It is important to check that the number of successes and number of failures in each sample is at least 10 because this helps ensure that the normal approximation of the binomial distribution is accurate.
When constructing a confidence interval for the difference between two population proportions, it is important to check that the number of successes and the number of failures in each sample is at least 10 because this helps ensure that the normal approximation of the binomial distribution is accurate. The normal approximation is often used in constructing confidence intervals for proportions because it simplifies the calculations, but it is only accurate if the sample size is large enough.
A common rule of thumb is that each sample should have at least 10 successes and 10 failures in order to ensure that the normal approximation is reasonable. This is because the Central Limit Theorem states that the sum of many independent and identically distributed random variables will approximately follow a normal distribution. When the sample size is large enough, the distribution of the sample proportions will be approximately normal, even if the individual observations are not.
If the number of successes and failures in each sample is less.
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what is 3/50+7/10 for adding and subtracting fractions
Answer:
37/50
Step-by-step explanation:
Step 1) Multiply 7/10 by 5/5 to get 35/50
Step 2) Add 3/50 and 35/50
Step 3) 3/50+ 35/50= 37/50
justify your reasons by determining the postulates, definitions, theorems, and properties used.
The angle 1 and angle 2 are congruent by alternate interior angles.
What is the angle sum property of triangle?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
1. Angle1 and angle2 are complementary. angle2 and angle 3 are complementary.
= sum of these angles is 180 degree because they are linear angles
2. m angle1+ m angle2 = 90° m/2+m/3 = 90°
=There sum makes right angle
3. m angle1+ m angle2 = m angle2 + m angle3
= sum of both the sides is 180 degree
4. m angle2 = m angle2
= sum of both the sides is equal
5. m angle1= m angle3
= sum of both the sides is equal
6. angle1 congruent angle3
=They are alternate interior angles.
Therefore, by the triangles properties angle 1 and angle 3 are congruent.
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How do you find the highest total surplus?
when the price is equal to the market equilibrium price, total surplus is maximized.
What is surplus?
Making the most of society's well-being is a desired goal for an economic system. Do free markets perform that? Buyers must profit from their purchases, and sellers must profit from their sales, in order to provide an answer. Consumer surplus is the difference between the price consumers are willing to pay and the price they actually pay for a commodity or service. When individuals buy something, they typically pay less than they would have otherwise. Similar to producers, sellers might command a higher price for a good than it costs them to make it; this is known as producer surplus because it occurs when the cost of production is less than the price at which the good is sold.
Consumer Surplus = Willingness to Pay Price − Market Price
Producer Surplus = Market Selling Price − Economic Cost
Total Surplus = Consumer Surplus + Producer Surplus
Only the most effective producers will be able to produce a product for less than the market price in highly competitive markets. Therefore, only those vendors will create a good.
Therefore, when the price is equal to the market equilibrium price, total surplus is maximized.
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A gardener will use up to 250 square feet for planting flowers and vegetables. She wants the area used for vegetables to be at least twice the area used for flowers. Let x denote the area (in square feet) used for flowers. Let y denote the area (in square feet) used for vegetables. Shade the region corresponding to all values of x and y that satisfy these requirements.
Answer:
Step-by-step explanation:
We can start by setting up the following system of inequalities to represent the requirements given in the problem:
x + y ≤ 250 (the total area used should not exceed 250 square feet)
y ≥ 2x (the area used for vegetables should be at least twice the area used for flowers)
To graph these inequalities, we can first graph the boundary lines for each inequality:
x + y = 250 (the boundary line for the first inequality, with points (250, 0) and (0, 250))
y = 2x (the boundary line for the second inequality, with points (0, 0) and (125, 250))
Then, we can shade the region that satisfies both inequalities, which is the region below the line x + y = 250 and to the right of the line y = 2x:
|
250-|__________________________
| / |
| / |
| / |
| / |
| / |
| / |
| / |
| / |
| / |
| / |
|/________________________|
0 125 250
The shaded region represents all values of x and y that satisfy the requirements given in the problem, where x is the area used for flowers and y is the area used for vegetables. The x and y values in this region can vary, as long as the total area used is less than or equal to 250 square feet and the area used for vegetables is at least twice the area used for flowers.
Answer:
To plot the region that satisfies the requirements, we can start by setting up the inequalities:
y ≥ 2x (the area used for vegetables is at least twice the area used for flowers)
x + y ≤ 250 (the total area used for planting is at most 250 square feet)
We can plot these inequalities on a coordinate plane to find the shaded region:
First, plot the line y = 2x (Load failedboundary line for the first inequality). This line passes through the origin and has a slope of 2, so we can plot additional points using this information. For example, when x = 50, y = 100 (since 100 is twice 50).
So, the shaded region on the coordinate plane corresponds to all values of x and y that satisfy the given requirements.
what is wrong with the following statement: boolean y = 12.5;
Answer:
we can not assign a floating-point number to a boolean variable
Step-by-step explanation:
The statement "boolean y = 12.5;" is incorrect or "wrong" because it is attempting to assign a floating-point value (12.5) to a boolean data type, which is a type of data that can only represent two values: true or false.
A boolean data type is a fundamental data type in programming and is commonly used in logic and decision-making structures. It is used to represent conditions that are either true or false, and can be used to control program flow, make decisions, and perform logical operations.
In the statement "boolean y = 12.5;", the value 12.5 is a floating-point value, which is a type of data that represents a decimal number with a fractional component. However, a boolean data type is not capable of representing such values, and can only represent two states: true or false.
In programming, attempting to assign a value of the wrong data type to a variable is known as a "type error" or a "type mismatch." Type errors can cause programs to fail, produce unexpected results, or behave in unintended ways.
To fix the statement "boolean y = 12.5;", the data type of the variable "y" should be changed to a data type that can represent decimal values, such as a floating-point data type like "double" or "float." Alternatively, if the intent of the statement was to assign a boolean value to the variable, the value of 12.5 should be replaced with a boolean expression that evaluates to either true or false.
In summary, the statement "boolean y = 12.5;" is incorrect or "wrong" because it attempts to assign a floating-point value to a boolean data type, which is not a valid data type for the value being assigned. Type errors like this can cause programs to fail, produce unexpected results, or behave in unintended ways, and must be corrected to ensure proper program operation.
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X
y
a) Complete the table of values for
y=x²- 2x + 5
1
2
-2 -1
13
-
b The aranh
0
5
-2
5
io
3
Answer:
See table below.
Step-by-step explanation:
Enter each x value into the equation x^2+2x+5 to find the value of y.
For example, when x = -2:
x^2-2x+5
(-2)^-2(-2)+5 for x = -2
4 + 4 + 5
y = 13
======
In the same manner:
x y
-2 13
-1 8
0 5
1 4
2 5
3 8
You want to build a sand castle on the seashore that will last two days. What two things should you consider?
Answer: sand and water
Sand : The first and most important thing you need to know about sand is that you can't do a thing with it unless it's wet. Here's why: when you add water to grains of sand, the liquid forms "bridges" that connect the granules to one another. This is why damp sand sticks together, so you can shape and carve it.
Water : Use lots of water. Dry sand in its natural state is lazy stuff. It wants to lie down and spread out into all sorts of nooks and crannies. The good news is that as long as you keep gravity working for you, there is really no way to add too much water. Which brings us to our second rule.2 Let it drain. If you've ever tried to make the base of a sandcastle by filling a plastic bucket with wet sand and then trying to unmould it, you've seen how important this rule is. With no place for the excess water to drain off, the sand makes a sucking, sticking, vacuum seal with the plastic and it becomes difficult, if not impossible, to remove the bucket.This is why successful sand sculptors do not use plastic buckets or other closed moulds but build their shapes by stacking handfuls of wet sand or by tamping it down in a topless and bottomless form.
Answer:
Placement and shape/size
Step-by-step explanation:
Placement: if the castle is to stay up for two days, you need to take into consideration the tide, and how far up on the seashore it will get. You need to know for a fact the ocean will not touch it, because if it does, chances are it will dig away at the foundation, making it topple over. You also need to make it in a place That little to no people will be there, so that they will not knock it over.
Shape/size: again, if it is to stay up for two days, you need to also consider the other weather than may occur. You need a good foundation that will not topple over. You need it tall enough that if some sand blows away, it will not matter. If it rains, you should have enough sand there that it would stay, and/or have something covering it, protecting it.
A cheetah can run 103 feet per second. A zebra can run x
feet per second. Use the Distributive Property to write and simplify an expression for how much farther the cheetah can run in 10 seconds.
expression: 10
(
)
simplified expression:
A cheetah can run 103 feet per second. A zebra can run x
feet per second. Use the Distributive Property to write and simplify an expression for how much farther the cheetah can run in 10 seconds.
expression: 10
(
)
simplified expression:
The expression of the distance between cheetah and zebra is (1030 – 10 x).
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The rate of cheetah Rc is given in the question, as follows:
Rc = 103 / sec
The rate of zebra Rz is given in the question, as follows:
Rz = x / sec
We have to determine the distance between the two are 10 seconds, that is:
distance = (103 – x) 10
Apply the Distributive Property in the above expression and we get
distance = 1030 – 10 x
Thus, the required expression is (1030 – 10 x).
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Including a 6% sales tax, a new bike costs $514.1. Find the cost of the bike before
tax.
the cost of the bike before tax
514.1/106%=$485
Graph the equation then find the solution
By graphing the system of equations, we can see that the solution is (4, -2)
How to solve the system of equations?Here we want to solve the system of equations:
y = (-3/2)*x + 4
y = (1/2)*x - 4
To solve this graphically, we just need to graph both equations on the same coordinate axis and find the point where the lines intersect.
The graph can be seen on the image at the end.
We can see that the solution is (4, -2)
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The histogram below shows information about the ages of the paintings in a gallery. 12 of the paintings in the gallery are over 90 years old. Work out an estimate for the number of the paintings that are over 70 years old.
The estimate for the number of the paintings that are over 70 years old is given as follows:
56.
How to obtain the estimate?The histogram shows the number of observations that appear in each range of the data-set.
12 of the paintings in the gallery are over 90 years old, hence the height of each small square is of:
12/(3 x 2) = 2 units.
Then the estimate of those over 70 years old is given as follows:
22 between 70 and 80.22 between 80 and 90.12 over 90.Hence the sum is given as follows:
22 + 22 + 12 = 56.
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URGENT!! WILL MARK BRAINLIEST!!!
The area of the parallelogram BEFD will be 100 square units.
What is the parallelogram area theorem?The area of parallelograms with the same base and corresponding parallels is the same. A parallelogram's area is the same as the area of a rectangle with the same base and height, or between the same parallels.
Given that the sides AB = 15, AD = 15 and the area of the quadrilateral ABCD is 100 square units.
From the theorem, the area of the parallelogram ABCD is equal to the area of the parallelogram BEDF.
Area of quadrilateral BEDF = 100 square units
Therefore, the area of the parallelogram BEFD will be 100 square units.
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G
E
C
D
28. Find x and y if CG=x+2y, EG=4, FG = 3x-y, and
DG=5.
Given the above values relative to the parallelogram, x = 2 and y = 1
What is a parallelogram?A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure.
Since the a parallelogram's diagonals are not all the same length, and they connect at the point of junction and have equal sides across the intersection, we can state that:
a
CG = EG and
FG = DG
Thus,
x+2y = 4; .........(1) and
3x-y = 5............(2)
Solving by substitution:
Let's make x the subject of the formula in (1)
x + 2y + (-2y) = 4 + (-2y)
x = -2y + 4 .......................................(3)
Substitute (3) into (2)
Where (2) is 3x-y = 5, thus;
3 (-2y + 4 )-y = 5.
-7y + 12 = 5
-7y + 12 -12 = 5 + -12
-7y = -1 (Divide both sides by -7)
y = 1 .............................(4)
Since y = 1, let's impute this in (1) x+2y = 4
x+2 (1) = 4
x = 4 -2
x = 2
Thus, x = 2, and y = 1
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Full Question;
Quadrilateral DEFC is parallelogram. Find x and y if CG = x + 2y, EG = 4, FG =3x-y, and DG = 5. Show your solution.
See attached image.
a certain group of women have a .92% rate of red/green colorblindness. if a woman is randomly selected, what is the probability that she dies not have red/green colorblindness?
The probability that a randomly selected woman does not have red/green colorblindness is 99.08%.
The probability that a randomly selected woman does not have red/green colorblindness is calculated by subtracting the given rate of red/green colorblindness from 100%. The formula for this probability is P(not colorblind) = 100% - .92% = 99.08%. The calculation is 100% - .92% = 99.08%. Therefore, the probability that a randomly selected woman does not have red/green colorblindness is 99.08.
Therefore, The probability that a randomly selected woman does not have red/green colorblindness is 99.08%. This was calculated using the formula P(not colorblind) = 100% - .92%.
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a)
3e - 2/4+30-4e/3=6
What does e =?
If the equation be 3e-2/4+30-4e/3=6 then the value of e be -14.1.
What is meant by expressions?A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression in mathematics.
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math. In mathematics, a numerical expression is a mixture of numbers and integers combined using addition, subtraction, multiplication, or division.
Let the given equation be [tex]$3 e-\frac{2}{4}+30-4 \cdot \frac{e}{3}=6$$[/tex]
Subtract [tex]$-\frac{2}{4}+30$[/tex] from both sides
[tex]$3 e-\frac{2}{4}+30-4 \cdot \frac{e}{3}-\left(-\frac{2}{4}+30\right)=6-\left(-\frac{2}{4}+30\right)$$[/tex]
Simplifying the above equation, we get
[tex]$3 e-4 \cdot \frac{e}{3}=-\frac{47}{2}$$[/tex]
Expand [tex]$3 e-4 \cdot \frac{e}{3}= \frac{5 e}{3}$[/tex]
[tex]$\frac{5 e}{3}=-\frac{47}{2}$$[/tex]
Multiply both sides by 3, then
[tex]$\frac{5 e}{3} \cdot 3=-\frac{47}{2} \cdot 3$$[/tex]
Simplifying the above equation, we get
[tex]$5 e=-\frac{141}{2}$$[/tex]
Divide both sides by 5
[tex]$\frac{5 e}{5}=\frac{-\frac{141}{2}}{5}$$[/tex]
Simplifying the above equation, we get
[tex]$e=-\frac{141}{10}$$[/tex]
e = -14.1
Therefore, the value of e be -14.1.
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Pls help or else am dead
The equation of a line is 3y + x - 15 = 0.
What is the equation of a line?
The set of points that make up a line in a coordinate system is represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. We may determine whether a given point lies on a line using the equation of any line.
Here, we have
Given: A(0,0), B(1,3)
The slope of AB = (3-0)/(1-0) = 3
The slope of a line perpendicular to AB = -1/3
y-intercept is 5
Equation of a line:
y - 5 = (-1/3)(x-0)
3y - 15 = -x
3y + x - 15 = 0
Hence, the equation of a line is 3y + x - 15 = 0.
Question: Given A(0,0) and B(1,3), find the equation of the line perpendicular to the y-intercept of 5
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You have a set of consecutive integers from (−5) to 5, inclusive. You multiply any three of the integers. What is the least positive integer you can get as the product?
The least positive integer we can get as the product is 2.
What is the least positive integer you can get?Here we have the following set of numbers:
{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
And we want to take the product between 3 of them and find the least positive integer that we can get as the product.
So it makes sence to choose the smallest absolute value numbers (not zero) such that one is positive and two are negative (we want two negative ones so the signs cancell eachother)
Then we will get:
1*(-1)*(-2) = 2
That is the least positive integer we can get as the product.
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Suppose G(x)=2x+3/x-4
find x such that G(x) = -3.
Answer:
I'm not entirely sure but maybe it's -11
Step-by-step explanation:
I'm sorry if it's wrong I tried what I think you need to do
I NEED HELP AGAINNNNN
1) Are the triangles ABC and PQR in the diagram congruent? GIVE REASONS for your answer.
2) In a piggy bank, there are x numbers of one dollar bills and 2x number of 50 dollar bills. Find the total amount of money in the piggy bank, in terms of x.
Answer:
no they are not equal just look at the picture carefully and you will realise it's not equal
K A can of beans has surface area 368 cm². Its height is 18 cm. What is the radius of the circular top? .... The radius of the circular top is 4.6 cm. (Do not round until the final answer. Then round to the nearest hundredth as needed.)
Answer: The surface area of a cylinder with height h and base with radius r can be calculated as:
A = 2πr^2 + 2πrh
We know the surface area (A) and the height (h) of the can of beans:
A = 368 cm²
h = 18 cm
We can substitute these values into the formula above and solve for r:
368 = 2πr^2 + 2πrh
368 = 2πr^2 + 2πr * 18
368 = 2πr^2 + 36πr
332 = 2πr^2 + 36πr
2πr^2 + 36πr - 332 = 0
We can use the quadratic formula to solve for r:
r = (-b ± √(b^2 - 4ac)) / 2a
where a = 2π, b = 36π, c = -332
r = (-36π ± √(36π^2 - 4 * 2π * -332)) / 2 * 2π
r = (-36π ± √(1296π^2 + 2664π)) / 4π
r = (-36π ± √(1296π^2 + 2664π)) / 4π
r = (-36π ± √(1296π^2 + 2664π)) / 4π
r = (-36π ± √(1656π)) / 4π
r = (-36π ± √(1656π)) / 4π
r = (-36π ± 40π^(1/2)) / 4π
There are two possible values for r, but only one will result in a positive value for r (the other will give a negative value). So we can use the positive value:
r = (-36π + 40π^(1/2)) / 4π
r = (40π^(1/2) - 36π) / 4π
r = (40π^(1/2) - 36π) / 4π
r = (40π^(1/2) - 36π) / 4π
r = (40 - 36π) / 4π
r = (40 - 36π) / 4π
We can approximate π as 3.14 to calculate the numerical value of r:
r = (40 - 36 * 3.14) / (4 * 3.14)
r = (40 - 113.04) / (4 * 3.14)
r = (40 - 113.04) / 12.56
r = (40 - 113.04) / 12.56
r = -73.04 / 12.56
r = -5.79
Since the radius must be positive, we reject this solution. The only valid solution is:
r = (40π^(1/2) - 36π) / 4π
r = (40π^(1/2) - 36π) / 4π
r = (6.32 - 36π) / 4π
r = (6.32 - 36 * 3.14) / (4 * 3.14)
r = (6.32 - 113.04) / 12.56
r = -106.72 / 12.56
r = -8.49
Since the radius must be positive, we reject this solution as well. There are no valid solutions for r, which means the original statement that "the radius of the circular top is 4.6 cm" is incorrect.
Step-by-step explanation:
The radius of the circular top is 4.6 cm.
What is surface area?
Surface area is total area on the surface of a three-dimensional shape.
The surface area of the can is made up of the sum of the areas of its top and bottom circular faces and its cylindrical side.
Let the radius of the circular top be "r".
The area of the circular top can be found using the formula:
A = πr^2
So, πr^2 = (1/2) * 368 cm²
r^2 = (368 / 2π) cm²
r = √(368 / 2π) cm
Using the value of π = 3.14, we get:
r = √(368 / (2 * 3.14)) cm
r = √(59.0079) cm
r = 4.6 cm
Therefore, The radius of the circular top is 4.6 cm.
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Consider the line 3x+5y=-1 What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?
Answer:
Parallel: m = -3/5
Perpendicular: m = 5/3
Step-by-step explanation:
First let's find the slope of the line.
To do so, we must make [tex]y[/tex] the subject of the line's equation. The slope would then be the coefficient of [tex]x[/tex].
[tex]3x + 5y = -1 \text{ // -3x} \\3x + 5y - 3x = -3x - 1\\\to 5y = -3x - 1 \text{ // :5}\\\\\frac{5y}5 = \frac{-3x - 1}5\\\\y = -\frac35x - \frac15[/tex]
Therefore, the slope of the line is [tex]m = -\frac35[/tex].
Parallel lines have similar slopes, therefore a line parallel to the line 3x + 5y = -1 would have a slope of -3/5.
If a line is perpendicular to our line, then its slope would be the negative invert of our line's slope. Therefore, its slope would be [tex]m = -\left(-\frac35\right)^{-1} \to -\left(-\frac53\right) \to \frac53[/tex]
Pls help me i need help
all the work in is the picture. lmk if anything is unclear, I'm happy to help
PLEASE HELP ME ASAP
Choose the letter of the correct
equation for the graph.
a. y = cos(x+)
b. y = cos(x - 5)
c. y = sin(x + π)
d. y = sin(x + 2)
e. y = sin(x) +
the above trigonometric function given in the graph will be y = sin(x + π)
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
In the given Trigonometric Functions
the graph is represented will be y = sin(x + π).
Hence the above trigonometric function given in the graph will be y = sin(x + π)
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Which expression to represents the phrase: "6 times a number plus 3."
6 x 3
6 x 3 + n
6n + 3
6n = 3
how many cubic feet of sand would you need to fill a space that 20 feet wide, 40 feet long, and a 6 inches thick?
The amount of sand needed, we will multiply 400 cubic feet by 1.5, which will give us 600 cubic feet of sand needed to fill the space.
The formula for finding the volume of a space is length x width x height. To find the cubic feet of sand needed to fill the space, we will need to calculate the volume of the space in cubic feet and then multiply it by the amount of sand needed to fill the space. To calculate the volume of the space, we will first convert the 6 inches to feet by dividing it by 12, which will give us 0.5 feet. We can then plug the numbers into the volume formula, which will look like this: 20 feet x 40 feet x 0.5 feet = 400 cubic feet. To find the amount of sand needed to fill the space, we will multiply the volume of the space by the amount of sand needed (which is usually 1.5 to 2 cubic feet per square foot). For this example, we will use 1.5 cubic feet. So to find the amount of sand needed, we will multiply 400 cubic feet by 1.5, which will give us 600 cubic feet of sand needed to fill the space.
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Shannon dreams of becoming the national spelling bee champion. She can already spell a lot of the words on her study list, but she needs to learn even more. This table shows the relationship between the time (in hours) that Shannon spends studying, x, and the total number of words on the study list that she can spell, y. x (hours) y (words) 1.1 93 1.3 95 1.6 98 1.8 100 According to the values in the table, do x and y have a proportional relationship? yes no
According to the values in the table, no, x and y does not have a proportional relationship. Therefore, the correct answer option is: B. no.
What is a proportional relationship?In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x represent the time (in hours).k is the constant of proportionality.y represent the total number of words.Next, we would determine the constant of proportionality (k) for the relationship between the x-values and y-values in this table as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 93/1.1 ≠ 95/1.3 ≠ 98/1.6 ≠ 100/1.8
Since the constant of proportionality (k) for the relationship between the x-values and y-values are different, we can logically deduce that this is not a proportional relationship.
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What is one of the solutions to the following system?
StartLayout Enlarged left-brace 1st Row y minus 3 = x 2nd row x squared minus 6 x + 13 = y EndLayout
The solutions to the system of equations is given as follows:
(-1,2) and (8,11).
How to solve the system of equations?The system of equations for this problem is defined as follows:
y - 3 = x.x² - 6x + 13 = y.From the first equation, we have that:
y = x + 3.
Replacing on the second, we have that:
x² - 6x + 13 = x + 3.
x² - 7x - 16 = 0.
We can factor the expression as follows:
(x - 8)(x + 1) = 0.
Hence the solutions are:
x - 8 = 0 -> x = 8 and y = x + 3 = 11.x + 1 = 0 -> x = -1 and y = x + 3 = 2.More can be learned about a system of equations at https://brainly.com/question/30374328
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Answer: B
Step-by-step explanation:
edge 2023
PLS HELP 100 points
A photographic negative is 5.4 cm by 1.35 cm. If you are going to enlarge the image on a 10.2 in by 2.4 in piece of photo paper, what is the largest length and width you can use to keep the photo in proportion to its negative?
Answer:
Step-by-step explanation:
To keep the photo in proportion to its negative, you need to maintain the same aspect ratio, which is the ratio of the width to the height of the image. The aspect ratio of the negative is 5.4 cm / 1.35 cm = 4. To maintain this aspect ratio, the aspect ratio of the enlargement must also be 4.
The aspect ratio of the photo paper is 10.2 in / 2.4 in = 4.25. So, the largest length and width that you can use to keep the photo in proportion to its negative is 2.4 in * 4 = 9.6 in and 9.6 in / 4 = 2.4 in, respectively.
Answer:
Length = 9.6 inWidth = 2.4 inStep-by-step explanation:
Conversion
1 inch ≈ 2.54 cmFirst convert the dimensions of the photo paper to centimeters:
[tex]\implies \sf 10.2\;in=10.2 \times 2.54=25.908\;cm[/tex]
[tex]\implies \sf 2.4\;in=2.4 \times 2.54=6.096\;cm[/tex]
Therefore, the dimensions of the photo paper in centimeters are:
25.908 × 6.096 cm (nearest thousandth)To determine the dimensions of the photo if the image is enlarged to fit on a 25.908 × 6.096 cm piece of photo paper, first calculate the scale factor by dividing the shortest side of the photo paper by the shortest side of the negative:
[tex]\sf Scale\;factor=\dfrac{6.096}{1.35}=4.51555...[/tex]
Multiply this scale factor by the longest side of the negative to determine the proportional length of the photo:
[tex]\implies \sf 4.51555...\times 5.4=24.384\;cm[/tex]
As 24.384 cm is less than the longest side of the photo paper, this scale factor will work to keep the photo in proportion to its negative.
Therefore, the largest length and width you can use to keep the photo in proportion to its negative is:
24.384 × 6.096 cm9.6 × 2.4 inthe adjoining figure shows a racing track consisting of two parallel stretches which is 119 M long and 10 metre wide its other two end are semicircular the inner distance between the two parallel Streches is 70 m evaluate and also find the distance around the track along its outer edge and the area of the track
The distance around the track along its outer edge is 740.4 meters and the area of the track is 2514 meter square.
A racing track consisting of two parallel stretches which are of 119 meters long and 10 meters wide.
The other two ends are semicircular the inner distance between the two parallel stretches is 70 m.
Radius of Exterior = ( 70 + 10 ) m = 80 m
The circumference formula is given by:
Circumference = 2πr
= 2 (3.14) (80)
= 2 (251.20)
= 502.4
Now we have to calculate the distance around the track
The Distance Around the Track = Circumference + 2 (Length)
= 502.4 + 2 (119)
= 502.4 + 238
= 740.4 meters
The Area of track = The Area of the outer circle - The Area of the inner circle
= π × R square - π × r square
= 6364 - 3850
= 2514 meter square
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Sarah invests £9600 at a simple interest rate of 8% per year.
Work out the value of investment after 3 years.