C. A customer buys some CDs at the discounted price and is told at checkout You
saved $18 today!" How much money did the customer spend?

the discount is 30% btw**

We know that RS is parallel to PQ by comparing RS and PQ and both vector have the same value and hence prove to be parallel.

We know that R, S, Q and P are midpoints of OC, CB, BA and OA, and we are given that OR = a, CS = b and OP = c

we have to prove that RS is parallel to PQ,

therefore we need to find, PQ = PA + AQ,

= c - c + a + b = a + b,

since we get that  PA = OP = c

therefore when we compare RS and PQ ,we get,

RS  =  PQ = a + b

now that it is clear that both the vectors are same and have the same value we can conclude that they are parallel.

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See attachment for reply.

Answer:

(4,0)

Step-by-step explanation:

(a) The value of st from the second constraint into the first constraint is yt = ct + (ct+1 - ct) = 2ct + ct+1, (b) The constraint for ct+1 is yt - 2ct, (c) u(ct) = ln(ct) + βln(yt - 2ct), (d) u'(ct) = 1/ct - 2β/(yt - 2ct), (e) 1/ct = 2β/(yt - 2ct), (f) The intuitive interpretation of the Euler Equation is that it represents the optimal intertemporal consumption choice, (g) β = 0.9524.

(a) To combine the two constraints, we can substitute the value of st from the second constraint into the first constraint:

yt = ct + st
yt = ct + (ct+1 - ct) = 2ct + ct+1

(b) Solving the constraint for ct+1, we get:

yt = 2ct + ct+1
ct+1 = yt - 2ct

(c) Plugging the constraint into ct+1 in the utility function, we have:

u(ct) = ln(ct) + βln(yt - 2ct)

(d) Differentiating the utility function with respect to ct, we get:

u'(ct) = 1/ct - 2β/(yt - 2ct)

(e) To derive the Euler Equation, we set the derivative of the utility function with respect to ct equal to 0:

0 = 1/ct - 2β/(yt - 2ct)

Simplifying, we have:

1/ct = 2β/(yt - 2ct)

(f) The intuitive interpretation of the Euler Equation is that it represents the optimal intertemporal consumption choice. It states that the marginal benefit of consuming one additional unit today (1/ct) is equal to the discounted marginal benefit of consuming one additional unit tomorrow (2β/(yt - 2ct)).

(g) If rho=0.05 and the real interest rate is 3%, we can calculate the value of β:

β = 1/(1+rho)

= 1/(1+0.05)

= 0.9524

To determine whether ct or ct+1 is larger, we need more information.

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The completed relative frequency table is given by the image shown at the end of the answer.

First we look at the row total of people who like to fly, which is of 70%, hence:

Amount those who can drive, we have that:

Amount those who cannot drive, we have that:

Thus the total frequency of the second row is given as follows:

0.17 + 0.13 = 0.30.

The table is given by the image shown at the end of the answer. I don't know if the values are the same but you will have to follow the same procedure to obtain the missing values.

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Answer:

I took the test

the answer is in the image below

Step-by-step explanation:

Answer:

sp of bicycle =5600

cp of bicycle =10

now,

profit(p)=sp-cp

=5600-10

=5,590

The profit of bicycle is Rs 5,599

The values of a, b, and c that represent the perimeter of the pool are a = 80, b = 0, and c = 100.

Step 1: Add the three dimensions together to find the total length of one side of the perimeter:
(4x^2 + 15) + (8x^2 + 10) + (8x^2) = 20x^2 + 25

Step 2: Since the perimeter has 4 equal sides (it's a rectangle), multiply the total length of one side by 4:
Perimeter = 4(20x^2 + 25) = 80x^2 + 100

Now, compare the perimeter polynomial with the general form ax^2 + bx + c:
80x^2 + 100 = ax^2 + bx + c

From this comparison, you can see that:
a = 80
b = 0 (since there is no term with x)
c = 100

So, the values of a, b, and c that represent the perimeter of the pool are a = 80, b = 0, and c = 100.

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Answer:

x = -9

Step-by-step explanation:

4x+10=-26

Subtract 10 from each side

4x+10-10=-26-10

4x = -36

Divide each side by 4

4x/4 = -36/4

x = -9

Answer:

I can't see the file

Step-by-step explanation:

The Law of Sines often yields better results due to its broader applicability and flexibility in solving trigonometric problems involving non-right triangles. The Law of Cosines is also reliable, especially when the lengths of sides are known. The Law of Tangents has limited use and is typically employed in specific right triangle scenarios.

To compare the results of the verification of the Law of Sines, Law of Cosines, and Law of Tangents, we can create a table showcasing the findings and analyze which law had better results:

Law               |                         Results                                |                             Accuracy

--------------------------------------------------------------------------------------------------------------------------------------------------------

Law of Sines      |  Satisfied for various triangle scenarios   | Dependent on angle and side accuracy

Law of Cosines   | Satisfied for various triangle scenarios   | Dependent on side accuracy

Law of Tangents | Satisfied for specific triangle scenarios   | Dependent on angle accuracy

The Law of Sines may often have better results because it is applicable to a broader range of triangle scenarios, allowing for more flexibility in solving trigonometric problems. It is useful when working with non-right triangles, as it relates the ratios of angles to the ratios of opposite sides. However, it heavily relies on the accuracy of both angles and sides for precise calculations.

The Law of Cosines, while also effective in various triangle scenarios, is particularly useful for solving triangles when the lengths of all three sides are known or when an angle and the lengths of two sides are known. It is less dependent on angle accuracy but relies more on side accuracy.

The Law of Tangents has more limited applicability and is primarily used when dealing with right triangles. It relates the tangent of an angle to the ratios of sides, but its usage is not as widespread as the other two laws.

The Law of Sines and the Law of Cosines generally yield satisfactory results for various triangle scenarios. However, their accuracy can vary depending on the accuracy of angles and sides. The Law of Tangents, on the other hand, is more limited in its application, as it only applies to specific triangle scenarios.

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The correct rule to describe the function g as a function of f and gives the correct rule is that g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

The correct rule to describe the function

g(x) = 3f(x)

in terms of the function f(x) = x³-2x²+7x-11 is that

g(x) = 3(x³-2x²+7x-11) and thus

g(x) = 3x³-6x²+21x-33.

In order to obtain the function g(x) from the given function f(x), it is necessary to multiply it by a constant, in this case 3.

Therefore, g(x) = 3f(x) means that g(x) is three times f(x).

Thus, we can obtain g(x) as follows:

g(x) = 3f(x) = 3(x³-2x²+7x-11) = 3x³-6x²+21x-33

Therefore, the correct rule to describe the function g as a function of f and gives the correct rule is that

g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

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According to Triangle Inequality Theorem,

adding ANY two sides (together) of a triangle must be GREATER than the third side.

Meaning, two sides CANNOT be less than the third side andCANNOT be equal to the third side.

Because when you add 3 and 16, you get 19.

19 is EQUAL to the third side, 19. This BREAKS the condition of the theorem.

ANSWER: No, the triangle cannot have the lengths of 3,16, and 19.

The answers would be z + w = -2 + 3i, z - w = 4 - 7i, and w - z = 4 + 7i after adding and subtracting two complex numbers.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

It is given that:

The complex numbers are:

z = 1 - 2i and w = -3 + 5i

z + w = 1 - 2i - 3 + 5i

z + w = -2 + 3i

z - w = 1 - 2i + 3 - 5i

z - w = 4 - 7i

w - z = 4 + 7i

Thus, the answers would be z + w = -2 + 3i, z - w = 4 - 7i, and w - z = 4 + 7i after adding and subtracting two complex numbers.

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Answer:

3

4

7

Step-by-step explanation:

got it right on edge

Answer:

(-3,2)

Step-by-step explanation:

the x component should be less than or equal to 3.

the y component is greater than -2.

Go through each option and you'll see that the only option that satisfies both conditions is 3.

Answer:

3.2

Step-by-step explanation:

Answer:

With the context you gave the awnser would be m≠5n

Step-by-step explanation:

Answer:

The probability a salamander has a length between 12.2cm and 16.5cm is 0.6930

Step-by-step explanation:

We start by finding the z-score of each

Mathematically;

z-score = (x - mean)/SD

for 12.2 cm

z-score = (12.2 - 15)/2 = -2.8/2 = -1.4

For 16.5 cm

z-score = (16.5 -15)/2 = 1.5/2 = 0.75

So the probability we want to calculate is;

P( -1.4 < z < 0.75)

we can calculate this using the normal distribution table

Mathematically;

P( -1.4 < z < 0.75) = P( z < 0.75) - P( z < -1.4)

= 0.2263 + 0.30738

= 0.69262

A,B, and C are interior while D is extorior

Step-by-step explanation: However ABCD are the same because they all mean a number and have their own angles Dis the most common number so its related to ABC. :)Hope this helps

Answer:

A,B, and C are interior while D is extorior

Step-by-step explanation: However ABCD are the same because they all mean a number and have their own angles Dis the most common number so its related to ABC.

Step-by-step explanation:

Answer:

$220

Step-by-step explanation:

first let's make the $12 bracelets as Type1 and the $8 bracelets as Type2,

then we calculate the amount she made by selling each type.

Eq.1 : No. of Type1 bracelets Selena made = 9

         Amount she sold them for = $12

         Amount she made by selling them = 9*12

                                                                                   = $108

Eq.2 : No. of Type2 bracelets Selena made = 14

          Amount she sold them for = $8

          Amount she made by selling them = 14*8

                                                                               = $112

Now we calculate the Total Amount she made

we add both of the amounts

$108 + $112

= $220

Hope this helps :)

All the real values of p such that 2(x - 4)(x - 2p) has a minimum value of -18 over all real values of x is p = 1 and p = -5.

Given that:

2(x + 4)(x - 2p)

It is required to find the values of p such that this expression has a minimum value of -18.

Expand the given expression.

2(x² + 4x - 2px - 8p)

2(x² + (4 - 2p)x - 8p)

2x² + (8 - 4p)x - 16p

The minimum value of the function can be found by first, setting the derivative equal to 0.

Differentiating,

4x + (8 - 4p) = 0

4x = 4p - 8

x = p - 2

Substitute x = p - 2 to the function 2(x + 4)(x - 2p).

When the value of the function is -18,

2(p - 2 + 4)(p - 2 - 2p) = -18

2(p + 2)(-p - 2) = -18

(p + 2)(-p - 2) = -9

(p + 2)² = 9

p + 2 = ±3

When p + 2 = 3, p = 1.

When p + 2 = -3, p = -5.

Hence the p values are 1 and -5.

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The given expression (8h + 2w - 5h + 3w) can fully be simplified as 3h + 5w.

An expression can be defined as a type of mathematical equation which is used to show the relationship that is existing between two or more variables and numerical quantities (integers).

In this exercise, you're required to fully simplify the given expression in the lowest terms. Thus, we would simplify the given expression completely by collecting like terms and performing the necessary arithmetic operations (addition and subtraction) as follows:

Collecting like terms, we have:

8h - 5h + 3w + 2w

Subtracting and adding the like terms respectively, we have:

3h + 5w.

In conclusion, we can logically deduce that the given expression (8h + 2w - 5h + 3w) can fully be simplified as 3h + 5w.

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Complete Question:

Fully simplify 8h + 2w - 5h + 3w.

Answer:

c

Step-by-step explanation:

In all these cases, no interaction means that the variables act independently on the response variable Y, and their combined effects are simply additive rather than multiplicative or otherwise interdependent.

No interaction in modeling response variable Y and explanatory variables X and Z means that the effect of each explanatory variable on the response variable is independent of the other explanatory variable. This can be illustrated using graphs or tables as follows:

a. When all variables are continuous (multiple regression), no interaction means that the slope of Y on X is constant regardless of the level of Z, and the slope of Y on Z is constant regardless of the level of X. In other words, the effect of X on Y is the same for all levels of Z, and the effect of Z on Y is the same for all levels of X.

b. When Y and X are continuous, and Z is categorical (analysis of covariance), no interaction means that the mean difference in Y between each level of Z is the same for all levels of X. In other words, the effect of Z on Y is the same for all levels of X.

c. When Y is continuous, and X and Z are categorical (two-way ANOVA), no interaction means that the mean difference in Y between each combination of X and Z is the same. In other words, the effect of X on Y is the same for all levels of Z, and the effect of Z on Y is the same for all levels of X.

d. When Y is binary, and X and Z are categorical (logistic regression), no interaction means that the odds ratio of Y on X is the same for all levels of Z, and the odds ratio of Y on Z is the same for all levels of X. In other words, the effect of X on the odds of Y is the same for all levels of Z, and the effect of Z on the odds of Y is the same for all levels of X.

a. Multiple regression (All variables are continuous): No interaction means that the effect of one explanatory variable (X) on the response variable (Y) does not depend on the value of the other explanatory variable (Z). In a graph, this would be represented by parallel lines or planes when plotting Y against X for different values of Z.

b. Analysis of covariance (Y and X are continuous, Z is categorical): No interaction suggests that the relationship between Y and X is consistent across different levels of the categorical variable Z. In a graph, this would appear as parallel regression lines for each category of Z.

c. Two-way ANOVA (Y is continuous, X and Z are categorical): No interaction means that the effect of one categorical variable (X) on the response variable (Y) is not influenced by the levels of the other categorical variable (Z). In a table, this would be evident by having similar differences between cell means across all combinations of X and Z.

d. Logistic regression (Y is binary, X and Z are categorical): No interaction implies that the odds of the binary response variable (Y) occurring do not depend on the combined effect of X and Z. In a table, the odds ratios for different levels of X and Z should be consistent, indicating no interaction between the two categorical variables.

In all these cases, no interaction means that the variables act independently on the response variable Y, and their combined effects are simply additive rather than multiplicative or otherwise interdependent.

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the EIR from this transaction is 16.25% (Option B, None of the above).

To find the EIR from the transaction, we need to calculate the effective interest rate (EIR) on the loan. The formula for EIR is:

EIR = [(1 + r/n)ⁿ - 1] x 100

where r is the nominal interest rate, and n is the number of compounding periods per year.

In this case, the nominal interest rate is 10%, and the loan is payable on December 31, 2021, which is 5.5 years from June 30, 2016. Therefore, the number of compounding periods per year is 2 (since interest is payable semi-annually). Substituting these values into the formula, we get:

EIR = [(1 + 0.10/2)₂ - 1] x 100 = 10.25%

However, the bank requires a maintaining balance of 6% for any amount borrowed. Therefore, the effective interest rate is increased by this amount. Adding 6% to the EIR, we get:

EIR = 10.25% + 6% = 16.25%

Therefore, the EIR from this transaction is 16.25% (Option B, None of the above).

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The number of years since 2000 where the passenger revenue was $930 million is 3.25 years.

It should be noted that the annual passenger revenue of a rail transport corporation from the year 2000 to the year 2020 is modeled by the formula R = −20t −15 + 1,010

where R is the annual revenue in million dollars

When the revenue is 930 million, the time will be illustrated as:

−20t −15 + 1,010

−20t −15 + 1,010 = 930

−20t −15 + 1,010 - 930 = 0

−20t + 65 = 0

Divide through

t = 65/20

t = 3.25 years.

Therefore, the number of years since 2000 where the passenger revenue was $930 million is 3.25 years.

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Kareem make muffin using a ratio of 3. 5 cup of flour for every 1. 75 cup of sugar. If he ha 3. 5 cup of sugar, flour doe he need to make the muffin is 7 cups.

The ratio that Kareem uses to make the muffin is 3.5 cups of flour for every 1.75 cups of sugar .

let the number of cups of flour be "y" and

the number of cups of sugar be "x" .

So , y ∝ x ,

y = k*x , where k is the constant of proportionality .

From the given data ,

3.5 = k*1.75

k = 3.5/1.75

k = 2 .

we have to find the cups of flour that Kareem needs , if he has 3.5 cups of sugar .

the equation becomes ,

y = 2*3.5

y = 7

Therefore , Kareem needs 7 cups of flour .

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other.

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Answer:

-½ + (root2 / 2) i + root½ i

Step-by-step explanation:

\( \frac{a}{b} - \frac{c}{d} = \frac{ad - cb}{bd} \)

I used this formula to do it but let me know if it's enough or you have to simplify it further

Answer:

45

Step-by-step explanation: