How many solutions does 1/2(6x-2)=2 have

[tex]\frac{2}{243} (82^\frac{3}{2} -1)[/tex] is the required length of the curve y = 4 + 6[tex]x^\frac{3}{2}[/tex]

Given equation of curve:

y = 4 + 6[tex]x^\frac{3}{2}[/tex]

length of the curve is given by L= [tex]\int\limits^a_b {\sqrt{1+(y^')^2} } \, dx[/tex]

where [tex]y^'[/tex] is derivative of y with respect to x

so [tex]y^'[/tex] = 6*(3/2) * [tex]\sqrt{x}[/tex]

=> 9 [tex]\sqrt{x}[/tex]

given a=1 and b=0

so L= [tex]\int\limits^1_0 {\sqrt{1+(9\sqrt{x})^2 } } \, dx[/tex]

L=  [tex]\int\limits^1_0 {\sqrt{1+81x } } \, dx[/tex]

let 1+81x be t

81dx = dt

as the value of x changes after the substitution of the value.

so now the L changes as:

L= 1/81 [tex]\int\limits{\sqrt{t } } \, dt[/tex]

L=1/81* [tex]\left \{ {{t=82} \atop {t=1}} \right.[/tex]  [tex]\frac{t^\frac{3}{2} }{\frac{3}{2} }[/tex]

the min value of t=1 and max value of t=82

L=[tex]\frac{2}{243} (82^\frac{3}{2} -1)[/tex]

so the exact length of the curve is given by L=[tex]\frac{2}{243} (82^\frac{3}{2} -1)[/tex]

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If we want the margin of error for the 90% confidence level to be about 1.5%, then a sample of 3002 is recommended.

In this problem, we want to find n for which  the margin of error for the 90% confidence level to be about 1.5%

From part (a), the 90% confidence interval is (0.435, 0.525)

the margin of error M = 0.015

0.015 = 1.645√(0.48 * 0.52)/n

(√n) ² = (0.015)²

n = 3001.9

n ≈ 3002

Therefore, a sample of 3002 is recommended.

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The complete question is:

Exercise 6.12 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they cannot a ord it. (a) Calculate a 90% con dence interval for the proportion of Americans who decide to not go to college because they cannot a ord it, and interpret the interval in context. (b) Suppose we wanted the margin of error for the 90% con dence level to be about 1.5%. How large of a survey would you recommend?

Step-by-step explanation:

To prove that AC = BD, we can use the symmetric property. The symmetric property states that if two quantities are equal, then their opposites are also equal.

In this case, we are given that AB = CD. Since AB and CD are opposite quantities (they are the lengths of the diagonals of a rectangle), we can use the symmetric property to conclude that AC = BD.

Therefore, the reason that can be used to justify statement 4 in the proof is the symmetric property.

Answer:

x = 3

Step-by-step explanation:

x + 6 = 9

Subtract 6 from both sides :

x = 9 - 6

x = 3

Hope this helped and have a good day

Answer:

x = 3

Step-by-step explanation:

x + 6 = 9  Subtract  from both sides of the equation

x + 6 - 6 += 9 - 6

x = 3

Check:

x + 6 = 9

3 + 6 = 9

9 = 9 Checks

Answer:

Step-by-step explanation

The tens digit of a certain two-digit number is 1/3 of the units digit. When the digits are reversed, the new number exceeds twice the original number by 2 more than the sum of the digits. Find the original number.

An integer to represent the situation, the temperature was 3° below zero is -3.

Integers include all whole numbers and negative numbers. This means if we include negative numbers along with whole numbers, we form a set of integers.

1) The stock market increased 75 points

Integer to represent the given situation is +75 or 75.

2) A loss of 15 yards

Integer to represent the given situation is -15

3) Nancy owes her friend $10

Integer to represent the given situation is -10

4) Frederick is located 290 feet above sea level

Integer to represent the given situation is 290 or +290

5) The temperature was 3° below zero

Integer to represent the given situation is -3.

Therefore, an integer to represent the situation, the temperature was 3° below zero is -3.

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The variable that researchers are trying to explain or predict is called the response variable. It is also sometimes called the dependent variable because it depends on another variable.

Variables used to explain or predict a response variable are called explanatory variables.

The students want to predict age using their height, so the explanatory variable is height and the response variable is age.

The values ​​of an ordinal variable have a meaningful order. For example, an education level (with possible values ​​of high school, bachelor's degree, and graduate degree) can be an ordinal variable.

"Hand" belongs to "Clock". "Experience" also belongs to "Year". So if he has 10 years of experience in the industry, no apostrophes are needed. An apostrophe is required if you have more than 10 years of experience.

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Answer:

Step-by-step explanation:

Using percentages we know that the total price of the book that Tommy will pay is $131.04.

What is the percentage?

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.

Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.

A% is a number that has neither dimensions nor a defined unit of measurement.

For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).

So, we know that the price of the book is 180.

Sales tax is 4%. So, the total price:

180/100 * 4 = 7.2$ ⇒ $187.2

Now, there is a 30% discount:

187.2/100 * 30 = $56.16

⇒ 187.2 - 56.16 = $131.04

Therefore, using percentages we know that the total price of the book that Tommy will pay is $131.04.

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Answer:

145 degrees

Step-by-step explanation:

the 2 angles are on a flat line so added together they equal 180 degrees

so we can subtract from 35 from 180 to find x

180-35

145

hopes this helps

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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The function f(x,y) is at origin [tex]\left|\frac{\sin x y}{x y}-1\right| < \varepsilon[/tex].

We can treat this function as h=xy and then it will looks like sin h/h because if we choose any path passing through original it will always continuous so above f(x,y) is continuous

[tex]$$f(x, y)= \begin{cases}\frac{\sin x y}{x y,} & \text { if } x y \neq 0 \\ 1, & \text { if } x y=0\end{cases}$$[/tex]

Choose y=mx path y→0, x→0

[tex]$$\begin{aligned}\lim _{\substack{x \rightarrow 0 \\y=\infty}} f(x, x) & =\lim _{x \rightarrow 0} \frac{\sin m x^2}{m x^2} \\& =\lim _{x \rightarrow 0} \frac{\cos m x^2 \cdot 2 m x}{2 m x}=1\end{aligned}$$[/tex]

Now consider,

[tex]$|f(n, y)-L 1=| \frac{\sin x-1}{n y}-1 \mid < \varepsilon$[/tex]

[tex]$$$\forall \varepsilon > 0$, and $|n| < \delta,|y| < d$$$=\left|\frac{\sin x y}{x y}-1\right| < \varepsilon$$[/tex]

Hence f(x,y) is continues at origin.

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Discuss the continuity of the function:

[tex]$$f(x, y)= \begin{cases}\frac{\sin x y}{x y,} & \text { if } x y \neq 0 \\ 1, & \text { if } x y=0\end{cases}$$[/tex]

∠1≅∠2 if RECT is the rectangle and M is the midpoint of EC.

A triangle is a three-sided polygon that consists of three edges and three vertices.

RECT is the rectangle and M is the midpoint of EC.

we need to prove angle one is congruent to angle two.

By given,RECT is the rectangle and M is the midpoint of EC.

∠E≅∠C

In the rectangle all the angles are 90 degrees.

∠EM≅∠MC.

As M is midpoint, it has equidistant from E and C.

ER≅CT both sides are congruent.

ΔERM≅ΔCTM both are similar triangles.

RM≅TM both sides are congruent.

∠1≅∠2 by SAS postulate.

Hence, RECT is the rectangle and M is the midpoint of EC then ∠1≅∠2

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Answer:

Step-by-step explanation:

Answer: About 0.2 gallons

Step-by-step explanation: 4/18=0.2 repeating, so each person gets about 0.2 gallons.

Each of her friend will get 4 and a half gallons of juice.

Division is one of the four main arithmetical operations by which we find the equal distribution of something.

Given that, At Lara's party, 4 gallon of fruit punch are shared equally among 18 friend.

To find how much each of them got, we will divide total amount of punch  by total number friends

Amount of juice each of them gets, = 18/4 = 4.5

Hence,  Each of her friend will get 4 and a half gallons of juice.

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Answer:

The price per cup would be 0.41 cents.

Step-by step explaination:

Answer:

$0.41

Step-by-step explanation:

To find the price per cup of milk, we first need to know how many cups are in a 3-quart carton.

1 quart is equivalent to 4 cups, so a 3-quart carton contains:

[tex]\sf 3\;quarts=3 \times 4 \;cups= 12\;cups[/tex]

Now, we can calculate the price per cup by dividing the total price by the number of cups:

[tex]\begin{aligned}\textsf{Price per cup} &= \dfrac{\textsf{Total price}}{\textsf{Number of cups}} \\\\&=\sf \dfrac{\$4.92}{12}\\\\&=\sf \$0.41\end{aligned}[/tex]

Therefore, the price per cup of milk is $0.41.

The value of α + β  is 4. Then the value of the expression 2⁻¹ x (α + β)² will be 8.

Let the equation be ax² + bx + c = 0 and the roots are α and β.

Then the sum of the roots will be

α + β = - b / a

And the product of the roots will be

α · β = c / a

The quadratic equation is given below.

x² - 4x + 1 = 0

The sum of the roots of the equation is given as,

α + β = - (-4) / 1

α + β = 4

Then the value of the expression will be given as,

⇒ 2⁻¹ x (α + β)²

⇒ 2⁻¹ x (4)²

⇒ 16 / 2

⇒ 8

The value of the expression 2⁻¹ x (α + β)² will be 8.

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The solution of the equation for values of a is 1/(x - 1)

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

a^2x - a = ax

Rewrite properly as

a²x - a = ax

Divide through by a

So, we have

ax - 1 = x

Collect the like terms

ax - x = 1

Factor out x

This gives

a(x - 1) = 1

Divide both sides by x - 1

a = 1/(x - 1)

Hence, the solution is 1/(x - 1)

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The expression that shows that Angie still owes victor is 20-d.

In algebra, an expression can be used to represent a value that may or may not be dependent on the values given to the variables that appear in the expression. The semantics associated with the expression's symbols are used to determine its value. The expression's context affects the semantic choice. Depending on the presumed order of operations by the context.

When an expression involves division by 0, for example, the semantic rules may state that it does not indicate any value; yet, despite having an undefined value, these expressions are still well-formed. Expressions generally have a wide range of meanings.

Given,

The number of dollars borrowed by Angie from victor is 20 dollars

And also given that Angie paid d dollars back to victor.

The expression that shows that Angie still owes victor is 20-d.

Therefore, the expression that shows Angie still owes victor is 20-d.

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The inverse function for this problem is defined as follows:

P^(-1)(x) = square root of (x + 100/5), x ≥ -100.

The function in this problem is defined as follows:

P(x) = 5x² - 100, x ≥ 0.

In which P(x) is the profit earned when x tamales are sold.

To obtain the inverse function, first we exchange the variable y = P(x) and x are follows:

x = 5y² - 100

Then the variable y must be isolated as follows:

5y² = x + 100

y² = (x + 100)/5

y = square root of (x + 100/5).

The domain must be the same domain of the square root function, that does not accept negative values hence:

P^(-1)(x) = square root of (x + 100/5), x ≥ -100.

This means that the first option is correct.

The problem is given by the image shown at the end of the answer.

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Answer:

the approximate percent increase of Misha's test score is 33% !

Step-by-step explanation:

Answer: 33.3333%

Step-by-step explanation:

Percent Increase Formula

c = x2-x1/x1

x2- final value

x1- initial value

c= 80-60/60 = 33.3333%

Answer:

Step-by-step explanation:

Number of pints | 16 | 32| 48|

Number of galll. |  2  | 4 | 6 |

Those are 3 ratios

16:2

32:4

and 48:6

You multiply by 2 to get 3 ratios

The choice that provides the best example of alliteration for the given sentence is tested terrifically on teaching. (Option C)

Alliteration is a literary device in which there is a noticeable repetition of initial consonant sounds in consecutive or nearby words in a phrase. It refers to the occurrence of the same sound or letter at the beginning of adjacent or closely connected words. Alliteration is created by repeated sound at the start of the words and not the repeated letter. For example, the phrase “kids’ coats” is alliterative, and the phrase “phony people” is not alliterative. In the given sentence, author can create alliteration by using tested terrifically in place was absolutely aced.

Note: The question is incomplete. The complete question probably is: In the sentence, the author wants to use alliteration. Which choice provides the best example of this? Ted absolutely aced his teaching exam. A) NO CHANGE B) was astounded at how well he did on C) tested terrifically on teaching.

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The correct option c. 20 cm, is the length of each sides of the regular pentagon.

A quadrilateral with five equal sides is known as a regular Pentagon.

Regular pentagon perimeter equals 5*side

Since we already know that a normal pentagon's perimeter is 100 cm.

Hence, 100 = 5*side

Side = 20 cm

Each side is 20 cm long.

As a result, the side of a regular pentagon is 20 cm long.

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Answer:

We get the approximate value of [n] as 5.

What is logarithm? What is a mathematical equation and expression?

A quantity representing the power to which a fixed number (the base) must be raised to produce a given number. We can write -

$$$\log_{b}({b^x})=x$$

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions.

A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have 31,100 is rounded to the nearest power of 10 and [N] represents a power of 10.

We can write -

We can write -10ⁿ = 31100

We can write -10ⁿ = 3110010ⁿ = 311 x 10²

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)n - 2 = 2.5

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)n - 2 = 2.5n = 4.5

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)n - 2 = 2.5n = 4.5n = 5 (approx.)

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)n - 2 = 2.5n = 4.5n = 5 (approx.)Therefore, we get the approximate value of [n] as 5.

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Answer: (x- 1/4)^2=9/16

Step-by-step explanation:

x^2 -1/2x =8/16

(x^2-1/2x +1/16)^2= 8/16+1/16)

(x- 1/4)^2=9/16

Answer:

77 melons

Step-by-step explanation:

[tex]11x \times x = 539 \\ 11 {x}^{2} = 539 \\ \frac{11x}{11} = \frac{539}{49} \\ {x}^{2} = 49 \\ \sqrt{ {x}^{2} } = \sqrt{49} \\ x = 7[/tex]

The oranges are 7

And the melons are 11 times the number of the oranges hence

11 x 7= 77

Answer:

There are 77 melons

Step-by-step explanation:

See picture below :)