The area of the aperture storing light is 0.196 [tex]m^{2}[/tex].
What are shapes?Mathematical figures which have a set of pre defined properties are known as shapes. For example, Square shape is a mathematical figure who has four sides and all of them are equal in length and all the four corner of square have an angle of 90 degree. Similarly if there a figure who has been formed by the help of four lines of equal length but the corners are not 90 degrees then it will be Rhombus and not Square.
Now for the given question:
Diameter of the mirror=50 cm
we convert dia. unit in meter as area is asked in meter.
Dia.= [tex]\frac{50}{100}[/tex]
= [tex]\frac{1}{2}[/tex]
Area of a circle=π× [tex](\frac{dia}{2} )^{2}[/tex]
=π×[tex](\frac{1}{4} )^{2}[/tex]
Area= π/16
π=3.14
Area=[tex]\frac{3.14}{16}[/tex]
= 0.196 [tex]m^{2}[/tex]
Hence area of the aperture is 0.196 [tex]m^{2}[/tex].
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a rectangular pyramid is sliced so the cross section is perpendicular to its base but does not pass through its vertex. what is the shape of the cross section?
When a rectangular pyramid is sliced by a plane that is perpendicular to its base but does not pass through its vertex, the resulting cross section is a trapezoid.
To understand why this is the case, it is helpful to visualize a rectangular pyramid. A rectangular pyramid is a three-dimensional figure with a rectangular base and four triangular faces that meet at a single point at the top, known as the vertex.
If a plane is passed through the pyramid perpendicular to the base but not through the vertex, it will intersect each of the four triangular faces of the pyramid at a different angle, resulting in a cross section that has four sides.
Since the base of the rectangular pyramid is a rectangle, the two opposite sides of the trapezoid cross section will be parallel, and the other two sides will be non-parallel. The shape and size of the trapezoid cross section will depend on the orientation of the plane with respect to the rectangular pyramid.
In summary, when a rectangular pyramid is sliced by a plane that is perpendicular to its base but does not pass through its vertex, the resulting cross section is a trapezoid with two parallel sides and two non-parallel sides.
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Farmer Quect started with 110 rews on his farm. Every hour, he destoryed 6 more of them. Farmer Mimstone started with 54 rews on her farm. Every hour she collected 9 more of them?
Write a systems of equations in slope intercept form. Farmer's rews (y), hours (x)
The systems of equations in slope intercept form is
y = -6x + 110
y = 9x + 54
What is Slope- intercept form?When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.
As, We know Slope-intercept form is
y = mx + b
where b is the starting value and m is the change per day.
Farmer Quect started with 110 rews on his farm. Every hour he destroyed 6 more of them.
So, the Equation to show the Situation
y = -6x + 110
and, Farmer Mimstone started with 54 rews on her farm. Every hour she collected 9 more of them.
So, the Equation to show the Situation
y = 9x + 54
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A school ordered `3` large boxes of markers. After giving `15` markers to each of `3` teachers, there were `90` markers left
How many markers were originally in each box?
Answer:
135 markers
Step-by-step explanation:
Let's call the number of markers in each large box "x."
After giving away 15 markers to each of 3 teachers, there were 90 markers left, so:
x - (15 * 3) = 90
Expanding the expression on the right side:
x - 45 = 90
Adding 45 to both sides:
x = 135
So, each large box originally contained 135 markers.
the coordinates of the endpoints of no are n(5,16) and o(19,9). point p is on no and divides it such that np:op is 4:3. what are the coordinates of p?
The coordinates of point P are (12, 12.5).
to put different elements or individuals in a coordinated effort.
To find the coordinates of point P, we can use the fact that P divides NO into two segments in the ratio of 4:3.
First, we can find the distance between points N and O using the distance formula:
d(NO) = sqrt((19-5)^2 + (9-16)^2) = sqrt(196 + 49) = sqrt(245)
Next, we can use the ratio of 4:3 to determine the distance between P and O:
d(OP) = (3/7) * d(NO) = (3/7) * sqrt(245)
Similarly, we can find the distance between P and N:
d(NP) = (4/7) * d(NO) = (4/7) * sqrt(245)
Now, we can use the midpoint formula to find the coordinates of P:
x-coordinate of P = (x-coordinate of N + x-coordinate of O) / 2 = (5 + 19) / 2 = 12
y-coordinate of P = (y-coordinate of N + y-coordinate of O) / 2 = (16 + 9) / 2 = 12.5
So the coordinates of point P are (12, 12.5).
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Indicate the method you would use to prove the two 's . If no method applies, enter "none".
SSS
ASA
SAS
AAS
None
As a result, no particular postulate can be used to demonstrate their congruence due to a lack of adequate data. So "None" is the correct response.
What in mathematics is a similarity?If two figures share the same form, congruent corresponding angles (which means the angles in the same locations of each shape are the same), and identical scale factors, they are said to be "similar figures." Equal scale factors signify a matched ratio between the lengths of their respective sides.
Two triangles can be seen in the illustration, and their corresponding angles are both equal.As a result, they match the AAA similarity requirement. However, no more details are provided to demonstrate their consistency.Although comparable triangles may not be congruent, congruent triangles are known to be similar.To know more about similarity visit:
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Answer: None
Step-by-step explanation: I Just did it
Clinton borrows a certain amount of money and pays the principle amount and the interest back after 5 years. Calculate the simple interest rate if Clinton pays back double the amount he borrowed
Answer: The simple interest will be 20%.
Step-by-step explanation:
we know the simple interest of borrowed amount is:
S.I.= (P x R x T)/100 ..... (i)
where P⇒ Principal amount
R⇒ rate of interest
T⇒ time
and
total Pays Back amount = Principal amount + S.I.
Hence S.I. = Pays Back amount - Principal amount
Now, as per the question: Clinton pays back Double of the amount hi borrowed. Means
if Principal amount = P
then Pays Back amount = 2P ⇒ S.I.= P
Rate of Interest = R
and Time = 5 years
P= (P x R x 5)/100
R= 100/5
R = 20%
Therefore, the simple interest is 20% annually.
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An account earns simple annual interest. $600 at 5% for 2 years
The total amount of interest earned at the end of 2 years is $60.
1. Calculate the interest earned in one year:
Interest = Principal × Rate × Time
Interest = 600 × 0.05 × 1
Interest = $30
2. Multiply the interest earned in one year by the number of years:
Total interest = 30 × 2
Total interest = $60
The total amount of interest earned at the end of 2 years is $60. This amount was earned by taking the principal amount of $600 and multiplying it by the rate of 5%, and then multiplying that product by the number of years, which in this case is 2. This calculation can be expressed as:
Total interest = Principal × Rate × Time
Total interest = 600 × 0.05 × 2
Total interest = $60
the complete question is :
An account earns simple annual interest. $600 at 5% for 2 years. How much interest will be earned on $600 invested at 5% simple annual interest for 2 years?
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the ratio of 9 minutes and 600 seconds in its simplest form
Answer:
Step-by-step explanation:
600 secs=600/60 mins=10 mins
9 mins= 9 mins
Therefore, 9 mins : 600 secs
=9 mins : 10 mins
=9:10
Can anybody answer the question I attached?
Answer:
36 bottles
Step-by-step explanation:
You want to know the number of bottles that must be painted and sold in order to make a profit of $120, given that 3 bottles can be purchased for $11, and each bottle can be sold for $7.
ProfitThe profit on each bottle is the difference between its cost and what it is sold for. The cost of 1 bottle is 1/3 of the cost of 3 bottles.
profit = selling price - purchase price
profit = $7/bottle - ($11/(3 bottles)) = $(21/3 -11/3)/bottle = $(10/3)/bottle
BottlesTo make a profit of $120, you need n bottles such that ...
(10/3)n = 120
n = 36 . . . . . . . . . multiply by 3/10
The club needs to buy, paint, and sell 36 bottles to raise $120.
HELP FOR 15 Points I SUCK AT MATH
The sum Given it can seen that according to the closure property of Rational numbers the addition of two rational numbers will sum up to a rational number provided that the rational numbers ≠ 0 and a set of rational number is closed under the closures property rule i.e x + y = y + x.
What is Closure Property of Integers ?
Closure Property of Integers states the sum or subtraction of two integers always gives an integer.
Rational number is defined as a number that can be made by dividing two integers.
Using the definition of rational and expanding the property, we can conclude that the sum of two rational numbers will result in a rational number.
using the closure property and based on the sum given, the addition of two rational numbers will sum up to a rational number provided that the rational numbers ≠ 0 and a set of rational number is closed under the closures property rule i.e x + y = y + x
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What is the standard function of f? F(x)=4(x+6)2+5
The standard function for F(x)=4(x+6)2+5, will be f(x)=8x+53.
What is the definition of a function?
A function is defined as a connection between a set of inputs and a single output. A function is a link between inputs that corresponds to exactly one output. Every function has a domain, a co-domain, and a range. A function is often denoted as f(x), where x represents the input. The general representation of a function is y = f(x).
There are several types of functions in mathematics. Here are a few examples:
An injective function or a one to one function exists when there is a mapping for a range for each domain between two sets.
Surjective functions, also known as Onto functions, are employed for transferring more than one element from domain to range.
A polynomial function is a function composed of polynomials.
Functions that may be used to inverse another function are known as inverse functions.
Now,
Given function is F(x)=4(x+6)2+5
=(4x+24)2+5
=8x+48+5
=8x+53
hence,
The standard function for F(x)=4(x+6)2+5, will be f(x)=8x+53.
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Please help me with this question real quick I didn't understand it if anyone can help please try to
you forgot to put the question
I increased a number by 5% twice how much id it increase by in percent.
Answer:
10%
Explanation:
You increased it by 5% twice, which is basically 5+5 or 5x2 which equals 10
Scatter Plot 8 grades, help please!!!
The of association represented in the graph is positive linear association.
option C
What is a positive correlation?
A positive correlation is a statistical relationship between two variables such that as one variable increases, the other variable also increases, and as one variable decreases, the other variable decreases as well.
In other words, positive correlation means that as the value of one variable goes up, the value of the other variable also goes up, and vice versa. The correlation is said to be positive because both variables move in the same direction.
The strength of the correlation can be measured using a correlation coefficient, which ranges from -1 to 1. A correlation coefficient of 1 indicates a perfect positive correlation, while a correlation coefficient of 0 indicates no correlation.
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Holly's height decreased by 21 is 62.
Use the variable h to represent Holly's height.
The algebraic expression is h - 21 = 62
How to represent as an algebraic expressionIf we let "h" be Holly's original height,
The phrase "Holly's height decreased by 21 is 62" can be translated into an algebraic expression as:
h - 21 = 62
This equation represents the relationship between Holly's original height and her current height, after a decrease of 21 units.
We can solve for h by adding 21 to both sides of the equation:
h - 21 + 21 = 62 + 21
h = 83
Hence, Holly's original height was 83 units.
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Fatina uses 7.8 pints of white paint and blue paint to paint her bedroom walls 3/5 of this amount is white paint and the rest is blue paint how many pints of blue paint did she use to paint her bedroom walls
Using the fractional value of blue paint to white paint, the number of pints of blue paint Fatina used to paint her bedroom walls is 3.12 pints.
What is a fractional value?A fractional value is a proportional quantity of the whole value.
Fractional values are depicted in decimals, fractions, or percentages.
The total quantity of white and blue paints used on the bedroom walls = 7.8 pints
The fraction of the white paint = 3/5
The fraction of the blue paint = 2/5 (1- 3/5)
2/5 of 7.8 = 3.12 pints
Thus, proportionately, we can conclude that the blue paint Fatina used was 3.12 pints.
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Kathy uses 3.12 pint of white paint to paint her bedroom walls
How many pints of blue paint did she use?Total amount of paint ( Blue and white paint)= 7.8 pints
Amount of blue paint=3/5 x 7.8 = 4.68Pints
amount of white paint = Total amount of paint - amount of blue paint
= 7.6 pints - 4.68 pints
=3.12 pint of white paint
In conclusion, she uses 3.12 pint of white paint to paint her bedroom walls
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read the story. clara snacked on a mix of almonds and pecans. she ate 3 almonds for every 1 pecan. pick the diagram that models the ratio in the story. if clara ate 10 more almonds than pecans, how many nuts did she eat altogether?
In all together, Clara ate 20 nuts.
A system of equations is a set of one or more equations involving a number of variables.
The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.
Given that Clara snacked on a mix of almonds and pecans. She ate 3 almonds for every 1 pecan. Clara ate 10 more almonds than pecans.
Let the number of pecans be x and the number of almonds is y.
We can write the system of equations as:
y = 3x
y = x + 10
Equating the value of {y}, we get -
3x = x + 10
2x = 10
x = 5 ...(1)
y = x + 10 = 15
y = 15 ...(2)
x + y = 15 + 5 = 20
Therefore, in together, Clara ate 20 nuts.
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A right triangle has acute angles c and d . If c=15/8 and sin d=8/17, what are cos d and cos c?
The value of the right triangle cos d = 15/17 and cos c = 8/17.
What are trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given that, the value of tan c = 15/8 and the value of sin d = 8/17.
From the trigonometric functions we can conclude that:
Opposite side to c = 15
Adjacent side to c = 8
Hypotenuse = 17
Opposite side to d = 8
Adjacent side to d = 15
The values of cos d is:
cos d = Adjacent side to d / Hypotenuse = 15/17
cos c = Adjacent side to c / Hypotenuse = 8/17
Hence the value of the right triangle cos d = 15/17 and cos c = 8/17.
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FIND THE PERIMETER AND AREA OF THE EQUILATERAL TRIANGLE
The area of an equilateral triangle is 16√3 m² and the perimeter of an equilateral triangle is 24 m.
What is area of an equilateral triangle?In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle. The area of an equilateral triangle is √3/4 ×a².
From the given figure, side of the equilateral triangle is 8 m.
Now, area of an equilateral triangle is
√3/4 ×8²
= √3/4 ×64
= 16√3 m²
The perimeter of an equilateral triangle is 3a.
Now, the perimeter is 3×8
= 24 m
Therefore, the area of an equilateral triangle is 16√3 m².
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Anna ate 5/8 of an orange and gave the other 3/8 to her brother.
The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference.
5/8 - 3/8 = x
5/8 = 5 ÷ 8
= 0.625
3/8 = 3 ÷ 8
= 0.375
0.625 - 0.375 = x
= 0.25
Therefore, the difference between the amount Anna ate and the amount she gave to her brother is 0.25.The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference. To solve this equation, we first need to convert the fractions into decimal values. 5/8 is equal to 5 divided by 8, which is equal to 0.625. 3/8 is equal to 3 divided by 8, which is equal to 0.375. We can then subtract 0.375 from 0.625 to get the difference. This gives us 0.25, which is the difference between the amount Anna ate and the amount she gave to her brother. Therefore, the answer to the equation 5/8 - 3/8 = x is x = 0.25.
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The complete question is
Anna ate 5 8 of an orange and gave the other 3 8 to her brother. Which equation can be used to find the difference between the amount Anna ate and the amount she gave her brother?
Anna ate 5 8 of an orange and gave the other 3 8 to her brother. Which equation can be used to find the difference between the amount Anna ate and the amount she gave her brother?
The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference.
5/8 - 3/8 = x
5/8 = 5 ÷ 8
= 0.625
3/8 = 3 ÷ 8
= 0.375
0.625 - 0.375 = x
= 0.25
Therefore, the difference between the amount Anna ate and the amount she gave to her brother is 0.25.The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference. To solve this equation, we first need to convert the fractions into decimal values. 5/8 is equal to 5 divided by 8, which is equal to 0.625. 3/8 is equal to 3 divided by 8, which is equal to 0.375. We can then subtract 0.375 from 0.625 to get the difference. This gives us 0.25, which is the difference between the amount Anna ate and the amount she gave to her brother. Therefore, the answer to the equation 5/8 - 3/8 = x is x = 0.25.
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1. suppose a point is to be selected at random from the unit square. write the sample space associated with this random experiment.
a) The x-range of a unit square is from o to 1 and y-range is also from 0 to 1
Sample space = {(x, y)} , 0≤x≤1, 0≤y≤1.
So, sample space associated with this random experiment is
{(x, y)} , 0≤x≤1, 0≤y≤1.
b) From the given data,
Sample space for A : {1, 3, 5, 7, 9, 11,...}
Sample space for B: {5, 10, 15, 20, 25,...}
Therefore, the sample space for A∩B will be the set of all odd natural numbers divisible by 5 which is
{5, 15, 25, 35,....}
c) First letter is the capital letter = 26 Possibilities
then four digits = 9*10*10*10
two lower case letters = 26*26
Total possible ways = 26*9*10*10*10*26*26
= 15,81,84,000 ways.
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Complete question:
Suppose a point is to be selected at random from the unit square. Write the sample space associated with this random experiment. 2. Let S = {0, 1, 2, 3, 4, ...), A = the set of odd natural numbers, and B = the set of natural numbers divisible by 5. What is the set An B? 3. A computer password consists of two lowercase letters followed by a capital letter and four digits. Find the total number of possible passwords.
Keisha must choose a shirt and a pair of pants for today's outfit. She has 4 shirts and 2 pairs of pants to choose from. How many different outfits can she make?
answer: 12
explanation:
if we have four variables, then how many equations will we have in our system of linear equations? 5 2 3
For four variables the required number of system of linear equations are at least option d. 4 equations.
Variable is represented by small alphabets : a , b, x, y , z, m , n ... so on.System of linear equations are set of equation relating variables with degree one. To solve the system of linear equations we need to have number of equations same as the number of variables.If there are two variables then we need to have minimum two system of linear equations .If there are n variables then there should be n system of linear equations.Therefore, if there are four variables in the system of linear equations then we should have option d. 4 equations.
The above question is incomplete , the complete question is:
If we have four variables, then how many equations will we have in our system of linear equations?
a. 5 b. 2 c. 3 d. 4
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\Plot the point (4, −3).
Start at the origin.
Move 4 units
Move 3 units
The point is at ___
Model |
^
On a coordinate plane, point A is 4 units to the left and 3 units up. Point B is 3 units to the left and 4 units up. Point C is 4 units to the right and 3 units up. Pound D is 4 units to the right and 3 units down.
The points A(-4,3) ; B(-3,4) ; C(4,3) ; D(4,-3) are plotted on the graph.
What is meant by a coordinate plane?
Two number lines combine to generate the two-dimensional surface known as the coordinate plane. The x-axis is a single horizontal number line. The y-axis is the name of the vertical number line which is the other number line. The origin is where the two axes come together. The coordinate plane can be used to graph points, lines, and other things.
The given points are
A is 4 units to the left and 3 units up which means A is (-4,3).
B is 3 units to the left and 4 units up which means B is (-3,4).
C is 4 units to the right and 3 units up which means C is (4,3).
D is 4 units to the right and 3 units down which means D is (4,-3).
All these 4 points are plotted on the coordinate plane and the graph is attached below.
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Add.The numerator should be expanded and simplified. The denominator should be either expanded or factored.\dfrac{8x}{x^2-49}+\dfrac{5}{x^2-4x-21}= x 2−498x + x 2−4x−215 =start fraction, 8, x, divided by, x, squared, minus, 49, end fraction, plus, start fraction, 5, divided by, x, squared, minus, 4, x, minus, 21, end fraction, equals
The simplified expression after factoring numerator and denominator is (x + 7) / x.
We can start by factoring the numerator and denominator of the first fraction:
x^2 - 49 = (x + 7)(x - 7)
The denominator can also be factored using the quadratic formula or by factoring as a product of two binomials:
x^2 - 4x - 21 = (x - 7)(x + 3)
So, the first fraction can be simplified as:
(x + 7)(x - 7)/[(x - 7)(x + 3)]
We can cancel out the (x - 7) factor in the numerator and denominator, leaving:
(x + 7)/(x + 3)
Next, we can simplify the second fraction by canceling out the common factor of (x + 3) in both the numerator and denominator:
(x + 3)/x
Putting it all together, we get:
[(x + 7)/(x + 3)] * [(x + 3)/x] = x + 7 / x
Therefore, the simplified expression is (x + 7) / x.
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____The given question is incorrect, the correct question is given below:
The numerator should be expanded and simplified. The denominator should be either expanded or factored.
Simplify (x^2-49)/(x^2-4x-21)*(x+3)/x
Cool Down: Bacteria Population
The graph shows the bacteria population on a petri dish as a function of the days d since an
antibiotic is introduced.
number of bacteria
1,000,000
Interpreting Exponential Functions
500,000
(0, 1000000)
(1, 900000)
2
(2, 810000)
4
time in days
6
8
00
10
The approximate value of f(4.5) is 550000.
What is the exponential function?Exponents are used in exponential functions, as the name suggests. But take note that an exponential function does not have a constant as its base and a variable as its exponent (A function is a power function rather than an exponential function if its base is a variable and its exponent is a constant).
From the given graph, the coordinate points are (0, 1000000), (1, 900000) and (2, 810000)
We know that, f(x)=mx+c
Here, (0, 1000000) and (1, 900000)
Now, m=(900000-1000000)/(1-0)
m=-100000/(1-0)
m=-100000
Substitute b=-100000 and (x, y)=(0, 1000000) in y=mx+c
1000000=-100000(0)+c
c=1000000
Substitute m=-100000 and c=1000000 in y=mx+c, we get
y=-100000x+1000000
The approximate value of f(4.5)
Now, y=-100000(4.5)+1000000
y=550000
Therefore, the approximate value of f(4.5) is 550000.
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A bag contains 2 red marbles and 3 black marbles. If Abby picks a marble without looking, returns it to the bag, and then draws a second marble, what is the probability that both marbles are red? Write your answer as a fraction.
The probability of getting both the marbles to be red will be 4/25.
What is probability?Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favorable outcomes to all outcomes.
Probability = Number of favorable outcomes / Number of samples
Given that two red and three black marbles are in a bag. If Abby takes a marble out of the bag without looking, puts it back, and then draws another marble.
The probability of getting red in the first draw,
P = 2 / 5
Now the marble is returned and again the probability of getting the red marble is,
P = 2 / 5
The probability of getting both the marbles red will be,
Pb = ( 2/ 5 ) x ( 2 / 5 )
Pb = 4 / 25
Therefore, there is a 4/25 chance that both marbles will be red.
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(a) without adding new vertices, add a single edge to the graph so that the new graph will have an euler path. which vertices does your new edge connect?
To add a single edge to a graph to create an Euler path, we must connect two existing vertices with an odd degree.
In graph theory, an Euler path is a path that visits every edge of a graph exactly once. However, not all graphs have an Euler path. If a graph has an Euler path, it must have either zero or two vertices with an odd degree. In this scenario, we are given a graph and are asked to add a single edge to create an Euler path.
To add a single edge to the graph, we must connect two existing vertices that have an odd degree. This is because adding a new vertex would change the degree of the graph and potentially affect the existence of an Euler path. Therefore, we must carefully consider the degree of each vertex before adding the edge.
Let's consider a graph:
A
/ \
B---C
/ \ / \
D---E---F
In this graph, vertices B, E, and F have an odd degree. To create an Euler path, we must connect two of these vertices with a new edge. Let's choose B and E, and add the edge (B, E) to the graph.
A
/ \
B---C
/ \ / \
D---E---F
Now, the graph has only one vertex with an odd degree, which is C. This means that the graph has an Euler path that starts at C, visits every edge exactly once, and ends at A.
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Simplify. -8/9 - (-2/9)
- 8/9 - (-2/9)
The answer I have gotten is -6/9
