Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Helen and Jordan decided to shoot arrows at a simple target with a large outer ring and a smaller bull's-eye. Helen went first and landed 3 arrows in the outer ring and 1 arrow in the bull's-eye, for a total of 174 points. Jordan went second and got 3 arrows in the outer ring and 4 arrows in the bull's-eye, earning a total of 444 points. How many points is each region of the target worth?
Answers
SOLUTION
Steps1: Define a parameter for the unknow
\(\begin{gathered} a=\text{outer ring point } \\ b=\text{bull's eye point} \end{gathered}\)Step2: Write out the equation for Helen
Since Helen landed 3arrows on the outer ring and 1 on the bull's eye and have a total of 174, the equation becomes
\(3a+b=174\)Step3: Wite out the equation for Jordan
Since Jordan Landed 3arrows on outer ring and 4arrows in the bull's eye with a total point of 444, the equation becomes
\(3a+4b=444\)Step4: Solve the system of equation with elimination method
To solve the equation, we label them eliminate the variables separately
hence
\(\begin{gathered} 3a+b=174\ldots Eq1 \\ 3a+4b=444\ldots Eq2 \end{gathered}\)Subtract Eq1 from Eq2 (Eq2-Eq1) to eliminate the variable a.
\(\begin{gathered} 3a_{}+4b=444 \\ 3a+b=174 \\ \text{Then} \\ 3b=270 \end{gathered}\)From the equation in the last line above divide both sides by 3, we have
\(\begin{gathered} \frac{3b}{3}=\frac{270}{3} \\ \text{then} \\ b=90 \end{gathered}\)To eliminate the variable b, Multiply Eq1 by 4 and subtract from Eq 2, we have
\(\begin{gathered} 4\times Eq1\rightarrow4(3a+b=174)=12a+4b=696 \\ \text{Then subtract from Eq2, we have } \\ 12a+4b=696 \\ 3a+4b=444 \\ \text{hence} \\ 9a=252 \end{gathered}\)From the equation in the last line above, divide both sides by 9, we obtain
\(\begin{gathered} \frac{9a}{9}=\frac{252}{9} \\ \text{Then} \\ a=28 \end{gathered}\)Hence
a=28,b=90.
Therefore
The outer ring worth 28 point
The bull's eye worth 90 point
Related Questions
Find the sum of the following finite geometric series.
Answers
The sum of the geometric sequence in this problem is given as follows:
5.77.
What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number, which is called the common ratio q.
The first term, the common ratio and the number of terms for this problem are given as follows:
\(a_1 = 10, q = -\frac{2}{3}, k = 8\)
The formula for the sum of the first n terms is given as follows:
\(S_n = a_1\frac{1 - r^n}{1 - r}\)
Hence the sum for this problem is given as follows:
\(S_8 = 10 \times \frac{1 - \left(-\frac{2}{3}\right)^8}{1 + \frac{2}{3}}\)
\(S_8 = 5.77\)
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The workers' union at a particular university is quite strong. About 96 of all workers employed by the university belong to the workers' union. Recently, the workers went on strike, and now a local TV station plans to interview 4 workers (chosen at random) at the university to get their opinions on the strike. What is the probability that exactly 2 of the workers interviewed are union members?
Answers
The probability that exactly 2 of the workers interviewed are union members is approximately 0.044.
To solve this problem, we can use the binomial probability formula, which is:
\(P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)\)
where:
n is the sample size (number of workers being interviewed)
k is the number of successes we are interested in (in this case, 2 of the workers being union members)
p is the probability of success (in this case, the probability that a worker is a union member)
(n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items (this can be calculated using the formula n! / (k! * (n - k)!))
Plugging in the values, we get:
\(P(X = 2) = (4 choose 2) * (0.96)^2 * (1 - 0.96)^(4 - 2)\)
\(= (6) * (0.96)^2 * (0.04)^2\)
= 0.04403136
Therefore, the probability that exactly 2 of the workers interviewed are union members is approximately 0.044.
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The measures of the angles of a triangle are shown in the figure below. Find the measure of the smallest angle.
44°
(5x+20)°
(9x+18)°
Answers
The smallest angle is 44°
Given that the sum of the interior angles of a triangle is 180 degrees :
44+5x+20+9x+18=180
14x=98
x=7
The angls of the triangle are:
44°
55°
81°
Clara is completing a math project.she has two ropes with length 126cm and 291cm.she wants to cut them into pieces of equal length without remainder.what is the greatest possible length of each smaller pieces of rope??this is my homework so pls kindly help me for the answer i would really appreciate it!✨
Answers
Answer:aw45
Step-by-step explanation:
w
In recent years, Sheffield Transportation purchased three used buses. Because of the frequent turnover in the accounting department, a different accountant was in charge of selecting the depreciation method for each bus, and various methods have been used. Information concerning the buses is summarized in the table below. Bus 1, Bus 2, Bus 3, For the declining-balance method, the company uses the declining method rate. For units-of-activity method, total miles are expected to be 125,000. Actual miles of use in the first 3 years were 2021, 27,000; 2022, 35,000; and 2023, 33,000.
(a1) For Bus #3, calculate depreciation expense per mile under units-of-activity method.
Answers
Under the units-of-activity method, the depreciation expense per mile for Bus #3 is $0.4616.
How is the depreciation expense per mile determined?The units-of-activity method is one of the depreciation methods in use.
Under the units-of-activity method, the depreciation expense per unit is determined by dividing the depreciable amount by the total units of activity.
The depreciation amount (the value of the asset subject to depreciation) is the net of the total cost less the salvage value.
Depreciable amount of Bus #3 = $57,700 ($66,500 - $8,800)
Expected total miles for Bus #3 = 125,000
Depreciation expense per mile for Bus #3 = $0.4616 ($57,700 ÷ 125,000)
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Question Completion:Bus Acquired Cost Salvage Useful Life Depreciation
Value in Years Method
1 1/1/12 $99,100 $7,900 4 Straight-line
2 1/1/12 128,000 11,000 4 Declining- balance
3 1/1/13 66,350 8,800 5 Unit-of-activity
Simplify 0.4(−4.5). (5 points)
Answers
Answer:
-1.8, multiply them, then add the negative sign
Step-by-step explanation:
Answer:
its -1.8
Step-by-step explanation:
i got it right on my exam :)
-Hope this helps!
The salaries of Kofi and Ama are in the ratio 3:5. If the salary of each is raised by ¢4000, the new ratio becomes 40:57. what is Ama's salary
Answers
Answer:
34000
Step-by-step explanation:
New Ratio = 40/57
Gap between numerator & denominator = 17
Original Ratio = 2/3
Gap between numerator & denominator = 1
=> Original Ratio can be restated as 34/51 to make gap of both ratios same.
Difference between two numerators OR denominators = 40 - 34 = 6 or 57 - 51 = 6
If gap is 6, sumit’s original salary = 51
If gap = 4000, sumit’s original salary is :
51/6 x 4000 = 34000
The salary of Amma is given as ¢11724.10.
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
The ratio of the salaries of Kofi and Ama is given as 3 : 5.
After adding 4000 to each ratio the new ratio becomes as 40 : 57.
Suppose the present salaries of Kofi and Ama be 3x and 5x respectively.
Then, as per the question following equation can be written as,
(3x + 4000)/(5x + 4000) = 40/57
=> 57(3x + 4000) = 40(5x + 4000)
=> 200x - 171x = 68000
=> 29x = 68000
=> x = 68000/29
= 2344.82
The Amma's salary is given by,
5x = 5 × 2344.82
= 11724.10
Hence, Amma's present salary is given as ¢11724.10.
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i need help with this problem
Answers
9514 1404 393
Answer:
(a) 4 in²
Step-by-step explanation:
The volume of a rectangular prism is given by the formula ...
V = Bh
where B is the area of the base, and h is the height of the prism.
We can find the area of the base by solving for B.
B = V/h
B = (12 in³)/(3 in)
B = 4 in² . . . . . . . . . . matches the first choice
find the dimensions (radius r and height h) of the cone of maximum volume that can be inscribed in a sphere of radius 2.
Answers
The dimensions of the radius is 4/3\(\sqrt{2}\) and that of height is 8/3.
Let r be the radius of the cone, be the radius of the sphere and h be the height of the cone.
Let's put DˆOB=x with limitations 0≤x≤π.
In the right-angled triangle DOB:
r=DB=Rsinx, OD=Rcosx, than
h=CD=OC+OD=R+Rcosx=R(1+cosx).
So the volume of the cone is:
V=1/3πr²h ⇒V=1/3π(Rsinx)²⋅R(1+cosx)
V=1/3πR³sin²x(1+cosx)
V'=1/3πR³⋅[2sinx⋅cosx⋅(1+cosx)+sin2x(−sinx)]
=1/3πR³sinx[2cosx(1+cosx)−sin2x]
=1/3πR³sinx(2cosx+2cos2x−sin2x)
=1/3πR³sinx(2cosx+2cos2x−1+cos2x)
=1/3πR³sinx(3cos2x+2cosx−1)
Now let's find the signum of the derivative, since sinx≥0 for every x in the limitations, then:
V'≥0⇒3cos²x+2cosx−1≥0
⇒Δ/4=(b/2)²−ac =1+3=4
cosx=(−b/2)±√Δ/4 / a
=−1±2/3,
So:
cosx≤−1∨cosx≥1/3
The first one has only the solution:
x=π
the second:
−arccos(1/3)≤x≤arccos(1/3), but for the limitations:
0≤x≤arccos(1/3).
The function gros from zero to arccos(1/3), and then it decreases.
So x=arccos(1/3) is the maximum requested.
Let's find now r and h:
r=Rsinx
=R√1−cos2x
= 2√1−(1/3)²
= 2√1−1/9
=2√9−1/9
=2√8/9
=2⋅2√2/3
=4/3√2
h=R(1+cosx)=2(1+1/3)
=2(3+1/3)
=8/3.
Therefore the radius is 4/3√2 and the height is 8/3.
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At the beginning of June, Max and Sean start saving money for the fair, which occurs 10 weeks later. Sean
starts out with $20 and saves just $2 per week. Max starts out with no money, but saves 5 dollars per week.
After how many weeks will Max have more money saved than Sean?
Answers
Answer:
Step-by-step explanation:
sean has 20 +2 : 2 x 7 = 14 + 20 = 34
max has 0 + 5: 5 x 7 = 35
so after 7 week max will have more money
helppppp! how do I find this?
Answers
Answer:
y=3x-6
Step-by-step explanation:
(2,0). y=mx+b or 0=3 × 2+b, or solving for b: b=0-(3)(2). b=-6.
(3,3). y=mx+b or 3=3 × 3+b, or solving for b: b=3-(3)(3). b=-6.
Plugging in the two points from the graph.
Hence, y=3x-6
The average body temperature of all healthy adults is 98.6 F. A doctor takes a random sample of 100 healthy adults and records the temperature of each. The average temperature of these 100 adults is 98.2 F and the standard deviation is 6.9 F. Identify the values of the statistic and the parameter(s).
Answers
Answer:
Explained below.
Step-by-step explanation:
A parameter is a valuable element of statistical analysis. It denotes the characteristics that are used to define a given population. It is used to define a particular attribute of the population. For instance, population mean, population standard deviation, population proportion and so on.
The parameter of interest is the average body temperature of all healthy adults, μ = 98.6°F.While making a statistical conclusion about the population under study, the parameter value is unknown. This is because it would not be possible to gather data from every single member of the population. So a sample is selected from the population to derive a conclusion about the parameter.
A statistic is the value of the characteristics that are computed using this sample. For instance, sample mean, sample standard deviation, sample proportion and so on.
The statistic is the average body temperature of 100 randoly selected healthy adults, \(\bar x=98.2^{o}F\).Which of the following tables represents a linear function? x −4 −1 0 1 2 y −4 2 −4 0 2 x 1 1 1 1 1 y −3 −2 −1 0 1 x −6 −1 0 2 3 y −7 negative sixteen thirds −5 negative thirteen thirds −4 x −2 −1 0 2 4 y −4 negative two thirds −1 two thirds 1 Question 5(Multiple Choice Worth 5 points) (Experimental Probability MC) A bag is filled with an equal number of red, yellow, green, blue, and purple socks. The theoretical probability of a child drawing 2 yellow socks from the bag with replacement is one fifth. If the experiment is repeated 175 times, what is a reasonable prediction of the number of times he will select 2 yellow socks? one fifth 10 25 35 Question 6(Multiple Choice Worth 5 points) (Identifying Functions LC) The graph represents a relation where x represents the independent variable and y represents the dependent variable. a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma negative 1, at 0 comma 2, at 1 comma 3, and at 5 comma 1 Is the relation a function? Explain. No, because for each input there is not exactly one output. No, because for each output there is not exactly one input. Yes, because for each input there is exactly one output. Yes, because for each output there is exactly one input. Question 7(Multiple Choice Worth 5 points) (Line of Fit MC) A movie theater wanted to determine the average rate that their diet soda is purchased. An employee gathered data on the amount of diet soda remaining in the machine, y, for several hours after the machine is filled, x. The following scatter plot and line of fit was created to display the data. scatter plot titled soda machine with the x axis labeled time in hours and the y axis labeled amount of diet soda in fluid ounces, with points at 1 comma 30, 1 comma 40, 2 comma 34, 3 comma 24, 3 comma 30, 4 comma 18, 5 comma 15, 5 comma 24, 6 comma 4, 6 comma 20, 7 comma 10, and 8 comma 0, with a line passing through the coordinates 3 comma 26.7 and 7 comma 7.66 Find the y-intercept of the line of fit an
Answers
The y-intercept of the line of fit is approximately 43.94 fluid ounces.
What is Probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
The answer is 35. If the theoretical probability of drawing two yellow socks is one fifth, then the experimental probability of drawing two yellow socks in one trial with replacement is also one fifth. Therefore, out of 175 trials, the number of times he will select two yellow socks can be predicted by multiplying the number of trials by the experimental probability: 175 * (1/5) = 35.
No, because for each input there is not exactly one output. The relation is not a function because for the input x = -5, there are two possible outputs: y = 1 and y = -1. Therefore, the relation violates the vertical line test, which requires that every vertical line intersects the graph at most once for the relation to be a function.
The y-intercept of the line of fit is approximately 43.94 fluid ounces. To find the y-intercept, we can look at the point where the line of fit intersects the y-axis (i.e., when x = 0). From the equation of the line of fit, we can see that the y-coordinate when x = 0 is approximately 43.94, which represents the initial amount of diet soda in the machine before it starts to be purchased.
Therefore, The y-intercept of the line of fit is approximately 43.94 fluid ounces.
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HELP ASAP
Question
Garret studies number of hours sleep per night among students who have a grade point average of 3.0–4.0 versus students who have a grade point average of 2.0–3.0.
His theory is that students who get more sleep will have a higher grade point average than students who get less sleep because they are more rested and, therefore, better able to concentrate.
In his samples, the mean number of hours of sleep students with a grade point average of 3.0–4.0 received each night was 6.8. The mean number of hours of sleep students with a grade point average of 2.0–3.0 received each night was 6.4.
Assuming there are no outliers or skew, do the results support Garret's theory?
Select from the drop-down menus to correctly complete the statements.
Since the samples were large and randomly chosen, we can use the samples to understand the populations.
Because the sample mean for students with a grade point average of 3.0–4.0 is
Choose...
a. less than
b. about the same
c.greater than
the sample mean for students with a grade point average of 2.0–3.0, the results
Choose...
a. tend to
b. do not tend to
Answers
The sample mean for students with a grade point average of 3.0–4.0 is greater than students with grade point average of 2.0 - 3.0, the results tend to
How to interpret Garret studies?From the question, we have the following highlights
The sample size is large enoughThe sample is at randomStudents who have a grade point average of 3.0 - 4.0 sleep for an average of 6.8 hoursStudents who have a grade point average of 2.0–3.0 sleep for an average of 6.4 hoursThere are no outliersFrom the above highlights, the sample mean for students with a grade point average of 3.0–4.0 is greater than students with grade point average of 2.0 - 3.0
This is because 6.8 is greater than 6.4
This means that Garret's theory about the hours of sleep is correct
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The question is in the picture above
Answers
Answer:
45 degrees
Step-by-step explanation:
90 - 45 = 45
When adding 32.6 to a certain number, the sum is 36.14, as seen below. What number should go in the box to complete the addition problem?
Answers
Answer:
3.54
Step-by-step explanation:
32.6 + x = 36.14
x = 36.14 - 32.6
x = 3.54
The unknown number is 3.54
Calculate a and b if
\( \sqrt{ \frac{ {7}^{2014} - {7}^{2012} }{12} } = a( {7}^{b} )\)
and a is not a multiple of 7.
Answers
Notice that
\(7^{2014} - 7^{2012} = 7^{2012} \bigg(7^2 - 1\bigg) = 7^{2012} \times 48 = 2^4 \times 3 \times 7^{2012}\)
\(12=2^2\times3\), so
\(\dfrac{7^{2014}-7^{2012}}{12} = 2^2 \times 7^{2012}\)
Then taking the positive square root gives
\(\sqrt{\dfrac{7^{2014}-7^{2012}}{12}} = \sqrt{2^2 \times 7^{2012}} = 2\times7^{1006}\)
so \(\boxed{a=2}\) and \(\boxed{b=1006}\).
Determining the Equation of a Function from a Graph
What is the equation of the translated function?
Answers
Answer: Given the graph of the function f(x) which is described by a parabola with the vertex at (0, 0) and the graph of the translated function g(x) which is described by a parabola with the vertex at (5, 2).
Notice, that the vertex of the translated function is 5 units to the right and 2 units up of the graph of f(x).
Thus, g(x) is obtained by translating the function f(x) 5 units to the right and 2 units up.
Recall that given a function described by a parabola with vertex at (h, k) as
A translation of a units to the right and b units up will result in
Therefore, the equation of the translated function, g(x) is given by
Step-by-step explanation:
please help! thank uu!~
Answers
The intermediate step in the form (x+a)²=b as a result of completing the square for the given equations is (x+4)²=18.
The given quadratic equation is x²+4x-9=-4x-7.
Here, x²+4x-9+4x=-7
x²+8x=-7+9
x²+8x=2 ------(i)
Choose coefficient of x, that is 8.
Half of coefficient of x is 4.
Take square of 4, that is 4²=16
Add 16 to both the sides of the equation, we get
x²+8x+16=2+16
(x+4)²=18
Therefore, the intermediate step in the form (x+a)²=b as a result of completing the square for the given equations is (x+4)²=18.
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Isaac was having cookies and milk with his
little brother. He got out a jug that held
16 cups of milk. Isaac drank 1 cups and
his brother drank 12 cups. How much
milk was left in the jug?
Answers
Answer:
There is now 3 cups of m ilk left in the jug.
Step-by-step explanation:
12+1=13 | 13-16=3
ANSWER: 3
The Simple interest on $160
for 6 month's at 5% per
annum
Answers
Answer:4$
Step-by-step explanation:
It the end of the day l need this last one
Answers
help me please its due 11:45
Answers
< is the correct answer
Find an equation of a line Parallel to x = 8 , through ( 6 , 5 ) .
Answers
What is the intermediate step in the form
(x+a)^2=b as a result of completing the square for the following question
Answers
The intermediate step in completing the square is\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\)
To complete the square for the equation \($(x+a)^2=b$\), we can follow these steps:
1. Expand the left side of the equation: \($(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$\).
2. Rewrite the equation by isolating the squared term and the linear term: \($x^2 + 2ax = b - a^2$\).
3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:
\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\).
4. Simplify the right side of the equation: \($x^2 + 2ax + (a^2) = b$\).
This step can be represented as: \(\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\]\)
This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.
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Man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and she wants to order between 15% and 20% extra of the material
Answers
The order for the extra materials that are ordered by the man will be between 17.31 ft² and 23.08 ft².
How to calculate the value?From the information, the man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and wants to order between 15% and 20% extra of the material.
It should be noted that 15% of the material will be:
= 15% × 115.4
= 17.31 ft²
It should be noted that 20% of the material will be:
= 20% × 115.4
= 23.08 ft²
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The questions on a multiple choice test have four answer choices.
Which of the following models could you use to simulate the outcome of guessing the correct answers to a 50-question test?
(HINT: Remember to choose a model with the same number of possible outcomes as each test question.)
Group of answer choices
A. flipping a coin 50 times
B. spinning a spinner with 4 equal sections 50 times
C. rolling a 6-sided die 50 times
D. spinning a spinner with 50 equal sections four times
Answers
Answer: spinning a spinner with 4 equal sections 50 times
Step-by-step explanation:
The models that one can use to simulate the outcome of guessing the correct answers to a 50-question test will be to spinn a spinner with 4 equal sections 50 times.
Flipping a coin 50 times is wrong since the coin only has two outcomes which are head and tail. Rolling a 6-sided die 50 times is also wrong.
Therefore, the correct option is B.
Please look at the photo. Thank you!
Answers
The zeros with each multiplicity are given as follows:
Multiplicity one: x = 6.Multiplicity two: x = 11.Multiplicity three: x = -6 and x = -5.How to obtain the multiplicities?The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.
Considering the linear factors of the function in this problem, the zeros are given as follows:
(x + 6)³ -> zero at x = -6 with multiplicity of 3.(x - 11)² -> zero at x = 11 with multiplicity of 2.x - 6 -> zero at x = 6 with multiplicity of 1.(x + 5)³ -> zero at x = -5 with multiplicity of 3.More can be learned about the Factor Theorem at brainly.com/question/24729294
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Use the graph of the function to find its domain and range. In interval notation.
Answers
Recall that the domain of a graph is all the values of the graph from left to right and the range is all the values of the graph from down to up.
From the given graph we get that the domain is the red set and the range is the blue set.
The red set in interval notation is:
\([-7,-2].\)The blue set in interval notation is:
\([-4,7].\)Answer:
\(\begin{gathered} Domain=[-7,-2], \\ Range=[-4,7]. \end{gathered}\)How many terms are in 2x-7+y?
Answers
.......
3
Step-by-step explanation:
There is three terms
X-+ are all terms I think