In geometry, the distance formula is a formula used to calculate the distance between two points in a plane. It is derived from the Pythagorean Theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The distance formula is an equation used to calculate the distance between two points in a plane. It is derived from the Pythagorean Theorem which defines the relationship between the three sides of a right triangle. To calculate the distance between two points, (x1, y1) and (x2, y2), the formula is:
d = √((x2-x1)^2 + (y2-y1)^2).
This means that the distance between the two points is equal to the square root of the sum of the squares of the differences between the x-coordinates and the y-coordinates. To find the answer, you must first subtract the two x-coordinates (x2-x1) and then square the result. Then you must subtract the two y-coordinates (y2-y1) and square the result. Finally, add the two squared results together and take the square root of the sum to get the distance between the two points.
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the u.s. census is an example of a huge descriptive research project that uses the entire population as the sample. what are some of the limitations of generalizing census findings back to the entire population? select all that apply.
Therefore, the limitations census of entire population can be described in major points like it can be Since surveys rely on self-reporting, some misrepresentation or mistake is unavoidable and further more
What is census?A key component of the U.S. Federal Statistical System, the United States Census Bureau, or Bureau of the Census, is in charge of gathering information on the population and economy of the United States.
Here,
Therefore ,the limitations of generalizing census findings back to the entire population are:-
The homeless population is underrepresented in the findings even though every home is required to complete a census report. This is because they are frequently impossible to reach, interview, and count.
People who do not speak either English or Spanish as their first language and whose primary language is one of those two are more likely to be overlooked in the census.
Since surveys rely on self-reporting, some misrepresentation or mistake is unavoidable.
The population fluctuates constantly, so it is unlikely that the population on the day the census results are released would closely resemble the population as described in the census.
Those who entered the country illegally but intend to stay do not submit a report.
Therefore , there are 5 major limitation described above .
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It is due jan 30th pls help
Answer:
slope of original line; m = -3/-4
=3/4
slope of parallel line = 3/4
slope of perpendicular line = m1*m2=-1
=(3/4)*m2=-1
=-4/3
equation passes through point (4,-3) is : 3x + 4y = -12
suppose that the population mean waist size is 85 cm and that the population standard deviation is 15 cm. how likely is it that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm? (round your answers to four decimal places.)
A random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm is 0.0749.
In the given question,
18-year-old American males stated that the sample mean waist circumference was 86.3 cm.
The populations mean waist size is 85 cm.
The population standard deviation is 15 cm.
We have to find, a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm.
H(0): μ = 85
H(A): μ > 85
Sample mean(X) = 86.3
Standard deviation(σ) = 15
Standard error of mean =σ/√n
Standard error of mean (SE) = 15/√277
SE = 15/16.6433
SE = 0.9013
z = (X- μ)/SE
z=(86.3-85)/0.9013
z = 1.4424
P(z > 1.4424) = 0.0749
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The right question is;
The National Health Statistics Reports dated Oct. 22, 2008 stated that for a sample size of 277. 18-year-old American males stated that the sample mean waist circumference was 86.3 cm.
Suppose that the population mean waist size is 85 cm and that the population standard deviation is 15 cm. how likely is it that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm? (Round your answers to four decimal places.)
A bag contains 6 red tiles, 8 blue tiles, and 6 green tiles. A tile is drawn , the color recorded, and then the tile placed back in the bag before a tile is drawn again. If this procedure is done 30 times, how many red tiles would you expect to draw?
Responses
Answer:
18 tiles
Step-by-step explanation:
There are 20 tiles in total. Red is 6 of the 20, or 6/20. That is 3/10 or 30%
Each draw has a 30% chance of being red. 30% or 20 tiles is 1.8 tiles. Over 30 draws, that would mean a total of 600 tiles are drawn, The overall chance of red is still 30%, so after 30 draws, the number of red tiles would be predicted to be 30% of 600:
(0.30)*(600) = 18 tiles will be red.
please help me ( I will give brainlist for correct answer)
Using the concept of unit price, we see that;
Unit price of Brand A = $0.3654
Unit price of Brand B = $0.3785
The better buy is Brand A
How to find the unit price?A unit price is defined as the price for one item or measurement, such as a pound, a kilogram, or a pint, which can then be used to compare the same type of goods sold in differing weights and amounts.
Now, we are told that brand A has a pack of 24 pencils for $8.77. Thus;
Unit price of Brand A = 8.77/24 = $0.3654
We are told that brand B has a pack of 26 pencils for $9.84. Thus;
Unit price of Brand B= 9.84/26 = $0.3785
Thus;
Unit price of Brand A = $0.3654
Unit price of Brand B = $0.3785
Thus, brand A has the cheaper unit price and is thus the better buy.
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suppose that from previous evidence, anthropologists had believed that for each 1 mm increase in chord length, cranial capacity would be expected to increase by 20 cm3. do the data given here strongly contradict prior belief? use a 0.05 level of significance.
The data does contradict with the prior evidence
To determine whether the data presented here are significantly inconsistent with previous assumptions, a statistical test was performed to verify that the observed relationship between tendon length and cranial volume was significantly greater than the expected relationship. You have to decide if they are different.
To do this, fit a line to the data using linear regression analysis and test the hypothesis that the slope of the line is equal to 20 cm3/mm. If the p-value for this hypothesis test is less than 0.05, you can conclude that the data are inconsistent with previous assumptions at the 0.05 significance level.
It is crucial to realize that this analysis assumes that the relationship between tendon length and cranial volume is linear.
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8 - 4y + (-2y) + 5.3
Answer:
-6y + 13.3 = 0
y = 13.3/6
Step-by-step explanation:
This equation don't need any step-by-step explanation :). Hope it helps!
Simplify the expression. negative 17 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 4 squared minus 4 and 7 tenths −4.26 −12.98 13.41 259.26
The simplified expression of the statement is -41.66
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
negative 17 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 4 squared minus 4 and 7 tenths
Rewrite properly
So, we have
(-17 - 3.7 + 9.15)/5 * 4² - 4.7
Evaluate the sum and the difference in the expression
So, we have
-11.55/5 * 4² - 4.7
Evaluate the exponent and the quotient
-2.31 * 16 - 4.7
So, we have
-36.96 - 4.7
Evaluate
-41.66
Hence, the solution is -41.66
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evaluate the double integral y^2/(x^2 y^2) where is the region that lies between the circles and by changing to polar coordinates.
The value of the double integral ∫∫[tex]\frac{y^{2} }{x^{2} +y^{2} }[/tex] dA is 131.95.
We know that in polar coordinates, the circle become r = 4 and r = 16. These are the limits on the radius. Clearly the limits on the angle are
0 ≤ θ ≤ 2π.
Therefore we get,
∫∫ [tex]\frac{y^{2} }{x^{2} + y^{2} }[/tex] dA = ∫ ∫ r²sin²θ / r² dr dθ
= ∫ sin²θ dθ ∫ r dr
= [ [tex]\frac{1}{2}[/tex]θ - [tex]\frac{1}{4}[/tex]sin(2θ)]₀²ⁿ[ [tex]\frac{1}{2}[/tex] r²]₄¹⁰
= [tex]\frac{1}{4}[/tex] (2π)(10² - 4²)
= 42π
∫∫ [tex]\frac{y^{2} }{x^{2} + y^{2} }[/tex] dA = 131.95.
What is Polar coordinates?
When each point on a plane of a two-dimensional coordinate system is decided by a distance from a reference point and an angle is taken from a reference direction, it is known as the polar coordinate system.
Polar coordinates are useful in calculating the equations of motion from a lot of mechanical systems. Polar coordinate means the magnitude and direction of a vector.
Polar coordinate system of locating points in a plane with reference to a fixed point O and a ray from the origin usually chosen to be the positive x-axis.
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Substitution Method: x+y (1)
2x-y=2 (2)
Find x and y.
Answer:
x = 8/3
y = 10/3
Step-by-step explanation:
We add (1) and (2) to get 3x = 8. This means that x = 8/3. We substitute it back into (1) to get 8/3 + y = 6 which shows that y = 10/3
Can the sides 30, 40, 50 be a right triangle?
Answer:
yes
Step-by-step explanation:
following the rule of the Pythagorean triple the answer is yes
Actually a 30 , 40 , 50 triangle is just a scaled up 3 , 4 , 5 triangle, which is a well known right angled triangle
Graph the image of the given triangle after the transformation with the rule (x, y)→(−x, y).
Select the "Polygon" button from the tool bar to plot your triangle. You may use the "Move" button to move the triangle after it is created.
Keyboard Instructions
Initial graph state
The horizontal axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
The vertical axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
Polygon with coordinates: (3, 4), (4, 7), (8, 2), (3, 4).
The given triangle is been reflected according to rule (x, y)→(−x, y) and the new coordinates are (-8, 2), (-3, 4), (-2, 7).
What is reflection?A reflection is a type of transformation that involves flipping a shape, known as the preimage, across a line, known as the line of reflection, to produce a new shape (called the image).
We can picture what would happen if you turned the form across the line to graph a reflection.
So, we have a triangle with coordinates:
(8, 2), (3, 4), (2, 7)
Now, we will reflect it according to the rule:
(x, y)→(−x, y)
Then, the coordinates will be:
(-8, 2), (-3, 4), (-2, 7)
(Refer to the graph attached below)
Therefore, the given triangle is been reflected according to rule (x, y)→(−x, y) and the new coordinates are (-8, 2), (-3, 4), (-2, 7).
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What is the median
of 98, 99, 100, 90,
98, 100?
The number of weaving errors in a twenty foot by ten foot roll of carpet has a mean of 0.8. What is the probability of observing more than 2 errors in the carpet
Answer:
0.0474
Step-by-step explanation:
mean = \mu = 0.8
Using the Poisson probability formula,
P(X = x) = (e-\mu * \mux ) / x!
P(X > 2) = 1 - P(x \le 2)
= 1 - P(x = 0) - P(x = 1) - P(x = 2)
= 1 - (e^-0.8 * 0.80 ) / 0! - (e^-0.8 * 0.8^1 ) / 1! - (e^-0.8 * 0.8^2 ) / 2!
= 0.0474
So, the answer is 0.0474
How do you simplify 10^3(10)^4?
The value after simplifying the number 10^3(10)^4 is 10⁷.
The simplification of given number can be done through the rule of exponent -
[tex] {a}^{m} [/tex] × [tex] {a}^{n} [/tex] = [tex] {a}^{m+n} [/tex], where m and n are the powers of a.
Now, keeping the values in formula -
Value = [tex] {10}^{3} [/tex] × [tex] {10}^{4} [/tex]
Based on the rule, the simplified for these powers will be
Value = [tex] {10}^{3+4} [/tex]
Performing addition of powers on Right Hand Side of the equation
Value = [tex] {10}^{7} [/tex]
Alternatively, the numbers can be expanded and multiplied. Further write the result in scientific notation as above. However, it will a long method which is not practical for very large numbers.
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PLEASE I REALLY NEED HELP, MY MATH CLASS IS DUE TOMORROW!!!!! ASAP!!!!!!
Answer:
13.3 ft
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a square}\\\\$A=s^2$\\\\where:\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\\\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle}\\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
The surface area of a square-based pyramid is made up of:
1 square (the base)4 congruent triangles (the sides)Given:
Total SA = 158 feet²s = 5 feeth = l feetFind the area of the square base and the area of one of the triangles by substituting the given values into the formulas:
[tex]\textsf{Area of the square base} = 5^2 = 25\; \sf ft^2[/tex]
[tex]\textsf{Area of one of the side triangles} = \dfrac{1}{2} \cdot 5 \cdot l= 2.5l \; \sf ft^2[/tex]
Substitute these values along with the given total surface area into the formula and solve for l:
[tex]\begin{aligned}\textsf{Total Surface Area}&=\sf square+4\;triangles\\\implies 158&=25+4\left(2.5l)\\158&=25+10l\\133&=10l\\l&=\dfrac{133}{10}\\l&=13.3\; \sf ft\end{aligned}[/tex]
Therefore, the missing length is 13.3 feet.
which type of analysis first equates groups on the basis of overall score and then evaluates differences in performance between the groups on particular items in an attempt to identify sources of bias?
The type of analysis used to identify the source of the bias is known as Differential Item Functioning Analysis.
Analysis
In statistics, analysis is to break a topic or concept down into its parts in order to inspect and understand it, and to restructure those parts in a way that makes sense to you.
Given,
Here we need to find the type of analysis used to identify sources of bias.
While we looking into the given question, we have used by ETS.
And it identifies items that are specifically biased against any ethnic, racial or gender group.
And we also know that the first analysis equates groups on the basis of overall scores.
By using these groups it evaluates differences in performance between sub groups on particular items.
And the Items that differ significantly between the groups are thrown out.
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Find the slope of every line that is perpendicular to this one.
Answer:
-4/7
Step-by-step explanation:
The slope of the given line is [tex]\frac{3-(-4)}{4-0}=\frac{7}{4}[/tex].
Perpendicular lines have slopes that are negative reciprocals of each other, so the answer is [tex]-4/7[/tex].
The slope of every line perpendicular to the line passing through (4, -3) and (0, -4) is -4.
We have,
Let's first find the slope of the given line passing through (4, -3) and
(0, -4):
slope = (change in y) / (change in x)
= (-4 - (-3)) / (0 - 4)
= (-4 + 3) / (-4)
= -1 / (-4)
= 1/4
The slope of the given line is 1/4.
Now, to find the slope of a line perpendicular to this line, we take the negative reciprocal of the slope:
[tex]slope_{perpendicular} = -1 / slope[/tex]
= -1 / (1/4)
= -4
Therefore,
The slope of every line perpendicular to the line passing through (4, -3) and (0, -4) is -4.
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In the United States, the common paper size is called letter size and measures 8. 5 by 11 inches. Let
V(x)= (8. 5-2x)(11-2x) (x) be the volume in cubic inches of a box made from a letter size paper
by cutting out squares of side length x in inches from each corner and then folding up the sides.
What is a reasonable domain for V in this context? Explain or show your reasoning.
PLs help
Answer:
0 < x < 4.5
Step-by-step explanation:
You want the reasonable domain of V(x) = (8.5 -2x)(11 -2x).
Reasonable domainThe equation describes volume (V) and cut length (x), so both need to be positive. Volume will be positive when ...
8.5 -2x > 0
4.25 > x
The reasonable domain is 0 < x < 4.5.
the coefficients of dummy variables in multiple regression models must always be positive. group of answer choices true false
The given statement "the coefficients of dummy variables in multiple regression models must always be positive." is True.
Regression model:
In statistics, regression model means a statistical technique that relates a dependent variable to one or more independent variables.
Given,
Here we have the statement the coefficients of dummy variables in multiple regression models must always be positive.
Now, we have to find whether the given statement is true or not.
In order to find the statement creditability, we must know the definition of the terms coefficient and dummy variables.
Dummy variable refers the variable that takes values of 0 and 1, where the values indicate the presence or absence of something
Where as the coefficient means a number or symbol by which another number or symbol is multiplied.
Based on this definition we have found that the given statement is true.
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Given the figure below, find the values of x and z. (5x − 1) (7x+1)=
please help!!!
will give brainlest answer
Answer:
[tex]x = 15 $^{\circ}$ ; z = 74$^{\circ}$[/tex]
Step-by-step explanation:
First, combine all like terms. Like terms are terms that have the same amount of the same variables:
[tex]m$\angle$(5x - 1) + m$\angle$(7x + 1) = 180$^{\circ}$\\\\[/tex]
[tex]m$\angle$(5x + 7x) + (1 - 1) = 180$^{\circ}$[/tex]
[tex]12x + 0 = 180$^{\circ}$[/tex]
Next, isolate the variable, x. Divide 12 from both sides of the equation:
[tex]12x = 180\\\frac{12x}{12} = \frac{180}{12}\\ x = \frac{180}{12}\\ x = 15 $^{\circ}$[/tex]
Next, plug in 15 for x in one of the given expressions. If you choose the right one (7x + 1), you will solve using the straight angle theorem. If you choose the bottom one (5x - 1), you will solve using the vertical angle postulate. Both will give you the same answer for x.
Firstly, if you want to solve using the straight angle theorem. The straight angle theorem is defined that all straight angles are 180 degrees. Solve using the straight angle theorem. Set both angle measurements equal to 180°:
[tex](z) + (7x + 1) = 180[/tex]
Plug in 15 for x and solve for the parenthesis:
[tex]z + 7(15) + 1 = 180 $^{\circ}$\\[/tex]
First, multiply 7 with 15:
[tex]z + (7 * 15) + 1 = 180 $^{\circ}$\\z +105 + 1 = 180$^{\circ}$\\[/tex]
Next, simplify by combining like terms:
[tex]z + (105 + 1) = 180 $^{\circ}$\\z + 106 = 180$^{\circ}$[/tex]
Next, isolate the variable, z, by subtracting 106 from both sides of the equation:
[tex]z + 106 = 180 $^{\circ}$\\z + 106 (-106) = 180 (-106)\\z = 180 - 106\\z = 74$^{\circ}$[/tex]
Your answer:
[tex]x = 15 $^{\circ}$ ; z = 74$^{\circ}$[/tex]
~
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“Let me give so much time to the improvement of myself that I shall have no time to criticize others.” what do you think about this one small paragraph please
Answer: I believe that this statement is very true. People shouldn’t be pushing others down when instead they could be pushing themselves up, improving them to be better.
Step-by-step explanation:
Answer:
THAT VERY RIGHT INSTEAD OF PEOPLE HELPING THEMSELVES THEY SPEND THEIR TIME CRITICIZING OTHERS KUDO TO U
What are biconditional statements math?
A biconditional statement is a statement that may be stated in the form “p if and only if q.” This implies “if p, then q” and “if q, then p.”
What are biconditional statements?
A biconditional statement is one that can be expressed as "p if and only if q," which implies "if p, then q" and "if q, then p."
For example, "If the polygon is a square, then it has four equal sides and four right angles," and "If a polygon has four equal sides and four right angles, then it is a square," are two examples of biconditional statements.
A biconditional statement is a combination of a conditional statement and its converse written in the if and only if form.
Two line segments are congruent if and only if they are of the same length.
Therefore, the biconditional statement is a statement that may be stated in the form “p if and only if q.” This implies “if p, then q” and “if q, then p.”
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n a conference, 75% of the attendees have been to germany, and 15% of the attendees have been to both england and germany. what is the probability that a randomly selected attendee has been to england, if it is known that they have been to germany? assume event e: the attendee has been to england; event g: the attendee has been to germany.
Simple probability is the calculation of an outcome or the chance of an event ever happening.
What is a probability in math?In common usage, the word "probability" is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%. The analysis of events governed by probability is called statistics.It is based on the possible chances of something to happen. The theoretical probability is mainly based on the reasoning behind probability. For example, if a coin is tossed, the theoretical probability of getting a head will be ½.Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes. Probability and odds are different concepts. Odds are the probability that something happens divided by the probability that it doesn't happen.The formula for probability states that the possibility of an event happening, or P(E), equals the ratio of the number of favorable outcomes to the number of total outcomes. Mathematically, it looks like this: P(E) = favorable outcomes/total outcomes.18.65% probability that the person is from Washington
Two events, A and B.
[tex]P(B/A)=\frac{P(B)*P(A/B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Arrived by train.
Event B: From Washington.
15% are from Washington
This means that [tex]P(B)=0.15[/tex]
12% of the attendees from Washington came to the conference by train.
This means that [tex]P(A/B)=0.12[/tex]
Probability of arriving by train:
6% of 60%(from California), 17% of 25%(from Oregon) or 12% of 15%(from Washington). So
[tex]P(A)=0.06*0.6+0.17*0.25+0.12*0.15=0.0965[/tex]
If an attendee is selected at random and found to have arrived by train,
[tex]P(B/A)=\frac{0.15+0.12}{0.0965} =0.1865[/tex]
=0.1865
18.65% probability that the person is from Washington
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a dealer sold a total of 60 of the three appliances listed in the table above for a total of $4,200. if the dealer sold twice as many food processors as mixers, what was the ratio of the number of blenders sold to the number of food processors sold?
On solving the provided question, we got to know that, Blenders sold as a percentage of food processors sold is 30/20, or 3/2.
What is equation?Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.
Compared to mixers, the dealer sold twice as many food processors.
Let M be the quantity of mixers sold.
Therefore, 2M is the quantity of food processors sold.
A total of 60 of the three appliances were sold by the dealer.
M + 2M = 3M
Thus, 3M is a representation of the whole sales of mixers and food processors.
60 appliances were purchased in total, thus 60 - 3M equals the quantity of blenders purchased.
Everything was sold by the merchant for a total of $4,200.
We get: (30)(M) + (120)(2M) + (50)(60 - 3M) = 4,200
30M + 240M + 3000 - 150M = 4200
130M + 3000 = 4200
120M = 1200
M = 10
The retailer so sold 10 mixers.
This indicates that the vendor sold 20 food processors and 30 food processors.
Blenders sold as a percentage of food processors sold is 30/20, or 3/2.
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For a Party, Jessica needs a sizable amount of money to buy balloons and party poppers. She goes to the store to buy Balloons for $0.20 for each balloon and party popper for $0.50 each. The total Price for the haul is $20. In total Jessica purchased 52 balloons and party poppers. Let x represent the number of balloons and y represents the number of party poppers, how many part supplies did Jessica buy?
I need elimination method and Substitution method
Someone please help
The number of party popper she bought is 32 and the number of balloons she bought is 18.
How many part supplies did she buy?The first step is to form a system of equations using the information provided in the question.
0.20x + 0.50y = $20 equation 1
x + y = 52 equation 2
The solution using the elimination method :
Multiply equation 2 by 0.20
0.20x + 0.20y = 10.40 equation 3
Subtract equation 3 from equation 2 :
0.30y = 9.60
Divide both sides of the equation by 0.30
y = 9.60 / 0.30
y = 32
The solution using the substitution method:
Make x the subject of the formula in equation 2
x = 52 - y equation 3
Substitute for x in equation 1 :
0.20(52 - y) + 0.50y = $20
10.40 - 0.20y + 0.50y = $20
Combine similar terms together
0.50y - 0.20y = $20 - $10.40
0.30y = $9.60
y = 9.60 / 0.30
y = 32
x = 50 - 32
x = 18
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solve the equation 5x+11=4x+18
Find the complex numbers
The complex numbers are
a. 11 - 3i
b. 2 + i
c. 5 - 6i
What is a complex number?A complex number is a number in the complex plane. It is written in the form r = a + bi where a and b are real numbers and i = √(-1). Also, a is the real part and ib is the complex part of the complex number
How to write the complex numbers?a. Given that the complex number is denoted by r = a + ib where
a = real part and ib = imaginary partSince we have for the given complex number
real part = 11 and complex part = -3iSo, r = real part + imaginary part = 11 + (-3i)
= 11 - 3i
So, the complex number is 11 - 3i
b. Given that the complex number is denoted by r = a + ib where
a = real part and ib = imaginary partSince we have for the given complex number
real part = 2 and imaginary part = iSo, r = real part + imaginary part = 2 + i
= 2 + i
So, the complex number is 2 + i
c. Given that the complex number is denoted by r = a + ib where
a = real part and ib = complex partSince we have for the given complex number
real part = 5 and imaginary part = -6√(-1)So, r = real part + imaginary part = 5 + [-6√(-1)]
= 5 - 6√(-1)
= 5 - 6i (since i = √(-1))
So, the complex number is 5 - 6i
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from a set of 7 math books, 12 science books, and 5 literature books, in how many ways can a student select 2 from each set?
The no. of ways or Probability can a student select 2 from each set of books = 13860
What is Probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
By multiplying the number of possibilities there are to choose books from each kind, separately, one can determine the maximum number of ways a student can choose two books from each subject.
Rule for Multiplication:
If an event A can be performed in m different ways and another event B in n different ways, then the two events together can be performed in (mn) different ways.
A combination problem is created by the various ways that math, science, and literature books might be chosen.
As a result, the total number of choices can be calculated as follows: (Number of math books chosen) x (Number of scientific books chosen) x (Number of literature books selection)
= C ( 7,2) * (12,2) * (5,2)
= C (7*6/2!) * (12*11/2!) * (5*4/2!)
= 21 * 66* 10
= 13860
The no. of ways or Probability can a student select 2 from each set of books = 13860
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Find the points on the graph of the function that are closest to the given point.
f(x) = x2, (0,9)
(x,y) smaller value
(x,y) larger value
The locations on the function's graph that are most near the specified point f(x) = x2, (0,9) are approximately 3 units to the right and left, respectively, or (sqr8.5, 8.5).
The initial estimate would be rough to the right and left by around 3 units, or (sqr8.5, 8.5), rounded to the nearest decimal place.
Visually, it is most likely just below y=9 and just below x=3. Additionally, roughly (-3, 9) slightly lower than 3 and 9
Connect the parabola's nearest point to the point at (0,9). Where the two intersect, its slope is the negative inverse of the parabola's slope. The derivative's slope is 2x for the equation f(x) = x2. -1/2x is its inverse negative. The line from (0,9) to the parabola's nearest point has a slope that is perpendicular to the tangent to the parabola at that location.
Get the equation of the line joining (0,9) and the nearest point (x,y) on the parabola using the point-slope formula: 8.5 or y=-1/2 + 9 = (-1/2x)(x)
The closest point's y coordinate is that. The square root of 8.5, including both positive and negative square roots, is the closest point's x coordinate (-sqr8.5, 8.5)
Sqr8.5 =[tex]\sqrt{8.5}[/tex], or approximately 2.91 or -2.91
The process entails finding the equation for the line connecting (0,9) with the parabola's nearest point and then setting the two equations equal. Set the line equation to y=(-1/2x), the parabola equation. The parabola equation is y=[tex]x^{2}[/tex] and the line equation is x + 9.
Equalize them, then find x using the square of the result. The closest point is at x,y. There are two places that are equally far from (0,9), both of which are as close as they can be to 3 at (3,9). (0,9). At the parabola point, that line is not perpendicular to the tangent line (3,9). The line must be perpendicular to the tangent line, which is the slope of the parabola, in order to be closest.
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