When n = energy efficiency and Pin = energy input and Pout = energy output, how can you mathematically represent the correct relationship between the energy you put in something and the energy you get out?
A. n = P out * P in
B. n = P out / P in
C. n = P out - P in ...?
Answer:
[tex]n=\frac{P_{out}}{P_{in}}[/tex]
Step-by-step explanation:
We know that,
[tex]\text{Energy efficiency}=\frac{\text{Energy out put}}{\text{Energy in put}}[/tex]
If [tex]P_{in}[/tex] represents the energy input,
[tex]P_{out}[/tex] represents the energy output,
And, n represents energy efficiency,
Hence, the required formula would be,
[tex]n=\frac{P_{out}}{P_{in}}[/tex]
i.e. OPTION B is correct.
Your math teacher manages a campground during summer vacation. He loves math so much that he has mapped the campground on a coordinate grid. The campsites have the following coordinate: Brighton Bluff at B(2,2), ponaganset peak at P(4,10) and harmony hill at h(12,2) he wants to build showers that are equidistant from all three campsites. Find the coordinates of the point where the shower should be placed.
Answer:
(5,5)
Step-by-step explanation:
Step 1) Find the perpendicular bisector of BP Step 2) Find the perpendicular bisector of BH Step 3) The intersection point of the perpendicular bisector is where the showers would be built. This is the circumcenter of the circumscribed circle. After doing all of this, you should get that answer.. (5,5)
Identify the type of conic section that has the equation 9x^2+ 16y^2 = 144 and identify its domain and range.
Answer:
B ) ellipse.Domain: { -4 ≤ x ≤ 4 }Range: { -3 ≤ y ≤ 3 }
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The equation [tex]\(9x^2 + 16y^2 = 144\)[/tex] represents an ellipse. Its domain is \([-4, 4]\) and its range is \([-3, 3]\).
The equation [tex]\(9x^2 + 16y^2 = 144\)[/tex] represents an ellipse. To identify its domain and range, we need to understand its shape and orientation.
Step 1: Standard Form of an Ellipse
The standard form of an ellipse with its center at the origin is [tex]\( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \)[/tex], where \( a \) and \( b \) are the semi-major and semi-minor axes lengths, respectively.
Step 2: Compare Equations
Comparing the given equation [tex]\( 9x^2 + 16y^2 = 144 \)[/tex] with the standard form, we see that [tex]\( a^2 = \frac{144}{9} = 16 \)[/tex] and [tex]\( b^2 = \frac{144}{16} = 9 \).[/tex]
Step 3: Determine Axis Lengths
This means the semi-major axis length \( a \) is [tex]\( \sqrt{16} = 4 \)[/tex]and the semi-minor axis length \( b \) is [tex]\( \sqrt{9} = 3 \).[/tex]Step 4: Shape of the Ellipse
Since \( a > b \), the ellipse is stretched more horizontally than vertically, meaning it's wider than it is tall.
Step 5: Domain and Range
The domain of the ellipse is determined by the values of \( x \) and the range by the values of \( y \). For this ellipse, the \( x \)-values vary from \( -4 \) to \( 4 \) (domain), and the \( y \)-values vary from \( -3 \) to \( 3 \) (range).
Therefore, the domain is \([-4, 4]\) and the range is \([-3, 3]\).
reflecting dish of a parabolic microphone has a cross-section in the shape of a parabola. The microphone itself is placed on the focus of the parabola. If the parabola is 60 inches wide and 30 inches deep, how far from the vertex should the microphone be placed?
A triangular tent flap measures 3 1/2 ft along the base and has a height of 4 1/2 ft. How much canvas is needed to make the flap
A piece of wood that is 3/4 meter long is being cut into smaller pieces that are each 1/10 meter long.which equation could be solved to find the number of pieces,n,that can be made?
A line tangent to a circle is ________ to a radius of the circle at the point of tangency.
congruent
perpendicular
parallel
similar
Answer:
Perpendicular... I had the same question and I got a 100%! Hope this helps!
If ABCDE is a regular pentagon and diagonals EB and AC intersect at O, then what is the degree measure of angleEOC?
If ABCDE is a regular pentagon and diagonals EB and AC intersect at O, then the degree measure of angle EOC is 108°.
In Mathematics and Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:
Sum of interior angles = 180 × (n - 2)
Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.
Sum of interior angles = 180 × (5 - 2)
Sum of interior angles = 180 × 3
Sum of interior angles = 540°.
Therefore, the measure of each interior angle is given by;
Interior angle of a pentagon = 540°/5
Interior angle of a pentagon = 108°
From triangle EAO, we have:
2m∠EOA = 180° - (54 + 54)°
m∠EOA = 72°/2
m∠EOA = 34°
Now, we can determine the measure of angle EOC;
m∠EOC = 180° - (34 + 34)°
m∠EOC = 108°
8 less than a number n is less than 11
Final answer:
To find the number n in the inequality '8 less than a number n is less than 11', we can set up and solve the inequality n - 8 < 11. The answer is that the number n is less than 19.
Explanation:
The question states that 8 less than a number n is less than 11. To solve this, we can set up the inequality:
n - 8 < 11
To isolate n, we can add 8 to both sides:
n < 11 + 8
n < 19
So, the answer is that the number n is less than 19.
what is the slope of
18x-15y=20?
Which lines are parallel if m4 = m5? Justify your answer.
The lines r and s are parallel
What are angles in parallel lines?
Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.
We can conclude three factors determining parallel lines ,
Alternate angles are equalCorresponding angles are equalCo-interior angles add up to 180°Given data ,
From the figure m4 = m5
And , m4 and m5 are alternate angles
Alternate angles are angles that occur on opposite sides of the transversal line and have the same size
So , m1 = m5 are corresponding angles
Or angle 1 = angle 5
Corresponding angles are the pairs of angles formed on the same side of the transversal that are either both obtuse or both acute and are equal in size.
Similarly , m2 = m6 or angle 2 = angle 6
Hence , the lines r and s are parallel by the properties of angles in parallel lines.
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Given the matrices A and B below, find A + B and 3A
The value of A+B is [tex]\left(\begin{array}{ccc}3&-3\\10&4.5\\10&-1\end{array}\right)[/tex] and the value of 3A is [tex]\left(\begin{array}{ccc}6&-9\\0&15\\21&-6\end{array}\right)[/tex] .
How to add two matrices?To add two matrices, we have to add the element present in the same position in the respective matrices.
(A+B)ij= Aij + Bij
where i is the no. of row and j is the no. of column.
How to multiply a scalar by the matrix?In order to multiply a scalar by the matrix, we have to multiply that scalar with every element of the matrix.
nA= nAij
Here given matrix is
A= [tex]\left(\begin{array}{ccc}2&-3\\0&5\\7&-2\end{array}\right)[/tex]
and the other matrix is
B= [tex]\left(\begin{array}{ccc}1&0\\10&-1/2\\3&1\end{array}\right)[/tex]
The sum of the matrix is A+B= [tex]\left(\begin{array}{ccc}2&-3\\0&5\\7&-2\end{array}\right)[/tex]+ [tex]\left(\begin{array}{ccc}1&0\\10&-1/2\\3&1\end{array}\right)[/tex]
⇒ A+B =[tex]\left(\begin{array}{ccc}2+1&-3+0\\0+10&5+(-1/2)\\7+3&-2+1\end{array}\right)[/tex]
⇒ A+B= [tex]\left(\begin{array}{ccc}3&-3\\10&4.5\\10&-1\end{array}\right)[/tex]
the value of 3A= 3 [tex]\left(\begin{array}{ccc}2&-3\\0&5\\7&-2\end{array}\right)[/tex]= [tex]\left(\begin{array}{ccc}6&-9\\0&15\\21&-6\end{array}\right)[/tex]
Therefore the value of A+B is [tex]\left(\begin{array}{ccc}3&-3\\10&4.5\\10&-1\end{array}\right)[/tex] and the value of 3A is [tex]\left(\begin{array}{ccc}6&-9\\0&15\\21&-6\end{array}\right)[/tex] .
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y=f(x)=1/x. Use algebra to find a simplified rational expression for the slope of the line between (3, f(3)) and (3+h, f(3+h))?? h cannot=0. ...?
Determine whether the following relation is a function.
{(3,7), (3,8), (3,-2), (3.4),(3,1)}
A) it is a function because the ordered pairs all have the same x-value.
B) it is not a function because there are multiple y-values paired with a single x-value.
C) it is a function because none of the ordered pairs have the same y-value.
D) it is not a function because none of the ordered pairs have the same y-value.
The relation is not a function it is not a function because there are multiple y-values paired with a single x-value. Option B.
Is the relation a function?A relation is a function only if every input is mapped into a single output.
Here we have the relation {(3,7), (3,8), (3,-2), (3.4),(3,1)}
Remember that the first number of each pair is the input, so we can see that all the inputs are the same one
So the input x = 3 is mapped into different outputs, thus, this is not a function.
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The correct option is B) it is not a function because there are multiple y-values paired with a single x-value.
To determine if a relation is a function, one must check if each x-value is associated with exactly one y-value. In other words, for every x, there should be one and only one y. This is known as the vertical line test in the context of graphs.
Let's examine the given set of ordered pairs: {(3,7), (3,8), (3,-2), (3,4), (3,1)}.
We can see that the x-value of 3 is repeated with different y-values: 7, 8, -2, 4, and 1.
This means that the x-value of 3 is associated with multiple y-values, which violates the definition of a function.
Therefore, the relation is not a function because it fails to satisfy the condition that each x-value must correspond to exactly one y-value.
The presence of multiple y-values for a single x-value is the key indicator that the relation is not a function.
What is the slope of the line whose equation is -3x y=12?
What is the smallest positive value for x where y=sin2x reaches its maximum? How do you figure this out? ...?
To find the smallest positive value for x where y = sin^2x reaches its maximum, we can set sin^2x = 1 and solve for x. The smallest positive value of x where y = sin^2x reaches its maximum is pi/2.
Explanation:To find the smallest positive value for x where y = sin^2x reaches its maximum, we need to consider the properties of the sine function. The sine function oscillates between -1 and +1, with the maximum value of sin^2x being 1. Since the maximum value of sin^2x is 1, we can set sin^2x = 1 and solve for x.
Applying the property of sin^2x = 1, we have:
sin^2x = 1
Taking the square root of both sides, sinx = ±1
Since we are looking for the smallest positive value of x, we take sinx = 1
This means that x = π/2 + 2πn, where n is an integer.
Therefore, the smallest positive value for x where y = sin^2x reaches its maximum is π/2.
Five people are sitting around a circle. Some always tell the truth, whilst others always lie. Each person claims to be sitting between two liars. How many of them are telling the truth?
A 0 B 1 C 2 D 3 E 4
The answer is: B. 1 - Only one of the five people is telling the truth.
In this scenario, we are given that five people are sitting around a circle. Some always tell the truth, while others always lie. Each person claims to be sitting between two liars.
Let's analyze the possibilities:
If all five people were telling the truth, each person's claim of sitting between two liars would be true. However, this would mean that all five people are telling the truth, which contradicts the given information.
If none of the five people were telling the truth, each person's claim of sitting between two liars would be false. However, this also contradicts the given information.
Given these two possibilities, we can conclude that there must be a combination of truth-tellers and liars among the five people.
Considering the options given:
A. 0: This suggests that none of the people are telling the truth. However, this contradicts the given information that some people always tell the truth.
B. 1: This suggests that only one person is telling the truth. In this case, this person's claim of sitting between two liars would be true, while the claims of the other four people would be false. This option aligns with the given information and is a valid possibility.
C. 2, D. 3, E. 4: These options suggest that multiple people are telling the truth. However, if more than one person tells the truth, their claims of sitting between two liars cannot all be true.
Based on the analysis, the answer is:
B. 1 - Only one of the five people is telling the truth.
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I don't know what to do ?
The equation 9(u – 2) + 1.5u = 8.25 models the total miles Michael traveled one afternoon while sledding, where u equals the number of hours walking up a hill and (u – 2) equals the number of hours sledding down the hill. Which is the value of u?
Answer:
2.5
Step-by-step explanation:
Given: The equation [tex]9(u - 2) + 1.5u = 8.25[/tex]models the total miles Michael traveled one afternoon while sledding.
To Find: Which is the value of u?
Solution:
[tex]9(u - 2) + 1.5u = 8.25[/tex]
[tex]9u - 18+ 1.5u = 8.25[/tex]
[tex]10.5u = 8.25+18[/tex]
[tex]10.5u =26.25[/tex]
[tex]u =\frac{26.25}{10.5}[/tex]
[tex]u =2.5[/tex]
Hence the value of u is 2.5
how to do rational numbers
The quotient of a number and –1.5 is 21
HELP ME ASAP!! Some red white and blue candies were placed in a bowl. Some contain nuts, and some do not. Suppose one of the candies were chosen randomly from all the candies in the bowl. According to the table below, if the candy is blue, what is the probability that is does not contain any nuts?
Red with nuts=10. Red without nuts=10. White with nuts=20. White without nuts=10. Blue with nuts=20. Blue without nuts=30.
A. 20%
B. 40%
C. 60%
D. 10%
Answer:
Option C: 60%
Step-by-step explanation:
The number of blue candies with nuts = 20
The number of blue candies without nuts = 30
The total number of blue candies = 20 + 30 = 50
As the chosen candy is blue, the probability that is does not contain any nuts will be = (The number of blue candies without nuts)/(Total number of blue candies)
So, the probability = 30/50 = 0.6 *100% = 60%
Answer: 20%
Step-by-step explanation:
A florist shop represents its first month’s sales with the equation y=168x+8, where x represents the number of days that the shop is open and y represents the sales in dollars. The owner of the shop would like to calculate the number of days it took to reach $3,200 in sales. Which would be used to solve the problem?
A-Substitute 3,200 for x.
B-Add 8 and 3,200.
C- Divide 3,192 by 168.
D-Isolate y in the equation.
Answer:
Option C is the answer.
Step-by-step explanation:
A florist sale is for it's first month is represented by the equation y = 168x + 8
Here y represents the sales in dollars and x represents number of days.
Now we have to calculate the number of days it took to reach $3200 in sales.
For this we will substitute $3200 in place of y and find the value of x by solving the equation.
3200 = 168x + 8
168x = 3200 - 8 = 3192
[tex]x=\frac{3192}{168}=19[/tex]
Therefore Option C. is the correct option.
Solve for x. -3(x-5)-2x=-10
A recipe calls for of a 1/3 cup of milk for 12 cookies. how many cups of milk are needed to make 108 cookies?
When you pay a bill in full, you are
A student earns $10 per hour for tutoring and $7 per hour as a teacher's aide. To have enough free time for studies, he can work no more than 20 hours per week. The tutoring center requires that each tutor spends at least three hours per week tutoring, but no more than eight hours per week. How many hours should he work to maximize his earnings?
hours of tutoring hours as a teacher's aide What is the maximum profit? $
He should work 20 hours every week to optimize his profits. The maximum profit will be $164.
What is a numerical expression?A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
He should tutor as many hours as possible because he is paid more for it. He may only work for a maximum of 20 hours every day. He must tutor for at least 3 hours but no more than 8 hours to optimum profit, he must tutor for 8 hours leaving 12 hours as a teacher's helper.
To optimize his profits, he should work 20 hours every week.
⇒ 8(10) + 12(7)
⇒ 80 + 84
⇒ 164
Therefore, he should work 20 hours every week to optimize his profit and the maximum profit will be $164.
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Which Equation represents this problem?
Pauline can spend $36 on bus fare each week. She needs to ride the bus 5 days a week. How much can she spend each day on bus fare?
A.
36 + b = 5
B.
5 x b = 36
C.
5 ÷ b = 36
D.
36 – b = 5
Marquis has a gross pay of $816. By how much will his gross pay be reduced if Marquis has the following items withheld?
federal tax of $92
Social Security tax that is 6.2% of his gross pay
Medicare tax that is 1.45% of his gross pay
state tax that is 22% of his federal tax
Answer:
His gross pay would be reduced $174.66.
Step-by-step explanation:
Gross pay of Marquis = $816
His withholding are :
Federal tax = $92.00
Social security tax = 6.2% of $816
= 0.062 × 816
= $50.592
Medicare tax = 1.45% × 816
= 0.0145 × 816
= $11.832
State tax = 22% × 92
= 0.22 × 92
= $20.24
Total withholding = 92 + 50.59 + 11.83 + 20.24
= $174.66
His net pay = $816 - $174.66 = $641.34
His gross pay would be reduced $174.66

Which points are solutions to the linear inequality y < 0.5x + 2? Check all that apply.
(–3, –2)
(–2, 1)
(–1, –2)
(–1, 2)
(1, –2)
(1, 2)
Answer:
Points (-3,-2), (-1,-2), (1,-2) and (1,2) are solutions to the given inequality.
Step-by-step explanation:
We are given the following inequality in the question:
[tex]y < 0.5x + 2[/tex]
We have to check which points give the solution to the given inequality.
1) (-3,-2)
Putting the values in the given inequality:
[tex]-2 < 0.5\times (-3) + 2\\-2 < 0.5\\\text{which is true}[/tex]
The above point is a solution to the given inequality.
2) (-2,1)
Putting the values in the given inequality:
[tex]1 < 0.5\times (-2) + 2\\1 < 1\\\text{which is not true}[/tex]
The above point is not a solution to the given inequality.
3) (-1,-2)
Putting the values in the given inequality:
[tex]-2 < 0.5\times (-1) + 2\\-2 < 1.5\\\text{which is true}[/tex]
The above point is a solution to the given inequality.
4) (-1,2)
Putting the values in the given inequality:
[tex]2< 0.5\times (-1) + 2\\2 < 1.5\\\text{which is not true}[/tex]
The above point is not a solution to the given inequality.
5) (1,-2)
Putting the values in the given inequality:
[tex]-2 < 0.5\times (1) + 2\\-2 < 2.5\\\text{which is true}[/tex]
The above point is a solution to the given inequality.
6) (1,2)
Putting the values in the given inequality:
[tex]2 < 0.5\times (1) + 2\\2 < 2.5\\\text{which is true}[/tex]
The above point is a solution to the given inequality.
Points (-3,-2), (-1,-2), (1,-2) and (1,2) are solutions to the given inequality.