Robyn has 4 important files saved on her computer.
To solve this problem, we can use a simple formula that relates the total space occupied by the files to the size of each file:
Total space occupied = Size of each file x Number of files
In this case, we know the total space occupied (84.6 megabytes) and the size of each file (21.15 megabytes), so we can rearrange the formula to solve for the number of files:
Number of files = Total space occupied ÷ Size of each file
Plugging in the values we know, we get:
Number of files = 84.6 megabytes ÷ 21.15 megabytes per file
Simplifying this expression gives us:
Number of files = 4
Therefore, Robyn has 4 important files saved on her computer.
It's important to note that this problem assumes that each file uses exactly 21.15 megabytes of memory. In reality, file sizes can vary depending on their content, so this may not always be the case. Additionally, it's worth noting that file size can be affected by various factors such as compression and encoding, so the actual size of a file on disk may differ from its theoretical size. Nonetheless, for the purposes of this problem, we can assume that each file uses exactly 21.15 megabytes of memory.
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20 POINTS.
Solve 4x+2 = 12 for x using the change of base formula
−1. 442114
−0. 207519
2. 55789
3. 79248
Answer:
Step-by-step explanation:
We can solve the equation 4x+2 = 12 for x using the change of base formula by isolating x on one side of the equation:
4x + 2 = 12
Subtracting 2 from both sides:
4x = 10
Dividing both sides by 4:
x = 2.5
We do not need to use the change of base formula to solve this equation as it is a simple linear equation that can be solved by basic algebraic manipulations. Therefore, none of the given options are correct.
PLESE HURRY 50 POINTSSS
Find the volume of the composite solid. Round your answer to the nearest tenth.
Answer:
about 1 cubic ft i think
Step-by-step explanation:
Pam and Erin start at the same point and begin rollerblading in different directions. Pam is rollerblading west at a speed of 2 miles per hour. Erin is rollerblading north at a speed of 4 miles per hour. After how many hours will they be exactly 14 miles apart? Round your answer to two decimal places
It will take 5.71 hours for Pam and Erin to be 14 miles apart.
If Pam and Erin start at the same point and rollerblade in different directions, then the total distance between them at any given time can be represented by the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
Let x represent the number of hours it takes for Pam and Erin to be 14 miles apart. Then, the distance traveled by Pam will be 2x, and the distance traveled by Erin will be 4x.
Using the Pythagorean Theorem, the equation that represents the distance between them can be written as 2x^2 + 4x^2 = 14^2.
Solving this equation, we get 6x^2 = 196, which can be written as x^2 = 32.75. Taking the square root of both sides, we get x = 5.71.
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Help me! Please (You dont need to do Both questions 1 and 2!)
1. Ben's mistake in solving the area of circle is, he has taken the value of diameter at the place of radius in formula.
2. Luna's mistake is, he did the incorrect squaring of radius 4.5.
Explain about the area of circle?The formula makes use of the diameter. The units are squared at all times. When the diameter is known, the area can be calculated by first determining the radius. The radius of the circle is the area. You can use circumference to determine area.
area of circle A = πr²
where, π = 3.14 and r is the radius of circle
r = diameter /2 = 9/2 = 4.5 cm
A = πr²
A = 3.14*(4.5)²
A = 3.14*20.25
A = 63.585 cm² (correct area)
Thus,
1. Ben's mistake in solving the area of circle is, he has taken the value of diameter at the place of radius in formula.
2. Luna's mistake is, he did the incorrect squaring of radius 4.5.
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a radioactive substance decays exponentially. a scientist begins with 110 milligrams of a radioactive substance. after 21 hours, 55 mg of the substance remains. how many milligrams will remain after 31 hours?
Starting with 110mg of a radioactive substance, after 21 hours, 55mg remains. Using the exponential decay model, after 31 hours, 39.3mg of the substance will remain.
We can use the formula for exponential decay, which is:
N(t) = N0 * e^(-λt)
where:
N0 is the initial amount of the substance
N(t) is the amount remaining after time t
λ is the decay constant
To solve for λ, we can use the fact that after 21 hours, 55 mg remains:
55 = 110 * e^(-λ*21)
Simplifying:
0.5 = e^(-λ*21)
Taking the natural logarithm of both sides:
ln(0.5) = -21λ
Solving for λ:
λ = ln(0.5) / (-21) ≈ 0.033
Now we can use this value of λ to find the amount remaining after 31 hours:
N(31) = 110 * e^(-0.033*31) ≈ 39.3 mg
Therefore, approximately 39.3 milligrams of the substance will remain after 31 hours.
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After identifying each of the mistakes that Ben and luna made, find the correct area of the circle. Round your answer to the nearest hundredth.
The area of the circle is 63.585 sq. cm.
What is area of circle?An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area. Each shape's area may be calculated by counting how many unit squares will fit inside of it.
Given that the diameter of the circle is 9 cm
The radius = 9/2 = 4.5 cm
The area of the circle is:
A = πr²
Substitute the values:
A = (3.14)(4.5)²
A = 63.585 sq. cm.
Hence, the area of the circle is 63.585 sq. cm.
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The complete question is:
A northbound car is going 12 miles per hour faster than a southbound car.
The cars are 276 miles apart 3 hours after passing each other on the interstate.
What is the speed of the northbound car?
Check the picture below.
so the cars are 276 miles apart, let's say the southbound car is going "r" mph fast, that means the northbound car is going "r + 12" mph fast as you see in the picture, so at some time they meet, hmmm wait, we know they're 3 hours apart from passing each other, so that means by the time they meet, 3 hours have passed, so by the time that happens, the northbound car has been traveling for 3 hours and the southbound car has been traveling for 3 hours as well.
Since we know they're 276 miles apart, let's say by the time they meet the southbound car has covered "d" miles, so the northbound car has covered the slack then, that is "276 - d" miles.
[tex]{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Southbound&d&r&3\\ Northbound&276-d&r+12&3 \end{array}\hspace{5em} \begin{cases} d=(r)(3)\\\\ 276-d=(r+12)(3) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{d=3r}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{276-(3r)~~ = ~~3(r+12)} \\\\\\ 276-3r=3r+36\implies 240-3r=3r\implies 240=6r \\\\\\ \cfrac{240}{6}=r\implies \stackrel{ Southbound~car }{40=r}\hspace{5em}\underset{ Northbound~car }{\stackrel{ 40~~ + ~~12 }{\text{\LARGE 52}}}[/tex]
The points Q(6, 3), R(-4,-3), S(-1,-8), and T(9,-2) form rectangle QRST.
Plot the points then click the "Graph Quadrilateral" button. Then find the area of the
rectangle.
The answer of the given question based on the finding the area of rectangle is QRST is approximately 116.56 square units.
What is Area?Area is a measure of the size or extent of a two-dimensional surface, like a shape or a region on a flat surface. It is typically measured in square units, like square meters (m²), square feet (ft²), or square centimeters (cm²).
To calculate the area of a shape, you need to know its dimensions and shape. The formula for finding the area of a shape depends on its shape. Area is an important concept in mathematics and geometry, and it is used in many real-life applications, such as measuring the size of land, determining the amount of material needed for a project, and calculating the volume of a container or room.
To find the area of the rectangle, we can use the distance formula to find the lengths of its sides. Then, we can use the formula for the area of a rectangle, which is the product of its length and width.
Length QR = √[(6 - (-4))² + (3 - (-3))²] = √[10² + 6²] = √(136)
Length ST = √[(9 - (-1))² + (-2 - (-8))²] = √[10² + 6²] = √(136)
Width QS = √[(6 - (-1))² + (3 - (-8))²] = √[7² + 11²] = √(170)
Width RT = √[(-4 - 9)² + (-3 - (-2))²] = √[13² + 1] = √(170)
Therefore, the area of the rectangle is:
Area = Length x Width = √(136) x √(170) = 116.56 (rounded to two decimal places)
So, the area of the rectangle QRST is approximately 116.56 square units.
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80% of ? = 60
HELP MEEE
PLSS
Answer:
48
Step-by-step explanation:
first multiply 60 by 0.80 the decimal version of the percentage then you get 48.00 or 48 as your anser
Subtract
−
5
x
2
−
9
x
−
5
−5x
2
−9x−5 from
4
x
2
−
5
x
+
3
4x
2
−5x+3.
Answer:
To subtract −5x² − 9x − 5 from 4x² − 5x + 3, we need to subtract the coefficients of each term with the same degree.
(4x² - 5x + 3) - (-5x² - 9x - 5)
4x² - 5x + 3 + 5x² + 9x + 5
9x² + 4x + 8
To subtract -5x² - 9x - 5 from 4x² - 5x + 3, you subtract each corresponding term, which results in 9x² + 4x + 8.
Explanation:If you would like to subtract -5x² - 9x - 5 from 4x² - 5x + 3, you need to subtract every term separately. So, the steps will look like the following:
subtract -5x² from 4x² which equals 9x²subtract -9x from -5x which equals 4xsubtract -5 from 3 which equals 8So, 4x² - 5x + 3 - (-5x² - 9x - 5) = 9x² + 4x + 8.
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If the triangle has sides with three different lengths what are all the possible whole number lengths for the sides that meet at a right angle
Answer:
Step-by-step explanation:
A) 6 inches. ( if the equation for the area of a triangle is
61 x 5 = 3,050 % 10, 381 X 27 = 1,143 % 9, 854 X 63 = 7,786 % 9, or 562 X 42 = 3,272, which equation is true, I don’t have the division sign so
Step-by-step explanation:
We can simplify each equation to determine which one is true:
61 x 5 = 305
10381 x 27 = 279,387
1143 ÷ 9854 x 63 = 0.00736 x 63 = 0.46368
562 x 42 = 23,604
Therefore, the only equation that is true is 562 x 42 = 23,604.
3.12 freeway level of service. a four-lane urban freeway (two lanes in each direction) was built in part using an abandoned canal. the design speed is 60 mph. the lanes are 10 feet wide without any shoulder on either side. if the traffic flow is 2500 vph with 25 percent trucks in the peak hour, what level of service is the freeway operation if there is an interchange every 0.33 mile? what is the density? g
The level of service for the urban freeway is level E, and the density is 61.25 vehicles per mile.
To determine the level of service for the urban freeway, we can use the Highway Capacity Manual (HCM) method, which considers factors such as traffic volume, speed, and density.
Based on the given traffic flow of 2500 vehicles per hour and a design speed of 60 mph, the capacity of the four-lane freeway can be calculated as 8000 vehicles per hour. Using this value, along with the interchange spacing of 0.33 miles, we can determine the density of the freeway, which is 61.25 vehicles per mile.
Using the HCM method, the level of service is determined by comparing the freeway density to the capacity, which results in a level of service of E. Level E indicates that the freeway is operating at or near its capacity, and delays are frequent.
In conclusion, the urban freeway has a level of service classified as E, and density of the freeway, which is the number of vehicles per mile, is calculated to be 61.25.
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f(x)=x^3-7x^2+25x-175 and f(7)=0
If we know that f(7) = 0, we can say that:
x - 7 is a factor of the function f(x).
This is because when we substitute x = 7 into the function, we get:
f(7) = 7^3 - 7(7)^2 + 25(7) - 175 = 0
This means that (x - 7) is one of the factors of the function.
Now we can use polynomial division or synthetic division to find the other factors. If we divide the function f(x) by (x - 7), we obtain:
x^2 - 4x + 25
Therefore, we can say that:
f(x) = (x - 7)(x^2 - 4x + 25)
The quadratic term, x^2 - 4x + 25, has no real roots because the discriminant is negative. Therefore, we can write the factorization of f(x) in terms of complex numbers as:
f(x) = (x - 7)(x - 2 + 5i)(x - 2 - 5i)
Thus, the complete factorization of f(x) is:
f(x) = (x - 7)(x - 2 + 5i)(x - 2 - 5i)
Si nous savons que f(7) = 0 alors,
x - 7 est un facteur de la fonction f(x).
on substitue x = 7 dans la fonction
f(7) = 7^3 - 7(7)^2 + 25(7) - 175 = 0
donc (x - 7) est l’un des facteurs de la fonction.
Maintenant, on utilise division polynomiale ou la division synthétique pour avoir les autres facteurs. Si on divise la fonction f(x) par (x - 7), on obtient:
x^2 - 4x + 25
Du coup peut dire que :
f(x) = (x - 7)(x^2 - 4x + 25)
Le terme quadratique, x^2 - 4x + 25, n’a pas de racines réelles car le discriminant est négatif. Par conséquent, nous pouvons écrire la factorisation de f(x) en termes de nombres complexes comme:
f(x) = (x - 7)(x - 2 + 5i)(x - 2 - 5i)
la factorisation complète de f(x) est:
f(x) = (x - 7)(x - 2 + 5i)(x - 2 - 5i)
Figure ABCDEFGH is a regular octagon. Segment AH is located at A(4, 5) and H(7, 5). What is the perimeter of ABCDEFGH? (1 point)
15 units
20 units
24 units
32 units
The perimeter of ABCDEFGH is 8s, with s = 3, so the perimeter of ABCDEFGH is 8x3 = 24 units.
The perimeter of a regular octagon can be calculated using the formula P = 8s, where s is the length of each side. To solve for the perimeter of ABCDEFGH, we need to first calculate the length of each side.We can use the distance formula to calculate the length of AH. The distance formula is [tex]d = √((x2-x1)^2 + (y2-y1)^2).[/tex] In this case, x1 = 4, y1 = 5, x2 = 7, and y2 = 5. Plugging these values into the formula, we get [tex]d = √((7-4)^2 + (5-5)^2) = √(3^2 + 0) = √9 = 3[/tex] units.Since each side of a regular octagon is equal, we can use the length of AH, 3 units, to calculate the perimeter of the octagon. The perimeter of ABCDEFGH is 8s, with s = 3, so the perimeter of ABCDEFGH is 8x3 = 24 units.
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you have three empty boxes and seven balls. how many ways can you distribute the balls among the three boxes so that each box contains at least one ball?
In conclusion there are 33 ways to distribute seven identical balls into three distinct boxes so that each box contains at least one ball.
How to solve?
This is a combinatorics problem known as distributing identical objects into distinct boxes with the condition that each box has at least one object.
There are three such cases: when the first box is empty, when the second box is empty, and when the third box is empty. Each of these cases can be represented by a single bar that is placed at the beginning or end of the line of stars. For example, the case where the first box is empty can be represented as:
|****|
There are three ways to place this single bar, so we need to subtract three from our previous count of 36 to get the final answer:
36 - 3 = 33
Therefore, there are 33 ways to distribute seven identical balls into three distinct boxes so that each box contains at least one ball.
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What is the verbal description of y=2/5x. WHO EVER ANSWERS WILL GET BRAINLIEST!!
The equation describes a linear relationship between two variables, where the output of the equation, y, is equal to two fifths of the input, x.
To calculate the value of y in the equation y=2/5x, we need to start by identifying the value of x. Once that is known, the value of y can be calculated by substituting x into the equation. For example, if x=10, then we can substitute 10 into the equation to get y=2/5 x 10. To solve this, we can multiply 2/5 by 10 to get 2x10/5, which simplifies to 20/5. Since dividing by 5 is the same as multiplying by 1/5, we can simplify this to 20/5 = 4. Therefore, when x=10, y=4.
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the complete question is
What is the verbal description of y=2/5x and identify the value of x
please help i will give 20 points if added demonstration on how to graph the answer
The solution is the factor 4y - 6x:. 2(2y - 3x) = 2(2y - 3x). 8 = 2• 4 =. 2(2y - 3x)
8. 2• 4
cancel the common factor: 2
= 2y - 3x. the answer is 2y - 3x
4 4
A random sample of 121 automobiles traveling on an interstate showed an average speed of 65 mph. From past information, it is known that the standard deviation of the population is 22 mph. If we are interested in determining an interval estimate for μ at 96. 6% confidence, the z value to use is
The interval estimate for the population mean, μ, is 65 ± 3.38 mph, or 61.62 to 68.38 mph.
The z-value for a 96.6% confidence level is 2.58. This value is used to determine the margin of error for a sample mean in a population. The formula for margin of error is ME = z*σ/√n, where σ is the population standard deviation, n is the sample size, and z is the z-value for the desired confidence level. In this case, ME = 2.58*22/√121 = 3.38 mph.Therefore, the interval estimate for the population mean, μ, is 65 ± 3.38 mph, or 61.62 to 68.38 mph.
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Meg wants to buy a new pair of skates. She can buy roller skates, figure skates, or hockey skates. A pair of skates can come in black, white, blue, or silver. How many different combinations can Meg choose from?
Meg has 12 different options to choose from when it comes to buying a new pair of skates based on combinations.
Meg has three options to choose from - roller skates, figure skates, and hockey skates, and four options for the color of her skates - black, white, blue, and silver. To find the total number of different combinations, we have to multiply the number of options for each category.
Total number of combinations of skates that Meg can choose from is:
3 (types of skates) x 4 (colors of skates) = 12
Meg has 12 different options to choose from when it comes to buying a new pair of skates.
It is important to note that this calculation assumes that Meg can choose any combination of skate type and color. If certain types of skates only come in certain colors, or if certain colors are only available for certain types of skates, then the number of possible combinations will be less than 12. Additionally, other factors such as size and brand of the skates may also affect the total number of options available to Meg.
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Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat of paint 0.03 cm thick to a hemispherical dome with a diameter of 30 meters.
The amount of paint needed in cubic centimeters to apply a coat of paint 0.03 cm thick to a hemispherical dome with a diameter of 30 meters is 1.413737 × 10¹⁰ cm³.
To estimate the amount of paint needed to apply a coat of paint 0.03 cm thick to a hemispherical dome with a diameter of 30 meters, we will use linear approximation.
The volume of a hemisphere with a diameter of 30 meters is given by:
V = (2/3)πr³Where r = 30/2 = 15 meters
We need to find the amount of paint required for a thickness of 0.03 cm.
We convert this to meters as:
0.03 cm = 0.0003 m
The linear approximation formula is given by:
ΔV ≈ dV/dx × Δx
where Δx = 0.0003 is the change in thickness, and
dV/dx is the rate of change of the volume with respect to thickness x.
We have:
V = (2/3)πr³ = (2/3)π(15)³ = 14137.2 m³
dV/dx = 4πr² = 1800π m²
Now, we can estimate the change in volume:
ΔV ≈ dV/dx × Δx = 1800π × 0.0003 = 0.1696 m³
The total amount of paint needed is:
V + ΔV = 14137.2 + 0.1696 = 14137.37 m³
We can convert this to cubic centimeters as:
1 m³ = 10⁶ cm³
So, the amount of paint needed in cubic centimeters is:
V = 14137.37 * 10⁶ cm³ = 1.413737 × 10¹⁰ cm³
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mad sounds ugh PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST sorry ik the Pic is dark my camera is broken
Answer:
B i think
Step-by-step explanation:
b
You push as hard as you can with a force of 20 N to move a table across the room, a distance of 15 m. How much work did it take you to move the table?
Answer:
Step-by-step explanation:
I’m not good at explaining but basically if you do 20n - 15n it would be 5n
I need help on this one
Answer:
Step-by-step explanation:
[tex]\sqrt{87x} =\sqrt{29\times3\times x}[/tex]
When [tex]x=21[/tex] we get:
[tex]\sqrt{87x} =\sqrt{29\times3\times 21}[/tex]
[tex]=\sqrt{29\times3\times3\times7}[/tex]
[tex]=3\sqrt{29\times7}[/tex]
[tex]=3\sqrt{203}[/tex]
So when [tex]x=21[/tex] we can simplify [tex]\sqrt{87x}[/tex].
Irene needs to make at least 25 dinners for a party,
including chicken dinners and vegetarian dinners.
She has $250 to spend. Chicken dinners cost $8.75
each and vegetarian dinners cost $5.50 each.
• c represents the number of chicken dinners.
v represents the number of vegetarian dinners.
Write a system of inequalities that represents Irene's
constraints.
First inequality,
Second inequality
The system of inequalities that represents Irene's constraints is:
c + v ≥ 25 (She needs to make at least 25 dinners) 8.75c + 5.50v ≤ 250.
The problem presents two types of dinners: chicken and vegetarian. Irene needs to make at least 25 dinners, so the total number of dinners must be greater than or equal to 25. The cost of chicken dinners and vegetarian dinners is also given, along with the total budget of $250. These constraints can be translated into mathematical inequalities using variables c and v to represent the number of chicken and vegetarian dinners, respectively.
The first inequality represents the constraint that the total number of dinners must be greater than or equal to 25:
c + v ≥ 25
The second inequality represents the constraint that the cost of the dinners cannot exceed the total budget of $250:
8.75c + 5.50v ≤ 250
Together, these two inequalities form a system of inequalities that represents Irene's constraints. The solution to this system will give the possible values of c and v that satisfy both constraints.
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Use the vectors u = (4, 4) and v = (-5, 1) to find the indicated quantity.
(u*v)v
(u*v)v=
State whether the result is a vector or a scalar.
The result is a
Therefore, the result of (u*v)v is a vector with components (80, -16).
What is vectors?In mathematics, a vector is a mathematical object that has both magnitude and direction. Vectors are used to represent physical quantities such as force, velocity, and acceleration, as well as abstract mathematical quantities such as points, lines, and planes. A vector is usually represented geometrically as an arrow in a coordinate system, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. Vectors can be added, subtracted, and multiplied by scalars, and these operations follow specific rules that make them a powerful tool for solving problems in mathematics, physics, engineering, and other fields. Vectors can have any number of dimensions, but in two-dimensional space, a vector can be represented as an ordered pair of numbers (x, y), where x and y represent the horizontal and vertical components of the vector, respectively. In three-dimensional space, a vector can be represented as an ordered triplet of numbers (x, y, z), and so on for higher dimensions.
Here,
To find (u*v)v, we first need to find the dot product of u and v, which is defined as:
u · v = (4, 4) · (-5, 1)
= (4 × -5) + (4 × 1)
= -20 + 4
= -16
Next, we need to multiply the dot product of u and v by v:
(u*v)v = (-16)(-5, 1)
= (80, -16)
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Which graph best represents y=x^+6x-1?
Answer:
ANSWER IS PROVIDED BELOW
hope this helps and good luck on your assignment
The b one please
i don't know
Answer:
Given :
By selling an article for rupees 144, a man loses 17
of his outlay. It is sold for rupees 189.
To do :
We have to find the gain or loss percent.
Solution :
Let the cost price of article be Rs. x
.
This implies,
SP =CP −Loss
=x−x7
=6x7
Therefore,
6x7=144
x=144×76
x=Rs. 168
If the article is sold for Rs. 189, then,
SP =Rs. 189
Profit =
SP − CP
=189−168
=Rs. 21
Gain %=GainCP×100%
=21168×100%
=12.5%
The gain percent is 12.5%
.
Step-by-step explanation:
if it helped you please mark me a brainliest :))
Write a model for m
Part a: Model for m∠A : cos A = 200/d.
Part b: If d = 300 m, m∠A = 48.19°.
Part c: If d = 550 m, m∠A = 68.67° .
Explain about the trigonometric ratios?The trigonometric functions sine, cosine, tangent, and its inverses make up these trigonometric ratios.
Given an angle measurement, so every function represents a distinct ratio in either a right triangle. Trigonometric ratios are the ratios of a right triangle's sides to one of the triangle's non-right angles. Remember that a right triangle has one right angle that is always 90 degrees in length.
In the given query:
Base = 200 m.
Hypotenuse = d m.
Part a: Model for m∠A :
cos A = Base/ Hypotenuse
cos A = 200/d.
Thus, Model for m∠A : cos A = 200/d.
Part b: If d = 300 m, m∠A = ?
cos A = 200/d.
cos A = 200/300
cos A = 2/3
m∠A = 48.19°
Part c: If d = 550 m, m∠A = ?
cos A = 200/d.
cos A = 200/550
cos A = 4/11
m∠A = 68.67°
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Twelve of the last 16 winners of the school science fair have been seventh grade students. mona placed 3 red marbles and 1 green marble in a bag to create a simulation to predict whether future science fair winners will be seventh graders. according to mona’s model, what is the probability that the next 4 winners will all be seventh grade students? startfraction 3 over 16 endfraction startfraction 81 over 256 endfraction three-fourths startfraction 7 over 8 endfraction
The probability that the next 4 science fair winners will all be seventh grade students is approximately 0.316
Assuming that the probability of winning the science fair is independent of grade level, the probability of a seventh grade student winning the science fair is 12/16 or 3/4, and the probability of a student of any other grade level winning is 1/4.
If Mona placed 3 red marbles (representing seventh grade winners) and 1 green marble (representing winners from other grade levels) in the bag, then the probability of drawing a red marble (representing a seventh grade winner) is 3/4, and the probability of drawing a green marble (representing a winner from another grade level) is 1/4.
Since the events of each science fair winner are independent, we can apply the multiplication rule of probability to determine the probability that the next 4 winners will all be seventh grade students
P(4 seventh grade winners) = (3/4)^4 = 81/256 or approximately 0.316.
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