As a result, y = -x + 1/2 is the equatiοn οf the tangent line tο the curve x² + y² = (2x² + 2y² - x)² at the pοsitiοn (0,1/2).
What is equatiοn?An equatiοn in mathematics is a claim that twο mathematical expressiοns are equivalent. An equatiοn has an equal sign, typically has οne οr mοre factοrs, and can be sοlved fοr by applying algebraic οr numerical techniques. Equatiοns are used tο represent real-wοrld phenοmena, resοlve issues, and make predictiοns in many branches οf mathematics, science, and engineering.
given:
We must first use implicit differentiatiοn tο determine the derivative οf the curve in οrder tο determine the equatiοn οf the tangent line tο the curve at the pοsitiοn (0,1/2).
By taking the derivative οf the equatiοn's twο sides with regard tο x, we arrive at:
dy/dx = 2x + 2y
(2x² + 2y²- x) * (4x - 1) (4x - 1)
When we sοlve fοr dy/dx and simplify this equatiοn, we get:
[(1 - 4x)(2x + 2y)] Equals dy/dx / [4(2x² + 2y² - x) - 2y(1 - 4x)]
The slοpe οf the tangent line at the pοint (0,1/2) can nοw be calculated by plugging in the numbers x = 0 and y = 1/2:
dy/dx = [(1 - 4(0))
(2(0) + 2(1/2))] / [4(2(0)² + 2(1/2)² - 0) - 2(1/2)(1 - 4(0))] = -1
Therefοre, the tangent line's slοpe at the pοsitiοn (0,1/2) is negative οne. We can use the pοint-slοpe fοrm οf a line tο determine the equatiοn οf the tangent line:
where (x1,y1) is the tangency pοint and m is the inclinatiοn οf the tangent line. When we enter the numbers we have, we οbtain:
y - 1/2 = -1(x - 0) (x - 0)
When we simplify this sοlutiοn, we οbtain:
y = -x + 1/2
As a result, y = -x + 1/2 is the equatiοn οf the tangent line tο the curve x² + y2 = (2x² + 2y² - x)² at the pοsitiοn (0,1/2).
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can someone help me with this problem please
here is the picture is just one
What is Function?
Function is the relationship between inputs where each input is related to exactly one output. It is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.
"y is a function of x" (denoted y = f(x)) means that y varies according to whatever value x takes on.
How to determine
Where F(x) = 2x^4 + x^2 - 10x + 1
So, to calculate f(-10)
f(x) = y
Where x = -10
f(-10) = 2(-10)^4 + (-10)^2 -10(-10) + 1
f(-10) = 2(10000) + 100 + 100 + 1
f(-10) = 20000 + 100 + 100 + 1
f(-10) = 20201
For f(2),
f(x) = y
Where x = 2
f(2) = 2(2)^4 +2^2 -10(2) + 1
f(2) = 2(16) + 4 -20 + 1
f(2) = 32 + 4 -20 + 1
f(2) = 17
For f(3)
f(x) = y
Where x = 3
f(3) = 2(3)^4 + 3^2 -10(3) + 1
f(3) = 2(81) + 9 -30 + 1
f(3) = 162 + 9 - 30 + 1
f(3) = 142
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
Since the center of the circle lies on the y-axis, the x-coordinate of the center must be 0.
Also, since the diameter of the circle is 12 units, the radius is half of that, or 6 units.
Using the standard form of the equation of a circle, which is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius, we can substitute the values we know and simplify the equations to see which ones match.
The equations that represent circles with a diameter of 12 units and a center that lies on the y-axis are:
x^2 + (y - 6)^2 = 36 (center is at (0, 6))
x^2 + (y + 6)^2 = 36 (center is at (0, -6))
Therefore, the two options that represent the circles with the given properties are:
x^2 + (y - 6)^2 = 36 and x^2 + (y + 6)^2 = 36.
Help me do this thing for a math project
Answer:10
Step-by-step explanation:3x2=6 and 4x1=4 4+6=10
Answer:
See below
Step-by-step explanation:
Perimeter = (7x2) + (2x2) = 18
Area (L x W) = Square + rectangle
= (3x2) + (4x1) = 6 + 4 = 10
(4a^-2)^-1/2 simplify
Answer: To simplify the expression, we can apply the exponent rule for powers of powers which states that to raise a power to another power, we multiply the exponents.
So,
(4a^(-2))^(-1/2) = 4a^(-2 * (-1/2)) = 4a^(1) = 4a
Therefore, (4a^-2)^-1/2 simplifies to 4a.
Step-by-step explanation:
3. What is the solution of the equation −4(n+5)=−32 - 4 ( n + 5 ) = - 32 ? −13 - 13 −12 - 12 3 3 13
The solution of the given equation -4(n+5)=-32 is n=3.
What is equations ?
An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign (=) between two expressions. The expressions on both sides of the equals sign have the same value. Equations are used to solve problems in mathematics and science.
To solve the equation, we need to isolate the variable n.
-4(n+5) = -32
Distribute -4 on the left side of the equation:
-4n - 20 = -32
Add 20 to both sides of the equation:
-4n = -12
Divide both sides by -4:
n = 3
Therefore, the solution of the given equation -4(n+5)=-32 is n=3.
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A radioactive element has a half-life of 34 years. How long will it take for 21% of a sample to remain after decay begins? Round your answer to the nearest year.
The number of years for 21% to remain is 78years
What is half life?The time required for half of the original population of radioactive atoms to decay is called the half-life.
half life = 0.693/decay constant
decay constant = 0.693/34
= 0.02
21% of N(o) = 21N(o)/100 = N(y)
from the formula
N(t) = Noe^-kt
21N(o)/100 = Noe^-kt
21N(o)=100 Noe^-kt
divide bother sides by N(o)
21 = 100e^-kt
e^-kt = 21/100
e^-kt = 0.21
-0.02 t= ln0.21
-0.02 t= -1.56t
t = 1.56/0.02
t = 78years
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Consider the function graphed to the right.
The function is increasing on (4, 6).
The function is decreasing on (- 6, - 2).
The function is constant on (-2, 4).
The domain of the function is, (- 6, 6).
The range of the function is, (- 3, 1).
What is increasing and decreasing functions?A function f(x) is said to be increasing if the increase in the independent variable results in an increase in the dependent variable.
A function f(x) is said to be increasing if the increase in the independent variable results in a decrease in the dependent variable.
The function is increasing on the intervals (4, 6).
The function is decreasing on the interval (- 6, - 2).
The function is constant on the interval (-2, 4).
The domain of the function is, (- 6, 6).
The range of the function is, (- 3, 1).
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find ratio of speed of car 15 km/hr and speed of cycle 30km/hr
QUESTION 1
Consider the following argument: Either there is a massive, multi-million dollar conspiracy at work, or else the electorate
have decided that Senator Wiggins is the best candidate for the position. The electorate have decided that Senator
Wiggins is the best candidate for the position. So, there is not a massive, multi-million dollar conspiracy at work. What is
the logical form of this argument?
O a. Modus Tollens
b. Disjunctive Syllogism
O c. Affirming the consequent
O d. Affirming a disjunct
Oe. Modus Ponens
Since the electorate have decided that Senator Wiggins is the best candidate for the position. The logical form of this argument is option b. Disjunctive Syllogism
What is Disjunctive Syllogism?The argument is presented in the form of a disjunctive syllogism, which involves a logical form that states that either one of two alternatives must be true, and one of them has been found to be true; therefore, the other must be false.
In this case, the two alternatives are:
There is a massive, multi-million dollar conspiracy at work.The electorate have decided that Senator Wiggins is the best candidate for the position.The argument concludes that the second alternative is true, which means that the first alternative must be false. Therefore, the argument logically deduces that there is not a massive, multi-million dollar conspiracy at work.Thus, the logical form of the argument is:
Either A or B.
Not A.
Therefore, B.
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A spectrophotometer used for measuring CO concentration [ppm (parts per million) by volume] is checked for accuracy by taking readings on a manufactured gas (called span gas) in which the CO concentration is very precisely controlled at 70 ppm. If the readings suggest that the spectrophotometer is not working properly, it will have to be recalibrated. Assume that if it is properly calibrated, measured concentration for span gas samples is normally distributed. On the basis of the six readings - 85, 77, 82, 68, 72 and 69 - is recalibration necessary? Carry out a test of the relevant hypotheses and report the P-value.
The p value is calculated as 0.116
How to solve for the p valueNull u = 70
alternate u ≠ 70
The alternate is a two tailed test
the test statistic calculation
t = x - u / s/√n
x = 85 + 77 + 82 + 68 + 72 + 69 / 6
= 75.5
standard deviation s = [tex]\sqrt{\frac{(85- 75.5)^2+(77- 75.5)^2+...(69- 75.5)^2}{6-1} }[/tex]
= 7.01
Test stat = (75.5 - 70) / 7.01/√6
= 1.92
degree of freedom = 6 - 1 = 5
this is 2 tailed
p value using excel = tdist( 1.8, 5 , 2)
= 0.116
We fail to reject the null hypothesis because it is greater than the level of significance
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Decide whether the probability described is theoretical or empirical. At one school, 59% of the students having lunch in the union are female, so the probability of a randomly selected student from the campus phone directory being male is 0.41.
The probability for this problem is an Empirical probability, as it is taken from an experiment.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
Empirical probability is based on observations or experimental data, for example, observing the number of students in a cafeteria and obtaining the percentage of male students and female students, as is done for this problem.
Theoretical probability, on the other hand, is based on mathematical analysis and is calculated using the principles of probability theory. It is the probability that an event will occur based on all possible outcomes. For example, a fair coin is equally as likely to be heads or tails.
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Compare the function g(x) = 3/x-2 +5 to the parent function f(x)= 1/x please describe how the function has been transformed from the parent function.
The function g(x) = 3/(x-2) + 5 is a transformation of the parent function f(x) = 1/x with a horizontal shift of 2 units to the right, a vertical stretch by a factor of 3, and a vertical shift of 5 units up.
What is the transformation of the functionThe function g(x) = 3/(x-2) + 5 is a transformation of the parent function f(x) = 1/x.
Here are the transformations that were applied to f(x) to obtain g(x):
1. Horizontal shift: The denominator of f(x) is x, which means that the vertical asymptote is at x = 0. By subtracting 2 from x in the denominator of g(x), we are shifting the vertical asymptote to x = 2. This is a horizontal shift of 2 units to the right.
2. Vertical stretch: The coefficient 3 in front of the fraction means that the function is stretched vertically by a factor of 3 compared to f(x). This means that the distance between the horizontal asymptotes (which are at y = 0 for f(x) and y = 5 for g(x)) is three times larger for g(x) than for f(x).
3. Vertical shift: The constant 5 added to the fraction means that the entire function is shifted vertically by 5 units compared to f(x). This means that the horizontal asymptote of g(x) is at y = 5 instead of y = 0.
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25 POINTS PLS HELP What is the arc length of an arc with radius 18 inches and central angle 22°? Leave the answer in
terms of . Show your work.
The arc length of the arc is (11/5)π inches, or approximately 6.926 inches (rounded to three decimal places).
We may use the following formula to determine the arc length of an arc having a radius of 18 inches and a centre angle of 22°:
(Central angle / 360°) x (2r) Equals arc length
where r denotes the arc's radius.
Inputting the values provided yields:
arc length is equal to (22°/360°) x (2x18 inches).
arc length is equal to 11/180 times 36 inches.
11.5 inches is the length of an arc.
As a result, the arc's length is (11/5) inches, or roughly 6.926 inches (rounded to three decimal places).
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m=1 b=4 what does y=
Answer:
Find the value of b using the formula for the equation of a line.
y = mx+b
Replace the known value of m in the slope y-intercept form of the equation.
y=(1)x+b
Replace the known value of b in the slope y-intercept form of the equation.
y=(1)x+4
Simplify the slope y-intercept form of the equation.
Remove parentheses.
y=(1)x+4
Multiply 1 by x
y=1x+4
Remove parentheses.
y=(1)x+4
Multiply x by 1
this is the answer : y=x+4
i hope this helps.
Suppose you have $600 to invest in a savings plan, and you want to compare 4 different ways you could invest the money.
Round answers to the nearest cent
Method 1: Find the balance after one year if you deposit all the money into an account that pays $2.50 in simple interest each month (this is a simple interest equation where the amount of interest stays the same each month).
Number
Method 2: Find the balance after one year if you deposit all the money into an account that pays 5% APR with monthly compounding.
Number
Method 3: Suppose if, instead of depositing the $600 all at once, you deposit nothing at the beginning and you divide up the $600 into 12 envelopes each with $50.
Find the balance after one year if you deposit one $50 envelope each month, all year, into an account that pays 5% APR with monthly compounding.
Number
Method 4: Suppose if, instead of depositing the $600 all at once, you make an initial deposit of $300 into an account that pays 5% APR at the beginning of the year and then you divide up the remaining $300 into 12 envelopes each with $25.
Find the balance after one year for the initial deposit of $300, if you also deposit one $25 envelope each month, all year, into the account that pays 5% APR with monthly compounding.
Number
Therefore , the solution of the given problem of interest comes out to be $630 , $659.15 , $638.89 and $345.57 .
What does interest actually mean?To determine simple interest, divide the sum by the cost of borrowing, the amount of time left, and other factors. Principal plus interest plus hours is the straightforward return strategy in marketing. The simplest approach to calculate interest is to use this method. The most popular method of calculating revenue is as a fraction of the principal amount.
Method 1: A basic interest rate of $2.50 per month for a year equals
=> $2.50 x 12 = $30 in interest.
The balance after a year equals $600 plus $30, or $630.
Response: $630
Step 2: Divide the monthly interest rate by 12 to get 0.4167%
Amount after a year:
=> $600 multiplied by (1 + 0.004167)/12 to arrive at $659.15
Response: $659.15
Option 3: $50 per month in deposits
Interest rate per month: 5% divided by 12 Equals 0.4167%
Surplus at the end of the year is equal to
=> $50 x (((1 + 0.004167)12 - 1) / 0.004167) x (1 + 0.004167) = $638.89
Response: $638.89
Method 4: Initial investment of $300, subsequent deposits of $25, and an interest rate of 5% divided by 12 equals 0.4167%.
Amount at the end of the year equals
=> $300 x (1 + 0.004167)12 + $25 x (((1 + 0.004167)12 - 1) / 0.004167) x (1 + 0.004167) = $345.57
Response: $345.57
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7.
The list below shows Wendy's bowling scores in her last five games.
112, 123, 136, 145, 159
Which measure of data best describes how much these bowling scores varied?
A Mean
B Median
C Mode
D Range
Answer:
Step-by-step explanation:
the range would be the answer as it shows the top and the bottom score.
Which graph represents a function with direct variation? A coordinate plane with a line passing through (negative 4, 0) and (0, negative 2). A coordinate plane with a line passing through (negative 5, 4) and (0, 3). A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3). A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4). Mark this and return
We can state this by responding to the provided question A direct function variation function is represented by the graph of this equation, which is a straight line going through the points (0, -2) and (-4, 0).
what is function?Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.
The coordinate plane with a line crossing between (0, -2) and (-2) is the graph that illustrates a function with direct variation (-4, 0).
If m is the line's slope and (x1, y1) is a point on the line, [tex]y - y1 = m(x - x1).[/tex]
The line's slope is as follows:
[tex]m = (y2 - y1)/(x2 - x1) = (-2 - 0)/(0 - (-4)) = 1/2[/tex]
The equation of the line going through (0, -2) and (-4, 0), expressed in point-slope form, is:
[tex]y - (-2) = 1/2(x - 0) (x - 0)[/tex]
When we simplify the equation, we obtain:
[tex]y = 1/2x - 2[/tex]
A direct variation function is represented by the graph of this equation, which is a straight line going through the points (0, -2) and (-4, 0).
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whats the square root of 9
Answer: 3
Step-by-step explanation:
hello! Find the slope of the line in the graph thanks!
The slope of the given line is [tex]m = \dfrac{1}{2}\\[/tex].
What is a slope?A line's slope is calculated as the tangent of the angle it makes with the x-axis. A straight line's slope remains constant throughout. Y = mx + b can be used to calculate a straight line's slope-intercept form.
Given that the line is passing through the points ( 0,1) and (-2, 0 ). The slope of the line is calculated by the application of the formula given below,
[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
The slope of the line is calculated by substituting the values of the coordinates in the formula,
[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m = \dfrac{1 - 0}{0 + 2 }[/tex]
[tex]m = \dfrac{1}{2}[/tex]
Therefore, the slope of the line will be [tex]m = \dfrac{1}{2}\\[/tex].
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Write the equation of the line that is perpendicular to y = -1/6x-2 and passes through the point (-2,-1)
Therefore , the solution of the given problem of equation comes out to be y = 6x + 11.
How do equations work?Mathematical formulas frequently use the same letter to try to impose uniformity between two claims. Many variable academic numbers are shown to be equal using mathematical equations, also known as assertions. The normalise divides 12 and b + 6 into two parts using the result y + 6 = 12 as an illustration. It is possible to determine the connection between each sign component and the number of lines. The significance of a symbol usually contradicts itself.
Here,
In slope-intercept form, the provided equation y = -1/6x - 2 has a slope of -1/6. Consequently, this line's perpendicular inclination is as follows:
=> m2 = -(1/-1/6) = 6
Now that we know the desired line's slope and the spot through which it passes (-2, -1). To determine the solution of a linear equation, we can use its point-slope form:
=> y - y1 = m(x - x1) (x - x1)
where m is the slope 6 and (x1, y1) is the position (-2, -1). By replacing these numbers, we obtain:
=> y + 1 = 6(x + 2) y + 1
=> 6x + 12 y + 1
=> 6x + 11 y - (-1)
=> 6(x - (-2))
As a result, the equation for the line passing through the position (-2, -1) and perpendicular to y = -1/6x - 2 is y = 6x + 11.
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Which expression is the simplest form of 223-22 + 3 (23 - 422)?
O A. 23 - 13x2
O B. 523 - 1322
О c. 323 - 1222
O D. 523 - 522
The simplification value of the expression is,
⇒ 5x³ - 12x²
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 2x³ - x² + 3 (x³ - 4x²)
Now, We can simplify the expression as;
⇒ 2x³ - x² + 3 (x³ - 4x²)
⇒ 2x³ - x² + 3x³ - 12x²
⇒ 5x³ - 12x²
Thus, The simplification value of the expression is,
⇒ 5x³ - 12x²
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2x+6 in distributive property then into a expression
Answer:
2(x+3)
Step by Step:
2(x)=2x
2(3)=6
2x+6=2(x+3)
2(x)+2(3) =2 (x+3)
a boy band has released two albums. Their first album should 5.9 x 10 to the 5th power copies. the second sold 1.3 x 10 to the 6th power copies. how many copies had the band boy sold
The total number of copies that the band sold is given as follows:
1.89 x 10^6 copies.
How to obtain the total number of copies sold?The total number of copies sold is obtained adding the number of copies of each album sold.
The amounts for each album are given as follows:
First album: 5.9 x 10^5 = 0.59 x 10^6.Second album: 1.3 x 10^6.When we add two numbers in scientific notation, they must have the same exponent, hence we add the bases keeping the exponents, as follows:
(1.3 + 0.59) x 10^6 = 1.89 x 10^6 copies.
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Calculate the cash discount and the net amount due the transaction (in $).
The cash discount is $353.20 and the net amount due is $17,306.80.
What are the purchase terms?Conditions of sale are the rules that govern a business transaction, including the cost, the method of payment, the delivery, and any other pertinent information. Normally, they are specified in a sales contract or invoice and acknowledged in advance of the transaction. The conditions of sale might alter based on the type of products or services being exchanged, the volume and complexity of the deal, and other elements.
We know that,
Cash discount = amount x discount rate
Net amount due = amount - cash discount
For 2/10:
Cash discount = $17,660 x 2% = $353.20
Net amount due = $17,660 - $353.20 = $17,306.80
Hence, the cash discount is $353.20 and the net amount due is $17,306.80.
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The principal P is borrowed at a simple interest rate r for a period of time t. Find the loan's future value A, or the total amount due at time t.
P=$1000, r=5.0%, t=6 months
Step-by-step explanation:
To calculate the future value of a loan with simple interest, we can use the formula:
A = P(1 + rt)
where A is the future value or total amount due, P is the principal, r is the interest rate, and t is the time period in years.
In this case, we have:
P = $1000
r = 5.0% = 0.05 (expressed as a decimal)
t = 6 months = 0.5 years (since there are 12 months in a year)
Plugging these values into the formula, we get:
A = $1000(1 + 0.05 x 0.5)
A = $1000(1.025)
A = $1025
Therefore, the future value or total amount due on the loan after 6 months is $1025.
he diameter of a circle is 18 feet. What is the circle's area?
Answer:
Step-by-step explanation:
[tex]A=\pi r^2\\[/tex]
[tex]=\pi \times 9^2[/tex] (radius = 9 feet)
[tex]=81\pi[/tex]
[tex]\approx 254.47[/tex] feet
What number a is 24% of 25?
Answer: 24 percent of 25 is 6.
Step-by-step explanation: The output of 24 percent of 25 is 6. To obtain this answer, we multiply 0.24 by 25.
PLEASE HELP WILL GIVE BRAINLISET POINTS !!
Answer:
Step-by-step explanation:
37
The mean of the following data values is 36.
19, 23, 35, 41, 42
Answer:
To find the mean of a set of data, we need to sum up all the values in the set and divide by the number of values.
Sum of the data values = 19 + 23 + 35 + 41 + 42 = 160
Number of data values = 5
Mean = Sum of data values / Number of data values = 160 / 5 = 32
However, we are given that the mean is 36. Since the calculated mean is lower than the given mean, it means that we are missing a value that is higher than the other values in the set.
Let's call this missing value x. Then, we have:
(19 + 23 + 35 + 41 + 42 + x) / 6 = 36
Multiplying both sides by 6, we get:
19 + 23 + 35 + 41 + 42 + x = 216
Simplifying the left-hand side, we get:
160 + x = 216
Subtracting 160 from both sides, we get:
x = 56
Therefore, the missing value is 56, and the complete data set is:
19, 23, 35, 41, 42, 56
Now, we can calculate the mean as:
Mean = (19 + 23 + 35 + 41 + 42 + 56) / 6 = 216 / 6 = 36
So, the mean of the data values is indeed 36.
Answer:
32
Step-by-step explanation:
To find the mean of a set of numbers, we add up all the numbers and then divide by the total number of values.
Adding up the values:
19 + 23 + 35 + 41 + 42 = 160
We have a total of 5 values, so we divide the sum by 5:
160 / 5 = 32
Therefore, the mean of the given data values is 32, not 36.
Find the value of x.
Answer:
Step-by-step explanation:
Angle sum of a triangle = 180°. So we get:
[tex]62+69+(4x+5)=180[/tex]
[tex]136+4x=180[/tex]
[tex]4x=44[/tex]
[tex]x=11[/tex]°
Answer:
x = 11
Step-by-step explanation:
We know that the sum of the interior angles in a triangle is added up to 180°.
Accordingly,
62 + 69 + 4x + 5 = 180
Combine like terms.
136 + 4x = 180
Subtract 136 from both sides.
4x = 180 - 136
4x = 44
Divide both sides by 4.
x = 11