which is the graph of the linear inequality 2x - 3y < 12

You probably forgot to mention the options. After a little research, I was able to get the complete question with the mentioned options you should have mentioned. The potential complete question is:

Ellen plans to leave an 18 percent tip with her $23.75 lunch bill. Which of these expressions could she use to determine her total bill?

Check all that apply.

(1.18)(23.75) 23.75 – [(0.18)(23.75)] 23.75 + [(0.18)(23.75)] (0.18)(23.75)

Answer:

The expression \(23.75\:+\:\left[\left(0.18\right)\left(23.75\right)\right]\) will determine her total bill.

Step-by-step explanation:

Total lunch bill = $23.75

As he pans to 18% tip of the total bill, so the expression will be:

\(=23.75\:+\:\left(\:18\%\:\:of\:\:23.75\:\right)\)

\(=23.75\:+\:\left(\:\frac{18}{100}\:\times \:23.75\:\right)\)

\(=23.75\:+\:\left(\:0.18\times \:23.75\:\right)\)

or

\(=23.75\:+\:\left[\left(0.18\right)\left(23.75\right)\right]\)

Therefore, the expression \(23.75\:+\:\left[\left(0.18\right)\left(23.75\right)\right]\) will determine her total bill.

Answer:

(1.18)(23.75)

23.75 + [(0.18)(23.75)]

Step-by-step explanation:

ur welcome

A department store chain that is entering a new area is looking at 16 possible locations for the placement of its 7 outlets. There are 57657600 many possible ways to the sites for the new stores.

Given that,

A department store chain that is entering a new area is looking at 16 possibility locations for the placement of its 7 outlets.

We have to find how many different possibility are there to choose the locations for the new businesses, provided that each site has an equal chance of being chosen.

By multiplying the number of possibilities each store has, we may determine the total number of ways.

It can be put on 16 sites for store 1. 15 locations can accommodate Store 2 (since store 1 is already on site 1). Up until shop 7, which has 10 sites, store 3 can be situated on 14 sites.

The quantity of ways is thus:

= 16 × 15 × 14 × 13 × 12 × 11 × 10

= 57657600

Therefore, there are 57657600 many possible ways to the sites for the new stores.

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Answer:

Area of circle = 33.17 yd²

Explanation:

First, we need to convert the number 3 ¼ yd into a decimal number, so:

Then, the area of a circle can be calculated using the following equation:

Where π is approximately 3.14 and r is the radius of the circle. So, if we replace π by 3.14 and r by 3.25 yd, we get:

Therefore, the answer is 33.17 yd²

The inequality \($uv^2 \leq (uv)^2$\) holds for any vectors u and v in \(R^2\). Equality holds when the vectors u and v are collinear or when one of them is the zero vector.

To prove the inequality \($uv^2 \leq (uv)^2$\), we can start by expressing the dot product of u and v in terms of their components. Let u = (\(u_1, u_2\)) and v = (\(v_1, v_2\)).

Then, the dot product of u and v is given by\(uv = u_1 v_1 + u_2 v_2\).

Now, consider the squared length of the projection of u onto v.

This can be calculated as \((uv)^2\) / \(||v||^2\), where ||v|| represents the length of vector v.

Since ||v||^2 = vv, we have \((uv)^2\) /\(||v||^2\) = \((uv)^2\) / (\($v \cdot v$\)).

On the other hand, the squared length of vector u can be expressed as \(u\cdot u = u1^2 + u2^2\).

Now, we can compare the two expressions: \(uv^2\) and \((uv)^2\) / (vv).

By substituting the expression for uv, we get \(uv^2\) = \((u_1 v_1 + u_2 v_2)^2\), and by substituting the expressions for \(||v||^2\) and uu, we get \((uv)^2\) / (vv) = (\(u_1^2 v_1^2 + u_2^2 v_2^2\)) / (\(v_1^2 + v_2^2\)).

It can be shown that \((u_1 v_1 + u_2 v_2)^2 \geq (u_1^2 v_1^2 + u_2^2 v_2^2)\) for any real numbers \(u_1, u_2, v_1, v_2\). Therefore, \(uv^2\) ≤ \((uv)^2\) / \((vv)\), which implies \(uv^2\) ≤ \((uv)^2\).

Equality holds in the inequality \($uv^2 \leq (uv)^2$\) when the vectors u and v are collinear or when one of them is the zero vector.

Geometrically, this inequality represents the fact that the squared length of the projection of vector u onto vector v is always less than or equal to the squared length of the projection of u onto v.

When the vectors are collinear, their projections coincide and the inequality becomes an equality. Similarly, when one of the vectors is the zero vector, its projection onto any other vector is zero, resulting in equality as well.

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Answer:

-372

Step-by-step explanation:

"Three hundred seventy-two feet" in words can be translated into 372 ft in numbers.

Sea level is often referred to as the integer 0. Altitudes above sea level are referred to as positive numbers, or numbers greater than 0 while altitudes below sea level are referred to as negative numbers, or numbers less than 0.

Because we're talking about 372 ft below sea level, this expresses the integer -372.

I hope this helps!

Answer:

This is not a function

Domain: -7, -6, -4, -8

Range: -8, -6, 5, 4

Step-by-step explanation:

This is not a function because one x-values repeats, -8. The x-value is the first value in a relation. Relations are written as (x,y)

Domain is the x-values in a relation. When writing the domain, make sure not to include repeats. In this case, the domain is -7, -6, -4, -8.

Range is the y-values in a relation. Also, don't repeat when writing range. The range of this function is -8, -6, 5, 4

-Chetan K

Answer:

m= -1/2

this is the answer

Answer:

6

Step-by-step explanation:

well 5 divided by 3/4 is 6.66666666667 which you can say is 6

\(\frac{-3}{5} > -2\) indicates that -3/5 is located on the right of -2 on the number line.

What is number line?

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

consider, \(\frac{-3}{5} > -2\)

Here, -3/5 = -0.6

-0.6 > -2

-0.6 is the number greater than -2.

So, -3/5 is located on the right side of -2.

Hence, -3/5  is located on the right of -2 on the number line.

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The following property: X (Y + Z ) = XY + XZ is known as the Distributive Property.

The distributive property is also known as the distributive law of multiplication over addition and subtraction. The name itself signifies that the operation includes dividing or distributing something. The distributive law is applicable to addition and subtraction.

X (Y + Z ) = XY + XZ (left distributive law) and (X + Y) Z = XZ + YZ (right distributive law). This property also allows like terms to be combined so AX + BX = (A + B)X.

This distributive law is also applicable to subtraction and is expressed as, A (B - C) = AB - AC. This means operand A is distributed between the other two operands.

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The triangle ABC has a surface area of 17.7 square units. Rounding to the nearest tenth of a square unit,

Heron's Formula can be used to calculate the triangle ABC's area. The equation reads as follows:

A = √[s(s-a)(s-b)(s-c)]

Where s is one-half of the triangle's circumference and a, b, and c are its three sides.

By summing the triangle's sides, we can determine the perimeter:

P = a + b + c

The formula below is used to get the other half of the perimeter.

s = P/2

For the triangle ABC, we have the sides a=3, b=5, and c=4.

Therefore, half of the perimeter is s = 8.

Now, Heron's formula can be used to determine the triangle ABC's surface area:

A = √[s(s-a)(s-b)(s-c)]

= √[8(8-3)(8-5)(8-4)]

= √[8(5)(3)(4)]

= 17.7 square units

Therefore, the triangle ABC has a surface area of 17.7 square units, Rounding to the nearest tenth of a square unit.

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Answer:

See the answer below

Step-by-step explanation:

Given data

We are given that the equation for the growth of the flower is

h=13+2.5w

From the expression we can see that 13 represents the initial height of the flower before it was planted

Answer:

4/11

Step-by-step explanation:

4x -9 =2

perform inverse operations

+9 to both sides

4x = 11

divid both sides by 4

x = 4/11

Answer:

x<4 and x>4

Step-by-step explanation:

4x-9<7 or 3x-10>2

Start with 4x-9<7

You want to get the variable alone. Since 9 is negative add it to both sides

4x-9(+9)<7(+9)

4x<16

You have to divide the 4 from both sides for the variable to be alone.

4x(/4)<16/4

x<4

Next 3x-10>2

Get the variable alone.

3x-10(+10)>2(+10)

3x>12

Divide 3 on both sides

3x(/3)>12(/3)

x>4

The solution to the given differential equation is L⁻¹{Y(s)} = (b³ t sin 2t) / (2 (sin bt - bt cos bt))

To solve the differential equation using the convolution theorem, we'll follow these steps:

Take the Laplace transform of both sides of the differential equation.

Use the convolution theorem to simplify the resulting expression.

Take the inverse Laplace transform to obtain the solution in the time domain.

Let's start with step 1:

Given differential equation: d²y/dt² - 4y = t cos 2t

Taking the Laplace transform of both sides, we get:

s²Y(s) - sy(0) - y'(0) - 4Y(s) = L{t cos 2t}

Where Y(s) represents the Laplace transform of y(t), y(0) is the initial condition for y(t) at t = 0, and y'(0) is the initial condition for dy/dt at t = 0.

The Laplace transform of t cos 2t can be found using the Laplace transform table:

L{t cos 2t} = -Im{d/ds[1 / (s² - (2i)²)]}

= -Im{d/ds[1 / (s² + 4)]}

= -Im{(-2s) / [(s² + 4)²]}

= 2Im{(s) / [(s² + 4)²]}

Now let's simplify the expression using the convolution theorem:

The Laplace transform of the convolution of two functions, f(t) and g(t), is given by the product of their individual Laplace transforms:

L{f * g} = F(s) G(s)

In our case, f(t) = y(t) and g(t) = 2Im{(s) / [(s² + 4)²]}.

Therefore, F(s) = Y(s) and G(s) = 2Im{(s) / [(s² + 4)²]}.

Multiplying F(s) and G(s), we get:

Y(s) G(s) = Y(s) 2Im{(s) / [(s² + 4)²]}

Now, we can rewrite the left-hand side of the equation using the convolution theorem:

Y(s) * 2Im{(s) / [(s² + 4)²]} = L{t cos 2t}

Taking the inverse Laplace transform of both sides, we have:

L⁻¹{Y(s) * 2Im{(s) / [(s² + 4)²]}} = L⁻¹{L{t cos 2t}}

Simplifying the right-hand side using the inverse Laplace transform table, we get:

L⁻¹{Y(s) * 2Im{(s) / [(s² + 4)²]}} = t sin 2t / 4

Now, we can apply the convolution theorem to the left-hand side of the equation:

L⁻¹{Y(s) * 2Im{(s) / [(s² + 4)²]}} = L⁻¹{Y(s)} * L⁻¹{2Im{(s) / [(s² + 4)²]}}

The inverse Laplace transform of 2Im{(s) / [(s² + 4)²]} can be found using the inverse Laplace transform table:

L⁻¹{2Im{(s) / [(s² + 4)²]}} = 1 / 2b³ (sin bt - bt cos bt)

Therefore, we have:

L⁻¹{Y(s)} * 1 / 2b³ (sin bt - bt cos bt) = t sin 2t / 4

From this, we can deduce the inverse Laplace transform of Y(s):

L⁻¹{Y(s)} = (t sin 2t / 4) / (1 / 2b³ (sin bt - bt cos bt))

Simplifying further:

L⁻¹{Y(s)} = (b³ t sin 2t) / (2 (sin bt - bt cos bt))

This is the solution to the given differential equation.

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Answer:

X < 7/2

Step-by-step explanation:

Move the variable to the left, separate into possible cases , solve, find the intersections, find the union, and then you get your solution.

Step-by-step explanation:

Given that:

|2x-7| = 7-2x

⇛2x-7 = 7-2x or -(7-2x)

since |x| = a ⇛ x = a or x = -a

⇛2x-7 = 7-2x or 2x-7 = 2x-7

Shift all variables on LHS and constant on RHS, changing it's sign.

⇛2x+2x = 7+7

Add the values on LHS and RHS.

⇛4x = 14

Shift the number 4 from LHS to RHS.

⇛x = 14/4

Write the fraction in lowest form by cancelling method.

⇛ x = {(14÷2)/(4÷2)}

⇛x = 7/2

There is no solution for negative value

x = 7/2

Please let me know if you have any other questions.

a) i) The pressure on the ground by snowshoe hare is 0.07 N/cm².

ii) The pressure on the ground by European hare is 0.15 N/cm².

b) The snowshoe hare is suited to living in snow because it has a larger surface area of feet.

a) The pressure on the ground can be calculated by dividing the force on the ground due to weight by the total surface area of the feet.

i) For the snowshoe hare, the pressure on the ground is:

Pressure = Force on ground / Total surface area of feet

Pressure = 14 N / 200 cm²

Pressure = 0.07 N/cm²

ii) For the European hare, the pressure on the ground is:

Pressure = Force on ground / Total surface area of feet

Pressure = 38 N / 250 cm²

Pressure = 0.15 N/cm²

b) The snowshoe hare is suited to living in snow because it has a larger surface area of feet than the European hare and exerts less pressure on the ground. This allows the snowshoe hare to move more easily over the snow without sinking.

Additionally, the snowshoe hare has fur on the soles of its feet, which provides additional insulation against the cold snow. These adaptations help the snowshoe hare survive in its snowy environment by allowing it to move and find food more easily.

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Answer:

r(x)= 11x

c(x) = 6x + 20

p(x) = r(x) - c(x)

= 11x -( 6x + 20)

= 11x - 6x - 20

= 5x - 20

The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z=\dfrac{X-\mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

\(Z=\dfrac{X-\mu}{\sigma}\)

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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gAnswer

Range of the sample means = 3.34

Explanation

The range is defined as the difference between the highest and the lowest number. Mathematically,

Range = Highest number - Lowest number

So, the range of the sample means is the difference between the highest and the lowest sample means.

Range of the sample means =

(Sample mean with the highest value) - (Sample mean with the lowest value)

From the table, we can calculate the sample means. The sample mean is given as the sum of the variables divided by the number of variables.

Note that we are told that Charles used only the shaded columns to calculate three sample means. The shaded columns, grouped include

4, 3, 3. Mean = 3.33

8, 5, 7. Mean = 6.67

6, 4, 3. Mean = 4.33

5, 3, 6. Mean = 4.67

Sample mean with the highest value = 6.67

Sample mean with the lowest value = 3.33

Range of the sample means = 6.67 - 3.33 = 3.34

Hope this Helps!!!

Answer:

lolololololololololololololololol

The rate at which the volume of the snowball is changing at the instant the radius is 6 cm is -241.27 cm³/min.

The volume of a sphere is given by the formula V = 4/3πr³, where r is the radius of the sphere. To find the rate at which the volume is changing, we need to take the derivative of this equation with respect to time, using the chain rule.

dV/dt = 4/3π(3r²) dr/dt

We know that the radius of the snowball is decreasing at a constant rate, so we can find the value of dr/dt by using the information given in the problem. The radius is decreasing from 34 cm to 18 cm in 30 minutes, which means that:

dr/dt = (34 - 18) cm / 30 minutes = -0.5333 cm/min

Now that we know the rate at which the radius is changing, we can substitute it into the equation for dV/dt and find the rate at which the volume is changing.

We know that the radius is 6 cm at the instant the volume is changing, so we can substitute that into the equation:

dV/dt = 4/3π(3r²) dr/dt = 4/3(π)(3)(6 cm)²(-0.5333 cm/min) = -241.27 cm³/min

So, the rate at which the volume of the snowball is changing at the instant the radius is 6 cm is -241.27 cm³/min.

Note that the negative sign indicates that the volume is decreasing.

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Answer:

Look at step-by-step explanation.

Step-by-step explanation:

The answer to 14 is 70 dollars.

The answer to 16 is 7 miles per hour or 7mph.

The required value of y for the unit circle is: 2/3

The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).

The equation of the circle is given by:

(x - h)² + (y - k)² = r²

where:

h, k is the coordinate of the center of the circle on coordinate plane.

r is the radius of the circle.

Here,

Equation of the unit circle is given as,

x² + y² = 1

Now substitute the given value in the equation,

5/9 + y² = 1

y² = 1 - 5/9

y² = 4/ 9

y = √(4/9)

y = 2/3

Thus, the required value of y for the unit circle is 2/3

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Answer:

14,400

Step-by-step explanation:

i=prt

p=40,000

r=0.09 have to turn percent to decimal

t=4

(40,000)(0.09)(4)

Answer:

Well, this is simple.

I=PRT

(Interest= Principle*Rate*Time)

So, simply divide both sides by PR

T=I/PR

Your answer is C: T = I divided by the quantity P times R

(This should have been represented as: T= I/PR)

~Hope this helps

Step-by-step explanation:

Answer:

c) 27.3%

Step-by-step explanation:

% = (part/whole)*100%

part = left handed = 11+4 = 15

whole = all students = 55

% = (15/55)*100% = 27.3 %

Answer:

27.3

Step-by-step explanation:

Total number of students=55

Total number of

left handed students =15

hence, take the % between them

15/55*100=27.2727...%= 27.3%

The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.

In this case, the mean weight is 340 grams, and the standard deviation is 5.2 grams.

CV = (Standard Deviation / Mean) * 100

CV = (5.2 / 340) * 100

CV ≈ 1.53%

Therefore, the correct answer is option B: 1.53%.

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Answer:

=360

explanation:

When you’re talking about rotation you go counterclockwise and each quadrant is another 90 degrees.

Answer:

360

Step-by-step explanation:

Answer:

-137.8

^^^^^Hope this Helps!