Answers
12 = 1/3x
The first thing you want to do when solving a system of equations is isolating one of the variables.
Since the second equation only contains x, we can isolate x in the first equation.
y - x = 9
y = x + 9
x = y - 9
You can also solve the second equation without any previous solving.
12 = 1/3x
Multiple both sides by 3/1 or 3
x = 36
Now we can set them equal to each other
36 = y - 9
y = 45
Answer: x = 36 and y = 45
Answer:
The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect. To solve a system is to find all such common solutions or points of intersection.
Step-by-step explanation:
Isolate x for 12=1/3x: x=36
[y - 36=9]
the solutions to the system of equation is:
y=45 x=36
Related Questions
NO LINKS!!
Use the properties to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive)
1. ln((xy)^5)
2. ln (seventh root(t))
3. ln (√x²/y^5)
Answers
Properties of log:
[tex]log\ ab=log\ a + log\ b[/tex][tex]log\ a/b =log\ a-log\ b[/tex][tex]log\ a^b=b\ log\ a[/tex]Evaluate given using the properties above:
Q1
[tex]ln((xy)^5) = 5ln(xy) = 5(ln x + ln y) = 5\ ln\ x + 5\ ln\ y[/tex]Q2
[tex]ln(\sqrt[7]{t} ) = ln(t^{1/7})=1/7\ ln\ t[/tex]Q3
[tex]ln(\sqrt{x^2}/y^5)=ln(x/y^5)= ln\ x - ln\ y^5 = ln\ x - 5\ ln\ y[/tex]Answer:
[tex]\textsf{1.} \quad 5 \ln x + 5 \ln y[/tex]
[tex]\textsf{2.} \quad \dfrac{1}{7} \ln t[/tex]
[tex]\textsf{3.} \quad \ln x - \dfrac{5}{2}\ln y \;\; \;\;\textsf{or} \;\;\;\; \ln x - 5\ln y[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Natural log laws}\\\\Product law: \;$\ln xy=\ln x + \ln y$\\\\Quotient law: $\ln \left(\dfrac{x}{y}\right) = \ln x - \ln y$\\\\Power law: \;\;\;\;$\ln x^n=n \ln x$\\\end{minipage}}[/tex]
Question 1Apply the power law followed by the product law:
[tex]\begin{aligned}\ln (xy)^5 & = 5 \ln (xy)\\ & = 5\left( \ln x + \ln y \right) \\ & = 5 \ln x + 5 \ln y\end{aligned}[/tex]
Question 2[tex]\textsf{Apply the exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}[/tex]
then apply the power law:
[tex]\begin{aligned}\ln \sqrt[7]{t} & = \ln t^{\frac{1}{7}} \\ & = \dfrac{1}{7} \ln t\end{aligned}[/tex]
Question 3It is not completely clear where the square root sign begins and ends, so I have provided answers for both permutations:
[tex]\begin{aligned}\ln \left(\sqrt{\dfrac{x^2}{y^5}}\right) & = \ln \left(\dfrac{\sqrt{x^2}}{\sqrt{y^5}}\right) \\\\& = \ln \left(\dfrac{x}{y^{\frac{5}{2}}}\right) \\\\&=\ln x - \ln y^{\frac{5}{2}}\\\\&=\ln x - \dfrac{5}{2}\ln y\end{aligned}[/tex]
[tex]\begin{aligned}\ln \left(\dfrac{\sqrt{x^2}}{y^5}\right)& = \ln \left(\dfrac{x}{y^5}\right) \\\\&=\ln x - \ln y^5\\\\&=\ln x - 5\ln y\end{aligned}[/tex]
A certain game keeps track of the maximum and minimum scores obtained so far. If num represents the most recent score obtained, which of the following algorithms correctly updates the values of the maximum and the minimum?
Answers
following algorithms correctly updates the values, If num is less than the minimum, set the minimum equal to num. Otherwise, if num is greater than the maximum, set the maximum equal to num.
What is algorithm ?An algorithm is a process used to carry out a computation or solve a problem. In either hardware-based or software-based routines, algorithms function as a detailed sequence of instructions that carry out predetermined operations sequentially.The game records the highest and lowest scores that were earned. This indicates that the game already has the highest and lowest score stored in its memory.
Now, if a new score, num, is achieved, the game must compare num with the minimum and maximum scores in order to update the minimum and maximum scores. The minimum score is updated to the score, num if the most recent score, num, is lower than the minimum score.
Additionally, the maximum score is updated to the score, num if the most recent score, num, is higher than the maximum score.
Complete Question :
A certain game keeps track of the maximum and minimum scores obtained so far. If num represents the most recent score obtained, which of the following algorithms correctly updates the values of the maximum and the minimum?
If num is greater than the minimum, set the minimum equal to num. Otherwise, if num is greater than the maximum, set the maximum equal to num.If num is less than the minimum, set the minimum equal to num. Otherwise, if num is greater than the maximum, set the maximum equal to num. If num is less than the minimum, set the minimum equal to num. Otherwise, if num is less than the maximum, set the maximum equal to num. If num is greater than the minimum, set the minimum equal to num. Otherwise, if num is less than the maximum, set the maximum equal to num.To learn more about algorithm refer,
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Complete the following.
(a) Consider the following statement.
The water temperature is 70.
Check all the statements below that are negations of this statement.
The water temperature is less than 80.
It is not the case that the water temperature is 70.
The water temperature is not 70.
(b) Consider the following conditional statement.
If the dress is red, then Keisha likes the dress.
What is the conclusion of this statement?
It is not true that Keisha owns a dress.
Keisha likes the dress.
The dress is red.
Keisha loves the dress.
The dress likes Keisha.
Answers
a) The option that is a negation of the given statement is; The water temperature is not 70.
b) The conclusion of the given conditional statement is; Keisha likes the dress.
How to Interpret Conditional Statements?In mathematics, a conditional statement is defined as a statement that can be written in the form “If P then Q,” where P and Q are sentences.
a) We are given the statement as;
The water temperature is 70.
Now, negation is a false/opposite form of the given statement and as such among the options, the only one that is a negation is that
"The water temperature is not 70."
b) We are given the conditional statement as;
If the dress is red, then Keisha likes the dress.
Thus, the conclusion of this is that likes the dress.
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A hospital director is told that 54% of the emergency room visitors are insured. The director wants to test the claim that the percentage of insured patients is under the expected percentage. A sample of 120 patients found that 60 were insured. Find the value of the test statistic. Round your answer to two decimal places.
Answers
According to question,
Given data,
A hospital director is told that 54% of the emergency room visitors are insured.
A sample of 120 patients found that 60 were insured.
We know that,
To determine the percentage,
we have to divide the value by the total value and then multiply the resultant by 100,
Percentage formula
Is /of=%?100
Or
Part/whole=%/100
With the help of formula,
Part/sample of patient=%/100
60×100/120=50%
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Neglecting air resistance and the weight of the propellant, determine the work done in propelling a 10-ton satellite to a height of 200 miles above Earth. Assume that the Earth has a radius of 4000 miles. O 4.190.48 mi-ton 1,142.86 mi-ton O 1,904.76 mi-ton 2,857.14 mi-ton 1,523.81 mi-ton
Answers
Therefore ,the the the work done in propelling a 10-ton satellite to a height of 200 miles above Earth is 1904.7619 million ton.
Analyze the equation.An expression is composed of a number, a variable, both, or neither, and specific operation symbols. An equation is made up of two expressions, which are separated by an equal sign.
Here,
Use F(x) = C/[tex]x^{2}[/tex]
Where c is a constant and x is the radius of the earth
F(x) is satellite weight
We have to find c.
thus,
=> 10 = c /[tex]4000^{2}[/tex]
=> c =160000000
Therefore,
=> F(x) = 160000000/ [tex]x^{2}[/tex]
Workdone ,
=> W = [tex]\int\limits^{4200}_{4000} {F(x)} \, dx[/tex]
=>W = [tex]\int\limits^{4200}_{4000} {160000000 /x^{2} } \, dx[/tex]
=>W =[tex]\left \{ {{4200} \atop {4000}} \right. \frac{-160000000 }{x}[/tex]
=> W =1904.7619 million ton
Therefore ,the the the work done in propelling a 10-ton satellite to a height of 200 miles above Earth is 1904.7619 million ton.
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Please help!!!!!!!!!!!!
Answers
The value of variable x in the equation is x = -3y + 5/ 2
How to solve an equation for a variable?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Therefore, the equation 2x + 3y = 5 can be solved for x as follows:
We have to make x the subject of the formula in the equation.
Subject of the formula is the variable which is expressed in terms of other variables involved in the formula.
Hence,
2x + 3y = 5
subtract 3y from both sides of the equation
2x + 3y = 5
2x + 3y - 3y = 5 - 3y
2x = 5 - 3y
divide both sides by 2
Therefore,
x = 5 - 3y / 2
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Last week Scott ran 43 miles less than James. Scott ran 5 miles. How many miles did James run?
A. 35
B. 44
C. 38
D. 48
Answers
Answer:
D) 48
Step-by-step explanation:
Let s = Scott
Let j - James
s = 5
s + 43 = j Substitute 5 for s
5 + 43 = j
48 = j
It is known that 25 % percent of Americans identify themselves as republican . In a random sample of n=20 Americans , what is the expected number of republicans ? It is known that 25 % percent of Americans identify themselves as republican . In a random sample of n=20 Americans , what is the standard deviation of the number of republicans ? ( Round to 2 decimal places )
Answers
Using percentages, we know that out of 20 people, 5 people that is 25% of the random sample consider themselves as republicans.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics.
We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.
So, we have a random sample of 20 people.
n = 20
And we also know that 25% of Americans identify themselves as republicans.
Then the number of republicans in 20 people would be:
20/100 * 25
.2 * 25
5
Therefore, using percentages, we know that out of 20 people, 5 people that is 25% of the random sample consider themselves as republicans.
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Rory is an independent filmmaker and has great ideas for several movies. For each short film or full-length movie she makes, she has to raise money. She figures that it will take 7 months to raise money for each short film and 7 months to raise money for each full-length movie. She has given herself at most 49 months to raise money for the films before she abandons the project.
1
While Rory is raising money, she also has to write the scripts. It will take her of a month to write each short film script and 2 months to write each full-length movie script. She is committed to spending at most 13 months on writing scripts.
a. What is the system of inequalities that models this scenario?
b. What is the graph of the solutions?
continued
Answers
The required inequality expressions are 7x + 7y ≤ 49 and x + 2y ≤ 13 an the graph has been plotted with clarity.
How to write an expression for linear inequality?The expression for inequality can be written by taking the suitable sign for the given problem and then relating the variable part to the constant terms.
(a) Suppose the number of short film and full movie are x and y respectively.
Then, the inequality expression for the given case can be written as follows,
The inequality for money raised is,
7x + 7y ≤ 49
And, the inequality for script writing is,
x + 2y ≤ 13
(b) These inequalities can be graphed as follows,
Hence, for the given case the required system of inequalities is 7x + 7y ≤ 49 and x + 2y ≤ 13 and the graph for the solution is drawn properly.
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2. The width, w, of a rectangular garden is x-2. The area of the garden is ³-2x-4. What is
an expression for the length of the garden?
Ox²-2x-2
Ox²+2x-2
Ox²-2x+2
Ox²+2x+2
Answers
Consequently, the rectangular garden's length is [tex]x^{2} +2x+2[/tex]
option D is correct
what is area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. Surface area refers to an open surface or the perimeter of a three-dimensional object, whereas plane region or plane area refers to a shape or planar lamina.
given
the width(w) of the rectangular garden= [tex]x[/tex][tex]-2[/tex]
area of the rectangular garden = [tex]x^{3} -2x-4[/tex]
The area of a rectangle is,
area = length × width(w) ,
If l is the rectangle's length,
w is the width of the rectangle,
By substituting values,
[tex]x^{3}-2x-4[/tex] = ([tex]x-2[/tex]) * length ( l )
[tex]l=\frac{x^{3}-2x-4 }{x-2}[/tex] = [tex]x^{2} +2x+2[/tex] (by long division method)
Consequently, the rectangular garden's length is [tex]x^{2} +2x+2[/tex]
option D is correct
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A quiz team of 5 children is to be selected from a class of 25 children. There are 15 girls and 10 boys in the class. (a) How many teams made up of 3 girls and 2 boys can be selected? (b) How many teams can be selected with at least 3 girls?
Answers
Using combination we get 20475 teams can made up of 3 girls and 2 boys and 37128 teams can be selected with at least 3 girls.
Why does combination mean?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.Since this is just a team of 5 children,
we have no of girls = 15
No of boys = 10
teams made up of 3 girls and 2 boys
girls out of 3 girls can be selected in ¹⁵C₃ ways and
2 boys out of 10 boys can be selected in ¹⁰C₂ ways.
[tex]\implies[/tex] ¹⁵C₃ X ¹⁰C₂
= 455*45 =20475 Ways
Teams can be selected with at least 3 girls
It is the probability of at least 3 girls which means P(3 girls,2 boys) or P(4 girls,1 boy) or P(5 girls, 0 boys)
[tex]\implies[/tex] ¹⁵C₃ X ¹⁰C₂ + ¹⁵C₄ X ¹⁰C₁ + ¹⁵C₅ X ¹⁰C₀
= 455 * 45 +1365*10+3003*1
=20475 +13650 +3003
=37128 ways
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Jen drew a scale drawing of a summer camp
Answers
Answer:
This is a statement. Not a question.
Step-by-step explanation:
Given the graph of f(x), determine the range of f−1(x).
Rational function with one piece decreasing from the left in quadrant 2 asymptotic to the line y equals 3 and passing through the point 0 comma 2 and asymptotic to the line x equals 2 and another piece decreasing from the left in quadrant 1 asymptotic to the line x equals 2 passing through the point 4 comma 4 asymptotic to the line y equals 3.
ℝ
(2, ∞)
(−∞, 2) ∪ (2, ∞)
(−∞, 3) ∪ (3, ∞)
Answers
Given the graph of f(x), the range of f⁻¹(x) is; (−∞, 2) ∪ (2, ∞)
How to find the range of the function?The range of a function is defined as the set that is composed by all the output values on a function. Thus, on the graph, the range of a function is composed by the values of y of the function.
For the inverse function, the input and the output are exchanged, and as such given the graph of a function, we can say that the range of the inverse function is given by the domain of the initial function, which is, the values of x of the graph of the original function.
From the description of the rational function, we are told that the asymptote is given as: x = 2
Thus, the domain of the graphed function, would be the same as the range of the inverse function, will be given by the interval:
(−∞, 2) ∪ (2, ∞).
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An account executive receives a base salary plus a commission. On $50,000 in monthly sales, the account executive receives $6500. On $60,000 in monthly sales, the account executive receives $6800.
(a) Determine a linear function that will yield the compensation y of the sales executive for a given amount of monthly sales x.
(b) Use this model to determine the account executive's compensation for $90,000 in monthly sales.
$
Answers
A) A linear function that will yield the compensation y of the sales executive for a given amount of monthly sales x is;
B) The account executive's compensation for $90,000 in monthly sales is; $300
How to model a linear equation?
The general equation of a line in slope intercept form is;
y = mx + b
where;
m is slope
b is y-intercept
x and y are provided in the problem: x = monthly sales and y = compensation
We will have to find m (Slope), which represents the commission percentage, and b (y-intercept), which represents the the base salary.
x₁ y₁ x₂ y₂
(50000, 6500) (60000, 6800)
Slope;
m = (y₂ - y₁) / (x₂ - x₁)
m = (6800 - 6500) / (60000 - 50000)
m = 300/10000
m = 3/100 = 0.03 = 3%
To find b, we have to take one of our ordered pairs [ (50000, 6500) or (60000, 6800) ] and plug it into the equation, y=mx+b.
Let's use (60000, 6800)
6800 = 0.03(60000) + b
6800 = 1200 + b
b = 6800 - 1200
b = $5600
The base salary = $5600
The equation is y = 0.03x + 5600
b) For $90000 in monthly sales, the executive's compensation is;
y = 0.03(90000) + 5600
y = 2700 + 5600
y = $300
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Solve:(6x^2+5x+1)÷(x+2)
Answers
Answer:
6x+6x2+3
Step-by-step explanation:
6x2+5x+1+x+2
Combine 5x and x to get 6x.
6x2+6x+1+2
Add 1 and 2 to get 3.
6x2+6x+3
What values of v and w make Δ P Q R ≅ Δ K J I ?
v=_____
w=_____
Answers
The values of v and w that will make ΔPQR congruent to ΔKJI are:
v = 12; w = 20.
What are Congruent Triangles?Based on the CPCTC, every corresponding sides and corresponding angles of two congruent triangles are equal to each other.
Therefore, given that ΔPQR ≅ ΔKJI
PR = KI, and QR = JI
Substitute the values:
5v = 6v - 12
5v - 6v = -12
-v = -12
v = 12
w - 1 = 3w - 41
w - 3w = 1 - 41
-2w = -40
w = -40/-2
w = 20
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if the circumference of a circle is 5cm, then the diameter is ____cm.
a. 5 cm
b. 31.4 cm
c. 15.7 cm
d. 1.57 cm
Answers
C=2πr
The circumference, “C,” is 5cm
5=2πr
Let’s rewrite the formula using the commutative property of multiplication so we can solve for “d:”
5=π2r
The order in which numbers are multiplied does not affect the product. Since the diameter is double the radius, 2r will equal the diameter since 2r equals r+r. So, we can substitute “d” in for 2r:
5=πd
Now, let’s solve for d
Divide both sides by pi:
5/π=d
1.591=d
We can check this back into the formula:
C=π(1.591)
C=4.998
So, your answer is 1.57 since it is the closest.
when conducting a study comparing more than two groups of parametric (normally distributed) data, which of the following statistical tests should be used? g
Answers
Answer:
.
Step-by-step explanation:
sorry i hit my daily limit and i need more answers
Question 1-28
What is the range of possible values for x?
B
A
8.2
11.7
(11x-4)
D
84°
C
Answers
The range of possible values for x is 4/11 < x < 8
How to determine the range of possible values for x?From the question, we have the following parameters that can be used in our computation:
Triangles = 2
On these triangles, we have the following angles
Angle 1 = 11x - 4
Angle 2 = 84
Angle 1 cannot exceed angle 2
So, we have
11x - 4 < 84
Add 4 to both sides
11x < 88
Divide
x < 8
Angle 1 cannot exceed be negative or 0
So, we have
11x - 4 > 0
Add 4 to both sides
11x > 4
Divide
x > 4/11
Hence, the range is 4/11 < x < 8
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For each diagram below, work out whether AB is a tangent to the circle, is not a
tangent to the circle, or if it is not possible to tell.
Justify your answers.
13 cm
5 cm
12 cm
10 cm
4 cm
11 cm
18 cm
18 cm
25 cm
Not drawn accurately
Answers
The tangent AB is for circle in figure (a).The correct option is (a).
What is the relation between the tangent and a circle?For a given circle there can only be one tangent at one point.
The tangent and the circle has only one point in common.
The tangent to a circle is always perpendicular to the radius at that point.
The tangent drawn to a circle is always at right angle to the radius at that point.
The given figures are examined one by one as follows,
(a) The sides of the triangle are given as 5, 12 and 13.
And, 13² = 5² + 12²
Which implies it is a right triangle by Pythagoras theorem.
(b) The sides of the triangle are given as 4, 10 and 11.
And, 11² ≠ 10² + 4²
Which implies it is not a right triangle by Pythagoras theorem.
(c) The sides of the triangle are given as 18, 25 and 18.
And, 25² ≠ 18² + 18²
Which implies it is not a right triangle by Pythagoras theorem.
Thus, only for figure (a) the criteria for the tangent satisfies.
Hence, the line segment AB is tangent to the circle given in figure (a).
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Emma wrote 8.4x+6.3x+12.6 as an equivalent expression for 4.2(2x+1.5x+3). She said that her equivalent expression is simplified. Do you agree? Explain.
Answers
Yes, I agree that this equivalent expression has been simplified.
The solutions to these issues are as follows
Reorder and gather like terms: (8.4x +6.3 x) +12.6
Collect coefficients for the like terms: (8.4 +6.3) × x +12.6
Calculate the sum or difference: 14.7 x +12.6
Answer : 14.7 x + 12.6
What exactly is equivalent expression, and how do we recognize it?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).
Distribute any coefficients.Combine any like terms on each side of the equation.Arrange the terms in the same order, usually x-term before constants.If all of the terms in the two expressions are identical, then the two expressions are equivalent.To learn more about coefficients refer to:
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NO LINKS!!
Find the average rate of change of the function from x1 to x2.
function f(x) = -9x + 4
x-values x1 = -5, x2 = 0
Answers
Answer:
-9
Step-by-step explanation:
Given function:
[tex]f(x)=-9x+4[/tex]
Given x-values:
x₁ = -5x₂ = 0Calculate the value of the function for the two given values of x:
[tex]\begin{aligned}\implies f(x_1)&=-9(-5)+4\\&=45+4\\&=49\end{aligned}[/tex]
[tex]\begin{aligned}\implies f(x_2)&=-9(0)+4\\&=0+4\\&=4\end{aligned}[/tex]
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Average rate of change of function $f(x)$}\\\\$\dfrac{f(b)-f(a)}{b-a}$\\\\over the interval $a \leq x \leq b$\\\end{minipage}}[/tex]
As -5 < 0:
a = x₁ = -5b = x₂ = 0Therefore:
[tex]\begin{aligned} \implies \textsf{Average rate of change}&=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}\\\\&=\dfrac{4-49}{0-(-5)}\\\\&=\dfrac{-45}{5}\\\\&=-9\end{aligned}[/tex]
Construct a cumulative frequency distribution
765-799| 22
Answers
The steps to construct a cumulative frequency distribution table are mentioned above.
What is cumulative frequency distribution? What is a mathematical function, equation and expression? cumulative frequency : A cumulative frequency is defined as the total of frequencies, that are distributed over different class intervals. function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is to construct a cumulative frequency distribution table.
Since the data is not given, we can write the steps to construct a frequency distribution table. The steps to create a cumulative frequency distribution table are mentioned below -
find the individual frequencies for each distinct value or category.arrange the obtained data in ascending order.the cumulative frequency of a distinct category is calculated by finding the sum of a category’s frequency and the total frequencies of all categories below it. the cumulative frequency of the first category equals the category’s individual frequency.Therefore, the steps to construct a cumulative frequency distribution table are mentioned above.
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what is a acute angle
Answers
Answer: Measure less 90 degrees
Step-by-step explanation: Less than 90 degrees measure acute angle. 90 degrees in right corner. Obtuse corners are larger than 90 degrees
can I get help with this practice I'm having a lot of trouble with this can I get some help
Answers
The formula to find the slope is m = (y₂ - y₁)/(x₂ - x₁), hence option B is correct and the slope of the line will be -1/2.
What is slope?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
As per the data mentioned in the question,
1.
The formula to find the slope of the line between two points is,
m = (y₂ - y₁)/(x₂ - x₁)
2.
The given points are,
(-4, 3) and (12, -5)
So, the slope of the line that connects given points,
m = (-5 - 3)/(12+4)
m = -8/16
m = -1/2
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An investor decides to invest some cash in an account paying12%
annual interest, and to put the rest in a stock fund that ends up earning 8%over the course of a year. The investor puts $1500more in the first account than in the stock fund, and at the end of the year finds the total interest from the two investments was $1880. How much money was invested at each of the two rates? Round to the nearest integer.
Answers
Let A be the amount of money invested at a 12% annual interest rate and B be the amount of money invested at a 8% annual interest rate.
We know that A = B + 1500, and the total interest earned by the two investments is $1880.
The interest earned by the investment at a 12% annual interest rate is 0.12 * A = 0.12A
The interest earned by the investment at a 8% annual interest rate is 0.08 * B = 0.08B
Therefore, we can write the following equation to represent the situation:
0.12A + 0.08B = 1880
Since A = B + 1500, we can substitute this into the equation to get:
0.12(B + 1500) + 0.08B = 1880
Solving for B, we get:
0.12B + 180 + 0.08B = 1880
Combining like terms, we get:
0.2B + 180 = 1880
Subtracting 180 from both sides, we get:
0.2B = 1700
Dividing both sides by 0.2, we get:
B = 8500
Since A = B + 1500, we can substitute this value into the equation to find the value of A:
A = 8500 + 1500 = 10000
Therefore, the investor invested $8,500 at an 8% annual interest rate and $10,000 at a 12% annual interest rate.
Answer:
Account A (12%)= $10,000
Account B (8% stock fund) = $8,500
Step-by-step explanation:
Annual Interest Formula
[tex]\large \text{$ \sf I=P\left(1+r\right)^{t} -P$}[/tex]
where:
I = Interest.P = Principal amount.r = Interest rate (in decimal form).t = Time (in years).Account A:
P = x + 1500r = 12% = 0.12t = 1 year[tex]\implies \sf Interest=(x+1500) (1+0.12)^1-(x+1500)[/tex]
[tex]\implies \sf Interest=(x+1500) (1+0.12)-(x+1500)[/tex]
[tex]\implies \sf Interest=(x+1500)+0.12(x+1500)-(x+1500)[/tex]
[tex]\implies \sf Interest=0.12(x+1500)[/tex]
[tex]\implies \sf Interest=0.12x+180[/tex]
Account B (stock fund):
P = xr = 8% = 0.08t = 1 year[tex]\implies \sf Interest=x (1+0.08)^1-x[/tex]
[tex]\implies \sf Interest=x (1+0.08)-x[/tex]
[tex]\implies \sf Interest=x+0.08x-x[/tex]
[tex]\implies \sf Interest=0.08x[/tex]
If the total interest from the two investments was $1880:
[tex]\implies \sf 0.12x+180+0.08x=1880[/tex]
[tex]\implies \sf 0.2x+180=1880[/tex]
[tex]\implies \sf 0.2x=1700[/tex]
[tex]\implies \sf x=8500[/tex]
Therefore, the money invested in each of the two accounts is:
Account A = $8,500 + $1,500 = $10,000Account B = $8,500Which of the following is a subspace of R^3? (A) All vectors of the form(0, a, a^2), (B) All vectors of the form(a+2, a, 0), (C) All vectors of the form (a, b, 2), (D) All vectors of the form(a, b, a-2b)
Answers
All vectors of the form(a, b, a - 2b) is a subspace of R³. So, the correct option is option(D).
Subspace:If W is a set of one or more vectors from a vector space V, then W is a subspace of V if and only if
If u and v are vectors in W, then u + v in W. ku is in W if k is any scalar and u is any vector in W.Now, check the options and find out the option which satisfy the subspace conditions.
A) All the vectors are of form (0, a,a²)
let (0,1,1) = u and v=(0,2,4) and both are belongs to { 0, a,a² : a∈R }, (0,0,0)∈ {0, a,a² : a∈R }.
u + v = (0,1,1) + (0,2,4) = (0,3, 5) not belongs to
{ 0, a,a² : a∈R }. So, this is not correct option.
B) Here, (0,0,0) does not belongs to
{0, a, a+2 : a∈R } because if a= 0 then a+2 =/ 0 .
So, it is also not subspace.
C) All vectors of the form (a, b, 2)
The third tuple is 2 which never be equal to zero. Hence, (0,0,0) does not belongs to (a, b, 2) and it is not form subspace.
D) All vectors of the form (a, b, a - 2b)
When a = 0 , b = 0 => (0,0,0) ∈(a, b, a - 2b)
let u = ( a1, b1 , a1- 2b1) and v = ( a₂, b₂ , a₂ - 2b₂)
and α∈R
u + v = ( a₁, b₁ , a₁- 2b₁ ) + ( a₂, b₂ , a₂ - 2b₂)
= ( a₁ +a₂ , b₁+b₂ , a₁+a₂ -2(b₁ - b₂)) €(a, b, a - 2b)
αu = α(a₁ , b₁ , a₁- 2b₁)
=( αa₁ , αb₁ , α(a₁ - 2b₁))∈(a, b, a - 2b)
both the conditions are satisfied, so it is Subspace of R³.
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Convergence or Divergence? Prove using a test.
Answers
√1+2•0/2+0+0
1/2
N—> ∞
Converges
*What two numbers have a sum of 352 and a difference of 104?
Answers
Answer:
124 and 228
Step-by-step explanation:
Two numbers will be presented as x and y
x + y = 352
x - y = 104
x + y + x - y = 352 + 104
2x = 456
Divide both side by 2
x = 228
x + y = 352
y = 352 - x
y = 352 - 228
y = 124
In Game 1, Emerson struck out 30 times in 90 times at bat. In Game 2, he struck out 40 times in 120 times at bat. In Game 3, Emerson struck out 42 times in 140 times at bat.
What percentage of times at bat did Emerson actually hit the ball?
%
Answers
Emerson actually hit the ball 32% of times at bat.
What is percentage ?
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.
Since in Game 1, Emerson struck out 30 times in 90 times at bat;
in Game 2, he struck out 40 times in 120 times at bat;
in Game 3, Emerson struck out 42 times in 140 times at bat;
To determine what percentage of times at bat did Emerson actually hit the ball, the following calculation must be performed:
(30 + 40 + 42) / (90 + 120 + 140) = X
112/350 = X
0.32 = X
Therefore, Emerson actually hit the ball 32% of times at bat.
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