Answer:
Step-by-step explanation:
I don’t understand this app how do I use it
A certain disease has an incidence rate of 0.4%. If the false negative rate is 8% and the false positive rate is 2%, compute the probability that a person who tests positive actually has the disease
Answer:
To compute the probability that a person who tests positive actually has the disease, we need to use Bayes' theorem:
P(D|P) = P(P|D) * P(D) / P(P)
where:
P(D|P) is the probability of having the disease given a positive test result
P(P|D) is the probability of testing positive given that the person has the disease (also known as sensitivity), which is 1 - false negative rate = 0.92 in this case
P(D) is the incidence rate of the disease, which is 0.4% = 0.004
P(P) is the probability of testing positive, which can be computed using the false positive rate as 1 - specificity = 1 - 0.98 = 0.02
Plugging in the values, we get:
P(D|P) = 0.92 * 0.004 / 0.02 = 0.184
Therefore, the probability that a person who tests positive actually has the disease is 0.184, or about 18.4%.
Find the area of triangle ABC to nearest tenth.
12. A = 20, c = 4 cm, b = 7 cm
13. C = 55, a = 10 m, b = 15 m
14. B = 42, a = 3 ft, c = 9 ft.
The areas of triangles ABC are
12. The area is 4.8 cm²
13. The area is 61.4 m²
14. The area is 9.0 ft²
What is the area of a triangle?The area of a triangle is the region occupied by the triangle.
12. Area of triangle ABC
Given that
A = 20, c = 4 cm, b = 7 cmArea of triangle ABC is A = 1/2bcsinA
= 1/2 × 7 cm × 4 cm × sin20°
= 7 cm × 2 cm × sin20°
= 14 cm² × sin20°
= 14 cm² × 0.3420
= 4.788 cm²
≅ 4.8 cm²
The area is 4.8 cm²
13. Area of triangle ABC
Given that
C = 55, a = 10 m, b = 15 mArea of triangle ABC is A = 1/2absinC
= 1/2 × 10 m × 15 m × sin55°
= 5 m × 15 m × sin55°
= 75 cm² × sin55°
= 75 cm² × 0.8192
= 61.436 cm²
≅ 61.4 cm²
The area is 61.4 cm²
14. Area of triangle ABC
Given that
B = 42, a = 3 ft, c = 9 ft mArea of triangle ABC is A = 1/2acsinB
= 1/2 × 3 ft × 9 ft × sin42°
= 1/2 × 27 ft² × sin42°
= 13.5 ft² × sin42°
= 13.5 ft² × 0.6691
= 9.033 ft²
≅ 9.0 ft²
The area is 9.0 ft²
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Please help me. it’s timed!!!! Use the drawing tools to form the correct answer on the graph.
Plot function h on the graph.
J-4,
lz + 5,
h (x)
=
x < -3
X -3
Answer:
The function h(x) is defined as:
h(x) = { x + 4, if x < -3
{ 2x + 5, if x >= -3
To plot this function on the graph, you would plot the points (-4, 0) and (-3, -1) for the first part of the function, and then plot the line with slope 2 passing through the point (-3, 2) for the second part of the function.
Step-by-step explanation:
Using the graph determine the coordinates of the xintercepts
Answer:
(-3,0), (1,0)
Step-by-step explanation:
The x-intercept is when the y = 0
In the graph, we see the line cross through the x-axis located at (-3,0), (1,0)
So, the x-intercepts are located at (-3,0) and (1,0)
Answer:
x intercepts are 1 and -3
Step-by-step explanation:
X intercepts are obtained by looking at a point where the parabola touches the x axis
Which of these statements is true? A.The radius of a circle is about three times its diameter.B. The diameter of a circle is equal to the radius.C. The diameter of a circle is two times the radius. D. The radius and the diameter are not related.
C. The diameter of a circle is two times the radius.
223.6/40 show your work
Answer:
5.590
Step-by-step explanation:
Answer: Using the linear model, a puppy grows _____ pounds each month. Fill in the blank.
Using the linear model, a puppy grows 6 pounds each month.
What is the point-slope form?In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (2, 20), an equation of this line in slope-intercept form can be calculated by using the point-slope form:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 20 = (80 - 20)/(12 - 2)(x - 2)
y = 60/10(x - 2) + 20
y = 6x - 12 + 20
y = 6x + 8
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Calculate the height of a lean-to roof that has a slanted height of 325 cm and an angle of elevation of 22 degrees. Round your answer to the nearest cm. Include a diagram.
The height of a lean-to roof that has a slanted height of 325 cm and an angle of elevation of 22 degrees is 131.30 cm.
What connection exists in trigonometry between the angle of elevation and the tangent function?The tangent function in trigonometry describes the relationship between an angle's adjacent and opposing sides. The angle of elevation is the angle formed by a horizontal line and a line leading from the observer's eye to a higher-than-horizontal object. When calculating an object's height with the tangent function, we utilize the angle of elevation and the length of the neighbouring side (in this example, the slanted height) to get the length of the opposing side (the height). As a result, the height of the object increases with increasing tangent value and elevation angle.
Given that, a roof has slanted height of 325 cm and an angle of elevation of 22 degrees.
Using the trigonometric functions:
tan(22) = h / 325
h = 325 * tan(22)
h ≈ 131.30 cm
Hence, the height of a lean-to roof that has a slanted height of 325 cm and an angle of elevation of 22 degrees is 131.30 cm.
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I need the steps to solve this question any help
The solution is:
Net income = $31,130
Total Assets = Owner's Equity and Liabilities = $104,230
What is income?Income can be stated as the consumption and saving opportunity gained by an entity within a specified timeframe, which is normally expressed in monetary terms. Income is that which means difficult to define conceptually and the definition may be different across fields.
here, we have,
The Income Statement of Profit or Loss and the Statement of Financial Position can be prepared as follows:
Sugar Almonds Ltd
Income Statement of Profit or Loss
For the Year Ended 31st December 2020
Particulars $ $
Sales Revenue 93,700
Cost of sales:
Opening inventory 12,000
Purchases 49,000
Closing inventory - income statement (24,350)
Cost of sales (36,650)
Gross profit 57,050
Operating expenses:
Administrative Expenses (850)
Rent paid (2,000)
Telephone (900)
Wages (21,650)
Travel expenses (330)
Total operating expenses (25,730)
Interest income (expense):
Interest paid (190)
Net income 31,130
Sugar Almonds Ltd
The Statement of Financial Position
As at 31st December 2020
Particulars $ $
Fixed Assets
Premises at cost 70,000
Vehicles at cost 5,800
Total Fixed Assets 75,800
Current Assets
Cash 630
Bank 2,100
Closing inventory - Statmt of fin positn 24,350
Trade Receivables 1,350
Total Current Assets 28,430
Total Assets 104,230
Owner's Equity
Capital 72,000
Drawings (6,450)
Net income 31,130
Total Owner's Equity 96,680
Current Liabilities
Trade Payables 6,400
VAT 1,150
Total Current Liabilities 7,550
Owner's Equity and Liabilities 104,230
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write cubed root 21 in the form 21k
The general format of the exponential expression is given as follows:
[tex]a^{\frac{n}{m}}[/tex]
In which:
The base is given by a.The exponent is given by n.The radicand is given by m.The radical form is given as follows:
[tex]\sqrt[m]{a^n}[/tex]
Meaning that the equivalence relation is given as follows:
[tex]\sqrt[m]{a^n} = a^{\frac{n}{m}}[/tex]
That is:
The radicand is the numerator of the fraction in the exponent.The radical is the denominator of the fraction in the exponent.Hence the relation for the cube root of 21 is given as follows:
[tex]\sqrt[3]{21} = 21^{\frac{1}{3}}[/tex]
(applying the conversion of the fractional exponent to a radical expression).
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The box plot displays the number of push-ups completed by 9 students in a PE class.
A box plot uses a number line from 9 to 45 with tick marks every 2 units. The box extends from 17.5 to 40.5 on the number line. A line in the box is at 30. The lines outside the box end at 10 and 42. The graph is titled Push-Ups In PE and the line is labeled Number of Push-Ups.
Which of the following represents the value of the lower quartile of the data?
42
40.5
17.5
10
Given that 17.5 is the bottom end of the box, the lower quartile's value equation (Q1) must fall between 17.5 and 30. Hence, the appropriate response is 17.5
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
25% of the data fall inside the lower quartile (Q1), which is represented by that number. Q1 is situated near the bottom of the box in the box plot.
According to the description, the box's boundary is at 30, and its size ranges from 17.5 to 40.5 on the number line. As a result, the median value of the middle 50% of the data is 30, with a range of 17.5 to 40.5.
There are some data points outside the middle 50% since the lines outside the box finish at 10 and 42.
Given that 17.5 is the bottom end of the box, the lower quartile's value (Q1) must fall between 17.5 and 30. Hence, the appropriate response is
17.5
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PLEASE HELP
Here is a graph of the function f defined by f(x) = a*b^x select all possible values of b
A. 0
B.1/10
C.1/2
D. 9/10
E. 1
F.1.3
G. 18/5
The possible values of b are 1/10, 1/2, 9/12, here we have to learn graph of a function. Diagram of question given below.
What is Graph of a Function?The graph of a function f in mathematics is the collection of ordered pairs where display style f(x)=y. These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the typical situation when x and f(x) are real integers.
Subset, If every element of a set P is also an element of a set Q, then set Q is a superset of set P and set A is a subset of set Q. P and Q might be equal; if not, then P is a legitimate subset of Q.
Here, when [tex]b=0,\ f(x) = a*0^{x} = 0[/tex]
[tex]b=1,\ f(x)=a*1^{x} = a[/tex]
[tex]b > 1,\ f(x)=a*b^{x}[/tex]
[tex]a < b < 1,\ f(x) = a*b^{x}[/tex]
[tex]So, b\in(0,1)=b=\frac{1}{10} ,\frac{1}{2} ,\frac{9}{10}.[/tex]
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ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST FOR ANSWERS
For the given sequence we have.
g(4) = 72g(n) = 2*g(n - 1)g(n) = 4*g(n - 2)g(n) = 8*g(n - 3)g(24)/g(21) = 8.How to describe the sequence?We have a sequence where each term is the double of the previous one.
So if we start with 9, we have:
g(1) = 9
g(2) = 2*9 = 18
g(3) = 2*18 = 36
g(4) = 2*36 = 72
That is the value of g(4).
Now the recursive formulas are trivial:
g(n) = 2*g(n - 1)
g(n) = 4*g(n - 2)
g(n) = 8*g(n - 3)
And finally, the quotient, we can write:
g(24)/g(21) as:
g(n)/g(n - 3)
And by the last recursive formula,we know that:
g(n) = 8*g(n - 3)
g(n)/g(n -3) = 8
So that is the answer there.
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These are two triangles, AB = 50, B = 40 degrees, and find the value of CE
The value of the length CE is 19.3 units
How to determine the length CEFrom the question, we have the following parameters that can be used in our computation:
The right triangle
Start by calculating the length AE using the following sine ratio
sin(B) = AE/AB
Substitute the known values in the above equation, so, we have the following representation
sin(40) = AE/50
So, we have
AE = 50 * sin(40)
Evaluate
AE = 32.14
From the figure, we can see that
Triangle CDE is 3/5 of triangle ABE
Using the above as a guide, we have the following:
CE = 3/5 * AE
So, we have
CE = 3/5 * 32.14
Evaluate
CE = 19.284
Approximate
CE = 19.3
Hence, the length is 19.3 units
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For a scientific experiment, a physicist must make sure that the temperature of a metal does not get colder than −51°C or the metal will not be usable. The physicist changes the metal's temperature at a steady rate of −3°C per hour.
We conclude that the physicists can change the temperature in 17 hours.
What is temperature?Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied on various reference points and thermometric substances for definition.
We know that a physicist must make sure that the temperature of a metal at 0° C gets no colder than -51° C.
The physicist changes the metal's temperature at a steady rate of -3° C per hour.
We calculate how long can the physicists change the temperature.
We get:
-51-0 / -3-0
= 17
Hence, We conclude that the physicists can change the temperature in 17 hours.
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HELPPP PLS thank you pls
The piecewise function graphed is given as follows:
y = x² + 4, x < 2.y = -x + 4, x ≥ 2.How to define the piecewise function?A piece-wise function is a function that has different definitions, based on the input x of the function.
For this problem, the intervals are given as follows:
x < 2.x ≥ 2.For the first interval, the interval is open due to the open circle, and the quadratic function is a translation up 4 units of y = x², hence^:
y = x² + 4, x < 2.
For the second interval, which is the closed interval, we have a decaying line with slope of -1 and x-intercept of 4, hence:
y = -x + b
0 = -4 + b
b = 4.
Hence:
y = -x + 4, x ≥ 2.
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Graph the following: f(x)= 1/2 x + 5 and (x)= 1/x
How many solutions are present?
a. 2
b. 3
c. 1
d. 0
Answer:
Below
Step-by-step explanation:
Where the graphs cross or touch each other is a solution.....see graph below ....how many solutions do YOU see ?
Can someone help I lost my brain cells xd 7 only
Answer: 81.75
Make 7 an improper fraction:
[tex]\frac{109}{12}[/tex] = [tex]\frac{k}{9}[/tex]
(9)(109) = 12k
981 = 12k
k = 81.75
Assume that during a three-hour period spent
outside, a person recorded the temperature and their
water consumption. The experiment was conducted
on 7 randomly selected days during the summer. The
data is shown in the table. Plot the data on a scatter
plot then add a line that is closest to all of the data
points.
Answer:
Plot the temperature on the x-axis and the water consumption on the y-axis.
For each day, plot a point on the scatter plot with the temperature and water consumption values.
Use a regression tool or calculate the slope and intercept of the line of best fit manually.
Draw a straight line through the data points that represents the trend in the data.
The equation for the line of best fit can be used to make predictions about water consumption given a certain temperature.
Step-by-step explanation:
The scatter plot shows that there is a positive relationship between temperature and water consumption.
Here is the scatter plot of the data:
Temperature (°F) | Water Consumption (fl. oz.)
------- | --------
75 | 12
80 | 15
85 | 18
90 | 21
95 | 24
100 | 27
The line that is closest to all of the data points is a line with a positive slope. This means that as the temperature increases, the water consumption also increases. The line does not perfectly fit all of the data points, but it does a good job of capturing the general trend.
Here is an explanation of how to interpret the scatter plot:
The points that are closer to the line indicate that the relationship between temperature and water consumption is stronger for those points.
The points that are further away from the line indicate that the relationship between temperature and water consumption is weaker for those points.
The line itself indicates the general trend of the data.
In this case, the line indicates that as the temperature increases, the water consumption also increases. However, there are some points that do not follow this trend. For example, the point at 95°F has a water consumption of 24 fl. oz., which is lower than the water consumption for the points at 90°F and 100°F. This suggests that there may be other factors that affect water consumption, such as the humidity or the activity level of the person.
Overall, the scatter plot shows that there is a positive relationship between temperature and water consumption. However, there are some points that do not follow this trend, which suggests that there may be other factors that also affect water consumption.
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Type the correct answer in each box.
Consider the expressions shown below.
-
Answer:
First one is b second one is a thrid is c
Step-by-step explanation:
Which of the following can be used to evaluate the series 5E n=1 6(0.6)n-1
Answer is C
A geometric series is an expression that results from adding all the elements in a geometric order. The right answer is B.
A geometric sequence is what?A geometric series is an expression that results from adding all the elements in a geometric order.
The given series is a geometric series in the form , where
The series has 5 terms, n = 5The first term of the series is 6, a₁ = 6The common ratio between the terms, r= 0.6Now, the geometry series' total can be expressed as,
[tex]\begin{aligned}\text { Sum } & =\mathrm{a}_1 \frac{\left(1-\mathrm{r}^{\mathrm{n}}\right)}{(1-\mathrm{r})} \\& =6 \frac{\left(1-0.6^5\right)}{(1-0.6)}\end{aligned}[/tex]
Hence, the correct option is C.
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function D gives the cost, in cents, of buying M mangoes at the fresh market. Which statement represents the meaning of the equation D(5)=100
According to the calculation D(5) = 100, the price of 5 mangoes at the fresh market will be $1.00, or 100 cents.
What is a formula or equation?Your example is an equation because a calculation is any formula with an equals symbol. Due to scientists' adoration of equal signs, equations are commonly used in mathematical expressions. A recipe is a collection of guidelines for producing a specific outcome.
The equation D(5) = 100 means that if you buy 5 mangoes at the fresh market, the cost will be 100 cents, or $1.00.
In general, the function D gives the cost (in cents) of buying M mangoes at the fresh market, so D(M) represents the cost of buying M mangoes. Therefore, D(5) means that we are evaluating the function D when M = 5, or when we buy 5 mangoes. The value of D(5) is 100 cents, or $1.00, which represents the cost of buying 5 mangoes at the fresh market.
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Find the value of 'x'.
A. 21
B. 49
C. 3
D. 7
7 cm
3x cm
x cm
21 cm
7 cm
im pretty sure u need to add more information to this question, but imma assume an answer
so if it's a square
21cm = 3xcm
7cm = xcm
so x = 7
A random survey of seventh- and eighth-grade students was conducted to find out how many hours is spent doing homework each night. Of the two sets of data, which has the greater median?
Cοmparing the medians fοund using the given bοx plοt, we fοund that the median οf eighth graders is greater than the median οf the seventh graders.
What is a bοx plοt?A bοx and whisker plοt, οften knοwn as a bοx plοt, shοws a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary.
A bοx is drawn frοm the first quartile tο the third quartile in a bοx plοt.
At the median, a vertical line passes thrοugh the bοx. It is generally used tο shοw whether a distributiοn is skewed οr nοt and whether there are any pοtential οutliers, οr οdd οbservatiοns, in the data set.
When cοmparing οr invοlving numerοus data sets, bοxplοts are alsο highly helpful. Graphs can be used tο determine hοw widely the data values vary οr are spread οut.
Frοm the bοx plοt given, we can summarize the fοllοwing,
Fοr seventh graders,
The first quartile Q1 = 3
The third quartile Q3 = 4
Interquartile range = Q3 - Q1 = 4-3 = 1
The median = 3.5
Fοr eighth graders,
The first quartile Q1 = 3.5
The third quartile Q3 = 4.5
Interquartile range = Q3 - Q1 = 4.5 -3.5 = 1
The median = 4
Therefοre cοmparing the medians fοund using the given bοx plοt, we fοund that the median οf eighth graders is greater than the median οf the seventh graders.
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The probability that a person with certain symptoms has hepatitis is 0.8. The blood test used to confirm this diagnosis gives positive results for 94% of people with the disease and 5% of those without the disease. What is the probability that an individual who has the symptoms and who reacts positively to the test actually has hepatitis?
The likelihood that someone with symptoms and a positive test has hepatitis is therefore 0.994, or almost 99.4%.
What is the probability that an individual who has the symptoms and who reacts positively to the test actually has hepatitis?We need to apply Bayes' theorem to determine the likelihood that a person with symptoms and a positive test actually has hepatitis. Let H stand for the occurrence that the person has hepatitis and T stand for the occurrence that the test is positive. Next, we have:
P(T | H) * P(H) / P(T | H) = P(H | T) (T)
where P(H) is the prior probability of the individual having hepatitis (which is 0.8), P(H) is the likelihood of the individual testing positive, and P(T) is the probability of testing positive given that the individual has hepatitis.
We must apply the law of total probability to determine P(T):
P(T) is equal to P(T | H)* P(H) plus P(T | not H)* P. (not H)
P(T | not H) is the complement of P(H), and P(not H) is the probability of testing positive if the person does not have hepatitis (0.05). (i.e., the probability of not having hepatitis, which is 0.2).
Now that the values have been inputted, we can calculate:
P(T) = (0.94 * 0.8) + (0.05 * 0.2) = 0.752 P(H | T) = (0.94 * 0.8) / 0.752 = 0.994
Although there is a strong likelihood that this is the case, it's crucial to remember that no medical test is error-free, and false positives and false negatives can still happen.
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What are the terms in the expression 3y+5+y
Answer: algebraic expression, coefficient
Step-by-step explanation:
Select all of the following sets in which the number 23 is an element
According to the definition of different number sets, 23 is an element of:
1) Natural number set
2) Whole number set
3) Integers set
4)Rational number set ( it can be written as 23/1)
A similar question is attached below.
What are the different number sets?
The different number sets are:
Natural numbersNatural numbers are the collection of positive integers from 1 to infinity. The letter "N" stands for the set of natural numbers.
Whole numbersNatural numbers with a zero are another name for whole numbers. The set is made up of non-negative integers without any fractional or decimal parts. The letter "W" stands for the whole number set.
Integers
The set of all whole numbers with a negative set of natural numbers is known as an integer. The letter "Z" stands for the integer set.
Rational numbersEvery integer that can be expressed as p/q, or as a ratio of one number to another, is referred to be a rational number. The letter "Q" can be used to signify a rational number.
Irrational numberThe number that cannot be represented by p/q. It denotes a number as being irrational if it cannot be expressed as a ratio of one to another. The letter "P" is used to signify it.
Therefore according to the definition of different number sets, 23 is an element of:
1) Natural number set
2) Whole number set
3) Integers set
4)Rational number set ( it can be written as 23/1)
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Find two values of θ, 0≤θ<2π, that satisfy the following equation.
Answer:
π/4, 7π/4
Step-by-step explanation:
You want the values of θ in the range 0 ≤ θ ≤ 2π such that cos(θ) = √2/2.
CosineThe cosine function has the value √2/2 for angles ±45° = ±π/4 radians and those angles added to an integer multiple of 2π. In the domain of interest, the angles are ...
θ = π/4 and 7π/4
THE ANSWER IS A & B!! Select the two values of x that are roots of this equation. x25x+3=0 A. x = B. D. X = X = X = 5+√13 2 5+√37 2 5-13 2 5-√37
The two x values that make up the equation's roots are:
x = [tex]\frac{5+\sqrt{13} }{2}[/tex]
x =[tex]\frac{5-\sqrt{13} }{2}[/tex]
These two items are the two answers to the problem.
what are equations?A mathematical definition of an equation is a claim that two expressions are equal and joined by the equals sign.
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.
from the question:
We can use the quadratic formula to determine the roots of the equation [tex]x^2 - 5x + 3 = 0.[/tex]
x = (-b ± [tex]\frac{b^2 - 4ac}{2a}[/tex])
where the quadratic equation's coefficients are a, b, and c.
With respect to our equation, we have:
a = 1, b = -5, and c = 3
These values are entered into the quadratic formula as follows:
x = (-(-5) ± [tex]\sqrt(-5)^2}[/tex] - 4(1)(3))) / 2(1)
x = (5 ± [tex]\frac{{13}}{2}[/tex])
The two x values that make up the equation's roots are:
x = [tex]\frac{5+\sqrt{13} }{2}[/tex]
x =[tex]\frac{5-\sqrt{13} }{2}[/tex]
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There are 5 numbers in a set of data. There are no repeated numbers in the set. Which
measure of data must represent a number in the set that is greater than 2 of the numbers in
the set and less than 2 of the numbers?
A Median
B Mean
с Mode
D Range
What is the answer pls help
The measure of data that must represent a number in the set that is greater than 2 of the numbers in the set and less than 2 of the numbers is the median.
The median is the middle value in a set of data when the values are listed in order from least to greatest (or greatest to least). If there are an odd number of values in the set, the median is the middle value. If there are an even number of values in the set, the median is the average of the two middle values.
If a number in the set is greater than 2 of the numbers and less than 2 of the numbers, then it falls between the first and last quartile of the data set. Therefore, the median, which represents the middle value in the data set, must also fall between the first and last quartile, and thus it must represent a number in the set that is greater than 2 of the numbers and less than 2 of the numbers.