgage paid per month by all homeowners in this area is ($1466.49, $1553.51). The banker should use a sample size of at least 285.
a) We want to find the margin of error for a 98% confidence interval. The critical value for a 98% confidence interval with 97 degrees of freedom is 2.326. The margin of error is then:
margin of error = critical value * (standard deviation / sqrt(sample size))
= 2.326 * (194 / sqrt(98))
≈ 43.51
So the margin of error is approximately $43.51.
b) The 98% confidence interval is given by:
sample mean ± margin of error
= $1510 ± 43.51
= ($1466.49, $1553.51)
So the 98% confidence interval for the mean amount of mortgage paid per month by all homeowners in this area is ($1466.49, $1553.51).
c) We want to find the sample size required to have a margin of error of $25. Solving the margin of error formula for sample size, we get:
sample size = (critical value * standard deviation / margin of error)^2
Since we want a 98% confidence interval, the critical value is 2.326. The standard deviation is still $194. Plugging in $25 for the margin of error, we get:
sample size = (2.326 * 194 / 25)^2
≈ 284.87
So the banker should use a sample size of at least 285.
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pls help , due at 12:00
The value of x is given as follows:
x = 5.4.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For the angle of 60º, we have that:
x is the adjacent side.9.3 is the opposite side.Hence we apply the tangent ratio to obtain the value of x as follows:
tan(60º) = 9.3/x
x = 9.3/tangent of 60 degrees
x = 5.4.
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Please help! Find the length of each arc. Do not round. Put answers in terms of pi.
Answer:
14π cm---------------------
Use the formula:
s = (θ/360) × 2πr,where θ is the central angle in degrees, r is the radius
We have:
θ = 315 and r = 8.Substituting the given values, we get:
s = (315/360) × 2π(8)s = (7/8) × 2π(8) s = 14πTherefore, the length of the arc is 14π cm.
Which expression is equal to x+8x+2⋅(x+2)(x−8)x2+13 ?
Responses
(x+8)(x−8)x3+26
(x+8)(x−8)x2+13
(x+8)2x3+26
(x+8)2x2+13
Answer:
Step-by-step explanation:
(x+8)(x−8)x2+13 is the answer
The given expression is:
x+8x+2⋅(x+2)(x−8)x2+13
To simplify this expression, you can start by simplifying the denominator:
2⋅(x+2)(x−8)x2+13 = 2(x2-6x-16)x2+13 = 2(x2-6x-16)x2 + 26x - 26x + 13
= 2(x2-6x-16)x2 + 26x + (-26x + 13)
Now you can rewrite the original expression as:
x+8x+(2(x2-6x-16)x2 + 26x + (-26x + 13))
= x(1 + 8x2(x2-6x-16)x2 + 26x + (-26x + 13))
x(2(x^2-6x-16)x^2 + 13)
We can simplify the expression inside the parenthesis first:
2(x^2-6x-16)x^2 = 2x^4 - 12x^3 - 32x^2
Substituting this back into the original expression, we get:
x(2x^4 - 12x^3 - 32x^2 + 13)
Multiplying out the brackets, we get:
2x^5 - 12x^4 - 32x^3 + 13x
Now, we can factor out a common factor of x:
x(2x^4 - 12x^3 - 32x^2 + 13)
= x(2x^4/x - 12x^3/x - 32x^2/x + 13/x)
= x(2x^3 - 12x^2 - 32x + 13/x)
Finally, we can factor the expression inside the brackets:
= x(2x^3 - 16x^2 + 4x^2 - 32x + 8x - 8 + 13/x)
= x(2x^2(x-8) + 4x(x-8) + 8(x-8) + 13/x)
= x(x-8)(2x^2+4x+8) + 13(x-8)/x
= (x-8)(x^3+2x^2+4x+13)/x
Now we can see that the expression can be written as:
(x-8)(x^3+2x^2+4x+13)/x
To simplify further, we can divide x into the numerator to get:
(x+8)(x−8)x^2+13
Therefore, the expression is equal to (x+8)(x−8)x2+13.
suppose that is continuous on and on . if the area between and the - axis on is 10, the average value of on this interval is
If the area between the function and the -axis on the interval [a, b] is 10 and the function is continuous on and on, then the average value of the function on this interval is between m and M, where m and M are the lower and upper bounds for the function on the interval.
To find the average value of a continuous function on an interval, we need to use the following formula:
Average value = (1 / b-a) * ∫[a,b] f(x) dx
where a and b are the endpoints of the interval, and ∫[a,b] f(x) dx represents the definite integral of the function over the interval.
In this case, we are given that the area between the function and the -axis on the interval [a, b] is 10. This means that ∫[a,b] f(x) dx = 10.
We don't know the values of a and b, but we do know that the function is continuous on and on, which means that it is continuous on the entire interval [a, b]. Therefore, we can assume that the function is integrable on this interval.
To find the average value of the function, we need to know the length of the interval [a, b]. This is given by the difference between the endpoints: b-a.
We don't know the value of b-a, but we do know that the function is continuous on and on, which means that it is bounded on this interval. This means that there exist numbers M and m such that m ≤ f(x) ≤ M for all x in [a, b].
We can use this information to find an upper bound and a lower bound for the average value of the function:
Lower bound = (1 / (b-a)) * ∫[a,b] m dx = m
Upper bound = (1 / (b-a)) * ∫[a,b] M dx = M
Therefore, the average value of the function on the interval [a, b] is between m and M. We cannot determine the exact value of the average value without knowing more information about the function or the interval.
In summary, if the area between the function and the -axis on the interval [a, b] is 10 and the function is continuous on and on, then the average value of the function on this interval is between m and M, where m and M are the lower and upper bounds for the function on the interval. The length of the interval [a, b] and the exact value of the function would be needed to find the exact value of the average value.
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The exterior angle of a triangle is 124°. What two measurement could represent the opposite interior angles?
The two opposite Interior angles of the triangle are y and 56°.
In a triangle, the sum of the measures of the interior angles is always 180°. the three interior angles of the triangle A, B, and C. The exterior angle, which is the angle formed by extending one of the sides of the triangle, is equal to the sum of the two non-adjacent interior angles.
So, if we call the two non-adjacent interior angles that form the exterior angle x and y, we can write:
x + y = 124° (1)
The third interior angle, C, can be found by subtracting the sum of the other two interior angles from 180°:
C = 180° - (x + y) (2)
We can use equation (1) to solve for one of the variables, say x, in terms of the other, y:
x = 124° - y
Substituting this into equation (2), we get:
C = 180° - (124° - y + y) = 56°
Therefore, the two opposite interior angles of the triangle are y and 56°. that there are different possible values for y, depending on which exterior angle we are considering. However, once we know one of the opposite interior angles, we can always find the other one by subtracting it from 180°.
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Please help me find bd
The value of BD is 6
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. The corresponding angles of similar triangles are equal.
Also the ratio of corresponding sides of similar triangles are equal.
Therefore;
12/x = x/3
x² = 12 × 3
x² = 36
x = √36
x = 6
Therefore the value of BD is 6
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Suppose x = 1, y = -1, and z = 1. What is the output of the following statement? (Please indent the statement correctly first.)
if (x > 0)
if (y > 0)
System.out.println("x > 0 and y > 0");
else if (z > 0)
System.out.println("x < 0 and z > 0");
A. x > 0 and y > 0;
B. x < 0 and z > 0;
C. x < 0 and z < 0;
D. no output
Based on the evaluation of the conditions, the output "x < 0 and z > 0" will be printed. Therefore, the correct answer is B. x < 0 and z > 0.
The correct indentation of the statement would be as follows:
if (x > 0)
if (y > 0)
System.out.println("x > 0 and y > 0");
else if (z > 0)
System.out.println("x < 0 and z > 0");
Given that x = 1, y = -1, and z = 1, let's evaluate the conditions:
The first if statement checks if x > 0, which is true since x = 1.
Since the condition in the first if statement is true, we move to the inner if statement, which checks if y > 0. However, y = -1, so this condition is false.
The inner if statement is followed by an else if statement that checks if z > 0. Since z = 1, this condition is true.
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if f is a one to one function and f(2)=3 what is f^-1(3)
Answer:
2
Step-by-step explanation:
F^-1 IS AN INVERSE, SO F(2)=3 THEREFORE F^-1(3) = 2
A real jeep can go up to 121 mph. A power wheels jeep goes 8 mph. What is the percent decrease?
Answer:93.3884%
Step-by-step explanation:
Based on the given conditions, formulate:(121-8)%121
Calculate the sum or difference:113/121
Rewrite a fraction as a decimal:0.933884
Multiply a number to both the numerator and the denominator: 0.933884* 100/100
Calculate the product or quotient: 93.3884/100
Rewrite a fraction with denominator equals 100 to a percentage: 93.3884%
. What is the total surface area? 52;4 Record your answer on the grid and fill in the bubbles. Be sure to use correct place value.
Based on the information, we can infer that the surface area of the rectangular prism is 485.5 in²
How to calculate surface area of rectangular prism?To calculate the surface area of the rectangular prism we must calculate the area of all the faces of the prism:
7.5 in * 18.5 in = 138.75 in² 4 in * 7.5 in = 30 in² 18.5 in * 4 in = 74 in²Now we must multiply each result by 2 because each of the faces is repeated 2 times.
138.75 in * 2 = 277.5 in² 30 in * 2 = 60 in² 74 in * 2 = 148 in²Finally, we must add the values to find the total surface area of the rectangular prism:
277.5 in² + 60 in² + 148 in² = 485.5 in²Note: This question is incomplete. Here is the complete information.
Attached Image
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work out the equation of the straight line shown below
Answer: The required equation of the straight line is: y = -5x+3
Step-by-step explanation:
we know, the equation of a straight line is :
y = mx + c ----(i)
where y = y coordinate, x = x coordinate, m = slope of the straight line, and c = intercept of the straight line.
Slope, m = tan theta = y2 - y1 / x2 - x1,
In this question, c = 3,
m = y2 - y1 / x2 - x1
Here, taking y2 = 3, y1 = -2, x2 = 0, x1 = -1 , we have,
=> m = 3 - (-2) / 0 -1
=> m = -5
Now, putting the values of m and c in equation (i) we get,
y = -5x + 3, which is the required solution.
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To solve for the equation of a straight line, we calculate the slope 'm' and y-intercept 'b' from the graph and substitute these values into the standard line equation y=mx+b.
Explanation:To work out the equation of the straight line we usually use the standard form of a linear equation which is y=mx+b, where 'm' is the slope of the line and 'b' is the y-intercept. The slope 'm' can be found by identifying two points on the line and applying the formula (y2 - y1) / (x2 - x1). The y-intercept 'b' is where the line crosses the y-axis. Once 'm' and 'b' have been calculated, they can be substituted into the equation format to find the equation of the line.
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Compare the functions
The function f(x) and g(x) have the same behavior for all real values except x = -1/4, as f(x) is not defined at x = -1/4.
How to define the domain and range of a function?The domain of a function is defined as the set containing all possible input values of the function, that is, all the values assumed by the independent variable x in the context of the function.The range of a function is defined as the set containing all possible output values of the function, that is, all the values assumed by the dependent variable y in the context of the function.The function f(x) is defined as follows:
f(x) = [(4x + 1)(x - 5)]/(4x + 1).
The denominator cannot be zero, hence the value that is outside the domain is given as follows:
4x + 1 = 0
4x = -1
x = -1/4.
For the other values, the 4x + 1 terms can be simplified, hence f(x) = g(x) = x - 5, meaning that they are equal.
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PLEASE HELP! I have no idea what I'm doing and it's kinda freaking me out ...thanks in advance
All the conic section are,
1) Parabola
2) Hyperbola
3) Ellipse
4) Circle
We have to given that;
We have to find the conic section for each condition.
1) when a plane crosses the generating line at the intersection of a single cone from a double-napped cone.
Then, We get Parabola is formed.
2) We know when a plane intersects on one nape of a double napped cone and then the cross section that is obtained is either a parabola, ellipse or a circle.
But if it passes through both the napes of a double napped cone then the cross-section obtained is a hyperbola.
Hence, the answer is Hyperbola.
3) When, A plane intersects at one cone of a double-napped cone for that the plane is neither parallel to the generating line nor perpendicular to the axis,
Then, Ellipse is formed.
4) When plane intersect at one cone of a double napped cone such that the plane is perpendicular for the generating line.
Then, We get Circle is formed.
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3. Find the measure of Arc BED. *
E
D
O 180 degrees
O142 degrees
O218 degrees
O 72 degrees
3
a
Page 3 of 10
Clear form
The measure of arc BED is 218 degree.
We know,
The total measure of a circle is 360°
Now, from the figure let us consider the Centre of circle at O.
Then, <DOL + <LOB +< BOD= 360
90 + 52 + <BOD= 360
142 + <BOD= 360
<BOD = 360- 142
<BOD = 218
Thus, the measure of arc BED is 218 degree.
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each of the digits $6,7,8,9$ is used no more than once to form an integer $n.$ how many possible $n$s are multiples of $3$?
There are $18$ possible integers $n$ that can be formed using the digits $6,7,8,9$ where each digit is used no more than once and the resulting integer is a multiple of $3$.
To determine if a number is divisible by $3$, we can add up its digits and see if that sum is divisible by $3$. Since $6+7+8+9 = 30$ is divisible by $3$, any integer formed by these four digits will be divisible by $3$ if and only if it contains at least one $9$.
There are four ways to choose the location of the $9$ in the integer. Once we've chosen the location for the $9$, we can fill the remaining three spots with the digits $6,7,$ and $8$ in any order. Since there are $3! = 6$ ways to order three distinct elements, there are $4\times 6 = 24$ ways to form an integer using the digits $6,7,8,9$ with no repetition that is divisible by $3$. However, we've counted the integer $9876$ twice, so there are actually only $18$ possible integers.
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Please answer as soon as possible!
The triangle ABC has its coordinates as shown below.
A:(3,3)
, B:(−2,−2)
, and C:(4,−4)
Triangle ABC is translated 2 units up, 3 units left and then dilated by a scale factor of 4 about the origin to form triangle A' B' C'. What are the coordinates of the vertex B' ? Enter your answer in the box below.
The translation of the triangle, 2 units up and 3 units to the left, followed by a dilation by a scale factor of 4 about the origin, indicates;
The coordinates of the vertex B is; (-20, 0)
What is a dilation transformation?A dilation transformation is one in which the size of the pre-image is transformed to produce the image, which may be smaller or increased in size.
The coordinates of the vertices of the triangles are;
A(3, 3), B(-2, -2), and C(4, -4)
The translation applied to the triangle are;
Vertical translation = 2 units up
Horizontal translation = 3 units to the left
The scale factor of the dilation = 4
The center of dilation = The origin
Therefore, we get;
The transformation applied to the vertices are as follows;
A(3 - 3, 3 + 2), B(-2 - 3, -2 + 2), and C(4 - 3, -4 + 2), which produces the coordinate points;
A(0, 5), B(-5, 0), and C(1, -2)
The dilation by a scale factor of 4, with the center of dilation at the origin, therefore, produces;
4 × (0, 5) ⇒ A'(0, 20)
4 × (-5, 0) ⇒ B'(-20, 0)
4 × (1, -2) ⇒ C'(4, -8)
The vertex of the coordinate B are therefore; (-20, 0)
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If you save 20% of your paycheck each week, how much would you save if you made $224 in a week. How much would you save in a month (4 weeks)?
If you save 20% of your paycheck each week, you would save $44.80 if you made $224 in a week. In a month (4 weeks), you would save a total of $179.20.
To determine how much you would save each week, you need to multiply your paycheck by the percentage you want to save:
$224 x 20% = $44.80
Therefore, you would save $44.80 each week if you made $224 and saved 20% of your paycheck.
To calculate how much you would save in a month, you need to multiply your weekly savings by the number of weeks in a month:
$44.80 x 4 = $179.20
Therefore, if you made $224 per week and saved 20% of your paycheck, you would save $44.80 each week and a total of $179.20 in a month.
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need to find the radius of sector b.
Answer:
7.7cm to 1 decimal place
Step-by-step explanation:
for 1st circle, area of full circle = π r² = π (12)² = 144π
area of sector for 1st circle = (42/360) X 144π = 16.8π
for sector of 2nd circle, area = 16.8π
area of sector = (103/360) π r² = 16.8π
π r² = (16.8π) ÷ (103/360)
= 184.469.....
r² = 58.718.....
r = 7.7 cm to 1 decimal place
Write and solve an inequality:
Cecilia earns a salary of $20,000 plus a commission of 15% of her sales. How much must her sales be in order to earn at least
$29,000 this year?
Her sales in order to earn at least $29,000 this year must be at least 60000
Calculating her sales in order to earn at least $29,000 this year?From the question, we have the following parameters that can be used in our computation:
Cecilia earns a salary of $20,000 Commission of 15% of her sales.Using the above as a guide, we have the following:
Earnings = 20000 + 15% * x
Where x is sales
The earnings is atleast 29,000
So, we have
20000 + 15% * x ≥ 29,000
This gives
15% * x ≥ 9,000
So, we have
x ≥ 60000
Hence, her sales must be at least 60000
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What multiplies to -112 and adds to 24
Answer: -4 and 28
Step-by-step explanation:
First, we will list factors of -112. Since we are multiplying to a negative number, we know that one number will be negative and one number will be positive.
±1, ±2, ±4, ±7, ±8, ±14, ±16, ±28, ±56 and ±112
Looking at this list of factors, we see 28 and 4. We know that 28 - 4 = 24, and 28 * -4 = -112. This means the answer to our question is:
-4 and 28
a laborer charges a fixed amount
of $100.00 for a day's weeding
contract plus an additional amount
for each acre of land cleared per day.
on a particular day, he was paid
$1500.00 for weeding 5 acres
of land, find.
the amount he received per acre
Answer: The laborer charges $100.00 for a day's weeding contract and was paid $1500.00 for weeding 5 acres of land. This means he received $1500.00 - $100.00 = $1400.00 for weeding 5 acres of land.
The amount he received per acre is $1400.00 / 5 acres = $280.00 per acre.
So the answer is 280
In angleABC, AB = 4.12, BC = 4, AC = 5. What is m 2 C?
A.25
B. 37.5
C. 43.93
D. 53.08
cos(C) = (4.12^2 + 4^2 - 5^2) / (2(4.12)(4)) ≈ 0.8197
C ≈ 36.99°
To find 2C, we simply multiply C by 2:
2C ≈ 73.98°
Therefore, the correct answer is D. 73.98.
For each diagram, write down whether the line segments are marked as parallel, perpendicular or equal-length. a) c) b) d) y
The relationships between the line segments in the diagrams are as follows:
a) Equal Length
b) Parallel
c) Perpendicular
d) Equal Length
Let's analyze each diagram and determine the relationships between the line segments.
a) Equal Length:
In this diagram, the two line segments appear to be of the same length. They do not appear to be parallel or perpendicular to each other. When the lengths of two line segments are equal and their orientation doesn't affect this equality, we say they are of equal length. In this case, both line segments simply share the same length without any specific angle relationship.
b) Parallel:
In this diagram, the two line segments run side by side in the same direction and do not intersect. When two lines follow this pattern, they are considered parallel. Parallel lines have the same slope, which means they maintain a constant distance between each other as they extend indefinitely.
c) Perpendicular:
In this diagram, the two line segments meet at a right angle, forming a perfect 90-degree angle where they intersect. When two lines intersect at a right angle, they are referred to as perpendicular. Perpendicular lines have slopes that are negative reciprocals of each other, meaning they intersect at right angles.
d) Equal Length:
Similar to the first diagram, in this case, the two line segments are of equal length. They are not parallel or perpendicular; they simply have the same length.
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Valentina made a scale drawing of a house and its lot. In real life, the porch is 20 feet wide. It is 38 inches wide in the drawing. What is the scale of the drawing?
Answer:Therefore, the scale of the drawing is 1 inch : 3.166 feet.
Step-by-step explanation:
To find the scale of the drawing, we need to determine the ratio of the size of the porch in the drawing to its actual size.
First, we need to convert 38 inches to feet:
38 inches ÷ 12 inches/foot = 3.1667 feet
Next, we can set up a proportion:
drawing size / actual size = scale factor
Let x be the scale factor. Then:
x / 20 feet = 3.1667 feet / 20 feet
Simplifying the right side:
3.1667 feet / 20 feet = 0.1583
Multiplying both sides by 20 feet:
x = 0.1583 × 20 feet
x = 3.166 feet
Therefore, the scale of the drawing is 1 inch : 3.166 feet.
the blades of a windmill turn on an axis that is 40 feet from the ground. the blades are 15 feet long and complete 3 rotations every minute. write a sine model, y
We get the following sine model for the vertical displacement y of a point on the blade at time t: y = 7.5 sin(2π(3t - 1)) + 40. This model gives the height above the ground of a point on the blade at time t, measured in minutes.
Assuming that the blades move in a circular motion, the vertical displacement of a point on a blade can be modeled using a sine function.
Let's start by finding the period of the function, which is the time it takes for the blade to complete one full rotation. Since the blade completes 3 rotations every minute, the period is:
T = 1/3 minutes
Next, we need to find the amplitude of the function, which is half the distance between the highest and lowest points of the blade's path. Since the blade is 15 feet long, the amplitude is:
A = 15/2 = 7.5 feet
Finally, we need to find the vertical displacement of the blade at time t, measured in minutes. Let's assume that t=0 corresponds to a blade pointing directly upwards. As the blade rotates, it moves in a circle with radius 15 feet, centered at a height of 40 feet above the ground. The vertical displacement of the blade is the y-coordinate of the point on the circle at angle θ, where θ is given by:
θ = 2π(3t - 1) (in radians)
This formula gives the angle in radians that the blade has rotated through at time t, taking into account the fact that the blade starts at a random angle at t=0. (The "-1" term ensures that the blade starts at the top at t=0.)
Putting it all together, we get the following sine model for the vertical displacement y of a point on the blade at time t:
y = 7.5 sin(2π(3t - 1)) + 40
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