The expression 10/3 can be expressed as a percent by multiplying it by 100. The result is approximately 333.33%.
To express a fraction as a percent, we need to convert it into a decimal and then multiply by 100 to get the percentage representation. In this case, we have 10/3 as the fraction.
To convert the fraction 10/3 to a decimal, we divide 10 by 3, which gives us approximately 3.3333. To express this decimal as a percentage, we multiply it by 100. Thus, 3.3333 * 100 = 333.33%.
Therefore, the expression 10/3 can be expressed as approximately 333.33% when converted to a percentage.
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What is the value of x in the equation 4(2x + 10) = 0?
-5
-7
5
7
Answer:
Step-by-step explanation:
4(2x+10)=0
8x+40=0
-40 -40
8x=-40
x=-5
Answer:
-5
Step-by-step explanation:
First you have to distribute 4 to 2x and 10, giving us 8x + 40 = 0. Then subtract 40 from both sides, giving us 8x = -40. Now divide -40 by 8, which gives us -5.
-4(z + 3) - 4(5 - 4z) solution
Answer:
12z-32
Step-by-step explanation:
-4z-12-20+16z
what is (−4)⋅(−4)⋅(−4)⋅y⋅y
Answer:
64y^2
Step-by-step explanation:
For the following estimated multiple linear regression equation,
Y = 8 + 45X_1 + 16X_2
a. what is the interpretation of the estimated coefficient of X_2
b. if R^2? (Goodness of Fit Coefficient) is 0.98 in this estimated regression equation, what does that tell you?
(a) The estimated coefficient of X₂ captures the average impact of X₂ on the response variable Y, given the specified regression model. (b) a higher R² value indicates a better fit of the model to the data and a higher degree of explained variability.
(a.) The estimated coefficient of X₂ in the multiple linear regression equation (Y = 8 + 45X₁ + 16X₂) represents the expected change in the dependent variable (Y) for a one-unit increase in the independent variable X₂, while holding all other independent variables constant.
In this case, the estimated coefficient of X₂ is 16, so for every one-unit increase in X₂, the expected change in Y is an increase of 16 units, assuming X₁ and other variables remain constant.
(b.) The coefficient of determination (R²) is a measure of the proportion of the total variation in the dependent variable (Y) that can be explained by the independent variables (X₁ and X₂) in the regression model. In this case, if the R² value is 0.98, it means that approximately 98% of the total variation in Y can be explained by the linear relationship between X₁, X₂, and the constant term.
A high R² value of 0.98 indicates a very strong fit of the regression model to the data. It suggests that 98% of the variability in the dependent variable Y is accounted for by the independent variables X₁ and X₂, while the remaining 2% may be attributed to other factors or random variation.
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Please help with 1 & 2!!! Will mean a lot!! And give brainly!!! Help plz due today
1. to find angle x:
angles on a straight line add to 180º : 180-92º = 88º
to find angle y:
exterior angle equals opposite interior angles: 88+22=110º
2. to find angle x:
angles on a straight line add to 180º : 180-118 = 62º
to find angle y:
exterior angle equals opposite interior angles: 62+52 = 114º
sorry if i got any of the angles wrong, the picture was a bit blurry and I couldn't tell that well, let me know if i got it wrong and i'll fix it
A small town is trying to establish a transportation system of large and small vans.
It can spend no more than $100,000 for purchasing both sizes of vehicles and no
more than $500 per month for maintenance. The town can purchase a small van for
$10,000 and maintain it for $100 per month. The large vans cost $20,000 each and
can be maintained for $75 per month. Each large van carries a maximum of 15
passengers and each small van carries a maximum of 7 passengers. Find the
maximum number of passengers the transportation system can handle given the
constraints. How many large and small vans will they need to maximize the
number of
passengers
it can service?
its a .......................................Step-by-step explanation:
Solve the following equation when x =
2 and y = 4.
3x + 2y + 4 =
Step-by-step explanation:
the answer is x=-4 ,y=-5
I do a one-way within-subjects ANOVA with one factor and four groups. How many groups would my participants be a member of? O 3 0 1 O 2 4 Question 8 2 pts Which sums of squares is only found in a one-way within-subjects ANOVA? O Between-persons sums of squares O Interaction sums of squares O Between-groups sums of squares Total sums of squares Within-groups sums of squares Question 9 2 pts I do a one-way within-subjects ANOVA and find that my overall model is significant. What do I do next? I would look at my b-weights to see which variables are significant o I would do a post-hoc Tukey test I would do a post-hoc Bonferroni test I would do a simple main effects analysis Question 10 2 pts True or false: On average, eta-squared, partial eta squared, and R-squared are all measures of effect size that refer to the proportion of variance explained within a study. True False 11 39 2 pts When doing a two-way between subjects ANOVA, how many F-tests would I normally run? O1 O2 04 D Question 12 2 pts Which sums of squares is only found in a two-way between-subjects ANOVA? Between-groups sums of squares Between persons sums of squares Within-groups sums of squares Total sums of squares Interaction sums of square?
1. The participants would be a member of all four groups. In a within-subjects ANOVA, participants are exposed to all levels of the factor, so they experience each group.
2. The within-groups sums of squares is only found in a one-way within-subjects ANOVA. This represents the variability within each group or condition.
3. In this case, you would typically conduct a post-hoc analysis to determine which specific groups or conditions differ significantly from each other. Common post-hoc tests for within-subjects ANOVA include the Bonferroni or Tukey tests. These tests help identify pairwise differences between the groups.
4. True. Eta-squared, partial eta-squared, and R-squared are all measures of effect size that indicate the proportion of variance explained within a study. They provide information about the strength and magnitude of the effect being studied.
5. When conducting a two-way between-subjects ANOVA, you would typically run two F-tests: one for each main effect and one for the interaction effect. The main effects assess the effects of each independent variable separately, while the interaction effect examines whether the combined influence of the variables is significant.
6. The between-groups sums of squares is only found in a two-way between-subjects ANOVA. It represents the variability between the different groups or levels of the independent variables.
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Consider an RC circuit in which the resistance R = 2, the capacitance C = 0.5 F, and the electromotive force E (t) = te-2t V. What is the differential equation governing the variation of c?
The differential equation governing the variation of the charge (c) in the given RC circuit is 2(d^2q/dt^2) + (1/0.5)(dq/dt) = d(E(t))/dt, where q represents the charge, t represents time, and E(t) represents the electromotive force of the circuit. This equation describes the relationship between the charge, current, and voltage in the RC circuit.
To compute the differential equation governing the variation of the charge (c) in the given RC circuit, we can start by using Kirchhoff's voltage law (KVL) and the relationship between charge, capacitance, and voltage.
Kirchhoff's voltage law states that the sum of the voltages in a closed loop in a circuit is equal to zero. In this case, the voltage across the resistor (VR) and the voltage across the capacitor (VC) must sum up to the electromotive force (E) of the circuit.
The voltage across the resistor can be calculated using Ohm's Law: VR = IR, where I is the current flowing through the circuit.
The voltage across the capacitor can be calculated using the formula: VC = (1 / C) ∫Idt, where ∫Idt represents the integral of the current over time.
Combining these equations, we have:
E(t) = VR + VC
E(t) = IR + (1 / C) ∫Idt
Differentiating both sides of the equation with respect to time, we get:
d(E(t)) / dt = d(IR) / dt + d((1 / C) ∫Idt) / dt
Since the resistance R and the capacitance C are constant values, their derivatives with respect to time are zero.
d(E(t)) / dt = R(dI / dt) + (1 / C)(I)
Substituting I with dq / dt, where q represents the charge c, we get:
d(E(t)) / dt = R(d^2q / dt^2) + (1 / C)(dq / dt)
Simplifying the equation, we obtain the differential equation governing the variation of c:
R(d^2q / dt²) + (1 / C)(dq / dt) = d(E(t)) / dt
In summary, the differential equation governing the variation of the charge (c) in the given RC circuit is:
2(d^2q / dt²) + (1 / 0.5)(dq / dt) = d(E(t)) / dt
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Use the given values to complete the table. Create quantities proportional to each other and graph them.
10
9
у
8
7
6
5
4
2
4
(4,2)
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
A group of adult males has foot lengths with a mean of 28.48 cm and a standard deviation of 1.41 cm. Use the range rule of thumb for identifying significant values to identify the limits separating values that are significantly low or significantly high. Is the adult male foot length of 31.6 cm significantly low or significantly high? Explain. Significantly low values are cm or lower. (Type an integer or a decimal. Do not round.)
Thus, the adult male foot length of 31.6 cm is significantly high since it falls outside the range of values considered normal for adult male foot length.
Range rule of thumb:The range rule of thumb is a formula used to calculate the range of the data that's spread around the mean. The range is the difference between the maximum and minimum data values. The range rule of thumb estimates the expected range for a normally distributed dataset by taking the difference between the maximum and minimum values, then multiplying that difference by 4. This estimate is usually only useful for datasets with more than 15 data points. Thus, using the range rule of thumb, the range of a normally distributed data set is approximately four times the standard deviation. Thus, the range of the adult male foot length is as follows:Range = 4 × Standard deviation= 4 × 1.41 cm= 5.64 cmWe can then identify the limits separating values that are significantly low or high as follows:Significantly low values are cm or lower: 28.48 - 2 x 1.41 = 25.66 cmSignificantly high values are cm or higher: 28.48 + 2 x 1.41 = 31.3 cmThus, the adult male foot length of 31.6 cm is significantly high since it falls outside the range of values considered normal for adult male foot length.
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What is |6 3/8 - 2| + |-8 5/8 + (-1)|?
Answer:
14
Step-by-step explanation:
I really need help please!!!!!
Step-by-step explanation:
area of a quadrilateral is b x h
if the base is 7 the height is x and the area is 63 then:
7x=63
divide both sides by 7
7/7x=63/7
x=9
Hope that helps :)
the economic stimulus act of 2008 focused on ________, whereas the american recovery and reinvestment act of 2009 focused on ________.
The Economic Stimulus Act of 2008 focused on providing tax relief, while the American Recovery and Reinvestment Act of 2009 focused on a combination of tax cuts, government spending, and investments for economic growth.
the Economic Stimulus Act of 2008 was enacted in response to the economic downturn that occurred during the Great Recession. Its main objective was to provide immediate relief to the economy by implementing tax incentives and rebates for individuals and businesses. The act aimed to encourage consumer spending and investment by putting more money into people's pockets and reducing the tax burden on businesses.
On the other hand, the American Recovery and Reinvestment Act of 2009 was a broader and more comprehensive economic stimulus package. It included a mix of tax cuts, grants, loans, and direct government spending on infrastructure projects, renewable energy, healthcare, education, and other areas. The goal was to not only provide short-term economic relief but also to make long-term investments that would promote sustainable economic growth and job creation.
Overall, while both acts were aimed at stimulating the economy, the focus of the Economic Stimulus Act of 2008 was primarily on tax relief, while the American Recovery and Reinvestment Act of 2009 encompassed a wider range of measures to boost the economy and address various sectors affected by the recession.
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Choose the item that does NOT have a measurable volume.
a dollar bill
air
a box of crackers
a water bottle
Answer:
Air
Step-by-step explanation:
You can't really measure air
Answer:
Air
Step-by-step explanation:
You cannot measure air because it is invisible.
The cumulative frequency of the 3rd bin in a frequency distribution table represents: a. The number of data values that are less than the maximum value of the 3rd bin. b. The percentage of data that falls into the 3rd bin. C. The cumulative deviation of the 3rd bin in percent. d. The frequency of data values that are larger than the minimum value of the 3rd bin.
The cumulative frequency of the 3rd bin in a frequency distribution table represents the number of data values that are less than the maximum value of the 3rd bin. The correct option is a.
What is a frequency distribution table?A frequency distribution table, often known as a frequency table, is a table that displays the frequency or amount of occurrences of different values in a dataset. Frequencies may be written as total values or as percentages of the total (relative frequency).
What is cumulative frequency?Cumulative frequency is the total frequency of values less than or equal to a given value in a dataset. The cumulative frequency of the 3rd bin in a frequency distribution table represents the total number of data values that are less than or equal to the maximum value of the 3rd bin.
Because it is a cumulative frequency, it contains all the values that came before it as well as its own frequency. The frequency distribution table is used to compute cumulative frequency.
The calculation of cumulative frequency may be done using the data's ascending or descending order.
Thus, the correct option is a.
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10g⁹ 2. Show that (Zn +n Xn) is a commutative ring with unity assuming it is a commutative additive n' group. Prove that or disprove 23 340 1 is divisible by 341 341 11 77
Given below are the step-by-step solutions to the provided questions:
1. Determine whether 23, 340, 1 is divisible by 341, 341, 11, 77. To prove 23, 340, 1 is divisible by 341, 341, 11, 77:341 is not a prime number since it is equal to 11 * 31, and it is the LCM of 11 and 31.So, 341 is a composite number. To check the divisibility of 23, 340, 1 by 341, we need to find the remainder of 23, 340, 1 when it is divided by 341.Since 341 = 11 * 31, the remainder of 23, 340, 1 when divided by 341 will be the same as the remainder when 23, 340, 1 is divided by 11 and 31, respectively.Remainder of 23, 340, 1 when divided by 11:340 + 23 + 1 = 364364 = 11 × 33Therefore, the remainder of 23, 340, 1 when divided by 11 is 0.Remainder of 23, 340, 1 when divided by 31:10^3 ≡ −1 (mod 31)340 ≡ 12 (mod 31)23 ≡ −8 (mod 31)−8 − 12 − 1 = −21 = −1 × 31Therefore, the remainder of 23, 340, 1 when divided by 31 is 10.Therefore, the remainder of 23, 340, 1 when divided by 341 is 0.Since the remainder is 0, then 23, 340, 1 is divisible by 341, 341, 11, and 77. Hence, the given statement is true.
2. Show that (Zn + nXn) is a commutative ring with unity assuming it is a commutative additive n' group.To prove that (Zn + nXn) is a commutative ring with unity assuming it is a commutative additive n' group:Firstly, we need to prove that Zn is a commutative ring with unity given that it is a commutative additive n' group.Commutativity of addition:a, b ∈ Zna + b = b + aAssociativity of addition:a, b, c ∈ Zna + (b + c) = (a + b) + cExistence of additive identity:n ∈ Zna + n = n + a = aAdditive inverse:For every a ∈ Zn there exists an element -a in Zn such that a + (-a) = (-a) + a = nExistence of multiplication:For a ∈ Zn and b ∈ Zn, their product ab is defined as ab ∈ Zn Multiplication is distributive over addition:For a, b, c ∈ Zna(b + c) = ab + ac and(a + b)c = ac + bcThus, we have proven that Zn is a commutative ring with unity given that it is a commutative additive n' group.Now we need to prove that (Zn + nXn) is a commutative ring with unity given that it is a commutative additive n' group.Zn is a commutative ring with unity and Xn is a commutative additive group. Hence, we have the following:Commutativity of addition:a, b ∈ (Zn + nXn)a + b = b + aAssociativity of addition:a, b, c ∈ (Zn + nXn)a + (b + c) = (a + b) + cExistence of additive identity:n ∈ (Zn + nXn)a + n = n + a = aAdditive inverse:For every a ∈ (Zn + nXn) there exists an element -a in (Zn + nXn) such that a + (-a) = (-a) + a = nExistence of multiplication:For a ∈ (Zn + nXn) and b ∈ (Zn + nXn), their product ab is defined as ab ∈ (Zn + nXn)Multiplication is distributive over addition:For a, b, c ∈ (Zn + nXn)a(b + c) = ab + ac and(a + b)c = ac + bcThus, (Zn + nXn) is a commutative ring with unity assuming it is a commutative additive n' group.
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Someone please help me I’ll give out brainliest please dont answer if you don’t know
Answer:
-5p+3
Step-by-step explanation:
-p-2-4p+5
-p-4p-2+5
-5p+3
If the coefficient of determination is 0.237, what percentage of the data about the regression line is explained?
Group of answer choices
o 76.3%
o 5.63%
o 23.7%
o 46.7%
The correct option is (C) 23.7%.
If the coefficient of determination is 0.237, the percentage of the data about the regression line that is explained is 23.7%.
The coefficient of determination is used to explain how much variability in a dependent variable is due to the independent variable in a regression analysis.
It is usually represented as R², which is a fraction between 0 and 1, or expressed as a percentage between 0% and 100%.
It measures the proportion of variability in the dependent variable that can be attributed to the independent variable(s).
In this problem, the coefficient of determination is given as 0.237, which means that 23.7% of the variability in the dependent variable is explained by the independent variable(s) in the regression line. Therefore, the correct option is (C) 23.7%.
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PLEASE HELP AND ILL GIVE BRAINLIEST
Answer:
2
Step-by-step explanation:
Subtract the number with the term both sides ( which is 9)
[tex] {x}^{2} + {y}^{2} - 6x + 4y = - 9[/tex]
Complete the square for the x terms and y terms.
( To complete the square divide the coefficient term by 2 and square it, then add that product to both sides.)
[tex] {x}^{2} - 6x + 9 + {y}^{2} +4y + 4 = - 9 + 9 + 4[/tex]
[tex] (x - 3) {}^{2} + (y + 2) {}^{2} = 4[/tex]
Take the square root of the right side to find the radius
[tex] \sqrt{4} = 2[/tex]
Which statement is true about a trend line? A regression line and a trend line are opposite terms. A regression line and trend line are equivalent terms. A trend line represents only the smallest data points. A trend line represents only the largest data points.
Answer:
A is incorrect! B. should be the correct answer
Step-by-step explanation
After some research, i found that the correct answer is most likely B. a regression line and trend line are equivalent terms
A trendline and a regression can be the same.
A regression line is based upon the best fitting curve Y= a + bX Most often it’s a least-squares fit (where the squared distances from the points to the line (along the Y-axis) is minimized).
It can be quadratic or logistic or otherwise, but most often it is linear.
A trendline is often constructed by smoothing of the results, making it less peaked. (often by using a moving average); but can also come from ARIMA projections or curve fitting techniques (such as regression).
Let me know if i helped you!
The statement that is true about a trend line is B. A regression line and trend line are equivalent terms.
It should be noted that the trend line doesn't represent only the largest data points. It can also represent the smallest data points.
The regression line and the trend line are not opposite terms but rather, the regression line and trend line are equivalent terms.
In conclusion, the correct option is B.
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Kianna says that Elena’s house is actually a reflection of her house across the y-axis.
Is Kianna right?
Answer: Kianna is incorrect, if Elena’s house was a reflection of her house across the y-axis, the coordinates would be (-4,2).
Step-by-step explanation:
Heather bought a ten-year maturity corporate bond when it was issued for $1,000. The bond has an
annual interest rate of seven percent and pays interest semi-annually. How much does she receive
every six months?
A. $90
B. $40
C. $30
D. $35
Heather receives $35 every six months from the corporate bond.
The correct answer to the given question is option D.
To calculate how much Heather receives every six months from the corporate bond, we need to determine the semi-annual interest payment.
The annual interest rate is given as seven percent. Since interest is paid semi-annually, we divide the annual interest rate by 2 to get the semi-annual interest rate:
Semi-annual interest rate = 7% / 2 = 3.5%
Next, we calculate the semi-annual interest payment by multiplying the face value of the bond ($1,000) by the semi-annual interest rate:
Semi-annual interest payment = $1,000 * 3.5% = $1,000 * 0.035 = $35
Therefore, Heather receives $35 every six months from the corporate bond.
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I need help with this question
Answer:
286 Degrees
Step-by-step explanation:
A circle is 360 degrees, and from the question, we know that it is asking for ACB, so it would be 360 - 74, which is 286 degrees
Brainliest Maybe?
Suppose the CDF F is a continuous real function and note that this does not imply F is differentiable. Assume for simplicity that F(0) = 0 and F(1) = 1 (this does not change the major statements below but makes the proof a bit cleaner). (j) Show that if X, Y are independent F-distributed RVs then for any n in N (ii) Conclude that P(X = Y) = 0 (remember that you cannot assume F has a density). Hint: n above can be arbitrarily large. (iii) Suppose X1,. . . , Xn is a sample drawn from F. Show that the probability that all Xi differ from one another is 1. in other words that P(exist i < j with Xi =Xj)=0.
For the CDF of a continuous real function, the answers are as follows:
(i) P(X = Y) = 0 because P(X ≤ Y) > 0 and P(X < Y) > 0 and both are strictly positive
(ii) P(exist i < j with Xi = Xj) = 0 which is a contradiction.
(i) Suppose the CDF F is a continuous real function and note that this does not imply F is differentiable. Assume for simplicity that F(0) = 0 and F(1) = 1 (this does not change the major statements below but makes the proof a bit cleaner). If X, Y are independent F-distributed RVs, then for any n in N, we have; P(X ≤ Y) = P(X ≤ Y, Y ≤ X) = P(X ≤ Y|Y ≤ X) P(Y ≤ X) = P(Y ≤ X|X ≤ Y) P(X ≤ Y) = P(X ≤ Y|X ≤ Y) P(X ≤ Y) = P(X = Y). Hence, P(X = Y) = P(X ≤ Y)P(Y ≤ X) = P(X ≤ Y)P(X ≤ Y) = P²(X ≤ Y).Since F is continuous, P(X ≤ Y) = P(X < Y) = P(X ≤ Y) - P(X = Y). Therefore, P(X = Y) = 0 because P(X ≤ Y) > 0 and P(X < Y) > 0 and both are strictly positive.
(ii) Conclude that P(X = Y) = 0 (remember that you cannot assume F has a density). As for the sample case, we show that P(exist i < j with Xi = Xj) = 0. Suppose, for the purpose of contradiction, that we have X1, . . . , Xn in F such that P(exist i < j with Xi = Xj) > 0. Then, there must be some distinct i < j such that Xi = Xj. Without loss of generality, we may assume i = 1 and j = 2. Then, the probability that this event occurs is; P(X1 = X2, X3 ≠ X1, . . . , Xn ≠ X1) = P(X2 ≤ X1, X3 ≠ X1, . . . , Xn ≠ X1) + P(X1 < X2, X3 ≠ X1, . . . , Xn ≠ X1)Since Xi are independent F-distributed RVs and P(X = Y) = 0, it follows that the probability of the first term in the sum above is zero. Therefore, P(exist i < j with Xi = Xj) = 0 which is a contradiction.
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When approximating Sºf(x)dx using Romberg integration, R33 gives an approximation of order: h10 h8 h4 h6 Romberg integration for approximating S. f(x)dx gives R21 = 7 and R22 = 7.21 then f(1) = 4.01 3.815 1.68 -0.5
Using Romberg integration, f(1) = 4.01.
Based on the given information, we can deduce the order of approximation for [tex]R_{33}[/tex] in Romberg integration as h10, h8, h4, h6. Additionally, we are given the values [tex]R_{21} = 7[/tex] and [tex]R_{22} = 7.21[/tex].
Romberg integration typically follows the pattern R(k, m), where k represents the number of iterations and m denotes the number of function evaluations per iteration.
From [tex]R_{21} = 7[/tex], we can determine that the approximation achieved after two iterations is 7.
From [tex]R_{22} = 7.21[/tex], we can conclude that the approximation achieved after two iterations is 7.21.
Since [tex]R_{21}[/tex] and [tex]R_{22}[/tex] represent the same number of iterations (k = 2), we can directly compare the results of these two approximations.
Therefore, the final answer is: f(1) = 4.01.
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help wrong answers reported
Answer:
65
Step-by-step explanation:
all triangles angles equal 180°
180-72-43=65
A manufacture has been selling 1350 television sets a week at $480 each. A market survey indicates that for each $15 rebate offered to a buyer, the number of sets sold will increase by 150 per week. a) Find the demand function p(x), where x is the number of the television sets sold per week. p(x) = b) How large rebate should the company offer to a buyer, in order to maximize its revenue? $ c) If the weekly cost function is 108000 + 160x, how should it set the size of the rebate to maximize its profit?
Given that a manufacture has been selling 1350 television sets a week at $480 each. A market survey indicates that for each $15 rebate offered to a buyer, the number of sets sold will increase by 150 per week.
a) The demand function is p(x) = 480 - 15x/150, Where x is the number of television sets sold per week.
b) The company should offer a rebate of $25 to maximize its revenue.
c) The company should offer a rebate of $23 to maximize its profit.
a) Demand function:
p(x) = 480 - 15x/150, Where x is the number of television sets sold per week.
b) To maximize revenue, we need to find the point where the marginal revenue equals zero.
Marginal revenue is the derivative of the revenue function.
Revenue function is given by R(x) = x p(x), where x is the number of television sets sold and p(x) is the price per set.
R(x) = x p(x)
R(n) = (1350 + 150n)(480 - 15n/150)
R(n) = 648000 - 2250n - 45n²
R’(n) = -2250 - 90n
For marginal revenue, we need
R’(n) = 0
2250 - 90n = 0
n = -2250/90
n = -25
So, the company should offer a rebate of $25 to maximize its revenue.
c) Cost function: C(x) = 108000 + 160x
Total revenue (TR) = x p(x)
= (1350 + 150n)(480 - 15n/150)
= 648000 - 2250n - 45n²
Total cost (TC) = C(x)
= 108000 + 160n
Profit (P) = TR - TCP
P = 648000 - 2250n - 45n² - (108000 + 160n)
P = 540000 - 2090n - 45n²
For maximum profit, we need
P’(n) = 0 -2090 - 90n
P'(n) = 0
2090 - 90n = 0
n = -2090/90
n = -23.2
Since n has to be a whole number, the number of TVs sold will be
1350 + 150n = 1350 + 150(-23)
= 1020.
Therefore, the company should offer a rebate of $23 to maximize its profit.
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Need help please thank you
Answer:
y = 4x+1
Step-by-step explanation:
We say that the decimal expansion 0.d1d2d3 ...dn ... is repeating if there is an m >0 such that dqm+r = dr for all q € N. Show that the set of all real numbers that have a repeating decimal expansion is a countable set.
The set of real numbers with a repeating decimal expansion is countable because it can be mapped to a countable set of unique pairs of rational numbers.
To show that the set of all real numbers with a repeating decimal expansion is countable, we can prove that it is at most countable.
Let's consider a repeating decimal number 0.d1d2d3...dn(dn+1...dn+m-1dn+m...). This can be represented as 0.d1d2d3...dn + (dn+1...dn+m-1dn+m...)/([tex]10^m - 1[/tex]).
We can see that for any repeating decimal number, the part before the repeating block (0.d1d2d3...dn) is a finite decimal representation, which is a rational number.
The part within the repeating block ((dn+1...dn+m-1dn+m...)/([tex]10^m - 1[/tex])) is also a rational number because it can be expressed as a fraction.
Since both the finite decimal part and the repeating block part are rational numbers, we can map each repeating decimal number to a unique pair of rational numbers (finite decimal part, repeating block part).
Now, we know that the set of rational numbers is countable. Therefore, if we can show that the set of unique pairs of rational numbers is countable, then the set of repeating decimal numbers is at most countable.
To show that the set of unique pairs of rational numbers is countable, we can use the fact that the Cartesian product of countable sets is countable.
Since the set of rational numbers is countable, the set of unique pairs of rational numbers (finite decimal part, repeating block part) is also countable.
Thus, we can conclude that the set of all real numbers with a repeating decimal expansion is at most countable.
To know more about a rational number follow
brainly.com/question/1535013
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