owing demand function: p = D(x) = = 105 – 2.1x = d the elasticity function. E(x) = =

Answer:

b= x

Step-by-step explanation:

\(\boxed{ {x}^{m} \times {x}^{n} = {x}^{m + n} }\)

Applying the law of indices above:

\(b = {x}^{ \frac{1}{4} } \times {x}^{ \frac{3}{4} } \)

\(b = {x}^{ \frac{1}{4} + \frac{3}{4} } \)

\(b = {x}^{ \frac{4}{4} } \)

\(b = {x}^{1} \)

∴b= x

Answer:

It is b = x

Step-by-step explanation:

From law of indices:

\( {a}^{b} \times {a}^{c} = {a}^{(b + c)} \)

for, multiplication: same coefficients, we sum up the powers.

\(b = {x}^{ \frac{1}{4} } \times {x}^{ \frac{3}{4} } \\ b = {x}^{( \frac{1}{4} + \frac{3}{4} ) } \\ b = {x}^{ \frac{4}{4} } \\ b = {x}^{1} \\ b = x\)

Answer:

Step-by-step explanation:

A. The Initial value is the starting value of her business which can be considered $350 since that is what she made the first year. The Slope can be calculated by subtracting the end profit from the initial profit and then dividing by the result of subtracting the end year by the initial year like so...

$350 initial value

\(\frac{750 - 350}{2014 - 2010} = \frac{400}{4} = \frac{100}{1 year} =\)  $100 a year increase

B. The equation for this scenario would be  y = 100x + 350

Answer:

100 each year and y=100x+350

Step-by-step explanation:

Answer:

10,000,000

Step-by-step explanation:

When it says 10 to the 7th power, that means to times by 7 whatever number you have. The power is how many times you need to multiply the other number. Not like 10x7, but 10x10, and so on.

The greatest common factor of the expression 2ax² + 2ax + 2a is 2a.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

2ax² + 2ax + 2a

There are three terms.

The greatest common factor in each term is 2a

Now,

2a (x² + x + 1)

Thus,

The expression with the greatest common factor is 2a (x² + x + 1).

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Answer:

- g - 6 ≤ 10.5

Step-by-step explanation:

Answer:

-g-6 is less than or equal to 10.5

Step-by-step explanation:

replace the g with 5.

Answer:

The given expression in factored form is (x + 2)(x - 3).

If the expression is set to zero, the solutions x = -2 and x = 3 are the roots of the graph of the equation.

Step-by-step explanation:

To factor a quadratic in the form ax² + bx + c, begin by finding two numbers that multiply to ac and sum to b.

Given quadratic:

\(x^2-x-6\)

Therefore:

\(\implies ac=1 \cdot -6=-6\)

\(\implies b=-1\)

Two numbers that multiply to -6 and sum to -1 are -3 and 2.

Rewrite b as the sum of these two numbers:

\(\implies x^2-3x+2x-6\)

Factor the first two terms and the last two terms separately:

\(\implies x(x-3)+2(x-3)\)

Factor out the common term (x - 3):

\(\implies (x+2)(x-3)\)

If the given expression is a function, then:

\(f(x)=(x+2)(x-3)\)

To find the solutions of the function, set it to zero and apply the zero-product property:

\((x+2)=0 \implies x=-2\)

\((x-3)=0 \implies x=3\)

Therefore, the solutions of the equation are x = -2 and x = 3.

These are the roots (x-intercepts) of the graph of the function.

Given:-

To find:-

Answer:-

Given expression to us is ,

\(\implies x^2 - x - 6 \\\)

Here we can write " - x " as the sum of -3x and x .

So we can write the given expression as ,

\(\implies x^2 - 3x + 2x - 6\\\)

\(\implies x ( x - 3) + 2(x -3) \\\)

\(\implies (x+2)( x-3)\\\)

Hence the factored form of the expression is (x+2)(x-3) .

By zeroes we mean the values , which when put in the equation at the place of variable here x , the value of expression becomes zero .

For finding the zeroes, we need to equate the given expression with 0 as ,

\(\implies (x+2)(x-3) = 0 \\\)

Here we can two values of x as ,

\(\implies \underline{\underline{ x = -2 , 3 }}\\\)

This means when we put x = -2 or x = 3 in the given equation , the equation becomes 0 .

and we are done!

The effect of eliminating a redundant constraint from a linear programming model depends on the specifics of the model and the constraint in question. It is important to analyze the model carefully to determine the effect that eliminating a constraint would have on the optimal solution.

No effect: If the constraint was indeed redundant, meaning that it did not affect the optimal solution, then eliminating it would have no effect on the optimal solution.

Improved solution: If the constraint was affecting the optimal solution, then eliminating it might result in a better solution. For example, if the constraint was limiting the feasible region of the solution, then eliminating it might expand the feasible region and result in a better solution.

Different solution: If the constraint was affecting the optimal solution, then eliminating it might result in a different solution. For example, if the constraint was forcing the optimal solution to go through a particular point, then eliminating it might result in a different solution.

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The value of y is given as follows:

y = 23.

Hence the angle measures are given as follows:

69º, 23º and 88º.

The sum of the measures of the internal angles of a triangle is of 180º.

The internal angles for the triangle in this problem have the measures given as follows:

Hence the value of y is obtained as follows:

3y + y + 4y - 4 = 180

8y = 184

y = 184/8

y = 23.

Hence the angle measures are given as follows:

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Answer:

Dylan's budget is $250, and she is buying pumpkins for $20 each and balloons for $2 each. We can represent the total cost of the pumpkins as 20x and the total cost of the balloons as 2y. The inequality that represents all possible ways she could buy pumpkins and balloons within her budget is:

20x + 2y <= 250

To find the maximum number of balloons she could buy, we can use the equation above and set x = 0, and then solve for y.

20(0) + 2y <= 250

2y <= 250

y <= 125

The maximum number of balloons she could buy is 125.

-3

Step-by-step explanation:

h^2/ h^2×g^3= 1/g^3= g^-3 -----> ?=-3

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

The inverse of the function f(x) = 3log(x²) is \(f^{-1}(x) = log_{10}\frac{x}{6}\).

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Given, A function f(x) = 3log(x²) for x > 0.

Ley, y = 3log(x²).

y = 2×3log(x).

y = 6log(x).

log(x) = y/6.

log(x) = y/6.

\(10^{log_{10}}(x) = log_{10}\frac{y}{6}\).

\(x = log_{10}\frac{y}{6}\).

\(y = log_{10}\frac{x}{6}\)

\(f^{-1}(x) = log_{10}\frac{x}{6}\).

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Answer:

9 dollars

Step-by-step explanation:

58.5 times .15 = 8.775 which can be rounded up to 9 dollars

If group of college students spent $58.50 for dinner and wanted to leave a 15% tip. Then $9 is the tip.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

A group of college students spent $58.50 for dinner

The students want to leave a tip of 15%.

We need to find how much they has to leave as tip.

Firstly we have to convert 15% to decimal.

We have to divide 15 by 100

15/100

0.15

Now we have to multiply 0.15 with 58.50 to find the 15% of 58.50

0.15×58.50

8.775

9

Hence, $9 is the tip the students has to leave.

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Answer:

the y-intercept is (0,21)

Answer:

(0,21)

Step-by-step explanation:

If you set x to 0, you can solve for the y-intercept. Plugging in 0 in this equation will give you 21. Therefore, the y-intercept is at (0,21).

Answer:

None of those answers seems correct to me

Correct equation of the graph is

y=2x

Step-by-step explanation:

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

From the question, we have the following parameters that can be used in our computation:

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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By applying a contradiction proof technique, we can prove that if z is less than 0, then x is greater than y. Given the values x = 2, y = 2, and z ∈ Z, along with the equations x = (1 - t)x + t(z) and y = (1 - k)y + k(z - x), we can substitute the given values to evaluate the expressions and show the desired inequality.

We are given the equations x = (1 - t)x + t(z) and y = (1 - k)y + k(z - x), and we want to prove that (z < 0) → (x > y) using a contradiction proof technique.
Assuming z < 0, we substitute the given values x = 2 and y = 2 into the equations and simplify:
x = (1 - t)x + t(z) => 2 = (1 - t) * 2 + t * z => 2 = 2 - 2t + tz
y = (1 - k)y + k(z - x) => 2 = (1 - k) * 2 + k * (z - 2) => 2 = 2 - 2k + k(z - 2)
Next, we observe that if z < 0, then tz < 0 and k(z - 2) < 0. Therefore, from the equation 2 = 2 - 2t + tz, we conclude that -2t + tz < 0, which implies 2 > x. Similarly, from the equation 2 = 2 - 2k + k(z - 2), we conclude that -2k + k(z - 2) < 0, leading to 2 > y.
Thus, we have shown that if z < 0, then x > y, fulfilling the desired implication (z < 0) → (x > y) using the contradiction proof technique.

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The simplified expression is [-6x² - 2x + 40]/[(x² - 6x+8)(x-2)]. To multiply and write the answer in the simplest form for the expression (x²+7x+10)/(7x-28) * (-6x+8)/(x²-4), you can follow these steps:

Simplify each expression separately

(x²+7x+10)/(7x-28) can be factored as (x+5)/(7(x-4)).

(-6x+8)/(x²-4) can be factored as -2(3x-4)/((x+2)(x-2)).

Multiply the numerators and denominators together:

(x+5)/(7(x-4)) * -2(3x-4)/((x+2)(x-2)) = [(x+5)(-2(3x-4))]/[7(x-4)(x+2)(x-2)].

Simplify the numerator:

Distribute -2 to (3x-4): (-2)(3x) + (-2)(-4) = -6x + 8.

Multiply (x+5) with -6x + 8: (x+5)(-6x+8) = -6x² - 2x + 40.

Simplify the denominator:

Multiply (x-4)(x+2)(x-2):

(x-4)(x+2)(x-2) = (x²-2x-4x+8)(x-2)

= (x²-6x+8)(x-2).

Write the simplified expression:

The simplified expression is [-6x² - 2x + 40]/[(x²-6x+8)(x-2)].

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Answer:the coefficient of the 2nd term is : 24

Step-by-step explanation:(6p + 2)^2 =

(6p + 2)(6p + 2) =

36p^2 + 12p + 12p + 4 =

36p^2 + 24p + 4

Answer:

-0.5

Step-by-step explanation:

-0.7 + 0.5 - 0.3 = -0.5

Answer:

1,3,5,6.

Step-by-step explanation:

ur welcome

One possible value of ∠U is 80° (to the nearest degree).

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.

To find the possible values of ∠U, we can use the Law of Cosines:

c² = a² + b² - 2ab cos(C)

Where c is the side opposite the angle we want to find (∠U), a and b are the other two sides, and C is the angle opposite side c.

In this case, we want to find ∠U, so we'll use side u as c and sides t and s (which we don't know yet) as a and b, respectively:

u² = t² + s² - 2ts cos(U)

Substituting the given values, we get:

340² = 620² + s² - 2(620)(s)cos(U)

Simplifying:

115600 = 384400 + s² - 1240s cos(U)

Subtracting 384400 and rearranging:

s² - 1240s cos(U) + 268800 = 0

Now we can use the quadratic formula to solve for s:

s = [1240 cos(U) ± √(1240² cos²(U) - 4(1)(268800))]/(2)

Simplifying under the square root:

s = [1240 cos(U) ± √(1537600 cos²(U) - 1075200)]/(2)

s = [1240 cos(U) ± √(409600 cos²(U) + 1742400)]/(2)

s = [620 cos(U) ± √(102400 cos²(U) + 435600)]

Since s must be positive, we can discard the negative solution, and we have:

s = 620 cos(U) + √(102400 cos²(U) + 435600)

Now we can use the fact that the sum of angles in a triangle is 180° to find ∠U:

∠U = 180° - ∠T - ∠S

Since we know ∠T = 110°, we just need to find ∠S. We can use the Law of Sines to do this:

sin(S)/s = sin(T)/t

sin(S) = (s/t)sin(T)

Substituting the values we know:

sin(S) = (620 cos(U) + √(102400 cos²(U) + 435600))/620 * sin(110°)

sin(S) ≈ (1.481 cos(U) + 2.225)/6.959

Now we can use a calculator to find the arcsin of both sides to get ∠S:

∠S ≈ arcsin((1.481 cos(U) + 2.225)/6.959)

Finally, we can substitute the values we found for ∠S and ∠T into the equation we found earlier for ∠U:

∠U = 180° - 110° - arcsin((1.481 cos(U) + 2.225)/6.959)

Simplifying:

∠U = 70° - arcsin((1.481 cos(U) + 2.225)/6.959)

Now we can use trial and error or a graphing calculator to find the values of ∠U that satisfy this equation. One possible solution is:

∠U ≈ 80°

Therefore, one possible value of ∠U is 80° (to the nearest degree).

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The experimental probability that at least two heads would be gotten is 11 / 25.

The theoretical probability that at least two heads would be gotten is 1/2.

Probability calculates the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Experimental probability is based on the result of an experiment that has been carried out multiples times.

Experimental probability = number of times at least two heads would be gotten / total number of tosses

( 5 + 6 + 6 + 5)/50 = 22/50 = 11 / 25

Theoretical probability = number of times at least two heads would be gotten / total number of possible outcomes

4 / 8 = 1/2

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Answer:

SD=10

Step-by-step explanation:

S=the intersection of the medians

SD=JD/3

SD=30/3

SD=10

The complex number 4 - 2i can be expressed as 4 - 2i in the form a + bi. In polar form, it can be written as 2√5(cos(-0.464) + isin(-0.464)). The magnitude or modulus of the number is 2√5, and the angle is approximately -0.464.

1. The complex number 4 - 2i can be expressed in the form a + bi, where a represents the real part and b represents the imaginary part. In this case, the real part is 4 and the imaginary part is -2, so the number can be written as 4 - 2i.

2. In polar form, a complex number can be represented as r(cosθ + isinθ), where r represents the magnitude or modulus of the number and θ represents the angle. To find the polar form of 4 - 2i, we need to calculate the magnitude and angle.

3. The magnitude (r) can be calculated using the formula r = √(a^2 + b^2). In this case, a = 4 and b = -2, so the magnitude is r = √(4^2 + (-2)^2) = √(16 + 4) = √20 = 2√5.

4. To find the angle (θ), we can use the formula θ = atan(b/a). Substituting the values, θ = atan((-2)/4) = atan(-0.5) ≈ -0.464. Therefore, the polar form of 4 - 2i is 2√5(cos(-0.464) + isin(-0.464)). In summary, the complex number 4 - 2i can be expressed as 4 - 2i in the form a + bi. In polar form, it can be written as 2√5(cos(-0.464) + isin(-0.464)). The magnitude or modulus of the number is 2√5, and the angle is approximately -0.464.

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Answer:

1. Combining like terms

2. Distributive property

3. Subtraction (both sides)

4. Addition(both sides)

5. Division

Step-by-step explanation:

The standard deviation used to calculate the test statistic for the one-sample z-test is option c, i.e. √(22(78)/200).

Let’s take p as the proportion of students from high school Y who watched the movie on opening night.

Then the sample proportion, ˆp = 22/200 = 0.11

We need to find out whether the proportion of all students in high school Y who saw the movie on opening night is greater than that of high school X. The sample proportion for high school X is 0.09.

We can use a one-sample z-test with the following hypotheses.

H₀: p ≤ 0.09

Hₐ: p > 0.09

The null hypothesis represents the assumption that the proportion of students in high school Y who watched the movie on opening night is less than or equal to that of high school X.

The alternative hypothesis represents the assumption that the proportion of students in high school Y who watched the movie on opening night is greater than that of high school X.We calculate the test statistic, z, as follows:

z = (ˆp - p₀) / σ

Where p₀ = 0.09 and σ is the standard deviation of the sample proportion.

We know that

σ = √[(p₀(1 - p₀)) / n]

Where n = 200.

σ = √[(0.09 x 0.91) / 200]

σ = 0.0274

Therefore,

z = (0.11 - 0.09) / 0.0274 = 0.7299

The p-value for this test is P(Z > 0.7299) = 0.2333

At the 5% level of significance, we fail to reject the null hypothesis since the p-value is greater than 0.05. Thus, we do not have sufficient evidence to conclude that the proportion of all students in high school Y who saw the movie on opening night is greater than that of high school X.

Hence option c is correct.

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