Based on the options provided, it seems that the question is asking whether the budgeted amount is enough to cover expenses, savings, and emergencies. The answer would be either A, B, C, or D.
A) No, it's short $207.0.
B) No, it's short $227.0.
C) Yes, there's a surplus of $207.0.
D) Yes, there's a surplus of $227.0.
Unfortunately, without more information about the specific budgeted amount and the actual expenses, savings, and emergencies, it is impossible to determine the correct answer. It is important to regularly track expenses and compare them to the budgeted amount to ensure that there is enough money to cover all necessary expenses and unexpected events. If there is a shortfall, it may be necessary to adjust the budget or find ways to increase income or decrease expenses to ensure financial stability.
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Find x.
Please help thank you
Calculate the bearing of U from T. U N 32° T
The bearing of U from T in the image is 32 degrees South by West of T
What is Bearing?In mathematics, bearings refer to the direction of an object or location in relation to two points. It is determined by the angle between the line joining them and that of the north.
Measured typically in degrees, it follows a cardinal system where 0° or 360° signifies North; East stands for 90°, South denotes at 180° while West represents 270°.
Thus, it can be seen that the bearing of U from T in the image is 32 degrees South by West of T
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Please help asap!! the image is attached, 35 points!!
Answer:
B
Step-by-step explanation:
Lisa's first step is to distribute, so you have to distribute all numbers.
(3+6x)-2(x+1)+5
3(1+2x)-2)x+1)+5
Hope this helps! :)
A cable rigging must be run from the ground through the top of a guidepost 10 feet high, and continue in a straight line to the face of a building that stands 20 feet from the post along the ground.
(a) How high up the building should the cable be attached if the area of the right triangle formed by the cable, ground, and building is to be minimized?
(b) If the length of the cable is to be minimized, what angle θ should it make with the face of the building?
(a) To minimize the area of the right triangle formed by the cable, ground, and building, we need to minimize the length of the cable. To do this, we can use the Pythagorean theorem:
c^2 = a^2 + b^2
where c is the length of the cable, a is the distance from the guidepost to the point where the cable is attached to the building, and b is the distance from that point to the ground.
Since we want to minimize c, we can differentiate the equation with respect to a and set the derivative equal to zero:
dc/da = 2a/c = 0
Solving for a, we get a = c/2. This means that the point where the cable is attached to the building should be halfway up the building, or 10 feet high.
(b) To minimize the length of the cable, we can use the principle of least action, which states that the path taken by the cable is the one that minimizes the integral of the tension along the cable.
Assuming that the tension in the cable is constant, we can use the law of sines to find the angle θ:
sin θ / 20 = sin (90° - θ) / c
where c is the length of the cable.
We want to minimize c, so we can differentiate the equation with respect to θ and set the derivative equal to zero:
d(c)/d(θ) = -20cos(θ) / sin^2(θ) + cos(θ) / sin(θ) * dc/d(θ) = 0
Solving for dc/d(θ), we get:
dc/d(θ) = 20c * tan(θ)
Substituting this into the original equation, we get:
-20cos(θ) / sin^2(θ) + cos(θ) / sin(θ) * 20c * tan(θ) = 0
Simplifying, we get:
cos(θ) / sin(θ) = tan(θ)
Solving for θ, we get:
θ = 45°
Therefore, to minimize the length of the cable, it should make an angle of 45° with the face of the building.
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Suppose that, using the simulation in Exercise 4 (Connections), you devise a patch configuration using stepping stones. In your first simulation run, you set the leave prairie probability to 0. 9 and turn probability in non-prairie to zero. You run the simulation once, with no fires. The simulated butterfly population size after 100 weeks increases from 25 to 132. What does this result tell you about the real-world Fender's blue butterfly population
The result should be interpreted with caution and cannot be directly extrapolated to the real-world Fender's blue butterfly populations, and the simulation does not take these factors into account.
Find out the result tell you about Fenders blue butterfly population?The result of the simulation suggests that in a hypothetical scenario where the Fender's blue butterfly population is restricted to stepping stones, and the leave prairie probability is set to 0.9, the population is likely to increase over time. However, it is important to note that the simulation represents an idealized scenario and may not reflect the complexity of real-world butterfly populations.
Furthermore, the absence of fires in the simulation may not reflect the natural habitat of Fender's blue butterfly, as fire is a crucial factor in maintaining prairie habitats. In the real world, fire suppression and habitat fragmentation are major threats to the survival of Fender's blue butterfly populations, and the simulation does not take these factors into account.
In summary, while the simulation result may provide insights into the potential effectiveness of using stepping stones to conserve butterfly populations, it should be interpreted with caution and cannot be directly extrapolated to the real-world Fender's blue butterfly population. Further research and monitoring of butterfly populations in their natural habitats are necessary to fully understand their dynamics and inform conservation efforts.
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Evaluate the following expression. Your answer must be in exact form: for example, type pi/6 for π/6 or DNE if the expression is undefined. arcsin (sin (-57π/10))=
For the following expression arcsin (sin (-57π/10)) is 3π/10.
The function arcsin(x) gives the angle in radians whose sine is x.
In this problem, we need to find the angle whose sine is equal to the sine of -57π/10.
First, we need to simplify -57π/10 to an angle in the range [-π/2, π/2] since the sine function has a range of [-1, 1]. To do this, we use the fact that sine has a period of 2π,
which means that sin(-57π/10) = sin((-57π/10) + 4π) = sin(3π/10).
So we need to find the angle θ such that sin(θ) = sin(3π/10).
Since sine is an odd function, we know that sin(-θ) = -sin(θ), so we can also say that sin(θ) = sin(-3π/10).
Therefore, there are two possible angles that satisfy the equation: θ = 3π/10 or θ = -3π/10.
However, since the range of the arcsine function is [-π/2, π/2], only the angle in that range that satisfies the equation is θ = 3π/10.
Therefore, we can write:
arcsin(sin(-57π/10)) = arcsin(sin(3π/10)) = 3π/10
The answer is 3π/10.
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An online furniture store sells chairs for $50 each and tables for $250 each. Every day, the store can ship no more than 26 pieces of furniture and must sell a minimum of $1900 worth of chairs and tables. Also, the store must sell a minimum of 14 tables. If a represents the number of tables sold and y represents the number of chairs sold, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
9, 10, 11, 12, 13.
Step-by-step explanation:
All possible values for the number of tables that the store must sell in order to meet the requirements are 9, 10, 11, 12, 13
Write the equation in factored form:
so x= what values?
What do the solutions for x mean?
x2−4x−21=0
Given the sequence an = n^7/n^4
The sequence is = _______
Given the sequence an = n^7/n^4, The sequence is = divergent. So, the answer is that the sequence is divergent.
The sequence an = n^7/n^4 can be simplified by cancelling out the common factor of n^4 in the numerator and denominator. This yields an = n^3.
Therefore, the sequence is simply the cubes of the positive integers, or 1, 8, 27, 64, 125, 216, ... and so on. This sequence grows without bound, as n gets larger, so it does not converge to any finite limit. In other words, the sequence an does not have a limit, and it is divergent.
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The lengths of the sides of a triangle are given. Classify each triangle as acute,
right, or obtuse.
19. 3, 4, 6
To start, compare c 2 to a 2 + b2
. Substitute the greatest length for c.
20. 9, 11, 16
19. The triangle with sides 3, 4, 6 is obtuse triangle.
20. The triangle with sides 9, 11, 16 is acute triangle.
How to Classify Triangles?In a triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side for the triangle to be considered "non-degenerate," which means it is a valid triangle with a positive area.
19. We have sides of 3, 4, and 6. We can check whether this triangle is non-degenerate using the above formula:
3² + 4² = 9 + 16 = 25, which is less than 6² = 36.
Therefore, this triangle is non-degenerate and we can classify it based on the size of its angles.
To do so, we can use the Pythagorean Theorem to find that the longest side (6) is opposite the largest angle, which is obtuse. Therefore, triangle #19 is an obtuse triangle.
20. For triangle #20, we have sides of 9, 11, and 16. Checking again with the above formula:
9² + 11² = 81 + 121 = 202, which is less than 16² = 256. So this triangle is also non-degenerate.
Using the same method as before, we can find that the longest side (16) is opposite the largest angle, which is acute. Therefore, triangle #20 is an acute triangle.
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Find the magnitude of v. v = 7i
|lv|| = _____
The magnitude of vector v is:
|v| = 7
The magnitude of v is simply the length of the vector v, which can be found using the Pythagorean theorem. The vector v is given as v = 7i.
To find the magnitude of v (|v|), use the formula:
|v| = √(x² + y²)
where x and y are the components of the vector v. In this case, x = 7 (from 7i) and y = 0 (since there is no j component).
Now, plug in the values of x and y into the formula:
|v| = √(7² + 0²)
|v| = √(49 + 0)
|v| = √(49)
|v| = 7
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On the same coordinate plane, mark all points (x,y) such that (A) y=x-2, (B) y=-x-2, (C) y=|x|-2
The marked points are (-2,-4), (-2,-1), (0,-2), (2,-1), and (2,-4), under the condition that they are on the same coordinate plane having (A) y=x-2, (B) y=-x-2, (C) y=|x|-2.
In the given graph points on the coordinate plane, we have to plot the points (x,y)
Here
x = horizontal axis
y = vertical axis.
In the given point A, y=x-2, we can continue at the origin (0,0) and move 2 units go down on the y-axis and 2 units right on the x-axis to plot point A at (2,0).
In the given point B, y=-x-2, we can continue at the origin (0,0) and transfer 2 units down on the y-axis and 2 units left on the x-axis to plot point B at (-2,0).
In the given point C, y=|x|-2, we can continue plotting two points for this equation.
When x is considered negative, we can procees at the origin (0,0) and transfer 2 units down on the y-axis and 2 units left on the x-axis to plot point C at (-2,0).
When x is positive, we can start at the origin (0,0) and move 2 units down on the y-axis and 2 units right on the x-axis to plot point C at (2,0).
Then, all points (x,y) such that (A) y=x-2, (B) y=-x-2, (C) y=|x|-2 are (-2,-4), (-2,-1), (0,-2), (2,-1), and (2,-4).
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The experimental probability that Anna can throw a football
through a hoop is 60%. How many throws out of 20 can Anna
predict she will make?
O 18
O 12
O14
O 10
Answer:
12
Step-by-step explanation
60/100 to get the probability of success
0.6 * 20 attempts = 12
If the equation is y = 2x^2 + 4x - 6 what is zero #1 (x,y) and zero #2 (x,y)
The zero #1 is (-3, 0) and the zero #2 is (1, 0).
To find the zeros of the quadratic equation y = 2x² + 4x - 6, we need to solve for the values of x when y = 0.
We can start by setting y to zero:
0 = 2x² + 4x - 6
Next, we can divide both sides by 2 to simplify the equation:
0 = x² + 2x - 3
We can then factor the left-hand side of the equation:
0 = (x + 3)(x - 1)
Using the zero product property, we can set each factor equal to zero and solve for x:
x + 3 = 0 or x - 1 = 0
x = -3 or x = 1
So the zeros of the quadratic function are (-3,0) and (1,0).
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Prove the following trigonometric identities
csc x - sin x - cosx cos x
To prove the trigonometric identity csc(x) - sin(x) - cos(x)cos(x), we will start by simplifying the left-hand side of the equation using trigonometric definitions and identities.
Recall that csc(x) = 1/sin(x). We will use this definition to rewrite the left-hand side of the equation:
1/sin(x) - sin(x) - cos(x)cos(x)
Now, we will find a common denominator for the terms in the equation. In this case, the common denominator is sin(x). To do this, we will multiply sin(x) to the second term:
(1 - sin^2(x) - cos(x)cos(x)sin(x)) / sin(x)
Next, we will use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to replace sin^2(x) in the expression:
(1 - (1 - cos^2(x)) - cos(x)cos(x)sin(x)) / sin(x)
Simplifying the expression, we get:
(cos^2(x) - cos(x)cos(x)sin(x)) / sin(x)
Now, we can factor out cos(x) from the numerator:
cos(x)(cos(x) - sin(x)) / sin(x)
This expression is equivalent to the given identity, so we have proven the trigonometric identity:
csc(x) - sin(x) - cos(x)cos(x) = cos(x)(cos(x) - sin(x)) / sin(x)
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Se van a repartir $10000 entre 3 personas de tal forma q la primera recibe $900 mas q la segunda y esta $200 mas q la tercera.La persona más beneficiada recibe en total: a- $4600. b- $4400. c- $4200. d- $4000
Answer:
The answer is A
Step-by-step explanation:
x = e⁴ᵗ, y = t + 4(a) Eliminate the parameter to find a Cartesian equation of the curve.(b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.
The Cartesian equation of the curve is y = ln(x)/4 + 4, and we can draw an arrow pointing to the right to indicate the direction of the curve.
(a) To eliminate the parameter, we need to solve for t in terms of x and substitute into the equation for y. From the equation x = e⁴ᵗ, we have t = ln(x)/4. Substituting into y = t + 4, we get y = ln(x)/4 + 4. Therefore, the Cartesian equation of the curve is y = ln(x)/4 + 4.
(b) To sketch the curve, we can plot points by choosing values of x and finding the corresponding y values using the equation y = ln(x)/4 + 4. As x increases, y increases but at a slower rate. This means that the curve is increasing but is becoming less steep.
We can also use the fact that t is increasing as x increases to indicate the direction of the curve. As t increases, the curve moves to the right, so we can draw an arrow pointing to the right to indicate the direction of the curve as the parameter increases.
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Does John Short qualify for overtime? Explain
1. 1. 3. How do you think management of Neat Upholsterers determine
whether a person has worked overtime? Do you think this is a fair
policy?
Regarding the second question, the management of Neat Upholsterers may determine whether a person has worked overtime by tracking their hours of work and comparing them to the standard working hours or the overtime policy defined in the employment contract or labor laws. This could involve using time cards, electronic systems, or other methods of tracking employee hours.
Whether this policy is fair or not depends on various factors, such as the specific overtime policy, the industry norms, the labor laws, and the bargaining power of the employees. If the overtime policy is reasonable, transparent, and consistent with the labor laws and the industry standards, and if the employees are compensated fairly for their extra work, then the policy could be considered fair. However, if the policy is exploitative, discriminatory, or violates the legal or ethical standards, then it could be considered unfair.
The equation, with a restriction on x, is the terminal side of an angle theta in standard position. 5x + y = 0, x ≥ 0 Give the exact values of the six trigonometric functions of theta. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. sin theta = (Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed. Rationalize all denominators.) B. The function is undefined.
Sin theta = -5/sqrt(26) Is the correct option , To find the six trigonometric functions of theta, we need to first find the values of x and y on the terminal side of theta. From the given equation, 5x + y = 0 and x ≥ 0, we can solve for y in terms of x:
y = -5x
Since x ≥ 0, we know that (x, y) lies in the fourth quadrant. We can now use the Pythagorean theorem to find the length of the hypotenuse:
r =[tex]sqrt(x^2 + y^2) = sqrt(x^2 + (-5x)^2) = sqrt(26x^2)[/tex]
Now we can find the six trigonometric functions:
sin(theta) = y/r = [tex]-5x/sqrt(26x^2) = -5/sqrt(26)[/tex]
cos(theta) = x/r =[tex]x/sqrt(26x^2) = 1/sqrt(26)[/tex]
tan(theta) = y/x = -5x/x = -5
csc(theta) = r/y = [tex]sqrt(26x^2)/(-5x) = -sqrt(26)/5[/tex]
sec(theta) = r/x = sqrt(26x^2)/x = sqrt(26)/1 = sqrt(26)
cot(theta) = 1/tan(theta) = -1/5
Therefore, the exact values of the six trigonometric functions of theta are:
sin(theta) = -5/sqrt(26)
cos(theta) = 1/sqrt(26)
tan(theta) = -5
csc(theta) = -sqrt(26)/5
sec(theta) = sqrt(26)
cot(theta) = -1/5
Answer: A. sin theta = -5/sqrt(26)
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Baron Blakk decided to start saving. He deposited seven thousand kroner at the start of each year. He always received a fixed interest rate of 2.3%. How much interest had he received in total after eight years? Give the answer to two decimal places.
The interest he had received in total after eight years is 1396.59 kroner
How much interest had he received in total after eight years?From the question, we have the following parameters that can be used in our computation:
Principal, P = 7000
Rate, r = 2.3%
Time, t = 8
The interest he had received in total after eight years is calculated as
I = P(1 + r)^t - P
Substitute the known values in the above equation, so, we have the following representation
I = 7000(1 + 2.3%)^8 - 7000
Evaluate
I = 1396.59
Hence, the total interest is 1396.59 kroner
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A local amusement park found that if the admission was $7, about 1000 customers per day were admitted. When the admission was dropped to $6, the park had about 1200 customers per day. Assuming a linear demand function, determine the admission price that will yield maximum revenue.
The admission price that will yield maximum revenue is $6.
To determine the admission price that will yield maximum revenue, we'll first find the linear demand function using the given data points: ($7, 1000) and ($6, 1200).
Let x represent the admission price and y represent the number of customers per day. We can calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given data points:
m = (1200 - 1000) / (6 - 7) = 200 / (-1) = -200
Now, we have the slope and a point, so we can use the point-slope form to find the linear demand function:
y - y1 = m(x - x1)
Using the point ($7, 1000):
y - 1000 = -200(x - 7)
Now, let's rewrite the equation to the slope-intercept form (y = mx + b):
y = -200x + 2400
The revenue (R) is equal to the product of the admission price (x) and the number of customers (y):
R = xy
Substitute the linear demand function (y = -200x + 2400) into the revenue equation:
R = x(-200x + 2400)
To maximize the revenue, we need to find the vertex of the parabola represented by this equation. The x-coordinate of the vertex is given by:
x_vertex = -b / 2a
In this case, a = -200 and b = 2400:
x_vertex = -2400 / (2 * -200) = 6
The admission price that will yield maximum revenue is $6.
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PLEASE HELP ME IMMEDIATELY!!!!!
The intervals where f is decreasing are given as follows:
None of the above.
When a function is increasing and when it is decreasing, looking at it's graph?Looking at the graph, we get that a function f(x) is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when the input variable represented x increases, the output variable represented by y also increases.Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down the graph, meaning that when the input variable represented by x increases, the output variable represented by y decreases.Hence the decreasing intervals of the function are given as follows:
-3.5 < x < -1.x > 2.5.Which are none of the options given in the problem.
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Complete the following to use the difference of two squares to find the product of 22 and 18.( + )( - ) =( )2 - ( )2 =396
The complete equation of two squares to find the product of 22 and 18 is (22 + 18)(22 - 18) = 396
When we can interpret an expression as the difference of two perfect squares, i.e. a2-b2, we can factor it as (a+b)(a-b).
To use the difference of two squares to find the product of 22 and 18:
First, find the average of the two numbers:
(22 + 18) ÷ 2 = 20
Then, find the difference between the two numbers:
22 - 18 = 4
Now we can write:
(20 + 4)(20 - 4) = 24 × 16 = 384
But we need to add the extra 12 to get 396:
(20 + 4)(20 - 4) + 12 = 396
So the completed equation is:
(22 + 18)(22 - 18) = 396
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1/2 (7)(4) + 6(5)=
I can not figure this out! Can you answer with middle school techniques?
The value of the given expression is 44. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
The four basic operations, also referred to as "arithmetic operations," are thought to explain all real numbers. Operations like division, multiplication, addition, and subtraction come before operations like quotient, product, sum, and difference in mathematics.
We are given an expression as [tex]\frac{1}{2}[/tex] (7) (4) + 6 (5).
We know that when there is no sign in between two numbers, it denotes multiplication.
So, we get
⇒ [tex]\frac{1}{2}[/tex] * (7) * (4) + 6 * (5)
⇒ 14 + 30
⇒ 44 (Using addition operation)
Hence, the value of the given expression is 44.
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A tool box has the dimensions of 9 in by 6 in by 7 in. If Mark plans to double one dimension to build a larger tool box, he believes he would double the volume of the tool box. Is he correct?
Yes, Mark is correct he believes that doubling one of the dimensions would double the volume of his toolbox.
Volume refers to the space occupied by a 3-Dimensional space. The volume of a cuboid is given by:
V = l * b * h
where l is the length
b is the breadth
h is the height
V = 9 * 6 * 7
= 378 cubic inches
If we double any of the dimensions, like
By doubling the 9 we get
V = 18 * 6 * 7
= 756 cubic inches
By doubling the 6 we get
V = 9 * 12 * 7
= 756 cubic inches
By doubling the 7 we get
V = 9 * 6 * 14
= 756 cubic inches
Then the volume of the toolbox is doubled as shown above.
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If f(x) = 2x2 - 6x² + 4x – 8 and g(x)= 0, find (fog)(x) and (gof)(x).
The final values is (fog)(x) = f(g(x)) = f(0) = -8.
In the given problem, we are given two functions, f(x) and g(x). The function f(x) is a polynomial function, and g(x) is a constant function equal to 0. We are asked to find the composition of these two functions, that is, (fog)(x) and (gof)(x).
The composition of two functions f(x) and g(x) is denoted by (fog)(x) and is defined as follows:
(fog)(x) = f(g(x))
This means that we first evaluate g(x) and then use the output of g(x) as the input of f(x) to get the final output of (fog)(x).
In this case, since g(x) = 0, we have:
(fog)(x) = f(g(x)) = f(0)
To evaluate f(0), we substitute x = 0 in the expression for f(x):
[tex]f(x) = 2x^2 - 6x^2 + 4x - 8[/tex]
[tex]f(0) = 2(0)^2 - 6(0)^2 + 4(0) - 8[/tex]
f(0) = -8
Therefore, (fog)(x) = f(g(x)) = f(0) = -8.
Now, to find (gof)(x), we need to evaluate g(f(x)). Since f(x) is a polynomial function, we can find its value for any value of x. However, since g(x) is a constant function equal to 0, its output is always 0 for any input x. Therefore, g(f(x)) = 0 for all values of f(x).
This means that (gof)(x) = g(f(x)) = 0 for all x.
In summary, we found that (fog)(x) = -8 and (gof)(x) = 0.
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a farmer made a loss of 28% by selling a gold for1440shillings what percentage profit would have made if he had sold the goat.for.sh 2100
The farmer would have made a profit of 5% if he had sold the goat for 2100 shillings.
Let's use the given terms and find out the percentage profit if the farmer had sold the goat for 2100 shillings.
Calculate the cost price of the goat
We know that the farmer made a loss of 28% by selling the goat for 1440 shillings. Let's represent the cost price as "CP".
We can write the equation:
[tex]CP \times (1 - loss% ) = selling price (SP)[/tex]
[tex]CP \times (1 - 0.28) = 1440[/tex]
Solve for CP
[tex]CP \times 0.72 = 1440[/tex]
CP = 1440 / 0.72
CP = 2000 shillings
Calculate the percentage profit
Now we want to find out the percentage profit if the farmer had sold the goat for 2100 shillings.
We can write the equation:
[tex](SP_{new - CP)} / CP \times 100 = profit[/tex]
[tex](2100 - 2000) / 2000 \times 100 = profit%[/tex]
[tex]100 / 2000 \times 100 = profit%[/tex]
5% = profit%.
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Classify each question as statistical or nonstatistical.
statistical
nonstatistical
what kind of dog does bruno have?
what is clara's brother's name?
what time did javed go to sleep?
how many siblings do you have?
what time do you go to sleep?
how many pets do you have?
The options that are statistical are:
how many pets do you have?
what time do you go to sleep?
how many siblings do you have?
The options that are non-statistical are:
what kind of dog does bruno have?
what is clara's brother's name?
what time did javed go to sleep?
How to identify statistical Data?A statistical question is defined as one that will obtain the data that will vary from one particular response to another. However, a non-statistical question is defined as one that will obtain data that is basically exact and then has only one response.
A question that will not provide a variety of different answers is referred to as not a statistical question. For example, we can say that 'how many siblings do I have?' is not referred to as statistical. The answer will definitely have just one response, and not many.
A non-statistical question in math is defined as a question that will not provide a variety of answers. Finally, non-statistical questions provide us with exact answers that do not change.
Thus, the options that are statistical are:
how many pets do you have?
what time do you go to sleep?
how many siblings do you have?
The options that are non-statistical are:
what kind of dog does bruno have?
what is clara's brother's name?
what time did javed go to sleep?
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Keegan deposited $675 in a savings account that pays 4.8% annual interest compounded quarterly.
Write the compound interest formula to represent Keegan's investment after 5 years.
How much money will Keegan have in the account after 5 years?
Keegan will have approximately $878.85 in the account after 5 years.
What is Compound interest ?
Compound interest is the interest that is earned not only on the initial amount of money invested (known as the principal), but also on any interest earned on that principal over time. In other words, compound interest is interest on interest.
The compound interest formula is given by:
A = P[tex](1 + r/n)^{nt}[/tex]
where A is the amount after t years, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, Keegan deposited $675, the annual interest rate is 4.8%, the interest is compounded quarterly, and the investment is for 5 years. Therefore, we can plug in these values into the formula to get:
A = 675[tex](1 + 0.048/4)^{20}[/tex]
A = 675[tex](1.012)^{20}[/tex]
A ≈ $878.85
Therefore, Keegan will have approximately $878.85 in the account after 5 years.
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The cone is formed from 3,200 ft3 of gravel. If the height of the cone is 24 feet, what is the radius, in feet, of the base of the cone? Use the π button on your calculator to determine the answer. Round your answer to the nearest tenth of afoot. The radius of the base of the cone is approximately ____ feet
The radius of the base of the cone is approximately 12.65 feet if The cone is formed from 3,200 ft of gravel.
Height of cone = 24 feet
The volume of the cone = [tex]3,200 ft^3[/tex]
To find the volume of the cone, the formula used here is:
V =π* [tex]r^2h[/tex]
Here, the values of V and H are known terms. we need to calculate the radius r of the cone.
π = 3.14 constant value
Substituting the values in the above equation, we get:
[tex]3,200 = (1/3)^2*(24)*[/tex] π
[tex]r^2[/tex]= 3,200 / (8π)
[tex]r^2[/tex] = 400 / π
r = 12.65
Therefore, we can conclude that the radius of the base of the cone is 12.65 feet.
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