The circumference and the area of the circular flower bed are given as follows:
Circumference: 12π units.Area: 36π units squared.What are the area and the circumference of a circle?The area of a circle of radius r is given by π multiplied by the radius squared, as follows:
A = πr²
The radius is half the diameter, hence it has the value given as follows:
r = 0.5d
r = 0.5 x 12
r = 6.
Then the area is obtained as follows:
A = π x 6²
A = 36π units squared.
The circumference is given by the multiplication of the diameter by π, hence:
C = 12π units.
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if you are using a simple-moving average and you want your forecast to ignore occasional noise in the data, which of the following is true? a. You want a stable forecast b. You want a responsible forecast c. You use more periods of data. d. You use fewer periods of data e.Only a and c f.Only b and d
if you are using a simple-moving average and you want your forecast to ignore occasional noise in the data, Only A & C are of the following is true .
What is the meaning of the simple moving average?
The average of a range of prices is determined by the number of periods that fall within the range using simple moving averages.
A technical indicator called a simple moving average can help forecast whether a price trend—be it bullish or bearish—will continue or reverse.
What is not necessary for simpler forecasting techniques?
various types and amounts of data are needed for various forecasting methodologies. Less information is necessary for simpler techniques, such as the time series techniques outlined below.
Complex models require a lot of data. It might be expensive to create precise forecasts.
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Determine whether the following statement is true or false.
Generally, the goal of an experiment is to determine the effect that the treatment will have on the response variable.
True, Generally, the goal of an experiment is to determine the effect that the treatment will have on the response variable.
What does a response variable in an experiment mean?
Response Continuum In an experimental investigation, this is the result that is assessed after manipulating the explanatory variable; it is also referred to as the dependent or outcome variable.
Its value is expected or its variation is explained by the explanatory variable.
What other name would you give the answer variable?
The term "dependent variable" is one more typical moniker for the response variable. The response variable is frequently referred to as just "the response" for short.
There are several more terms for the predictor variables, including "explanatory variables," "independent variables," "predictors," and "regressors."
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A right cone has a base with diameter 6 units. The volume of the cone is 72π cubic units.
What is the length of a segment drawn from the apex to the edge of the circular base?
Round to the nearest tenth. This is a multi-step problem.
The segment drawn from the apex to the edge of the circular base is _______ units.
Answer:
6
Step-by-step explanation:
The radius of the base of the cone is 3 units, since the diameter is 6 units. Let's call the height of the cone "h".
We can use the formula for the volume of a cone to find h:
V = (1/3)πr^2h
72π = (1/3)π(3^2)h
72π = (1/3)π(9)h
72π = 3πh
h = 72/3
h = 24
Now we can use the Pythagorean theorem to find the length of the segment:
a^2 + h^2 = c^2
a^2 + 24^2 = 6^2
a^2 = 36
a = 6
So the segment drawn from the apex to the edge of the circular base is 6 units, rounded to the nearest tenth.
true/false. an experiment was run to compare four groups. the standard deviations were 4974, 6585, 3288, 5488. in this case, it is reasonable to assume all groups have equal variances.
False. It is not reasonable to assume all groups have equal variances in this case.
The standard deviation is a measure of variability or spread of the data. If the standard deviations of different groups are significantly different, then it suggests that the spread of the data within each group is also different. When comparing multiple groups, equal variances are typically assumed so that a valid statistical test can be performed.
If the variances are unequal, then a different type of test, such as Welch's ANOVA, should be used. In this case, the large difference in the standard deviations of the four groups (4974, 6585, 3288, 5488) suggests that it is not reasonable to assume equal variances and a different test should be used.
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Helpppp meeeeeeee (35 points)
Answer:
B.
Step-by-step explanation:
It is B because the height of the triangle is 9 and the height of B is 9. The bottom side of the triangle is 16 and the bottom of B is 16. The other labeled side is 10 and the side parallel to that side is 10 in figure B.
Could someone help me with this please!
Answer: x = 3
Step-by-step explanation:
6x + 5 = 3x + 14
subtract 5 from both sides:
6x + 5 - 5 = 3x + 14 - 5
6x = 3x + 9
subtract 3x from both sides:
6x - 3x = 3x + 9 - 3x
3x = 9
divide both sides by 3:
3x/3 = 9/3
x = 3
Answer:
x=
Step-by-step explanation:
collect like terms
6x-3x =14x-5
3x=9
x=
given the following information for langs, inc., calculate per share dividend dollar amount (that is, the dividends per share), rounded to the nearest cent (i.e., $5.21843
The per share dividend dollar amount paid out by Langs Inc. in 2020 is $0.50.
To calculate the per-share dividend dollar amount, we first need to calculate the total dividends paid out in 2020. We can find this by subtracting the retained earnings at the end of 2019 from the retained earnings at the end of 2020: $4,326,800 - $4,216,800 = $110,000. This $110,000 represents the total dividends paid out in 2020, since the company only uses retained earnings to pay dividends.
Next, we divide the total dividends by the number of shares outstanding at the end of 2020: $110,000 / 220,000 shares = $0.50. This is the per share dividend dollar amount, rounded to the nearest cent.
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Complete Question:
Given the following information for Langs, Inc., calculate per share dividend dollar amount (that is, the dividends per share), rounded to the nearest cent (i.e., $5.21843 = $5.22) that the company paid out in 2020:
Retained earnings reported on December 31, 2019 balance sheet: $4,216,800 Retained earnings reported on December 31, 2020 balance sheet: $4,326,800 Net Income reported on December 31, 2019 income statement: $658,700 Net Income reported on December 31, 2020 income statement: $547,900 Number of shares of common stock outstanding at the end of 2019: 206,600 shares Number of shares of common stock outstanding at the end of 2020: 220,000 sharesHelp!
Solve. Separate your answers with a comma.│x+7│=2
The values of x in the expression are -5, -9
How to determine the solution to the expressionFrom the question, we have the following parameters that can be used in our computation:
|x + 7| = 2
Remove the absolute bracket
So, we have the following representation
x + 7 = -2 or x + 7 = 2
Evaluate the like terms
x = -9 or x = -5
Hence, the values are -5 and -9
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let A be a 2x2 matrix. given the following descriptions, determine the following elementary matrices and their inverses. The elementary matrix E1 multiplies the first row of A by 1/2
For a matrix A, the determined matrices are
a) Matrix E₁ is [tex]E₁ = \begin{bmatrix} \frac{1}{2} & \frac{ - 3}{2} \\ -1 & 3\end{bmatrix} [/tex]
and it's inverse is equals to zero.
b) Matrix E₂ and it's inverse E₂⁻¹ are
[tex]E₂ = \begin{bmatrix} 1 & -3 \\ - 5& - 1\end{bmatrix} [/tex]
[tex]E₂⁻¹ = \begin{bmatrix} \frac{ - 1}{16} & \frac{3}{16} \\ \\ \frac{5}{16} & \frac{1}{16} \end{bmatrix}[/tex]
We have a matrix 2×2, A such that
[tex]A= \begin{bmatrix} 1 & -3 \\ -1 & 3\end{bmatrix}[/tex]
and we have to determine the matrix E₁ with their inverses. Also, matrix E₁ is generated by multiplying the first row of matrix A by 1/2. As we see elements of first row of matrix are 1 and -3.
[tex]E₁ = \begin{bmatrix} 1 \times \frac{1}{2} & -3 \times \frac{1}{2} \\ -1 & 3\end{bmatrix}
[/tex]
[tex]E₁ = \begin{bmatrix} \frac{1}{2} & \frac{ - 3}{2} \\ -1 & 3\end{bmatrix} [/tex]
The inverse of A is A⁻¹only when AA⁻¹= A⁻¹A = I.
Steps to determine the inverse of a 2x2 matrix:
Swap the positions of a and d, where a --> first row first element and d --> second row 2nd element.Put negatives in front of b and c, where b --> first row 2nd element and c --> 2nd row first element. Divide everything by the determinant (ad-bc).Determinant of E₁ = ad - bc , here a =1/2 , b = -3/2 , c= -1 and d = 3. So, |E₁ | = 1/2× 3 - (-3/2)×(-1) = 3/2 - 3/2 = 0 . Thus, Inverse of E₁⁻¹ = 0 .
b) When we multiplies the second row of A by -4 then the elementary matrix E₂ is form. [tex]E₂ = \begin{bmatrix} 1 & -3 \\ -1 + (- 4)& 3 + ( - 4)\end{bmatrix}[/tex]
[tex]E₂ = \begin{bmatrix} 1 & -3 \\ - 5& - 1\end{bmatrix}[/tex]
Now, we have determine the Inverse of E₂. The determinant of |E₂| = -1× 1 - (-5)×(-3) = -1 - 15 = -16
So, inverse of matrix is , E₂⁻¹
[tex]E₂⁻¹ = \frac{1}{16}\begin{bmatrix} - 1 & - ( -3) \\ - ( - 5)& 1\end{bmatrix}[/tex]
[tex]E₂⁻¹ = \frac{1}{16} \begin{bmatrix} -1 & 3 \\ 5& 1\end{bmatrix}[/tex]
[tex]E₂⁻¹ = \begin{bmatrix} \frac{ - 1}{16} & \frac{3}{16} \\\\\frac{5}{16} & \frac{1}{16} \end{bmatrix}[/tex]
Hence, we get the required inverse.
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Complete question:
Let A be a 2 x 2 matrix. Given the following descriptions, A = [ 1 -3 ; -1 3]
determine the following elementary matrices and their inverses.
a. The elementary matrix E1 multiplies the first row of A by 1/2 .
b. The elementary matrix E2 adding the second row of A by -4
a polynominal has a zero at 4 (multiplicity 2) and 0 (multiplicity 1) what is the function
The function would be; [tex]f(x)= x^4 + 6x^3 + 12x^2 + 8x[/tex]
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
Given that a polynominal has a zero at 4 (multiplicity 2) and 0 (multiplicity 1)
Required polynomial;
[tex]= x(x + 2)^3 \\= x(x^3 + 6x^2 + 12x + 8) \\= x^4 + 6x^3 + 12x^2 + 8x[/tex]
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Barry took out a 20-year loan for $55,000 at an APR of 6.8%, compounded
monthly, and he is making monthly payments of $419.84. Assuming that his
balance is $31,019.97 with 8 years left on the loan, how much would he save
by paying off the loan 8 years early?
The solution is, A = $94193.421., would he save by paying off the loan 8 years early.
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
here, we have,
We must determine the amount owed for the first 8 years.
The monthly compound interest formula is:
A = P(1+r/12)^12t - Xnt
given,
P = $55,000
r = 6.8%
t = 8
Xnt = $419.84
solving we get,
A = 94193.421
Hence, The solution is, A = $94193.421.
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express the negation of the statement in terms of quantifiers without using the negation symbol. [10 pts.] a. b. \
Negating a statement in terms of quantifiers means expressing the opposite of the statement using quantifiers such as "for all" (∀) and "there exists" (∃) instead of using negation symbols like "not". The key to negating a statement using quantifiers is to switch the quantifiers and negate the predicate.
For example, the negation of the statement "For all x, P(x)" is "There exists x such that not P(x)" because we have switched the universal quantifier "for all" to the existential quantifier "there exists" and negated the predicate P(x). On the other hand, the negation of the statement "There exists x such that P(x)" is "For all x, not P(x)" because we have switched the existential quantifier to the universal quantifier and negated the predicate.
Similarly, the negation of a statement involving "and" or "or" can be found by negating each component and switching the connective. For example, the negation of "P(x) and Q(x)" is "P(x) or not Q(x)" or "not P(x) or Q(x)".
In this context, the negation statements are:
a) There exists x such that x <= 1
b) There exists x such that x > 2
c) For all x, x < 4
d) For all x, x >= 0
e) There exists x such that x >= -1 and x <= 2
f) For all x, x >= 4 and x <= 7
The complete question is given below:
"
Express the negation of each of these statements in terms of quantifiers without using the negation symbol.
a) ∀x(x>1)
b) ∀x(x≤2)
c) ∃x(x≥4)
d) ∃x(x<0)
e) ∀x((x<−1)∨(x>2))
f) ∃x((x<4)∨(x>7))
"
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triangle $xyz$ is equilateral, with $o$ as its center. a point $p$ is chosen at random, inside the triangle. find the probability that point $p$ is closer to point $o$ than to any of the vertices. (in other words, find the probability that $op$ is shorter than $xp,$ $yp,$ and $zp.$)
The probability that point p is closer to point o than to any of the vertices is 0.3737.
The probability that point p is closer to point o than to any of the vertices can be found by considering the ratio of the area of the equilateral triangle xyz to the area of its circumscribed circle. This ratio is [tex]$\frac{3\sqrt{3}}{4\pi}$[/tex]. We can use this ratio to calculate the probability that point $p$ is closer to point o than to any of the vertices:
[tex]$P(op < xp, yp, zp) = \frac{3\sqrt{3}}{4\pi} = 0.3737$[/tex]
Therefore, the probability that point $p$ is closer to point $o$ than to any of the vertices is 0.3737.
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Noah found a shirt at the nearby clothing store that was 20 percent off. The total price after the discount is $58.20, which includes $3.80 in taxes.
The original price of the shirt was $68
How to find the original price?We know that the price after a discount of the 20% and an added $3.80 in taxes is $58.20
Then we can write:
$58.20 = P*(1 - 0.2) + $3.80
Where the factor (1- 0.2) corresponds to a discount of 20%.
Solving that for P we will get:
P = ($58.20 - $3.80)/0.8
P = $68
That is the original price of the shirt.
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Jill has 2/5 of a cup of powdered sugar. She sprinkles 1/6 of the sugar onto a plate of brownies and sprinkles the rest onto a plate of lemon cookies. How much sugar does Jill sprinkle on the brownies?
The amount of sugar that Jill sprinkles on the brownies will be 1/15 cusp.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Jill has 2/5 of a cup of powdered sugar. She sprinkles 1/6 of the sugar onto a plate of brownies and sprinkles the rest onto a plate of lemon cookies.
Then the amount of sugar that Jill sprinkles on the brownies is given as,
⇒ (2/5) x (1/6)
⇒ 2 / 30
⇒ 1/15
The amount of sugar that Jill sprinkles on the brownies will be 1/15 cusp.
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What is the next fraction in this sequence? Simplify your answer.
2 4
8 16
27.
3, 9, 27, 81, ...
Submit
Answer: 32/243
Step-by-step Explanation: multiply 16/81 by 2/3
A high school softball team needs to raise $915 to cover the cost of new equipment. They decide to have a car wash where they will charge $3 for cars, c, and $5 for trucks or SUVs, t. The combined number of $3 carwashes for cars, c, and $5 carwashes for trucks or SUVs, t, needed can be represented by the equation If only 5 cars are washed, how many trucks or SUVs need to be washed to raise the full $915?
a) The combined number of $3 carwashes for cars, c, and $5 carwashes for trucks or SUVs, t, needed can be represented by the equation y = c + t.
b) If only 5 cars are washed, the number of trucks or SUVs needed to be washed to raise the full $915 is 180.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal or equivalent.
Equations use the equation symbol (=) to show the equality of expressions.
The total amount needed for the new equipment = $915
The charge for a car wash per car = $3
The charge for cash wash per truck or SUV = $5
Let the number of cars = c
Let the number of trucks or SUVs = t
Equations:c + t = y... Equation 1
3c + 5t = 915... Equation 2
If the number of cars, c = 5
From equation 2:
3c + 5t = 915
3(5) + 5t = 915
15 + 5t = 915
5t = 900
t = 180
Thus, from equation 2, we can determine that if cars are 5, the trucks or SUVs must be 180 to meet the target.
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a) b) c) d) By how much is 78 greater than-12? By how much is -23 less than 23? What must be added to -6 to give 105? What must be added to 15 to give -30?
Answer:
a) 90
b) 46
c) 111
d) -45
Step-by-step explanation:
78 is greater than -12 by 90 (78 + (-12) = 66)
-23 is less than 23 by 46 (23 + (-23) = 0)
To give 105, 111 must be added to -6 (105 + (-6) = 99)
To give -30, -45 must be added to 15 (-30 + 15 = -15)
What are the lengths of the sides of the trapezoid shown at the right if the perimeter of the trapezoid is 17 cm?
The side lengths of Trapezoid are 4 cm, 5 cm, 4 cm and 4 cm.
What is Perimeter?The perimeter of a form is the space surrounding its edge.
A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter.
Given:
Perimeter of Trapezoid = 17 cm
So, the Perimeter of Trapezoid
17 = Sum of parallel sides + Sum of non parallel side
17 = x + x+ 1 + 2√x + 2√x
17 = 2x + 4√x + 1
2x + 4√x = 16
2x + 4√x - 16 = 0
x + 2√x = 8
2√x = 8- x
Now, Squaring both side
4x = 64 + x² - 16x
x² - 16x -4x + 64 = 0
x² - 20x + 64 = 0
x² - 16x - 4x + 64 = 0
x(x-16) -4( x- 16)= 0
x= 16, 4
So, the sides lengths are
x= 4 cm, x+1 = 5 cm, 2√x = 4 cm, 2√x = 4 cm.
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Question
Which models represent the sum?
1.2 + 0.3
Select each correct answer.
Responses
Ten by 10 grid of 100 squares. The first column and 2 squares of the second column are shaded one color. The next three columns are shaded another color.
Image with alt text: Ten by 10 grid of 100 squares. The first column and 2 squares of the second column are shaded one color. The next three columns are shaded another color.
One column, divided into 10 small squares. Two small squares. Plus sign. Three columns, each divided into 10 small squares.
Image with alt text: One column, divided into 10 small squares. Two small squares. Plus sign. Three columns, each divided into 10 small squares.
Two 10 by 10 grids of 100 squares. All 10 columns of first square and 2 columns of the second square shaded one color. Three columns of the second square shaded a different color.
Image with alt text: Two 10 by 10 grids of 100 squares. All 10 columns of first square and 2 columns of the second square shaded one color. Three columns of the second square shaded a different color.
Large square divided into a 10 by 10 grid of 100 small squares. Two columns, each divided into 10 small squares. Plus sign. Three columns, each divided into 10 small squares.
Image with alt text: Large square divided into a 10 by 10 grid of 100 small squares. Two columns, each divided into 10 small squares. Plus sign. Three columns, each divided into 10 small squares.
Number line from 0 to 4 by tenths. An arrow shows a jump starting at 0 and ending 2 marks past 1. Another arrow shows a jump starting at 2 marks past 1 and ending at 5 marks past 1.
The models that represent the sum 1.2 + 0.3 are
Option 3 and Option 5
Why are they the models?For Option 3:
The first square represents 1.2, with all 10 columns shaded in one color. The next two columns represent 0.3, shaded in a different color. The sum of 1.2 and 0.3 is 1.5, which is represented by the combination of the two squares.
For Option 5:
On the number line, the first arrow represents 1.2, starting from 0 and ending 2 marks past 1, which is equal to 1.2. The second arrow represents 0.3, starting from 2 marks past 1 and ending at 5 marks past 1, which is equal to 1.5. The sum of 1.2 and 0.3 is 1.5, which is represented by the end point of the second arrow on the number line.
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(3x)^-3 show work pls
Answer: -81x
Step-by-step explanation:
3x times -3= -9x
-9x times -3= 27x
27x times -3= -81x
perform operation and write result in standard form:
(√19+√11i)(√19-√11i)
The value of expression (√19+√11i)(√19-√11i) is 30.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (√19+√11i)(√19-√11i)
Square root of nineteen plus square root of eleven i times to the Square root of nineteen minus square root of eleven times i
We have an algebraic property
(a+b)(a-b)=a²-b²
Take a as √19 and b as √11 i
(√19+√11i)(√19-√11i)=(√19)²-(√11i)²
=19-11(-1)
=19+11
=30
Hence, the value of (√19+√11i)(√19-√11i) is 30.
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given the following integral and value of n, approximate the following integral using the methods indicated (round your answers to six decimal places):
The approximate value of [tex]$\int_{0}^{2} x^4 dx$[/tex] using the trapezoidal rule is 16.
Integral : [tex]$\int_{0}^{2} x^n dx$[/tex]
n = 4
Approximation Method : Trapezoidal Rule
The trapezoidal rule is a numerical integration technique used to approximate the definite integral of a function. It works by approximating the region under the curve of the function with a series of trapezoids, and calculating the area of those trapezoids to estimate the integral.
In the given problem, we have to approximate the definite integral of [tex]$x^4$[/tex] from 0 to 2. The trapezoidal rule for approximating a definite integral is given by
[tex]$\int_{a}^{b} f(x)dx \approx \frac{h}{2} \left( f(a) + f(b) + 2 \sum_{i=1}^{n-1} f(x_i) \right)$[/tex]
where [tex]$f(x)$[/tex] is the function, [tex]$a$[/tex] and [tex]$b$[/tex] are the lower and upper limits of the integral, h is the width of each trapezoid, and $n$ is the number of trapezoids.
In our case, [tex]$f(x) = x^4$, $a = 0$, $b = 2$, $h = \frac{2 - 0}{2} = 1$[/tex] and n = 2.
Substituting these values into the formula, we get
[tex]$\int_{0}^{2} x^4 dx \approx \frac{1}{2} \left( 0 + 16 + 2 \left(x_1^4 + x_2^4 \right) \right)$[/tex]
where [tex]$x_1 = \frac{2 - 0}{2} = 1$ and $x_2 = \frac{2 + 0}{2} = 1$[/tex].
Substituting these values, we get
[tex]$\int_{0}^{2} x^4 dx \approx \frac{1}{2} \left( 0 + 16 + 2 \left(1^4 + 1^4 \right) \right) = 16$[/tex]So, the approximate value of [tex]$\int_{0}^{2} x^4 dx$[/tex] using the trapezoidal rule is 16.
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Find the median and mean of the data set below: 21 , 40 , 48 , 26 , 32 , 31
What does the problem asks for:
--> mean and median
Let's calculate the mean:
[tex]\text{Mean}=\dfrac{\text{sum of all the numbers}}{\text{number of numbers given}}[/tex]
--> the sum of all the numbers = 21 + 40 + 48 + 26+ 32 + 31 = 198
--> number of numbers given: 6
==> let's calculate
[tex]\text{Mean}=\dfrac{198}{6} =33[/tex]
Let's calculate the median
--> Median definition: middle number in an ordered sequence
==> let's order the sequence: 21, 26, 31, 32, 40, 48
--> since there are an even number of numbers, there isn't an exact
middle number
--> thus, we must find the mean of the two numbers closest to the
middle
[tex]\text{Median} = \dfrac{31+32}{2} =\dfrac{63}{2} =31.5[/tex]
Answer: 31.5
Step-by-step explanation:
21, 26, 31, 32, 40, 48
Median
31+32= 63
63÷2= 31.5
Mean
21+26+31+32+40+48=198
198÷6=33
Find the correct volume and round to the nearest tenth. Please I need help!!! Answer both questions
The volume of the given cylinder would be = 1.33mm³
How to calculate the volume of cylinder?The formula that can be used to calculate the volume of the cylinder = v = πr²h
Where,
π = 3.14
r= 0.5mm
h= 1.7 mm
V = 3.14×0.5²×1.7
V= 3.14× 0.25×1.7
V= 1.3345
V= 1.33mm³ ( to the nearest tenth)
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I NEED HELP ASAP PIECEWISE FUNCTION !!!!!
a. The family pays $336.
b. The family's payment when the dental charge is $4500 is $2375.
c. The model that relates payment and charges are,
250 + 0.2x, x < 1500 and 250 + 0.5x, x > 1500.
What is a piecewise function?A function that is piecewise defined by numerous subfunctions, each of which has a separate domain interval for which it is applicable.
Piecewise definition is more of an expression of the function than it is a property of the function.
a. Determining the family's payment if the dental charge is $680.
$650 falls in the category of the first $250 paid by the family and the rest 80% paid by the insurance company.
So, $(680 - 250) = $430.
Therefore, The family pays 250 + 0.2x (when x < 1500).
= 250 + 0.2(430).
= 250 + 86.
= $336.
b. The family's payment when the dental charge is $4500 is,
= 4500 - 250.
= $4250.
So, 250 + 0.5(4250) (when x > 1500).
= 250 + 2125.
= $2375.
c. The model that relates payment and charges are,
250 + 0.2x. (x < 1500) and 250 + 0.5x (x > 1500).
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Select all of the linear transformations from ℝ3 to ℝ3 that are invertible. There may be more than one correct answer.A. Identity transformationB. Projection onto the xz-planeC. Reflection in the y-axisD. Rotation about the x-axisE. Dilation by a factor of 6F. Projection onto the z-axis
A linear transformation is a function from one vector space to another that preserves each vector space's underlying (linear) structure. A linear transformation can also be referred to as a linear operator or map.
The correct answers are A, D, and E.
A linear transformation from ℝ3 to ℝ3 is invertible if and only if it is bijective, meaning it is both one-to-one and onto.
The following linear transformations are invertible:
A. Identity transformation: The identity transformation maps every vector to itself and is one-to-one, so it is invertible.
D. Rotation about the x-axis: A rotation about the x-axis is a bijective linear transformation that maps each point in ℝ3 to another point in ℝ3 in a one-to-one manner, so it is invertible.
E. Dilation by a factor of 6: A dilation by a factor of 6 scales every vector by 6, and the scaling factor is nonzero, so this transformation is bijective and invertible.
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the two systems have the same coefficient matrix but different right-hand sides. solve both systems simultaneously by eliminating the first entry in the second row of the augmented matrix: [ ] and then performing back substitutions for each of the columns corresponding to the right-hand sides.
The first system points are (2,-1) and the second system points are (-2,3).
The elementary row operations can be used to solve a system of equations in an easy way and used to find the rank of a matrix.
There are three types of elementary row operations:
1) Interchanging two rows.
Interchanging the first and second rows is given by R₁ ↔ R₂.
2) Multiplying/dividing a row by a scalar.
If the first row is multiplied by some scalar, with 3, it is measured as
R₁ → 3R₁.
3) Multiplying/dividing a row by some scalar and adding/subtracting to the corresponding elements of another row.
If the first row is multiplied by 3 and added to the second row, we can write it as R₁ → 3R₁ + R₂ (or) R₂ → R₂ + 3R₁.
Now by using the elementary row operation we can find the system of equations:
The given systems are:
2x₁+x₂=3 2x₁+x₂=-1
4x₁+3x₂=5 4x₁+3x₂=1
and the matrix is
[tex]\left[\begin{array}{cccc}2&1|&3&-1\\4&3|&5&-1\\\end{array}\right][/tex]
Apply elementary row operation
R₂-2R₁
[tex]\left[\begin{array}{cccc}2&1|&3&-1\\4&3|&5&-1\\\end{array}\right]--- > \left[\begin{array}{cccc}2&1|&3&-1\\0&1|&-1&3\\\end{array}\right][/tex]
Now Apply R₁-R₂
[tex]\left[\begin{array}{cccc}2&0|&4&-4\\0&1|&-1&3\\\end{array}\right][/tex]
Apply R₁/2
[tex]\left[\begin{array}{cccc}1&0|&2&-2\\0&1|&-1&3\\\end{array}\right][/tex]
The two linear systems are
x₁+0=2 x₁+0=-2
0+x₂=-1 0+x₂=3
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Describe the mistake that was made in solving the following equation:
The mistake is in the second step, where the sign of the "4" is changed. The real solution is x = -5
Which one is the mistake in the solution of the equation?Here we have the solution of the following equation:
4x + 6 = 2x - 4
First, they subtract 2x from both sides, then we will get:
4x + 6 - 2x = 2x - 4 - 2x
2x + 6 = -4
While notice that in the image, in this step they wrote:
2x + 6 = 4
They changed the sign of the 4, there is the mistake.
Now we can keep solving our equation:
2x + 6 = -4
2x = -4 - 6
2x = -10
x = -10/2
x = -5
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For which values of x is the expression undefined?
x+8/3x+4
The value of x that makes the expression undefined is given as follows:
x = -4/3.
How to make the expression undefined?The expression for this problem is presented as follows:
(x + 8)/(3x + 4).
As it is a fractional expression, it will be undefined when the denominator assumes a value of zero.
The denominator of a fraction is the value at the bottom, hence it is given as follows:
3x + 4.
Hence the value of x that makes the expression undefined is obtained as follows:
3x + 4 = 0
3x = -4
x = -4/3.
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