The computation illustrate that there'll be 13 cases and 2 additional units.
How to illustrate the information?From the information given, it was stated that 80 units are needed, 6. units per case.
Therefore, the number of cases will be:
= 80/6
= 13 remainder 2.
Therefore, there'll be 13 cases and 2 additional units
Complete information
80 units are needed, 6. units per case. What is the number of cases and the number of additional units?
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The marital status distribution of the U.S. male population, ages 15 and older, is as follows: 35.4% never married, 53.6% married, 2.7% widowed, and 8.3% divorced/separated. A random sample of 300 U.S. young adult males, 18 to 24 years old, found 141 never married, 132 married, 3 widowed, and 24 divorced/separated. Using α = 0.10, is this evidence that males in this age group follow a different distribution than all males in the U.S.? Write the hypotheses, calculate the expected counts, check the condition, calculate the test statistic, and use either the critical value approach or the p-value approach to make a conclusion about the question being asked.
The hypothesis illustrates that the males in the group don't follow a same distribution as all the males that are in the United States.
How to illustrate the information?Based on the information given, it should be noted that the degree of freedom given in this case will be:
= 4 - 1
= 3
By using the Excel function, the p-value is given as 0.0002. In this case, we've to reject the null hypothesis if the p value is less than 0.1.
Therefore, we will reject the null hypothesis in this case. In inferential statistics, the null hypothesis is that two possibilities are the same. It is observed difference is due to chance alone. Using statistical tests, it is possible to calculate the likelihood that the null hypothesis is true
Therefore, the hypothesis illustrates that the males in the group don't follow the same distribution as all the males that are in the United States.
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Please draw the number line and show me if possible:)
The solution to the given inequality expression is expressed as x ≥ 6
Solving inequalitiesGiven the inequality expression shown below;
5x-9/7≥3
Cross multiply
(5x -9)≥7(3)
Expand
5x-9≥21
Add 9 to both sides
5x ≥ 21 + 9
5x ≥ 30
x ≥6
The solution to the given inequality expression is expressed as x ≥ 6
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Can someone help me with this plss
Answer:
6. Quadrant four
7. Quadrant three
8. Quadrant one
Step-by-step explanation:
These questions give you points to graph and then asks which quadrants they are graphed in. Here is a visual.
The acute angle between the lines x – 3y – 6 = 0 and y = 2x + 5 is
Answer:
Step-by-step explanation:
eq. of line x-3y-6=0
3y=x-6
y=1/3 x-6/3
or
y=1/3 x-2
its slope m1=1/3
y=2x+5
slope m2=2
if α is the angle between the lines then
[tex]tan~\alpha =|\frac{m1-m2}{1+m1m2} |=|\frac{\frac{1}{3} -2}{1+1/3\times 2}| =|\frac{1-3\times2}{3+2}| =5/5=1=tan 45\\\alpha =45^\circ\\[/tex]
See attachment for the full question
The inverse of the demand function is; P = 9 - 0.25Q
The profit-maximizing price and quantity are; $8.5 and 2 units.
The maximum profit is; $1
How to find the inverse of a function?
A) The demand function we are given is;
Q = 36 - 4P
Making P the subject gives the inverse demand function;
P = (36 - Q)/4
P = 9 - Q/4
P = 9 - 0.25Q
B) The profit-maximization point is the point at which MR = MC.
MR refers to the marginal revenue and MC is the marginal cost.
MC can be calculated as the first derivative of the cost function:
C(Q) = 4 + 4Q + Q²
MC = C'(Q) = 2Q + 4
Total Revenue = Price * Quantity
Total Revenue = (9 - 0.25Q) * Q
Total Revenue = 9Q - 0.25Q²
MR is gotten by differentiating Total Revenue to get;
MR = 9 - 0.5Q
Applying the condition MR = MC, we have;
9 - 0.5Q = 4 - 2Q
Solving for Q gives Q = 2
Thus, profit maximizing quantity is 2.
Thus, profit maximizing price will be;
P(2) = 9 - 0.25(2)
P(2) = $8.5
C) Formula for Maximum Profit is;
Profit = Total Revenue - Total Cost
Total Revenue = 8.5 * 2
Total revenue = $17
Total Cost is;
C(2) = 4 + 4(2) + 2²
C(2) = $16
Thus;
Maximum Profit = 17 - 16 = $1
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∫[tex]\frac{xdx}{(x^{2}+4)^{3} }[/tex]
Substitute [tex]u=x^2+4[/tex] and [tex]du=2x\,dx[/tex]. Then the integral transforms to
[tex]\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \int \frac{du}{u^3}[/tex]
Apply the power rule.
[tex]\displaystyle \int \frac{du}{u^3} = -\dfrac1{2u^2} + C[/tex]
Now put the result back in terms of [tex]x[/tex].
[tex]\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \left(-\dfrac1{2u^2} + C\right) = -\dfrac1{4u^2} + C = \boxed{-\dfrac1{4(x^2+4)^2} + C}[/tex]
A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them that the last 18 houses that sold in their neighborhood took an average time of 100 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 20 days. (You may find it useful to reference the z table.)
a. What assumption regarding the population is necessary for making an interval estimate for the population mean?
multiple choice
Assume that the central limit theorem applies.
Assume that the population has a normal distribution.
b. Construct the 99% confidence interval for the mean sale time for all homes in the neighborhood. (Round final answer to 2 decimal places.)
The 99% Confidence interval for the mean sale time for all homes in the neighborhood is:87.857, 112.143.
Confidence intervala. The assumption is: Assume that the population has a normal distribution.
The CI is exact for the normal populations and for small samples the z-interval method should be used in a situation where the variable is normally distributed.
b. Confidence interval:
CI=Sample mean±z-score×Standard deviation/√Size of the sample
CI=100-2.576×20/√18, 100+2.576×20/√18
CI=100-12.143, 100+12.143
CI=87.857, 112.143
Therefore the 99% Confidence interval is 87.857, 112.143.
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How much will you have saved after 6 years by contributing $1,200 at the end of each year if you expect to earn 11% on the investment?
Savings after 6 years would be $ 1992.
What are savings?Savings is the money that remains after expenses and other commitments have been subtracted from income.
Savings are the sum of money that would otherwise be lying about, not being risked on investments or used for consumption.
Savings and investing can be compared because the latter includes putting money at risk in an effort to try to increase wealth.
Indicators of household debt or a negative net worth include negative savings.
According to the question,
Amount contributed(P)= $1200
Rate(R)= 11%
Time(T)= 6 years
Interest(SI)=P*R*T/100
= 1200*11*6/100
= 792
Savings after 6 years = P+ SI
= 1200 + 792
= $ 1992
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Write down the 2×2 matrices representing the following transformations of the plane. (i) Reflection in the y-axis, (ii) Reflection in the line y = x (iii) Rotation through 180◦ about the origin (iv) Enlargement from the origin with scale factor λ.
The 2 x 2 matrices of the transformations are
[tex]\left[\begin{array}{cc}-1&0\\0&1\end{array}\right][/tex], [tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right][/tex], [tex]\left[\begin{array}{cc}-1&0\\0&-1\end{array}\right][/tex] and [tex]\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right][/tex]
(i) Reflection in the y-axisThe rule of reflection in the y-axis is
(x, y) ⇒ (-x, y)
This is represented as:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&y\end{array}\right][/tex]
When solved using a graphing calculator, we have:
[tex]\left[\begin{array}{cc}-1&0\\0&1\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&y\end{array}\right][/tex]
Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}-1&0\\0&1\end{array}\right][/tex]
(ii) Reflection in the line y = xThe rule of reflection in the line y = x is
(x, y) ⇒ (y, x)
This is represented as:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}y&x\end{array}\right][/tex]
When solved using a graphing calculator, we have:
[tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}y&x\end{array}\right][/tex]
Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}0&1\\1&0\end{array}\right][/tex]
(iii) Rotation through 180◦ about the originThe rule of rotation through 180◦ about the origin is
(x, y) ⇒ (-x, -y)
This is represented as:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&-y\end{array}\right][/tex]
When solved using a graphing calculator, we have:
[tex]\left[\begin{array}{cc}-1&0\\0&-1\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}-x&y\end{array}\right][/tex]
Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}-1&0\\0&-1\end{array}\right][/tex]
(iv) Enlargement from the origin with scale factor λ.The rule of the enlargement from the origin with scale factor λ.
(x, y) ⇒ (λx, λy)
This is represented as:
[tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}\lambda x&\lambda y\end{array}\right][/tex]
When solved using a graphing calculator, we have:
[tex]\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}\lambda x&\lambda y\end{array}\right][/tex]
Hence, the 2 x 2 matrix is [tex]\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right][/tex]
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what percentage was the price of the shirt reduced
Suppose f(x)=2^x. What is of g(x)=f(3x)?
Answer:
All you need to do is suppose x = 3x :
[tex] \tt \: g(x) = \boxed{ \tt{2^{3x} }} [/tex]
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what is the value of x 44 inches and 55 inches triangle
Answer: I don't know what you are talking about, but if x is the area, then the answer is 1,210.
Step-by-step explanation: 44 x 55 x 1/2 = 1,210. The formula for the area of a triangle is 1/2 times length times height. Therefore, x = 1,210
Hope this helps.
If
xn = (n−1)cos(n2 +n+1) 2n−1
EXERCISES
then xn has a convergence subsequence.
The proof using Bolzano-Weierstrass Theorem is suggestive of the fact that the bounded sequence that is given has a subsequence that is convergent.
What is Bolzano-Weierstrass Theorem?The Bolzano-Weierstrass theorem, is a key conclusion regarding convergence in a finite-dimensional Euclidean space in mathematics, notably in real analysis.
According to the theorem above, each bounded sequence in Rⁿ has a convergent subsequence.
***See proof in the attached document.
Hence the given sequence is bounded. It is safe therefore to state that given Bolzano-Weierstrass theorem, the stated real bounded sequence has a convergent subsequence.
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To support the tree a guy wire 8.1 m long is attached to the trunk and then secured in the ground find the height of the leafty part of the tree to the nearest tenth
The height of the leafy part will be 6m.
How to calculate the height?Other part of the question:
At the same time, a vertical pole 3m high vast s shadow 4m long.
Based on the information given, the height will be:
h/8 = 3/4
h = (3 × 8)/4
h = 6
Therefore, the height is 6m.
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Find the value of t0 such that the following statement is true: P(-t0 ≤ t ≤ t0) = .95 where df = 15. Group of answer choices
The value of To from the t table will be 2.131
How to get the value?The following can be deduced from the information:
P(-t0 < t < t0) = 0.95
2*P(t < t0) - 1 = 0.95
P(t < t0) = 0.975
df = 15
From t-table (column 1-0.975 = 0.025) in the row 15. Therefore, t0 = 2.131.
In conclusion, the answer is 2.131.
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A model house has a scale of 1 in : 2 ft. if the real house is 26 ft wide then how wide is the model house.
Answer: 13 in.
Step-by-step explanation:
All you need to do is divide 26 by 2 in this case.
How much should be invested now at an interest rate of 6.5% per year, compounded continuously, to have $1500 in two years?
Do not round any intermediate computations, and round your answer to the nearest cent.
If necessary, refer to the list of financial formulas.
Answer:
$1317.14
Step-by-step explanation:
compounded continuously formula is A=Pe^rt
given that you want to have $1500 in 2 years while the rate is 6.5%, you have A, r, and t of the formula and you are just looking for the P.
plugging everything in...
1500=P (e)^2x0.065
P=1500/1.139
P=1317.14
Ross Martin arrived at the following tax information gross salary 56,145 interest earnings 205 dividend income 65 standard deduction 12,000 itemized deductions 11,250 adjustments to income 1200 what amount with Ross report as taxable income income
The amount that Ross report as taxable income will be $31965.
What is a taxable income?Taxable income refers to the base upon which an income tax system imposes the tax.
In other words, the taxable income is the income over which the government imposed tax. It includes some or all items of income and is reduced by expenses and other deductions.
From the information:
Gross salary = $56,145
Interest earnings = $205
Dividend income = $65
Standard deduction = $12,000
Itemized deductions = $11,250
Adjustments to income = $1,200
The taxable income is given by:
= Gross salary + Interest earnings + Dividend income - Standard deduction - Itemized deductions - Adjustment to income
= 56145 + 205 + 65 - 12000 - 11250 - 1200
= $31965
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Help would really be needed asap!
Answer:
C
Step-by-step explanation:
For lines AC and EF, line FC is a transversal.
Angles ACF and EFC are same side interior angles.
Since their measures add to 180°, then the lines are parallel.
Answer: Choice C
NO LINKS!! Please help me with this problem.
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Information : The given ellipse is a horizontal ellipse, and it's centre lies on origin, as the foci are given on x - axis.
The foci of the ellipse can be written in form :
[tex]\qquad \sf \dashrightarrow \: ( \pm ae , 0)[/tex]
So,
[tex]\qquad \sf \dashrightarrow \: ae = 5[/tex]
and Vertex of the ellipse can be written as
[tex]\qquad \sf \dashrightarrow \: (\pm a,0)[/tex]
so, we get a = 11Now, plug the value in first equation ~
[tex]\qquad \sf \dashrightarrow \: ae = 5[/tex]
[tex]\qquad \sf \dashrightarrow \: 11e = 5[/tex]
[tex]\qquad \sf \dashrightarrow \: e = \cfrac{5}{11} [/tex]
Now, we have to find b (length of semi minor axis)
we can use the formula ~
[tex]\qquad \sf \dashrightarrow \: b {}^{2} = {a}^{2} (1 - {e}^{2} )[/tex]
[tex]\qquad \sf \dashrightarrow \: b {}^{2} = 121(1 - \frac{25}{121} )[/tex]
[tex]\qquad \sf \dashrightarrow \: b {}^{2} = 121( \frac{121 - 25}{121} )[/tex]
[tex]\qquad \sf \dashrightarrow \: b {}^{2} = 96[/tex]
Now, we can write the equation of ellipse as :
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {x}^{2} }{ {a}^{2} } + \cfrac{ {y}^{2} }{ {b}^{2} } = 1[/tex]
[ plug the values ]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {x}^{2} }{ {121}^{} } + \cfrac{ {y}^{2} }{ {96}^{} } = 1[/tex]
Answer:
[tex]\dfrac{x^2}{121}+\dfrac{y^2}{96}=1[/tex]
Step-by-step explanation:
General equation of an ellipse:
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]
where:
center = (h, k)Vertices = (h±a, k) and (h, k±b)Foci = (h±c, k) and (k, h±c) where c²=a²−b²Major Axis: longest diameter of an ellipseMinor Axis: shortest diameter of an ellipseMajor radius: one half of the major axisMinor radius: one half of the minor axisIf a > b the ellipse is horizontal, a is the major radius, and b is the minor radius.
If b > a the ellipse is vertical, b is the major radius, and a is the minor radius.
Given:
foci = (-5, 0) and (5, 0)vertices = (-11, 0) and (11, 0)Therefore, the ellipse is horizontal with its center at (0, 0):
⇒ h = 0 and k = 0
⇒ a = 11
⇒ c = 5
To find b², use c² = a² − b²:
⇒ 5² = 11² − b²
⇒ b² = 11² − 5²
⇒ b² = 96
Therefore, the standard form of the equation of the ellipse is:
[tex]\implies \dfrac{(x-0)^2}{11^2}+\dfrac{(y-0)^2}{96}=1[/tex]
[tex]\implies \dfrac{x^2}{121}+\dfrac{y^2}{96}=1[/tex]
10-A biased die is thrown thirty times and the number of sixes seen is eight. ( The probability of face six is 8 = 4 ) If the die is thrown a further twelve times find:
30 15
(a) the probability that a six will occur exactly twice; (b) the expected number of sixes: () = ;
(c) the variance of the number of sixes.
Using the binomial distribution, we have that:
a) There is a 0.2111 = 21.11% probability that a six will occur exactly twice.
b) The expected number of sixes is of 3.2.
c) The variance of the number of sixes is of 2.35.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the parameters are given by:
p = 8/30 = 0.2667, n = 12.
Item a:
The probability is P(X = 2), hence;
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{12,2}.(0.2667)^{2}.(1-0.2667)^{10} = 0.2111[/tex]
Item b:
The expected number of the binomial distribution is:
E(X) = np.
Hence:
E(X) = 12 x 8/30 = 3.2.
Item c:
The variance of the binomial distribution is:
V(X) = np(1-p).
Hence:
E(X) = 12 x 8/30 x 22/30 = 2.35.
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how can I solve for x? Answers ASAP
Using the inscribed angle theorem, the value of x is: 9.
What is the Inscribed Angle Theorem?Note that an intercepted arc is regarded as part of the circumference of a circle, which is between a chord and a tangent. Thus, based on the inscribed angle theorem, the inscribed angle measure = 1/2(the intercepted arc measure).
So, we would have:
m∠DEF = 1/2(arc DE)
m∠DEF = 4x + 19
arc DE = 360 - (28x - 2) = 360 - 28x + 2
arc DE = 362 - 28x
Plug in the values
4x + 19 = 1/2(362 - 28x)
Solve for x
2(4x + 19) = 362 - 28x
8x + 38 = 362 - 28x
8x + 28x = 362 - 38
36x = 324
x = 324/36
x = 9
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which of the following best describes the graph below?
Answer:
I think it's B
Step-by-step explanation:
because it's a function,it's 5 to 4 not one to one
An advertiser claims that 80% of people stream their TV, 10% have cable, and the rest do not watch TV. To evaluate this claim, they take a sample and calculate a test statistic of
. If their rejection region is, what would their conclusion be?
The conclusion that they would arrive at based on the rejection region would be to reject the null hypothesis.
What is the rejection region?This is the region that tells us that we are not to accept the null. The conclusion would be to reject the null.
This happens when the rejection region is found to be around the area that is in the critical value.
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what is the measure of the reference angle for a 102 degree angle? A. 78 degrees B. 68 degrees C. 57 degrees D. 12 degrees
Answer:
A. The reference angle measures 78 degrees
what is the measure of XYZ?
46°
94°
a. 46°
b. 140°
c. 94°
d. 70°
Answer:
46+96=140°_÷__^_^^^^=^
A farmer finds there is a linear relationship between the number of bean stalks, n , she plants and the yield, y , each plant produces. When she plants 30 stalks, each plant yields 30 oz of beans. When she plants 33 stalks, each plant produces 29 oz of beans. Find a linear relationship in the form y=mn+b that gives the yield when n stalks are planted.
The equation y = -0.5x +45 represent the linear relationship.
According to the statement
We have given that the When she plants 30 stalks, each plant yields 30 oz of beans and When she plants 33 stalks, each plant produces 29 oz of beans.
And we have to find the linear relationship between the plants which are stalks.
So, For this purpose,
When we consider this graph as a straight line, the two points lying on the line would be
(30, 30) and (34, 28) taking n as horizontal and y vertical
Using two point equation we find that
the equation of the line is
y-y1 / y2-y1 = x-x1 / x2-x1
Substitute the points as x =n and put the other values in it then
y-30 / 28-30 = x-30 / 34-30
Then
y = -0.5x +45
This represent the relationship.
So, The equation y = -0.5x +45 represent the linear relationship.
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a coin is flipped 10 times and the result is recorded. How many outcomes are in the event n(A)?
There are 1024 outcomes in the event
How to determine the number of outcomes?The given parameters are:
Device = coin
Number of flips = 10
A coin has 2 faces.
So, the number of outcomes is
Outcome = Faces^Flip
This gives
Outcome = 2^10
Evaluate
Outcome = 1024
Hence, there are 1024 outcomes in the event
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Answer:
[tex]1024[/tex]
Step-by-step explanation:
Each and every flip of our coin has two possible outcomes on the whole: it is either the heads or the tails. Besides, it resembles the bit in computing, right? Indeed, it has two options likewise: it can be either [tex]0[/tex] or [tex]1[/tex]. For now on I suggest thinking neither in heads nor in tails, but in bits. Suppose the heads is [tex]0[/tex], the tails is [tex]1[/tex]. Let us slightly simplify the condition, namely: suppose that the number of flips is [tex]3[/tex]. Then, our possible outcomes:
[tex]000 \\ 001 \\ 010 \\ 011 \\ 100 \\ 101 \\ 110\\ 111[/tex]
Take a look at the first number. In case it is [tex]0[/tex], we have [tex]4[/tex] outcomes because we can put either [tex]0[/tex] or [tex]1[/tex] not only on the second place, yet also on the third one. Abiding by the same logic, we also have [tex]4[/tex] outcomes when the first one is [tex]1[/tex]. In mathematics: [tex]2 * 2 * 2 = 2^3 = 8[/tex] outcomes.
As for the initial condition, it does not globally differ from our simplification, it just has more flips, hence it is not just a walk in the park to list all the possible outcomes anymore in this case, it is time-consuming otherwise. Even though, it is still not a big deal to count it: [tex]2 * ... * 2 = 2^{10} = 1024[/tex] outcomes.
in how many ways can the letters in the word payment be arranged if the letters are taken 6 at a time
Considering the definition of permutation, in 5040 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 6 at a time.
What is PermutationPermutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.
That is, permutations refer to the action of arranging all the members of a set in some sort of order or sequence.
In other words, permutations (or Permutations without repetition) are ways of grouping elements of a set in which:
take all the elements of a set.the elements of the set are not repeated.order matters.To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:
[tex]mPn=\frac{m!}{(m-n)!}[/tex]
where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.
This caseIn this case, you have:
the letter word "PAYMENT", where the number of letters is 7.the letters are taken 6 at a time.Then, you know that:
m= 7n=6Replacing in the definition of permutation:
[tex]7P6=\frac{7!}{(7-6)!}[/tex]
Solving:
[tex]7P6=\frac{7!}{1!}[/tex]
7P6= 5040
Finally, in 5040 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 6 at a time.
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Match each expression to the scenario it represents.
Expressions
Scenario
the price of a game that’s been discounted
18% off its list price (x)
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the price of a toy that sells for 18% more
than the amount (x) needed to build the toy
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the volume of water remaining in a tank after
of its original volume (x) is drained out
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the total amount of flour in a bakery after receiving new stock equal to of its current stock (x)
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The expression matched with each scenario is;
Scenario 1: 0.82x
Scenario 2: 1.18x
Scenario 3: 7/10x
Scenario 4: 13/10x
AlgebraThe price of a game that’s been discounted
18% off its list price (x)
Total price = x
Discount = 18%x = 0.18x
New price = x - 0.18x
= 0.82x
The price of a toy that sells for 18% more
than the amount (x) needed to build the toy
Original price = x
Percentage increase = 18%x = 0.18x
New price = x + 0.18x
= 1.18x
The volume of water remaining in a tank after 3/10 of its original volume (x) is drained out
Original volume = x
Volume drained = 3/10x
New volume = x - 3/10x
= 7/10x
The total amount of flour in a bakery after receiving new stock equal to 3/10 of its current stock (x)
Original stock = x
New stock = 3/10x
Total stock = x + 3/10x
= 13/10x
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