The Correct statement about Standardized units is (c) Standardized units are units that have the same meaning for everyone who uses them. When using standardized units, people can communicate measurements and know they mean same thing to both people.
The Standardized Units are a set of units of measurement that have been universally recognized and adopted for specific quantities.
The International System of Units (SI) is the most widely used system of standardized units, and includes units for measuring length, mass, time, electric current, temperature, and other physical quantities.
The Standardized Units play a crucial role in scientific experiments, as well as in manufacturing processes, and in providing precise information on medication dosages, food labeling, and other important areas.
Therefore , standardized units ensure uniformity and comparability of measurements across different fields and geographic locations.
What is meant by standardized units and why are they useful?
Choose the correct answer below.
(a) Standardized units are the units that were once standard but have since been phased out for more precise definitions of measurements. They are useful for historical reason, as knowledge of these older units allows people to translate the measurements of the past into the units of today.
(b) Standardized units are the units that have been determined by a monarchy. They allow educated peoples who use them to distinguish themselves from the common folk who do not.
(c) Standardized units are units that have the same meaning for everyone who uses them. When using standardized units, people can communicate measurements and know that they mean the same thing to both people.
(d) Standardized units are units that are about the same for each person. For example the length of a person's foot is a foot. These units are useful because, for example, anyone with a foot can use their own to get a measurement.
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consider the two functions shown below. assume the blue line represents a(x) and the pink line represents b(x). how do the second derivatives of the two functions with respect to x compare?
The second derivative of a(x) is larger than the second derivative of b(x) for the given x values.
The second derivative of a function with respect to x is the rate of change of the first derivative with respect to x. The second derivative of a function measures the "curvature" of the graph. In the case of the two functions shown, the blue line represents a(x) and the pink line represents b(x). By looking at the graph, we can see that the first derivative of a(x) is steeper than that of b(x). Therefore, the second derivative of a(x) will be larger than the second derivative of b(x). This can be seen by looking at the graph and noting that the blue line has a greater curvature or "bend" than the pink line. In other words, the second derivative of a(x) is larger than the second derivative of b(x) for the given x values.
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find the average value of the following function on the given interval. draw a graph of the function and indicate the average value. f(x); [0,1] for any integer n greater than 1
The average value is the intersection point between the function and the line, which is at (0,1+C).
The average value of a function on an interval can be calculated using the following formula: Average Value = (1/b-a)∫a b f(x)dx. In this case, the function is f(x) and the interval is [0,1]. To calculate the average value, we must first calculate the integral of the function on the given interval. The integral of f(x) is nx^n-1 + C, where C is a constant. Using the fundamental theorem of calculus, we can evaluate the integral from 0 to 1 to be 1 + C.
The average value of the function on the given interval is then (1/1-0)∫0 1 (1+C)dx, which simplifies to 1+C. Therefore, the average value of the function on the given interval is 1 + C.
Graphically, the average value of the function on the given interval can be seen by plotting the graph of the function, which is a parabola with a vertex at (0,0), and a line at y=1+C. The average value is the intersection point between the function and the line, which is at (0,1+C).
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two step equations -16 - 5x = -16
Answer:
-16 - 5x = -16
-5X=-16+16
-5X=0
X=5
Step-by-step explanation:
a scale of 1:900,000 is ________ a scale of 1:24,000
A scale of 1:900,000 is 36 times smaller than a scale of 1:24,000.
This can be expressed mathematically as a ratio: 1:900,000 = 1:24,000 / 36. To calculate the scale factor between two maps, divide the denominator of the larger scale by the denominator of the smaller scale. In this example, the scale factor is 36.
A scale of 1:900,000 means that one unit on the map represents 900,000 units of the same type in the real world. For example, one centimeter on the map could represent 900,000 centimeters in real life, or 9 kilometers. A scale of 1:24,000 would mean that one unit on the map represents 24,000 units of the same type in the real world. For example, one centimeter on the map could represent 24,000 centimeters in real life, or 0.24 kilometers.
The scale factor is the number that is used to compare the size of one map to another. In this example, a map with a scale of 1:900,000 is 36 times smaller than a map with a scale of 1:24,000. This means that the features on the 1:900,000 map are 36 times smaller than the same features on the 1:24,000 map. Therefore, the 1:900,000 map is not as detailed as the 1:24,000 map.
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X el largo de un escritorio es 6 pulgadas mas que su ancho. expresar el largo de la mesa en términos de su ancho W
The algebraic expression representing the length of the desk as a function of the width is given as follows:
L = W + 6.
How to obtain the algebraic expression?The two variables in the context of this problem are given as follows:
Length L.Width W.The length is 6 inches greater than the width of the desk, hence the algebraic expression representing the length of the desk as a function of the width is given as follows:L = W + 6.
TranslationThe problem asks for the algebraic expression representing the length of the desk as a function of the width.
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A scatter plot is shown on the coordinate plane.
scatter plot with points plotted at 1 comma 9, 3 comma 7, 4 comma 5, 4 comma 6, 5 comma 3, 6 comma 4, 7 comma 4, 8 comma 4, 9 comma 2, and 10 comma 1
Which of the following graphs shows a line on the scatter plot that fits the data?
scatter plot with points plotted at 1 comma 9, 3 comma 7, 4 comma 5, 4 comma 6, 5 comma 3, 6 comma 4, 7 comma 4, 8 comma 4, 9 comma 2, and 10 comma 1, with a line drawn through 7 comma 4 and 9 comma 2
scatter plot with points plotted at 1 comma 9, 3 comma 7, 4 comma 5, 4 comma 6, 5 comma 3, 6 comma 4, 7 comma 4, 8 comma 4, 9 comma 2, and 10 comma 1, with a line drawn through 4 comma 6 and 9 comma 2
scatter plot with points plotted at 1 comma 9, 3 comma 7, 4 comma 5, 4 comma 6, 5 comma 3, 6 comma 4, 7 comma 4, 8 comma 4, 9 comma 2, and 10 comma 1, with a line drawn through 4 comma 5 and 8 comma 1
scatter plot with points plotted at 1 comma 9, 3 comma 7, 4 comma 5, 4 comma 6, 5 comma 3, 6 comma 4, 7 comma 4, 8 comma 4, 9 comma 2, and 10 comma 1, with a line drawn through 6 comma 4 and 7 comma 4
The correct graph that shows a line on the scatter plot that fits the data is the one with a line drawn through the points (1,7 and 2,6).
What is Graph?In mathematics, a graph is a visual representation of a set of objects, called vertices or nodes, that are connected by lines or arcs, called edges or links. Graphs are commonly used to represent and analyze relationships between different entities, such as people, places, or things.
here, we have,
The vertices in a graph can represent anything, such as cities on a map, people in a social network, or molecules in a chemical reaction. The edges between vertices represent the connections or relationships between them. For example, in a social network graph, the edges might represent friendships between people, while in a transportation network, the edges might represent roads or train tracks connecting different cities.
Graphs are used in many areas of mathematics and science, including computer science, physics, biology, and social science. They are a powerful tool for analyzing and visualizing complex systems and relationships, and have many practical applications, such as in route planning, network analysis, and social network analysis.
The correct graph that shows a line on the scatter plot that fits the data is the one with a line drawn through the points (1,7 and 2,6).
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a bag of fertilizer covers 3000 square feet of lawn. find how many bags of fertilizer should be purchased to cover a rectangular lawn 170 feet by 40 feet. round up to the nearest whole bag of fertilizer.
9.53 fertilizer bags are required to cover a lawn that is rectangular and is 260 feet by 120 feet.
How to find the Calculation?The nitrogen fertilizer type known as urea is inexpensive. This is as a result of its high nitrogen content and the ensuing low costs of storage and transportation.
When all that is required for a soil fertility program is nitrogen, urea can be the best fertilizer to use.
Finding the location of the lawn is the first stage.
Area: 110 feet by 260 feet.
28600 square feet.
Calculating how many bags of fertilizer to purchase is the next step.
Bags = Area x 3,000 feet
Bags: 28600 feet / 3000 feet
9.53 bags total are in the bag.
Inconclusion 9.53 sacks of fertilizer should be bought to cover a lawn that is rectangular and measures 260 feet by 120 feet.
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In ΔABC, a= 270 inches, m∠C=164° and m∠A=8°. Find the length of c to the nearest 10th of an inch
Answer:
456.9 inches
Step-by-step explanation:
We can use the law of sines to find c:
c = (a / sin C) = (270 inches / sin 164°)
To find the sine of an angle in degrees, we can use a scientific calculator or a trigonometry table. Rounding to the nearest 10th of an inch, c = approximately 456.9 inches.
Answer: It's 534.7
Step-by-step explanation:
I sacrificed my chance of getting it right to see the answer. It's right That I guarantee. btw brainiest, please?
determine the magnitude and coordinate direction angles of f3 so that the resultant of the three is 0
The magnitude of f3 is 6.403N and the coordinate direction angle is 247.9°
We can calculate the magnitude and coordinate direction angle of f3 using the vector triangle method.
We assume that the coordinate direction angle of f1 is 0° and the coordinate direction angle of f2 is 90°.
Using the law of cosines, we can determine the magnitude of f3, which is 6.403N:
f3^2 = f1^2 + f2^2 -2f1f2cos180°
f3^2 = 5^2 + 8^2 -2(5)(8)cos180°
f3^2 = 25 + 64 -80
f3^2 = 49
f3 = 6.403N
We can then use the law of sines to determine the coordinate direction angle of f3, which is 247.9°:
sinθ3 = f2sin180°/f3
sinθ3 = (8)(180°)/6.403
sinθ3 = 147.6°
θ3 = 247.9°
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M is the midpoint of AB
Answer:
Midpoint=(−12,−2)
As a decimal:
Midpoint=(−0.5,−2)
Step-by-step explanation:
M=(xM,yM)
M=(x1+x22,y1+y22)
M=(3+−42,3+−72)
M=(−12,−42)
M=(−12,−2)
As a decimal:
M=(−0.5,−2)
Distance Solution: Between Endpoints
d=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√
d=(−4−3)2+(−7−3)2−−−−−−−−−−−−−−−−−−√
d=(−7)2+(−10)2−−−−−−−−−−−−√
d=49+100−−−−−−−√
d=149−−−√
d=12.206556
Solve the initial value problem t^2dy/dt - t = 1 + y + ty, y(1)=2
y =
For given expression, solution will be y=(t-1)/(1+t).
What are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
Given expression is t^2dy/dt-t=1+y+ty
After differentiation : As (d/dx) (x^n ) = nx^{n-1}
2t-t=1+y+ty
t-1=y(1+t)
y=(t-1)/(1+t)
for y(1)=2
2+2t=1-t
3t=-1
t=-1/3
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11). Find the area of the enclosed figure below.
Total area of the enclosed figure is given as 66 sq. units.
What is Area of a figure ?The quantity of unit squares that cover a closed figure's surface is its area. Square units like cm2 and m2 are used to measure area. A shape's area is a two-dimensional measurement.
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 common ways to depict square units, which are the same as areas, are square inches, square feet, etc.
The space around by a shape's perimeter or boundary is known as its area. Using particular mathematical methods, we may determine the area of shape for various geometric forms.
In the shape there is 2 triangles and 3 rectangle
Area of the bottom triangle = 1/2 * 3*4 = 6 sq. units
Area of the top triangle = 1/2 * 4*2 = 4 sq. units
Area of the bottom rectangle = 8*3 = 24 sq. units
Area of the middle rectangle = 8*3 = 24 sq. units
Area of the top rectangle = 4*2 - 8 sq. units
Total area of the enclosed figure is given as 6+4+ 24+ 24+ 8 = 66 sq. units.
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(1/6+2 2/3)x(1 1/4-1/2)
Answer:2.12
Step-by-step explanation:
How to convert 80 kg to lbs?
When 80 kg is converted to lbs it will be equal to 176.36980975 pounds (lb).
How to convert kg to lb?The conversion factor of 2.20462 can be used to convert kilograms (kg) to pounds (lbs). To calculate the number of pounds, multiply the number of kilograms by 2.20462.Here in this case,
80kg x 2.20462
= 176.36980975 pounds.
It should be noted that this conversion is for the international standard, and the conversion formula may vary depending on the country.Also, keep in mind that the pound (lb) and kilogram (kg) are weight units and should not be confused with mass, which is measured in ounces (oz) and grams (g). Weight is more commonly used in everyday life to measure things like body weight and food weight, whereas mass is more commonly used in scientific settings.To learn more about unit conversion refer to :
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PLEASE HELP SOLVE THIS SLOPE
Answer:
D
Step-by-step explanation:
1. Find which of these 4 (four) has a y-intercept of positive 4, in this case, B and D. Recall, that the y-intercept means when X is 0 (zero) what is the value of Y?
2. Find the slope of B and D
The formula to find slope is change in y/change in x (Y/X)
B:
X: 0 - 4 = -4
Y: 4 - 0 = 4
4/-4 = -1
D:
X: 0 - -4 = 4
Y: 4 - 0 = 4
4/4 = 1
When the students select their random samples and plot the results on a dotplot, which of the following should they expect to see?
The dots, which represent the sample proportions obtained by the students,
A) will all be at the same number.
B) will be wildly unpredictable.
C) will be clustered around 0 and 1.
D) will be centered around p, the true population proportion.
The correct option is "will be centered around p, the true population proportion."
What are random sample?Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.
Given that, the students select their random samples and plot the results on a dot plot, the dots, represent the sample proportions obtained by the students,
Since, the dots are representing the sample proportions, we know,
The population proportion is equal to the mean of the sampling distribution of the sample proportion.
Hence, the correct option is "will be centered around p, the true population proportion."
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Madelyn has a home-based business making and selling scented soaps. She initially spent $50 to purchase soap-making equipment, and the materials for each kilogram of soap cost $6. Madelyn sells the soap for $8 per kilogram. Eventually, she will sell enough soap to cover the cost of the equipment. Write a system of equations.
Answer:
25
Step-by-step explanation:
$50
Cost=$6
Selling price=$8
Profit=$8-$6=$2
50/2=25
given rectangular prism ABCD
choose all of the terms that best describe each of the sets of lines or points.
points E, H, and J
[] non-coplanar
[] coplanar
[] equidistant
[] non- collinear
[] collinear
The best describe each of the sets of lines or points will be coplanar, equidistant, and collinear. Then the correct options are B, C, and E.
What are collinear points?An axis is a term used to describe a line on which points are located, particularly if that line is connected to a triangle or other geometric shape. Since two factors determine a line, two points are transparently collinear. If the points are in a line, then the points are collinear points.
Let A, B, C, and D be the collinear points. Then the condition of the collinear will be
AB + BC + CD = AD
The collinear points lie in the same plane. Then the points are coplanar too.
From the graph, the distance between points E, H, and J will be the same.
The best describe each of the sets of lines or points will be coplanar, equidistant, and collinear. Then the correct options are B, C, and E.
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the mean composite score for seniors who took the sat in 2018 was 1068. if the standard deviation for this same year was 180, what is the raw score for a person with a z score of –0.42?
A person with a Z-score of -0.42 would have a raw score of 992.4 on the SAT taken in 2018.
The standard deviation is a measure of how much the data varies from the mean. A Z-score is a standardized value that represents the number of standard deviations a raw score is from the mean.
To find the raw score given a Z-score, we can use the following formula:
raw score = mean + Z-score * standard deviation
For the mean composite score of 1068 and a standard deviation of 180, we can plug in the values for the Z-score of -0.42:
raw score = 1068 + (-0.42) * 180
raw score = 1068 - 75.6
raw score = 992.4
Note: The Z-score of -0.42 indicates that the raw score is 0.42 standard deviations below the mean.
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Ernesto has 29 cups of water. Is this enough water to make 15 batches of green slime for a class project? Explain.
8. There are 16 tablespoons in 1 cup. How many tablespoons of cornstarch would Ernesto need to make 20 batches of green slime ?
help please???????????
Answer:240!
16 xs 15 = 240
Step-by-step explanation:
Answer: 240
Step-by-step explanation:
16 x 15 = 240 :)
Suppose we observe the following rates: 1R1 = .08, 1R2 = .12, and E(2r1) = 14. If the liquidity premium theory of the term structure of interest rates holds, what is the liquidity premium for year 2? Hint: Ry[(1+R)+E(277)+4)...Q+E(x7)+Lx)} N-1 O 6.15% O 2.15% O 14.00% O 8.45% O 12.45%
If the liquidity premium theory of the term structure of interest rates holds, 0.498% is the liquidity premium for year 2.
What is liquid premium theory?Any additional compensation that is necessary to attract investment in assets that cannot be quickly and effectively converted into cash at fair market value is known as a liquidity premium. Because it is more difficult to sell than a short-term bond, a long-term bond, for instance, will have a higher interest rate. According to the principle of the liquidity premium, bond investors favour short-dated assets that are highly liquid and have a short sales cycle over those that are longer-dated. According to another tenet of the theory, fluctuations in interest rates provide investors with compensation for greater pricing and default risks.
Given that,
1 + 1R₂= {(1 + 1R₁)(1 + E(2r₁) + L₂)}1/2
or, 1.12 = (1.8)(1.14 + L₂)1/2
or, (1.12)2/1.18 = 1.14 + L₂
or, 1.898 = 1.14 + L₂
or, L₂ = 0.498%
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Two teams need to raise $100 each for their end-of-the-year field trips. Team A wants to sell popcorn at the Spring Fling Carnival, and Team B wants to sell cotton candy. It costs $15 to rent a popcorn machine and it costs $25 to rent a cotton candy maker. The cost of additional supplies for the popcorn is $0.05 per bag. The additional cost for the cotton candy is $0.10 per stick. Team A will sell the bags of popcorn for $0.50 each. Team B will sell the cotton candy for $0.75 per stick.
At what point do both teams earn the same amount of profit? How do you know and
how much profit is earned?
Team A needs to sell 255 bags of popcorn to reach their goal of $100.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Team A will sell the bags of popcorn for $0.50 each.
Team B will sell the cotton candy for $0.75 per stick.
Let the number of bags of popcorn sold by Team A be "x".
So, the total cost for the popcorn machine rental and supplies is
= $15 + 0.05x.
To reach their goal of $100
$100 = 0.5x - ($15 + 0.05x)
$100 = 0.5x - $15 - 0.05x
$115 = 0.45x
x = $115 / 0.45
x = 255 bags of popcorn
Thus, Team A needs to sell 255 bags of popcorn.
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If a polynomial equation P(x)= 0 has 3+4i as a solution, what other solution must it have?
Answer: 3 - 4i
Step-by-step explanation:
For the given polynomial p(x) , if 3 +4i is a root then, 3 - 4i is also the root of p(x).
Consider the given polynomial equation p(x) = 0 It is given that the polynomial P(x) has one root 3 + 4i .
According to complex conjugate theorem, if V is a polynomial and x + iy is a root of given polynomial then its conjugate x - iy is also the root of the polynomial.
Thus, for the given polynomial p(x) if 3 +4i is a root then, 3 - 4i is also the root of p(x).
If a polynomial equation P(x) = 0 has (3 + 4i) as a solution, the other solution it must have (3 - 4i).
What is a polynomial?
Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Conjugate complex numbers are those that only differ in the imaginary part's sign.
a + bi and a - bi, where a and b are real numbers, are generally conjugate, as are, for instance, 2 + 3i and 2 - 3i, -5 - 7i and -5 + 7i, and so on.
Due to the fact that their output is always a genuine number.
The general case is -
= (a + bi)(a - bi)
= a² - abi + abi - (b²)(i²)
= a² + b²
The real example is -
= (2 + 3i)(2 - 3i)
= 2² + 3²
= 4 + 9
= 13
Complex roots for a polynomial equation P(x) = 0 with real coefficients are always represented as conjugate pairs.
So, the following equation must contain (3 - 4i) as a second root if the coefficients are real.
Therefore, P(x) has second root (3 - 4i).
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question content area top part 1 find the average rate of change of the function over the given intervals. f(x)=11x3 11; a) [6,8], b) [−1,1]
the average rate of change = (f(1) - f(-1))/(1-(-1)). Substituting in the values of f(-1) and f(1), we get (143 - (-143))/2
a) Average rate of change of the function over [6,8] = (f(8) - f(6))/(8-6) = (11(83) - 11(63))/2 = 882/2 = 441
b) Average rate of change of the function over [-1,1] = (f(1) - f(−1))/(1-(−1)) = (11(13) - 11(-13))/2 = 244/2 = 122
a) To find the average rate of change of the function f(x)=11x3 over the interval [6,8], first calculate the value of the function at x=6 and x=8. This gives us f(6) = 11(63) = 729 and f(8) = 11(83) = 1728. Then, the average rate of change = (f(8) - f(6))/(8-6). Substituting in the values of f(6) and f(8), we get (1728 - 729)/2 = 882/2 = 441.
b) To find the average rate of change of the function f(x)=11x3 over the interval [-1,1], first calculate the value of the function at x=-1 and x=1. This gives us f(-1) = 11(-13) = -143 and f(1) = 11(13) = 143. Then, the average rate of change = (f(1) - f(-1))/(1-(-1)). Substituting in the values of f(-1) and f(1), we get (143 - (-143))/2
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pls answer will buy you a reward or brainly premium after answer
The height of the tree is obtained as 27.7 m
What is the height of the light pole?We have to note that in the solution of the problem that the tangent of the angle is going to come in to play. The tangent if one of the trigonometric ratios and the other ratios are the cos and the sine.
We know that the tangent of the angle is;
tan 36 = opposite/adjacent
Opposite of the angle = x + 5
(Where x is the height of the tree)
Adjacent of the angle = 45 m
We would then have that;
tan 36 = x + 5/45
45 tan 36 = x + 5
x = (45 tan 36) - 5
x = 27.7 m
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Find the values of x and y that ensure each quadrilateral is a parallelogram.
Top of quadrilaterial is: 3x-4y
Bottom of quadrilaterial is: 18
Right of it is: 7
Left of it is: 5x+y
As the sides of the parallelogram are equal, the values of x and y that ensure each quadrilateral is a parallelogram are 2 and -3.
What is 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. A parallelogram is a sort of quadrilateral with opposing pairs of sides that are parallel and equal. A parallelogram is a form of quadrilateral in geometry. It has four sides and is two-dimensional. A parallelogram's most significant qualities are that its opposite sides are parallel and congruent, and its opposite angles are equal.
Here,
3x-4y=18
5x+y=7
multiply 2nd equation by 4 and solve,
3x-4y=18
20x+4y=28
23x=46
x=2
5*10+y=7
y=-3
The values of x and y that ensure each quadrilateral is a parallelogram is 2 and -3 as the side of parallelogram are equal.
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a sample of 137cs (half-life = 30.1 years) decays at a rate of 10^10 decays per second. how long (in years) will it take the decay rate to decrease to 10^7 decays per second?
It will take 19.44 years for the decay rate of 137Cs to decrease to 10^7 decays per second.
The decay rate of 137Cs is given by the formula:
A = A0 * e^(-λt)
Where A is the decay rate, A0 is the initial decay rate (10^10 decays per second), λ is the decay constant (ln(2)/30.1 years) and t is the time in years.
To calculate the time, t, required for the decay rate to decrease to 10^7 decays per second, we solve for t and substitute the given values into the equation:
[tex]t = (ln(A0/A))/λ\\t = (ln(10^10/10^7))/(ln(2)/30.1)\\t = 19.44 years[/tex]
Therefore, it will take 19.44 years for the decay rate of 137Cs to decrease to 10^7 decays per second.
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Real number system using the given theme and its description formulate three conditional statements not written in if then form and convert the three conditional statements into if - then form
Conditional statements using the theme of the real number system:
The product of two positive real numbers is positive.The sum of a positive real number and a negative real number is positive if the magnitude of the negative number is less than the positive number.The quotient of two real numbers is positive if the numerator is positive and the denominator is negative.Conditional statements in if-then form:
If x and y are positive real numbers, then xy is positive.If a is a positive real number and b is a negative real number with |b| < a, then a + b is positive.If x is a positive real number and y is a negative real number, then x/y is positive.Conditional statements are statements in logic and mathematics that assert the truth of a statement based on certain conditions. They are usually written in the form "if P, then Q", where P is a condition and Q is a conclusion that follows from P. Conditional statements are used to make decisions or test certain conditions in programming, mathematics, and everyday life.
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Four aerial photographers will need 6 batteries to operate their drone. Each found a different website that sells rechargeable batteries.
A first quadrant coordinate plane titled Website A is shown. The horizontal axis is labeled batteries. The vertical axis is labeled cost in dollars. A dotted line is graphed through the points zero comma forty, one comma forty-two, and continues through six comma fifty-two. An advertisement is titled Website B. Zapper. Rechargeable batteries, two dollars and thirty cents each. Battery charger, thirty-five dollars.
The table is titled Website C and has two columns and six rows. The first column is batteries. The second column is cost in dollars. One battery, thirty-nine dollars and ten cents. Two batteries, forty-one dollars and twenty cents. Three batteries, forty-three dollars and thirty cents. Five batteries, forty-seven dollars and fifty cents. Six batteries, forty-nine dollars and sixty cents. A caption reads, Website D: y equals three and five tenths x plus twenty-eight.
For each website, find the cost of 6 rechargeable batteries and a charger. Which website has the best price?
Answer: The cheapest option is Website B.
Step-by-step explanation:
The cost of 6 rechargeable batteries and a charger from each website is:
Website A: 6 batteries * $52/battery = $312
Website B: 6 batteries * $2.30/battery + $35/charger = $16.80 + $35 = $51.80
Website C: 6 batteries * $49.60/battery = $297.60
Website D: 6 batteries * $3.5 x + $28 = $63 + $28 = $91
The cheapest option is Website B with a cost of $51.80.
find the volume of the solid obtained by rotating the region bounded by the curves y=1−x2 and y=0 about the x-axis.
The volume of the region will be 4/3 cubic unit with the help of integration.
What is integration?
Integration is the calculation of an integral. Integrals in maths are used to find many useful quantities such as areas, volumes, displacement, etc. When we speak about integrals, it is related to usually definite integrals. The indefinite integrals are used for antiderivatives. Integration is one of the two major calculus topics in Mathematics, apart from differentiation(which measure the rate of change of any function with respect to its variables).
Definite Integral
An integral that contains the upper and lower limits then it is a definite integral. On a real line, x is restricted to lie. Riemann Integral is the other name of the Definite Integral.
A definite Integral is represented as:
∫f(x)dx from a to b.
Indefinite Integral
Indefinite integrals are defined without upper and lower limits. It is represented as:
∫f(x)dx = F(x) + C
Where C is any constant and the function f(x) is called the integrand.
Now,
For volume
Integrate y=1-x^2 for x=-1 to 1.
volume=1-x^2.dx
V=x-x^3/3
=1-1/3+1-1/3
=2-2/3
Hence,
Volume=4/3 cubic unit
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