Jordan’s family went to dinner and bought four meals for $8.00 each. They had a coupon for 25% off. What was their total bill after the coupon

The values of f ◦ g is equal to (x + 2)^2 + 1 and g ◦ f is equal to x^2 + 3.

f ◦ g is the composition of functions f and g, which means that for any x in the domain of g, we substitute g(x) into f(x) to get f(g(x)) = (x + 2)^2 + 1.

g ◦ f is the composition of functions g and f, which means that for any x in the domain of f, we substitute f(x) into g(x) to get g(f(x)) = x^2 + 1 + 2

So f ◦ g = (x + 2)^2 + 1 and g ◦ f = x^2 + 3

It's important to notice that the order of the functions matters when composing them, f ◦ g is not the same as g ◦ f. The composition of functions is a fundamental concept in mathematics and it's used to chain multiple functions together to create a new function.

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The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

Given data: Initial velocity, u = 0 ft/sec

Acceleration, a = g = 32.2 ft/sec²

The maximum rate of fall, vmax = 80 mph

Time, t = 2 seconds

Air resistance constant, Ar = 0.2

We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.

The governing equation for the velocity of the skydiver is given by the following:

ma = -m * g + k * v²

where, m = mass of the skydive

r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.

The equation can be written as,

v' = -g + (k / m) * v²

Here, v' = dv/dt = acceleration

Hence, the modified Euler's formula for the velocity can be written as

v1 = v0 + h * v'0.5 * (v'0 + v'1)

where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²

As the initial velocity of the skydiver is zero, we can write

v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))

v1 = 62.732 mph

Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

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Answer:

8 inches

Step-by-step explanation:

The volume of a hemisphere is half the volume of a sphere.

Therefore, the sum of the volumes of the two hemisphere-shaped scoops of ice cream (with diameters of 4 inches), is equal to the volume of a sphere with diameter of 4 inches.

If the melted ice cream fills the cone exactly to the top without overflowing, the volume of the cone with diameter of 4 inches must be equal to the volume of a sphere with diameter of 4 inches.

As the diameter of a circle is twice its radius, then the radius of the sphere and cone is r = 2 inches.

The formulas for the volume of a cone and the volume of a sphere are:

\(\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}\)   \(\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\\\end{minipage}}\)

The depth of the cone is its height.

Therefore, to calculate how deep the cone must be so that the melted ice cream will fill the cone exactly to the top without overflowing, set the two equations equal to each other, substitute r = 2, and solve for h (the depth of the cone).

\(\begin{aligned}\textsf{Volume of a cone}&=\textsf{Volume of a sphere}\\\\\dfrac{1}{3} \pi (2)^2 h & = \dfrac{4}{3} \pi (2)^3\\\\\dfrac{1}{3} \pi \cdot 4 h & = \dfrac{4}{3} \pi \cdot 8\\\\\dfrac{4}{3} \pi h& = \dfrac{32}{3} \pi \\\\\dfrac{4}{3} h& = \dfrac{32}{3} \\\\4 h& = 32 \\\\h&=\dfrac{32}{4}\\\\h&=8\; \sf inches\end{aligned}\)

Therefore, the depth of the cone must be 8 inches.

The cone must be at least 8 inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing.

1. The opening of the ice cream cone has a diameter of 4 inches. This means that the radius of the cone's opening is 4/2 = 2 inches.

2. The two hemisphere-shaped scoops of ice cream have diameters of 4 inches each. This means that the radius of each scoop is 4/2 = 2 inches.

3. When the ice cream melts, it will take up the space between the scoops and fill the cone. In order for the melted ice cream to fill the cone exactly to the top without overflowing, the depth of the cone must be equal to the combined height of the two ice cream scoops.

4. The height of each hemisphere-shaped scoop can be calculated using the formula for the volume of a sphere, which is (4/3)πr³, where r is the radius.

  - For each scoop, the radius is 2 inches, so the height of each scoop is (4/3)π(2)³ = (4/3)π(8) = (32/3)π.

5. Since there are two scoops, the combined height of the two scoops is 2 * (32/3)π = (64/3)π.

6. Therefore, the cone must be at least (64/3)π inches deep in order for the melted ice cream to fill the cone exactly to the top without overflowing. This is approximately equal to 67.03 inches.

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Answer:

96

Step-by-step explanation:

6a²

Put a as 4.

6(4)²

Solve for power first.

6(16)

Multiply both terms.

= 96

x^2+2x-24 is the correct answer

The value of x is the sum of angle ABO and angle CDO because they are the acute angles made out of parallel lines.

Parallel lines are lines that are always the same distance apart and never intersect. They maintain a constant distance from each other as they extend indefinitely in both directions

Recall one of the theorem:

- Alternate angles made by 2 parallel lines are always equal.

Applying this theorem,

angle ABO + angle CDO = angle BOD

50° + 30° = x°

x° = 80°

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Answer:

Step-by-step explanation:

If diameter is 5, then the radius is 2.5 cm.

Area of circle = πR²

Area = 3.14 * 2.5^2 = 3.14 * 6.25 = 19.625

Circumference = π * Diameter

Circumference = 3.14 * 5 = 15.7

Answer:

Step-by-step explanation:

Objective: find the circumference and area of a circle.

Given values; diameter: 5cm, pie: 3.14.

Step one:

Circumference: pie x diameter

= 3.14 x 5cm = 15.7 cm (circumference)

Step two:

Area: ( pie x radius to the power of 2)

= 3.14 x 6.25 cm

= 19.625 (area)

The algebraic expression is 2/3(2y + y)

The length of the 2/3 feet long

It is broken into two parts x and y

If x is twice the length of y, we have

x = 2y

The algebraic expression is 2/3/x + y , if x = 2y

We have that,

2/3(2y + y)

Thus, the algebraic expression is 2/3(2y + y)

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Answer:

\(5(x - 2) = x + 1 \\ 5x - 10 = x + 1 \\ 5x - x = 1 0+ 1 \\ 4x = 11 \\ x = \frac{11}{4} \)

We were given that:

At equilibrium, we have:

Answer:

x=-48

Step-by-step explanation:

-1/4x=12

-1/4x(-4)=12(-4)

x=-48

Hence, x=-48.

Answer:

83.333333333333%

Step-by-step explanation:

A z-score of 2.14 indicates that Katie's score on the test is quite high and unusual, and places her in the top 2% of the scores in the population.

Katie scored a 93 on a test and her calculated z score was 2.14, that means that her score is 2.14 standard deviations above the mean of the test scores.

A z score represents the number of standard deviations a data point is from the mean of the data set.

A positive z score means that the data point is above the mean, while a negative z score means that the data point is below the mean.

The mean of the test scores was, 80 with a standard deviation of 5, then Katie's z score would be calculated as:

z = (x - μ) / σ

= (93 - 80) / 5

= 2.6

Z scores are useful for comparing data points from different data sets or for comparing data points within the same data set that are measured on different scales.

Katie's score is 2.6 standard deviations above the mean.

A z score of 2.14 would mean that Katie's score is slightly below this value, but still significantly above the mean.

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The value of   Sin(a + b) =   \(-\frac{3+4\sqrt{15} }{20}\) and value of

Cos (a -b) = 119/400

Given,

In the question;

Sin(a) = 1/4 and cos(b) = -3/5

with a and b both in the interval [\(\frac{\pi }{2} ,\pi\))

To find the sin(a + b) and cos (a - b)

Now, According to the question:

We know that :

Sin (b) =   \(\sqrt{1-cos^2b}\) = 4/5

Cos (a) = - \(\sqrt{1-sin^2a} = - \frac{\sqrt{15} }{4}\)

∴ Sin(a + b) = Sin(a) Cos(b) + Cos(a) Sin(b)

  Sin(a + b) = 1/4. (-3/5) + \(-(\frac{\sqrt{15} }{4} )\) . 4/5

   Sin(a + b)  =   \(-\frac{3+4\sqrt{15} }{20}\)

∴ Cos (a -b) = \(cos^2a -sin^2b\)

Cos (a -b) = \((-\frac{\sqrt{15} }{4} )^2\) - \((\frac{4}{5} )^2\)

Cos (a -b) = 119/400

Hence, The value of   Sin(a + b) =   \(-\frac{3+4\sqrt{15} }{20}\) and value of

Cos (a -b) = 119/400 .

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Answer:

B) 2,000.

Step-by-step explanation:

As the mean is 6000 the total number of students = 5*6000

= 30,000.

If graduates are excluded we have 4*7000 = 28,000 students.

So the number at graduate level

=  30,000 - 28,000

= 2,000.

When a double cone is sliced at the apex by a plane perpendicular to the base of the cone, the resulting conic section is a parabola.

Option B is the correct answer.

We have,

A parabola is a type of conic sect ion that can be defined as the locus of points equidistant from a fixed point (the focus) and a fixed line (the directrix).

In the case of slicing a double cone at the apex, the resulting conic section will have the characteristic shape of a parabola.

The slicing plane intersects both sides of the double cone, creating a curved shape that opens upward or downward, depending on the orientation of the cone.

The vertex of the parabola corresponds to the point of intersection of the slicing plane with the double cone.

Therefore,

When a double cone is sliced at the apex by a plane perpendicular to the base, a parabola is formed.

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The complete question:

Which degenerate conic is formed when a double cone is sliced at the apex by a plane perpendicular to the base of the cone?

A. Circle

B. Parabola

C. Ellipse

D. Hyperbola

The amount of interest that the customer will pay is given as follows:

$31.88.

The balance of an account after t periods is given as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are explained as follows:

Hence the interest accrued is given as follows:

I(t) = Prt.

The parameters for this problem are given as follows:

P = 2530.16, r = 0.00042, t = 30.

Hence the interest is given as follows:

I(30) = 2530.16 x 0.00042 x 30

I(30) = $31.88.

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Answer:

g > -6

Step-by-step explanation:

-6(g+4) < 12 (Given)

-6g - 24 < 12 (Distributive Property of Inequality)

-6g < 36 (Addition Property of Inequality)

g > -6 (Division Property of Inequality)

Sign Changes Since it was divided by a Negative number.  

According to the question c is a circle centered at the​ origin, oriented​ counterclockwise, that encloses disk r in the plane The two-dimensional curl of the vector field \(\(f = 2x, 2y\) is \(0\)\).

To calculate the curl of a vector field, we use the formula \(\(\text{curl}(f) = \frac{\partial f_y}{\partial x} - \frac{\partial f_x}{\partial y}\)\).

For the given vector field \(\(f = 2x, 2y\)\), the partial derivatives are

\(\(\frac{\partial f_y}{\partial x} = 0\) and \(\frac{\partial f_x}{\partial y} = 0\)\).

Substituting these values into the curl formula, we have \(\(\text{curl}(f) = 0 - 0 = 0\)\).

Therefore, the two-dimensional curl of the vector field \(\(f = 2x, 2y\) is \(0\)\).

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The line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1, 1), and the line segment from (1,1) to (0,1) is equal to 2/5.

What is integral?

The value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.

To evaluate the line integral using Green's theorem, we need to find a vector field F = (P, Q) such that ∇ × F = Qₓ - Pᵧ, where Qₓ represents the partial derivative of Q with respect to x, and Pᵧ represents the partial derivative of P with respect to y.

Let's consider F = (P, Q) = (x²y², xy).

Now, let's calculate the partial derivatives:

Qₓ = ∂Q/∂x = ∂(xy)/∂x = y

Pᵧ = ∂P/∂y = ∂(x²y²)/∂y = 2x²y

The curl of F is given by ∇ × F = Qₓ - Pᵧ = y - 2x²y = (1 - 2x²)y.

Now, let's find the line integral using Green's theorem:

∫[C] (Pdx + Qdy) = ∫∫[R] (1 - 2x²)y dA,

where [R] represents the region enclosed by the curve C.

To evaluate the line integral, we need to parameterize the curve C.

The arc of the parabola y = x² from (0, 0) to (1, 1) can be parameterized as r(t) = (t, t²) for t ∈ [0, 1].

The line segment from (1, 1) to (0, 1) can be parameterized as r(t) = (1 - t, 1) for t ∈ [0, 1].

Using these parameterizations, the region R is bounded by the curves r(t) = (t, t²) and r(t) = (1 - t, 1).

Now, let's calculate the line integral:

∫∫[R] (1 - 2x²)y dA = ∫[0,1] ∫[t²,1] (1 - 2t²)y dy dx + ∫[0,1] ∫[0,t²] (1 - 2t²)y dy dx.

Integrating with respect to y first:

∫[0,1] [(1 - 2t²)(1 - t²) - (1 - 2t²)t²] dt.

Simplifying:

∫[0,1] [1 - 3t² + 2t⁴] dt.

Integrating with respect to t:

[t - t³ + (2/5)t⁵]_[0,1] = 1 - 1 + (2/5) = 2/5.

Therefore, the line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1,1), and the line segment from (1,1) to (0,1) is equal to 2/5.

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Answer:

(D)

Step-by-step explanation:

If it has a leading coefficient of 1, then it can not (A) or (B) because they have a two in front of it. Next, we can check the roots -2 and 7. -2 goes with (x+2), while 7 goes with (x-7). Therefore, you can already see that the answer is (D). To make sure. let us check the root 5 with multiplicity of 2. 5 goes with (x-5), implying that there must be 2 (x-5)'s. Only (D) satifies that as well, so the answer must be (D).

Answer:

D on edge

Step-by-step explanation:

L = lengh

W = width

french reasoning ( hello from France ) !

The base of the house is a rectangle where the length of a rectangle is 8 more than the width.

=> L = W + 8

and

Its area is 240 ft sq

W x L = 240

L = W + 8

W x L = 240

=> W x (W+8) = 240

W² + 8W - 240 = 0

Δ = 8² - 4*1*(-240) = 32²

W' = (-8 + 32) / 2 = 12 ft

W'' = (-8 - 32) / 2 = impossible

at the end

W the width = 12 ft

and then the lengh = 12 + 8 = 20

area = 12 x 20 = 240 ft²

Step-by-step explanation:

See image below

The system of equations that could be used to determine the number of pounds of apples sold and the number of pounds of strawberries sold will be x + y = 35 and 2x + 3y = 80.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, each pound of apples sells for $2 and each pound of strawberries sells for $3. Aiden made $80 from selling a total of 35 pounds of apples and strawberries.

Suppose the number of pounds of apples and strawberries is x and y respectively.

If the total of 35 pounds of apples and strawberries as a result,

x + y = 35-------(1)

If each pound of apples sells for $2 and each pound of strawberries sells for $3. Aiden made $80 then,

2x + 3y = 80---------(2)

Multiply equation 1 by 2 and subtract from equation 2 as

2x + 3y -2(x+y) = 80 - 2(35)

y = 10

Substitute the value of y we get x = 25

As a result, there are 25 pounds of apples and 10 pounds of strawberries in all.

Thus, the system of equations that could be used to determine the number of pounds of apples sold and the number of pounds of strawberries sold will be x + y = 35 and 2x + 3y = 80.

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We need to know the total earnings and total expenses for the day. Without this information, we cannot accurately determine Leo's profit. If you can provide additional details or the complete notebook entries, I would be happy to assist you in calculating the profit.

To determine Leo's profit for the first day, we need more information than what is provided in the question. The notebook shows the money earned and spent, but the given information stops at "10," without specifying whether it represents money earned or money spent. Additionally, we don't have any other earnings or expenses mentioned in the question.

To calculate the profit, we need to know the total earnings and total expenses for the day. Without this information, we cannot accurately determine Leo's profit. If you can provide additional details or the complete notebook entries, I would be happy to assist you in calculating the profit.

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Step-by-step explanation:

The equation is   sinθ * cosθ - sinθ = 0

θ = 0 + 2kπ

θ = 2kπ where k is any integer

The solutions to the equation are: {0 degree, 180 degree, 360 degree, 360 degree + 180 degree n, where n is any integer}

Hence, the correct option is C.

The given equation is:

sin theta × cos theta - sin theta = 0

We can factor out the sine theta:

sin theta (cos theta - 1) = 0

This means that either sin theta = 0 or cos theta - 1 = 0.

If sin theta = 0, then theta = 0, 180 degrees, 360 degrees, etc.

If cos theta - 1 = 0, then cos theta = 1, which means that theta = 0 degrees and 360 degrees.

Therefore, the solutions to the equation are:

{0 degree, 180 degree, 360 degree, 360 degree + 180 degree n, where n is any integer}

So the answer is C.

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Okay, here are the steps to solve this problem:

* Kariro had y cows

* Ali had 3 times as much as Kariro, so Ali had 3y cows

* Nabwiso had half as much as Kariro, so Nabwiso had y/2 cows

* In total, they had:

** Kariro: y cows

** Ali: 3y cows

** Nabwiso: y/2 cows

* So in total: y + 3y + y/2 = 180

* 4.5y = 180

* y = 40

* So:

** Kariro had 40 cows

** Ali had 3 * 40 = 120 cows

** Nabwiso had 40/2 = 20 cows

Therefore, if the total cows was 180, then Nabwiso had 20 cows.

Let me know if you have any other questions!