Shopping and Discounts
How do I write this into an equation or something.
Best Buy is selling TVs for 30% off the original price. The TV you want to purchase is $1,499.00. What will be the sale price at 30% off? How much will you save?

Answer:

25x^2 +40x+16

Step-by-step explanation:

(5x + 4)²​

(5x+4)(5x+4)

FOIL

first  5x*5x = 25x^2

outer  5x*4 = 20x

inner 4*5x = 20x

last = 4*4 = 16

Add them together

25x^2 +20x+20x+16

Combine like terms

25x^2 +40x+16

Answer:

\( {(5x + 4)}^{2} \\ = {(5x)}^{2} + 2 \times 4 \times 5x + {4}^{2} \\ = 25 {x}^{2} + 40x + 16 \\ thank \: you\)

Answer:

Step-by-step explanation:

1). Geometric mean of a and b = \(\sqrt{a\times b}\)

   Therefore, geometric mean of 2 and 50 = \(\sqrt{2\times 50}\)

                                                                       = 10

2). By geometric mean theorem,

   \(\frac{JM}{KM}=\frac{KM}{ML}\)

   \(\frac{6}{e}=\frac{e}{24}\)

   e² = 6 × 24

   e = √144

   e = 12

  Similarly, \(\frac{JL}{KJ}=\frac{KJ}{JM}\)

   \(\frac{6+24}{d}=\frac{d}{6}\)

   d² = 6 × 30

   d = √180

   d = 6√5

   And \(\frac{JL}{KL}=\frac{KL}{ML}\)

   \(\frac{6+24}{c}=\frac{c}{24}\)

   c² = 30 × 24

   c = √720

   c = 12√5

answer

\(y = \frac{4}{3}x - 8\)

explanation

\(4x - 3y = 24\)

\( - 3y = 24 - 4x\)

\(3y = - 24 + 4x\)

\(y = - 8 + \frac{4}{3} x\)

\(y = \frac{4}{3}x - 8\)

The optimal solution for the given linear programming model is:

max z = 38

when x1 = 5, x2 = 10, x3 = 0

To solve the given linear programming model using the simplex algorithm, we start by converting the inequalities into equations and introducing slack variables. The initial tableau is constructed with the coefficients of the decision variables and the right-hand side constants.

Next, we apply the simplex algorithm to iteratively improve the solution. By performing pivot operations, we move towards the optimal solution. In each iteration, we select the pivot column based on the most negative coefficient in the objective row and the pivot row based on the minimum ratio test.

After several iterations, we reach the optimal tableau, where all the coefficients in the objective row are non-negative. The optimal solution is obtained by reading the values of the decision variables from the tableau.

In this case, the optimal solution is z = 38 when x1 = 5, x2 = 10, and x3 = 0. This means that to maximize the objective function, the decision variables x1 and x2 should be set to 5 and 10 respectively, while x3 is set to 0.

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Based on the function shown on the graph, the statement that is true is: D. The candle started at 9 mm and shrinks 5 mm every 4 minutes.

A function is a relationship between input and output values.

On a graph, the average rate of change represents the unit rate, while the point where the line intercepts the y-axis is the initial value or starting value.

Therefore:

The starting value = 9 mm (the candle length when it started burning).

In conclusion, based on the function shown on the graph, the statement that is true is: D. The candle started at 9 mm and shrinks 5 mm every 4 minutes.

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The Graph of quadratic functions gives parabolas that are U-shaped, and wide or narrow depending upon the coefficients of the function.

The graph of quadratic functions is a technique to study the nature of the quadratic functions graphically. The shape of the parabola is determined by the coefficient 'a' of the quadratic function f(x) = ax2 + bx + c, where a, b, c are real numbers and a ≠ 0.

the vertex of a quadratic function is. \(f(x)=a(x-h)^2+k, where (h,k)\) is the vertex of parabola. When a>0 then function will be open upward if a<0 then function will be opens downward.

Steps to plot graph of quadratic function.

a\(x^2\) is imply a vertical scaling of the parabola, if a<0 the parabola will also flip its mouth from the positive to negative side.

\(a(x+\frac{b}{2a} )^2\) This is a horizontal shift of magnitude |\(\frac{b}{2a}\)| units. The direction of the shift will be decided by the sign of b/2a. The new vertex of the parabola will be at (-b/2a,0).

This transformation is a vertical shift of magnitude |\(\frac{D}{4a}\)| units. The direction of the shift will be decided by the sign of \(\frac{D}{4a}\). The final vertex of the parabola will be at (\(\frac{-b}{2a} ,\frac{-D}{4a}\)).

So, The Graph of quadratic functions gives parabolas that are U-shaped, and wide or narrow depending upon the coefficients of the function.

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Answer:

$3.45

Step-by-step explanation:

15% of 23 is 3.45

Answer: y=-35

Step-by-step explanation:

The question is 25+y=-10

Now, since we want the value of y, we can see that we have to remove the 25 that is added to it. So, we subtract both sides as it an equal side, and -10-25= -35 So, y=-35

25+y=-10

-25       -25

y=-10-25=-35

Hope this helps

Answer: C) She slept until noon.

Answer:

(A) 4x2 - 4x + 1

Step-by-step explanation:

We can factor 4 out of each of these choices and see which ones can be factored as a perfect square

(A) 4x² - 4x + 1

= 4(x² - 1x + 1/4)

If x² - x + 1/4  is to be a perfect square, since the coefficient of x is negative it must be of the form (x - a)²
(x - a)² = x² - 2ax + a²

With a = 1/2, a² = 1/4

-2ax = -2 x 1/2 x = -1x = -x

So 4x2 - 4x + 1 is a perfect square and can be factored as
4(x - 1/2)²

(a) p(2), that is, P(X = 2)The cdf is given by: F(x) = 0 x < 00.06 0 ≤ x < 10.16 1 ≤ x < 20.33 2 ≤ x < 30.69 3 ≤ x < 40.92 4 ≤ x < 50.99 5 ≤ x < 61 6 ≤ x

The probability mass function p(x) can be derived from the cdf by taking differences:

p(x) = F(x) − F(x-1)Thus the probability mass function p(x) is as follows: p(x) = 0.06  x = 10.1  x = 20.17 x = 30.36  x = 40.23 x = 50.07 x = 60.01 x = 6The probability P(X = 2) can be found as follows: P(X = 2) = p(2) = 0.17(b) P(X > 3)The probability can be found as follows: P(X > 3) = P(4 ≤ X) = 1 - P(X < 4) = 1 - F(3) = 1 - 0.33 = 0.67(c) P(2 ≤ X ≤ 5)The probability can be found as follows: P(2 ≤ X ≤ 5) = F(5) - F(1) = 0.99 - 0.1 = 0.89(d) P(2 < X < 5)

The probability can be found as follows: P(2 < X < 5) = F(4) - F(2) = 0.92 - 0.17 = 0.75.

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Answer:

The common factors are 1, 2, 3, and 6. The greatest common factor would be 6.

Answer:

B

Step-by-step explanation:

Using the rule of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

\(a^{0}\) = 1

Given

\(9^{c}\) × \(9^{-c}\)

= \(9^{(c-c)}\)

= \(9^{0}\)

= 1 → B

Answer:

0.25 Liters

Step-by-step explanation:

1 milliliter = 0.001 Liter

250 milliliters = 0.001 x 250 = 0.25 Liters

So, there are 0.25 Liters in 250 milliliters.

Answer:

.25 liters

Step-by-step explanation:

1 milliliter is .001 liter so .001 multiplied by 250 equals .25

:) hope that helps

The principle values of the given logarithms is

\(i (π/2 + 2πk),\)

where k is an integer.

The solution to the evaluation is

\( = (a-b)^(-Arg(a-b)) [cos(ln|a-b|) + i sin(ln|a-b|)]\)

The principal value of a logarithm is the value of the logarithm that lies within a certain range of values, typically (-π, π] or [0, 2π).

The principal value is usually denoted with the symbol "Log"

For instance, the principal value of the logarithm of a negative number or a complex number is typically given as:

\(Log(z) = ln|z| + i Arg(z)\)

where

ln denotes the natural logarithm,

|z| denotes the absolute value of z,

i is the imaginary unit, and

Arg(z) denotes the principal argument of z (i.e., the angle that the complex number makes with the positive real axis).

For the expression (√-1), the principal value of the logarithm is:

\(Log(√-1) = ln|√-1| + i Arg(√-1) \\

= ln|1| + i (π/2 + 2πk) \\

= i (π/2 + 2πk )\)

Note that there are infinitely many possible values for the logarithm of a complex number, due to the periodicity of the trigonometric functions involved.

To evaluate (a+b)i and (a-b)^i in the form a+bi, where a and b are real numbers:

\((a+b)i = ai + bi \\

(a-b)^i = e^(i Log(a-b)) \\

= e^(i (ln|a-b| + i Arg(a-b))) \\

= e^(-Arg(a-b)) e^(i ln|a-b|) \\

= (a-b)^(-Arg(a-b)) [cos(ln|a-b|) + i sin(ln|a-b|)]\)

where e is the base of the natural logarithm, and Arg(a-b) denotes the principal argument of the complex number a-b.

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Answer:

(-6,-3) (-5,-1) (-4,1) (-3,-1) (-2,-1)

Step-by-step explanation:

i hope thats what you wanted.

Q6: Approximately 68.3% of the cherry tomatoes sold by Berkeley Bowl fall within the specified diameter limits of 20 mm to 32 mm.

Q7: To achieve half of the Six Sigma Quality, the standard deviation of the process should be approximately 0.22 mm for Berkeley Bowl's cherry tomatoes.

In Q6, we can use the concept of the normal distribution to determine the percentage of tomatoes within the specification limits. Since the average diameter is 26 mm and the standard deviation is 3 mm, we can assume a normal distribution and calculate the percentage of tomatoes within one standard deviation of the mean. This corresponds to approximately 68.3% of the tomatoes falling within the specified limits.

In Q7, achieving Six Sigma Quality means that the process has a very low defect rate. In this case, half of the Six Sigma Quality means reducing the variability in diameter to half the acceptable range.

The acceptable range is 32 mm - 20 mm = 12 mm. To achieve half the range, the standard deviation should be approximately half of 12 mm, which is 6 mm. Since the standard deviation is given as 3 mm, the process would need to be improved to reduce the standard deviation to approximately 0.22 mm for it to meet half of the Six Sigma Quality.

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The probability that a bridge hand will have exactly 2 queens is 0.45%.

To find the probability of getting a bridge hand with exactly 2 queens, we need to use the binomial probability formula. The formula is:

P(exactly k successes) = (n choose k) * p^k * (1-p)^(n-k)

Where:

n is the total number of trials

k is the number of successes in the trials

p is the probability of success in a single trial

In this case, the total number of trials is 13 (since a bridge hand consists of 13 cards), and the number of successes we want is 2 (since we want exactly 2 queens). The probability of success in a single trial is the probability of drawing a queen, which is 4/52 (since there are 4 queens in a deck of 52 cards).

Plugging these values into the formula, we get:

P(exactly 2 queens) = (13 choose 2) * (4/52)² * (48/52)¹¹

= (78) * (1/169) * (4/13)¹¹

= (4/169) * (4/13)¹¹

This simplifies to:

P(exactly 2 queens) = (4/169) * (4/13)¹¹

= (4/169) * (4/169)¹¹

= (4/169)¹²

The final probability is approximately 0.0045 or 0.45%. This means that the probability of getting a bridge hand with exactly 2 queens is quite low.

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I hope this helps you

Question wants sum of two functions

g(x) +k(x)

9x^2-5+3x-1

9x^2+3x-6

3(3x^2+x-2)

3(3x-2)(x+1)

Answer:

SSS

Step-by-step explanation:

Can't be AA. (no angles given)

Can't be SAS. No angles Given

Can't be not. (CPCTC)

The total charge for a rental that includes insurance is C = 21.85 + 0.85M.

The given equations are known as linear equations. Linear equations are equations that that has a single variable raised to the power of 1. When drawn on a graph, a linear equation is a straight line.

The mathematical operation that would be used to determine the total cost is addition. Addition is the process of adding two or more numbers.

The total cost for rental is the sum of the standard charge and the cost of insurance.

Total cost = cost of insurance + standard charge

(16.95 +0.60M) + (4.90+0.25M)

Add similar terms: (16.95 + 4.90) + (0.60M + 0.25M)

C = 21.85 + 0.85M

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Volume of the cylinder = 1130.4 m³

volume of the cylinder = 1780.4 m³

Volume of cylinder = πr²h

1) diamter = 12 m

diameter = 2(radius)

radius = diamter/2 = 12/2 = 6 m

height = h = 10m

let π = 3.14

Volume of the cylinder = 3.14 × 6² × 10

Volume of the cylinder = 1130.4 m³

2) radius = 9 in

height 7 in

Volume of cylinder = πr²h

Volume of the cylinder = 3.14 × 9² × 7

Volume of the cylinder = 1780.38

To the nearest tenth, volume of the cylinder = 1780.4 m³

Answer: 0.7

Step-by-step explanation:

April has 30 days, and we know that it rained in 9 of them.

Then the probability that there will be rain in a random day, can be estimated as the quotient between the number of days where was rain and the total number of days, this probability will be:

P = 9/30 = 0.3

And we can extrapolate this probability to May.

Then we can estimate that the first day of May, the probability of rain will be around 0.3

Then the probability that it does not rain in the first day of may will be:

1 - 0.3 = 0.7

Answer:

Step-by-step explanation:

Answer: $755.9

Explanation:

The total cost of all repairs is the sum of the timing belt kit cost, the brake pads cost, and the labor cost.

Since they require 4.6 hours for the timing belt kit and 1.8 hours for the brake pads. the total labor cost is:

$95 * (4.6 hours + 1.8 hours )

$95 * (6.4 hours)

$608

Because the labor rate is $95/hour

Therefore, the total cost of repair is:

$89.95 + $57.95 + $608 = $755.9

So, the answer is $755.9