.Calculate pay in the following cases- 2+4+3= 10 marks

a) Mark works at a rock concert selling programs. He is paid $20 for showing up,

plus 45 cents for each program that he sells. He sells 200 programs. How

much does he earn working at the rock concert?

b) Mary wood is an architect working for New Horizons. She makes every month a salary of 5500.

i What is her annual income?

ii What is her gross earnings per pay period.

iii How much does she earn per period if paid semi-monthly

iv How much does she earn per period if paid weekly.

c) Danny Keeper is paid $12.50 per hour. He worked 8 hours on Monday and Tuesday, 10 hours on Wednesday and 7 hours on Thursday. Friday was a public holiday and he was called in to work for 10 hours. Overtime is paid time and a half. Time over 40 hours is considered as overtime. Calculate regular salary and overtime. Show all of your work. 

Answer:

y = 3(x + 1)² - 7

Step-by-step explanation:

y = 3x² + 6x - 4

First, factor out the coefficient of the quadratic eq'n:

y = 3(x² + 2x - ⁴/₃)

Use the "complete the square" rule;

The "x² + 2x" should be rewritten as "(x + 1)² - 1", i.e. place into squared brackets x (without the power 2) and add half the coefficient of the x-term, you then need to subtract the square of the constant term in the squared brackets and then simplify:

y = 3((x + 1)² - 1 - ⁴/₃)

y = 3((x + 1)² - ⁷/₃)

Finally, multiply the 2 terms you end up with by the 3, factored out initially:

y = 3(x + 1)² - 7

Answer:

y = - 2x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (1,1) ← 2 points on the line

m = \(\frac{1-3}{1-0}\) = - 2

The line crosses the y- axis at (0, 3) ⇒ c = 3

y = - 2x + 3 ← equation of line

Answer:

Step-by-step explanation:

The area of a parallelogram is base times height.

In this case it would be:

(3x +1) (5x-4)

Then multiply to simplify.

Use FOIL

15x² - 12x + 5x - 4

Simplify again

15x² - 7x - 4

Answer:

independent

Step-by-step explanation:

because it asked ronald to roll a dice and flip a quarter, no one else he did it himself

Step-by-step explanation:

if you don't even understand the question, this is also something you need to tell your teacher. it is his/her job to make you understand it.

a probability is always

desired cases / possible cases

so, if we pick a single student randomly, how many possible options do we have ?

we have 2+5+6+9 = 22 students (as the 4 categories in the table are mutually exclusive).

therefore, our possible cases to pick a student are 22.

now, how many of these 22 students represent our desired cases ?

male, who does not have an A : 9

so, the probability to pick a student who is male and does not have an A is

9/22 = 0.409090909...

Answer:

I may be wrong, but I believe the answer is $200.

Answer:

p.

Step-by-step explanation:

p is the independent variable.

The dependent one is h.

The value of h depends on the value of p.

Considering the vertex of a quadratic equation, the greatest rectangular area that the farmer can enclose with 100 m is of 625 m².

A quadratic equation is modeled by the rule presented as follows:

y = ax^2 + bx + c

The vertex has these following coordinates.

\((x_v, y_v)\)

In which:

Considering the coefficient a, we have that the vertex can represent either a maximum or a minimum point in the function, as follows::

In this problem, the coefficients of the quadratic equation representing the area are given as follows:

a = -1, b = 50.

The greatest rectangular area that the farmer can enclose with 100 m is the y-coordinate of the vertex of the quadratic equation, hence:

\(y_v = -\frac{50^2 - 4(-1)(0)}{4(-1)} = 625\)

The area is of 625 m².

The quadratic equation for the area is:

A(w) = -w² + 50w

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Answer:

625

explanation:

trust

Step-by-step explanation:

-1/4, -1/5, -1/6, -1/7, -1/8, 1/8, 1/7, 1/6, 1/5, 1/4

The signed decimal value in CX is 144, and the unsigned decimal value in ECX is also 144.



The assembly instructions provided are performing bitwise operations on the ECX register. Here's a brief solution:The instruction "xor ecx, ecx" is XORing the ECX register with itself, effectively setting it to zero. This means the value in CX (the lower 16 bits of ECX) will also be zero.The instruction "mov ch, 0x90" is moving the hexadecimal value 0x90 (144 in decimal) into the CH register (the higher 8 bits of CX). Since the lower 8 bits (CL) of CX are already zero, the value in CX will be 0x0090 in hexadecimal or 144 in decimal.

To calculate the signed decimal value in CX, we consider it as a 16-bit signed integer. Since the most significant bit (MSB) of CX is zero, the signed decimal value will be positive, i.e., 144.The unsigned decimal value in ECX is obtained by considering the full 32 bits of ECX. Since ECX was set to zero earlier and only the higher 8 bits (CH) were modified to 0x90, the unsigned decimal value in ECX will be 0x00000090 in hexadecimal or 144 in decimal.

Therefore, the signed decimal value in CX is 144, and the unsigned decimal value in ECX is also 144.

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Answer:

5^-18

Step-by-step explanation:

here is the answer please mark me as the brainliest

The values of f(0), f′(0), f′′(0), and f′′′(0) are 4, -3, 0.4, and -24 respectively.

Given information:

The function f (x) is approximated near a = 0 by the 3rd degree taylor polynomial t3(x) = 4 −3x + (x^2 / 5) − (4x^3).We are to find the values of f (0), f ′(0), f ′′(0), and f ′′′(0).

Calculations: We are given the 3rd degree Taylor polynomial as:t3(x) = 4 −3x + (x^2 / 5) − (4x^3)

To find f(x) and its derivatives, we will differentiate the polynomial to different orders.

Differentiating t3(x) w.r.t x we get: $$t_3^{(1)}(x) = -3 + \frac{2x}{5} - 12x^2$$

Differentiating t3(x) again w.r.t x, we get: $$t_3^{(2)}(x) = \frac{2}{5} - 24x$$Differentiating t3(x) once again w.r.t x, we get: $$t_3^{(3)}(x) = -24$$Now, we have found f(x) and its derivatives using the Taylor polynomial. So, we can find their respective values at x = 0.

Substituting x = 0 in t3(x), we get:$$t_3(0) = 4$$Therefore, f(0) = 4.Substituting x = 0 in t3′(x), we get:$$t_3′(0) = -3$$Therefore, f′(0) = -3.Substituting x = 0 in t3′′(x), we get:$$t_3′′(0) = \frac{2}{5}$$Therefore, f′′(0) = 0.4.Substituting x = 0 in t3′′′(x), we get:$$t_3′′′(0) = -24$$

Therefore, f′′′(0) = -24.

Answer:

Therefore, the values of f(0), f′(0), f′′(0), and f′′′(0) are 4, -3, 0.4, and -24 respectively.

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The integral for the volume V of the cut out is 2016πr^3.

The volume V of the cut out can be found using the integral:
V = ∫[A(x)]dx
Where A(x) is the area of the cross section of the cut out at a given x-value and the integral is taken over the length of the cut out.

In this case, the cross section of the cut out is a circle with radius 12r, so A(x) = π(12r)^2 = 144πr^2.
The length of the cut out is the diameter of the cylinder, or 2(7r) = 14r.
Therefore, the integral for the volume V of the cut out is:
V = ∫[144πr^2]dx from x = 0 to x = 14r
V = 144πr^2∫dx from x = 0 to x = 14r
V = 144πr^2(14r - 0)
V = 2016πr^3
So the integral for the volume V of the cut out is 2016πr^3.

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The probability of AL's number will be a whole number multiple of bill's and bill's number will be a whole number multiple of call's is 1÷ 80

The problem can be solved using Butte force approach

We can solves this in two cases

If Cal's number is :

If Bill's number is , Al’s can be any of 4, 6, 8, 10.

If Bill's number is , Al’s can be any of 6, 9.

If Bill's number is , Al’s can be 8.

If Bill's number is , Al’s can be 10.

Otherwise, Al's number could not be a whole number multiple of Bill's.

If Cal's number is 2 :

If Bill’s number is , Al's can be 8.

Otherwise, Al’s number could not be a whole number multiple of Bill's while Bill’s number is still a whole number multiple of Cal’s.

Otherwise, Bill's number must be greater than , i.e. Al’s number could not be a whole number multiple of Bill’s.

Clearly, there are exactly  cases where Al's number will be a whole number multiple of Bill's and Bill's number will be a whole number multiple of Cal’s. Since there are 10×9×8 possible permutations of the numbers Al, Bill, and Cal were assigned, the probability that this is true is

9÷10×9×8

C = 1÷80

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The speed of the plane and wind in km/hr is 187.5 and 37.5 respectively.

A linear equation has highest degree of 1.

According to the given question a small plane flies for 3 hours to an airport 450 kilo meters away against a strong headwind. the plane then returns to its starting location flying with the wind, taking 2 hours.

Form these we can form two linear equations in two variables.

Assuming speed of the plane to be x km/hr and speed of wind to be y km/hr.

We know Distance = speed × time.

3( x - y) = 450. and 2( x + y) = 450.

3x - 3y = 450...(i) and 2x + 2y = 450...(ii)

multiplying eqn (i) by 2 and eqn (ii) by 3 and solving we get

x = 187.5 km/hr and y = 37.5 km/hr.

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Answer:

d) 1/2 ÷ 4 = 1/2 • 4/1

Step-by-step explanation:

when dividing fractions use keep change flip (keep the first fraction, change the sign to multiplication, flip the second fraction)

when multiplying just multiply straight across

FICA tax contribution for an employee, multiply their gross pay by the Social Security and Medicare tax rates.

FICA is a U.S. federal payroll tax. It stands for the Federal Insurance Contributions Act and is deducted from each paycheck. Your nine-digit number helps Social Security accurately record your covered wages or self-employment. As you work and pay FICA taxes, you earn credits for Social Security benefits.

For both of them, the current Social Security and Medicare tax rates are 6.2% and 1.45%, respectively. So each party – employee and employer – pays 7.65% of their income, for a total FICA contribution of 15.3%. To calculate your FICA tax burden, you can multiply your gross pay by 7.65%.

For example, if an employee’s taxable wages are $700 for the week, their social security contribution would be: $700.00 x 6.2% = $43.40. Their Medicare contribution would be: $700.00 x 1.45%= $10.15.

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Answer:

I think it is $66 at first sorry if wrong

A traingle has the verticies A(1,-3), B(-2,-10), and C(4,-13) so, The length of the perimeter of the triangle is √58 + 3√5 + √109.

To find the length of the perimeter of the triangle with vertices A(1, -3), B(-2, -10), and C(4, -13), we need to calculate the distances between these points.

The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula:

Distance = √((x2 - x1)² + (y2 - y1)²)

Let's calculate the distances between the vertices:

Distance AB:

x1 = 1, y1 = -3 (coordinates of A)

x2 = -2, y2 = -10 (coordinates of B)

Distance AB = √((-2 - 1)² + (-10 - (-3))²) = √((-3)² + (-7)²) = √(9 + 49) = √58

Distance BC:

x1 = -2, y1 = -10 (coordinates of B)

x2 = 4, y2 = -13 (coordinates of C)

Distance BC = √((4 - (-2))² + (-13 - (-10))²) = √((6)² + (-3)²) = √(36 + 9) = √45 = 3√5

Distance AC:

x1 = 1, y1 = -3 (coordinates of A)

x2 = 4, y2 = -13 (coordinates of C)

Distance AC = √((4 - 1)² + (-13 - (-3))²) = √((3)² + (-10)²) = √(9 + 100) = √109

Now, we can calculate the perimeter by adding up the distances:

Perimeter = AB + BC + AC = √58 + 3√5 + √109

As a result, the triangle's circumference measures √58 + 3√5 + √109.

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Answer:

c√a^b the first option is the correct one

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The graph has a line with a slope of 1/2 beginning at the origin and extending as far as you like into the first quadrant.

The confidence interval is $57006 ± $4624.68.

The given information in the problem is as follows:SHSU wants to test whether there is any difference in salaries for business professors (group 1) and criminal justice professors (group 2).A sample of 48 business professors is selected.The average salary of business professors is 5∈431.A sample of 49 criminal justice professors is selected.The average salary of criminal justice professors is $572788.

The population standard deviations are known and equal to $9000 for business professors and $7500 for criminal justice professors.The university wants to test if there is a difference between the salaries of these 2 groups, using a significance level of 5%.We are asked to compute the test statistic needed for performing this test and round our answer to 2 decimals.It is a two-tailed test as we want to check if there is a difference between two groups of professors.

Hence, the level of significance is α = 5/100 = 0.05. The degrees of freedom (df) is given by the following formula:df = n1 + n2 - 2Here, n1 = 48 (sample size of group 1), n2 = 49 (sample size of group 2).Thus,df = 48 + 49 - 2 = 95.Using the given formula, the test statistic is calculated as follows:t = (x1 - x2 - D) / [(s1²/n1) + (s2²/n2)]^0.5Where,x1 = 5∈431 (sample mean of group 1)x2 = 572788 (sample mean of group 2)s1 = $9000 (population standard deviation of group 1)s2 = $7500 (population standard deviation of group 2)n1 = 48 (sample size of group 1)n2 = 49 (sample size of group 2)D = 0 (null hypothesis).

On substituting the given values in the formula,t = (5∈431 - 572788 - 0) / [(9000²/48) + (7500²/49)]^0.5t = -1.96The test statistic needed for performing this test is -1.96 (rounded to 2 decimals).Now, we need to find the confidence interval for the difference in salaries for business professors and criminal justice professors.

The given information in the problem is as follows:SHSU wants to construct a confidence interval for the difference in salaries for business professors (group 1) and criminal justice professors (group 2).A sample of 41 business professors is selected.The average salary of business professors is $581153.A sample of 49 criminal justice professors is selected.The average salary of criminal justice professors is $62976.

The population standard deviations are known and equal to $9000 for business professors, respectively $7500 for criminal justice professors.The university wants to estimate the difference in salaries between the two groups by constructing a 95% confidence interval.We are asked to compute the 95% confidence interval.

It is given that the population standard deviations are known and equal to $9000 for business professors, respectively $7500 for criminal justice professors. The level of significance (α) is 5% which means that the confidence level is 1 - α = 0.95.The formula for the confidence interval is given by:CI = (x1 - x2) ± tα/2 [(s1²/n1) + (s2²/n2)]^0.5Where,CI = Confidence Intervalx1 = $581153 (sample mean of group 1)x2 = $62976 (sample mean of group 2)s1 = $9000 (population standard deviation of group 1)s2 = $7500 (population standard deviation of group 2)n1 = 41 (sample size of group 1)n2 = 49 (sample size of group 2)tα/2 is the t-value at α/2 level of significance and degrees of freedom (df = n1 + n2 - 2).

Here,tα/2 = t0.025 = 1.96 (at 0.025 level of significance, df = 41 + 49 - 2 = 88).On substituting the given values in the formula,CI = (581153 - 62976) ± 1.96 [(9000²/41) + (7500²/49)]^0.5CI = $57006 ± $4624.68The confidence interval is $57006 ± $4624.68.

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Answer:

y = 3x+1

Step-by-step explanation:

Find slope of line

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-1}{1-0}=\frac{3}{1}=3\)

The y-intercept is when x=0, so this would be y=1, making the equation y=3x+1

Answer:

31

Step-by-step explanation:

f(-9) = -(-9)-5

= 9-5

= 4

f(-9) - 9(-3) = 4 - (-27)

= 31

Answer:

$33.60

Step-by-step explanation:

Answer:

33.60

Step-by-step explanation:

20% of 42 is 8.40. Subtract that from 42 to get your answer.

Answer:

The answer is -15