Solve the equation 2^(x-2)+2^3-x=3. Also prove that the roots also satisfies 4^(x)-6*2^(x+1)+32=0

Shanika ends up paying more for her utilities, and she paid $35.875 more than Vanesa.

1. Standard Use Plan

2. Interval Use Plan

3. Both women use 1,325 kWh for the given 30 day period

As given to us Shanika is using the Standard use plan, and her usage is  1,325 kWh. so,

        \(400\times 7.5\\=3,000\ \rm cent\)

        \(400\times 10\\=4,000\ \rm cent\)

        \((1325-800)\times 12.5\\= 525 \times 12.5\\= 6,562.5\ cent\)

The total bill of Shanika

\(3,000\cent + 4,000\ cent +6,562.5\ cent\\= 13,562.5\ cent\\= \$135.625\)

Thus, the total bill of Shanika is $135.625.

As given to us Vanesa is using the Interval use plan. Also, Vanesa uses 500 kWh during on-peak hours and 825 during off-peak hours.

       = Amount of electricity used x Rate of electricity

       = 500 kWh x 15 cents/kWh

       = 7,500 cent

       = Amount of electricity used x Rate of electricity

       = 825 kWh x 3 cents/kWh

       = 2,475 cent

The total bill of Vanesa

= 7,500 cent + 2,475 cent

= 9,975 cent

= $99.75

Thus, the total amount paid by Vanesa is $99.75.

Therefore, the amount paid by Shanika is more.

The difference between the bill amount of both the womens

= total bill of Shanika - total bill of Vanesa

= $135.625 - $99.75

= $35.875

Hence, Shanika ends up paying more for her utilities, and she paid $35.875 more than Vanesa.

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Answer:c

Step-by-step explanation:

Substitution is the best method to use when one of the equations in the system is already solved for one variable. This involves substituting the solved equation into the other equations in the system, allowing the variable to be eliminated, and then solving the resulting equation.

Substitution is the best method to use when one of the equations in the system is already solved for one variable. This method involves substituting the solved equation into the other equations in the system, allowing the variable to be eliminated. The resulting equation will have fewer variables, making it easier to solve. Additionally, this method can be used to eliminate variables from equations that cannot be solved directly. For example, if two equations are given that cannot be solved for a common variable, substitution can be used to eliminate the variable from both equations and turn them into equations in one variable. This makes it easier to solve the system of equations.

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The answer to the question is option B: "The slot machine didn't give me a winning amount for over an hour, so chances now are going to be that I hit the jackpot soon."

The first paragraph explains how slot machines and cell phones can create a sense of excitement and false hope, leading to addictive behaviors. It highlights the manipulation by app designers and the negative impact on interpersonal relationships. The second paragraph asks for an example of the Gambler's Fallacy.

The answer to the question is option B: "The slot machine didn't give me a winning amount for over an hour, so chances now are going to be that I hit the jackpot soon." This statement reflects the Gambler's Fallacy, which is the belief that previous outcomes will influence future outcomes in a game of chance. In this case, the person assumes that because they haven't won for a while, their chances of hitting the jackpot have increased. However, each spin of the slot machine is independent and has no connection to previous outcomes. The Gambler's Fallacy is a common misconception that can lead to risky and irrational behavior in gambling situations.

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The estimated value of y when x1=12, x2=1, and x3=-1 is -204. This is calculated by substituting the given values into the equation ˆy=−184−7x1+47x2+20x3.

ˆy=−184−7(12)+47(1)+20(-1)

ˆy=−184-84+47-20

ˆy=−204

In the multiple regression equation

ˆy=−184−7x1+47x2+20x3

the estimated value of y can be determined by substituting the given values of x1, x2, and x3 into the equation. For example, given

x1=12, x2=1, and x3=-1,

the estimated value of y can be calculated as follows: ˆy=−184−7(12)+47(1)+20(-1). This simplifies to

ˆy=−184-84+47-20, or ˆy=-204.

The equation takes the form of a linear equation, with each independent variable x1, x2, and x3 multiplied by a coefficient, and then added together to give the estimated value of y. In this example, the coefficient for x1 is -7, for x2 is 47, and for x3 is 20. This means that if x1 increases by 1 unit, then the estimated value of y will decrease by 7 units; if x2 increases by 1 unit, then the estimated value of y will increase by 47 units; and if x3 increases by 1 unit, then the estimated value of y will increase by 20 units. Using the multiple regression equation, therefore, the estimated value of y can be calculated when the values of the independent variables are known. In this example, given x1=12, x2=1, and x3=-1, the estimated value of y is -204.

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The complete question is

In the following multiple regression equation, what is the value of x2 when x1 = 15.5 and ˆy is estimated to be -412?ˆy=78−20x1−10x2x2=2)Given the following multiple regression equation:ˆy=−184−7x1+47x2+20x3Determine the estimated value of y whenx1=12x2=1x3=−1ˆy=−204

Using a die to simulate your quiz score allows you to incorporate randomness into the guessing process and estimate the probability of passing the quiz by chance.

To simulate your quiz score using a die, you can assign each answer choice to a number on the die. Since there are six answer choices (A, B, C, D, E, F) and a standard die has six sides, you can assign each choice to one side of the die.

Here's how you can set up the simulation:

Label each face of the die with one of the answer choices (A, B, C, D, E, F).

Roll the die for each question and record the letter that corresponds to the face that comes up.

Repeat this process for all 10 questions to get your simulated quiz score.

Once you have your simulated quiz score, you can calculate the number of correct answers and compare it to the passing grade criteria. For example, if the passing grade requires getting at least 6 out of 10 questions correct, count how many of your simulated quiz answers match the correct answers. If the count is equal to or greater than 6, consider it a passing grade; otherwise, it's a failing grade.

To determine the probability of receiving a passing grade by guessing, you can repeat the simulation many times (e.g., 1000 times) and keep track of the number of times you get a passing grade. Divide the number of successful outcomes (passing grades) by the total number of trials (simulations) to calculate the probability.

It provides a straightforward and tangible way to visualize and understand the concept of probability in this scenario.

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Answer:

11

Step-by-step explanation:

(2x + 7) - (2x - 4)

2x + 7 - 2x + 4

7 + 4 = 11

Answer:

Furthermore, it turns out that rotations by 180^\circ180  

∘

180, degrees or -90^\circ−90  

∘

minus, 90, degrees follow similar patterns:

R_{(0,0),180^\circ}(\tealD{x},\purpleC{y})=(-\tealD{x},-\purpleC{y})R  

(0,0),180  

∘

​

(x,y)=(−x,−y)R, start subscript, left parenthesis, 0, comma, 0, right parenthesis, comma, 180, degrees, end subscript, left parenthesis, start color #01a995, x, end color #01a995, comma, start color #aa87ff, y, end color #aa87ff, right parenthesis, equals, left parenthesis, minus, start color #01a995, x, end color #01a995, comma, minus, start color #aa87ff, y, end color #aa87ff, right parenthesis

R_{(0,0),-90^\circ}(\tealD{x},\purpleC{y})=(\purpleC{y},-\tealD{x})R  

(0,0),−90  

∘

​

(x,y)=(y,−x)R, start subscript, left parenthesis, 0, comma, 0, right parenthesis, comma, minus, 90, degrees, end subscript, left parenthesis, start color #01a995, x, end color #01a995, comma, start color #aa87ff, y, end color #aa87ff, right parenthesis, equals, left parenthesis, start color #aa87ff, y, end color #aa87ff, comma, minus, start color #01a995, x, end color #01a995, right parenthesis

We can use these to rotate any point we want by plugging its coordinates in the appropriate equation.

Step-by-step explanation:

Step-by-step explanation:

the same "conversion process" applies.

whatever expression was in place of the old x gets a negative sign and moves into the spot of y.

and whatever expression was in place of the old y moves into the spot of x.

so, in general, we could say

the original is (f(x), g(y)).

and the 90° rotation is then

(f(x), g(y)) -> (g(y), -f(x))

add on : that means, of course, that if the old x was already a negative number, it turns via "--" into a positive number for the new y.

last but not least : we are talking here about a 90° clockwise rotation. right?

because for the counterclockwise rotation it is

(f(x), g(y)) -> (-g(y), f(x))

Answer:

$175

Step-by-step explanation:

you need to specify if harriet got the 7 portion or the 5 portion. I'll answer as if she got the 7 portion.

They split it into 12 portions because the ratio is 7:5 and 7+5=12. So do $300/12=25

Assuming Maya got the 5 portion, do $25 x 5 = $125, so Maya got $125.

Assuming Harriet got the 7 portion, do $25 x 7 = $175, so Harriet got $175.

Answer:

163m

Step-by-step explanation:

you find the perimeter of the rectangle then you multiply by three

17  is the value of discriminant for quadratic equation.

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                               The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

General form of a quadratic equation is

ax² + bx + c = 0

The Discriminant of the quadratic equation is denoted by D and defined as

D = b² - 4ac

The given Quadratic equation is

√2x² - 5x + √2 = 0

Comparing with the general equation of quadratic equation ax² + bx + c = 0 we get

a = √2 , b = - 5 , c = √2

Value of Discriminant

      = b² - 4ac

      = (-5)² - 4 * √2 * √2

       = 25 - 8

       = 17      

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The missing number in the unit conversion problem is composed as follows:

9 ft = 108 inches.

The missing number is obtained applying the proportions in the context of the problem.

The unit conversion rate between ft and inches is given as follows:

1 feet = 12 inches.

Hence the number of inches in 9 feet is obtained multiplying 9 by 12, as follows:

9 x 12 = 108 inches.

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The vertices of image L'M'N' are L'(-5, -1), M'(0, -1) and N'(-5, -2). Therefore, option C is the correct answer.

Given that, triangles LMN has vertices at L(-1, 5), M(-1, 0) and N(-2, 5).

The vertices of image L'M'N' if the preimage is rotated 90 degree counterclockwise.

90° counterclockwise rotation: (x, y) becomes (-y, x).

Here,

L(-1, 5)→L'(-5, -1)

M(-1, 0)→M'(0, -1)

N(-2, 5)→N'(-5, -2)

Therefore, option C is the correct answer.

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Step-by-step explanation:

A decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point.

Answer: 9/16 as a decimal is 0.5625

9-16-as-a-decimal-is-0.5625

Let's look into the two methods to write 9/16 as a decimal.

Explanation:

Method 1: Writing 9/16 as a decimal using the division method

To convert any fraction to decimal form, we just need to divide its numerator by denominator.

Here, the fraction is 9/16 which means we need to perform 9 ÷ 16

This gives the answer as 0.5625. So, 9/16 as a decimal is 0.5625

Method 2: Writing 9/16 as a decimal by converting the denominator to powers of 10

Step 1: Find a number such that we can multiply by the denominator of the fraction to make it 10 or 100 or 1000 and so on.

Step 2: Multiply both numerator and denominator by that number to convert it into it's an equivalent fraction.

Step 3: Then write down just the numerator, putting the decimal point in the correct place, that is, one space from the right-hand side for every zero in the denominator.

9/16 = (9 × 625) / (16 × 625) = 5625/10000 = 0.5625

Irrespective of the methods used, the answer to 9/16 as a decimal will always remain the same.

You can also verify your answer using Cuemath's Fraction to Decimal Calculator.

Thus, 9/16 as a decimal is 0.5625

Answer: 45

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

The answer is D. When a translation on the x-value is positive, it moves to the right. When a translation on the y-value is positive, it moves up. So, (x+4,y+4) moves up 4 units, and right 4 units.

-hope it helps

The answer is option D

The associated right triangle has one angle θ whose tangent is x/6, and the adjacent side has length 6 while the opposite side has length x.

To evaluate the integral, we use the trigonometric substitution x = 6 tan(θ). Then, dx = 6 sec2(θ) dθ, and substituting in the integral we get:

∫(x^2)/(36+x^2) dx = ∫(36 tan^2(θ))/(36 + 36 tan^2(θ)) (6 sec^2(θ) dθ)

= ∫tan^2(θ) dθ

To solve this integral, we use the trigonometric identity tan^2(θ) = sec^2(θ) - 1, so we get:

∫tan^2(θ) dθ = ∫(sec^2(θ) - 1) dθ

= tan(θ) - θ + C

Substituting back x = 6 tan(θ) and simplifying, we get the final result:

∫(x^2)/(36+x^2) dx = 6(x/6 * √(1 + x^2/36) - atan(x/6) + C)

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Answer:

hi

Step-by-step explanation:

As per the trigonometric substitution the value of the integrals are

a) ∫ x² + 4 / x² dx is 2 tan θ

b) ∫ (16 - 9x²) / x² dx is (4/3) sec θ

c) ∫ (5x² - 3) / x² dx is (1/√3)tanθ

Let's take a look at the given integrals:

a) ∫ x² + 4 / x² dx

For this integral, we can use the trigonometric substitution x = 2tanθ. This substitution simplifies the integral and allows us to solve it using trigonometric identities.

b) ∫ (16 - 9x²) / x² dx

To solve this integral, we can use the trigonometric substitution x = (4/3)secθ. This substitution simplifies the expression under the integral sign and allows us to use trigonometric identities to solve the integral.

c) ∫ (5x² - 3) / x² dx

For this integral, we can use the trigonometric substitution x = (1/√3)tanθ. This substitution simplifies the integral and allows us to use trigonometric identities to solve it.

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The end behavior of the graph of q(x) is as x approaches positive infinity, q(x) approaches negative infinity, and as x approaches negative infinity, q(x) also approaches negative infinity. (Choice C)

To determine the end behavior of the graph of q(x), we examine the leading term of the polynomial function, which is the term with the highest exponent. In this case, the leading term is -2x^8.

As x approaches positive infinity, the leading term -2x^8 becomes very large and negative, causing the entire polynomial q(x) to approach negative infinity. Therefore, as x approaches positive infinity, q(x) approaches negative infinity.

Similarly, as x approaches negative infinity, the leading term -2x^8 becomes very large and negative, causing the entire polynomial q(x) to also approach negative infinity. Therefore, as x approaches negative infinity, q(x) approaches negative infinity.

Thus, the correct answer is choice C: As x approaches positive infinity, q(x) approaches negative infinity, and as x approaches negative infinity, q(x) also approaches negative infinity.

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Answer: 0

Step-by-step explanation:

The measure of the angle if the measure of its two adjacent supplementary angles add up to 100 degrees is 80 degrees.

Let the measure of the angle be x.

We are given that the measure of its other two supplementary angles is 100°

We know that:

The sum of the supplementary angles is equal to 180°.

So, we get that:

100° + x = 180°

Subtract 100° from both the sides:

x = 180° - 100°

Simplify the expression:

x = 80°

Therefore, we get that, the measure of the angle if the measure of its two adjacent supplementary angles add up to 100 degrees is 80 degrees.

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Answer:

45

Step-by-step explanation:

Answer:

49.7 \(cm^{2}\)

Step-by-step explanation:

Although it is hidden a bit, we are actually given the circumference of the circle, which is 25 cm.

We know that C = 2πr, so we can substitute variables to find the radius (r).

25 = 2πr

r = 25/(2π)

r = 3.9788... cm

The area of a circle is A = π\(r^{2}\), so:

A = π \(3.9788^{2}\)

A = 49.7359... \(cm^{2}\)

A ≈ 49.7 \(cm^{2}\)

A 6 pack of bouncy ball costs 2.76$ and the unit price of a bouncy ball is $0.46

To find the unit price of the bouncy balls, we need to divide the total cost by the number of bouncy balls in the pack. Since there are 6 bouncy balls in the pack and the cost is $2.76, we can calculate the unit price as follows: Unit price = total cost ÷ number of units

Unit price = $2.76 ÷ 6

Unit price = $0.46

Therefore, the unit price of a bouncy ball is $0.46.

Unit price is a measure of the cost of a single unit of a product. It is calculated by dividing the total cost of a product by the number of units in the package. The unit price is helpful when comparing the costs of different package sizes or brands of the same product. It allows consumers to make informed decisions about their purchases based on the value they receive for their money. Unit pricing is required by law in some countries, including the United States, to ensure transparency in pricing and to protect consumers from deceptive marketing practices. Overall, knowing the unit price of a product can help consumers save money and make more informed purchasing decisions.

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The algebraic expression that represents the amount that Sohail got is given as follows:

[10(x - 8)]².

His break lasted x days and he was out of station for 8 days, hence the number of days that Sohail worked is given as follows:

x - 8 days.

Each day he earned Rs 10, hence the total amount earned can be modeled as follows:

10(x - 8).

After the amount was squared, the expression is given as follows:

[10(x - 8)]².

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Answer:

B

Step-by-step explanation:

4 times 5 = 20

-2 times 1 = -2

20 - -2 = 18

Answer:

\(sin^2x\)

Step-by-step explanation:

To simplify the expression (1 - cos x)(1 + cos x), we can use the difference of squares identity, which states that \(a^2 - b^2 = (a + b)(a - b).\)

Let's apply this identity to the given expression:

\((1 - cos x)(1 + cos x) = 1^2 - (cos x)^2\)

Now, we can simplify further by using the trigonometric identity \(cos^2(x) + sin^2(x) = 1.\) By rearranging this identity, we have \(cos^2(x) = 1 - sin^2(x).\)

Substituting this into our expression, we get:

\(1^2 - (cos x)^2 = 1 - (1 - sin^2(x))\)

Simplifying further:

\(1 - (1 - sin^2(x)) = 1 - 1 + sin^2(x)\)

Finally, we get the simplified expression:

\((1 - cos x)(1 + cos x) = sin^2(x)\)

To simplify the expression \(\sf\:(1-\cos x)(1+\cos x)\\\), follow these steps:

Step 1: Apply the distributive property.

\(\longrightarrow\sf\:(1-\cos x)(1+\cos x) = 1 \cdot 1 + 1 \cdot \\\)\(\sf\: \cos x -\cos x \cdot 1 - \cos x \cdot \cos x\\\)

Step 2: Simplify the terms.

\(\longrightarrow\sf\:1 + \cos x - \cos x - \cos^2 x\\\)

Step 3: Combine like terms.

\(\longrightarrow\sf\:1 - \cos^2 x\\\)

Step 4: Apply the identity \(\sf\:\cos^2 x = 1 - \sin^2 x\\\).

\(\sf\:1 - (1 - \sin^2 x)\\\)

Step 5: Simplify further.

\(\longrightarrow\sf\:1 - 1 + \sin^2 x\\\)

Step 6: Final result.

\(\sf\red\bigstar{\boxed{\sin^2 x}}\\\)

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)