4) A teacher has an annual income of $51,750. The income tax the teacher has to pay is 7%. What is the amount of income tax in dollar and cents the teacher has to pay?
A) $3,448.25
B) $3,622.50
C) $3,891.10
D) $3,933.01

Answer:

Step-by-step explanation:

Given:

Simplify equation for perimeter and solve for W:

Find L:

Answer:

I really need help with this question.*

Answer:

There is no question

Step-by-step explanation:

Hope you have a great day!!

Answer:

no entiendo, perdóname, suerte

500 children ages 5-11 were asked the following question:

"Do you read books for fun every day?"

Results are shown in the two-way table below.

             Boy    Girl     Total

Yes         48      75       123

No          182     195     377

Total      230    270     500

A proportion is the number of desired outcomes divided by the number of total outcomes.

There are 500 children and 230 are boys.

230/500 = 0.46

There are 230 boys and 48 read books for fun every day.

48/230 = 0.21

There are 270 girls and 75 read books for fun every day.

75/270 = 0.28

Based on the results from b and c, it would seem more likely for a girl to read books for fun than for a boy.

There are 500 children and 123 read books for fun.

P = 123/500 = 0.25

There are 500 children and 75 are girls who read books for fun.

P = 75/500 = 0.15

There are 500 children. The favorable cases are the girls (270) plus the children who read books for fun (123) minus the girls who read books for fun (75).

P = (270 + 123 - 75)/500 = 0.64

There are 270 girls and 75 of them read books for fun.

P = 75/270 = 0.28

Learn more about proportions here: https://brainly.com/question/25259185

Answer:

Mary:604

Mona:796

Step-by-step explanation:

Answer:

Ms. Mary spend $302

Ms. Mona spend $ 686

Step-by-step explanation: We know that Ms. Mary spend $192 less than Ms. Mona.

So we are to divide $988 by 2 which is 494

now both have $494 each but Ms. Mona spend 192 so we are to add 192 + 494 to get the right sum of how much money Ms. Mona have and take away 494-192 to get the right sum of how much money Ms. Mary spend.

192 + 494 = 686

494 - 192 = 302

Answer:

C, 18.

Step-by-step explanation:

Since 24 divided by 8 is 3, which means that

8x3 = 24, then the amount of boys must be solved using the equation 6x3 which equals 18.

We first compute the partial derivatives of f(x, y):

f(x, y) = 5x² + 5y² - 10x + 21

∂f/∂x = 10x - 10

∂f/∂y = 10y

The critical points of f occur where both ∂f/∂x and ∂f/∂y are equal to zero. This only happens at the point (x, y) = (1, 0). (And this point does lie inside R.)

Next, compute the Hessian matrix H(x, y) for f :

[tex]H(x, y) = \begin{bmatrix}\frac{\partial^2f}{\partial x^2} & \frac{\partial^2f}{\partial x\partial y} \\ \frac{\partial^2 f}{\partial y\partial x} & \frac{\partial^2f}{\partial y^2}\end{bmatrix} = \begin{bmatrix}10&0\\0&10\end{bmatrix}[/tex]

Since det(H(x,y)) = 100 is positive for all x and y, this means the critical point (1, 0) is a local minimum, and we have f(1, 0) = 16.

Next, we check for extrema along the boundary of R, which is comprised of a semicircle with radius 2 and the line segment connecting (-2, 0) and (2, 0).

• Parameterize the semicircular portion by

x(t) = 2 cos(t)

y(t) = 2 sin(t)

with 0 ≤ t ≤ π. Then

f(x(t), y(t)) = 20 sin²(t) + 20 cos²(t) - 20 cos(t) + 21

which is simplifies to a function of one variable t,

g(t) = 41 - 20 cos(t)

Find the extrema of g over the interval [0, π] : we have critical points when

g'(t) = 20 sin(t) = 0

which happens at t = 0 and t = π. At these points, we get local extreme values  of

•• t = 0   =>   x = 2 and y = 0   =>   f(2, 0) = 21

•• t = π   =>   x = -2 and y = 0   =>   f(-2, 0) = 61

• Over the line-segment portion, we take y = 0, so f(x, y) again reduces to a function of one variable:

f(x, 0) = 5x² - 10x + 21

Completing the square, we have

5x² - 10x + 21 = 5 (x - 1)² + 16

which has a maximum value of 16 when x = 1 (and this happens to be the critical point (1, 0) we found earlier).

So, over the region R, f(x, y) has

• an absolute maximum of 61 at the point (-2, 0), and

• an absolute minimum of 16 at (1, 0)

Answer:

5

Step-by-step explanation:

The answer is 60/12 becuase we can simfly both of theese mixed numbers into an improper fraction, wich will be 4/3*15/4. We do the multiplication, and we get 60/12. 60/12 can be simplifed to 5 becuase 60 divided by 12 is 5

Answer:

38.5 in

Step-by-step explanation:

11.25 in + 11.25 in + 8 in + 8 in

= 38.5 in

[tex]\\ \sf\longmapsto (5x^3+5x^2+5)-(6x^3-6x^2+8x-5)[/tex]

[tex]\\ \sf\longmapsto 5x^3+5x^2+5-6x^3+6x^2-8x+5[/tex]

[tex]\\ \sf\longmapsto 5x^3-6x^3+5x^2+6x^2-8x+5+5[/tex]

[tex]\\ \sf\longmapsto -x^3+11x^2-8x+10[/tex]

[tex]\\ \sf\longmapsto x^3-11x^2+8x-10[/tex]

[tex]\large \boldsymbol{} \longmapsto (5x^3+5x^2+5) -(6x^3-6x^2+8x-5 ) \\\\\\ \longmapsto5x^3+5x^2+5-6x^3+6x^2-8x+5 \\\\\\ \longmapsto 5x^3-6x^3+5x^2+6x^2-8x+5+5 \\\\\\ \longmapsto \boxed{ - x^3+11x^2-8x+10}[/tex]

Using a system of equations, the height of the tree would be 12.80 meters.

Equating the height and shadows of the tree and pole :

Height of pole / shadow of pole = height of tree / shadow of tree

Representing the equation thus :

Let the height of the tree = h

3/4 = h/17

Cross multiply

4h = 17 × 3

4h = 51

Divide both sides by 4

h = 51/4

h = 12.75.

Hence, the height of the tree to the nearest tenth of a meter is 12.80 meters.

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60

Step-by-step explanation:

(-47)-(-107)

(-47)-1(-107)

-47+107

=60

Answer:

Step-by-step explanation:

The vertex is given (-1, 4).

The axis of symmetry is a vertical line and passes through vertex.

Since the x- coordinate of vertex is  - 1, the line of symmetry is x = - 1.

Answer:

x=-1

Step-by-step explanation:

Parabola is symmetric on both sides of the vertex

The axis of symmetry is the x coordinate of vertex

Here the vertex is (-1,4)

So axis of symmetry is x=-1

The equation that can be used to determine the original length of the pool is 205.85 = 11.6(l + 3.7)

Let l be the original length of the pool.

Since the length of the pool is increased by 3.7 m, the new length L = l + 3.7.

Also, the area of the pool A = 205.85 square meter and it is a rectangle with width, W = 11.6 meters,

So, A = LW

Substituting the values of the variables into the equation, we have

A = LW

205.85 = (l + 3.7)11.6

So, the equation that can be used to determine the original length of the pool is 205.85 = 11.6(l + 3.7)

Learn more:

https://brainly.com/question/12932084

Answer:

Step-by-step explanation

205.85=11.6(l+3.7)

Answer:

You need 6 lbs of red potatoes

32oz of cream cheese

43oz cream of potatoe soup

Step-by-step explanation:

Multiply all by 4

Answer:

[tex]\displaystyle m = \frac{5}{3}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Coordinate Planes

Step-by-step explanation:

Step 1: Define

Identify

Point (-1, 4)

Point (2, 9)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m.

The circle that passes through the vertices of triangle ΔABC (A, B, C) is the

circumscribing circle of triangle ΔABC.

The area of the circle that passes through vertices A, B, and C, is (C) 26·π

Reasons:

The given parameters are;

Side length of isosceles triangle ΔABC; [tex]\overline{AB}[/tex] = [tex]\overline{AC}[/tex] = 3·√6

Radius of circle tangent to [tex]\overline{AB}[/tex] at B and [tex]\overline{AC}[/tex] at C = 5·√2

Required:

Area of the circle that passes through vertices A, B, and C

Solution:

Angle ∠BAO is given as follows;

[tex]\angle BAO = arctan\left(\dfrac{5 \cdot \sqrt{2} }{3 \cdot \sqrt{6}} \right) = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}[/tex]

Therefore;

[tex]\angle BOA = 90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)[/tex]

[tex]\overline{BC} = 2 \times 5 \cdot \sqrt{2} \times sin\left(90^{\circ} - arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right) = 15\cdot \sqrt{\dfrac{6}{13} }[/tex]

∠ABO' = ∠BAO' (Base angles of isosceles triangle ΔABO')

[tex]\angle BAO' = \angle BAO = \mathbf{arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)}[/tex]

Therefore;

[tex]\angle BO'A = 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)[/tex]

From sine rule, we have;

[tex]\dfrac{\overline{AB}}{sin \left(\angle BO'A \right)} = \mathbf{\dfrac{\overline{BO'}}{sin \left(\angle BAO' \right) \right)}}[/tex]

Which gives;

[tex]\mathbf{\dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)}} = \dfrac{\overline{BO'}}{sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right)}[/tex]

Using a graphing calculator, we get;

[tex]\overline{BO'} = \dfrac{3 \cdot \sqrt{6} }{sin \left( 180^{\circ} - 2 \times arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right)\right)} \times sin \left(arctan\left(\dfrac{5 \cdot \sqrt{3} }{9} \right) \right) = \sqrt{26}[/tex]

The radius of the circumscribing circle [tex]\overline{BO'}[/tex] = √(26)

Therefore, area of the circumscribing circle, [tex]A_{O'}[/tex] = π·(√(26))² = 26·π

The area of the circle that passes through vertices A, B, and C, is (C) 26·π

Learn more here:

https://brainly.com/question/17147358

The possible question options obtained from a similar question online are;

(A) 24·π (B) 25·π (C) 26·π (D) 27·π (E) 28·π

Answer:

I should think the median

Answer:

q=13

Step-by-step explanation:

(8q-5)°+81°=180° (angles on a str line)

   8q-5+81=180

            8q=180+5-81

                =104

              q=104÷8

                =13

Using supplementary angle theorem

[tex]\\ \sf\longmapsto 8q-5+81=180[/tex]

[tex]\\ \sf\longmapsto 8q+76=180[/tex]

[tex]\\ \sf\longmapsto 8q=104[/tex]

[tex]\\ \sf\longmapsto q=13[/tex]

Size of final payment is $6392.43

Given that formula for compound interest is P(1+r/n[tex])^{nt}[/tex]

where P is initial principal

r is interest rate

n is compound times per period

t is time in years

We find all the variables in the formula in order to get our answer.

Initial principal = 96000 less 25%= 72000

interest rate = 9%

number of compound times= 12

time in years =4.25 years (whole period is 4.5 years since number of payments to complete balance will take 54 months)

Hence principal and CI after 4 years and 3 months(the second to last payment)

72000(1+0.09/12)^12x4.25=$105,393.6

We use $105,393.6 as our principal to calculate the whole interest and principal for the period in order to find last payment

105393.6(1+0.09/12)^12x0.25=$107,786.03

interest for the final month = $107786.03-$105,393.6=$2392.43

To get our final payment, we add the principal payment of $4000 to final compounded interest =$6392.43

Answer:

Step-by-step explanation:

Slope- intercept form:

Given points:

The slope is:

Use point (2, 4) to find the value of the y-intercept:

Answer:

To find the area of a square with the scale factor of 3, you multiply the side lengths by 3, so (3*L)*(3*W)= Area of your square.

Step-by-step explanation: I hope that this helps, ask questions in the comments below.(if you have any).

The area of the imagined square will be 90 units² by increased with a scale factor of 3.

You must specify the extent of the shape's enlargement when describing one.

The scale factor is the ratio of two dimensions such that one figure is large and another is small.

As per the imagined square with dimensions of 10 units.

Applied the scale factor 3 in the length of the square(since it has only one dimension).

10 x 3 = 30 units.

Thus, each side of the square will be 30 units in length.

Hence "By adding a scale factor of 3, the envisioned square's area will expand to 90 units²".

To learn more about scale factors,

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#SPJ5

Answer:

Step-by-step explanation:

Answer:

0.6 cm

Step-by-step explanation:

15/25=0.6

Answer:

0.6 Is the answer

Step-by-step explanation:

Hope this helped ¬∪ω∪¬

Answer:

3/8

Step-by-step explanation:

-4<x>/=5

Answer:

2/3 ​sandwich.

Step-by-step explanation:

No Explanation

Answer:

45

Step-by-step explanation:

15+15+15=45

that would increase her practice time by 45 minutes