Marty's friend Tom makes and hourly wage of $15.00 per hour. Using that there are 40 hours in a standard work week, there are 52 weeks in a year, Social Security Tax is $6.20 for every $100 earned, Medicare Tax is $1.45 for every $100 earned, and the following income tax designations, calculate the following (round your answers to the nearest penny if needed):

a. Tom's annual income is:_______
b. Tom's annual social security tax is:_______
c. Tom's annual medicare tax is:______

Answer:

Graph is attached.

Step-by-step explanation:

We are to graph the following inequalities:

y > 2x + 4 ... (i)

x + y ≤ 6 ... (ii)

We can graph these inequalities on an online graphing calculator but its recommended that you graph them on your physical graph book.

Your graph is attached below. The shaded region is the required part.

The graph of a system of inequalities represents the solution of the inequalities

The solution to the system of inequalities is [tex]\mathbf{y > \frac 23}[/tex] and [tex]\mathbf{x \le \frac{16}3}[/tex]

The system of inequalities is given as:

[tex]\mathbf{y > 2x + 4}[/tex]

[tex]\mathbf{x + y \le 6 }[/tex]

See attachment for the graphs of [tex]\mathbf{y > 2x + 4}[/tex] and [tex]\mathbf{x + y \le 6 }[/tex]

From the graph, we have:

[tex]\mathbf{y > \frac 23}[/tex]

[tex]\mathbf{x \le \frac{16}3}[/tex]

Read more about system of inequalities at:

https://brainly.com/question/19526736

Answer:

BC ≈ 10.94

Step-by-step explanation:

Base on the triangle we were given 2 sides and an angle. We were also asked to find the last length BC.

we can use cosine rule to find the side BC.

Base on cosine rule

a² = b² + c² - 2bc cos A

a = BC

b = AC = 14

c = AB = 10

a² = 14² + 10² - 2 × 14 × 10 cos 51°

a² = 196  + 100 - 280  cos 51°

a² = 296 - 280 × 0.62932039105

a² = 296 - 176.209709494

a² = 119.790290506

square root both sides

a = √119.790290506

a = 10.9448750795

BC ≈ 10.94

Answer:

BC = 10.94

Step-by-step explanation:

its a las of cosines

a² = b² + c² - 2bc cos A

AB = 10

AC = 14

angle A = 51°

BC² = 10² + 14² - (2 * 10 * 14 cos 51°)

BC = sqrt 119.8

BC = 10.94

Answer:

a) The student cannot receive an A in the class.

b) The student must score 119 in the third exams to make an A.  This is clearly not possible, since he cannot make 119 in a 100-points exam.

c) The student can make a B but he must score at least 84 in the third exam.

Step-by-step explanation:

To make an A, the student must score 315 (350 x 90%) in both home and the three exams.

The student who scored 35 (7 + 8 + 7 + 5 + 8) in the homework and 161 (81 + 80), getting a total of 196, is short by 119 (315 - 196) scores in making an A.

To make a B, the student must score 280 (350 x 80%) or higher but not reaching 315.

B ≥ 280 and < 315.

Since, the student had scored 196, he needs to score 84 and above to make a B in the last exam.

Answer:

(a) H₀: p = 0.11 vs. Hₐ: p > 0.11.

(b) A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).

Step-by-step explanation:

A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus.

From past data, it is believed that 11% of all Americans are left-handed.

The college wants to know if the data provide enough evidence to show that students at this college have a higher percentage of left-handed people than the general American population.

(a)

The hypothesis can be defined as follows:

H₀: The percentage of left-handed people in the college is 11%, i.e. p = 0.11.

Hₐ: The percentage of left-handed people in the college is more than 11%, i.e. p > 0.11.

(b)

A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).

In this case, a type I error would be committed if it is concluded that the percentage of left-handed people in the college is more than 11% when in fact it is 11%.

And, a type II error would be committed if it is concluded that the percentage of left-handed people in the college is 11% when in fact it is more than 11%.

Answer:

The 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries is (0.6151, 0.7615).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 154, \pi = \frac{106}{154} = 0.6883[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6883 - 1.96\sqrt{\frac{0.6883*0.3117}{154}} = 0.6151[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6883 + 1.96\sqrt{\frac{0.6883*0.3117}{154}} = 0.7615[/tex]

The 95% confidence interval for the true proportion of the households that spend more than $125 a week on groceries is (0.6151, 0.7615).

Answer:

Look at the numbers on the sides. If they are not spaced out very far, it's centimeters. If they are spaced out very far, it's inches

Step-by-step explanation:

this is how you read a ruler

Answer:

Start at 0

Step-by-step explanation:

Start at 0, then see how far the object goes.

Answer:

  B.  zero

Step-by-step explanation:

The slope of a line can be computed as ...

  slope = rise/run

When the line is horizontal, the "rise" is zero over any "run", so the slope is zero.

Step-by-step explanation:

Using the trigonometric identity

sin(a - b) = sin a cos b - cos a sin b

So sin 79° cos 19° - cos 79° sin 19° can be written as

sin ( 79 - 19) = sin 60

And

[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]

Hope this helps you

Answer:

  x + y + z = 14

Step-by-step explanation:

If the points are designated A, B, C, then ...

  AB × AC = (7, -7, 0) × (7, 0, -7) = (49, 49, 49).

That is, a vector perpendicular to the plane is (1, 1, 1), so the equation of the plane can be ...

  (1, 1, 1)·(x, y, z) = (1, 1, 1)·A

  x + y + z = 14

Answer:

For the Square

Base length is 6 units

Height is 4 units

Volume is 48 cubic units

Volume of 4 square pyramids is 192 cubic units

(Rectangular)

Base length is 12 units

Base width is 8 units

Height is 6 units

Volume is 192 cubic units

Step-by-step explanation:

Square pyramids is a geometric shape having square base. The appex is perpendicularly at the center of the square. If all the edges are equal it is equilateral square pyramid.

Rectangular pyramids have four sided base and four triangle sides that are coming together to the appex. Each base and appex  form a triange called lateral face. The triangular faces are non rectangular base. Pyramid with n side have n + 1 vertices and 2n edges.

Answer:

D. 569.39 m^3

Step-by-step explanation:

First, we can split up the solid into two shapes: a cone and a cylinder.

Then we can find the volume of the cone

The formula is v= pi r^2 h/3

We know the radius is four and so is the height.

Plug it in and we get 67.02 m^3

Next is the cylinder

Formula is pi r^2 h

We know that the radius is 4 and the height is 10

Plus it in and we get 502.65 m^3

We add 67.02 and 502.65 together to get the total volume.

Answer is D. 569.39 m^3

Mine is a bit higher than D since I used a pi button instead of 3.14

Answer:

Hey there! The answer to your question will be below

Step-by-step explanation:

The answer to your question is -1/2

-1/2x + 1/4

= -1/2

Hope that helps

By:xBrainly

Answer:

17

Step-by-step explanation:

The closest perfect cube (to 360) is 343 (7^3) .

360-343 = 17

Subtract 17.

Answer:

You should subtract 17 from 360 to make a perfect cube

Step-by-step explanation:

Answer:

A

The  test statistics is  [tex]t = -1.7[/tex]

B

The  Null and  Alternative hypothesis are

      [tex]H_o : \mu = 47.2[/tex]   and  [tex]H_a : \mu \ne 47.2[/tex]

Step-by-step explanation:

From the question we are told that

    The population mean is  [tex]\mu = 47.2 miles/gallon(MPG)[/tex]

    The sample size is  [tex]n = 250 \ van[/tex]

     The  sample mean is  [tex]\= x = 47.0[/tex]

      The sample  standard deviation is  [tex]\sigma = 1.9[/tex]

      The level of significance is  [tex]\alpha = 0.02[/tex]

Given that the value which the manufacturer gave the automobile is  47.2 and  it is believed that this is not correct, then  

The  Null Hypothesis is  

        [tex]H_o : \mu = 47.2[/tex]

The alternative Hypothesis  is  

        [tex]H_a : \mu \ne 47.2[/tex]

The test statistics can be mathematically evaluated as  

        [tex]t = \frac{\= x- \mu}{\frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

        [tex]t = \frac{\= 47- 47.2}{\frac{1.9 }{\sqrt{250} } }[/tex]

       [tex]t = -1.7[/tex]

Answer:

95% confidence intervals about the population mean is

(51.7656 , 60.2344)

Step-by-step explanation:

Step(i):-

Given random sample of size 'n' =17

Given mean of the sample 'x⁻' = 56

Given standard deviation of sample 's' = 10

95% confidence intervals about the population mean is determined by

[tex](x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )[/tex]

Degrees of freedom

ν = n-1 = 17-1 =16

t₀.₀₅ = 1.7459  (from t-table)

Step(ii):-

95% confidence intervals about the population mean is determined by

[tex](x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )[/tex]

[tex](56 - 1.7459 \frac{10}{\sqrt{17} } ,56 + 1.7459 \frac{10}{\sqrt{17} } )[/tex]

( 56 - 4.2344 , 56 + 4.2344)

(51.7656 , 60.2344)

Conclusion:-

95% confidence intervals about the population mean is

(51.7656 , 60.2344)

Answer:

cos∅ = 16√481/481

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

cos∅ = adjacent/hypotenuse

tan∅ = opposite/adjacent

Step 1: Find hypotenuse

15² + 16² = c²

c = √481

Step 2: Find cos∅

cos∅ = 16/√481

cos∅ = 16√481/481

Answer:

D

Step-by-step explanation:

There isn't enough information to find a y-intercept.

Answer: -7/12

Step-by-step explanation: an number multiplied by 1 is itself

Answer:

True

Step-by-step explanation:

Coefficient of realism called alpha which is a decimal number between 0 and 1. This number provides the optimistic view. The number 1 - [tex]\alpha[/tex] is amount of emphasis that is placed in pessimistic outcome. If the coefficient of realism alpha is 1 then criterion of realism will yield same result as maxi max criterion.

Answer:

[tex] A.\angle 1\: \\\\D. \angle 3[/tex]

Step-by-step explanation:

[tex] \angle 1\: \&\: \angle 3[/tex] are remote interior angles of [tex] \angle 6[/tex]

Answer:

16%

Step-by-step explanation:

Find the z-score.

z = (x − μ) / σ

z = (93 − 85) / 8

z = 1

This means 93 is one standard deviation above the mean.

According to the empirical rule, 68% of a normal distribution is between -1 and +1 standard deviations.  So 32% is either less than -1 or greater than +1 standard deviations.  Normal curves are symmetrical, so 16% is greater than +1 standard deviations.

Answer:

A. converse

Step-by-step explanation:

Let's first define some concepts:

Statement             If p , then q

Converse        If q , then p  

Inverse                If not p , then not q  

Contrapositive If not q , then not p

From the statement we have:

a ⇒b

b ⇒a

if you look at the definitions then:

The second statement is the converse of the first

Answer:

Converse

Step-by-step explanation:

Got Correct On ASSIST.

Answer:

( 2,1) is the center of dilation and 4 is the scale factor

Step-by-step explanation:

A' = k( x-a) +a, k( y-b)+b  where ( a,b) is the center of dilation and k is the scale factor

3,1 becomes 6,1

6,1 = k( 3-a) +a, k( 1-b)+b

6 = 3k -ka+a

1 = k -kb +b

4,1 becomes 10,1

10,1 = k( 4-a) +a, k( 1-b)+b

10 = 4k -ka+a

1 = k -kb +b

Using these two equations

6 = 3k -ka+a

10 = 4k -ka+a

Subtracting the top from the bottom

10 = 4k -ka+a

-6 = -3k +ka-a

------------------------

4 = k

Now solving for a

6 = 3k -ka+a

6 = 3(4) -4a+a

6 =12 -3a

Subtract 12

6-12 = -3a

-6 = -3a

Divide by -3

-6/-3 = -3a/-3

2 =a

Now finding b

1 = k -kb +b

1 = 4 - 4b+b

1 =4 -3b

Subtract 4

-3 = -3b

Divide by -3

1 = b

Answer:

Dilation factor: 4.  

Center of dilation: (2, 1).  

Step-by-step explanation:

The distance between the old vertices was 4 - 3 = 1. The distance between the new vertices is 10 - 6 = 4. 4 / 1 = 4. That means that the dilation factor is 4.  

Now that we have a dilation factor, we can use the formulas x1 = d(x-a) +a and y1 = d( y-b)+b to solve for the center of dilation.  

In this case, d = 4, x1 = 10, x = 4, y1 = 1, and y = 1.  

10 = 4(4 – a) + a

10 = 16 – 4a + a

10 = 16 – 3a

-3a + 16 = 10

-3a = -6

a = 2

1 = 4(1 – b) + b

1 = 4 – 4b + b

1 = 4 – 3b

-3b + 4 = 1

-3b = -3

b = 1

And so, your center of dilation will be (2, 1).  

Hope this helps!  

Answer:

4

  [tex]P(X \ge 219 ) = 0.093[/tex]

5

 [tex]P(X \ge 219 ) = 0.1038[/tex]

Step-by-step explanation:

From the question we are told that  

    The percentage of hair dryers that are defective is p=2%  [tex]= 0.02[/tex]

      The  sample size is  [tex]n =10000[/tex]

       The  random number is  x = 219

The mean of this data set is evaluated as

     [tex]\mu = n* p[/tex]

substituting values

     [tex]\mu = 10000 * 0.02[/tex]

    [tex]\mu =200[/tex]

The standard deviation is evaluated as

      [tex]\sigma = \sqrt{[\mu (1 -p)]}[/tex]

substituting values  

      [tex]\sigma = \sqrt{[200 (1 -0.02)]}[/tex]

     [tex]\sigma = 14[/tex]

Since it is  a one tail test the degree of freedom is  

      df =  0.5

So  

   [tex]x_l = x- 0.5[/tex]

   [tex]x = 219 - 0.5[/tex]

    [tex]x = 218.05[/tex]

Now applying normal approximation

    [tex]P(X \ge 219 ) = P(z > \frac{x - \mu}{\sigma} )[/tex]

substituting values  

    [tex]P(X \ge 219 ) = P(z > \frac{218.5 - 200}{14} )[/tex]

    [tex]P(X \ge 219 ) = P(z > 1.32} )[/tex]

From the z-table  

    [tex]P(X \ge 219 ) = 0.093[/tex]

Considering Question 5  

The  random number is  x = 90

      The mean is  [tex]\mu = n * p[/tex]

Where  n = 100

   and  p  =  0.85

So  

     [tex]\mu = 0.85 *100[/tex]    

     [tex]\mu = 85[/tex]

The standard deviation is  evaluated as

     [tex]\sigma = \sqrt{[\mu (1 -p)]}[/tex]

substituting values  

      [tex]\sigma = \sqrt{[85 (1 -0.85)]}[/tex]        

     [tex]\sigma = 3.5707[/tex]      

Since it is  a one tail test the degree of freedom is  

      df =  0.5

Now applying normal approximation

    [tex]P(X \ge 90 ) = P(z > \frac{x - \mu}{\sigma} )[/tex]

   substituting values  

    [tex]P(X \ge 219 ) = P(z > \frac{89.5 - 85}{3.5707} )[/tex]

    [tex]P(X \ge 219 ) = P(z > 1.2603} )[/tex]

From the z-table  

   [tex]P(X \ge 219 ) = 0.1038[/tex]

Answer:

y <= (2/5)x - 3/2

Step-by-step explanation:

y-intercept is -3/2

slope = 2/5

shading is below the line

Answer: y <= (2/5)x - 3/2

Answer:

18

Step-by-step explanation:

The pattern in this sequence is that you add 7 from the previous number to get the next number (-10 + 7 = -3, -3 + 7 = 4, etc). The next item will be 11 + 7 + 18. Hope this helps!

The next item in the sequence is 18.

You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences.

The sequence is  -10 ,-3, 4, 11,........

this sequence is following pattern ,you add 7 from the previous number to get the next number

First term =  -10 + 7 = -3,

Second term =-3 + 7 = 4, .

The next item will be 11 + 7 = 18.

Therefore, The next item in the sequence is 18.

Learn more about sequence brainly.com/question/12474324 here

#SPJ2

Answer:

c

Step-by-step explanation:

next

Answer:

length of side BC = 11.9cm

The complete question found on brainly (ID: 14303570 ) is stated below:

Find the length of side BC.

Give your answer to 1 decimal place.

∠A = 58°

AC = 14cm

Find attached the diagram of the triangle.

Step-by-step explanation:

From the diagram

∠A = 58°

∠B = 90°

AC = 14cm

The triangle is a right angled triangle

To get the length side of BC, we would

apply trigonometry SOHCAHTOA.

In this question the sine ratio would be appropriate since we know the hypotenuse but we are looking for the opposite side (BC).

Sine ratio: Sin58° = opposite/hypotenuse

Sin58° = BC/AC

Sin58° = BC/14

BC = 14sin58°

BC = 14 × 0.8480

BC = 11.9cm

length of side BC = 11.9cm (1 decimal place)

Answer:

a) Discrete random variable

b) Continous random variable.

Step-by-step explanation:

a) As the number of people can take only integer values, from 0 to n (0, 1, 15, 256, for example, but not 5.6) and not decimals values, we can say that it is a discrete variable.

b) In this case, the weight of a Upper T dash bone steak is a physical variable and can take decimals positive values (0.645 lbs for example).

Then, this variable is a continous variable.