money paid by employer to Alan is $ 155.09
word problemA word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.
money paid for dinner by employer=$20.20
money paid for lunch by employer =$10.70
money paid for breakfast by employer =$6.93
according to question,
in this problem we will simply multiply quantity of dinners with amount
to get our answer.
so as given in problem Alan scheduled 4 dinners , 5 lunches and 3 breakfast
(4×$20.20)+(5×$10.70)+(3×$6.93)
80.8+53.5+20.79
=$ 155.09
hence money paid by employer to Alan is $ 155.09
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On a hike, Maria walked up a hill in 30 minutes, and then she ran back down the hill in 10 minutes. Which of the following graphs could model the total distance Maria hiked?
The graph that describes the motion of Maria is the graph in Option B.
What is displacement?Displacement is the term that is used to describe the distance covered in a specified direction.
We are told that Maria walked up a hill in 30 minutes, and then she ran back down the hill in 10 minutes. The graph that describes this motion is the graph in Option B.
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Oscar bought some markers, notebooks, and packs of sticky notes for his office. He bought the same number of markers as notebooks. He bought three more packs of sticky notes than markers and notebooks combined. He paid $1.05 for each marker, $2.25 for each notebook, and the packs of sticky notes were $1.95. How many of each kind of office supply did Oscar buy if he paid $49.05 in all?
Using a system of equations, it is found that Oscar bought 6 markers, 6 notebooks and 15 packs of sticky notes.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of markers.Variable y: Number of notebooks.Variable z: Number of packs of notes.He bought the same number of markers as notebooks, hence:
x = y.
He bought three more packs of sticky notes than markers and notebooks combined, hence:
z = 3 + x + y
z = 3 + 2x.
He paid $1.05 for each marker, $2.25 for each notebook, and the packs of sticky notes were $1.95. He spent $49.05 in total, hence:
1.05x + 2.25y + 1.95z = 49.05.
Then:
1.05x + 2.25x + 1.95(3 + 2x) = 49.05.
7.2x = 43.2
x = 43.2/7.2
x = 6.
The amounts are as follows:
y = 6.z = 3 + 2(6) = 15.He bought 6 markers, 6 notebooks and 15 packs of sticky notes.
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For the following sample, calculate ss. then, compute the sample variance and standard deviation. scores: 5, 2, 2, 7, 9
The sample standard deviation is 7.6 and the sample variance is 2.76.
for the scores 5, 2, 2, 7, 9.
According to the question,
Sample size n = 5
Sample Mean = [5+2+2+7+9]/5
= 5
Formula for sample standard deviation = (x-mean)²/n
= [(5-5)²+(2-5)²+(2-5)²+(7-5)²+(9-5)²]/5
= [0+9+9+4+16]/5
= 38/5
= 7.6
Formula for sample variance = √sample standard deviation
=√7.6
=2.76.
Hence, the sample standard deviation is 7.6 and the sample variance is 2.76.
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Given the following table with selected values of f (x) and g(x), evaluate f (g(4)).
x –6 –4 1 3 4
f (x) 4 –1 –6 1 3
g(x) 1 4 3 –4 –6
–4
–1
1
4
The value of f(x) when x is -6 is 1.
Composite functionsComposite functions are also known as function of a function. In order to get a composite functions f(g(x)).
g(4) = -6 (the value of g(x) when x is equivalent to 4 is -6)
f(g(x))= f(g(4)) = f(-6)
f(-6) = 1
The value of f(x) when x is -6 is 1.
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Pls help with b
The diameters of two circular pulleys are 6cm and 12 cm, and their centres
are 10cm apart.
a. Angle a = 72.54 degrees
b. Hence find, in centimetres correct to one decimal place, the length of a
taut belt around the two pulleys
What is the ratio of the amount of the 30% solution to the amount of 5% solution used to create the 10% solution?
The ratio comes out to be 1:4.
What is ratio?
A ratio in mathematics shows how many times one number is contained in another. For instance, if a mixture of milk and water contains eight liters of water and six liters of milk, the ratio of water to milk is eight to six. Similarly, the ratio of water to the overall amount of mixture is 8:14, while the ratio of milk to water is 6:8.
Calculating the Ratio of the Solution:
Let us assume that x is the quantity of 30% of the solution and y be that of 5% solution, then,
30% of x + 5% of y = 10% of (x + y)
0.3x + 0.05y = 0.1 (x + y)
0.3x + 0.05y = 0.1x + 0.1y
0.3x - 0.1x = 0.1y - 0.05y
0.2x = 0.05y
Thus, the required ratio is,
0.2x / 0.05y = 1
x / y = 0.05 / 0.2
x / y = 5 / 20
x:y = 1 : 4
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780tonnes 650kilograms ÷13
Answer:
60 kilograms
Step-by-step explanation:
The graph shown here is the graph of which of the following rational
functions?
Considering it's asymptotes, the rational function shown in the graph is:
C. [tex]F(x) = \frac{1}{(x + 2)(x - 1)}[/tex]
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.In this graph, there are vertical asymptotes at x = -2 and x = 1, hence the denominator of the function is:
(x + 2)(x - 1).
The horizontal asymptote is of y = 0, hence the function can be given by:
C. [tex]F(x) = \frac{1}{(x + 2)(x - 1)}[/tex]
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y=x+3
y=-x-1
i need to find the solution of equations
Answer:
[tex]\huge\boxed{\sf \{(-2,1)\}}[/tex]
Step-by-step explanation:
Given equations:
y = x + 3
y = -x - 1
By comparing the above equations, we get:
x + 3 = -x - 1
Add x to both sides
x + x + 3 = -1 2x + 3 = -1Subtract 3 to both sides
2x = -1 - 3
2x = -4
Divide 2 to both sides
x = -4/2
x = -2Substitute x = -2 in first equation.
y = x + 3
y = -2 + 3
y = 1So,
Solution Set = {(x,y)}={(-2,1)}[tex]\rule[225]{225}{2}[/tex]
Answer:
[tex]x = - 2 \\ y = 1[/tex]
Step-by-step explanation:
The above are Simultaneous equations.
What are Simultaneous equations?Simultaneous equations are two or more algebraic equations which share same variables like X,Y or X,Y and Z.
They are called simultaneous equations because they can be solved the same time.
From the question,
[tex]y = x + 3 - - - - - - (1) \\ y = - x - 1 - - - - - - (2) \\ Substitute \: equation \: (2)into \: (1) \\ - x - 1 = x + 3 \\ Collect \: liketerms \\ - x - x = 3 + 1 \\ - 2x = 4 \\ Divide \: bothsides \: by \: - 2 \\ \frac{ - 2x}{ - 2} = \frac{4}{ - 2} \\ x = - 2 \\ Substitute \: the \: value \: of \: x \: into \: equation \: (1) \\ y = x + 3 \\ y = - 2 + 3 \\ y = 1 \\ Therefore \: x = - 2 \: \: and \: y = 1[/tex]
Rita divides avogadro’s number (approximately 6.02214 times. 1023) by 2.055 to calculate the number of atoms in a sample. which expression gives her result to the correct number of significant figures? 2.93 times. 1023 2.930 times. 1023 2.9305 times. 1023 2.93048 times. 1023
The correct answer is 2.930 × [tex]10^{23}[/tex]
What is Avogadro's number?
Avogadro's number, which is equal to 6.02214076 1023, is the quantity of units in one mole of any material (defined as its molecular weight in grams). Depending on the substance and the nature of the reaction, the units may be electrons, atoms, ions, or molecules (if any).
You have two numbers here. While number 2.0550 is stated with five significant figures, Avogadro's number is supplied with four. This implies that you must provide four significant figures with your result.
(6.022 × [tex]10^{23}[/tex]) / 2.0550 = 2.930 × [tex]10^{23}[/tex]
Therefore, the correct answer is 2.930 ×[tex]10^{23}[/tex] .
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Instructions: Find the length of the missing sides. Round your
answers to the nearest tenth. (Hint: Always make sure to label
your triangle first with your reference angle)
Degree 54
Hypotenuse 24
How do i find x and y?
The values of x and y are 19 and 14 respectively.
How to determine the lengthGiven the hypotenuse = 24
Opposite = x
Adjacent = y
Let's use the sine ratio to find the opposite side
sin of angle = opposite/hypotenuse
sin 54 = x/24
Cross multiplysin 54 × 24 ,= x
x = 19.42
x = 19
To find the adjacent side, we use cosine ratio
cos = adjacent/hypotenuse
cos 54 = y/25
Cross multiply
cos 54 × 24 = y
y = 14
Thus, the values of x and y are 19 and 14 respectively.
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A pendulum is swinging next to a wall. the distance d(t) (in cm) between the of the pendulum and the wall as a function of time t (in seconds) can be modeled by a sinusoidal expression of the form a * sin (b * t) + d at t = 0, when the endulum is exactly in the middle of its swing, the bob is 5 cm away from the wall. the bob reaches the closest point to the wall, which is 3 cm from the wall, 1 second later. find d(t). (t should be in radians)
The equation of the function d(t) is d(t) = -2sin(π/2 t) + 5
How to determine the function d(t)?The function is given as:
d(t) = a * sin(b * t) + d
The bob is 5 cm away from the wall implies that the vertical shift is 5.
This means that
d = 5
So, we have
d(t) = a * sin(b * t) + 5
The bob reaches the closest point to the wall, which is 3 cm from the wall.
So, the amplitude is
A = 3 - 5
Evaluate
A= -2
So, we have:
d(t) = -2 * sin(b * t) + 5
The period is calculated as:
B = 2π/t
Where
t = (5 + 3)/2
This gives
t = 4
Substitute t = 4 in B = 2π/t
B = 2π/4
Evaluate
B = π/2
So, we have:
d(t) = -2sin(π/2 t) + 5
Hence, the equation of the function d(t) is d(t) = -2sin(π/2 t) + 5
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Which graph shows the system
x²+y=2
x²+y²=9?
Green’s Sport Shop offers its salespeople an annual salary of $10,000 plus a 6% commission on all sales above $20,000. Every employee receives a Christmas bonus of $500. What are Mr. Cahn’s total earnings in a year in which his sales amounted to $160,000?
(A) $18,900
(B) $18,400
(C) $19,600
(D) $20,100
Mr. Cahn’s total earnings in a year is $18,900.
What is the total earnings?The total earnings is a function of the annual salary, commission and Christmas bonus.
Total earnings = annual salary + commission + Christmas bonus
Commission = 6% x (160,000 - 20,000)
6% x $140,000
0.06 x 140,000 = $8,400
Total earnings = $8,400 + 10,000 + $500 = $18,900
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Which equation represents x, the side length of the greater square? x2 (x – 2)2 = 10 x2 2x2 = 10 x2 (x – 2)2 = 100 x2 2x2 = 100
Step-by-step explanation:
10x2(x-2)2=100x2x2 2x2
I really need help for my hw please
Answer:
5.46
111
86
367.2
49
467
use labels
Step-by-step explanation:
1. [tex]\frac{39}{2} times . 0.28[/tex]
[tex]\frac{39}{2} times \frac{28}{100} =\frac{1092}{200} \\[/tex]
[tex]\frac{1092}{200} = \frac{273}{50}[/tex]
Answer 273/50 or 5.46 inches
2. [tex]\frac{97}{87} times \frac{100}{1} =\frac{9700}{87}[/tex]
Answer 9700/87= 111%ft
3. [tex]\frac{146}{1} divided \frac{170}{1}[/tex]
[tex]\frac{146}{1}times\frac{1}{170} =\frac{146}{170}[/tex]
Answer=146/170=73/85=
86%tons
4. [tex]\frac{136}{1} times\frac{270}{100} =\frac{36720}{100}[/tex]
Answer=367.2%ft
5 .[tex]\frac{60}{123}[/tex]=49%inches
6.[tex]\frac{56}{1} times\frac{100}{12} =[/tex]467%inches
What is the equation of the line that is used to show the reflection of a relation and its inverse?
help please and thank u <3
The graph and inverse of a function are reflections of each other along the line y = x.
A relation made up of ordered pairs (x, y) has as its inverse the set of all ordered pairs (y, x).
When a point is mirrored over the line y = x, the x- and y-coordinates swap places. Similarly, when a point is mirrored over the line y = -x, the x- and y-coordinates swap places and become negated.
Therefore,
The point (x, y)'s reflection over the line y = x is (y, x).
The point (x, y)'s reflection over the line y = - x is (-y, -x).
Thus, the graph and inverse of a function are reflections of each other along the line y = x.
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A waste management survey collected data about the types of materials that were recycled by three different states in
2008
20082008. The table at left shows the approximate amount of each material recycled measured in thousands of tons. Based on the information in the table at left, as a percentage, approximately what is the relative frequency of plastics recycled in New Mexico in plastics recycled in all three states combined?
As a percentage, the relative frequency of plastics recycling in New Mexico in 2008 compared to plastics recycled in all three states combined is approximately 11%.
What is relative frequency?A relative frequency measures the proportion of events that occur within a class out of the total number of observations.
When using relative frequency, the results are usually displayed in percentages, proportions, and fractions.
Data and Calculations:Year State Recycled Plastics Relative
(thousands of tons) Frequency
2008 New Mexico 500 0.111 (500/4,500)
2008 New York 1,500 0.333 (1,500/4,500)
2008 Texas 2,500 0.566 (2,500/4,500)
Total 4,500 1
Thus, the relative frequency of plastics recycling in New Mexico in 2008 compared to plastics recycled in all three states combined is approximately 11%.
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Answer: 9%
Step-by-step explanation:
just did the question
eli ate one-third of a pie on friday, one-fourth of the pie on saturday, and the final 50 ounces of the pie on sunday. how many ounces of pie did eli eat on saturday
If Eli ate one third of a pie on friday ,one fourth proportion of the pie on saturday and 50 ounces of the pie on sunday then it is found that she ate 30 ounces of pie.
Given that Eli ate one third of a pie on friday, one fourth of the pie on saturday, and final 50 ounces of the pie on sunday which is left out.
We have to find the amount of pie that she ate one saturday.
We are given fraction and we know that sum of all fractions of something is equal to 1.
Let the proportion that she ate on sunday be x.
1/3+1/4+x=1
Taking LCM.
(4+3+12x)/12=1
7+12x=12
12x=12-7
12x=5
x=5/12
So the left out out portion that she ate on sunday is 5/12 of the pie.
We are given that she ate 50 ounces on sunday so the total pie will be 12/5*50=120 ounces.
Portion eaten by Eli on saturday =1/4
Pie that she ate on saturday=1/4*120
=30 ounces.
Hence Eli ate 30 ounces of pie on saturday.
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Determine the x-intercept(s) of the rational function:
f(x) = (x ^ 2 - 16)/(x ^ 2 - 2x - 3)
Answer:
(-4,0) and (4,0)
Step-by-step explanation:
The x-intercepts occur for values of x where f(x) = 0.
f(x) = 0 when the nominator ([tex]x^{2} - 16[/tex]) = 0.
[tex]x^{2} -16[/tex] is a difference of squares,
so you can factor it as (x + 4)(x – 4)
When x = –4 or x = 4, the nominator is 0, and f(x) = 0
PLEASE HELP IM SUPER STUCK
Replace x with the value in the table and solve for y
-3: 2(-3)/3 + 4 = -6/3 + 4 = -2+4 = 2
0: 2(0)/3 +4 = 0/3 + 4 = 0+4 = 4
3: 2(3)/3 + 4 = 6/3 + 4 = 2 + 4 = 6
6: 2(6)/3 + 4 = 12/3 + 4 = 4+4 = 8
Answer:
When x = -3:
y = 2(-3)/3 + 4
y = 2
When x = 0:
y = 2(0)/3 + 4
y = 4
When x = 3:
y = 2(3)/3 + 4
y = 6
When x = 6:
y = 2(6)/3 + 4
y = 8
A relatively prime date is a date for which the number of the month and the number of the day are relatively prime. For example, June 17 is a relatively prime date because the greatest common factor of 6 and 17 is 1. How many relatively prime dates are in the month with the fewest relatively prime dates
There are 11 prime dates in it.
The prime numbers between 1 and 30 are 1, 2,3,5,7,11,13,17,19,23,29
Relative prime:
Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.
Hence There are 11 prime dates in the month of June.
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Answer: 10
Step-by-step explanation:
Since exactly 1 in every $n$ consecutive dates is divisible by $n$, the month with the fewest relatively prime days is the month with the greatest number of distinct small prime divisors. This reasoning gives us June ($6=2\cdot3$) and December ($12=2^2\cdot3$). December, however, has one more relatively prime day, namely December 31, than does June, which has only 30 days. Therefore, June has the fewest relatively prime days. To count how many relatively prime days June has, we must count the number of days that are divisible neither by 2 nor by 3. Out of its 30 days, $\frac{30}{2}=15$ are divisible by 2 and $\frac{30}{3}=10$ are divisible by 3. We are double counting the number of days that are divisible by 6, $\frac{30}{6}=5$ days. Thus, June has $30-(15+10-5)=30-20=\boxed{10}$ relatively prime days.
Which factorization could represent the number of water bottles and weight of each water bottle?
The factorization that could represent the number of water bottles and weight of each water bottle is 12(5x^2 + 4x + 2). Option B
What is factorization?The term factorization has to do with the process of obtaining common factors in an expression. It involves dividing each term in the expression with a factor that is common to all the terms in the expression.
The factorization that could represent the number of water bottles and weight of each water bottle is 12(5x^2 + 4x + 2).
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Missing parts;
Mara carried water bottles to the field to share with her team at halftime. The water bottles weighed a total of 60x2 + 48x + 24 ounces. Which factorization could represent the number of water bottles and weight of each water bottle? 6(10x2 + 8x + 2) 12(5x2 + 4x + 2) 6x(10x2 + 8x + 2) 12x(5x2 + 4x + 2)
On their website, a property management company states that the mean monthly rent for apartments on the east side of town is $700. A researcher for a consumer advocacy group believes that, due to the construction of newer apartment complexes in neighboring towns, the mean monthly rent on the east side, , is now lower. A random sample of 12 monthly rents for apartments on the east side has a mean of $687, with a standard deviation of $17. Assume that current monthly rents for apartments on the east side are approximately normally distributed. Based on the sample, is there enough evidence to conclude, at the 0.05 level of significance, that the population mean monthly rent is now less than what is stated on the website?
Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places.
(a) State the null hypothesis and the alternative hypothesis . (b) Determine the type of test statistic to use. (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value. (Round to three or more decimal places.) (e) Can we conclude that the mean monthly rent for apartments on the east side is less than what is stated on the website?
The null hypothesis is μ≥700 and alternative hypothesis is μ<700, the type of test statistic is t statistic, the statistical test value is -2.650, the critical value is -1.796 and the null hypothesis is reject.
Given the average monthly rent for apartments on the east side of the cities is $700, and the mean for a random sample of 12-month rents for apartments on the east side is $687, with a standard deviation of $17.
Statistical hypothesis testing is an important technique in inferential statistics. Used to test hypotheses about population parameters. Statistical tests are used to compute test statistics and p-values. Finally, use this test statistic and the p-value to make a decision about rejecting the null hypothesis.
(a) Let μ be the population and monthly rent. the null and alternative hypotheses are given below.
Null Hypothesis: μ≥700
Alternative hypothesis: μ< 700 This is a left-sided hypothesis test.
(b) Here, the sample size is less than 30 and the population mean is unknown. Therefore, a one-sample t-test can be used here. Therefore, the t statistic is the test statistic.
(c) Given [tex]\bar{x}[/tex]=687, s=17 and n=12, the test statistic is computed as
[tex]\begin{aligned}t&=\frac{\bar{x}-\mu_{0}}{s/\sqrt{n}}\\ &=\frac{687-700}{17/\sqrt{12}}\\ &=-2.64901888216\\ &=-2.650\end[/tex]
(d) For n-1=12-1=11 degrees of freedom
The critical value for a significance level of 0.05 with 11 degrees of freedom is
[tex]\begin{aligned}t_{crit}&=-1.7959\\ &=-1.796\end[/tex]
(e) Reject the null hypothesis because the statistical test value (-2.650) is less than the critical value (-1.796). There is ample evidence to support the claim that the average monthly rent for East Side apartments is lower than stated on the website.
Hence, The value of test statistic and critical value has a mean of $687 and a standard deviation of $17, which are -2.650 and -1.796.
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three decreased by eleven times a number
Step-by-step explanation:
3 - 11x
x is "a number".
so, the request is to multiply it by 11 and subtract the result from 3.
Can anyone solve question 2 and 10 with step by step explaination??
Answer:
Question 2: 4 1/2
Question 10: $7.24
Step-by-step explanation:
Question 2:
1 1/2/x = 3/9
x: total pages read3: minutes first spent9: minutes spent total1 1/2: pages read in 3 minutesto solve for x, we need to use 1 1/2/x and multiply it by x:
1 1/2/x * x
then we need to have 3/9 multiplied by x:
3/9 * x
this is equal to 1 1/2 = 3/9 * x
now you need to multiply both sides by the opposite of 3/9 = 9/3
3/2 * 9/3 = 3/9 * 9/3 * x which equals 9/2 = 4 1/2
final answer: 4 1/2
Question 10:
Jeff bought 3 boxes of cereal $2.99 each which comes up to $8.97,
he bought one gallon of milk for $4.98,
and 4 bananas for $0.50 each which in total is $2.00.
total amount spent: 8.97 + 4.98 + 2.00 = $15.95
We know there is a 20% off discount so what we have to do is take 20% off $15.95!
20%= $3.19
15.95 - 3.19 = 12.76
The total is now $12.76. But, Jeff payed with a $20.00 bill. Because of this, he will get $7.24 back. 12.76 + 7.24 = 20
Final answer: $7.24
4+5(7-1)+8/2
Simplify
Answer:38
Step-by-step explanation:4+5×6+4=4+30+4=38
Given the equation, y=2x+6, what is its slope?
Select one:
O a. 6
Ob. 2
O c. 3
O d. 1
Answer:
B, 2
Step-by-step explanation:
The slope in a y=mx+b equation is m. The m in your equation is 2.
Therfore, your slope is 2.
Select one or more expressions that together represent all solutions to the equation.
Your answer should be in radians.
Assume n is any integer.
30 cos (30x) + 14 = -16
Choose all answers that apply:
Answer:
D. π/30 + n(π/15)
Step-by-step explanation:
The given equation can be solved by isolating the cosine function and using the inverse function to find the angles.
Solution30cos(30x) +14 = -16
30cos(30x) = -30 . . . . . . subtract 14
cos(30x) = -1
This is an extreme value of the cosine function that first occurs where the argument is π, and repeats every 2π after that:
30x = π +2nπ
x = π/30 +n(π/15) . . . . . odd multiples of π/30
__
Additional comment
The answer choices other than D include all multiples of π/30, or only even multiples of π/30. Either way, they are not part of the correct answer.
The name of this bronze-casting process relies on a modeled original form made from a pliable material. This method is known as ________.
The bronze-casting process that depends on a modelled original form is: lost-wax casting.
What is Lost-wax Casting?Lost-wax casting is a bronze-casting process which is also referred to as the cire-perdue. In this type of metal casting, a wax model is created when a molten metal is usually poured into a mold. The wax model is then melted and drained.
In summary, the name for this bronze-casting process that relies on this wax model is called: lost-wax casting.
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