A new car is purchased for 19900 dollars. The value of the car depreciates at 7.5% per year. What will the value of the car be, to the nearest cent, after 8 years?

Final answer:

The degree of the term [tex]4xy^2z[/tex] is 4, calculated by summing up the exponents of all variables in the term.

Explanation:

The degree of a monomial like [tex]4xy^2z[/tex] is found by adding up the exponents of all the variables in the term. In this case, the exponent of x is 1, the exponent of y is 2, and the exponent of z is 1. Therefore, the degree of [tex]4xy^2z[/tex] is 1+2+1 = 4.

The degree of a polynomial is an important concept in algebra that tells you the highest degree of any term in the polynomial. For this reason, understanding how to calculate the degree of individual terms like 4xy^2z is crucial for working with polynomials. Remember, coefficients, like the number 4 in this expression, do not affect the degree of the term.

The degree of the term [tex]\(4xy^2z\)[/tex] is 4.

To find the degree of the term [tex]\(4xy^2z\)[/tex], we add up the exponents of all the variables present in the term.

In the term [tex]\(4xy^2z\)[/tex], we have:

- (x) with an exponent of 1,

- (y) with an exponent of 2,

- (z) with an exponent of 1.

Adding up the exponents:

[tex]\[1 + 2 + 1 = 4\][/tex]

So, the degree of the term [tex]\(4xy^2z\)[/tex] is 4.

Answer:

Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16 ⇒ answer (a)

Step-by-step explanation:

* Lets revise some facts about the parabola

- Standard form equation for a parabola of vertex at (0 , 0)

- If the equation is in the form  x² =  4py, then  

- The axis of symmetry is the y-axis,  x = 0  

- 4p  equal to the coefficient of y in the given equation to

  solve for  p

- If  p  >  0, the parabola opens up.

- If  p <  0, the parabola opens down.

- Use  p  to find the coordinates of the focus,  (0  ,  p)

- Use  p  to find equation of the directri ,   y= − p

- Use  p  to find the endpoints of the focal diameter,  (±2p  ,  p)

* Now lets solve the problem

- The vertex of the parabola is (0 , 0)

∵ -1/16x² = y ⇒ multiply each side by -16

∴ x² = -16y

∴ 4p = -16 ⇒ ÷ 4 tbe both sides

∴ p = -4

∵ The focus is (0 , p)

∴ The focus is (0 , -4)

∵ The directrix is y = -p

∴ The directrix is y = -(-4) = 4 ⇒ y = 4

∵ The endpoints of the focal diameter,  (±2p  ,  p)

∴ The focal width = 2p - (-2p) = 4p

∴ The focal width = 4 ×  I-4I = 16

* Vertex: (0, 0); Focus: (0, -4); Directrix: y = 4; Focal width: 16

Answer:

A

Step-by-step explanation:

i just took the edg quiz

Answer:

308.2 - 293.8 = 14.4 km

14.4 - 2.3 = 12.1

So the library is 12.1 km from the park.

Library is 12.1 km far from the park.

Distance is the total movement of an object without any regard to direction.

Given that, Aidan rode his bike 2.3 km from home to the library. Then he biked to the park. When he left home, his odometer read 293.8 km. When he reached the park, it read 308.2 km.

Total Distance reading in Odometer after reaching Library =

293.8  + 2.3 = 296.1 km

Reading in Odometer after reaching park = 308.2 km

308.2 - 296.1 = 12.1 km

Hence, Library is 12.1 km far from the park.

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[tex]\bf f(x)=-2x^2+11x\implies \left. \cfrac{df}{dx}=-4x+11 \right|_{x=9}\implies -4(9)+11\implies -25[/tex]

Answer:

a) -25

Step-by-step explanation:

First you have to find the derivative of F(x):

[tex]f(x)=2x^{2} +11x\\Derivative=2(2x)+1(11)\\Derivative=4x+11[/tex]

Now you just have to calculate the vale of f(x) when x=9

[tex]-4x+11=\\-4(9)+11=\\-36+11=-25[/tex]

So when x=9, the derivative of [tex]f(x)=2x^{2} +11x[/tex] is equal to -25

Answer:

The answer is C. m<1=60 degrees  m<2=30 degrees and m<3 equals 60 degrees

Step-by-step explanation: So, if 1 was 60 degrees then half of it is 30 degrees which is the angle for two. Them 3 is the same degree as 1.

Answer:

y=5,902,060*(.957)^t

Step-by-step explanation:

Since the original amount would be decreasing and it's an exponential one, hence the "every year", we can determine that it's an exponential decay equation.

The exponential delay equation is y=A*(1-r)^t. The y is the remaining amount, A is the original amount, r is the rate in decimal form, and t is for years. "1-r" is for decreasing rates and "1+r" is for increasing rates.

First thing we need to do is turn the rate, 4.3%, from a percentage to a decimal. You can do this by moving the decimal two places to the right, which gives you 0.043.

Now plug the numbers into the equation.

y=5,902,060*(1-0.043)^t

Simplify what's inside the parenthesis and get your final equation.

y=5,902,060*(.957)^t

Answer:

F = 5,902,060(0.957)[tex]F = 5,902,060(0.957)^{t}[/tex]

Step-by-step explanation:

Answer:

7,400

Step-by-step explanation:

First, we have to see that this is an arithmetic sequence... since to get the next element we add 1 to it.  (a geometric sequence would be a multiplication, not an addition)

So, we have a, the first term (a = 53), and we have the difference between each term (d = 1), and we want to find the SUM of the first 80 terms.

To do this without spending hours writing them down, we can use this formula:

[tex]S = \frac{n}{2} * (2a + (n - 1) * d)[/tex]

If we plug in our values, we have:

[tex]S = \frac{80}{2} * (2 * 53 + (80 - 1) * 1) = 40 * (106 + 79 * 1)[/tex]

S = 40 * (106 + 79) = 40 * 185= 7,400

Answer:   If you want to find out how much 20 percent of 5.4 is, you have to multiply, the equation would be

5.4 x .2 = 1.08, so it will give you 1.08 more

Step-by-step explanation:

Answer:

i feel like the answer is y=-3x - 1 but at the same time i think its wrong.

Step-by-step explanation:

Answer:y=-3x - 1

Step-by-step explanation:

Answer: I don't what your're asking but I guess it's 37 and 39.

Step-by-step explanation:

37- 38-39

Answer: First Option

[tex]A = 790.90 cm^2[/tex]

Step-by-step explanation:

The surface area of a circular cone is equal to the area of the cone surface plus the area of the circular base

[tex]A = \pi r ^ 2 + \pi rs[/tex]

Where r is the radius of the base and s is the inclined height of the pyramid.

In this case we know that:

[tex]r = \frac{19}{2}[/tex]

[tex]s = 17[/tex]

Then the surface area of the cone is:

[tex]A = \pi (9.5) ^ 2 + \pi (9.5)(17)[/tex]

[tex]A = 790.90 cm^2[/tex]

Answer:

  [tex]15x^4y^5z^2[/tex]

Step-by-step explanation:

The applicable rule of exponents is ...

  (a^b)(a^c) = a^(b+c)

[tex]3xy^4z^2\cdot 5x^2yx=(3\cdot 5)x^{1+2+1}y^{4+1}z^2=15x^4y^5z^2[/tex]

_____

Comment on the rule of exponents

You can see where the rule comes from when you consider that an exponent signifies repeated multiplication.

x² = x·x . . . . . . the 2 signifies that x is a factor 2 times

x³ = x·x·x . . . . the 3 signifies that x is a factor 3 times

The product of these is ...

  (x²)(x³) = (x·x)(x·x·x) = x·x·x·x·x = x⁵ = x²⁺³

Answer:

UR BAD AT SPELLING KID

Step-by-step explanation:

Answer:

The expected value would be a gain of 1,5

Step-by-step explanation:

For any calculation of expecte value you should multiply the probability of every chance with his value or gain, for example, for this dice

If your roll 1

p(1) = 1/6, and his gain is -1

If your roll 2

p(2) = 1/6, and his gain is -2

If your roll 3

p(3) = 1/6, and his gain is -3

If your roll 4

p(4) = 1/6, and his gain is 4

If your roll 5

p(5) = 1/6, and his gain is 5

If your roll 6

p(6) = 1/6, and his gain is 6

So the expecte value would be

E = p(1)*(-1) + p(2)*(-2)+p(3)*(-3)+p(4)*(4)+p(5)*5+p(6)*6

p(1)=p(2)=p(3)=p(4)=p(5)=p(6)=1/6 because this dice is a cube, with even chances to fall in any face.

E = (1/6)*(-1-2-3+4+5+6)

E=(1/6)*(-6+15)

E=(1/6)*(9)

E=1,5

The expected value would be a gain of 1,5

Answer:

Mean: 5.6428571428571

Median: 5

Step-by-step explanation:

The mean is 5.64 and the median is 5 for the given data. This can be obtained by using formula for mean and median.

For finding mean and median the data should be in ascending order,

Mean = sum of observations / total number of observations

When 'n' is odd, Median = [tex](\frac{n+1}{2})^{th}term[/tex]

When 'n' is even, Median =  [tex]\frac{(\frac{n}{2})^{th} term +(\frac{n}{2}+1)^{th} term }{2}[/tex]  , where n is the number of observations.

First write the data in ascending order,

2,2,3,4,4,5,5,5,6,6,7,9,10,11

Mean = [tex]\frac{2+2+3+4+4+5+5+5+6+6+7+9+10+11}{14}[/tex] =79/14 = 5.64

Median=(5 + 5 )/2 = 5

Hence the mean is 5.64 and the median is 5 for the given data.

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Answer:

−3(1.5n−1)−3(1.5n−1)

Step-by-step explanation:

To factor the expression −4.5n+3−4.5n+3, find the GCF between each term.  Using the GCF 3, divide each term by 3 and rewrite it as −3(1.5n−1)−3(1.5n−1).

The other options are not the factors because they give the wrong signs of at least one term in the expression.

−1.5(−3n+2)−1.5(−3n+2)  = 4.5n -3 + 4.5n - 3

−1.5(3n+2)−1.5(3n+2)  = -4.5n - 3 - 4.5n - 3

−3(1.5n+1) = -4.5n - 3

Answer:

The answer is A. 755 m2; 815 m2

Step-by-step explanation:

The answer is A) 472m^2; 486 m^2.

Let a, b, and c be the sides of the base and h be the height of the prism

a = 2 m

b = 7 m

c = 7.28 m

h = 29 m

The lateral surface area is:

LA = a*h + b*h + c*h = h * (a + b + c)

LA = 29 * (2 + 7 + 7.28) = 29 * 16.28 ≈ 472 m²

The surface area is:

SA = LA + 2 * 1/2 * a * b

SA = 472 + 2 * 7 = 472 + 14 = 486 m²

Answer:

The lateral surface area is 755 sq.m. and total surface area is 785 sq.m.

Step-by-step explanation:

Let a, b, and c be the sides of the base and h be the height of the prism.

a = 5 m

b=6 m

c=11.21 m

h = 34 m

Lateral surface area of triangular prism = [tex](a+b+c)h[/tex]

                                                                 = [tex](5+6+11.21)34[/tex]

                                                                 =755.14 sq.m.

Total surface are of triangular prism = Lateral surface area + area of 2 triangles

                                                         =[tex]755.14+2 (\frac{1}{2} \times b\times h)[/tex]

                                                         =[tex]755.14+2 (\frac{1}{2} \times 5\times 6)[/tex]

                                                         =[tex]785.14[/tex]

Thus the lateral surface area is 755 sq.m. and total surface area is 785 sq.m.

Option B is correct.

Answer:

[tex]12+2g[/tex]

Step-by-step explanation:

Let the variable g represents Gail's savings.

Then twice Gail's savings will be 2g.

The sum of 12 and twice Gail's savings is

[tex]12+2g.[/tex]

Hence, the algebraic expression that translate the phrase "The sum of 12 and twice Gail's savings" is [tex]12+2g.[/tex]

[tex]\vec f(x,y,z)=(2yze^{2xyz}+4z^2\cos(xz^2))\,\vec\imath+2xze^{2xyz}\,\vec\jmath+(2xye^{2xyz}+8xz\cos(xz^2))\,\vec k[/tex]

Let

[tex]\vec f=f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k[/tex]

The curl is

[tex]\nabla\cdot\vec f=(\partial_x\,\vec\imath+\partial_y\,\vec\jmath+\partial_z\,\vec k)\times(f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k)[/tex]

where [tex]\partial_\xi[/tex] denotes the partial derivative operator with respect to [tex]\xi[/tex]. Recall that

[tex]\vec\imath\times\vec\jmath=\vec k[/tex]

[tex]\vec\jmath\times\vec k=\vec i[/tex]

[tex]\vec k\times\vec\imath=\vec\jmath[/tex]

and that for any two vectors [tex]\vec a[/tex] and [tex]\vec b[/tex], [tex]\vec a\times\vec b=-\vec b\times\vec a[/tex], and [tex]\vec a\times\vec a=\vec0[/tex].

The cross product reduces to

[tex]\nabla\times\vec f=(\partial_yf_3-\partial_zf_2)\,\vec\imath+(\partial_xf_3-\partial_zf_1)\,\vec\jmath+(\partial_xf_2-\partial_yf_1)\,\vec k[/tex]

When you compute the partial derivatives, you'll find that all the components reduce to 0 and

[tex]\nabla\times\vec f=\vec0[/tex]

which means [tex]\vec f[/tex] is indeed conservative and we can find [tex]f[/tex].

Integrate both sides of

[tex]\dfrac{\partial f}{\partial y}=2xze^{2xyz}[/tex]

with respect to [tex]y[/tex] and

[tex]\implies f(x,y,z)=e^{2xyz}+g(x,z)[/tex]

Differentiate both sides with respect to [tex]x[/tex] and

[tex]\dfrac{\partial f}{\partial x}=\dfrac{\partial(e^{2xyz})}{\partial x}+\dfrac{\partial g}{\partial x}[/tex]

[tex]2yze^{2xyz}+4z^2\cos(xz^2)=2yze^{2xyz}+\dfrac{\partial g}{\partial x}[/tex]

[tex]4z^2\cos(xz^2)=\dfrac{\partial g}{\partial x}[/tex]

[tex]\implies g(x,z)=4\sin(xz^2)+h(z)[/tex]

Now

[tex]f(x,y,z)=e^{2xyz}+4\sin(xz^2)+h(z)[/tex]

and differentiating with respect to [tex]z[/tex] gives

[tex]\dfrac{\partial f}{\partial z}=\dfrac{\partial(e^{2xyz}+4\sin(xz^2))}{\partial z}+\dfrac{\mathrm dh}{\mathrm dz}[/tex]

[tex]2xye^{2xyz}+8xz\cos(xz^2)=2xye^{2xyz}+8xz\cos(xz^2)+\dfrac{\mathrm dh}{\mathrm dz}[/tex]

[tex]\dfrac{\mathrm dh}{\mathrm dz}=0[/tex]

[tex]\implies h(z)=C[/tex]

for some constant [tex]C[/tex]. So

[tex]f(x,y,z)=e^{2xyz}+4\sin(xz^2)+C[/tex]

The curl of a vector field can be calculated by finding the determinant of a 3x3 matrix constructed from the unit vectors, partial derivatives, and the components of the vector field. The existence of a function f(x,y,z) such that f⃗ =∇f would imply that the vector field is conservative, meaning it has zero curl.

In mathematics and vector calculus, the curl of a vector field is a vector operator that shows the rotation or the circular motion of the vectors in a vector field. It is denoted by ∇×F. The given vector field f⃗ (x,y,z)=(2yze^(2xyz)+4z²cos(xz²)î⃗ +(2xze^(2xyz)j⃗ +(2xye^(2xyz)+8xzcos(xz²))k). The curl can be obtained by finding the determinant of a matrix.

Consider a 3x3 matrix composed of î, ĵ, and k (in the first row), partial derivates (∂/∂x, ∂/∂y, ∂/∂z) (in the second row), and the vector field components (in the third row). Now, you need to calculate the determinant of this matrix to find the curl of the vector field.

The existence of function f(x,y,z) such that f⃗ =∇f would imply that the vector field is conservative. For a vector field to be conservative, it needs to have zero curl. So, once we have the curl, if it equates to zero, it implies the existence of such a function. Otherwise, no such function exists.

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Answer:

Each property with the appropriate example is given below.

1. c.Transitive property

If 3 + 4 = 7 and 6 + 1 = 7, then 3 + 4 = 6 + 1

2. a.Distributive property

2x + 6 = 2(x + 3)

3. d.Commutative property

7 * 3 = 3 * 7

4. e.Multiplicative inverse property

½ * 2 = 1

5. b.Associative property

(x + y) + z = x + (y + z)

Answer:

[tex]64.98\°[/tex]

Step-by-step explanation:

we know that

In the right triangle of the figure

[tex]tan(A)=\frac{BC}{AB}[/tex] ---> opposite side to angle A divided by the adjacent side to angle A

substitute the values

[tex]tan(A)=\frac{15}{7}[/tex]

[tex]A=arctan(\frac{15}{7})=64.98\°[/tex]

the answer for this question is ( d)

The least steep graph is y=1/2x+3.

Hence, the least steep graph is y=1/2x+3.

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For this case we have that the volume of the rectangular prism is given by:

[tex]V = A_ {b} * h[/tex]

Where:

[tex]A_ {b}:[/tex] It is the area of the base

h: It's the height

We have that the base is a triangle, so, the area of the base is the area of the triangle:

[tex]A_ {b} = \frac {9 * 4} {2} = 18 \ units ^ 2[/tex]

The height of the prism is 18 units.

So, the volume is:

[tex]V = 18 * 18 = 324 \ units ^ 3[/tex]

ANswer:

[tex]324 \ units ^ 3[/tex]

Option C

The volume of the triangular prism is 324 cubic feet (option c).

To calculate the volume of a triangular prism, you can use the formula:

Volume = (1/2) * base * height * length

In your case:

Base (b) = 9 ft

Height (h) = 4 ft

Length (H) = 18 ft

Now, plug these values into the formula:

Volume = (1/2) * 9 ft * 4 ft * 18 ft

First, multiply the numbers:

Volume = (1/2) * 9 * 4 * 18

Now, perform the multiplications step by step:

Volume = (1/2) * 36 * 18

Volume = 18 * 18

Volume = 324 cubic feet

So, the volume of the triangular prism is 324 cubic feet.

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Answer:

Step-by-step explanation:

Use FOIL: (a + b)(c + d) = ac + ad + bc + bd

(4 - 8i)(2 - 7i)

= (4)(2) + (4)(-7i) + (-8i)(2) + (-8i)(-7i)

= 8 - 28i - 16i + 56i²

combine like terms

= 8 + (-28i - 16i) + 56i²

= 8 - 44i + 56i²

Answer:

Answer to Create a simple fraction calculator that can add and subtract any number of fractions and writes the answer as a reduced... ... writes the answer as a reduced fraction. Your program will read input from stdin and write output on stdout.

Step-by-step explanation:

Answer:

none. he didn't pour water, he poured juice.

Step-by-step explanation:

Option: B is the correct answer.

         B)  0.31

Let A denote the event that a person is a sophomore.

Let B denote the event that a person has attended volleyball game.

A∩B denote the event that a person is a sophomore and attend volleyball game.

Let P denote the probability of an event.

We are asked to find:

P(A∩B)

From the table provided to us we see that:

A∩B=42

Hence,

P(A∩B)=42/137=0.3065 which is approximately equal to 0.31

         Hence, the probability is:

                      0.31

Answer: it's 0.48

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

There are 8 ounces in a cup

8*3=24

24/2(for 2 oz. containers)=12

Answer:

There were 12 full containers packaged for the sale.

Step By Step Explanation:

3 cups of lemonade equals 24 ounces. So take 24 divided by 2 and you get your answer of 12 full 2-ounce containers of lemonade packaged for the sale.

Answer:

Option C is correct.

Step-by-step explanation:

We need to find the values of a and b.

We are given:

[tex]8y^2-12y + 4 \,\,by\,\, 4y\\8y^2-12y +4/4y\\8y^2/4y -12y/4y +4/4y = a+b+1/y\\2y -3+1/y = a+b+1/y[/tex]

From the equation [tex]2y -3+1/y = a+b+1/y[/tex] we can find value of a and b

a = 2y and b= -3

So, Option C is correct.

Answer:

0.375

Step-by-step explanation:

1/4= 0.25

0.25/2=1/8

0.125=1/8

0.125x3=3/8

0.375=3/8

The remaining portion of the pizza is 0.375.

A decimal is a number that consists of a whole and a fractional part.

Given that, Mikayla and her two friends made a pizza and cut it into 8 equal sized slices. Of which Makayla and her friends ate 5 slices of pizza,

The whole pizza be represented by 1,

Now, they sliced the pizza into 8 equal parts, and ate 5 of it,

Therefore,

Remaining = 1-5/8

= 3/8

= 0.375

Hence, the remaining portion of the pizza is 0.375.

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Answer:

arcsin(x/4)

Step-by-step explanation:

Sinθ =x/4

θ= sin-¹(x/4)

θ= arc sin (x/4)

The expression represents θ in terms of x will be θ = arcsin (x/4).

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

Given that sin θ = x/4.

Then the expression represents θ in terms of x will be

sin θ = x/4

     θ = arcsin (x/4)

Thus, the correct option is B.

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