John's net pay is calculated by subtracting deductions for Medicare, Social Security, state and federal taxes, and insurance from his gross pay of $500. The total deductions amount to $168.25, resulting in a net pay of $331.75.
Explanation:Calculation of John's Net Pay
To calculate John's net pay, we need to subtract all the deductions from his gross pay. Since his gross pay is $500, we will apply the following deductions:
Medicare tax: 1.45% of $500 = $7.25
Social Security tax: 6.2% of $500 = $31.00
State tax: 2% of $500 = $10.00
Federal income tax: 20% of $500 = $100.00
Insurance deduction: $20.00
Add up all deductions: $7.25 (Medicare) + $31.00 (Social Security) + $10.00 (State Tax) + $100.00 (Federal Tax) + $20.00 (Insurance) = $168.25
John's net pay is therefore calculated by subtracting the total deductions from his gross pay: $500.00 - $168.25 = $331.75.
Dennis ran a mile in 593.7 seconds. Martina ran a mile in 573.36 seconds. What was the difference in their running times ?
A . 5.14 seconds
B . 6.01 seconds
C . 20.34 seconds
D . 26.01 seconds
Choose the fraction that goes in the blank? 1/2 < _ < 4/5
I don't understand how they got 2/3
A video game sets the points needed to reach the next level based on the function g(x) = 7(3)^x − 1, where x is the current level. The hardest setting promises to multiply the points needed in each level according to the function h(x) = 4x. How many points will a player need on the hardest setting of level 4?
A player will need 2,264 points on the hardest setting of level 4 as calculated by evaluating g(4) using the function g(x) = 7(3)^x - 1 and then applying the function h(x) = 4x.
To calculate the number of points a player will need on the hardest setting of level 4, we need to consider the function h(x) = 4x provided in the context of the question. However, the question also mentions the function g(x) = 7(3)^x - 1, which indicates the points needed to reach the next level normally. Since we need to find the hardest setting value, we will use the function h(x) but before that, we need to evaluate g(4) to find out the base points at level 4.
To find g(4), we substitute x = 4 into g(x):
g(4) = 7(3)^4 - 1 = 7(81) - 1 = 567 - 1 = 566
Now we apply the function h(x) to this value to get the points on the hardest setting:
h(g(4)) = 4 × 566 = 2264
Therefore, a player will need 2,264 points on the hardest setting of level 4.
estimate the product 731+207
Set up a system of equations for the following scenario. Then solve for the system. Three students buy different combinations of tickets for a baseball game. The first student buys 2 senior, 1 adult, and 2 student tickets for $51. The second student buys 1 adult and 5 student tickets for $55. The third student buys 2 senior, 2 adult, and 7 student tickets for $75. Set up a system of equations to find the price of each ticket.
Find the surface of a cylinder with a base diameter of 4yd and a height of 6yd
Which equation does the graph of the systems of equations solve? two linear functions intersecting at 4, 1 the answers are one fourthx + 2 = 2x − 7 one fourthx + 2 = −2x − 7 −one fourthx + 2 = 2x − 7 −one fourthx + 2 = −2x − 7
Factor 2a^5b + 2a^4b^2 + 2a^3b^3.
A.)2a^2b(a^2+a
Given the Vectors s=(-3,2) and t= (-9,-4), find 6s and s+t
Ivan was given two data sets, one without an outlier and one with an outlier.
Data without an outlier: 108, 113, 105, 118, 124, 121, 109
Data with an outlier: 108, 113, 105, 118, 124, 121, 109, 61
How is the median affected by the outlier?
Answer:
b
Step-by-step explanation:
The outlier affects the median of the data sets collected by Ivan by reducing the median.
What is an outlier?An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The outlier in the data set is 62. Median is the number at the center of a data set.
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How do you subtract an integer from another integer without using a number line or counters? Give an example.
A brace for a shelf has the shape of a right triangle. Its hypotenuse is 8 inches long and the two legs are equal in length. How long are the legs of the triangle?
At a certain time, the length of a rectangle is 5 feet and its width is 3 feet. At that same moment, the length is decreasing at 0.5 feet per second and the widthis increasing at 0.4 feet per second.
What is the length of the diagonal at that time?
How fast is the length of the diagonal changing? Is this length increasing or decreasing?
subtract, 8 3/8 - 10 1/6
With 400,000 sq ft or 16% of total office space. How much space did the city have
Find f(-5), if f(x) = -x^2 - 2x+1
yesterday's low temperature was -2.5 degrees celsius. today's low temperature is 5 times as low as yesterday's low temperature. what was the low temperature today?
Answer:
The temperature is -12.5 degrees Celsius.
Step-by-step explanation:
The daily maximum temperature, or high, describes how warm you can expect the air to be, usually from 7 a.m. to 7 p.m. The daily minimum temperature, or low, tells how much the air is expected to cool, usually overnight from 7 p.m. to 7 a.m.
A basketball is thrown with an initial upward velocity of 25 feet per second from a height of 8 feet above the ground. The equation h=-16t^2+25t+8 models the height in feet t seconds after it is thrown. After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground. About how long after it was thrown does it go into the hoop?
Answer:
A quadratic equation is in the form of [tex]ax^2+bx+c =0[/tex]........[1], then the solution for this equation is given by:
[tex]x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
As per the statement:
The equation is given by:
[tex]h=-16t^2+25t+8[/tex]
where, h is the height in feet t seconds after it is thrown.
After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground.
⇒h = 10 feet
then;
[tex]-16t^2+25t+8=10[/tex]
Subtract 10 from both sides we have;
[tex]16t^2-25t+2=0[/tex]
On comparing this equation with [1] we have;
a =16 , b =-25 and c =2
then;
[tex]t= \frac{25 \pm \sqrt{(-25)^2-4(16)(2)}}{2(16)}[/tex]
⇒[tex]t= \frac{25 \pm \sqrt{625-128}}{32}[/tex]
⇒[tex]t= \frac{25 \pm \sqrt{497}}{32}[/tex]
as we want the time when it was falling so ,
[tex]t= \frac{25 + \sqrt{497}}{32}[/tex]
Simplify:
[tex]t \approx 1.48[/tex] sec
Therefore, 1.48 sec long after it was thrown does it go into the hoop
Stacy is walking his dog on a path and his dog wiggled out of his collar. If the dog is 30 feet lower than the owner and the angle of elevation from the dog to the owner is 10 degrees, find the distance from the dog to the owner.
if I have 3 layers of 14 cases per layer of an item,how many total cases should I have
The total number of cases I should have is 42.
How many cases should I have?
Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
Total number of cases = number of layers x cases per layer
14 x 3 = 42
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The sum of differences between the group mean and the grand mean summed over all groups for a given set of observations is called _____ variance.
a plane takes 2hr to travel 1000mi with the wind. it can travel only 880mi against the wind in the same amount of time. find the speed of the wind and the speed of the plane in still air
Autumn is thinking about buying a car. The table below shows the projected value of two different cars for three years.
Number of years 1 2 3
Car 1 (value in dollars) 38,000 32,000 26,000
Car 2 (value in dollars) 38,000 32,300 27,455
Part A: What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? Explain your answer. (2 points)
Part B: Write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)
Part C: Autumn wants to purchase a car that would have the greatest value in 6 years. Will there be any significant difference in the value of either car after 6 years? Explain your answer, and show the value of each car after 6 years. (4 points)
The value of Car 1 decreases linearly and can be described by a linear function. Without an exact exponential function for Car 2, we'll assume it may have a slower depreciation rate compared to Car 1. Autumn should consider Car 2 to likely have greater value after 6 years.
Explanation:Part A: Identifying the Type of Function
To determine which type of function best describes the value of each car after a fixed number of years, we must look at the rate at which the car's value decreases. For Car 1, the value decreases by a constant amount each year ($6,000), which suggests a linear function. Conversely, Car 2 does not decrease by the same amount each year, but rather by amounts that seem to be getting progressively larger, hinting at an exponential function.
Part B: Writing the Functions
The linear function for Car 1 can be represented as f(x) = -6,000x + 44,000, since we start at $44,000 and decrease by $6,000 each year. For Car 2, an exponential decay function may fit the data; however, with only three points provided, determining the exact exponential function would require more complex regression analysis which we do not perform here. Assuming the rate of depreciation remains similar, we might estimate the function for Car 2 using a linear approximation for simplicity.
Part C: Future Car Value Comparison
Extending the linear depreciation model for Car 1, its value after 6 years would be f(x) = -6,000(6) + 44,000 = $8,000. A precise prediction for Car 2 after 6 years cannot be determined without an accurate exponential function, but it's apparent that Car 2 depreciates less rapidly than Car 1. Therefore, Autumn would likely find that Car 2 retains more value over 6 years.
If the constant c is chosen so that the curve given parametrically by ct, c 2 8 t 2 , 0 ≤ t ≤ 3 , is the arc of the parabola 8y = x 2 from (0, 0) to (4, 2), find the coordinates of the point p on this arc corresponding to t = 2.
By solving the given equations using the provided information, and assuming the constant c = 4/3, we can find the coordinates of the point P on the curve corresponding to t = 2 are (8/3, 32/9). There is a probable discrepancy in the question which causes two different solutions for c, therefore making the canonical form of the parabola ambiguous.
Explanation:The given parametric curve has its equations as x = ct and y = c/8 * t^2. We're given that it's the arc of the parabola 8y = x^2 from (0, 0) to (4, 2), meaning that we can set x = ct = 4 and y = c/8 * t^2 = 2 when t=3 (the upper limit of t) to find the value of the constant c. Solving these equations gives c=4/3 and c=48. Since c must be the same in both equations, there seems to be a discrepancy here, which could possibly originate from a mistake in the question. However, if we only use c from the first equation (x = ct), we get c = 4/3.
The question asks for the coordinates of the point on the curve corresponding to t = 2. Substituting t = 2 into x = ct and y = c/8 * t^2 gives x = 8/3 and y = 32/9, assuming c = 4/3. So, the coordinates of the point would be (8/3, 32/9).
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Consider the function f(x) = (x − 3)2(x + 2)2(x − 1). The zero has a multiplicity of 1. The zero −2 has a multiplicity of?
The zero with a multiplicity of 1 is x = 1, and the zero x = -2 has a multiplicity of 2.
How to find the multiplicity of zeros in a polynomial?For a general polynomial like:
[tex]p(x) = (x - x_1)^n*(x - x_2)^m*...[/tex]
The zero x₁ has a multiplicity of n (same as the exponent in the term where the zero appears), while the zero x₂ has a multiplicity m.
Now let's go to our polynomial:
[tex]f(x) = (x - 3)^2(x + 2)^2(x - 1)[/tex]
Here we can see that the only zero with a multiplicity of 1, is x = 1, while the zero x = -2 has a multiplicity of 2.
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Answer:
first one is 1 and second is 2
Step-by-step explanation:
just got it right
The radius of a circular park is 114 yd. To the nearest yard, what is the circumference of the park?
circumference = 2 x pi x r
using 3.14 for pi
2 x3.14x114=715.92
round to 716 yards
Answer:
The circumference of a circle is 715.92 yd.
Step-by-step explanation:
Formula
[tex]Circumference\ of\ a\ circle = 2\pi r[/tex]
Where r is the radius of a circle.
As given
The radius of a circular park is 114 yd.
[tex]\pi = 3.14[/tex]
Put in the formula
[tex]Circumference\ of\ a\ circle = 2\times 3.14\times 114[/tex]
Circumference of a circle = 715.92 yd
Therefore the circumference of a circle is 715.92 yd.
Classify the four angles of the quadrilateral.
A
B
C
D
90°
105°
75°
90°
Right , Acute, Obtuse
∠A
∠B
∠C
∠D
All the angles of the quadrilateral are,
⇒ ∠A = Right angle
⇒ ∠B = Obtuse angle
⇒ ∠C = Acute angle
⇒ ∠D = Right angle
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Now, We know that;
Any angle which is greater than 90° is called obtuse angle and less than 90° is called acute angle and 90° is called Right angle.
Here, The four angles of the quadrilateral are,
⇒ ∠A = 90°
⇒ ∠B = 105°
⇒ ∠C = 75°
⇒ ∠D = 90°
Hence, We get;
⇒ ∠A = Right angle
⇒ ∠B = Obtuse angle
⇒ ∠C = Acute angle
⇒ ∠D = Right angle
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What are two numbers whose sum is 11 and whose product is -60?
You are hiking on a trail that leads to the top of a mountain. At 12 P.M. you reach an elevation of 3700 feet. At 4 P.M. you reach an elevation of 4500 feet. What is your mean hourly change in elevation?
Answer: 200 ft per hour
Step-by-step explanation:
Given : You are hiking on a trail that leads to the top of a mountain.
At 12 P.M. you reach an elevation of 3700 feet. At 4 P.M. you reach an elevation of 4500 feet.
The formula for the mean hourly change in elevation is :-
[tex]\dfrac{\text{Change in elevation}}{\text{Time in hours}}[/tex]
From the given information, the change in elevation=4500 ft-3700 ft= 800 ft
Time taken = 4 hours [From 12 pm to 4 pm]
Now, Mean hourly change in elevation=[tex]\dfrac{800}{4}=200[/tex]
Hence, the mean hourly change in elevation = 200 ft
Suppose that it costs $25 to place a classified advertisement in the newspaper, plus $4 for each line. Then the cost to place an ad x lines long is given by y dollars, where y= 4x + 25.
express as an ordered pair the fact that a 14 line cost $81. _
Express as an ordered pair the fact that an ad costing $37 is 3 lines long. _