By using the alternating series estimation theorem we found that the number of terms we need to add in order to find the sum with an error less than 0.0001 is 7.
We must employ one of the convergence tests to determine whether the provided series is convergent or divergent. The alternating series test, which states that a series converges if it takes the form ∑ [tex](-1)^{n}[/tex] x an, where 'an' is a decreasing sequence of positive terms, is the most applicable test for this series.
∑ [tex](-1)^{n}[/tex] x an
a n = [tex]\frac{(n + 1)}{(n^2 + 2n + 3)}[/tex]
by taking the derivative of the expression for a n, this sequence is decreasing and showing that it is always negative. given by a'n = [tex]\frac{(n + 1)}{(n^2 + 2n + 3)}[/tex] [tex]- \frac{(n + 1) X 2)}{(n^2 + 2n + 3)^2}[/tex]
= [tex]\frac{(-2n - 2)}{(n^2 + 2n + 3)^2}[/tex]
for all values of n it is negative, therefore the sequence a n is decreasing. Thus, given series satisfies the conditions of the alternating series test. Therefore, the series is convergent.
The alternating series estimation theorem can be used to determine how many terms are required to be added in order to find the total with an error of less than 0.0001. This asserts that the first disregarded term in an alternating series is smaller than the error in the series' sum. The error in the sum of the series with N + 1 terms is therefore smaller than the value of the (N + 1)th term in the series if we add N terms to the series and the error is less than E.
Find the first term in the series that is less than 0.0001 in order to calculate the number of terms we must add to the series in order to find the total with an error smaller than 0.0001.
given series that a 1 = [tex]\frac{2}{4}[/tex] = 0.5, a 2 = [tex]\frac{3}{9}[/tex] = 0.333, a 3 = [tex]\frac{4}{16}[/tex] = 0.25, and a 4 = [tex]\frac{5}{25}[/tex] = 0.2. Since the first term that is less than 0.0001 is a 7 = [tex]\frac{8}{64}[/tex] = 0.125, Adding, 7 terms to the series in order to find the sum with an error less than 0.0001.
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nora has $640 to spend at a bicycle store for some new gear and biking outfits. assume all prices listed include tax. she buys a new bicycle for $418.55. she buys 2 bicycle reflectors for $19.39 each and a pair of bike gloves for $27.23. she plans to spend some or all of the money she has left to buy new biking outfits for $38.86 each. use the drop-down menu below to write an inequality representing oo, the number of outfits she can buy while staying within her budget.
Layla should by not more than 4 outfits in order not to exceed her budget
The inequality expression is n ≤ 4
price of a new bicycles = $418.55
2 bicycle reflectors = $19.39
a pair of bike gloves = $27.23
new biking outfits = $38.86 each
Nora's total money to spend at a bicycle store = $38.86
How to write the required inequalityLayla's spending will never exceed the total spending at the bike shop, so it will be less than or equal to the total of other items
We write the expression as;
$640 ≤ $418.55 + 2 * $19.39 + $27.23 + n * $38.86
where n represents the number of the new biking outfits
$640 - ( $418.55+ 2 * $19.39 + $27.23 ) ≤. + n * $38.86
( $640 - ( $418.55 + 2 * $19.39 + $27.23 ) ) / $38.86≥ n
( $640 - $484.56 ) / $38.86 ≥ n
( $155.44) / $38.86 ≥ n
4 ≥ n
Layla should by not more than 4 outfits in order not to exceed her budget
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Assume that the game playthrough times for a newly released puzzle game has a mean of 49.8 minutes and a standard deviation of 4.2 minutes. A sample of size n39 playthrough times is randomly selected from a gaming population. What is the probability that the sample.mean is in between 50 minutes and 51 minutes? You may use a calculator or the portion of the z-table given below. Round your answers to three decimal places where appropriate
The probability that the sample mean is in between 50 minutes and 51 minutes is 0.345.
How to calculate probability?
n = sample size = 39
σ = standard deviation =4.2
μ = population mean = 49.8
Probability is the chance that an event can occur, in this case probability is used to measure the chance sample mean is between 50 minutes and 51 minutes. So,
P(50 ≤ x ≤ 51) = P([tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex] ≤ z ≤ [tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex])
= P([tex]\frac{50-49.8}{\frac{4.2}{\sqrt{39}}}[/tex] ≤ z ≤ [tex]\frac{51-49.8}{\frac{4.2}{\sqrt{39}}}[/tex])
= P(0.30 ≤ z ≤ 1.78)
= P(z ≤ 1.78) - P(z ≤ 0.3)
using z table and we get,
= 0.9625 - 0.6179
= 0.3446
= 0.345
Thus, the probability is 0.345 for the sample mean is within 50 and 51.
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Which of the following represents a one to one function?A.Students to thier height B.Students to their weight C.Students to their LRN D.Students to their age
(Option C. Students to their LRN) In this case, each student has a unique LRN, meaning that it can be used in a one-to-one function where each student is mapped to their LRN.
Which of the following represents a one-to-one function?Option C. Students to their LRNA one-to-one function is a type of function where each element in the domain has one and only one image in the range. In this case, each student can be mapped to their LRN (Learning Reference Number) in a one-to-one function. This means that for every student, there is a unique LRN, and for every LRN, there is a unique student. This type of function is useful for keeping track of individual student information, as each student has a unique LRN associated with them.
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Find the point in the first quadrant where the line y = 4 x intersects a circle of radius 5 centered at the origin.
The graph of the point of intersection is given below.
The point of intersection.
(5/√17, 20/√17) and (-5/√17, 20/√17)
What is a circle?A circle is a two-dimensional figure with a radius and circumference of
2πr.
The equation of a circle is x² + y² = r²
We have,
The equation of a circle
x² + y² = r²
r = 5
x² + y² = 25 ______(1)
The line.
y = 4x _____(2)
Now,
The line intersects the circle.
The point of intersection.
x² + (4x)² = 25
x² + 16x² = 25
17x² = 25
x = √(25/17)
x = ± 5/√17
x = 5/√17 and x = -5/√17
Now,
At x = 5/√17,
y = 4 x 5/√17
y = 20/√17
At x = -5/√17,
y = 4 x 5/√17
y = 20/√17
Thus,
The point of intersection.
(5/√17, 20/√17) and (-5/√17, 20/√17)
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What is 47 = 2(k+3) +3(k-3) ? This is my missing work from being absent so pleas help me.
Answer: K=10
Step-by-step explanation:
To begin, you should multiply out the terms in front of the parentheses. This results in: 47=2k+6+3k-9
Next, we can combine like terms: 47=5k-3
Add 3 to both sides: 50=5k
Divide both sides by 5: 10=k
k=10
Given the vector u equal to 7 (cos 330°, sin 330°) and vector v equal to
4 (cos 90°, sin 90°), find the sum u + v and write your answer in magnitude and
direction form with the magnitude rounded to the nearest tenth and the direction
rounded to the nearest degree, 0° ≤0 < 360°.
The magnitude of u + v is 6.08 and the direction of the vector u + v is 4.7°.
What is rounded to the nearest tenth?
To write a decimal number up to one decimal place, round it to the nearest tenth. This is done in a way that leaves one digit after the decimal point after rounding.
Given that vector u is 7 (cos 330°, sin 330°)
Vector v equal to is 4 (cos 90°, sin 90°)
Calculating the value of cos 330° and sin 330°:
cos 330°
= cos (3×90° + 60°)
= sin 60°
= √3/2
sin 330°
= sin (3×90° + 60°)
= -cos 60°
= -1/2
The vector u can be written as 7 (cos 330°, sin 330°) = 7(√3/2, -1/2) =(7√3/2, -7/2) = 7√3/2 i - 7/2j
The vector v can be written as 4 (cos 90°, sin 90°) = 4(0,1) = (0,4) = 0i + 4j
Add vector u and v:
u + v
= 7√3/2 i - 7/2j + 0i + 4j
= 7√3/2 i + 1/2 j
= 6.06 i + 0.5 j
The magnitude of the vector u+v is √( 6.06² + .5²) = 6.08
The angle is
tan θ = y/x
tan θ =0.5/6.06
θ = 4.7°
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Question 10(Multiple Choice Worth 5 points)
(Proportional Relationships LC)
Does the graph represent a proportional relationship?
graph with a line from 0 comma 0 and going through 25 comma 8
No, it is not proportional because the line does not go through (0, 0).
No, it is not proportional because the graph is curved.
Yes, it is proportional because it is a line that goes through (0, 0).
Yes, it is proportional because the x-axis and y-axis are numbered correctly.
Since the graph has a line from 0 comma 0 and going through 25 comma 8, C. Yes, it is proportional because it is a line that goes through (0, 0).
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.
Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.
By critically observing graph of this proportional relationship (see attachment), we can logically deduce that it starts from the origin (0, 0) and as such, it is proportional.
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Casual sneaker sales represent 4.5% and athletic shoe sales represent 3.2%
of total store sales. If the total store sales are $900,000, what are the dollar
sales for each department?
Answer: Casual sneaker sales = $40,500 & Athletic shoe sales = $28,800
Step-by-step explanation:
If the total store sales are $900,000 and you already have the percentages of the casual sneaker sales and athletic shoe sales, then you move the decimal point in each percentage two digits to the left, or simply multiply the percentage by .01, then take that number and multiply it by the total, $900,000
Ex:
4.5%(0.01) = .045
3.2%(0.01) = .032
.045(900,000) = 40,500
.032(900,000) = 28,800
Independent random samples, each containing 80 observations, were selected from two populations. The samples from populations 1 and 2 produced 33 and 28 successes, respectively.
Test H0:(p1−p2) = 0 against Ha:(p1−p2) ≠ 0. Use α = 0.05
The test statistic should be: _______
The P-value is _______
From two populations, independent random samples were drawn, each having 80 observations. The test statistic should be z = 2.18 because samples from populations 1 and 2 yielded 33 and 28 successes, respectively.
P-value is set at 0.030.
State the null and alternate hypotheses in step one.
H0: (p1-p2) = 0
Ha: (p1-p2) ≠ 0
Step 2: Calculate the test statistic
We can calculate the test statistic using the formula:
z = (p1-p2)/√(p(1−p)(1/n1+1/n2))
where,
p = (successes in sample 1 + successes in sample 2)/(n1+n2)
= (33 + 28)/(80 + 80)
= 61/160
= 0.30
n1 = sample size of population 1
= 80
n2 = sample size of population 2
= 80
Therefore,
z = (p1-p2)/√(p(1−p)(1/n1+1/n2))
= (33/80 - 28/80)/√(0.38125(1−0.38125)(1/80+1/80))
=2.18
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In a recent year, companies spent a total of $87.5 billion on newspaper, television, and radio ads. The total amount spent on television and
radio ads was only $2.9 billion more than the amount spent on newspaper ads alone. The amount spent on newspaper ads was $5.4 billion
more than what was spent on television ads. How much was spent on each form of advertising? (Hint: Let the variables represent numbers of
billions of dollars.)
How much was spent on newspaper ads? $
How much was spent on television ads? $
How much was spent on radio ads? $ billion
billion
billion
Answer:
newspaper ads: $42.3 billiontelevision ads: $36.9 billionradio ads: $8.3 billionStep-by-step explanation:
You want the amount spent on ads in each medium given the total and relations between amounts spent for newspaper, television, and radio ads.
SetupLet n, t, r represent the amounts spent on ads in newspapers, television, and radio, respectively. The given relations tell you ....
n +t +r = 87.5
-n +t +r = 2.9
n -t = 5.4
SolutionThe augmented coefficient matrix can be reduced to row-echelon form using a suitable calculator or spreadsheet. This tells you the amounts spent in each medium. The attachment shows this.
newspaper ads: $42.3 billiontelevision ads: $36.9 billionradio ads: $8.3 billion__
Additional comment
The value of n can be found by subtracting the second equation from the first. That can be used in the third equation to find t, and both of those values can be used in either of the first two equations to find r.
Write an equation of a circle whose
center is (-1,3) and passes through the
point (7,-2).
Answer: (x + 1)^2 + (y - 3)^2 = 65
Step-by-step explanation:
Answer: (x+1)²+(y-3)²=89
Step-by-step explanation:
An equation of a circle: (x-a)²+(y-b)=R²
The center of a circle is (-1,3), hence a=-1 b=3
(x-(-1))²+(y-3)=R²
(x+1)²+(y-3)²=R² (1)
Substitute the coordinate (7,-2) belonging to the circle into equation (1):
(7+1)²+(-2-3)²=R²
8²+(-5)²=R²
64+25=R²
89=R²
Thus, R²=89
Hence,
(x+1)²+(y-3)²=89
Exercise 1
Directions: Describe the end behaviors of the following functions:
1. f(x) = x5 – 19x3 + 48x
2. f(x) = - x4 - 49x2 - 5
3. f(x) = x2 - 10x + 16
4. f(x) = - x (x + 9) (x - 1)
5. f(x) = 4x2 - 2x + 1
On solving the derivatives we got - 6x5-15 , 4x² - 98x , x-5)²-9, -3x²-16x+9 , -2
What is derivative?Differentiation is the rate at which a function changes with regard to a variable in mathematics (in mathematics, the rate of change of a function with respect to a variable). The usage of derivatives is necessary while solving calculus and differential equation problems.
1. f(x) = 6x5-15 DERIVATIVE
2.f(x) = 4x² - 98x DERIVATIVE
3. f(x) = (x-5)²-9
4.f(x)= -3x²-16x+9 DERIVATIVE
5.f(x)=-2 DERIVATIVE
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What is the Herfindahl-Hirschman Index for a market with two firms, one having 99.5 percent of the market and the other having 0.5 percent?
Answer:A topic sentence is used to bring
to a paragraph.
Step-by-step explanation:
A topic sentence is used to bring
to a paragraph.
I need this please help me
Answer: m∠A = 72°, m∠C = 56°
Step-by-step explanation: All triangles interior angles add up to 180, This is an isosceles triangle which by rule mean that angles m∠A and m∠B and the same value of 72°. Now it becomes an equation to find m∠C, of
72 + 72 + x = 180.
144 + x = 180
x = 56
For any positive integer x, let x^R be the integer whose binary representation is the reverse of the binary representation of x. (Assume no leading 0s in the binary representation of x.) Define the function R^+: N rightarrow N where R+(x) = x + x^R. a. Let A_2 = { | R^+ (x) = y}. Show A_2 elementof L. b. Let A_3 = { | R^+ (R^+ (x) = y}. Show A_3 elementof L.
Define the function [tex]R^{+}[/tex]: N ⇒ N where R+(x) = x + [tex]x^{R}[/tex]
(a) Let A₂ = {(x,y) | [tex]R^{+}[/tex] (x) = y} language A₂ ∈L.
(b) Let A₃ = {(x,y) | [tex]R^{+}[/tex] ([tex]R^{+}[/tex] (x)) = y} language A₃ ∈L.
Given that,
For any positive integer x, let [tex]x^{R}[/tex] be the integer with the opposite of x's binary representation in terms of representation. (Assume that x's binary form has no leading 0s.) Specify the function [tex]R^{+}[/tex]: N ⇒ N where R+(x) = x + [tex]x^{R}[/tex]
(a) Let A₂ = {(x,y) | [tex]R^{+}[/tex] (x) = y}. Show A₂ ∈L.
(b) Let A₃ = {(x,y) | [tex]R^{+}[/tex] ([tex]R^{+}[/tex] (x)) = y}. Show A₃ ∈L.
We know that,
Consider the Turing machine M, which computes the inverse of x for every positive inter. The result will also be x if the computation is done using both the integer x and its inverse.
This is because the result of adding a binary number 1 to 0 is always 1. The criterion is that the binary representation of x must not contain 0. In this case, a positive integer x is converted into binary representation.
Only x values with a binary representation of 1 will be accepted by the Turing machine. Even the Turing machine will accept inverse-of-x values with binary representations of 0.
Therefore, It is proved that language A₃ ∈L.
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Which one is not a polynomial? (a) 4x² + 2x-1 (b) x²-1
(c) y² + 5y + 1
So option b. x² -1 is the correct option of the given statement Because option b satisfy the requirement of not a polynomial.
In mathematics, what does a polynomial mean?An expression for a polynomial can be generated using only the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables (also known as indeterminates) and coefficients make up a polynomial.
What makes a polynomial unique?It is possible to identify the polynomials by seeing which formulae only include the operations addition, subtraction, multiplication, and non-negative integer exponents. Expressions that include extra operations are regarded as non-polynomial expressions. Specify the grounds for the expressions' non-polynomial status.
Which regulations apply to polynomials?Any function in an equation that uses only positive integer exponents or non-negative integer powers of a variable is known as a polynomial function. These equations include, for instance, the cubic equation, the quadratic equation, and others. A polynomial with an exponent of 1 is, for instance, 2x+5.
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hese are curves obtained by the intersection of right circular cone and a plane.
a. Parabola
b. Ellipse
c. Hyperbola
d. Conic sections
Answer: conic sections
Step-by-step explanation: the other options are a part of conic sections that are named depending on the angle of the plane relative to the cone, and the intersection.
Identify or mark the missing side or angle that would make triangle ABC congruent to triangle PDF by SAS.
Answer:
Mark the sides BC and DF as congruent---------------------------------------------------
We are given a side and an adjacent angle and need to identify the missing side or angle for proof by SAS.
SAS is side-angle-side and requires two sides and the included angle to be congruent on both triangles.
The missing bit is the other side of the marked angle B and D:
sides BC or DF.You have $16 to buy apples for an apple crisp recipe. Apples cost $2 each. Write and solve an inequality that represents the numbers of apples you can buy.
The inequality to buy an apple can be given as 2x ≤ 16
The number of apples we can buy is 8
What is an inequality?
An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.
We are given that we have only$16 dollar to buy apples and each costs $2
Let the number of apples we can buy be x
Hence the inequality can be given as
2x ≤ 16
Now dividing both sides by 2 we get,
x ≤ 8
Hence we can buy at most 8 apples
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Evaluate âˆD(1+z2)dVâˆD(1+z2)dV where DD is the solid region bounded below by the upper portion of the cone z2=3x2+3y2z2=3x2+3y2 and above by the sphere x2+y2+z2=4.
Answer: 1
Step-by-step explanation:
sume of angles of a triangel greater than 180 degrees when teh triange is so large that it extends to cosmological scales
In hyperbolic geometry, the angle sum of a triangle is always less than 180 degrees.
A lune is a wedge of a sphere with angle θ, represented by L(θ) in the proof.
α, β, and γ are the three angles of the triangle.
4πr²+4area[αβγ]=2L(α)+2L(β)+2L(γ)
2(2πr²+2area[αβγ])=2(L(α)+L(β)+L(γ))
2πr²+2area[αβγ]=L(α)+L(β)+L(γ)
At this point, we need to use a theorem that states that a lune whose corner angle is θ radians has an area of 2θr².
2πr²+2area[αβγ]=2αr²+2βr²+2γr²
2πr²+2area[αβγ]=2r²(α+β+γ)
π+area[αβγ]r²=α+β+γ
At this point, it is clear that the sum of the angles is equal to π plus the area[αβγ]r² (which cannot be zero).
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Which functions are decreasing? Select all answers that are correct. Responses The function consists of four sections. Section 1 is a line from begin ordered pair negative 3 comma 4 end ordered pair to begin ordered pair negative 1 comma 4 end ordered pair. Section 2 is a line from begin ordered pair negative 1 comma 4 end ordered pair to begin ordered pair 1 comma 0 end ordered pair. Section 3 is a line from begin ordered pair 1 comma 0 end ordered pair to begin ordered pair 3 comma 2 end ordered pair. Section 4 is a line from begin ordered pair 3 comma 2 end ordered pair to begin ordered pair 5 comma negative 2 end ordered pair. Image with alt text: The function consists of four sections. Section 1 is a line from begin ordered pair negative 3 comma 4 end ordered pair to begin ordered pair negative 1 comma 4 end ordered pair. Section 2 is a line from begin ordered pair negative 1 comma 4 end ordered pair to begin ordered pair 1 comma 0 end ordered pair. Section 3 is a line from begin ordered pair 1 comma 0 end ordered pair to begin ordered pair 3 comma 2 end ordered pair. Section 4 is a line from begin ordered pair 3 comma 2 end ordered pair to begin ordered pair 5 comma negative 2 end ordered pair. The function goes through begin ordered pair negative 4 comma negative 2.5 end ordered pair, begin ordered pair negative 3 comma negative 5 end ordered pair, begin ordered pair negative 2 comma negative 2 end ordered pair, begin ordered pair 0 comma 5 end ordered pair, begin ordered pair 2 comma negative 2 end ordered pair, begin ordered pair 3 comma negative 5 end ordered pair and begin ordered pair 4 comma negative 2.5 end ordered pair. Image with alt text: The function goes through begin ordered pair negative 4 comma negative 2.5 end ordered pair, begin ordered pair negative 3 comma negative 5 end ordered pair, begin ordered pair negative 2 comma negative 2 end ordered pair, begin ordered pair 0 comma 5 end ordered pair, begin ordered pair 2 comma negative 2 end ordered pair, begin ordered pair 3 comma negativ
The sections of the function that are decreasing, defined by the ordered pairs are;
Section 2; (-1, 4) to (1, 0)
Section 4; (3, 2), to (5, -2)
The part of the second function that is decreasing is; (2, -2) to (3, -5)
What is a function?A function is a definition of the mapping of the set of input variables unto the set of the output variables.
The points in the specified functions are;
Section 1 line ; (-3, 4) to (-1, 4)
Section 2 line ; (-1, 4) to (1, 0)
Section 3 line ; (1, 0) to (3, 2)
Section 4 line ; (3, 2) to (5, -2)
The points through which the function goes through are; (-4, -2.5), (3, -5), (-2, -2), (0, 5), (2, -2), (3, -5), (4, 2.5) and (5, -2)
A function is decreasing when the positive increase in the x-value of the function is accompanied by a decrease in the y-value.
The sections of the functions that are decreasing are;
Section 2 line ; (-1, 4) to (1, 0),
Section 4; (3, 2) to (5, -2)
Parts of the function that is decreasing is; (2, -2), (3, -5)
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PLEASE HELP!!
(Solving System of Equations from Context)
Jordan is working two summer jobs, making $13 per hour lifeguarding and $10 per hour walking dogs. Last week Jordan earned a total of $177 and worked 3 more hours lifeguarding than hours walking dogs. Determine the number of hours Jordan worked lifeguarding last week and the number of hours he worked walking dogs last week.
Answer:
Jordan worked 18 hours lifeguarding and 15 hours walking dogs.
Step-by-step explanation:
To solve this problem, we can set up a system of two equations to represent the given information. Let "L" represent the number of hours Jordan worked lifeguarding and "W" represent the number of hours he worked walking dogs.
The first equation will represent the total amount of money Jordan earned:
13L + 10W = 177
The second equation will represent the difference in hours between the two jobs:
L - W = 3
We can solve this system of equations using either substitution or elimination.
Using substitution, we can solve for one variable in terms of the other and substitute that expression into the other equation to solve for the other variable.
Solving the second equation for L, we get:
L = W + 3
Substituting this expression for L into the first equation, we get:
(W + 3) + 10W = 177
Combining like terms, we get:
11W + 3 = 177
Subtracting 3 from both sides, we get:
11W = 174
Dividing both sides by 11, we get:
W = 15.818181818181818
Since the number of hours worked must be a whole number, we can round down to 15 hours. Substituting this value back into the equation L = W + 3, we get:
L = 15 + 3 = 18
Therefore, Jordan worked 18 hours lifeguarding and 15 hours walking dogs.
Jeff Ryan bought 200 shares of BUI for $19.50. Eight weeks later he sold the stock for $20.75. Assuming a 3% commission, his bottom line was a gain of:
Multiple Choice
$250.00
$374.50
$8.50
$257.50
His bottom line was a gain from selling and 3% commission is $257.50.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
The cost price of 200 shares of BUI is (19.50×200) = $3900.
The selling price of 200 shares of BUI is (20.75×200) = $4150.
The net gain is (4150 - 3900) = $250 and with 3% commission it is,
= (103/100)×250.
= $257.50.
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Point A is the incenter of triangle DEF.
Which must be true? Select three options
A.Point A is the center of the circle that passes through points D, E, and F.
B.Point A is the center of the circle that passes through points X, Y, and Z.
C.ZA≅YA
D.EA≅FA
E.AX≅AY
The three options that describe the in-center of the given triangle are;
B. Point A is the center of the circle that passes through points X, Y, and Z.
C. ZA ≅ YA
E. AX ≅ AY
What is the in center of the triangle?The incenter of a triangle is defined as the point of intersection point of all the three interior angle bisectors of the given triangle. This means that, it can also be said to be the point where all the internal angle bisectors of the triangle cross each other.
Now, we are told that Point A is the incenter of triangle DEF. From the definition above, we can deduce that;
An inscribed circle can be drawn with center A passing through points X, Y and Z.
Similarly, since it passes through X, Y and Z, then it means that ZA≅YA, AX≅AY.
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an escalator has a slope of 3/4 after traveling forward 128 feet, the escalator is 96 feet above the floor. Write this word problem in point slope form
The point slope form of the slope of escalator and distance is y-24 = 3/4(x-32).
The general point slope form is given by the equation -
y - y1 = m (x - x1)
Now we are given the slope as 3/4. So, keeping the values of y1 and x1 in the equation. Let us assume the points as (32, 24). As per the points, 32 is x1 and 24 is y1.
y - 24 = 3/4(x - 32)
y - 24 = 3x/4 - 3/4×32
Performing division on Right Hand Side of the equation
y - 24 = 3x/4 - 3×8
y - 24 = 3x/4 - 24
Rewriting the equation
y - 3x/4 = - 24 + 24
Solving the equation on Right Hand Side of the equation
y - 3x/4 = 0
y = 3x/4
Thus, the equation is y - 24 = 3/4(x - 32).
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which equation represents the line that passes through the points (- 3, 7) and (9, - 1) ^ prime; which equation represents a line that is parallel to the line y=-3x+4; what is the equation of the line passing through the points (2/5 19/20); what is the slope-intercept form of a line that passes through points (2, 11) and (4, 17)?; what method can be used to write the equation of a line in slope-intercept form given two points?; what is the equation of the line that passes through the points (15, 9) and (-2, 9)?; which is a characteristic of the line that passes through the points (6, 10) and (12, 7)?; which can be the first step in finding the equation of the line that passes through the points
1. The equation of the line is:
y=-2x/3 + 5
2. The equation of the line in slope intercept form is:
y=3x+5
1. Given:
we have two points:
(-3,7) = (x₁,y₁)
(9,-1) = (x₂,y₂)
equation of the line is:
y - y₁ = m(x-x₁)
₁first calculate slope m = y₂-y₁/x₂-x₁
m = -1-7/9-(-3)
m = -8/12
m = -2/3
now, y - 7 = -2/3 (x-(-3)
y-7=-2/3(x+3)
y-7=-2x/3-2
y=-2x/3-2+7
y=-2x/3 + 5
hence equation of the line is y=-2x/3 + 5
2. Given two points:
(2, 11) and (4, 17)
(2, 11) = (x₁,y₁)
and (4, 17) = (x₂,y₂)
slope intercept form:
y=mx+c
we need to calculate the m value:
m = 17-11/4-2
m = 6/2
m=3
now substitute in the given form:
y - 11 = 3(x-2)
y-11=3x-6
y=3x-6+11
y=3x+5
Hence we get the required answer.
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what is 2 1/6 + 4 3/6 as a fraction
Answer:
6 2/3
Step-by-step explanation:
2 1/6 + 4 3/6
6 4/6
6 2/3
Given A(1,4), B(-2,5)and C(3, 4), which coordinate pair will make AB perpendicular to CD ?
The coordinate pair of D that will make AB perpendicular to CD is ( 4,7)
How are lines perpendicular in a coordinate?The slopes of perpendicular lines are opposite reciprocals of each other. Their product is -1.
The slope of a line is given as ( y1-y2)/(x1-x2)
for AB and CD to be perpendicular
( y2-y1)/(x2-x1) × ( y4-y3)/(x4-x3) = -1
therefore (5-4)/-2-1 = ( y4-y3)/(x4-x3)
1/-3 ×(y4-4)/(x4-3) = -1
(y4-4)/(x4-3) = 3/1
therefore 3= y4-4 and 1 = x4-3
therefore y4 = 3+4= 7
and x4 = 1+3= 4
therefore the coordinate of D = (x4,y4) for AB perpendicular to CD = (4,7)
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Evaluate 2xx ÷ 3yy for x = 1 2 and y = 3 5 -show the steps
The value of 2xx ÷ 3yy is 288/1225
What is simplification?In mathematics, simply or simplification is reducing the expression/fraction/problem to a simpler form. It makes the problem easy with calculations and solving.
Given that, an expression 2xx ÷ 3yy, where x = 12 and y = 35
2x12x12/3x35x35 = 288/1225
Hence, The value of 2xx ÷ 3yy is 288/1225
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