An employee earned $3,300 working for an employer in the current year. the current rate for fica social security is 6.2% payable on earnings up to $117,000 maximum per year and the rate for fica medicare 1.45%. the employer's total fica payroll tax for this employee is:
If one calendar year had two consecutive months with Friday the thirteenth, which months would they be?
arman needs 4 1/2 inches of cable to make A,3 3/4 inches to make B, and 5 1/8 inches to make C. He used a 12 inch piece of cable to make A and B.
Answer:
8 1/4
Step-by-step explanation:
lim θ→π/4 1 - tan θ / sin θ - cos θ
how to prove a polygon is a rectangle?
Convert 85°to radians
1 degree = 0.0174533 radians
85* 0.0174533 = 1.4835305 radians
Round answer as needed
Answer:
17pi/36 (PLATO answer)
Step-by-step explanation:
solve, explain why the algorithm works
3892
-2567
Harland just got his second major credit card, so his credit score rose from 671 to 711. According to the following table for a $150,000 mortgage, how much less per year would Harland have to pay on a $150,000 mortgage with the new credit score?
Answer:
2004
Step-by-step explanation:
Ocean currents influence all of the following except
temperature
climate
radiation from the sun
weather
BE is the midsegment of triangle ACD. The value of x is:
5.
20.
35.
40.
there is a cafe at the park it is 13 meters long and 8 meters wide. what is the area of the cafe
A maintenance man has 12 keys on his key ring. if he tries the keys at random on a storage room door, discarding those that do not work, what is the probability that he will get the door open on his 4th try?
Final answer:
The probability that the maintenance man will open the storage door on his fourth try with 12 keys is 1/12.
Explanation:
The question asks for the probability that the maintenance man will open a storage room door on his fourth try with 12 unique keys at his disposal. This is a classic probability problem that involves permutations.
To solve this, we consider the scenario as a sequence of independent events. He has 1 out of 12 chances to pick the correct key on the first try, 1 out of 11 on the second try (after discarding the first incorrect key), 1 out of 10 on the third try, and so on. However, we want the first three attempts to be unsuccessful and the fourth to be successful.
Thus, the probability that the first three keys are incorrect is (11/12) * (10/11) * (9/10), and the probability the fourth key is correct is 1/9. The overall probability of the desired outcome is the product of these probabilities, which simplifies to:
(11/12) * (10/11) * (9/10) * (1/9) = 1/12.
Which number produces an irrational number when multiplied by 0.4?
Evaluate x 1 - x -1 + x 0 for x = 2
a) 0
b)1/2
c)1 1/2
d)2 1/2
The solution of expression is, 7/2.
What is an expression?A mathematical expression is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.
We have to give that,
An expression is,
⇒ x¹ + x⁻¹ + x⁰
Now, Substitute x = 2 in the above expression and find the value,
⇒ x¹ + x⁻¹ + x⁰
⇒ 2¹ + 2⁻¹ + 2⁰
⇒ 2 + 1/2 + 1
⇒ 3 + 1/2
⇒ (6 + 1)/2
⇒ 7/2
Therefore, The solution is, 7/2
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the circle is centered at the origin and the length of its radius is 4. what is
the circles equation
Answer: [tex]x^2+y^2=16[/tex]
Step-by-step explanation:
The general equation of a circle having center at (h,k) and radius r is given by :-
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Given: Radius of the circle : r= 4 units
The center of the circle : (h,k)=(0,0)
Now, the equation of a circle having center at (0,0) and radius 4 units is given by :-
[tex](x-0)^2+(y-0)^2=4^2\\\\\Rightarrow\ x^2+y^2=16[/tex]
Answer:
X²+Y²=16
Step-by-step explanation:
A p e x
Explain how to use the standard normal table to find the probability associated with the shaded area under the curve.
Answer:
The standard normal table gives areas under the curve to the left of z-scores.
Find the probability in the standard normal table that a value is to the left of 1.9.
Find the probability in the standard normal table that a value is to the left of 0.4.
Subtract the probability of a value being to the left of 0.4 from the probability of a value being to the left of 1.9.
Step-by-step explanation:
edge2020
In order to find the probability associated with the shaded area under the curve using the standard normal table, you should subtract the probability of a value left of 0.4 from the probability of a value left of 1.9.
How do you find the probability associated with the shaded area?We are trying to find the probability of the area between 1.9 and 0.4 so the first thing to do is to find the probability that a value is to the left of 1.9 from the Standard normal table.
After this is done, you then find the probability that the value is left of 0.4.
To find the probability of the middle area, subtract the value to the left of 0.4 from that of the value left of 1.9
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Pentagon RSTUV is circumscribed about a circle. What is the value of x if RS = 6, ST = 9, TU = 7, UV = 15, and VR = 14?
Starting at vertex V going until vertex S, we make our calculations.
VR = 14
Rx = x
therefore, xS = VR – Rx
xS = 14 – x ---> 1
Now starting at vertex V going left to vertex S, we make our next set of calculations. Assuming x is on VR but nearer R
VR = 14 - x
at UV = 15 – (14 – x)
at UV = 1 + x
at TU = 7 – (1 + x)
at TU = 6 – x
at ST = 9 – (6 – x)
at ST = 3 + x ---> 2
Equate 1 and 2:
14 – x = 3 + x
2 x = 11
x = 5.5
To find the value of x in the circumscribed pentagon RSTUV with given sides, we set up an equation based on the sum of the lengths of the opposite sides. After solving the equation, we determined that x is 25.
Pentagon RSTUV and the Value of x
Given that pentagon RSTUV is circumscribed about a circle, we need to find the value of x,
where RS = 6, ST = 9, TU = 7, UV = 15, and VR = 14.
For a polygon circumscribed about a circle, the sum of the lengths of the pairs of opposite sides must be equal. Therefore, we can set up the equation:
RS + TU + x = ST + UV + VR
Substituting the given values:
6 + 7 + x = 9 + 15 + 14
Simplifying the right-hand side:
6 + 7 + x = 3813 + x = 38x = 38 - 13x = 25Thus, the value of x is 25.
EASY 5 POINTS!!! Choose the equation that correctly uses the Pythagorean Theorem for the given right triangle.
Answer:
Option C
Step-by-step explanation:
In the given right angle triangle
Hypotenuse = 4.5 cm
Height = 2.5 cm
and base = g cm.
Pythagoras theorem says
(hypotenuse)² = (base)² + (height)²
So by putting the values in the formula
(4.5)² + (2.5)² + g²
Option C is the answer.
Ahmed is working at the burger joint. His boss pays him $6.50 per hour and promises a raise of $0.25 per hour every 6 months. Which sequence describes Ahmed's expected hourly wages in dollars, starting with his current wage?
Answer:
Sequence will be $6.50, $6.75, $7.0, $7.25.......
Step-by-step explanation:
Ahmed is working at the burger joint and he was paid by his boss $6.50 per hour.
His boss promised him to raise $0.25 per hour every six months.
So we have to find the sequence which describes Ahmed's expected hourly wages starting with his current wage.
As at every 6 months increase in wages is $0.25 so the sequence formed will be an arithmetic sequence with common difference of 0.25 and first term 6.50
Sequence will be $6.50, $6.75, $7.0, $7.25,.........
Verify that the divergence theorem is true for the vector field f on the region
e. give the flux. f(x, y, z) = 3xi + xyj + 4xzk, e is the cube bounded by the planes x = 0, x = 3, y = 0, y = 3, z = 0, and z = 3.
To verify the divergence theorem, we need to calculate the flux of the vector field through the surface of the cube and compare it with the divergence of the vector field integrated over the volume of the cube.
Explanation:To verify the divergence theorem for the given vector field f(x, y, z) = 3xi + xyj + 4xzk on the region e, which is a cube bounded by the planes x = 0, x = 3, y = 0, y = 3, z = 0, and z = 3, we need to calculate the flux of the vector field through the surface of the cube and compare it with the divergence of the vector field integrated over the volume of the cube.
The flux, Ƭ, can be calculated using the surface integral of the vector field over each face of the cube. According to the divergence theorem, this should be equal to the volume integral of the divergence of the vector field over the entire volume of the cube.
By calculating both sides of the equation, we can verify that the divergence theorem holds true for the given vector field on the specified region.
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P(1+r)t Using the expression above, choose the correct answers for the new balance and the amount of interest earned in the following compound interest problem. $950 at 7% for 8 years, compounded annually. Total Amount = $ Interest Amount = $
Final answer:
The new balance after 8 years with an initial $950 at a 7% annual interest rate compounded annually is $1632.77, and the amount of interest earned is $682.77.
Explanation:
The compounded interest formula is P(1+r)^t, where P is the principal amount, r is the annual interest rate (in decimal form), and t is the time in years. To find the new balance and amount of interest earned for $950 at 7% for 8 years, compounded annually, we use the formula with P = $950, r = 0.07 (7% as a decimal), and t = 8.
First, we calculate the new balance:
Total Amount = $950(1 + 0.07)^8
Total Amount = $950(1.07)^8
Total Amount = $950 * 1.718186
Total Amount = $1632.77 (rounded to two decimal places)
Subsequently, to find the amount of interest earned, we subtract the original principal from the total amount:
Interest Amount = Total Amount - Original Principal
Interest Amount = $1632.77 - $950
Interest Amount = $682.77
Therefore, the new balance after 8 years is $1632.77, and the interest earned is $682.77.
Rewrite the expression x^2-12x as a(x-h)^2+k
If CD is the perpendicular bisector of AB, then the value of x is:
10.
5.
22.
11.
Complete parts (a) and (b) using the probability distribution below.
The number of overtime hours worked in one week per employee
Overtime hours
0 1 2 3 4 5 6
Probability
0.026 0.072 0.154 0.303 0.215 0.164 0.066
(a) Find the mean, variance, and standard deviation of the probability distribution.
Find the mean of the probability distribution.
μ = 3.4
σ2 = 2.0
σ = 1.4
Choose the correct answer below.
A.
An employee works an average of 2.0 overtime hours per week with a standard deviation of approximately 1.4 hours.
B.
An employee works an average 3.4 of overtime hours per week with a standard deviation of approximately 4 hours.
C.
An employee works an average of 1.4 overtime hours per week with a standard deviation of approximately 3.4 hours.
D.
An employee works an average of 3.4 overtime hours per week with a standard deviation of approximately 1.4 hours.
The mean number of overtime hours worked is 3.4 with a standard deviation of approximately 1.4 hours, which corresponds to option D.
Explanation:The correct answer for the given probability distribution of overtime hours worked per employee in one week is D. An employee works an average of 3.4 overtime hours per week with a standard deviation of approximately 1.4 hours.
To find the mean (μ) of the probability distribution, we multiply each possible value by its corresponding probability and then sum all these products. The mean of this distribution is given as 3.4, which is found by summing up the product of each value of overtime hours and its corresponding probability:
μ = (0 * 0.026) + (1 * 0.072) + (2 * 0.154) + (3 * 0.303) + (4 * 0.215) + (5 * 0.164) + (6 * 0.066) = 3.4
The variance (σ2) is calculated by taking each value's deviation from the mean, squaring it, multiplying by the probability, and summing all these values. The variance for this distribution is given as 2.0:
σ2 = Σ [(x - μ)2 * P(x)] = 2.0
And the standard deviation (σ) is simply the square root of the variance:
σ = √σ2 = 1.4
A person in a casino decides to play blackjack until he loses a game, but he will not play more than 3 games. let l denote a loss and w denote a win. what is the sample space for this random experiment
The sample space for the random experiment of playing blackjack until a loss or a maximum of three games are played is represented by the set {l, wl, ww}.
Explanation:The sample space for this scenario comprises of all possible outcomes of playing "blackjack" until the person loses or has played three games. We represent win and loss by w and l respectively. By these definitions, we get the following possibilities: l (losing on the first game), wl (winning the first game then losing the second), and ww (winning the first two games and decide not to play a third game or it wasn't possible to play a third game). This assumes that the player stops after either losing a game or after playing the third game, even if he won that.
Note that the scenario where the player wins all three games (www) is not included in the sample space because the problem states that the player will stop playing as soon as they lose a game.
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Graph y=3x^2 -5 and it's inverse
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y=3x^{2}-5[/tex] -----> quadratic equation of a vertical parabola open upward
Find the inverse function
Exchange variables x for y and y for x
[tex]x=3y^{2}-5[/tex]
Isolate the variable y
[tex]3y^{2}=x+5[/tex] -----> inverse function (horizontal parabola open to the right)
or
[tex]y=(+/-)\sqrt{\frac{x+5}{3}}[/tex]
using a graphing tool
see the attached figure
The graph of function and it's inverse of the graph is shown in image.
We have to given that,
To graph the function y = 3x² - 5 and it's inverse.
Here, The equation is,
y = 3x² - 5
So, We can find it's inverse as,
y = 3x² - 5
y + 5 = 3x²
(y + 5) / 3 = x²
x² = (y + 5)/3
x = √(y + 5)/3
Hence, the inverse of function is,
f ⁻¹ (x) = √ (x + 5)/3
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The value of the given digits in the numbers 7s in 775 823 159
3y^2-16y+16
could someone help me walk through this?
Use the position equation
s = −16t^2 + v0t + s0
as the model for the problem.
A cargo plane flying at 6000 feet over level terrain drops a 700-pound supply package.
(a) How long will it take the package to strike the ground? (Round your answer to two decimal places.)
(b) The plane is flying at 600 miles per hour. How far will the package travel horizontally during its descent? (Round your answer to two decimal places.)
A. To solve for the time it takes for the package to strike the ground, all we have to do is to plug in the given values in to the position equation:
s = −16 t^2 + v0 t + s0
Where,
s = distance of the plane from the ground = - 6000 ft (negative since the package moves from top to bottom)
t = time for it to strike the ground = unknown
v0 = 0 since the package starts from rest
s0 = 0 since we take the plane as the reference point
Substituting the given values:
- 6000 = -16 t^2 + 0 * t + 0
16 t^2 = 6000
t^2 = 375
t = 19.36 s
B. s = v * t
where v = 600 miles / hr = 0.17 miles / s
s = (0.17 miles / s) * 19.36 s
s = 3.23 miles = 17,054 ft
Sam used his calculator to find the answer and wrote down cos 1.75 = 0.999. Does this seem like a reasonable answer to you? What might he have done wrong on his calculator?
Since pi is equivalent to 3.14 and means 180°, therefore 1.75 which is about half of pi should be at almost 90°. The cos of a 90° angle which is located on the y axis should be zero, therefore cos 1.75 must be near zero. However in this case it is near one, clearly his calculator is in degree mode that is why he got an erroneous answer.
What Sam can do to get the correct answer would be to convert his calculator into radian mode or convert the given 1.75 rad into degrees:
θ = 1.75 rad (180° / π rad)
θ = 100.2676
cos 100.2676 = -0.1782 which is now correct since it is nearer to zero