Calculate the amount of simple interest earned. $6,000 at 12% for 7 years The interest is $

Answer: t=2.59

Step-by-step explanation:

This is a matter of clearing out the equation

set 1151=800e^0.14t

1151/800=e^0.14t

ln(1151/800)/0.14=t

t=2.59

The equation of the normal plane is 4y = 4π, or equivalently, y = π.

The word osculate comes from the Latin osculatus, which is a past participle of the verb osculari, which means "to kiss." Thus, an osculating plane is one that "kisses" a submanifold.

To find the osculating plane and normal plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, π, 1), we need to follow these steps:

Step 1: Find the first and second derivatives of the curve with respect to t.

x' = 2cos2t

y' = 1

z' = -2sin2t

x'' = -4sin2t

y'' = 0

z'' = -4cos2t

Step 2: Evaluate the derivatives at t = π.

x'(π) = 2cos2π = 2

y'(π) = 1

z'(π) = -2sin2π = 0

x''(π) = -4sin2π = 0

y''(π) = 0

z''(π) = -4cos2π = -4

So the velocity vector at the point (0, π, 1) is v = ⟨2, 1, 0⟩, the acceleration vector is a = ⟨0, 0, -4⟩, and the curvature vector is κv = ⟨0, 4, 0⟩.

Step 3: Use the velocity and acceleration vectors to find the normal vector of the osculating plane.

The normal vector of the osculating plane is given by the cross product of the velocity and acceleration vectors:

n = v × a = ⟨2, 1, 0⟩ × ⟨0, 0, -4⟩ = ⟨4, 0, 0⟩

Step 4: Use the normal vector and the point (0, π, 1) to find the equation of the osculating plane.

The equation of the osculating plane is given by:

4(x - 0) + 0(y - π) + 0(z - 1) = 0

Simplifying, we get:

4x - 4 = 0

So the equation of the osculating plane is 4x = 4, or equivalently, x = 1.

Step 5: Use the curvature vector to find the normal vector of the normal plane.

The normal vector of the normal plane is given by the curvature vector:

n' = κv = ⟨0, 4, 0⟩

Step 6: Use the normal vector and the point (0, π, 1) to find the equation of the normal plane.

The equation of the normal plane is given by:

0(x - 0) + 4(y - π) + 0(z - 1) = 0

Simplifying, we get:

4y - 4π = 0

So, the equation of the normal plane is 4y = 4π, or equivalently, y = π.

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The equation of the plane that passes through the line of intersection of x - z = 3 and y + 3z = 3 and is perpendicular to x + y - 4z = 6 is x + y - 4z = 3.

The point-normal form of the equation of a plane is given by:

N · (<x - x0>, <y - y0>, <z - z0>) = 0

Where (x0, y0, z0) is a point on the plane and N = is a normal vector to the plane, we have the point-normal form of the equation of a plane. The dot product of the vector from the supplied location to any point on the plane with the normal vector to the plane yields this form of the equation. The equation states that any vector located in the plane with the normal vector has a zero dot product. The scalar equation of the plane can also be found by expanding the dot product, and it takes the form axe + by + cz = d, where d = N (x0, y0, z0).

Given the equation of the planes is x − z = 3 and y + 3z = 3.

Now, find the direction vector of the line of intersection:

Set z = t:

x = t + 3 and y = 3 - 3t

The direction vector is <1, -3, 1>.

2. Determine the normal vector:

The plane is perpendicular to the plane x + y - 4z = 6, so:

normal vector of x + y - 4z = 6, which is <1, 1, -4>.

3. Using point normal form we have:

(3, 0, 0)

The point satisfies the equation:

x - z = 3 and y + 3z = 3 when z = 0

Thus,

<1, 1, -4> · <x - 3, y, z> = 0

x + y - 4z = 3

Hence, the equation of the plane that passes through the line of intersection of x - z = 3 and y + 3z = 3 and is perpendicular to x + y - 4z = 6 is x + y - 4z = 3.

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Answer:

[tex]3( {2}^{2} ) - {2}^{2} + 4 = 12[/tex]

[tex] {2}^{3} + b( {2}^{2} ) + 43(2) - 126 = 4b - 204[/tex]

[tex]4b - 32 = 12[/tex]

[tex]4b = 44[/tex]

[tex]b = 11[/tex]

For this value of b, these graphs will intersect at (2, 12). Please use your graphing calculator to confirm that this is the only point of intersection.

Answer:

1. 90

2. 468

Step-by-step explanation:

Answer:

Question 1). 45 in

Question 2). 234 m

Step-by-step explanation:

Area = base x height x 1/2

10 x 9 = 90

90 x 1/2 = 45

Question 2)

30 x 15.6 = 468

468 x 1/2 = 234 m

The function is nonlinear because the variable x is raised to the second power. So, the correct option is D) .

A linear function is a mathematical equation that can be represented by a straight line. It is a function in which the independent variable, say "x," is raised only to the first power, and the dependent variable, say "y," is not multiplied or divided by any variable. Linear functions have a constant rate of change, which means that the slope of the line is the same at all points.

The general form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point at which the line crosses the y-axis. The slope m represents the rate of change of y with respect to x, and can be calculated as the change in y divided by the change in x between any two points on the line.

A linear function is a function that has a constant rate of change, meaning that as x increases by a certain amount, y also increases by a constant amount. A linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

In the given equation y = x²  + 9, the variable x is raised to the second power, which means that the rate of change of y with respect to x is not constant. This is the characteristic of a nonlinear function. Moreover, the graph of the function is a parabola, which is also a characteristic of a nonlinear function.

Therefore, the correct answer is D) The function is nonlinear because the variable x is raised to the second power.

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The complete question is :

Which statement explains the type of function that is represented by the equation y=x² +9?

A The function is linear because it contains more than one term.

B) The function is linear because the variable x is raised to the second power.

C) The function is nonlinear because it contains more than one term.

D) The function is nonlinear because the variable x is raised to the second power.

Answer:  33.51 cubic units.

Step-by-step explanation: The equation for the volume of a circle is:

V = (4/3)πr³

where r is the sweep of the circle.

Since the distance across of the circle is given as 4, we are able discover the span by partitioning the distance across by 2:

r = d/2 = 4/2 = 2

Presently we are able plug within the esteem of the sweep into the equation for the volume:

V = (4/3)π(2³) = (4/3)π(8) = 32/3π

Answer: 33.51

Step-by-step explanation:

The formula is 4/3 pi r^3. The radius is 2. If you do the equation, you get roughly 33.51.

The polynomial function of least degree that has zeros of x=0, x=2i, and x=3, and with all coefficients real is:

Since the zeros of the polynomial function are given as

x=0, x=2i, and x=3,

we can write the function in factored form as follows:

f(x) = a(x-0)(x-2i)(x-3)

where

a is a constant coefficient and the factors correspond to the given zeros.

Since all coefficients must be real, we know that the complex conjugate of 2i, which is -2i, must also be a zero of the function. Therefore, we can rewrite the function as:

f(x) = a(x-0)(x-2i)(x+2i)(x-3)

Expanding this expression gives:

f(x) = a(x² + 4)(x-3)

Multiplying out the brackets and collecting like terms, we get:

f(x) = ax³ - 3ax² + 4ax - 12a

To find the value of 'a', we can use the fact that the coefficient of the x³ term is 1. Thus, we have:

a = 1/(1*4) = 1/4

Substituting this value of 'a' in the above expression, we get:

f(x) = (1/4)x³ - (3/4)x² + x - 3

Therefore, the polynomial function of least degree that has zeros of x=0, x=2i, and x=3, and with all coefficients real is:

Option A: f(x) = x² - 3x³ + 4x² - 12x

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According to the given information, the function has no cusp.

What is a function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

The given piecewise function is:

c(x) = 39, when x ≤ 6

c(x) = 39 + 5(x - 6), when x > 6

A cusp is a point on the graph where the function changes direction very abruptly, like a sharp turn. This happens when the derivative of the function is not defined at that point.

The derivative of the function is:

c'(x) = 0, when x ≤ 6

c'(x) = 5, when x > 6

Since the derivative is defined and continuous at x = 6, there is no cusp at that point. Therefore, the function has no cusp.

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Answer:

To mathematically prove that Marc hit the ball near the top of the tower, he could use the equation h(x) = -16x^2 + 120x, where h is the height of the ball and x is the number of seconds the ball is in the air.

First, Marc would need to determine the maximum height the ball reached during its flight. This can be found by using the vertex formula, which is x = -b/2a. In this case, a = -16 and b = 120, so x = -120/(2*-16) = 3.75 seconds.

Next, Marc can substitute this value back into the original equation to find the maximum height the ball reached. h(3.75) = -16(3.75)^2 + 120(3.75) = 135 feet.

Since the tower is 300 feet tall, Marc could conclude that if the ball hit near the top of the tower, it would have reached a height close to 300 feet. Since the ball reached a maximum height of 135 feet, it is unlikely that it hit the top of the tower.

However, this calculation assumes that the tower is directly in line with Marc's shot and that the ball did not have any horizontal movement. In reality, the tower could have been to the left or right of the shot, and the ball could have had some horizontal movement, which would affect its height at impact. Therefore, this calculation can only provide a rough estimate and cannot definitively prove whether or not the ball hit near the top of the tower.

Answer:

A parallelogram with congruent diagonals, a parallelogram with a right angle, a parallelogram with perpendicular diagonals.

Step-by-step explanation:

By definition, a rectangle is nothing but a parallelogram with one right angle. One of the properties of a rectangle is that its perpendiculars are congruent. Finally, the diagonals of a rectangle are congruent (this can be proved by finding congruent triangles split by the diagonals, using CPCTC, etc.).

There are 52 quarters and 15 half-dollars

Let's represent the number of half-dollars as "x" and the number of quarters as "y".

From the problem statement, we know that:

x + y = 67 (because there are a total of 67 coins)

y = 3x + 7 (because the number of quarters is 7 more than three times the number of half-dollars)

We can use substitution to solve for x:

x + (3x + 7) = 67

4x + 7 = 67

4x = 60

x = 15

So there are 15 half-dollars. We can use this to find the number of quarters:

y = 3x + 7

y = 3(15) + 7

y = 52

So there are 52 quarters.

Therefore, there are 52 quarters and 15 half-dollars.

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The negation is the fourth option.

6 + 3 ≠ 9 or 6 - 3 ≠ 9

The negation of an equation is an inequality such that we just change the equal sign, by the "≠" sign.

Here we start with the two equations.

6 + 3 = 9 or 6 - 3 = 9

Just change the equal signs for different signs:

6 + 3 ≠ 9 or 6 - 3 ≠ 9

That is the negation, fourth option.

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The composite functions (f/g)(x) and (f-g)(x) are (2x-1)/√(3x-5) and (2x-1) -√(3x-5)

To calculate (f/g)(x), we need to divide f(x) by g(x):

(f/g)(x) = f(x)/g(x) = (2x-1)/√(3x-5)

The domain of (f/g)(x) is the set of all x-values for which the denominator √(3x-5) is not equal to zero and non-negative

3x-5 ≥ 0, or x ≥ 5/3

Therefore, the domain of (f/g)(x) is x ≥ 5/3.

To calculate (f-g)(x), we need to subtract g(x) from f(x):

(f-g)(x) = f(x) - g(x) = (2x-1) - √(3x-5)

The domain of (f-g)(x) is the set of all x-values for which the expression inside the square root is non-negative:

3x-5 ≥ 0, or x ≥ 5/3

Therefore, the domain of (f-g)(x) is x ≥ 5/3.

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The number of red tiles in the box given the chance ratio of red to blue tiles is 18. The surface area of the rectangular prism is 2600 square inches.

Number of red tiles = x

Number of blue tiles = 12 + x

Total tiles = x + 12 + x

= 12 + 2x

Ratio of red = 3

Ratio of blue = 5

Total ratio = 3 + 5 = 8

Number of red tiles = 3 / 8 × 12+2x

x = 3(12 + 2x) / 8

x = (36 + 6x) / 8

8x = 36 + 6x

8x - 6x = 36

2x = 36

x = 36/2

x = 18 tiles

Therefore, The number of red tiles in the box given the chance ratio of red to blue tiles is 18.

b) To find the surface area of the rectangular prism, we need to find the area of each of its faces and add them together. Looking at the net, we see that there are three pairs of identical rectangles: the top and bottom faces, the front and back faces, and the left and right faces. Each of these rectangles has dimensions of 23 inches by 8 inches.

Therefore, the surface area of the rectangular prism is:

=2 * (23 in. * 8 in.) (top and bottom faces)

=2 * (36 in. * 8 in.) (front and back faces)

=2 * (23 in. * 36 in.) (left and right faces)

= 368 + 576 + 1656

= 2600 square inches

Therefore, the surface area of the rectangular prism is 2600 square inches.

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The ordered pair (0, 2) lies on the graph.

The ordered pair (-1, 0) lies on the graph.

The ordered pair (-1, 0) lies on the graph.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

The exponential function f(x) = -32x+5 can be written in the form of

f(x) = [tex]a(b^{x})+c[/tex], where a, b, and c are constants. Comparing with the given function, we have a = -3, b = 2, and c = 5.

To find the ordered pairs that lie on the graph of the exponential function, we can plug in different values of x and calculate the corresponding values of y using the function. Here are some examples:

When x = 0, we have f(0) = [tex]-3(2^{0})[/tex] + 5 = 2. Therefore, the ordered pair (0, 2) lies on the graph.

When x = 1, we have f(1) = [tex]-3(2^{1})[/tex] + 5 = -1. Therefore, the ordered pair (1, -1) lies on the graph.

When x = -1, we have f(-1) = [tex]-3(2^{-1})[/tex] + 5 = 6/2 - 3 = 0. Therefore, the ordered pair (-1, 0) lies on the graph.

We can continue this process to find more ordered pairs that lie on the graph of the exponential function.

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The outcome that Regis is likely to get after randomly drawing one tile from the bag would be 0. That is option A.

To calculate the outcome of the event is to calculate the probability of selecting a tile with a number when one tile is drawn at random.

Probability = possible outcome/sample space.

Possible outcome = 1

sample space = 8

probability = 1/8 = 0.125

The probability is approximately = 0

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Answer:

finding the perimeter, you sumthe distance all round that is 7+7.5+17.8+6=38.3

38.3 is the perimeter

Arun's purple paint will be redder.

Percentage is a way of expressing a proportion or a fraction as a number out of 100. It is represented by the symbol "%". For example, if you say that 20% of students in a class scored an A grade in a test, it means that 20 out of every 100 students received an A grade.

Deondra mixed 6 cups of blue paint and 7 cups of red paint, so the percent of red paint in her mixture is:

7 / (6 + 7) × 100% = 53.8%, which rounds to 54%.

Arun mixed 2 cups of blue paint and 3 cups of red paint, so the percent of red paint in his mixture is:

3 / (2 + 3) × 100% = 60%.

Since Arun's mixture has a higher percentage of red paint, his purple paint will be redder than Deondra's.

Therefore, the answer is Arun's purple paint will be redder.

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Answer:

Summer for 9th Graders: 0.14

Fall for 10th Graders: 0.15

Spring overall total: 0.36

Summer overall total: 0.22

Fall overall total: 0.33

Winter overall total: 0.09

Step-by-step explanation:

Relative frequencies are related to percentages so you can find the answer through that given the total from each grade.

However, adding or subtracting makes the process easier (in my opinion) to find the relative frequency

Check the picture below.

Answer: 4.8%

Step-by-step explanation: the total amount of pens in the drawer is (10+12+3)  = 25

the amount of red pens in the drawer is 3

the probability of picking out a red pen from the drawer = 3/25

the amount of blue pens in the drawer is 10

the probability of picking out a red pen from the drawer = 10/25

the probability of picking out a red pen then a blue pen afterwards = (10/25 x 3/25) = 4.8%

In triangle ABC

a) The value of x = 29⁰

b) The angle c equal to 93⁰

A triangle is a closed plane figure that is formed by connecting three line segments, also known as sides, at their endpoints. The three endpoints, or vertices, where the sides of the triangle meet are not collinear. Triangles are important in mathematics and geometry because they are the simplest polygon that can exist in two-dimensional space.

In a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can use this fact to find the value of x and angle c.

We know that:

angle a = 35⁰

angle b = 52⁰

angle c = 3(x+2)⁰

Using the fact that the sum of all interior angles in a triangle is 180 degrees, we can write:

angle a + angle b + angle c = 180

Substituting the values we know, we get:

35 + 52 + 3(x+2) = 180

Simplifying the equation, we get:

87 + 3x + 6 = 180

3x + 93 = 180

3x = 87

x = 29

Therefore, x = 29⁰

To find angle c, we can substitute the value of x into the equation we were given for angle c:

angle c = 3(x+2)

angle c = 3(29+2)

angle c = 3(31)

angle c = 93

Therefore, angle c is equal to 93⁰.

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The circumference and approximate area of the given​ circle is 69.08 inches & 380.14 square inches.

What is circumference?

Circumference is the distance around the edge of a circular object or a round shape. It is the length of the boundary or perimeter of the circle. The formula is given by C = 2πr, where C is the circumference, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.

The circumference of a circle is given by the formula:

C = 2πr

where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.

Using this formula and plugging in the given value of radius:

C = 2 x 3.14 x 11

C = 69.08 inches (rounded to two decimal places)

So the circumference of the circle with 11 inches radius is approximately 69.08 inches.

The area of a circle is given by the formula:

A = πr²

Again, using the given value of radius and approximating π to 3.14:

A = 3.14 x 11²

A = 3.14 x 121

A = 380.14 square inches (rounded to two decimal places)

So the approximate area of the circle with 11 inches radius is approximately 380.14 square inches.

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Answer:

3,4,5 is the answer

Step-by-step explanation:

for the explanation using pythagoras theoem

[tex] {3}^{2} + {4}^{2} = {5 \\ }^{2} \\ 3 \times 3 + 4 \times 4 = 5 \times 5 \\ 9 + 16 = 25 \\ 25 = 25[/tex]

may you give me branliest as you promised

Therefore, Dorie needs to sell the dress for $349.93 in order to mark it back to its regular selling price.

What is selling price?

Selling price refers to the price at which a product or service is sold to customers. It is the amount of money that a buyer pays to the seller in exchange for the product or service. The selling price is usually higher than the cost price, which is the amount that the seller paid to acquire or produce the product or service. The difference between the selling price and the cost price is called the profit margin, and it is the profit that the seller makes on the sale of the product or service.

If a dress had been marked down 70%, this means that it is being sold for only 30% of its original selling price.

Let P be the original selling price of the dress. Then:

0.3P = $104.98

Solving for P, we get:

P = $104.98 / 0.3

P = $349.93

Therefore, Dorie needs to sell the dress for $349.93 in order to mark it back to its regular selling price.

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Answer:

Axis of symmetry =1

vertex =(1,2)

y intercept =0

min/max= -6,2

domain= 0,1,2

range =y≥1,2

The solution of the differential equation y'' + y = t with the initial conditions y(0)=1 and y'(0)=-2 is y(t)= 1-2t+te-t.

Equation is a mathematical statement that expresses the equality of two expressions. It shows the relationship between two or more variables and can be written using symbols, numbers, and operations. Equations are used to describe physical laws, to make calculations, and to solve problems. Examples of equations include the Pythagorean theorem, Newton's laws of motion, and linear equations.

We solve this differential equation using Laplace inverse, with the initial conditions y(0)=1 and y'(0)=-2. First, we take the Laplace transform of the equation:

L[y''+y]=L[t]

Using the properties of Laplace transform, we can write this as:

s2Y(s)-sy(0)-y'(0)+Y(s)= (1/s)

Substituting the initial conditions and rearranging terms, we have:

Y(s)= (1/s) + (2/s2) + (1/s2)

We can then invert the Laplace transform to get the solution of the original equation:

y(t)= 1-2t+te-t

Therefore, the solution of the differential equation y'' + y = t with the initial conditions y(0)=1 and y'(0)=-2 is y(t)= 1-2t+te-t.

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Answer:

3 and -16

Step-by-step explanation:

To find two numbers that add up to 13 but multiply to -48, we can start by making a list of the factors of -48:

1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 16, -16, 24, -24, 48, -48

We can see that the only two numbers in this list whose sum is 13 are 3 and -16. To verify that these numbers multiply to -48, we can simply multiply them together:

3 x (-16) = -48

Therefore, the two numbers that add up to 13 but multiply to -48 are 3 and -16.

Answer: -3, 16

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

A. $24

Step-by-step explanation:

Given:

Solve for average tip:

Answer:

Thus, the waiter's average tip per table is $24.

The answer is A.