Rosa want to buy a new TV priced at 499.99 The TV is on sale for 15% off but the cashier informs her that if she applies for a store credit card she can have an additional 10% off. How much will Rosa pay after the discounts and 6% tax have been applied? Write and solve an equation to find the final price.

The results of the expressions involving logarithms are listed below:

Case 1: 1 / 2

Case 2:

Subcase a: 0

Subcase b: 11 / 2

Subcase c: - 11 / 2

In this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c

㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c

㏒ₐ cᵇ = b · ㏒ₐ c

Now we proceed to determine the result of each case:

Case 1

㏒ ∛8 / ㏒ 4

(1 / 3) · ㏒ 8 / ㏒ 2²

(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)

㏒ 2 / (2 · ㏒ 2)

1 / 2

Case 2:

Subcase a

㏒ [b / (100 · a · c)]

㏒ b - ㏒ (100 · a · c)

㏒ b - ㏒ 100 - ㏒ a - ㏒ c

3 - 2 - 2 + 1

0

Subcase b

㏒√[(a³ · b) / c²]

(1 / 2) · ㏒ [(a³ · b) / c²]

(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²

(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · 2 + (1 / 2) · 3 + 1

3 + 3 / 2 + 1

11 / 2

Subcase c

㏒ [(2 · a · √b) / (5 · c)]⁻¹

- ㏒ [(2 · a · √b) / (5 · c)]

- ㏒ (2 · a · √b) + ㏒ (5 · c)

- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c

- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- 1 - 2 - (1 / 2) · 3 - 1

- 4 - 3 / 2

- 11 / 2

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Answer:

Step-by-step explanation:

10.00 amps

  Among the given options (A, B, C, D), the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

In a population regression model, we are interested in modeling the relationship between a dependent variable (Y) and one or more independent variables (X1, X2, etc.). The model equation consists of the regression coefficients (β0, β1, β2, etc.) that represent the effect of each independent variable on the dependent variable, and the error term (e) that captures the unexplained variation in the data.
Among the given options, only option D includes all the necessary components of a population regression model with two independent variables (k = 2). It includes the dependent variable Y, the regression coefficients β0, β1, and β2 for the independent variables X1 and X2, respectively, and the error term e.
Options A, B, and C are incorrect because they either omit the error term or have an incomplete equation. The error term is crucial in accounting for the unobserved factors and random variation in the relationship between the variables.
Therefore, the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.

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Answer:

n < -10

Step-by-step explanation:

In order to get the variable n by itself subtract 7 from both sides across the inequality

n + 7 < -3

  -7     -7

n   <  -10

Answer:

They are not Congruent = A

Step-by-step explanation:

Its not congruent because the left one is slightly a little bit bigger than the right. If you look close enough you can see that. Plus if you add the lines together the right one is slightly tilted.

Answer:

6 ways

Step-by-step explanation:

Given that:

Number of options, n = 4

Combo, r = 2

Using Combination :

nCr = n! ÷ (n-r)! r!

4C2 = 4! ÷ (4-2)!2!

4C2 = 4! ÷ 2!2!

4C2 = (4 * 3) / (2 * 1)

4C2 = 12 / 2

4C2 = 6

Answer:

Step-by-step explanation:

2.

u would use probability for that which gives them the answer

4.

looking at the chart it may be a 14% chance

5.

i would use 3 coins so that the number of coins is equivalent to the amount of pets they have. so that they can see what pets they may have (cats or dogs)

Answer: first blank: jen

second blank: mean

Step-by-step explanation:

N/A

The questions tests on indices. Write 125 in form of its prime factors. Apply the power rule (a^m)^(1/n)=a^(m/n). In prime factor form 125 = 5×5×5

125 = 5^3

(125^3)^(1/3) = 5^(3×1/3) = 5

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Answer:

The answer is option B.

Step-by-step explanation:

Before the regulations were applied to the field of chemistry, the elements, their characteristics and other information related to them were so disorganized that this was causing the progress in the field to slow down.

So the committees decided to regulate things such as the names of any newly discovered elements, any properties it had so that it could be put to use in a more effective way.

The correct answer for this question is option B.

I hope this answer helps.

The early committees regulated how the newly discovered elements were named.

Around the  mid-1800s to the early 1900s, chemical discoveries soared rapidly due to the invention of new equipment that made research a lot more easier.

Around 1919, the international union of pure and applied chemistry set up committees to regulate the naming of new elements and compounds hence strict rules were set up for the naming of newly discovered elements and compounds.

Hence, the early committees regulated how the newly discovered elements were named.

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Answer:

D, \(y=\frac{-5}{2x}+3\)

Answer:

x = 4°

Step-by-step explanation:

10x+2°+62° = 25x+4°{ the exterior angle formed by producing the side of triangle is equal to two non-adjacent angle}

or, 10x + 64° = 25x+4°

or, 10x-25x = 4°-64°

or, -15x = -60°

or, x = -60°/-15

or, x = 4°

82 kg is equal to 180.77844 pounds and 2892.24704 ounces.

Weight is a measure of how heavy an object is, and it is typically measured in units such as pounds (lbs) and ounces (oz). The kilogram (kg) is also a unit of weight, and it is the base unit of mass in the International System of Units (SI).

To convert the pounds to ounces, we know that 1 pound is equal to 16 ounces. To get the ounces from pounds, we can multiply the pounds by 16, so 180.77844 pounds is equal to 2892.24704 ounces.

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A club is forming a committee to plan its annual Holiday Dance. One person will serve as Chair of the committee, another will be Vice-Chair and there will be two other members.  this is an example of a combination

Combining is a way of calculating the total score for an event, regardless of the order of the scores. To calculate the combination, use the formula nCr = n! /r! * (n - r)!, where n is the total number of items and r is the number of items selected at one time.

The combination is a mathematical technique that determines the number of possible arrangements within a collection of items, regardless of the order of selection.

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The revised MeanMedian2 class allows the user to input up to 20 values, with the option to stop entering numbers by inputting 9999. It calculates both the mean and median of the provided values.

To implement this functionality, the MeanMedian2 class can prompt the user to enter values in a loop until either 20 values are entered or the user inputs 9999. The entered values can be stored in a list. Once the user is done entering values, the class can compute the mean and median. For the mean, it can sum all the values in the list and divide by the number of values. For the median, it needs to handle two scenarios: an odd number of values and an even number of values. If the list has an odd number of values, the median can be obtained by simply finding the middle value. However, if there is an even number of values, the two middle values can be averaged to get the median.

With this revised class, users can easily input any number of values, up to 20, and get accurate mean and median calculations. Additionally, the option to quit by entering 9999 provides a convenient way for users to stop entering values whenever they want. This updated implementation improves the flexibility and usability of the MeanMedian2 class.

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Answer: 64 minutes

Step-by-step explanation:

Start by finding the rate how many minutes does it take to ride a km by dividing 48 by 15

48/15= 3.2

Now multiply 3.2 by 20 to find how many minutes it will take to ride 20 km

3.2x20=64

9514 1404 393

Answer:

  (a) 6² +3² +1² +1² = 47

  (b) 5² +4² +2² +1² +1² = 47

  (c) 3³ +4² +2² = 47

Step-by-step explanation:

It can work reasonably well to start with the largest square less than the target number, repeating that approach for the remaining differences. When more squares than necessary are asked for, then the first square chosen may need to be the square of a number 1 less than the largest possible.

The approach where a cube is required can work the same way.

(a) floor(√47) = 6; floor(√(47 -6^2)) = 3; floor(√(47 -45)) = 1; floor(√(47-46)) = 1

__

(b) floor(√47 -1) = 5; floor(√(47-25)) = 4; ...

__

(c) floor(∛47) = 3; floor(√(47 -27)) = 4; floor(√(47 -43)) = 2

Answer:

n=1.3

Step-by-step explanation:

just plug it in for n and see results

1-Step-by-step explanation:

Answer:

GCF = 6, Sum = 60.

Step-by-step explanation:

Substitute 6 into our distribution equation:

6(3) + 6(7) = (18 + 42) = 60

Check:

6(3)+6(7) = 60.

(This is an easier way to find the GCF, by substitution)

Checking Continued:

18: 1, 2, 3, 6, 9, 18

42: 1, 2, 3, 6, 7, 14, 21, 42

6 is the GCF.

The population variance estimate for the denominator of the F ratios for the main and interaction effects is built by averaging the estimates of the variation of scores inside each cell.

The results of two independent variables on a dependent variable are revealed by a two-way ANOVA, which is an extension of the one-way ANOVA (analysis of variances).

Numerous fields, including finance, economics, science, medical, and social science, use ANOVA.

The mean of a quantitative variable is estimated using a two-way ANOVA in relation to the values of two categorical variables. When attempting to determine the combined impact of two independent factors on a dependent variable, use a two-way ANOVA.

When you want to determine how two factors affect a response variable and whether or not the two factors interact with the response variable, you should utilise a two-way ANOVA.

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Answer:

speed of train A = 70 + 20 = 90 miles per hour

speed of train B = 70 miles per hour 

Step-by-step explanation:

Let

speed of train B = a

speed of train A = a + 20

Recall

speed = distance/time

The travel time is same for both train. Therefore, let us make time subject of the formula in the speed equation.

Time = distance/speed

270/a + 20 = 210/a

cross multiply

270a = 210(a + 20)

270a = 210a + 4200

270a - 210a = 4200

60a = 4200

divide both sides by 60

a = 4200/60

a = 70

speed of train A = 70 + 20 = 90 miles per hour

speed of train B = 70  miles per hour

Answer: 72π meters squared.

Step-by-step explanation: Given that the radius is 6 meters, use the sphere surface area formula to find the surface area of the half-sphere;

The time taken by the bacterias to reach 3,700 will be 2.81 days.

It is given in the question that:-The the number of bacteria, B left parenthesis d right parenthesis, in a certain population increases according to the following function, where time, d, is measured in days:

\(B(d)=2425\ e^{0.15d\)

\(3700= 2425\ e^{0.15d}\\\\\\e^{0.15d}=\dfrac{3700}{2425}\\\\\\0.15d=ln\dfrac{3700}{2425}\\\\\\\)

d   =   2.81  days

Hence the time taken by the bacteria to reach 3,700 will be 2.81 days.

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There are two points that satisfy the system of equations:

(0.79, 0.37)

(-3.79, -12.37)

The system of equations is:

y = 3x - 3

y = -x^2

To determine which point from a specified set satisfies the system of equations, we need to find the values of x and y that satisfy both equations simultaneously.

Substituting y = 3x - 3 into the second equation, we get:

3x - 3 = -x^2

Rearranging this equation, we get:

x^2 + 3x - 3 = 0

Using the quadratic formula, we can solve for x:

x = (-3 ± sqrt(3^2 - 41(-3))) / (2*1) = (-3 ± sqrt(21)) / 2

Therefore, there are two possible values of x that satisfy the system of equations:

x = (-3 + sqrt(21)) / 2 ≈ 0.79

x = (-3 - sqrt(21)) / 2 ≈ -3.79

To find the corresponding values of y, we can substitute these values of x into either equation. For example, if we use y = 3x - 3, we get:

y ≈ 0.37 (when x ≈ 0.79)

y ≈ -12.37 (when x ≈ -3.79)

Therefore, there are two points that satisfy the system of equations:

(0.79, 0.37)

(-3.79, -12.37)

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The value of a is 3.

The value of b is -14.

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

The function of the graph is,

y = 2x² + ax + b

The graph intersects the x-axis at the points (-7/2, 0) and (2, 0).

Now,

Since, The graph intersects the x-axis at the points (-7/2, 0) and (2, 0).

Hence, The points must satisfy the graph of the function.

So, Points (-7/2, 0) and (2, 0) are satisfy the function y = 2x² + ax + b.

When point (-7/2, 0) satisfy the function y = 2x² + ax + b

Then,

0 = 2 × (-7/2)² + a × (-7/2) + b

0 = 49/2 - 7a/2 + b

7a/2 - b = 49/2 .... (i)

And, When point (2, 0) satisfy the function y = 2x² + ax + b

Then,

0 = 2 × (2)² + a×2 + b

2a + b = -8    .... (ii)

Add equation (i) and (ii) we get;

7a/2 - b + 2a - b = 49/2 + (-8)

11a/2 = 33/2

11a = 33

a = 3

And, 2a + b = -8

2 × 3 + b = -8

b = -8 - 6

b = -14

Hence, The value of a is 3.

The value of b is -14.

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Points A, B and C are collinear and X is a bisector of ∠A.

To prove that A, B, and C are collinear, we need to show that they lie on the same straight line.

So, we have the following statements and reasons

Therefore, we have proved that A, B, and C are collinear.

To prove that X is a bisector of ∠A, we need to show that ∠AXB = ∠CXB. We can do this using a two-column proof:

Therefore, we have proven that X is a bisector of ∠A.

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Answer: The answer is C on edge.

Answer:

answer is C 2,635

Step-by-step explanation:

a) A vector function for the line segment from P to Q is:

r(t) = (1 - t) i - 3t j + (10-11t) k

b) A vector function for the part of the parabola from (-1,-2) to (2,-8) is:

r(t) = ti - 2t² j

c) A vector function for the part of the circle traced out counterclockwise from (4,0) to (0,-4) is:

r(t) = (4cos(t)) i + (4sin(t)) j, for 0 ≤ t ≤ (7π/4)

(a) For a vector function r(t) for the line segment from P(1, -3,10) to Q(0,7,-1), we can use the formula:

r(t) = (1 - t)P + tQ

where P and Q are the initial and terminal points of the line segment, respectively, and t is a parameter between 0 and 1.

Plugging in the values, we get:

r(t) = (1 - t)(1,-3,10) + t(0,7,-1)

Expanding and simplifying, we get:

r(t) = (1-t, -3 + 10t, 10 - 11t)

So a vector function for the line segment from P to Q is:

r(t) = (1 - t) i - 3t j + (10-11t) k

(b) For a vector function r(t) for the part of the parabola y=-2x² from (-1,-2) to (2,-8), we can use the formula:

r(t) = (x(t), y(t), z(t))

where x(t) is the parameterization for x and y(t) = -2x(t)^2 is the parameterization for y.

We can choose any parameterization for z(t) that we like, as long as it is continuous and differentiable.

For this problem, we can use z(t) = 0 to keep the curve in the xy-plane. Then we have:

x(t) = t

y(t) = -2t²

z(t) = 0

So a vector function for the part of the parabola from (-1,-2) to (2,-8) is:

r(t) = ti - 2t² j

(c) For a vector function r(t) for the part of the circle of radius 4 centered at the origin, traced out counterclockwise with initial point (4,0) and terminal point (0,−4), we can use the formula:

r(t) = (x(t), y(t), z(t))

where x(t) and y(t) are parameterizations for the circle and z(t) can be any continuous and differentiable function that keeps the curve in the xy-plane.

For this circle, we can use the parameterizations:

x(t) = 4cos(t)

y(t) = 4sin(t)

z(t) = 0

Then a vector function for the part of the circle traced out counterclockwise from (4,0) to (0,-4) is:

r(t) = (4cos(t)) i + (4sin(t)) j, for 0 ≤ t ≤ (7π/4)

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