2. Last year a certain toy car cost $50, but this year the price was dropped to $20. By what percentage was the price dropped?​

To find the boundary points, you need to determine the range of u and v that define the first octant.

The first octant is defined by the following conditions:
- u ≥ 0
- v ≥ 0
- 6 - 3u - 2v ≥ 0 (since z must be positive in the first octant)

To find the range of u, solve the inequality 6 - 3u - 2v ≥ 0 for u:

6 - 2v ≥ 3u
(6 - 2v)/3 ≥ u

Since u must be non-negative, the lower bound of the integral is u = 0. To find the upper bound, set the right-hand side of the inequality equal to 0:

(6 - 2v)/3 = 0
6 - 2v = 0
v = 3

Therefore, the range of v is 0 ≤ v ≤ 3.

Putting it all together, the integral to find the volume of the part of the plane 3x+2y+z = 6 that lies in the first octant is:

∫₀³ ∫₀^(6-3u-2v) 1 dz dv du.

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The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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"0" was the gift tax in 2018.

Gift taxes are paid by either the giver or the recipient?

A gift tax is not present. There is no gift tax because gifts up to $15,000 are tax-free.

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344865

Explanation

Use the following formula:

In this case, n=830, thus you get your answer by entering 830 in the formula like this:

so, the answer is

344865

The decimal value of the floating-point number 110000001111110... is approximately -0.000000015935.

A 32-bit binary number is the floating-point number 010000010110100000... We must interpret its components in accordance with the IEEE 754 standard for single-precision floating-point representation before we can convert it to decimal.

The number's sign is represented by the first bit, which is 0. The number is positive because it is zero.

The exponent is represented by the next eight bits, 10000010 The bias value, which is 127 for single-precision, needs to be subtracted in order to determine the exponent's decimal value. As a result, the value of the exponent is -25: 10000010 - 127.

The binary fractional part is represented by the remaining 23 bits, which are 110100000... Summing the series of 2(-i) for each bit I that is set to 1, we convert the fractional part to a decimal fraction for the purpose of determining its decimal value. The series is as follows, starting with the leftmost bit:

The decimal value of the floating-point number is then calculated as follows: 1/2 + 1/8 + 1/16 + 1/32 = 0.53125.

The floating-point number 010000010110100000... has a decimal value of approximately 0.0000000938776, which is equal to (-1)0 * 1.53125 * 2(-25).

8th Question: The 32-bit binary number 110000001111110... is a floating-point number. Using the same procedure as before:

The number's sign is represented by the first bit, which is 1. The number is negative because it is 1.

The exponent is represented by the next eight bits, 10000011 We get the exponent value of 10000011 - 127 = -24 when we subtract the bias value of 127.

In binary, the fractional part of the number is represented by the remaining 23 bits, which are 111110... Switching it over completely to a decimal division gives us the series:

1/2 plus 1/4 plus 1/8 plus 1/16 plus 1/32 equals 0.96875, so the floating-point number's decimal value is as follows:

The floating-point number 110000001111110... has a decimal value of (-1)1 x 1.96875 x 2 (-24), which is approximately -0.000000015935003662109375.

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The perimeter of a shape with 4 sides is equal to the sum of its sides multiplied by itself, which in this case is 4 multiplied by 4, resulting in a perimeter of 16.

Step 1: Calculate the length of each side by multiplying 4 by 4.

Step 2: Add the lengths of each side together to get the perimeter.

Step 3: The perimeter of the shape with 4 sides is equal to 16.

The perimeter of a shape is the sum of the lengths of its sides. To calculate the perimeter of a shape with 4 sides, you need to find the length of each side. To do this, you can multiply the length of one side by itself. For example, if the length of one side is 4, the length of each side would be 4 multiplied by 4, which is 16. Therefore, the perimeter of a shape with 4 sides is equal to 16. To calculate the perimeter of a different shape with an unknown number of sides, you can add up the lengths of each side to get the total perimeter. This is a useful way to measure the size of a shape and can be used to calculate the area of a shape by dividing the perimeter by the number of sides.

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Answer:

11^5

Step-by-step explanation:

11^5 because your multiplying 11 by itself 5 times

The coordinates of A'', B'' and C'' are (-1, 4), (-4, 3) and (-1, 2) respectively.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

Given triangle has coordinates,

A(2, -2), B(5, -3) and C(2, -4).

First the triangle is translated by the rule (x, y) → (x - 1, y + 6)

A(2, -2) becomes A'(2 - 1, -2 + 6) = A'(1, 4).

B(5, -3) becomes B'(5 - 1, -3 + 6) = B'(4, 3)

C(2, -4) becomes C'(2 - 1, -4 + 6) = C'(1, 2)

Then the translated triangle is reflected across the Y axis.

When reflected a point (x, y) across the Y axis, y coordinate remains same and x coordinate flips.

A'(1, 4) becomes A''(-1, 4)

B'(4, 3) becomes B''(-4, 3)

C'(1, 2) becomes C''(-1, 2)

Hence the vertices of the triangle after undergoes translation and reflection becomes A''(-1, 4), B''(-4, 3) and C''(-1, 2).

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Answer:

5

Step-by-step explanation:

0 is 10ths 5 is 100ths

We can be 95% confident that the true population mean TV viewing time is between 3.812 and 4.388 hours.

To calculate the 95% confidence interval, we use the formula:

CI = x' ± Zα/2 * (σ/√n)

Where:

x' = sample mean

Zα/2 = the Z-score associated with the desired confidence level (in this case, 95%, so Zα/2 = 1.96)

σ = population standard deviation

n = sample size

Substituting the given values, we get:

CI = 4.1 ± 1.96 * (1.3/√78)

Calculating the standard error (SE) first:

SE = σ/√n

SE = 1.3/√78

SE ≈ 0.147

Then we substitute the SE value in the CI formula:

CI = 4.1 ± 1.96 * 0.147

CI = 4.1 ± 0.288

CI = (3.812, 4.388)

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Answer:

(2x+2)+(x+34)=180°[by linear pair]

3x+36=180°

3x=180°-36°

3x=144

x=144/3

x=48

Answer:

1.63

Step-by-step explanation:

Answer:

1.63

Step-by-step explanation:

Discount amount = price x discount percentage as a decimal:

Discount amount = 62.00 x 0.15 = 9.30

Discount = $9.30

Answer:

$52.70

Step-by-step explanation:

In this scenario, we are interested in testing a hypothesis about the proportion of first-year college students who are undecided about their major. The claimed proportion is 0.47, but the researcher believes this value is too high. To test this hypothesis, the researcher surveys a random sample of 450 first-year college students and finds that 189 of them are undecided about their major.

To find the p-value in this problem, we need to conduct a hypothesis test. Let's define the terms first:

1. Proportion: The proportion of first-year college students who are undecided about their major, claimed to be 0.47.
2. Hypothesis: We are testing if the claimed proportion (0.47) is too high.
3. Sample: A random sample of 450 first-year college students, with 189 undecided about their major.

Now, let's follow the steps of a hypothesis test:

Step 1: Define the null hypothesis (H0) and alternative hypothesis (H1).
H0: p = 0.47 (The proportion is equal to 0.47)
H1: p < 0.47 (The proportion is less than 0.47)

Step 2: Calculate the test statistic.
Test statistic = (Sample proportion - Claimed proportion) / Standard error
Sample proportion = 189 / 450 = 0.42
Standard error = sqrt[(0.47 * (1 - 0.47)) / 450] ≈ 0.0229

Test statistic = (0.42 - 0.47) / 0.0229 ≈ -2.18

Step 3: Find the p-value using the test statistic from a Z-distribution table or calculator.
The test statistic is -2.18, which corresponds to a p-value of approximately 0.0146.

Step 4: Compare the p-value to the chosen significance level (alpha).
The p-value is between 0.01 and 0.05.

Therefore, the answer is: C. between 0.01 and 0.05.

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Answer:

a.  Yes

b.  Yes

c. Yes

d. Degree 8

Step-by-step explanation:

a. Yes, n(x) is a polynomial of one single term (also called monomial) because it contains variables raised to positive integers.

b. Yes, m(x) is a polynomial of also one single term (also called monomial) because it contains variables raised to positive integers.

c. The quotient of n(x) / m(x) can be reduced to a polynomial of one single term as follows:

\(\frac{n(x)}{m(x)} =\frac{6\,x^5\,y^7}{2\,x^3\,y} =3\,x^2\,y^6\)

which as can be seen, also contains variables raised to positive integers.

d. The degree of the polynomial resultant is the addition of the powers of all variables present (x and y) which results in: 2 + 6 = 8

Therefore the degree of this polynomial is 8.

The type of data collection involved in this scenario is "survey research."

The type of data collection involved in this scenario is "survey research." Survey research is a method of gathering information from a sample of individuals through the use of questionnaires or interviews.

In this case, the marketing research firm is using a questionnaire to collect data about adults' beverage preferences.

This method allows the firm to gather information about people's opinions, preferences, and experiences, which can be used to make informed decisions about marketing strategies and product development.

The data collected from this type of research is usually quantitative, which means it can be analyzed using statistical methods. The results obtained from the survey research can be used to draw conclusions about the population from which the sample was drawn.

Survey research is a useful method for marketing research because it allows researchers to collect a large amount of data from a relatively small sample of individuals.

Additionally, the data collected from survey research can be used to inform marketing strategies, product development, and other business decisions.

So it is conculded that the type of data collection involved in this scenario is "survey research."

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Answer:

What I would do is to basically just find what b equals.

The equations given are x - 5y = 3 and 3x - 2y = -4. To find the solution to this system of equations, we need to find the values of x and y that satisfy both equations simultaneously.

One way to solve this system of equations is by substitution. We can solve one equation for x or y, and then substitute that expression into the other equation to eliminate one variable. Let's solve the first equation for x:

x - 5y = 3

x = 5y + 3

Now we can substitute this expression for x into the second equation:

3x - 2y = -4

3(5y + 3) - 2y = -4

15y + 9 - 2y = -4

13y = -13

y = -1

We can now substitute this value for y back into either equation to find the value of x:

x - 5y = 3

x - 5(-1) = 3

x + 5 = 3

x = -2

Therefore, the solution to the system of equations x - 5y = 3 and 3x - 2y = -4 is (-2, -1). This is the point where the solid line and dotted line intersect, as shown in the image.

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The probability that Aja wins at most 111 prizes in the 555 boxes is approximately 0.9999 (rounded to the nearest hundredth).

To calculate the probability that Aja wins at most 111 prizes in 555 boxes, we need to find the cumulative probability up to 111 prizes.

Given:

Number of boxes: 555

Probability of winning a prize: 111 in 444 boxes

Let's calculate the probability using the binomial probability formula:

P(X ≤ 111) = Σ P(X = k) for k = 0 to 111

Using the binomial probability formula, we have:

P(X ≤ 111) = Σ (C(555, k) * (111/444)^k * (333/444)^(555-k)) for k = 0 to 111

Calculating this sum directly would be computationally intensive. However, we can approximate the cumulative probability using statistical software or calculators.

Using a statistical calculator or software, we find that P(X ≤ 111) is approximately 0.9999.

The answer is P(X ≤ 111) = 0.9999.

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Step-by-step explanation:

14(3.8) ×3 + 2(1/2)×3×4

= 159.6 + 12

= 171. 6

(a) Evaluating the natural logarithm of the moment generating function of 5X at the point t = 0.86:

To find the natural logarithm of the moment generating function of 5X, we substitute 5t into the moment generating function px(t). Therefore, the moment generating function of 5X is (0.47e^(5t) + 1 - 0.47)^15. Evaluating this at t = 0.86 gives us (0.47e^(5*0.86) + 1 - 0.47)^15. By calculating the numerical value of this expression, we can find the natural logarithm of the moment generating function of 5X at t = 0.86.

(b) Finding the expectation of 5X:

To find the expectation of 5X, we can differentiate the moment generating function of 5X with respect to t and then evaluate it at t = 0. This gives us the first moment, which corresponds to the expectation. By differentiating the moment generating function (0.47e^(5t) + 1 - 0.47)^15 with respect to t and evaluating it at t = 0, we obtain the expectation of 5X.

(c) Evaluating the natural logarithm of the moment generating function of 5X + 8 at the point t = 0.86:

To find the natural logarithm of the moment generating function of 5X + 8, we substitute 5t into the moment generating function px(t) and add 8 to the resulting expression. Therefore, the moment generating function of 5X + 8 is (0.47e^(5t) + 1 - 0.47)^15 + 8. Evaluating this at t = 0.86 gives us (0.47e^(5*0.86) + 1 - 0.47)^15 + 8. By calculating the numerical value of this expression, we can find the natural logarithm of the moment generating function of 5X + 8 at t = 0.86.

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Answer:

\(R_1>R_2>R_3\)

Step-by-step explanation:

As per Ohm's law,

V = IR

I = Current

R = Resistance

V = Voltage

This law states → R = \(\frac{V}{I}\)

If we graph the relation between Voltage and Current, linear graph represents the Resistance.

Greater the slope of the line will represent greater resistance.

Therefore, \(R_1>R_2>R_3\)

The radius of convergence of the series sigma cnx9n will be R raised to the power 1/9.

Radius=a straight line extending from the center of a circle or sphere to the circumference or surface: The radius of a circle is half the diameter. the length of such a line.

The radius of convergence of the sum of the two series will be 5.

sigma (cnxn + dnxn) = sigma cnxn + sigma dnxn, and if both the series on the right-hand side converge.

The LHS converges for values of x on which both the series on the RHS converge. Hence, the LHS will converge on the intersection of the convergence of the two RHS series.

( if 5 < |x| < 6, the second series will converge, but the first will not.)

The series sigma cnx9n has radius of convergence R raised to the power 1/9.The series sigma cnxn has radius of convergence R. This means that it converges for |x| < R.The series sigma cnx9n can be written as sigma cn(x9)n

This means that the series converges for |x9| < R.

Therefore, the radius of convergence of the series sigma cnx9n will be R raised to the power 1/9.

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Given that nth partial sum is sn = a1 + a2 + ⋯ + an. Therefore, the difference of two consecutive partial sums is given as;sn − sn − 1 = (a1 + a2 + ⋯ + an) - (a1 + a2 + ⋯ + an−1)

By cancelling a1, a2, a3 up to an−1, we obtain;sn − sn − 1 = anIn other words, the nth term of a sequence is the difference between two consecutive partial sums. In a finite arithmetic sequence, the sum of the n terms is given asSn = (n/2)[2a1 + (n − 1)d] where; Sn is the nth term, a1 is the first term and d is the common difference.Substituting the given values;a1 = 1, d = 4, and n = 10Sn = (10/2)[2 × 1 + (10 − 1) × 4]Sn = (5 × 19 × 4) = 380Hence, the sum of the first ten terms of the sequence with first term 1 and common difference 4 is 380.

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In a linear equation, 9.14 does he save by paying off the loan when the next payment is due .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Jan  293  18  311  1,507 16.25%

Feb  296  15  311  1,212 32.67%

Mar 298           12  311   913 49.25%

Apr  301            9  311   612 66.00%

May  304    6  311  308 82.92%

Jun  308    3  311    0        100.00%

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Answer:

Turning it 90 degrees clockwise.

Step-by-step explanation:

They are opposite, and 360 degrees is a complete turn. 360-270=90

Answer:

HF is 20 m away from the tower which makes it the base of a triangle

tan 30= opp/adj=PF/HF

PF=tan 30°(20)=11.547

tan 50=T F/20 ⇒ T F=20*tan 50= 23.835

PT= T F-PF= 23.835-11.547=12.288 m

b ) the distance from point H to the power is the hypotenuse

cos 50=adj/hyp

hypo(HT)= 20/cos 50=31.114

(HF at a new angle=40)

tan 40=opp/adj = T F/HF

HF=T F/tan40=23.835/tan 40=28.405