Henri buys 126 inches of a fabric that costs $12 for each yard. How much does Henri pay for the fabric?

Inequality will become 2x + 3y < 9

What do you mean by inequality?

In mathematics, an inequality is a relationship in which two numbers or other mathematical expressions compare unequal. [1] Most commonly used to compare two numbers on the number line based on size.

The notation a < b means that a is less than b.

The notation a > b means that a is greater than b.

From the given graph , we get two passing points are (3,1) and (0,3)

Equation of the line having two passing points as (a,b) and (c,d) is

\(y-b=\frac{d-b}{c-a}(x-a)\)

Equation of line having passing point (3,1) and (0,3) is

\(y-1=\frac{3-1}{0-3}(x-3)\)

\(y-1=\frac{2}{-3}(x-3)\)

-3(y-1) = 2(x-3)

-3y + 3 = 2x - 6

2x + 3y - 6 - 3 = 0

2x + 3y - 9 = 0

As the line given in graph is dashed line therefore, inequality will become 2x + 3y < 9

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x = 2.67 is the solution to the equation -6x + (3)(2x) = 16.

What is the Algebraic Equations?

Algebraic equations are mathematical statements that describe a relationship between two or more variables, where one variable is expressed in terms of the others.

To solve the equation -6x + (3)(2x) = 16, we can simplify the expression on the left-hand side first:

-6x + (3)(2x) = -6x + 6x = 0x = 0

Next, we isolate the x term on one side of the equation by subtracting 16 from both sides:

0x = 0 - 16 = -16

Finally, we can solve for x by dividing both sides of the equation by -6:

x = -16 / -6 = 2.67 (rounded to two decimal places).

So, x = 2.67 is the solution to the equation -6x + (3)(2x) = 16.

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The probability of getting at least 6 heads is3/256 or 0.0117

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.

Probability is a measure of how likely something is to occur. Calculating probability involves dividing the total number of outcomes by the number of possible ways an event may occur.

Given that,

A fair coin is tossed = 8 time.

We have to find the probability of getting at least 6 heads.

Since, the probability of getting head, when one coin is tossed = 1/2

And the probability of getting tale = 1/2  

The probability of getting head at least  6 times when coin is tossed 8 times can be given as,

The head can come 6 times, then probability = \((1/2)\x^{6} (1/2)\x^{2}\) =  (1/2)⁸

The head can come 7 times, then probability = (1/2)⁷(1/2) = (1/2)⁸

The head can come 8 times, then probability = (1/2)⁸

The probability of getting head at least 6 times

= (1/2)⁸ + (1/2)⁸ +  (1/2)⁸ = 3(1/2)⁸ = 3/256 = 0.0117

The probability of getting at least 6 heads is3/256 or 0.0117

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Answer:

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Step-by-step explanation:

The value of 650 ft.² divided by 2/3 of an hour is 975 ft² per hour

The mathematical statement is given as

650 ft.² divided by 2/3 of an hour

This can be represented properly as:

650 ft.² / 2/3 of an hour

2/3 of an hour is

2/3 of an hour = 2/3 hr

So, we have

650 ft.² / 2/3 of an hour = 650 ft.² / (2/3 hr)

Evaluate the quotient

650 ft.² / 2/3 of an hour = 975 ft² per hour

Hence, the value of 650 ft.² divided by 2/3 of an hour is 975 ft² per hour

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Answer:

Step-by-step explanation:

In order to properly fit the website for Faria mobile devices such as tablets and smartphones, the company will need to make sure that the website is optimized for different screen sizes. The original website was designed for a screen dimension of 16" x 9", but mobile devices have varying screen sizes. The company can use the dimensions listed in the table to ensure that the website looks and functions properly on the five mobile devices they are researching.

The given point is (3,6), and the vertex is (1,2). This means

We use the vertex form of a quadratic function.

Let's replace the given values to find a.

Once we have a, we can write the function using the vertex-form and the vertex point.

Answer: 8x

Answer: 12x - 3y

hope it helps.

Answer:

Step-by-step explanation:

(This is technically a personal opinion question) In MY opinion all government run things from libraries to schools to the military come from taxes. If you don't agree with how the government spends the money that you pay in taxes yet enjoy/use government facilities then you have no room to complain and not pay your taxes.

Answer:

No

Step-by-step explanation:

To determine whether the given set of ordered pairs {(49,13),(61,36),(10,27),(76,52),(23,52)} represents a function, check if each x-value is associated with a unique y-value.

Check the x-values in the set: 49, 61, 10, 76, and 23. There are no repeated x-values.  Still need to check if each x-value has a unique corresponding y-value.

Check the y-values: 13, 36, 27, 52, and 52. There is one repeated y-value, 52, for the pairs (76, 52) and (23, 52).

Conclusion: the y-value 52 is associated with 2 different x-values, therefore the given set of ordered pairs does not represent a function.

Answer:

\(V(x) = 66.02\ \text{in}^3 \ \vert \ _x_=_1_._9_6\)

Step-by-step explanation:

The volume of a rectangular prism is found using the formula: V = lwh.

In order to write a formula in terms of the variable x, we need to write expressions for the length, width, and height of the rectangle.

We can say the length is the bottom of the base of the prism. To find this value, we can subtract x and x from 15 and divide this by 2, since there are two equal rectangles (base and lid).

We can say the width is the side of the base of the prism. To find this value, we can subtract 2x from 10.

The height of the prism can be x, which is the labeled length of the rectangle next to the base and lid.

Now we are able to write a formula for volume in terms of x.

The domain of the volume is where x > 0, 2x < 10, and 2x < 15.

This is because our expressions for length (\(\frac{15-2x}{2}\)), width (10-2x), and height (x) cannot go below 0, because you cannot have a negative value for measurement - realistically.

Therefore, if we take into account all of these restrictions on x, the domain is where 0 < x < 5.

x cannot be > 5 since that would not satisfy 2x < 10.

The domain of V for this problem situation is D: (0, 5).

In order to find the maximum volume of the rectangular prism using our formula we derived, we can use the idea of optimization in calculus.

Start by taking the derivative of V(x).

Set the derivative equal to 0. This gives us the critical point(s) in order to determine the extreme values of the function, aka where the max and min occur.

Solve for x by using the quadratic formula.

Input this into your calculator and you should get:

We are going to use x = 1.96 since 6.37 is NOT in the domain of V(x).

Now, since this value of x is going to give the maximum volume of this rectangular prism, or cardboard box, we can plug it back into the V(x) equation for volume to determine the maximum volume of the box.

The maximum volume of the cardboard box is 66.02 in³ and the value of x that gives this is 1.96.

The correct answer is, by choosing a = -2 and b = 1, we satisfy both inequalities .a < b:

To make both inequalities true, we need to select values for a and b that satisfy the given conditions:

a < b: This inequality means that the value of a should be less than the value of b.

|b| < |a|: This inequality means that the absolute value of b should be less than the absolute value of a.

One possible solution that satisfies both conditions is:

a = -2

b = 1

With these values, we have:

-2 < 1 (a < b)

|-1| < |2| (|b| < |a|)

Therefore, by choosing a = -2 and b = 1, we satisfy both inequalities.a < b:

This inequality states that the value of a should be less than the value of b. In other words, a needs to be positioned to the left of b on the number line. To satisfy this condition, we can choose a to be any number that is less than b. In the example I provided, a = -2 and b = 1, we can see that -2 is indeed less than 1, fulfilling the requirement.

|b| < |a|:

This inequality involves the absolute values of a and b. The absolute value of a number is its distance from zero on the number line, always resulting in a non-negative value. The inequality states that the absolute value of b should be less than the absolute value of a. To satisfy this condition, we can choose b to be any number with a smaller absolute value than a. In the example I provided, |1| is less than |(-2)|, as 1 is closer to zero than -2, fulfilling the requirement.

By selecting a = -2 and b = 1, we satisfy both inequalities: a < b and |b| < |a|. The specific values of -2 and 1 were chosen as an example, but there are multiple other values that would also satisfy the given conditions. The important aspect is that a is indeed less than b, and the absolute value of b is smaller than the absolute value of a.

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Answer: ∠16 and ∠11

Step-by-step explanation:

      All of these answer options include ∠16, so we know we're looking for an angle that is corresponding to ∠16. A corresponding angle is an angle that is in the same relative position. We will look at ∠9, ∠11, ∠2, and ∠12 since those are the given answer options, and see which is corresponding.

The correct corresponding angles are ∠16 and ∠11.

You may need to delete the dollar sign and/or the comma when typing in the answer.

=======================================================

Work Shown:

\(A = P*e^{rt}\\\\50,000 = P*e^{0.019*20}\\\\50,000 = P*e^{0.38}\\\\P = \frac{50,000}{e^{0.38}}\\\\P \approx 34,193.0704606\\\\P \approx 34,193.07\\\\\)

Side note: the 'e' is a special constant roughly equal to 2.71828...

Answer:A

Step-by-step explanation:

To find the rate of decay, we need to use the formula A(t) = P(0.82)^t, where A(t) is the amount after t years, P is the initial amount, and 0.82 is the decay factor.

The decay factor is equal to 1 minus the decay rate, so we can solve for the decay rate as follows:

0.82 = 1 - r

r = 1 - 0.82

r = 0.18

Therefore, the rate of decay is 18%, which corresponds to answer choice A.

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let REPEAT \(_{TM\)= { | M is a TM, and for all s ∈ L(M), s = uv where u = v }

To prove that REPEAT \(_{TM\)  is undecidable.

Let  REPEAT \(_{TM\) {| M is a TM that does not accept M}

Then, we form a TM  u for L by applying TM v as a subroutine.

Assume Repeat   is decidable

Let M be the algorithm that  TM which decides the REPEATU = on input "s" simulate the M

Accept; if M ever enters the accept state

Reject; if M ever enters the reject state

U does not decide the REPEAT as it may loop over s

so REPEAT is undecidable

Answer:

left one on 3rd row

Step-by-step explanation:

using the rules of exponents/ radicals

\(a^{-m}\) = \(\frac{1}{a^{m} }\)

\(a^{\frac{m}{n} }\) = \(\sqrt[n]{a^{m} }\)

given

\(12^{-\frac{4}{7} }\)

= \(\frac{1}{12^{\frac{4}{7} } }\)

= \(\frac{1}{\sqrt[7]{12^{4} } }\)

The parent function that has a domain of all real values of x and a range of y ≥ 0 is :  Absolute value

What is Function ?

A function is a mathematical relationship between two sets of values, typically represented by variables, where each input (or domain value) maps to a unique output (or range value). In other words, a function assigns exactly one output value to each input value.

The absolute value function, denoted as |x|, has a domain of all real values of x, meaning it can accept any real number as input. The range of the absolute value function is y ≥ 0, which means that the output (or the absolute value of x) will always be greater than or equal to 0.

Reciprocal, cubic, and linear functions do not satisfy the criteria of having a range of y ≥ 0 for all real values of x. The reciprocal function, for example, has a domain that excludes 0, as division by zero is undefined, and its range does not include negative values. The cubic and linear functions, in general, can have a range that includes negative values depending on their coefficients and shifts.

Therefore, The parent function that has a domain of all real values of x and a range of y ≥ 0 is :  Absolute value

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Answer:

The answer is B.

Step-by-step explanation:

In order to solve this problem, you need to combine like terms, which in this case, are the x's. So, if you add the numbers with the x's together, you get 3x + 12y. The 12y remains untouched because there are no other terms with the same variable.

Hope this helped,

Philip

Brainliest always appreciated! <3

Answer: -5x^2 + 2

Step-by-step explanation:

Answer:

x ≥ _

Step-by-step explanation:

I can't see the numbers, however the number under the closed dot would be the number to insert there. Leave x alone.

The value of AB is,

⇒ AB = 5.9

(rounded to nearest tenth)

We have to given that,

A right triangle ABC is shown.

Now, By trigonometry formula,

we get;

⇒ cos 33° = Base / Hypotenuse

Substitute all the values, we get;

⇒ cos 33° = AB / 7

⇒ 0.84 = AB / 7

⇒ AB = 0.84 × 7

⇒ AB = 5.88

⇒ AB = 5.9

(rounded to nearest tenth)

Thus, We get;

AB = 5.9

(rounded to nearest tenth)

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Answer:

KL = 7, so B is the correct answer.

The group of individuals fitting a description is called option D: Population, this is because, in statistics, a population is seen as am entire group of individuals, items, or elements that tends to have or share a common characteristics.

The term "population" describes the complete group of people or things that you are interested in investigating. It is the group of individuals or thing(s) about which you are attempting to draw conclusions.

There are infinite and finite populations. A population with a set quantity of people or things is said to be finite. An endless population is one that has an infinite amount of people or things.

Therefore, the correct option is D

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See full text below

A group of individuals fitting a description is the _____

Which of the term below fit the description above.

A.census

B.sample

C.parameter

D.population

Answer:

C. \( y = -\frac{1}{2}x - \frac{7}{2} \)

Step-by-step explanation:

We can get the equation in slope-intercept form if we know the slope (m) and the y-intercept (b).

Since the line is parallel to -2x + 4y = 8, it will have the same slope as the equation.

Converting -2x + 4y = 8 into the slope-intercept form, we would have:

4y = -2x + 8

y = -2x/4 + 8/4

y = -½x + 2

Theregore, slope, m, of the line that is parallel bro 4y = -2x + 8 is -½.

To find the y-intercept, b, substitute (x, y) = (-5, -1) and m = -½ in y = mx + b.

Thus:

-1 = (-½)(-5) + b

-1 = ⁵/2 + b

-1 - ⁵/2 = b

(-2 - 5)/2 = b

-⁷/2 = b

b = -⁷/2

To get the equation of the line, substitute b = -⁷/2, and m = -½ in y = mx + b.

The equation would be:

\( y = -\frac{1}{2}x - \frac{7}{2} \)

Hence, there are roughly 1.75 ounces of trail mix in each bag.

What does amount look like?

She put an incredible/exorbitant amount of time into planning her garden. A candidate's ability to spend money is now restricted under the new law. We have a lot of resources at our disposal. = We have such a lot of resources at our disposal.

We must sum up the weight of the cashews, almonds, and walnuts and divide it by the quantity of bags to determine how many ounces inside each bag.

Total weight of the trail mix = 20 + 10.2 + 15.3 = 45.5 ounces

Number of bags = 26

Weight per bag = (Total weight of trail mix) ÷ (Number of bags)

Weight per bag = 45.5 ÷ 26 ≈ 1.75 ounces

Therefore, each bag of trail mix contains approximately 1.75 ounces.

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(i)  The partial fraction decomposition of\(100/(x^7 * (10 - x))\) is\(100/(x^7 * (10 - x)) = 10/x^7 + (1/10^5)/(10 - x).\) (ii) The expression for t in terms of x is t = 10 ± √(100 + 200/x).

(i) To express the rational function 100/(\(x^7\) * (10 - x)) in partial fractions, we need to decompose it into simpler fractions. The general form of partial fractions for a rational function with distinct linear factors in the denominator is:

A/(factor 1) + B/(factor 2) + C/(factor 3) + ...

In this case, we have two factors: \(x^7\) and (10 - x). Therefore, we can express the given rational function as:

100/(\(x^7\) * (10 - x)) = A/\(x^7\) + B/(10 - x)

To determine the values of A and B, we need to find a common denominator for the right-hand side and combine the fractions:

100/(x^7 * (10 - x)) = (A * (10 - x) + B * \(x^7\))/(\(x^7\) * (10 - x))

Now, we can equate the numerators:

100 = (A * (10 - x) + B * \(x^7\))

To solve for A and B, we can substitute appropriate values of x. Let's choose x = 0 and x = 10:

For x = 0:

100 = (A * (10 - 0) + B * \(0^7\))

100 = 10A

A = 10

For x = 10:

100 = (A * (10 - 10) + B *\(10^7\))

100 = B * 10^7

B = 100 / 10^7

B = 1/10^5

Therefore, the partial fraction decomposition of 100/(\(x^7\) * (10 - x)) is:

100/(\(x^7\) * (10 - x)) = 10/\(x^7\) + (1/10^5)/(10 - x)

(ii) Given the differential equation: dx/dt = (1/100) *\(x^2\) * (10 - x)

We are also given x = 1 when t = 0.

To solve this equation and obtain an expression for t in terms of x, we can separate the variables and integrate both sides:

∫(1/\(x^2\)) dx = ∫((1/100) * (10 - x)) dt

Integrating both sides:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) + C

Where C is the constant of integration.

Now, we can substitute the initial condition x = 1 and t = 0 into the equation to find the value of C:

-1/1 = (1/100) * (10*0 - (1/2)*\(0^2\)) + C

-1 = 0 + C

C = -1

Plugging in the value of C, we have:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

To solve for t in terms of x, we can rearrange the equation:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Multiplying both sides by -1, we get:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

Simplifying further:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Now, we can isolate t on one side of the equation:

(1/100) * (10t - (1/2)t^2) = 1 - 1/x

10t - (1/2)t^2 = 100 - 100/x

Simplifying the equation:

(1/2)\(t^2\) - 10t + (100 - 100/x) = 0

At this point, we have a quadratic equation in terms of t. To solve for t, we can use the quadratic formula:

t = (-(-10) ± √((-10)^2 - 4*(1/2)(100 - 100/x))) / (2(1/2))

Simplifying further:

t = (10 ± √(100 + 200/x)) / 1

t = 10 ± √(100 + 200/x)

Therefore, the expression for t in terms of x is t = 10 ± √(100 + 200/x).

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Answer:

i dont know

Step-by-step explanation:

there is no questions